diff --git "a/batch_s000013.csv" "b/batch_s000013.csv" new file mode 100644--- /dev/null +++ "b/batch_s000013.csv" @@ -0,0 +1,10395 @@ +source,target + The resultscan be seen in ‘Table 3., The resultscan be seen in Table 3. + Phe average error. (fromten hall skies) is below 12'4 down to a lux limit of 0.6 Jv (70 GLIz) and 0.4 Jy (100 CGLIz)., The average error (fromten half skies) is below $12\%$ down to a flux limit of $0.6$ Jy (70 GHz) and $0.4$ Jy (100 GHz). + Phe determination of these cumulants would allow us, The determination of these cumulants would allow us +not only does the higher S/N data show smaller scatter (as expected. and indicated by the corresponcingly smaller error bars) but also exhibit Gaussian uncertainties. whereas the poorer quality data shows indications of a bias towards larger index values.,"not only does the higher S/N data show smaller scatter (as expected, and indicated by the correspondingly smaller error bars) but also exhibit Gaussian uncertainties, whereas the poorer quality data shows indications of a bias towards larger index values." + This is particularly true of GC IX043 which appears as an outlier in al [our panels of Figure 5 and has the lowest S/N of the sample., This is particularly true of GC K043 which appears as an outlier in all four panels of Figure \ref{fig:ssp1} and has the lowest S/N of the sample. + Concentrating solely on the ugher S/N data. we find that the models (plotted such that they are cllectively degenerate in age ancl exhibit ony a metallicity sequence) reproduce the cata very well.," Concentrating solely on the higher S/N data, we find that the models (plotted such that they are effectively degenerate in age and exhibit only a metallicity sequence) reproduce the data very well." + “Phis is also the case Lor our composite metal-poor and metal-rich CC's., This is also the case for our composite metal-poor and metal-rich GCs. + There is a sugeestion of a systematic olfset in the Mg6 Ales erid. since the composite GCs lic slightly above the &rids. although the olfset is not large.," There is a suggestion of a systematic offset in the Mg – $_2$ grid, since the composite GCs lie slightly above the grids, although the offset is not large." +" For comparison purposes. we also show the position of the central nuclear line-strengths of NGC 524 (through a standard 1.47. 4"" aperture). taken from Trager (1998)."," For comparison purposes, we also show the position of the central nuclear line-strengths of NGC 524 (through a standard $\arcsec \times $ $\arcsec$ aperture), taken from \citeANP{Trager98} (1998)." + Two of the GCs in Figure 5 appear to have metallicities similar to that of NGC 524 itself., Two of the GCs in Figure \ref{fig:ssp1} appear to have metallicities similar to that of NGC 524 itself. + In principle. α Κο ratios may be derived from these plots. but we defer further clisettssion Of this subject to the next section.," In principle, $\alpha$ /Fe] ratios may be derived from these plots, but we defer further discussion of this subject to the next section." + For the rest of this analysis. we concenrate on the 14 GC's which have higher S/N. In Figure 6 we compare our data with the Alaraston&Thomas (2000) mocels. for the H (Pe5270 | be5335)/2. Mg». 111. Ley and L9i indices. and the combined. Mgle] index.," For the rest of this analysis, we concentrate on the 14 GCs which have higher S/N. In Figure \ref{fig:ssp2} we compare our data with the \citeANP{Maraston00} (2000) models, for the $\langle$ $\rangle$ (Fe5270 + Fe5335)/2, $_2$, $\beta$, $\gamma_A$ and $\delta_A$ indices, and the combined [MgFe] index." + To assist in our interpretaticon of the erids. an additional metallicity interval at Fell] = O.S4 has been included in the mocdoels shown in Figure 6.. by linear interpolation between he Fel] = 1.35 and )33 lines.," To assist in our interpretation of the grids, an additional metallicity interval at [Fe/H] = –0.84 has been included in the models shown in Figure \ref{fig:ssp2}, by linear interpolation between the [Fe/H] = –1.35 and –0.33 lines." + lt is clear that the individual data-points for the GC's populate a arge area of the SSP grid. parameter space., It is clear that the individual data-points for the GCs populate a large area of the SSP grid parameter space. + In the lower tyvo panels of Figure ο the distribution in 112 is broadly οnsistent with the observational errors following the old-agec loci of the grids., In the lower two panels of Figure \ref{fig:ssp2} the distribution in $\beta$ is broadly consistent with the observational errors following the old-aged loci of the grids. + The H4 index also behaves similarly: heavever itis clear that we can only measure L5 poorly., The $\delta_{\rm A}$ index also behaves similarly; however it is clear that we can only measure $\gamma_{\rm A}$ poorly. + We have also plotted the nuclear line-streneths of NGC 5241πο taken from “Tragerctal. (1998). which indicate an old. metal-rich stellar svstem.," We have also plotted the nuclear line-strengths of NGC 524 itself, taken from \citeANP{Trager98} (1998), which indicate an old, metal-rich stellar system." +higher than our values. while the VCS 5 values for the power-law galaxies are uniformly. lower.,"higher than our values, while the VCS $\gamma'$ values for the power-law galaxies are uniformly lower." + The dynamic range of the VCS +/ values is thus overall smaller than ours. and many of the VCS ! values place the galaxies in the intermediate zone between cores aud. power-laws.," The dynamic range of the VCS $\gamma'$ values is thus overall smaller than ours, and many of the VCS $\gamma'$ values place the galaxies in the intermediate zone between cores and power-laws." + In a number ol cases. often where Ferrareseetal.(20060). claimed the existeuce of large uuclei. the agreement between the two samples is expecially poor. with the VCS 5 values falling in the range of core ealaxies [or svstems that we lad classified as power-laws.," In a number of cases, often where \citet{lf} claimed the existence of large nuclei, the agreement between the two samples is especially poor, with the VCS $\gamma'$ values falling in the range of core galaxies for systems that we had classified as power-laws." + The ACS/WEC imagery used by the VCS study. aud the WEDPC2 and. WEPCI imagery that dominate the present sample provide essentially equivalent information., The ACS/WFC imagery used by the VCS study and the WFPC2 and WFPC1 imagery that dominate the present sample provide essentially equivalent information. + A comparison of WFEPC2/PCI aud ACS/WEC PSFs shows that WEPC2 actually provides significantly better angular resolution (Figure 9))., A comparison of WFPC2/PC1 and ACS/WFC PSFs shows that WFPC2 actually provides significantly better angular resolution (Figure \ref{fig:psf}) ). + The FWHM of the WEPC2/PCT F555W is 07061. while that of the ACS/WEC FL75W PSE is 07092. or larger.," The FWHM of the WFPC2/PC1 F555W is $0\asec061,$ while that of the ACS/WFC F475W PSF is $0\asec092,$ or larger." + The use of (Fruchter&Hook2002) to rectify the ACS images slightly degrades its resolution further., The use of \citep{driz} to rectify the ACS images slightly degrades its resolution further. + The present sample bas 19 galaxies at Virgo distance or closer. and a substantial number that are no more than umore clistaut: both the present aud VCS samples are probing the same plivsical scales in the galaxies.," The present sample has 49 galaxies at Virgo distance or closer, and a substantial number that are no more than more distant; both the present and VCS samples are probing the same physical scales in the galaxies." + Reearcdless of the resolution dilfereuce between WEPC2 and ACS. PSE-deconvolution provides a modelindepeucent approach to correct ASTtnagery for the “wines” of the PSF outside theAST diffraction limit aud to isolate the profile analysis from the residual blurring interior to the diffraction limit that remains even after deconvolution.," Regardless of the resolution difference between WFPC2 and ACS, PSF-deconvolution provides a model-independent approach to correct imagery for the “wings” of the PSF outside the diffraction limit and to isolate the profile analysis from the residual blurring interior to the diffraction limit that remains even after deconvolution." + The decouvolutiou tests presented in (1992b).. Laueretal. (1995).. Laueretal. (1993).. Restetal. (2001).. aud ave established that this methodology. works well forAST studies of brightness profiles: they also yield well-understood resolution limits.," The deconvolution tests presented in \citet{l92b}, \citet{l95}, \citet{l98}, \citet{rest}, and \citet{l05} have established that this methodology works well for studies of brightness profiles; they also yield well-understood resolution limits." + The ACS images cau be decouvolved as well to correct for ferences between the ACS aud WEPC2 PSFs outside the resolution limit., The ACS images can be deconvolved as well to correct for differences between the ACS and WFPC2 PSFs outside the resolution limit. + We demonustrate this with direct. Comparisons of decouvolved ACS and WEPC2 or WEPCI proliles for several galaxies --- COMMON., We demonstrate this with direct comparisons of deconvolved ACS and WFPC2 or WFPC1 profiles for several galaxies in common. +" Figure 10. compares proliles measured [roi PSF-cleconvolved ACS E175W. ""«drizzled"" images to those obtained from cdecouvolved WEPCI F555W images (Laueretal.1995). for eight galaxies iu common. and Crom decouvolved WEPC2 F552W images (Laueretal.2005) [or two galaxies in common."," Figure \ref{fig:acsdecon} compares profiles measured from PSF-deconvolved ACS F475W “drizzled"" images to those obtained from deconvolved WFPC1 F555W images \citep{l95} for eight galaxies in common, and from deconvolved WFPC2 F555W images \citep{l05} for two galaxies in common." + We present more extensive comparisons between ACS aud WEPCI than between ACS aud WEPC2 because this is the more challenging test: the WEPCI imagery was blurred by a strongly aberrated PSF., We present more extensive comparisons between ACS and WFPC1 than between ACS and WFPC2 because this is the more challenging test; the WFPC1 imagery was blurred by a strongly aberrated PSF. + Further. most of the power-law galaxies in coummon with the VCS sample were observed with WEDPCI rather than WEPC2: the steep central cusps in power-laws present a ereater challenge for deconvolution than do core galaxies.," Further, most of the power-law galaxies in common with the VCS sample were observed with WFPC1 rather than WFPC2; the steep central cusps in power-laws present a greater challenge for deconvolution than do core galaxies." + The agreemente between all tliree cameras in all cases is excellent. with differences between the," The agreement between all three cameras in all cases is excellent, with differences between the" +"two clusters, its density would came out overestimated because background and foreground galaxies not physically associated with it would wrongly contribute to the In order to comply with criteria that are generally adopted in the literature (namely 1 Mpc, 1000 kms~!), so that the results from this work could be easily compared with other reference papers, but also keeping an eye on the physical structures that constitute the CS, we decided to evaluate the density adopting the following compromise strategy.","two clusters, its density would came out overestimated because background and foreground galaxies not physically associated with it would wrongly contribute to the In order to comply with criteria that are generally adopted in the literature (namely $1$ Mpc, $1000~$$\rm km s^{-1}$ ), so that the results from this work could be easily compared with other reference papers, but also keeping an eye on the physical structures that constitute the CS, we decided to evaluate the density adopting the following compromise strategy." +" First we compress the ""Fingers of God"" of Coma and Abell 1367 in the redshift space by assigning to galaxies belonging to the ""Fingers of God"" a velocity equal to the average velocity of the cluster, plus or minus a random Gaussian distributed AV comparable to the transverse size of the cluster on the plane of the sky, assuming that clusters have approximately a spherical shape in 3-D. (We assume that the transverse size is 2 deg and 1 deg for Coma and A1367, corresponding to 248 and 124 kms""! respectively)."," First we compress the ""Fingers of God"" of Coma and Abell 1367 in the redshift space by assigning to galaxies belonging to the ""Fingers of God"" a velocity equal to the average velocity of the cluster, plus or minus a random Gaussian distributed $\Delta V$ comparable to the transverse size of the cluster on the plane of the sky, assuming that clusters have approximately a spherical shape in 3-D. (We assume that the transverse size is 2 deg and 1 deg for Coma and A1367, corresponding to 248 and 124 $\rm km s^{-1}$ respectively)." +keV aud Ady=2.82 keV aud a metal abuudauce Z—0.21 provides a good fit to the integrated spectrum.,"keV and $kT_2= +2.82$ keV and a metal abundance $Z = 0.21$ provides a good fit to the integrated spectrum." +(Pitjeva2009) and INPOP (Fiengaοἱal.20098) ephemericdes by including some vears of continuous radiometric ranging data to Cassini in addition to data of several types spanning the last century. (Pitjeva2008:Fiengaοἱal.2009b) both are non-zero al a statistically significant level (80 aud 1.26. respectively) and thev are compatible each other since their difference is equal to 4+10 mas |.,"\citep{Pit09} and INPOP \citep{INPOP} + ephemerides by including some years of continuous radiometric ranging data to Cassini in addition to data of several types spanning the last century, \citep{Pit08,Fie09} + both are non-zero at a statistically significant level $3\sigma$ and $1.2\sigma$, respectively) and they are compatible each other since their difference is equal to $4\pm 10$ mas $^{-1}$." + At themonent*.. no corrections A estimated with the DE ephemerides by NASA JPL are available.," At the, no corrections $\Delta\dot\varpi$ estimated with the DE ephemerides by NASA JPL are available." + lorio(2009a) unsuccessfully examined several possible ανασα] explanations in terms of both mundane. standard: Newlonian/relativislic gravitational phivsies ancl οἱ modified models of gravity.," \citet{Ior09} unsuccessfully examined several possible dynamical explanations in terms of both mundane, standard Newtonian/relativistic gravitational physics and of modified models of gravity." + Anyway. further analvses of extended data sets from Cassini with different dynamical force models are required to firmly. establish the existence of the anomalous perihelion precession of Saturn as a genuine physical effect.," Anyway, further analyses of extended data sets from Cassini with different dynamical force models are required to firmly establish the existence of the anomalous perihelion precession of Saturn as a genuine physical effect." + llere we will show that the existence of a localized distant body. (planet X/Nemesis). modeled in neither EPM nor INPOP ephenmerides. is a good candidate to explain a secular peribelion precession of Saturn having the characteristics of(2): indeed. contrary (o a massive ring usually adopted to model the action of the minor asteroids and of the Trans Neptunian Objects (TNOs). it vields a retrograde secular perihelion precessions and (he constraints on its distance for different postulated values of ils mass are consistent with several theoretical predictions put forth to accommodate some features of the Edgeworth-Ixuiper bell (Κακα&Mukai2008).," Here we will show that the existence of a localized distant body (planet X/Nemesis), modeled in neither EPM nor INPOP ephemerides, is a good candidate to explain a secular perihelion precession of Saturn having the characteristics of: indeed, contrary to a massive ring usually adopted to model the action of the minor asteroids and of the Trans Neptunian Objects (TNOs), it yields a retrograde secular perihelion precessions and the constraints on its distance for different postulated values of its mass are consistent with several theoretical predictions put forth to accommodate some features of the Edgeworth-Kuiper belt \citep{Lyk}." +. Concerning Nemesis. it would be an undiscovered stellar companion of the Sun which. moving along a highlv elliptical!.. would periodically disturb the Oort cloud being responsible of the periodicity of about 26 Alvr in extinction rates on the Earth over the last 250 Myr (Whitmire&al.1984): : (he Nemesis hypothesis has also been used to explain (he measurements ol the ages of 155 lunar spherules from the Apollo 14 site (Muller2002).," Concerning Nemesis, it would be an undiscovered stellar companion of the Sun which, moving along a highly elliptical, would periodically disturb the Oort cloud being responsible of the periodicity of about 26 Myr in extinction rates on the Earth over the last 250 Myr \citep{Nem1,Nem2}; the Nemesis hypothesis has also been used to explain the measurements of the ages of 155 lunar spherules from the Apollo 14 site \citep{Mul02}." +. See e.g. for huther details., See e.g. \citet{IorNem} for further details. + Interestingly. such a proposed explanation of the anomalous perihelion precession of Saturn in terms of pointlike dark matter is. to a certain extent. to be considered as degenerate since also the MOdified Newtonian Dynamics (MOND) (Milgrom1953) predicts certain subtle effects in the planetary region of the solar svstem," Interestingly, such a proposed explanation of the anomalous perihelion precession of Saturn in terms of pointlike dark matter is, to a certain extent, to be considered as degenerate since also the MOdified Newtonian Dynamics (MOND) \citep{Mil83} predicts certain subtle effects in the planetary region of the solar system" +fibre radius of 1.25 aresec. and under the assumption of an exponential surface brightness profile. a mean scale length of 2.9 aresec. a mean effective radius of 3.6 arcsec (Jerjen Dressler 19972) and for the case that the fibre had been ideally centred onto the galaxy.,"fibre radius of 1.25 arcsec, and under the assumption of an exponential surface brightness profile, a mean scale length of 2.9 arcsec, a mean effective radius of 3.6 arcsec (Jerjen Dressler 1997a) and for the case that the fibre had been ideally centred onto the galaxy." + Two fields were excluded from the analysis because of their much lower yield due to problems with the autoguider., Two fields were excluded from the analysis because of their much lower yield due to problems with the autoguider. + The limit in surface brightness which could be reached here confirms that projects aiming at the systematic measurement of redshifts for dwarf galaxies in nearby clusters are feasible. even with a multi-fibre instrument.," The limit in surface brightness which could be reached here confirms that projects aiming at the systematic measurement of redshifts for dwarf galaxies in nearby clusters are feasible, even with a multi-fibre instrument." + The only requirement is a large field of view., The only requirement is a large field of view. + 0.5cm Correction for the earth motion was then carried out. leading to heliocentric corrected redshifts for both the cross-correlation and the emission-line redshifts.," 0.5cm Correction for the earth motion was then carried out, leading to heliocentric corrected redshifts for both the cross-correlation and the emission-line redshifts." + For 32 galaxies the redshifts obtained here could be compared to those obtained previously by one of us (Stein 1996)., For 32 galaxies the redshifts obtained here could be compared to those obtained previously by one of us (Stein 1996). + Note that cross-correlation errors for the brightest galaxies in Stein (1996) might be slight underestimations. due to the fact that the template had been constructed using a sample of these same bright galaxies.," Note that cross-correlation errors for the brightest galaxies in Stein (1996) might be slight underestimations, due to the fact that the template had been constructed using a sample of these same bright galaxies." + Thus. the scaling factor between internal (Tonry Davis 1979) and external errors is determined using only galaxies in the calibration sample with errors of 20 or above.," Thus, the scaling factor between internal (Tonry Davis 1979) and external errors is determined using only galaxies in the calibration sample with errors of 20 or above." + With an error scaling factor of 1.7 the differences between redshifts in both datasets are perfectly consistent with the resulting external errors., With an error scaling factor of 1.7 the differences between redshifts in both datasets are perfectly consistent with the resulting external errors. + À zero-point shift of 26 was then applied to the cross-correlation data., A zero-point shift of 26 was then applied to the cross-correlation data. + Only for six galaxies it was possible to obtain both cross-correlation and emission-line redshifts., Only for six galaxies it was possible to obtain both cross-correlation and emission-line redshifts. + Again. the distribution of differences is in good agreement with the expectations. given the uncertainties in both measurements.," Again, the distribution of differences is in good agreement with the expectations, given the uncertainties in both measurements." + Finally. a weighted mean of emission and absorption (cross-correlation) redshifts was taken.," Finally, a weighted mean of emission and absorption (cross-correlation) redshifts was taken." + We measured redshifts for 115 galaxies., We measured redshifts for 115 galaxies. + The data are listed in 55a. 5b. and 5e combined with data from the CCC such as morphological type. total apparent D mmagnitude. ane SB.g.," The data are listed in 5a, 5b, and 5c combined with data from the CCC such as morphological type, total apparent $B$ magnitude, and $_{\rm eff}$." + Galaxies with no previous redshift measurement are subdivided into two lists according to cluster members 55a) and background objects 55b)., Galaxies with no previous redshift measurement are subdivided into two lists according to cluster members 5a) and background objects 5b). + 55e contains the data for galaxies which already had a redshift measured and are confirmed cluster members., 5c contains the data for galaxies which already had a redshift measured and are confirmed cluster members. + Among our galaxies there are 101 with velocities smaller than 5414ο., Among our galaxies there are 101 with velocities smaller than 5414. +.. This velocity corresponds to the 3 upper limit for the velocity distribution of Cen45 (LCD) and was used as a cut-off to discriminate between cluster members and background galaxies., This velocity corresponds to the $\sigma$ upper limit for the velocity distribution of Cen45 (LCD) and was used as a cut-off to discriminate between cluster members and background galaxies. + Actually. the remaining 14 velocities lie between [00000 and 0000 which makes a separation unambiguous.," Actually, the remaining 14 velocities lie between 000 and 000 which makes a separation unambiguous." + Our cluster sample was complemented by 19 redshifts taken from the literature (DCL: LC: Stein 1996)., Our cluster sample was complemented by 19 redshifts taken from the literature (DCL; LC; Stein 1996). + Finally. the dataset upon which the following analysis is based consists of redshifts for 120 cluster members located in the central cluster area.," Finally, the dataset upon which the following analysis is based consists of redshifts for 120 cluster members located in the central cluster area." + A weighted average was taken in case of nultiple redshifts. after homogenization of zero-point-shifts and sealing of errors among the four sources.," A weighted average was taken in case of multiple redshifts, after homogenization of zero-point-shifts and scaling of errors among the four sources." + The completeness of this data set is very high with respect to apparent magnitude and effective surface brightness., The completeness of this data set is very high with respect to apparent magnitude and effective surface brightness. + Redshifts are available for 96 percent of all known cluster galaxies brighter than 7217.5., Redshifts are available for 96 percent of all known cluster galaxies brighter than $B_{\rm T}$ =17.5. + At the limit of Br=18.5 our redshift sample is still complete to 78 percent.," At the limit of $B_{\rm +T}$ =18.5 our redshift sample is still complete to 78 percent." +" This latter magnitude corresponds to Mp=— 15.3. assuming a cluster distance modulus of (0.M(44,233.79 (Jerjen Dressler 1997b) and including an extinction. term of 4520.42."," This latter magnitude corresponds to $M_{B_{\rm T}}=-$ 15.3, assuming a cluster distance modulus of $(m-M)_{\rm Cen}$ =33.79 (Jerjen Dressler 1997b) and including an extinction term of $A_{\rm B}$ =0.42." +" For $B,.g the completeness levels are 93 percent at Baaresee?. and 78 percent at Baaresce 7. respectively."," For $_{\rm eff}$ the completeness levels are 93 percent at $\,B$ $^{-2}$ and 78 percent at $B$ $^{-2}$, respectively." + 55a and 5b contain data for 50 galaxies with new measured velocities among which 36 galaxies are cluster members according to our selection criterion., 5a and 5b contain data for 50 galaxies with new measured velocities among which 36 galaxies are cluster members according to our selection criterion. + Their Hubble type mixture is (1/3/11/21)., Their Hubble type mixture is (1/3/11/21). + The composition of the background sample is (0/3/6/5)., The composition of the background sample is (0/3/6/5). + For the latter sample the morphological information may not necessarily be true any more because the classification had been done under the assumption of cluster membership., For the latter sample the morphological information may not necessarily be true any more because the classification had been done under the assumption of cluster membership. + The new measured redshifts shall be used to estimate the accuracy of the morphological based cluster membership for dwarf galaxies in the CCC., The new measured redshifts shall be used to estimate the accuracy of the morphological based cluster membership for dwarf galaxies in the CCC. + For this purpose we compare in 22 the number of cluster members and background objects for the two dwarf families individually., For this purpose we compare in 2 the number of cluster members and background objects for the two dwarf families individually. + In 11. we give the three membership classes as listed in the CCC., In 1 we give the three membership classes as listed in the CCC. + 22 and 3 give the observed numbers of late-type dwarfs of a particular membership class divided into members (m) and background (b) according to their redshifts., 2 and 3 give the observed numbers of late-type dwarfs of a particular membership class divided into members (m) and background (b) according to their redshifts. + From 22 and 3 we derive the fraction of real cluster members in 44 which can be compared to the percentages listed in 11., From 2 and 3 we derive the fraction of real cluster members in 4 which can be compared to the percentages listed in 1. + The same analysis is done for the early-type dwarfs in the columns 5-7., The same analysis is done for the early-type dwarfs in the columns 5–7. + As can be seen. the numbers in 11. 4 and 7 are in good agreement.," As can be seen, the numbers in 1, 4 and 7 are in good agreement." + The case is slightly, The case is slightly +is that. higher observation density makes detection of high eccentricity planets more likely.,is that higher observation density makes detection of high eccentricity planets more likely. + The subsets of 1179949 show significant. variations in Di(e;). but is there a difference between stars?," The subsets of 179949 show significant variations in $D^\prime_{\mathrm{int}}(e_i)$, but is there a difference between stars?" +" Figure 14 shows Di,(e;) for each of the three objects. 1179949. 220782 and 338382."," Figure \ref{fig:eselfunc1} shows $D^\prime_{\mathrm{int}}(e_i)$ for each of the three objects, 179949, 20782 and 38382." + The shape of the curves. while in general decreasing at higher eccentricities. is dilleren [or each object.," The shape of the curves, while in general decreasing at higher eccentricities, is different for each object." + For example. when e;0.1 1179049 has the lowest fraction of planets redetected. however when e;2OS 1 iw the highest.," For example, when $e_i\le 0.1$ 179949 has the lowest fraction of planets redetected, however when $e_i\ge 0.8$ it has the highest." +" Thus data sampling ai quality are fundamental to the selection elfects. present in planet search observations and. a simple parametrisation of the detectability of cxoplanct parameters using ""whole-of-survey” metrics e.g. 2 done.", Thus data sampling and quality are fundamental to the selection effects present in planet search observations and a simple parametrisation of the detectability of exoplanet parameters using ``whole-of-survey'' metrics – e.g. \citet{Cumming04} –. + As an example. consider the case of 1179949.," As an example, consider the case of 179949." +" Of. the three sets. of observations we discuss here. the 1179949 data have the highest median measurement uncertainty ty, and one might naively expect it’s detectabilities to. he the lowest."," Of the three sets of observations we discuss here, the 179949 data have the highest median measurement uncertainty $^{-1}$ ), and one might naively expect it's detectabilities to be the lowest." + However. the observation density (equal to the observation time-span/number of observations or 7NTZN) is the highest at ddays/epoch. whieh should counteract the first elect to some degree.," However, the observation density (equal to the observation time-span/number of observations or $\Delta T/N$ ) is the highest at days/epoch, which should counteract the first effect to some degree." + It is not intuitively clear how to parametrise ancl compare the cetectability of the 1179949 observations. with. for example. that of the 338382. observations which have lower observation density but also lower median measurement. uncertainty without the simulations we have carried. out in this study.," It is not intuitively clear how to parametrise and compare the detectability of the 179949 observations, with, for example, that of the 38382 observations – which have lower observation density but also lower median measurement uncertainty – without the simulations we have carried out in this study." + Therefore carrying out simulations on a star-by-star basis is the way to understand the selection ellects in Doppler velocity. planet searches., Therefore carrying out simulations on a star-by-star basis is the way to understand the selection effects in Doppler velocity planet searches. + In the previous section. we examined DX(0;).. the detectability at each ο. which is at all 2? and AJ;.," In the previous section, we examined $D^\prime_{\mathrm{int}}(e_i)$ , the detectability at each $e_i$, which is at all $P_i$ and $M_i$." + This is fine [or the case of these simulations. where we know the input parameter valuespriori.," This is fine for the case of these simulations, where we know the input parameter values." +" Llowever. as this is never the case for actual Doppler planet data it is useful to consider our detectability at each 6,,: Le. the eccentricities rather than the input eccentricities."," However, as this is never the case for actual Doppler planet data it is useful to consider our detectability at each $e_m$; i.e. the eccentricities rather than the input eccentricities." + We call this quantity Dii0)., We call this quantity $D^\prime_{\mathrm{int}}(e_m)$. +" Leis determined by counting the number of correct detections i.c. false positives are excluded: in. equally spaced bins of e,,. normalised by the number of —-simulations in cach of bin."," It is determined by counting the number of correct detections – i.e. false positives are excluded – in equally spaced bins of $e_m$ , normalised by the number of simulations in each of bin." +We] now compare thetwo quantities.S (ο).' and,"We now compare thetwo quantities, $D^\prime_{\mathrm{int}}(e_m)$ and" +as a polytrope and that pοςT?[sin(za)/(12)]?/ (see Eq. [6]]).,as a polytrope and that $\rho \propto T^{3} \propto [sin(\pi x)/(\pi x)]^{3/4}$ (see Eq. \ref{eq:rho}] ]). +" However, the external layers of a SN typically have a steeper power-law distribution caused by the"," However, the external layers of a SN typically have a steeper power-law distribution caused by the" +finding extended the underprediction of high-mass subhalos to an underprediction of luminous satellites. implying that the MW-MCs system is unusual.,"finding extended the underprediction of high-mass subhalos to an underprediction of luminous satellites, implying that the MW-MCs system is unusual." + Similarly. Okamotoetal.(2010) explored a range of feedback models to add galaxies to some of the high resolution Aquarius halos (Springeletal.2008).," Similarly, \citet{Okamoto10} explored a range of feedback models to add galaxies to some of the high resolution Aquarius halos \citep{Springel08}." +. It was again difficult to readily reproduce halos with lummosities as bright as the MCs., It was again difficult to readily reproduce halos with luminosities as bright as the MCs. + Having looked in detail at a handful of simulated objects. however. this work indicates that there may be significant halo-to-halo scatter in the number of such massive objects.," Having looked in detail at a handful of simulated objects, however, this work indicates that there may be significant halo-to-halo scatter in the number of such massive objects." + The idea of intrinsic scatter in the subhalo population was expanded on in Ishiyamaetal. (2009a)., The idea of intrinsic scatter in the subhalo population was expanded on in \cite{Ishiyama09}. +". While this work did not concentrate specifically on MC-like subhalos. they did consider the range in number of subhalos with vj,sub!Verhos20.1."," While this work did not concentrate specifically on MC-like subhalos, they did consider the range in number of subhalos with $v_{max,sub}/v_{max,host} > 0.1$." + This work showed an extremely large variation (20-60) in the number of such massive subhalos a galaxy-sized halos would host., This work showed an extremely large variation (20-60) in the number of such massive subhalos a galaxy-sized halos would host. + In contrast to the semi-analytic modeling just discussed. Libeskindetal.(2007) used hydrodynamic simulations to model the luminosity functions for the satellites around MW-like host halos.," In contrast to the semi-analytic modeling just discussed, \cite{Libeskind07} used hydrodynamic simulations to model the luminosity functions for the satellites around MW-like host halos." + Their simulation identified 9 MW-like central galaxies and found that they. on average. have 1.6 satellites brighter than My.2—16 and a third of them had satellites with luminosities comparable to the LMC.," Their simulation identified 9 MW-like central galaxies and found that they, on average, have 1.6 satellites brighter than $M_V = +-16$ and a third of them had satellites with luminosities comparable to the LMC." + The recent Millennium-II and Bolshor simulations (Boylan-Kolchinetal.2010:Klypin2010) have. for the first time. allowed us to probe cosmological volumes to understand the predictions for the satellite populations of MW-like halos.," The recent Millennium-II and Bolshoi simulations \citep{BoylanKolchin10,Klypin10} have, for the first time, allowed us to probe cosmological volumes to understand the predictions for the satellite populations of MW-like halos." + The properties of these simulations are summarized in Table 1., The properties of these simulations are summarized in Table 1. + Boylan-Kolchinetal.(2010) (hereafter BKΙΟ) quantified the likelihood for 10'7M halos to host massive satellite galaxies in the Millennium-II ..simulation. finding that subhalos similar to the MCs are quite rare.," \citet{BoylanKolchin10} + (hereafter BK10) quantified the likelihood for $10^{12} \msol$ halos to host massive satellite galaxies in the Millennium-II simulation, finding that subhalos similar to the MCs are quite rare." + In this paper. we expand on this work by making similar measurements. for the Bolshor simulation. which used WMAP7 cosmological parameters. and using an abundance matching technique to make detailed comparisons between the Bolshoi predictions and the measurements from Liuetal.(2010).," In this paper, we expand on this work by making similar measurements for the Bolshoi simulation, which used WMAP7 cosmological parameters, and using an abundance matching technique to make detailed comparisons between the Bolshoi predictions and the measurements from \cite{Liu10}." +. Our goal is to understand just how well reproduces the statistical properties of bright satellites., Our goal is to understand just how well reproduces the statistical properties of bright satellites. + Note that this is the reverse question from the one that was asked in a companion paper. Bushaetal.(2010)..," Note that this is the reverse question from the one that was asked in a companion paper, \cite{Busha10c}." + That work assumed a satellite population and asked what the implications were for the properties of the host halo. including its mass.," That work assumed a satellite population and asked what the implications were for the properties of the host halo, including its mass." + Here. we assume a host halo mass and ask about the implications for the subhalo population.," Here, we assume a host halo mass and ask about the implications for the subhalo population." + There ts no reason for both questions to give the same answer: while Bushaetal.(2010) showed that a halo which hosts two MC-like satellites most likely has a mass near 1.2«10'M.. there is no reason to assume that a typical 1.2«I0'7M.. halo will have the MC:an as satellites.," There is no reason for both questions to give the same answer: while \cite{Busha10c} showed that a halo which hosts two MC-like satellites most likely has a mass near $1.2 \times 10^{12} \msol$, there is no reason to assume that a typical $1.2 \times 10^{12}\msol$ halo will have the MCs as satellites." + We begin by giving an overview of the Bolshoi simulation ins 2.. and then investigate the properties of massive dark matter satellites around dark matter host halos in $3.. focusing on the mass ranges for hosts and satellites that are most relevant to the MW system.," We begin by giving an overview of the Bolshoi simulation in \ref{sec:sims}, and then investigate the properties of massive dark matter satellites around dark matter host halos in \ref{sec:halos}, focusing on the mass ranges for hosts and satellites that are most relevant to the MW system." + The analysis here is similar to that of BKIO., The analysis here is similar to that of BK10. + In $4.. we assign galaxy luminosities to our suite of dark matter halos and extend the results for a sample with similar selection cuts as for observations.," In \ref{sec:luminosities}, we assign galaxy luminosities to our suite of dark matter halos and extend the results for a sample with similar selection cuts as for observations." + In this way. we are able to make detailed comparisons to the observational work of (Liuetal.2010.hereafterLIO) concerning the satellite population around MW-magnitude galaxies.," In this way, we are able to make detailed comparisons to the observational work of \cite[][hereafter L10]{Liu10} concerning the satellite population around MW-magnitude galaxies." + Section 4.4 gives the results of this analysis — see especially Figure 8.., Section \ref{sec:comparisons} gives the results of this analysis — see especially Figure \ref{fig:nsats_obs_sim}. + Finally. in 35.. we expand this study to include the satellite population of a more general distribution of hosts. and $6 summarizes our conclusions.," Finally, in \ref{sec:generalproperties}, , we expand this study to include the satellite population of a more general distribution of hosts, and \ref{sec:conclusions} summarizes our conclusions." + Throughout this paper. we adopt the convention /=0.7 (the value that was used in the Bolshoi simulation) when reporting values from either simulations or observations.," Throughout this paper, we adopt the convention $h = +0.7$ (the value that was used in the Bolshoi simulation) when reporting values from either simulations or observations." + We use the dark matter halos identified in the Bolshoi simulation (Klypinetal.2010:Trujillo-Gomez2010).," We use the dark matter halos identified in the Bolshoi simulation \citep{Klypin10, TrujilloGomez10}." +" This simulation modeled a 250 /r!Mpe comoving box using cosmological parameters similar to those derived by WMAP7 (Komatsuetal.2010): ©,,=0.27. O4=0.73. oy=0.82. i20.95. and h20.7."," This simulation modeled a 250 $\hmpc$ comoving box using cosmological parameters similar to those derived by WMAP7 \citep{Komatsu10}: $\Omega_m = 0.27$ , $\Omega_{\Lambda} = 0.73$, $\sigma_8 = 0.82$, $n=0.95$, and $h = 0.7$." + The simulation volume contains 2048? particles. each with a mass of 1.35«10°7!M.. and was run using the ART code (Kravtsovetal.1997).," The simulation volume contains $2048^3$ particles, each with a mass of $1.35 \times 10^8~\hinv\msol$ and was run using the ART code \citep{Kravtsov97}." +. 180 snapshots from the simulation were saved and analyzed., 180 snapshots from the simulation were saved and analyzed. + One of the unique aspects of this simulation ts the high level of spatial resolution employed. allowing objects to be resolved down to a physical scale of 1 A7'kpe.," One of the unique aspects of this simulation is the high level of spatial resolution employed, allowing objects to be resolved down to a physical scale of 1 $\hkpc$." + This gives us excellent ability to track halos as they merge with and are disrupted by larger objects. allowing us to track them even as they pass near the core of the host halo.," This gives us excellent ability to track halos as they merge with and are disrupted by larger objects, allowing us to track them even as they pass near the core of the host halo." + A summary of these simulation parameters is presented in Table Τ.., A summary of these simulation parameters is presented in Table \ref{table:simulations}. + Because we discuss our work in the context of the BKΙΟ results. we also present the same parameters for the Millennium II simulation (Boylan-Kolchinetal. 2009).. on which the ΒΚ10 results were based.," Because we discuss our work in the context of the BK10 results, we also present the same parameters for the Millennium II simulation \citep{BoylanKolchin09}, on which the BK10 results were based." + Halos and subhalos were identified using the BDM algorithm (Klypin&Holtzman1997)., Halos and subhalos were identified using the BDM algorithm \citep{Klypin97}. +.. The algorithm identifies maxima in. the density field and examines the neighboring region to identify bound particles., The algorithm identifies maxima in the density field and examines the neighboring region to identify bound particles. + In this way. it treats both halos and subhalos identically.," In this way, it treats both halos and subhalos identically." + Subhalos are just identified as objects living within the virial radius of a larger objects., Subhalos are just identified as objects living within the virial radius of a larger objects. +" Because of the high level of mass and spatial resolution. BDM results in a halo catalog that is complete down to a maximum circular velocity v4,250 km s!, where Vinay=Max(GmnDE This corresponds to à virial mass of roughly 10/57!M..."," Because of the high level of mass and spatial resolution, BDM results in a halo catalog that is complete down to a maximum circular velocity $\vmax = 50$ km $^{-1}$, where $\vmax = {\rm max}\left(\sqrt{{GM( and IL euission lines known from previous low-resolution spectroscopy (Castro-Tirado 11996)., The K band top panel shows the strong $\gamma$ and I emission lines known from previous low-resolution spectroscopy (Castro-Tirado 1996). + Similarly. we see Brackett series in cluission frou 11-1 4) to 15-1 A) iu the IT baud.," Similarly, we see Brackett series in emission from 11-4 $\eta$ ) to 15-4 $\lambda$ ) in the H band." + We do uot fine eudssiou as reported |w Castro-Tirado ((1996). Eikeuberry (1998) anc ((2000). supporting their conclusion that this is a variable feature probadv related to the N-rav state aud jet ejection activity.," We do not find emission as reported by Castro-Tirado (1996), Eikenberry (1998) and (2000), supporting their conclusion that this is a variable feature probably related to the X-ray state and jet ejection activity." + We note that during our 1999 ISAAC observation of GRS 1915105 was in a state of low activity at N-ravs and radio. though the time from the last radio flare and towards the rext radio flare were different to the ((2000) observation.," We note that during our 1999 ISAAC observation of GRS 1915+105 was in a state of low activity at X-rays and radio, though the time from the last radio flare and towards the next radio flare were different to the (2000) observation." + Both. the II as we Las lires are clearly rexἼνος. vaving FWIIM — 1015 aat a resolution of 5 (α ithe ID bou.," Both, the H as well as lines are clearly resolved, having FWHM $\sim$ 10–15 at a resolution of 5 (in the H band)." + Iftus were die to rotational Doppler adenine. it would correspond to a velocity of e sm 200300 kiu/s. In nost cases. these lines are οΗΝ but have a ceutra depression.," If this were due to rotational Doppler broadening, it would correspond to a velocity of $v$ $i$ $\sim$ 200–300 km/s. In most cases, these lines are not gaussian, but have a central depression." + Caven the Ct that he inchlation of the binary svsteni ds 7TUdeg#2¢ce (MiraIC Rodneuez 1991) oue indeed may alicipate a double-li edsrape., Given the fact that the inclination of the binary system is $i \sim 70\deg\pm2\deg$ (Mirabel Rodriguez 1994) one indeed may anticipate a double-lined shape. + We do not fd P Cre xofiles iu he Dr5 aud II as reported by ((2000)., We do not find P Cyg profiles in the $\gamma$ and I as reported by (2000). + Iu acdcition. we fiuc fortjo first time several absortion ines which allow us to make a rough ideutification of the donor in the CRS 19151105 binary.," In addition, we find for the first time several absorption lines which allow us to make a rough identification of the donor in the GRS 1915+105 binary." + Iu tιο WN uid we clearly ideutifv 300 absorption baud heads characteristic of a low te3uperature (TTOU| Is) star (c.g. Wletmmanun Hall 1986)., In the K band we clearly identify $^{12}$ CO absorption band heads characteristic of a low temperature $T< 7000$ K) star (e.g. Kleinmann Hall 1986). + Though weak. we also identity the CO (2.0 yand CO (3.1) trausilolis. indicating a bhunuimositv class IIT or brighter (e.g. Wallace Iüukle 1997).," Though weak, we also identify the $^{13}$ CO (2,0) and $^{13}$ CO (3,1) transitions, indicating a luminosity class III or brighter (e.g. Wallace Hinkle 1997)." + We also ileutifv t1 Na. doublet (2.2062L/2.20897 gnu). aud possibly the Ca triplet you). ALT (9.0088 μπι). aud the MgII doublet au) m absorption.," We also identify the Na doublet (2.20624/2.20897 $\mu$ m), and possibly the Ca triplet $\mu$ m), I (2.10988 $\mu$ m) and the I doublet $\mu$ m) in absorption." + Note that the CN doublet jiu). which In superelauts is more proniuneut than Al/Mg. is not detected.," Note that the CN doublet $\mu$ m), which in supergiants is more prominent than Al/Mg, is not detected." + Iu the II baud. we iceutiv Mell jn) hough 2CO (LL) may also conrbute) “CO (6.3) and CO (8.5) iu a ratio which is consistent with MEI standards (Mover 11998). axl II (16718.9/16750.6 jn).," In the H band, we identify I $\mu$ m) (though $^{12}$ CO (4,1) may also contribute), $^{12}$ CO (6,3) and $^{12}$ CO (8,5) in a ratio which is consistent with MK standards (Meyer 1998), and I (16718.9/16750.6 $\mu$ m)." + Comparing the 2.32.1 in ea spectrum from 20/21 July 1999 with hat taken on 21/25 July 2000 (after heliocentric correction). we find tvat the CO band head systems are shifted hy 60 lau's yolativ to cach other.," Comparing the 2.3–2.4 $mu$ m spectrum from 20/21 July 1999 with that taken on 24/25 July 2000 (after heliocentric correction), we find that the CO band head systems are shifted by 60 km/s relativ to each other." + The easiest interpretalon is Dopder moion. aud therefore midicates that the CO absorp10 ris indeed of photospheric origin aud not due to absorptio Lina static. cold. eieuustellar ecu.," The easiest interpretation is Doppler motion, and therefore indicates that the CO absorption is indeed of photospheric origin and not due to absorption in a static, cold, circumstellar medium." + Tus. we couchde tji we have identified the «onor in CRS 1915105. iux that it is a late-tvpe. K-M giant.," Thus, we conclude that we have identified the donor in GRS 1915+105, and that it is a late-type, K-M giant." + We have tried to coufirm the DIuunositv class more quantitatively by using the veiline-independent indicator r=loglLEW{302.O0)ΓΗ(Na)EW(Ca))| (Raiiirrez 11997).," We have tried to confirm the luminosity class more quantitatively by using the veiling-independent indicator $~~~~~r = \log [EW(^{12}{\rm CO} (2,0))/(EW({\rm Na}) + EW({\rm Ca}))]$ rez 1997)." + Because oftie low significance of tie Ca triplet. our measurement has a laree error: r=O0.25+0.20.," Because of the low significance of the Ca triplet, our measurement has a large error: $r = 0.25 \pm 0.20$." + This value falls in between the ranges covered by dwirfs 0.2z5e 50.0) and elants 15r SO.6) (Ramirrez 119097)., This value falls in between the ranges covered by dwarfs $r$ 0.0) and giants $r$ 0.6) rez 1997). + T1ο ratio of equivalent wiIths of 12CO to PCO which depends ou Iuuinositv class (Campbell 119903. has heen measured for the seven transitions covered. (ower panel of Fig. 2))," The ratio of equivalent widths of $^{12}$ CO to $^{13}$ CO which depends on luminosity class (Campbell 1990), has been measured for the seven transitions covered (lower panel of Fig. \ref{kspec}) )" + to 3+l. again supporting a giaut classification.," to $\sim 3 \pm 1$, again supporting a giant classification." + Usiug the IT band spectra. we also considered the veilme-iuxependent temperature/Iuuinositv discriminant EW(OT 1.6901 jun)/EW(Mg 1.5765. pon} vs. EW(CO 1.6610 µια. | CO L6187 μι)ΤΝλος 1.5765 flu) as proposed w Mover (1998).," Using the H band spectra, we also considered the veiling-independent temperature/luminosity discriminant EW(OH 1.6904 $\mu$ m)/EW(Mg 1.5765 $\mu$ m) vs. EW(CO 1.6610 $\mu$ m + CO 1.6187 $\mu$ m)/EW(Mg 1.5765 $\mu$ m) as proposed by Meyer (1998)." +" The OII line is. unfortunately, only marginally detected. aud therefore only the huninosity class caunot be : ↸⊳∪∐↴∖↴⊓⋅⋜"," The OH line is, unfortunately, only marginally detected, and therefore only the luminosity class cannot be constrained." +↧∐∐∖≺↧∙↽∕∏∐∖↑↸∖∐∏⋉∖↥⋅⋜↧⊓∐⋅↸∖↸∖↴∖↴↑∐⊔⋜↧↑↸∖⋅↖⇁↕↸∖↕≼⇂↴∖↴∿↓≺∖∩↸⇅⋅ ⋅ ∖⊐⋃⋃EN Is. which would sugseest a late-C 00r dX spectral type (IIoudashelt," The temperature estimate yields $\sim$ $^{+200}_{-500}$ K, which would suggest a late-G or K spectral type (Houdashelt" +trend Chat we see in all the models of starless cores. ie. the first scenario. (an example is shown in Fig. 9)),"trend that we see in all the models of starless cores, i.e. the first scenario, (an example is shown in Fig. \ref{mod_pre}) )" + is that. once the final density is reached (at (5.27x 109 ves). the molecular abundances of the observed species evolve since thev stabilize. changing by no more (han a few hundredthis with respect to the final value: the higher the depletion efficiency (he shorter the time needed to reach the stable state.," is that, once the final density is reached (at $\times$ $^6$ yrs), the molecular abundances of the observed species evolve since they stabilize, changing by no more than a few hundredths with respect to the final value: the higher the depletion efficiency the shorter the time needed to reach the stable state." + Another general trend is that the column density ol has a double peak. the first maximum is reached soon after the final density is reached. the second is the final value.," Another general trend is that the column density of has a double peak, the first maximum is reached soon after the final density is reached, the second is the final value." + This double peak behavior was also found by other authors (e.g. Gwenlanοἱal. 2000))., This double peak behavior was also found by other authors (e.g. \citealt{gwenlan00}) ). + In Fig., In Fig. + 9. we show the evolution of the column densities of the observed species in a starless core (ie. in the first scenario) with a density of 5x10! and à FR=0.2. that corresponds toa percentage of CO on grains of ad 7x 108 ves.," \ref{mod_pre} we show the evolution of the column densities of the observed species in a starless core (i.e. in the first scenario) with a density of $\times$ $^4$ and a FR=0.2, that corresponds to a percentage of CO on grains of at $\times$ $^6$ yrs." +" At lime around 9x 109 vrs the observed species stabilize their abundances and the predicted column densities of CS. and fall in the range of the observed values while NIL, and agree within a factor of 15."," At time around $\times$ $^6$ yrs the observed species stabilize their abundances and the predicted column densities of CS, and fall in the range of the observed values while $_3$ and agree within a factor of 15." +" A good agreement with the observations is also found al early limes. around 5.5x 109 vrs. for a slightly higher depletion efficiency (FR=0.4). however. also in this case. NIL, is between one and two orders of magnitude higher (hen observed."," A good agreement with the observations is also found at early times, around $\times$ $^6$ yrs, for a slightly higher depletion efficiency (FR=0.4), however, also in this case, $_3$ is between one and two orders of magnitude higher then observed." + In Fig., In Fig. + LO we show the column densities of the observed species vs time in (he best [fit model of the second scenario. ie. where a voung protostar is present in the core.," \ref{mod_pro} we show the column densities of the observed species vs time in the best fit model of the second scenario, i.e. where a young protostar is present in the core." + The general behaviour of Cs. NII; and is similar to the previous scenario while and CIL;OLII behave differently.," The general behaviour of CS, $_3$ and is similar to the previous scenario while and $_3$ OH behave differently." + In particular does not show the second peak and ΠΟΠ decreases quickly., In particular does not show the second peak and $_3$ OH decreases quickly. + The reason why methanol, The reason why methanol +Galactic winds and outllows are the primary mechanism by which galaxies deposit energy. anc metalenrichecl gas into the intergalactic. medium. This can greatly. alfect. the evolution of the LGAL and the subsequent formation of other generations of galaxies.,"Galactic winds and outflows are the primary mechanism by which galaxies deposit energy and metal-enriched gas into the intergalactic medium This can greatly affect the evolution of the IGM, and the subsequent formation of other generations of galaxies." + Feedback by galactic outflows can provide an explanation for the observed high mass-to-light ratio of dwarl galaxies ancl the abundance of dwarf galaxies in the Local Group. and can solve various problems with galaxy. formation mocels.," Feedback by galactic outflows can provide an explanation for the observed high mass-to-light ratio of dwarf galaxies and the abundance of dwarf galaxies in the Local Group, and can solve various problems with galaxy formation models," +are significant: we find tvpical changes of oover (he full range of coronal temperatures for O abundance variations of a factor of 2.,are significant: we find typical changes of over the full range of coronal temperatures for O abundance variations of a factor of 2. + When the other abundant light elements C ancl N are allowed to scale with the ο) abundance the diagnostic fares slightly less well but does provide discrimination between the photospherie compositions of GS and (2005)., When the other abundant light elements C and N are allowed to scale with the O abundance the diagnostic fares slightly less well but does provide discrimination between the photospheric compositions of GS and . +. The O abundance is llower than that of GS. and the ο Ka EWs differ by20-25%.," The O abundance is lower than that of GS, and the O $\alpha$ EWs differ by." +.. For a given exciting X-ray spectrum. changes in [Inorescent line strength with different photospheric parameters depend on changes in theshell of the fluorescent line in question.," For a given exciting X-ray spectrum, changes in fluorescent line strength with different photospheric parameters depend on changes in the of the fluorescent line in question." + For a solar composition. two other sources of opacity in (the vicinitw of the O edge are C and N. The chemical compositions of GS and differ by «10 iin O/C and O/N ratios. ancl the lockstep changes in these elements that dilutes the ellect of the dillerent O abundances relative to I1 on the O ἵνα EW.," For a solar composition, two other sources of opacity in the vicinity of the O edge are C and N. The chemical compositions of GS and differ by $< 10$ in O/C and O/N ratios, and the lockstep changes in these elements that dilutes the effect of the different O abundances relative to H on the O $\alpha$ EW." + Despite this slightly lower sensitivity of the [Inorescent line to the elobal chemical composition. accurate measurements of the O Ίνα EWs still potentially provide a new and relatively direct means of assessing the veracity of the GS and mixtures.," Despite this slightly lower sensitivity of the fluorescent line to the global chemical composition, accurate measurements of the O $\alpha$ EWs still potentially provide a new and relatively direct means of assessing the veracity of the GS and mixtures." + The line EW is also sensitive to (he abundances adopted [or the exciting coronal spectrum., The line EW is also sensitive to the abundances adopted for the exciting coronal spectrum. + This is due to the large contribution of the O VII He-lke complex to the source of ionising photons for coronal temperatures logZ'«6.5., This is due to the large contribution of the O VII He-like complex to the source of ionising photons for coronal temperatures $\log T < 6.5$. + To a lesser extent. Fe L-shell ancl Ne. Meg and $i [-like and Ile-like lines also make a contribution for temperatures up to lopLT7.0.," To a lesser extent, Fe L-shell and Ne, Mg and Si H-like and He-like lines also make a contribution for temperatures up to $\log T\sim 7.0$." + We have examüned (he sensitivity (o coronal abundances by comparison of O Ίνα line EWs computed for coronal spectra generated using GS and compositions. as illustrated in Figure 3..," We have examined the sensitivity to coronal abundances by comparison of O $\alpha$ line EWs computed for coronal spectra generated using GS and compositions, as illustrated in Figure \ref{f:ew}." + The former are hieher than the latter by an amount that decreases [from [for temperatures logT<6.3 where the O VII lines dominate. to ~LOY aat logο6.8 1.0.," The former are higher than the latter by an amount that decreases from for temperatures $\log T \leq 6.3$ where the O VII lines dominate, to $\sim 10$ at $\log T \sim 6.8$ –7.0." +" Differences at higher temperatures are largely due to the lower Ne. Mg. Si and Fe abundances in the composition (bv 74. 12. 10 and respectively),"," Differences at higher temperatures are largely due to the lower Ne, Mg, Si and Fe abundances in the composition (by 74, 12, 10 and respectively)." + In addition to uncertainties in the solar O content. coronal abundance variations are also expected as a result of chemical fractionation. in which the abundances of elements with low first lonisation potentials are seen to differ from photospheric values by. factors of up to ~11992)..," In addition to uncertainties in the solar O content, coronal abundance variations are also expected as a result of chemical fractionation, in which the abundances of elements with low first ionisation potentials are seen to differ from photospheric values by factors of up to $\sim +4$." + In this context. we emphasise (hat in a practical application of the fIuorescence technique the photospheric abundance would be deduced by comparing the model fluorescent EWs computed for different photospheric abundances and (he," In this context, we emphasise that in a practical application of the fluorescence technique the photospheric abundance would be deduced by comparing the model fluorescent EWs computed for different photospheric abundances and the" +30% of the currently observed Li or 11erely be a secondary source of Li in the galaxy.,$\%$ of the currently observed Li or merely be a secondary source of Li in the galaxy. +the proximity of these lines. the best. model describes the entire observed spectrum (except Ho) very well.,"the proximity of these lines, the best model describes the entire observed spectrum (except $\alpha$ ) very well." + This velocity measurement method. have multiple sources of error., This velocity measurement method have multiple sources of error. + One of them may be the systematic bias due the approximations in the model (LII. power-LIaw atmosphere. simple source function. ete.).," One of them may be the systematic bias due the approximations in the model (LTE, power-law atmosphere, simple source function, etc.)." + However. the comparison of our results with those [rom full NULL models (822)) show no systematic bias in the case of SNe 1999em and 2005ces.," However, the comparison of our results with those from full NLTE models \ref{sec_results}) ) show no systematic bias in the case of SNe 1999em and 2005cs." + The agreement between the velocities from these two very cillerent modeling codes are within X10 percent., The agreement between the velocities from these two very different modeling codes are within $\pm 10$ percent. + For SN 2006bp the dillerences are higher. but it will be shown below that for this SN the models do not describe well the spectral features we use. contrary tothe moclels (822)).," For SN 2006bp the differences are higher, but it will be shown below that for this SN the models do not describe well the spectral features we use, contrary tothe models \ref{sec_results06bp}) )." + Another source of error may be the correlation between the parameters., Another source of error may be the correlation between the parameters. + In Fig., In Fig. + 3. we present contour plots of the V hyperspace around its minimum. as a function of i14 and several other parameters that can allect the shape of the fitted A5169 feature.," \ref{contur} we present contour plots of the $\chi^2$ hyperspace around its minimum, as a function of $v_{model}$ and several other parameters that can affect the shape of the fitted $\lambda5169$ feature." + The thick black contour curve corresponds to 50% higher V7 than the minimum value., The thick black contour curve corresponds to 50 higher $\chi^2$ than the minimum value. +" I is visible that correlation is indeed. present (1.0. the contours are distorted) between 0,,,5,4 ancl the power-law exponent n or the optical depth rp.", It is visible that correlation is indeed present (i.e. the contours are distorted) between $v_{model}$ and the power-law exponent $n$ or the optical depth $\tau_{Fe}$. + The correlation is much less between Cyrede and Tp Of and Mg. whose features mav blend with A5169.," The correlation is much less between $v_{model}$ and $\tau_{ref}$ of and , whose features may blend with $\lambda5169$." +" Lowever. even for the correlated parameters. selecting n or τε, very far from their optimum value can alter 0,54 only bv a few hundred km +."," However, even for the correlated parameters, selecting $n$ or $\tau_{Fe}$ very far from their optimum value can alter $v_{model}$ only by a few hundred km $^{-1}$." +" Thus. we conclude that uncertainties in finding the minimum of 47 do not cause errors in co, that significantly exceed. the uncertainty due to the spectral resolution of the observed spectra (which is usually between 200 - 300 kim ly "," Thus, we conclude that uncertainties in finding the minimum of $\chi^2$ do not cause errors in $v_{model}$ that significantly exceed the uncertainty due to the spectral resolution of the observed spectra (which is usually between 200 - 300 km $^{-1}$ )." +A possible source of uncertainty may be that during the final fitting the wavelength interval around the used spectral feature is chosen somewhat subjectively., A possible source of uncertainty may be that during the final fitting the wavelength interval around the used spectral feature is chosen somewhat subjectively. + However. our tests showed that changing the limits reasonably has negligible ellect on the final velocities.," However, our tests showed that changing the limits reasonably has negligible effect on the final velocities." + ]t is emphasized. that. although the final fitting is restricted to a vicinity of a well-defined. spectral line. this method is certainly more reliable than the measurement of only the location ofthe οἱ the same feature.," It is emphasized that although the final fitting is restricted to a vicinity of a well-defined spectral line, this method is certainly more reliable than the measurement of only the location of the of the same feature." + As it was discussed above. the minimum can be significantly and systematically altered by signal-to-noise. spectral resolution. blending. ete.," As it was discussed above, the minimum can be significantly and systematically altered by signal-to-noise, spectral resolution, blending, etc." + The fitting of a model spectrum to the feature is expected to overcome these dillieulties. provided the underlving model is not too [ar from reality.," The fitting of a model spectrum to the feature is expected to overcome these difficulties, provided the underlying model is not too far from reality." +" UsingSYNOW as described. above. we determined. the best-fitting. parameters of all SNe spectra from See. οὃν,"," Using as described above, we determined the best-fitting parameters of all SNe spectra from Sec. \ref{sec_data}." +" The resulting mioclel velocities are collected in Table 11 in Appendix D. The best-fittingSYNOW parameters. such as T, For each atom/ion. the power-law exponent n and eycde together with the chosen Z,55,. can be found in Table in Appendix €. In Table Bl we also list theey, and Dus velocities."," The resulting model velocities are collected in Table \ref{vel} in Appendix B. The best-fitting parameters, such as $\tau_{ref}$ for each atom/ion, the power-law exponent $n$ and $v_{model}$ together with the chosen $T_{phot}$, can be found in Table \ref{synowtable} in Appendix C. In Table \ref{vel} we also list the$v_{Fe}$ and $v_{H\beta}$ velocities." + For SNe 1999em. 2005es ancl 2006bp.. we collected. the photospheric velocities from: CMFGEN. models of Dessart&LHillier(2006) ancl Dessartetal.(2008).," For SNe 1999em, 2005cs and 2006bp, we collected the photospheric velocities from $\tt CMFGEN$ models of \citet{dessart2006} and \citet{dessart2008}." +. These are included in Table Bl as Όρη., These are included in Table \ref{vel} as $v_{nlte}$. + Velocities from the ecross-correlation technique (Sect. 22)), Velocities from the cross-correlation technique (Sect. \ref{sec_cross}) ) + were obtained using two sets of template spectra., were obtained using two sets of template spectra. + The first set contained the 22 observed spectra of SN. 1999em. (set. #11). while the second set was based on the CMFGEN mocels mentioned above (set 22).," The first set contained the 22 observed spectra of SN 1999em (set 1), while the second set was based on the $\tt CMFGEN$ models mentioned above (set 2)." +" The velocities ofthe template spectra were re, for set #11 and 0,5, for set #22.", The velocities ofthe template spectra were $v_{Fe}$ for set 1 and $v_{nlte}$ for set 2. + We cross-correlated all the observed spectra with the two sets separately on the wavelength range of 4500 5500Α.. and the resulting velocities are also in Table BI as v.," We cross-correlated all the observed spectra with the two sets separately on the wavelength range of 4500 – 5500, and the resulting velocities are also in Table \ref{vel} as $v_{cc}$." + Fie., Fig. + 4 shows tna against phase for all studied SNe (top left. panel). and the ratio of tia to all the other velocities.," \ref{velocities} shows $v_{model}$ against phase for all studied SNe (top left panel), and the ratio of $v_{model}$ to all the other velocities." + The caleulated: velocities all show the expected decline with phase as the photosphere moves deeper anc deeper within the ejectra. toward slower expanding lavers.," The calculated velocities all show the expected decline with phase as the photosphere moves deeper and deeper within the ejectra, toward slower expanding layers." + Similar plots containing the ratio tyronefle. and Robsflee as Cunetions of phase. are presented in Fig. 5..," Similar plots containing the ratio $v_{model} / v_{cc}$ and $v_{abs} / v_{cc}$ as functions of phase, are presented in Fig. \ref{velcc}." + In the followings we provide some details of deriving these velocities for cach object ancl discuss some object-specilie dillerences between them., In the followings we provide some details of deriving these velocities for each object and discuss some object-specific differences between them. +" When determining t,o. Wilh SYNOW.. £2 was fitted or the first 6 spectra. then the A5169 feature was used or the remaining 16 spectra."," When determining $v_{model}$ with , $H\beta$ was fitted for the first 6 spectra, then the $\lambda5169$ feature was used for the remaining 16 spectra." + The resulting velocities are tween L1000 and 1800 kms 1., The resulting velocities are between $11000$ and $1800$ km $^{-1}$. + As seen in the bottom right xiuiel of Eig. 4.. ," As seen in the bottom right panel of Fig. \ref{velocities}, ," +μι and μι are about the same for the carly phases (before the appearance of the lines). while ater cus tends to be higher than Όροι.," $v_{model}$ and $v_{H\beta}$ are about the same for the early phases (before the appearance of the lines), while later $v_{H\beta}$ tends to be higher than $v_{model}$." +" Also. between day [15 and dày |40. 60,27 ds à slightly higher than er, (Fig."," Also, between day +15 and day +40, $v_{model}$ is a slightly higher than $v_{Fe}$ (Fig." + 4 bottom left panel)., \ref{velocities} bottom left panel). +" After day |40 6,5 drops below ey, and their ratio Increases toward later phases.", After day +40 $v_{model}$ drops below $v_{Fe}$ and their ratio increases toward later phases. + The velocities fron: models of (Dessart&Llill, The velocities from models of \citep{dessart2006} (Fig. +"ier2006) (Lig. 4 top right panel) agree with ey,cuc7.", \ref{velocities} top right panel) agree with $v_{model}$. + Phe cross-Correlation with set. #22 (Fie.5 bottom: panels) gave similar results for the first few points. but. overestimate Cone between davs |22 and. |80.," The cross-correlation with set 2 \ref{velcc} bottom panels) gave similar results for the first few points, but overestimate $v_{model}$ between days +22 and +80." +" ""ον mostly fall between Cg sand epo which is expected. since we eross-correlated the range of 4500 0500A.. where these features appear."," They mostly fall between $v_{H\beta}$ and $v_{Fe}$, which is expected, since we cross-correlated the range of 4500 – 5500, where these features appear." + The SYNOW model velocities of the L1 spectra that cover the second of halfthe plateau phase are between 3400 and 1700 km s+., The model velocities of the 11 spectra that cover the second half of the plateau phase are between $\sim$ 3400 and 1700 km $^{-1}$. + These are similar to those of SN 1999em at the same phase., These are similar to those of SN 1999em at the same phase. + Both ep. and eg; ave higher thaney. at all epochs. especially the latter with a factor of about 1.8 (Fig. 4)).," Both $v_{Fe}$ and $v_{H\beta}$ are higher than$v_{model}$ at all epochs, especially the latter with a factor of about $1.8$ (Fig. \ref{velocities}) )." + No model was available for SN. 2004dj., No model was available for SN 2004dj. + C'ross- with both template sets gavevery similar results., Cross-correlation with both template sets gavevery similar results. +" They are only slightly higher than both ruc. and vj, (Fig.5)).", They are only slightly higher than both $v_{model}$ and $v_{Fe}$ \ref{velcc}) ). + Forthe first 6 spectra the model was optimized for £13. then for the A5169 feature.," Forthe first 6 spectra the model was optimized for $H\beta$ , then for the $\lambda 5169$ feature." + Theresulting model velocities ave between 9700 and 1800 kms + (Fig. 4))., Theresulting model velocities are between 9700 and 1800 km $^{-1}$ (Fig. \ref{velocities}) ). + The, The +of GALEX | 0117 by comparing our non-L'TIS analysis to LEE results (Section 3.3.2).,of GALEX $+$ 0117 by comparing our non-LTE analysis to LTE results (Section 3.3.2). + Our original spectral svntheses were computed with the ine list available on the CD-ROAL No., Our original spectral syntheses were computed with the line list available on the CD-ROM No. + 23 of Ixurucz&Bell(1995) /kurucz23/sekur., 23 of \citet{kur1995} . +html.. For each ton. we now compare he oscillator strengths. (fi) and Stark line. broadening xwameters. (D) listed. by Ixurucz&Bell(1995). to the rest available theoretical and. experimental data.," For each ion, we now compare the oscillator strengths $f_{\rm ij}$ ) and Stark line broadening parameters $\Gamma$ ) listed by \citet{kur1995} to the best available theoretical and experimental data." +" Data on ine oscillator strengths are also available at the National Institute of Standards and Lechnoloey We noted that the isotopic shift in the 7°21 Πλοτος doublet is only [0.85 (Drullinger.Wineland.&Jerequist1980). and. therefore. we do not expect observable ellects on the MgiAHSI doublet in ""resolution spectra."," Data on line oscillator strengths are also available at the National Institute of Standards and Technology We noted that the isotopic shift in the $^{26-24}$ $\lambda$ 2798 doublet is only $+0.85$ $^{-1}$ \citep{dru1980} + and, therefore, we do not expect observable effects on the $\lambda$ 4481 doublet in $^{-1}$ -resolution spectra." + Similarly. other isotopic shifts (ce... οοἱ 781) may be neglected in the present study. (seeBerengut.Dzuba.&Flambaum 2003)..," Similarly, other isotopic shifts (e.g., $^{30}{\rm Si}/^{28}{\rm Si}$ ) may be neglected in the present study \citep[see][]{ber2003}. ." + The rich silicon. lino. spectrum in GALEN J1931[0117 prompted a detailed review of available data., The rich silicon line spectrum in GALEX J1931+0117 prompted a detailed review of available data. + Table 2. lists and compares fi from popular data compilations (CD23 and NIST) to homogeneous. theoretical. or experimental data sets., Table \ref{tbl-2} lists and compares $f_{\rm ij}$ from popular data compilations (CD23 and NIST) to homogeneous theoretical or experimental data sets. +.. We. noted considerable variations in oscillator strengths. in particular in the À3862 triplet and in A5041.024.," We noted considerable variations in oscillator strengths, in particular in the $\lambda$ 3862 triplet and in $\lambda$ 5041.024." +. Discrepancies of the order of 40 to would. allect individual abundance measurements in equal measures., Discrepancies of the order of 40 to would affect individual abundance measurements in equal measures. + For example. the ratio of CD23 data to experimental fi; values is 1.06 but varies with a standard deviation σ—38'4 while the NIST data that are largely based on the experimental values vary by only with an average ratio of 0.98. and the theoretical data (Artruetal.LOST) vary by with an average ratio of 0.98.," For example, the ratio of CD23 data to experimental $f_{\rm ij}$ values is 1.06 but varies with a standard deviation $\sigma=$ while the NIST data that are largely based on the experimental values vary by only with an average ratio of 0.98, and the theoretical data \citep{art1981} vary by with an average ratio of 0.98." + The adoption of one data set over another will not have a large effect on the average abundance. but. individual line measurements are less reliable.," The adoption of one data set over another will not have a large effect on the average abundance, but individual line measurements are less reliable." + Strong saturated lines are sensitive to line broadening parameters., Strong saturated lines are sensitive to line broadening parameters. + “Table 3/— lists full-width. at. half-maximunm: (FWHAI= Pu) Stark widths and shifts due to electron impacts for strong optical lines., Table \ref{tbl-3} lists full-width at half-maximum $\equiv 2w$ ) Stark widths and shifts due to electron impacts for strong optical lines. +" Ixurucz&Bell(1995) tabulate the circular. frequeney per electron. P that we converted into the PWLIM at 5,=107 ? using the formula: where e is the speed of light.", \citet{kur1995} tabulate the circular frequency per electron $\Gamma$ that we converted into the FWHM at $n_e=10^{17}$ $^{-3}$ using the formula: where $c$ is the speed of light. +Lanz.Dimitrijevic.&Artru(1988) tabulates FWILAT values for electron. and. proton impacts separately., \citet{lan1988} tabulates FWHM values for electron and proton impacts separately. + For most lines the proton contribution to the total width is 21054 up to1, For most lines the proton contribution to the total width is $\approx$ up to. +5/4... ENIM from ]|xurucz&Bell(1995). are on average Thelareer than the experimental values with a standard deviation of while the values from Lanz.Dimitrijevic.&Artru(1955) are only lower than the experimental values with a stanelare deviation of21%., The FWHM from \citet{kur1995} are on average larger than the experimental values with a standard deviation of while the values from \citet{lan1988} are only lower than the experimental values with a standard deviation of. + The execllent agreement between Lanz.Dimitrijevic.&Artru(1988). and the experiments prompted. us to explore two options in computing detailed. silicon line spectra., The excellent agreement between \citet{lan1988} and the experiments prompted us to explore two options in computing detailed silicon line spectra. + In option Lowe adopted. the silicon oscillator strengths. from Artruetal.(1981) and the line broadening parameters for electrons anclprotons from Lanz.Dimitrijevic.&Artru(1988)., In option 1 we adopted the silicon oscillator strengths from \cite{art1981} and the line broadening parameters for electrons andprotons from \citet{lan1988}. +". The aepening parameters are tabulated at 5. 10. 20. and C dx with estimated: uncertainties of less than at 5»,=107 em (or a depth zj£z2 in the atmosphere)."," The line broadening parameters are tabulated at 5, 10, 20, and $\times10^3$ K with estimated uncertainties of less than at $n_e=10^{17}$ $^{-3}$ (or a depth $\tau_R\approx 2$ in the atmosphere)." +" Also. the clleet of Stark shifts are. included using the experimental data of Gonzálezctal.(2002) although we have no information onthe scaling of d, with temperature or on M magnitude of Stark shifts due to ions (protonsin this case)."," Also, the effect of Stark shifts are included using the experimental data of \citet{gon2002} although we have no information onthe scaling of $d_e$ with temperature or on the magnitude of Stark shifts due to ions (protons in this case)." + The ellect of Stark shifts is apparent in radial velocity measurements of the AADOVAL-5055 ancl AA5967-5978 MNopts (seeTable1 ., The effect of Stark shifts is apparent in radial velocity measurements of the $\lambda\lambda$ 5041-5055 and $\lambda\lambda$ 5967-5978 multiplets \citep[see Table~\ref{tbl-1} . + byIn option 2. we emploved the cata Cfi; and D) iil lxurucz (1995)... and neglected the ellect of Stark shifts.," In option 2, we employed the data $f_{\rm ij}$ and $\Gamma$ ) compiled by \citet{kur1995}, and neglected the effect of Stark shifts." + Unlike silicon. the magnesium abundance measurement. is based on a single doublet.," Unlike silicon, the magnesium abundance measurement is based on a single doublet." + The red. Mg11AT989. multiplet shows evidence of Stark shifts (Vennes.Ixawka.&Németh2010a) although the spectrum is particularly noisy in the vicinity. of the multiplet.," The red $\lambda$ 7989 multiplet shows evidence of Stark shifts \citep{ven2010a} + although the spectrum is particularly noisy in the vicinity of the multiplet." + On the other hand. the strong TAKS1 doublet is well exposed.," On the other hand, the strong $\lambda$ 4481 doublet is well exposed." + Because of its strength. the Dine profile is particularly sensitive to. broadening parameters. although quoted oscillator strength: values.are consistent (NISTandIxurucz&Bell1995) within = 2%..," Because of its strength, the line profile is particularly sensitive to broadening parameters, although quoted oscillator strength valuesare consistent \citep[NIST and][]{kur1995} + within $\la2$ ." + The compilation of Ixurucz&Bell) does not provide a Stark width for the Mgl1A4481. doublet. which is then estimated in using the formula (Castelli2005) ," The compilation of \citet{kur1995} does not provide a Stark width for the $\lambda$ 4481 doublet which is then estimated in using the formula \citep{cas2005} + " +applicable to large gas-grain chemical networks.,applicable to large gas-grain chemical networks. + Such a scheme must provide rate continuity over the stochastic-deterministic threshold at (N(7))=1., Such a scheme must provide rate continuity over the stochastic--deterministic threshold at $\langle N(i) \rangle = 1$. + Any functional form must also be integrable using standard differential equation-solving techniques (i.e. the Gear algorithm)., Any functional form must also be integrable using standard differential equation-solving techniques (i.e. the Gear algorithm). +" Below, further modifications to, and restrictions on, the basic equations (11) and (12) are formulated."," Below, further modifications to, and restrictions on, the basic equations (11) and (12) are formulated." + The switch-over between the modified rate and the standard rate may produce a discontinuity in the rates at (N(i))=1., The switch-over between the modified rate and the standard rate may produce a discontinuity in the rates at $\langle N(i) \rangle =1$. +" Dependent on the relative rates of all the processes involved, this may present an impediment to accurate calculations."," Dependent on the relative rates of all the processes involved, this may present an impediment to accurate calculations." +" Therefore, a simple empirical function, f, is introduced to make the transition smoother whilst preserving a fast switch-over."," Therefore, a simple empirical function, $f$, is introduced to make the transition smoother whilst preserving a fast switch-over." +" Under this scheme, production rates arealways modified according to: where: This has the effect that when (N(A)),(N(B))«1, the rate is always ""stochastic"", whilst quickly tending towards the deterministic rate as either (N(A)) or (N(B)) rises above unity."," Under this scheme, production rates are modified according to: where: This has the effect that when $\langle N(A) \rangle, \langle N(B) \rangle < 1$, the rate is always “stochastic”, whilst quickly tending towards the deterministic rate as either $\langle N(A) \rangle$ or $\langle N(B) \rangle$ rises above unity." +" For example, if species A and B both attain abundances of 10 atoms/molecules per grain, the deterministic contribution to the total production rate will be of the normal deterministic rate."," For example, if species $A$ and $B$ both attain abundances of 10 atoms/molecules per grain, the deterministic contribution to the total production rate will be of the normal deterministic rate." + Expressions (14) (15) therefore allow the modified rate contribution to replace a fraction of the total deterministic rate that corresponds to the reaction of 1 atom/molecule of species A with 1 atom/molecule of species B., Expressions (14) (15) therefore allow the modified rate contribution to replace a fraction of the total deterministic rate that corresponds to the reaction of 1 atom/molecule of species $A$ with 1 atom/molecule of species $B$. +" Equation (13) is also applied, meaning that if Rjo4(AB)>kap:(N(A))-(NCB)), the total rate is equal to the unmodified deterministic rate."," Equation (13) is also applied, meaning that if $R_{mod}(AB) > k_{AB} \cdot \langle N(A) \rangle \cdot \langle N(B) \rangle$, the total rate is equal to the unmodified deterministic rate." +" The continuous rate-modification scheme outlined above is used to examine the water and methanol systems, at 15 K, as investigated by Barzel&Biham(2007b)."," The continuous rate-modification scheme outlined above is used to examine the water and methanol systems, at 15 K, as investigated by \cite{barzel2}." +". The former scheme includes reactions between surface species H, O, and OH, resulting in Hz, O» and H2O production."," The former scheme includes reactions between surface species H, O, and OH, resulting in $_2$, $_2$ and $_2$ O production." +" The latter scheme also includes reactions with CO, HCO, H2CO, and CH30, leading to the production of methanol, CH30H, and carbon dioxide, CO»."," The latter scheme also includes reactions with CO, HCO, $_2$ CO, and $_3$ O, leading to the production of methanol, $_3$ OH, and carbon dioxide, $_2$." +" The reactions, fluxes, and binding energies are indicated in Tables 1 2."," The reactions, fluxes, and binding energies are indicated in Tables 1 2." + It should be noted that the methanol system investigated by Barzel Biham does not include any activation-energy barriers., It should be noted that the methanol system investigated by Barzel Biham does not include any activation-energy barriers. +" In fact, activation energies substantially complicate the behaviour of the methanol system; see Section 6."," In fact, activation energies substantially complicate the behaviour of the methanol system; see Section 6." +" Figures 3 4 show population sizes and production rates of key species, for the water and methanol systems, respectively."," Figures 3 4 show population sizes and production rates of key species, for the water and methanol systems, respectively." + Populations obtained from the new method (Section 4.1) are very well matched to the master-equation results of Barzel Biham., Populations obtained from the new method (Section 4.1) are very well matched to the master-equation results of Barzel Biham. +" Production rates are accurate at high and very low values of S, but values near the stochastic-deterministic threshold are more obviously inaccurate, whilst obeying the correct trend."," Production rates are accurate at high and very low values of $S$, but values near the stochastic–deterministic threshold are more obviously inaccurate, whilst obeying the correct trend." +" However, the new method is a very good first approximation."," However, the new method is a very good first approximation." + What are the underlying physical reasons for the disagreements?, What are the underlying physical reasons for the disagreements? + The production rates obtained from the new method rise to the rate equation values at lower values of S than the master-equation results., The production rates obtained from the new method rise to the rate equation values at lower values of $S$ than the master-equation results. +" This occurs before any reactants approach a population of 1, as the rate limit of equation (13) is reached before this."," This occurs before any reactants approach a population of 1, as the rate limit of equation (13) is reached before this." +" Hence, the empirical function that is used to switch over at the (N(i))=1 threshold is not the cause."," Hence, the empirical function that is used to switch over at the $\langle N(i) \rangle = 1$ threshold is not the cause." +" In fact, the modified rates are too fast because competition between surface processes has not been considered."," In fact, the modified rates are too fast because competition between surface processes has not been considered." +" At low values of S, reactions are extremely fast, due to the fast reaction rates of all reactants; see equation (3)."," At low values of $S$, reactions are extremely fast, due to the fast reaction rates of all reactants; see equation (3)." +" As S increases, reaction becomes slower, and the possibility arises that one or other reactant may evaporate before the two meet in the same binding site and react."," As $S$ increases, reaction becomes slower, and the possibility arises that one or other reactant may evaporate before the two meet in the same binding site and react." +" For hydrogen atoms in the water and methanol systems, using the binding energies shown in Table 2, Κηχ=Kevap(H) when S~460 sites per grain."," For hydrogen atoms in the water and methanol systems, using the binding energies shown in Table 2, $k_{HX}=k_{evap}(H)$ when $S \simeq 460$ sites per grain." +Our individual limits are siguificautlv better than the studies at 2=3. πο if there are significaut nunibers of ealaxies with lower escape fractious (eg. fiero)~0.20.,"Our individual limits are significantly better than the studies at $z=3$, so if there are significant numbers of galaxies with lower escape fractions (eg. $f_{\mathrm{esc,rel}}\sim 0.20$," + rather than unitv). we would be able to detect thei.," rather than unity), we would be able to detect them." + We see no evidence for this scenario iu our sample., We see no evidence for this scenario in our sample. + Comparing our findings. which are in agreement with all other 2<1 f; measurements. with :~23 studies (?7) nuplies that the average escape fraction evolves with redshift. but the cause of this evolution reais nuknown.," Comparing our findings, which are in agreement with all other $z<1$ $f_{\mathrm{esc}}$ measurements, with $z\sim3$ studies \citep{2006ApJ...651..688S,2009ApJ...692.1287I} implies that the average escape fraction evolves with redshift, but the cause of this evolution remains unknown." + It should be noted. however. that foreground contanunation which is likely more severe at higher redshift. ταν account for some of the apparent evolution seen between 2= Laud 3. by this work aud others (??7)..," It should be noted, however, that foreground contamination which is likely more severe at higher redshift, may account for some of the apparent evolution seen between $z=1$ and 3, by this work and others \citep{2010arXiv1001.3412S,2010MNRAS.404.1672V,2006MNRAS.371L...1I}." + We proceed by focusing on possible imechauisunis that could explain the lack of large escape fraction galaxies at lol., We proceed by focusing on possible mechanisms that could explain the lack of large escape fraction galaxies at $z\sim1$. + When comparing biel and low-redshift ealaxy saluples. there is always some degree of uucertaimty reearding the true analog nature of the two populations.," When comparing high- and low-redshift galaxy samples, there is always some degree of uncertainty regarding the true analog nature of the two populations." + As discussed in Section 2 and shown in Figure | we selected a sample of LBC analogs sharing many of he same properties of the 7. and ? 2—3 LBCs.," As discussed in Section \ref{sec:selection} and shown in Figure \ref{fig:surf_bright}, we selected a sample of LBG analogs sharing many of the same properties of the \citet{2006ApJ...651..688S} and \citet{2009ApJ...692.1287I} $z\sim3$ LBGs." + Figure 10 further hiehliehts their similarities showiug he distribution of reddening. stellar mass and rest-παλιο UV luminosity in these sources is simular to the distribution in LBCs.," Figure \ref{fig:ebv_mass} further highlights their similarities showing the distribution of reddening, stellar mass and rest-frame UV luminosity in these sources is similar to the distribution in LBGs." + The similarity in mass together with the UVoptical colors of the UVLCs miplies that hey iav still be uudergoiusg an carly. major episode of star formation rather than a small burst on top of a iddenu older population (alsosee?.forthesamereason LBGs}..," The similarity in mass together with the UV–optical colors of the UVLGs implies that they may still be undergoing an early, major episode of star formation rather than a small burst on top of a hidden older population \citep[also see][for the same reason applied +to LBGs]{2004ApJS..154...97B}." +" Ultimately, this sample of LBC analogs shares Muuerous smiluities to the parent LBC population. but since only —105415% of LBCs have been observed with sguificaut LyC detections. perhaps this subclass of LBCs has other processes at work allowing or aidius iu the escape of LyC plotous."," Ultimately, this sample of LBG analogs shares numerous similarities to the parent LBG population, but since only $\sim10\%-15\%$ of LBGs have been observed with significant LyC detections, perhaps this subclass of LBGs has other processes at work allowing or aiding in the escape of LyC photons." + Galaxy niergers offer au intriguing explanation for the Increased escape fraction seen at 2~3., Galaxy mergers offer an intriguing explanation for the increased escape fraction seen at $z\sim3$. + 7. noted that UVLGs typically exhibit faint tidal features sugecstive of aimeregcr or recent interaction., \citet{2008ApJ...677...37O} noted that UVLGs typically exhibit faint tidal features suggestive of a merger or recent interaction. + They therefore propose that the super starbursts in LDCs are trigeered by eas-rich mergers., They therefore propose that the super starbursts in LBGs are triggered by gas-rich mergers. + Similarly. ?— showed that of LBCs have structures akin to local starburst merecrs aud may be driven by similar processes.," Similarly, \citet{2009AJ....138..362P} showed that of LBGs have structures akin to local starburst mergers and may be driven by similar processes." + As ealaxies collide. strong eravitational auc tidal forces can expel loug streams of stars. and ignite violent starbursts at rates of a few to hundreds of M. vrt (?77)..," As galaxies collide, strong gravitational and tidal forces can expel long streams of stars, and ignite violent starbursts at rates of a few to hundreds of $M_{\odot}$ $^{-1}$ \citep{1982ApJ...252..455S,2000ApJ...530..660B,2010ApJ...709.1067B}." + During a merger. the tidal fields distort the ealaxies racially. drawing out galactic material iuto long tails. pluues aud bridges (e.g...2?)..," During a merger, the tidal fields distort the galaxies radially, drawing out galactic material into long tails, plumes and bridges \citep[e.g.,][]{1972ApJ...178..623T,1996ApJ...464..641M}." + The ID I reservoirs can become disturbed. aud the neutral gas pulled away from the sources of ioniziug radiation producing low-cohuun deusitv lines of sight (??) through the ealaxics. in turn allowing the escape of LyC photons.," The H I reservoirs can become disturbed, and the neutral gas pulled away from the sources of ionizing radiation producing low-column density lines of sight \citep{2000AJ....119.1130H,2008AJ....135..548D} through the galaxies, in turn allowing the escape of LyC photons." + Simulations bv? sugeest that the escape fraction in major merecrs can be large (οντως 30%) compared to nonduergers Gf< 10%) alone specific lines of sight.," Simulations by \citet{2008ApJ...672..765G} suggest that the escape fraction in major mergers can be large $f_{\mathrm{esc,rel}}\gsim30\%$ ) compared to non-mergers $f_{\mathrm{esc,rel}}<10\%$ ) along specific lines of sight." + Within our suuple of 32 sealaxies. 1l had morphologies consistent with merecr activity.," Within our sample of 32 galaxies, 11 had morphologies consistent with merger activity." + We independently stacked cight of these spectra (removing three due to their larger spatial extent) aud fud fire<2% (80 upper linüt).," We independently stacked eight of these spectra (removing three due to their larger spatial extent) and find $f_{\mathrm{esc,rel}}<2\%$ $3\sigma$ upper limit)." + Tf mereiue is a viable mechanisin for clearing pathways in the ISM for LyC photons. the orientation of the svstem along the line of sight is also a likely factor. requiring a laree suple of UV. luminous mergers," If merging is a viable mechanism for clearing pathways in the ISM for LyC photons, the orientation of the system along the line of sight is also a likely factor, requiring a large sample of UV luminous mergers." + Therefore. we cannot sav whether mergers are an important factor as our saple size is at present too sinall.," Therefore, we cannot say whether mergers are an important factor as our sample size is at present too small." + Currently. there is a lack of deep high-resolution rest-frame optical nuaeine ofthe LDGs with larger escape fractions. aud the interpretation of UV morphologies remains problematic (?)..," Currently, there is a lack of deep high-resolution rest-frame optical imaging of the LBGs with larger escape fractions, and the interpretation of UV morphologies remains problematic \citep{2007ApJ...656....1L}." + Future near-IR observations with oof the :~3 LBC leakers will shed light ou this hypothesis., Future near-IR observations with of the $z\sim3$ LBG leakers will shed light on this hypothesis. + As discussed carlicr in the section. galaxy mergers are capable of clearing patlwavs. exposing UV bright stars.," As discussed earlier in the section, galaxy mergers are capable of clearing pathways, exposing UV bright stars." + If merecrs do facilitate the escape of LyC radiation heu an evolving merger rate. may be responsible for he observed evolution in [οταν ," If mergers do facilitate the escape of LyC radiation then an evolving merger rate, may be responsible for the observed evolution in $f_{\mathrm {sc,rel}}$." +Numerous observational studies auc simulations haven shown that the ealaxv nerecr rate evolves with+ redshift.a eoiug. as ~(1+|:)27H CQUNTTTTy.," Numerous observational studies and simulations haven shown that the galaxy merger rate evolves with redshift, going as $\sim(1+z)^{2-3}$ \citep{2001ApJ...546..223G,2003AJ....126.1183C,2007ApJS..172..320K,2007ApJ...659..976H,2007ApJ...659..931B,2008MNRAS.386..909C,2010ApJ...709.1067B}." + The factor of 3-1 iuerease m iuerger rate jetween id and 3 as seen observationally. would also increase the number of lines of sights aud range of encounter paramcters observed in 2—3 galaxy mergers o» the same factor.," The factor of 3-4 increase in merger rate between $z\sim$ 1 and 3 as seen observationally, would also increase the number of lines of sights and range of encounter parameters observed in $z\sim3$ galaxy mergers by the same factor." + This would in tur increase the ikelihood of detecting LyC at higher redshift., This would in turn increase the likelihood of detecting LyC at higher redshift. + The LyC€ escape fraction is limited by the distribution of neutral lvdrogen along a Lue of sight aud likely depends on galactic parameters;, The LyC escape fraction is limited by the distribution of neutral hydrogen along a line of sight and likely depends on galactic parameters. + We now consider what ealaxy properties could evolve with redshift that reduce he cficiency of galactic outflows/climmeys in leaking LvC€ photons from Iuuinous galaxies., We now consider what galaxy properties could evolve with redshift that reduce the efficiency of galactic outflows/chimneys in leaking LyC photons from luminous galaxies. + Typical galaxies Gucluding UW bright galaxies) have )en Shown to be 1.5-3 times smaller at 2~3 than heir local counterparts (2??)..," Typical galaxies (including UV bright galaxies) have been shown to be 1.5-3 times smaller at $z\sim3$ than their local counterparts \citep{2006ApJ...650...18T,2002ApJ...579L...1P,2004ApJ...600L.107F}." + Although our sample was selected to have similar UV surface brightuesses as 2~3 LBCs (refer to Figure 1)). little is known about the rue optical sizes of LBGs or the gas distribution.," Although our sample was selected to have similar UV surface brightnesses as $z\sim3$ LBGs (refer to Figure \ref{fig:surf_bright}) ), little is known about the true optical sizes of LBGs or the gas distribution." + The velocities of galactic winds or outilows have been fond to © proportional to the SFR in LBCs (?).. therefore LBC and LBG analogs. having similar SER should ium principle eenerate outflows with similar velocities (a few huudred Sos ly," The velocities of galactic winds or outflows have been found to be proportional to the SFR in LBGs \citep{2006MNRAS.373..571F}, therefore LBG and LBG analogs, having similar SFR should in principle generate outflows with similar velocities (a few hundred km $^{-1}$ )." +" However. smaller salaxies would have higher SERs per uuit volume. which cau result iu more efficient ealactic winds (7). more casily clearing pathways or ""ehinmnev-like"" structures. aud im turni allowing for higher ""eaol (?).."," However, smaller galaxies would have higher SFRs per unit volume, which can result in more efficient galactic winds \citep{2005ARA&A..43..769V}, more easily clearing pathways or “chimney-like” structures, and in turn allowing for higher $f_{\mathrm{esc,rel}}$ \citep{2003ApJ...599...50F}." + With smaller galaxies. aud ligher-deusity starbursts comes the potential for a larger fraction of stars born iu very colpact star clusters. including super star clusters (SSCs).," With smaller galaxies, and higher-density starbursts comes the potential for a larger fraction of stars born in very compact star clusters, including super star clusters (SSCs)." + SSCs cau have thousands of vouung (50M) stars within a μαΠο radius of —10pc (7)., SSCs can have thousands of young $<$ 50Myr) stars within a half-light radius of $\sim$ 10pc \citep{2005ARA&A..43..769V}. + These extreme concentrations of hot O aud D stars can ercatly Hupact the state of the ISAL driving powerful galactic winds (like those seen iu M82). openime chanucls for LvC photons to escape.," These extreme concentrations of hot O and B stars can greatly impact the state of the ISM driving powerful galactic winds (like those seen in M82), opening channels for LyC photons to escape." + SSCs have been detected in the tidal tails (2). and outer regions of galaxies. which could explain the spatially offset LyC cussion (to the optical Cluission) detected bv ? ina few 2~3 LBCs.," SSCs have been detected in the tidal tails \citep{2009AAS...21334401C} and outer regions of galaxies, which could explain the spatially offset LyC emission (to the optical emission) detected by \citet{2009ApJ...692.1287I} in a few $z\sim3$ LBGs." + There is also some evidence that SSCs found in the local group, There is also some evidence that SSCs found in the local group +SO galaxies under study relevant to this analysis. as follows: Co.,"S0 galaxies under study relevant to this analysis, as follows: Col." + 1: the galaxy. denomination: Co., 1: the galaxy denomination; Col. + 2: alternate (NGC/IC) galaxy. denomination: Col., 2: alternate (NGC/IC) galaxy denomination; Col. + 3: the morphological classification: Co., 3: the morphological classification; Col. + 4: the H-band etlective radius rg and its error: Col., 4: the H-band effective radius $r_{e H}$ and its error; Col. + 5: the classification according to the IH-band prolile «lecomposition (see Col., 5: the classification according to the H-band profile decomposition (see Col. + 5 of Tab., 5 of Tab. + 2): , 2); Col. +6: the 1I-band bulge-to-total luminosity ratio (sce Col., 6: the H-band bulge-to-total luminosity ratio $B/T_H$ (see Col. + 6 of Tab., 6 of Tab. + 2): ., 2); Col. + T: the D-band elfective radius rg and its error: ., 7: the B-band effective radius $r_{e B}$ and its error; Col. +Sithe classification according to the D-band profile decomposition (see Col., 8: the classification according to the B-band profile decomposition (see Col. + 5 of Tab., 5 of Tab. + 2): , 2); Col. +9: the B-band bulge-to-total luminosity ratio p (see Col., 9: the B-band bulge-to-total luminosity ratio $B/T_B$ (see Col. + 6 of Tab., 6 of Tab. + 2): , 2); Col. +10: the observed. total L-banc magnitude LL and its error: Col., 10: the observed total H-band magnitude H and its error; Col. + 11: the observed total B-band magnitude D and its CDDOL., 11: the observed total B-band magnitude B and its error. + llereafter. no correction. for Galactic extinction. in direction either of the Virgo cluster or of the Coma cluster will be applied to the B- and L-bancl magnitudes. since this correction is negligible for our purposes.," Hereafter no correction for Galactic extinction in direction either of the Virgo cluster or of the Coma cluster will be applied to the B- and H-band magnitudes, since this correction is negligible for our purposes." + No correction [or internal extinction to the photometric parameters. of individual galaxies will be applied either., No correction for internal extinction to the photometric parameters of individual galaxies will be applied either. + lig., Fig. + 2 shows the distribution of the LS VCC early-tvpe clwarls listed in Tab., 2 shows the distribution of the 18 VCC early-type dwarfs listed in Tab. + 1 in the plane defined by the decimal ogarithm of the ratio o£ reg and rg (regir ag) and by the otal color index LL. Individual galaxies are represented w empty circles. asterisks or filled. circles if their surface xightness profile follows. either a ce Vaucouleurs-Iaw. a | disk decomposition. or an exponential-Iaw (tvpe 1. 2 or 3. respectively cf," 1 in the plane defined by the decimal logarithm of the ratio of $r_{e B}$ and $r_{e H}$ $r_{e B}/r_{e H}$ ) and by the total color index $-$ H. Individual galaxies are represented by empty circles, asterisks or filled circles if their surface brightness profile follows either a de Vaucouleurs-law, a $+$ disk decomposition, or an exponential-law (type 1, 2 or 3, respectively – cf." + Sect., Sect. + 2)., 2). + In panels a and sh) objects are classified. according to profile decomposition either in he IHI-band or in the B-band (cf., In panels `a' and `b' objects are classified according to profile decomposition either in the H-band or in the B-band (cf. + Tab., Tab. + 2). respectively.," 2), respectively." + Fig., Fig. + 2 shows that:, 2 shows that: +The relation. between far-infrarecl emission. and. the racio emission from galaxies at all redshifts is surprisingly tight (deJongetal.1985:HelouConclon1992:Ciar-pett2002) and leads to the conclusion that both trace recent star-[ormation. in the local ancl distant Universe.,"The relation between far-infrared emission and the radio emission from galaxies at all redshifts is surprisingly tight \citep{deJong85, Helou85, Condon92, Garret02} and leads to the conclusion that both trace recent star-formation, in the local and distant Universe." + ‘The far-infrared cmiussion is believed. to arise. from. the thermal emission of dusty clouds surrounding regions of star formation. whereas the radio emission arises [ron cosmic-ray electrons. accelerated in supernova remnants. of the dying stars. which emit svachrotron racliation.," The far-infrared emission is believed to arise from the thermal emission of dusty clouds surrounding regions of star formation, whereas the radio emission arises from cosmic-ray electrons accelerated in supernova remnants of the dying stars, which emit synchrotron radiation." + lt ds however unclear why there should be such a correlation between the thermal far-infrared emission. and the non-thermal radio emission over such a wide range of galaxy types ancl masses. from starburst svstenis to more normal galaxies.," It is however unclear why there should be such a correlation between the thermal far-infrared emission and the non-thermal radio emission over such a wide range of galaxy types and masses, from starburst systems to more normal galaxies." + As a result of this. many models resort toa relatively significant amount of fine tuning. such as assuming a much stronger magnetic field than what is estimated. via minimum energy arguments (e.g.Thompsonetal.2006).," As a result of this, many models resort to a relatively significant amount of fine tuning, such as assuming a much stronger magnetic field than what is estimated via minimum energy arguments \citep[e.g.][]{Thompson06}." +".. A full discussion of such arguments is bevond the scope of this paper: however. we refer to the reader to Lackietal.(2009) and Lacki&""Thompson(2009) who provide a detailed discussion of the various physical interpretations of the [ar-infrared.racio correlation (Εν)."," A full discussion of such arguments is beyond the scope of this paper; however, we refer to the reader to \citet{Lacki1} and \citet{Lacki2} who provide a detailed discussion of the various physical interpretations of the far-infrared--radio correlation (FIRC)." + Observationally. recent work has concentrated on exploring the FIRC as a function of redshift. mainly. because of the preponderance of deep.Spifzer ancl radio data over relatively small <10 square degree areas (c.g.Appletonetetal. 2010).," Observationally, recent work has concentrated on exploring the FIRC as a function of redshift, mainly because of the preponderance of deep and radio data over relatively small $<10$ square degree areas \citep[e.g.][]{Appleton04, Frayer06, Ibar08, Murphy09,Michalowski10, Sargent10,Bourne10}." +. Phis has led to several authors suggesting hat 1e FIRC remains unchanged out to high redshift (2221.5) (c.g.Sargentctal.2010)... whereas others suggest a shallow ecrease in the ratio between far-infrared. luminosity and radio Luminosity (e.g.Sevmourctal.2009).," This has led to several authors suggesting that the FIRC remains unchanged out to high redshift $z\gtsim 1.5$ ) \citep[e.g.][]{Sargent10}, whereas others suggest a shallow decrease in the ratio between far-infrared luminosity and radio luminosity \citep[e.g.][]{Seymour09}." +.. Constraining rw evolution of the FIRC is important as it may clp oi understanding of the physical mechanism which results in such a tight correlation between the thermal and non- emission., Constraining the evolution of the FIRC is important as it may help our understanding of the physical mechanism which results in such a tight correlation between the thermal and non-thermal emission. + For example. metallicity and temperature," For example, metallicity and temperature" +back the orbit of to show that a αναισα] disk runaway eveut ago is very likely the ejection mechanisi in this case.,back the orbit of to show that a dynamical disk runaway event ago is very likely the ejection mechanism in this case. + has a total velocity referred to the local standard of vest (LSR) of (Aaitzenetal.1998) inakiug it the second fastest runaway star after the massive B-type giautIID271791., has a total velocity referred to the local standard of rest (LSR) of \citep{maaap339} making it the second fastest runaway star after the massive B-type giant. +. The various sinularitics between both stars were motivation to us to re-investieate the origin of60350., The various similarities between both stars were motivation to us to re-investigate the origin of. +. To this ai we carried out a quantitative analysis of a lugh-resolition spectra using non-local thermodyuanic equilibrimu (NLTE) techniques for the first time., To this aim we carried out a quantitative analysis of a high-resolution spectrum using non-local thermodynamic equilibrium (NLTE) techniques for the first time. + Stellar paramctors were thus revised and elemental abundances constrained (Sect. 22))., Stellar parameters were thus revised and elemental abundances constrained (Sect. \ref{spectroscopy}) ). + The results together with proper motions from the new reduction of the Catalog were used to determine the current three-dineusional (3D) space velocity., The results together with proper motions from the new reduction of the Catalog were used to determine the current three-dimensional (3D) space velocity. + The following kincmatic analysis sugeested that the star originated iu or near the Crux-Scutiun spiral armi (Sect. ?7))., The following kinematic analysis suggested that the star originated in or near the Crux-Scutum spiral arm (Sect. \ref{kinematics}) ). + Finally we discuss the kinematic paramucters and the clemenutal abuudauce pattern in the liebt of the rivaling formation scenarios. ilc. binary supernova versus dynamical cluster ejection (Sect. ?7)).," Finally we discuss the kinematic parameters and the elemental abundance pattern in the light of the rivaling formation scenarios, i.e., binary supernova versus dynamical cluster ejection (Sect. \ref{discussion}) )." + was observed in 2008 December with he high-resolution echelle spectroeraph of the 9.2 wan Tobby-Eberly Telescope (ITET) at the McDonald Observatory., was observed in 2008 December with the high-resolution echelle spectrograph of the $9.2$ m Hobby-Eberly Telescope (HET) at the McDonald Observatory. + Three individual spectra with resolving over A/AA=15000 and useful wavelength rangeAA.. were co-added. resulting in a signal-to-noise ratio AAJ](S/N) avounud 110 in the blue visual range.," Three individual spectra with resolving power $\lambda/\Delta \lambda=15\,000$ and useful wavelength range, ] were co-added, resulting in a signal-to-noise ratio (S/N) around $140$ in the blue visual range." + Additionally. hree intermecdiate-resolution spectra taken in 2009 May and July with the 3.5 uuu telescope at Calar Alto. Spain. and its loneslt TWIN spectrograph were available chlareing the spectral coverage down toAA... naling accessible the high-order Baliner lines aud the Balmer jump.," Additionally, three intermediate-resolution spectra taken in 2009 May and July with the $3.5$ m telescope at Calar Alto, Spain, and its long-slit TWIN spectrograph were available enlarging the spectral coverage down to, making accessible the high-order Balmer lines and the Balmer jump." + The quantitative spectral analysis was carried out following the hybrid NLTE approach discussed by Nieva&Przvbilla(2006.2007.2008) aud Przvbillaetal. (2006): liue-blanketed LTE 1inodel atinosplieres were computed with ATLAS9 (νο 1993).. while NLTE liue formation calculations were performiecl using updated versions of DETAIL and SURFACE (Cuddings1981:Butler&Giddings 1985).," The quantitative spectral analysis was carried out following the hybrid NLTE approach discussed by \citet{niapjl639, niaap467, niaap481} and \citet{praap445}: line-blanketed LTE model atmospheres were computed with ATLAS9 \citep{ku93}, , while NLTE line formation calculations were performed using updated versions of DETAIL and SURFACE \citep{giphd, bu9}. ." +. State-ofthe-art model atoms were adopted allowing absolute elemental abuudauces to be obtained with hieh accuracy (κος. Przvbillaetal.2008a.) for anu overview).," State-of-the-art model atoms were adopted allowing absolute elemental abundances to be obtained with high accuracy (see \citealt{prapjl688,prapj684} for an overview)." + Atinospheric parameters and eleiieutal abundauces were derived by detailed line-profile analysis aud fitting of the spectral euergy distribution (SED)., Atmospheric parameters and elemental abundances were derived by detailed line-profile analysis and fitting of the spectral energy distribution (SED). + The fundamental atmospheric paranieters0.15. incroturbuleut velocity and projected rotational velocity were primarily coustrained— from Baluer and lines as well as the ionization equilibrimm.," The fundamental atmospheric parameters, microturbulent velocity and projected rotational velocity were primarily constrained from Balmer and lines as well as the ionization equilibrium." + Elemental abundances were then obtained by matching the nieasurable lines of the individual chemical species while keeping all other stellar parameters fixed (see Fig. 1))., Elemental abundances were then obtained by matching the measurable lines of the individual chemical species while keeping all other stellar parameters fixed (see Fig. \ref{abundance_uncertainties}) ). + Tn the eud. a final svuthetic spectrum was computed which excellently reproduces the observation (sec Fie. 2)).," In the end, a final synthetic spectrum was computed which excellently reproduces the observation (see Fig. \ref{comparison}) )," + coufinüuug the B-type nature of60350., confirming the B-type nature of. +. Tuterestinely. a helm abundance higher than solar.=11.21.. was required to match the Ποια lines. the depth of the Daliuer lines aud the SED sinultaneouslv (see Fig. 3)).," Interestingly, a helium abundance higher than solar, was required to match the helium lines, the depth of the Balmer lines and the SED simultaneously (see Fig. \ref{sed}) )." + The resulting abuudances (averaged over all lines of au clement) are τος iu Table 1.., The resulting abundances (averaged over all lines of an element) are listed in Table \ref{stellar}. + spectra vielded a barvceutric radial velocityAll of|. equivalent to iu very eood agreement with deDoerctal.(1988) who fouud|.," All spectra yielded a barycentric radial velocity of, equivalent to in very good agreement with \citet{deaap202} who found." + Bearing in mind the different time intervals between cach measurement. the star is unlikely a binary.," Bearing in mind the different time intervals between each measurement, the star is unlikely a binary." + Comparing the location of in the (Tig.logg) diagram to evolutionary tracks (Schalleretal.1992) of solar inetallicity as shown in Fig.," Comparing the location of in the $\left(T_{\rm eff},\log g \right)$ diagram to evolutionary tracks \citep{scaaps96} of solar metallicity as shown in Fig." + [allowed its mass and age to be constrained., \ref{evolution} allowed its mass and age to be constrained. + The distance to could then be calculated from AL. V. Tog. logg aud extinction Ay=VV)=O0.07mae using the method described by Raispecketal.(2001) to bekpc.," The distance to could then be calculated from $M$, $V$, $T_{\rm eff}$, $\log g$ and extinction $A_V=3.1\,E(B-V)=0.07\,\rm mag$ using the method described by \citet{raaap379} to be." +. The precision of the analysis was restricted by an interplav of three effects: Ij Les in a telpcrative region where the opticalTWIP spectrum shows very few strone but nium weak metal lines., The precision of the analysis was restricted by an interplay of three effects: I) lies in a temperature region where the optical spectrum shows very few strong but many weak metal lines. + II) A considerable fraction ofthelatter is s11icared out due to the high projected rotational velocity esiu/., II) A considerable fraction ofthelatter is smeared out due to the high projected rotational velocity . +. IIT) The, III) The +1997)]] to —2 [the singular isothermal sphere (SIS) case (Gott&Gunn1974:Gott1984)]] while maintaining the same mass density in lenses. the integral lensing probability increases by. more (han two orders of magnitudes lor the flat model of the Universe (LOO2).,"] to $-2$ [the singular isothermal sphere (SIS) case \citep{got74,tur84}] ] while maintaining the same mass density in lenses, the integral lensing probability increases by more than two orders of magnitudes for the flat model of the Universe (LO02)." + Therefore. lensing also sensitivelv probes small scale structure.," Therefore, lensing also sensitively probes small scale structure." + This complicates matters and renders it is hazardous (ο use observed lensing statistics to draw inferences with regard to cosmology before determining the sensitivity to other factors., This complicates matters and renders it is hazardous to use observed lensing statistics to draw inferences with regard to cosmology before determining the sensitivity to other factors. + In LOQ2. we have shown that in order to explain the observed numbers of lenses found in the JVAS/CLASS survey. at least. (wo populations of dark halos must exist in nature.," In LO02, we have shown that in order to explain the observed numbers of lenses found in the JVAS/CLASS survey, at least two populations of dark halos must exist in nature." + CNme population. which corresponds to normal galaxies. has masses <10M. and a steep inner densitv profile (azz2. i.e. SIS) presumably determined by the distribution of baryonic natevial in the inner parts of the other one. which corresponds (0 groups or clusters of galaxies. has masses >10!M. and a shallow inner density profile (a1.4. ie. similar to NEW).," One population, which corresponds to normal galaxies, has masses $\la 10^{13} M_\odot$ and a steep inner density profile $\alpha \approx 2$, i.e. SIS) presumably determined by the distribution of baryonic material in the inner parts of the other one, which corresponds to groups or clusters of galaxies, has masses $\ga 10^{13} M_\odot$ and a shallow inner density profile $\alpha \la 1.4$, i.e. similar to NFW)." + A similar conclusion has been obtained by Porciani&Macau(2000). [or explaining the number of lenses found in the CASTLES survey., A similar conclusion has been obtained by \citet{por00} for explaining the number of lenses found in the CASTLES survey. + These results are consistent with the theoretical studies on the cooling of massive gas clouds: there is a critical mass of halos ~10M. below which cooling of the corresponding barvonic component will lead to concentration of the barvous to the inner parts of the mass profile al. 1986).," These results are consistent with the theoretical studies on the cooling of massive gas clouds: there is a critical mass of halos $\sim 10^{13} M_\odot$ below which cooling of the corresponding baryonic component will lead to concentration of the baryons to the inner parts of the mass profile \citep{ree77,blu86}." +. In this paper we investigate (he lensing statistics produced by a compound population of halos., In this paper we investigate the lensing statistics produced by a compound population of halos. +" We assume (hat there are three populations of halos in (he Universe: Population A: LOMATAL.2x10""hHAL. a=1.3 [GNFW (generalizedNEW.Zhao 1996)]]: Population C: AZ<10hTAL... a=L3 (GNEW). where { is the IIubble constant in units of 100 kms ! |."," We assume that there are three populations of halos in the Universe: — Population A: $10^{10} h^{-1} M_\odot < M < 2\times 10^{13} h^{-1} +M_\odot$ , $\alpha = 2$ (SIS); — Population B: $M > 2\times 10^{13} h^{-1} M_\odot$, $\alpha = 1.3$ [GNFW \citep[generalized NFW,][]{zha96}] ]; — Population C: $M < 10^{10} h^{-1} M_\odot$, $\alpha = 1.3$ (GNFW), where $h$ is the Hubble constant in units of 100 km $^{-1}$ $^{-1}$." + Population A corresponds Lo spiral ancl elliptical galaxies. whose centers are dominated by baryonic matter.," Population A corresponds to spiral and elliptical galaxies, whose centers are dominated by baryonic matter." + Population D corresponds to groups or clusters of galaxies. whose centers are dominated by dark matter.," Population B corresponds to groups or clusters of galaxies, whose centers are dominated by dark matter." + Population C corresponds todwarl galaxies or subgalactie objects. whose centers lack barvons," Population C corresponds todwarf galaxies or subgalactic objects, whose centers lack baryons" +When we increase the 1tunber of the Gauss-Seidel iteration during a cycle of the inulti-grid iteration. we get a higher recuctiou in the residual per cycle at the expeuse of lounger computation ime.,"When we increase the number of the Gauss-Seidel iteration during a cycle of the multi-grid iteration, we get a higher reduction in the residual per cycle at the expense of longer computation time." + The recluction per uuii| colnputaion load is higher when we the Catss-Seicdel iteration is »erforijecd several times each., The reduction per unit computation load is higher when we the Gauss-Seidel iteration is performed several times each. + We tried the successive over relaxaion (SOR) itsteacl the Causs-Seicdel iteration to accelerate he converge but failec., We tried the successive over relaxation (SOR) instead the Gauss-Seidel iteration to accelerate the converge but failed. + Wren SOR ts used as the pre- aud post-relaxation in our imulti-ericl iteration. the residual iucreases sometiues cdepeucii[n]0 ou the initial guess.," When SOR is used as the pre- and post-relaxation in our multi-grid iteration, the residual increases sometimes depending on the initial guess." + SOR works well ouly when use one level of the grid. Le.. when the grid is iol nestec.," SOR works well only when use one level of the grid, i.e., when the grid is not nested." + We also tried to improve the interpolatiou formia. Equation (19)). lor a higher order accuracy.," We also tried to improve the interpolation formula, Equation \ref{interpolation1}) ), for a higher order accuracy." + We [οιud that our iter:ion did uot converge whet we used a higher order interpolation formula., We found that our iteration did not converge when we used a higher order interpolation formula. + Thougl we Ceui not εἶοιy existence of a successful i1erpolation formula. we could uot find it.," Though we can not deny existence of a successful interpolation formula, we could not find it." + We evaluated the computation oad of our multi-erid algorithin by measuring the computation time., We evaluated the computation load of our multi-grid algorithm by measuring the computation time. + A UNIX workstation. SGI 05 (MIPS R10000 250 MHz) was used for the measurement.," A UNIX workstation, SGI O2 (MIPS R10000 250 MHz) was used for the measurement." + The computation iine was Lnueasured with the subroutine DTIME., The computation time was measured with the subroutine DTIME. + Figure 9 shows the execution imme per FMG evcle., Figure \ref{etime.eps} shows the execution time per FMG cycle. +" When Tje abscissa deuotes the effective total number. Noell = finas""+ dnde logarithinie scale."," When The abscissa denotes the effective total number, $ N _{\rm cell} $ = $ +\ell _{\rm max} \, N ^3 $, in the logarithmic scale." + The ordinate denotes the logarithia of the computation liive. /.," The ordinate denotes the logarithm of the computation time, $ t $." + The dashed lies clenote the relajons. CPU ime xοι and CPU time.," The dashed lines denote the relations, CPU time $ \propto \, N _{\rm cell} $ and CPU time." +" We uade this pkX |wy chaugiug (gas al aN in the range of 2""dí10 and 5«ONx«12k."," We made this plot by changing $ \ell _{\rm max} $ and $ N $ in the range of $ 2 \, \le \, \ell \, \le \, 10 $ and $ 8 \, \le \, N +\, \le \, 128 $." + As slOW Lin Figure 9.. the coriputation load is p'oportional o the Αι when Noο32.," As shown in Figure \ref{etime.eps}, the computation load is proportional to the $ N _{\rm cell} $ when $ N \, \ge \, 32 $." + This Ineaus thi ilour aleorithin is scalabe for ποται auc arge nested erids., This means that our algorithm is scalable for medium and large nested grids. +" WeaSO lleastl'ed the computation time with the super compuer Fujitsu VPP5000 at National Astronomica Obse""alory. Japau."," We also measured the computation time with the super computer Fujitsu VPP5000 at National Astronomical Observatory, Japan." +" When N=256 a1| {Wax5. the CPU time is 0.21 sec per FMCG evele,"," When $ N \, = \, 256 $ and $ \ell _{\rm max} \, = \, 5 $, the CPU time is 0.21 sec per FMG cycle." + This CPU time is reasonably small σοιiparecl with the CPU time for solving the hivcdrodsnamical eqlation on the same nested grid., This CPU time is reasonably small compared with the CPU time for solving the hydrodynamical equation on the same nested grid. + Tlis CPU time is uot scalable to the number of cells siuce the suyer computer has vector processors aud its CPU time is not proportional to the computation load., This CPU time is not scalable to the number of cells since the super computer has vector processors and its CPU time is not proportional to the computation load. + As shown in the previous section. our numerical method provides an accurate solution with a reasonably small computation cost.," As shown in the previous section, our numerical method provides an accurate solution with a reasonably small computation cost." + The computation load is scalable in the seuse that it is proportional to the uumber of the cells contained iu the nested grid., The computation load is scalable in the sense that it is proportional to the number of the cells contained in the nested grid. + Our discrete Poissou equatiou is robust iu the sense that it cau be applied also to AMI as far as a parent cell is subcdivided into, Our discrete Poisson equation is robust in the sense that it can be applied also to AMR as far as a parent cell is subdivided into +with the highest overdensity particle. we strouud each potential deusitv maxima by a sphere of radius ring=105.!spe aud exclude all particles within this sphere from further search.,"with the highest overdensity particle, we surround each potential density maximum by a sphere of radius $r_{\rm find}=10h^{-1}\ \rm kpc$ and exclude all particles within this sphere from further search." + The search radius is defined by the size of sunallest svstenis we aiu to ileutifv., The search radius is defined by the size of smallest systems we aim to identify. + We verified that the results do not chanee if this radius is decreased by a factor ofup to four., We verified that the results do not change if this radius is decreased by a factor of up to four. + After all potential halo centers ave identified. we the deusity distribution aud velocitiesof surrounding particles analyzeto test whethercenter corresponds to a bound chup.," After all potential halo centers are identified, we analyze the density distribution and velocities of surrounding particles to test whether the center corresponds to a gravitationally bound clump." + Specifically. thewe coustruct the density. circular velocity. and velocity dispersion profiles around cach ceuter and iteratively remove wnbotud particlesdetails).," Specifically, we construct the density, circular velocity, and velocity dispersion profiles around each center and iteratively remove unbound particles." + We then coustruct final profiles using ouly bound particles and use them to calculate such halo properties as the naxinuun circular velocity Vj. mass M. ete.," We then construct final profiles using only bound particles and use them to calculate such halo properties as the maximum circular velocity $V_{\rm m}$, mass $M$, etc." + The virial radius is 11020inegless for the sublialos within a arecr host as their outer lavers are tidally stripped aud the extent of the halo is truncated., The virial radius is meaningless for the subhalos within a larger host as their outer layers are tidally stripped and the extent of the halo is truncated. + The definition of the outer voundary of a subhalo and its mass are thus somewhat aüubieuous., The definition of the outer boundary of a subhalo and its mass are thus somewhat ambiguous. + We adopt theradius. ἐν. at which he logarithmic slope of the deusitv profile constructed roni the bound particles becomes larger than 0.5 as we do not expect the density profile of the CDM. halos o be flatter than this slope.," We adopt the, $r_{\rm t}$, at which the logarithmic slope of the density profile constructed from the bound particles becomes larger than $-0.5$ as we do not expect the density profile of the CDM halos to be flatter than this slope." + Empirically. this definition roughly correspouds to the radius at which the density of he eravitationally bound particles is equal to the backeround rost halo density. albeit witha large scatter.," Empirically, this definition roughly corresponds to the radius at which the density of the gravitationally bound particles is equal to the background host halo density, albeit witha large scatter." + For some walos rg is larger than their virial radius., For some halos $r_{\rm t}$ is larger than their virial radius. +" Iu this case. we seta,—Rey."," In this case, we set $r_{\rm t}=R_{\rm vir}$." + Throughout this paper. we will denote the ΠΕ of the virial mass and mass within r. simply as AM.," Throughout this paper, we will denote the minimum of the virial mass and mass within $r_{\rm t}$, simply as $M$." + For ΠΕeach halo we also construct the circular velocity xofile V.tr)=ναλέςΕν aud compute the maximi circular velocity profile V4., For each halo we also construct the circular velocity profile $V_{c}(r)=\sqrt{GM( of the outer two planets, however, the LL solution does 0.1)not give a quantitatively acceptable answer."," Given the moderate eccentricity $e > 0.1$ ) of the outer two planets, however, the LL solution does not give a quantitatively acceptable answer." +" Consequently, we recompute the eccentricity ratios using the Gaussian averaging method, as described in section 2.4, utilizing the LL solution as an initial guess in the root-finding algorithm."," Consequently, we recompute the eccentricity ratios using the Gaussian averaging method, as described in section 2.4, utilizing the LL solution as an initial guess in the root-finding algorithm." + The resulting curves are plotted in figures (4) and (5)., The resulting curves are plotted in figures (4) and (5). +" It is noteworthy that although the Gaussian and LL solutions are qualitatively similar, higher-order secular terms clearly make a noticeable contribution to the fixed-point solution."," It is noteworthy that although the Gaussian and LL solutions are qualitatively similar, higher-order secular terms clearly make a noticeable contribution to the fixed-point solution." +" Although the error bars on the orbital elements are still large, it is noteworthy that the observed system is consistent with a fixed point configuration."," Although the error bars on the orbital elements are still large, it is noteworthy that the observed system is consistent with a fixed point configuration." +" Thus, further observation of the system is warranted, given that if the system is found to be in a stationary state, it would yield not only the true masses, but also a constraint on the tidal quality factor of the inner-most planet."," Thus, further observation of the system is warranted, given that if the system is found to be in a stationary state, it would yield not only the true masses, but also a constraint on the tidal quality factor of the inner-most planet." +" 'The domain of applicability of the method described in this paper does not extend to ""large"" planets that we require AP...)«1 in order to solve for (recall sin(I))"," The domain of applicability of the method described in this paper does not extend to “large"" planets (recall that we require $\Lambda_{tidal}^{p} \ll 1$ in order to solve for $\sin(I)$ )." +" However, for massive, close-in planets, the sin(I) degeneracy can be resolved from spectral characterization of the host star alone (Snellen et al 2010)."," However, for massive, close-in planets, the $\sin(I)$ degeneracy can be resolved from spectral characterization of the host star alone (Snellen et al 2010)." +" In such case, the orbital precession rate yields information on athe radius and the interior structure of the planet."," In such a case, the orbital precession rate yields information on the radius and the interior structure of the planet." +" If only a single planet is present in the system, then the method described by Ragozzine Wolf (2009) can be employed."," If only a single planet is present in the system, then the method described by Ragozzine Wolf (2009) can be employed." +" Namely, if the planet is sufficiently close to its host star, the orbital precession rate may be as high as a few "," Namely, if the planet is sufficiently close to its host star, the orbital precession rate may be as high as a few degrees/year." +"In this case, direct observation of the orbital precession degrees/year.can be related to the sum of equations (7) -(9)."," In this case, direct observation of the orbital precession can be related to the sum of equations (7) -(9)." +" As already discussed above, however, the first"," As already discussed above, however, the first" +of Be/X-rav binary pulsars are usually hard.,of Be/X-ray binary pulsars are usually hard. + A fluorescent iron emission line at GA keV is observed in the spectrum of most of the X-ray pulsars., A fluorescent iron emission line at 6.4 keV is observed in the spectrum of most of the X-ray pulsars. + Lt is possible that most. of these systems have a soft X-ray excess above the power-law continuum component., It is possible that most of these systems have a soft X-ray excess above the power-law continuum component. + However. detection of the the soft excess depends on the value of absorption column density (Paul et al.," However, detection of the the soft excess depends on the value of absorption column density (Paul et al." + 2002: Naik Paul 2004a. 2004b and references therein).," 2002; Naik Paul 2004a, 2004b and references therein)." + The transient N-rav pulsar was discovered. on 1993 July 1 by the BATSE experiment onboard the(CORO) (Stollberg ct al., The transient X-ray pulsar was discovered on 1993 July 14 by the BATSE experiment onboard the (Stollberg et al. + 1993)., 1993). + X-ray pulsations of 93.587 s were detected in the 20-120 keV οποίον range of BAVSE., X-ray pulsations of 93.587 s were detected in the 20-120 keV energy range of BATSE. + From ASCA observation. the X-ray. pulse profile of the pulsar was found to have a clouble-peak structure with a well-defined. sharp intensity minimum and a less prominent seconcary minimum (Tanaka et al.," From ASCA observation, the X-ray pulse profile of the pulsar was found to have a double-peak structure with a well-defined, sharp intensity minimum and a less prominent secondary minimum (Tanaka et al." + 19921.Το BATSE spectrum was described. by an optically thin thermal bremsstrahlung model withAY = 25 keV. Following the discovery. the optical ancl infrared observations of the optical counterpar o revealed the presence of strong Balmer emission lines and infrared excess (Coe et al.," 1993).The BATSE spectrum was described by an optically thin thermal bremsstrahlung model with = 25 keV. Following the discovery, the optical and infrared observations of the optical counterpart to revealed the presence of strong Balmer emission lines and infrared excess (Coe et al." + 1994)., 1994). + Base on these results. the svstem was classified as a massive NALLY systeni consisting of a neutron star as the compac object and a Be or a supergiant primary.," Based on these results, the system was classified as a massive binary system consisting of a neutron star as the compact object and a Be or a supergiant primary." + After 260 days of his outburst. a second outburst was detected by BATSE (Finger ct al.," After 260 days of this outburst, a second outburst was detected by BATSE (Finger et al." + 19904)., 1994). + Assuming this 260 d as the orbita »eriod. of the pulsar. Finger et al. (," Assuming this 260 d as the orbital period of the pulsar, Finger et al. (" +1994). estimated. the mass of the binary companion to be 3-8M. indicating the system as a high mass X-rav binary.,1994) estimated the mass of the binary companion to be 3-8$M_\odot$ indicating the system as a high mass X-ray binary. + The ROSAT PSPC observation of the pulsar. in the declining. phase of the discovery outburst by BATSE in 1993. clearly. detected the 93.4 s pulsation with a couble-peaked pulse profile in O.1-2.4 keV lieht curve (Petre Gehrels L994).," The ROSAT PSPC observation of the pulsar, in the declining phase of the discovery outburst by BATSE in 1993, clearly detected the 93.4 s pulsation with a double-peaked pulse profile in 0.1-2.4 keV light curve (Petre Gehrels 1994)." + A search. in the archive of ENOSATYMedium-Energy Experiment (ALLE) observation. centered on LID SS661. revealed. the presence of the pulsed. emission. at. the same period curing the 1993 outburst (Macomb. Shrader. Schultz 1994).," A search in the archive of EXOSAT/Medium-Energy Experiment (ME) observation, centered on HD 88661, revealed the presence of the pulsed emission at the same period during the 1993 outburst (Macomb, Shrader, Schultz 1994)." + The X-rav spectrum (0.510 keV range) was found to be highly absorbed (Ng=0.7LOalomsem 7) and. described bv a hard power-law with a photon index of ~1.2.," The X-ray spectrum (0.8–10 keV range) was found to be highly absorbed $N_H += 0.7\times10^{22} atoms cm^{-2}$ ) and described by a hard power-law with a photon index of $\sim$ 1.2." + A combined analysis of data from the CGRO and ASCA observations. though non-simultaneous. shortly. after. the peak of the discovery outburst. reported that the broadband spectrum of the pulsar can be well approximated by a power-law with an exponential cutolf and a 6.4 keV iron emission line (Shrader ct al.," A combined analysis of data from the CGRO and ASCA observations, though non-simultaneous, shortly after the peak of the discovery outburst, reported that the broadband spectrum of the pulsar can be well approximated by a power-law with an exponential cutoff and a 6.4 keV iron emission line (Shrader et al." + 1999)., 1999). + The pulse profile was also found to be energy dependent. a couble-peaked profile detected by ASCA that evolved into a single-peaked. profile as detected by BATSE.," The pulse profile was also found to be energy dependent, a double-peaked profile detected by ASCA that evolved into a single-peaked profile as detected by BATSE." + Analyzing the BATSE and Rossiraydiminglvcplorer(PNT E)/SM Εαν histories. Shracer et al. (," Analyzing the BATSE and $Rossi +X-ray Timing Explorer (RXTE)$ /ASM flux histories, Shrader et al. (" +1999) suggested the orbital period of the svstem to be 7135 days.,1999) suggested the orbital period of the system to be $\sim$ 135 days. + However. Levine Corbet (2006) detected a 248.9 day periodicity in the [NXTE Xll-sky Monitor (ASAI) X-ray light curve by analyzing data accumulated over nearly 10 vears.," However, Levine Corbet (2006) detected a 248.9 day periodicity in the $RXTE$ All-sky Monitor (ASM) X-ray light curve by analyzing data accumulated over nearly 10 years." + This periodicity was found by visual identification of periodically occurring outbursts in the ASM light curve., This periodicity was found by visual identification of periodically occurring outbursts in the ASM light curve. + An independent. analysis of pulse period. variations during outbursts. using DATSIS data. estimated the orbital period precisely. to be 247.8 d (Coe et al.," An independent analysis of pulse period variations during outbursts, using BATSE data, estimated the orbital period precisely to be 247.8 d (Coe et al." + 2007) which is good agreement with the orbital period. determined. from. the recurrence of the X-ray outbursts in ASAT light curve., 2007) which is good agreement with the orbital period determined from the recurrence of the X-ray outbursts in ASM light curve. + Following the detection of an intense outburst [rom with the Burst Alert Telescope (BAT) on Swift on 2007 November 17 (Ixrimm ct 22007). the accreting N-rav pulsar was observed. with various. N-rav observatories.," Following the detection of an intense outburst from with the Burst Alert Telescope (BAT) on Swift on 2007 November 17 (Krimm et 2007), the accreting X-ray pulsar was observed with various X-ray observatories." + The RATE observations detected the pulsar up to ~70 keV along with the regular 793.75 s pulsations (Wilms et al., The RXTE observations detected the pulsar up to $\sim$ 70 keV along with the regular $\sim$ 93.75 s pulsations (Wilms et al. + 2007)., 2007). + Suzaku performed a TOO observation of the pulsar on 2007 November 30., Suzaku performed a TOO observation of the pulsar on 2007 November 30. + The results obtained from the analysis of the Suzaku observation are presented in this paper., The results obtained from the analysis of the Suzaku observation are presented in this paper. + The transient pulsar was observed with the Suzaku during the declining phase of the 2007 November outburst., The transient pulsar was observed with the $Suzaku$ during the declining phase of the 2007 November outburst. + We used public data (ver-2.1.6.16) for the Suzaku Target of Opportunity (LOO) observation of the pulsar in the present work., We used public data (ver-2.1.6.16) for the $Suzaku$ Target of Opportunity (TOO) observation of the pulsar in the present work. + The ΝΤΛΟΑΤ monitoring of the pulsar showed that the outburst lasted for 20 davs., The RXTE/ASM monitoring of the pulsar showed that the outburst lasted for $\sim$ 20 days. + During this outburst. the peak luminosity was about 90 mCrab (7 ASM counts s +).," During this outburst, the peak luminosity was about $\sim$ 90 mCrab $\sim$ 7 ASM counts $^{-1}$ )." + During this outburst. the pulsar was observed. with the ΗΝΓΙΟ ancl σητα observatories.," During this outburst, the pulsar was observed with the RXTE and $Suzaku$ observatories." + The RNTE/ASAL (1.5-12 keV) and Swift(BAL (15-50 keV) one-dav averaged light curves of between 2007 September 29 and 2008 January 20 are shown in the top and bottom panels of Figure 1.. respectively.," The RXTE/ASM (1.5-12 keV) and Swift/BAT (15-50 keV) one-day averaged light curves of between 2007 September 29 and 2008 January 20 are shown in the top and bottom panels of Figure \ref{asm}, respectively." + The region between the vertical lines in the figure. indicates the observation of the pulsar with the Suiza., The region between the vertical lines in the figure indicates the observation of the pulsar with the $Suzaku$. + This TOO observation was carried out at “XLS nominal” pointing position Lor cllective exposures of 42 ks., This TOO observation was carried out at “XIS nominal” pointing position for effective exposures of 42 ks. +" The ALS was operated. with 71/4 window"" option which gives a time resolution of 2 sec. covering a field of view of 17.8 44."," The XIS was operated with “1/4 window” option which gives a time resolution of 2 sec, covering a field of view of $'$ $\times$ $'$ .4." + Suzaku. the filth Japanese X-ray astronomy. satellite (Alitsucla et al.," $Suzaku$ , the fifth Japanese X-ray astronomy satellite (Mitsuda et al." + 2007). was launched on 2005 July 10.," 2007), was launched on 2005 July 10." + [t covers 0.2600 keV. οποιον range with the two sets of, It covers 0.2–600 keV energy range with the two sets of +the maenetized aunulus.,the magnetized annulus. + The domain is au anuulus with radius raugiug frou 0.08 to 0.32 and height 0.0375 units., The domain is an annulus with radius ranging from 0.08 to 0.32 and height 0.0375 units. + The vertical boundaries are periodic., The vertical boundaries are periodic. + The iuner aud outer radial boundaries are fixed-value. arranged by preventing time evolution for particles with radius ereater than 0.3 or less than O.1.," The inner and outer radial boundaries are fixed-value, arranged by preventing time evolution for particles with radius greater than 0.3 or less than 0.1." + The initial deusitv is 1.0 evervwhere., The initial density is 1.0 everywhere. +" A vertical magnetic field is imposed with radial profile D.(r)=Bob,(re). where By=0.0821 aud which eives a magnetized aunulus."," A vertical magnetic field is imposed with radial profile $B_z(r) = B_0 +b_p(r)$, where $B_0=0.0824$ and which gives a magnetized annulus." +" The sound speed im the magnetized auuulus was set το c,=0.821. and the internal enerev in the nonanaguetized region adjusted so that the total pressure (thermal plus magnetic) is conustaut."," The sound speed in the magnetized annulus was set to $c_s = 0.824$, and the internal energy in the non-magnetized region adjusted so that the total pressure (thermal plus magnetic) is constant." + The radial velocity is perturbed with Spatially constant resolutions of A=1/210. À=1/320. and A=1/100 were used corresponding to A=1/9A\LR. A=1λνμαι. Al/lbAxg where Αν=0.0375 is the wavelength of the fastest erowineg AIRT mode at r=O17.," The radial velocity is perturbed with Spatially constant resolutions of $\lambda=1/240$, $\lambda=1/320$, and $\lambda=1/400$ were used corresponding to $\lambda = 1/9 \lambda_\mathrm{MRI}$, $\lambda = 1/12 \lambda_\mathrm{MRI}$, $\lambda = 1/15 \lambda_\mathrm{MRI}$ where $\lambda_\mathrm{MRI}=0.0375$ is the wavelength of the fastest growing MRI mode at $r=0.17$." + We then measure the erowth of the most unstable uode at r= 0.17., We then measure the growth of the most unstable mode at $r=0.17$ . + Fieure 13. shows the radial magnetic Ποια configuration achieved at time 0.91 (or 2.13 orbits at ¢= O17) for all three resolutions., Figure \ref{figflocktestslice} shows the radial magnetic field configuration achieved at time $0.94$ (or $2.13$ orbits at $r=0.17$ ) for all three resolutions. + To calculate he mode amplitude AZ. we use a convolution defined directly on the particles. iustead of eridding aud Fourier ranstormune the data.," To calculate the mode amplitude $M$, we use a convolution defined directly on the particles, instead of gridding and Fourier transforming the data." + The motivations are the same as when this procedure was used for the I&elviu-Iehuholtz est., The motivations are the same as when this procedure was used for the Kelvin-Helmholtz test. + Iu this case. where all suis run over the I points; aud The chosen width of the couvolution σ=2.7«109 imiunnizes the radial range that influcuces the measurement. while still ¢iving sufficieutly low sample niolse.," In this case, where all sums run over the $N$ points, and The chosen width of the convolution $\sigma=2.7\times10^{-6}$ minimizes the radial range that influences the measurement, while still giving sufficiently low sampling noise." + We plot the evolution of the mode amplitude iu Figure ll together with the maxuuuu erowth rate of exp(0.750) predicted by a linear perturbation analysis of vertical field AMIRI., We plot the evolution of the mode amplitude in Figure \ref{figflocktest_18} together with the maximum growth rate of $\exp(0.75\Omega)$ predicted by a linear perturbation analysis of vertical field MRI. + The modeled growth rates are reasonably cousisteut with the prediction from tle linear analysis for the fastest erowing mode., The modeled growth rates are reasonably consistent with the prediction from the linear analysis for the fastest growing mode. + huportautlv. iu the context of the findines of Flocketal.(2010).. where spuriously high erowth rates were observed. we fud erowtli rates slieltly lower than the theoretical maxima value.," Importantly, in the context of the findings of \cite{2010A&A...516A..26F}, where spuriously high growth rates were observed, we find growth rates slightly lower than the theoretical maximum value." + To determine if Phurbas can be used for practical conrputations. we need to establish some guidelines for its relative ability to resolve particular phenomena.," To determine if Phurbas can be used for practical computations, we need to establish some guidelines for its relative ability to resolve particular phenomena." + This should be doue cautiously. as different classes of algoritlins have differcut properties iu cach flow regime.," This should be done cautiously, as different classes of algorithms have different properties in each flow regime." + An equivalence or difference between algorithms in one reenne may not hold across differcut regimes., An equivalence or difference between algorithms in one regime may not hold across different regimes. + Iu any case. it is expected that an wustructured mesh or unstructured meshless method will have a lower effective resolution than a structured mesh inethod.," In any case, it is expected that an unstructured mesh or unstructured meshless method will have a lower effective resolution than a structured mesh method." + This is because a given munber of resolving clements can represcut the largest possible set of waveleugths when they are arranged in a regular manner., This is because a given number of resolving elements can represent the largest possible set of wavelengths when they are arranged in a regular manner. + Civen these caveats. we can compare the test results that we have preseuted here to examples computed with Eulerian. uesh-based schemes.," Given these caveats, we can compare the test results that we have presented here to examples computed with Eulerian, mesh-based schemes." + The first example is the circularly polarized Alfvéóuu wave test., The first example is the circularly polarized Alfvénn wave test. + The lowest resolution. three-dimensional. Athena results in a rectaugulhuw domain published in Stoneetal.(2008.Fie.33) correspond to 20 aud 39 cells per waveleugth. computed with third order spatial reconstruction aud IILLD fuxes.," The lowest resolution, three-dimensional, Athena results in a rectangular domain published in \citet[][Fig. 33]{2008ApJS..178..137S} + correspond to $20$ and $39$ cells per wavelength, computed with third order spatial reconstruction and HLLD fluxes." + The Phurbas results ou this test at A=1/8 and A=1/16 of a wavceleusth appear to roughly equal the accuracy. of the 20 and 39 cells per wavelength Athena results in the seuse that the final amplitude of the wave in the Phurbas results is closer to the analytically correct value even though there are fewer resolution clemeuts used per waveleneth., The Phurbas results on this test at $\lambda = 1/8$ and $\lambda = 1/16$ of a wavelength appear to roughly equal the accuracy of the $20$ and $39$ cells per wavelength Athena results in the sense that the final amplitude of the wave in the Phurbas results is closer to the analytically correct value even though there are fewer resolution elements used per wavelength. + This result should be interpreted cautiously. as the two codes lave different aud unoulinear nuuerical dissipation.," This result should be interpreted cautiously, as the two codes have different and nonlinear numerical dissipation." + Nevertheless. this cau be interpreted to mean that the Phurbas effective resolution A is roughly equal to two Athena cells as a measure of resolution. (," Nevertheless, this can be interpreted to mean that the Phurbas effective resolution $\lambda$ is roughly equal to two Athena cells as a measure of resolution. (" +On average. there should be one particle in cach volume of radius A.),"On average, there should be one particle in each volume of radius $\lambda$ .)" + Tn this sense Phurbas with a third-order polvnomual fit is competitive with a spatially third-order exid codo., In this sense Phurbas with a third-order polynomial fit is competitive with a spatially third-order grid code. + A possibly more operationally useful comparison cau be drawn from the results of the linear phase IRI erowtl test., A possibly more operationally useful comparison can be drawn from the results of the linear phase MRI growth test. + Flockotal.(2010). claim that in the code Pluto (Migeuoueetal.2007) with piecewise linear reconstructions and an HILED σαι solver. 10 cells per wavelength are required to resolve the erowth of AMIRI.," \citet{2010A&A...516A..26F} claim that in the code Pluto \citep{2007ApJS..170..228M} with piecewise linear reconstructions and an HLLD Riemann solver, 10 cells per wavelength are required to resolve the growth of MRI." + Our test iu section 3.5. shows Phurbas requires ~9 A per MRI wavelength to resolve the exowth., Our test in section \ref{sec_flocktest} shows Phurbas requires $\sim 9$ $\lambda$ per MRI wavelength to resolve the growth. + Thus. for this test we can sav that one =LA.," Thus, for this test we can say that one $\ \approx 1 \lambda$." + The alegorithiu used by Flocketal.(2010). has a stencil size of five cells. while Phurbas can be said to have a stencil size of 2ry=LGA. so the same rough proportionality holds between the two algorithms when expressed in terms of stencil size.," The algorithm used by \citet{2010A&A...516A..26F} has a stencil size of five cells, while Phurbas can be said to have a stencil size of $2 r_f =4.6\lambda$, so the same rough proportionality holds between the two algorithms when expressed in terms of stencil size." + The iain advantage of Plurbas is its Lagrangian mature., The main advantage of Phurbas is its Lagrangian nature. + Euleriau codes suffer from nunerical dissipation hat varies with the speed aud direction of the flow across the erid., Eulerian codes suffer from numerical dissipation that varies with the speed and direction of the flow across the grid. + Phurbas formulation cleanly avoids this jehavior., Phurbas's formulation cleanly avoids this behavior. + For svstenis wheres the bulk velocity varies as a iuultiple or large fraction of the wave speeds. this ueaus Phurbas can capture the dow with more uniformi fidelity across the domain.," For systems where the bulk velocity varies as a multiple or large fraction of the wave speeds, this means Phurbas can capture the flow with more uniform fidelity across the domain." + Techniques that add an extra advection step to an Eulerian method (e.c.Masset2000: can oulyefficicutly handle simple How geometries.," Techniques that add an extra advection step to an Eulerian method \citep[e.g.][]{2000A&AS..141..165M,2009ApJ...697.1269J} can onlyefficiently handle simple flow geometries." + Moreover. in Phurbas. the time step is oulv dependent ou Calilean-invariant quantities.," Moreover, in Phurbas, the time step is only dependent on Galilean-invariant quantities." + For flow with bulk velocities greater than the signal speeds that, For flow with bulk velocities greater than the signal speeds that +as CAIRSs directly. stellar population svnthesis model mus oe considered.,"as CMRs directly, stellar population synthesis model must be considered." + We adopt a model by Ixodama Arimoto (1997) as such a population svnthesis model., We adopt a model by Kodama Arimoto (1997) as such a population synthesis model. + Luminosity ancl colour of stars cannot be theoretically estimate without uncertainties because the stellar evolution nioclels hemselves include the uncertainties., Luminosity and colour of stars cannot be theoretically estimated without uncertainties because the stellar evolution models themselves include the uncertainties. + For example. as for the convection of stellar gas. we have only a phenomenologica heory Cmixing length. theory).," For example, as for the convection of stellar gas, we have only a phenomenological theory (`mixing length theory')." + However. their model. is adequate for our purpose of investigating the slope of the CAIR.," However, their model is adequate for our purpose of investigating the slope of the CMR." + Once we understand the properties of galaxies such as the CMIR physically ancl qualitatively. even if the stellar population model is changed. we fit immediately our results with observations by changing parameters mentioned above.," Once we understand the properties of galaxies such as the CMR physically and qualitatively, even if the stellar population model is changed, we fit immediately our results with observations by changing parameters mentioned above." + The EME which we adopt is the Salpeter type with a slope of 1.35. and the mass range is OAL.~ GOAL..," The IMF which we adopt is the Salpeter type with a slope of 1.35, and the mass range is $0.1$ $_{\odot}\sim 60$ $_{\odot}$." + The range of stellar metallicity Z; of simple stellar populations is 0.0001~0.05., The range of stellar metallicity $Z_{*}$ of simple stellar populations is $0.0001\sim 0.05$. + In Section ??.. we divide the stellar component into discl ancl bulge components.," In Section \ref{sec:sf}, we divide the stellar component into disc and bulge components." + Morphology of cach galaxy is determined. by the £-bancl bulge-to-cise luminosity ratio (B/D)., Morphology of each galaxy is determined by the $B$ -band bulge-to-disc luminosity ratio $B/D$ ). + Simien de Vaueouleurs (1986). showed. that he Llubble tvpe of galaxies correlates with the D-band uminosity 2/0., Simien de Vaucouleurs (1986) showed that the Hubble type of galaxies correlates with the $B$ -band luminosity $B/D$ . + In this paper. galaxies with 2/251.52 are identified as ellipticals. 0.680<1.52 as SOs. and DfD<0.68 as spirals. according to their results.," In this paper, galaxies with $B/D\geq 1.52$ are identified as ellipticals, $0.68\leq B/D<1.52$ as S0s, and $B/D<0.68$ as spirals, according to their results." + Lt is shown hat this method for classification reproduces observations well by Ixaullmann et al. (, It is shown that this method for classification reproduces observations well by Kauffmann et al. ( +1993) and Baugh. Cole brenk (1996).,"1993) and Baugh, Cole Frenk (1996)." + In this section. we explore the origin of the CMI," In this section, we explore the origin of the CMR." + In this paper. because we investigate how the CALR depends on the physical processes such as star formation. supernova fecdback. and so on. we fix the cosmological parameters to the standard CDM model. that is. £2=1A0. 50km | +. ο=0.06. and os=0.67.," In this paper, because we investigate how the CMR depends on the physical processes such as star formation, supernova feedback, and so on, we fix the cosmological parameters to the standard CDM model, that is, $\Omega=1, +\Lambda=0, H=50$ km $^{-1}$ $^{-1}$, $\Omega_{b}=0.06$, and $ +\sigma_{8}=0.67$." + We refer to the moclels considered bv the models A. D. € aad D as shown in Table 1.," We refer to the models considered by the models A, B, C and D as shown in Table 1." + In this table. we also show models from E to J. which are adopted in the next section.," In this table, we also show models from E to J, which are adopted in the next section." + The fifth column. UV. is explained in Section ??..," The fifth column, UV, is explained in Section \ref{sec:uv}." + Phe sixth column. burst. is shown in Section ??..," The sixth column, burst, is shown in Section \ref{sec:merger}." + The vield y is equal to 0.038=2Z. in all the models., The yield $y$ is equal to $0.038=2Z_{\odot}$ in all the models. + In WO. y=1.22. in the low feedback model.," In KC, $y=1.2Z_{\odot}$ in the low feedback model." + Lowever. in order to see the ellects of the feedback and so on. we fix the value of the vield in all models.," However, in order to see the effects of the feedback and so on, we fix the value of the yield in all models." + 1n the following sections. we take notice of only the slopes of CMIti. because the luminosity of galaxies can be translated by considering the following reason.," In the following sections, we take notice of only the slopes of CMRs, because the luminosity of galaxies can be translated by considering the following reason." + Stars are formed. according to the IME., Stars are formed according to the IMF. + Mass of luminous stars is larger than O.OSAL.. which is determined by the criterion of nuclear burning.," Mass of luminous stars is larger than $\sim 0.08$ $_{\odot}$, which is determined by the criterion of nuclear burning." + However. there is a possibility hat invisible stars with mass smaller than O.OSAL. are ormed.," However, there is a possibility that invisible stars with mass smaller than $0.08$ $_{\odot}$ are formed." + LW there are many invisible stars in galaxies. the galaxies become faint compared to the case that all stars are uminous.," If there are many invisible stars in galaxies, the galaxies become faint compared to the case that all stars are luminous." + “Phe ratio of the invisible stars to the luminous stars is (treated: as a [ree parameter in the previous work., The ratio of the invisible stars to the luminous stars is treated as a free parameter in the previous work. + Therefore the absolute value of luminosity can be adjusted w this parameter., Therefore the absolute value of luminosity can be adjusted by this parameter. + Lhe suitable value of this parameter will » determined by considering other observational quantities., The suitable value of this parameter will be determined by considering other observational quantities. + Thus this parameter does not alfect the slope of the CAI., Thus this parameter does not affect the slope of the CMR. + 1n . we show the CMldIis in the models A and D with Aner=2 which is the value adopted by WC.," In \ref{fig:cmrab}, we show the CMRs in the models A and B with $\alpha_{hot}=2$ which is the value adopted by KC." + Ehe dots denote galaxies identified as ellipticals. and the solid lines show the observational CARs (Bower οἱ al.," The dots denote galaxies identified as ellipticals, and the solid lines show the observational CMRs (Bower et al." + 1992)., 1992). + The criterion to xck out ellipticals among all galaxies is shown in Section 7aed., The criterion to pick out ellipticals among all galaxies is shown in Section \ref{sec:mor}. + Asin KC. in the model A with high feedback clliciency. he slopes of the CAIRs are in roughlv agreement with he observations. but the dispersion is larger than that of observations. 0.04 mag.," As in KC, in the model A with high feedback efficiency, the slopes of the CMRs are in roughly agreement with the observations, but the dispersion is larger than that of observations, $\sim 0.04$ mag." + This is due to the recent. star ormation owing to long star formation time-scale. τι=20 Gyr.," This is due to the recent star formation owing to long star formation time-scale, $\tau_{*}^{0}=20$ Gyr." + On the other hand. in the model B with low feedback elliciency. the slopes of the οΑς are nearly Lat.," On the other hand, in the model B with low feedback efficiency, the slopes of the CMRs are nearly flat." + At the xieht-end. the colour becomes redder about O.1-0.2 mag. and at the faint-enc (My~ 15). about. 0.2-0.3 mag. compared to that in the modelA. In order to see the physical relation between the reddening and the feedback intensity. we investigate the age- and metallicitv-Iuminosity relations.," At the bright-end, the colour becomes redder about 0.1-0.2 mag, and at the faint-end $M_{V}\sim -18$ ), about 0.2-0.3 mag, compared to that in the modelA. In order to see the physical relation between the reddening and the feedback intensity, we investigate the age- and metallicity-luminosity relations." +Fig.,Fig. + 10 presents contour plots of stars in the simulated rolwine ealaxy at f=1600 Myrs (820 Myrs after the oerieenter passage)., 10 presents contour plots of stars in the simulated polar-ring galaxy at $t=1600$ Myrs (820 Myrs after the pericenter passage). + At that time the donor galaxy has flow away at about 250 kpe distance (which of course. can appear much closer in sky projection) and does nof erturb the target anv more.," At that time the donor galaxy has flown away at about 250 kpc distance (which of course, can appear much closer in sky projection) and does not perturb the target any more." + As for the polar ring. it has ecole more regular than on the earlier stages shown iu Fig.," As for the polar ring, it has become more regular than on the earlier stages shown in Fig." + 9. even if still asviinuetrical.," 9, even if still asymmetrical." + This model reproduces he main characteristics of AM. 1931-563: Let us note that the matter transferred from the douor o the target galaxy is not only gas., This model reproduces the main characteristics of AM 1934-563: Let us note that the matter transferred from the donor to the target galaxy is not only gas. + As can be seen iu Fig., As can be seen in Fig. + 9. some stars frou the donor are also captured i the xolar disk. without being dispersed. but most of them have )cen formed just before the ring. inside the tidal bridgc.," 9, some stars from the donor are also captured in the polar disk, without being dispersed, but most of them have been formed just before the ring, inside the tidal bridge." + That soue stars are formed before the ring mav lead to an over-estiniatioi of the age of the ring. vet these stars do rot dominate the mass and are not much older than the ring. so that this over-cstimation may nof excece 24107 vr.," That some stars are formed before the ring may lead to an over-estimation of the age of the ring, yet these stars do not dominate the mass and are not much older than the ring, so that this over-estimation may not exceed $\times 10^8$ yr." +" A sinall fraction of dark matter is also acereted frou hne donunor eaaxy. but for our model with non-rotatiug dark haoes, this does not exceed of the domor dark Lass,"," A small fraction of dark matter is also accreted from the donnor galaxy, but for our model with non-rotating dark haloes, this does not exceed of the donnor dark mass." + At least four scenarios cau be proposed to account for voung. massive polar rugs surrounding pre-existing host ealaxies: The last three ones cau be regarded as hree subtypes the accretion scenark»," At least four scenarios can be proposed to account for young, massive polar rings surrounding pre-existing host galaxies: The last three ones can be regarded as three subtypes of the accretion scenario." + Let Us note that the first and third of these variants do no predic the presence : conirpanionus around PRCs. wuch is supported by servations.," Let us note that the first and third of these variants do not predict the presence of companions around PRGs, which is supported by observations." + For example Brocea et al. (," For example, Brocca et al. (" +1997) find that statistically. the environments of PRCs show no excess of ose coniaΠοis. which is consisteit with the uajoritv of PRCs forming via either kong-ternu sectlay gas accretion or via mergers In which the οςΜΙΣΟΙ Is estrovec.,"1997) find that statistically, the environments of PRGs show no excess of close companions, which is consistent with the majority of PRGs forming via either long-term secular gas accretion or via mergers in which the companion is destroyed." + Towever. this does not 11le out accretion Yolla eas-ricli donor. for the donor may have left he scene.," However, this does not rule out accretion from a gas-rich donor, for the donor may have left the scene." + Torice et: (2002a.b) favor the merger scenark> of two ¢isk. ealaxies. frou the study of stelar »opulatious and morphological structure of the host: however. the costraints are 1O strong euouel. Since du oan scenario. enas can be acCreec by t1ο host aud mduce star formation. wlie the host Is porurbed. so that a large range of 5‘lar ages sLOU.d coexist in the rturbed host.," Iodice et al (2002a,b) favor the merger scenario of two disk galaxies, from the study of stellar populations and morphological structure of the host; however, the constraints are not strong enough, since in any scenario, gas can be accreted by the host and induce star formation, while the host is perturbed, so that a large range of stellar ages should coexist in the perturbed host." +" The prex""ce or Lot of a diffuse eivelope of stars arouud the PRC is LOVE COISune (see BC03).", The presence or not of a diffuse envelope of stars around the PRG is more constraining (see BC03). + The major merger «xnario las 1 shown to be ess likely than the fida accretion iulo. especially or inclined rings {06000).," The major merger scenario has been shown to be less likely than the tidal accretion scenario, especially for inclined rings (BC03)." + Aloreover. 10 asviunetrie rue of AM. 1931-563 cinuuot νο well fitted bv. this scenario.," Moreover, the asymmetric ring of AM 1934-563 cannot be well fitted by this scenario." + Tudeed. this scenido assunes that the host σαιAXV as ποσο with a “victim cisk galaxy iat has even bir ο the polar ring.," Indeed, this scenario assumes that the host galaxy as merged with a ”victim” disk galaxy that has given birth to the polar ring." +" Since t1ο southern part of the riie ] ANL 1931-563 is more exteided than t16 northern onc. f center of this “victim, σαaxv should o south of the host ealaxy. which should ial: ot1e southern part of the volar ving brieliter that t16 OLheru one."," Since the southern part of the ring in AM 1934-563 is more extended than the northern one, the center of this “victim” galaxy should be south of the host galaxy, which should make the southern part of the polar ring brighter that the northern one." + Ou the contrary. f1ο rorthern part o the ving is brighter than the southeru one.," On the contrary, the northern part of the ring is brighter than the southern one." + We have cjecked. iu ESuulatious of DCUS that t1C nore extended AL Q: the ring is at least as hunuinous astje shortest part. when tie Ting is formed in a major nerser.," We have checked in simulations of BC03 that the more extended part of the ring is at least as luminous as the shortest part, when the ring is formed in a major merger." + We lave explaiuec aboxο that the disruption of a small companion. duriug a niünor merecr. is uulikelv to lave orlned the polar ring of AM 1931-563. for the rine NOTE certainly appear unuclosed. because the orbit of the conauion is uuclosed iself.," We have explained above that the disruption of a small companion, during a minor merger, is unlikely to have formed the polar ring of AM 1934-563, for the ring would certainly appear unclosed, because the orbit of the companion is unclosed itself." + Moreover. forming a massive enough ring. without disturbing the host disk too wich. In asrong constraint on the mass of this companion.," Moreover, forming a massive enough ring, without disturbing the host disk too much, is a strong constraint on the mass of this companion." + ο1 the contrary. f1ο accretion scenario invoking a fida nass transfer from a massive donor. without galaxy merger. has been shown to succeed in reproducing the characteristics of AM |931-563.," On the contrary, the accretion scenario invoking a tidal mass transfer from a massive donor, without galaxy merger, has been shown to succeed in reproducing the characteristics of AM 1934-563." + Furthermore. the small velocity dispersion of this group (see Sect.," Furthermore, the small velocity dispersion of this group (see Sect." + 3.1) could result, 3.1) could result +produce additional. structure at a few given. Lrequencics.,produce additional structure at a few given frequencies. + The general scheme of propagating Iluctuations can still be correct but. additional assumptions need to be mace. for example. assuming that a few annuli have much enhanced variability power will certainly. produce a bumpy PSD and might reproduce the steps in the lag spectra. as suggested by Nowak(2000). and also Ixotovetal.(2001).," The general scheme of propagating fluctuations can still be correct but additional assumptions need to be made, for example, assuming that a few annuli have much enhanced variability power will certainly produce a bumpy PSD and might reproduce the steps in the lag spectra, as suggested by \citet{Nowak00} and also \citet{Kotov}." +. The extended. emitting region in our model is responsible for the high frequency bend in the PSD. and the associated racial emissivity profiles produce the energy dependence of the PSD and the time lags.," The extended emitting region in our model is responsible for the high frequency bend in the PSD, and the associated radial emissivity profiles produce the energy dependence of the PSD and the time lags." + In this section we will summarise the speetral-timing properties produced. by the. moclel. consider the implications of the model for the size of the emitting region. and discuss some possible improvemoents.," In this section we will summarise the spectral-timing properties produced by the model, consider the implications of the model for the size of the emitting region, and discuss some possible improvements." + Keeping the local variability time-scales tied. το the propagation time-scale produces time lage spectra of power law slope ~l or Uatter. and lags of ~110% of the variability time-scale. for a wide range of moclel parameters.," Keeping the local variability time-scales tied to the propagation time-scale produces time lag spectra of power law slope $\sim -1$ or flatter, and lags of $\sim 1 -10\%$ of the variability time-scale, for a wide range of model parameters." + As discussed in Sections 4. and 5.. these simple assumptions produce lag spectra that mateh the cata well in time-scale dependence ancl amplitude.," As discussed in Sections \ref{agn} + and \ref{xrb}, these simple assumptions produce lag spectra that match the data well in time-scale dependence and amplitude." + We note once again that these laes arise solely due to the clillerence in emissivity. profiles of the N-rav. energy. bands ancl do not involve any other spectral evolution of the emitting region., We note once again that these lags arise solely due to the difference in emissivity profiles of the X-ray energy bands and do not involve any other spectral evolution of the emitting region. + The amplitude of the lags depends mostly on the emissivity indices of the energy. bands. increasing rapiclly with their difference. up to As~1. above which the lag values tend to saturate.," The amplitude of the lags depends mostly on the emissivity indices of the energy bands, increasing rapidly with their difference, up to $\Delta \gamma \sim 1$, above which the lag values tend to saturate." + Significant lags can appear between enerev bands. characterised by similar emissivity profiles and. correspondingly. similar PSD shapes.," Significant lags can appear between energy bands characterised by similar emissivity profiles and, correspondingly, similar PSD shapes." + In particular. the PSD of €vg X-1 in the high/soft state shows weak energy dependence (see Section 5.1). but the PSD ratio and lags can still be reproduced simultaneously with close emissivity indices for each energy band (As~ 0.5). provided that the propagation time-scale is slightly longer than the local luctuation time-scale. and assuming that the inner clise radius is small.," In particular, the PSD of Cyg X-1 in the high/soft state shows weak energy dependence (see Section 5.1), but the PSD ratio and lags can still be reproduced simultaneously with close emissivity indices for each energy band $\Delta \gamma \sim 0.5$ ), provided that the propagation time-scale is slightly longer than the local fluctuation time-scale, and assuming that the inner disc radius is small." + Ehe power-law shape of the lag spectra is quite robust. its slope depends. only weakly on. disc structure parameters (LfB)-a.," The power-law shape of the lag spectra is quite robust, its slope depends only weakly on disc structure parameters $(H/R)^2\alpha$." + Incidentally. the stability of the lag spectra might explain the behaviour seen in. e.g. (νο X-1. in different spectral states.," Incidentally, the stability of the lag spectra might explain the behaviour seen in, e.g. Cyg X-1, in different spectral states." + Fhis object shows very dillerent PSD and energy spectra in the high/soft and Iowhard. states. indicative of dillerent. disc configurations. but surprisingly similar lags (Pottschmidtetal.," This object shows very different PSD and energy spectra in the high/soft and low/hard states, indicative of different disc configurations, but surprisingly similar lags \citep{Pottschmidt}." +2000).. A comparison with AGN and BUNKB data in the high/soft state shows that the filtering ellect of the extended emitting region. acting on a simple 1/f underlying PSD shape. can broadly reproduce their PSD shape and energy dependence.," A comparison with AGN and BHXRB data in the high/soft state shows that the filtering effect of the extended emitting region, acting on a simple $1/f$ underlying PSD shape, can broadly reproduce their PSD shape and energy dependence." + Cve N-1 in the low/hare state. however. requires a more complex PSD.," Cyg X-1 in the low/hard state, however, requires a more complex PSD." + In either case. the extended emitting region introduces a bend in the PSD in addition to any intrinsic curvature. ancl produces the energy. dependence of he filtered. PSDs.," In either case, the extended emitting region introduces a bend in the PSD in addition to any intrinsic curvature, and produces the energy dependence of the filtered PSDs." + Note that the bending power-Iaw. used to fit AGN data. is only an approximation to the actual PSDs produced. by he fluctuating-acerction model.," Note that the bending power-law, used to fit AGN data, is only an approximation to the actual PSDs produced by the fluctuating-accretion model." + The filtered. PSD bends down continuously at. high. frequencies ancl has no well-defined. high-frequency power Law slope., The filtered PSD bends down continuously at high frequencies and has no well-defined high-frequency power law slope. + The cdillerence tween the bending power-law mocel and the filtered PSDs can be appreciated in Fig. Ll.," The difference between the bending power-law model and the filtered PSDs can be appreciated in Fig. \ref{psd_surr_ngc}," + where the single-bend PSD it overestimates the power in the highest. frequency. bins., where the single-bend PSD fit overestimates the power in the highest frequency bins. + Llowever. as this region of the PSDs from real data is often wavily alected by Poisson noise. the associated. error bars and scatter are large and it is not. possible to appreciate any deviations from a simple power law slope.," However, as this region of the PSDs from real data is often heavily affected by Poisson noise, the associated error bars and scatter are large and it is not possible to appreciate any deviations from a simple power law slope." + Therefore. even better ACN data would. be needed to discern if the model can replicate the exact. PSD shape or if additional variability components are needed.," Therefore, even better AGN data would be needed to discern if the model can replicate the exact PSD shape or if additional variability components are needed." + We also note here that. although Itevnivtsev.Gilfanov&Churazov(2000). fit the ügh/soft state PSD from combined data from 1996 June 4-18 with a simple power law (index -2.1) up to ~200 112. he signal-to-noise at these frequencies is still fairly low. and he PSD during that time is known vary in shape between observations (Cuietal.1997)... which makes interpretation of the underlving shape even more dillicult.," We also note here that, although \citet{RevHifreq} fit the high/soft state PSD from combined data from 1996 June 4-18 with a simple power law (index -2.1) up to $\sim200$ Hz, the signal-to-noise at these frequencies is still fairly low, and the PSD during that time is known vary in shape between observations \citep{Cui97}, which makes interpretation of the underlying shape even more difficult." +" Axclssonctal.(2005) have recently demonstrated that the high/soft state ""SD can be fitted with weak Lorentzians to a ~Lf power-law component with an exponential cut-olf.", \citet{Axelsson} have recently demonstrated that the high/soft state PSD can be fitted with weak Lorentzians to a $\sim 1/f$ power-law component with an exponential cut-off. + This last component is reminiscent of our simulated PSDs., This last component is reminiscent of our simulated PSDs. + Therefore. our model may be considered as representative of the times when the Lorentzians in the PSD are verv weak or absent.," Therefore, our model may be considered as representative of the times when the Lorentzians in the PSD are very weak or absent." + In our model. thick cise parameters. a(44/R)?=0.3. in the inner regions of the accretion Low and inner radius Moin=6 put the break frequency. around. 10eIi. (e. 2 - 20 Hz for a LOAD. black hole. 103 for a 10A4. ).," In our model, thick disc parameters, $\alpha (H/R)^2=0.3$, in the inner regions of the accretion flow and inner radius $r_{\rm min}= 6$ put the break frequency around $10^{-4}-10^{-3}c/R_{\rm g}$ (i.e. $\sim$ 2 - 20 Hz for a $10 M_{\odot}$ black hole, $2\times +10^{-5}-2\times 10^{-4}$ for a $10^6 M_{\odot}$ )." +" ""οσο values are in general2. agreement with the average break frequencies of ΑΝ and. DIIXIUDs. indicating that Ductuations on the viscous time-scales of a gcometrically Chick accretion Low are appropriate to explain he variability."," These values are in general agreement with the average break frequencies of AGN and BHXRBs, indicating that fluctuations on the viscous time-scales of a geometrically thick accretion flow are appropriate to explain the variability." + A geometrically thick disc is necessary to srocluce the observed high frequency Huctuations as frequencies., A geometrically thick disc is necessary to produce the observed high frequency fluctuations as frequencies. + I£ the [uctuations were instead. produced on dynamical time-scales. or à magnetic time-scale related ο this. as in e.g. Wineetal.(2004).. then a thinner Low might be allowed.," If the fluctuations were instead produced on dynamical time-scales, or a magnetic time-scale related to this, as in e.g. \citet{King}, then a thinner flow might be allowed." + However. the Uuctuations need. not only »* produced: but also propagated. which poses a dilliculty or much thinner accretion Lows. as fluctuations on time-scales much shorter than the propagation time-scale are casily clampecl (Churazoyetal.," However, the fluctuations need not only be produced but also propagated, which poses a difficulty for much thinner accretion flows, as fluctuations on time-scales much shorter than the propagation time-scale are easily damped \citep{Churazov}." +2001)... This. of course. does not rule out an additional thin disc. possibly underlving the thick How. that might contribute to the Dux but not to the variability.," This, of course, does not rule out an additional thin disc, possibly underlying the thick flow, that might contribute to the flux but not to the variability." + In our implementation of the variability model. the X-ray emitting region extends out to large radii.," In our implementation of the variability model, the X-ray emitting region extends out to large radii." + Phe bend in the PSD is produced. by the radial distribution of variability time-scales anc cniissivity profiles alone and is not related to a characteristic time-scale at the maximum racius of emission., The bend in the PSD is produced by the radial distribution of variability time-scales and emissivity profiles alone and is not related to a characteristic time-scale at the maximum radius of emission. + l'herefore. an outer οσο to the emitting region might be allowed. but is not required.," Therefore, an outer edge to the emitting region might be allowed but is not required." + The steep emissivity, The steep emissivity +The profile of angular velocity in (he convection zone is determined by a balance of angular momentum transport [rom meridional flow and a reduction in meridional How from buovaney force at the subacliabatic laver.,The profile of angular velocity in the convection zone is determined by a balance of angular momentum transport from meridional flow and a reduction in meridional flow from buoyancy force at the subadiabatic layer. +" We run simulations for seventeen cases. with Table | showing the parameters for each Case,"," We run simulations for seventeen cases, with Table \ref{param} showing the parameters for each case." + In this section. we discuss (he cases wilh angular velocities up to 16 times the solar value (represented by Q.). placing an emphasis on the morphology. of stellar differential rotation.," In this section, we discuss the cases with angular velocities up to 16 times the solar value (represented by $\Omega_\odot$ ), placing an emphasis on the morphology of stellar differential rotation." + Fie., Fig. + 3 shows the results of our calculations which correspond to cases 1-5 in Table 1.., \ref{rapid} shows the results of our calculations which correspond to cases 1-5 in Table \ref{param}. + It is found that the larger stellar angular velocity is. the more likely it is [or differential rotation to be in the Tavlor-Proudiman state. in whieh the contour lines of the," It is found that the larger stellar angular velocity is, the more likely it is for differential rotation to be in the Taylor-Proudman state, in which the contour lines of the" +implies a nean iron abundance of about 0.25 dex at 5 kpe towards the inner disk (and -0.25 towards the outer disk).,implies a mean iron abundance of about 0.25 dex at 5 kpc towards the inner disk (and -0.25 towards the outer disk). + Allowing for an intrinsic dispersion similar to what is measured on the local iron distribution (0.15 dex). we easily reach (within 1 or 2 sigma) the highest metallicities that are observed at the solar radius. which means that the oxvgen gradient measured on Type II PNe is well compatible with abundances measured in the local stellar population.," Allowing for an intrinsic dispersion similar to what is measured on the local iron distribution (0.15 dex), we easily reach (within 1 or 2 sigma) the highest metallicities that are observed at the solar radius, which means that the oxygen gradient measured on Type II PNe is well compatible with abundances measured in the local stellar population." + In order to increase (he significance of the PN results we explore the literature Lor object classes whose a-element abundances and gradients have been studied., In order to increase the significance of the PN results we explore the literature for object classes whose $\alpha$ -element abundances and gradients have been studied. + Several studies concerning II IE regions and voung stars are available. while the only possible comparison with an older population is that of open clusters.," Several studies concerning H II regions and young stars are available, while the only possible comparison with an older population is that of open clusters." + In Table 4 we list gradient slopes and (heir uncertainties (in column 2) and distance ranges (column 3) from different (racers (column 4). where the authors have measured directly the oxveen abundances of the (racers.," In Table 4 we list gradient slopes and their uncertainties (in column 2) and distance ranges (column 3) from different tracers (column 4), where the authors have measured directly the oxygen abundances of the tracers." + Most tracers are very voung stars. whose eradients have been plotted in Figure 8 with open circles.," Most tracers are very young stars, whose gradients have been plotted in Figure 8 with open circles." + These voung stellar data seem {ο fit in well with the voung PNe of our sample. eiving continuity to the plot.," These young stellar data seem to fit in well with the young PNe of our sample, giving continuity to the plot." + Our basic list of open clusters is (he one designed by Magrini et al. (, Our basic list of open clusters is the one designed by Magrini et al. ( +2009). to which we added a few more clusters from (he most recent literature.,"2009), to which we added a few more clusters from the most recent literature." + The various parameters are eiven in Table 5 with columns (1) through (2) providing the name. age. distance from the Galactic center.," The various parameters are given in Table 5 with columns (1) through (3) providing the name, age, distance from the Galactic center." + Iron abundances. referred. to solar. are listed in column (4).," Iron abundances, referred to solar, are listed in column (4)." + References to the iron abundances are as in Magrini et al. (, References to the iron abundances are as in Magrini et al. ( +2009).,2009). + Columns (5) through (8) of Table 5 give the oxvgen abundance ratios (o iron. the oxvgen abundances relative {ο solar. the actual oxvgen abundance caleulated for the solar value given in the individual papers. anc," Columns (5) through (8) of Table 5 give the oxygen abundance ratios to iron, the oxygen abundances relative to solar, the actual oxygen abundance calculated for the solar value given in the individual papers, and" + Columns (5) through (8) of Table 5 give the oxvgen abundance ratios (o iron. the oxvgen abundances relative {ο solar. the actual oxvgen abundance caleulated for the solar value given in the individual papers. ancl," Columns (5) through (8) of Table 5 give the oxygen abundance ratios to iron, the oxygen abundances relative to solar, the actual oxygen abundance calculated for the solar value given in the individual papers, and" +"As discussed in3.1,, when the model parameters that determine the density and temperature profiles at TA are unconstrained or poorly constrained, the fully parametric approach can be biased towards self-similar scaling relations.","As discussed in, when the model parameters that determine the density and temperature profiles at $r_\Delta$ are unconstrained or poorly constrained, the fully parametric approach can be biased towards self-similar scaling relations." +" As an explicit illustration of this, consider a 8 model description of the gas density in conjunction with a simple, non-isothermal temperature profile, This function is a simplification of the form used by(2006),, namely eliminating the ‘cool core’ term, which is intended to describe the profile at small radii."," As an explicit illustration of this, consider a $\beta$ model description of the gas density in conjunction with a simple, non-isothermal temperature profile, This function is a simplification of the form used by, namely eliminating the `cool core' term, which is intended to describe the profile at small radii." +" To illustrate the case where these models are effectively unconstrained, we generated random realizations by sampling independent, uniform values of the model parameters within the ranges given inA1."," To illustrate the case where these models are effectively unconstrained, we generated random realizations by sampling independent, uniform values of the model parameters within the ranges given in." +". The radial scales in the density and temperature models, Τε and Τε, were allowed to take values between zero and raa. max4/3f T"," The radial scales in the density and temperature models, $\rc$ and $\rt$, were allowed to take values between zero and $\rmax = \mathrm{max} \sqrt{3\beta T_0}$ ." +"his is the maximum value of rc for which the isothermal To.8 model has a real solution for ra 10)); while the same is not true of this non-isothermal model, allowing larger values does not change the resulting picture qualitatively."," This is the maximum value of $\rc$ for which the isothermal $\beta$ model has a real solution for $r_\Delta$ ); while the same is not true of this non-isothermal model, allowing larger values does not change the resulting picture qualitatively." +" 8 was allowed to vary over a range somewhat wider than that seen in observations, while the temperature exponents, b and c, were varied over approximately the range allowed by(2006)."," $\beta$ was allowed to vary over a range somewhat wider than that seen in observations, while the temperature exponents, $b$ and $c$, were varied over approximately the range allowed by." +". To provide an adequate baseline to observe the resulting scaling behavior, the temperature normalization, To, was sampled uniformly in the logarithm between 1 and 1000."," To provide an adequate baseline to observe the resulting scaling behavior, the temperature normalization, $T_0$, was sampled uniformly in the logarithm between 1 and 1000." +" For each realization, an implicit solution for ra 3)) was searched for numerically, and models for which there was no real solution were discarded."," For each realization, an implicit solution for $r_\Delta$ ) was searched for numerically, and models for which there was no real solution were discarded." + A sample of the resulting density and temperature profiles is shown inAl., A sample of the resulting density and temperature profiles is shown in. +". The model profiles are clearly not self-similar in any meaningful sense, but, because their variation is independent of mass, the slopes of the mean scaling relations take on the self-similar values (right panel of 1))."," The model profiles are clearly not self-similar in any meaningful sense, but, because their variation is independent of mass, the slopes of the mean scaling relations take on the self-similar values (right panel of )." +" For clarity, we have culled models where rc/rA>0.7 from the figure; these models produce an asymmetric tail to low masses, but do not change the scaling relation slope."," For clarity, we have culled models where $\rc/r_\Delta>0.7$ from the figure; these models produce an asymmetric tail to low masses, but do not change the scaling relation slope." +" The x-axis of the figure shows the emission-weighted projected temperature within ra, calculated from the n(r) and T(r) profiles, although the precise definition of T does not affect the conclusions."," The x-axis of the figure shows the emission-weighted projected temperature within $r_\Delta$, calculated from the $n(r)$ and $T(r)$ profiles, although the precise definition of $T_\Delta$ does not affect the conclusions." + Here we offer some brief thoughts on the task of obtaining hydrostatic mass estimates using minimal assumptions, Here we offer some brief thoughts on the task of obtaining hydrostatic mass estimates using minimal assumptions +age of the Universe at each redshift considered).,age of the Universe at each redshift considered). + While there is some room for confusion with z«1 galaxies — which due to dust emission in the F560W filter (not taken into account in our models) may potentially produce similar colours in this diagram — such objects are not likely to display apparent magnitudes in the same range as high-redshift pop III galaxies., While there is some room for confusion with $z<1$ galaxies – which due to dust emission in the F560W filter (not taken into account in our models) may potentially produce similar colours in this diagram – such objects are not likely to display apparent magnitudes in the same range as high-redshift pop III galaxies. +" Hence, objects that end up in the upper left corner of Fig. 8,"," Hence, objects that end up in the upper left corner of Fig. \ref{typeA_MIRIcolcol}," +" and have apparent magnitudes in the range expected for high-redshift galaxies, are likely to be zzz 7-8 pop III galaxies even in the absence of additional redshift constraints."," and have apparent magnitudes in the range expected for high-redshift galaxies, are likely to be $z\approx 7$ –8 pop III galaxies even in the absence of additional redshift constraints." +" While this scheme would seem to give a cleaner selection of pop III galaxy candidates than that proposed by Inoue(2011b),, it suffers from one obvious drawback: the lower sensitivity of MIRI implies a minimum mass for detection that is an order of magnitude higher than in the case where only NIRCam filters are used (see Fig. 5))."," While this scheme would seem to give a cleaner selection of pop III galaxy candidates than that proposed by \citet{Inoue b}, it suffers from one obvious drawback: the lower sensitivity of MIRI implies a minimum mass for detection that is an order of magnitude higher than in the case where only NIRCam filters are used (see Fig. \ref{Mmin_singlez}) )." +" Even in the case of 100 h exposures per filter, the mass converted into stars would need to be on the order of ~10’Mo to allow detection in the F560W and F770W filters."," Even in the case of 100 h exposures per filter, the mass converted into stars would need to be on the order of $\sim 10^7\ M_\odot$ to allow detection in the F560W and F770W filters." +" The maximum mass that stellar populations consisting entirely of pop III stars can reach is unknown, but current simulations suggest that unenriched halos are unlikely to attain total masses in excess of M~105Mg at z>7 (Trentietal. 2009)."," The maximum mass that stellar populations consisting entirely of pop III stars can reach is unknown, but current simulations suggest that unenriched halos are unlikely to attain total masses in excess of $M\sim 10^8\ M_\odot$ at $z>7$ \citep{Trenti et al.}." +". To produce~10°Meg worth of pop III stars, essentially all of the baryons in a M~105Mo object would need to be converted into stars (somehow evading negative feedback effects) in a limited amount of time (up to ~107 yr), which seems highly unrealistic."," To produce$\sim 10^7\ M_\odot$ worth of pop III stars, essentially all of the baryons in a $M\sim 10^8\ M_\odot$ object would need to be converted into stars (somehow evading negative feedback effects) in a limited amount of time (up to $\sim 10^7$ yr), which seems highly unrealistic." +" By hunting for pop III galaxies behind lensing clusters with magnification µzz100 (MACSJ0717.5+3745;e.g.Zitrin 2010),, the required stellar population mass can in principle be lowered to ~10°Mo "," By hunting for pop III galaxies behind lensing clusters with magnification $\mu\approx 100$ \citep[MACS J0717.5+3745; e.g.][]{Zitrin et al.,Zackrisson et al. c}, , the required stellar population mass can in principle be lowered to $\sim 10^5\ M_\odot$ " +[or (10)) are sunimarized in Table 1 for different: phases.,for \ref{107a}) ) are summarized in Table \ref{tab1} for different phases. + lig., Fig. + lis a plot of Πίο). 962). log gel). ο) for one whole pulsation. INSGS).," 1 is a plot of $T_{\rm e}(\varphi)$ , $\vartheta(\varphi)$, $\log g_{\rm e}(\varphi)$ , $h_0(R,\varphi)$ for one whole pulsation. $\Delta T_{\rm e}(\varphi)$," + Aloeg(y2) are plotted in the lower panels of Fig. 2.., $\Delta\log g_{\rm e}(\varphi)$ are plotted in the lower panels of Fig. \ref{fig2}. + Assuming random errors of 40.02 for the colour indices will result in AY.=Εθν and Aloeg.=+£0.04., Assuming random errors of $\pm 0.02$ for the colour indices will result in $\Delta T_{\rm e}=\pm 10\mbox{K}$ and $\Delta\log g_{\rm e}=\pm 0.04$. + These values are indicated by the dotted horizontal lines., These values are indicated by the dotted horizontal lines. + Condition Lis satisfied in the phase points Lvine below or close to the clotted lines., Condition I is satisfied in the phase points lying below or close to the dotted lines. + At phases [ving. above the dotted. lines. the monochromatic Hux of statie models and SU Dra dillers significantly on a level which has noticeable ellect on the broad band colours (BV(De:," At phases lying above the dotted lines, the monochromatic flux of static models and SU Dra differs significantly on a level which has noticeable effect on the broad band colours $UBV(RI)_C$." + The assumed Al] L6.E(BVW)=0.015 were verified by a variation procedure (Bareza&Benkó2009).," The assumed $[M]=-1.6$, $E(B-V)=0.015$ were verified by a variation procedure \citep{barc3}." +. In the shock free phases yo=0.15.0.5.0.55. minimization of AT.(uz).Adoggol) resulted in A]=100-010. E(BV)=0.015£0.01.," In the shock free phases $\varphi=0.15,0.5,0.55$, minimization of $\Delta +T_{\rm e}(\varphi),\Delta\log g_{\rm e}(\varphi)$ resulted in $[M]=-1.60\pm 0.10$, $E(B-V)=0.015\pm 0.01$." + To demonstrate the difference between good ancl poor QSAA. the histograms of the 30 logge.Ze values are plotted in the upper panels of Fig.," To demonstrate the difference between good and poor QSAA, the histograms of the 30 $\log g_{\rm e},T_{\rm e}$ values are plotted in the upper panels of Fig." + 2 for 4;=0.5.0.98 of SU Dra and BD |67 τος.," \ref{fig2} for $\varphi=0.5,0.98$ of SU Dra and BD +67 708." + Phev show normal distributions with small scatter for the non-variable BD. |67 TOS and SU Dra at y=0.5., They show normal distributions with small scatter for the non-variable BD +67 708 and SU Dra at $\varphi=0.5$. + At =0.98 the distribution is almost uniform., At $\varphi=0.98$ the distribution is almost uniform. + At the next phase point 4=1 merely 14 intersections of US(loggoCh.Clos.MJ.ΕΣντο Le. 14. pairs of loggo.T; were found instead of 30 pairs.," At the next phase point $\varphi=1$ merely 14 intersections of $\{T_{\rm e}^{(i)}(\log g_{\rm e},{\rm CI}_1,{\rm CI}_2,[M],E(B-V))\}_ +{i=1,2}$, i.e. 14 pairs of $\log g_{\rm e},T_{\rm e}$ were found instead of 30 pairs." + Phus. at ος21 the observed. colours diller significantly from those of any static model of Ixurucz(1997).," Thus, at $\varphi \approx 1$ the observed colours differ significantly from those of any static model of \citet{kuru1}." +. Llowever. it is interesting to note that the small errors Aloeg.=0.03. AT.=191 indicate a phase island at y=0.93 with observed and static mocel colours in agreement for some 0.017zc10 minutes.," However, it is interesting to note that the small errors $\Delta\log g_{\rm e}=0.03$, $\Delta T_{\rm e}=12\mbox{K}$ indicate a phase island at $\varphi=0.93$ with observed and static model colours in agreement for some $0.01P\approx 10$ minutes." + This happens to be the phase of the hump on the light curve when the inward and outward motions encounter and. produce a shock (Smith1995).., This happens to be the phase of the hump on the light curve when the inward and outward motions encounter and produce a shock \citep{smit1}. + In the interval 0.92«45<1.05 the atmosphere is in a state of maximal compression by the shock coming from the sub-photospheric lavers and {1 is nearly minimal., In the interval $0.92 < \varphi < 1.05$ the atmosphere is in a state of maximal compression by the shock coming from the sub-photospheric layers and $R$ is nearly minimal. + ‘This is the risine branch andthe start of the descending branch in the light curve., This is the rising branch andthe start of the descending branch in the light curve. + Therefore. the values of logg..ἐν. obtained from QSSA. if they can be found at all. must be considered as a first approximation only.," Therefore, the values of $\log g_{\rm e},T_{\rm e},\vartheta$ obtained from QSSA, if they can be found at all, must be considered as a first approximation only." + This is rellected in large Aloe q«. AZ. except for qz0.93.," This is reflected in large $\Delta \log g_{\rm e}$ , $\Delta T_{\rm e}$ except for $\varphi \approx 0.93$." + To get raf) ete for (LOD). VO and Ώου.1). were differentiated by midpoint formulae.," To get $v(r,t)$ etc for \ref{107a}) ), $\vartheta(t)$ and $h_0(R,t)$ were differentiated by midpoint formulae." + Fig., Fig. + 3aa is a plot of the functions ία.E). for the phases f= P. ge=0.15-0.35.0.5.0.55 with ai’!(4.40)=0.," \ref{fig3}a a is a plot of the functions ${\cal M}(d,t)$ for the phases $t=\varphi P$ , $\varphi=0.15\mbox{-}0.35,0.5,0.55$ with $a^{\rm (dyn)}(R,t)=0$." + The average and standard vror of M.d are given in Table 2. from the pairs 25 and yo=0.15.0.3.0.35.0.55). (μι=0.35 and } in (10)) as our best. values denoted by —," The average and standard error of ${\cal M},d$ are given in Table \ref{tab2} from the pairs $(\varphi_1=0.25$ and $\varphi_2=0.15,0.3,0.35,0.55)$, $(\varphi_1=0.35$ and $\varphi_2=0.55)$ in \ref{107a}) ) as our best values denoted by $[\ast]$." + yo=0.35 Condition Lis moderately violated but Condition LL is satisfied and a’(2.1D)gAR0x0.07. therefore. this phase was included in getting dM! of αι," At $\varphi=0.35$ Condition I is moderately violated but Condition II is satisfied and $a^{\rm (dyn)}(R,t)/g_{\rm + s}(R,t)\approx -0.07$, therefore, this phase was included in getting $d,{\cal M}$ of $[\ast]$." + Condition I is satisfied at 42=0.2.0.5. however. these phases had to be excluded from the mass and distance determination because of the large aU--=02.05)5.8.3.3ms7 and q=O52.38. respectively.," Condition I is satisfied at $\varphi=0.2,0.5$, however, these phases had to be excluded from the mass and distance determination because of the large $a^{\rm + (dyn)}(R,\varphi=0.2,0.5)=5.8,-3.3\:\mbox{ms}^{-2}$ and $q=-0.52,38$, respectively." + Using our best solution for .Vf ancld. the radius variation. velocities. and the components of acceleration were computed in physical units and are plotted inFig. 3bb-," Using our best solution for ${\cal M}$ and$d$, the radius variation, velocities, and the components of acceleration were computed in physical units and are plotted inFig.\ref{fig3}b b-d." + Velocities ancl accelerations are plotted. only for. the phases of more or less good QSAA (ως 0.15-0.3.0.5.0.55). including the slightly shocked phases y= 0.35-0.45.," Velocities and accelerations are plotted only for the phases of more or less good QSAA $\varphi=0.15\mbox{-}0.3,0.5,0.55$ ), including the slightly shocked phases $\varphi=0.35\mbox{-}0.45$ ." + At the phases «e=O.15.0.25.0.3.0.35.0.55 aPRu)=TOS.16.65.93ems7 and Condition Lis satisfied. [amenrp)(11D]< 0.13.Le. aPORus) is small incomparison with the other acceleration. ternis in (3).," At the phases $\varphi=0.15,0.25,0.3,0.35,0.55$ $a^{\rm (dyn)}(R,\varphi)=-79,8,-16,65,93\:\mbox{cms}^{-2}$ and Condition I is satisfied, $\vert a^{\rm (dyn)}(R,t)/g_{\rm s}(R,t)\vert < 0.13$ ,i.e. $a^{\rm (dyn)}(R,\varphi)$ is small incomparison with the other acceleration terms in \ref{1.100}) )." + |g)&O.L is expected. from Alogg.= 0.04. δι=0.39. 0.02. 0.06. 0.10. 0.13. were. found.," $\vert q\vert\approx 0.1$ is expected from $\Delta \log g_{\rm e}=0.04$ , $q(R,\varphi)=0.39,$ $0.02,$ $0.06,$ $-0.10,$ $-0.13$ were found." + Thus. Condition. Lb is indeed: satisfied.," Thus, Condition II is indeed satisfied." +Phe outlier value 0.39 is produced. by cancellation of OrfOl=—30.5mis ,The outlier value $0.39$ is produced by cancellation of $\partial v/\partial t\approx -30.5\:\mbox{ms}^{-2}$ +thought it would be useful to check whether we could detect auv other edge. or check how strict the upper liuits are.,"thought it would be useful to check whether we could detect any other edge, or check how strict the upper limits are." + We take NCC) 1051 as basis for comparison., We take NGC 4051 as basis for comparison. + In NGC 1051. the absorber is rather Mehly ionized. with OVIII being the strongest edee witιτ LlicUl then NeX with r=0.8d0.1.," In NGC 4051, the absorber is rather highly ionized, with OVIII being the strongest edge with $\tau$ = $1.1 \pm 0.4$, then NeX with $\tau$ $0.8 \pm 0.4$." + The OVII «dee is weaker with 720.35: I[xoniossa Fink. 1997.," The OVII edge is weaker with $\tau$ =0.35; Komossa Fink, 1997." + Usiis the ratio Toy) TNX as typical for the relative clepths in a lighly ionized absorber. we can conclude that our non-doetection of edges other than the oue near 1.1 seV in PGIIOL]226 is still consistent with a standard wiwin absorber i.e. our upper luüts on 7 are not strict οrough to rule out a warm absorber m relativistic outflow.," Using the ratio $\tau$$_{OVIII}$ $\tau$$_{NeX}$ as typical for the relative depths in a highly ionized absorber, we can conclude that our non-detection of edges other than the one near 1.1 keV in PG1404+226 is still consistent with a standard warm absorber i.e. our upper limits on $\tau$ are not strict enough to rule out a warm absorber in relativistic outflow." + Foursvectra were taken in February 1996 with IIST/FOS aud gcrafiues C130. CIO90II. (27) and CiLOO with iuteeration times 2300. 530. 120 aud 120 seconds respecively.," Four spectra were taken in February 1996 with HST/FOS and gratings G130, G190H, G270 and G400 with integration times 2300, 530, 120 and 120 seconds respectively." + The total observed wavecheth range covered is 1087 - 1773 with a nominal resolution of 1300 (Fig.6)., The total observed wavelength range covered is 1087 - 4773 with a nominal resolution of 1300 (Fig.6). + The spectra were taken through the 0.86 arcsec diameter aperture., The spectra were taken through the 0.86 arcsec diameter aperture. + Standard reduction procedires were performed., Standard reduction procedures were performed. + The wavelength scale of the spectrum taken with G19MI was shifted by |1.5A. to be consistent with the ot101) spectra.," The wavelength scale of the spectrum taken with G190H was shifted by +1.5, to be consistent with the other spectra." + PC 11YL|226 was oserved with IUE ou Julv ] 2 davs after the ROSAT oervatious.," PG 1404+226 was observed with IUE on July 1994, 2 days after the ROSAT observations." +" The spectrum. SWP 51119. has a total integration time of 315r, ii (accumulated in 12 parts). and was taken through the large aperture aud at low dispersion."," The spectrum, SWP 51419, has a total integration time of 315 minutes (accumulated in 12 parts), and was taken through the large aperture and at low dispersion." + Compared with the UST spectra taken LS mouthts later the coutimuui fiux iu July 1991 is zm 1.3 tinies brighter iu the common observed waveleugth range 1265 to but the Ίνα line kept the sale intensity., Compared with the HST spectra taken 18 monthts later the continuum flux in July 1994 is $\approx$ 1.3 times brighter in the common observed wavelength range 1265 to but the $\alpha$ line kept the same intensity. + The modest S/N aud spectral POCsoll of the IUE spectra would xevent the detection of the absorption lines seen iu the IST spectra., The modest S/N and spectral resolution of the IUE spectrum would prevent the detection of the absorption lines seen in the HST spectra. + No change iu the cuuissiou/absorption profile of Ίσα (Fie.7) cau be detected by comparing the IUE spectirmm aud the C130 spectrin rehbinued at2A., No change in the emission/absorption profile of $\alpha$ (Fig.7) can be detected by comparing the IUE spectrum and the FOS-G130 spectrum rebinned at. + Table 3 lists the emission line imtensities (Ilj = 50 lau 1 Ἐν ου = 0. distance = 617 Mpce).," Table 3 lists the emission line intensities $_{0}$ = 50 km $^{-1}$ $^{-1}$, $_{0}$ = 0, distance = 617 Mpc)." + We note the presence of some weak enission lues: (1) an unideutified line at (rest waveleneth LOTOA) noticed in a few other quasar spectra (Laor et al 1995: Taman et al 1997) (2) a line at 1290 wwhich we ideutifiv with 1175.7., We note the presence of some weak emission lines: (1) an unidentified line at (rest wavelength ) noticed in a few other quasar spectra (Laor et al 1995; Hamann et al 1997) (2) a line at 1290 which we identifiy with $^*$ 1175.7. + This line is seen in UST spectra of Zwl and Laor et al (1997) sugeest that it is produced by resonance scattering of contimmuun photons by ions. a niechauis which requires large velocity eradicuts ( 1000 kins 1) within emitting cloud of the BLR.," This line is seen in HST spectra of IZw1 and Laor et al (1997) suggest that it is produced by resonance scattering of continuum photons by $^*$ ions, a mechanism which requires large velocity gradients $\approx$ 1000 km $^{-1}$ ) within emitting cloud of the BLR." + We identify two absorption systems in the IIST. spectra which. in the source frame. are separated by ~1920 kin +.," We identify two absorption systems in the HST spectra which, in the source frame, are separated by $\sim 1920$ km $^{-1}$." + Tn the blue svstem the absorption lines appear in the blue Πακ of the Ένα and CIV. emission lines at 800 luus ! from the peak., In the `blue' system the absorption lines appear in the blue flank of the $\alpha$ and CIV emission lines at 800 km $^{-1}$ from the peak. + Iu the που system the absorption lues appear on the red flaik of the emission lines at 1100 kan + from the peak., In the `red' system the absorption lines appear on the red flank of the emission lines at 1100 km $^{-1}$ from the peak. + Ilt is known that in radio quiet. ACN/QOuasars. the lieh ionization lines such as CTV are blucshitted with resect to the systemic velocity oa few hundred to a few thousand kin | (e.g. van Cronimgenun 1987. Corbin 1995. Sulentic et al.," It is known that in radio quiet AGN/Quasars, the high ionization lines such as CIV are blueshifted with respect to the systemic velocity by a few hundred to a few thousand km $^{-1}$ (e.g. van Groningen 1987, Corbin 1995, Sulentic et al." + 1995) this dueshiff beime generally iuerpreted as evidence for a wind outflowing from the facc' of the accretion disk turned owards us;, 1995) this blueshift being generally interpreted as evidence for a wind outflowing from the face of the accretion disk turned towards us. + On this basis. we:weue that the red absorption," On this basis, we argue that the red absorption" +stars of varying mass and age.,stars of varying mass and age. +" With an uncertainty in [Fe/H] of +0.1, the masses of these stars could be determined to within 4 to7%."," With an uncertainty in $[\rm{Fe}/\rm{H}]$ of $\pm0.1$, the masses of these stars could be determined to within 4 to." +. Age can generally be determined to within 1 Gyr., Age can generally be determined to within 1 Gyr. + The precision of the age is heavily influenced by theuncertainty in ὄνρο and the position of the star in the C-D diagram., The precision of the age is heavily influenced by theuncertainty in $\delta\nu_{02}$ and the position of the star in the C-D diagram. + Many of these stars are being observed for an extended period of time withKepler and the precision of these measurements will undoubtedly improve., Many of these stars are being observed for an extended period of time with and the precision of these measurements will undoubtedly improve. +" With supporting ground-based spectroscopic observations and detailed modeling involving the individual frequencies, the fundamental properties of these stars will become well-determined and the data should provide significant tests of stellar models."," With supporting ground-based spectroscopic observations and detailed modeling involving the individual frequencies, the fundamental properties of these stars will become well-determined and the data should provide significant tests of stellar models." + Figure 4 shows the observational e diagram., Figure \ref{fig2} shows the observational $\epsilon$ diagram. +" Observations cannot determine the radial order n directly, and so it is possible for ε to be uncertain by +1, particularly in the subgiants (Av in the range 20-80 "," Observations cannot determine the radial order $n$ directly, and so it is possible for $\epsilon$ to be uncertain by $\pm1$, particularly in the subgiants $\Delta\nu$ in the range 20–80 $\mu$ Hz)." +"For these, we have taken e to be in the range 0.7-1.7,wHz). but note there is some ambiguity for stars near the extremes of this range."," For these, we have taken $\epsilon$ to be in the range 0.7–1.7, but note there is some ambiguity for stars near the extremes of this range." + The measurement of e is complicated by its close relationship to Av: a small change in Av can induce a large change in e., The measurement of $\epsilon$ is complicated by its close relationship to $\Delta\nu$: a small change in $\Delta\nu$ can induce a large change in $\epsilon$. +" We have also measured e using an alternative method: the variation of the large separation with frequency was measured as described by ?,, before the radial modes were globally fit and e derived, taking into account the mean curvature."," We have also measured $\epsilon$ using an alternative method: the variation of the large separation with frequency was measured as described by \citet{Mosser10}, before the radial modes were globally fit and $\epsilon$ derived, taking into account the mean curvature." +" À comparison of the values obtained by the two methods showed good agreement, although small systematic offsets exist, typically about 0.1."," A comparison of the values obtained by the two methods showed good agreement, although small systematic offsets exist, typically about 0.1." + This offset is probably due to the combined effects of curvature (departure from equation (1))) and the slightly different range of frequencies over which Av and e were measured., This offset is probably due to the combined effects of curvature (departure from equation \ref{asymp}) )) and the slightly different range of frequencies over which $\Delta\nu$ and $\epsilon$ were measured. + A single method must be applied to both models and data used to ensure consistency., A single method must be applied to both models and data used to ensure consistency. + In this Letter we have used the method outlined in Section ??.., In this Letter we have used the method outlined in Section \ref{sec3}. + The observed stars in Figure 4 are offset to the right of the models., The observed stars in Figure \ref{fig2} are offset to the right of the models. +" This offset is well-known from helioseismology, in which there is a discrepancy between the observed and computed oscillation frequencies of the Sun arising from improper modeling of the near-surface layers (??).."," This offset is well-known from helioseismology, in which there is a discrepancy between the observed and computed oscillation frequencies of the Sun arising from improper modeling of the near-surface layers \citep{Dziembowski88,C-D96}. ." +" A rigorous comparison of the observations with models requires that the offset be taken into account, either by a proper modeling of near-surface"," A rigorous comparison of the observations with models requires that the offset be taken into account, either by a proper modeling of near-surface" +sample shown in Fig.,sample shown in Fig. + 5 where the cross-correlation function peaks at an angular distance of 1. bubble radius with a significance of 9m., \ref{fig:crosscol} where the cross-correlation function peaks at an angular distance of 1 bubble radius with a significance of $\sigma$. + In the immediate environment of a bubble the highest probability location to find an IMS YSO is projected against the rim of the bubble., In the immediate environment of a bubble the highest probability location to find an RMS YSO is projected against the rim of the bubble. + Aloreover. it ds clear from inspecting Fig.," Moreover, it is clear from inspecting Fig." + 2. that the surface density of YSOs is not only enhanced at an angular olfset of1 bubble radius. but that it is enhanced over the entire. angular scale. of the bubbles out to an angular οκο of 2 bubble radii.," \ref{fig:surfdens} that the surface density of YSOs is not only enhanced at an angular offset of 1 bubble radius, but that it is enhanced over the entire angular scale of the bubbles out to an angular offset of 2 bubble radii." +" We can see this by comparing the mean surface clensity of YSOs ""μαρια 2 bubble radii ancl ""outside"" 2 bubble radii.", We can see this by comparing the mean surface density of YSOs “inside” 2 bubble radii and “outside” 2 bubble radii. + The mean surface density of YSOs within an angular olfset of 2 bubble radii is S.O+1.7 YSOs/unit area compared a value of 3.20.2 YSOs/unit area at an angular ollset of 2 bubble radii or greater., The mean surface density of YSOs within an angular offset of 2 bubble radii is $\pm$ 1.7 YSOs/unit area compared a value of $\pm$ 0.2 YSOs/unit area at an angular offset of 2 bubble radii or greater. + jX two sample unequal variance (heteroscedastic) t test of these two subsamples returns a probability. of only that these two subsamples are drawn from populations with the same mean., A two sample unequal variance (heteroscedastic) t test of these two subsamples returns a probability of only that these two subsamples are drawn from populations with the same mean. + Hence we have demonstrated. that there is a statistically significant overdensity of massive YSOs associated with the bubbles compared to the hackground. with an enhanced. probability of finding these YSOs projected. against the rim. of the xibbles.," Hence we have demonstrated that there is a statistically significant overdensity of massive YSOs associated with the bubbles compared to the background, with an enhanced probability of finding these YSOs projected against the rim of the bubbles." + What do these results imply?, What do these results imply? + Firstly. there is a greater concentration of massive star formation towards the bubbles han in the wider environment.," Firstly, there is a greater concentration of massive star formation towards the bubbles than in the wider environment." + This result is confirmed hy he surface density of MMD 6.7 Cillz masers (see Fig. 4)).," This result is confirmed by the surface density of MMB 6.7 GHz masers (see Fig. \ref{fig:mmb_surfdens}) )," + which trace a YSO population independently of mid-infrared emission., which trace a YSO population independently of mid-infrared emission. + A greater concentration of star formation towards he bubbles implies that the bubbles are either cllicicnt at ooducing YSOs. or that they are found in regions of high YSO surface density.," A greater concentration of star formation towards the bubbles implies that the bubbles are either efficient at producing YSOs, or that they are found in regions of high YSO surface density." + This is the classic chicken ancl egg scenario applied to massive star formation: do the bubbles »ecede the high surface density of YSOs. or does the high surface density of YSOs precede (or occur. sipultaneously with) the formation of the bubbles?," This is the classic chicken and egg scenario applied to massive star formation: do the bubbles precede the high surface density of YSOs, or does the high surface density of YSOs precede (or occur simultaneously with) the formation of the bubbles?" + 3elore considering this question more fully. we must ing in the second of our results that there is an enhanced oobabilitv of finding YSOs projected. against the rim of he bubbles (ie. at an angular olfset of 1: bubble radius)," Before considering this question more fully, we must bring in the second of our results – that there is an enhanced probability of finding YSOs projected against the rim of the bubbles (i.e. at an angular offset of 1 bubble radius)." + Dv inspecting the autocorrelation of the IMS. YSOs we showed in Section 2.3 that this elfect is not likely to be due o intrinsic clustering within the RAIS sample on. similar angular scales to the bubble radii., By inspecting the autocorrelation of the RMS YSOs we showed in Section \ref{sect:autocol} that this effect is not likely to be due to intrinsic clustering within the RMS sample on similar angular scales to the bubble radii. + Phe ancillary question raisecl by this result is: why are the YSOs more likely to be ound projected against the rim of the bubbles., The ancillary question raised by this result is: why are the YSOs more likely to be found projected against the rim of the bubbles. + ie. what is special about the bubble rims?, i.e. what is special about the bubble rims? + The bubble rims are traced by sym PATE emission which originates from the photon-clominatec region between the ionisation front being driven out by the LIL region. within the bubble and the surrounding neutral medium., The bubble rims are traced by $\mu$ m PAH emission which originates from the photon-dominated region between the ionisation front being driven out by the HII region within the bubble and the surrounding neutral medium. + The rim of the bubbles thus shows the interface between LIL region and surrounding neutral gas., The rim of the bubbles thus shows the interface between HII region and surrounding neutral gas. + For a spherical bubble morphology one would expect the column density of gas to be greater at the bubble rims due to the greater path length through the neutral material towards the rims., For a spherical bubble morphology one would expect the column density of gas to be greater at the bubble rims due to the greater path length through the neutral material towards the rims. + So at first elance. the higher surface density of YSOs projected against the bubble rims may simply reflect. the higher column density at the rim of the bubbles. i.c. the YSOs trace molecular column density.," So at first glance, the higher surface density of YSOs projected against the bubble rims may simply reflect the higher column density at the rim of the bubbles, i.e. the YSOs trace molecular column density." + However. while the sample of bubbles that have been observed at. relatively high angular resolution in molecular ines (27) do show a peaked molecular column density profile at à normalised) bubble radius of 1. the column cdensity alls olf much less sharply than the YSO surface. density.," However, while the sample of bubbles that have been observed at relatively high angular resolution in molecular lines \citep{beaumont2010} do show a peaked molecular column density profile at a normalised bubble radius of 1, the column density falls off much less sharply than the YSO surface density." + Inspection of Figure 2 from ? shows that at a normalised xibble radius of 1.5 the CO intensity can be roughly half of hat at a normalised radius of L., Inspection of Figure 2 from \citet{beaumont2010} shows that at a normalised bubble radius of 1.5 the CO intensity can be roughly half of that at a normalised radius of 1. + Phis suggests that the YSOs may not trace the column density distribution. although much closer scrutiny of the bubbles in a non-optically thick racer is required to confirm this hypothesis.," This suggests that the YSOs may not trace the column density distribution, although much closer scrutiny of the bubbles in a non-optically thick tracer is required to confirm this hypothesis." + Moreover. the CO contrast between the centre of the bubbles and their rims is often extreme (2). whereas the YSO surface density within an angular olfset of 2 bubble radii is everywhere higher than the background level.," Moreover, the CO contrast between the centre of the bubbles and their rims is often extreme \citep{beaumont2010} whereas the YSO surface density within an angular offset of 2 bubble radii is everywhere higher than the background level." + Vhus we cannot confidentIy. sav that the YSO surface density traces the gas column density around the bubbles., Thus we cannot confidently say that the YSO surface density traces the gas column density around the bubbles. + The YSO surface density is strongly peaked at an olfset of 1 bubble radius and decreases sharply bevond this value., The YSO surface density is strongly peaked at an offset of 1 bubble radius and decreases sharply beyond this value. + )evond an angular ollset of 2 bubble radii the surface density of. YSOs is essentially undistinguishable from the background. level., Beyond an angular offset of 2 bubble radii the surface density of YSOs is essentially undistinguishable from the background level. + The angular cross-correlation function shows a similar steep drop —-| bevond an angular distance of 2 bubble radii the bubbles and RAIS YSOs are essentiallyuncorrelated., The angular cross-correlation function shows a similar steep drop — beyond an angular distance of 2 bubble radii the bubbles and RMS YSOs are essentially. +.. Vhe implication of this is that whatever causes the rise in YSO surface density is closely related to the rim of the bubbles., The implication of this is that whatever causes the rise in YSO surface density is closely related to the rim of the bubbles. + The bubble radius is a dynamic value and expected to increase over time as stellar winds or radiation pressure causes the bubbles to expand., The bubble radius is a dynamic value and expected to increase over time as stellar winds or radiation pressure causes the bubbles to expand. + Combined with this is the fact that the massive YSOs and. UC LIL regions identified by the RAIS survey typically tend to have lifetimes around a few 103 toa few 107 vears (2). and so should trace very recent star formation., Combined with this is the fact that the massive YSOs and UC HII regions identified by the RMS survey typically tend to have lifetimes around a few $^{4}$ to a few $10^{5}$ years \citep{mottram2011b} and so should trace very recent star formation. + The sum of these pieces. of information leads us to conclude that it is likely that the bubbles predate the YSOs., The sum of these pieces of information leads us to conclude that it is likely that the bubbles predate the YSOs. + Ifthe bubbles formed in an environment with a high surface density of YSOs (e.g.intheturbulenthighlyfragmentecinitialconditionssuggestedby 2).. then the distribution should not peak at the rim of the bubble as the bubble radius is time-dependent.," If the bubbles formed in an environment with a high surface density of YSOs \citep[e.g.~in the turbulent highly fragmented initial conditions suggested by][]{dale2011}, then the distribution should not peak at the rim of the bubble as the bubble radius is time-dependent." + Similar arguments have been usec by ο for YSOs detected a he edges of shells in. Carina., Similar arguments have been used by \citet{preibisch2011} for YSOs detected at the edges of shells in Carina. + Also in this case the extent of the enhanced YSO surface density should. also not be related to the current racius of the bubble why are bubbles found in regions of enhance YSO surface density occupying twice their angular radius?, Also in this case the extent of the enhanced YSO surface density should also not be related to the current radius of the bubble – why are bubbles found in regions of enhanced YSO surface density occupying twice their angular radius? + Finally. the relative timescales of the massive YSOs and those required for the expansion of the bubbles imply hat the YSOs formed the bubbles.," Finally, the relative timescales of the massive YSOs and those required for the expansion of the bubbles imply that the YSOs formed the bubbles." + We thus conclude hat a significant [fraction of the YSOs seen against the rim of the bubbles were likely triggered by the expansion of the rubble., We thus conclude that a significant fraction of the YSOs seen against the rim of the bubbles were likely triggered by the expansion of the bubble. + A greater understanding of the clynamical timescales or the expansion of the bubbles and also the molecular environment of the bubbles are required. to confirm this ivpothesis., A greater understanding of the dynamical timescales for the expansion of the bubbles and also the molecular environment of the bubbles are required to confirm this hypothesis. + Pinpointing the YSO formation to have occurred alter the bubble was formed is crucial to cisentaneling cause and effect in the star formation surrounding the bubbles., Pinpointing the YSO formation to have occurred after the bubble was formed is crucial to disentangling cause and effect in the star formation surrounding the bubbles. + Currently. only a few bubbles have had their. dynamical lifetimes estimated and more studies similar to those of ? are required over a larger sample of bubbles.," Currently, only a few bubbles have had their dynamical lifetimes estimated and more studies similar to those of \citet{watson2009} are required over a larger sample of bubbles." + Comparing the YSO clistribution to the gas distribution is also crucial to investigate dillerences in the population of YSOs at the rims of bubbles. for example to determine whether," Comparing the YSO distribution to the gas distribution is also crucial to investigate differences in the population of YSOs at the rims of bubbles, for example to determine whether" +CLUSTTERS OF GALAXIES CBenoist! Müunchen. Germany Copennhagen. Demnark The recent. discovery. of apparently massive ancl relaxed: clusters of galaxies at redshifts 220.5 ollers a unique opportunity to study the evolution of gravitationally bound svstems over an extended. look-back time.,"TERS OF GALAXIES }$, C. $^{1}$ unchen, Germany } nhagen, Denmark } The recent discovery of apparently massive and relaxed clusters of galaxies at redshifts $z\gsim0.5$ offers a unique opportunity to study the evolution of gravitationally bound systems over an extended look-back time." + Moreover. if such systems are proven to be massive. especially those at + their sheer existence can impose stringent constraints on viable cosmological 20.8.modelsS].," Moreover, if such systems are proven to be massive, especially those at $z\gsim0.8$, their sheer existence can impose stringent constraints on viable cosmological models." + In addition. a large sample of confirmed clusters. spanning a broad redshift range. is of great interest for constraining moclels of formation and evolution of earlv-tv galaxies and scale structure. and for the selection of targetsin dillerent peredshift: intervals for," In addition, a large sample of confirmed clusters, spanning a broad redshift range, is of great interest for constraining models of formation and evolution of early-type galaxies and large-scale structure, and for the selection of targetsin different redshift intervals for" + (Rottecringetal.2003).. (Lonsdaleetal.2009) 2009).. (Oosterloo (Boothetal.2009):; (Jolustouctal.2008).," \citep{rbf03}, \citep{lcm+09} \citep{ecc+09}. \citep{Welch09,Dewdney09,Jonas09,ovc09}. \citep{ovc09}; \citep{bbjf09}; \citep{jtb+08}." +. We divide radio transieuts iuto four categories based ou two attributes., We divide radio transients into four categories based on two attributes. + The first is the duration of the sje phenomenon (shorter than or greater than a few seconds)., The first is the duration of the basic phenomenon (shorter than or greater than a few seconds). + The secoud is their location (within the Calaxy or extra-galactic)., The second is their location (within the Galaxy or extra-galactic). + Roughly speaking the duration maS o coherent versus incohercut cliission aud the location o repeated versus catacbesinice eveuts., Roughly speaking the duration maps to coherent versus incoherent emission and the location to repeated versus cataclysmic events. + Pulsars aud related phenomenon (eiut pulses. nulli18o oulsus. erratic pulsars. roating radio transieuts. aid uagnetars) are the dominant category of short duration radio trausieuts at meter and centimneter wavoleusths.," Pulsars and related phenomenon (giant pulses, nulling pulsars, erratic pulsars, rotating radio transients, and magnetars) are the dominant category of short duration radio transients at meter and centimeter wavelengths." + There are no secure examples of short duration radio rausicuts that are located bevoud the local Group., There are no secure examples of short duration radio transients that are located beyond the local Group. + Flare stars and associated phenomena are prine examples of oue duration radio transicuts of Galactic origin., Flare stars and associated phenomena are prime examples of long duration radio transients of Galactic origin. + The focus of this paper is long duration trausicuts of extra-galactic origin., The focus of this paper is long duration transients of extra-galactic origin. + Known examples iu this group are supernovae (Weileretal.2010) aud ginuuarav burst afterelows (Gehrelsetal.2009).," Known examples in this group are supernovae \citep{wps+10} + and gamma-ray burst afterglows \citep{grf09}." +. Iu both cases. the radio eniüssion arises as the fast moving debris mteracts with the circustellar matter.," In both cases, the radio emission arises as the fast moving debris interacts with the circumstellar matter." + Ii Table 1 we «παχο the areal density of racio-cuuitting supernovae (iucludiug the sub-classes) aud GRB afterglows., In Table \ref{tab:ListOfTrans} we summarize the areal density of radio-emitting supernovae (including the sub-classes) and GRB afterglows. +" Note the areal density of ""live transicuts” (transicuts present at anv even instant of time) of both supernovae and CRB afterelows is less than 0.05 per square degree.", Note the areal density of “live transients” (transients present at any given instant of time) of both supernovae and GRB afterglows is less than 0.05 per square degree. + Iu 2007. Bower ct reported on the analysis of a single feld observed hereafter.every BOT]week as a part of the Very Large Axrav. (VLA) calibration progriun.," In 2007, Bower et \nocite{bsb+07} [hereafter, B07] reported on the analysis of a single field observed every week as a part of the Very Large Array (VLA) calibration program." + The observations were conducted at GGIIz aud CCTz and lasted 22 wears., The observations were conducted at GHz and GHz and lasted 22 years. + The 9114 epochs and the lLweekly cadence inakes this data set a most valuable set to probe the decimeter baud for loug duration trausieuts at the subanilliJausky level., The 944 epochs and the weekly cadence makes this data set a most valuable set to probe the decimeter band for long duration transients at the sub-milliJansky level. +" These authors reported the discovery of eight transicuts found iu only one epoch (hereafter. ""iugle-epoch: duration. 20nuuimutes"," These authors reported the discovery of eight transients found in only one epoch (hereafter “single-epoch”; duration, minutes" +where didt=OfOF|veNV ods the Lagrangian time derivative. £4 is the CR pressure. ος is the CR energy density. & is the CR cliffsion coefficient. 5; is the CR source terii due to the central AGN activity. pg. is the iron density. and all other variables have their usual meanings.,"where $d/dt \equiv \partial/\partial t+{\bf v} \cdot \nabla $ is the Lagrangian time derivative, $P_{\rm c}$ is the CR pressure, $e_{\rm + c}$ is the CR energy density, $\kappa$ is the CR diffusion coefficient, $\dot{S_{\rm c}}$ is the CR source term due to the central AGN activity, $\rho_{\rm Fe}$ is the iron density, and all other variables have their usual meanings." +" Pressures aud euergy densities are related via P=(>De aud BP.=(τιle. where we assume ~=h/8 ands,=1/3."," Pressures and energy densities are related via $P=(\gamma-1)e$ and $P_{\rm c}=(\gamma_{\rm c}-1)e_{\rm c}$, where we assume $\gamma=5/3$ and $\gamma_{\rm c}=4/3$." + Equation (5)) describes the couservation of iron mass., Equation \ref{hydro5}) ) describes the conservation of iron mass. + Since we focus ou the effect of ACN outbursts on tle iron distribution and follow the cluster evolution for a timescale much shorter than eurichinoeut times (2.5 Cor: 7)). we ignore the iron source term.," Since we focus on the effect of AGN outbursts on the iron distribution and follow the cluster evolution for a timescale much shorter than enrichment times $\gtrsim 5$ Gyr; \citealt{bohringer04}) ), we ignore the iron source term." + The iron abuudance Z iu unitsof the solar value is proportional to PE/p., The iron abundance $Z$ in unitsof the solar value is proportional to $Z\propto \rho_{\rm Fe}/\rho$ . + Thus the iron density pg. in equation (5)) may be replaced by Zp., Thus the iron density $\rho_{\rm Fe}$ in equation \ref{hydro5}) ) may be replaced by $Z \rho$. + Siuce both the gas mass aud irou lass are conserved. the metallicity Z is also conserved: and therefore provides a tracer for the ICM eas. which is helpful in understanding how ACN outburstsaffect and mix the ICM.," Since both the gas mass and iron mass are conserved, the metallicity $Z$ is also conserved: and therefore provides a tracer for the ICM gas, which is helpful in understanding how AGN outburstsaffect and mix the ICM." + Iu the eas energv equation (3)). we inchide radiative cooling with a volume cooling rate nye(T.Z). where the cooling function A(7.Z) is adopted from ?.— and depends ou both gas temperature TZ and metallicity Z.," In the gas energy equation \ref{hydro3}) ), we include radiative cooling with a volume cooling rate $n_{\rm i}n_{\rm e}\Lambda(T,Z)$, where the cooling function $\Lambda(T,Z)$ is adopted from \citet{sd93} + and depends on both gas temperature $T$ and metallicity $Z$." + The jou umber deusitv 5»; is related to the proton nuuber deusifv ay via sj= Lloeg. aud thus the molecular weight is 4—0.61., The ion number density $n_{\rm i}$ is related to the proton number density $n_{\rm H}$ via $n_{\rm i}=1.1n_{\rm H}$ and thus the molecular weight is $\mu=0.61$. +" The gas temperature is related to the gas pressure aud density via the ideal gas law: where Ay is Boltzmann's coustaut aud i, is the atomic lass unt.", The gas temperature is related to the gas pressure and density via the ideal gas law: where $k_{\rm B}$ is Boltzmann's constant and $m_{\mu}$ is the atomic mass unit. + Equatious (1)) (5)) ave solved im (r0:) evlindrica coordinates using a two-dimensional Eulerian code «λίαν to ZEUS 2D να iu particular. we have incorporated iuto the code a background eravitationa potential. CR diffusion. CR cucrey equation. aud mon equation of mass conservation.," Equations \ref{hydro1}) ) $-$ \ref{hydro5}) ) are solved in $(r, z)$ cylindrical coordinates using a two-dimensional Eulerian code similar to ZEUS 2D \citep{stone92}; ; in particular, we have incorporated into the code a background gravitational potential, CR diffusion, CR energy equation, and iron equation of mass conservation." + The computational eric consists of 100 equally spaced zones in both coordinates out to 100 kpe plus additional 100 logarithiuically-spacec zoues out to 1 Alpe., The computational grid consists of $100$ equally spaced zones in both coordinates out to $100$ kpc plus additional $100$ logarithmically-spaced zones out to $1$ Mpc. + For all the three fluids. we adopt reflective boundary conditions at the origin aud outflow boundary conditions at the outer boundary.," For all the three fluids, we adopt reflective boundary conditions at the origin and outflow boundary conditions at the outer boundary." + Our model aud methods are geucrallv applicable to all relaxed clusters. but for concreteuess. we adopt «λαο. paraimcters appropriate for the typical CC cluster Abell 1795. which has been well observed by both aud (2???) ," Our model and methods are generally applicable to all relaxed clusters, but for concreteness, we adopt simulation parameters appropriate for the typical CC cluster Abell 1795, which has been well observed by both and \citep{tamura01, ettori02, vikhlinin06}. ." +"For initial profiles of AL795. we first build au analytic fit to the deprojected 3-dimnieunsional eas temperature profile derived. from observations. which acquired data out to ~1 Mpe covering our eutire coniputational eril: where the constant a is chosen to be a= 5. T,=2.5 keV is the observed central temperature of A1795.and Ty isthebest-fit temiperature profile of ?. which providesan excellent fit to Chandra data of AT795 from LO kpe to l Mpc: where"," For initial profiles of A1795, we first build an analytic fit to the deprojected $3$ -dimensional gas temperature profile derived from observations, which acquired data out to $\sim 1$ Mpc covering our entire computational grid: where the constant $\alpha$ is chosen to be $\alpha=5$ , $T_{\rm in}=2.5$ keV is the observed central temperature of A1795,and $T_{\rm V}$ is thebest-fit temperature profile of \citet{vikhlinin06} which providesan excellent fit to data of A1795 from $40$ kpc to $1$ Mpc: where" +wave equation: where the operator PF is given by Here z is the distance to the magnetic axis of symmetry.,wave equation: where the operator $F$ is given by Here $x$ is the distance to the magnetic axis of symmetry. +" Although in the presence of a mixed poloidal and toroidal field the equations still give rise to a continuous set of solutions, the calculations are significantly complicated as the continuum modes are affected by the toroidal component of the field, by gravity, and by compressibility."," Although in the presence of a mixed poloidal and toroidal field the equations still give rise to a continuous set of solutions, the calculations are significantly complicated as the continuum modes are affected by the toroidal component of the field, by gravity, and by compressibility." + For the sake of simplicity we will ignore toroidal fields in our dynamic simulations., For the sake of simplicity we will ignore toroidal fields in our dynamic simulations. +" We will however, calculate the continuum frequencies for a mixed poloidal and toroidal field in the Appendix B. For determining the spectrum of the core continuum, the appropriate boundary conditions are €4(x=xc)0, where χε(Φ) marks the location of the crust-core interface."," We will however, calculate the continuum frequencies for a mixed poloidal and toroidal field in the Appendix B. For determining the spectrum of the core continuum, the appropriate boundary conditions are $\xi_{\phi}(\chi=\chi_c)=0$, where $\chi_c(\phi)$ marks the location of the crust-core interface." +" With this boundary condition, Equation (26)) constitutes a Sturm-Liouville problem on each separate flux surface i»."," With this boundary condition, Equation \ref{poedts}) ) constitutes a Sturm-Liouville problem on each separate flux surface $\psi$." +" Using the stellar structure model and magnetic field configuration from section 4.1, we can calculate the eigenfunctions and eigenfrequencies for each flux surface w."," Using the stellar structure model and magnetic field configuration from section 4.1, we can calculate the eigenfunctions and eigenfrequencies for each flux surface $\psi$." + The reflection symmetry of the stellar model and the magnetic field with respect to the equatorial plane assures that the eigenfunctions of Eq. (26)), The reflection symmetry of the stellar model and the magnetic field with respect to the equatorial plane assures that the eigenfunctions of Eq. \ref{poedts}) ) + are either symmetric or anti-symmetric with respect to the equatorial plane., are either symmetric or anti-symmetric with respect to the equatorial plane. + We can therefore determine the eigenfunctions by integrating Eq. (26)), We can therefore determine the eigenfunctions by integrating Eq. \ref{poedts}) ) + along the magnetic field lines from the equatorial plane x=0 to the crust-core interface x=xc(v).," along the magnetic field lines from the equatorial plane $\chi = +0$ to the crust-core interface $\chi = \chi_c \left( \psi \right)$." +" Let us consider the odd modes here for which £5(0)=0, and solve Eq. (26))"," Let us consider the odd modes here for which $\xi_{\phi} \left( 0 \right) = 0$, and solve Eq. \ref{poedts}) )" +" with the boundary condition £5(x.)=0 at the crust-core interface; for even modes, the boundary condition is d£;(0)/dx=0."," with the boundary condition $\xi_{\phi} \left(\chi_c \right) = +0$ at the crust-core interface; for even modes, the boundary condition is $d\xi_{\phi} \left( 0 \right)/d\chi=0$." + We find the eigenfunctions by means of a shooting method; using fourth order Runge-Kutta integration we integrate from x=0 to x=x..," We find the eigenfunctions by means of a shooting method; using fourth order Runge-Kutta integration we integrate from $\chi += 0$ to $\chi = \chi_c$." +" The correct eigenvalues o,, and eigenfunctions £,(x) are found by changing the value of o until the boundary condition at En is satisfied.", The correct eigenvalues $\sigma_n$ and eigenfunctions $\xi_n \left( \chi \right)$ are found by changing the value of $\sigma$ until the boundary condition at $\xi_n$ is satisfied. + In this way we gradually increase the value of σ until the desired number of harmonics is obtained., In this way we gradually increase the value of $\sigma$ until the desired number of harmonics is obtained. + In figure 12 we show a typical resulting core-continuum.," In figure \ref{core_cont1} + we show a typical resulting core-continuum." +" According to Sturm-Liouville theory the normalized eigenfunctions £, of Eq. (26))", According to Sturm-Liouville theory the normalized eigenfunctions $\xi_n$ of Eq. \ref{poedts}) ) + form an orthonormal basis with respect to the following inner product:, form an orthonormal basis with respect to the following inner product: +the conventional law Τ(λ)οςA7? (Draine1989).,the conventional law $\tau (\lambda) \propto \lambda^{-1.75}$ \citep{Dr89}. +". In this assumption, the total flux density is written as follows, where rp and ηλαν are the flux density amplitudes of the starburst and AGN templates {235 and f29 normalized at 6 um, respectively."," In this assumption, the total flux density is written as follows, where $\eta_{\rm SB}$ and $\eta_{\rm AGN}$ are the flux density amplitudes of the starburst and AGN templates $f^{\rm SB}_{\nu}$ and $f^{\rm AGN}_{\nu}$ normalized at 6 $\mu$ m, respectively." +" We can estimate the only two free parameters (the ratio of sp to ηλαν and το, which is the 6 pom optical depth to the AGN) by fitting the spectrum."," We can estimate the only two free parameters (the ratio of $\eta_{\rm SB}$ to $\eta_{\rm AGN}$ and $\tau_{6}$, which is the 6 $\mu$ m optical depth to the AGN) by fitting the spectrum." +" From these, we can get the intrinsic AGN contribution to the 6 jum flux density, ag=nacn/(Nacn+risp)."," From these, we can get the intrinsic AGN contribution to the 6 $\mu$ m flux density, $\alpha_{6} = \eta_{\rm AGN} / (\eta_{\rm AGN} + \eta_{\rm SB})$." +" In addition, we can also estimate the AGN contribution to the total infrared luminosity (this roughly corresponds to the bolometric luminosity, Loi, for ULIRGs), oo=nacn/(Nacnt+Knsp), where K=RACN/RS®, and RAGN and R?P are the ratios of the intrinsic flux at 6 wm to the total infrared flux of AGN and starbursts, respectively; in local ULIRGs, logRAGN= logRSP=1005, yielding K~35 (Nardini et al."," In addition, we can also estimate the AGN contribution to the total infrared luminosity (this roughly corresponds to the bolometric luminosity, $L_{\rm bol}$, for ULIRGs), $\alpha_{\rm bol} = \eta_{\rm AGN} / (\eta_{\rm AGN} + K \eta_{\rm SB}) $, where $K = R^{\rm AGN}/R^{\rm SB}$, and $R^{\rm AGN}$ and $R^{\rm SB}$ are the ratios of the intrinsic flux at 6 $\mu$ m to the total infrared flux of AGN and starbursts, respectively; in local ULIRGs, $\log R^{\rm AGN} = -0.36^{+0.06}_{-0.07}$ , $\log R^{\rm SB} = -1.91^{+0.02}_{-0.02}$, yielding $K \sim 35$ (Nardini et al." +" in —0.36*905,prep.).", in prep.). +" The model--1.91 has been successfully applied to a sample of local ULIRGs, obtaining two important results: 1) despite the complexity of the spectra, all the sources were successfully fitted, showing that the relative AGN/starburst contribution and the extinction of the AGN component are responsible for most of the observed variety; 2) the expected AGN/starburst contributions to the bolometric luminosity reproduce closely the total observed luminosity."," The model has been successfully applied to a sample of local ULIRGs, obtaining two important results: 1) despite the complexity of the spectra, all the sources were successfully fitted, showing that the relative AGN/starburst contribution and the extinction of the AGN component are responsible for most of the observed variety; 2) the expected AGN/starburst contributions to the bolometric luminosity reproduce closely the total observed luminosity." +" This is an important test for our model: the bolometric contributions are obtained from the 6 jum spectral decomposition only (and from the average bolometric ratios, which have a fixed value for all objects), therefore the comparison between the predicted and observed total luminosities is an independent check of the results."," This is an important test for our model: the bolometric contributions are obtained from the 6 $\mu$ m spectral decomposition only (and from the average bolometric ratios, which have a fixed value for all objects), therefore the comparison between the predicted and observed total luminosities is an independent check of the results." + Here we apply the same model to high-redshift sources., Here we apply the same model to high-redshift sources. +" In doing so, we assume that a) the intrinsic SED, and b) the bolometric ratios, are the same at low and high redshift."," In doing so, we assume that a) the intrinsic SED, and b) the bolometric ratios, are the same at low and high redshift." + We discuss the implications and the limits of these assumptions in 84., We discuss the implications and the limits of these assumptions in 4. + The stacked spectra for the two samples of submm- and 24 um-selected galaxies are shown in Fig., The stacked spectra for the two samples of submm- and 24 $\mu$ m-selected galaxies are shown in Fig. +" 1, together with our deconvolution in the AGN and starburst components."," 1, together with our deconvolution in the AGN and starburst components." +in the FGM-based BLFs (see the closed contours in Fig. 39).,in the FGM-based BLFs (see the closed contours in Fig. \ref{fig:gauss_lf}) ). + This structure is introduced by the Gaussian copula. and from the physical point of view. it might not be strongly desired.," This structure is introduced by the Gaussian copula, and from the physical point of view, it might not be strongly desired." + The FGM-based BLF has a more ideal shape., The FGM-based BLF has a more ideal shape. + Second. since the univariate LF shapes are different at FIR and FUV. the ridge of the BLF is not a straight line but clearly nonlinear.," Second, since the univariate LF shapes are different at FIR and FUV, the ridge of the BLF is not a straight line but clearly nonlinear." + This feature is more clearly visible in higher correlation cases in Figure 3.. but always exists for the whole range of p.," This feature is more clearly visible in higher correlation cases in Figure \ref{fig:gauss_lf}, but always exists for the whole range of $\rho$." + This trend is indeed found in the {ην diagram (Martinetal.2005)., This trend is indeed found in the $\lir$ $\luv$ diagram \citep{martin05}. +. The underlying physies is that galaxies with high SFRs are more extinguished by dust (e.g.Buatetal.2007a.b).," The underlying physics is that galaxies with high SFRs are more extinguished by dust \citep[e.g.][]{buat07a,buat07b}." +. Observational applications including this topic will be presented elsewhere (Takeuchi et 2010. in preparation).," Observational applications including this topic will be presented elsewhere (Takeuchi et 2010, in preparation)." + Since we have an explicit form of a BLF. we can discuss the flux selection effect formally.," Since we have an explicit form of a BLF, we can discuss the flux selection effect formally." + For simplicity. we consider the bivariate case ssample selected at two bands). but it will be straightforward to extend the formulation to a multiwavelength ease (or more generally. selected using any physical properties).," For simplicity, we consider the bivariate case sample selected at two bands), but it will be straightforward to extend the formulation to a multiwavelength case (or more generally, selected using any physical properties)." +" The flux selection is described in terms of luminosity as putting a lower bound LP"" on a CL —L:2) plane.", The flux selection is described in terms of luminosity as putting a lower bound $\llim$ on a luminosity--luminosity $L_1$ $L_2$ ) plane. +" The lower bound luminosity LE"" is defined by the flux (density) detection limit SI?"" as a function of redshift.", The lower bound luminosity $\llim$ is defined by the flux (density) detection limit $S^{\rm lim}$ as a function of redshift. + In most surveys. a certain wavelength band is chosen as the primary selection band. like B-band. Ks-band. 60jm-selected. ete.," In most surveys, a certain wavelength band is chosen as the primary selection band, like -band, s-band, $60\;\mu$ m-selected, etc." + The schematic description of a survey is presented in Figure 4.., The schematic description of a survey is presented in Figure \ref{fig:selection_effect}. +" If we select a sample of objects (in our case galaxies) at band |. the objects with £L, \llim_1 (z)$ and $L_2 > \llim_2 (z)$." +" Hence. on the £,—L» plane. the 2-dim distribution of the detected objects is expressed as where © is a solid angle. and © is the Heaviside step function detined as The quantity S° is proportional to the surface number density of objects detected in both bands on the {ιο plane."," Hence, on the $L_1$ $L_2$ plane, the 2-dim distribution of the detected objects is expressed as where $\Omega$ is a solid angle, and $\Theta$ is the Heaviside step function defined as The quantity $\sdet$ is proportional to the surface number density of objects detected in both bands on the $L_1$ $L_2$ plane." + We start from a primary selection at band |. then we would have objects detected at band | but not detected at band 2.," We start from a primary selection at band 1, then we would have objects detected at band 1 but not detected at band 2." + In such a case we only have upper limits for these objects., In such a case we only have upper limits for these objects. +" The 2-dim distribution of the upper limits at band 2 is similarly formulated as The superseript UL? stands for ""upper limit at band 27.", The 2-dim distribution of the upper limits at band 2 is similarly formulated as The superscript UL2 stands for “upper limit at band 2”. + In statistical terminology. the upper limit case. wwe know there is an object but we do only have the upper tor lower) limits of a certain quantity. is referred to as “censored”.," In statistical terminology, the upper limit case, we know there is an object but we do only have the upper (or lower) limits of a certain quantity, is referred to as “censored”." + Though we can detine the distribution XUL.Es) by Eq. (09. ," Though we can define the distribution $\sult (L_1, L_2)$ by Eq. \ref{eq:ul2}) )," +since the sample objects belonging to this category appear only as upper limits on the plot. a special statistical treatment. referred to as the survival analysis. is required to estimate »ial£2) from the data.," since the sample objects belonging to this category appear only as upper limits on the plot, a special statistical treatment, referred to as the survival analysis, is required to estimate $\sult (L_1, L_2)$ from the data." + Since we select objects at band |. we do not have upper limits at band |. because we do not know if there would be an object below the limit.," Since we select objects at band 1, we do not have upper limits at band 1, because we do not know if there would be an object below the limit." +" This case is called ""truncated"" in statistics.", This case is called “truncated” in statistics. + If we select objects at band 2. we can formulate the 2-dim distribution of detected objects and upper limits exactly in the same way as the band | selected sample.," If we select objects at band 2, we can formulate the 2-dim distribution of detected objects and upper limits exactly in the same way as the band 1 selected sample." + For the objects detected at both bands. the 2-dim distribution is expressed by Eq. (38)).," For the objects detected at both bands, the 2-dim distribution is expressed by Eq. \ref{eq:detect}) )." + The objects detected at band 2 but not detected at band | is expressed as ↕↑⊲∖↖∁∁⋡∙⋯∣∏⋯∣∁∣∠↕⊥⊔⊔↿∖∶⊐⋡∙⋯↳∣∠⊳↕∙↘⊔⊔↿∖∶⊐⇂≯⇂⊾∁∁↥⊰∁∣⋝⊽↥⋂∁∣⊔↳∐⋂∙⋮↾↾∣↧∁∫∖⋡−∁⋯⊾⇂⊾∁∁⊓∩⋂⋅∁∖⊽∩∣⊔⊓⋯⊤∙∥⊾⋝⊽∁⇈⊲∁∁↾⋅∁↾∁⋅⋅∖↖," The objects detected at band 2 but not detected at band 1 is expressed as If we can model $\llim_1 (z)$ and $\llim_2 (z)$ precisely including the $K$ -correction, evolutionary effect, etc.," +∁∁⋡∙⋯⊔⊰∁↾∣↧∁∩∣↴⊰∁∏⊽∁↲∣↴↥∖∩∙∣∏⋡∙∣↾∁ luminosity distribution to estimate the correlation coefficient. or more generally the dependence structure of two luminosities through Eqs. (38))-(40)).," we can use the observed bivariate luminosity distribution to estimate the correlation coefficient, or more generally the dependence structure of two luminosities through Eqs. \ref{eq:detect}) \ref{eq:ul2}) )." + We can deal with these cases in a unified manner with techniques developed in survival analysis., We can deal with these cases in a unified manner with techniques developed in survival analysis. + We discuss this issue ina subsequent work (Takeuchi et 22010. in preparation).," We discuss this issue in a subsequent work (Takeuchi et 2010, in preparation)." + The star formation rate (SFR) is one of the most fundamental quantities to investigate the formation and evolution of galaxies., The star formation rate (SFR) is one of the most fundamental quantities to investigate the formation and evolution of galaxies. + The SFR is often estimated from the FUV flux of galaxies (or other related observables like Ha ete.), The SFR is often estimated from the FUV flux of galaxies (or other related observables like $\alpha$ etc.) +" after ""correcting"" the dust extinction.", after “correcting” the dust extinction. + However.," However," +appropriately.,appropriately. + The number of stars per magnitude (7) and colour interval (7. .7) was integrated to the magnitude limit of this survey., The number of stars per magnitude $I$ ) and colour interval $I-J$ ) was integrated to the magnitude limit of this survey. + The derived M-dwarf isonumbers are compared to our data in Fig. 6.., The derived M-dwarf isonumbers are compared to our data in Fig. \ref{Figcontamination}. + The conclusion is that it is not likely that the proposed new Pleiades BDs are field M dwarfs., The conclusion is that it is not likely that the proposed new Pleiades BDs are field M dwarfs. + Eight new Pletades candidates have been identified. four of which are possible BDs.," Eight new Pleiades candidates have been identified, four of which are possible BDs." + Three of the four brightest new candidates have proper motions consistent with Pletades membership (Hambly. priv.," Three of the four brightest new candidates have proper motions consistent with Pleiades membership (Hambly, priv." + comm.)., comm.). + Two probable members (NPL22 32) stick out from the single-star sequence and are analyzed as binaries together with the spectroscopic binary PPL15 (NPL35)., Two probable members (NPL22 32) stick out from the single-star sequence and are analyzed as binaries together with the spectroscopic binary PPL15 (NPL35). + À number of faint very red objects were also found., A number of faint very red objects were also found. + Two of those were measured also in A and show colours similar to GDI65B and are possible field BDs., Two of those were measured also in $K$ and show colours similar to GD165B and are possible field BDs. + In Fig., In Fig. + 7. this survey 1s compared to several other recent surveys., \ref{Figcomparison} this survey is compared to several other recent surveys. + Known nonmembers have been excluded., Known nonmembers have been excluded. + The dispersion of the Steele et al., The dispersion of the Steele et al. + (1993.1995) data can probably be explained by photometric uncertainty. since most of their I magnitudes are photographic.," \cite*{steele93,steele95} data can probably be explained by photometric uncertainty, since most of their $I$ magnitudes are photographic." + Note that the faint Pleiades sequence is slightly bluer than the Baraffe et al., Note that the faint Pleiades sequence is slightly bluer than the Baraffe et al. + (1998) model., \cite*{baraffe98} model. + Part of this may be due to incomplete line lists and not yet included dust formation in the models., Part of this may be due to incomplete line lists and not yet included dust formation in the models. + Note also that Mermilliod et al., Note also that Mermilliod et al. + (1997) found from Hippareos data that the Pleiades cluster is peculiar in the sense that its main sequence is ~0.1 mag fainter than other nearby clusters. such as the Hyades and Praesepe.," \cite*{mermilliod97} found from Hipparcos data that the Pleiades cluster is peculiar in the sense that its main sequence is $\sim0.4$ mag fainter than other nearby clusters, such as the Hyades and Praesepe." + The reason for this peculiarity is not known. and may also hide part of the model deviation.," The reason for this peculiarity is not known, and may also hide part of the model deviation." + The objects in Table 2 that are of special interest are individually discussed and compared to other papers below.N," The objects in Table \ref{Tabphotometry} that are of special interest are individually discussed and compared to other papers below.," +PL11. and have proper motions consistent with membership (Hambly. priv.," and have proper motions consistent with membership (Hambly, priv." + comm.).," comm.)," + although not present in HHJ., although not present in HHJ. + NPL22 is also a possible binary. best fitted by two components of equal brightness. Z4=Ij16.3NPL24. and have proper motions that are not consistent with membership. (," NPL22 is also a possible binary, best fitted by two components of equal brightness, $I_\mathrm{A}=I_\mathrm{B}=16.3$, and have proper motions that are not consistent with membership. (" +ΡΡΙ12) and have uncertain proper motions.,PPL12) and have uncertain proper motions. + NPL30 has a radial velocity consistent with membership (Staufferetal.1994b)., NPL30 has a radial velocity consistent with membership \cite{stauffer94b}. +. NPL32 is very close to a bright star. which due to blending makes the photographie proper motion uncertain.," NPL32 is very close to a bright star, which due to blending makes the photographic proper motion uncertain." + If NPL32 is à member. its position above the Pleiades sequence indicates an unresolved binary. best fitted by Iq =17.1. fy=15.0. (," If NPL32 is a member, its position above the Pleiades sequence indicates an unresolved binary, best fitted by $I_\mathrm{A}=17.4$ , $I_\mathrm{B}=18.0$. (" +HHJ26) is. as also found by Steele et al. (1993).,"HHJ26) is, as also found by Steele et al. \cite*{steele93}," +. an RE nonmember. (, an $RI$ nonmember. ( +PPLI5) has been measured by several authors recently (Stauffer et al.,PPL15) has been measured by several authors recently (Stauffer et al. + 1994a: Basri et al., 1994a; Basri et al. +" 1996: ZMR). and also found to be a spectroscopic binary (Basri&Martin1997).,From the primary component's possible loeit in our colour-magnitude diagrams. the secondary’s mass is ~0.03 M... consistent with ZMR."," 1996; ZMR), and also found to be a spectroscopic binary \cite{basri97}.From the primary component's possible locii in our colour-magnitude diagrams, the secondary's mass is $\sim0.03$ $_{\odot}$, consistent with ZMR." + The 7 magnitudes would be 7/4=17.96 Hm=21.3., The $I$ magnitudes would be $I_\mathrm{A}=17.96$ $I_\mathrm{B}=21.3$. + A heavier and brighter secondary would force the primary below the disk sequence., A heavier and brighter secondary would force the primary below the disk sequence. + are all below the BD limit., are all below the BD limit. + NPL37 shows a slight brightness enhancement at the edge of the stellar profile., NPL37 shows a slight brightness enhancement at the edge of the stellar profile. + It is not clear wether this is a background star or galaxy or if NPL37 itself i$ a compact galaxy. (, It is not clear wether this is a background star or galaxy or if NPL37 itself is a compact galaxy. ( +Teidel).,Teide1). + Our result is 7—19.26. 7=16.15.," Our result is $I=19.26$, $J=16.18$." + The values given in ZMR and ZRM are 7=18.50and J= 16.37. The ./ magnitude agrees fairly well. but the difference in 7 (0.16 mag) is clearly exceeding the error-bar limits.," The values given in ZMR and ZRM are $I=18.80$and $J=16.37$ The $J$ magnitude agrees fairly well, but the difference in $I$ $0.46$ mag) is clearly exceeding the error-bar limits." + Teidel, Teide1 +to the BGL and the intergranular lane.,to the BGL and the intergranular lane. +" Using NST TiO and observations, we discovered that small-scale intergranular jets, first described in Goodeetal.(2010b),, are associated with bright granular lanes (BGLs) developing inside photospheric granules."," Using NST TiO and observations, we discovered that small-scale intergranular jets, first described in \cite{goode_apjl_2010}, are associated with bright granular lanes (BGLs) developing inside photospheric granules." + The BGLs are thought to be a signature of vortex tubes and they were first found in solar and simulation data by Steineretal.(2010)., The BGLs are thought to be a signature of vortex tubes and they were first found in solar and simulation data by \citet{Steiner_2010}. +". We summarize our new findings as follows: i) our conservative estimate is that more than half of a total of 100 well identified tiny intergranular jets are co-spatial and co-temporal with the occurrence of BGLs, although not each BGL event is accompanied with small-scale chromospheric activity; ii) along with the BGL, a vortex tube also develops a well-defined bright grain located between the BGL and the dark intergranular lane; and iii) vortex-tube signatures may reach the lower chromosphere and can be detected in off-band images."," We summarize our new findings as follows: i) our conservative estimate is that more than half of a total of 100 well identified tiny intergranular jets are co-spatial and co-temporal with the occurrence of BGLs, although not each BGL event is accompanied with small-scale chromospheric activity; ii) along with the BGL, a vortex tube also develops a well-defined bright grain located between the BGL and the dark intergranular lane; and iii) vortex-tube signatures may reach the lower chromosphere and can be detected in off-band images." +" The bright grain, described here, appears to correspond to the plateau in the model intensity profile presented in Figure 5 in Steineretal.(2010)."," The bright grain, described here, appears to correspond to the plateau in the model intensity profile presented in Figure 5 in \cite{Steiner_2010}." +". According to the simulation data, the darkish space between the bright grain and the BGL coincides with the axis of the vortex tube."," According to the simulation data, the darkish space between the bright grain and the BGL coincides with the axis of the vortex tube." +" The interpretation is that due to low pressure and temperature, the opacity above the vortex tube is reduced thus allowing us to peer deeper into its relatively cooler interior."," The interpretation is that due to low pressure and temperature, the opacity above the vortex tube is reduced thus allowing us to peer deeper into its relatively cooler interior." + What is the bright grain then?, What is the bright grain then? + Is it part of the vortex tube?, Is it part of the vortex tube? + Does this interpretation hold when we consider the fact that the vortex tube can each the chromosphere?, Does this interpretation hold when we consider the fact that the vortex tube can reach the chromosphere? +" As it follows from simulations, the associated magnetic field, is generally wrapped up in such a way, that the field is mainly aligned with the flow, i.e., it is rather perpendicular to the vortex tube axis."," As it follows from simulations, the associated magnetic field, is generally wrapped up in such a way, that the field is mainly aligned with the flow, i.e., it is rather perpendicular to the vortex tube axis." + The high-speed flow above the vortex tube reaches p to the top of the photosphere with velocities up to 8 km ! and sweeps the magnetic field in the horizontal direction to the intergranular lane., The high-speed flow above the vortex tube reaches up to the top of the photosphere with velocities up to 8 km $^{-1}$ and sweeps the magnetic field in the horizontal direction to the intergranular lane. +" It may be that this field collides with the nearby intergranular field of possibly opposing polarity, which has the potential to cause some chromospheric activity."," It may be that this field collides with the nearby intergranular field of possibly opposing polarity, which has the potential to cause some chromospheric activity." +" We do not know, however, if BGL events seen in images of granulation possess magnetic fields strong enough to cause detectable chromospheric activity."," We do not know, however, if BGL events seen in images of granulation possess magnetic fields strong enough to cause detectable chromospheric activity." + Polarization measurements with the baloon-borne solar telescope failed to detect magnetic field signal associated with a vortex tube (Steineretal.2010)., Polarization measurements with the baloon-borne solar telescope failed to detect magnetic field signal associated with a vortex tube \citep{Steiner_2010}. +". A brief review of published Hinode/SP data (e.g.,Centenoetal.2007;2010) indicates that Hinode/SP intensity maps may have insufficient spatial resolution to reliably discern a BGL event, so that no reliable conclusions on the association between a BGL and the magnetic field can be made."," A brief review of published Hinode/SP data \citep[e.g.,][]{centeno2007,lites_2008,2010ApJ...713.1310I, gomory_2010} + indicates that Hinode/SP intensity maps may have insufficient spatial resolution to reliably discern a BGL event, so that no reliable conclusions on the association between a BGL and the magnetic field can be made." +" Nevertheless, Centenoetal.(2007,leftpanelintheirFig-ure1) studied a flux-emergence event associated with a particular pattern in the intensity maps that could be interpreted as an evolving BGL."," Nevertheless, \citet[][left panel in their Figure 1]{centeno2007} studied a flux-emergence event associated with a particular pattern in the intensity maps that could be interpreted as an evolving BGL." +" OrozcoSuárezetal.(2008) presented data for two flux-emergence events, where increased circular polarization polarization was spatial with enhanced brightness within a granule."," \cite{orozco} presented data for two flux-emergence events, where increased circular polarization polarization was co-spatial with enhanced brightness within a granule." + Zhangetal.(2009) reported that granules tend to fragment when magnetic fields emerge within them., \cite{Zhang_granule_fragmentation} reported that granules tend to fragment when magnetic fields emerge within them. + Simulations by Tortosa-Andreu&Moreno-Insertis(2009) seem to confirm the latter by showing that surface temperature structures change as field emerges., Simulations by \cite{tortosa_andreu} seem to confirm the latter by showing that surface temperature structures change as field emerges. +" On the other hand, Gómóryetal.2010) argue that an emerging loop leaves no detectable brightness pattern on the host granule."," On the other hand, \cite{gomory_2010} argue that an emerging loop leaves no detectable brightness pattern on the host granule." +" Stenflo(2011) underscored the possible existence of two distinct populations of the solar magnetic fields: i) strong, or collapsed, fields predominantly located in the intergranular lanes and manifested via photospheric bright points and ii) weak, or uncollapsed, flux occupying both intergranular lanes and bright granules with a wea preference for the bright granular cells."," \cite{stenflo_2011} underscored the possible existence of two distinct populations of the solar magnetic fields: i) strong, or collapsed, fields predominantly located in the intergranular lanes and manifested via photospheric bright points and ii) weak, or uncollapsed, flux occupying both intergranular lanes and bright granules with a weak preference for the bright granular cells." + The uncollapsed population is thought to represent weaker turbulent fields with spatial scales too small to be fully resolved with today's state-of-the-art instrumentation., The uncollapsed population is thought to represent weaker turbulent fields with spatial scales too small to be fully resolved with today's state-of-the-art instrumentation. +" In this case, we suggest that the intergranular Jets, associated with the development of BGLs, may be a manifestation of these weaker turbulent fields, the bulk of which apparently remains hidden at spatial scales below 200 km (Stenflo2011)."," In this case, we suggest that the intergranular jets, associated with the development of BGLs, may be a manifestation of these weaker turbulent fields, the bulk of which apparently remains hidden at spatial scales below 200 km \citep{stenflo_2011}." +. The intergranular jets are much smaller and weaker than all previously known jet-like events., The intergranular jets are much smaller and weaker than all previously known jet-like events. +" At the same time, they appear much more numerous than the larger events, leading us to the speculation that the total energy released by these tiny events may not be negligible in the total energy balance."," At the same time, they appear much more numerous than the larger events, leading us to the speculation that the total energy released by these tiny events may not be negligible in the total energy balance." + Authors thank BBSO observers and the instrument team for their contribution to this study., Authors thank BBSO observers and the instrument team for their contribution to this study. + VY work was partly supported under NASA GI NNX08AJ20G and LWS TR&TT NNGO-5GN34G grants., VY work was partly supported under NASA GI NNX08AJ20G and LWS T NNG0-5GN34G grants. + VA acknowledges partial support from NSF grant ATM-0716512., VA acknowledges partial support from NSF grant ATM-0716512. +" PG, VA and VY are partially supported by NSF (AGS-0745744), NASA (NNY 08BA22C)."," PG, VA and VY are partially supported by NSF (AGS-0745744), NASA (NNY 08BA22G)." + PG is partially supported by AFOSR (FA9550-09-1-0655)., PG is partially supported by AFOSR (FA9550-09-1-0655). + OS acknowledges insightful discussions on small-scale filament formation within the ISSI International Team lead by Ι.Ν. Kitiashvili at ISSI (International Space Science Institute) in Bern., OS acknowledges insightful discussions on small-scale filament formation within the ISSI International Team lead by I.N. Kitiashvili at ISSI (International Space Science Institute) in Bern. +to those found in the Taurus Molecular Cloud.,to those found in the Taurus Molecular Cloud. + The observation of abundant ο in L1251À coustitutes the first detection of anions iu a protostcllar cuvelope outside of the Taurus-Auriga complex. aud indicates that anious are Likely to be widespread throughout Calactic star-forming regions where carbon chains are present.," The observation of abundant $_6$ $^-$ in L1251A constitutes the first detection of anions in a protostellar envelope outside of the Taurus-Auriga complex, and indicates that anions are likely to be widespread throughout Galactic star-forming regions where carbon chains are present." + The techuique of using UC3N aud CT as proxies for the detection of less abundaut. larger carbon chains aud anions shows strong promise as a leans for obtainiug further detections of these inolecules iu low-inass forming regions in the future.," The technique of using $_3$ N and $_4$ H as proxies for the detection of less abundant, larger carbon chains and anions shows strong promise as a means for obtaining further detections of these molecules in low-mass star-forming regions in the future." + This researcli was supported by the NASA Exobicloey Program and the Coddard Center for Astrobioloey., This research was supported by the NASA Exobiology Program and the Goddard Center for Astrobiology. + Astrophysics at QUB is supported by a eraut from STFC., Astrophysics at QUB is supported by a grant from STFC. +Karl-Sehhwarzschild-Str.2.85748labelsect:intro Variability is a dominant observational signature in pre-main sequence (pre-MS) stellar evolution.,"hwarzschild-Str.\tikzmark{mainBodyEnd0} \tikzmark{mainBodyStart1}2,\tikzmark{mainBodyEnd1} \tikzmark{mainBodyStart2}85748\tikzmark{mainBodyEnd2} \tikzmark{mainBodyStart3}Garching,\tikzmark{mainBodyEnd3} \tikzmark{mainBodyStart4}Germany\tikzmark{mainBodyEnd4} \tikzmark{mainBodyStart5}}\tikzmark{mainBodyEnd5} + +%\titlerunning{X-ray emission from Z\,CMa during outburst and from its jet} + +\date{Received $<$29-01-2009$>$ / Accepted $<$16-03-2009$>$} + + +\abstract{ +Accretion shocks have been recognized as important X-ray emission mechanism +for pre-main sequence stars. Yet the X-ray properties of FUor outbursts, events that are caused by +violent accretion, have been given little attention. We have observed the FUor +object Z\,CMa during optical outburst and quiescence with {\em Chandra}. No significant +changes in X-ray brightness and spectral shape are found, suggesting that the X-ray +emission is of coronal nature. Due to the binary nature of Z\,CMa +the origin of the X-ray source is ambiguous. However, the moderate hydrogen column +density derived from our data makes it unlikely that the embedded primary star +is the X-ray source. The secondary star, which is the FUor object, +is thus responsible for both the X-ray emission +and the presently ongoing accretion outburst, which seem however to be unrelated phenomena. +The secondary is also known to drive a large outflow and jet, that we detect here for the +first time in X-rays. The distance of the X-ray emitting outflow +source to the central star is higher than in jets of low-mass stars. +} + +% context heading (optional) +{ +}\tikzmark{mainBodyStart6}}\tikzmark{mainBodyEnd6} +% aims heading (mandatory) +{ +}\tikzmark{mainBodyStart7}}\tikzmark{mainBodyEnd7} +% methods heading (mandatory) +{ +}\tikzmark{mainBodyStart8}}\tikzmark{mainBodyEnd8} +% results heading (mandatory) +{ +}\tikzmark{mainBodyStart9}}\tikzmark{mainBodyEnd9} +% conclusions heading (optional) +{ +}\tikzmark{mainBodyStart10}} Variability is a dominant observational signature in pre-main sequence (pre-MS) stellar evolution." + Besides the ubiquitous short-duration flares related to magnetic reconnection events. various types of long-term outbursts are reported: FUor events are characterized by optical intensity changes of up to [ mmag and a fading phase of decades. EXor events are less extreme and shorter (months to few years).," Besides the ubiquitous short-duration flares related to magnetic reconnection events, various types of long-term outbursts are reported: FUor events are characterized by optical intensity changes of up to $4$ mag and a fading phase of decades, EXor events are less extreme and shorter (months to few years)." + Both types of outburst are associated with a sudden increase of the accretion rate. such that the disk outshines the central star leading to characteristic spectral signatures (e.g.?)..," Both types of outburst are associated with a sudden increase of the accretion rate, such that the disk outshines the central star leading to characteristic spectral signatures \citep[e.g.][]{Hartmann96.1}." + The spectra of FUor objects resemble that of F-G supergiants. while EXor objects are of later spectral type.," The spectra of FUor objects resemble that of F-G supergiants, while EXor objects are of later spectral type." + The FUor and EXor phenomena are probably recurrent. about once every 10! yyrs for the FUors and every few years in the case of EXors.," The FUor and EXor phenomena are probably recurrent, about once every $10^4$ yrs for the FUors and every few years in the case of EXors." + Only a minor fraction of pre-MS stars ts classified as FUor or EXor (??)..," Only a minor fraction of pre-MS stars is classified as FUor or EXor \citep{Abraham04.1, Herbig08.1}." + Different mechanisms have been proposed as triggers for the outbursts: dynamical interaction with a close binary companion (??).. thermal instability in a disk with high accretior from a surrounding envelope (?).. and changes in the magnetic field configuration (?)..," Different mechanisms have been proposed as triggers for the outbursts: dynamical interaction with a close binary companion \citep{Bonnell92.1, Reipurth04.1}, thermal instability in a disk with high accretion from a surrounding envelope \citep{Bell94.1}, , and changes in the magnetic field configuration \citep{vandenAncker04.1}." + In recent years accretion has been recognized to make an important contribution to the X-ray emission of pre-MS stars (??).. making FUor and EXor objects interesting targets for ray studies.," In recent years accretion has been recognized to make an important contribution to the X-ray emission of pre-MS stars \citep{Kastner02.1, Stelzer04.3}, making FUor and EXor objects interesting targets for X-ray studies." + Plasma temperatures of up to a few 10 KK can be produced in the accretion shocks that form when matter is funneled along the magnetic field lines onto the stellar surface., Plasma temperatures of up to a few $10^6$ K can be produced in the accretion shocks that form when matter is funneled along the magnetic field lines onto the stellar surface. + In the first dedicated X-ray survey of FUor objects ? have detected two of four stars withXMM-Newton., In the first dedicated X-ray survey of FUor objects \cite{Skinner09.1} have detected two of four stars with. + None of their targets were in a state of recent optical outburst during the X- observation., None of their targets were in a state of recent optical outburst during the X-ray observation. + Only two EXors have been observed in X-rays during an optical outburst. with contradictory results (22)..," Only two EXors have been observed in X-rays during an optical outburst, with contradictory results \citep{Kastner06.1, Audard05.2}." + The X-ray spectrum of the prototype OOri shows surprisingly a complex absorption pattern: While the harder emission is strongly absorbed and can be ascribed to an embedded stellar corona. the origin of the weakly absorbed soft emission is unclear (?)..," The X-ray spectrum of the prototype Ori shows surprisingly a complex absorption pattern: While the harder emission is strongly absorbed and can be ascribed to an embedded stellar corona, the origin of the weakly absorbed soft emission is unclear \citep{Skinner06.1}." + Possible scenarios include the overlaid effect of a binary companion. accretion shocks. and shocked jets.," Possible scenarios include the overlaid effect of a binary companion, accretion shocks, and shocked jets." + Indeed. ? showed recently that the unresolved soft component in the X-ray spectrum of the pre-MS star TTau can be explained as emission from a post-shock cooling zone in the innermost part of its optical outflow.," Indeed, \cite{Guenther09.1} showed recently that the unresolved soft component in the X-ray spectrum of the pre-MS star Tau can be explained as emission from a post-shock cooling zone in the innermost part of its optical outflow." + Soft emission (few MK) is only an indirect means of inferring outflows in X-rays and a signature that is easily confused with contributions from aceretion., Soft emission (few MK) is only an indirect means of inferring outflows in X-rays and a signature that is easily confused with contributions from accretion. + Direct detection of X-ray emission from pre-MS jets by means of a displacement with respect to the central coronal source has been achieved only in a handful of cases (seemaryin ?).., Direct detection of X-ray emission from pre-MS jets by means of a displacement with respect to the central coronal source has been achieved only in a handful of cases \citep[see summary in][]{Bonito07.1}. + In this article we examine the X-ray properties of ZCCMa during its recent optical outburst. we compare them to its quiescent state. and we present the X-ray detection of its jet.," In this article we examine the X-ray properties of CMa during its recent optical outburst, we compare them to its quiescent state, and we present the X-ray detection of its jet." +" ZCCMais a 0.1"" pre-MS binary.", CMa is a $0.1^{\prime\prime}$ pre-MS binary. + While the south-east (SE) FUor object dominates the light at optical wavelengths. the north-west (NW) component is a powerful infrared (IR) source (?)..," While the south-east (SE) FUor object dominates the light at optical wavelengths, the north-west (NW) component is a powerful infrared (IR) source \citep{Koresko91.1}." + The FUor star has ~3M... and is located just below the birthline in the HR diagram (2)..," The FUor star has $\sim 3\,{\rm M_\odot}$ and is located just below the birthline in the HR diagram \citep{Hartmann89.3}." + Assuming that the IR source is coeval. it can be modeled as a HII star with 16NL. (2)..," Assuming that the IR source is coeval, it can be modeled as a III star with $16\,{\rm M_\odot}$ \citep{vandenAncker04.1}." + The optically dominating component ts. therefore. the secondary in the binary system.," The optically dominating component is, therefore, the secondary in the binary system." + This star is likely responsible both for the FUor phenomena and for the jet and molecular outflow observed at radio and optical wavelengths (2??).. ," This star is likely responsible both for the FUor phenomena and for the jet and molecular outflow observed at radio and optical wavelengths \citep{Poetzel89.1, Evans94.1, Velazquez01.1}." +The long-term lightcurve of ZCCMa exhibits features of both FUor and EXor-like events: Optical outbursts of ~ 1mmag are superposed on a two decade long decay (2).., The long-term lightcurve of CMa exhibits features of both FUor and EXor-like events: Optical outbursts of $\sim 1$ mag are superposed on a two decade long decay \citep{vandenAncker04.1}. + An alternative explanation for the irregular light. variations of CCMa is scattered light fromthe embedded primary that penetrates an envelope of variable thickness (?).. , An alternative explanation for the irregular light variations of CMa is scattered light fromthe embedded primary that penetrates an envelope of variable thickness \citep{Hartmann96.1}. . +In 22008 CCMa started a largeoptical outburst (see Fig. 1))., In 2008 CMa started a largeoptical outburst (see Fig. \ref{fig:opt_lc}) ). + Visual brightness are available for the initial gradual increase by ~1.5 mmag., Visual brightness are available for the initial gradual increase by $\sim 1.5$ mag. + Further visual observations, Further visual observations +dvnamo theory is the best accepted wav to fit to the experimental data. (he moclels used to describe these facts are different for every object described.,"dynamo theory is the best accepted way to fit to the experimental data, the models used to describe these facts are different for every object described." + This paper tries to solve this problem with the use of a model that (ries to explain all these features without the need specificities., This paper tries to solve this problem with the use of a model that tries to explain all these features without the need specificities. + In (his paper we propose a model of magnetic field generation based on a (hermocvuaniuc point of view which uses the relation between thermocdwvnamie forces and fIuxes as the starting point., In this paper we propose a model of magnetic field generation based on a thermodynamic point of view which uses the relation between thermodynamic forces and fluxes as the starting point. + In the model. a redistribution of the charge is obtained from (he gravitational energy of the planet through the action of pressure.," In the model, a redistribution of the charge is obtained from the gravitational energy of the planet through the action of pressure." + From (his charge distribution and the rotation of the planet. the magnetic field is generated.," From this charge distribution and the rotation of the planet, the magnetic field is generated." + Several advantages of (this model are: 1) Its ability (ο spontaneously break the spherical sviumetry of the svstem to vield a field with axial svimmetiv: 2) (he possibility to obtain a tilt of the dipole moment relative to (he axis of rotation: 3) a possible explanation of why Uranus and Neptune. that have laree lls. have hieher quadrupole moment (han (he other planets: 4) an explanation of why Saturn. with a hieh axisvnuuetric field. has a low quacaupole moment.," Several advantages of this model are: 1) Its ability to spontaneously break the spherical symmetry of the system to yield a field with axial symmetry; 2) the possibility to obtain a tilt of the dipole moment relative to the axis of rotation; 3) a possible explanation of why Uranus and Neptune, that have large tilts, have higher quadrupole moment than the other planets; 4) an explanation of why Saturn, with a high axisymmetric field, has a low quadrupole moment." + The possibility of reversing (he dipole is open. ancl predicts that the field. during a transition may become more quadrupolar (han the stable normal or reverse state (as observed in (he past).," The possibility of reversing the dipole is open, and predicts that the field during a transition may become more quadrupolar than the stable normal or reverse state (as observed in the past)." + The detailed dynamics of the transition is out of the scope of this paper that only pretends to present the main lines of (ie moclel., The detailed dynamics of the transition is out of the scope of this paper that only pretends to present the main lines of the model. + The inclusion of an analvsis of the multipolarityv of the fields obtained is also out of the scope of this article. but. this feature is implicitilv considered in the model because of its geonelrv.," The inclusion of an analysis of the multipolarity of the fields obtained is also out of the scope of this article, but this feature is implicitily considered in the model because of its geometry." + This paper doesnt attempt to replace the eeodvnaimo moclel that fits so well in the case of the Earth (Glatzmaier&Roberts(2000. 1996))). but (tries to propose a general mechanism for the different planets to generate a magnetic field.," This paper doesn't attempt to replace the geodynamo model that fits so well in the case of the Earth \cite{GLATZ4, GLATZ5}) ), but tries to propose a general mechanism for the different planets to generate a magnetic field." + Instead of it. the energy needed for the eeneration of the field comes [rom (he more universal gravitational field. present all over the Universe.," Instead of it, the energy needed for the generation of the field comes from the more universal gravitational field, present all over the Universe." + To describe in an unified way the behaviors of such different planets. it is logical to ask for a model relatively independent of the microscopic details. (is is the reason why we have turned here to a global thermodynamic analysis. al a macroscopic level. rather (han directly going to the mechanistic details. which may be different in dillerent planets.," To describe in an unified way the behaviors of such different planets, it is logical to ask for a model relatively independent of the microscopic details, this is the reason why we have turned here to a global thermodynamic analysis, at a macroscopic level, rather than directly going to the mechanistic details, which may be different in different planets." + The model could be used in posterior papers. as a generator of magnetic fields in more eeneral objects of the Universe like the main sequence stars or the neutron stars.," The model could be used in posterior papers, as a generator of magnetic fields in more general objects of the Universe like the main sequence stars or the neutron stars." +"show that this behavior is due to the presence of themodes, and we shall derive their frequencies and amplitudes.","show that this behavior is due to the presence of the, and we shall derive their frequencies and amplitudes." +" In this section we deal with the system of coupled harmonic oscillators, and one should be able to find its normal modes using the standard techniques (Landau and Lifshitz mechanics, 823)."," In this section we deal with the system of coupled harmonic oscillators, and one should be able to find its normal modes using the standard techniques (Landau and Lifshitz mechanics, 23)." +" However, the fact that all small oscillators are attached to the large one, and there is no direct coupling between the small oscillators, allows us a significant shortcut (in Appendix A, we treat a more general problem of large oscillators coupled to a multitude of the core modes)."," However, the fact that all small oscillators are attached to the large one, and there is no direct coupling between the small oscillators, allows us a significant shortcut (in Appendix A, we treat a more general problem of large oscillators coupled to a multitude of the core modes)." +" We proceed as follows: Suppose that we impose on the large oscillator a periodic motion with angular frequency €) by driving it externally with theforce Fe,=Fo(Q)exp(iOt)."," We proceed as follows: Suppose that we impose on the large oscillator a periodic motion with angular frequency $\Omega$, by driving it externally with theforce $F_{\rm ext}=F_0(\Omega) \exp(i\Omega t)$." + This motion in turn drives the small oscillators according to Eq. (1)):, This motion in turn drives the small oscillators according to Eq. \ref{vier}) ): + which has the steady state solution: where we have omitted the time dependent factor exp(#Qt) on both sides., which has the steady state solution: where we have omitted the time dependent factor $\exp(i \Omega t)$ on both sides. + The combined force feont of the small oscillators acting back on the large one (see Eq. (2))), The combined force $f_{\rm cont}$ of the small oscillators acting back on the large one (see Eq. \ref{vijf}) )) +" is given by According to Newton’s second law, If Ω corresponds to the normal-mode frequency, then Fo(Q)= 0."," is given by According to Newton's second law, If $\Omega$ corresponds to the normal-mode frequency, then $F_0(\Omega)=0$ ." + Hence by substituting Eq. (5)), Hence by substituting Eq. \ref{no8}) ) + into Eq. (6)), into Eq. \ref{secondlaw}) ) +" we getthe following eigenvalue equation for Ω: In the continuum limit N— oo, the above equation becomes"," we getthe following eigenvalue equation for $\Omega$ : In the continuum limit $N\rightarrow\infty$ , the above equation becomes" +halo.,halo. +" Note that, because of the limited time resolution, we may actually underestimate the peak velocity of gas particles that reach a maximum speed and then slow down significantly within the time interval of two simulation outputs (At2140 Myr)."," Note that, because of the limited time resolution, we may actually underestimate the peak velocity of gas particles that reach a maximum speed and then slow down significantly within the time interval of two simulation outputs $\Delta t \gta 140$ Myr)." +" The scatter plot shows that enriched gas particles can often reach velocities in excess of 600kms-!, with a few of them moving as fast as ~800—1000kms~!, a value that is consistent with the highest velocity material observedin LBGs at 2Sz3 by Steideletal.(2010)."," The scatter plot shows that enriched gas particles can often reach velocities in excess of $600\,\kms$, with a few of them moving as fast as $\sim 800-1000\,\kms$, a value that is consistent with the highest velocity material observedin LBGs at $2 \lta z \lta 3$ by \citet{Steidel10}." +. The mass and metal-weighted outflow average speed typically ranges between 200 and 400 kms-!., The mass and metal-weighted outflow average speed typically ranges between 200 and 400 $\kms$. +" From redshift 9.3 to 3.0, the total mass of the main host halo increases from 5.0x10?Mo to 2.4x1011Ma."," From redshift 9.3 to 3.0, the total mass of the main host halo increases from $5.0\times 10^{9}\,\msun$ to $2.4\times 10^{11}\,\msun$." +" The mean outflow speed increases for 5S;zS59.3 and decreases again at zS;5, so there is no obvious correlation between halo mass and the peak outflow velocity in ErisMC."," The mean outflow speed increases for $5\lta z \lta 9.3$ and decreases again at $z\lta 5$, so there is no obvious correlation between halo mass and the peak outflow velocity in ErisMC." +" Similarly, we find only a weak correlation between the maximum wind velocity and star formation rate."," Similarly, we find only a weak correlation between the maximum wind velocity and star formation rate." +" However, if we define the mass averaged mean outflow velocity at distance r as: where N is the total number of outflow gas particles in a radial shell of thickness dr =0.02 R,i; at distance r, m; is the mass of particle i and v; its outflow radial velocity (relative to the host’s ;"," However, if we define the mass averaged mean outflow velocity at distance $r$ as: where N is the total number of outflow gas particles in a radial shell of thickness $dr=$ 0.02 $R_{\rm vir}$ at distance $r$, $m_i$ is the mass of particle $i$ and $v_{r,i}$ its outflow radial velocity (relative to the host's center)." +" There is a correlation between the mean outflow center).velocity and the peak circular velocity of the host, as shown in Figure 16.."," There is a correlation between the mean outflow velocity and the peak circular velocity of the host, as shown in Figure \ref{fig16}." + Figure 17 shows the metallicity of inflowing and outflowing material at ErisMC's virial radius as a function of redshift., Figure \ref{fig17} shows the metallicity of inflowing and outflowing material at ErisMC's virial radius as a function of redshift. +" Galactic outflows are enriched to a typical metallicity in the range 0.1—0.2Z@ since redshift ~9, with little dependence on cosmic time."," Galactic outflows are enriched to a typical metallicity in the range $0.1-0.2\,Z_\odot$ since redshift $\sim 9$, with little dependence on cosmic time." +"The mean metallicity of inflowing gas shows a more marked evolution, as it increases by about one dex in the interval 9=zκ3.5.","The mean metallicity of inflowing gas shows a more marked evolution, as it increases by about one dex in the interval $9\gta z\gta 3.5$." + This is a consequence of more processed material falling back onto ErisMC in a “halo fountain” (Oppenheimeretal.2010) as well as being accreted via infalling satellites.," This is a consequence of more processed material falling back onto ErisMC in a “halo fountain"" \citep{Oppenheimer10} as well as being accreted via infalling satellites." + Only half of the inflowing material at Ryir is unprocessed primordial gas., Only half of the inflowing material at $R_{\rm vir}$ is unprocessed primordial gas. +" The gas metallicity of inflowing gas at z <5 (Z~0.01 Za) is typical of the metallicity observed in Damped Lyo and Lyman-Limit systems (e.g.,Wolfeetal.2005)."," The gas metallicity of inflowing gas at z $\la 5$ $Z\sim 0.01\,Z_{\odot}$ ) is typical of the metallicity observed in Damped $\alpha$ and Lyman-Limit systems \citep[e.g.,][]{Wolfe05}." +". 'The mass loading factor characterizes the amount of material involved in a galactic outflow, and is defined as n= My,/SFR, where M,, is the rate at which mass is ejected."," The mass loading factor characterizes the amount of material involved in a galactic outflow, and is defined as $\eta = \dot{M_{w}}/$ SFR, where $\dot{M_{w}}$ is the rate at which mass is ejected." +" Observations of galactic outflows powered by starbursts suggest a wide range of mass loading factors, η=0.01— 10, with no obvious correlation with the star formation rates of their hosts (Veilleux,Cec"," Observations of galactic outflows powered by starbursts suggest a wide range of mass loading factors, $\eta = 0.01 - 10$ , with no obvious correlation with the star formation rates of their hosts \citep{Veilleux05}." +"il,& In low-resolution cosmological simulations, the mass 2005)..loading factor is one of the input parameters"," In low-resolution cosmological simulations, the mass loading factor is one of the input parameters" +phase and the residuals against time when the main signal is subtracted.,phase and the residuals against time when the main signal is subtracted. + There is no significant periodic trend nor linear drift in the O-C residuals. with a standard deviation of 4.1ms7!.. Le.. marginally above the individual errors.," There is no significant periodic trend nor linear drift in the O-C residuals, with a standard deviation of 4.1, i.e., marginally above the individual errors." + All parameters of the orbit and the planet are given in Table 2.. together with their estimated error.," All parameters of the orbit and the planet are given in Table \ref{TablePlanets}, together with their estimated error." + Observations of 220868 consist in 48 HARPS measurements obtained over 1705 days between November Ist 2003 and July 2nd 2008., Observations of 20868 consist in 48 HARPS measurements obtained over 1705 days between November 1st 2003 and July 2nd 2008. + The mean uncertainty on the radial velocity measurements is 1.5ms!'., The mean uncertainty on the radial velocity measurements is 1.5. +. The measurements are given in Table + (electronic version only)., The measurements are given in Table \ref{rv2} (electronic version only). + Figure 2 shows the velocities as a function of time. as well as the Keplerian orbit with a period of 380.85 days that best fits the data.," Figure \ref{obs2} shows the velocities as a function of time, as well as the Keplerian orbit with a period of 380.85 days that best fits the data." + The residual values. after subtraction of the fit. are also shown against time.," The residual values, after subtraction of the fit, are also shown against time." + There is no significant trend in these residuals. characterized by a standard deviation of 1.7 ms7!.," There is no significant trend in these residuals, characterized by a standard deviation of 1.7 ." +. The reduced γ΄ of the fit is 1.27., The reduced $\chi^2$ of the fit is 1.27. + The best orbital solution is a strongly eccentric orbit (ο= 0.75) with a semi-amplitude of 100.34ms!., The best orbital solution is a strongly eccentric orbit $e=$ 0.75) with a semi-amplitude of 100.34. +. The inferred minimum mass of the companion responsible for this velocity variation is 1.99 and a semi-major axis of 0.947 AU is derived from the third Kepler law., The inferred minimum mass of the companion responsible for this velocity variation is 1.99 and a semi-major axis of 0.947 AU is derived from the third Kepler law. + The periastron distance 1s 0.54 AU. which corresponds to a transit probability of0., The periastron distance is 0.54 AU which corresponds to a transit probability of. +7%.. The bisector test was applied and excludes that the velocity variations are due to stellar activity., The bisector test was applied and excludes that the velocity variations are due to stellar activity. + A trend which is confirmed by the long rotation period., A trend which is confirmed by the long rotation period. + We gathered 39 HARPS measurements of 773267 over a time span of 1586 days. from November 27th 2004 and May 3|st 2008.," We gathered 39 HARPS measurements of 73267 over a time span of 1586 days, from November 27th 2004 and May 31st 2008." + Small individual uncertainties are obtained. with a mean value of 1.8ms7!.," Small individual uncertainties are obtained, with a mean value of 1.8." +. Data are shown in Table 8 and in Figure 3.., Data are shown in Table \ref{rv3} and in Figure \ref{obs3}. + The observed velocity variations were fitted with a Keplerian orbit., The observed velocity variations were fitted with a Keplerian orbit. + The best solution corresponds to a period of 1260 days. eccentricity of 0.256 and semi-amplitude of 64.29ms!.," The best solution corresponds to a period of 1260 days, eccentricity of 0.256 and semi-amplitude of 64.29." +. The scatter of the residuals is compatible with the radial-velocity uncertainty and these residuals show no specific trend., The scatter of the residuals is compatible with the radial-velocity uncertainty and these residuals show no specific trend. + The ο—C standard deviation is 1.7 and reduced yo is 1.19., The $O-C$ standard deviation is 1.7 and reduced $\chi^2$ is 1.19. + The bisector variations are not correlated to the velocity variations or in phase with the signal. which excludes the stellar variability as being the cause of it.," The bisector variations are not correlated to the velocity variations nor in phase with the signal, which excludes the stellar variability as being the cause of it." + Here again. the estimated rotation period of the star is long. and spot-related activity cannot be considered as a potential origin for the observed signal.," Here again, the estimated rotation period of the star is long, and spot-related activity cannot be considered as a potential origin for the observed signal." + The miimum mass of the inferred companion is 3.06 and a semi-major axis of 2.198 AU is calculated for this 3.44 year period companion., The minimum mass of the inferred companion is 3.06 and a semi-major axis of 2.198 AU is calculated for this 3.44 year period companion. + We gathered 41 measurements of 1131664 over 1463 days with HARPS. from May 21st 2004 and May 23rd 2008.," We gathered 41 measurements of 131664 over 1463 days with HARPS, from May 21st 2004 and May 23rd 2008." + Individual uncertainties have a mean value of 2ms7!., Individual uncertainties have a mean value of 2. +. A long-term velocity variation is observed (Figure 4)). which is best fitted with a Keplerian orbit of 195]. days. 0.638 eccentricity and a large semi-amplitude K of 359.5ms!.," A long-term velocity variation is observed (Figure \ref{obs4}) ), which is best fitted with a Keplerian orbit of 1951 days, 0.638 eccentricity and a large semi-amplitude $K$ of 359.5." +. The residuals after subtraction of this signal have a standard deviation of only imsand no specific trend., The residuals after subtraction of this signal have a standard deviation of only 4and no specific trend. + The reduced y of the fit is 2.97., The reduced $\chi^2$ of the fit is 2.97. +of which were new discoverics. observed with the 2.2120 ESO/MPTI telescope at La Silla. Chile.,"of which were new discoveries, observed with the 2.2m ESO/MPI telescope at La Silla, Chile." + Additional V and I data were obtained by Cucrenetal.(2001) at Las Campanas aud Cerro Tololo., Additional V and I data were obtained by \citet{2004AJ....128.1167G} at Las Campanas and Cerro Tololo. + Deep. ucar-infrared J aud Is baud observations were obtained with ESO VET using the ISAAC caluera. resulting in a final distauce modulus (10)AM)y=26.37dE0.05(random)+0.03(systematic) (Cuierenctal.2005)..," Deep, near-infrared J and K band observations were obtained with ESO VLT using the ISAAC camera, resulting in a final distance modulus $(m-M)_0=26.37 \pm 0.05 \,{\rm (random)} \pm 0.03 \,{\rm (systematic)}$ \citep{2005ApJ...628..695G}." + The superb angularC» resolution offered bv the IIubble Space Telescope has recently open the possibility of determining the distance to NCC 300 using the Tip of the Red Giant Brauch (TRGB)., The superb angular resolution offered by the Hubble Space Telescope has recently open the possibility of determining the distance to NGC 300 using the Tip of the Red Giant Branch (TRGB). + A set of IST WEPC2 fields were analyzed by. Sakaiand Butleretal.(2001).. ancl more recently by Tikhonovetal. (2005)..," A set of HST WFPC2 fields were analyzed by \citet{2004ApJ...608...42S} and \citet{2004AJ....127.1472B}, and more recently by \citet{2005A&A...431..127T}. ." + The derived distance moduli are (aALJy=26.65+0.09. ΕΥ=26.5640.07£013. and (50.ALy=26.50+ 0.15. respectively.," The derived distance moduli are $(m-M)_0=26.65 \pm 0.09$, $(m-M)_0=26.56 \pm 0.07 \pm 0.13$, and $(m-M)_0=26.50 \pm 0.15$ , respectively." + Iun this paper. we present the first TRGB distance based on deep ACS observations of NCC 300.," In this paper, we present the first TRGB distance based on deep ACS observations of NGC 300." + These data are the deepest ever obtained for this galaxy. aud they sample both the inner bulec and the outer disk.," These data are the deepest ever obtained for this galaxy, and they sample both the inner bulge and the outer disk." + The paper is organized as follows: Section 2. presents the data. the reduction techniques we adopted. and the resulting color- ciagraus (CAID).," The paper is organized as follows: Section \ref{data} presents the data, the reduction techniques we adopted, and the resulting color-magnidute diagrams (CMD)." + We describe the TRGB method and its application to NCC 300 in Section 3.., We describe the TRGB method and its application to NGC 300 in Section \ref{distance}. + We discuss our results in Section 1 and a brief sununuiary is preseuted in Section 5.., We discuss our results in Section \ref{discussion} and a brief summary is presented in Section \ref{conclusions}. + The ACS observations used to derive a new TRGB distance to NGC 300 were obtained durus UST Cycle 11. as part of program CO-9192 (PI: Bresolin). from July 2002 to December 2002.," The ACS observations used to derive a new TRGB distance to NGC 300 were obtained during HST Cycle 11, as part of program GO-9492 (PI: Bresolin), from July 2002 to December 2002." + The iain purpose of these observations was to conrplenieunt the extensive eround-hased CCD photometry of Cepheid variable stars and blue superet stars collected in the framework of the Avaucaria project., The main purpose of these observations was to complement the extensive ground-based CCD photometry of Cepheid variable stars and blue supergiant stars collected in the framework of the Araucaria project. + Two-orhit IST visits allowed o obtain deep photometry in the F155W. EF555W (1080 seconds). and FalWY (1110 seconds) filters.," Two-orbit HST visits allowed to obtain deep photometry in the F435W, F555W (1080 seconds), and F814W (1440 seconds) filters." + A total of six fields were observed., A total of six fields were observed. + Stellar photometry was performed with the DOLPILOT (version 1.0) package. an adaptation of IISTphot (Dolphin2000). to ACS images.," Stellar photometry was performed with the DOLPHOT (version 1.0) package, an adaptation of HSTphot \citep{2000PASP..112.1383D} to ACS images." + Pre-conrputer Point Spread Functions were adopted. and the final calibrated photometry was then transformed to the standard BVT svstem using the equations provided by Siriannietal.(2005)..," Pre-computer Point Spread Functions were adopted, and the final calibrated photometry was then transformed to the standard BVI system using the equations provided by \citet{2005astro.ph..7614S}." + The transformation frou one photometric svstem to another inevitably introduces additional uncertaitics but it secnis necessary given that most of the calibrations of the absolute magnitude of the TRGB are in the I baud., The transformation from one photometric system to another inevitably introduces additional uncertainties but it seems necessary given that most of the calibrations of the absolute magnitude of the TRGB are in the I band. + For a more extended discussion of the issues related to calibration sec Bresolinotal., For a more extended discussion of the issues related to calibration see \citet{Bresolin:rb}. +(2005). As an example of the quality of the results. the final calibrated CMDs are shown in Figures 1 and 2 for Fields 1 aud 3. respectively.," As an example of the quality of the results, the final calibrated CMDs are shown in Figures \ref{cmd_1.ps} and \ref{cmd_3.ps} for Fields 1 and 3, respectively." + Field 1 is situated close to the eastern outer edge. while Field 3 i centered ou the nucleus of the galaxy (see.Bresolinetal.2005.foramapoftheob-servedFields).," Field 1 is situated close to the eastern outer edge, while Field 3 is centered on the nucleus of the galaxy \citep[see][for a map of the observed Fields]{Bresolin:rb}." + All the CAIDs show a very well pronenmuced secpuede? of blue vouugo stars. reaching down to the lower age Imt of isochroue sets (60Aber.Carardietal. 20001).," All the CMDs show a very well pronounced sequence of blue young stars, reaching down to the lower age limit of isochrone sets \citep[$\sim 60$ Myr,][]{2000A&AS..141..371G}." + Blic-loop stars occupy the ceutral region of the diagrams. and a well defined red eiut brauch (ROB) extends from I ~22 down to the photometric detection limit. I 26.," Blue-loop stars occupy the central region of the diagrams, and a well defined red giant branch (RGB) extends from I $\sim 22$ down to the photometric detection limit, I $\sim 26$." + A full discussion of the CMD features. along with a reconstruction of the star formation history. will be prescuted in a forthcoming paper.," A full discussion of the CMD features, along with a reconstruction of the star formation history, will be presented in a forthcoming paper." + The distance estimates based on the RGB tip rest ou a solid physical basis: low-inass stars reach he end of their ascent alone the RGB with a degenerate helimu core aud they ignite helimm ring within a very narrow rause of luminosity (Salarisetal.2002.andreferencestherein).., The distance estimates based on the RGB tip rest on a solid physical basis: low-mass stars reach the end of their ascent along the RGB with a degenerate helium core and they ignite helium burning within a very narrow range of luminosity \citep[][and references therein]{2002PASP..114..375S}. + The otenutial of the method was revealed in a seminal per by Lee aud collaborators (Leeetal.1993).. along with a first attempt at objectively estimate he position of the tip on the CMD based on a digital edge-detection (ED) filter iu the form |-2.0.2]. applied to the I band Iniuositv function.," The potential of the method was revealed in a seminal paper by Lee and collaborators \citep{1993ApJ...417..553L}, along with a first attempt at objectively estimate the position of the tip on the CMD based on a digital edge-detection (ED) filter in the form [-2,0,2], applied to the I band luminosity function." + This filter effectively responds to changes iu the slope of the luninositv function and cdisplavs a peak corresponding to the TROB., This filter effectively responds to changes in the slope of the luminosity function and displays a peak corresponding to the TRGB. + À refined version of this method was presented in Sakai (1996).. , A refined version of this method was presented in \citet{1996ApJ...461..713S}. . +More receutlv. a differcut approach was sugeested by Méndezetal. (2002)...," More recently, a different approach was suggested by \citet{2002AJ....124..213M}. ." + To avoid problems related tobinning. this method uses a inaninnuu-likelihood (ML) analysis to ect the," To avoid problems related tobinning, this method uses a maximum-likelihood (ML) analysis to get the" +llowever. because of distorted morphology of DDO210 at ligh spatial resolutions. au attempt to derive the kinematical ceuter from a elobal fit to the velocity fields at these resolutious did not vield reliable results.,"However, because of distorted morphology of DDO210 at high spatial resolutions, an attempt to derive the kinematical center from a global fit to the velocity fields at these resolutions did not yield reliable results." + Heuce. the ceuter for the higher resolution velocity fields was fixed to a value obtained from the lower resolution velocity fields.," Hence, the center for the higher resolution velocity fields was fixed to a value obtained from the lower resolution velocity fields." + I—1.2. half of the clusters by number) represent ofthe FUV luminosity.," The younger, attenuated clusters (defined to have $U - B \leq -0.5$ and $\beta > -1.2$, half of the clusters by number) represent ofthe FUV luminosity." + The older. unattenuated clusters (defined to have U—B>—0.5. 1/6 of the clusters by number) have only of the FUV luminosity.," The older, unattenuated clusters (defined to have $U - B > -0.5$, 1/6 of the clusters by number) have only of the FUV luminosity." + Noting that the clusters are selected to have U<12 (and therefore are being selected to be reasonably young) and possible differences between the cluster and field SF histories. this result tentatively ascribes much of the observed ‘redness’ of the LMC to dust effects: older stellar populations tend to be UV-faint and do not affect the global ./ estimate as significantly.," Noting that the clusters are selected to have $U < 12$ (and therefore are being selected to be reasonably young) and possible differences between the cluster and field SF histories, this result tentatively ascribes much of the observed `redness' of the LMC to dust effects: older stellar populations tend to be UV-faint and do not affect the global $\beta$ estimate as significantly." + This interpretation is consistent with the detailed results of stellar population modeling., This interpretation is consistent with the detailed results of stellar population modeling. + show that the possible offset AJ} between young and older stellar populations is ~O.5. as. to first order. stars that are bright enough to affect the FUV luminosity of a galaxy with even a small amount of ongoing SF have very blue ./ values.," show that the possible offset $\Delta\beta$ between young and older stellar populations is $\sim$ 0.5, as, to first order, stars that are bright enough to affect the FUV luminosity of a galaxy with even a small amount of ongoing SF have very blue $\beta$ values." + One intriguing feature of 1s the population of seemingly unattenuated clusterswith —1=XI but blue U—B colors., One intriguing feature of \\ref{fig:bica} is the population of seemingly unattenuated clusterswith $-1 \la \beta \la 1$ but blue $U - B$ colors. + While theLMC sounding rocket images are photographie and relatively old1987).. extensive checks against UIT. IUE. D2B- TDI and ANS data have not indicated any significant," While theLMC sounding rocket images are photographic and relatively old, extensive checks against UIT, IUE, D2B-Aura, TD1 and ANS data have not indicated any significant" +after adding two free parameters iuto the model.,after adding two free parameters into the model. + Heuce. he introduction of the Caussiuu is statistically justified.," Hence, the introduction of the Gaussian is statistically justified." + Note. however. that the resulting line equivalent width pecolmes c 12 keV whic jds unacceptably laree.," Note, however, that the resulting line equivalent width becomes $\sim$ 12 keV which is unacceptably large." + Since he temperature of the emission colmponcut is lower thau l keV. it seems uulikelv that this cussion line comes roni the hot plasima itself.," Since the temperature of the emission component is lower than 1 keV, it seems unlikely that this emission line comes from the hot plasma itself." + The fluorescent iron enission ine is. on the other had. expected to emanate frou he white dwarf surface ilhuuinated by the hard XN-rav cnussion.," The fluorescent iron emission line is, on the other hand, expected to emanate from the white dwarf surface illuminated by the hard X-ray emission." + Iowever. its eqiuvalent width is estimated to ο c 110 eV (Georee aud Fabian 1991. Done 1991. Deudinore 1995) if the white dwarf surface is solar composition of heavy elemoeuts.," However, its equivalent width is estimated to be $\sim$ 140 eV (George and Fabian 1991, Done 1994, Beardmore 1995) if the white dwarf surface has solar composition of heavy elements." + Therefore. the equivalent width deterred from the fit iudicates an abundance of theorder of ~LOO times Solar. which is in stroug contraciction to the abuidauce frou the R&SS modcl. ~ (1 (Table 1)).," Therefore, the equivalent width determined from the fit indicates an abundance of theorder of $\sim$ 100 times Solar, which is in strong contradiction to the abundance from the S model, $\sim$ 0.1 (Table \ref{ASCApara}) )." + We cowclude that he partialcovering absorXtion model cannot reproduce the observed spectrum ina physically οςyusistent mauner., We conclude that the partial-covering absorption model cannot reproduce the observed spectrum in a physically consistent manner. + As the next step. we hewe tried to fit the hard excess coniponeont siowii 1i," As the next step, we have tried to fit the hard excess component shown in Fig." +" Fie. 1l bv introducinge a second R&SS com20icut,", \ref{LC} by introducing a second S component. + T1C TOSilt ofthe Ht is shown in Fie. 5..," The result of the fit is shown in Fig. \ref{WARARAGA}," + aud the best ft parameters are shown in the 6th coli of Table 1.., and the best fit parameters are shown in the 6th column of Table \ref{ASCApara}. + The fi In aeceptable with+ a reduced 47P value of (0.7 sugeesting hat he X-rav spectrum of consists of maultemperature optically thin tjicrinal plasiia cussion components.," The fit is acceptable with a reduced $\chi^2$ value of 0.74, suggesting that the X-ray spectrum of consists of multi-temperature optically thin thermal plasma emission components." + The obtained flux is LS«10 Pores te 2. iutf16 band 210 keV. Note that this f still suggests a very hieh abundance of6 tiues Solar with a lower limit of 2.5 times Solar. which seenis too high or cataclysuic variades. because they are eoncrally consiere¢ to be old systems.," The obtained flux is $\times 10^{-13}$ erg $^{-1}$ $^{-2}$ in the band 2–10 keV. Note that this fit still suggests a very high abundance of 6 times Solar with a lower limit of 2.5 times Solar, which seems too high for cataclysmic variables, because they are generally considered to be old systems." + Receutly. Wellier ((1998) compiled spectra o :15 i1CVs from archival data.," Recently, Hellier (1998) compiled spectra of 15 mCVs from archival data." + A total of 11svectra out of the 15 show a siguificaut fluorescent iron Cluission line at 6.11 keV. as well as the two thermal plasna conponoents at 6.68. keV. and 6.97 keV. Amone theii. the fluorescent courponeut probably originates frou fhe white dwarf surface (Dono. Osborne aud Beardmore 1995).," A total of 14 spectra out of the 15 show a significant fluorescent iron emission line at 6.41 keV, as well as the two thermal plasma components at 6.68 keV and 6.97 keV. Among them, the fluorescent component probably originates from the white dwarf surface (Done, Osborne and Beardmore 1995)." + Although the statistics of our data is not good erough to resolve these three coluponents. it is necessary to include the fluorescent iron line iuto the mode in evaluating the abundance correctly.," Although the statistics of our data is not good enough to resolve these three components, it is necessary to include the fluorescent iron line into the model in evaluating the abundance correctly." + We thus µανο iutrocποσα a Caussian πο as representing tιο iron li1e of fluorescence origin., We thus have introduced a Gaussian line as representing the iron line of fluorescence origin. + The result is sunumarized iu f1ο ast column of Table 1.., The result is summarized in the last column of Table \ref{ASCApara}. + Although the best fit abtudance is reduced ta ~ 1.9. the equivalent width of the fluorescent ion line becomes ALOTid 2 keV. This value aealji indicates an abuudauce of more than 1) times Solar.," Although the best fit abundance is reduced to $\sim$ 0.9, the equivalent width of the fluorescent iron line becomes around 2 keV. This value again indicates an abundance of more than 10 times Solar." + Clearly. the abuicdaunices estimated frou he iuteusities of won lines of the rot plasma oriei rand of the Huorescencee origi should IO οςusisteut.," Clearly, the abundances estimated from the intensities of iron lines of the hot plasma origin and of the fluorescence origin should be consistent." + Tus point will |ο ciscussed i l1., This point will be discussed in 4. + Note also hat the hig1 abundancee can aftec the estimation of he ]volometric hnuiuositv o ft1ο hard component. since he iie enudssioi predominates among all the cooling Xocesses in ΓΗ the temperature of which is less han 2 keV (MeCray. 1987).," Note also that the high abundance can affect the estimation of the bolometric luminosity of the hard component, since the line emission predominates among all the cooling processes in the plasma the temperature of which is less than 2 keV (McCray 1987)." + We therefore caleulate the lometzc Iuninositv of the hard optically thin thermal coniponent later in relation with the anudauce., We therefore calculate the bolometric luminosity of the hard optically thin thermal component later in relation with the abundance. + Greer. Remillard aud Motch (1995. 1998) reported that the flux of the soft blackbody component is ereater than that of the ατα thin thermal plasima cussion bv two orders of magnitude iu the bai 0.12.1 keV. We have attempted to re-exaije this extreme soft excess in combination with the hard N-rav data.," Greiner, Remillard and Motch (1995, 1998) reported that the flux of the soft blackbody component is greater than that of the hard thin thermal plasma emission by two orders of magnitude in the band 0.1–2.4 keV. We have attempted to re-examine this extreme soft excess in combination with the hard X-ray data." + pointed our times between 1992 October and 1993 Sepember., pointed four times between 1992 October and 1993 September. + We have extracted a meanROSAT PSPC spectrtun from the observation on 1993 September 11/12 (the exposure time of which was 13 ksec. the longest of a] the pointing observations).," We have extracted a mean PSPC spectrum from the observation on 1993 September 11/12 (the exposure time of which was $\sim$ 13 ksec, the longest of all the pointing observations)." + Details of the observations are prescutec iu Creer. Remillard aud Motch (1998) (see also Caxeimer. Remillard and Motel 1995).," Details of the observations are presented in Greiner, Remillard and Motch (1998) (see also Greiner, Remillard and Motch 1995)." + Since the ROSAT observation is not simuultaneous with the observation. we lave first checked if the," Since the observation is not simultaneous with the observation, we have first checked if the" +Acknowledgments: M. Leubner acknowledges the hospitality of the Austrian Academy of sciences at (he Space Research Institute in Graz.,Acknowledgments: M. Leubner acknowledges the hospitality of the Austrian Academy of Sciences at the Space Research Institute in Graz. + The authors are grateful to N. Ness (Bartol Res., The authors are grateful to N. Ness (Bartol Res. + Inst.), Inst.) + for providing ACE data and to BR. Lepping and IX.W. Ogilvie (NASA-GSFC) for providing WIND data and M. Volwerk for reading the manuscript., for providing ACE data and to R. Lepping and K.W. Ogilvie (NASA-GSFC) for providing WIND data and M. Volwerk for reading the manuscript. +AM CVn stars and ultra-compact X-ray binaries (UCXBs) are interacting double stars with orbital periods less than about one hour. with white dwarf or neutron star accretors 22).,"AM CVn stars and ultra-compact X-ray binaries (UCXBs) are interacting double stars with orbital periods less than about one hour, with white dwarf or neutron star accretors ." +.. This distinguishing property implies that the orbits are so tight. that only compact. evolved donors. such as helium stars. white dwarfs or low-mass stars with hydrogen-deticient envelopes. fit in.," This distinguishing property implies that the orbits are so tight, that only compact, evolved donors, such as helium stars, white dwarfs or low-mass stars with hydrogen-deficient envelopes, fit in." + Indeed the optical spectra of these systems lack any convincing sign of hydrogen but instead show helium lines in absorption or emission in the AM CVn systems 2).. or weak C/O or He/N lines in emission in the UCXBs (2222).," Indeed the optical spectra of these systems lack any convincing sign of hydrogen but instead show helium lines in absorption or emission in the AM CVn systems , or weak C/O or He/N lines in emission in the UCXBs ." + For one of the UCXBs. 4U have found double peaked O and Ne lines in the spectrum.," For one of the UCXBs, 4U1626-67 have found double peaked O and Ne lines in the spectrum." + The short orbital periods and close proximity of AM CVn stars and UCXBs make them the brightest Galactic gravitational wave sources22)., The short orbital periods and close proximity of AM CVn stars and UCXBs make them the brightest Galactic gravitational wave sources. +. In recent years many new ultra-compact binaries have been discovered2222222). bringing the total number of known AM CVn stars to 22 and the known number of (candidate) UCXBs to 27.," In recent years many new ultra-compact binaries have been discovered, bringing the total number of known AM CVn stars to 22 and the known number of (candidate) UCXBs to 27." + Three formation channels have been proposed for the formation of interacting ultra-compact binaries. schematically depicted in Fig.," Three formation channels have been proposed for the formation of interacting ultra-compact binaries, schematically depicted in Fig." + |., \ref{fig:P_Mdot} . + 22).. e , $\bullet~$ +We have used the L-ATLAS Science. Demonstration Phase data to investigate the evolution of the Ες over he redshift range 0<2«0.5.,We have used the H-ATLAS Science Demonstration Phase data to investigate the evolution of the FIRC over the redshift range $0 nieht18oO indicate the robustuess of the ¢etermination., If the three latter values of the gradients are similar to those obtained with the least-squared fitting might indicate the robustness of the determination. + This is the situation for LGC 6205. with al e values ol the gradieuts rangiug [roi1 —0.2 to —0.E dex/kpc.," This is the situation for UGC 6205, with all the values of the gradients ranging from $-0.2$ to $-0.4$ dex/kpc." + An average value of —0.31 dex/kdC witt a clispersici1 of 0.03 will be couskerect., An average value of $-0.31$ dex/kpc with a dispersion of $0.03$ will be considered. + Another remarkable results presetted in Table 1 is the steepness of the graclient. being lareer ilal he values obtained fo nost. of tle [n]eidaxies studied so far (e.g. see Table | i Vila-Costas Eduunds 1992J," Another remarkable results presented in Table 1 is the steepness of the gradient, being larger than the values obtained for most of the galaxies studied so far (e.g. see Table 4 in Vila-Costas Edmunds 1992)." + Why?, Why? + One mieht think tlat this galaxy shows very extreme anuixlance values. but |e ost external region. located a 3.1 kpc. lias a metallicity of 7.7 dex while he most internal regiols have 1neallicities of 8.7 dex.," One might think that this galaxy shows very extreme abundance values, but the most external region, located at 3.1 kpc, has a metallicity of $7.7$ dex while the most internal regions have metallicities of $8.7$ dex." + The «ης'euce is only of 1 dex. which is uo so large.," The difference is only of $1$ dex, which is not so large." + There are other spiral salaxies wlhi such. differece in their abundances. or larger. as Sl (Garnett 5hieks 1987).," There are other spiral galaxies with such difference in their abundances, or larger, as M81 (Garnett Shields 1987)." + Tie poiut he ‘eis that M81 s very mnuch larger than UCC 6205., The point here is that M81 is very much larger than UGC 6205. + 50. UGC 6205 has the same cifTereice in the abuidauce tha oller galaxies but the galactocenric distances of the Hila‘e sinaller.," So, UGC 6205 has the same difference in the abundance than other galaxies but the galactocentric distances of the are smaller." + Therefore. so large gracie," Therefore, so large gradient." + The next cuestiou to be addressed is whie ristle 'eelon responsible [or stch a steep gradient., The next question to be addressed is which is the region responsible for such a steep gradient. + One might thi1ς that those regious witl low S/N are responsible for the slope because their abundance valie iruielit not be so reliabe., One might think that those regions with low S/N are responsible for the slope because their abundance value might not be so reliable. + This is not t‘tie for several reasous: irstlyv. the gradients obtained with he W2 aud V3 nethocs. whicl inced only those high S/N regions. give only slightly. shallower gradients.," This is not true for several reasons: firstly, the gradients obtained with the $N2$ and $N3$ methods, which included only those high S/N regions, give only slightly shallower gradients." + Moreover. he values cdeterinined without the leas-squared fitting are of the same orcer except when tlie gralent is ¢eleriulrect from the most aud ess metallic regions which is of —1.1 dex/kpe. aud it will be ignore because of its doubtful meaniig.," Moreover, the values determined without the least-squared fitting are of the same order except when the gradient is determined from the most and less metallic regions which is of $-1.1$ dex/kpc, and it will be ignored because of its doubtful meaning." +€) Another way to check the reliability of tle steep gradient. is. as previously sakl. using an average abundance for different ranges of ealactocentric distances: 0-0.6 kpe. Q.6-1.2 kpc. 1.2-1.5 kpc. 1.5-2.1 kpc. 2.1-3.0 kpe. axd 3.0-:1.600 Kk0€.," Another way to check the reliability of the steep gradient, is, as previously said, using an average abundance for different ranges of galactocentric distances: $0$ $0.6$ kpc, $0.6$ $1.2$ kpc, $1.2$ $1.8$ kpc, $1.8$ $2.4$ kpc, $2.4$ $3.0$ kpc, and $3.0$ $3.600$ kpc." + As sakl. the variations of the abundance are," As said, the variations of the abundance are" +relationship between galaxy and halo properties.,relationship between galaxy and halo properties. + We thank Danilo Marchesini. Qi Guo. Simon White. and Chuck Steidel for useful discussions. as well as the anonvinous referee for a constructive report.," We thank Danilo Marchesini, Qi Guo, Simon White, and Chuck Steidel for useful discussions, as well as the anonymous referee for a constructive report." + This work ds based data made public by URIDSS. SXDS. aud SWIRE teams.," This work is based data made public by UKIDSS, SXDS, and SWIRE teams." + R.F.Q. is supported by a NOVA Postdoctoral Fellowship., R.F.Q. is supported by a NOVA Postdoctoral Fellowship. + Support frou: National Science Foundation graut CAREER ÀAST-0119678 is also eratefiully acknowledged., Support from National Science Foundation grant CAREER AST-0449678 is also gratefully acknowledged. +Each photou packet euütted is characterized by a position. direction vector. frequency. and a Stokes vector (L OQ. U. V) hat describes the total iuteusitv aud the linear and circular polarization.,"Each photon packet emitted is characterized by a position, direction vector, frequency, and a Stokes vector (I, Q, U, V) that describes the total intensity and the linear and circular polarization." + The code is written in a noduluw way that allows support for different exid ecometries to be easilv added., The code is written in a modular way that allows support for different grid geometries to be easily added. + At the moment. three-dineusioual cartesian. splerical-polar. aud cvlindrical-polar evids cau be used. as well as two types of adaptive cartesian exids.," At the moment, three-dimensional cartesian, spherical-polar, and cylindrical-polar grids can be used, as well as two types of adaptive cartesian grids." + Tle first is a standard exid. m which each cubic cell can be recursively split equally iuto cight smaller cubic cells.," The first is a standard grid, in which each cubic cell can be recursively split equally into eight smaller cubic cells." + The second is the type of exid conuuonlv used iu adaptive mesh refineiicut (AAIR) bvdrodyuauical codes., The second is the type of grid commonly used in adaptive mesh refinement (AMR) hydrodynamical codes. + Here. a coarse erid ds firs chned on the zero-th level of refinement. and with increasing levels. iucreasingly finer erids can be used im areas where high resolution is needed.," Here, a coarse grid is first defined on the zero-th level of refinement, and with increasing levels, increasingly finer grids can be used in areas where high resolution is needed." + Because they couceutrate the resolution where it is needed. variable resolution evids such as octrecs aud AMR allow radiation ransfer to be computed on density erids with effective resolutions that would be prolibitive with regular cartesian grids.," Because they concentrate the resolution where it is needed, variable resolution grids such as octrees and AMR allow radiation transfer to be computed on density grids with effective resolutions that would be prohibitive with regular cartesian grids." +" The dust properties required are the frequency-depeudent mass extinction cocficicut y, aud albedo iz. as well as the scattering properties of the dust."," The dust properties required are the frequency-dependent mass extinction coefficient $\chi_\nu$ and albedo $\omega_\nu$, as well as the scattering properties of the dust." + At this time. supports auisotropic wavelenetl-cdependcut scattering of randomly orieuted erains. using a {σοι Mueller matrix (C27): Support for aligned nou-sphlierical dust erains. which aro described by a full. 16-clement matrix. will be Huplemented in future (6.9.?2)..," At this time, supports anisotropic wavelength-dependent scattering of randomly oriented grains, using a 4-element Mueller matrix \citep{Chandrasekhar:60, Code:95:400}: Support for aligned non-spherical dust grains, which are described by a full 16-element matrix, will be implemented in future \citep[e.g.][]{whitney:02:205}." + To keep the Fortran code as general as possible. he mean opacities and enüssivities of the dust are pre-conmiputed bv the Python library as a funuctiou of the specific energv absorption rate of the dust rather than he dust temperature (c.f. refsec:temperature)).," To keep the Fortran code as general as possible, the mean opacities and emissivities of the dust are pre-computed by the Python library as a function of the specific energy absorption rate of the dust rather than the dust temperature (c.f. \\ref{sec:temperature}) )." +" For dust in LTE. the euissivities are even by jy=hy,DL). and the mean opacities are the usual Planck aud Rossecland mcan opacities to extinction and absorption."," For dust in LTE, the emissivities are given by $j_\nu = \kappa_\nu\,B_\nu(T)$, and the mean opacities are the usual Planck and Rosseland mean opacities to extinction and absorption." + Towever. it is also possible to specity mean opacities and enmüssivities that do not assume LTE (e.g. rofsecipali)).," However, it is also possible to specify mean opacities and emissivities that do not assume LTE (e.g. \\ref{sec:pah}) )." + Thus. assumptions about LTE are made at the level of the dust fles. rather than in the radiative transter code itself.," Thus, assumptions about LTE are made at the level of the dust files, rather than in the radiative transfer code itself." +" The code implements the propagation of photon packets in the following wav: a photon packet is euüutted from a source. randonlv selected frou a probability distribution uction defined by the relative Iuuinosityv of the different sources,"," The code implements the propagation of photon packets in the following way: a photon packet is emitted from a source, randomly selected from a probability distribution function defined by the relative luminosity of the different sources." + This sampling cau be done either in the stancard wav to give a number of photon packets proportional to he source luminosity. or to eive equal uuubers of photous o each source. which requires weighting the energv of he photons.," This sampling can be done either in the standard way to give a number of photon packets proportional to the source luminosity, or to give equal numbers of photons to each source, which requires weighting the energy of the photons." + The direction and frequency of the photon wicket are randomly sampled accordingly for the type and the spectrum of the source it originates from. usiug standard siuupliug with uo weighting.," The direction and frequency of the photon packet are randomly sampled accordingly for the type and the spectrum of the source it originates from, using standard sampling with no weighting." + A random optical depth to extinction 7 is sampled from the probability distribution function exp(7) by sampling a randon munber ¢ uniformly between 0 and 1. and taking 7= luc.," A random optical depth to extinction $\tau$ is sampled from the probability distribution function $\exp{(-\tau)}$ by sampling a random number $\zeta$ uniformly between 0 and 1, and taking $\tau=-\ln{\zeta}$ ." + The photon packet is then propagated aloug a ταν uutil it either escapes the erid. or reaches the sampled optical depth. whichever happeus first.," The photon packet is then propagated along a ray until it either escapes the grid, or reaches the sampled optical depth, whichever happens first." + If the photon packet has not escaped the exid. it will then interact WwoH.h the dust.," If the photon packet has not escaped the grid, it will then interact with the dust." + A random uuuber ¢ is sampled muiformiy between 0 and 1. aud if it is larger than the albedo of the dust. the photon packet is absorbed: otherwise it is scattered.," A random number $\zeta$ is sampled uniformly between 0 and 1, and if it is larger than the albedo of the dust, the photon packet is absorbed; otherwise it is scattered." + Once the photon packet is scattered or re-enitted. a new optical depth is sampled. and the process is repeated until the photon packet escapes from the exid.," Once the photon packet is scattered or re-emitted, a new optical depth is sampled, and the process is repeated until the photon packet escapes from the grid." + Very optically thick regions are an issue iu basic Moute-Carlo radiative transfer. as photon packets cau ect trapped in these regions and require iu some cases millions of absorptions/re-cuuissious aud scatterings to escape.," Very optically thick regions are an issue in basic Monte-Carlo radiative transfer, as photon packets can get trapped in these regions and require in some cases millions of absorptions/re-emissions and scatterings to escape." + Receutly. proposed a nodified random wall (MRW) algoritlan that allows photon packets to propagate cticiently in very optically thick regions by erouping nianv scatterines and absorptious/re-enissions iuto sinele larger steps.," Recently, \cite{min:09:155} proposed a modified random walk (MRW) algorithm that allows photon packets to propagate efficiently in very optically thick regions by grouping many scatterings and absorptions/re-emissions into single larger steps." + The photon packet propagation described previously is done im a grid made up of cells of coustaut density aud temperature., The photon packet propagation described previously is done in a grid made up of cells of constant density and temperature. + Therefore if the mean optical depth o the edge of a cell is much larger than unity. one can set up a sphere whose radius is simaller than the distance to the closest wall. inside which the deusity will," Therefore if the mean optical depth to the edge of a cell is much larger than unity, one can set up a sphere whose radius is smaller than the distance to the closest wall, inside which the density will" +"c,.",$c_g$. +" Indeed. from the viewpoint of Jupiter's rest frame. c, is completely irrelevant. since the eravitational field is static (again. ignoring Jupiter's acceleration)."," Indeed, from the viewpoint of Jupiter's rest frame, $c_g$ is completely irrelevant, since the gravitational field is static (again, ignoring Jupiter's acceleration)." +" The velocitv-dependent prelactor is a combination of a gravitomagnetic effect (the Fact (hat (he gravitational field is nol a scalar quantitv. but contains both a vector aud tensorial part) and a simple Doppler effect in (ranslorming from Jupiter's rest frame to the barycentric [αμ],"," The velocity-dependent prefactor is a combination of a gravitomagnetic effect (the fact that the gravitational field is not a scalar quantity, but contains both a vector and tensorial part) and a simple Doppler effect in transforming from Jupiter's rest frame to the barycentric frame." + We (hus conclude that the e/e corrections to the Shapiro time delay are normal 1.5DN corrections (hat occur when there are moving bodies. but that thev havenothing to do wilh (he speed of propagation of gravity. insofar as il affects (he retardation of gravitational interactions.," We thus conclude that the $v/c$ corrections to the Shapiro time delay are normal 1.5PN corrections that occur when there are moving bodies, but that they have to do with the speed of propagation of gravity, insofar as it affects the retardation of gravitational interactions." +" Furthermore. as a potential test of alternative gravitational theories. measuring these v/ce terms is not promising. because a variety. of solar svstem measurements already constrain a, and > to such a degree that ο«&4x10o7 under relatively weak assumptions or |C|<5x10? under assumptions that invoke so-called. ""preferred-Iramie"" tests of the parameter a, (see Will(2001) for the latest bounds on the PPN parameters)."," Furthermore, as a potential test of alternative gravitational theories, measuring these $v/c$ terms is not promising, because a variety of solar system measurements already constrain $\alpha_1$ and $\gamma$ to such a degree that $|\zeta | < 4 \times 10^{-3}$ under relatively weak assumptions or $|\zeta | < 5 \times 10^{-5}$ under assumptions that invoke so-called “preferred-frame” tests of the parameter $\alpha_1$ (see \citet{livrev} for the latest bounds on the PPN parameters)." + In fact. the VLBI measurements are sensitive mainly to the velocity dependence in (he logarithinic term. not to the prefactor.," In fact, the VLBI measurements are sensitive mainly to the velocity dependence in the logarithmic term, not to the prefactor." + Therefore. measurements of the propagation of radio waves past Jupiter do not directly. constrain the propagation speed of the gravitational interaction.," Therefore, measurements of the propagation of radio waves past Jupiter do not directly constrain the propagation speed of the gravitational interaction." + The remainder of this paper provides details., The remainder of this paper provides details. + In Sec., In Sec. + 2. we describe (he assumptions and basic equations (hat go into our calculation., \ref{basic} we describe the assumptions and basic equations that go into our calculation. + Section 3.B carries oul the integrations {ο fined the time delay., Section \ref{lienard} carries out the integrations to find the time delay. + In Sec., In Sec. + 4. we give concluding remarks., \ref{discussion} we give concluding remarks. +" We assume that. whatever theory of gravity is in force. it is amelric theory. that is il has a spacetime metric g,, that governs the interactions and motions of all non-gravilational fields and all 7""test particles."," We assume that, whatever theory of gravity is in force, it is a theory, that is it has a spacetime metric $g_{\mu\nu}$ that governs the interactions and motions of all non-gravitational fields and all “test” particles." + In particular. we will assume that light ravs move on null eeodesics of the spacetime metric.," In particular, we will assume that light rays move on null geodesics of the spacetime metric." + We will assume (hat atomic clocks measure proper time as given by the invariant interval of the spacetime metric., We will assume that atomic clocks measure proper time as given by the invariant interval of the spacetime metric. + By choosing the units determined by such physical measurements appropriately. we may make the speed of light as measured by anv [freely falling observer unity.," By choosing the units determined by such physical measurements appropriately, we may make the speed of light as measured by any freely falling observer unity." + Henceforth we will use units in whieh C—e=1., Henceforth we will use units in which $G=c=1$. + We then assume that the theory of gravity. has a post-Newtonian limit that can be written in the following form:, We then assume that the theory of gravity has a post-Newtonian limit that can be written in the following form: +"One interesting and important topic in (he secular evolution of low-mass N-rav. binaries (LMXDs) is the so-called. ""biburcation period"" fj. the initial binary orbital period which separates the formation of converging svstems (which evolve wilh decreasing orbital periods until the donor becomes degenerate) [rom the diverging svstems (which evolve with increasing orbital periods until the donor star loses its envelope and a wide detached binary is formed) CIntukovetal.1985).","One interesting and important topic in the secular evolution of low-mass X-ray binaries (LMXBs) is the so-called “bifurcation period"" $P_{\rm bif}$, the initial binary orbital period which separates the formation of converging systems (which evolve with decreasing orbital periods until the donor becomes degenerate) from the diverging systems (which evolve with increasing orbital periods until the donor star loses its envelope and a wide detached binary is formed) \citep{tutukov85}." +. The first svstematic investigations on the bifurcation period were done by Pylvser&Savonije(1933.1989).," The first systematic investigations on the bifurcation period were done by \citet{pylyser88,pylyser89}." +. Neglecting mass loss from the binary svstem and asstuning angular momentum loss due to magnetic braking, Neglecting mass loss from the binary system and assuming angular momentum loss due to magnetic braking +can be traced in the same py array [rom this approaching racial velocity right back to the svstemic racial velocity.,can be traced in the same pv array from this approaching radial velocity right back to the systemic radial velocity. +" The ""spike is also intercepted by Slit 3 ( Ixnot 5 in Fig.", The `spike' is also intercepted by Slit 3 ( Knot 5 in Fig. + 3(c) and ‘Table 1) where it now has & SSO kms|., 3(c) and Table 1) where it now has $\approx$ $-$ 850 $\kms$. +" The present kinematical observations of the ‘spike’ along Slit 2 should. be interpreted. along with those from it but nearer to 5 Carinae in Paper 1 (EW: slit. positions S I2"" S. fig.", The present kinematical observations of the `spike' along Slit 2 should be interpreted along with those from it but nearer to $\eta$ Carinae in Paper 1 (EW slit positions $^{\prime\prime}$ $^{\prime\prime}$ S – fig. + 5 in that paper)., 5 in that paper). + The py arrays across the ‘spike’ for these two previous positions reveal a spatially resolved: velocity. feature that extends continuously out. to x TOO kms.+ from the svstemic racial velocity., The pv arrays across the `spike' for these two previous positions reveal a spatially resolved velocity feature that extends continuously out to $\approx$ $-$ 700 $\kms$ from the systemic radial velocity. + The ‘spike’ identified in Fig., The `spike' identified in Fig. + 1 and seen in Fig., 1 and seen in Fig. +" 4(h) ias a width of a lew areseconds within the ""inner shell of collisionally tonizecl gas (see Paper 1) ancl decreases from zo at Hoopfrom 5 ""Carinac (where it is MENintercepted » Slit mE2) to at (Slit qe3).", 4(b) has a width of a few arcseconds within the `inner shell' of collisionally ionized gas (see Paper 1) and decreases from $\approx$ at from $\eta$ Carinae (where it is intercepted by Slit 2) to at (Slit 3). + An elongated. cavity.. with thin outllowing walls was sugeeste as an explanation of this feature in Paper 1.," An elongated cavity, with thin outflowing walls was suggested as an explanation of this feature in Paper 1." + Lt was proposed that the spike-ike appearance arose as the cavity walls were viewed angentiallv., It was proposed that the spike-like appearance arose as the cavity walls were viewed tangentially. +" The present. kinematical observations (which ave further from a Carinac than the earlier. ones). and he LIST imagery suggest that the ""spike! could. be a jet ic.", The present kinematical observations (which are further from $\eta$ Carinae than the earlier ones) and the HST imagery suggest that the `spike' could be a jet ie. + à narrow. collimated outllow exhibiting some form of acceleration or directional variation to produce a change of ftom 650kmsFL to. S50kms.! between its interception by Slits 3.," a narrow, collimated outflow exhibiting some form of acceleration or directional variation to produce a change of from $-$ 650 $\kms$ to $-$ 850 $\kms$ between its interception by Slits 2 3." + An estimate of the outllow velocity of the ‘spike’. if a jet. depends critically on its orientation with respect to the plane of the sky.," An estimate of the outflow velocity of the `spike', if a jet, depends critically on its orientation with respect to the plane of the sky." + One guide to this angle. a. could be the measured orientation for LES (see Fig.," One guide to this angle, $\alpha$, could be the measured orientation for E5 (see Fig." + 1)., 1). +" This has been derived [rom the proper motion of 5"" feentury of E5 from η Carinae (Walborn Blanco 1989) which. for a distance of 2.6 kpe combined with the radial velocity dilference of = 140 kms (Table 1) gives an outflow: velocity of 620 kins tilled at à = 13 to the sky for this group of knots ES marked in Fig."," This has been derived from the proper motion of $^{\prime\prime}$ /century of E5 from $\eta$ Carinae (Walborn Blanco 1989) which, for a distance of 2.6 kpc combined with the radial velocity difference of $\approx$ $-$ 140 $\kms$ (Table 1) gives an outflow velocity of 620 $\kms$ tilted at $\alpha$ = $^{\circ}$ to the sky for this group of knots E5 marked in Fig." + 1., 1. +" With this same angle a speed of &3800 knis is then predicted by the measured: value of = S50 kms| for the tip of the ""spike.", With this same angle a speed of $\approx$ 3800 $\kms$ is then predicted by the measured value of = $-$ 850 $\kms$ for the tip of the `spike'. + For a constant velocity away from 7 Carinac the ‘spike’ would then have originated in an eruptive event around: 1900., For a constant velocity away from $\eta$ Carinae the `spike' would then have originated in an eruptive event around 1890. + This is near the time of major outbursts listed by Walborn Liller (1971)., This is near the time of major outbursts listed by Walborn Liller (1977). +" Perhaps. the orientation. of the ""spike"" can estimated more realistically i£ it assumed that its directional variationssky. which give an apparent change of 15"" between where 1t is intercepted by Slits 2 and 3.2 are of similar magnitude to directional changes perpendicular to the plane of the sky."," Perhaps, the orientation of the `spike' can estimated more realistically if it assumed that its directional variations, which give an apparent change of $^{o}$ between where it is intercepted by Slits 2 and 3, are of similar magnitude to directional changes perpendicular to the plane of the sky." +" This would cause the racial velocity dillerence of 200 Kms.1 between these (o positions even if, more realistically. no acceleration is assumed."," This would cause the radial velocity difference of $-$ 200 $\kms$ between these two positions even if, more realistically, no acceleration is assumed." +" In this case a2 3T"" js predicted with a jet speed of LOTT kmsο giving an age of z 360 vr for the tip of the ‘spike’. which is before records of the eruptions of 4 Carinae are available though this speed must be subject to large uncertainties."," In this case $\alpha~\approx$ $^{o}$ is predicted with a jet speed of 1077 $\kms$ giving an age of $\approx$ 360 yr for the tip of the `spike', which is before records of the eruptions of $\eta$ Carinae are available though this speed must be subject to large uncertainties." + Incidentallv. the converging sides of the “spike” can be explained as part of a jet structure if the Hl] emission is from recollimation shocks (cf.," Incidentally, the converging sides of the `spike' can be explained as part of a jet structure if the [N ] emission is from recollimation shocks (cf." + Paper 3)., Paper 3). + X model of the spectrum of Davidson et al. (, A model of the spectrun of Davidson et al. ( +1986) ofan ΑΠ) bright knot in the outer shell of the a Carinae nebula (by John Ravnion and reported in Meaburn et al. (,1986) of an [N ] bright knot in the outer shell of the $\eta$ Carinae nebula (by John Raymond and reported in Meaburn et al. ( +1988)) eave a shock velocity of 140 kms.7.,1988)) gave a shock velocity of 140 $\kms$. + In any case. the shock velocities cannot be higher than this value for the small knots in the outer shel of η Carinae to be ionized by radiative shocks.," In any case, the shock velocities cannot be higher than this value for the small knots in the outer shell of $\eta$ Carinae to be ionized by radiative shocks." +" Since Ν.Π emission requires the shocks to be x 100 kms+. the aspec ratio of the convergent. part of the spike will be roughly Cua/(2.ων be. c 5: in projection for a jet speed. of 1077 kms which is easilv satisfied by the observed. high aspect ratio of the ""spike."," Since [N ] emission requires the shocks to be $\leq$ 100 $\kms$, the aspect ratio of the convergent part of the spike will be roughly $v_{\rm jet}/(2~v_{\rm shock})$, i.e. $\geq$ 5:1 in projection for a jet speed of 1077 $\kms$ which is easily satisfied by the observed high aspect ratio of the `spike'." + Unusual kinematical features also occur along Slits 4 Ὁ over the ridge marked. care’ in Fig., Unusual kinematical features also occur along Slits 4 5 over the ridge marked `arc' in Fig. + 1 which appears to originate near the knot marked I5., 1 which appears to originate near the knot marked E5. + Incidentally. a detailed inspection of the LIST image in Fig.," Incidentally, a detailed inspection of the HST image in Fig." +" 2 reveals that. both I5 and the northern end of the ""arc are. composed. of a conglomeration of emission line knots as small as 0.37 across.", 2 reveals that both E5 and the northern end of the `arc' are composed of a conglomeration of emission line knots as small as $^{\prime\prime}$ across. +" It is in the profiles from. Slit 4 over this ""arc. that the strange loop (discussed. in Sect.", It is in the profiles from Slit 4 over this `arc' that the strange loop (discussed in Sect. + 2) in the pv arrays occurs (Slit 4 Ixnots 1 3 in Fie., 2) in the pv arrays occurs (Slit 4 Knots 1 – 3 in Fig. + 3(d) anc Table. 1)., 3(d) and Table 1). + The kinematical features over I5 are themselves complex (Fig., The kinematical features over E5 are themselves complex (Fig. + 3(0))., 3(c)). +" X ""parabola, of emission in the py array (Slit 3 extended Knot 2). 15"" across. extends out to 400 kimis from the systemic radial velocity though the peak of the emission from L5 can be seen. in the contour map of the surface brightnesses shown in Fig."," A `parabola' of emission in the pv array (Slit 3 extended Knot 2), $^{\prime\prime}$ across, extends out to $-$ 400 $\kms$ from the systemic radial velocity though the peak of the emission from E5 can be seen, in the contour map of the surface brightnesses shown in Fig." + 6. to be at c 14) kms," 6, to be at $\approx$ $-$ 140 $\kms$." + Assuming the interpretation of the loop as à coherent feature of emission. (though see. the reservations expressed in Sect., Assuming the interpretation of the loop as a coherent feature of emission (though see the reservations expressed in Sect. + 2) an attempt has been mace to reproduce the approaching ‘loop’ in the py array in Fie., 2) an attempt has been made to reproduce the approaching `loop' in the pv array in Fig. + 3(d) from the ‘are’ sketehed in Fig., 3(d) from the `arc' sketched in Fig. + 1: using the model shown in Fig., 1 using the model shown in Fig. + το)., 7(c). + Here a conical shell is assumed to have vratio of thickness to radius of 0.15., Here a conical shell is assumed to have a ratio of thickness to radius of 0.15. + Phe ionized gas within is shell is given. somewhat arbitarilv. a How velocity along --s surface of 1500 kms+ (similar to the well-verified speed X the jet in Paper 3).," The ionized gas within this shell is given, somewhat arbitarily, a flow velocity along its surface of 1500 $\kms$ (similar to the well-verified speed of the jet in Paper 3)." + Ehe full opening angle of the cone from 16 image in Fig., The full opening angle of the cone from the image in Fig. + 2 and the AAT photograph is taken to be 6., 2 and the AAT photograph is taken to be $^\circ$. +" The angle between the axis of the cone and the plane of re sky is 1S"".", The angle between the axis of the cone and the plane of the sky is $^\circ$. +" The slit is oriented at 30° with respect to the uis of the cone to simulate approximately its orientation to je ""arc in Fig.", The slit is oriented at $^\circ$ with respect to the axis of the cone to simulate approximately its orientation to the `arc' in Fig. + 1., 1. + The predictions of this model (Fig., The predictions of this model (Fig. + T(b)) 'onvincineglv. match the contour plot of the observed. array of profiles in Fig., 7(b)) convincingly match the contour plot of the observed array of profiles in Fig. + τα). (if these are all assumed. to be of origin)., 7(a) (if these are all assumed to be of origin). +o Uniform volume cniissivity ofthe line emission. within the cone would give rise to à completely ‘Losec ellipse in the predicted py array in Fig., Uniform volume emissivity of the line emission within the cone would give rise to a completely closed ellipse in the predicted pv array in Fig. + 7(b)., 7(b). + However. in the model. the volume emissivity has been reduced in one section of the cone until a reasonable match was achieved to 16 brightness variations within the observed loop in the py urav.," However, in the model, the volume emissivity has been reduced in one section of the cone until a reasonable match was achieved to the brightness variations within the observed loop in the pv array." + This self consistent set of key parameters (the opening uigle. the speed and the angle between the cone's axis and Ίο sky) is constrained to within ten percent by the racial," This self consistent set of key parameters (the opening angle, the speed and the angle between the cone's axis and the sky) is constrained to within ten percent by the radial" +"of the 31 cluster candidates which coufirmed them as groups and. clusters of galaxies with 10720.3$ are presented. + For comparison. at 20.3 the RINOS survey . found a siface density of 0.33+0.15 clusters ? (to a sinilu. slightly lower flux limit).," For comparison, at $z>0.3$ the RIXOS survey \cite{ca} found a surface density of $0.33 \pm 0.15$ clusters $^{-2}$ (to a similar, slightly lower flux limit)." + The WARPS finds 0.512:0.22 clusters, The WARPS finds $0.84\pm 0.22$ clusters +n et al. 1996)).,n et al. \cite{martin96}) ). + Theoretical evolutionary models (which do not include grain formation in very cool atmospheres) predict that these objects become much redder with colours (R—I) > 3 (Chabrier et al. 1996))., Theoretical evolutionary models (which do not include grain formation in very cool atmospheres) predict that these objects become much redder with colours $(R-I)$ $\ge$ 3 (Chabrier et al. \cite{chabrier96}) ). +" Thus, they might be extremely faint in R wavelengths, greatly hindering their detection."," Thus, they might be extremely faint in $R$ wavelengths, greatly hindering their detection." +" On the other hand, field stars do exhibit a turn-off in (R—I) at around M7 spectral type, with stars of later types having bluer colours (Bessell 1991))."," On the other hand, field stars do exhibit a turn-off in $(R-I)$ at around M7 spectral type, with stars of later types having bluer colours (Bessell \cite{bessell91}) )." +" The fluxes and colours of the Pleiades BDs fainter than Teidell and Calar33 are unknown, but we expect them to have spectral energy distributions which resemble those of the coolest objects in the field."," The fluxes and colours of the Pleiades BDs fainter than 1 and 3 are unknown, but we expect them to have spectral energy distributions which resemble those of the coolest objects in the field." + It could turn out that the (R—I) colour is no longer useful to discriminate low luminosity cluster members from field objects., It could turn out that the $(R-I)$ colour is no longer useful to discriminate low luminosity cluster members from field objects. +" The (1—J) colour, however, gets monotonically redder for lower temperatures (both for observed and theoretical predictions), implying that the slope of the spectral pseudocontinuum between J and J wavelengths clearly increases."," The $(I-J)$ colour, however, gets monotonically redder for lower temperatures (both for observed and theoretical predictions), implying that the slope of the spectral pseudocontinuum between $I$ and $J$ wavelengths clearly increases." +" As the Z filter is centered at nnm, we expect a similar behaviour with / and Z."," As the $Z$ filter is centered at nm, we expect a similar behaviour with $I$ and $Z$." +" Although the efficiency of the CCD drops considerably in the Z-band, this effect is compensated by the increased brightness of BDs at these near-IR wavelengths."," Although the efficiency of the CCD drops considerably in the $Z$ -band, this effect is compensated by the increased brightness of BDs at these near-IR wavelengths." + The (J—Z) colour has been shown to be a useful discriminant for Pleiades BDs by Cossburn et al. (1997))., The $(I-Z)$ colour has been shown to be a useful discriminant for Pleiades BDs by Cossburn et al. \cite{cossburn97}) ). +" Other photometric searches for substellar objects in the Pleiades carried out with R and J (Jameson Skillen 1989; Zapatero Osorio et al. 1997b,,"," Other photometric searches for substellar objects in the Pleiades carried out with $R$ and $I$ (Jameson Skillen \cite{jameson89}; Zapatero Osorio et al. \cite{osorio97b}," + Π) provide a high number of mid- and late-M stars that do not belong to the cluster and are contaminating the surveys., I) provide a high number of mid- and late-M stars that do not belong to the cluster and are contaminating the surveys. + It is desiderable to find a strategy which avoids these field contaminants and facilitates a more efficient tool for detecting true members., It is desiderable to find a strategy which avoids these field contaminants and facilitates a more efficient tool for detecting true members. + In II the success rate was only25%:: two out of the eight proposed cool candidates have been confirmed as Pleiades BDs (Reboloet al. 1996))., In I the success rate was only: two out of the eight proposed cool candidates have been confirmed as Pleiades BDs (Reboloet al. \cite{rebolo96}) ). +" The authors argue that this was due to the detection of reddened late-M dwarfs (Zapatero Osorio et al. 1997c,,"," The authors argue that this was due to the detection of reddened late-M dwarfs (Zapatero Osorio et al. \cite{osorio97c}," + III)., II). + The use of longer wavelength filters would help to jump over this obstacle., The use of longer wavelength filters would help to jump over this obstacle. +" Raw frames were processed using standard techniques within the (Image Reduction and Analysis Facility) environment, which included bias subtraction, flat-fielding and correction for bad pixels by interpolation with values from the nearest-neighbour pixels."," Raw frames were processed using standard techniques within the (Image Reduction and Analysis Facility) environment, which included bias subtraction, flat-fielding and correction for bad pixels by interpolation with values from the nearest-neighbour pixels." +" The photometric PSF fitting analysis was carried out using routines within DAOPHOT, which provides image profile information needed to discriminate between stars and galaxies."," The photometric PSF fitting analysis was carried out using routines within DAOPHOT, which provides image profile information needed to discriminate between stars and galaxies." + Instrumental RI magnitudes were corrected for atmospheric extinction and transformed into the RI Cousins system using observations of standard stars from Landolt’s (1992)) list., Instrumental $RI$ magnitudes were corrected for atmospheric extinction and transformed into the $RI$ Cousins system using observations of standard stars from Landolt's \cite{landolt92}) ) list. + Special care was taken in including red standard stars in order to ensure a reliable transformation for the reddest candidates: the field 998 contains many photometric standards covering colours from AO to M7 spectral type., Special care was taken in including red standard stars in order to ensure a reliable transformation for the reddest candidates: the field 98 contains many photometric standards covering colours from A0 to M7 spectral type. + The calibration of Z magnitudes required more observational effort as there are no real data for standards available in the literature., The calibration of $Z$ magnitudes required more observational effort as there are no real data for standards available in the literature. +" We have not performed an absolute flux calibration for this filter, but obtained (1—Z) colours with respect to a given spectral type."," We have not performed an absolute flux calibration for this filter, but obtained $(I-Z)$ colours with respect to a given spectral type." +" Using the same Landolt fields as observed through the other two filters at culmination (airmass = 1.1), we set Z = I for those standard stars with (R—I) ~ 0 (A0-type)."," Using the same Landolt fields as observed through the other two filters at culmination (airmass = 1.1), we set $Z$ = $I$ for those standard stars with $(R-I)$ $\sim$ 0 (A0-type)." + The adopted (1—Z) colours are shown in Table 2.., The adopted $(I-Z)$ colours are shown in Table \ref{sa98}. + Observations of these fields at different elevations allowed us to correct Z instrumental magnitudes for atmospheric extinction., Observations of these fields at different elevations allowed us to correct $Z$ instrumental magnitudes for atmospheric extinction. + Errors for Z instrumental magnitudes as provided by IRAF routines are plotted in Fig. 2.., Errors for $Z$ instrumental magnitudes as provided by IRAF routines are plotted in Fig. \ref{error}. + The best power law fit to the errors in I for the bulk of data is superimposed in the figure for comparison., The best power law fit to the errors in $I$ for the bulk of data is superimposed in the figure for comparison. +" Summarizing, uncertainties in the INT photometry range from <0.05mmag at I,Z ~20.5, 19.7 to about mmag at 22, mmag, respectively."," Summarizing, uncertainties in the INT photometry range from $\le$ mag at $I$ $Z$ $\sim\,20.5$, 19.7 to about mag at 22, mag, respectively." + We present in Fig., We present in Fig. +" 3 the resulting J vs. (I—Z) diagram where data for the Pleiads 33, 115 and 11 (which are present in three of our fields) are combined with the new observations."," \ref{iz} the resulting $I$ vs. $(I-Z)$ diagram where data for the Pleiads 3, 15 and 1 (which are present in three of our fields) are combined with the new observations." + We remark that Z magnitudes are not on a standard system., We remark that $Z$ magnitudes are not on a standard system. + Completeness and limiting magnitudes of our survey were derived following the same procedure described in Stauffer et al. (1994)), Completeness and limiting magnitudes of our survey were derived following the same procedure described in Stauffer et al. \cite{stauffer94}) ) +" and perll. We estimate them to be /,Z~ 21, 20.5 for"," and I. We estimate them to be $I$ $Z \sim\,21$ , 20.5 for" +caleulatious outlined ChristyD)...(19," \cite{Christy-1964}, \citep{Baker-1965,Christy-1966b}." +6 (Baker Tugele&Then(1973) convection 1966a.b:Tune1967:Cough1977).," \cite{Tuggle-1973} \citep{Cox-1966a,Cox-1966b,Unno-1967,Gough-1977}." + Stellingwort(1982a.b.198[a.b.c). adequately resolving these eradieuts is imirportaut for accurate modeling.," \cite{Stellingwerf-1982a, Stellingwerf-1982b, Stellingwerf-1984a, Stellingwerf-1984b, Stellingwerf-1984c} adequately resolving these gradients is important for accurate modeling." + Golinevr(1992a.).1993) aud Dori&Feuchtinecr(1991)— have both included. adaptive ervids too better resolve the steep. gradients i the ionization zones as they sweep through the envelope during pulsation.," \cite{Gehmeyr-1992a, Gehmeyr-1992b,Gehmeyr-1993} and \cite{Dorfi-1991} have both included adaptive grids too better resolve the steep gradients in the ionization zones as they sweep through the envelope during pulsation." + Using a version of Stellinswerf's time-dependent convective. model with. his. adaptive: scheme. Geluneyr was able to produce a red edge at roughly. the observed effective temperature.," Using a version of Stellingwerf's time-dependent convective model with his adaptive scheme, \citeauthor{Gehmeyr-1992a} was able to produce a red edge at roughly the observed effective temperature." + He notes that the effective temperature of the red edge is depeudenut ou the parameters used for the couvective model. and that the predicted temperature of the red οσο could vary by a few hundred degrees I&clviu depending on the values used for the convective nodel paramcters.," He notes that the effective temperature of the red edge is dependent on the parameters used for the convective model, and that the predicted temperature of the red edge could vary by a few hundred degrees Kelvin depending on the values used for the convective model parameters." + Also. there are differences )etween Celunevi’s light amplituce-vise time relationship and the observed relatiouship iu voth slope aud zero point.," Also, there are differences between Gehmeyr's light amplitude-rise time relationship and the observed relationship in both slope and zero point." + Feuchtinecr&Dorf(1996) used their adaptive code to calculate light and radial velocity curves which exhibit shapes vpieal of RR Lyrae stars., \cite{Dorfi-1996} used their adaptive code to calculate light and radial velocity curves which exhibit shapes typical of RR Lyrae stars. + À second potential difficulty is an accurate representation of the surface boundary. which Feuchtiger&Dorf ested by including a model atinosplere aud found hat its iuclusiou did not impact the pulsational characteristics of the moctel.," A second potential difficulty is an accurate representation of the surface boundary, which \citeauthor{Dorfi-1996} tested by including a model atmosphere and found that its inclusion did not impact the pulsational characteristics of the model." + Marconietal.(2003) used the 1D. Lagrangian. ivdrodyuamnics code described by Bono&Stelling-wert(0091) and Donoetal.(L997a.b) to compute RR Lerae models to compare with the RR Lvrae starsobserved in M3;," \cite{Marconi-2003} used the 1D, Lagrangian, hydrodynamics code described by \cite{Bono-1994} and \cite{Bono-1997a,Bono-1997b} to compute RR Lyrae models to compare with the RR Lyrae starsobserved in M3." +" Tn order to. fully spocity the problem Marconietal. needed to. choose a mixing-lenugth parameter. aud adopted both H/ID,=1.5 aud 2.0. where fis the iixiug-leugth and ZI, is the pressure scale height."," In order to fully specify the problem \citeauthor{Marconi-2003} needed to choose a mixing-length parameter, and adopted both $l/H_p=1.5$ and $2.0$ , where $l$ is the mixing-length and $H_p$ is the pressure scale height." + They fouud that iu order to match the boundaries of RR, They found that in order to match the boundaries of RR +the elliptical mocels do not represent any physical entity. as expected considering the Iarge residuals when these models are subtracted.,"the elliptical models do not represent any physical entity, as expected considering the large residuals when these models are subtracted." + The faülure on fitting the surface brightness profiles is another indication that the IGL components are very irregular and. cannot be described by a regular mocel. as it happens in the diffuse component of clusters of galaxies.," The failure on fitting the surface brightness profiles is another indication that the IGL components are very irregular and cannot be described by a regular model, as it happens in the diffuse component of clusters of galaxies." + We can conclude from this. already. that the compact groups are far [rom being a relaxed ane virialized structure.," We can conclude from this, already, that the compact groups are far from being a relaxed and virialized structure." +" The analysis of the colour maps of the reconstructed ΕΙ, components of all groups do not. show any kind. of substructures. such as blue regions that could be associated tostar forming regions in the IGL."," The analysis of the colour maps of the reconstructed IGL components of all groups do not show any kind of substructures, such as blue regions that could be associated to star forming regions in the IGL." +" Blue star forming regions in the diffuse component. as found in the Coma cluster by 7.. could. be the origin of the dillerence. we find. between the mean colour. of the ΓΙ, and the one of the galaxy component. when the IGL is bluer than the galaxies."," Blue star forming regions in the diffuse component, as found in the Coma cluster by \citet{ada05}, could be the origin of the difference we find between the mean colour of the IGL and the one of the galaxy component, when the IGL is bluer than the galaxies." + In the case of our study. those regions. if they exist. could be too disperse to be individually identified in our colour maps.," In the case of our study, those regions, if they exist, could be too disperse to be individually identified in our colour maps." + Some group properties can be used as dynamical evolution indicators. such as fraction of earlv-tw galaxies (or of late-tvpe galaxies). crossing time and magnitudepe. cdillerence between the first and the second-ranked: galaxies. (2X2).," Some group properties can be used as dynamical evolution indicators, such as fraction of early-type galaxies (or of late-type galaxies), crossing time and magnitude difference between the first and the second-ranked galaxies $\Delta m_{12}$ )." + Now we have an additional dynamical evolution indicator. the fraction of IGL present in the group.," Now we have an additional dynamical evolution indicator, the fraction of IGL present in the group." + In a first qualitative effort. we analyzed. the relation between these indicators in our sample.," In a first qualitative effort, we analyzed the relation between these indicators in our sample." + We restricted. this analvsis to the groups studied here and in ? in order to have a homogeneously analyzed sample and the analysis is only qualitative due to small number of objects. only 6 groups.," We restricted this analysis to the groups studied here and in \citet{dar05} in order to have a homogeneously analyzed sample and the analysis is only qualitative due to small number of objects, only 6 groups." +" We can see the relations between the fraction of IGL in the B band. (Pre). the fraction of early-twpe galaxies (Pryor). the crossing time (/4,,: and Xm». in figure 5.."," We can see the relations between the fraction of IGL in the $B$ band $F_{IGL}$ ), the fraction of early-type galaxies $F_{Egal}$ ), the crossing time $t_{cross}$ ) and $\Delta m_{12}$, in figure \ref{figcorr}." + The fractions of IGL in the 2 and & band are very similar. and for this kind of study do not. present any dilference in the relation with the other indicators.," The fractions of IGL in the $B$ and $R$ band are very similar, and for this kind of study do not present any difference in the relation with the other indicators." + HCG 15 and 51 are presented with two cata points each. for the quintet ancl sextet configurations.," HCG 15 and 51 are presented with two data points each, for the quintet and sextet configurations." + For LIC; SS we have found new recession velocity measurements (?).., For HCG 88 we have found new recession velocity measurements \citep{nis00b}. . +" The new measurements increase the velocity. dispersion of thegroup from 31 to 93kms allowing the estimate of the deprojected velocity. dispersion. (134kms 1j and reducing the crossing time from 8.7 to 0.065LL,. therefore we included a “new point” for this group in the relations between foros. and other quantities."," The new measurements increase the velocity dispersion of thegroup from $31$ to $93~{\rm +km~s^{-1}}$, allowing the estimate of the deprojected velocity dispersion $134~{\rm km~s^{-1}}$ ) and reducing the crossing time from $8.7$ to $0.065~{\rm H_0^{-1}}$, therefore we included a “new point” for this group in the relations between $t_{cross}$ and other quantities." + This decrease in. the crossing time do not alter the conclusions about this object elven in 2.. since the value is still considerably. high.," This decrease in the crossing time do not alter the conclusions about this object given in \citet{dar05}, , since the value is still considerably high." + The relations. with Arps show no clear tendency., The relations with $\Delta m_{12}$ show no clear tendency. + Relations between fren. Begar and foros. Can be. in a first approximation. described in a linear relation. if the clearly discrepant. objects are. excluded.," Relations between $F_{IGL}$, $F_{Egal}$ and $t_{cross}$ can be, in a first approximation, described in a linear relation, if the clearly discrepant objects are excluded." +" We excluded. the ""old"" high £544. value of HC SS from the fits for relations with this quantity and LCG 35. that shows a very. high fraction of earlv-tvpe galaxies. was excluded from the fits for relations with f."," We excluded the “old” high $t_{cross}$ value of HCG 88 from the fits for relations with this quantity and HCG 35, that shows a very high fraction of early-type galaxies, was excluded from the fits for relations with$F_{Egal}$ ." + These relations show the agreement. in aqualitative way. between our new dynamical evolution," These relations show the agreement, in aqualitative way, between our new dynamical evolution" +Supernovac (SNe) have a profound. influence upon many diverse. areas of astrophwsies.,Supernovae (SNe) have a profound influence upon many diverse areas of astrophysics. + They. are the kev source of heavy elements in the universe. driving cosmic chemical evolution.," They are the key source of heavy elements in the universe, driving cosmic chemical evolution." + Their cnergy input can initiate episodes of star formation. and they are themselves the product. of the complex physics underlying the final stages of stellar evolution.," Their energy input can initiate episodes of star formation, and they are themselves the product of the complex physics underlying the final stages of stellar evolution." + The homogeneous nature of the thermonuclear Type la SNe provides the most mature ancl direct. probe of dark energy., The homogeneous nature of the thermonuclear Type Ia SNe provides the most mature and direct probe of dark energy. + Despite this importance in astrophysics. we understancl surprisingly little about the physics governing SN explosions.," Despite this importance in astrophysics, we understand surprisingly little about the physics governing SN explosions." + Only the progenitors of the core. collapse Type HP SNe have been directly. identified: the physical nature of other SN tvpes remains uncertain (forreviewsseeLlillebranct&Niemever2000:Smartt 2009)...," Only the progenitors of the core collapse Type IIP SNe have been directly identified: the physical nature of other SN types remains uncertain \citep[for reviews +see][]{2000ARA&A..38..191H,2009ARA&A..47...63S}." + We remain ignorant about many aspects of SN rates. light-curves. spectra. demographics. and the dependence ο these properties on environment. progenitor composition. and explosion physics.," We remain ignorant about many aspects of SN rates, light-curves, spectra, demographics, and the dependence of these properties on environment, progenitor composition, and explosion physics." + In part. this is due to the historical dillicultv ancl technical challenges associated with locating SNe in the required numbers to create statistically meaningful samples. particularly at low redshift where high quality follow-up data can most easily. be attained.," In part, this is due to the historical difficulty and technical challenges associated with locating SNe in the required numbers to create statistically meaningful samples, particularly at low redshift where high quality follow-up data can most easily be attained." + This situation has changed with the availability of large format CCD detectors., This situation has changed with the availability of large format CCD detectors. + Automated. wide-feld transient searches on dedicated 1-2m class telescopes and facilities are underway. typically observing thousands of square degrees every. few days (e.g.Ixeller.ctal.2007:Lawet 2009)..," Automated, wide-field transient searches on dedicated 1-2m class telescopes and facilities are underway, typically observing thousands of square degrees every few days \citep[e.g.][]{2007PASA...24....1K,2009PASP..121.1395L}." +" These Hux-Hamited ""rolling searches! select. transient events without regard. to host galaxy properties or tvpe.", These flux-limited `rolling searches' select transient events without regard to host galaxy properties or type. + This large amount of imagine cata naturally generates its own particular logistical challenges in dealing with the data low. and identilving transient astrophysical objects of interest in the cata Ceandidates) for scientific study. and analysis.," This large amount of imaging data naturally generates its own particular logistical challenges in dealing with the data flow, and identifying transient astrophysical objects of interest in the data (`candidates') for scientific study and analysis." + Of particular importance is the rapid identification of new candidates once the imaging data has been obtained and. processed., Of particular importance is the rapid identification of new candidates once the imaging data has been obtained and processed. + Though many aspects of survey operations. such as image processing. can be efficiently. pipelined. the identification of new transient sources remains challenging. with human operators Cscanners) invariably charged with wading through new detections on a nightly basis.," Though many aspects of survey operations, such as image processing, can be efficiently pipelined, the identification of new transient sources remains challenging, with human operators (`scanners') invariably charged with wading through new detections on a nightly basis." + Though computer algorithms can assist with identifving objects of interest in the data. this scanning can still absorb a significant amount of researcher time.," Though computer algorithms can assist with identifying objects of interest in the data, this scanning can still absorb a significant amount of researcher time." + (X related. issue is spectroscopic follow-up. a limited. resource that must be prioritised ancl allocated: efficiently. to. the. detected candidates. with the absolute minimum of false candidates observed.," A related issue is spectroscopic follow-up, a limited resource that must be prioritised and allocated efficiently to the detected candidates, with the absolute minimum of false candidates observed." + Two high-redshift SN. searches highlight these challenges., Two high-redshift SN searches highlight these challenges. + The Supernova Legacy Survey (SNLS:e.g.Astierctal. used the MegaC'am instrument on the 3.6m CanadaHawaii Telescope to survey 4 deg? with a cadence ofa few days., The Supernova Legacy Survey \citep[SNLS; e.g.][]{2006A&A...447...31A} used the MegaCam instrument on the 3.6m Canada--France--Hawaii Telescope to survey 4 $^{2}$ with a cadence of a few days. + Following automated cuts on signal-to-noise and candidate shape. cach square degree would: typically. generate ~200 candidates for each night of observation (Perrettetal.2010)...," Following automated cuts on signal-to-noise and candidate shape, each square degree would typically generate $\sim$ 200 candidates for each night of observation \citep{2010AJ....140..518P}." + Visual inspection would: decrease this number to ~20 plausible real transients., Visual inspection would decrease this number to $\sim$ 20 plausible real transients. + Phe Sloan Digital Sky Survey-LL Supernova Survey (SDSS-SN:e.g.Fricmanetal.2008) usec the SDSS 2.5m telescope to survey a larger area of 300 deg. though to a shallower depth than SNLS (Sakoetal.2008)..," The Sloan Digital Sky Survey-II Supernova Survey \citep[SDSS-SN; +e.g.][]{2008AJ....135..338F} used the SDSS 2.5m telescope to survey a larger area of 300 $^{2}$, though to a shallower depth than SNLS \citep{2008AJ....135..348S}." + After the removal of moving (solar system) objects. in the first season (3 month »riod). human scanners viewed. 30005000 objects each night spread. over six scanners (100.000. over the whole season).," After the removal of moving (solar system) objects, in the first season (3 month period), human scanners viewed 3000–5000 objects each night spread over six scanners $>$ 100,000 over the whole season)." + Although this number was radically reduced. in ater seasons as more automated procedures were developed (714.000 during season 2). the burden on human scanners was still laree (Sakoetal.2008)..," Although this number was radically reduced in later seasons as more automated procedures were developed $\sim$ 14,000 during season 2), the burden on human scanners was still large \citep{2008AJ....135..348S}." + With new wide-field ransient surveys generating many more candidates. than hese two surveys. advances in both automated. techniques and human scanning are clearly required.," With new wide-field transient surveys generating many more candidates than these two surveys, advances in both automated techniques and human scanning are clearly required." + This paper details a new method for sorting through SN candidates. based. upon the citizen science project “Galaxy Zoo (Lintottetal.2008.2010)..," This paper details a new method for sorting through SN candidates, based upon the citizen science project `Galaxy Zoo' \citep{2008MNRAS.389.1179L,2010arXiv1007.3265L}." + New candidate transient events are uploaded to the Galaxy Zoo Supernovae website. and are visually examined and classified. by members of he public. guided by a tutorial ancl associated: decision ree.," New candidate transient events are uploaded to the Galaxy Zoo Supernovae website, and are visually examined and classified by members of the public, guided by a tutorial and associated decision tree." + Each canclicdate is examined. and classified by multiple »ople and given an average score. with the candidates ranked and made available for further investigation in real-ime.," Each candidate is examined and classified by multiple people and given an average score, with the candidates ranked and made available for further investigation in real-time." + The advantages of this approach are considerable., The advantages of this approach are considerable. + First. the burden of candidate scanning is larecly removed rom the science team running the survey.," First, the burden of candidate scanning is largely removed from the science team running the survey." + Second. each candidate is inspected. multiple times (versus once by a scanner in previous transient surveys). reducing the chances hat the candidate could. be missed.," Second, each candidate is inspected multiple times (versus once by a scanner in previous transient surveys), reducing the chances that the candidate could be missed." + Fhird. with a large number of people scanning candidates. more candidates can be examined in a shorter amount of time — ancl with he global Zooniverse (the parent project of Galaxy Zoo) user base this can be done around the clock. regarclless of the local time zone the science team happens to be owed in.," Third, with a large number of people scanning candidates, more candidates can be examined in a shorter amount of time – and with the global Zooniverse (the parent project of Galaxy Zoo) user base this can be done around the clock, regardless of the local time zone the science team happens to be based in." + This speed can even allow interesting candidates o be followed up on the same night as that of the SNe discovery. of particular interest to. quickly evolving SNe or transient. sources.," This speed can even allow interesting candidates to be followed up on the same night as that of the SNe discovery, of particular interest to quickly evolving SNe or transient sources." + Fourth. the large number of human classifications collected can be used. to. improve machine learning algorithms for automated SNe classification.," Fourth, the large number of human classifications collected can be used to improve machine learning algorithms for automated SNe classification." + This paper reports the results from. the carly operations (over 3 month period) of this system., This paper reports the results from the early operations (over $\sim$ 3 month period) of this system. + 1n section 2.. we describe the Palomar Transient Factory. data from which were used in the tests and running of Galaxy Zoo Supernovae.," In section \ref{sec:palom-trans-fact}, we describe the Palomar Transient Factory, data from which were used in the tests and running of Galaxy Zoo Supernovae." + Section 3. describes Galaxy Zoo Supernovac. including the ranking svstem for candidates used by the citizenscience classifiers.," Section \ref{sec:oper-galaxy-zoo} describes Galaxy Zoo Supernovae, including the ranking system for candidates used by the citizenscience classifiers." + Section 4. has details of the tests and. first results of the Galaxy Zoo Supernovae operation., Section \ref{sec:results} has details of the tests and first results of the Galaxy Zoo Supernovae operation. + We discuss the future direction of this project in section 5.., We discuss the future direction of this project in section \ref{sec:future}. . + Vhe Palomar Transient Factory (PEE) is a wide-field survey exploring the optical transient sky., The Palomar Transient Factory (PTF) is a wide-field survey exploring the optical transient sky. + The survey is built, The survey is built +1984).,. +. The troilite abundance is Q4;=7-68x10.! (Pollacketal.1994).., The troilite abundance is $\zeta_{troi}=7.68\times 10^{-4}$ \citep{Pollack}. + Graphite optical properties are taken from Weinegartner&Draine(2001) [or graphite. and the silicates are assumed to be pyroxenes GUgosFei9/04). with optical properties from (1995)..," Graphite optical properties are taken from \citet{Weingartner} for graphite, and the silicates are assumed to be pyroxenes $Mg_{0.8}\,Fe_{0.2}\,SiO_{3}$ ), with optical properties from \citet{Dorschner}." +" Also. we consider an interstellar medium dust size distribution with n(a)xa.77. with minima and maxinmn sizes yj,=0.005:/m and (yg,=0.25jan. respectively."," Also, we consider an interstellar medium dust size distribution \citep{Mathis1} with $n(a)\propto a^{-3.5}$, with minimum and maximum sizes $a_{min}=0.005\mu$ m and $a_{max}=0.25\mu$ m, respectively." + To show the dependence of the SED on the input parameters we change one parameter al a (ime and compare the resultant SED (o that of the fiducial model., To show the dependence of the SED on the input parameters we change one parameter at a time and compare the resultant SED to that of the fiducial model. + We first consider the change of parameters in (he wall. and then the change of parameters in (he optically thin reeion inside the hole.," We first consider the change of parameters in the wall, and then the change of parameters in the optically thin region inside the hole." +" We assume that (he apparent separation of (he stars on the plane of (he sky is the same as the observed separation d,53.6d:0.5nmurs—1.52:0.07AU. &lIxraus 2003)..", We assume that the apparent separation of the stars on the plane of the sky is the same as the observed separation $d_{ap}=53.6\pm 0.5mas = 7.5 \pm 0.07 AU$ \citep{Ireland}. + This assumption implies a fixed semi-major axis. a.," This assumption implies a fixed semi-major axis, $a$." +" Note that the system configuration changes with time. thus. the d, will change. for a fixed a."," Note that the system configuration changes with time, thus, the $d_{ap}$ will change, for a fixed $a$." + In the modeling. the inner boundary. of the CD disk is circular. which is the simplest assumption.," In the modeling, the inner boundary of the CB disk is circular, which is the simplest assumption." + However. in principle ils shape can be non-axisvinnetric.," However, in principle its shape can be non-axisymmetric." + From the results of the hydrocwnamical simulations of Artwmowiez&Lubow(1996). and G&nther&lxlev.(2002).. we nole (hal in the line that connects both stars. the disk material is approaching the outer lagrangian points.," From the results of the hydrodynamical simulations of \citet{Artymowicz2} + and \citet{Gunther1}, we note that in the line that connects both stars, the disk material is approaching the outer lagrangian points." + Thus. in order (o quantily the difference between axisvimmnetric ancl non-axisvmmnietric models. we model (he shape of the wall as an ellipse wil ils seniminor axis along this line.," Thus, in order to quantify the difference between axisymmetric and non-axisymmetric models, we model the shape of the wall as an ellipse with its semiminor axis along this line." + This is an easv way to get à non-axisvmmeltrie wall. however. only a hyvdrodynamical simulation applied to svstems like Colxu Tau/4 will allow us to accurately characterize the wall.," This is an easy way to get a non-axisymmetric wall, however, only a hydrodynamical simulation applied to systems like CoKu Tau/4 will allow us to accurately characterize the wall." + Thus. the wall presented here is just one of many possibilities.," Thus, the wall presented here is just one of many possibilities." +" Fieure 19. shows models with the parameters of the fiducial configuration. but. with a semiminor axis for the CD disk of b=Ry,—(0.4.0.3.0.2.0.1.0.0)a."," Figure \ref{fig-noaxisim} shows models with the parameters of the fiducial configuration, but with a semiminor axis for the CB disk of $b=R_{cb}-(0.4,0.3,0.2,0.1,0.0)a$." + Note that the flux decreases for smaller 5. which seems unplivsieal. due to the fact that the temperature of the wall closest to the stars is larger.," Note that the flux decreases for smaller $b$, which seems unphysical, due to the fact that the temperature of the wall closest to the stars is larger." + Ilowever. the projected area perpendicular to the line of sight decreases in such a wav that the second ellect dominates the observed emission.," However, the projected area perpendicular to the line of sight decreases in such a way that the second effect dominates the observed emission." + The main result is that the changes are restricted to wavelengths longer than 120m. thus. the silicates band is not modified.," The main result is that the changes are restricted to wavelengths longer than $12\mu$ m, thus, the silicates band is not modified." + The changes are larger around. 30jan. but this is," The changes are larger around $30\mu$ m, but this is" +"In eq.(6)) Mpy 15 the Mueller matrix for the transmission of a polarizer. Myjig(9) is for the transmission (reflection) of a HWP. Spre is the Stokes vector for the emission of a polarizer (HWP). and S, the Stokes vector for the emission of the dust.","In $\,$ \ref{e6}) ) $M_{PT}$ is the Mueller matrix for the transmission of a polarizer, $M_{HT(R)}(\theta)$ is for the transmission (reflection) of a HWP, $S_{P(H)E}$ is the Stokes vector for the emission of a polarizer (HWP), and $S_d$ the Stokes vector for the emission of the dust." + With respect to the ideal case. a real HWP modifies the sstropphyssiccal polarized signal reducing the amplitude and the offfset of the transmitted signal.," With respect to the ideal case, a real HWP modifies the cal polarized signal reducing the amplitude and the fset of the transmitted signal." +" In fact. in our example the amplitude of the signal transmitted by a real HWP. AS with respect to the ideal one. ALS at GHz is APA?eas- 0.93: and. similarly. for the offset: O?..,/O?,.|;=0.93."," In fact, in our example the amplitude of the signal transmitted by a real HWP, $A^S_{real}$ , with respect to the ideal one, $A^S_{ideal}$, at $\,$ GHz is $A^S_{real}/A^S_{ideal}|_{545}=0.93$ ; and, similarly, for the offset: $O^S_{real}/O^S_{ideal}|_{545}=0.93$." +" The reduction in both the amplitude and the offset increases at high frequencies: at GHz we find. in fact: 0.88 and OP,Οἱise=0.83."," The reduction in both the amplitude and the offset increases at high frequencies; at $\,$ GHz we find, in fact: $A^S_{real}/A^S_{ideal}|_{1250}=0.88$ and $O^S_{real}/O^S_{ideal}|_{1250}=0.85$." + Our simulation for the amplitude of the signal (the offset is removed through a low pass filter) clearly shows that to increase the efficiency. of the polarimeter 1t Is necessary to cool down to cryogenic tempperratturres both the polarizer and the HWP 5)).," Our simulation for the amplitude of the signal (the offset is removed through a low pass filter) clearly shows that to increase the efficiency of the polarimeter it is necessary to cool down to cryogenic res both the polarizer and the HWP $\,$ \ref{fig:4}) )." + From (6)) the radiation emitted by the polarizer and reflected back by the HWP produces a cos4nAé- siggnal with the same phase as the astrophysical source. whe the wires of the polarizer are aligned to the polarization vector of the signal (Salatino de Bernardis. 2010)).," From $\,$ \ref{e6}) ) the radiation emitted by the polarizer and reflected back by the HWP produces a $\cos{4 n \Delta \theta}$ gnal with the same phase as the astrophysical source, when the wires of the polarizer are aligned to the polarization vector of the signal (Salatino de Bernardis, \cite{Salatino10}) )." + Depending οἱ the in-band spectrum of the incoming signal. this emissior can add to the astrophysical signal. mimicking a spurious increase of its amplitude.," Depending on the in-band spectrum of the incoming signal, this emission can add to the astrophysical signal, mimicking a spurious increase of its amplitude." + Rotating the polarizer by 35.726. this emission becomes out of phase with respect to the astrophysical signal.," Rotating the polarizer by $35.^{\circ}26$, this emission becomes out of phase with respect to the astrophysical signal." + Moreover. the pollarrizzed emission of the HWP. which directly crosses the polarizer. produces a signal modulated at 2nAé in the detected signal.," Moreover, the zed emission of the HWP, which directly crosses the polarizer, produces a signal modulated at $2 n \Delta \theta$ in the detected signal." +" The C, parameter is dominated by the temperature of the polarizer.", The $C_A$ parameter is dominated by the temperature of the polarizer. + Only if the HWP is warmer than about 10K the polarized emission from the crystal contaminates the cos4nAé@ signal.," Only if the HWP is warmer than about $\,$ K the polarized emission from the crystal contaminates the $\cos{4 n \Delta \theta}$ signal." + Given its definition. C4. includes. all the terms contributing to the signal. including any cos2A0 term.," Given its definition, $C_A$ includes all the terms contributing to the signal, including any $\cos{2n\Delta\theta}$ term." +" Moreover. the C4, parameter depends also on the cos21A0 component because the non linear behavior of incoherent detectors produces a cos4nrAé@ signal if the cos27Aé@ one is too large."," Moreover, the $C_A$ parameter depends also on the $\cos{2 +n\Delta \theta}$ component because the non linear behavior of incoherent detectors produces a $\cos{4 n \Delta \theta}$ signal if the $\cos{2 n \Delta \theta}$ one is too large." + This additional signal can be sevverral order of magnitudes larger than the dust emission., This additional signal can be ral order of magnitudes larger than the dust emission. + Given the larger emissivity of the HWP with respect to the one of the polarizer (by at least one order of magnitude) and the low reflectivity of the HWP itself. the Co parameter Is dominated by the HWP temperature.," Given the larger emissivity of the HWP with respect to the one of the polarizer (by at least one order of magnitude) and the low reflectivity of the HWP itself, the $C_O$ parameter is dominated by the HWP temperature." + We run our model for a 300K waveplate. and found that the signal produced by the HWP is 10+ times larger than the dust signal.," We run our model for a 300K waveplate, and found that the signal produced by the HWP is $10^4$ times larger than the dust signal." + This poses extreme requirements for the stabbillitty of the polarimeter. which are completely relaxed for a cryogenic waveplate.," This poses extreme requirements for the ty of the polarimeter, which are completely relaxed for a cryogenic waveplate." + Both parameters decrease with frequency., Both parameters decrease with frequency. + This is because the refraction indices and the absorption coefficients increase with frequency. but the emission of interstellar dust at 30K increases faster (at least for frequencies «1500 GHz): the net result is a decrease of the fractional disturbance.," This is because the refraction indices and the absorption coefficients increase with frequency, but the emission of interstellar dust at $\,$ K increases faster (at least for frequencies $<$ $\,$ GHz): the net result is a decrease of the fractional disturbance." + The C4 parameter (Fig.5)) decreases quickly with the polarizer temperature. and it is «0.1 for both channels when the wire grid is cooled below K. The Cy parameter. instead. decreases quickly with the HWP temperature it becomes 9.8-1077and 3.5-1077 at K. and 6.5107 and 8.5-1077 when cooling down the HWP to 4.5K (higher and lower frequency respectively).," The $C_A$ parameter $\,$ \ref{fig:4}) ) decreases quickly with the polarizer temperature, and it is $<$ 0.1 for both channels when the wire grid is cooled below $\,$ K. The $C_O$ parameter, instead, decreases quickly with the HWP temperature it becomes $\cdot10^{-4}$and $\cdot10^{-2}$ at $\,$ K, and $\cdot 10^{-5}$ and $\cdot10^{-3}$ when cooling down the HWP to $\,$ K (higher and lower frequency respectively)." + We have also checked that our results are not very sensitive to reasonable changes in the parameters of the dust spectrum., We have also checked that our results are not very sensitive to reasonable changes in the parameters of the dust spectrum. +velocity at low latitudes in the vicinity of the tachocline.,velocity at low latitudes in the vicinity of the tachocline. +" Here we examine this finding further, by seeking such a periodicity in the angular momentum or kinetic energy."," Here we examine this finding further, by seeking such a periodicity in the angular momentum or kinetic energy." + We calculate the discrete Fourier transforms of the results illustrated in Figure 2 to see whether there is a significant peak in the power spectra around a frequency of 0.75 γι]., We calculate the discrete Fourier transforms of the results illustrated in Figure 2 to see whether there is a significant peak in the power spectra around a frequency of 0.75 $^{-1}$. + The outcome is presented in Figure 6., The outcome is presented in Figure 6. +" Evidently, no such peak is apparent."," Evidently, no such peak is apparent." +" The power spectra in the vicinity of the tachocline appear to contain no particularly significant peak, although those in the upper layers of the convection zone do contain an obvious peak in the lowest frequency bin allowed in the discrete Fourier transform: this corresponds to the solar-cycle variation."," The power spectra in the vicinity of the tachocline appear to contain no particularly significant peak, although those in the upper layers of the convection zone do contain an obvious peak in the lowest frequency bin allowed in the discrete Fourier transform: this corresponds to the solar-cycle variation." +" We have looked at many different depth and latitude ranges; the results are all similar to those shown in the figure, irrespective of whether the seismic data employed were from GONG or from MDI."," We have looked at many different depth and latitude ranges; the results are all similar to those shown in the figure, irrespective of whether the seismic data employed were from GONG or from MDI." +" Therefore, apart from a possible periodicity characteristic of solar-cycle variation, we find no evidence for periodicity at any depth."," Therefore, apart from a possible periodicity characteristic of solar-cycle variation, we find no evidence for periodicity at any depth." +" For illustrative purposes, we present in Figure 7 the temporal variation in the low-latitude region of the tachocline (0.70R5xr< 0.749) in both rotational kinetic energy and angular momentum, inferred from MDI as well as GONG data."," For illustrative purposes, we present in Figure 7 the temporal variation in the low-latitude region of the tachocline $0.70R_\odot\le r\le 0.74R_\odot$ ) in both rotational kinetic energy and angular momentum, inferred from MDI as well as GONG data." + This is the region in which Howe et al. (, This is the region in which Howe et al. ( +2000b) and Komm et al. (,2000b) and Komm et al. ( +2003) found the greatest amplitude of the 1.3-year oscillations.,2003) found the greatest amplitude of the 1.3-year oscillations. +" It is clear from the figure that there is reasonable agreement between GONG and MDI data, and that the variation in angular momentum is similar to that in the rotational kinetic energy."," It is clear from the figure that there is reasonable agreement between GONG and MDI data, and that the variation in angular momentum is similar to that in the rotational kinetic energy." +" However, no significant temporal variation is evident; in particular, there is no very clear sign of a 1.3-year oscillation."," However, no significant temporal variation is evident; in particular, there is no very clear sign of a 1.3-year oscillation." +" From our inferences of the angular velocity throughout the solar interior, it is possible to calculate the quadrupole and higher-order multipole moments of the Sun's gravitational field, and study their possible temporal variation."," From our inferences of the angular velocity throughout the solar interior, it is possible to calculate the quadrupole and higher-order multipole moments of the Sun's gravitational field, and study their possible temporal variation." + Figure 8 illustrates the even-order moments J; — Jj» inferred from both GONG and MDI data., Figure 8 illustrates the even-order moments $J_2$ – $J_{12}$ inferred from both GONG and MDI data. + To ascertain whether temporal variation in these quantities is related to solar activity we have calculated the coefficients of their correlation with the 10.7 cm radio flux., To ascertain whether temporal variation in these quantities is related to solar activity we have calculated the coefficients of their correlation with the 10.7 cm radio flux. + We identify the phase of any possible solar-cycle variation by fitting to the moments sinusoids with a period of 11 years., We identify the phase of any possible solar-cycle variation by fitting to the moments sinusoids with a period of 11 years. +" The results are summarized in Table 1, in which are listed the temporal averages of the moments as well as the relative amplitudes and phases (in years, relative to the phase of the 10.7 cm radio flux) of the fitted sinusoidals."," The results are summarized in Table 1, in which are listed the temporal averages of the moments as well as the relative amplitudes and phases (in years, relative to the phase of the 10.7 cm radio flux) of the fitted sinusoidals." +" As one might expect, the quadrupole moment J» exhibits no noticeable temporal variation: the sinusoidal fits have very low (relative) amplitudes, and the phases inferred from the GONG and MDI data are different."," As one might expect, the quadrupole moment $J_2$ exhibits no noticeable temporal variation: the sinusoidal fits have very low (relative) amplitudes, and the phases inferred from the GONG and MDI data are different." + There appears to be a substantial difference between the mean value of J> calculated from the GONG and the MDI data., There appears to be a substantial difference between the mean value of $J_2$ calculated from the GONG and the MDI data. + This is most probably a result of already known differences in the splitting coefficients (Schou et al., This is most probably a result of already known differences in the splitting coefficients (Schou et al. + 2002)., 2002). + Similar differences between GONG and MDI estimates for J> were found by Pijpers (1998)., Similar differences between GONG and MDI estimates for $J_2$ were found by Pijpers (1998). + We note in passing that Emilio et al. (, We note in passing that Emilio et al. ( +"2007), using measurements by MDI, find strong variation in the figure of the Sun, which is contrary to their earlier results (Kuhn et al.","2007), using measurements by MDI, find strong variation in the figure of the Sun, which is contrary to their earlier results (Kuhn et al." +" 1998); however, most of the distortion from sphericity is the direct response to the centrifugal force on the rotating surface layers, and not from the asphericity of the gravitational field."," 1998); however, most of the distortion from sphericity is the direct response to the centrifugal force on the rotating surface layers, and not from the asphericity of the gravitational field." +" The temporal variation in the distortion observed at the solar surface is certainly associated with the magnetic field, which itself is correlated with the zonal bands of alternate fast and slow rotation, and is probably confined to layers near the surface."," The temporal variation in the distortion observed at the solar surface is certainly associated with the magnetic field, which itself is correlated with the zonal bands of alternate fast and slow rotation, and is probably confined to layers near the surface." +" Of course, the uncertainty in the estimate of the gravitational distortion obtained from the shape of the surface of the Sun is much greater than the uncertainty with which J» can be obtained from seismic measurements."," Of course, the uncertainty in the estimate of the gravitational distortion obtained from the shape of the surface of the Sun is much greater than the uncertainty with which $J_2$ can be obtained from seismic measurements." + Kuhn et al. (, Kuhn et al. ( +"1998) found significant temporal variation in the P4(cos0) component of distortion at the solar surface, although their errors are much larger in this component.","1998) found significant temporal variation in the $P_4(\cos\theta)$ component of distortion at the solar surface, although their errors are much larger in this component." +" Accordingly, we seek a corresponding variation in Jy."," Accordingly, we seek a corresponding variation in $J_4$." +" It appears in Figure 8 that there is indeed some systematic variation, for inferences from both GONG and MDI data behave similarly"," It appears in Figure 8 that there is indeed some systematic variation, for inferences from both GONG and MDI data behave similarly." +" However, the amplitude of the sinusoid fitted to the GONG data is only about of that of the corresponding MDI sinusoid, and, moreover, the phases differ by about 1.3 years."," However, the amplitude of the sinusoid fitted to the GONG data is only about of that of the corresponding MDI sinusoid, and, moreover, the phases differ by about 1.3 years." +" The correlation coefficients between the inferred values of J4 and the 10.7 cm radio flux are only 0.29 and 0.51 for GONG and MDI data respectively, although these quite low values appear to be a consequence mainly of the phase difference."," The correlation coefficients between the inferred values of $J_4$ and the 10.7 cm radio flux are only $0.29$ and $0.51$ for GONG and MDI data respectively, although these quite low values appear to be a consequence mainly of the phase difference." +" However, the results do suggest that J4 may undergo temporal variation with an amplitude of about 10719, which is of the mean, and that this variation is correlated with solar activity."," However, the results do suggest that $J_4$ may undergo temporal variation with an amplitude of about $10^{-10}$, which is of the mean, and that this variation is correlated with solar activity." + The variation is much less than, The variation is much less than +WNNS wind. so for simplicity we use WANS euissivities for both winds.,"WN8 wind, so for simplicity we use WN8 emissivities for both winds." + As Leywn>Loop. this has little effect ou the resulting cussion.," As $L_{\rm cw,WN} \gg L_{\rm cw,OB}$, this has little effect on the resulting emission." + We also incorporate the IIRC-I effective area frou data distributed with the PIAIAIS ποιαος COCLO. and assume a distance of 650 pe (Morris 2000)).," We also incorporate the HRC-I effective area from data distributed with the PIMMS source code, and assume a distance of 650 pc (Morris \cite{M2000}) )." + The size iu degrees of cach cell iu the livdrodyuanic eid varies with each 1nodel for mode cw.22 cach cell is 2.112ς10° degrees square)., The size in degrees of each cell in the hydrodynamic grid varies with each model for model 2 each cell is $2.142 \times 10^{-6}$ degrees square). + Each IIRC-I pixel is 3.66&10/7 degrees square. so for mode 22 cach IIRC-I pixel covers the same area of skv as 292 lydrodvuamic cells.," Each HRC-I pixel is $3.66 \times 10^{-5}$ degrees square, so for model 2 each HRC-I pixel covers the same area of sky as 292 hydrodynamic cells." + We have therefore rebiunec the svuthetic nuages to the same scale as the URC-I pixels. and have positioucd the WR star at coordinates (20360.61.ιο21 07.1). to match. the ceutrok position of the radio contours in Fie. 2..," We have therefore rebinned the synthetic images to the same scale as the HRC-I pixels, and have positioned the WR star at coordinates $20\;36\;43.64,\;\;+40\;21\;07.4$ ), to match the centroid position of the radio contours in Fig. \ref{fig:xrayradio}." + The companion star has been set at a position angle of 351° from the WR- W97 and N98)., The companion star has been set at a position angle of $351^{\circ}$ from the WR-star W97 and N98). + All images are convolved with a Cassia profile of 0.I EWIIM to approximate the ITRC-I PSF., All images are convolved with a Gaussian profile of $0.4\arcsec$ FWHM to approximate the HRC-I PSF. + Fig., Fig. + 1 shows the svuthetic nuages from each lydrodvuaiic model assuming a5 ksec exposure., \ref{fig:comb_lincont} shows the synthetic images from each hydrodynamic model assuming a 5 ksec exposure. + For ease of comparison. cach inage has the same field of view as Fig.," For ease of comparison, each image has the same field of view as Fig." + 2 and the same coutour levels contours linearly spaced by 0.366 cts}., \ref{fig:xrayradio} and the same contour levels contours linearly spaced by 0.366 cts). + The muuber of counts m each dace is listed in Table 2.., The number of counts in each image is listed in Table \ref{tab:models}. + The coutoirs of the actual observation in Fie., The contours of the actual observation in Fig. + 2 have a small additional broadening through our use of CSMOO'TIL which is estimated to result in a total uet suoothing of approximately 0.12” PWHAL.," \ref{fig:xrayradio} have a small additional broadening through our use of CSMOOTH, which is estimated to result in a total net smoothing of approximately $0.42\arcsec$ FWHM." + Therefore this showld not overly affect he comparison., Therefore this should not overly affect the comparison. + Tιο offset mentioned m Sec., The offset mentioned in Sec. +2. has again been applied.,\ref{sec:analysis} has again been applied. + Of iuuuediate note is the eratifvine fact that the predicte FEWIIM from the svuthetic nuages (220.7. 0.87) is in rough agreement with the value inferred roni the data in Sec. 2.., Of immediate note is the gratifying fact that the predicted FWHM from the synthetic images $\approx 0.7-0.8\arcsec$ ) is in rough agreement with the value inferred from the data in Sec. \ref{sec:analysis}. + We also note that it appears to correlate with j aud 7., We also note that it appears to correlate with $\eta$ and $i$. + The range iu model luminosity is appareut from the wmmber and extent of the contour levels in cach Huaec. and it is evident that model cw_ll is too bright and model ew_99 too faint.," The range in model luminosity is apparent from the number and extent of the contour levels in each image, and it is evident that model 1 is too bright and model 9 too faint." + Because of the selt-consisteut eeneration of cach model. the position of the peak emission los at approximately the same coordinates in cach image.," Because of the self-consistent generation of each model, the position of the peak emission lies at approximately the same coordinates in each image." + However. the contours appear more circular and more ub xiehteued for higher values of the system inclination. 7 (sce also Fig. 5)).," However, the contours appear more circular and more limb brightened for higher values of the system inclination, $i$ (see also Fig. \ref{fig:xeus_comb}) )." + For instance. models 33 aud ll ave essentially the same count rate. vet he emission from nodel ll is much more couceutrated as witnessed by its larger number of contours.," For instance, models 3 and 4 have essentially the same count rate, yet the emission from model 4 is much more concentrated as witnessed by its larger number of contours." + The difference iu the concentration of the emission vetween the models is best illustrated through profiles across the shock cone as shown in Fie. 5. , The difference in the concentration of the emission between the models is best illustrated through profiles across the shock cone as shown in Fig. \ref{fig:xeus_comb}. . +The profile is clearly broader with duereased i aud increased /., The profile is clearly broader with increased $\eta$ and increased $i$. + While this width can only be used iu comparison with observations to determine some combination of jg and { (they cannot be deteriuned independently frou this coluparison alone). it is perhaps possible for these to be uniquely. determined if further additional comparisons between the models aud the data are made.," While this width can only be used in comparison with observations to determine some combination of $\eta$ and $i$ (they cannot be determined independently from this comparison alone), it is perhaps possible for these to be uniquely determined if further additional comparisons between the models and the data are made." + For instance. the normalization of the profile is dependent ou tle X- luminosity from the colliding WNS wind. since the shocked WR wind dominates the total colliding winds X- huniuositv.," For instance, the normalization of the profile is dependent on the X-ray luminosity from the colliding WN8 wind, since the shocked WR wind dominates the total colliding winds X-ray luminosity." + With fixed values for Afws aud cx... and since the shocked WNS wind is largely adiabatic. Lex:κ FAD.," With fixed values for $\Mdot_{\rm WN}$ and $v_{\infty_{\rm WN}}$, and since the shocked WN8 wind is largely adiabatic, $L_{\rm cw} \propto f/D$ ." + Were f is a measure of the shape of the wi-wind collisiou (aud so is a function of 5j). aud the separation of tle stars; D. is related to the seperation ont10 sky. Dau by Doa=Dassin.," Here $f$ is a measure of the shape of the wind-wind collision (and so is a function of $\eta$ ), and the separation of the stars, $D_{\rm sep}$, is related to the seperation on the sky, $D_{\rm sky}$, by $D_{\rm sep} = D_{\rm sky}/{\rm sin}\;i$." + Hence Ley is a (complicated) function of jj aud 7. The width of the euission audthe luuinosity therefore vield two constraiuts on two uuknuowus. audia principle jg od i may be determined.," Hence $L_{\rm cw}$ is a (complicated) function of $\eta$ and $i$ The width of the emission andthe luminosity therefore yield two constraints on two unknowns, andin principle $\eta$ and $i$ may be determined." + We note that the observed circularity of the emission also appears to vary. and if may," We note that the observed circularity of the emission also appears to vary, and it may" +"n, being the electron number density.",$n_{e}$ being the electron number density. +" For the ""Fe plasma with Z=26. we have ρα [rom equation (10)."," For the $^{56}$ Fe plasma with $Z$ =26, we have $k_{FT} a_{I}$ =0.548 from equation (10)." + IIubbard Slattery (1971) have carried out a Monte Carlo simulation of the ions screened with the dielectric function of the electron liquid., Hubbard Slattery (1971) have carried out a Monte Carlo simulation of the ions screened with the dielectric function of the electron liquid. + They have shown that for πα<0.5 the results that take into account the electron dielectric function are close to the results corresponding to (he ions imbedded in the negative background., They have shown that for $k_{FT} a_{I} \lesssim 0.5$ the results that take into account the electron dielectric function are close to the results corresponding to the ions imbedded in the negative background. + Therefore. we are justified in using the liquid structure [factor corresponding to the ions imbedded in the negative background. (classical one-component plasma).," Therefore, we are justified in using the liquid structure factor corresponding to the ions imbedded in the negative background (classical one-component plasma)." + In this paper we use the liquid structure [actor of the classical one-component plasma calculated. by. Ichimaru. Ivetomi. Tanaka (1957) using the improved hvpernetted-chain scheme.," In this paper we use the liquid structure factor of the classical one-component plasma calculated by Ichimaru, Iyetomi, Tanaka (1987) using the improved hypernetted-chain scheme." + Thev have presented a numerical table for D—2. 5. 10. 20. 40. 80. 125. ancl 160.," They have presented a numerical table for $\Gamma$ =2, 5, 10, 20, 40, 80, 125, and 160." + We supplement (his table by the table presented in Itoh et al. (, We supplement this table by the table presented in Itoh et al. ( +1983) by using the same method [or the case of P=1.,1983) by using the same method for the case of $\Gamma$ =1. + In passing. it should be noted that those who wish to calculate the anele-dependent cross section should use the tables of the liquid structure factor 5(/) presented in Ichimaru. Ivetomi. Tanaka (1987) and also in Hoh et al. (," In passing, it should be noted that those who wish to calculate the angle-dependent cross section should use the tables of the liquid structure factor $S(k)$ presented in Ichimaru, Iyetomi, Tanaka (1987) and also in Itoh et al. (" +1983).,1983). + Constructing analvtie fitting formulae for SCA) would be extremely difficult. since (4) has oscillatory behavior.," Constructing analytic fitting formulae for $S(k)$ would be extremely difficult, since $S(k)$ has oscillatory behavior." + It would be best (o use numerical (ables rather than analvtice fitting formulae lor 5(k)⋅, It would be best to use numerical tables rather than analytic fitting formulae for $S(k)$. + ↕∐∏≸↽↔↴⋯⋅≼↲⊋∖���⇁↩⋟∖⊽∐⋯∖⇁⊔∐↲↕⋅≼↲⋟∖⊽∏∐⋟∖⊽∪↓⋟⊔∐↲≺∢≀↧↴↥≺∢∏↥≀↧↴∐∪∐↓⋟∪↕⋅∣⇆⊽∕∖∕∖↕∐≼↲≺⇂, In Figure 2 we show the results of the calculation for $$ in equation (15). +∏≀↕↴∐∪∐⊔⇀↱≻↕⋟⋅↼≚⋟∖⊽↕∐↕∐≀↧↴↕⋅ ≸↽↔↴↕⋅≀↕↴↕↽≻∐∐≀↧⊔∖⊽∣↽≻≼↲≼↲∐↕↽≻↕⋅≼↲⋟∖⊽≼, A similar graph has been presented in Bruenn Mezzacappa (1997). +↲∐∩↲≺⇂↕∐∐↕⋅⋯↲∐∐≪↽∖↽⇀∖↕≼↲∠∠≀↧↴≺∢≀↧↴↕↽≻↕↽≻≀↧↴⊔≤∍≤∏↕⋝⋅↴⊺↥∐↲⋡∖↽∐≀↧↴∖↽≼↲∏⋟∖⊽≼↲≼⇂∐∪↕⋅∪∖∖⊽∐∠∎⋟∖⊽≼⊥≤∍≤∍⊤∓⋝ fitting formula., They have used Horowitz's (1997) fitting formula. + In Figuree 3 we compare our results with Ilorowitz's fittinge formula., In Figure 3 we compare our results with Horowitz's fitting formula. + We find that llorowitz's results for e<1.0 greatlv diller from our results., We find that Horowitz's results for $\epsilon \leq 1.0$ greatly differ from our results. + It appears that this is due to (he inaccurate treatment done by Horowitz to caleuate the small- behavior of (he liquid structure [actor S(5) that cannot be directly obtained from the Monte Carlo results because ol the finite size of the simulation., It appears that this is due to the inaccurate treatment done by Horowitz to calcuate the $k$ behavior of the liquid structure factor $S(k)$ that cannot be directly obtained from the Monte Carlo results because of the finite size of the simulation. + We have used the correct small- (e;À 1) behavior of the liquid structure factor (Ichimaru 1982: Πο et al., We have used the correct $k$ $a_{I}k < 1$ ) behavior of the liquid structure factor (Ichimaru 1982; Itoh et al. + 1983): We [ind that the present more accurate caleulation leads (o a more dramatic reduction of the neutrino-nucleus scattering cross section lor ex1.0 than has been caleulated by, 1983): We find that the present more accurate calculation leads to a more dramatic reduction of the neutrino-nucleus scattering cross section for $\epsilon \leq 1.0$ than has been calculated by +and 100 mJy at 7 and θα wavelengths. respectively.,"and 100 mJy at 7 and 13mm wavelengths, respectively." + A more detailed view of Haring activity, A more detailed view of flaring activity +the dark energy density plays a role in observable quantities. and as a corollary. until what epoch one can hope to reconstruct either its energy density or its equation of state parameter.,"the dark energy density plays a role in observable quantities, and as a corollary, until what epoch one can hope to reconstruct either its energy density or its equation of state parameter." + As we have seen in section 3.. the SNla Hubble diagram poorly constrains a possible transition epoch in the equation of state of the dark energy component.," As we have seen in section \ref{secanalysis}, the SNIa Hubble diagram poorly constrains a possible transition epoch in the equation of state of the dark energy component." + As we have stated. this appears somewhat paradoxical as data extending up to redshift 2 fail to reveal a transition occurring at redshifts as low as 0.25. at which the dark energy component is still dominant.," As we have stated, this appears somewhat paradoxical as data extending up to redshift 2 fail to reveal a transition occurring at redshifts as low as 0.25, at which the dark energy component is still dominant." +" Indeed. in a model with Qo=0.7. €,=0.3 today. with weconstant and equal to —|. the matter to dark energy transition. defined when Oo(z)=QC)= 0.5. occurs at redshift z,=ο—]~0.33."," Indeed, in a model with $\Omega_\QUINT = 0.7$, $\Omega_\MAT += 0.3$ today, with $w_\QUINT$constant and equal to $-1$, the matter to dark energy transition, defined when $\Omega_\QUINT (z) += \Omega_\MAT(z) = 0.5$ , occurs at redshift $z_e = (\Omega_\QUINT / +\Omega_\MAT)^{\frac{1}{3}} - 1 \sim 0.33$." + Let us now consider two alternatives., Let us now consider two alternatives. + First. we can consider a pure cosmological constant model. with we=—1 also at early times.," First, we can consider a pure cosmological constant model, with $w_\QUINT = -1$ also at early times." + Second. we can consider a model where wo~O for 2>z2z.," Second, we can consider a model where $w_\QUINT \sim 0$ for $z > z_\TRANS = z_e$." +" In the first case. one has a usual ACDM model. whereas in the second ease. one has a model close to a flat Einstein- Sitter model at epoch z>z,."," In the first case, one has a usual $\Lambda$ CDM model, whereas in the second case, one has a model close to a flat Einstein-de Sitter model at epoch $z > z_e$." + An observer at z=σι should easily be able to distinguish between the two models. just as we are able to distinguish between à ACDM with Qo=0.5 and a flat Einstein-de Sitter model today.," An observer at $z = z_\TRANS$ should easily be able to distinguish between the two models, just as we are able to distinguish between a $\Lambda$ CDM with $\Omega_\QUINT += 0.5$ and a flat Einstein-de Sitter model today." + Now. are we able to distinguish today between these two models. which differ only in z>z?," Now, are we able to distinguish today between these two models, which differ only in $z > +z_\TRANS$?" + Surprisingly. the answer is no 1f one considers supernovae data only. as is convincingly illustrated by Fig.2..," Surprisingly, the answer is no if one considers supernovae data only, as is convincingly illustrated by \ref{fig:HD}." + The explanation of this apparent paradox is as follows., The explanation of this apparent paradox is as follows. + Present data favour dark energy because high redshift supernovae are dimmer than expected in a flat Einstein-de Sitter universe., Present data favour dark energy because high redshift supernovae are dimmer than expected in a flat Einstein-de Sitter universe. + This is usually expressed as a difference of magnitude between the two models one considers for some standard candle at some redshift. the exact value of which depend on the quality of the data.," This is usually expressed as a difference of magnitude between the two models one considers for some standard candle at some redshift, the exact value of which depend on the quality of the data." + The magnitude is essentially the logarithm of the luminosity distance as a function of the redshift., The magnitude is essentially the logarithm of the luminosity distance as a function of the redshift. +" Let us define dM) and dz) the luminosity distance as a function of the redshift in à ACDMmodel with Q4.=Q,,0.5 today. and in à flat Einstein-de Sitter model."," Let us define $d_L^\Lambda(z)$ and $d_L^{\rm EdS}(z)$ the luminosity distance as a function of the redshift in a $\Lambda$ CDMmodel with $\Omega_\Lambda = \Omega_\MAT = 0.5$ today, and in a flat Einstein-de Sitter model." + Let us assume these two models can be distinguished., Let us assume these two models can be distinguished. +" Let us now consider dz) and do) the luminosity distance rredshift relation in à ACDM modelwith Q,=0.7. Q,,=0.3 today. and a dark energy model with οὐ= 0.7. Q,,=0.3 today. with wo experiencing a sudden transition from 0 to 21 at z= z."," Let us now consider $\tilde +d_L^\Lambda(z)$ and $d_Q(z)$ the luminosity distance redshift relation in a $\Lambda$ CDM modelwith $\Omega_\Lambda = 0.7$, $\Omega_\MAT = 0.3$ today, and a dark energy model with $\Omega_Q = +0.7$ , $\Omega_\MAT = 0.3$ today, with $w_\QUINT$ experiencing a sudden transition from $0$ to $-1$ at $z = z_\TRANS$ ." + An observer at z=τι would therefore measure either dz or qz)., An observer at $z = z_\TRANS$ would therefore measure either $d_L^\Lambda(z')$ or $d_L^{\rm EdS} (z')$ . + The epoch corresponding to a redshift of Z (18)). 6.., The epoch corresponding to a redshift of $z'$ \ref{dmt}) \ref{figcomp}. +Thus. ὃς can be estimated. by combining a measured timescale with statistical information about caustic orientations and velocities.,"Thus, $S_{s}$ can be estimated by combining a measured timescale with statistical information about caustic orientations and velocities." + Eqn 3 demonstrates a systematic uncertainty in our determination of source size that is proportional to the uncertainty in the estimate of the event duration., Eqn \ref{size} demonstrates a systematic uncertainty in our determination of source size that is proportional to the uncertainty in the estimate of the event duration. + Eqn 3 defines our measure of source size. however its interpretation is dependent on the intensity profile of the source.," Eqn \ref{size} defines our measure of source size, however its interpretation is dependent on the intensity profile of the source." + The lower panel in Fig., The lower panel in Fig. + 3. shows an example of an extended: source light-curve for image A (54= 10.4) computed using the method described in Wyithe Webster 9)., \ref{cross} shows an example of an extended source light-curve for image A $\gamma_{A}=+0.4$ ) computed using the method described in Wyithe Webster (1999). + One half ofa double peaked event is highlighted bv a »ox and reproduced in the top panel of Fig., One half of a double peaked event is highlighted by a box and reproduced in the top panel of Fig. + 3. for two source intensity profiles: a Gaussian profile(light line) and a top-iat. profile (clark line)., \ref{cross} for two source intensity profiles: a Gaussian profile (light line) and a top-hat profile (dark line). + Cross-sections of the intensity. profiles are shown in the central panel of Fig., Cross-sections of the intensity profiles are shown in the central panel of Fig. + 3. and comparison of hese with the corresponding λος demonstrates that ος is approximately the source diameter for à top-hat source olile. but twice the half width S; for a Gaussian profile.," \ref{cross} and comparison of these with the corresponding HMEs demonstrates that $S_{s}$ is approximately the source diameter for a top-hat source profile, but twice the half width $S_{s}$ for a Gaussian profile." + Probability distributions for normal caustic velocity pou|imsenuus) ave computed assuming various. values Or ic galactic transverse. velocity.," Probability distributions for normal caustic velocity $p_{c}(v_{\perp}\,|\,\langle m\rangle,v_{tran})$ are computed assuming various values for the galactic transverse velocity." +" By differentiating the cumulative distribution. «(V to which clusteringὃν alfects the method.," Deeper IR surveys will provide more accurate knowledge of $\omega(\theta)$ on arcminute scales, allowing us to better understand the degree to which clustering affects the method." + Future studies. of clusters with wide-field optical-infrarecl cata (e.g. with the VISTA telescope. //www-star.qmw.ac.uk/~jpe/vista)) covering a wide wavelength range could. provide more accurately selected background: populations via photometric redshifts and allow us to add another sample of independent mass profiles to be compared. with those derived. from. velocity dispersions. X-rav measurements. and strong and weak lensing.," Future studies of clusters with wide-field optical-infrared data (e.g. with the VISTA telescope, ) covering a wide wavelength range could provide more accurately selected background populations via photometric redshifts and allow us to add another sample of independent mass profiles to be compared with those derived from velocity dispersions, X-ray measurements, and strong and weak lensing." + The problem. posed by the uncertainty in the backeround number counts can be overcome by selecting similar clusters (e.g. by their A-rav temperatures) and stacking the depletion signal accordinglv to obtain an average cluster mass profile: a feasible project for future I1 survey telescopes., The problem posed by the uncertainty in the background number counts can be overcome by selecting similar clusters (e.g. by their X-ray temperatures) and stacking the depletion signal accordingly to obtain an average cluster mass profile; a feasible project for future IR survey telescopes. + We thank. Peter. Schneider. Lindsav Wing. Ancy Tavlor and νοημα Wuijken for useful discussions. and Felipe Alenanteau [for assistance with the CISSEL9G mocdels.," We thank Peter Schneider, Lindsay King, Andy Taylor and Konrad Kuijken for useful discussions, and Felipe Menanteau for assistance with the GISSEL96 models." + The Cambridge. Infrared Survey. Instrument. is. available thanks to the generous support of Itavmond. and. Beverly sackler., The Cambridge Infrared Survey Instrument is available thanks to the generous support of Raymond and Beverly Sackler. + ALEC wishes to acknowledge the support of the Canadian: Cambridge Trust and the Worshipful Company of Scientific Instrument Makers., MEG wishes to acknowledge the support of the Canadian Cambridge Trust and the Worshipful Company of Scientific Instrument Makers. + AR) was supported by the European Ελ Lensing network and. by a Wolfson College Fellowship., AR was supported by the European TMR Lensing network and by a Wolfson College Fellowship. + This. research has been conducted under the auspices of the European “PAIR network “Gravitational Lensing: New Constraints on Cosmology and the Distribution of Dark Alatter”. macle possible via generous financial support from the European Commission The likelihood. function for the lensing depletion has been derived. by SINE. for the case of a complete sample of background galaxies.," This research has been conducted under the auspices of the European TMR network “Gravitational Lensing: New Constraints on Cosmology and the Distribution of Dark Matter”, made possible via generous financial support from the European Commission The likelihood function for the lensing depletion has been derived by SKE, for the case of a complete sample of background galaxies." + Llere we generalize their results to include the οσοι of incompleteness in the sample., Here we generalize their results to include the effect of incompleteness in the sample. +pulsation code. LNA. (Castor1971).. modified to allow a ganna law gas. is nuposed so that the model pulsates around the equilibria poiut in either the fundamental or the first overtouc modes.,"pulsation code, LNA, \citep{Castor-1971}, modified to allow a gamma law gas, is imposed so that the model pulsates around the equilibrium point in either the fundamental or the first overtone modes." + The simulation volume is separated iuto cells bounded by intersecting surfaces., The simulation volume is separated into cells bounded by intersecting surfaces. + These surfaces are defined at coustant values of the three independeut variables AL... 0. aud o.," These surfaces are defined at constant values of the three independent variables $M_r$, $\theta$, and $\phi$ ." + Dependent quantities p. E. aud P are defined. at cell ceuters and depeudeut quantities r. C4. tur. Co. and co are defined at appropriate cell interfaces.," Dependent quantities $\rho$, $E$, and $P$ are defined at cell centers and dependent quantities $r$, $v_r$, $v_{0r}$, $v_\theta$, and $v_\phi$ are defined at appropriate cell interfaces." + The models used for testing have 107 radial. 10 theta. aud 10 phi zoues.," The models used for testing have 107 radial, 10 theta, and 10 phi zones." + The inner 10 radial zones are haucdled in 1D as discussed in 82., The inner 10 radial zones are handled in 1D as discussed in \ref{sec:HERLS}. + The zoue uuuber at which the switch between LD and 3D is made is chosen by the user., The zone number at which the switch between 1D and 3D is made is chosen by the user. + For the test cases used in this paper the tota lass of he star was 0.575 M. with an initial mass spaciug of L5«109 M. at the surface. and increasing by each shell into the star.," For the test cases used in this paper the total mass of the star was 0.575 $_\sun$, with an initial mass spacing of $4.5\times 10^{-9}$ $_\sun$ at the surface, and increasing by each shell into the star." + Both the 0 and o zones have a spacing of l.so that the total simulation volume covers 100 square degrees.," Both the $\theta$ and $\phi$ zones have a spacing of $^\circ$, so that the total simulation volume covers 100 square degrees." + The equations outlined in 82.1. are in differential form and are approxinated by appropriate finite difference expressions., The equations outlined in \ref{sec:cons-eqs} are in differential form and are approximated by appropriate finite difference expressions. +" Spatial differcutials are approximated bw differeuces between quantities at either cell ceuters or cell interfaces: depeuding ou whether the quantity being""T updated im time is interface ceutered or cell centered. respectively."," Spatial differentials are approximated by differences between quantities at either cell centers or cell interfaces depending on whether the quantity being updated in time is interface centered or cell centered, respectively." + Temporal differentials are approximated by differences between the current erid state and the updated erid state divided by the time step. Af. computed asa fraction of the ΙΙΙ time step allowed by the Courant condition for the model as a whole.," Temporal differentials are approximated by differences between the current grid state and the updated grid state divided by the time step, $\Delta t$, computed as a fraction of the minimum time step allowed by the Courant condition for the model as a whole." + This then allows us to explicitly solve for the updated erid state given the current erid state and the time step., This then allows us to explicitly solve for the updated grid state given the current grid state and the time step. + Equation (10)) is written in finite volume form with fluxes defined at cel faces., Equation \ref{eq:mass-cons-fv}) ) is written in finite volume form with fluxes defined at cell faces. + The velocities required for these fluxes are already interface centered: however. the densities are not.," The velocities required for these fluxes are already interface centered; however, the densities are not." + In eeneral quantities that are needed at interfaces but defined at cell centers. aud quantities that are needed at cell centers but defined at interfaces are approximated by averages of adjaceut quantities.," In general, quantities that are needed at interfaces but defined at cell centers, and quantities that are needed at cell centers but defined at interfaces are approximated by averages of adjacent quantities." + We lave used artificial viscosity given by to smooth out shocks with a threshold velocity of onc-hundredth of the local sound specd for turning on the artificial viscosity aud have used weighted donor cell to stabilize advection ternis. with a weight of 0.1 on the upwind terms aud 0.9 for ceutered terms.," We have used artificial viscosity given by to smooth out shocks with a threshold velocity of one-hundredth of the local sound speed for turning on the artificial viscosity and have used weighted donor cell to stabilize advection terms, with a weight of 0.1 on the upwind terms and 0.9 for centered terms." + The order of calculation follows that of Deupree(LO77aj) with a few iuinor modifications., The order of calculation follows that of \cite{Deupree-1977a} with a few minor modifications. + We start by updating the three velocities using equations (3... {νι aud 5)) from time iL/2 ton |2 usine quantities at (p. Gp). rand 2) aud quantities at Dol2 Ce. 0. 0o. and eo}.," We start by updating the three velocities using equations \ref{eq:rad-mom-cons}, \ref{eq:theta-mom-cons}, and \ref{eq:phi-mom-cons}) ) from time $n-1/2$ to $n+1/2$ using quantities at $n$ $\rho$, $\langle\rho\rangle$, $r$, and $P$ ) and quantities at $n-1/2$ $v_r$ , $v_{r0}$ $v_\theta$, and $v_\phi$ )." + Next the exid velocity is caleulatec at time »|1/2 using equation (15)) working from inner boundary of the model to the surface in a recursive manner., Next the grid velocity is calculated at time $n+1/2$ using equation \ref{eq:rad-grid-vel}) ) working from inner boundary of the model to the surface in a recursive manner. + The updated radius Is coniputec with equation (7))., The updated radius is computed with equation \ref{eq:r-update}) ). + The cusityv ds updated ποια 5 to 9|1 using the equation for lnass conservation (eq. [LO|)).," The density is updated from $n$ to $n+1$ using the equation for mass conservation (eq. \ref{eq:mass-cons-fv}] ])," +" with quautities at n Cp andr). aud quantities atv |1/2 ορ. 0,9. Co. alle to)."," with quantities at $n$ $\rho$ and $r$ ), and quantities at $n+1/2$ $v_r$, $v_{r0}$, $v_\theta$, and $v_\phi$ )." + The euergv is updated in a similar manner., The energy is updated in a similar manner. + The equation of state then allows us to conrpute the pressure at the new time step from the updated density aud specific internal energy., The equation of state then allows us to compute the pressure at the new time step from the updated density and specific internal energy. + The code we have developed to perform these calculations has been uamed SPIIERLS (Stellar Pulsation with a lIlorizoutal Eulerian Radial Lagrangian Scheme)., The code we have developed to perform these calculations has been named SPHERLS (Stellar Pulsation with a Horizontal Eulerian Radial Lagrangian Scheme). + SPIIERLS has Όσο designed Toni 16 beginning to allow for parallel calculatious using MPI protocols., SPHERLS has been designed from the beginning to allow for parallel calculations using MPI protocols. + The parallel design allows or domain decomposition in all three directions with ie ability to vary the umuber of ghost cells (used to express the boundary couditions of the ocal domain) copied from other processors., The parallel design allows for domain decomposition in all three directions with the ability to vary the number of ghost cells (used to express the boundary conditions of the local domain) copied from other processors. + Note hat boundary coucitious in this sense are not he global boundary conditions of the calculation »t onlv the information required from other oxocessors to be able to perform the calculations ou the processor iu question., Note that boundary conditions in this sense are not the global boundary conditions of the calculation but only the information required from other processors to be able to perform the calculations on the processor in question. + Equations (3)). C1). (53). (6)). (103). depend ou onlylocal quantities and are casily applied to the local erids ou each processor.," Equations \ref{eq:rad-mom-cons}) ), \ref{eq:theta-mom-cons}) ), \ref{eq:phi-mom-cons}) ), \ref{eq:E-cons}) ), \ref{eq:mass-cons-fv}) ) depend on onlylocal quantities and are easily applied to the local grids on each processor." + The equation to calculate the exid velocity (eq. |15]]), The equation to calculate the grid velocity (eq. \ref{eq:rad-grid-vel}] ]) + requires information across all jo and & spaces, requires information across all $j$ and $k$ space. + Usiug this equation with domain decomposition in the y aud & directions would require additional message passingwhich has not vet been naploeimiented. and thus currently limits," Using this equation with domain decomposition in the $j$ and $k$ directions would require additional message passingwhich has not yet been implemented, and thus currently limits" +about 4 arcsec south of the nucleus in their44/57 NICALOS colour index map.,about 4 arcsec south of the nucleus in their WFPC2--NICMOS colour index map. + We see a multi-armed spiral pattern in our images (Fig., We see a multi-armed spiral pattern in our images (Fig. + 28). in agreement with ltegan Alulehaey (1999) who describe he global morphology of this galaxy as multi-armed.," 2g), in agreement with Regan Mulchaey (1999) who describe the global morphology of this galaxy as multi-armed." + There is a lot of structure in our ground-based. images. but a detailed comparison with the colour index maps obtained by τοσα Mulchaey. (1999) is cillieult due to the lower spatial resolution of our images.," There is a lot of structure in our ground-based images, but a detailed comparison with the colour index maps obtained by Regan Mulchaey (1999) is difficult due to the lower spatial resolution of our images." + TheS57 NUR image (Fig., The NIR image (Fig. + 1) is he one used by Reean Mulchaey. ancl shows the rather aunt spiral structure in the CNR.," 1) is the one used by Regan Mulchaey, and shows the rather faint spiral structure in the CNR." + Our colour index map shows that this galaxy has a small red nucleus. classified as S32.," Our colour index map shows that this galaxy has a small red nucleus, classified as Sy2." + The ellipticity of the isophotes reaches a maximum at a racius of 9 aresec., The ellipticity of the isophotes reaches a maximum at a radius of 9 arcsec. + This could correspond to a ring. a small bar or a triaxial bulec.," This could correspond to a ring, a small bar or a triaxial bulge." + The radial colour profiles C/.—AN and ff A) follow a characteristic shape. becoming very red close to the nucleus. with the colour most likely due to emission from dust heated by the AGN radiation field.," The radial colour profiles $J-K$ and $H-K$ ) follow a characteristic shape, becoming very red close to the nucleus, with the colour most likely due to emission from dust heated by the AGN radiation field." + The colours become bluer until a certain radius (the location of the ring). after which they remain constant.," The colours become bluer until a certain radius (the location of the ring), after which they remain constant." + Such a profile shape is onlv seen in the AGNs of our sample., Such a profile shape is only seen in the AGNs of our sample. + Ehe cdillerence in colour between the nucleus and the ring radius is about 0.2 magnitudes in both J Nand liWy., The difference in colour between the nucleus and the ring radius is about 0.2 magnitudes in both $J-K$ and $H-K$. + Buta Crocker (1903) classify this galaxv as having a nuclear ring. based on their Lla data.," Buta Crocker (1993) classify this galaxy as having a nuclear ring, based on their $\alpha$ data." + Elmegreen οἱ al. (, Elmegreen et al. ( +1997). using Nllt. observations. did not detect any ring.,"1997), using NIR observations, did not detect any ring." + According to them. the ring consists of very young stars which do not show up in the NIB.," According to them, the ring consists of very young stars which do not show up in the NIR." + However. we can see a well-defined ring in our JA and dfA images (Fig.," However, we can see a well-defined ring in our $J-K$ and $H-K$ images (Fig." + 2h)., 2h). + There is a pair of dust lanes which connect the bar to the nuclear ring in the south and north., There is a pair of dust lanes which connect the bar to the nuclear ring in the south and north. + Phe reddest colours are seen where the dust lanes merge with the nuclear ring., The reddest colours are seen where the dust lanes merge with the nuclear ring. + Colina et al. (, Colina et al. ( +1997). present a UV. (~ 2200A)).LST image of the CNR of NGC 4303. which shows spiral structure outlining massive SE. continuing all the way into the unresolved: core on the NE side of the nucleus.,"1997) present a UV $\sim2200$ ) image of the CNR of NGC 4303, which shows spiral structure outlining massive SF, continuing all the way into the unresolved core on the NE side of the nucleus." + The UV SE spiral is strongest on the side opposite to where we see the largest concentrations of dust (darkest patches in bie., The UV SF spiral is strongest on the side opposite to where we see the largest concentrations of dust (darkest patches in Fig. + 2h) in our NIR colour index maps., 2h) in our NIR colour index maps. + Our5T H-band image shows some spiral structure in the NER but emission is dominated by the central bulge component., Our $H$ -band image shows some spiral structure in the NIR but emission is dominated by the central bulge component. + There are strong isophotal twists within the central 7 aresec. and a possible nuclear bar with a radius of 2 aresec," There are strong isophotal twists within the central 7 arcsec, and a possible nuclear bar with a radius of 2 arcsec" +The investigation of stellar populations is very important to understand the formation and evolution of our Galaxy.,The investigation of stellar populations is very important to understand the formation and evolution of our Galaxy. + The Milky Way (MW) has a composite structure with several subsystems., The Milky Way (MW) has a composite structure with several subsystems. + The main three stellar populations of the MW in the solar neighborhood are the thin disk. thick disk. and the halo.," The main three stellar populations of the MW in the solar neighborhood are the thin disk, thick disk, and the halo." + These populations have different kinematic and chemical properties., These populations have different kinematic and chemical properties. + The subdivision between the disk and halo was first identified since long ago. but the thick disk was discovered far more recently by Gilmore Reid (1983)). who analysed the stellar density distributior as a function of distance from the Galactic plane.," The subdivision between the disk and halo was first identified since long ago, but the thick disk was discovered far more recently by Gilmore Reid \cite{Gilmore}) ), who analysed the stellar density distribution as a function of distance from the Galactic plane." + There is no obvious predetermined way to identify purely thick or thin disk stars in the solar neighborhood., There is no obvious predetermined way to identify purely thick or thin disk stars in the solar neighborhood. + There are essentially three ways of distinguishing local thick and thir disk stars: a purely kinematical approach (e.g. Bensby etal.2003.. 2005:," There are essentially three ways of distinguishing local thick and thin disk stars: a purely kinematical approach (e.g. Bensby etal.\cite{Bensby-03}, \cite{Bensby-05};" +:Reddy et al. 20060).," Reddy et al. \cite{Reddy}) )," + a purely chemical methoc(e.g., a purely chemical method(e.g. + Navarro et al. 2011).," Navarro et al. \cite{Navarro}) )," + and by looking at a combinatior of kinematics. metallicities.and stellarages (e.g. Fuhrmani 1998:: Haywood 2008a)).," and by looking at a combination of kinematics, metallicities,and stellarages (e.g. Fuhrmann \cite{Fuhrmann}; Haywood \cite{Haywood-08a}) )." + The kinematic selection is à much more commonly appliec method than the chemical approach. because it is much easier to measure the velocity of a star thanto determine its chemical composition (particularly its a-enhancement).," The kinematic selection is a much more commonly applied method than the chemical approach, because it is much easier to measure the velocity of a star thanto determine its chemical composition (particularly its $\alpha$ -enhancement)." + However. the chemical distinction. of the disks can be more useful and reliable. at least. because chemistry ts a relatively more stable property of a star. that is intimately connected to the time and place of its birth. whereas spatial positions and kinematics are evolving properties.," However, the chemical distinction of the disks can be more useful and reliable, at least, because chemistry is a relatively more stable property of a star, that is intimately connected to the time and place of its birth, whereas spatial positions and kinematics are evolving properties." + During the past few years. there have been several studies directed to the detailed elemental abundance investigations of stars in different subpopulations.," During the past few years, there have been several studies directed to the detailed elemental abundance investigations of stars in different subpopulations." + However. spectroscopic studies are in general limited to small samples of afew hundred stars atmost (e.g. Feltzing Gustafsson1998:; Bensby etal. 2003.2005.20071:," However, spectroscopic studies are in general limited to small samples of afew hundred stars atmost (e.g. Feltzing Gustafsson\cite{Feltzing & Gustafsson}; Bensby etal. \cite{Bensby-03,Bensby-05,Bensby-2007};" + Soubiranet al. 2005::, Soubiranet al. \cite{Soubiran05}; + Reddy et al. 2006:; Ramí, Reddy et al. \cite{Reddy}; +rrez et al. 2007)), rez et al. \cite{Ram=0000EDrez}) ) + and only a few studies havebeen basedon samples aslarge as 1000stars (e.g. Gazzano et al. 2010::, and only a few studies havebeen basedon samples aslarge as 1000stars (e.g. Gazzano et al. \cite{Gazzano-10}; + Gazzano 2011:; Petigura Marcy 201 1)., Gazzano \cite{Gazzano-11}; Petigura Marcy \cite{Petigura-11}) ). + To investigate [a/Fe abundances in the thin andthick disks with relatively large samples. some studies combine data from different sources (e.g. Navarro et al. 2011)).2011).," To investigate $\alpha$ abundances in the thin andthick disks with relatively large samples, some studies combine data from different sources (e.g. Navarro et al. \cite{Navarro})." + However. both methods are far less precise than those obtained with high-resolution spectroscopy. and prevent us from seeing any separation gap between the thin and thick disks.," However, both methods are far less precise than those obtained with high-resolution spectroscopy, and prevent us from seeing any separation gap between the thin and thick disks." +" To minimize any type of external and internal ""errors"". one needs to have as large and as homogeneous a sample as possible. with reliable measurements of their chemical and kinematic features."," To minimize any type of external and internal “errors”, one needs to have as large and as homogeneous a sample as possible, with reliable measurements of their chemical and kinematic features." + In this Letter. we investigate the possible differences in the elemental abundance trends for stars of different subpopulations.μα using a stellar sampleof 1112 long-liveddwarf stars.," In this Letter, we investigate the possible differences in the elemental abundance trends for stars of different subpopulations, using a stellar sampleof 1112 long-liveddwarf stars." +" To separate and investigate the different Galactic stellar subsystems. we focus on the [a/Fe] ratio (here ""a refers to the average abundance of Mg. Si. and Ti)."," To separate and investigate the different Galactic stellar subsystems, we focus on the $\alpha$ ratio (here $\alpha$ ” refers to the average abundance of Mg, Si, and Ti)." + The extensive and full investigation. of this sample. will be more focused on the abundance difference between stars with and without planets and be presented in an upcoming paper where we will mso describe the observations. data reductions. and abundance dalysis 1n detail.," The extensive and full investigation of this sample, will be more focused on the abundance difference between stars with and without planets and be presented in an upcoming paper where we will also describe the observations, data reductions, and abundance analysis in detail." + The sample used in this workconsists of 1112 FGK stars observedwithin the context of the HARPSGTO programs. hereafter called HARPS-1 (Mayor et al. 2003)).," The sample used in this workconsists of 1112 FGK stars observedwithin the context of the HARPSGTO programs, hereafter called HARPS-1 (Mayor et al. \cite{Mayor}) )," + HARPS-2 (Lo Curto et al. 20100).," HARPS-2 (Lo Curto et al. \cite{Lo Curto}) )," + and HARPS-4 (Santos et al. 20115)., and HARPS-4 (Santos et al. \cite{Santos_11}) ). + The stars are slowly-rotating. non-evolved. and in general have a low level of activity.," The stars are slowly-rotating, non-evolved, and in general have a low level of activity." + The individual spectra of each star were reduced using the HARPSpipeline andthen combined. with ~ ~20 - , The individual spectra of each star were reduced using the HARPSpipeline andthen combined with $\sim$ $\sim$ $\sim$ +means (hat the mass distribution f(n./) is expressed in the calulation of the C. but remains implicit in the definition of the ODEs (Eq.,"means that the mass distribution $f(m,t)$ is expressed in the calulation of the $C_k$, but remains implicit in the definition of the ODEs (Eq." + 26)., 26). + Thus. the method is semi-inmplicit. because the RIIS of the equations above can be expressed in terms of the moments (as defined in Eq.," Thus, the method is semi-implicit, because the RHS of the equations above can be expressed in terms of the moments (as defined in Eq." + 2)., 2). + Equations (26) are then integrated using the fourth order Iunge-Ixutta method. ancl mav be compared with the results of 2.2.1 and the direct integration of Eq. (," Equations (26) are then integrated using the fourth order Runge-Kutta method, and may be compared with the results of 2.2.1 and the direct integration of Eq. (" +1).,1). + This semi-implicit approach (tracks (he evolving kernel through the integration of Equations (24) and (25) alter every timestep. (hus the computational time involved is similar to the explicit ease.," This semi-implicit approach tracks the evolving kernel through the integration of Equations (24) and (25) after every timestep, thus the computational time involved is similar to the explicit case." +" In order to update the kernel. one may solve for the new my, after each A/ using the equation (¢4 1) The new normalization coefficient e can then be found from the definition of A,=p."," In order to update the kernel, one may solve for the new $m_L$ after each $\Delta t$ using the equation $q\ne 1$ ) The new normalization coefficient $c$ can then be found from the definition of $M_1 = \rho$." + We (hen reintegrate Equations (24) and (25) under the powerlaw assumption. and then proceed to fit the C'(Gmn./) with a finite series in fractional powers of m.," We then reintegrate Equations (24) and (25) under the powerlaw assumption, and then proceed to fit the $C_k(m,t)$ with a finite series in fractional powers of $m$." + Although. in principle. anv other (wo moments could be used to obtain ij. M4. which les between Ms and M4. and because it roughly characterizes the evolution of the largest particle (see discussion at the end of 2.2). seems the most consistent. choice.," Although, in principle, any other two moments could be used to obtain $m_L$, $M_q$, which lies between $M_2$ and $M_1$, and because it roughly characterizes the evolution of the largest particle (see discussion at the end of 2.2), seems the most consistent choice." + The q-th moment is calculated using the Lagrange polvnomial interpolation scheme (Eqs., The $q$ -th moment is calculated using the Lagrange polynomial interpolation scheme (Eqs. + 3 aud 9)., 8 and 9). + The advantage of the moments method lies in the ability to express the differential equations in terms of the moments of the distribution (i.e.. their integrated properties).," The advantage of the moments method lies in the ability to express the differential equations in terms of the moments of the distribution (i.e., their integrated properties)." + IL a more explicitly mass-dependent approach is adopted (as is the case in 2.2.1. and the semi- approach described here). then the computational Gime significantly increases.," If a more explicitly mass-dependent approach is adopted (as is the case in 2.2.1, and the semi-implicit approach described here), then the computational time significantly increases." + One can improve the speed of computation by calculating the C. periodically. or in tlie extreme case. onlv al /=0 which would make (he approach truly. (e.g.. 2.1).," One can improve the speed of computation by calculating the $C_k$ periodically, or in the extreme case, only at $t=0$ which would make the approach truly (e.g., 2.1)." + The advantage of an implicit approach is Chat it becomes Fully general (the form of f is only assumed at the onset). ancl also in the time it takes to solve (<1 minute).," The advantage of an implicit approach is that it becomes fully general (the form of $f$ is only assumed at the onset), and also in the time it takes to solve $< 1$ minute)." + The bulk of the time is spent in (he integration of equations (24) and (25) which would occur only once., The bulk of the time is spent in the integration of equations (24) and (25) which would occur only once. + The disadvantage. of course. is (hat (he particle velocity distribution is not updated as it changes with time (due to. e... changes in the bounds of the size distribution).," The disadvantage, of course, is that the particle velocity distribution is not updated as it changes with time (due to, e.g., changes in the bounds of the size distribution)." + We present examples of both extremes in 3., We present examples of both extremes in 3. + If one wanted to implement a mass- or velocitv-dependent sticking coefficient 9. it can readily be included in the integration to obtain the C.," If one wanted to implement a mass- or velocity-dependent sticking coefficient $S$, it can readily be included in the integration to obtain the $C_k$." +" The additional imelusion of source and sink terms due to erosion. fragmention. or gravitational growth in (his senii-implicil formalism would require that we fit these terms in a similar manner to the C5, so that their"," The additional inclusion of source and sink terms due to erosion, fragmention, or gravitational growth in this semi-implicit formalism would require that we fit these terms in a similar manner to the $C_k$ so that their" +DL—L9T.o=0.20). but was fairlv consistent. within either eroup.,"$\Gamma=1.97, \sigma=0.20)$, but was fairly consistent within either group." + The cluster sources were found to comprise +40 per cent magnetic systems. based. on the photon. index distribution.," The cluster sources were found to comprise $\sim 40$ per cent magnetic systems, based on the photon index distribution." + Our measured photon index of P=1.510.11 places CV1 on the borderline between the magnetic and non-magnetic distributions., Our measured photon index of $\Gamma=1.51\pm0.11$ places CV1 on the borderline between the magnetic and non-magnetic distributions. + However. the combination of our result with the photon index result of Webbctal.(2004).. which. although consistent with our value. ranges to softer values. tips the balance slightly in favour of a non-magnetic CY classification for the object.," However, the combination of our result with the photon index result of \citet{webb04}, which, although consistent with our value, ranges to softer values, tips the balance slightly in favour of a non-magnetic CV classification for the object." + In the optical. the characteristics of the ~15-d 2004 Alay outburst of M22. €CV1 covered. by our observations are consistent with previous reports of ~15 d. 23 mag eruptions of the svstem by Sahuetal.(2001).. Dondοἱal.(2005). ancl Pletrukowiezοἱal.(2005).," In the optical, the characteristics of the $\sim$ 15-d 2004 May outburst of M22 CV1 covered by our observations are consistent with previous reports of $\sim$ 15--20 d, 2–3 mag eruptions of the system by \citet{sahu01}, \cite{bond05} and \cite{piet05}." +.. These outburst characteristics arealso consistent with normal outbursts of DN. whieh typically have durations from 2 d (Warner1995).. where this duration is also correlated with the recurrence time for outbursts.," These outburst characteristics arealso consistent with normal outbursts of DN, which typically have durations from 2--20 d \citep{warner95}, where this duration is also correlated with the recurrence time for outbursts." + Pictrukowiezetal.(2005) estimated the outburst recurrence time for CV1 to be greater than 150 cl our observations are consistent with this limit., \cite{piet05} estimated the outburst recurrence time for CV1 to be greater than 150 d – our observations are consistent with this limit. + The typical duration of outbursts of CV. at 1520 d. would tend to favour a longer orbital period estimate of the order of LO h or more (e.g.Ak.Ozkan&Mattei2002).," The typical duration of outbursts of CV1, at 15–20 d, would tend to favour a longer orbital period estimate of the order of 10 h or more \citep*[e.g.][]{ak02}." +. In addition. the outburst properties ofCVI are not unlike those of non-magnetic dwarf novae of longer orbital period. such as BY Con. which undergoes outbursts with an amplitude of 3 mag and a 30-cl duration separated by 150 d (although these tend to be more symmetrical in rise and decay. than those of CVI).," In addition, the outburst properties of CV1 are not unlike those of non-magnetic dwarf novae of longer orbital period, such as BV Cen, which undergoes outbursts with an amplitude of $\sim3$ mag and a 30-d duration separated by 150 d (although these tend to be more symmetrical in rise and decay than those of CV1)." + Ifmagnelie.. €CN1 cannot be a polar because. their absent dises preclude. outhursts.," If, CV1 cannot be a polar because their absent discs preclude outbursts." + On the other. hand. intermediate polars (LPs) with their partially. truncated inner disces do exhibit outbursts.," On the other hand, intermediate polars (IPs) – with their partially truncated inner discs – do exhibit outbursts." + However. the outburst characteristics of CVT are not consistent with any particular example of the known IPs.," However, the outburst characteristics of CV1 are not consistent with any particular example of the known IPs." + Gis Por. with its infrequent outbursts which persist. for. two months. remains an anomalous system.," GK Per, with its infrequent outbursts which persist for two months, remains an anomalous system." + Other IP systems such as EX Lva exhibit a similar outhurst amplitude to CV1. ~3.5 mag. but these outbursts last only 23 d and have a longer recurrence ime of ~2 vr (LHellieretal.1989)... while IPs such as TV Col and. V1223 Ser show even shorter duration Low-amplitude outbursts that [ast only ~0.5 d. Thus. on the vasis of its outburst properties. CVI does not resemble a magnetic svstem.," Other IP systems such as EX Hya exhibit a similar outburst amplitude to CV1, $\sim3.5$ mag, but these outbursts last only 2–3 d and have a longer recurrence time of $\sim2$ yr \citep{hell89}, while IPs such as TV Col and V1223 Sgr show even shorter duration low-amplitude outbursts that last only $\sim0.5$ d. Thus, on the basis of its outburst properties, CV1 does not resemble a magnetic system." + We can also eliminate the class οσο on the morphology. of the outburst light curve: even hough our sampling Is too sparse to detect superhumps (the modulation which is the defining characteristic of the SU UAla class) in the ouburst light curve. we find no evidence or the extended. sloping plateau of brightness associated with superoutbursts.," We can also eliminate the class based on the morphology of the outburst light curve: even though our sampling is too sparse to detect superhumps (the modulation which is the defining characteristic of the SU UMa class) in the ouburst light curve, we find no evidence for the extended, sloping plateau of brightness associated with superoutbursts." + Similarly. Pietrukowiezetal.(2005) ound no evidence for the presence of superhunmps in. the 2000 August outburst [light curve.," Similarly, \citet{piet05} found no evidence for the presence of superhumps in the 2000 August outburst light curve." + This leaves the longer-»eriod. CGem--type DN as the group of CVs with the most similar properties to CVI (e.g. BY Con)., This leaves the longer-period -type DN as the group of CVs with the most similar properties to CV1 (e.g. BV Cen). + Echevarria&Jones(1984). show that for a sample of field DN.the (BV) ancl (€DB) colours are well correlated with orbital period. with those svstems having £u<5i h being significantly bluer than those with P>7 h. Conversely. or the same sample. the A2) and (22£) colours do not appear to be well correlated with μι ," \citet{echev84} show that for a sample of field DN, the $(B-V)$ and $(U-B)$ colours are well correlated with orbital period, with those systems having $P_{\mathrm{orb}}<5\frac{1}{2}$ h being significantly bluer than those with $P_{\mathrm{orb}}>7$ h. Conversely, for the same sample, the $(V-R)$ and $(R-I)$ colours do not appear to be well correlated with $P_{\mathrm{orb}}$ ." +Based on its (7Vo colour of 0.3250.13 mag. CVI appears to be consistent with wing Pao>Th. Phe blackbodsy temperature of 9000 Ix inferred from the (46Vy colour is consistent with emission rom the accretion disc.," Based on its $(U-V)_0$ colour of $0.13\pm0.13$ mag, CV1 appears to be consistent with having $P_{\mathrm{orb}}> 7$ h. The blackbody temperature of $\sim 9000$ K inferred from the $(U-V)_0$ colour is consistent with emission from the accretion disc." + Andersonctal.(2003). found that the (2450.75) and (Vonlx) colours of CVI are. unusually rec for a CV. about0.2 mag and 0.1 mag recward of the main sequence. respectively.," \citet{ack03} found that the $B_{439}-R_{675}$ ) and $V_{606}-I_{814}$ ) colours of CV1 are unusually red for a CV, about0.2 mag and 0.1 mag redward of the main sequence, respectively." + AX possible explanation for these red. colours. previously mentioned. by Andersonetal... is that a secondary. larger than a normal main-sequence star dominates the optical emission of the svstem.," A possible explanation for these red colours, previously mentioned by \citeauthor{ack03}, is that a secondary larger than a normal main-sequence star dominates the optical emission of the system." +" Baralle&Ixolb(2000) show that for longer orbital period (L4,6 hh) CVs. the degree of nuclear evolution of the secondary. is crucial in setting its spectral type. with the most evolved donors having spectral tvpes significantly. later than their main-sequence analogues."," \citet{baraffe00} show that for longer orbital period $P_{\mathrm{orb}}\gtrsim6$ h) CVs, the degree of nuclear evolution of the secondary is crucial in setting its spectral type, with the most evolved donors having spectral types significantly later than their main-sequence analogues." + Some degree of nuclear evolution of the donor olf the main sequence could explain the location of CVI in the CMDs of. Andersonetal..., Some degree of nuclear evolution of the donor off the main sequence could explain the location of CV1 in the CMDs of \citeauthor{ack03}. + An enhance contribution to the V-band from such a secondary mieh also explain the relatively low UV excess inferred from the ο— V) colour (see Section ??))., An enhanced contribution to the -band from such a secondary might also explain the relatively low UV excess inferred from the $U-V$ ) colour (see Section \ref{sec:colours}) ). + Although an establishe example of an evolved. globular cluster CV. secondary may be found in the dwarf nova AKO 9 in 47 Tuc (see the CAIDs of Albrowctal.2001: Edmondsetal.2003a αι the calculations of Ixniggeetal. 2003)). the (V£) colours of many other globular cluster CVs (e.g.Cooletal.1998:Edmondsctal.2003a)/ suggest a lesser. if any. degree of nuclear evolution of the donors in these systems.," Although an established example of an evolved globular cluster CV secondary may be found in the dwarf nova AKO 9 in 47 Tuc (see the CMDs of \citealt{albrow01}; \citealt{edmonds03a} and the calculations of \citealt{knigge03}) ), the $V-I$ ) colours of many other globular cluster CVs \citep[e.g.][]{cool98,edmonds03a} suggest a lesser, if any, degree of nuclear evolution of the donors in these systems." + We note that the location of CV1 on the (ια fers) and. (Vos Ia) €MDs of Andersonet al... together with its UV. and. X-ray. colours. could. also be explained if CV1 were part of a hierarchical triple svstem in which the third star were a main-sequence star of mass comparable to the secondary star in CVI.," We note that the location of CV1 on the $B_{439}-R_{675}$ ) and $V_{606}-I_{814}$ ) CMDs of \citeauthor{ack03}, , together with its UV and X-ray colours, could also be explained if CV1 were part of a hierarchical triple system in which the third star were a main-sequence star of mass comparable to the secondary star in CV1." + I would be of interest to determine whether such à system could. survive in the core of M22., It would be of interest to determine whether such a system could survive in the core of M22. + Alternatively. the (ως Ress) ancl (Vous Ix44) colours could. be accounted for by the presence of a line-of-sight main-sequence star.," Alternatively, the $B_{439}-R_{675}$ ) and $V_{606}-I_{814}$ ) colours could be accounted for by the presence of a line-of-sight main-sequence star." + The relatively low density of stars in the vicinity of CV1 in the image make this unlikely. but it cannot be ruled out.," The relatively low density of stars in the vicinity of CV1 in the image make this unlikely, but it cannot be ruled out." + A useful discriminant of the subtype of a CV is the ratio of X-ray to ultra-violet and/or optical (us., A useful discriminant of the subtype of a CV is the ratio of X-ray to ultra-violet and/or optical flux. + Verbuntetal.(1997). demonstrated that the cillerent classes of CV can be subcdivided as follows: SU UMa and U Gem-type CVs. Bx £Pop~Ol PN PSopt~0.01. for Z Cam-type CVs:finally. UN UAla-type (or novalike)) CVs have the lowest ratios at Ps δνop~ 0.001.," \citet{verbunt97} demonstrated that the different classes of CV can be subdivided as follows: SU UMa and U Gem-type CVs, $ F_{\mathrm{X}} $ $ F_{\mathrm{uv + opt}} \sim0.1$; $ +F_{\mathrm{X}} $ $ F_{\mathrm{uv + opt}} \sim0.01$ for Z Cam-type CVs;finally, UX UMa-type (or ) CVs have the lowest ratios at $ F_{\mathrm{X}} $ $ F_{\mathrm{uv + opt}} \sim 0.001$ ." + Calculating the ratio of X-ray to UV plus optical Lux in an equivalent manner for CV1. we find fs ffiop 70.07 (where the ciscrepaney with the result of," Calculating the ratio of X-ray to UV plus optical flux in an equivalent manner for CV1, we find $F_{\mathrm{X}}$ $F_{\mathrm{uv + +opt}} \sim $ 0.07 (where the discrepancy with the result of" +(Figure 9)) for overdensities produced by either an OLR. or IL. this curvature is seen as a result of the selection ellects and the constraint in J.,"(Figure \ref{fig:pol_GCS}) ) – for overdensities produced by either an OLR or ILR, this curvature is seen as a result of the selection effects and the constraint in $\bolJ$." +" ] have explored. models with resonances at other frequeney ratios (and thus with cifferent relationships between 6, and @,). and found that it is possible to produce overdensities in @ that are qualitatively very similar to those shown here."," I have explored models with resonances at other frequency ratios (and thus with different relationships between $\theta_r$ and $\theta_\phi$ ), and found that it is possible to produce overdensities in $\bolth$ that are qualitatively very similar to those shown here." + While it may be possible to tell one from another for given observations (such as those of the LIvacdes) it is certainly a very complicated task. and one that will require careful modelling and analysis.," While it may be possible to tell one from another for given observations (such as those of the Hyades) it is certainly a very complicated task, and one that will require careful modelling and analysis." + In this paper L have re-cxamined the distribution of stars in the Solar neighbourhood in angle coordinates following the claim by SLO that the ναός moving group is related to an ILR., In this paper I have re-examined the distribution of stars in the Solar neighbourhood in angle coordinates following the claim by S10 that the Hyades moving group is related to an ILR. + Using a dvnamical “torus” model LE showed the significant impact of selection effects. associated: with surveving a finite (small) volume upon the distribution of stars in angle coordinates taken from a phase-mixed model., Using a dynamical “torus” model I showed the significant impact of selection effects associated with surveying a finite (small) volume upon the distribution of stars in angle coordinates taken from a phase-mixed model. + Using models which contain resonant components in addition to à phase-mixed background LI have demonstrated the important effects that the distribution of resonant stars in action have on the observed distribution in angle (again because of selection ellects)., Using models which contain resonant components in addition to a phase-mixed background I have demonstrated the important effects that the distribution of resonant stars in action have on the observed distribution in angle (again because of selection effects). + ‘The distribution of the stars associated with the LEvades moving group in action (Ligure 10)) ? (?) 2 7)), The distribution of the stars associated with the Hyades moving group in action (Figure \ref{fig:actions}) \cite{HaSePr11} \citep{GAIA01} \ref{fig:UVaxes} \ref{fig:UV_GCS}) + ‘The distribution of the stars associated with the LEvades moving group in action (Ligure 10)) ? (?) 2 7))., The distribution of the stars associated with the Hyades moving group in action (Figure \ref{fig:actions}) \cite{HaSePr11} \citep{GAIA01} \ref{fig:UVaxes} \ref{fig:UV_GCS}) +relonization may be siguificautly delaved until a population of harder sources appears.,reionization may be significantly delayed until a population of harder sources appears. + The large fluctuations in the optical depth observed with STIS and FUSE [2] suggest reiouization occurs late. around +~3.," The large fluctuations in the optical depth observed with STIS and FUSE \cite{2} suggest reionization occurs late, around $z\sim 3$." + There is supporting evidence from the hardenime of the UV-backerounud. as deduced youn nietal line ratios although these results remain controversial 101.," There is supporting evidence from the hardening of the UV-background, as deduced from metal line ratios although these results remain controversial \cite{3}." + An independent approach is to study the temperature of the ICAL., An independent approach is to study the temperature of the IGM. + Photo-eating aud adiabatic expansion introduce a tight deusitv-teuiperature relation 0l. P=Totpfipi)Ἐν for the low density ICM responsible for producing the Lyinan-a forest.," Photo-heating and adiabatic expansion introduce a tight density-temperature relation \cite{4}, $ +T=T_0(\rho/\langle\rho\rangle)^{\gamma-1}\,,$ for the low density IGM responsible for producing the $\alpha$ forest." + A sudden injection of entropy resulting from reiouizatiou will increase Ty aud make the eas nearly isothermal. >~1.," A sudden injection of entropy resulting from reionization will increase $T_0$ and make the gas nearly isothermal, $\gamma\sim 1$." + Detecting reionization lhrough a sudden entropy imerease has the advautage that one determines the epoch at which a significant fraction of the volume of the wuiverse is over x the ionization front., Detecting reionization through a sudden entropy increase has the advantage that one determines the epoch at which a significant fraction of the volume of the universe is overrun by the ionization front. + Schave et al., Schaye et al. + used Lydrodvuamiucal simulations to demoustrate that the density-tempecrature relation introduces a cut-off in the scatter plot of columns density yy; versus Hine width b [0].., used hydrodynamical simulations to demonstrate that the density-temperature relation introduces a cut-off in the scatter plot of column density $N_\H$ versus line width $b$ \cite{5}. + They used a set of many high resolutio- siauulations to calibrate the relation between the position of the cut-off aud (I5. 5).," They used a set of many high resolution simulations to calibrate the relation between the position of the cut-off and $(T_0,\gamma$ )." + Applviug the calibration to the cut-off measured in ten high-resolutio- spectra. they found evideuce for a rise in Zy arouud a redshift 2~3.3. and au associated dip iu 5. which they associated with reionization.," Applying the calibration to the cut-off measured in ten high-resolution spectra, they found evidence for a rise in $T_0$ around a redshift $z\sim 3.3$, and an associated dip in $\gamma$, which they associated with reionization." + Ricotti. Gnedin Shull (0])) applied a similar technique. but calibrated with pseudo livdrodvuauical simulations. to published line lists. aud ound a simular temperature increase. although their error bars are large and heir result is consistent with a non-evolviug τρ as well.," Ricotti, Gnedin Shull \cite{6}) ) applied a similar technique, but calibrated with pseudo hydrodynamical simulations, to published line lists, and found a similar temperature increase, although their error bars are large and their result is consistent with a non-evolving $T_0$ as well." + Bryan Machacek 0|. also found evidence for a high value of Ty. but McDonald et al.," Bryan Machacek \cite{7} also found evidence for a high value of $T_0$, but McDonald et al." + [0]. did rot find an increase iu Zi around 2=3.3. although they used larecly the same data as Schaye ct al.," \cite{8} + did not find an increase in $T_0$ around $z=3.3$, although they used largely the same data as Schaye et al." + Zaldarriage 10 applied a wavelet analysis similar to the one discussed here to look for temperature changes in the spectrum of QSO 112212531 which might be a relie from reionization. aud constrained them to be sunaller than a factor of 2.5.," Zaldarriage \cite{9} applied a wavelet analysis similar to the one discussed here to look for temperature changes in the spectrum of QSO 1422+231 which might be a relic from reionization, and constrained them to be smaller than a factor of 2.5." + A discrete wavelet is a localised function with a finite bandwidth., A discrete wavelet is a localised function with a finite bandwidth. + This makes wavelets useful for characterising line widtls ina spectrum. since the amplitude of the wavelet will be related to the width of the line. and the position of the wavelet to the position of the line.," This makes wavelets useful for characterising line widths in a spectrum, since the amplitude of the wavelet will be related to the width of the line, and the position of the wavelet to the position of the line." + The decomposition is moreover unique. for a given wavelet basis.," The decomposition is moreover unique, for a given wavelet basis." + Theuus Zaroubi [0] used the Daubechies 20 wavelet to characterise temperature fluctuations in snmlated a spectra., Theuns Zaroubi \cite{10} used the Daubechies 20 wavelet to characterise temperature fluctuations in simulated $\alpha$ spectra. + They demonstrated how the wavelet amplitudes are laree when the gas is cold and the lines narrow. andverse.," They demonstrated how the wavelet amplitudes are large when the gas is cold and the lines narrow, and." + They also showed how the cunulative distribution of wavelet auplitudes can be used to characterise the eas temperature. aud to judge whether two stretches of spectrum have differcut temperatures or not.," They also showed how the cumulative distribution of wavelet amplitudes can be used to characterise the gas temperature, and to judge whether two stretches of spectrum have different temperatures or not." + Here.," Here," +The nature of the IGME in filaments. on the contrary. remains largely unknown. because the study. of RAL outside clusters is still scarce (e.g..Nuetal.2006): detecting the RAI due to the IGAIF in filaments is difficult with current facilities. and also removing the galactic loreground is not a trivial task.,"The nature of the IGMF in filaments, on the contrary, remains largely unknown, because the study of RM outside clusters is still scarce \citep[e.g.,][]{xkhd06}; detecting the RM due to the IGMF in filaments is difficult with current facilities, and also removing the galactic foreground is not a trivial task." + The next generation radio interferometers including je Square Wilometer Array (SIVA). and upcoming SIVA pathfinders. the Australian SIVA Pathfinder (ASIXAP) and the South. African. Karoo Array Telescope (AleerAT). as well ihe Low Frequency Array (LOFAR). however. are expected to be used to study the RM.," The next generation radio interferometers including the Square Kilometer Array (SKA), and upcoming SKA pathfinders, the Australian SKA Pathfinder (ASKAP) and the South African Karoo Array Telescope (MeerKAT), as well the Low Frequency Array (LOFAR), however, are expected to be used to study the RM." + Particularly. the ΝΑ could measure RM for ~LO” polarized extragalactic sources across the sky with an average spacing of ~60 aresec between lines of sight (LOSs) (see.e.g..Car-2004:INrauseetal.2009.andreferencest herein).. enabling us to investigate 1e IGME in the large-scale structure (LSS) of the universe.," Particularly, the SKA could measure RM for $\sim 10^8$ polarized extragalactic sources across the sky with an average spacing of $\sim 60$ arcsec between lines of sight (LOS's) \citep[see, e.g.,][and references therein]{car04,kra09}, enabling us to investigate the IGMF in the large-scale structure (LSS) of the universe." + Attempts to theoretically predict the IM due to the IGME have been made: for instance. Ίναetal.(1998) and Dolagοἱal.(2005) used hvdiodynamie simulations for cosmological structive formation to study RM in the LSS. and more recently used ATID simulations to study RAL for clusters.," Attempts to theoretically predict the RM due to the IGMF have been made: for instance, \citet{rkb98} and \citet{dol05} used hydrodynamic simulations for cosmological structure formation to study RM in the LSS, and more recently \citet{dub08} used MHD simulations to study RM for clusters." + However. the properties of the IGAIF. especially in filaments. such as the strength aud coherence leneth as well as the spatial distribution. are largely unknown. hindering the theoretical study of RAI in the LSS of the uhiverse.," However, the properties of the IGMF, especially in filaments, such as the strength and coherence length as well as the spatial distribution, are largely unknown, hindering the theoretical study of RM in the LSS of the universe." + Recently. Ryuetal.(2008). proposed a physically motivated model for the IGME. in which a part of the gravitational energy released curing structure lormation is transferred to (he magnetic field energy as a result of the Gurbulent diamo amplification of weak seed fields in the LSS of the universe.," Recently, \citet{rkcd08} proposed a physically motivated model for the IGMF, in which a part of the gravitational energy released during structure formation is transferred to the magnetic field energy as a result of the turbulent dynamo amplification of weak seed fields in the LSS of the universe." + In the model. the IGAIF follows largely the matter distribution in the cosmic web and the strength is predicted to be (3)~10 nG in filaments.," In the model, the IGMF follows largely the matter distribution in the cosmic web and the strength is predicted to be $\langle B\rangle \sim 10$ nG in filaments." + Cho studied various characteristic length scales of magnetic fields in turbulence with very weak or zero mean magnetic field. aud showed that the coherence length defined for RAI is 3/4 times the integral scale in (he incompressible limit.," \citet{cr09} studied various characteristic length scales of magnetic fields in turbulence with very weak or zero mean magnetic field, and showed that the coherence length defined for RM is 3/4 times the integral scale in the incompressible limit." + They predicted that in filaments. the coherence length for RM would be a few x1007.| kpe with the IGMP of and the RM due to the magnetic field would be of order ~1radm?," They predicted that in filaments, the coherence length for RM would be a few $\times\ 100\ h^{-1}$ kpc with the IGMF of \citet{rkcd08} and the RM due to the magnetic field would be of order $\sim 1\ {\rm rad\ m^{-2}}$." + In (his paper. we study RM in the LSS of (he universe. focusing on RAL through filaments. using simulations for cosmological structure formation along with the model IGME of Ryu and Cho&Raw(2009).," In this paper, we study RM in the LSS of the universe, focusing on RM through filaments, using simulations for cosmological structure formation along with the model IGMF of \citet{rkcd08} and \citet{cr09}." +. Specilicallv. we present the spatial distribution. probability distzibution function (PDF) ancl power spectrum of the RM. and discuss the prospect of possible observations of the RM.," Specifically, we present the spatial distribution, probability distribution function (PDF) and power spectrum of the RM, and discuss the prospect of possible observations of the RM." + In sections 2 and 3. we describe our model and the results.," In sections 2 and 3, we describe our model and the results." + Discussion is in Section 4. and Summary and Conclusion follows in Section 4.," Discussion is in Section 4, and Summary and Conclusion follows in Section 4." +"To better see the impact of an overabundance of satellites on the clustering of galaxies, we randomly remove from the SAM mock samples 80% of the red satellites.","To better see the impact of an overabundance of satellites on the clustering of galaxies, we randomly remove from the SAM mock samples $80\%$ of the red satellites." + The resulting galaxies correlation functions are shown in Fig. 14.., The resulting galaxies correlation functions are shown in Fig. \ref{rem_sat}. +" This figure shows that, by excluding most of SAM red satellites, the amplitude of the correlation function of red galaxies is dramatically reduced, particularly on small scales."," This figure shows that, by excluding most of SAM red satellites, the amplitude of the correlation function of red galaxies is dramatically reduced, particularly on small scales." +" Model predictions obtained excluding 80 per cent of the red satellites are in quite good agreement with observational measurements but at 0.2}$ 2 keV) shows a point-like morphology, consistent with the FWHM PSF simulations, while soft band $\sf{<}$ 2 keV) shows an extended morphology (see Figure \ref{fig:PSF}) )." + The soft N-vav image shows a complex exteuded enission with a bipolar structure aligued aloug PA~122° (Figure 2))., The soft X-ray image shows a complex extended emission with a bipolar structure aligned along ${\sf \sim 122^{\circ}}$ (Figure \ref{fig:X_OIII}) ). + It extends 8.5 arcsec to the NW and 6.5 aresec to the SE., It extends 8.5 arcsec to the NW and 6.5 arcsec to the SE. + As already mentioned. 5573 shows a biconical morphology in the |O emission. which resenibles that observed in the soft N-ravs.," As already mentioned, 573 shows a biconical morphology in the [O III] emission, which resembles that observed in the soft X-rays." +ΠΗ The ratio of |OIII| to TD recombination lines is cohbunonly asstuned to be an indicator of the ionization, The ratio of [OIII] to H recombination lines is commonly assumed to be an indicator of the ionization +is the only selection applied to the radio sample for Follow-up spectroscopy.,is the only selection applied to the radio sample for follow-up spectroscopy. + Part of this large dataset. is. presented by Ceorgakakis et al. (, Part of this large dataset is presented by Georgakakis et al. ( +1999).,1999). +" Galaxies are grouped on the basis of spectral features ancl diagnostic emission-line ratios into (1) svstems exhibiting absorption-line features only. (i) star-lorming galaxies. (ii) narrow emission line Seyfert 2s. (iv) broad line Sevfert Ls and (v) ""unclassified objects."," Galaxies are grouped on the basis of spectral features and diagnostic emission-line ratios into (i) systems exhibiting absorption-line features only, (ii) star-forming galaxies, (iii) narrow emission line Seyfert 2s, (iv) broad line Seyfert 1s and (v) “unclassified” objects." + The latter have at least one narrow emission line identified in their optical spectra (allowing redshift determination) but the poor S/N ratio. or the small number of emission lines within the observable window. or the presence of instrumental features contaminating emission lines prevented a reliable spectral classification (Georgakakis et al.," The latter have at least one narrow emission line identified in their optical spectra (allowing redshift determination) but the poor S/N ratio, or the small number of emission lines within the observable window, or the presence of instrumental features contaminating emission lines prevented a reliable spectral classification (Georgakakis et al." + 1999)., 1999). +" A new set of hieh quality deep multiwavelength (ωςI photometric data has. recently been obtained or à subregion of the PDS partly overlapping with the hoenix/NMM. field using the Wide Field. lmager at he AAT (BV A-bands) and the ESO mm (C-band) clescopes complete to £xs24 and (C&22.5 mmag respectively,", A new set of high quality deep multiwavelength $UBVRI$ photometric data has recently been obtained for a subregion of the PDS partly overlapping with the Phoenix/XMM field using the Wide Field Imager at the AAT $BVRI$ -bands) and the ESO m $U$ -band) telescopes complete to $I\approx24$ and $U\approx22.5$ mag respectively. + Near-inlrared (NER) photometric observations (J and A-bands) complete to ἐνzz ISmmae have also oen Obtained for the 30aarcmin diameter area of the hoenix/NMM survey using OSIRIS at the CTIO mim elescope., Near-infrared (NIR) photometric observations $J$ and $K$ -bands) complete to $K\approx18$ mag have also been obtained for the arcmin diameter area of the Phoenix/XMM survey using OSIRIS at the CTIO m telescope. + The UV. optical and NUR data will be presented in a series of forthcoming papers.," The UV, optical and NIR data will be presented in a series of forthcoming papers." +" A subregion of the PDS centered al 11A(J2000)2011252: 4533/10.0"" was surveved by theXNMM-Ne4on. on 2002. May 5.", A subregion of the PDS centered at $01^{\rm h}12^{\rm m}52^{\rm s}$; $-45^{\circ}33^{\prime}10.0^{\prime\prime}$ was surveyed by the on 2002 May 5. + The observation consists of a single pointing with an exposure time of z 50kks., The observation consists of a single pointing with an exposure time of $\approx50$ ks. + “Phe EPIC (European Photon Imaging Camera: Strtideler et al., The EPIC (European Photon Imaging Camera; Strüdder et al. + 2001: Turner et al., 2001; Turner et al. + 2001) cameras were operated. in full frame mode with the medium filter applied., 2001) cameras were operated in full frame mode with the medium filter applied. + The data have been analysed: using the Science Analysis Software (SAS 5.3)., The data have been analysed using the Science Analysis Software (SAS 5.3). + Event files for the PN and the two MOS detectors have been produced. using the and tasks of SAS respectively., Event files for the PN and the two MOS detectors have been produced using the and tasks of SAS respectively. + The event iles were sereened for high particle background: periods »w rejecting times with Κον count rates. higher han 20 and Geets/l00s for the PN and the two MOS cameras respectively., The event files were screened for high particle background periods by rejecting times with keV count rates higher than 20 and cts/100s for the PN and the two MOS cameras respectively. + Lhe adopted count rates are a trace olf between maximum. cllective exposure time ane low xwlicle background. contamination., The adopted count rates are a trade off between maximum effective exposure time and low particle background contamination. + Higher thresholds. clo not significantly increase the exposure time while lower hresholds severely reduce the effective exposure time., Higher thresholds do not significantly increase the exposure time while lower thresholds severely reduce the effective exposure time. + The N ancl MOS good time intervals are 39444 ancl ss respectively., The PN and MOS good time intervals are 39444 and s respectively. + The difference between the PN and the MOS exposure times is due to varving start ancl end. times of he detectors., The difference between the PN and the MOS exposure times is due to varying start and end times of the detectors. + Only events corresponding to patterns O4 or the PN and 0.12 for two MOS cameras have been kept., Only events corresponding to patterns 0–4 for the PN and 0–12 for two MOS cameras have been kept. + To increase the signaltonoise ratio and to reach fainter Iluxes the PN and the MOS event files have been combined into a single event list using the task of SAS., To increase the signal–to–noise ratio and to reach fainter fluxes the PN and the MOS event files have been combined into a single event list using the task of SAS. + Images in celestial coordinates with pixel size of aaresce have been extracted in the spectral bands SkkoV. (total). 2kkeV. (soft) and SkkeW (hard) for he merged event file.," Images in celestial coordinates with pixel size of arcsec have been extracted in the spectral bands keV (total), keV (soft) and keV (hard) for the merged event file." + Events with energies below 0.5 or above SkkeV are not used here because of the reduced elective area at these energies., Events with energies below 0.5 or above keV are not used here because of the reduced effective area at these energies. + Also. below k5kkeV. the background. is elevated due to the Galactic X-ray emission component. (Lumb et al.," Also, below keV the background is elevated due to the Galactic X-ray emission component (Lumb et al." + 2002)., 2002). + “Pherefore. shotons with energies <0.5 and 7SkkeV primarily increase he background and do not improve the signalto.noise ratio of the final image.," Therefore, photons with energies $<0.5$ and $>8$ keV primarily increase the background and do not improve the signal–to–noise ratio of the final image." + Exposure maps accounting for vignetting. CCD gaps anc bad. pixels have been constructed for cach spectral band.," Exposure maps accounting for vignetting, CCD gaps and bad pixels have been constructed for each spectral band." + Source detection was independently. performed. in the total SkkeV). soft 2kkeV) ancl hard kkeV) band images using the task of SAS with a significance threshold. of 4a.," Source detection was independently performed in the total keV), soft keV) and hard keV) band images using the task of SAS with a significance threshold of $4\,\sigma$." + A byproduct of the source extraction algorithm is the construction of background maps for cach spectral band., A byproduct of the source extraction algorithm is the construction of background maps for each spectral band. + We detect 19τ. 128 and. SS N- sources in the 0.5-8. 0.52 skkeV spectral bands respectively.," We detect 137, 128 and 88 X-ray sources in the 0.5-8, 0.5–2 keV spectral bands respectively." +" Ehe 40 limiting fluxes in these spectral bands are f(0.5SkeV)=107C. {52keV)z9101"" and f(2/SkeV)z2.10Moreslem7."," The $4\,\sigma$ limiting fluxes in these spectral bands are $f(\rm 0.5 - 8 \,keV) \approx 10^{-15}$, $f(\rm 0.5 - 2 +\,keV) \approx 9 \times 10^{-16}$ and $f(\rm 2 - 8 \,keV) \approx +2 \times 10^{-15} \rm \, erg \, s^{-1} \, cm^{-2}$." + A small number of X-rav [aint sources are only detected. in cither the solt (total of 11) or the hard (total of 9) bands and. are nussed from the total band due to the elevated background., A small number of X-ray faint sources are only detected in either the soft (total of 11) or the hard (total of 9) bands and are missed from the total band due to the elevated background. + A detailed. analysis of the nature of the X-ray sources detected in the Phoenix/NMM survey will be presented in a forthcoming paper (CGoeorgakakis et al., A detailed analysis of the nature of the X-ray sources detected in the Phoenix/XMM survey will be presented in a forthcoming paper (Georgakakis et al. + in. preparation)., in preparation). + To convert counts to lus the Energy Conversion Factors (ECE) of individual detectors are calculated assuming a power law spectrum with P=2.0 (e.g. Bauer et al., To convert counts to flux the Energy Conversion Factors (ECF) of individual detectors are calculated assuming a power law spectrum with $\Gamma=2.0$ (e.g. Bauer et al. +" 2002) and Galactic absorption Ny=2«10""em.? appropriate for the PDS.", 2002) and Galactic absorption $N_H=2\times 10^{20} \rm {cm^{-2}}$ appropriate for the PDS. + The mean ECP for the mosaic of all three electors is estimated by weighting the ECs of individual detectors by the respective exposure time., The mean ECF for the mosaic of all three detectors is estimated by weighting the ECFs of individual detectors by the respective exposure time. + For the encircled nergy correction. accounting for the energy fraction outside the aperture within which source counts are accumulated. =μαὉ adopt the calibration performed. by Ghizzardi (2001a. 10110).," For the encircled energy correction, accounting for the energy fraction outside the aperture within which source counts are accumulated, we adopt the calibration performed by Ghizzardi (2001a, 2001b)." + These studies use both PN and MOS observations of point sources to formulate the PSE for different energies ancl oll-axis angles., These studies use both PN and MOS observations of point sources to formulate the PSF for different energies and off-axis angles. + In. particular. a Wing profile is fit to the data with parameters that are a function of both οποιον ancl oll-axis angle.," In particular, a King profile is fit to the data with parameters that are a function of both energy and off-axis angle." + The. encircled. energy correction for the merged. PN|MOS. image is estimated by weighting the corrections of individual detectors by the respective exposure time., The encircled energy correction for the merged PN+MOS image is estimated by weighting the corrections of individual detectors by the respective exposure time. + In any rate the dilference between the PN and MOS. encireled energy. corrections found by CGhizzordi (2001a. 2001b) is negligible.," In any rate the difference between the PN and MOS encircled energy corrections found by Ghizzardi (2001a, 2001b) is negligible." +Leo T is well bevoucl this clistance threshold aud uine of the eleven new Milky Way satellites are within 200 kpc.,Leo T is well beyond this distance threshold and nine of the eleven new Milky Way satellites are within $200$ kpc. + We make the most conservative estimate. by assuming that we have a complete sample of dwarls within 200 kpc.," We make the most conservative estimate, by assuming that we have a complete sample of dwarfs within $200$ kpc." + Additional selection bias lor the new cdwarfs comes primarily [rom the limits of the SDSS coverage ou the sky., Additional selection bias for the new dwarfs comes primarily from the limits of the SDSS coverage on the sky. + To account lor this. we apply the zero-th order correction of multiplying the number of new dwarls by 5.15 (?)..," To account for this, we apply the zero-th order correction of multiplying the number of new dwarfs by 5.15 \citep{Tollerudetal08}." + This correction assumes au isotropi distribution of satellites when observed from the Galactic center., This correction assumes an isotropic distribution of satellites when observed from the Galactic center. + With this simple assuumptious we estimate that the nuuber of Milky Way satellites with Calactocentric distance <200 kpe is abot SOELE including the 29 previously kuow satellites.," With this simple assumptions we estimate that the number of Milky Way satellites with Galactocentric distance $<200$ kpc is about $85 \pm 14$, including the 29 previously know satellites." + The error estimate is due to slot noise., The error estimate is due to shot noise. + However. bright satellites of the Milky Way are clistributecdl very auisotropically (??).. so the asstuuption of isotropy may uot be a good one.," However, bright satellites of the Milky Way are distributed very anisotropically \citep{Kroupa:05, Zentner:05}, so the assumption of isotropy may not be a good one." + In addition. the luminous satellites cau be racially biased. so the abundauce ofthe faintest satellites within 50 kpc may uot be easily corrected to larger distances without prior knowledge of this bias.," In addition, the luminous satellites can be radially biased, so the abundance of the faintest satellites within 50 kpc may not be easily corrected to larger distances without prior knowledge of this bias." + Aud. of course. satellites of different Iuminosity aud surface brightuess will have different. completeness Limits.," And, of course, satellites of different luminosity and surface brightness will have different completeness limits." + These selection biases have beeu considered iu detail in a recent paper by 2.., These selection biases have been considered in detail in a recent paper by \cite{Tollerudetal08}. + This study finds that there may be between 300 to 600 luminous satellites within the virial radius of the Milky Way., This study finds that there may be between 300 to 600 luminous satellites within the virial radius of the Milky Way. + Their estimate lor the number of luminous satellites within a Gialactocentrie distance of about 200 kpe is 120. that is slightly larger than our simple (auc more couservative) estimate.," Their estimate for the number of luminous satellites within a Galactocentric distance of about $200$ kpc is 120, that is slightly larger than our simple (and more conservative) estimate." + Iu this section. we use the results of publislied N-body simulatious to estimate the uumber of dark halos in the Milky Way that have. or had. a circular velocity e.>20 kin/s. By definition. dwarf galaxies formed in these dark halos are not pre-reionization fossils.," In this section, we use the results of published N-body simulations to estimate the number of dark halos in the Milky Way that have, or had, a circular velocity $v_c>20$ km/s. By definition, dwarf galaxies formed in these dark halos are not pre-reionization fossils." + If we find that the munber ol observed Milky Way satellites exceeds the estimated uumber of these massive halos we must conclude that at least a fraction of the observed Milky Way satellites are pre-reionization lossils., If we find that the number of observed Milky Way satellites exceeds the estimated number of these massive halos we must conclude that at least a fraction of the observed Milky Way satellites are pre-reionization fossils. + GIX06 have estimated that pre-reionization fossils may constitute about 1/3 of Milky Way cwarts. based ou detailed comparisons between predicted aud observed Calactocentrie distributions of dwarf satellites.," GK06 have estimated that pre-reionization fossils may constitute about $1/3$ of Milky Way dwarfs, based on detailed comparisons between predicted and observed Galactocentric distributions of dwarf satellites." + [t is clear that if we simply count the number of dark halos within the Milky Way virial radius with c.x20 kms. their number is much smaller than the current number of observed Luminous satellites.," It is clear that if we simply count the number of dark halos within the Milky Way virial radius with $v_c \simgt 20$ km/s, their number is much smaller than the current number of observed luminous satellites." + However. a significant fraction of dark halos that today have e;«20 km/s were once more massive. due to tidal tripping (2) .," However, a significant fraction of dark halos that today have $v_c < 20$ km/s were once more massive, due to tidal tripping \citep{KravtsovGnedinKlypin04} ." + If the stars in these halos survive tidal stripping [or as long as the dark matter. they may inceed account for a fraction or all of the newly discovered ultra-[alnt dwarf.," If the stars in these halos survive tidal stripping for as long as the dark matter, they may indeed account for a fraction or all of the newly discovered ultra-faint dwarfs." + ? [avor the idea that tidal strippiug of the dark matter halo does not affect the stellar properties of the dwarf galaxy., \cite{KravtsovGnedinKlypin04} favor the idea that tidal stripping of the dark matter halo does not affect the stellar properties of the dwarf galaxy. + Thus. this model is qualitatively similar to our inodel lor pre-reiouization fossils. save a rescaling of the mass of the dark halos hosting the dwarfs.," Thus, this model is qualitatively similar to our model for pre-reionization fossils, save a rescaling of the mass of the dark halos hosting the dwarfs." +scale through light scattered. by the dust. grains that will inevitably be entrained by the wind.,scale through light scattered by the dust grains that will inevitably be entrained by the wind. + The origin of crvstalline dust) erains detected. in protoplanctary dises via infra-red. (LR) spectroscopy. (e.g. Jouwman et al., The origin of crystalline dust grains detected in protoplanetary discs via infra-red (IR) spectroscopy (e.g. Bouwman et al. + 2001) and directly. within our own solar system (e.g. Wooden et al., 2001) and directly within our own solar system (e.g. Wooden et al. + 1999). is. still a matter. of discussion., 1999) is still a matter of discussion. + The source of all dust in star formation - the ISM - is inferred to be entirely amorphous (c.g. Ixemper et al., The source of all dust in star formation - the ISM - is inferred to be entirely amorphous (e.g. Kemper et al. + 2005)., 2005). + Spectroscopy of dises (van Boekel et. al., Spectroscopy of discs (van Boekel et al. + 2005: Apai et al., 2005; Apai et al. + 2005) indicates a non-neeligible level of crystalline dust outside the crystalline radius. where erains are hot enough (Z> SOOIWK) to be thermally annealed. and converted into crystalline grains.," 2005) indicates a non-negligible level of crystalline dust outside the crystalline radius, where grains are hot enough $T>800$ K) to be thermally annealed and converted into crystalline grains." + This discovery has. lead to the development of dise models with radial mixing to allow crystalline grains that formed in the hot inner disc to be transported to larger radii (e.g. Morfill. Νους 1984: Gail 2001. 2002: Wehrstedt. Cail 2002: Dockelee-Alorvan et al.," This discovery has lead to the development of disc models with radial mixing to allow crystalline grains that formed in the hot inner disc to be transported to larger radii (e.g. Morfill Voelk 1984; Gail 2001, 2002; Wehrstedt Gail 2002; Bockelee-Morvan et al." + 2002: Dullemond et al., 2002; Dullemond et al. + 2006: LHlughes Armitage 2010)., 2006; Hughes Armitage 2010). + Another suggestion put. forward. by Shu et al. (, Another suggestion put forward by Shu et al. ( +1996). is that. ervstzline grains could. be czuried outwards by a x-winel.,"1996), is that crystalline grains could be carried outwards by a x-wind." + Given that the crystallization radius of <1-2AU is smaller than the minimum launch radius for a photoevaporative wind 22:44 around Llerbig Ac/Be stars and lower mass stars. the photoevaporative wind cannot be the direct source of the crystalline grains at larger radii. but could work in combination with racial mixing to produce the observed. enhancement.," Given that the crystallization radius of $<$ 1-2AU is smaller than the minimum launch radius for a photoevaporative wind $>2AU$ around Herbig Ae/Be stars and lower mass stars, the photoevaporative wind cannot be the direct source of the crystalline grains at larger radii, but could work in combination with radial mixing to produce the observed enhancement." + Furthermore crystallinity around edge-on disces can be used to probe the source of the dust in the extended: emission. since a disce origin will eive rise to crystalline dust. grains in the wind while an in-falline envelope will contain only amorphous grains.," Furthermore crystallinity around edge-on discs can be used to probe the source of the dust in the extended emission, since a disc origin will give rise to crystalline dust grains in the wind while an in-falling envelope will contain only amorphous grains." + In this paper we present a simple model to investigate the imprint of photoevaporation on the extended. emission observed. around. edge-on Llerbig Ac/Be stars., In this paper we present a simple model to investigate the imprint of photoevaporation on the extended emission observed around edge-on Herbig Ae/Be stars. + We will compare our model to current observations of edge-on cliscs along with following the fate of crystalline grains in the wind as they are transported to large radius., We will compare our model to current observations of edge-on discs along with following the fate of crystalline grains in the wind as they are transported to large radius. + In Section ?? we describe the model. including the hyelrocynamic ancl radiative transfer methods.," In Section \ref{model} we describe the model, including the hydrodynamic and radiative transfer methods." + In Section ο we present svnthetic images obtained [rom the models., In Section \ref{sec:images} we present synthetic images obtained from the models. + In Section. ?? we describe the results of crystallinity calculations for the wind., In Section \ref{sec:cryst} we describe the results of crystallinity calculations for the wind. + We compare our results to observations of edge-on discs in Section ?? and we summarise our moin findings in Section ?7.., We compare our results to observations of edge-on discs in Section \ref{sec:compare} and we summarise our main findings in Section \ref{sec:conclusions}. + Considering the force balance on a cust grain. it is easy to show that small cust particles are entrained in a photoevaporative wind. which carries them. out to larec distances.," Considering the force balance on a dust grain, it is easy to show that small dust particles are entrained in a photoevaporative wind, which carries them out to large distances." + ‘Takeuchi et al. (, Takeuchi et al. ( +"2005) showed that the drag force on a grain is approximately: where ma. py and e are. respectively: the mass. the density and the radius of à dust grain (assumed to be spherical) and po and e, are the density and velocity of the wind.","2005) showed that the drag force on a grain is approximately: where $m_d$, $\rho_d$ and $a$ are, respectively; the mass, the density and the radius of a dust grain (assumed to be spherical) and $\rho_w$ and $v_w$ are the density and velocity of the wind." +" At large raclius (ές)7 1) the Dow is approximately spherical implving poc, [alls olf as 1/77.", At large radius $z/R>1$ ) the flow is approximately spherical implying $\rho_wv_w$ falls off as $1/r^2$. +" Since gravity. also falls oll as 1/77 and v, increases monotonically with radius. then if à grain is still entrained several scale heights above the aunching surface. it will be entrained permanently. allowing dust to be carried to very large distance from the star. since he drag force will dominate over gravity."," Since gravity also falls off as $1/r^2$ and $v_w$ increases monotonically with radius, then if a grain is still entrained several scale heights above the launching surface, it will be entrained permanently, allowing dust to be carried to very large distance from the star, since the drag force will dominate over gravity." + We build a simplified. model to test. the possibility of extended emission. [rom dust grains cue to a ohotoevaporative wind. and we choose a set of assumptions hat allows us to place an upper limit on this expected evel of emission.," We build a simplified model to test the possibility of extended emission from dust grains due to a photoevaporative wind, and we choose a set of assumptions that allows us to place an upper limit on this expected level of emission." + Namely we assume that the entire cust »opulation is able to reach the launching surface of the wind via some turbulent mechanism and ignore the effects of settling ancl grain growth., Namely we assume that the entire dust population is able to reach the launching surface of the wind via some turbulent mechanism and ignore the effects of settling and grain growth. + Our simple mocel ignores the details of the bound regions of the and thus ignores any emission. produced. by this region. includingon£g the wind itself and its contributions to emission.," Our simple model ignores the details of the bound regions of the and thus ignores any emission produced by this region, including the wind itself and its contributions to emission." + This simplification means our model will not be accurate near the mid-plano. where emission from dust in the discs upper atmosphere dominates over the wind emission.," This simplification means our model will not be accurate near the mid-plane, where emission from dust in the disc's upper atmosphere dominates over the wind emission." + Therefore. we are unable to reproduce the observed intensities and optical depths seen at several scale height above and below the mid-plane in an edgc-on dise: however. here we are interested in the extended emission. which. in the absence of an infalling envelope is dominated by the photoevaporative wind.," Therefore, we are unable to reproduce the observed intensities and optical depths seen at several scale height above and below the mid-plane in an edge-on disc; however, here we are interested in the extended emission, which, in the absence of an infalling envelope is dominated by the photoevaporative wind." + Our model naturally produces a wingnut morphology similar to that seen in several scattered. light images (c.g. Perrin et al., Our model naturally produces a `wingnut' morphology similar to that seen in several scattered light images (e.g. Perrin et al. + 2006). and. produces a spatially variable dust. distribution. due to the cdillerent. maximum grain size that can be entrained along cach streamline.," 2006), and produces a spatially variable dust distribution, due to the different maximum grain size that can be entrained along each streamline." + The radial morphology. of the streamlines then vields that. at a eiven evlindrical radius. the maximum grain size increases with height. resulting in a spatial variation of colour in the scattered. light. images.," The radial morphology of the streamlines then yields that, at a given cylindrical radius, the maximum grain size increases with height, resulting in a spatial variation of colour in the scattered light images." + Furthermore crvstalline. grains entrained in the wind are transported outwards from regions of the disc with higher ervstallinity [ractions resulting in an enhancement of crystalline grains in the wind over the discs underlying cistrubtion., Furthermore crystalline grains entrained in the wind are transported outwards from regions of the disc with higher crystallinity fractions resulting in an enhancement of crystalline grains in the wind over the disc's underlying distrubtion. + We can split the method. for constructing scattered light images into three separate parts: (i) hyvdrodynamic calculations of the photoevaporative wind: (ii) calculation of the dust profile. distribution ancl crystallinity based. on the hydrodynamic solution: (iii) radiative transfer moceling of the dust. distribution., We can split the method for constructing scattered light images into three separate parts: (i) hydrodynamic calculations of the photoevaporative wind; (ii) calculation of the dust profile distribution and crystallinity based on the hydrodynamic solution; (iii) radiative transfer modeling of the dust distribution. + As the mass-loss rates are not well known for Llerbig Ae/Be stars we have left the ionizing luminosity (which sets the mass-loss rates) for an EUV driven wind (Llollenbach et al., As the mass-loss rates are not well known for Herbig Ae/Be stars we have left the ionizing luminosity (which sets the mass-loss rates) for an EUV driven wind (Hollenbach et al. + 1994) as a free parameter and consider the elect of changing niws-loss rates on the morphology. colour of the emission and cevstallinity distribution in the wines.," 1994) as a free parameter and consider the effect of changing mass-loss rates on the morphology, colour of the emission and crystallinity distribution in the winds." + We consider an EUV wind from a primordial disc around a 2.5M. star with a range in ionizing luminosity from 107 to lah s! , We consider an EUV wind from a primordial disc around a $_\odot$ star with a range in ionizing luminosity from $10^{41}$ to $10^{45}$ $^{-1}$ +such as that formed in the simulations has a relatively sanall density coutrast between the equatorial plane aud the polar regions. advection dominated flows are also hot enough that the eas is only weakly bound to the central mass.,"such as that formed in the simulations has a relatively small density contrast between the equatorial plane and the polar regions, advection dominated flows are also hot enough that the gas is only weakly bound to the central mass." + Detailed solutions show that the Bernoulli coustaut. which measures the enerev the eas would possess if adiabatically uoved to immfuitv. is positive for an often wide range of angles close to the poles (Naravan Yi 1991: 1995).," Detailed solutions show that the Bernoulli constant, which measures the energy the gas would possess if adiabatically moved to infinity, is positive for an often wide range of angles close to the poles (Narayan Yi 1994; 1995)." + Although the outcome depends additionally ou the outer boundary coucitious aud the detailed plysics of outflow eeneration. this positivity of Be is likely to iuplv that outflows are a generic feature of advection dominated disks (o Naravan Yi 1995: Dlaudford Beechuanu 1999).," Although the outcome depends additionally on the outer boundary conditions and the detailed physics of outflow generation, this positivity of ${\rm Be}$ is likely to imply that outflows are a generic feature of advection dominated disks ( Narayan Yi 1995; Blandford Begelman 1999)." + For our purposes. we cau distinguish two extreme possibilities. in which outflows are either sclsimular or ecucrated exclusively frou the iuner disk at Roc.Self-sinidlaer," For our purposes, we can distinguish two extreme possibilities, in which outflows are either self-similar or generated exclusively from the inner disk at $R \simeq R_{\rm ns}$." + outflows from advection dominated: flows represcut the model considered by Blauclford Beecluan (1999)., outflows from advection dominated flows represent the model considered by Blandford Begelman (1999). + Tn this case the fraction of accreting mass lost iu the outflow is the same for each decade in disk radius. so that the remaining mass accretion rate through the disk decreases iuwards as ALxRe with 0100 K) cools mainly through CO. H:O. and H» ro-vibrational transitions1995).,"Warm molecular gas $T > 100$ K) cools mainly through CO, $_2$ O, and $_2$ ro-vibrational transitions." +. The ground state lines of CO. up to J=6—5. are extensively studied from the ground in à large number of galaxies up to a redshift z~0.04.," The ground state lines of CO, up to $J=6-5$, are extensively studied from the ground in a large number of galaxies up to a redshift $z\sim +0.04$." + Unfortunately. the atmosphere makes it impossible tostudy CO transitions with J>8 and HO rotational lines.," Unfortunately, the atmosphere makes it impossible tostudy CO transitions with $J > 8$ and $_2$ O rotational lines." + It is these lines. however. that are tracing the warm molecular gas.," It is these lines, however, that are tracing the warm molecular gas." + Moreover. these lines are sensitive to extreme UV irradiation from star-formation and X-rays due to supermassive black-hole accretion.," Moreover, these lines are sensitive to extreme UV irradiation from star-formation and X-rays due to supermassive black-hole accretion." +" Some high-/ CO lines have been observed in bright galactic objects such as the Orion Bar and Sagittarius A1999)., and the Class 0 object L1448-mm1999)."," Some $J$ CO lines have been observed in bright galactic objects such as the Orion Bar and Sagittarius A, and the Class 0 object L1448-mm." +. It is only recently that significant progress is being made in the study of the warm molecular interstellar medium (ISM) in nearby galaxies., It is only recently that significant progress is being made in the study of the warm molecular interstellar medium (ISM) in nearby galaxies. + Both high-J as well as rotational water lines have been observed abundantly after the launch of the Herschel Space observatory. that is operating between wavelengths =55—672 jm. The successful HerCULES open time key program has observed 29 close (U)LIRGs with both SPIRE and PACS instruments. revealing CO lines up CO J=14-13 (while current follow-up PACS observations might detect even higher transition) and H»O lines in Mrk 231 that are of comparable strengths2010).," Both $J$ as well as rotational water lines have been observed abundantly after the launch of the Herschel Space observatory, that is operating between wavelengths $\lambda=55-672$ $\mu$ m. The successful HerCULES open time key program has observed 29 close (U)LIRGs with both SPIRE and PACS instruments, revealing CO lines up CO $J=14-13$ (while current follow-up PACS observations might detect even higher transition) and $_2$ O lines in Mrk 231 that are of comparable strengths." +. These CO and H?O lines are at least in part produced in regions of the galaxy exposed to X-rays. so-called XDRs2005).. but emission produced through shock excitation may also contribute as observed for OH in Mrk 2312010).," These CO and $_2$ O lines are at least in part produced in regions of the galaxy exposed to X-rays, so-called XDRs, but emission produced through shock excitation may also contribute as observed for OH in Mrk 231." +. Moreover. Herschel-PACS also detected a lot of high-/ CO lines as well as H»O and OH in embedded objects. such as DK Chamaeleontis and in disk atmospheres. ο.σ.. HD 1005462010).. where X-rays also affect the chemical-thermal structure.," Moreover, -PACS also detected a lot of $J$ CO lines as well as $_2$ O and OH in embedded objects, such as DK Chamaeleontis and in disk atmospheres, e.g., HD 100546, where X-rays also affect the chemical-thermal structure." + Even though this paper focuses on an applicatior to ULIRGs. it will have applications to other objects as well.," Even though this paper focuses on an application to ULIRGs, it will have applications to other objects as well." + Understanding the excitation and chemistry of these important molecules is therefore key in studying the dominant physical processes in the ISM and star-formation., Understanding the excitation and chemistry of these important molecules is therefore key in studying the dominant physical processes in the ISM and star-formation. + CO is a linear molecule. and the radiation transfer models allow to calculate far-infrared to millimeter spectra relatively easy for a given physical structure.," CO is a linear molecule, and the radiation transfer models allow to calculate far-infrared to millimeter spectra relatively easy for a given physical structure." + Models predicting CO emission. where both the thermal-chemical structure and radiation transfer are calculated simultaneously have more problems to reach agreement.," Models predicting CO emission, where both the thermal-chemical structure and radiation transfer are calculated simultaneously have more problems to reach agreement." + The case for H»O is even worse. due to its complex nature: high critical densities nq>107—10'° em in combination with high opacities. infrared-pumping and maser actively. makes an excitation calculation extremely challenging.," The case for $_2$ O is even worse, due to its complex nature: high critical densities $n_{\rm crit} > 10^8 - 10^{10}$ $^{-3}$ in combination with high opacities, infrared-pumping and maser actively, makes an excitation calculation extremely challenging." + Also. the excitation state in which water will enter the gas-phase after desorption or evaporation from a dust grain is very uncertain.," Also, the excitation state in which water will enter the gas-phase after desorption or evaporation from a dust grain is very uncertain." + A first guess in this would be to divide the excess energy over the levels using equipartion. so 1/3 translational. 1/3 rotational and 1/3 vibrational excitation. with a Boltzmann distribution for the sub-levels.," A first guess in this would be to divide the excess energy over the levels using equipartion, so 1/3 translational, 1/3 rotational and 1/3 vibrational excitation, with a Boltzmann distribution for the sub-levels." + The formation of molecular hydrogen. H>. in the ISM has been a long-standing problem.," The formation of molecular hydrogen, $_2$, in the ISM has been a long-standing problem." + At extrenely low metallicities. when no dust is present. H» either forms through the H route1991). or through a three-body reaction (H+H+H—H» +H).," At extremely low metallicities, when no dust is present, $_2$ either forms through the $^-$ route, or through a three-body reaction $\rm H + H + H \rightarrow H_2 + H$ )." + The three-body reaction dominates at very high densities1998)., The three-body reaction dominates at very high densities. + For normal ISM conditions. Η- is predominantly formed on dust grains. and much progress has been made over the past two decades. both experimentially as Well as theoretically. in understanding this (much faster) formation of H» on the surfaces of grainstherein).," For normal ISM conditions, $_2$ is predominantly formed on dust grains, and much progress has been made over the past two decades, both experimentially as well as theoretically, in understanding this (much faster) formation of $_2$ on the surfaces of grains." + In general. the understanding is that CO is formed in the gas-phase. but the origin of gas-phase water 1s not so clear-cut.," In general, the understanding is that CO is formed in the gas-phase, but the origin of gas-phase water is not so clear-cut." +" It is possible to form water in the gas-phase through either a chain of 1eutral-neutral reactions containing a number of temperature barriers. or through ton-molecule reactions when the gas Is moderately tonized (v,~ 107)."," It is possible to form water in the gas-phase through either a chain of neutral-neutral reactions containing a number of temperature barriers, or through ion-molecule reactions when the gas is moderately ionized $x_e\sim +10^{-5}$ )." + The formation of water on interstellar dust can also be an efficient route in diffuse and dense clouds ., The formation of water on interstellar dust can also be an efficient route in diffuse and dense clouds . +. Several routes to form water can be considered. involving stccessive hydrogenation of oxygen either with Η» or H. Because species can stay on the dust. they," Several routes to form water can be considered, involving successive hydrogenation of oxygen either with $_2$ or H. Because species can stay on the dust, they" +N-rav flashXRF) is a kiud of recently ideutified explosion.,X-ray flash(XRF) is a kind of recently identified explosion. + Its nost properties are qualitatively simular to those of gamma-ray burst(GRD) such as duration. teniporal structure. spectrun and spectral evolution except peak. enerev and flux.," Its most properties are qualitatively similar to those of gamma-ray burst(GRB) such as duration, temporal structure, spectrum and spectral evolution except peak energy and flux." + A-rav flash’s peak euergv and fiux are lower. but their distributions just smoothly join the eauua-ray burst. there secus to © no obyious borderline between ARF aud CRD.," X-ray flash's peak energy and flux are lower, but their distributions just smoothly join the gamma-ray burst, there seems to be no obvious borderline between XRF and GRB." + These similarities led to the sugeestion that the N-rav. flash is in fact “Neray rich” eanunrayv burs (Kkippeu et al.," These similarities led to the suggestion that the X-ray flash is in fact ""X-ray rich"" gamma-ray burst (Kippen et al." + 2003). uavbe they have sale origins except for different conditions.," 2003), maybe they have same origins except for different conditions." + The similarity between NRF aud CRB sugeests that the N-rav flash melt come from an off-axis nonunuiforni eanunu-rav burst jetWoosley ethenal., The similarity between XRF and GRB suggests that the X-ray flash might come from an off-axis nonuniform gamma-ray burst's jet(Woosley et al. + 2003: Rossi ct al., 2003; Rossi et al. + 2002: Zhang Meszaros 2002)., 2002; Zhang Meszaros 2002b). + W. a burst is observed at the center of the jet. it will|ο detected as a normal eunmua-ray burs.," When a burst is observed at the center of the jet, it will be detected as a normal gamma-ray burst." +" Dut the ]mrst tend tobe “dirtw when it ds observed at a large viewing augle (Zhang A\eszaros 20020). off-axis ejected iatter takes less ποον"" and has lower Lorentz factor."," But the burst tend to be ""dirty"" when it is observed at a large viewing angle (Zhang Meszaros 2002b), off-axis ejected matter takes less energy and has lower Lorentz factor." + So its Ei will shift to Nevay responsibility. aud it will1νο observed as an N-ray flash.," So its $E_{\rm p}$ will shift to X-ray responsibility, and it will be observed as an X-ray flash." + Iu this paper. we adopt a structured jet model where all the cuerey ancl mass of ejected matter per unit solid anele and the initial bulk Lorentz factor depend on the angle distance 0 from the ceuter as power laws e(0)xο Fingi)Tossx(0/042. ?00).(0)N(0/0) CNeszaros et al.," In this paper, we adopt a structured jet model where all the energy and mass of ejected matter per unit solid angle and the initial bulk Lorentz factor depend on the angle distance $\theta$ from the center as power laws $\epsilon(\theta)\propto(\theta/\theta_{\rm c})^{-k}$ , $m_{\rm +ej}(\theta)\propto(\theta/\theta_{\rm c})^{-k_{2}}$, $\gamma(\theta)\propto(\theta/\theta_{\rm c})^{-k_{1}}$ (Meszaros et al." + 1998: ot al., 1998; Rossi et al. + , 2002). +We take k=2 for a uonunifori jet. Bossi et al.," We take $k=2$ for a nonuniform jet, Rossi et al." + have shown that 1.5x&<2.2 is the reasonable value for fitting observations wellBossi ( al., have shown that $1.5\leq k\leq 2.2$ is the reasonable value for fitting observations well(Rossi et al. + 2002)., 2002). +" Frail ct a.(2001) had eiveu the jet angles distribution with known redshift ezunnia-rav bursts,", Frail et al.(2001) had given the jet angles distribution with known redshift gamma-ray bursts. + The jet's opening rele are range from 0.05 to 0.[ rad(Frail et al., The jet's opening angle are range from 0.05 to 0.4 rad(Frail et al. + 2001). id most common value is 0.12 rad(Perna et al.," 2001), and most common value is 0.12 rad(Perna et al." + 2003)., 2003). + The ganuua-ray euergies released are narrowly clustered around E.5«LW %eres(Frail et al.," The gamma-ray energies released are narrowly clustered around $E_{\gamma}\sim 5\times10^{50}{\rm +ergs}$ (Frail et al." + 2001)., 2001). + We introduce our model aud eive out some analytical solutious in Sect.2., We introduce our model and give out some analytical solutions in Sect.2. + Iu Sect.3 we present numerical results of spectra and fluxes for both wniform aud nonuuiforiu jets. and calculate the gamma-ray bursts to N-rav flashes observational ratio.," In Sect.3 we present numerical results of spectra and fluxes for both uniform and nonuniform jets, and calculate the gamma-ray bursts to X-ray flashes observational ratio." +" Finally. we give a discussion aud draw sole conclusions im Sect.1,"," Finally, we give a discussion and draw some conclusions in Sect.4." + We consider a relativistic outflow where the enerev per nuit solid angle depend as power law ou the aneular distance from the ceuter 0 (Meszaros et al., We consider a relativistic outflow where the energy per unit solid angle depend as power law on the angular distance from the center $\theta$ (Meszaros et al. + 1998: Zhang Meszaros 2002a: Rossi et al., 1998; Zhang Meszaros 2002a; Rossi et al. + 2002):<0., 2002):. +" and the ejected inatter per unit solid angle and the bulk Lorentz factor also depend on ϐ as power laws: nn4(00)=mgο.""2. (0)=s(0)(0/0,)P: (eoxO0 0)."," and the ejected matter per unit solid angle and the bulk Lorentz factor also depend on $\theta$ as power laws: $m_{\rm +ej}(\theta)=m_{\rm ej}(0)(\theta/\theta_{\rm c})^{-k_{2}}$, $\gamma(\theta)=\gamma(0)(\theta/\theta_{\rm c})^{-k_{1}}$ $\theta_{\rm c}\leq\theta\leq\theta_{\rm j}$ )." +" The deceleration radius at @ is rad)Lin,Bel)(OF67E3ratsjka2hb0963 ."," The deceleration radius at $\theta$ is $r_{\rm +d}(\theta)=(\frac{3\epsilon(\theta)}{4\pi n\gamma(\theta)^{2}{\rm +m}_{\rm p}{\rm c}^{2}})^{1/3}=r_{\rm +d}(0)(\frac{\theta}{\theta_{\rm c}})^{(-k+2k_{1})/3}$ ." + All our calculations will|vo done at the time when an outflow just reaches its deceleration radius where the blast wave is formed., All our calculations will be done at the time when an outflow just reaches its deceleration radius where the blast wave is formed. + Because of the beaming effect of large Lorentz factor at this time. there is no obvious observation difference between isotropic aud anisotropic outfiows.," Because of the beaming effect of large Lorentz factor at this time, there is no obvious observation difference between isotropic and anisotropic outflows." + That means a jetted outflow with a viewing augle O.. is observationally simular to an isotropic outflow with bulk Lorentz factor +=5(0.)., That means a jetted outflow with a viewing angle $\theta_{\rm v}$ is observationally similar to an isotropic outflow with bulk Lorentz factor $\gamma=\gamma(\theta_{\rm v})$. + So we can use the solutions from. an isotropic explosion modcldiffe(Sart Piran 1999) to do an analysisby choosing ut Lorentz factor at different viewing angle £A. (vuΕνJrnax((0)=MaxtO)Fiaax(] These equations describe the emission features from a shock between outflows aud external iiedimus.," So we can use the solutions from an isotropic explosion model (Sari Piran 1999) to do an analysis by choosing different Lorentz factor at different viewing angle $\theta_{\rm v}$: $(\nu F_{\nu})_{\rm max}(\theta)=\nu_{\rm max}(\theta)F_{\nu +,\rm max}(\theta)$ These equations describe the emission features from a shock between outflows and external mediums." + Generally a external shock is not ideal for reproducing lughly variable burst(Sari et al1998). but it can reproduce a burst with several peaks(Panaiteseu Alesziros 1998) aud παν therefore be applicable to the class of long. «που bursts(Meszaros 1999).," Generally a external shock is not ideal for reproducing a highly variable burst(Sari et al,1998), but it can reproduce a burst with several peaks(Panaitescu Meszaros 1998) and may therefore be applicable to the class of long, smooth bursts(Meszaros 1999)." +gaars later in the clusters life.,stars later in the cluster's life. + We used the properties of 1e entire cluster core rather than that of the sub-cluster [massive stars because the low to intermediate mass stars ji we were considering here have not had time to mass segregate., We used the properties of the entire cluster core rather than that of the sub-cluster of massive stars because the low to intermediate mass stars that we were considering here have not had time to mass segregate. + Using equation 13 of Leonard.(1989)... we found i only + collisions should have occurred. in the first 5 p»Ive.," Using equation 13 of \citet{1989AJ.....98..217L}, we found that only 4 collisions should have occurred in the first 5 Myr." + Even if we assume that the cluster conditions remain 1e same until the stars of this mass reach the AGB phase (about 30 Myr). only a few dozen collisions will occur. and only approximately of those will produce stars with masses between 3 and SAL.," Even if we assume that the cluster conditions remain the same until the stars of this mass reach the AGB phase (about 30 Myr), only a few dozen collisions will occur, and only approximately of those will produce stars with masses between 3 and 8." +.. Therefore. we will neglect the contribution of collisionally-created AGB stars.," Therefore, we will neglect the contribution of collisionally-created AGB stars." + Now we caleulate the contribution of the AGB stars rom both the first and. second stellar generations., Now we calculate the contribution of the AGB stars from both the first and second stellar generations. + We use vields for Z=0.001 for both the first ane second generation populations (Ventura&1)Antona2008.2009)..," We use yields for Z=0.001 for both the first and second generation populations \citep{2008A&A...479..805V, + 2009A&A...499..835V}." + Phese vields will be incorrect for the AGB2 stars formed from the ejecta of he runaway collision and fast rotating massive stars. as the iclium and light clement content of these stars is initially increased.," These yields will be incorrect for the AGB stars formed from the ejecta of the runaway collision and fast rotating massive stars, as the helium and light element content of these stars is initially increased." + “The structure of helium-rich. stars is. clillerent han that of normal stars. and the hvdrogen-burning eveles are dependent on the abundanees of the catalyst elements.," The structure of helium-rich stars is different than that of normal stars, and the hydrogen-burning cycles are dependent on the abundances of the catalyst elements." + Therefore. we should not simply. scale the vields from the normal ACD stars to estimate the vielcls of high-helium stars.," Therefore, we should not simply scale the yields from the normal AGB stars to estimate the yields of high-helium stars." + The helium abundances will be higher than given by the normal star vields because even. unprocessed material will be enriched in helium., The helium abundances will be higher than given by the normal star yields because even unprocessed material will be enriched in helium. + However. the number of second-eeneration AGB stars is low (~ 65). and so we will take the conservative assumption that their vields are the same as the first generation population.," However, the number of second-generation AGB stars is low $\sim$ 65), and so we will take the conservative assumption that their yields are the same as the first generation population." + In addition. helium-rich AGB stars have lifetimes which are z shorter than stars of the same mass but normal helium.," In addition, helium-rich AGB stars have lifetimes which are $\approx$ shorter than stars of the same mass but normal helium." + In our simple model. this does not alfect our results because we simply Lgum up all the contributions from AGB stars with Lifetimes gajorter than our ceutolL," In our simple model, this does not affect our results because we simply sum up all the contributions from AGB stars with lifetimes shorter than our cutoff." + ELowever. a more detailed model will need to include this lifetime elfect.," However, a more detailed model will need to include this lifetime effect." + First. we assume that all ACID. stars between 3 and 6 contribute to the material which forms the third generation.," First, we assume that all AGB stars between 3 and 6 contribute to the material which forms the third generation." +— The AGB stars produce almost. twice as much material as the massive stars (6084. M)., The AGB stars produce almost twice as much material as the massive stars (6084 ). + The. helium abundance of this population is Y=0.29. which is higher than the standard value but still not as high as the Y-0.4 inferred. for clusters such as NGC 2808.," The helium abundance of this population is Y=0.29, which is higher than the standard value but still not as high as the Y=0.4 inferred for clusters such as NGC 2808." + The AGB ejecta is slightly enhanced. in oxygen compared to the initial value (O/Fe] = 0.55 up from O04). and is significantly enhanced. in sodium {ΝαΡο = 1.04. up from -0.2).," The AGB ejecta is slightly enhanced in oxygen compared to the initial value ([O/Fe] = 0.55, up from 0.4), and is significantly enhanced in sodium ([Na/Fe] = 1.04, up from -0.2)." + The sodium enhancement is much larger than that seen in most globular clusters. and the AGB stars alone do not produce stars with low oxvgen/high sodium. values that are seen in elobular clusters.," The sodium enhancement is much larger than that seen in most globular clusters, and the AGB stars alone do not produce stars with low oxygen/high sodium values that are seen in globular clusters." + Dilution with primordial material reduce both the sodium and oxvgen abundances. but an oxygen depletion of approximately 1 dex is impossible to accomplish with these AGB vields.," Dilution with primordial material reduce both the sodium and oxygen abundances, but an oxygen depletion of approximately 1 dex is impossible to accomplish with these AGB yields." + Similarly. this population produces some aluminum without much change in magnesium.," Similarly, this population produces some aluminum without much change in magnesium." + This population is labelled ‘all AGB in figures 1. - 4.., This population is labelled `all AGB' in figures \ref{fig:Yhist} - \ref{fig:AlMgdiagram}. + llowever. AGB stars have lifetimes of over 300 Alvr.," However, 3 AGB stars have lifetimes of over 300 Myr." + Εις time is long enough that SNla may have started to pollute the cluster and. disrupt the gas., This time is long enough that SNIa may have started to pollute the cluster and disrupt the gas. + Also. the most massive AGB stars started losing their mass after only ~ 50 Myr. and it is not clear that this material would have remained in the cluster. waiting for the ejecta of the lower mass stars.," Also, the most massive AGB stars started losing their mass after only $\sim$ 50 Myr, and it is not clear that this material would have remained in the cluster, waiting for the ejecta of the lower mass stars." + Lt is more likely that the longest possible time for the AGB ejecta to collect is more like 100 Myr. which is the lifetime of à 5 AGB star.," It is more likely that the longest possible time for the AGB ejecta to collect is more like 100 Myr, which is the lifetime of a 5 AGB star." + Lowe restrict ourselves to only the most massive AGB stars (5-6 M.). then the sodium and oxygen vields are more consistent with the observations. and in [act are very similar to those from the runaway | FRAIS population.," If we restrict ourselves to only the most massive AGB stars (5-6 ), then the sodium and oxygen yields are more consistent with the observations, and in fact are very similar to those from the runaway + FRMS population." + Under this assumption. ACD stars only contribute ~ 2100 to the new generation. an amount of mass which is comparable to that of the first generation.," Under this assumption, AGB stars only contribute $\sim$ 2100 to the new generation, an amount of mass which is comparable to that of the first generation." + This population also produces more aluminum and shows a very slight magnesium dilution., This population also produces more aluminum and shows a very slight magnesium dilution. + This population is labelled ‘high mass AGD' in figures 1. - 4.., This population is labelled `high mass AGB' in figures \ref{fig:Yhist} - \ref{fig:AlMgdiagram}. . + If we combine the second and third generation. we have 9.5 .Lo? of material. or less than of the initial cluster.," If we combine the second and third generation, we have 9.5 $\times 10 +^3$ of material, or less than of the initial cluster." + Lowe compare the number of stars that will still be in the elobular cluster at current time (less massive than 0.8 }). the two new generations have created 25 000 stars and there are approximately 2.6 ©107 stars fron: the first eeneration.," If we compare the number of stars that will still be in the globular cluster at current time (less massive than 0.8 ), the two new generations have created 25 000 stars and there are approximately 2.6 $\times 10^5$ stars from the first generation." + We are still required to lose of the initial low-mass stars in order to have our vounger generations form half the cluster at the current day., We are still required to lose of the initial low-mass stars in order to have our younger generations form half the cluster at the current day. + VPhese numbers assume that all AGB stars contribute to the third generation. which is the most &enerous assumption one can make about total mass. but is almost certainly an overestimate as discussed above.," These numbers assume that all AGB stars contribute to the third generation, which is the most generous assumption one can make about total mass, but is almost certainly an overestimate as discussed above." + The other wav to mitigate this mass problem. is to allow primordial material to mix into the gas which will orm either the second. or third. generation (or possibly xh)., The other way to mitigate this mass problem is to allow primordial material to mix into the gas which will form either the second or third generation (or possibly both). + While this will certainly help boost the mass of that eencration. it will also change the abundances.," While this will certainly help boost the mass of that generation, it will also change the abundances." + In figures and 4.. we have drawn lines of dilution for the second and he two possible third generations.," In figures \ref{fig:NaOdiagram} + and \ref{fig:AlMgdiagram}, we have drawn lines of dilution for the second and the two possible third generations." + The amount of dilution ranges from. almost none near the points labelled. by the »xolluters. to a huge amount of mass as the line nears the ximordial abundance.," The amount of dilution ranges from almost none near the points labelled by the polluters, to a huge amount of mass as the line nears the primordial abundance." + We fee that it is more likely that he second generation would be polluted than the third. and so we calculated the tota amount of mass needed to xing the helium abundance down to some values of interest.," We feel that it is more likely that the second generation would be polluted than the third, and so we calculated the total amount of mass needed to bring the helium abundance down to some values of interest." + For example. only 1500 is needed to bring the helium abundance to Y=O.4. but 77 00€) brings Yto 0.25.," For example, only 1500 is needed to bring the helium abundance to Y=0.4, but 77 000 brings Yto 0.25." + This is comparable to the mass ofthe initial generation., This is comparable to the mass of the initial generation. +a vertical line indicating a fixed wwould move to the left.,a vertical line indicating a fixed would move to the left. +" If the N/H ratio is lower than assumed, the displacement would also be to the left."," If the N/H ratio is lower than assumed, the displacement would also be to the left." +" Of course both assumptions could be incorrect in different senses and one error can correct for the other, but without a good knowledge of both the nitrogen ionization ratio and the relative abundance of nitrogen and hydrogen, the method is suspect."," Of course both assumptions could be incorrect in different senses and one error can correct for the other, but without a good knowledge of both the nitrogen ionization ratio and the relative abundance of nitrogen and hydrogen, the method is suspect." +" In an attempt to identify the range of probable values of the nitrogen ionization ratio, we have extracted this information from our calculated models."," In an attempt to identify the range of probable values of the nitrogen ionization ratio, we have extracted this information from our calculated models." +" For the models that most closely match the distribution of the Barnard’s Loop,Bubble,, and WIM observations the ionization ratio varies little."," For the models that most closely match the distribution of the Barnard's Loop, and WIM observations the ionization ratio varies little." +" The nitrogen ionization ratio for log U=-3.67 and T,4,—331000 varies only from 1.007 to 1.014 over the range of Z/H from -0.5 to 0.5 dex.", The nitrogen ionization ratio for log U=-3.67 and 31000 varies only from 1.007 to 1.014 over the range of Z/H from -0.5 to 0.5 dex. +" The ionization ratio for log U=-3.07 and Ts,ar=440000 varies only from 1.012 to 1.035 over the range of Z/H from -0.5 to 0.5 dex.", The ionization ratio for log U=-3.07 and 40000 varies only from 1.012 to 1.035 over the range of Z/H from -0.5 to 0.5 dex. +" This confirms that variations in the ionization ratio do not play an important role, as previously assumed and calculated."," This confirms that variations in the ionization ratio do not play an important role, as previously assumed and calculated." + This is in excellent agreement with the predictions of Sembach et al. (, This is in excellent agreement with the predictions of Sembach et al. ( +2000).,2000). +" Unfortunately, in the study of Madsenetal.(2006),, which drew on the Sembach et al. ("," Unfortunately, in the study of \cite{mad06}, which drew on the Sembach et al. (" +"2000) models a value of the nitrogen ionization ratio of 0.8 was adopted, whereas this is actually the value for N*/N. This error was not corrected when the results were repeated in a review article 2009).","2000) models a value of the nitrogen ionization ratio of 0.8 was adopted, whereas this is actually the value for $^{+}$ /N. This error was not corrected when the results were repeated in a review article \citep{haf09}." +". This makes the electron temperatures they present to be too large, for their assumed abundance."," This makes the electron temperatures they present to be too large, for their assumed abundance." +" In the original study of Haffneretal.(1999) a nitrogen ionization ratio of 1.0 was adopted, which means that those temperatures should be correct, if the nitrogen abundance they adopted of N/H=7.5 x 10~° is both correct and uniform."," In the original study of \citet{haf99} a nitrogen ionization ratio of 1.0 was adopted, which means that those temperatures should be correct, if the nitrogen abundance they adopted of N/H=7.5 x $^{-5}$ is both correct and uniform." +" The more important limitation of the I([N H])/I(Ha)) ratio method is the other scaling factor, the N/H ratio."," The more important limitation of the I([N ) ratio method is the other scaling factor, the N/H ratio." + We argue in 33.6 that in the case of Barnard's Loop that there is a Z/H abundance enhancement of about 0.15 dex that (alone) would shift a line of fixed, We argue in 3.6 that in the case of Barnard's Loop that there is a Z/H abundance enhancement of about 0.15 dex that (alone) would shift a line of fixed +"a ""uniform weighting"", thus we may assume that the same sensitivity can be reached with a larger beam, obtained for example by “natural weighting"".","a “uniform weighting”, thus we may assume that the same sensitivity can be reached with a larger beam, obtained for example by “natural weighting”." +" However, the survey sensitivity may be limited by the rms confusion level."," However, the survey sensitivity may be limited by the rms confusion level." + This is given by Condon 1987; Kronberg et al., This is given by Condon 1987; Kronberg et al. +" 2007): where 612 is the beam size in arcsec, and v is Miz)the frequency in MHz."," 2007): where $\theta_{1,2}$ is the beam size in arcsec, and $\nu$ is the frequency in MHz." + Of course all the issues discussed above will be clarified during the commissioning phase of LOFAR., Of course all the issues discussed above will be clarified during the commissioning phase of LOFAR. +" Thus we decided to present calculations in several cases, specifically €-F=0.25, 0.6 and 1 mJy/beam to cover a range of possible LOFAR sensitivities?."," Thus we decided to present calculations in several cases, specifically $\xi\cdot F\,=0.25$, $0.6$ and $1$ mJy/beam to cover a range of possible LOFAR sensitivities." +. Vertical dashed lines in Fig., Vertical dashed lines in Fig. + 1 show the minimum power of a halo at z~0.05 detectable by LOFAR surveys assuming €-F=0.25.0.6 and 1 mJy/beam.," \ref{Fig.RHLF} show the minimum power of a halo at $z\sim 0.05$ detectable by LOFAR surveys assuming $\xi\cdot F=0.25, 0.6$ and $1$ mJy/beam." +" The important point is that with increasing survey sensitivity new populations of radio halos are expected to be unveiled, with the detectable number of ultra steep spectrum halos increasing in deeper surveys."," The important point is that with increasing survey sensitivity new populations of radio halos are expected to be unveiled, with the detectable number of ultra steep spectrum halos increasing in deeper surveys." +" LOFAR observations will allow to study the distribution of radio halos in the radio-X-ray luminosity diagram at low radio frequencies, so far an unexplored issue."," LOFAR observations will allow to study the distribution of radio halos in the radio–X-ray luminosity diagram at low radio frequencies, so far an unexplored issue." +" The vast majority of ultra-steep spectrum halos visible at low frequencies are expected to be associated with galaxy clusters of intermediate X-ray luminosity, Ly~3—6:10 erg/s, and should be less luminous than radio halos that are presently observed at GHz frequencies."," The vast majority of ultra-steep spectrum halos visible at low frequencies are expected to be associated with galaxy clusters of intermediate X-ray luminosity, $L_X\sim 3-6\cdot 10^{44}$ erg/s, and should be less luminous than radio halos that are presently observed at GHz frequencies." +" This should affect the radio—X-ray luminosity correlation of halos at low frequencies, that is expected to be steeper and with larger scatter than that at 1.4 GHz."," This should affect the radio–X-ray luminosity correlation of halos at low frequencies, that is expected to be steeper and with larger scatter than that at 1.4 GHz." +" To address this issue quantitatively we assume vo=120 MHz, and following C06 and C09 we use Monte Carlo procedures based on the extended Press Schechter (1974; Lacey Cole 1993) formalism to obtaini) the population of galaxy clusters, with their mass (and X-ray luminosity), in the redshift interval z=0—0.5, and the population of radio halos, with their v,, associated with these clusters."," To address this issue quantitatively we assume $\nu_0=120$ MHz, and following C06 and C09 we use Monte Carlo procedures based on the extended Press Schechter (1974; Lacey Cole 1993) formalism to obtain the population of galaxy clusters, with their mass (and X-ray luminosity), in the redshift interval $z=0-0.5$, and the population of radio halos, with their $\nu_s$, associated with these clusters." + We use homogeneous models and the set of model parameters given in the previous section., We use homogeneous models and the set of model parameters given in the previous section. + From these simulations we extract the population of radio halos that can be detected by observations at νο=120 MHz according to their radio luminosity and πα)., From these simulations we extract the population of radio halos that can be detected by observations at $\nu_0=120$ MHz according to their radio luminosity and $f_{min}(z)$. +" In particular, the luminosity at 120 MHz of radio halos with ys=1.4 GHz, in clusters with X-ray luminosity Ly, is obtained from the P(1.4)—Ly correlation, assuming a spectral index a=1.3 and allowing for a random scatter 6P/P=+2 (see discussion in Sect.2)."," In particular, the luminosity at 120 MHz of radio halos with $\nu_s\geq 1.4$ GHz, in clusters with X-ray luminosity $L_X$, is obtained from the $P(1.4)-L_X$ correlation, assuming a spectral index $\alpha=1.3$ and allowing for a random scatter $\delta P/P=\pm 2$ (see discussion in Sect.2)." + The luminosity at 120 MHz of radio halos with a given v; is obtained according to Eq. 2.., The luminosity at 120 MHz of radio halos with a given $\nu_s$ is obtained according to Eq. \ref{Eq:Pnu_P1p4}. . +" In particular, we calculated halo statistics by assuming the following frequency ranges: v,=120—240 MHz, 240—600 MHz, 600—1400 MHz."," In particular, we calculated halo statistics by assuming the following frequency ranges: $\nu_s=120-240$ MHz, $240-600$ MHz, $600-1400$ MHz." + Eq., Eq. +" 2 also implies that halos with v;€v,0, and high Galactic latitudes, |b]2 20) and finin(z) from Eq. 4.."," Finally, we assume the LOFAR sky coverage (the Northern hemisphere, $\delta\geq0$, and high Galactic latitudes, $|b|\geq 20$ ) and $f_{min}(z)$ from Eq. \ref{fmin}." +" The resulting theoretical distribution of radio halos in the P(120)-Lx diagram is shown in Fig. 2,,"," The resulting theoretical distribution of radio halos in the $P(120)-L_X$ diagram is shown in Fig. \ref{Fig.Lr_Lx}," + assuming £F=1.0.6 and 0.25 mJy/beam (colored open dots; from left to right).," assuming $\xi\cdot F=1, 0.6$ and $0.25$ mJy/beam (colored open dots; from left to right)." + Different colored dots indicate halos with different values of v; (the same color code usedin Fig. 1))., Different colored dots indicate halos with different values of $\nu_s$ (the same color code usedin Fig. \ref{Fig.RHLF}) ). +" Halos with different v, fill different regions, with radio halos with smaller v; "," Halos with different $\nu_s$ fill different regions, with radio halos with smaller $\nu_s$ " +been attempted by a number of groups (Beasley οἱ 22002: Schiavon οἱ al.,been attempted by a number of groups (Beasley et 2002; Schiavon et al. + 2002a.b: Puzia el 22002: Maraston et 22003: Leonardi Rose 2003). our work benefits [rom the combination of a homogeneous set of high S/N integrated GC spectra newly collected. by our eroup. with the LST CALDs of several (ens of Galactic GCs. most of them reaching the QC tui-olE by Piotto et ((2002).," 2002a,b; Puzia et 2002; Maraston et 2003; Leonardi Rose 2003), our work benefits from the combination of a homogeneous set of high S/N integrated GC spectra newly collected by our group, with the HST CMDs of several tens of Galactic GCs, most of them reaching the GC turn-off, by Piotto et (2002)." + We demonstrate the ability of well-calibrated models. combined with high S/N spectra. to single out the contribution of DIID stars to the integrated light of GCs.," We demonstrate the ability of well-calibrated models, combined with high S/N spectra, to single out the contribution of BHB stars to the integrated light of GCs." + We use a combination of an Fe-sensitive index and an index comprised of the ratio of two Balmer line EWs to uniquely constrain (he DIID contribution to the integrated light., We use a combination of an Fe-sensitive index and an index comprised of the ratio of two Balmer line EWs to uniquely constrain the BHB contribution to the integrated light. + This enables us to disünguish.spectra. uly intermecdiate-age or voung clusters [rom those which are old. but whose Balmer lines are strengthened by the contaminating light of BIID stus.," This enables us to distinguish, truly intermediate-age or young clusters from those which are old, but whose Balmer lines are strengthened by the contaminating light of BHB stars." + We envisage a direct application of our method to studies of extragalactic GC svstems. where the determination of GC ages and metal abundances can vielcl insight into the star formation and merger histories of the host ealaxies (e.g. Cohen. Blakeslee Coté 2003: Larsen οἱ al.," We envisage a direct application of our method to studies of extragalactic GC systems, where the determination of GC ages and metal abundances can yield insight into the star formation and merger histories of the host galaxies (e.g. Cohen, Blakeslee Côtté 2003; Larsen et al." + 2003: Hempel et 22003)., 2003; Hempel et 2003). + We collected integrated spectra for 40 Galactic GC's with the R-C spectrograph on the 4m Blanco telescope al CTIO in April 2003., We collected integrated spectra for 40 Galactic GCs with the R-C spectrograph on the 4m Blanco telescope at CTIO in April 2003. + We scanned a 5:55-long slit across the core diameter of each target. GC., We scanned a 5-long slit across the core diameter of each target GC. + For the GC's located towards the bulge. on-target exposures were interspersed with raster scans of adjacent skv regions ~5! aaway [rom the GC centers.," For the GCs located towards the bulge, on-target exposures were interspersed with raster scans of adjacent sky regions $\sim$ away from the GC centers." + The instrumental setup consisted of grating INPGLI. with 632 ]/mm. and a Loral CCD with 3k x Ik I5jan-sized pixels.," The instrumental setup consisted of grating KPGL1, with 632 l/mm, and a Loral CCD with 3k $\times$ 1k $\mu$ m-sized pixels." + The resulting spectra cover the range 6435À with 2.84 FWIIM resolution., The resulting spectra cover the range ${\rm\AA}$ with ${\rm\AA}$ FWHM resolution. + The exposure times were scaled to vield spectra with S/N Z 100 per resolution element., The exposure times were scaled to yield spectra with S/N $\simgreat$ 100 per resolution element. + Data reduction used standard ΗΑΕ routines for longslit spectra., Data reduction used standard IRAF routines for longslit spectra. + Final 1D integrated spectra were obtained by extracting an aperture covering (the core diameter along (he slit direction., Final 1D integrated spectra were obtained by extracting an aperture covering the core diameter along the slit direction. + Since (he exposures were trailed over a core diameter perpendicular to the slit. the resulting 1D spectra are representative of the stellar content in the cores of the GC's.," Since the exposures were trailed over a core diameter perpendicular to the slit, the resulting 1D spectra are representative of the stellar content in the cores of the GCs." + The spectra were flux calibrated using observations of [lux standards taken (throughout the observing run., The spectra were flux calibrated using observations of flux standards taken throughout the observing run. + The 1D integrated spectra had (heir resolution degraded to match that of the Lick/IDS svstem. and EWs of absorption lines were measured following the definitions of Worthev et ((1994) and Worthey Ottaviani (1997).," The 1D integrated spectra had their resolution degraded to match that of the Lick/IDS system, and EWs of absorption lines were measured following the definitions of Worthey et (1994) and Worthey Ottaviani (1997)." + Consistency. wilh the Lick/IDS index system was achieved by comparing EWs measured in spectra ol standard Lick/IDS stars. taken (hroughout the observing run. wilh standard values from Worthev et ((1994).," Consistency with the Lick/IDS index system was achieved by comparing EWs measured in spectra of standard Lick/IDS stars, taken throughout the observing run, with standard values from Worthey et (1994)." +Απ πια other studies;,by many other studies. +" Santoro&Shull(2006). fouud individual critical ietallicities for C. Fe. Si. aud O aud suggested that for densities aud temperatures conducive o Pop III star formation. these species contribute nore to the cooling rate than atomic lvdrogen or II,."," \citet{SS06} found individual critical metallicities for C, Fe, Si, and O and suggested that for densities and temperatures conducive to Pop III star formation, these species contribute more to the cooling rate than atomic hydrogen or $\text{H}_2$." + Suüthetal.(2009) fouud that there exists a critical metallicity window. due in part to the CMD cluperature floor. which regulates the transition.," \citet{SMI09} found that there exists a critical metallicity window, due in part to the CMB temperature floor, which regulates the transition." + In a series of papers (COimmukai2000:Oumkaiotal.2005.2008) dust was shown to have a sienificaut impact ou the Pop ΠΠ transition.," In a series of papers \citep{OMU00, OMU05,OMU08} dust was shown to have a significant impact on the Pop III/II transition." + Its inclusion lowers the critical mctallicity derived frou pure metal line cooling bv several orders of magnitude., Its inclusion lowers the critical metallicity derived from pure metal line cooling by several orders of magnitude. + Dust eraius act as a catalyst for molecule formation aud radiate thermally. however these effects ecnerally become naportaut late in the pre-stellar gas contraction phase when deusitv is hieh.," Dust grains act as a catalyst for molecule formation and radiate thermally, however these effects generally become important late in the pre-stellar gas contraction phase when density is high." + Schueider& Onmulku(2009) aveued that the interplay of dust and aetal cooling is the kev driver. toecther with the CAIB temperature floor.," \citet{SO09} argued that the interplay of dust and metal cooling is the key driver, together with the CMB temperature floor." + À differcut view was developed in a series of studies (Jappseuctal.2007. 2009a.b).. now taking iuto account molecular cooling.," A different view was developed in a series of studies \citep{JAP07, Jappsen:09a,JAP09}, now taking into account molecular cooling." + According to these authors. metallicity plavs uo vole in the fragimoeutation of collapsing clouds while initial conditions. set by the details of galaxy formation. the CXMB temperature. turbulence. aud rotation. dominate he Pop.," According to these authors, metallicity plays no role in the fragmentation of collapsing clouds while initial conditions, set by the details of galaxy formation, the CMB temperature, turbulence, and rotation, dominate the Pop." + III/II transition., III/II transition. + This star formation mode ransition is clearly a couples. gradual process. regulated in part by all of these factors.," This star formation mode transition is clearly a complex, gradual process, regulated in part by all of these factors." + Most studies of the critical metallicity to date have octsed ou ~109AL. DAL halos. or niünuihalos. as the mumordal star formation cuviroument.," Most studies of the critical metallicity to date have focused on $\sim 10^{6} \,M_\odot$ DM halos, or minihalos, as the primordial star formation environment." + Iowever. the uajoritv ofthe first Pop II stars likely formed in deeper »teutial wells. possibly iu halos that can cool via atomic ivdrogeu cooling (c.g..Brounetal.2009).," However, the majority of the first Pop II stars likely formed in deeper potential wells, possibly in halos that can cool via atomic hydrogen cooling \citep[e.g.,][]{Betal09}." +. Whereas the quasi-lydrostatic. roughly spherical nature of barvouic collapse inside of nuiuihalos admits modeling of low uctallicity cooling iu a rather straightforward fashion. he bydrodvuamics inside the first galaxies is much nore complex.," Whereas the quasi-hydrostatic, roughly spherical nature of baryonic collapse inside of minihalos admits modeling of low metallicity cooling in a rather straightforward fashion, the hydrodynamics inside the first galaxies is much more complex." + Sinulations with realistic cosmological initial couditious have receutlv demonstrated how cold accretion streams feed dense. turbulent gas to the center of the galaxy. where second generation star formation will take place (c.g..Cacifetal.2008:Wise&Abel2007. 2008).," Simulations with realistic cosmological initial conditions have recently demonstrated how cold accretion streams feed dense, turbulent gas to the center of the galaxy, where second generation star formation will take place \citep[e.g.,][]{GB08,WA07,WA08}." +. Siuce detailed. simulations of the fragmentation properties m such a cloud with different levels of pre-chrichiment are still lacking. it is timely to carry out an exploratory survey of the crucial pluavsics involved im the fracimentation of such shocked. stream-fed eas.," Since detailed simulations of the fragmentation properties in such a cloud with different levels of pre-enrichment are still lacking, it is timely to carry out an exploratory survey of the crucial physics involved in the fragmentation of such shocked, stream-fed gas." + These cosmic filaanecuts play a pivotal role in ealaxy formation by adding a third accretion mode to the two processes that have traditionally been thought to partake in galaxy formation., These cosmic filaments play a pivotal role in galaxy formation by adding a third accretion mode to the two processes that have traditionally been thought to partake in galaxy formation. + Spheroidal galaxy coupoucuts were thought to have been built by eas chauucliug in ealactic inergers (Tooure1977:White&Rees1978) and disk compouents by accretion from a shock-heated interealactic media (ICAL) curing virialization (Rees&Ostriker1977:Sill τοῦ).," Spheroidal galaxy components were thought to have been built by gas channeling in galactic mergers \citep{TOO77, WR78} and disk components by accretion from a shock-heated intergalactic medium (IGM) during virialization \citep{RO77, SIL97}." + Tot accretion occurs when gas is shock heated to approximately the virial temperature close to the virial radius of the DM halo: the eas then cools. falls iusvard. aud civeularizes in the ealactic disk.," Hot accretion occurs when gas is shock heated to approximately the virial temperature close to the virial radius of the DM halo; the gas then cools, falls inward, and circularizes in the galactic disk." + Receutlv. however. a new iode of accretion has been found to dominate iu ligh-7 cosinological peak halos at lüeh redshift (Dekel&Biruboim2006:Dekeletal.2009).," Recently, however, a new mode of accretion has been found to dominate in $\sigma$ cosmological peak halos at high redshift \citep{DB06,DEK09}." +. This mode. coined cold flow accretion. occurs along cosmic filaancuts that feed gas directly to the inuer parts of a galaxy. leading to shocks at radii nich smaller than the halo virial radius (sec.also.Wise&Abel2007:Binuev2001.," This mode, coined `cold flow accretion,' occurs along cosmic filaments that feed gas directly to the inner parts of a galaxy, leading to shocks at radii much smaller than the halo virial radius \citep[see, also,][]{WA07,Binney:04}." + This differs qualitatively from hot accretion in that the infalline eas passes through the virial shock unaffected. has a much higher density. aud is deposited much closer to the center of the galaxy.," This differs qualitatively from hot accretion in that the infalling gas passes through the virial shock unaffected, has a much higher density, and is deposited much closer to the center of the galaxy." + Cold accretion is theoretically very. appealing., Cold accretion is theoretically very appealing. + It preseuts a solution to the observed bluc-cred galaxy bimodality (Baldryet.al.2001).., It presents a solution to the observed blue-red galaxy bimodality \citep{BAL04}. . + It provides a natural explanation for high redshift ealaxies with large star formation rates (SFRs) but no evidence of a major merger (c.g...Genzeletal.2006).," It provides a natural explanation for high redshift galaxies with large star formation rates (SFRs) but no evidence of a major merger \citep[e.g.,][]{Genzel:06}." +. Also. cold accretion naturally arises in may simmlatious of ealaxy formation (I&eresetal.2005:Dekel&DBiruboin2008:οσα&Iaehnelt2009).. suggesting this type of accretion is natural to lagh-o7 peak halos at high redshifts within ACDM models.," Also, cold accretion naturally arises in many simulations of galaxy formation \citep{KER05, DB06, WA07, GB08, +HAR08,Regan:09}, suggesting this type of accretion is natural to $\sigma$ peak halos at high redshifts within $\Lambda$ CDM models." + DAI halos with masses ~105M. represeut the sinallest structures that eau be classified as first galaxies (INitavama&Yoshida2005:Readetal.2006:WiseAbel2007:Greifetal.2008:τοι 2009).," DM halos with masses $\sim 10^{8} \,M_\odot$ represent the smallest structures that can be classified as `first galaxies' \citep{KY05, REA06, WA07, GB08, Betal09}." +. Talos of this mass have virial temperatures Ta.>10+ which allows efficieut cooling via excitation of atomic Lbydrogcu (e.g...Taianetal.1997:TeeiiarkMiralda-Escude&Rees1998:BarkanaLoch1999:Oh 1999).," Halos of this mass have virial temperatures $T_{\text{vir}} > 10^{4} \,\text{K}$ which allows efficient cooling via excitation of atomic hydrogen \citep[e.g.,][]{Haiman:97,TEG97,MiraldaEscude:98,Barkana:99,Oh:99}." + This is the halo mass scale where we first expect to see sustained. possibly sclfreeulated. star formation. similar to the preseut-dav case.," This is the halo mass scale where we first expect to see sustained, possibly self-regulated, star formation, similar to the present-day case." + Finally. in 105AM. halos. οgas accreting along cosmic filameuts will drive supersouic turbulence (Wise&Abel2007:αςctal.2008:Re-ean&Ilaehuelt2009:IKlessenTennehbelle 2009).. fundamentally changing the star formation cdoyununuies (Padoan&Nordlund2002:MacLowIxlessen.2001:Melxee&Ostriker 2007).," Finally, in $10^{8}\,M_\odot$ halos, gas accreting along cosmic filaments will drive supersonic turbulence \citep{WA07, GB08,Regan:09,KLE10}, fundamentally changing the star formation dynamics \citep{PN02,MacLow:04, MOst07}." +. Tu this work. as in many others. we define a first galaxy to be oue of the first DAL halos to form with mass =5«101AY... thus mecting the requirement that eas heated to the virial temperature is able to cool through bydrogen excitation (or Lyaian-a) enudssion.," In this work, as in many others, we define a first galaxy to be one of the first DM halos to form with mass $\geq5\times10^{7}\,M_{\odot}$, thus meeting the requirement that gas heated to the virial temperature is able to cool through hydrogen excitation (or $\alpha$ ) emission." + A further motivation for this work is wuderstancding the formation of low-Iuninuosity dwarf splieriodal satellite ealaixes (dSph) and elobular clusters (CC's)., A further motivation for this work is understanding the formation of low-luminosity dwarf spheriodal satellite galaixes (dSph) and globular clusters (GCs). + These structures have similar huuinositics. stellar masses. eenerallv no gas nor recent star formation. and coutaiu metal-poor. old stellar populations.," These structures have similar luminosities, stellar masses, generally no gas nor recent star formation, and contain metal-poor, old stellar populations." + However. GCs are sinall (—Lo 10pe) and do not ποσο to coutaiu much DM while dSph galaxies are 1imch larger (7100 pc) aud are heavily dominated bx DM as indicated by their large mass-to-light ratios (Mateo1998:Strigarictal.2008).," However, GCs are small $\sim 1-10\,\text{pc} $ ) and do not seem to contain much DM while dSph galaxies are much larger $>100\,\text{pc} $ ) and are heavily dominated by DM as indicated by their large mass-to-light ratios \citep{MAT98,STR08}." +. It is clear these are two structurally distinct populatious (e.e..INormencdy1985:Delokurovetal.2007).. but it is necessary to unuderstaud the cosinological circumstances of their formation.," It is clear these are two structurally distinct populations \citep[e.g.,][]{KOR85,BEL07}, but it is necessary to understand the cosmological circumstances of their formation." + To auswer whether the first galaxies are progenitors to dSph galaxies. GCs. or both requires an πιοαποας of star formation iu these objects.," To answer whether the first galaxies are progenitors to dSph galaxies, GCs, or both requires an understanding of star formation in these objects." + With this iu miud. we investigate the fragmentation properties of the metal-pre-cnriched cold flow accretion i| protogalaxics αἲ high redshift. aud explore imuplieatious for star formation in these —objects.," With this in mind, we investigate the fragmentation properties of the metal-pre-enriched cold flow accretion in protogalaxies at high redshift, and explore implications for star formation in these objects." + Dense. metal-enriched barvouic streams flow alongthe filameuts of the cosmic web and penetrate deep into a protogalaxy.," Dense, metal-enriched baryonic streams flow alongthe filaments of the cosmic web and penetrate deep into a protogalaxy." + The multiple (c.g.. ternary) streams collide with cach other. or collide with a turbuleutlh-supported," The multiple (e.g., ternary) streams collide with each other, or collide with a turbulently-supported" +"hydrostatic state. is given by where V—Vaq is the superadiabatic temperature gradient with Vag=1.1/5. V—(OluT/Olnp)... where 5,ατα| το).","hydrostatic state, is given by where $\nabla-\nabla_{\rm ad}$ is the superadiabatic temperature gradient with $\nabla_{\rm ad} = 1-1/\gamma$, $\nabla = (\pd \ln T/\pd +\ln p)_{z_{\rm m}}$, where $z_{\rm m}=\onehalf(z_3+z_2)$ ." +" The amount of stratification is determined by the parameter fy=(5.l)eT,/(gd). which ts the pressure scale height at the top of the domain normalized by the depth of the unstable layer."," The amount of stratification is determined by the parameter $\xi_0 =(\gamma-1) +c_{\rm V}T_4/(gd)$, which is the pressure scale height at the top of the domain normalized by the depth of the unstable layer." + We use in all cases £y=0.12. which results in a density contrast of about 120.," We use in all cases $\xi_0 =0.12$, which results in a density contrast of about 120." +" We define the fluid and magnetic Reynolds numbers via where (4, 1s the rms value of the velocity fluctuations and Ay=2z/d is assumed as a reasonable estimate for the wavenumber of the energy-carrying eddies."," We define the fluid and magnetic Reynolds numbers via where $\urms$ is the rms value of the velocity fluctuations and $\kef += 2\pi/d$ is assumed as a reasonable estimate for the wavenumber of the energy-carrying eddies." + Our definitions of the Reynolds numbers are smaller than the usually adopted ones by a factor of 27., Our definitions of the Reynolds numbers are smaller than the usually adopted ones by a factor of $2\pi$. +" The amount of shear is quantified by where Uy, is the amplitude and d, the width of the imposed shear profile (see below).", The amount of shear is quantified by where $U_0$ is the amplitude and $d_{\rm s}$ the width of the imposed shear profile (see below). + The equipartition magnetic field is defined by where the angular brackets denote horizontal average., The equipartition magnetic field is defined by where the angular brackets denote horizontal average. +" For a better comparison between the magnetic and kinetic energies. we evaluate D, at the center of the shear layer. :=zu."," For a better comparison between the magnetic and kinetic energies, we evaluate $\Beq$ at the center of the shear layer, $z=z_{\rm ref}$." + The simulations were performed with theCopr!.. which uses sixth-order explicit finite differences in space and third order accurate time stepping method.," The simulations were performed with the, which uses sixth-order explicit finite differences in space and third order accurate time stepping method." + In the horizontal .c and 4 directions we use periodic boundary conditions and at the vertical €:) boundaries we use stress-free boundary conditions for the velocity. For the magnetic field vertical field condition is used on the upper boundary whereas perfect conductor conditions are used at the lower boundary. respectively.," In the horizontal $x$ and $y$ directions we use periodic boundary conditions and at the vertical $z$ ) boundaries we use stress-free boundary conditions for the velocity, For the magnetic field vertical field condition is used on the upper boundary whereas perfect conductor conditions are used at the lower boundary, respectively." + The upper boundary thus allows magnetic helicity flux whereas at the lower boundary does not., The upper boundary thus allows magnetic helicity flux whereas at the lower boundary does not. + This is likely to be representative of the situation in a real star where magnetic helicity can escape via the surface but does not penetrate into the core., This is likely to be representative of the situation in a real star where magnetic helicity can escape via the surface but does not penetrate into the core. + In order to mimic the tachocline at the base of the solar convection zone we introduce a shear profile where τν is the reference position of the shear layer., In order to mimic the tachocline at the base of the solar convection zone we introduce a shear profile where $z_{\rm ref}$ is the reference position of the shear layer. +" Given the uncertainties of the radial position and width of the tachocline we perform parameter studies where τν and d, are varied.", Given the uncertainties of the radial position and width of the tachocline we perform parameter studies where $z_{\rm ref}$ and $d_{\rm s}$ are varied. + Furthermore. it is of general interest to study how dynamo excitation is depends on varying Uy and the ratio of Ugfd...," Furthermore, it is of general interest to study how dynamo excitation is depends on varying $U_0$ and the ratio of $U_0/d_{\rm s}$." + With the purpose of addressing the questions raised in the introduction we perform a sertes of simulations with the model described above where some properties of the shear layer are varied., With the purpose of addressing the questions raised in the introduction we perform a series of simulations with the model described above where some properties of the shear layer are varied. + We first study the hydrodynamie properties of the system and the conditions for dynamo excitation., We first study the hydrodynamic properties of the system and the conditions for dynamo excitation. + The results of this parameter study are summarized in Table 1.., The results of this parameter study are summarized in Table \ref{tab:1}. + Then we study the topological and buoyant properties of the magnetic fields generated in some characteristic runs and compare them with models with different aspect ratio and higher resolution (see Table 2))., Then we study the topological and buoyant properties of the magnetic fields generated in some characteristic runs and compare them with models with different aspect ratio and higher resolution (see Table \ref{tab:2}) ). + We finalize this section with the study of the magnetic feedback on the plasma motion and the computation of the turbulent coefficients that govern the evolution of scale magnetic fields in our simulations., We finalize this section with the study of the magnetic feedback on the plasma motion and the computation of the turbulent coefficients that govern the evolution of large-scale magnetic fields in our simulations. + In our simulation setup. two kinds of hydrodynamical instabilities may develop. namely the Kelvin-Helmholtz (KH) instability due to the imposed shear and stratification. and the convective instability due to the superadiabatic stratification in the middle layer.," In our simulation setup, two kinds of hydrodynamical instabilities may develop, namely the Kelvin-Helmholtz (KH) instability due to the imposed shear and stratification, and the convective instability due to the superadiabatic stratification in the middle layer." + From hydrodynamical runs. we find that the convective instability develops early. at με~LOL whereas the KH-instability develops at μεcz100 in runs with the strongest shear.," From hydrodynamical runs, we find that the convective instability develops early, at $t \urms \kef \approx 40$, whereas the KH-instability develops at $t \urms \kef \approx 100$ in runs with the strongest shear." + After a few hundred time units the velocity reaches a statistically steady state (constant rms-velocity). and the toroidal velocity achieves the desirec shear profile.," After a few hundred time units the velocity reaches a statistically steady state (constant rms-velocity), and the toroidal velocity achieves the desired shear profile." + A thermally relaxed state (constant thermal energy). however. is reached only after a few thousand time units.," A thermally relaxed state (constant thermal energy), however, is reached only after a few thousand time units." + This time depends on the radiative conductivity (A) but also on the imposed shear. which produces viscous heating that modifies the thermal stratification of the system as 1t may be seen in the top panels of Fig. 1..," This time depends on the radiative conductivity $K$ ) but also on the imposed shear, which produces viscous heating that modifies the thermal stratification of the system as it may be seen in the top panels of Fig. \ref{fig:strat}." + The final velocity profile which includes shear. convection. and the KH instability. does not allow the possibility of including rotation in the model.," The final velocity profile which includes shear, convection, and the KH instability, does not allow the possibility of including rotation in the model." + If it is done. the system develops mean field motions inthe horizontal direction which are undesirable in the present study.," If it is done, the system develops mean field motions inthe horizontal direction which are undesirable in the present study." +" In order to study the dynamo excitation we follow the evolution of an initial random seed magnetic field of the order of 10 ""B,", In order to study the dynamo excitation we follow the evolution of an initial random seed magnetic field of the order of $10^{-5}\Beq$ . + Since there is no rotation and because the vertical, Since there is no rotation and because the vertical +resulting Lyapunoy exponent is SeO45as. where eux0.75 is the maximum unstable growth rate for the of magnetorotational instability (Balbus&Llawley 1998).,"resulting Lyapunov exponent is $0.458 \omega_{\mathrm{max}}$, where $\omega_{\mathrm{max}} = +0.75\Omega$ is the maximum unstable growth rate for the of magnetorotational instability \citep{bh98}." +. AIL of our experiments vield a Lyapunov exponent comparable to wis:, All of our experiments yield a Lyapunov exponent comparable to $\omega_{\mathrm{max}}$. + That the Lvapunov exponent would be on order of the maximum MIAO growth rate is not surprising., That the Lyapunov exponent would be on order of the maximum MRI growth rate is not surprising. + Ht is precisely the linearly unstable. exponentially growing AIRE that is feeding the turbulence. and driving exponential divergence of the state vector.," It is precisely the linearly unstable, exponentially growing MRI that is feeding the turbulence, and driving exponential divergence of the state vector." + To examine this more carefully. a series of experiments was performed on shearing boxes with a varicty of background: shear gq parameters ancl for both sinusoidal vertical ancl toroidal initial field. configurations.," To examine this more carefully, a series of experiments was performed on shearing boxes with a variety of background shear $q$ parameters and for both sinusoidal vertical and toroidal initial field configurations." + Because the maximum linear growth rate of the MIU is qí2 (Balbus&Lawley1998).. the ensemble of simulations spans an interesting range of MIU growth rates.," Because the maximum linear growth rate of the MRI is $q/2$ \citep{bh98}, the ensemble of simulations spans an interesting range of MRI growth rates." + We would expect the Lyapunoy exponent to be proportional to q as well., We would expect the Lyapunov exponent to be proportional to $q$ as well. + Figure S. displays the volume averaged. percent state vector dillerence. histories for these runs.," Figure \ref{e2plot} displays the volume averaged, percent state vector difference histories for these runs." + The curves are abeled by their gq values. with solid. lines for the vertica ield runs ane dashed lines for the toroidal field runs.," The curves are labeled by their $q$ values, with solid lines for the vertical field runs and dashed lines for the toroidal field runs." + The corresponding first. Lyapunoy exponent values. normalizec V Way are 0.521. 0.458. 0.422. and. 0.583 for the vertica ield cases. in order of descending gq value. anc 0.484. ane Y.644 for the toroidal field q=1.5 and q=1.3 runs.," The corresponding first Lyapunov exponent values normalized by $\omega_{\mathrm{max}}$ are $0.521$ , $0.458$, $0.422$ and $0.583$ for the vertical field cases, in order of descending $q$ value, and $0.484$ and $0.644$ for the toroidal field $q=1.5$ and $q=1.3$ runs." + Clearly. he first Lvapunov exponents are positive. and of the same magnitude. normalized by exis.," Clearly, the first Lyapunov exponents are positive, and of the same magnitude, normalized by $\omega_{\mathrm{max}}$." + I should also be noted tha irst Lyapunov exponents were calculated at many points in ime in the simulations. always with similar results.," It should also be noted that first Lyapunov exponents were calculated at many points in time in the simulations, always with similar results." + In summary. the Lyapunov exponents in MIVl-driven AID turbulence simulations are all positive. and. when normalized bv μον. they all lic within in a range of 0.4 to 0.6.," In summary, the Lyapunov exponents in MRI-driven MHD turbulence simulations are all positive, and, when normalized by $\omega_{\mathrm{max}}$, they all lie within in a range of 0.4 to 0.6." + Phere is a slight trend of larger Lyapunov exponent for larger q value (non-normalized)., There is a slight trend of larger Lyapunov exponent for larger $q$ value (non-normalized). + Previous experiments also found stronger overall levels of turbulence with larger q values (Llawley.Balbus.&Winters1999): in à sense. a larger Lyapunov exponent is “more turbulent.”," Previous experiments also found stronger overall levels of turbulence with larger $q$ values \citep{hbw99}; in a sense, a larger Lyapunov exponent is “more turbulent.”" + Finally. the chaos parameters of the turbulence are independent of the initial magnetic field. configuration.," Finally, the chaos parameters of the turbulence are independent of the initial magnetic field configuration." + Initial. vertical magnetic fields have similar Lyapunov exponent. values as initial toroidal magnetic fields., Initial vertical magnetic fields have similar Lyapunov exponent values as initial toroidal magnetic fields. + Shearing box simulations of the MIU constitute an excellent numerical laboratory in which to study chaos in turbulent How., Shearing box simulations of the MRI constitute an excellent numerical laboratory in which to study chaos in turbulent flow. + Their compactness ancl simple boundary. conditions make them a very convenient svstem to study. but they also require care to interpret.," Their compactness and simple boundary conditions make them a very convenient system to study, but they also require care to interpret." + For example. the variance of the the Dow fluctuations. which may be of direct. astrophysical interest because of its connection with radiative emission. is a function of the box size adopted (cf.," For example, the variance of the the flow fluctuations, which may be of direct astrophysical interest because of its connection with radiative emission, is a function of the box size adopted (cf." + figure 2))., figure \ref{ziso}) ). + In this paper. we have demonstrated the extreme sensitivity o£. MEIID. turbulence to infinitesimal deviations in the Blow.," In this paper, we have demonstrated the extreme sensitivity of MHD turbulence to infinitesimal deviations in the flow." + This was done by several cilferent moethocls: showing that invariant scaling laws fail when implemented numerically. for both vertical ancl toroidal initial fieles. and externally imposing tinv perturbations on an established turbulent Dow and following the growing deviations in the subsequent evolution. of the original and the perturbed system.," This was done by several different methods: showing that invariant scaling laws fail when implemented numerically, for both vertical and toroidal initial fields, and externally imposing tiny perturbations on an established turbulent flow and following the growing deviations in the subsequent evolution of the original and the perturbed system." + Estimates of the largest Lyapunov exponent in a variety of turbulent flows with different field. geometries vieldeck values near the characteristic growth rate of the linear. MEL., Estimates of the largest Lyapunov exponent in a variety of turbulent flows with different field geometries yielded values near the characteristic growth rate of the linear MRI. + This is an indication that the linear physics of the instability plays an active role in defining the highly nonlinear turbulent cvnamics of these Lows., This is an indication that the linear physics of the instability plays an active role in defining the highly nonlinear turbulent dynamics of these flows. + One wav this could come about would. be if the cnerey input into a Ixolmosgorov-like cascade was essentially the linear MILL., One way this could come about would be if the energy input into a Kolmogorov-like cascade was essentially the linear MRI. + The most important practical consequence of this behavior is that the nongaussian statistical properties. of chaotic Hows severely limit the extent to which a modeling can be used αποσαν., The most important practical consequence of this behavior is that the nongaussian statistical properties of chaotic flows severely limit the extent to which $\alpha$ modeling can be used uncritically. + VPhough Maxwell ancl viscous stress have some formal properties in common (Balbus&Papaloizou —|.1999).. the averaging procedure necessary for a semi-local treatment of the turbulence is à. very delicate: matter.," Though Maxwell and viscous stress have some formal properties in common \citep{bp99}, the averaging procedure necessary for a semi-local treatment of the turbulence is a very delicate matter." + A time base of hundreds: of orbits ds clearly necessary to establish a meaningful estimate of the characteristic stress., A time base of hundreds of orbits is clearly necessary to establish a meaningful estimate of the characteristic stress. + La astrophwsical svstems. especially those in transience. it may not be possible to ascribe an instantaneous à value to the stress. and there may be no recourse other than detailed numerical modeling.," In astrophysical systems, especially those in transience, it may not be possible to ascribe an instantaneous $\alpha$ value to the stress, and there may be no recourse other than detailed numerical modeling." + We acknowledge support. under. NSE grant. AST-0070979. and NASA erant NACG5-9266.," We acknowledge support under NSF grant AST-0070979, and NASA grant NAG5-9266." + Some of the simulations described here werecarried out on computational platforms ab the NSE-supported National Center for Supercomputing Applications and the San Diego Supercomputer Center., Some of the simulations described here werecarried out on computational platforms at the NSF-supported National Center for Supercomputing Applications and the San Diego Supercomputer Center. + (Miniati2005).," \citep{miniati00, ryuetal03}." +.. VX (Ryuetal.2002:Plrominer2006:Kang2007;al.2008:Vazzaοἱ2009).. (e.g..," $M \la$ \citep{ryuetal03, psej06, kangetal07, skillman08, hoeft08, vazza09}." +Markevitchal.2002.2005:Markeviteh.&Vikhlinin2007) (e.$..Dagchietal.Finognenoyοἱal.2010:vanWeerenet2010). (Bell1973:Drury.1983:Malkov&Drury2001).. (e.g..Amato&Blasi2006:," \citep[e.g.,][]{markev02, markev05, markev07} \citep[e.g.,][]{bdnp06, fsnw10, wrbh10} \citep{bell78, dru83,maldru01}. \citep[e.g.,][]{ab06,veb06,kj07}." +measured at of the peak intensity (after contimmun subtraction).,measured at of the peak intensity (after continuum subtraction). + Dots are VLAIOs (ass ΤΕ where lis nicasured by fitting the profiles (filled dots from this paper. open dots from Aluzerolle et al. 2003):," Dots are VLMOs (mass $\simless 0.2$ ), where is measured by fitting the profiles (filled dots from this paper, open dots from Muzerolle et al. \cite{Mea03}) );" + peutagous are VELMOSs with values of ibigh enough to produce measurable veiling iu the optical (White aud Dasri 2003: Muzerolle et al. 2000... 2003:," pentagons are VLMOs with values of high enough to produce measurable veiling in the optical (White and Basri \cite{WB03}; Muzerolle et al. \cite{Mea00}, \cite{Mea03};" + Barrado v Navascuéss et al. 20013)., Barrado y Navascuéss et al. \cite{BMJ04}) ). + The total sample spans a range of mnasses from about 0.01 ο OS, The total sample spans a range of masses from about 0.04 to 0.8. + Fig., Fig. + 3 shows that our determinations of aaeree with the eeneral treud shown by other objects rou the literature. aud that there is coutiuuitv between ueasurenieuts obtaiued from veiling (which are fully iudepenudenu of the width) aud those derived from »profiles.," \ref{haw} shows that our determinations of agree with the general trend shown by other objects from the literature, and that there is continuity between measurements obtained from veiling (which are fully independent of the width) and those derived from profiles." +" Iu the sub-stellay τοσο, the width. which can © derived directly from the observations. is considered a eood indicator of accretion. with the separation between accretors aud ion-accretors set at width between 200 ({(Javawardana et al. 2003b))"," In the sub-stellar regime, the width, which can be derived directly from the observations, is considered a good indicator of accretion, with the separation between accretors and non-accretors set at width between $\sim$ 200 (Jayawardana et al. \cite{Jay03b}) )" + aud ~ 270 (AWlute aud Dasii 2003))., and $\sim$ 270 (White and Basri \cite{WB03}) ). + Fi, Fig. +e.ο 3 οΙΕ result., \ref{haw} confirms this result. + Adopting ~200 aas a limit. one would missclassify one accreting object out of 23 (MIIO-LL with Mao15«10.TALL aad width of 151kis: Muzerolle et al. 2003))," Adopting $\sim$ 200 as a limit, one would missclassify one accreting object out of 23 (MHO-4, with $\sim 1.5\times 10^{-11}$ and width of 154; Muzerolle et al. \cite{Mea03}) )" + and two non accretors out of the37 for which there are upper limits (Muzerolle et al., and two non accretors out of the37 for which there are upper limits (Muzerolle et al. + 2003 and this paper)., \cite{Mea03} and this paper). +" Finthermore., Fig."," Furthermore, Fig." + 3 shows that there is a rather goodl correlation between the width aud oover the whole range of mass from BDs to TTS. so that it is possible to use the observed width not only to discriminate between accretors and non-accretors but also to eot an approximate estimate of the accretion rate. WwoH.hout performing detailed model fits.," \ref{haw} shows that there is a rather good correlation between the width and over the whole range of mass from BDs to TTS, so that it is possible to use the observed width not only to discriminate between accretors and non-accretors but also to get an approximate estimate of the accretion rate, without performing detailed model fits." + We show in Fig., We show in Fig. + the best-fit relation between these two quantities for width 2200s. which can be expressed ax: where Ha10 is the width in iud Ds mντ," \ref{haw} the best-fit relation between these two quantities for width $>200$, which can be expressed as: where $\rm H\alpha 10$ is the width in and is in." +"ι, The spread is rather laree. aud can be due in part to the fact that iu most cases the measurements used to derive aed the Hel-resolution pprofiles have not been obtained sinultaucously."," The spread is rather large, and can be due in part to the fact that in most cases the measurements used to derive and the high-resolution profiles have not been obtained simultaneously." + We slow. as an illustration of possible problems. the rather unusual case of the TTS DF Tau which has au accretion rate of about 10.*/vz.. based on veiling from medium-resolution spectroplotometric data obtained in 1996 (Gullbring et al. 19983).," We show, as an illustration of possible problems, the rather unusual case of the TTS DF Tau which has an accretion rate of about $10^{-7}$, based on veiling from medium-resolution spectrophotometric data obtained in 1996 (Gullbring et al. \cite{Gea98}) )." + Theh resolutiou profiles of several Bahuer lines obtained non-sinultaueouslv. from 1988 to 1990 bv Edwards et al. (199 1)).," High resolution profiles of several Balmer lines obtained non-simultaneously from 1988 to 1990 by Edwards et al. \cite{Eea94}) )," + show broad enmussjou iu all the lines. In with large discrepancies between them: in particular. the wwidth is smaller than that of the higher Balmer lues.," show broad emission in all the lines, but with large discrepancies between them; in particular, the width is smaller than that of the higher Balmer lines." + One could certainly improve the correlation if larger aud slinultanecous sets of data for TTS were available., One could certainly improve the correlation if larger and simultaneous sets of data for TTS were available. + vvalues derived in this wav are necessarily inaccurate for individual objects. aud should be used with care.," values derived in this way are necessarily inaccurate for individual objects, and should be used with care." + Nevertheless. they can be very useful when dealing with large samples of objects.," Nevertheless, they can be very useful when dealing with large samples of objects." + Our near-IR spectroscopy docs not allow us to resolve the lue profiles. aud we can only measure equivalent widths. listed in Table 1.," Our near-IR spectroscopy does not allow us to resolve the line profiles, and we can only measure equivalent widths, listed in Table 1." + Of the 9 Chamacleon I objects. lis detected in ouly 1.," Of the 9 Chamaeleon I objects, is detected in only 1." + For the others. we cau set upper limits to the equivalent width (30) of about 0.30.9 À.," For the others, we can set upper limits to the equivalent width $\sigma$ ) of about 0.3–0.9 ." +. Iu Ophiucus. ou the contrary. we detect comission in 7 of the 10 observed objects.," In Ophiucus, on the contrary, we detect emission in 7 of the 10 observed objects." +derived and We also calculated the expected fluxes assuming a synchrotron model with a typical spectral index of 0.55 from the radio flux of 29 mJy within the aperture.,derived and We also calculated the expected fluxes assuming a synchrotron model with a typical spectral index of 0.55 from the radio flux of 29 mJy within the aperture. + The expected fluxes range from 0.38 mJy to 0.14 mJy. which are below the limits measurable with the present data.," The expected fluxes range from 0.38 mJy to 0.14 mJy, which are below the limits measurable with the present data." + The soft X-ray image (Figure 3dd and 3ee and contours on Figure 5bb) does not show emission from the jet., The soft X-ray image (Figure \ref{xrI}d d and \ref{xrI}e e and contours on Figure \ref{xrIcon}b b) does not show emission from the jet. + The resolved northwest radio jet coincides with a region of low Χ-ray emission. most likely a small ~15” X-ray cavity created by the expansion of the radio plasma. previously described by Kim&Fabbiano(2003).," The resolved northwest radio jet coincides with a region of low X-ray emission, most likely a small $\sim15\arcsec$ X-ray cavity created by the expansion of the radio plasma, previously described by \citet{kim03}." +. As illustrated in Figure See. the dust emission is faint at the position of the radio jet.," As illustrated in Figure \ref{xrIcon}c c, the dust emission is faint at the position of the radio jet." + The bend in the northwestern Jet is located just south of the first IR knot. along the northwestern dust protrusion.," The bend in the northwestern jet is located just south of the first IR knot, along the northwestern dust protrusion." + Temietal.(2005) found that the morphology of the non-stellar emission was similar to that of the emission detected by the (ISO) (Xilourisetal.2004)., \citet{tem05} found that the morphology of the non-stellar emission was similar to that of the emission detected by the (ISO) \citep{xil04}. +. They concluded that. while much of the excess emission at was likely due to PAH emission atjim... warm. small dust grains also contributed.," They concluded that, while much of the excess emission at was likely due to PAH emission at, warm, small dust grains also contributed." + The similarity of the features at and supports this interpretation., The similarity of the features at and supports this interpretation. + The extended non-stellar emission has significant structure at all wavelengths as shown in Figure 3. and Figure 5:: In the galaxy core. the soft image and the image show a roughly north-south elongation approximately 17225 (8.2 kpe) in each direction (Figures 3dd. 3ee) which does not follow the distribution of the stars.," The extended non-stellar emission has significant structure at all wavelengths as shown in Figure \ref{xrI} and Figure \ref{xrIcon}: In the galaxy core, the soft image and the image show a roughly north-south elongation approximately 25 (8.2 kpc) in each direction (Figures \ref{xrI}d d, \ref{xrI}e e), which does not follow the distribution of the stars." + Instead. this emission is roughly perpendicular to the major axis of NGC 1316 and may be from hot gas that was moved by the outburst.," Instead, this emission is roughly perpendicular to the major axis of NGC 1316 and may be from hot gas that was moved by the outburst." + The larger field of view (Figure 4)) shows further filamentary emission— north of the nucleus and a pair of X-ray cavities., The larger field of view (Figure \ref{xmm}) ) shows further filamentary emission north of the nucleus and a pair of X-ray cavities. + These cavities. likely created by the expansion of radio plasma. are marked with yellow circles of 230” (25 kpe) radii.," These cavities, likely created by the expansion of radio plasma, are marked with yellow circles of $\arcsec$ (25 kpc) radii." +" The western cavity is centered at (3722716, 114/00"") and the southeastern cavity is centered at (3723?3*, 115/40"")."," The western cavity is centered at $3^{h}22^{m}16^{s}$, $\arcmin$ $\arcsec$ ) and the southeastern cavity is centered at $3^{h}23^{m}3^{s}$, $\arcmin$ $\arcsec$ )." +" Each cavity lies 320"" (34.8 kpe in the plane of the sky) from the nucleus.", Each cavity lies $\arcsec$ (34.8 kpc in the plane of the sky) from the nucleus. +" There are three regions of enhanced emission along the edges of these cavities. approximately located at (3722""28,5*, 37711742""), (322""2-p,. -377009'35""). and (323""00*. 377111/33""). which are likely due to increased gas density as the hot ISM is compressed by the expanding cavities."," There are three regions of enhanced emission along the edges of these cavities, approximately located at $3^{h}22^{m}28.5^{s}$, $\arcmin$ $\arcsec$ ), $3^{h}22^{m}24^{s}$, $\arcmin$ $\arcsec$ ), and $3^{h}23^{m}00^{s}$, $\arcmin$ $\arcsec$ ), which are likely due to increased gas density as the hot ISM is compressed by the expanding cavities." + No radio emission is detected in these X-ray cavities. a situation previously seen in Abell 4059 (Heinzetal.2002). M87 (Formanetal.2007).. and the Perseus cluster (Fabianetal. 2006).," No radio emission is detected in these X-ray cavities, a situation previously seen in Abell 4059 \citep{hei02}, M87 \citep{for07}, and the Perseus cluster \citep{fab06}." +. While the centers of the radio lobes line up with the AGN. there are indications that this system may be experiencing some sloshing of the hot gas.," While the centers of the radio lobes line up with the AGN, there are indications that this system may be experiencing some sloshing of the hot gas." + Specifically. the X-ray cavities are centered 1755 and 3/22 south of the nucleus and Ekersetal.(1983) found low-level radio emission between the lobes ~7’ south of the nucleus.," Specifically, the X-ray cavities are centered 5 and 2 south of the nucleus and \citet{eke83} found low-level radio emission between the lobes $\sim7\arcmin$ south of the nucleus." +" To quantitatively. measure the significance of the cavities seen in the image. we plot in. Figure 7 the azimuthal surface brightness of the soft 2.0 keV) exposure-corrected background-subtracted image (Figure 4)) taken in an annulus extending from 180” (19.6 kpe) to 375"" (40.8 kpe) from the nucleus after the image was smoothed with a 28722 Gaussian."," To quantitatively measure the significance of the cavities seen in the image, we plot in Figure \ref{azprof} the azimuthal surface brightness of the soft (0.5-2.0 keV) exposure-corrected background-subtracted image (Figure \ref{xmm}) ) taken in an annulus extending from $\arcsec$ (19.6 kpc) to $\arcsec$ (40.8 kpc) from the nucleus after the image was smoothed with a 2 Gaussian." +" The azimuthal profile shows that the regions between80-140"". (1.e. southeast of the nucleus). and between220-280""... (1.e. to the west). have significantly lower surface brightness than the rest of the annulus."," The azimuthal profile shows that the regions between, (i.e. southeast of the nucleus), and between, (i.e. to the west), have significantly lower surface brightness than the rest of the annulus." + These regions coincide with the cavities identified (yellow circles) in Figure 4.., These regions coincide with the cavities identified (yellow circles) in Figure \ref{xmm}. + The bright regions north of the nucleus and along the cavity edges in Figure 4 coincide with the significantly brighter regions in. the azimuthal plot (Figure 7))., The bright regions north of the nucleus and along the cavity edges in Figure \ref{xmm} coincide with the significantly brighter regions in the azimuthal plot (Figure \ref{azprof}) ). + The three regions of enhanced ray emission along the cavity edges are noted in Figure 7.., The three regions of enhanced X-ray emission along the cavity edges are noted in Figure \ref{azprof}. + We tested whether the variations in. azimuthal surface brightness could be the result of abundance or gas density variations., We tested whether the variations in azimuthal surface brightness could be the result of abundance or gas density variations. + The maximum surface brightness change would require a factor of 2.3 difference in elemental abundance (1.8. the lower surface brightness region would have an elemental abundance that of the brighter regions)., The maximum surface brightness change would require a factor of 2.3 difference in elemental abundance (i.e. the lower surface brightness region would have an elemental abundance that of the brighter regions). + While such an abundance gradient would be relatively long lived. against diffusion. even if it proceeds as fast as predicted for heavy ions in a fully ionized plasma (Sarazin1988.Spitzer1956).. such a distribution of metals mimicking cavity structures seems particularly contrived.," While such an abundance gradient would be relatively long lived against diffusion, even if it proceeds as fast as predicted for heavy ions in a fully ionized plasma \citep{sar88,spi56}, such a distribution of metals mimicking cavity structures seems particularly contrived." + An alternative explanation for the surface brightness variations is for the isobaric gas to have a density in the regions of lower surface brightness 0.66 times that of the gas to the north and south of the nucleus., An alternative explanation for the surface brightness variations is for the isobaric gas to have a density in the regions of lower surface brightness 0.66 times that of the gas to the north and south of the nucleus. + Such a difference in density requires either that the lower surface, Such a difference in density requires either that the lower surface +June 10 with the fourth &.21 telescope at the European Southern Observatory. Paranal. using the FORS2 imaging spectrograph with au MIT CCD inosaic. the L200R exi. the 60135 blocking filter. aud a fixed slit width of 0.7 arcsecoud.,"June 10 with the fourth 8.2m telescope at the European Southern Observatory, Paranal, using the FORS2 imaging spectrograph with an MIT CCD mosaic, the 1200R grism, the GG435 blocking filter, and a fixed slit width of 0.7 arcsecond." + This instruinental configuration vields a waveleneth ranee of 5750-7310 wwith a resolution of about 0.76 FEWIIM., This instrumental configuration yields a wavelength range of 5750-7310 with a resolution of about 0.76 FWHM. + SE2002 obtained a total of 15 spectra of J1650 i somewhat mareinal seem (typically between 1.0 aud 1.5 areseconds}., SF2002 obtained a total of 15 spectra of J1650 in somewhat marginal seeing (typically between 1.0 and 1.5 arcseconds). + They also obtained the spectra of six bright CG- and K-tvpe dwarts using the same instruuental configuration., They also obtained the spectra of six bright G- and K-type dwarfs using the same instrumental configuration. + We obtained these data from the ESO archive. aud used tasks in to perform the CCD reductions aud to extract the spectra.," We obtained these data from the ESO archive, and used tasks in to perform the CCD reductions and to extract the spectra." +" Since the Bat field and wavelength calibration images were obtained exclusively during the davtime hours at Paranal. it was uecessary to correct for flexure in the spectrograph by applying small corrections (< 0.6A)) to the wavelength scales extracted spectra using bright night-sky omissionof thelines, ."," Since the flat field and wavelength calibration images were obtained exclusively during the daytime hours at Paranal, it was necessary to correct for flexure in the spectrograph by applying small corrections $\le 0.6$ ) to the wavelength scales of the extracted spectra using bright night-sky emission lines." + ⊺∐↸∖⋀∖↕⋜↧∶↴⋁↸∖∐⋜↧∐∐∶↴⋁∐↑↸⊳↿∐⋅↖↽↸∖∪↕⋅∐⊓⋅↱≻∩↴∖↴∐∪↖↖↽↸∖≺↧ ⋡↽ considerable variability. so we phased the data on the period reported by SE2002 (P=0.212 davs).," The Magellan light curve of J1650 showed considerable variability, so we phased the data on the period reported by SF2002 $P=0.212$ days)." + To our surprise. the lieht curve phased ou that period showed considerable scatter.," To our surprise, the light curve phased on that period showed considerable scatter." + Cousequeutly. we searched the Magellan light curve for periodicities using the ELC code with its genetic fitting algorithiu (Orosz Ilauschiklt 2000: Orosz et 22002).," Consequently, we searched the Magellan light curve for periodicities using the ELC code with its genetic fitting algorithm (Orosz Hauschildt 2000; Orosz et 2002)." + About 1.106.000. ellipsoidal models were generated aud compared with the data using the absolute as⋅⋅ the merit function: ⋅.ouly where εί) denotes the model value computed at vy. yy is the observed quautitv at the sane or). aud σι is the uncertainty ML ," About 1,106,000 ellipsoidal models were generated and compared with the data using the absolute deviation as the merit function: where $y(x_i;a)$ denotes the model value computed at $x_i$, $y_i$ is the observed quantity at the same $x_i$ , and $\sigma_i$ is the uncertainty in $y_i$." +This merit function is more robust than the 47 difunction because it is less sensitive to a few outlying poiuts., This merit function is more robust than the $\chi^2$ function because it is less sensitive to a few outlying points. + Models were computed using a period range of 0.15 to 0.50 davs., Models were computed using a period range of 0.15 to 0.50 days. + After all of the fits were performed. tle ierit function hwpersurface was projected onto the trial period axis (see Orosz ct 22002 for a more in-depth discussion of this error estimation technique): the resulting periodoeram is shown iu the top of veffiel..," After all of the fits were performed, the merit function hypersurface was projected onto the trial period axis (see Orosz et 2002 for a more in-depth discussion of this error estimation technique); the resulting periodogram is shown in the top of \\ref{fig1}." + The absolute deviation has a miüuimuuuu value at a trial period of 0.3205 davs. aud a secoudazy ninnmuun at a tral period of 0.3785 clave.," The absolute deviation has a minimum value at a trial period of 0.3205 days, and a secondary minimum at a trial period of 0.3785 days." + reffie?— (top) shows the Magellan light curve phased on a period of P=0.3205 days;, \\ref{fig2} (top) shows the Magellan light curve phased on a period of $P=0.3205$ days. + There is no dip in the absolute deviation near the period reported by SF2002 (P=0.212 days). aud tlie licht curve phased on that period is essentially a scatter plot (bottom of reffig2)).," There is no dip in the absolute deviation near the period reported by SF2002 $P=0.212$ days), and the light curve phased on that period is essentially a scatter plot (bottom of \\ref{fig2}) )." +" As a check on our results. we used the ""pdai task in IRAP. which is an iuplemoenutation of the phase dispersion. technique of Stellingwerf (1978)."," As a check on our results, we used the `pdm' task in IRAF, which is an implementation of the phase dispersion technique of Stellingwerf (1978)." + A similar periodogram was obtained., A similar periodogram was obtained. + To estimate the error on our photometric measurement of the orbital period. we did additional fits usine ⊏∫⇀≼⊲⋅↴∖↴∩⊾↸∖∐↸∖↑↕↸⊳⋜↧↕∩⊾∪↥⋅↕↑∐⋯⋜⋯≼↧↑∐↸∖∐∪∐⊔⋜↧∖⇉⋜↧↴∖↴↑↕∐∖ nerit function.," To estimate the error on our photometric measurement of the orbital period, we did additional fits using ELC's genetic algorithm and the normal $\chi^2$ as the merit function." + We fiud a lo uncertaüuty of about )Q007 day. so we adopt P=0.3205+0.0007 day.," We find a $1\sigma$ uncertainty of about 0.0007 day, so we adopt $P=0.3205\pm 0.0007$ day." + We then analyzed the VLT spectra in au attempt to understand the disaerecment of our photometric period with the spectroscopic period reported by SE2002., We then analyzed the VLT spectra in an attempt to understand the disagreement of our photometric period with the spectroscopic period reported by SF2002. + We tried to extract radial velocities usine the standard. cross-correlatiou echnique of Toury Davis (1979. iupleimenuted in the IRAF cfscor’ task).," We tried to extract radial velocities using the standard cross-correlation technique of Tonry Davis (1979, implemented in the IRAF `fxcor' task)." + However. we found hat the spectra were very noisy aud viclded a few mareinal measurements of velocity.," However, we found that the spectra were very noisy and yielded only a few marginal measurements of velocity." + We deviation herefore. used the .vrestframe™- analysis that we developed for ITL705-250 (Remillard et 11996)., We therefore used the “restframe” analysis that we developed for H1705-250 (Remillard et 1996). +" This↴⋅ technique⋅ is ⋅⋅⋅simular to the .“skew mapping⋅⋅⊀ echnique. sometimes. used for. cataclysmic. .variables (διὰ, Cameron. Tuckuott 1993: Vande Putte et 22003). aud is quite simple to eniplox."," This technique is similar to the “skew mapping” technique sometimes used for cataclysmic variables (Smith, Cameron, Tucknott 1993; Vande Putte et 2003), and is quite simple to employ." + Suppose one has a time series of spectroscopic observatious., Suppose one has a time series of spectroscopic observations. +" If tho spectra are Doppler shifted to zevo velocity and coadded using the correct orbital elemeuts tthe period P. the seuiauplitude Ao aud the time of maxima velocity Z9). then t ↕↸∖⋜∏⋝↴∖↴∪↥⋅↻↑↕∪∐↕≯↸∖⋜↧⊓∐⋅↸∖↴∖↴∪↕≯↑∐↸∖↸⊳∪∐∏≻⋜∐∐∪∐↴∖↴⋜∐⋅ willEappear;wv at the owsameN waveleugthscavoleneths i all. of: the individual;Iv. spectra,"," If the spectra are Doppler shifted to zero velocity and coadded using the correct orbital elements the period $P$, the semiamplitude $K_2$ and the time of maximum velocity $T_0$ ), then the absorption features of the companion star willappear at the same wavelengths in all of the individual spectra." +αραΈλι 'Consequently.in- the Deslines iu," Consequently, the lines in" +αραΈλι 'Consequently.in- the Deslines iu7," Consequently, the lines in" +comelary X-ray emission. electron acceleration in solar flares. supernova renmnant shock waves and Acvection Dominated Accretion Flows (ADAFS) (Vaishergetal.1983:INranoselskikhοἱ1988:Luo.Wei.&Feng2003:MeClementsetal. 1997).. and observed in situ together with accelerated. electrons at ILallev's comet (Gringanzetal.1986:Klimov1936).,"cometary X-ray emission, electron acceleration in solar flares, supernova remnant shock waves and Advection Dominated Accretion Flows (ADAFS) \citep{vaisberg83,krasno85,bingham97,shapiro99,bingham00, +begelman88,luo03,mcclements97}, and observed in situ together with accelerated electrons at Halley's comet \citep{gringauz86,klimov86}." +.. A cold plasma theory for lower-hybrid waves is given in the Appendix of Laming(2001a)., A cold plasma theory for lower-hybrid waves is given in the Appendix of \citet{laming01a}. +. Here we summarize the theory. with finite electron aud ion temperatures., Here we summarize the theory with finite electron and ion temperatures. +" The dispersion relation is (seee.gLamine2001b) where J=DUEZ2{tXJg»(Áus)Ώ.exp(=)Htv3ede. Jjουο and v?E=hyT;/m,. and o(:)ς=—z/Vs|κα.ον)yy—z)dl is. the usual plasma dispersion.n functionBn (Ty; and mm,; are electron aud ion temperatures and masses respectively and Ay is Boltzinann's constant)."," The dispersion relation is \citep[see e.g][]{laming01b} + where $I={m_e\over k_{\rm B}T_e}\int _0^{+\infty} +J_0^2\left(k_{\perp}v_{\perp} \over\Omega +_e\right)\exp\left(-m_ev_{\perp}^2 \over +2k_{\rm B}T\right)v_{\perp}dv_{\perp}$, $v_e^2=k_{\rm B}T_e/m_e$ and $v_i^2=k_{\rm B}T_i/m_i$ , and $\phi\left(z\right)=-z/\sqrt{\pi}\int _{-\infty} +^{\infty}\exp\left(-t^2\right)/\left(t-z\right) dt$ is the usual plasma dispersion function $T_{e,i}$ and $m_{e,i}$ are electron and ion temperatures and masses respectively and $k_{\rm B}$ is Boltzmann's constant)." +" Specializing to w>>ο and ο>>koc .sodhat J~1—Kk[OP ancl οa/2Gefev;)expC-«7/2h7) and taking wy,>>OQ. and e—x. The instability is illustrated schematically in Figure 1."," Specializing to $\omega >> \sqrt{2}kv_i$ and $\Omega _e >> k_{\perp}v_{e\perp}$, so that $I\simeq 1-k_{\perp}^2v_{e\perp}^2/ +\Omega _e^2$ and $\phi \simeq 1 +i\sqrt{\pi /2}\left(\omega /kv_i\right) +\exp\left(-\omega ^2/2k^2v_i^2\right)$ and taking $\omega _{pe}>>\Omega _e$ and $c\rightarrow\infty$, The instability is illustrated schematically in Figure 1." + The density is increasing towards the right. and the density gradient is perpendicular to the magnetic field.," The density is increasing towards the right, and the density gradient is perpendicular to the magnetic field." + A local anisotropy in the ion distribution develops in the direction formed by (he cross product ol density eracdient and magnetic field. which in (he representation of Figure 1 is into or out of the page.," A local anisotropy in the ion distribution develops in the direction formed by the cross product of density gradient and magnetic field, which in the representation of Figure 1 is into or out of the page." + This is similar (0 a scenario envisaged by Begelman&Chinel(1988).. who were interested in electron-ion equilibration in two temperature accretion [lows.," This is similar to a scenario envisaged by \citet{begelman88}, who were interested in electron-ion equilibration in two temperature accretion flows." + We consider the effect of a density gradient in a uniform magnetic field., We consider the effect of a density gradient in a uniform magnetic field. + In such a situation the ion distribution function is given by where the magnetic field B=Dz. ancl the densitv gradient. (lnος)οἲ is related to L bv n(L.r/dn)=L.," In such a situation the ion distribution function is given by where the magnetic field $\vec{B} = B\vec{z}$, and the density gradient $\left(dn/dx\right) \vec{x}$ is related to $L$ by $n\left(dx/dn\right) =L$." + We consider the growth of lower hybrid waves in the protonsexcited bv minor ions with large evroradii., We consider the growth of lower hybrid waves in the protonsexcited by minor ions with large gyroradii. + The growth rate for each minor ion species is given bv, The growth rate for each minor ion species is given by +Motion of stars relative to their local iuterstellar medi is frequeut/usual process in galaxies.,Motion of stars relative to their local interstellar medium is frequent/usual process in galaxies. + Neutral atous penetrate into the Solar System due to the relative motion of the Sun with respect to the interstellar medium., Neutral atoms penetrate into the Solar System due to the relative motion of the Sun with respect to the interstellar medium. + This flow of neutral atoms through a heliosplere has bee- investigated in iuauv papers. e.g. Fahr (1996). Lee et al. (," This flow of neutral atoms through a heliosphere has been investigated in many papers, e.g. Fahr (1996), Lee et al. (" +2009). MóObbius et al. (,"2009), Möbbius et al. (" +2009).,2009). + Motion of dust in interplanetary space can be affected bv the neutral gas penetrating into the heliosphere., Motion of dust in interplanetary space can be affected by the neutral gas penetrating into the heliosphere. + Iuflucuce of this effect ou dvnaiics of dust particles is usually ignored iu literature., Influence of this effect on dynamics of dust particles is usually ignored in literature. + The Povuting-Robertson effect. the racial solar wind and the gravitational perturbation of planet(s) are usually taken into account. (Siidlichovsk® Nesvorny 1991: Liou Zook 1997: Liou Zool 1999: Ikuchner Tolman 2003).," The Poynting-Robertson effect, the radial solar wind and the gravitational perturbation of planet(s) are usually taken into account (Šiidlichovský Nesvorný 1994; Liou Zook 1997; Liou Zook 1999; Kuchner Holman 2003)." + Scherer (2000) has calculated secular tine derivatives of angular momentum aud Laplace-Runec-Lenz vector of a dust particle under the action of interstellar eas flow., Scherer (2000) has calculated secular time derivatives of angular momentum and Laplace-Runge-Lenz vector of a dust particle under the action of interstellar gas flow. +" But Scherer’s calculations coutain several iucorrectuesses,", But Scherer's calculations contain several incorrectnesses. + Ue has come to the conclusion that scii-iajor axis of the dust particle iucreases exponentially (Scherer 2000. p. 331).," He has come to the conclusion that semi-major axis of the dust particle increases exponentially (Scherer 2000, p. 334)." + This paper preseuts that semiauajor axis of the dust particle decreases uudoer the action of interstellar eas flow. in the framework of the perturbation theory.," This paper presents that semi-major axis of the dust particle decreases under the action of interstellar gas flow, in the framework of the perturbation theory." + Motion of dust particles iu the zone ofthe Edgeworthli-Iuiper belt under the action of the interstellar flow of eas has been investigated by IElackka et al. (, Motion of dust particles in the zone of the Edgeworth-Kuiper belt under the action of the interstellar flow of gas has been investigated by Klačkka et al. ( +2009a).,2009a). + The authors have calculated secular time derivatives of orbital elements only for the case when interstellar eas velocity vector les in the orbital plane of the dust particle aud direction of the velocity vector is parallel with y-axis., The authors have calculated secular time derivatives of orbital elements only for the case when interstellar gas velocity vector lies in the orbital plane of the dust particle and direction of the velocity vector is parallel with $y$ -axis. + This paper overcomes these restrictions., This paper overcomes these restrictions. + Moreover. it presents sole main properties of dust dynamics under the action of the iuterstellar eas.," Moreover, it presents some main properties of dust dynamics under the action of the interstellar gas." + Acceleration of a spherical dust particle caused by the flow of neutral gas can be given in the form (Scherer 2000) where vy is velocity of the neutral hydrogen atom. v is velocity of the dust erain. ep is the drag cocficient. 544 is the collision parameter.," Acceleration of a spherical dust particle caused by the flow of neutral gas can be given in the form (Scherer 2000) where $\vec{v}_{H}$ is velocity of the neutral hydrogen atom, $\vec{v}$ is velocity of the dust grain, $c_{D}$ is the drag coefficient, $\gamma_{H}$ is the collision parameter." + For the collision parameter we cau write where mig is mass of the neutral livdrogen atom. 0j; 15 the concentration of interstellar neutral hydrogen atoms. A= rR Docis the geometricalB cross section+ of. the spherical- dust grain of radius δ aud mass s.," For the collision parameter we can write where $m_{H}$ is mass of the neutral hydrogen atom, $n_{H}$ is the concentration of interstellar neutral hydrogen atoms, $A$ $=$ $\pi {R}^{2}$ is the geometrical cross section of the spherical dust grain of radius $R$ and mass $m$." + Theconcentration of interstellar hydrogen ayy is not constant iu the cutire wcliosphere., Theconcentration of interstellar hydrogen $n_{H}$ is not constant in the entire heliosphere. + For heliocentric distances r less than 1 AU Dg decreases precipitously from its value in the outer icliosphere toward the Sun. due to ionization (Lee et al.," For heliocentric distances $r$ less than 4 AU $n_{H}$ decreases precipitously from its value in the outer heliosphere toward the Sun, due to ionization (Lee et al." + 2009)., 2009). + But iu the outer heliosphere. kr C (30. AU. NU AU). we Call assume that the concentration of the jieutral Bvdrogen atonis is coustant pj = 0.05 ? (Fale 1996).," But in the outer heliosphere, $r$ $\in$ (30 AU, 80 AU), we can assume that the concentration of the neutral hydrogen atoms is constant $n_{H}$ $=$ 0.05 $^{-3}$ (Fahr 1996)." + The same assumption can be used also behind the solar wind termunation shock., The same assumption can be used also behind the solar wind termination shock. + The shock was crossed hy Voyager Lat a helioceutric distance 91 AU aud by Vovager 2 at 8I AU (Richardson et al., The shock was crossed by Voyager 1 at a heliocentric distance 94 AU and by Voyager 2 at 84 AU (Richardson et al. + 2008)., 2008). + We wil assune that the speed of interstellar gas is much ereater than the speed of the dust eram iu the stationary frame associate with the Sun (e « ey)., We will assume that the speed of interstellar gas is much greater than the speed of the dust grain in the stationary frame associated with the Sun $v$ $\ll$ $v_H$ ). + This approximation leads o approximately coustaut value of ep cc 2.6 (Baines ct al., This approximation leads to approximately constant value of $c_D$ $\approx$ 2.6 (Baines et al. + 1965: Banaszkiewicz et al., 1965; Banaszkiewicz et al. + 1001: Ixlackka et al., 1994; Klačkka et al. + 20092)., 2009a). + We want to find influence of the Sow of iuterstellar eas on secular evolution of particles orbit., We want to find influence of the flow of interstellar gas on secular evolution of particle's orbit. + We will asstune that the dust particle is under the action of solar eravitation aud the flow of neutral gas., We will assume that the dust particle is under the action of solar gravitation and the flow of neutral gas. + Hence we have equation of motiou where jp = . GAL... ! Gis the gravitational coustaut. A. is niass of the Sun. i is position vector of tlhe dust particle," Hence we have equation of motion where $\mu$ $=$ $G M_{\odot}$ , $G$ is the gravitational constant, $M_{\odot}$ is mass of the Sun, $\vec{r}$ is position vector of the dust particle" +density of the supershell. 1 the hydrogen mass. and ¢ the age of the shell.,"density of the supershell, $m_H$ the hydrogen mass, and $t$ the age of the shell." + Using the values v2v;=1500kms and N2107em™. we get where Noy2N/107em? and Exi=E/10?eres.," Using the values $v = v_{exp} = 1500 \kms$ and $N=10^{20}\cm^{-2}$ , we get where $N_{20}=N/10^{20}\cm^{-2}$ and $E_{53}= E/10^{53}\ergs$." + In Fig., In Fig. + 3 are shown the size and age of the supershell as well as the volume number density of the ambient medium with Es; being a free parameter., 3 are shown the size and age of the supershell as well as the volume number density of the ambient medium with $E_{53}$ being a free parameter. + For à range of input energy. 0.01.}{_\sim} 0.7$ keV, indicating the presence of an additional plasma component." + This excess can be modeled with an optically thin thermal APEC model (?) as indicated by the blue thick curve in Fig. 11.., This excess can be modeled with an optically thin thermal APEC model \citep{smith01} as indicated by the blue thick curve in Fig. \ref{epicspectra}. + The APEC model component assumes collisional equilibrium for ionization and excitation processes which is observable as bremsstrahlung continuum plus emission lines., The APEC model component assumes collisional equilibrium for ionization and excitation processes which is observable as bremsstrahlung continuum plus emission lines. + Optically thin emission has been seen in various, Optically thin emission has been seen in various +be smaller. (heir expected values of (f./fi) drop even faster. so the discrepancy would be even larger.,"be smaller, their expected values of $(f_x/f_V)$ drop even faster, so the discrepancy would be even larger." + On the other hand. if the object were an AGN at the redshift of 2294. it would tvpically have a V—4 color of ~2. so my~23 and f.fy~0.4. a ratio that is within the expected range for AGN.," On the other hand, if the object were an AGN at the redshift of 294, it would typically have a $V\!-\!K$ color of $\sim2$ , so $m_V\sim23$ and $f_x/f_V\sim0.4$, a ratio that is within the expected range for AGN." + The most likely explanation lor the duplicity in the Chandra image is therefore that Chere are two active nuclei associated with 2294: one associated with the compact radio nucleus aud heavily obscured at rest-Drune optical wavelengths and in soft X-raàvs (Fabianοἱal.2003).. the otherassociated with the stellar object 07909 (~3 kpc) east of the radio source and intrinsically less powerful. but. having relatively little extinction.," The most likely explanation for the duplicity in the Chandra image is therefore that there are two active nuclei associated with 294: one associated with the compact radio nucleus and heavily obscured at rest-frame optical wavelengths and in soft X-rays \citep{fab03}, the otherassociated with the stellar object 9 $\sim8$ kpc) east of the radio source and intrinsically less powerful, but having relatively little extinction." + If we asstune no extinction for the eastern nucleus ancl assume the estimate of [or the intrinsic N-rav flux of the radio nucleus. the eastern nucleus has an intrinsic X-ray. luminosity roughly an order of magnitude lower than that of the radio nucleus.," If we assume no extinction for the eastern nucleus and assume the estimate of \citet{fab03} for the intrinsic X-ray flux of the radio nucleus, the eastern nucleus has an intrinsic X-ray luminosity roughly an order of magnitude lower than that of the radio nucleus." + There is no indication of radio emission from this second active nucleus in the 6 em VLA map of MeCarthyetal.(1990).. but Chis [act alone cannol set verv stringent limits on its radio/X-ray flux ratio.," There is no indication of radio emission from this second active nucleus in the 6 cm VLA map of \citet{mcC90}, but this fact alone cannot set very stringent limits on its radio/X-ray flux ratio." + The position of the radio nucleus of 2294 determined here places it ~078 north of the position given by Stockton.Canalizo.&Büdgwavy(1999) and ~079 west of the position eiven bv Quirrenbachetal.(2001)., The position of the radio nucleus of 294 determined here places it $\sim0\farcs8$ north of the position given by \citet{sto99} and $\sim0\farcs9$ west of the position given by \citet{qui01}. +. Within the errors of the determination. the nucleus is coincident wilh a modest peak within the diffuse component seen in the A-band imaging data.," Within the errors of the determination, the nucleus is coincident with a modest peak within the diffuse component seen in the $K$ -band imaging data." + While this position of the radio nucleus undercuts the specific argument made by Quirrenbachetal.(2001). that 2294 is à merger in progress. since (he radio source can no longer be identified with the eastern stellar component. their conclusion is nevertheless reallirmed by the fact that both the radio nucleus aud the eastern stellar object appear to be X-rav sources.," While this position of the radio nucleus undercuts the specific argument made by \citet{qui01} that 294 is a merger in progress, since the radio source can no longer be identified with the eastern stellar component, their conclusion is nevertheless reaffirmed by the fact that both the radio nucleus and the eastern stellar object appear to be X-ray sources." + The apparent presence of (yo active nuclei in such close proximity places 2294 within a a small. but important. class.," The apparent presence of two active nuclei in such close proximity places 294 within a a small, but important, class." + A recent cottage industry has developed in mining survevs for eravitationallv lensed QSOs to extract double QSOs that are the result of gravitational lensing. but. instead. are (vue binaries (¢.g..Mortlock.Webster.&Francis1999).," A recent cottage industry has developed in mining surveys for gravitationally lensed QSOs to extract double QSOs that are the result of gravitational lensing, but, instead, are true binaries \citep[\eg][]{mor99}." +. Such cases are important for at least two reasons: (1) If they are found as subsets of large survey whose selection properties are well determined. such as the Large Bright Quasar Survey (LBQS) or the Sloan Digital Skv Survey (SDSS). their statistics can provide evidence for the importance ol interactions and mergers in triggering nuclear activity (Djorgovski 1999): and (2) with a sufficiently large sample. they can provide evidence on mean," Such cases are important for at least two reasons: (1) If they are found as subsets of large survey whose selection properties are well determined, such as the Large Bright Quasar Survey (LBQS) or the Sloan Digital Sky Survey (SDSS), their statistics can provide evidence for the importance of interactions and mergers in triggering nuclear activity \citep{djo91,koc99}; ; and (2) with a sufficiently large sample, they can provide evidence on mean" +levels (i). (ii) and Git) within the model limitations and what data quality is required. for this.,"levels (i), (ii) and (iii) within the model limitations and what data quality is required for this." + In refsecidata.. we apply our method to nine Milky. Way dwarf galaxies with measured radial velocities aid proper motions.," In \\ref{sec:data}, we apply our method to nine Milky Way dwarf galaxies with measured radial velocities and proper motions." + Finally. in refsec:iconclusions we present our conclusions.," Finally, in \\ref{sec:conclusions} we present our conclusions." + In this section. we use the Via Lactea L(VL1) simulation ofa Milkv Way mass galaxy (2).. to determine how well we recover satellite orbits in the face of measurement crrors and a time varying gravitational potential.," In this section, we use the Via Lactea I (VL1) simulation of a Milky Way mass galaxy \citep{2007ApJ...667..859D}, to determine how well we recover satellite orbits in the face of measurement errors and a time varying gravitational potential." +" We extract from the simulation three sets ofsubhalost:: the 50 most massive today (24). the 50 most massive before redshift +=10.59 (270) and the 50 most massive before redshift >=10.59. taking. depletion. by a disc ..into account (στι."" "," We extract from the simulation three sets of: the 50 most massive today $z^{50}_0$ ), the 50 most massive before redshift $z=10.59$ $z^{50}_{10}$) and the 50 most massive before redshift $z=10.59$, taking depletion by a disc into account $z^{50}_{10}(r_{d}))$ ." +In. all cases. we include only subhalos with mass AJ710AZ. and distance to the centre of the main halo kr« 150kkpe at redshift z=0.," In all cases, we include only subhalos with mass $M > 10^7 M_\odot$ and distance to the centre of the main halo $r< 150$ kpc at redshift $z=0$." + This represents the mass and radius range where we find the Milky Way ciwarfs (c£, This represents the mass and radius range where we find the Milky Way dwarfs (c.f. + Table 1. in section refsecithedata))., Table \ref{tab:dwarfdata1} in section \\ref{sec:thedata}) ). +" In the dise. depletedsample we exclude all orbits having pericentres rj,«rí before extracting the sample. motivated by recent work by 2.."," In the disc depletedsample we exclude all orbits having pericentres $r_p 0.5$ ). + This low contras neaus that only very little facular brieliteniueg is seen near he limb and thus leads to au earlier ouset of the spot-induced darkening. as illustrated on the right-hand plots of Fie. 10..," This low contrast means that only very little facular brightening is seen near the limb and thus leads to an earlier onset of the spot-induced darkening, as illustrated on the right-hand plots of Fig. \ref{fig:timeseries2}." + We note that at 1.55 jnu. there is rather poor aerectuent between the model calculations auc the SIM data during May 2004.," We note that at 1.55 $\mu$ m, there is rather poor agreement between the model calculations and the SIM data during May 2004." + In particular. we fud that the SIM data show a reversal in the relative spot strength diving Max.," In particular, we find that the SIM data show a reversal in the relative spot strength during May." + The first spot (centred around May. 15th) is sienificautly strouger than the spot at the end of May in all wavebauds. except at 1.55 san. where the second spot appears darker.," The first spot (centred around May 15th) is significantly stronger than the spot at the end of May in all wavebands, except at 1.55 $\mu$ m, where the second spot appears darker." + This could indicate that the temperature eradicut in the two spots is differcut. although we caunot exclude macorrected data fluctuations.," This could indicate that the temperature gradient in the two spots is different, although we cannot exclude uncorrected data fluctuations." + We lave presented and compared SATIRE model calculations and measurements of spectral solar variability onu rotational time scales., We have presented and compared SATIRE model calculations and measurements of spectral solar variability on rotational time scales. + The data and calculations cover a 3-mouth fiue span from λίαν to July 9001., The data and calculations cover a 3-month time span from May to July 2004. + Iu addition. we also compare modelled aud observed time series of the total mradiauce variability aud the variability in a nuuber of selected wavelength bauds.," In addition, we also compare modelled and observed time series of the total irradiance variability and the variability in a number of selected wavelength bands." + Such coluparisons are particularly timely as SORCE/SIM is able to provide uuprecedeuted observations over most of he range starting iu the UV at approxinatelv 220 mu and iucludiug the visible as well as the near infrared up o 1.6 jun. We find excellent. agreciment between the modelled otal solar iradiance variations and the SORCE/TIM ueasureienuts., Such comparisons are particularly timely as SORCE/SIM is able to provide unprecedented observations over most of the range starting in the UV at approximately 220 nm and including the visible as well as the near infrared up to 1.6 $\mu$ m. We find excellent agreement between the modelled total solar irradiance variations and the SORCE/TIM measurements. + The absolute value of the waveleueth-inteerated SORCE/SIAL measurements is in line with he expected model fluxes. aud its variability agrees well except on a sinall uuuber of days when the data quality was poorer (see Fie. 3)).," The absolute value of the wavelength-integrated SORCE/SIM measurements is in line with the expected model fluxes, and its variability agrees well except on a small number of days when the data quality was poorer (see Fig. \ref{fig:TSI}) )." +" We find correlation cocticicuts of 0.97 aud 0.92 when comparing the mocelled total solar radiance with TIAL and the waveleneth inteerated SIM nmieasurements, respectively."," We find correlation coefficients of 0.97 and 0.92 when comparing the modelled total solar irradiance with TIM and the wavelength integrated SIM measurements, respectively." + The modelled aud iueasured spectral variability over the three months is stmumarised in Fie., The modelled and measured spectral variability over the three months is summarised in Fig. + 5 for wavelenetls between 220 and 1600 aim., \ref{fig:var_all} for wavelengths between 220 and 1600 nm. + Overall we find good agrecnient between the model and the observations.," Overall, we find good agreement between the model and the observations." + Aercoicut is particularly good between LOO auc 1300 n1., Agreement is particularly good between 400 and 1300 nm. + Tu the UV. where we also compare the SIM imieasuremeuts to UARS/SUSIM. the agreement is somewhat patchy: sole strong individual lues. such as the Mg h&kk doublet. match verv well others. such as Mg1 and Ca UWI. aeree ouly poorly.," In the UV, where we also compare the SIM measurements to UARS/SUSIM, the agreement is somewhat patchy; some strong individual lines, such as the Mg k doublet, match very well, others, such as Mg and Ca K, agree only poorly." + This is not too surprisius as we use opacity distribution aud assinie LTE throughout., This is not too surprising as we use opacity distribution and assume LTE throughout. + Uiteubroek&Briand(1995). have shown that NLTE cffects can explain much of the different beliaviour of the Me and Mg resonance lines., \citet{uitenbroek1995} have shown that NLTE effects can explain much of the different behaviour of the Mg and Mg resonance lines. + We also note that the resolution of our calculatious is insufficient to resolve even the strong lines aud to capture their complex behaviour., We also note that the resolution of our calculations is insufficient to resolve even the strong lines and to capture their complex behaviour. + The role of spectral resolution in the context of line variability has been discussed. e.g.. in Whiteetal. (2000)..," The role of spectral resolution in the context of line variability has been discussed, e.g., in \citet{white2000issi}." + In the waveleneth range between approximatcly 10 nu aud 350 nni possibly even up to 390 mu. the rsponse of both SORCE/SIM and UARS/SUSIM is too poor to determine solar variability ou the rotational time scale.," In the wavelength range between approximately 310 nm and 350 nm, possibly even up to 390 nm, the response of both SORCE/SIM and UARS/SUSIM is too poor to determine solar variability on the rotational time scale." + The best estimate of variability at those wavelengths is currently provided by the SATIRE model., The best estimate of variability at those wavelengths is currently provided by the SATIRE model. + The model calculations allow us to isolate the facular and spot contribution., The model calculations allow us to isolate the facular and spot contribution. + This. together with the lieht-curves. illustrates very clearly the change from facular dominated variability. at short waveleneths to dominated variability above approximately LOO naui.," This, together with the light-curves, illustrates very clearly the change from facular dominated variability at short wavelengths to spot-dominated variability above approximately 400 nm." + Tn the visible. the observed aud modelled inadiauce variability iatches well. though the decrease in the variability at longer wavelengths appears somewhat steep in the model compared to the observations.," In the visible, the observed and modelled irradiance variability matches well, though the decrease in the variability at longer wavelengths appears somewhat steep in the model compared to the observations." + We fiud. e.g. that the SATIRE model overestimates the variability between about GOO aud 800 nm by up to 20% compared," We find, e.g., that the SATIRE model overestimates the variability between about 600 and 800 nm by up to 20 compared" +In recent vears we have witnessed. considerable progress in the search for extra-solar planets.,In recent years we have witnessed considerable progress in the search for extra-solar planets. +" Since the first detection of a ""Hot Jupiter around. the main-sequence star 51 Peg (?)). the number of extra-solar planets has rapidly risen. and currently approaching500."," Since the first detection of a `Hot Jupiter' around the main-sequence star 51 Peg \citealt{Mayor95}) ), the number of extra-solar planets has rapidly risen, and currently approaching." + Most of these discoveries are the result of racial velocity (RV) searches., Most of these discoveries are the result of radial velocity (RV) searches. + More recently. an increasing number of extra-solar planets (2 SO) have been detected by dedicated: planetary. transit surveys including ILVEnet (2)). Drs (e.g. 2: 7: 7)). OGLE (?.. 2003). XO (?2)). and. WASD. the Ulx Wide-Anele Search for Planets (?)).," More recently, an increasing number of extra-solar planets $>80$ ) have been detected by dedicated planetary transit surveys including HATnet \citealt{Bakos04}) ), TrES (e.g. \citealt{Brown00}; ; \citealt{Dunham04}; \citealt{Alonso04}) ), OGLE \citealt{Udalski02}, 2003), XO \citealt{McCullough05}) ), and WASP, the UK Wide-Angle Search for Planets \citealt{Pollacco06}) )." + Planet detection via the transit. technique involves searching for periodic dips in stellar lisht curves as a planet occludes a small fraction of the visible disc of the host star once per orbit., Planet detection via the transit technique involves searching for periodic dips in stellar light curves as a planet occludes a small fraction of the visible disc of the host star once per orbit. + Only planets with thei orbital planes aligned. within a few degrees to the line of sight will exhibit a transit. the probability of such an alignment being around for typical ‘hot Jupiter systems.," Only planets with their orbital planes aligned within a few degrees to the line of sight will exhibit a transit, the probability of such an alignment being around for typical `hot Jupiter' systems." + This introduces a constraint on the number of observable systems and explains the relatively low number of transiting planets when compared to racial velocity studies., This introduces a constraint on the number of observable systems and explains the relatively low number of transiting planets when compared to radial velocity studies. + Importantly. when combined with I measurements. planetary.transits oller," Importantly, when combined with RV measurements, planetarytransits offer" +The appropriately normalized twophoton spectrum iu ternis of the variable ως is: 'The: |ees7DG)=E2.,The appropriately normalized two–photon spectrum in terms of the variable $x$ is: The $ \int^{x_{12}}_{-\infty}\Phi(x) d x = 2$. +" For our *purposes the frequencyn distribution+H ofn the Ey, photons can be approximated by a delta fiction on the V aNIS. πο With αν(έν the ratio of Ly,, redshift rate to the two decay rate can be calculated from equatious (13)) aud (11))."," For our purposes the frequency distribution of the ${\rm Ly}_{\alpha} \,$ photons can be approximated by a delta function on the $\nu$ axis, so With $n_{1s}(t)$, the ratio of ${\rm Ly}_{\alpha}$ redshift rate to the two--photon decay rate can be calculated from equations \ref{rsr}) ) and \ref{rph2}) )." + This ratio depends on the cosmology., This ratio depends on the cosmology. + For the 2>1 transition ucelecting the Lin the denominator of equation (13)) and using the numerical values. oue arrives at The redshift of the newbor photous is eiven by equation (22)) in terms of the variables ur and 7.," For the $2 \rightarrow 1 \,$ transition neglecting the $-1$ in the denominator of equation \ref{rsr}) ) and using the numerical values, one arrives at The redshift of the new–born photons is given by equation \ref{lapleq}) ) in terms of the variables $x$ and $\tau$." +" spectrum at different redshifts is shown in Figure | L1. QO,=0.1. hf= 1) aud Fieure 5 (O0=1. ο= h= 1)."," The spectrum at different redshifts is shown in Figure 4 $ \Omega = 0.1$ , $\Omega_b =0.1$, $h=1$ ) and Figure 5 $ \Omega = 1$, $\Omega_b =0.01$, $h=1$ )." + When the barvou deusitv is ow. the ὃν > Is rausition plavs a minor role.," When the baryon density is low, the 2s $\rightarrow $ 1s transition plays a minor role." + These results disagree with DelAutonio Rybicki (1993). who state that the energev distribution of photons emitted by the 2s>Ls transition rather stronely vealed at ν=np.2 aud tho 25.»1s transitions eive no iore than iference in the free electron densities and the line streneth.," These results disagree with Dell'Antonio Rybicki (1993), who state that the energy distribution of the photons emitted by the $2s \rightarrow 1s$ transition rather strongly peaked at $\nu =n_{{\rm Ly}_{\alpha}}/2$ and the $2s\rightarrow 1s$ transitions give no more than difference in the free electron densities and the line strength." + Our results (Fie., Our results (Fig. + 1 aud Fig., 4 and Fig. + 5) show that the spectrum of 25>ls photons is broad (see also Spitzer Greenstein 1951)., 5) show that the spectrum of $2s\rightarrow 1s$ photons is broad (see also Spitzer Greenstein 1951). +" ""Though for certain cosniologies he contribution of these photons is small but as it is demoustrated in Figure 6. for other set of xranmeters this contribution is quite considerable."," Though for certain cosmologies the contribution of these photons is small, but as it is demonstrated in Figure 6, for other set of parameters this contribution is quite considerable." +" Iu the models with Heh © aud low ο the twophoton transitions are negligible. but for h?0,cOL they are more nportaut. aud for the flat. Heh 5 model they are dominant."," In the models with high $\Omega$ and low $\Omega_b$ the two–photon transitions are negligible, but for $h^2 \Omega_b \ge 0.1$ they are more important, and for the flat, high $\Omega_b$ model they are dominant." + Ia spite of the above meutioucd disagreement our recombination history curve (Fig., In spite of the above mentioned disagreement our recombination history curve (Fig. + 2) agrees well with tha of DellAntonio Bybicki (1993). because by colmputing this function μον took iuto account also the Ps > Ls ftransifions.," 2) agrees well with that of Dell'Antonio Rybicki (1993), because by computing this function they took into account also the 2s $\rightarrow$ 1s transitions." +" Figure 7 shows a part of the CMD radiation spectrum or differeut cosmological xuanmneters, where the distortion due to recombinations is the nost nuportant."," Figure 7 shows a part of the CMB radiation spectrum for different cosmological parameters, where the distortion due to recombinations is the most important." + The wdrogen recombination eius When iu the background radiation there are less energetic photons than bydrogen atoms., The hydrogen recombination begins when in the background radiation there are less energetic photons than hydrogen atoms. + Consequently. the spectrum of the plotous issuiug roni the recombination has a maxiuun uear the Plauck-curve.," Consequently, the spectrum of the photons issuing from the recombination has a maximum near the Planck-curve." + The other maxima in this spectrmm corresponds o the twophoton transitions. is longwards fro tle first naxiununm at hÉÁgyuo=(Bo DQ)/25.1 ον. aul is uuder the Planckcurve.," The other maximum in this spectrum corresponds to the two–photon transitions, is longwards from the first maximum at $h \nu_{{\rm max},2} = +(B_2 - B_1)/2 = 5.1$ eV, and is under the Planck–curve." + The 2s>1s photous iufiueuces he distortion in two wavs.," The $2s +\rightarrow 1s$ photons influences the distortion in two ways." + First. the short wavelength wart of their spectimm is above the Plauck-curve aud eive a direct contribution to the distortion (Figure 6).," First, the short wavelength part of their spectrum is above the Planck-curve and give a direct contribution to the distortion (Figure 6)." + Second. he umber of recombinations are eiven by the number of wdrogen atoms.," Second, the number of recombinations are given by the number of hydrogen atoms." +" Ifa considerable part of recombinations lappens by twoploton decavs. there are less redslüfted Lv, photons. the amplitude aud shape of their spectrum changes."," If a considerable part of recombinations happens by two–photon decays, there are less redshifted $_{\alpha}$ photons, the amplitude and shape of their spectrum changes." + For giveu Ὁ aud h there are more plotous above the Plauckcurve when both O aud R are large.," For given $\Omega_b\,$ and h there are more photons above the Planck–curve when both $\Omega \,$ and R are large." + When 9 aud hn are given. the spectrum with the larger O5 Les above all the others.," When $\Omega\,$ and h are given, the spectrum with the larger $\Omega_b \,$ lies above all the others." +" For a fixed value of O and 9, the spectrum with larger 5 ds larecr."," For a fixed value of $\Omega$ and $\Omega_b \,$ the spectrum with larger $h$ is larger." + Iu Figure 7 we compare our spectrum with that of DollAutouio Rybicki (1993)., In Figure 7 we compare our spectrum with that of Dell'Antonio Rybicki (1993). + Tu the 120 ju Ay. where ny ds 1ie Ixeplerian mean 1100] about the cener of mass of Pluto and Charon. we found that the azinmuthal period. £)=οπή shorter than tie Ixeplerian orbital period aud that the periapse aud asceicing uode (rel:dive to Pluto-Charon orbital plane) precess at nearly. equal rates in opposite directions (prograde Lor periapse ancl 'etrograde for the node).," With $\nu_0 > n_0 > n_K > \kappa_0$, where $n_K$ is the Keplerian mean motion about the center of mass of Pluto and Charon, we found that the azimuthal period $P_0 = 2\pi/n_0$ is shorter than the Keplerian orbital period and that the periapse and ascending node (relative to the Pluto-Charon orbital plane) precess at nearly equal rates in opposite directions (prograde for the periapse and retrograde for the node)." + We have also performecl a series of direct nuunerical orbit integrallons with different. assumecl masses for P2 aix PL. aud he restlts presented i1 Section 3 show the increasing ellects of the proximity of the orbits of P2 aud P:| to the 3:2 mean-nmotior commensurability with increasing masses.," We have also performed a series of direct numerical orbit integrations with different assumed masses for P2 and P1, and the results presented in Section 3 show the increasing effects of the proximity of the orbits of P2 and P1 to the 3:2 mean-motion commensurability with increasing masses." + As shown i1 Fie. 1..," As shown in Fig. \ref{fig:period}," + he deviation [rom Ivejxler's thirc law is already detected in the uuperturbed Ixeplerian Iit of BOYYS (whichi was previously polutec out by BGYYS as discrepaucies in the total mass o. Pluto-Claron iiferred from {1e orbits of Charon. P2. aud P1).," the deviation from Kepler's third law is already detected in the unperturbed Keplerian fit of BGYYS (which was previously pointed out by BGYYS as discrepancies in the total mass of Pluto-Charon inferred from the orbits of Charon, P2, and P1)." + Since the other non-Ixeplerian behaviors de»eud oi the masses of P2 and P1. a dynamical fit to the data that accouutsfor the inteactions amoug Cjiaron. P2. are P1 shouk," Since the other non-Keplerian behaviors depend on the masses of P2 and P1, a dynamical fit to the data that accountsfor the interactions among Charon, P2, and P1 should" +"unigrids and will accel cliscrete sources of ionizing radiation and radiative transler in order to capture the heating ancl clumping more accurately,",unigrids and will add discrete sources of ionizing radiation and radiative transfer in order to capture the heating and clumping more accurately. + We will also include source Gun-on al z>9 ιο test the decrease and recovery of ο. as seen in Figures 3 and 4.," We will also include source turn-on at $z > 9$ to test the decrease and recovery of $C_H$, as seen in Figures 3 and 4." + Finally. we plan to carry oul more detailed modeling of theIEI (21-cim) signal. coupled to the kinetic and spin temperatures driven by heating al z>7.," Finally, we plan to carry out more detailed modeling of the (21-cm) signal, coupled to the kinetic and spin temperatures driven by heating at $z > 7$." + As described earlier. the curation of (he reionization (ransition and (he 21-em emission during the heating phase could. provide diseriminants of various SFR. histories al 2>6.," As described earlier, the duration of the reionization transition and the 21-cm emission during the heating phase could provide discriminants of various SFR histories at $z > 6$." + This work was supported bv grants to the Astrophysical Theory Program [rom NASA and ASTO7-07474 from NSF) at the University of Colorado Boulder., \acknowledgments This work was supported by grants to the Astrophysical Theory Program (NNX07-AG77G from NASA and AST07-07474 from NSF) at the University of Colorado Boulder. + We thank Joanna Dunkley. Chris Carilli. Richard Ellis. and Piero Macau for useful discussions on reionizalion aud CMD optical depth statistics.," We thank Joanna Dunkley, Chris Carilli, Richard Ellis, and Piero Madau for useful discussions on reionization and CMB optical depth statistics." + We are grateful to the referee lor suggesting additional model comparisons with the ionizing background al 2=5—6., We are grateful to the referee for suggesting additional model comparisons with the ionizing background at $z = 5-6$ . +The essential ingredieut of defining a dviuuuical eutropy 1s coarseeraimiug. that leads to sviubolie dynamics.,"The essential ingredient of defining a dynamical entropy is coarse–graining, that leads to symbolic dynamics." + Suppose that the Wilbert space of the svsteni is partitioned iuto cells. corresponding to projection operators ων so that their sun is the ideutity operator: »D=f," Suppose that the Hilbert space of the system is partitioned into cells, corresponding to projection operators $P_k$, so that their sum is the identity operator: $\sum_k P_k = I$." + Caven auy initial state c. quanti evolution vields the vector ο) at any future (or past) time jr. with οZ and 7 an observation delay.," Given any initial state $\psi$, quantum evolution yields the vector $\psi(j)$ at any future (or past) time $j \tau$, with $j \in \mathbf Z$ and $\tau$ an observation delay." + Clearly. the probability that the quautum svsteu is found in imacrostate & at time j is given by the square modulus of ο).," Clearly, the probability that the quantum system is found in macro–state $k$ at time $j$ is given by the square modulus of $P_k \psi (j)$." +" The ""quantuii historv of a vector c ds the result of repeated projections ο followed by unitary evolution."," The “quantum history” of a vector $\psi$ is the result of repeated projections on macro--states, followed by unitary evolution." + If the choice of the macrostate at time j is oeidicated by 0;. aud if the string of clioices at successive times is cutered iu the vector σ of leugth J. 6—(09.04.....Tay1) (this ds called a “word” in sviibolic vaandces) the quantum history of the vector c is For couveuieunce of notation we shall put The ‘amplitude’ (05.05). when averaged over initial conditions c. as we shall do momentarily is the analogue of the measure of the classical phase space cvlinder associated with the sviubolic dvnamics σ.," If the choice of the macrostate at time $j$ is indicated by $\sigma_j$ , and if the string of choices at successive times is entered in the vector $\mathbf{\sigma}$ of length $J$, $\mathbf{\sigma}=(\sigma_0,\sigma_1,\ldots,\sigma_{M-1})$ (this is called a “word” in symbolic dynamics) the quantum history of the vector $\psi$ is For convenience of notation we shall put The “amplitude” $(\psi_\sigma, \psi_\sigma)$, when averaged over initial conditions $\psi$, as we shall do momentarily, is the analogue of the measure of the classical phase space cylinder associated with the symbolic dynamics $\sigma$." + The formal analogy is completed by notiug the equivalence of ( with the inverse of the classical map., The formal analogy is completed by noting the equivalence of $U$ with the inverse of the classical map. +" In both classical and quanti clvnamics these probabilities add up to one: 35,(6s.608)=1. In quantum mechanics. though. interference reigns and the products (605.Ga) are non-null also when στσ’."," In both classical and quantum dynamics these probabilities add up to one: $\sum_\sigma (\psi_\sigma, \psi_\sigma) = 1.$ In quantum mechanics, though, interference reigns and the products $(\psi_\sigma, +\psi_{\sigma'})$ are non-null also when $\sigma \neq \sigma'$." + IkohuogorovSinai eutropy is constructed starting from the measures of the cxliuders o., Kolmogorov–Sinai entropy is constructed starting from the measures of the cylinders $\sigma$. + Iu the A-F. quanti formulation [33].. eutropy is derived by the spectra of the decoherence matrix D with cutrics D. defined by where Av is the dimension of the Wilbert space. the dageer indicates the adjoint aud clearly Ü3=CU04. D=D.," In the A-F. quantum formulation \cite{alik}, entropy is derived by the spectrum of the decoherence matrix $D$ with entries $D_{\sigma,\sigma'}$, defined by where ${\cal N}$ is the dimension of the Hilbert space, the dagger indicates the adjoint and clearly $U^\dagger = +U^{-1}$, $P_k^\dagger = P_k$." + Observe that D is a 27ος square matrix. Heritean. of uuit-trace and non-negative.," Observe that $D$ is a $2^J \times 2^J$ square matrix, Hermitean, of unit-trace and non-negative." + In the classical case. this matrix is diagonal.," In the classical case, this matrix is diagonal." + In the quautwm case. one defines the Shannon - Alicki - Fanucs (S-A-F) eutropy 5(4) of the system histories of leugth J with projections {Phas Technically. the A-F cutropy associated with the partition {2} is the limit SCA)SCF1) as J tends to infinity. as in the caseof KS cutropy.," In the quantum case, one defines the Shannon - Alicki - Fannes (S-A-F) entropy $S(J)$ of the system histories of length $J$ with projections $\{P_k\}$ as Technically, the A-F entropy associated with the partition $\{P_k\}$ is the limit $S(J)-S(J-1)$ as $J$ tends to infinity, as in the caseof KS entropy." + For systenis with Suitedimensional Hilbert spaces it is null., For systems with finite–dimensional Hilbert spaces it is null. + Nonetheless we ascribe particular importance to the S-A-F eutropies 567) even before the limit is taken, Nonetheless we ascribe particular importance to the S-A-F entropies $S(J)$ even before the limit is taken +It mav be possible. however. to discriminate between alternative formation iechanisius by cxamining the relative scaling of the fractionation ratios.,"It may be possible, however, to discriminate between alternative formation mechanisms by examining the relative scaling of the fractionation ratios." + For example. erain surface formation uplies that whereas. to first order. eas phase chemistry implics (using equatious [10 [12]]) The fact that the caleulated. values of A for the three isotoponuers alwavs have the same ratio wrespective of their absolute values is apparent frou Fie.," For example, grain surface formation implies that whereas, to first order, gas phase chemistry implies (using equations \ref{r3}] \ref{r1}] ]) The fact that the calculated values of $R$ for the three isotopomers always have the same ratio irrespective of their absolute values is apparent from Fig." + 2. where the vertical separation of the curves for the three isotopomers is coustaut.," 2, where the vertical separation of the curves for the three isotopomers is constant." + For doublv-deuterated anunonia. the predicted ratios are simular. with the observed value of RPONITID)=0.1 inplviug respective values of FCNITD»o)=0.05 and 0.03 for eas phase aud surface chemistry.," For doubly-deuterated ammonia, the predicted ratios are similar, with the observed value of $R(\damm) = 0.1$ implying respective values of $R(\ddamm) = 0.05$ and 0.03 for gas phase and surface chemistry." + Although the observed value of 0.05 agrees with our eas phase scheme. the observational uncertaimties are too large to rule out surface formation.," Although the observed value of 0.05 agrees with our gas phase scheme, the observational uncertainties are too large to rule out surface formation." + However. for triply-deuterated amunonia. the eas phase scheme predicts a fractionation almost twice as large: when scaled to the aabunudauce this iuplies a irafio 2.5 times ercater than the value predicted by surface chemustry (where we have used the relation ΕςΣΠ=ΠΟ)«RONIIDo)< RONID)D): cour definition of & in S1).," However, for triply-deuterated ammonia, the gas phase scheme predicts a fractionation almost twice as large; when scaled to the abundance this implies a ratio 2.5 times greater than the value predicted by surface chemistry (where we have used the relation $\tdamm/\ammonia = R(\tdamm)\times +R(\ddamm)\times R(\damm)$ ; our definition of $R$ in $\S +1$ ." + With the observed values .(NII3)=10* and R(NIL)D)=0.1. we predict (ND)z10Hl," With the observed values $x(\ammonia) = 10^{-7}$ and $R(\damm) += 0.1$, we predict $x(\tdamm) \approx 10^{-11}$." + Hence. if οσα be detected (or au upper limit detezruiued) in L131N. it nav be possible to determine whether the anunonia is ornmed in the gas or on the grains.," Hence, if can be detected (or an upper limit determined) in L134N, it may be possible to determine whether the ammonia is formed in the gas or on the grains." + It is worth stressing that the kind of scaliug relatious or multipl-deuterated fractionation ratios expressed by equations (18)) aud (19)) are applicable iu. geucral o all molecules., It is worth stressing that the kind of scaling relations for multiply-deuterated fractionation ratios expressed by equations \ref{surfscale}) ) and \ref{gasscale}) ) are applicable in general to all molecules. + Thus. whereas the fractionation of sinely-deuterated molecules reflects both the formation uechanisui of the molecule aud the underlving D/II ratio in the precursors. the relative fractionation ratios of uultipl-deuterated molecules reflect ouly the formation uechanisui.," Thus, whereas the fractionation of singly-deuterated molecules reflects both the formation mechanism of the molecule and the underlying D/H ratio in the precursors, the relative fractionation ratios of multiply-deuterated molecules reflect only the formation mechanism." + This fact was first appreciated by Turner (1990). who used the DoCO:IIDCO:II;CO ratios to show hat formaldehyde iu the Orion Compact Ridge should lave a grain surface origin.," This fact was first appreciated by Turner (1990), who used the $_2$ $_2$ CO ratios to show that formaldehyde in the Orion Compact Ridge should have a grain surface origin." + We have shown that large abundauces of aud οσα be produced by gas pliase chemistry in the interiors of cold dense clouds., We have shown that large abundances of and can be produced by gas phase chemistry in the interiors of cold dense clouds. + Auuuouia is deuterated via deuterou transfer from species such as ID!. DCO!. aud NoD. followed by dissociative recombination.," Ammonia is deuterated via deuteron transfer from species such as $_2$ $^+$, $^+$, and $_2$ $^+$ , followed by dissociative recombination." + This mechanisu is able to match the observed fractionation ratios of both species if the underlying ND! /NIT! ratio. R. equals 0.1.," This mechanism is able to match the observed fractionation ratios of both species if the underlying $^+$ $^+$ ratio, $\bar{R}$, equals 0.1." + Grain surface formation of anumnonia produces distinct fractionation ratios. however the uncertainties in the observed abundances mean that we cannot definitively conclude that deuterated lis bee formed in the eas.," Grain surface formation of ammonia produces distinct fractionation ratios, however the uncertainties in the observed abundances mean that we cannot definitively conclude that deuterated is being formed in the gas." + Because the scaling of the fractionation ratios expected from these two processes is not the same. this raises the possibility that the ivafios mav ultimately be used to deteriunue the origiu of these molecules.," Because the scaling of the fractionation ratios expected from these two processes is not the same, this raises the possibility that the ratios may ultimately be used to determine the origin of these molecules." + Iu particular. this could be resolved with the detection ofND;.. which we predict to have an abuudance of ~104 inLIBIN..," In particular, this could be resolved with the detection of, which we predict to have an abundance of $\sim 10^{-11}$ in." + Cas phase formation appears more feasible than surface chemistry since it is able to account for the observed aabunudance without recourse to uncertain surface processes and desorption mechanisms., Gas phase formation appears more feasible than surface chemistry since it is able to account for the observed abundance without recourse to uncertain surface processes and desorption mechanisms. + A further problem for the erain siutace hivpothesis is the fact that the large value of R(NTILD)) in LISLN requires a σας phase atomic D/II ratio of 0.05. but theoretical models predict au equilibrimm value of ouly a few times LO? at LOIS (Millar 1989: Roberts Millay 2000).," A further problem for the grain surface hypothesis is the fact that the large value of $R$ ) in L134N requires a gas phase atomic D/H ratio of 0.05, but theoretical models predict an equilibrium value of only a few times $10^{-3}$ at K (Millar 1989; Roberts Millar 2000)." + We also find that the large. observed molecular D/II ratios can only be reproduced if heavy elements are partially depleted outo erain surfaces., We also find that the large observed molecular D/H ratios can only be reproduced if heavy elements are partially depleted onto grain surfaces. + Therefore. it appears that the deutermuuu cussion peak in L131N traces a stnall reeion where significant amounts of CO. No and ο are frozen onto grains.," Therefore, it appears that the deuterium emission peak in L134N traces a small region where significant amounts of CO, $_2$ and O are frozen onto grains." + A similar region of cuhanced D fractionation is known to exist in TMC-1 (Cuéllin 1982). a dark cloud that appears to be plivsicallv simular toL131N.," A similar region of enhanced D fractionation is known to exist in TMC-1 (Guéllin 1982), a dark cloud that appears to be physically similar to." +. The fact that there appear to be several infrared sources located behind LI31N (Suell 1981) may allow the molecular depletion iuto ice mantles to be measured aud crudely mapped., The fact that there appear to be several infrared sources located behind L134N (Snell 1981) may allow the molecular depletion into ice mantles to be measured and crudely mapped. + Alternatively. these spatial eradicuts may be due to the energy available when ious aud neutrals have slightly different velocities.," Alternatively, these spatial gradients may be due to the energy available when ions and neutrals have slightly different velocities." +" In this case. &, becomes the dominant term in the denominator of the expression for S (equ. [3]."," In this case, $k_r$ becomes the dominant term in the denominator of the expression for ${\cal S}$ (eqn. \ref{calS}] ])," + which is consequently reduced (Charley 1998)., which is consequently reduced (Charnley 1998). + Another explanation may be the existence of chemical bistability in iuterstellar clouds: Cerin (1997) showed that molecular D/IL ratios are typically reduced by a factor of ten in the high ionization phase steady-state solution. as opposed to the low ionization phase.," Another explanation may be the existence of chemical bistability in interstellar clouds; Gerin (1997) showed that molecular D/H ratios are typically reduced by a factor of ten in the high ionization phase steady-state solution, as opposed to the low ionization phase." + Nevertheless. it seenis more likely that depletion is the cause of the lich deuteration in LISLN. since the latter mechanisms act to reduce S whereas depletion causes & to increase.," Nevertheless, it seems more likely that depletion is the cause of the high deuteration in L134N, since the latter mechanisms act to reduce $\cal S$ whereas depletion causes $\cal S$ to increase." + It is interesting to note that the observed range of Rin LISIN is always >0.05: this is what one would expect for a LOWS cloud with no depletion. aud is in fact the value derived frou DCO! observations of a laree nunibor of cold clouds (Caréllin 1982: Butner 1995).," It is interesting to note that the observed range of $\bar{R}$ in L134N is always $\gtrsim 0.05$; this is what one would expect for a K cloud with no depletion, and is in fact the value derived from $^+$ observations of a large number of cold clouds (Guéllin 1982; Butner 1995)." + The fact that the fractionation in L131N is determined to be above this canonical cold cloud. value is evidence for selective deuterimu enhancement iu this particular region. as opposed to a reduction of the fractionation iu the surrounding eas.," The fact that the fractionation in L134N is determined to be above this canonical cold cloud value is evidence for selective deuterium enhancement in this particular region, as opposed to a reduction of the fractionation in the surrounding gas." + On the other hand. Cerin (L997) observed a value of R(DCO!)20.003 in the lüeh latitude cloud. MCLD | 21.9. ten times lower than the ‘normal value.," On the other hand, Gerin (1997) observed a value of $R({\rm DCO^+}) = +0.003$ in the high latitude cloud MCLD $+$ 24.9, ten times lower than the `normal' value." + Iu this instance. it would appear that some mechanisin is deed operating to suppress the D/II chhaucement.," In this instance, it would appear that some mechanism is indeed operating to suppress the D/H enhancement." + If the depletion is particularly huge. the value of R can become as large as unity (Milla 2000).," If the depletion is particularly large, the value of $\bar{R}$ can become as large as unity (Millar 2000)." + Iu this case. chemical models predict large abundances of HDCO aud DoCO (Roberts Millar 2000). so it may be fruitful to search for DoCO in dark clouds.," In this case, chemical models predict large abundances of HDCO and $_2$ CO (Roberts Millar 2000), so it may be fruitful to search for $_2$CO in dark clouds." + Note. however. that deuterated formaldehydemay not in fact be as abundant as predicted by these models where it is asstuued that IH5C'O is deuterated via the same mecliauisum," Note, however, that deuterated formaldehydemay not in fact be as abundant as predicted by these models where it is assumed that $_2$ CO is deuterated via the same mechanism" + Note. however. that deuterated formaldehydemay not in fact be as abundant as predicted by these models where it is asstuued that IH5C'O is deuterated via the same mecliauisumi," Note, however, that deuterated formaldehydemay not in fact be as abundant as predicted by these models where it is assumed that $_2$ CO is deuterated via the same mechanism" +Sevlert galaxies are the closest. ancl most. common class of galaxies containing Active Galactic Nuclei (AGN) and. although their active nuclei are relatively weak. they exhibit many of the properties of their more luminous counterparts. xuticularly quasars.,"Seyfert galaxies are the closest and most common class of galaxies containing Active Galactic Nuclei (AGN) and, although their active nuclei are relatively weak, they exhibit many of the properties of their more luminous counterparts, particularly quasars." + As such they represent ideal sites for he study of the AGN phenomenon and its relationship to he host galaxy environment. which is dillicult to observe in more distant and powerful AGN.," As such they represent ideal sites for the study of the AGN phenomenon and its relationship to the host galaxy environment, which is difficult to observe in more distant and powerful AGN." + Observations of the A21-em. spectral line of neutral ivdrogen (LLL) provide valuable information on eas kinematics in nearby galaxies. anc may allow us to investigate models for XGN and their hosts on à wide range of scales. [rom the outer-most regions. where the gas may be alfected by tidal interactions. down to the cireumnuclear regions. where it may play. a role in the fuelling of AGN.," Observations of the $\lambda$ 21-cm spectral line of neutral hydrogen (HI) provide valuable information on gas kinematics in nearby galaxies, and may allow us to investigate models for AGN and their hosts on a wide range of scales, from the outer-most regions, where the gas may be affected by tidal interactions, down to the circumnuclear regions, where it may play a role in the fuelling of AGN." + In particular. - which are seen in nearly of galaxies when studied in the near HX (Alulehaey Regan. 1997)- may be an cllicient mechanism for transporting eas from the outer parts of a galaxy towards the active nucleus. where other transport processes become important (Roberts. Van Albada Luntley. 1979: Shlosman. Degelman Frank. 1990: Larson 1994).," In particular, - which are seen in nearly of galaxies when studied in the near IR (Mulchaey Regan, 1997)- may be an efficient mechanism for transporting gas from the outer parts of a galaxy towards the active nucleus, where other transport processes become important (Roberts, Van Albada Huntley, 1979; Shlosman, Begelman Frank, 1990; Larson 1994)." + Since neutral gas may respond in a hiehly non-incar way to even small deviations from axial svnunetry. it is an excellent tracer of the underlving gravitational potential of a barred galaxy Cleuben οἱ αἱ.," Since neutral gas may respond in a highly non-linear way to even small deviations from axial symmetry, it is an excellent tracer of the underlying gravitational potential of a barred galaxy (Teuben et al.," + 1986). but limitations in angular resolution and. sensitivity," 1986), but limitations in angular resolution and sensitivity" +spurious results and a high level of noise in the final reconstruction. while larger values oversmooth the results.,"spurious results and a high level of noise in the final reconstruction, while larger values oversmooth the results." + Even when the emitting plasma is strictly isothermal. the MCMC technique ts unable to distinguish between a truly isothermal solution and a Gaussian DEM with FWHM=0.05: also. the MCMC technique is able to separate multiple near-isothermal EM components only if their separation in temperature is AlogZ7=0.20.," Even when the emitting plasma is strictly isothermal, the MCMC technique is unable to distinguish between a truly isothermal solution and a Gaussian DEM with FWHM=0.05; also, the MCMC technique is able to separate multiple near-isothermal EM components only if their separation in temperature is $\Delta \log T=0.20$." + Atomic data uncertainties can affect the results by providing less accurate peak EM values and shifting the EM peak temperature. but the Alog7=0.20 resolving power of the MCMC technique is unaffected.," Atomic data uncertainties can affect the results by providing less accurate peak EM values and shifting the EM peak temperature, but the $\Delta \log T=0.20$ resolving power of the MCMC technique is unaffected." + The number of available tons does not affect the quality of the reconstruction. providec these ions are formed over a temperature range larger than the range where the plasma EM ts significant.," The number of available ions does not affect the quality of the reconstruction, provided these ions are formed over a temperature range larger than the range where the plasma EM is significant." + A smaller ton formation temperature range decreases the temperature resolution achieved by the MCMC technique., A smaller ion formation temperature range decreases the temperature resolution achieved by the MCMC technique. + The work of Enrico Landi is supported by NASA grants NNXIOAMI7G and NNXIIAC20G. Fabio Reale acknowledges support from Italian Ministero dell'Università e Ricerca and from Agenzia Spaziale Italiana (ASI). contract 1/015/07/0.," The work of Enrico Landi is supported by NASA grants NNX10AM17G and NNX11AC20G. Fabio Reale acknowledges support from Italian Ministero dell'Universitá e Ricerca and from Agenzia Spaziale Italiana (ASI), contract I/015/07/0." + Paola Testa was supported by NASA contract NNMO07AB07C to the Smithsonian Astrophysical Observatory., Paola Testa was supported by NASA contract NNM07AB07C to the Smithsonian Astrophysical Observatory. + We thank the referee for valuable comments that helped us improve the manuscript., We thank the referee for valuable comments that helped us improve the manuscript. +"Following (2005),, we use Q,=0.3, Ωκ= 0.0, Q4=0.7 and Πρ=100h km s~! Mpc-!.","Following \citet{2005AJ....129.2562B}, we use $\Omega_m = 0.3$ , $\Omega_k = 0.0$ , $\Omega_\Lambda = 0.7$ and $H_0 = 100 h$ km $^{-1}$ $^{-1}$." +" The most general form of the counts-in-cells distribution is denoted by f(N,V) which gives the probability of finding N galaxies in a region of space with volume V."," The most general form of the counts-in-cells distribution is denoted by $f(N,V)$ which gives the probability of finding $N$ galaxies in a region of space with volume $V$." + There are two approaches to studying this distribution., There are two approaches to studying this distribution. + The first approach is to let V be constant resulting in fy(N) which gives the distribution of the number of galaxies N for cells of a given volume V., The first approach is to let $V$ be constant resulting in $f_V(N)$ which gives the distribution of the number of galaxies $N$ for cells of a given volume $V$. +" This method is simple to use, yet powerful."," This method is simple to use, yet powerful." + The measurement of fy generally involves examining cells in 3D space or in (N)projection and counting the number of galaxies in each cell., The measurement of $f_V(N)$ generally involves examining cells in 3D space or in projection and counting the number of galaxies in each cell. +" In addition, the moments of fy(N) are closely related to the volume integrals of the Fronscorrelation functions of all (cs πε 2000)) and the orderscorrelation functions can be measured from the moments of (FryGaztanaga][1994)..&"," In addition, the moments of $f_V(N)$ are closely related to the volume integrals of the correlation functions of all orders (e.g. \citealt{1980lssu.book.....P, 1985ApJ...289...10F, 2000dggc.book.....S}) ) and the correlation functions can be measured from the moments of $f_V(N)$ \citep{1994ApJ...425....1F}." + For example the relation fy(N)between the volume integrals of the 2-point and 3-point correlation functions and the moments of the counts-in-cells distributionare given by where N is the mean number of galaxies in a cell and the volume integral of the N-point correlation function with £4=1 depends on the cell volume V., For example the relation between the volume integrals of the 2-point and 3-point correlation functions and the moments of the counts-in-cells distributionare given by where $\overline{N}$ is the mean number of galaxies in a cell and the volume integral of the $N$ -point correlation function with $\overline{\xi}_1 = 1$ depends on the cell volume $V$. + This property allows us to compare the counts-in-cells results with observations of the two-point correlation function., This property allows us to compare the counts-in-cells results with observations of the two-point correlation function. + 'To get the measured value of the two-point correlation function €2(r) we rewrite equation for the 2-galaxy case as This is a conditional average correlation where one galaxy is located at the center of the volume so one power of V in the denominator is removed by using polar coordinates relative to the central galaxy of the arbitrary volume., To get the measured value of the two-point correlation function $\xi_2(r)$ we rewrite equation for the 2-galaxy case as This is a conditional average correlation where one galaxy is located at the center of the volume so one power of $V$ in the denominator is removed by using polar coordinates relative to the central galaxy of the arbitrary volume. + We can invert the integral using a finite difference scheme with an interval of Ar to approximate the value of éo(r) such that where from equation and V is the volume of the cell which depends on the shape of the cell., We can invert the integral using a finite difference scheme with an interval of $\Delta r$ to approximate the value of $\xi_2(r)$ such that where from equation and $V$ is the volume of the cell which depends on the shape of the cell. + This gives us a means of determining the two-point correlation function from a series of measurements of fy over a range of scales., This gives us a means of determining the two-point correlation function from a series of measurements of $f_V(N)$ over a range of scales. +" The other approach to studying(IN) f(V,N) is to let N be constantresulting in /w(V) which gives the distribution of the volume V occupied by N galaxies of which the void probability function (VPF), where N=0, is a special case (e.g. [1986))."," The other approach to studying $f(V,N)$ is to let $N$ be constantresulting in $f_N(V)$ which gives the distribution of the volume $V$ occupied by $N$ galaxies of which the void probability function (VPF), where $N=0$, is a special case (e.g. \citealt{1986ApJ...301....1C}) )." + A theoretical approach to f/w(V) is complicated by the fact that the distribution depends on the correlation function at all scales rather than a scale determined by a particular value of V., A theoretical approach to $f_N(V)$ is complicated by the fact that the distribution depends on the correlation function at all scales rather than a scale determined by a particular value of $V$. +" This scale dependence can be found either empirically from the dependence of the variance of the fv(N) distribution on V, or from a model assumption of the form of £4(V)."," This scale dependence can be found either empirically from the dependence of the variance of the $f_V(N)$ distribution on $V$, or from a model assumption of the form of $\overline{\xi}_2(V)$." + These give the analytic form of fn(V)., These give the analytic form of $f_N(V)$. +" To avoid these complications, most attempts to study fw(V) have focused on the VPF because use of the reduced void probability 1986) considerably simplifies the analysis by expressing fo(V) in terms of NÉ."," To avoid these complications, most attempts to study $f_N(V)$ have focused on the VPF because use of the reduced void probability \citep{1986ApJ...306..358F} considerably simplifies the analysis by expressing $f_0(V)$ in terms of $\overline{N}\overline{\xi}_2$." +" 'The reduced void probability, given byprovides a means of isolating the scale-dependence of the void probability function because y is a function that depends only on Λέο, and N&, is easily derived from the variance of fy(N)."," The reduced void probability, given byprovides a means of isolating the scale-dependence of the void probability function because $\chi$ is a function that depends only on $\overline{N}\overline{\xi}_2$, and $\overline{N}\overline{\xi}_2$ is easily derived from the variance of $f_V(N)$." +" However, this simplification is only possible for voids in the GQED and NBD because, for N>1, fw(V) depends on N and £s separately."," However, this simplification is only possible for voids in the GQED and NBD because, for $N \geq 1$, $f_N(V)$ depends on $\overline{N}$ and $\overline{\xi}_2$ separately." +" Moreover, the void distribution is relatively insensitive to information on large cell sizes because large cells are unlikely to be completely empty."," Moreover, the void distribution is relatively insensitive to information on large cell sizes because large cells are unlikely to be completely empty." + For these reasons we focus on the simpler fy(V) approach in this paper and introduce the statistical descriptions of the counts-in-cells distribution., For these reasons we focus on the simpler $f_V(N)$ approach in this paper and introduce the statistical descriptions of the counts-in-cells distribution. + The gravitational quasi-equilibrium distribution was first derived from thermodynamics and subsequently from statistical mechanics 1984)(Ahmad by assuming that galaxy clustering evolveset al.through a sequence of quasi- states., The gravitational quasi-equilibrium distribution was first derived from thermodynamics \citep{1984ApJ...276...13S} and subsequently from statistical mechanics \citep{2002ApJ...571..576A} by assuming that galaxy clustering evolves through a sequence of quasi-equilibrium states. + The resulting distribution is given by where N=7nV is the average expected number of galaxies in a cell of volume V and 7 is the average number density of galaxies., The resulting distribution is given by where $\overline{N}=\overline{n}V$ is the average expected number of galaxies in a cell of volume $V$ and $\overline{n}$ is the average number density of galaxies. + Here b——W/2K is the ratio of the gravitational correlation energy W to twice the kinetic energy A of peculiar velocities relative to the Hubble flow and it represents a measure of clustering., Here $b=-W/2K$ is the ratio of the gravitational correlation energy $W$ to twice the kinetic energy $K$ of peculiar velocities relative to the Hubble flow and it represents a measure of clustering. +" A physical description of b is given by tobe which relates b to the mass of a galaxy m, the number density of galaxies 7 and the kinetic temperature of the galaxies T."," A physical description of $b$ is given by\citet{2002ApJ...571..576A} tobe which relates $b$ to the mass of a galaxy $m$ , the number density of galaxies $\overline{n}$ and the kinetic temperature of the galaxies $T$ ." + Here G is the gravitational constant., Here $G$ is the gravitational constant. +" (1984)..Originally an ansatz proposed by the physical origin of b was only later understood through work done by Baslaw&Fang! on the first and second laws of thermodynamics, and through the statistical mechanical derivation of the GQED by[Ahmad] ⋅"," Originally an ansatz proposed by \citet{1984ApJ...276...13S}, , the physical origin of $b$ was only later understood through work done by \citet{1996ApJ...460...16S} on the first and second laws of thermodynamics, and through the statistical mechanical derivation of the GQED by \citet{2002ApJ...571..576A}. ." +" (1984)..Originally an ansatz proposed by the physical origin of b was only later understood through work done by Baslaw&Fang! on the first and second laws of thermodynamics, and through the statistical mechanical derivation of the GQED by[Ahmad] ⋅⋅"," Originally an ansatz proposed by \citet{1984ApJ...276...13S}, , the physical origin of $b$ was only later understood through work done by \citet{1996ApJ...460...16S} on the first and second laws of thermodynamics, and through the statistical mechanical derivation of the GQED by \citet{2002ApJ...571..576A}. ." +rs dn each cluster model (Acami et al.,"$r_{\rm s}$, in each cluster model (Adami et al." + 1998)., 1998). + In order to derive the three dimensional (3D) density field (pr). where rds the distance from the center of the cluster) from XGH). we can use the following formula (Binney Tremaine 1987): We numerically estimate the spherical svmiumetric ptr) profile for a given SCA) in a model.," In order to derive the three dimensional (3D) density field ${\rho}(r)$ , where $r$ is the distance from the center of the cluster) from $\Sigma (R)$, we can use the following formula (Binney Tremaine 1987): We numerically estimate the spherical symmetric $\rho (r)$ profile for a given $\Sigma (R)$ in a model." + Each particle is given an initial orbital eccentricity (6) and a pericenter distance (r5) for a given cluster potential., Each particle is given an initial orbital eccentricity $e$ ) and a pericenter distance $r_{\rm p}$ ) for a given cluster potential. + We give each particle e so that the e-clistribution for N particles has a Gaussian with the mean e value and the dispersion of e being eio and συ. respectively.," We give each particle $e$ so that the $e$ -distribution for $N$ particles has a Gaussian with the mean $e$ value and the dispersion of $e$ being $e_{\rm m, 0}$ and ${\sigma}_{0}$, respectively." + Since we adopt spherical distributions of particles. we cdo not introduce initial anisotropy in. velocity dispersion for the ur. jy. and z directions: the velocity ellipsoid of particles can be anisotropic in racial (7) direction only.," Since we adopt spherical distributions of particles, we do not introduce initial anisotropy in velocity dispersion for the $x$, $y$, and $z$ directions: the velocity ellipsoid of particles can be anisotropic in radial $r$ ) direction only." +" In this calculation. we consider that the mean orbital eccentricity of galaxies in a cluster (64,0) is 0.6. which is consistent with recent high-resolution cosmological simulations (Cihigna ct al."," In this calculation, we consider that the mean orbital eccentricity of galaxies in a cluster $e_{\rm m,0}$ ) is 0.6, which is consistent with recent high-resolution cosmological simulations (Ghigna et al." + 1998)., 1998). + We however investigate dillerent. Live sets of models with 0.5noxcuoE0.7 and OLxay0.3.," We however investigate different five sets of models with $0.5\le e_{\rm m, 0} \le 0.7$ and $0.1 \le {\sigma}_{0} \le 0.3$." +" We investigate racial profiles of (projected) line-of-sight velocity dispersions (o1, (111) and velocity dispersions within 200 kpc (σι) for ""selected. particles” ancl all ones.", We investigate radial profiles of (projected) line-of-sight velocity dispersions ${\sigma}_{\rm los}(R)$ ) and velocity dispersions within 200 kpc ${\sigma}_{m}$ ) for “selected particles” and all ones. + We investigate ση within 200 kpc. mainky because all UCDs ave located within the central 200 kpe of the Fornax (c.g. Drinkwater ct al.," We investigate ${\sigma}_{m}$ within 200 kpc, mainly because all UCDs are located within the central 200 kpc of the Fornax (e.g., Drinkwater et al." + 2003: Gregg et al., 2003; Gregg et al. + 2007)., 2007). +" We consider that particles with cifferent mj, and ο can have dilferent kinematics. ancl accordingly we investigate a,.(42) and σι, [or ""selected. particles” with 57 (0) being within a certain parameter range."," We consider that particles with different $r_{\rm p}$ and $e$ can have different kinematics, and accordingly we investigate ${\sigma}_{\rm los}(R)$ and ${\sigma}_{m}$ for “selected particles” with $r_{\rm p}$ $e$ ) being within a certain parameter range." +" We introduce two Κον parameters: (1) à which (y of selected: particles are smaller than and (2) ei, which e of the particles are larger than.", We introduce two key parameters; (1) $r_{\rm th}$ which $r_{\rm p}$ of selected particles are smaller than and (2) $e_{\rm th}$ which $e$ of the particles are larger than. + We consider that ry and ei are Κον. because our previous simulations of UCD formation based on the threshing scenario suggest that these two are important for UCD formation.," We consider that $r_{\rm th}$ and $e_{\rm th}$ are key, because our previous simulations of UCD formation based on the threshing scenario suggest that these two are important for UCD formation." +" We investigate the models with 25 kpe xny< 175 kpe and 0.5Sey,<=0.7 for a given ey,;o and συ."," We investigate the models with 25 kpc $\le r_{\rm th} \le $ 175 kpc and $0.5 \le e_{\rm th} \le 0.7$ for a given $e_{\rm m,0}$ and ${\sigma}_0$." +" We mainly show the results of the ""standard"" model (M1) with eo=0.6 and συ=0.2. because the adopted parameters are the most reasonable in the present studs:"," We mainly show the results of the “standard” model (M1) with $e_{\rm m,0}=0.6$ and ${\sigma}_0=0.2$, because the adopted parameters are the most reasonable in the present study." + The. parameter. values of other four models (M2. M3. M4. ancl M5) are given in the ‘Table 1.," The parameter values of other four models (M2, M3, M4, and M5) are given in the Table 1." + Since most UCDs are located at 50 κρος2 200 kpe in the Fornax cluster (Ciregg et al., Since most UCDs are located at 50 $ \le R \le $ 200 kpc in the Fornax cluster (Gregg et al. +" 2007).n we estimate m, [or particles with 50 kpe10$ ) based on the results of these future cosmological simulations. + Figure 1 clearly shows that o.(2?) is significantly. steeper ancl systematically smaller in selected particles with than in all ones for the central 200 kpe of the standard, Figure 1 clearly shows that ${\sigma}_{\rm los}(R)$ is significantly steeper and systematically smaller in selected particles with $r_{\rm p}70$, because the hot spot solutions in the simulations give filling factors below." +. The more probable option is that the hot spots are shock [τοῖς caused by gas accretion [rom the disk onto the object., The more probable option is that the hot spots are shock fronts caused by gas accretion from the disk onto the object. + This is also supported by the presence of Hoa emission in the spectra. which is likely to be dominated by accretion as well (Sect. 4)).," This is also supported by the presence of $\alpha$ emission in the spectra, which is likely to be dominated by accretion as well (Sect. \ref{spec}) )." + The lack of variability in Ho over timescales ofdd (EN varies by <10. 15) is in line with the presence of stable accretion-related spots., The lack of variability in $\alpha$ over timescales of d (EW varies by $<10-15$ ) is in line with the presence of stable accretion-related spots. + LE accretion is the origin of the hot spots. the long-term: variability. in FU Tau A indicates substantial changes in the accretion configuration (geometry or accretion rate) on timescales of Nears.," If accretion is the origin of the hot spots, the long-term variability in FU Tau A indicates substantial changes in the accretion configuration (geometry or accretion rate) on timescales of years." + In addition to the optical variabilitv. FU Tau also exhibits moderate changes of ~ 0.2mamag at wavelengths of pim on timescales of vears (4th section in Table 3)). which are significantly larger than the photometric error.," In addition to the optical variability, FU Tau also exhibits moderate changes of $\sim 0.2$ mag at wavelengths of $\,\mu m$ on timescales of years (4th section in Table \ref{amps}) ), which are significantly larger than the photometric error." + The best explanation for the infrared. variations is changes in the disk structure or temperature. which could be related to changes in the accretion How.," The best explanation for the infrared variations is changes in the disk structure or temperature, which could be related to changes in the accretion flow." + FU Tau A is anomalous in its observed properties. primarily in (wo aspects: 1) In comparison with Taurus objects of similar spectral tvpe and temperature. FU Tau (X shows strong X-ray," FU Tau A is anomalous in its observed properties, primarily in two aspects: 1) In comparison with Taurus objects of similar spectral type and temperature, FU Tau A shows strong X-ray" +be produced by a cut-off in the electron energy. distribution. rather than a cooling break.,"be produced by a cut-off in the electron energy distribution, rather than a cooling break." + Observations in the X-ray. band of hard ((hard. X-ravs trailing in time behind soft. N-ravs) in MINN 421(Alaraschi.etal.1999) suggest (hat at (he peak energy (he acceleration and loss (me scales of the racialine particles are comparable (Ixirk.Rieger.&Alastichiaclis1997)., Observations in the X-ray band of hard (hard X-rays trailing in time behind soft X-rays) in MKN 421\citep{maraschi99} suggest that at the peak energy the acceleration and loss time scales of the radiating particles are comparable \citep{kirk97}. +. The corresponding electron spectrum is hard: p<2., The corresponding electron spectrum is hard: $p<2$. + This difference in electron spectrum max reflect a fundamental difference in the underlying particle acceleration mechanism in these (vo distinct. classes of objects., This difference in electron spectrum may reflect a fundamental difference in the underlying particle acceleration mechanism in these two distinct classes of objects. + This work was supported by the European Union TMLB programme under contract FMBRX-CT98-0163., This work was supported by the European Union TMR programme under contract FMRX-CT98-0168. + Consider a blob containing a uniform distribution of electrons., Consider a blob containing a uniform distribution of electrons. + In the rest frame of the blob. the differential number of electrons in interval ds’ moving within the solid angle € is e!TAFE πο where V is the volume of the blob.," In the rest frame of the blob, the differential number of electrons in interval $d\gamma'$ moving within the solid angle $\Omega'$ is ) = V ) where $V$ is the volume of the blob." + In the [frame the blob moves along the -r-axis at speed eo. and the clirection {ο the observer makes an angle 0 with this axis.," In the frame the blob moves along the $x$ -axis at speed $c\beta$, and the direction ${\bf\hat{n}}$ to the observer makes an angle $\theta$ with this axis." +" The radiation flix £F, observed is proportional to the product of the single particle emissivity and the electron distribution integrated over the emitting volumetime.", The radiation flux $F_\nu$ observed is proportional to the product of the single particle emissivity and the electron distribution integrated over the emitting volume. + This can be wrillen dini(s..p))ocA2) /e) Apart [rom the argument of the delta function. the only dependence of the integrand on / arises from the limits of (he integration over the moving blob. so that nuo)," This can be written dt ) ) Apart from the argument of the delta function, the only dependence of the integrand on $t$ arises from the limits of the integration over the moving blob, so that )" +Westerluncl (1961). discovered. that the 41day. Cepheid LS Pup was surrounded by a remarkable nebulosity.,Westerlund (1961) discovered that the 41day Cepheid RS Pup was surrounded by a remarkable nebulosity. + This is in the shape of rudimentary rings but with much distorted structure ane condensations., This is in the shape of rudimentary rings but with much distorted structure and condensations. + Llavlen (1972) showed that portions of the nebulosity varied in the period of the Cepheic but with with various phase lags., Havlen (1972) showed that portions of the nebulosity varied in the period of the Cepheid but with with various phase lags. + A very. beautiful set of measurements of phase lags at various points in the nebula has recently: been obtained by Iervella ct al. (, A very beautiful set of measurements of phase lags at various points in the nebula has recently been obtained by Kervella et al. ( +2008) (= ]xervella et al.).,2008) (= Kervella et al.). + In general. the expected phase lag at à point Fimay be written: llere Ad; is the fractional. phase lag. N; the whole number of pulsation periods elapsed. D is the distance to RS Pup in parsecs. 0; is the angular distance of 7 from the star in aresec. P? is the pulsation period in davs aud a; is the angle between the line joining the star to / and the plane of the sky (positive if? is further away than the star. negative if it is nearer).," In general, the expected phase lag at a point $i$ may be written: Here $\Delta \phi_{i}$ is the fractional phase lag, $N_{i}$ the whole number of pulsation periods elapsed, $D$ is the distance to RS Pup in parsecs, $\theta_{i}$ is the angular distance of $i$ from the star in arcsec, $P$ is the pulsation period in days and $\alpha_{i}$ is the angle between the line joining the star to $i$ and the plane of the sky (positive if $i$ is further away than the star, negative if it is nearer)." + The measured. quantities are Ao; and 8;., The measured quantities are $\Delta \phi_{i}$ and $\theta_{i}$. + P is assumed known ancl here it is taken as 41.4389 days ( Ixervella et al)., $P$ is assumed known and here it is taken as 41.4389 days ( Kervella et al.). + In an attempt to determine D. Iwervella et al.," In an attempt to determine $D$, Kervella et al." + assume a;=constant0., assume $\alpha_{i} = \rm {constant} =0$. + That is they assume that all the features measured. by them lie in the plane of the sky and the values of IN; are then chosen to obtain the best fit to this model., That is they assume that all the features measured by them lie in the plane of the sky and the values of $N_{i}$ are then chosen to obtain the best fit to this model. + The justification for this assumption is that if the nebulosity consisted of a series of thin. uniform. spherical shells centred on the star. then the deviation of all measured. points [rom the plane of the sky would be small.," The justification for this assumption is that if the nebulosity consisted of a series of thin, uniform, spherical shells centred on the star, then the deviation of all measured points from the plane of the sky would be small." + However an examination of the structure of the nebulosity (for instance from the figures in Ixervella et al.), However an examination of the structure of the nebulosity (for instance from the figures in Kervella et al.) + shows that it is far from corresponding to this idealized moclel., shows that it is far from corresponding to this idealized model. + Phere is much distortion and density variation in the rudimentary rings., There is much distortion and density variation in the rudimentary rings. + Ixervella et al., Kervella et al. + place special emphasis on the ten condensations or blobs shown in their fig 7., place special emphasis on the ten condensations or blobs shown in their fig 7. + The existence of such blobs is not consistent with the idealized model and leaves open the question of whether they or other features are actually in. or near. the plane of the sky.," The existence of such blobs is not consistent with the idealized model and leaves open the question of whether they or other features are actually in, or near, the plane of the sky." +" In view of these uncertainties it cannot be claimed that a definitive distance to RS Pup can be found based on the ""in-the-plane"" assumption."," In view of these uncertainties it cannot be claimed that a definitive distance to RS Pup can be found based on the “in-the-plane"" assumption." + In the next section this assumption is dropped ancl it is shown that a simple and astrophysically interesting model for the nebulosity is found if a distance for RS Pup is adopted from a. period-Iuminosity relation., In the next section this assumption is dropped and it is shown that a simple and astrophysically interesting model for the nebulosity is found if a distance for RS Pup is adopted from a period-luminosity relation. + van Leeuwen et al (, van Leeuwen et al. ( +2007) established à. redcdening-free period-Iuminosity relation in VL based on LIST (Benedict et al.,"2007) established a reddening-free period-luminosity relation in $V,I$ based on HST (Benedict et al." + 2007) and revised Hipparcos parallaxes., 2007) and revised Hipparcos parallaxes. + This together with the data in table I of that paper leads to a predicted distance of 1728pe for RS Pup., This together with the data in table A1 of that paper leads to a predicted distance of 1728pc for RS Pup. + Adopting this distance it is possible to use eq., Adopting this distance it is possible to use eq. + 1 to study the three dimensional structure of the nebulosity., 1 to study the three dimensional structure of the nebulosity. + In principle the values of Α can be arbitrarily assigned., In principle the values of $N_{i}$ can be arbitrarily assigned. + However they should obviously be chosen to account for apparent continuities in the structure and to conform to some simple. physically reasonable model.," However they should obviously be chosen to account for apparent continuities in the structure and to conform to some simple, physically reasonable model." + It was quickly found by trial and error that there is à Consistent set of values of IN; in which the points measured bv [xervella et al., It was quickly found by trial and error that there is a consistent set of values of $N_{i}$ in which the points measured by Kervella et al. + are further away than the star on the south side and nearer on the north. ic. an inclined. disc model is indicated.," are further away than the star on the south side and nearer on the north, i.e. an inclined disc model is indicated." + “Phis is indeed the simplest model. if the uniform spherical shell model is rejected.," This is indeed the simplest model, if the uniform spherical shell model is rejected." + La such a mocel the values of N; have to chosen such that (N;|2N6;)65 values are as near constant as possible in a given direction from the star and vary smoothly with direction., In such a model the values of $N_{i}$ have to chosen such that $(N_{i} +\Delta \phi_{i})/\theta_{i}$ values are as near constant as possible in a given direction from the star and vary smoothly with direction. + The details, The details + CrotonLucia&Blaizot2007)). (Schawinskietal.2007:BunelyIxXaviraj2008:Schawinskietal.2003).. (Dundyetal.2008:INaviraj2008).," \citealt{Croton2006,Delucia2007}) \citep{Schawinski2007,Bundy2008,Kaviraj2008,Schawinski2008}. \citep{Bundy2008,Kaviraj2008}." +. 5—12;0n Ho. 4000.1 (<1—2 1999)), $5-12\mu$ $\delta$ $\AA\/$ $<1-2$ \nocite{balogh99}) + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ " + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\e" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\ep" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\eps" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsi" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsil" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsilo" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsilon" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsilon\" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsilon\g" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). ," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsilon\gt" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). €," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsilon\gta" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). €2," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsilon\gta " + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). €20," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsilon\gta 0" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). €20.," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsilon\gta 0." + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). €20.1," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsilon\gta 0.1" + 26 1013 zz10?M. 2=6.4. (2—6)x10. 10?—104...2=30 LOYAL. exO.1. /jq4=0.45Gvr. M(0). €20.1," $z\approx 6$ $10^{47}$ $\approx 10^9 M_\odot$ $z=6.4$ $(2-6)\times 10^9 M_\odot$ $10^2-10^4 M_\odot$$z=30$ $10^9 M_\odot$ $\epsilon\simeq0.1$ $t_{\rm Edd}=0.45\,{\rm Gyr} $ $M(0)$ $\epsilon\gta 0.1$" +Marsden. D.. Lingenfelter. R.E. Rothschild. R.E. 2001a. ApJ 547. Marsden. D.. Lingenlelter. RE. Rothschild. ROE. 2001b. Alenou. Ix.. Perna. R. Hernquist. L. 2001a. Alenou. Ix.. Perna. E. Hernuquist. L. 2001b. Mereghetti. 5. 1999. to appear in The Neutron Star - Blackhole Connection. C. IxXouveliotou. J. van Paraclijs J. Ventura. eds. (INIuwer: Dordrecht). Alichel. F.C. 1988. Nature. 333. Michel. F.C. Dessler. A.J. 1981. ApJ. 251. Michel. F.C. Dessler. &.J. 1983. Nature. 303. Alineshige. 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P.M. et al.," 2000, PASP, 112, Woods, P.M. et al." + 1999. ApJ 519.," 1999, ApJ 519," +"is proportional tov "") is 1.3140.24.",is proportional to $\nu^{-\alpha}$ ) is $1.31\pm0.24$. + This is rather typical for AGNs on short time scales (Lawrence&Papaclakis1993)., This is rather typical for AGNs on short time scales \citep{law93}. +. Using the 0.75 keV data from the long-look observation. Papadakisetal.(2002) detected a high frequency break al Hz and a slope of L24(rji below the break frequency.," Using the 0.7–5 keV data from the long-look observation, \citet{papa01} detected a high frequency break at $(2.3\pm0.6)\times10^{-3}$ Hz and a slope of $^{+0.03}_{-0.04}$ below the break frequency." + Although the break Tequency cannot be detected in our data due to the Poisson noise. (he slope that we measure is consistent with their result.," Although the break frequency cannot be detected in our data due to the Poisson noise, the slope that we measure is consistent with their result." + We analvzed (he MEGZI and ZI spectra., We analyzed the $\pm$ 1 and $\pm$ 1 spectra. + The errors quoted in this section are 90% [or a single parameter of interest (N47= 2.71)., The errors quoted in this section are 90 for a single parameter of interest $\Delta\chi^2=2.71$ ). + Calibration errors for absolute [Iux are nol taken into account: Thev are estimated to be less than 10 and 20 lor the 1.5G6 keV band and the most of the other energy bands.respectivelv?.," Calibration errors for absolute flux are not taken into account; They are estimated to be less than 10 and 20 for the 1.5–6 keV band and the most of the other energy bands,." +. Calibration uncertaintv for the relative flux between WEG and MEG is accounted for bv introducing a constant parameter into the mocel., Calibration uncertainty for the relative flux between HEG and MEG is accounted for by introducing a constant parameter into the model. + First. we tried to fit the data in the whole energv band with a model consisting of a power-law and Galactic absorption (Vu —6.4x107em7: Dickey Lockman. 19907).," First, we tried to fit the data in the whole energy band with a model consisting of a power-law and Galactic absorption $N$ $=6.4\times10^{20}~{\rm cm}^{-2}$; Dickey Lockman, )." + To look at the large scale behavior. we rebinned the spectra coarsely. so that the energy resolution is similar to that of the SIS. and so that each energv. bin contains more than 25 photons.," To look at the large scale behavior, we rebinned the spectra coarsely, so that the energy resolution is similar to that of the SIS, and so that each energy bin contains more than 25 photons." + The residuals showed svstematic bumps with amplitude larger (han the calibration errors in the softest and hardest energy bands., The residuals showed systematic humps with amplitude larger than the calibration errors in the softest and hardest energy bands. + First we fitted the data only in the 25 keV band and obtained a reasonable 47 value of 96.1 for LIO degrees of [reedom (d.o.E.)., First we fitted the data only in the 2–5 keV band and obtained a reasonable $\chi^2$ value of 96.1 for 110 degrees of freedom (d.o.f.). + The photon-index and the unabsorbed 2.10 keV this are 2.5640.06 and (2.422-0.06) x10.ergem7s1 respectively.," The photon-index and the unabsorbed 2–10 keV flux are $2.56\pm0.06$ and $\pm$ $\times10^{-11}~{\rm erg~cm^{-2}~s^{-1}}$, respectively." + Fig., Fig. + 3 shows (he data ancl the best-fit model mentioned above and extrapolated to the whole energy band., \ref{fig:pl} shows the data and the best-fit model mentioned above and extrapolated to the whole energy band. + Excess emission below about 1.5 keV is seen clearly in the ratio plots., Excess emission below about 1.5 keV is seen clearly in the ratio plots. + We tried to model the soft excess component in three wavs., We tried to model the soft excess component in three ways. + Throughout we fixed neutral, Throughout we fixed neutral +convolve our model with the point-spread. function. (PSI) of the observations. and take the binning into account that results from the finite pixelsize of the CCD.,"convolve our model with the point-spread function (PSF) of the observations, and take the binning into account that results from the finite pixelsize of the CCD." + We therefore constructed a two-dimensional velocity field of the extracted rotation curve. such that and we convolved this field with a kernel as described in the appendix of Qian et al. (1995)...," We therefore constructed a two-dimensional velocity field of the extracted rotation curve, such that and we convolved this field with a kernel as described in the appendix of Qian et al. \nocite{1995MNRAS.274..602Q}." +" This kernel takes into account the blurring caused by the atmosphere and the instrument (EWLAL = 1.4"". for the oobservations of NGC 2974. see. Emscllem et al. 2004))"," This kernel takes into account the blurring caused by the atmosphere and the instrument (FWHM = $^{\prime \prime}$, for the observations of NGC 2974, see Emsellem et al. \nocite{2004MNRAS.352..721E}) )" + and the spatial resolution of the reduced observations (0.87 for SAURON)).," and the spatial resolution of the reduced observations $^{\prime + \prime}$ for )." + We extracted. the velocity along the major axis of the convolvecl velocity mocel and used the resulting rotation curve to fit our observations., We extracted the velocity along the major axis of the convolved velocity model and used the resulting rotation curve to fit our observations. +" The best fit is shown in Figure 6.. and has a core radius 42.—2."" (~0.2 kpe)."," The best fit is shown in Figure \ref{fig:fit_vphi}, and has a core radius $R_c = 2.1^{\prime + \prime}$ $\sim 0.2$ kpc)." + Under. the assumptions of Equation (6)). the asvmmeltric drift correction of Equation C XIS)) reduces to where T is the observed velocity. X ds the surface brightness of the ionised gas and ay the radial dispersion of the eas.," Under the assumptions of Equation \ref{eq:vmod}) ), the asymmetric drift correction of Equation \ref{eq:adc3}) ) reduces to where $\overline{v_\phi}$ is the observed velocity, $\Sigma$ is the surface brightness of the ionised gas and $\sigma_R$ the radial dispersion of the gas." + The last two terms in the equation are connected to the shape of the velocity ellipsoid. with & indicating the alignment of the ellipsoid. see Appendix A..," The last two terms in the equation are connected to the shape of the velocity ellipsoid, with $\kappa$ indicating the alignment of the ellipsoid, see Appendix \ref{sec:adc}." + To determine the slope of the surface brightness profile. we run kinemetry on the [flux map. extracting the surface brightness along cllipses with the same position angle and Uattening as the ones used to describe the velocity field.," To determine the slope of the surface brightness profile, we run kinemetry on the flux map, extracting the surface brightness along ellipses with the same position angle and flattening as the ones used to describe the velocity field." + To decrease the noise we fit a double exponential function to the profile. and determine the slope needed for the asymmetric drift correction from this parametrisation.," To decrease the noise we fit a double exponential function to the profile, and determine the slope needed for the asymmetric drift correction from this parametrisation." + The observed surface brightness profile and its fit are shown in Figure 7.., The observed surface brightness profile and its fit are shown in Figure \ref{fig:dens_fit}. + s with the velocity. profile. we convolved our model of the surface brightness during the fit with the kernel of Qian et al," As with the velocity profile, we convolved our model of the surface brightness during the fit with the kernel of Qian et al." +. to take seeing and sampling into account.," \nocite{1995MNRAS.274..602Q} + to take seeing and sampling into account." + ap can be obtained from the observed velocity dispersion σ using Equation X13))., $\sigma_R$ can be obtained from the observed velocity dispersion $\sigma$ using Equation \ref{eq:obs}) ). + Along the major axis. and under the assumptions made above. this expression simplifies to with Ayo defined in Equation (7)). and adopting from the velocity prolile.," Along the major axis, and under the assumptions made above, this expression simplifies to with $R_{\mathrm{mod}}$ defined in Equation \ref{eq:rmod}) ), and adopting $R_c = 2.1^{\prime \prime}$ from the velocity profile." + We choose &=(0.5. which is a tvpical value for a disc galaxy (e.g. Went de Zeeuw 1991)). but we also experimented. with other values for this parameter.," We choose $\kappa = 0.5$, which is a typical value for a disc galaxy (e.g. Kent de Zeeuw \nocite{1991AJ....102.1994K}) ), but we also experimented with other values for this parameter." + Varving & between 0 ancl 1 resulted in differences in V; of approximately LO|. and we adopt this value into the error bars of our final rotation curve.," Varying $\kappa$ between 0 and 1 resulted in differences in $V_c$ of approximately 10, and we adopt this value into the error bars of our final rotation curve." + ‘To obtain the slope of ay we follow the same procedure as for the surface brightness. extracting the profile of ma from the velocity dispersion map with kinemetry.," To obtain the slope of $\sigma_R$ we follow the same procedure as for the surface brightness, extracting the profile of $\sigma_{\mathrm{obs}}$ from the velocity dispersion map with kinemetry." +" We assume for the moment that turbulence is negligible in the galaxy (uui, =O) and subtract quadratically eina=LO {from a...", We assume for the moment that turbulence is negligible in the galaxy $\sigma_{\mathrm{turb}} = 0$ ) and subtract quadratically $\sigma_{\mathrm{thermal}} = 10$ from $\sigma_{\mathrm{obs}}$. + We convert the resulting ton.=ara. into σι using the relation in Equation (11)).," We convert the resulting $\sigma_{\mathrm{obs}} = +\sigma_{\mathrm{grav}}$ into $\sigma_R$ using the relation in Equation \ref{eq:sigma_simple}) )." + We parametrise this prolile by This profile has a core in the centre (introduced. by Husa). so that we can better reproduce the fattening of the profile towards the centre.," We parametrise this profile by This profile has a core in the centre (introduced by $R_{\mathrm{mod}}$ ), so that we can better reproduce the flattening of the profile towards the centre." + Again. we convolved our mocel to take seeing and sampling into account curing the fit.," Again, we convolved our model to take seeing and sampling into account during the fit." + The top panel of FigureS. shows the resulting profile and fit. as well as the observed. velocity. clispersion.," The top panel of Figure\ref{fig:sigma_fit} shows the resulting profile and fit, as well as the observed velocity dispersion." + We first assume that turbulence plavs no role in this galaxy. and we use ap às computed above to calculate the asvnnmetric drift. correction (Equation 9)).," We first assume that turbulence plays no role in this galaxy, and we use $\sigma_R$ as computed above to calculate the asymmetric drift correction (Equation \ref{eq:adc_text}) )." + The resulting rotation curve. as well as the observed rotation curve of the ionisecl gas. is shown in the top panel of Figure 9..," The resulting rotation curve, as well as the observed rotation curve of the ionised gas, is shown in the top panel of Figure \ref{fig:asym}. ." + To check our asymmetric drift corrected rotation curve, To check our asymmetric drift corrected rotation curve +SNRs and pulsars within the inner Galaxy nuelt emit VIIE 5 ravs but only a few 5 ταν sources were previously known.,SNRs and pulsars within the inner Galaxy might emit VHE $\gamma$ rays but only a few $\gamma$ ray sources were previously known. + Although the ILESS Collaboration indicates a clear positional coincidence of ils sources wilh a known SNR. or pulsar only in a limited number of cases. the distribution of Galactic latitude of the seventeen VITE 5 ray sources detected by TESS agrees quite well with the distributions of all SNRs catalogued by Green(2004) ancl of all pulsars catalogued by Manchesteretal.," Although the HESS Collaboration indicates a clear positional coincidence of its sources with a known SNR or pulsar only in a limited number of cases, the distribution of Galactic latitude of the seventeen VHE $\gamma$ ray sources detected by HESS agrees quite well with the distributions of all SNRs catalogued by \cite{Green:2004gr} and of all pulsars catalogued by \cite{Manchester}." +(2005).. Assuming. for example. that SNRs are a single class of counterparts with isotropic luminosity 1.95xI0eres! to the new ILESS sources and taking lor them a simple radiative model. Aharonianetal.(200G6a) found that the location of these sources favours a scale height of less (han 100 pe. consistent with the hypothesis (hat these sources are either SNRs or pulsars in a massive star forming region.," Assuming, for example, that SNRs are a single class of counterparts with isotropic luminosity $1.95 \times {10}^{34} \, {\mathrm{erg}} \, {\mathrm{s^{-1}}}$ to the new HESS sources and taking for them a simple radiative model, \cite{Aharonian:2005kn} found that the location of these sources favours a scale height of less than 100 pc, consistent with the hypothesis that these sources are either SNRs or pulsars in a massive star forming region." + Therefore although for only a few of HESS sources a firm identification with counterparts al other wavelengths exists. there are some suggestions that many of the HESS sources might coincide wilh supernova remnants (SNRs) or pulsar wind nebulae (DWNe).," Therefore although for only a few of HESS sources a firm identification with counterparts at other wavelengths exists, there are some suggestions that many of the HESS sources might coincide with supernova remnants (SNRs) or pulsar wind nebulae (PWNe)." + In fact (wo of the TESS sources have SNRs as counterparts. and five of these most recently discovered HESSsources are associated with pulsar wind nebulae (Funk|2007)..," In fact two of the HESS sources have SNRs as counterparts, and five of these most recently discovered HESSsources are associated with pulsar wind nebulae \citep{Funk}." + SNRs are an established source class in VII 5 rav astronomy., SNRs are an established source class in VHE $\gamma$ ray astronomy. + Possible correlations between SNRs and unidentified EGRET and HESS sources have been proposed since the release of (he [ist EGRET catalogue (Sturmer&Dermer1995:Espositoetal.1996).. and later for the third EGRET catalogue bv (Romeroetal.1999:Combi2001).," Possible correlations between SNRs and unidentified EGRET and HESS sources have been proposed since the release of the first EGRET catalogue \citep{Sturmer,Esposito}, and later for the third EGRET catalogue by \citep{Romero,Combi}." +. PWNe formed Irom voung pulsars with age less than a million vears are considered as potential gamma-ray emitters 2005)., PWNe formed from young pulsars with age less than a million years are considered as potential gamma-ray emitters \citep{Manchester:2004}. +. Though a voung age is not a sufficient condition for a pulsar to generate a PWN., Though a young age is not a sufficient condition for a pulsar to generate a PWN. + The spin-down energv loss is (he kev parameter to determine whether a voung energetic pulsar forms a PWN (Golthelf2003)., The spin-down energy loss is the key parameter to determine whether a young energetic pulsar forms a PWN \citep{Gotthelf:2003}. +. The ratio between 5-rav loud versus 5-ray quiel pulsars is uncertain., The ratio between $\gamma$ -ray loud versus $\gamma$ -ray quiet pulsars is uncertain. +" Gotthelf(2003) suggests that all pulsars with dI/dl>dE/dl,,=3.4x10erg/s ave N-rav. bright. manifest a distinct pulsar wind nebula (PWN). and are associated with a supernova event."," \citet{Gotthelf:2003} + suggests that all pulsars with $dE/dt > dE/dt_c = 3.4 \times {10}^{36} erg/s$ are X-ray bright, manifest a distinct pulsar wind nebula (PWN), and are associated with a supernova event." + By studying the Chandra data on the 28 most energetic pulsars of the Parkes Multibeam Pulsar Survey (Manchester2005) Gotthelf(2004) found that 15 pulsars with E>3.4.x10ergs/s ave X-ray bright. show a resolved PWN. and are associated with evidence of a supernova event.," By studying the Chandra data on the 28 most energetic pulsars of the Parkes Multibeam Pulsar Survey \citep{Manchester:2004} \citet{Gotthelf:2004} found that 15 pulsars with $\dot E > 3.4 \times {10}^{36} ergs/s$ are X-ray bright, show a resolved PWN, and are associated with evidence of a supernova event." + This suggests that about 2.5 per cent of the radio loud pulsar have à PWN and might emit 5-ravs., This suggests that about 2.5 per cent of the radio loud pulsar have a PWN and might emit $\gamma$ -rays. + Supernova remnants and pulsars are (he radio counterparts of two of the high energyeanmma rav candidates. SNRs and PWNe. and their spatial distribution is known from many observations ab radio wavelengths.," Supernova remnants and pulsars are the radio counterparts of two of the high energygamma ray candidates, SNRs and PWNe, and their spatial distribution is known from many observations at radio wavelengths." + The pulsar surface densitv o »sp(r). plotted in Fig. 2.. ," The pulsar surface density $\sigma_{PSR}(r)$ , plotted in Fig. \ref{fig2}, ," +is filled by the following shifted Gamma function (Yusifov&Wick2004:Lorimeretal. ," is fitted by the following shifted Gamma function \citep{Yusifov:2004fr,Lorimer:2004,Lorimer:2006} + " +andl oligarch formation is short compared to the GGyr PAIS contraction time (D'Antona1994;Baralfeetal.1998:Siess 2000).. Che timing of planetesimal formation sets (he nature of icv/rocky planets wilh distance from a low mass star.,"and oligarch formation is short compared to the Gyr PMS contraction time \citep{1994ApJS...90..467D,1998A&A...337..403B,2000A&A...358..593S}, the timing of planetesimal formation sets the nature of icy/rocky planets with distance from a low mass star." +" On its Havashi track. the huminositv of a M, star fades by a factor of several hundred at roughly. constant effective temperature."," On its Hayashi track, the luminosity of a $M_{\odot}$ star fades by a factor of several hundred at roughly constant effective temperature." +" During (his period. &,,,4, moves inward by a [actor of +15 20."," During this period, $a_{snow}$ moves inward by a factor of $\sim$ 15–20." + Just outside the moving snow line. ice condensation increases σ (Mj) bv a factor of ~ 4 (8) (Havashi1981): ἐν decreases by a factor of 3.," Just outside the moving snow line, ice condensation increases $\sigma$ $M_{iso}$ ) by a factor of $\sim$ 4 (8) \citep{1981PThPS..70...35H}; $t_{iso}$ decreases by a factor of 3." + This moving snow line enables rapid formation ol icy oligarchs that can collide and merge into super-Eartls., This moving snow line enables rapid formation of icy oligarchs that can collide and merge into super-Earths. + Disk evolution is also an important feature of planet formation around low mass stars., Disk evolution is also an important feature of planet formation around low mass stars. + In the standard MMSN. model. σ is fixed in time and scales with the stellar radius on ihe main sequence (e.g.ILavashi1981)..," In the standard MMSN model, $\sigma$ is fixed in time and scales with the stellar radius on the main sequence \citep[e.g.][]{1981PThPS..70...35H}." +" ILowever. when PAIS stars actively accrete from a circumstellar disk. magnetic interactions between (he star and the disk appear to lock. the inner disk radius J2;, al a fixed distance relative to the stellar radius. £=ἐν~3. ab several Myr (e.g.Eisneretal.2005).."," However, when PMS stars actively accrete from a circumstellar disk, magnetic interactions between the star and the disk appear to `lock' the inner disk radius $R_{in}$ at a fixed distance relative to the stellar radius, $\xi \equiv +R_{in}/R_\star \sim 3$, at several Myr \citep[e.g.][]{2005ApJ...623..952E}." + Although the duration of this phase isnot the observed change in £ lor disks around solar-tvpe stars is a factor of ~2 3 (Eisneretal.2005)..," Although the duration of this phase isnot well-constrained, the observed change in $\xi$ for disks around solar-type stars is a factor of $\sim 2$ –3 \citep{2005ApJ...623..952E}." + IE disks around low mass stars remain locked for the entire PAIS phase. ihe maximum decrease in the inner disk radius is à factor of ~1520.," If disks around low mass stars remain locked for the entire PMS phase, the maximum decrease in the inner disk radius is a factor of $\sim$ 15–20." + This change is much larger than the observed variation of £: thus we assume € = constant., This change is much larger than the observed variation of $\xi$; thus we assume $\xi$ = constant. + To conserve mass ancl angular momentum. c and (he outer disk radius must evolve. which impacts Ad; and the formation (ümescales for oligarchs ancl planets.," To conserve mass and angular momentum, $\sigma$ and the outer disk radius must evolve, which impacts $M_{iso}$ and the formation timescales for oligarchs and planets." +" To construct a moclel for disk evolution. we adopt where 2, is in units of solar radii. e=8ggcem 7. and a, is the radial distance from the star in AU."," To construct a model for disk evolution, we adopt where $R_\star$ is in units of solar radii, $\sigma_0 = 8$ $^{-2}$, and $a_{{\textrm{{\tiny AU}}}}$ is the radial distance from the star in AU." + Setting the scale factor 3~ vields the usual 2(MMSN) for a £M. star ad MMvr. when a large fraction of the solid mass in the terrestrial zone of the Solar Svstem is in large bodies.," Setting the scale factor $\beta \sim 3$ yields the usual $\sigma$ (MMSN) for a $M_{\odot}$ star at Myr, when a large fraction of the solid mass in the terrestrial zone of the Solar System is in large bodies." + Consistent with observations (Nattaetal.2000:Seholz2006)... we scale σ and the disk mass linearly with the stellar mass.," Consistent with observations \citep{2000prpl.conf..559N,2006ApJ...645.1498S}, we scale $\sigma$ and the disk mass linearly with the stellar mass." +" For a MMwr old 0.25AL. star. this scaled MAISN has ο=2 and My;=0.0264, integrated [rom 34, to 50AXAU [for a eas/solids ratio of 100."," For a Myr old $0.25\,M_\odot$ star, this scaled MMSN has $\beta = 2$ and $M_{disk} = 0.026 +M_\star$ integrated from $3 R_\star$ to AU for a gas/solids ratio of 100." +" To provide a smooth transition from fj,=1 foreSea, to fi,=4 for @Zau. (Havashi 1981).. we include a parameter Jj.=1+CN,—1)/(1+e"") where"," To provide a smooth transition from $f_{ice} = 1$ for $a \lesssim a_{snow}$ to $f_{ice} = 4$ for $a \gtrsim a_{snow}$ \citep{1981PThPS..70...35H}, , we include a parameter $f_{ice}=1+(\Delta_{ice}-1)/(1+e^x)$ where" +(Aland Mz., and. +.. Equations (À&.2)) or (ΑΟ) completely determines the respouse to the perturbation induced by the perturber., Equations \ref{alapl}) ) or \ref{alapl1}) ) completely determines the response to the perturbation induced by the perturber. + For b=0 (no external perturbation). one obtains the following nonlinear eigenvalue problem (5)].," For ${\bf b}=0$ (no external perturbation), one obtains the following nonlinear eigenvalue problem (s)]." + The eigenvalues of this problem are the frequencies of the point modes of the stellar system: frequencies with Re(s)>0 correspond to unstable erowing modes while for stable damped modes ReCs)<0., The eigenvalues of this problem are the frequencies of the point modes of the stellar system: frequencies with $Re(s)>0$ correspond to unstable growing modes while for stable damped modes $Re(s)<0$. + Solution of equation (CÀ.2)) describes the evolution iu frequency space., Solution of equation \ref{alapl}) ) describes the evolution in frequency space. + In order to eect the time evolution of the perturbation we need to perform the inverse Laplace transform of equation (A.2))., In order to get the time evolution of the perturbation we need to perform the inverse Laplace transform of equation \ref{alapl}) ). + This viclds the following expression for the coefficieuts αι.(f) where. to simplify the notation. we have definedX," This yields the following expression for the coefficients ${\bf a}_{l\g_3}(t)$ where, to simplify the notation, we have defined." +p Equation (AL1}) does not take iuto account the zeros of det D(s) which are the point modes of the primary svsteu., Equation \ref{tco}) ) does not take into account the zeros of det ${\bf D}(s)$ which are the point modes of the primary system. + Since we will cousider ouly systems known to be stable. there are no modes with Res}>0. while moces with Re(s)«0 will be damped aud die away with time.," Since we will consider only systems known to be stable, there are no modes with $Re(s)>0$, while modes with $Re(s)<0$ will be damped and die away with time." + Nevertheless. as shown in Weinbere (1991). for ime models some modes cau be very weakly damped and persist long after their excitation.," Nevertheless, as shown in Weinberg (1994), for King models some modes can be very weakly damped and persist long after their excitation." + When the effects of damped modes are included. Equation (ALL) is valid for ¢>»x while for finite time it has an additional term for cach such mode.," When the effects of damped modes are included, Equation \ref{tco}) ) is valid for $t \rightarrow +\infty$ while for finite time it has an additional term for each such mode." + Altogetherwe fud where sy denote the frequeucies of the damped modes., Altogetherwe find where $s_d$ denote the frequencies of the damped modes. + Miuunerical evaluation of equation (A16)) requires truucatiug the infinite sum over 54 (the suis over the indices 2» aud 75 ranec from 7 to ήν see Tremaine Weinhere 1981)., Numerical evaluation of equation \ref{dm}) ) requires truncating the infinite sum over $\g_1$ (the sums over the indices $\g_2$ and $\g_3$ range from $-l$ to $l$; see Tremaine Weinberg 1984). +" After checking the convergence of the solution. the final value adopted is “yu.=6 for the low-conceutratiou Kine model studied in 83 aud 51,44=10 for the hieh-couceutration Nine model considered in 8&1."," After checking the convergence of the solution, the final value adopted is $\g_{1max}=6$ for the low-concentration King model studied in 3 and $\g_{1max}=10$ for the high-concentration King model considered in 4." + Similarky. the stan over the radial basis niust be truncated," Similarly, the sum over the radial basis must be truncated." + Since the the adopted biorthogonal functions are tailored to the equilibrium model Γρ=10 is sufficieut for the convergence., Since the the adopted biorthogonal functions are tailored to the equilibrium model $n_{max}=10$ is sufficient for the convergence. +" All the integrals have been calculated by Roubere's method with the muuber of poiuts chosen so to euuzuitee a maxima error of z Lat,", All the integrals have been calculated by Romberg's method with the number of points chosen so to guarantee a maximum error of $\approx10^{-4}$ . +BB to be measured should. vield a precise mass estimate for BD. This would make possible an interesting comparison with V209 z DD and PCI-V36. which have similar orbital periods to but that ave both members of metal-poor globular clusters.,"B to be measured should yield a precise mass estimate for $-$ B. This would make possible an interesting comparison with V209 $\omega$ B and PC1-V36, which have similar orbital periods to but that are both members of metal-poor globular clusters." + Lt seems clear that the formation of mmust have involved. extensive mass loss from a red. giant star. but the mechanism for the mass loss is not so clear.," It seems clear that the formation of must have involved extensive mass loss from a red giant star, but the mechanism for the mass loss is not so clear." + The progenitor of BB must have had a mass O.SAL: to evolve olf the main-sequence within the lifetime of the Galaxy. so this star has lost &Tadhuter1993) comes from the FR I ike radio morphology of these sources.," Additionalevidence for the relative misalignment of 0923+392 \citep{kollgaard90} and 0405-123 \citep{morganti93} + comes from the FR II like radio morphology of these sources." + Criveu the relaive nulsalirment of BQs we ask how the SED of the aligned. version of these sources looks. aud ow tlese aligned sources Compare with soICes ound in current blazar samples.," Given the relative misalignment of BQs we ask how the SED of the aligned version of these sources looks, and how these aligned sources compare with sources found in current blazar samples." +" We examine botl Cases for tLe optical-UV flux. being only sy""nchrotron or having au adcditioual thermal contributio1 roma 1 aecretiou disc.", We examine both cases for the optical–UV flux being only synchrotron or having an additional thermal contribution from an accretion disc. + We usethe jet formaIsla ο. 2.. moclified to include IC losses due to au exteri€ photon fiek aud an augle depeucent emission fo ‘both a constant Lorentz factor and an accelerati& jet 1998).," We use the jet formalism of \citet{kirk97}, modified to include IC losses due to an external photon field and an angle dependent emission for both a constant Lorentz factor and an accelerating jet \citep{georganopoulos98}." +. Iu lus work the IC emission is not modeled., In this work the IC emission is not modeled. + Mocleliig the hard X-ray. eluissiou. whic1 is probably due o SSC (Ixuboetal.1998).. is highly complicatecL for the inhomogeneous jets stucliec here.," Modeling the hard X-ray emission, which is probably due to SSC \citep{kubo98}, is highly complicated for the inhomogeneous jets studied here." + Althougi we cannot address the bard X-ray. emission (tantitatively. we cau discuss qualitatively the scalit& of the observed lard X-ray [lux of the BQs as a functiou of beaming. since the beaming behavior of the IC component is well understood (Dermer1902).," Although we cannot address the hard X-ray emission quantitatively, we can discuss qualitatively the scaling of the observed hard X-ray flux of the BQs as a function of beaming, since the beaming behavior of the IC component is well understood \citep{dermer95}." +. We sttdy first a coustant Lorentz factor P jet together with a tlermal component moceled as black bod(v (BB radiation., We study first a constant Lorentz factor $\Gamma$ jet together with a thermal component modeled as black body (BB) radiation. + In Figure 1 we plot the SED [for a ratee of angles 0 between the jet axis ancl the line of sight., In Figure \ref{fig1} we plot the SED for a range of angles $\theta$ between the jet axis and the line of sight. +" The jet emission is strongly alected by Doppler boosting aud. as 0 decreases. the uou-lerinal SED shiftsmostly upward to higler appareit Duuniuosities with a slight shift to higher peaX [requeicies. since Lox8°""Lg and voxpg. where a is the spectral index. o js the ustal Dop)er factor 6=I/(I(1—8pcos0)). aid the subscript 0 refers O quantities in the flow coiloving Taime."," The jet emission is strongly affected by Doppler boosting and, as $\theta$ decreases, the non–thermal SED shiftsmostly upward to higher apparent luminosities with a slight shift to higher peak frequencies, since $L\propto \delta^{3+\alpha} L_{0}$ and $\nu\propto \delta \nu_{0}$, where $\alpha$ is the spectral index, $\delta$ is the usual Doppler factor $\delta=1/(\Gamma(1-\beta_{\Gamma}\cos\theta))$, and the subscript $0$ refers to quantities in the flow comoving frame." + 5iuce the BB and the BLR eimissiol are not a funcjon o [0.1je relative contributior ol the tlerinal component and the ecuivalen width (EW) of the eniissiou lires (which are not plotted here. but we assuiued to have a fraction of he BB huminosi v)a'e reclueed as 0 decreases.," Since the BB and the BLR emission are not a function of $\theta$, the relative contribution of the thermal component and the equivalent width (EW) of the emission lines (which are not plotted here, but are assumed to have a fraction of the BB luminosity) are reduced as $\theta$ decreases." + We expec the IC componeut to either follov the increase o ‘the svuch'Oolron one if it is due to SSC eiiss]on or (o inerease even faser if it is due to EC emissio .sdnce Losex8”[2] and Leox617 (Dernjer1995).," We expect the IC component to either follow the increase of the synchrotron one if it is due to SSC emission or to increase even faster if it is due to EC emission, since $L_{SSC}\propto +\delta^{3+\alpha}$ and $L_{EC} \propto \delta^{4+2\alpha}$ \citep{dermer95}." +. In both cases. ancl cdeyencling on μεν. t1e aligned source will ook like au LBL or acassical FSRQ. possibly siinilar to 3C 279. a source sowing evidence of a hermal compouent iuls optical-UV spectrum. (Pianetal. 1999)..," In both cases, and depending on $L_{BLR}$ , the aligned source will look like an LBL or a classical FSRQ, possibly similar to 3C 279, a source showing evidence of a thermal component in its optical–UV spectrum \citep{pian99}. ." + It is interestiug to note that or 3C 279. logμι=[LT6 eres “(Cao&Jiang 1999).. in the με range of theBOs examined lere.," It is interesting to note that for 3C 279, $\log L_{BLR}=44.76$ erg $^{-1}$ \citep{cao99}, , in the $L_{BLR}$ range of theBQs examined here." +" 2003:(ο,ο,Dressler1980:Baoeh2001:Weinmnann"," \citep[e.g.][]{dressler80,balogh98,gomez03,kauffmann04,weinmann06}." +etal.2006).. lol Cirützbaucljietal.2011a).," $z \sim 1$ \citep[e.g.][]{cucciati06, cooper07, + elbaz07, ideue09, salimbeni09, scodeggio09, tran10, grutzbauch11a}." +. -- (seealsoScovilleetal.2007:201]:Cooperetal.2010).. transition at τον1.," $z \sim $ \citep[see + also][]{scoville07,patel09b,patel11,cooper10}, transition at $z \sim 1$." + However there are several reasons το doubt he existence of such ao stroug transition., However there are several reasons to doubt the existence of such a strong transition. + Cave he apparently smooth erowth of the red sequence over COsanic time (Dranuueretal.2009:WilliamsctIlbertetal.2010:Iajisawa 2011).. it. wouk| be odd if this erowth occurred preferentially iu overdelse regions atf 2«1 but avoided them at +>1.," Given the apparently smooth growth of the red sequence over cosmic time \citep{brammer09, williams09, ilbert10, + kajisawa11}, it would be odd if this growth occurred preferentially in overdense regions at $z < 1$ but avoided them at $z > 1$." + Iustead. there are several examples of clusters at 2—1.5 that already. have. proniüneut populations of passive galaxies in place (e.g.MeCarthyetal.2007:I&urk2009:Wilsonetal.2009:Strazzullo 2010).," Instead, there are several examples of clusters at $z \sim 1.5$ that already have prominent populations of passive galaxies in place \citep[e.g.][]{mccarthy07,kurk09,wilson09,strazzullo10}." +". Studiof eaOs:laxyv chisterineg have also found that red galaxies teud to be more clustered thanblue galaxies at 2z1.5 (c.g,al. 2010).. which also suggests that they reside in deleler enuvironnieuts;"," Studies of galaxy clustering have also found that red galaxies tend to be more clustered than blue galaxies at $z \gtrsim 1.5$ \citep[e.g.][]{grazian06,quadri07,quadri08,hartley10}, which also suggests that they reside in denser environments." + Moreover. if nothing else. it is natural to expect that more massive galaxies at 2>1 should teud to lie in deuser euvironnmienuts. and eiven that more massive eaOs:laxies are also more Likely to have their star formation qleuched. (“downsizing”). this would sugeest that the SF-density relation should extend to +>1.," Moreover, if nothing else, it is natural to expect that more massive galaxies at $z +> 1$ should tend to lie in denser environments, and given that more massive galaxies are also more likely to have their star formation quenched (“downsizing”), this would suggest that the SF-density relation should extend to $z > 1$." + Several of the studies that lave performed direct CRinuates of environmental densitics have used large maples of galaxies with spectroscopic redshifts. howevery plesainimg spectroscopic redshifts for large aud unbiased na at το5—l ds very. difficult.," Several of the studies that have performed direct estimates of environmental densities have used large samples of galaxies with spectroscopic redshifts, however obtaining spectroscopic redshifts for large and unbiased samples at $z > 1$ is very difficult." + Quiescent Os:axies. which are verv faint in the observer's optiical. aὉ especially hard το observe. and it is these eaaxies that are of particular interest when studvius the SF-density relation.," Quiescent galaxies, which are very faint in the observer's optical, are especially hard to observe, and it is these galaxies that are of particular interest when studying the SF-density relation." + À second. although perhaps less siguifücant. diffüceultwv for spectroscopic studieSN 18 obainimg sufficicutly deuse spectroscopicsampling of eaOs:axies in overdense regions.," A second, although perhaps less significant, difficulty for spectroscopic studies is obtaining sufficiently dense spectroscopicsampling of galaxies in overdense regions." + Other studies have estimated euvironmental deusities Usius photometric redshifts., Other studies have estimated environmental densities using photometric redshifts. + This has the obwTOUS, This has the obvious +"amplitude of the excursion in the positional data associated with these separations can be calculated by simulating the data at the line-peak, convolving them with the seeing and determining the spectro-astrometric trace (cf. ?)).","amplitude of the excursion in the positional data associated with these separations can be calculated by simulating the data at the line-peak, convolving them with the seeing and determining the spectro-astrometric trace (cf. \citealt{baines_2006}) )." +" In both cases, the photo-center is precisely halfway because the line peaks are equally bright as the star."," In both cases, the photo-center is precisely halfway because the line peaks are equally bright as the star." +" We therefore would expect, based on the above, that in the present data line excursions of up to 2.2 mas (α Col) and 1.6 mas (Z Tau) can be observed."," We therefore would expect, based on the above, that in the present data line excursions of up to 2.2 mas $\alpha$ Col) and 1.6 mas $\zeta$ Tau) can be observed." +" This is the maximum observable separation, as the above computation assumes that all line emission arises from a thin ring with a rotation speed corresponding to the line peak."," This is the maximum observable separation, as the above computation assumes that all line emission arises from a thin ring with a rotation speed corresponding to the line peak." +" Not all emission at the line peak comes from a single ring however, as the projected velocities for smaller, faster, rings will be observed as well at the observed Doppler shifts."," Not all emission at the line peak comes from a single ring however, as the projected velocities for smaller, faster, rings will be observed as well at the observed Doppler shifts." + To assess this effect we performed some simple model calculations., To assess this effect we performed some simple model calculations. +" We assume the star to be surrounded by a geometrically thin, Keplerian rotating disk reaching onto the stellar surface, with the line flux per unit area following a simple power law in radius."," We assume the star to be surrounded by a geometrically thin, Keplerian rotating disk reaching onto the stellar surface, with the line flux per unit area following a simple power law in radius." +" The main input parameters of the model are the stellar radius, rotation speed, the inclination and emission line strength (which are all fairly well known), the remaining free parameters are the disk's outer radius and the exponent of the power law."," The main input parameters of the model are the stellar radius, rotation speed, the inclination and emission line strength (which are all fairly well known), the remaining free parameters are the disk's outer radius and the exponent of the power law." +" The model produces a two dimensional position-velocity diagram, which is binned up and smoothed to represent our pixel sizes of 5 kms!, 85 mas and seeing of 500 mas respectively."," The model produces a two dimensional position-velocity diagram, which is binned up and smoothed to represent our pixel sizes of 5 $^{-1}$, 85 mas and seeing of 500 mas respectively." +" From the resulting data, the spectro-astrometry is then measured."," From the resulting data, the spectro-astrometry is then measured." +" Changing the outer radius of the model disk increases the spectro-astrometric excursions, which then occur at lower velocities, as expected from Keplerian rotation."," Changing the outer radius of the model disk increases the spectro-astrometric excursions, which then occur at lower velocities, as expected from Keplerian rotation." + A stronger line flux will yield a larger spectro-astrometric excursion because the photo-centre shifts more in the direction of the emission line., A stronger line flux will yield a larger spectro-astrometric excursion because the photo-centre shifts more in the direction of the emission line. +" In the extreme case of optically thick emission, the powerlaw will have a flat slope and the emerging line flux wil be dominated by the outer parts of the disk."," In the extreme case of optically thick emission, the powerlaw will have a flat slope and the emerging line flux will be dominated by the outer parts of the disk." +" In the other extreme, that of optically thin emission, the power law depends on the density distribution."," In the other extreme, that of optically thin emission, the power law depends on the density distribution." +" For an isothermal, flaring Keplerian disk, the surface density, and by implication the flux per unit area, has an r? powerlaw dependence (cf. ?))."," For an isothermal, flaring Keplerian disk, the surface density, and by implication the flux per unit area, has an $r^{-2}$ powerlaw dependence (cf. \citealt{carciofi_2006}) )." +" As a consequence, the line emission moves towards the inner parts of the disk."," As a consequence, the line emission moves towards the inner parts of the disk." +" The main positional excursions will thus occur at higher velocities, closer to the star and therefore be smaller than in the optically thick case."," The main positional excursions will thus occur at higher velocities, closer to the star and therefore be smaller than in the optically thick case." + Changing the exponent of the powerlaw also affects the shape of the emission line., Changing the exponent of the powerlaw also affects the shape of the emission line. +" A shallower exponent, more representative of the optically thick case, puts more flux at lower velocities, while a steeper power law, closer to the optically thin situation, results in narrower lines, with the line peak at higher velocities."," A shallower exponent, more representative of the optically thick case, puts more flux at lower velocities, while a steeper power law, closer to the optically thin situation, results in narrower lines, with the line peak at higher velocities." +" In general though, unless the exponent gets too steep, the excursions are of similar magnitude when the same line-to-continuum ratio is simulated."," In general though, unless the exponent gets too steep, the excursions are of similar magnitude when the same line-to-continuum ratio is simulated." +" We performed a large parameter study, but for the purposes of this paper, we will restrain ourselves to one illustrative example representative of both objects."," We performed a large parameter study, but for the purposes of this paper, we will restrain ourselves to one illustrative example representative of both objects." + We set the line-to-continuum ratio to be 2 (as per the spectra in Fig., We set the line-to-continuum ratio to be 2 (as per the spectra in Fig. +" 1 and derived above), use a stellar rotational velocity of 475 kms""! (halfway the values for both objects) and an inclination of 55? (also roughly halfway the two objects) and use a stellar radius of 0.2 mas."," \ref{specast} and derived above), use a stellar rotational velocity of 475 $^{-1}$ (halfway the values for both objects) and an inclination of $^{\rm o}$ (also roughly halfway the two objects) and use a stellar radius of 0.2 mas." +" For the outer radius of the disk we take 10, 30 and a maximum of 70 stellar radii (cf. ?))."," For the outer radius of the disk we take 10, 30 and a maximum of 70 stellar radii (cf. \citealt{marlborough_1997}) )." + The resulting data are shown in Fig. 2.., The resulting data are shown in Fig. \ref{specastmod}. + The top panel presents the resulting model line profiles., The top panel presents the resulting model line profiles. +" As expected, the lines are doubly peaked with peak separations that are larger for smaller disk radii."," As expected, the lines are doubly peaked with peak separations that are larger for smaller disk radii." +" The separations range from 110kms! for the largest disk to 160 and 270 kms'! for the smallest disks, respectively."," The separations range from $\sim$ $^{-1}$ for the largest disk to 160 and 270 $^{-1}$ for the smallest disks, respectively." +" This trend is explained by the fact that these velocities correspond to the Keplerian rotation speeds at the maximum possible radii, where most of the line flux originates if the emission is optically thick."," This trend is explained by the fact that these velocities correspond to the Keplerian rotation speeds at the maximum possible radii, where most of the line flux originates if the emission is optically thick." + The most notable differences between the model line profiles and the observed line profiles are the relative narrowness of the line peaks and the little emission at low projected velocities., The most notable differences between the model line profiles and the observed line profiles are the relative narrowness of the line peaks and the little emission at low projected velocities. +" This is probably due to the fact that the model disks are assumed to be geometrically thin, resulting in low projected emitting surface areas at low velocities."," This is probably due to the fact that the model disks are assumed to be geometrically thin, resulting in low projected emitting surface areas at low velocities." +" In reality the disks are flared, and therefore the emitting area will be much larger, in particular at these low velocities."," In reality the disks are flared, and therefore the emitting area will be much larger, in particular at these low velocities." +" In addition, line broadening is not taken into account here."," In addition, line broadening is not taken into account here." +" For a proper treatment, radiative transfer models such as those by ? will be an excellent tool."," For a proper treatment, radiative transfer models such as those by \citet{carciofibjorkman_2006} will be an excellent tool." +" Using such advanced models is beyond the scope of this paper, in which we wish to obtain a rough figure for the excursions only."," Using such advanced models is beyond the scope of this paper, in which we wish to obtain a rough figure for the excursions only." + We also note that the blue peak of Z Tau is much stronger than the red peak., We also note that the blue peak of $\zeta$ Tau is much stronger than the red peak. +" This is most likely due to one-armed oscillations in its disk, which give rise to such asymmetry,"," This is most likely due to one-armed oscillations in its disk, which give rise to such asymmetry," +or AR©vulg.,or $\Delta R\approx v_{sh}t_d$. +" The resulting density p=¢/rez,fy. when combined with the shock jump condition for the radiation pressure. gives a temperature comparable to that in equation (7))."," The resulting density $\rho=c/\kappa v_{sh}^2 t_d$, when combined with the shock jump condition for the radiation pressure, gives a temperature comparable to that in equation \ref{temp}) )." + These results can be compared to the numerical results of Morivaetal.(2010)., These results can be compared to the numerical results of \cite{moriya10}. +".. Taking their model sl3w2r20m2Pe3 with Fs,=3. Af=1.3. and D,=1. the breakout radius in our model is AH,=5.9xLOM em. which is inside the outer radius of 2x1015 em in the numerical model."," Taking their model s13w2r20m2e3 with $E_{51}=3$, $M_{e1}=1.3$, and $D_*=1$, the breakout radius in our model is $R_d=5.9\times 10^{14}$ cm, which is inside the outer radius of $2\times 10^{15}$ cm in the numerical model." +" Substituting (he parameters into equation (5). the radiated energy is £7,=1.43x1050 eves. which is close to the 2.0xLO"" eres found in the numerical model (Morivaetal.2010)."," Substituting the parameters into equation (5), the radiated energy is $E_{rad}=1.4\times 10^{50}$ ergs, which is close to the $2.0\times 10^{50}$ ergs found in the numerical model \citep{moriya10}." +. The numerical result may be larger. in part. because the shock wave generates power in ihe more extended. cireiumstellar medium.," The numerical result may be larger, in part, because the shock wave generates power in the more extended circumstellar medium." +" We also examined the scaling of E,,; with the parameters and found reasonable agreement wil (he numerical results.", We also examined the scaling of $E_{rad}$ with the parameters and found reasonable agreement with the numerical results. + The scaling depends on the supernova density gradient. which is only approximately treated here.," The scaling depends on the supernova density gradient, which is only approximately treated here." + Estimates of the observable color temperature of the radiation require considerations of whether radiation equilibrium is attained in the emitting region., Estimates of the observable color temperature of the radiation require considerations of whether radiation equilibrium is attained in the emitting region. + Following Nakar (2010).. we define a thermal coupling coellident y=npp/UÜanysr(Inp)). where κΤην is (he photon number density in thermal equilibrium. j is Doltzinann's constant. and tip¢¢(Ten)=3.5xοelU? tem ? is the production rate of photons by the free-lree process.," Following \cite{nakar10}, we define a thermal coupling coefficient $\eta=n_{BB}/(t_d\dot n_{ph,ff}(T_{BB}))$, where $n_{BB}\approx aT^4_{BB}/3k_BT_{BB}$ is the photon number density in thermal equilibrium, $k_B$ is Boltzmann's constant, and $\dot n_{ph,ff}(T_{BB})=3.5\times 10^{36}\rho^2T^{-1/2}$ $^{-1}$ $^{-3}$ is the production rate of photons by the free-free process." + If sufficient photons are produced to maintain the blackbody niumnber density. or 7S1. thermal equilibrium is achieved.," If sufficient photons are produced to maintain the blackbody number density, or $\eta\la 1$, thermal equilibrium is achieved." +" Using equations (1)) and (7)) for / and Typ. and p=vp,(B) (taking into account the factor 7 compression in the shock wave). we estimate a for the breakout shell: For the standard parameters. (he breakout shell is mareinally in thermal οΙΙΙ."," Using equations \ref{td}) ) and \ref{temp}) ) for $t_d$ and $T_{BB}$, and $\rho=7\rho_w(R_{fs})$ (taking into account the factor 7 compression in the shock wave), we estimate $\eta$ for the breakout shell: For the standard parameters, the breakout shell is marginally in thermal equilibrium." + As the radiation propagates into the tmshocked mass loss region. the lower clensity results in a deviation from thermal equilibrium.," As the radiation propagates into the unshocked mass loss region, the lower density results in a deviation from thermal equilibrium." + The Irequency dependence of the opacity can play a role (Morivaetal.2010) and we do not treat the details of spectrum production here., The frequency dependence of the opacity can play a role \citep{moriya10} and we do not treat the details of spectrum production here. + The loss of radiative energy from the shocked region results in the formation of a dense shell at radius AH. as seen in munerical simulations(Grassbere 1911)..," The loss of radiative energy from the shocked region results in the formation of a dense shell at radius $R$, as seen in numerical simulations\citep{grassberg71,falk77}." + The expansion of the shell into additional mass loss produces continuing power for the supernova. L=πρι(epey). where the wind velocity ο may be affected by preshock radiative acceleration.," The expansion of the shell into additional mass loss produces continuing power for the supernova, $L=2\pi R^2 \rho_w (v_{fs}-v_w)^3$, where the wind velocity $v_w$ may be affected by preshock radiative acceleration." + The simulations of Morivaetal.(2010). show some evidence [or acceleration. but it is only significant near the breakout radius because of the r? dependence of the radiative flux. aud we neglect it here.," The simulations of \cite{moriya10} show some evidence for acceleration, but it is only significant near the breakout radius because of the $r^{-2}$ dependence of the radiative flux, and we neglect it here." +" The expansion of /2 can be described by the (hin shell approximation (Chevalier 1982).. vielding 2= 0.94/2,;."," The expansion of $R$ can be described by the thin shell approximation \citep{chevalier82}, , yielding $R=0.94 R_{cd}$ ." + The resulting power is, The resulting power is +account for of the median gas turbulence.,account for of the median gas turbulence. + For five out of the eleven z~0.6 clumpy galaxies. it was possible to compare the positions of emission and absorption lines using FORS? spectra from Rodriguesetal.(2008).," For five out of the eleven $\sim$ 0.6 clumpy galaxies, it was possible to compare the positions of emission and absorption lines using FORS2 spectra from \cite{rodrigues08}." +. Only J033224.60-274428.1 shows a significant shift (— IO0km/s. Puechetal. 201020). which suggests substantial winds in this galaxy.," Only J033224.60-274428.1 shows a significant shift $\sim$ 100km/s, \citealt{puech09b}) ), which suggests substantial winds in this galaxy." + Therefore. feedback from. star formation is probably not the main driver for the high velocity dispersion observed in z~0.6 elumpy galaxies.," Therefore, feedback from star formation is probably not the main driver for the high velocity dispersion observed in $\sim$ 0.6 clumpy galaxies." + Inter-clump gravity could account for an additional contribution in z~0.6 clumpy galaxies (Lehnertetal.2009)... which is not sufficient to account for the observed level of turbulence.," Inter-clump gravity could account for an additional contribution in $\sim$ 0.6 clumpy galaxies \citep{lehnert09}, which is not sufficient to account for the observed level of turbulence." + Another source of turbulence could be associaed with cold gas accretion., Another source of turbulence could be associated with cold gas accretion. + In their semi-analytic model. Khociar&Silk(2009). calibrated a relation between the cold gas accretion rate and the associated generated gas velocity dispersion using z-2 galaxies.," In their semi-analytic model, \cite{khochfar08} calibrated a relation between the cold gas accretion rate and the associated generated gas velocity dispersion using $\sim$ 2 galaxies." + Using the same calibration. I estimate tha to generate the observed level of gasturbulence in z~0.6 clumov galaxies. an accretion rate of ~ 34M../vr would be required.," Using the same calibration, I estimate that to generate the observed level of gasturbulence in $\sim$ 0.6 clumpy galaxies, an accretion rate of $\sim$ $_\odot$ /yr would be required." + Thi sis one order of magnitude above what is expected from full numerical simulations (see Keresetal.2009 and discussion below in Sect., This is one order of magnitude above what is expected from full numerical simulations (see \citealt{keres09} and discussion below in Sect. + 4.2)., 4.2). + Finally. the turbulence in z~0.6 clumpy galaxies could be merger-driven.," Finally, the turbulence in $\sim$ 0.6 clumpy galaxies could be merger-driven." +" Simulated gas-rich remnants from major mergers (e.g.. Robertson&Bullock 2008)) indeed show similar V,/c ratios in the rebuilt disks compared to observed values (Puechetal.2007)."," Simulated gas-rich remnants from major mergers (e.g., \citealt{robertson08}) ) indeed show similar $V_{rot}/\sigma$ ratios in the rebuilt disks compared to observed values \citep{puech07}." +. In order to relax towards local galaxies. the stellar phase of 7-0.6 clumpy galaxies needs to get stabilized by increasing Ον. by at least ~25% on average.," In order to relax towards local galaxies, the stellar phase of $\sim$ 0.6 clumpy galaxies needs to get stabilized by increasing $Q_{stars}$ by at least $\sim$ on average." +" This could be achieved by increasing V, through gas accretion within the optical radius.", This could be achieved by increasing $V_{rot}$ through gas accretion within the optical radius. + Alternatively. this can also be achieved through the stabilizing influence of a growing bulge as described by Bournaud&Elmegreen (2009). ," Alternatively, this can also be achieved through the stabilizing influence of a growing bulge as described by \cite{bournaud09}. ." +"Finally. if self-gravity drives disk turbulence (Burkertetal.2009).. then one expects that z-0.6 clumpy galaxies get stabilized by increasing their velocity dispersion to ~49 km/s in order to reach Q,,,—1."," Finally, if self-gravity drives disk turbulence \citep{burkert09}, then one expects that $\sim$ 0.6 clumpy galaxies get stabilized by increasing their velocity dispersion to $\sim$ 49 km/s in order to reach $_{eff}$ =1." + This is relatively close to the median value observed in z~0.6 RD galaxies. with 4743 km/s. Cold streams are thought to be an important process triggering instability. as z~2 disks are expected to be fueled by such cold streams. which could maintain a dense gaseous disk that can undergo gravitational fragmentation into clumps (Dekelet 2009b)...," This is relatively close to the median value observed in $\sim$ 0.6 RD galaxies, with $\pm$ 3 km/s. Cold streams are thought to be an important process triggering instability, as $\sim$ 2 disks are expected to be fueled by such cold streams, which could maintain a dense gaseous disk that can undergo gravitational fragmentation into clumps \citep{dekel09b}. ." + Indeed. 7-2 clumpy galaxies are thought to livein -[0'M. dark matter haloes (e.g.. Dekeletal. 2009)). in which such cold flows are expected to take place (Dekeletal. 2009)..," Indeed, $\sim$ 2 clumpy galaxies are thought to livein $\sim$ $^{12}$ $_\odot$ dark matter haloes (e.g., \citealt{dekel09}) ), in which such cold flows are expected to take place \citep{dekel09}. ." +"In the collisionally-dominated resistive limit, the resulting magnetic diffusivity is a scalar, the familiar Ohmic resistivity.","In the collisionally-dominated resistive limit, the resulting magnetic diffusivity is a scalar, the familiar Ohmic resistivity." +" This is simply because collisions occur in all directions, therefore the impulse they communicate to the charges is randomly oriented."," This is simply because collisions occur in all directions, therefore the impulse they communicate to the charges is randomly oriented." +" In the other limits, however, where at least some charged species are well tied to the magnetic field, the diffusivity is a tensor."," In the other limits, however, where at least some charged species are well tied to the magnetic field, the diffusivity is a tensor." +" Previous studies on the magnetic activity of discs (e.g. Wardle1999;Sano&Stone2002a,b;Salmeron&Wardle2003,2005;Salmeron 2011,, hereafter WS11) have highlighted the importance of incorporating in these studies all the three field-matter diffusion mechanisms described above, as their relative importance is a strong function of location within the disc."," Previous studies on the magnetic activity of discs (e.g. \citealt{W99, SS02a, SS02b, SW03, SW05, WS11}, hereafter WS11) have highlighted the importance of incorporating in these studies all the three field-matter diffusion mechanisms described above, as their relative importance is a strong function of location within the disc." +" This is illustrated in Fig. 1,,"," This is illustrated in Fig. \ref{fig:diff}," +" which shows the regions where the ambipolar, Hall and Ohmic diffusivity terms dominate in a Log B - Log ny plane (e.g.Wardle 2007), assuming that the charged particles are ions and electrons, in a weakly-ionised plasma."," which shows the regions where the ambipolar, Hall and Ohmic diffusivity terms dominate in a Log $B$ – Log $n_{\rm H}$ plane \citep[e.g.][]{W07}, assuming that the charged particles are ions and electrons, in a weakly-ionised plasma." +" As expected, ambipolar diffusion is dominant at low densities and strong fields whereas the opposite is true for the Ohmic regime."," As expected, ambipolar diffusion is dominant at low densities and strong fields whereas the opposite is true for the Ohmic regime." +" The large, intermediate region of parameter space between these two limits is dominated by the Hall diffusivity."," The large, intermediate region of parameter space between these two limits is dominated by the Hall diffusivity." +" For example, for r21 AU the"," For example, for $r = 1$ AU the" +which is high enough to rule out a pre-existing dwarf galaxy.,which is high enough to rule out a pre–existing dwarf galaxy. + An additional hint is given by comparing the UV-to-optical SED of C2 and C5., An additional hint is given by comparing the UV–to–optical SED of C2 and C5. +" As we have seen earlier in the present section, they are remarkably similar."," As we have seen earlier in the present section, they are remarkably similar." + The most likely possibility is that this region is the tip of a tidal tail., The most likely possibility is that this region is the tip of a tidal tail. + High resolution HI observations would certainly yield precious information regarding the exact nature of the C2 clump., High resolution HI observations would certainly yield precious information regarding the exact nature of the C2 clump. +" The gas depletion timescale, which is the time it would take to convert the molecular gas reservoir into stars at the current SFR, can vary between different objects, but it is unclear whether and how it varies within a given interacting system."," The gas depletion timescale, which is the time it would take to convert the molecular gas reservoir into stars at the current SFR, can vary between different objects, but it is unclear whether and how it varies within a given interacting system." + ? showed that collision debris have a depletion timescale of the molecular gas similar to that of spiral galaxies., \cite{braine2001a} showed that collision debris have a depletion timescale of the molecular gas similar to that of spiral galaxies. +" However, how this timescale changes as a function of the morphology in an interacting system is still an open question."," However, how this timescale changes as a function of the morphology in an interacting system is still an open question." + In Table 5 we list the depletion timescale of the molecular gas in the CO(1—0) beams., In Table \ref{tab:SFR} we list the depletion timescale of the molecular gas in the CO(1–0) beams. +" The shortest depletion timescale corresponds to the starburst in the eastern nucleus, which is also observed in other nuclear regions."," The shortest depletion timescale corresponds to the starburst in the eastern nucleus, which is also observed in other nuclear regions." + This is expected as starbursts tend to have a shorter depletion timescale (?).., This is expected as starbursts tend to have a shorter depletion timescale \citep{kennicutt1998b}. + The tidal features C3 and C5 show a longer depletion timescale around 2x10? yr that is typical of what can be observed in spiral galaxies and in collision debris in general (?)..," The tidal features C3 and C5 show a longer depletion timescale around $2\times10^9$ yr that is typical of what can be observed in spiral galaxies \citep{kennicutt1998b,bigiel2011a} and in collision debris in general \citep{braine2001a}." + C2 however has a shorter depletion timescale., C2 however has a shorter depletion timescale. + This may be due to an age effect as usual SFR estimators assume a constant SFR which causes an overestimate the current SFR if it is actually declining., This may be due to an age effect as usual SFR estimators assume a constant SFR which causes an overestimate the current SFR if it is actually declining. + The Schmidt-Kennicutt law links the gas surface density to the SFR surface density: Xsrgος, The Schmidt–Kennicutt law links the gas surface density to the SFR surface density: $\mathrm{\Sigma_{SFR}\propto\Sigma_{gas}^N}$. + Whether and how this law varies is subject of an on-goingYN. debate in the ," Whether and how this law varies is subject of an on–going debate in the literature \citep{kennicutt1998b,gao2004a,kennicutt2007a,leroy2008a,bigiel2008a,blanc2009a,rahman2011a,liu2011a}." +Deviations between quiescent star-forming galaxies and interacting systems can have important implications regarding our understanding of galaxy formation and evolution., Deviations between quiescent star-forming galaxies and interacting systems can have important implications regarding our understanding of galaxy formation and evolution. +" The fundamental reason is that the ISM (interstellar medium) of high redshift galaxies is turbulent (?), and that they are gas rich (??)."," The fundamental reason is that the ISM (interstellar medium) of high redshift galaxies is turbulent \citep{forster2006a}, and that they are gas rich \citep{tacconi2010a,daddi2010a}." +" Nearby interacting systems, by having an enhanced turbulence, can be seen as analogues of high redshift galaxies."," Nearby interacting systems, by having an enhanced turbulence, can be seen as analogues of high redshift galaxies." +" Recent high resolution simulations by ? show that interacting galaxies deviate from the standard Schmidt-Kennicutt law seen in spiral disks, which could be explained by the effect of gas turbulence and fragmentation."," Recent high resolution simulations by \cite{teyssier2010a} show that interacting galaxies deviate from the standard Schmidt–Kennicutt law seen in spiral disks, which could be explained by the effect of gas turbulence and fragmentation." + Whether star formation proceeds similarly to the Schmidt-Kennicutt law in local interacting galaxies is therefore important to gain insight into the mode of star formation at high redshift., Whether star formation proceeds similarly to the Schmidt–Kennicutt law in local interacting galaxies is therefore important to gain insight into the mode of star formation at high redshift. + In a first step we examine how the molecular hydrogen column density and the SFR surface density in the different regions in Arp 158 compare to the relation derived by ? in the case of spiral galaxies., In a first step we examine how the molecular hydrogen column density and the SFR surface density in the different regions in Arp 158 compare to the relation derived by \cite{bigiel2008a} in the case of spiral galaxies. + The SFR in Arp 158 corresponds to the 244FUV measurement in Table 5 which is the same to that used by ?.., The SFR in Arp 158 corresponds to the 24+FUV measurement in Table \ref{tab:SFR} which is the same to that used by \cite{bigiel2008a}. +" Even though there are only a few measurements, the SFR and the H» surface densities span more than one order of magnitude and are well correlated with each other in Arp 158."," Even though there are only a few measurements, the SFR and the $_2$ surface densities span more than one order of magnitude and are well correlated with each other in Arp 158." +" The NC, C3 and C5 regions follow the same relation as spiral galaxies, which is consistent with the results found by ? on TDG."," The NC, C3 and C5 regions follow the same relation as spiral galaxies, which is consistent with the results found by \cite{braine2001a} on TDG." + The NE and C2 regions exhibit clear excesses of their SFR in comparison to their molecular gas surface density., The NE and C2 regions exhibit clear excesses of their SFR in comparison to their molecular gas surface density. + This is easily explainable for NE as it is a nuclear starburst., This is easily explainable for NE as it is a nuclear starburst. + This finding confirms observational and theoretical results for starburst galaxies., This finding confirms observational and theoretical results for starburst galaxies. + Another possibility for NE and C2 is that the molecular gas is more concentrated than star formation so that averaging over the beam would underestimate the molecular gas surface density., Another possibility for NE and C2 is that the molecular gas is more concentrated than star formation so that averaging over the beam would underestimate the molecular gas surface density. +" However, if the gas and star formation are equally extended it would move the points mostly parallel to the ? relation."," However, if the gas and star formation are equally extended it would move the points mostly parallel to the \cite{bigiel2008a} relation." + Interferometric observations of the entire system would be required to answer this question., Interferometric observations of the entire system would be required to answer this question. + Another possibility is that a strong burst quickly depleted the molecular gas reservoir or that star formation tracers give a significantly overevaluated SFR., Another possibility is that a strong burst quickly depleted the molecular gas reservoir or that star formation tracers give a significantly overevaluated SFR. +" In all cases, if the burst SFH is decreasing, the standard SFR estimators which assume a constant SFR over 100 Myr will likely overestimate the actual SFR."," In all cases, if the burst SFH is decreasing, the standard SFR estimators which assume a constant SFR over 100 Myr will likely overestimate the actual SFR." +" As star-formation in collision debris tends to be more bursty compared to star-formation averaged over a galactic disk, this could artificially enhance the derived SFR in these regions."," As star--formation in collision debris tends to be more bursty compared to star–formation averaged over a galactic disk, this could artificially enhance the derived SFR in these regions." + When, When +remark that while. following their predictions. in our Monte Carlo simulations we assign a 0.13 probability [or a remnan to contain a BLL. the precise BL fraction is. in reality. subjec to a certain degree of uncertainty.,"remark that while, following their predictions, in our Monte Carlo simulations we assign a 0.13 probability for a remnant to contain a BH, the precise BH fraction is, in reality, subject to a certain degree of uncertainty." + Even taking rigorously the results of Leger ct al. (, Even taking rigorously the results of Heger et al. ( +2003). one needs to note tha their NS vs DILE fraction (cfr.,"2003), one needs to note that their NS vs BH fraction (cfr." + thei fig.5) was compute assuming a fraction of about iol Type Ib/e SNe. ane οἱ Type Η.," their fig.5) was computed assuming a fraction of about of Type Ib/c SNe, and of Type II." + Our sample. on the other hand. contains about of Type Ib/c and of Type LL SNe.," Our sample, on the other hand, contains about of Type Ib/c and of Type II SNe." + How the remnant fraction would change in this case is clillicul to predict., How the remnant fraction would change in this case is difficult to predict. + Leger ct al., Heger et al. + point out how normal Tvpe Ib/c SNe are not produced. by single stars until the metallicity. is well above solar., point out how normal Type Ib/c SNe are not produced by single stars until the metallicity is well above solar. + In this case. the remnants would be al NSs.," In this case, the remnants would be all NSs." + At lower metallicities. on the other hand. most. Tvpe Ibfe SNe are produced in binary systems where the binary companion helps in removing the hydrogen envelope of the collapsing star.," At lower metallicities, on the other hand, most Type Ib/c SNe are produced in binary systems where the binary companion helps in removing the hydrogen envelope of the collapsing star." + Given these uncertainties. while adopting for our simulations the ΕΟΝ fraction estimated by Leger et al.," Given these uncertainties, while adopting for our simulations the BH/NS fraction estimated by Heger et al." + for solar metallicity. we also ciscuss how results would vary for cillerent values of the DII and NS components.," for solar metallicity, we also discuss how results would vary for different values of the BH and NS components." + Pan object is à DIL. à low level of X-ray luminosity (< erg/s. Le. smaller than the lowest measurement/limit in our SN data set) is assigned to it.," If an object is a BH, a low level of X-ray luminosity $<10^{35}$ erg/s, i.e. smaller than the lowest measurement/limit in our SN data set) is assigned to it." + This is the most conservative assumption that we can make in order to derive constraints on the luminosity distribution of the NS component., This is the most conservative assumption that we can make in order to derive constraints on the luminosity distribution of the NS component. + Loan object is a NS. then its birth period and magnetic Ποια is drawn from the ACC clistribution as described. above. and it is evolved to its current age (equal to the age of the corresponding SN at the time of the observation) with 124.31).," If an object is a NS, then its birth period and magnetic field is drawn from the ACC distribution as described above, and it is evolved to its current age (equal to the age of the corresponding SN at the time of the observation) with \ref{eq:spin}) )." +" The corresponding X-ray luminosity is then drawn from a lIog-Gaussian clistribution with mean given by the PO2 relation. and dispersion σε,=VonlogLp OL."," The corresponding X-ray luminosity is then drawn from a log-Gaussian distribution with mean given by the P02 relation, and dispersion $\sigma_{L_x}=\sqrt{\sigma_a^2[\log\dot{E}_{\rm rot}]^2 ++ \sigma_b^2}$ ." + Figure 1 (top panel) shows the predicted. distribution of the most frequent of the pulsar Luminosity over all the Monte Carlo realizations of the entire sample. of ‘Table 1., Figure 1 (top panel) shows the predicted distribution of the most frequent of the pulsar luminosity over all the Monte Carlo realizations of the entire sample of Table 1. + Ehe shaded. region indicates the lo dispersion in the model., The shaded region indicates the $1\sigma$ dispersion in the model. + This has been determined by computing the most compact region containing of the random realizations of the sample., This has been determined by computing the most compact region containing of the random realizations of the sample. + Also shown is the distribution of the X-rav luminosity (both detections and upper limits) of the SNe (ele., Also shown is the distribution of the X-ray luminosity (both detections and upper limits) of the SNe (cfr. + Table 1)., Table 1). + Since the measured. N-rav. luminosity of each object is the sum of that of the SN itself and that of the putative pulsar embedded in it. for the purpose of this work X-rav detections are also treated as upper limits on the pulsar luminosities.," Since the measured X-ray luminosity of each object is the sum of that of the SN itself and that of the putative pulsar embedded in it, for the purpose of this work X-ray detections are also treated as upper limits on the pulsar luminosities." + This is indicated by the arrows in ligure 1., This is indicated by the arrows in Figure 1. + Our NX-rav analysis. in all those cases where a measurement was possible. never revealed column densities hish enough to allect the observed 2-10. keV [lux significantlv.," Our X-ray analysis, in all those cases where a measurement was possible, never revealed column densities high enough to affect the observed 2-10 keV flux significantly." + However. if a laree fraction of the X-ray luminosity (when not due to the pulsar) does not. come from the innermost region of the remnant. then the inferred Ny would. be uncerestimatecd with respect to the total column clensity to the pulsar.," However, if a large fraction of the X-ray luminosity (when not due to the pulsar) does not come from the innermost region of the remnant, then the inferred $N_{\rm H}$ would be underestimated with respect to the total column density to the pulsar." + “Phe total optical depth to the center of the SN as a function. of the SN age, The total optical depth to the center of the SN as a function of the SN age +Laney 2000): where Nj is the number of free parameters. and N the number of observed periods.,"Laney 2000): where $N_{\rm p}$ is the number of free parameters, and $N$ the number of observed periods." +" In our case. N,—2 (stellar mass and effective temperature)."," In our case, $N_{\rm p}= 2$ (stellar mass and effective temperature)." + The smaller the value of BIC. the better the quality of the fit.," The smaller the value of BIC, the better the quality of the fit." + We obtain BIC=0.85. which is substantially larger than the BIC value of the best fit model of BKOII (BIC= -0.41).," We obtain ${\rm BIC}= 0.85$, which is substantially larger than the BIC value of the best fit model of 11 ${\rm BIC}= -0.41$ )." + This means that our period fit is somewhat poorer than theirs., This means that our period fit is somewhat poorer than theirs. + Notwithstanding this. our asteroseismological model still provides a very satisfactory fit to the periods of KIC 8626021.," Notwithstanding this, our asteroseismological model still provides a very satisfactory fit to the periods of KIC 8626021." + The last column in Table 2 shows the rate of period change of the fitted pulsation modes., The last column in Table \ref{table2} shows the rate of period change of the fitted pulsation modes. + Our calculations predict all of the pulsation periods to with time (IT;> 0). in accordance with the decrease of the Brunt-Váàisállá frequency in the core of the model induced by cooling.," Our calculations predict all of the pulsation periods to with time $\dot{\Pi}_k>0$ ), in accordance with the decrease of the Brunt-Väiisällä frequency in the core of the model induced by cooling." + Note that at the effective temperature of KIC 8626021. cooling has the largest effect on Il. while gravitational contraction. which should result in a of periods with time. becomes negligible and no longer affects the pulsation periods.," Note that at the effective temperature of KIC 8626021, cooling has the largest effect on $\dot{\Pi}_k$, while gravitational contraction, which should result in a of periods with time, becomes negligible and no longer affects the pulsation periods." + Until now. no measurement of Π in a DBV has been assessed. although important efforts to measure the rate of period change in at least one star at the blue edge (EC 20058-5234: Dalessio et al.," Until now, no measurement of $\dot{\Pi}$ in a DBV has been assessed, although important efforts to measure the rate of period change in at least one star at the blue edge (EC $-$ 5234; Dalessio et al." + 2010) are being currently carried out. and a possible determination of the rate of period change for other DBV star (PG 1351-4489) has beer reported (Redaelli et al.," 2010) are being currently carried out, and a possible determination of the rate of period change for other DBV star (PG 1351+489) has been reported (Redaelli et al." + 2011)., 2011). + The main features of our best-fit model are summarized i Table 3.. where we also include the parameters of KIC 8626021 extracted from OEAI1I and the seismological model derivec by BKOIIT.," The main features of our best-fit model are summarized in Table \ref{table3}, where we also include the parameters of KIC 8626021 extracted from EA11 and the seismological model derived by 11." + In the Table. the quantity My corresponds to the total content of He of the envelope of the model.," In the Table, the quantity $M_{\rm He, total}$ corresponds to the total content of He of the envelope of the model." + li order to make the comparison easy. we include in the table the four parameters employed by BKÓII that define the chemical profiles at the core and envelope of their models.," In order to make the comparison easy, we include in the table the four parameters employed by 11 that define the chemical profiles at the core and envelope of their models." + Note that BKO1I do not specify the value of My of their best-fit model.," Note that 11 do not specify the value of $M_{\rm He, total}$ of their best-fit model." + The location of the best-fit model for KIC 8626021 both according to our study and that of BK@11 in the logZ4j—e plane is shown in Fig. |.., The location of the best-fit model for KIC 8626021 both according to our study and that of 11 in the $\log T_{\rm eff}-\log g$ plane is shown in Fig. \ref{hr}. + Both asteroseismic studies lead to the conclusion that KIC 8626021 should be closer to the blue edge of the DBV instability strip than spectroscopy suggests., Both asteroseismic studies lead to the conclusion that KIC 8626021 should be closer to the blue edge of the DBV instability strip than spectroscopy suggests. + The results of our asteroseismological analysis point to a higher stellar mass of KIC 8626021 than predicted by spectroscopy., The results of our asteroseismological analysis point to a higher stellar mass of KIC 8626021 than predicted by spectroscopy. + We arrive at such conclusion through both the period spacing and the individual periods exhibited by the star., We arrive at such conclusion through both the period spacing and the individual periods exhibited by the star. + Regarding the effective temperature. our work indicates a higher 7; than the spectroscopic measurement.," Regarding the effective temperature, our work indicates a higher $T_{\rm eff}$ than the spectroscopic measurement." + Our results also ditfer somewhat from those of the seismological analysis of BKOI1., Our results also differ somewhat from those of the seismological analysis of 11. + Specifically. we obtain αἱ asteroseismological model that is more massive and cooler thar that of BK@I1.," Specifically, we obtain an asteroseismological model that is more massive and cooler than that of 11." + The fact that in both independent analysis a good match to the observed periods is found can be understood on the basis of the asymptotic behavior of g-mode pulsations. that predicts that a lower effective temperature is compensated by a higher mass.," The fact that in both independent analysis a good match to the observed periods is found can be understood on the basis of the asymptotic behavior of $g$ -mode pulsations, that predicts that a lower effective temperature is compensated by a higher mass." + What is interesting and exciting is that. i spite of the substantial differences in the white dwarf modeling (in particular. the quite different composition. profiles. that lead to significant differences in the pulsation periods) both analysis agree that KIC 8626021 is a hot DBV.," What is interesting and exciting is that, in spite of the substantial differences in the white dwarf modeling (in particular, the quite different composition profiles, that lead to significant differences in the pulsation periods) both analysis agree that KIC 8626021 is a hot DBV." + This is in agreement with analyses based on the average period spacing and also with the fact that low period modes are present in KIC 862602]'s pulsation spectrum. as is also observed for the hot DBV EC20058.," This is in agreement with analyses based on the average period spacing and also with the fact that low period modes are present in KIC 8626021's pulsation spectrum, as is also observed for the hot DBV EC20058." + In this paper we have presented a detailed asteroseismic analysis of KIC 8626021. the first pulsating DB white dwarf star discovered by theMission.. on the basis of the full evolutionary DB white-dwarf models presented in Althaus et al. (," In this paper we have presented a detailed asteroseismic analysis of KIC 8626021, the first pulsating DB white dwarf star discovered by the, on the basis of the full evolutionary DB white-dwarf models presented in Althaus et al. (" +20093) which were computed for a wide range of stellar masses and He envelopes.,2009a) which were computed for a wide range of stellar masses and He envelopes. + These DB white dwarf models are characterized by consistent chemical profiles for both the core and the envelope., These DB white dwarf models are characterized by consistent chemical profiles for both the core and the envelope. + These chemical profiles are the result of the computation of the full and complete evolution. of the, These chemical profiles are the result of the computation of the full and complete evolution of the +Fig. 4..,Fig. \ref{fig_sed}. + We also calculated a density map using existing photometric redshift catalogs in COSMOS (??) in Fig. 1..," We also calculated a density map using existing photometric redshift catalogs in COSMOS \citep{ilbert_cosmos_2009,whitaker_newfirm_2011} in Fig. \ref{fig_density}." + The overdensities are completely absent in the public i—band selected catalog of ?.., The overdensities are completely absent in the public $i-$ band selected catalog of \citet{ilbert_cosmos_2009}. +" Only a weak impression of the overdensities is apparent in the K,—band selected catalog of ?..", Only a weak impression of the overdensities is apparent in the $K_s-$ band selected catalog of \citet{whitaker_newfirm_2011}. +" This substantiates the critical role that deep, near-IR imaging with medium-band filters willplay in understanding environment and galaxy evolution at redshifts z>1.5."," This substantiates the critical role that deep, near-IR imaging with medium-band filters willplay in understanding environment and galaxy evolution at redshifts $z>1.5$." +" We note the candidate cluster satisfies the Spitzer/IRAC color based selection criteria of ?,, used to discover a z=1.62 cluster (?).."," We note the candidate cluster satisfies the Spitzer/IRAC color based selection criteria of \citet{papovich_angular_2008}, used to discover a $z=1.62$ cluster \citep{papovich_spitzer-selected_2010}." +" However, unlike the IRAC selection, our catalogs provide accurate photometric redshifts, thus reducing spurious detections from foreground interlopers and enabling the secure identification of an overdensity at z~2.2."," However, unlike the IRAC selection, our catalogs provide accurate photometric redshifts, thus reducing spurious detections from foreground interlopers and enabling the secure identification of an overdensity at $z\sim2.2$." +" To quantify the,ig statistical significance of the overdensities, we first estimated the mean and intrinsic scatter in the nearest neighbor density map of Fig. 1.."," To quantify the statistical significance of the overdensities, we first estimated the mean and intrinsic scatter in the nearest neighbor density map of Fig. \ref{fig_density}." +" 'To avoid biasing these values by the strong overdensities themselves, we use the mean density (n;=2.6 aremin?) and its standard deviation (o,7=1.4 from adjacent redshift slices (z—1.92.1 and z?)—2.3 2.5)."," To avoid biasing these values by the strong overdensities themselves, we use the mean density $n_7=2.6$ $^{-2}$ ) and its standard deviation $\sigma_{n7}=1.4$ $^{-2}$ ) from adjacent redshift slices $z=1.9-2.1$ and $z=2.3-2.5$ )." + These statistics reflect the distribution of nearest neighbor densities evaluated only at the locations of all galaxies in a redshift slice., These statistics reflect the distribution of nearest neighbor densities evaluated only at the locations of all galaxies in a redshift slice. +" We find that the overdensities are =20, 50, and 10e deviations for A, B, and C, respectively."," We find that the overdensities are $\approx20$, $50$, and $10\sigma$ deviations for A, B, and C, respectively." + We also performed a bootstrap resampling of the rredshifts., We also performed a bootstrap resampling of the redshifts. +" At each instance, we shuffled all redshifts in our catalog and generated a 7th nearest-neighbor density map."," At each instance, we shuffled all redshifts in our catalog and generated a 7th nearest-neighbor density map." +" To robustly identify overdensities in the resampled maps, we tuned(DETECT_THRESH, SEEING_FWHM) to detect only overdensities A B in the real density map."," To robustly identify overdensities in the resampled maps, we tuned, ) to detect only overdensities A B in the real density map." + In only 3 of the 1000 resampled maps was overdensity detected., In only 3 of the 1000 resampled maps was overdensity detected. +" When tuned to find the less significant overdensity C, detects only 65 overdensities in the resampled maps."," When tuned to find the less significant overdensity C, detects only 65 overdensities in the resampled maps." + Note the number of valid analogs in the resampled maps would decrease further if we tried to match the tight spatial configuration of the real overdensities., Note the number of valid analogs in the resampled maps would decrease further if we tried to match the tight spatial configuration of the real overdensities. +" As a final check, we analyzed 121 mock density maps from simulated light cones produced by the Mock Galaxy Factory (Bernyk et al."," As a final check, we analyzed 121 mock density maps from simulated light cones produced by the Mock Galaxy Factory (Bernyk et al." +",in prep.).",",in prep.)." +" These are based upon the Millennium Simulation (?) and semi-analytical models of?.. After introducing fake redshift errors, we matched the number of observed galaxies in the Z—FOURGE COSMOS field by selecting an R-band absolute magnitude limit Mg<—21.6 (roughly 24.5 at z= 2.2) and found a consistent scatter 2.0+0.7 3) with our own estimate."," These are based upon the Millennium Simulation \citep{springel_simulations_2005} and semi-analytical models of\citet{croton_many_2006}.. After introducing fake redshift errors, we matched the number of observed galaxies in the $Z-$ FOURGE COSMOS field by selecting an $R$ -band absolute magnitude limit $M_R<-21.6$ (roughly $K_s\la24.5$ at $z=2.2$ ) and found a consistent scatter $\sigma_{n7}=2.0\pm0.7$ $^{-2}$ ) with our own estimate." +" The above arcminresults confirm that overdensities A B are robust, while overdensity C appears to be slightly less significant."," The above results confirm that overdensities A B are robust, while overdensity C appears to be slightly less significant." + Its close proximity to A B raises the intriguing possibility that it is associated with the AB system., Its close proximity to A B raises the intriguing possibility that it is associated with the AB system. + We therefore include overdensity C in the following., We therefore include overdensity C in the following. +" Of the 313 galaxies in the redshift slice 2.1€z«2.3 over the full ZCFOURGE COSMOS field, 29 galaxies are within 30"" of a z=2.2 overdensity."," Of the 313 galaxies in the redshift slice $2.1\le z\le2.3$ over the full $Z-$ FOURGE COSMOS field, 29 galaxies are within $30\arcsec$ of a $z=2.2$ overdensity." + We consider these candidate overdensity galaxies., We consider these candidate overdensity galaxies. + Fig., Fig. +5 shows observed color-magnitude diagrams for all galaxies having 2.1€z<2.3.,\ref{fig_cmd} shows observed color-magnitude diagrams for all galaxies having $2.1\le z\le2.3$. + The J;—Hj color probes continuum on both sides of the bbreak and avoids rest-frame Ha inK;., The $J_1-H_l$ color probes continuum on both sides of the break and avoids rest-frame $\alpha$ in. +. The histograms in Fig., The histograms in Fig. + 5 show that the non-overdensity or “field” distribution is dominated by blue galaxies (J1—H;« 1.6) while the overdensity galaxies have a higher fraction of red galaxies., \ref{fig_cmd} show that the non-overdensity or “field” distribution is dominated by blue galaxies $J_1-H_l<1.6$ ) while the overdensity galaxies have a higher fraction of red galaxies. +" We calculated the red galaxy fractions, freq= of each overdensity."," We calculated the red galaxy fractions, $f_{red}=N_{red}/N_{total}$ , of each overdensity." +" Here γεια is the number of galaxies Nred/Neotal,with J;—H;>1.6 at allmagnitudes within r«30” of an overdensity at 2.1 1$, we obtain from the $\sigma$ confidence limits: $1 \la \beta \la 4.5$ $\cal C$ 1) and $1 +\la \beta \la 4$ $\cal C$ 2)." +" If we fit a SFR of (1|2)"" from :=1 to IL. there is no lowerlint ou a since at least one of the well-fitting models has little or uo star formation prior to +=1."," If we fit a SFR of $(1+z)^{\alpha}$ from $z=1$ to 4, there is no lowerlimit on $\alpha$ since at least one of the well-fitting models has little or no star formation prior to $z=1$." + The upper limit from these natural sccuarios is aZ1 for both cosimologies.," The upper limit from these natural scenarios is $\alpha \la +1$ for both cosmologies." + The f;-figas paraiueterization is linited iu its scope for changes of SER with time., The $\tin$ $\tsf$ $\zform$ parameterization is limited in its scope for changes of SFR with time. + Therefore. to further testohistory. we look at the oa- Jr piruneterization.," Therefore, to further test, we look at the $\alpha$ $\beta$ $r$ parameterization." + Fieure 7 shows best-fit regions in 4 versus with k=1.1 for both cosimologics., Figure \ref{fig:alpha-versus-beta} shows best-fit regions in $\alpha$ versus $\beta$ with $r=1.1$ for both cosmologies. + Iu these scenarios. the galaxies start fully constituted with eas (there is no iufall) aud consistent evolution of the metallicity is implemented.," In these scenarios, the galaxies start fully constituted with gas (there is no infall) and consistent evolution of the metallicity is implemented." + Constaut metallicity scenarios were also tested but found not to be cousisteut within the 30 lianit on FOM D. Howe take à SER normalization of 1.1. meaning a total mass of stars formed between τ=5 and 2=0 equal to 1.1 times the mass of gas available. there is a degeneracyv across the plane of à. versus 2; (Figure 7)).," Constant metallicity scenarios were also tested but found not to be consistent within the $\sigma$ limit on FOM B. If we take a SFR normalization of 1.1, meaning a total mass of stars formed between $z=5$ and $z=0$ equal to 1.1 times the mass of gas available, there is a degeneracy across the plane of $\alpha$ versus $\beta$ (Figure \ref{fig:alpha-versus-beta}) )." + Scenarios with ο<0 cannot be ruled out for a72.5.However. this would imply a in the SFR arouud 2=1 which is in disaerecnieut with παν cosmic SER density studies based on photometry.," Scenarios with $\beta<0$ cannot be ruled out for $\alpha>2.5$.However, this would imply a in the SFR around $z=1$ which is in disagreement with many cosmic SFR density studies based on photometry." + These also represcut, These also represent +The free cherey then reads where —l/Tpg ds inverse teniperaturc«,The free energy then reads where $\beta =1/T_{BH}$ is inverse temperature. +"s The donünuaut contribution from the even horizon to Fis The contribution of the horizou to the eutropy S are where A=liv,D is: the horizouH area.", The dominant contribution from the even horizon to $F$ is The contribution of the horizon to the entropy $S$ are where $A=4\pi r_H^2$ is the horizon area. + So+ we reproduce the correct relationH of. S*X AAanorimalized- to the Bekenstcin-Wawking. expression.. je.B 5*=Spyή17).," So we reproduce the correct relation of $S\propto A$ .normalized to the Bekenstein-Hawking expression, i.e., $S=S_{BH}=A/(4l_p^2)$." +D Then.d from. the eq.(98)) we obtain the field umber /N as follows The mmuber NV is independent of the parameters of the black hole. aud same as eq.(75)).," Then, from the \ref{entropy}) ) we obtain the field number $N$ as follows The number $N$ is independent of the parameters of the black hole, and same as \ref{NN}) )." + Iu suuumuierv: A semi-classical reasoning leads to the nou-commuutativity of space and time coordinates near the horizon of static ron-extreme black hole. and reuders the classical horizon spreading to.," In summery: A semi-classical reasoning leads to the non-commutativity of space and time coordinates near the horizon of static non-extreme black hole, and renders the classical horizon spreading to." + Iun enus of the backeround metric of the black hole with the. a quantum feld theory in curved space without ultraviolet divergeney near the horizou is formulated.," In terms of the background metric of the black hole with the, a quantum field theory in curved space without ultraviolet divergency near the horizon is formulated." +" In tus foriiulisiu. the black hole thermodynamics is reproduced. correctly without both ambiguity aud acditional hypothesis in the deriviug the holes Tawking raciatious aud eutrop105, aid a new iteresting prediction on he umber of radiative ficld 1iodes is provided."," In this formulism, the black hole thermodynamics is reproduced correctly without both ambiguity and additional hypothesis in the deriving the hole's Hawking radiations and entropies, and a new interesting prediction on the number of radiative field modes $N$ is provided." + Sλος1Πςally. the 1nain results are follows: 1. Tawlking vacations rightly emerge as an effect of quantun tunneling through the quantiii horizon. and lence the ambiguities due to cole across the sinetlarity ou the classical horizon were eot rid of: 2. t IHTooft's brick wall thickness hyvothesis aud the boundary condition iuosed for the field considered iu his brick wall mode were got rid of also. aud related plivsies lias been interpreted: 3. The preseut theory is paraueter free.," Specifically, the main results are follows: 1, Hawking radiations rightly emerge as an effect of quantum tunneling through the quantum horizon, and hence the ambiguities due to going across the singularity on the classical horizon were got rid of; 2, 't Hooft's brick wall thickness hypothesis and the boundary condition imposed for the field considered in his brick wall model were got rid of also, and related physics has been interpreted; 3, The present theory is parameter free." + So. the theory has power to predict the multiplicity Αν of radiative field modes according to the requirement of normalization of Tawkine-Bekcustcin entropy.," So, the theory has power to predict the multiplicity $N$ of radiative field modes according to the requirement of normalization of Hawking-Bekenstein entropy." + It has been fotnd hat NVx162., It has been found that $N\simeq 162$. + Finally. two discussions are in order: 1) We conclude in this paper that the blac klrole eutropy aud the ILvkiug temperature have been produced successfully anc siniltauc01sly in the QETauodel in curved space with «quautuni horizon.," Finally, two discussions are in order: 1) We conclude in this paper that the black hole entropy and the Hawking temperature have been produced successfully and simultaneously in the QFT-model in curved space with quantum horizon." + Physicallv. this iuplies that this model uot only cau be used to rightly count the mücro-states of the black hole (coirespondius to derive its entropy). but also can be used to rightly caleulate the quanti funelliue amplitudes across the horizon for the particles creating by strong gravitational fields (correspouding to derive the Hawking," Physically, this implies that this model not only can be used to rightly count the micro-states of the black hole (corresponding to derive its entropy), but also can be used to rightly calculate the quantum tunnelling amplitudes across the horizon for the particles creating by strong gravitational fields (corresponding to derive the Hawking" + a.. R ∙ ∙∙ ⋜↧↕−∐∖↸⊳↑↴∖↴↴∖↴↕∶↴∙⊾∐↕∱∎⊔⊳⋜⋯∏⋅↖↽↑↕∐∖↕∐∐↸∖↥⋅↴∖↴⊓⋅⋯⊳⊓∐⋅↸∖⋜⋯≼↧↑↕⋯↴∖↴↑↕∐∖∣∣⊢ af x OL AU from their parcut star raises fuudunental aboutD their ∙and uueration process∙↻↥⋅↸∖↴∖↴↸∖∐↑↕⋅↖↽≼∐∖↑↸∖↸⊳↑↸∖≼↧⊓⋅⋜⋯↴∖↴↕↑↴∖↴∙∐⋜⋯∐∖↕⋅↖⇁∐↕≻⊇∩≝⊔⋅↱⊐≺∖↴⋝∙↖↖↽↕↑∐↙∣∶ O.O1GAU about the infiuence formationof the parent star through with radiation or tidal effects., The increasing number of discovered giant planets orbiting at $\simle$ 0.1 AU from their parent star raises fundamental questions about their formation and migration process and about the influence of the parent star through irradiation or tidal effects. + The recent discovery of an extended atmosphere for the transiting exoplauet ID209155b (VidabMadjar et al., The recent discovery of an extended atmosphere for the transiting exoplanet HD209458b (Vidal-Madjar et al. + 2003) hielliehts the ocenrence of atniospherie evaporation for these closc-in plaucts., 2003) highlights the occurence of atmospheric evaporation for these close-in planets. +" Whether such evaporation due to heating |roni the iucideutincident stellar‘ 8flux leads tto majora]. masst 1loss -e duringthe peplanet1 lifetilitetinie. ‘and1 h1 whether»this ]process ‘affects& siguificantly""i the structure of the ]planet‘ 7aud thus its i ? relatiouship1‘ndu] is. ‘an open] question.i which hisis of primeoi nuportauce]‘ for our uuderstaudiug‘o of psplanetary ⋠⋅⋅system ↕∪↥⋅⊔⋜↧⊓∪∐"," Whether such evaporation due to heating from the incident stellar flux leads to major mass loss during the planet lifetime, and whether this process affects significantly the structure of the planet and thus its $m$ $R$ relationship is an open question, which is of prime importance for our understanding of planetary system formation." +∙⋀∖↸∖↖↖↽↸∖↖⇁⋜↧↕∏⋜↧⊓∪∐↴∖↴∪↕⋜↧↑⋯∪↴∖↴↻∐↸∖↥⋅↕↸⊳↑∐↸∖∐⊔⋜↧ evaporationvaporation rafrates byy LaunuerLe eret alal. (, New evaluations of atmospheric thermal evaporation rates by Lammer et al. ( +(2003.3. Loa.LO3). baseba onu exospleric heating ‘by stellarov NUV radiation.⋅ vick sienificautly larecrEO rates‘ than‘ the ]previous estimatesUU assundue eteJeans escape at the effective⋅ temperature o the planet.,"2003, L03), based on exospheric heating by stellar XUV radiation, yield significantly larger rates than the previous estimates assuming Jeans escape at the effective temperature of the planet." + The first attempt of LOS to model such a complex process vields au escape rate in good aereciuen the. observational deteriuiuatious. of⋅⋅ Vidal-Madjar .description et ↙al.1 (, The first attempt of L03 to model such a complex process yields an escape rate in good agreement with the observational determinations of Vidal-Madjar et al. ( +"2003) ""Pfor IID209209]55b.:5] ]providingidi ocicouragingfee: support for. further} exploration.","2003) for HD209458b, providing encouraging support for further exploration." + Moreover. since stellar NUV fluxes vary sieuificauthyg with time aud can he mas MINCE o: vouns ∪↕⋅≺∐∖↥⋅∪⊔⋪↧∩⊾∐↕∏≺∐∖↴∖↴↕⋪∐⋅∩⊾↸∖↕⋅⋪↧↑↖⇁↸∖↥⋅↖↽↖↽∪∏∐∩⋪↧∩⊾↸∖↴∖↴∙↑↕↓↸∖↴∖↴↸∖as evaporation rates are muuch larger at the planet carly evolutionary stages.," Moreover, since stellar XUV fluxes vary significantly with time and can be order of magnitudes larger at very young ages, these evaporation rates are much larger at the planet early evolutionary stages." + LO3 thus suggestOO that mass loss could be au important event iu the life of close-in exoplauets. coutrarily to what was previously thought.," L03 thus suggest that mass loss could be an important event in the life of close-in exoplanets, contrarily to what was previously thought." + It is the purpose of this letter to explore this issue bv taking Πο account cousistently the thermal escape rates of L023 along the evolution of strongly irradiated planets (Daraffe ct al., It is the purpose of this letter to explore this issue by taking into account consistently the thermal escape rates of L03 along the evolution of strongly irradiated planets (Baraffe et al. + 2003. hereafter DOJ).," 2003, hereafter B03)." + Since an important issue of this analysis is to determine whether evaporation ↽∕∏∐∖∐⊔⊳↥⋅↸∖⋜↕↴∖↴∐↕∶↴∙⊾↕∐∐⊔↴⋝↸∖↥⋅∪↕≺∐↴∖↴↸⊳∪↖⇁↸∖↥⋅↸∖≺↧∶↴∙⊾↕⋜⋯↑↻↕⋜∐∐∖↑↴∖↴∪↥⋅↴⋝↕⊓∐∶↴⋁ velationship of exoplancts. we focns on the case of ∙ questions ct al.," Since an important issue of this analysis is to determine whether evaporation affects significantly the inner structure and thus the $m$ $R$ relationship of exoplanets, we focus on the case of presently detected transits, namely HD209458b, with $a=0.046$ AU (Charbonneau et al." +" 2000) and OGLE-TR-56b. and ο —0,023AU(Ionacki et al."," 2000) and OGLE-TR-56b, with $a=0.023$ AU (Konacki et al." + 2003)., 2003). + The evolutionary calculations are based on the consisten coupling∙↜ between. the imnradiated⋅∙∙⋅ atmospheric↴∙⋅ aud interior⋅∙⋅∙ structures as described: in: DOS.. aud iu: Barman et al. (," The evolutionary calculations are based on the consistent coupling between the irradiated atmospheric and interior structures as described in B03, and in Barman et al. (" +2001)⊀↽ for¢ the atinosphere model calculations.,2001) for the atmosphere model calculations. +: Such: a consisteu: treatment of the irradiated: atimospheric: structure and the internal.: partially: radiative∙∙ structure successfully ↥⋅↸∖↻↥⋅∪≼⊔∐⊳↸∖↴∖↴↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖⇁↸∖≺↧↴≻⋜∐⋅⋜↕⋯↸∖↑↸∖↥⋅↴∖↴∪↕↑∐↸∖⊓⋅⋜⋯↴∖↴↕↑↻↕⋜∐∐∖ : : ≼↽≻," Such a consistent treatment of the irradiated atmospheric structure and the internal, partially radiative structure successfully reproduces the observed parameters of the transit planet OGLE-TR-56b (Chabrier et al." +⊂∶↕⇀⊏∶↙, 2004). +∏⊰≓∏⋯⋝≼⊂⊲∐⋮∏⋝∏⋠∖↕⋠∖↾⋮↕↕∙⋮⋂⋂↓⋟∙ Details: of: the inodel used to derive: thermal rates⋅ can be found in⋅ LOS., Details of the model used to derive thermal evaporation rates can be found in L03. +∙ The↴ basic⋅⋅ idea .. yelies⋅ on the factui that the euergv deposition bv stellar NUV cads to exospheric temperatures higher than the blow-off temperature for IT. Therefore. the classical Jeaus of thermal escape iuust be replaced bw a with lydrodvuamic modoeliug of the expansion aud mass loss.," The basic idea relies on the fact that the energy deposition by stellar XUV leads to exospheric temperatures higher than the blow-off temperature for H. Therefore, the classical Jeans' description of thermal escape must be replaced by a hydrodynamic modeling of the expansion and mass loss." + The: energv-linüted⋅⋅ atinosphlierie: mass loss rate AL can be written: where J} is the ratio between the expausiou radius fy. where the bulk of the NUV. radiation is absorbed. aud the planetary radius Rp aud p=(Qun)/(UIzej) is the lean plauct deusity.," The energy-limited atmospheric mass loss rate $\dot M$ can be written: where $\beta$ is the ratio between the expansion radius $R_1$, where the bulk of the XUV radiation is absorbed, and the planetary radius $R_{\rm P}$ and $\rho = (3 m)/( 4 \pi R_{\rm P} ^3)$ is the mean planet density." + LOS estiuate 3 by applying the hydrodynamic of modelWatson et al. (, L03 estimate $\beta$ by applying the hydrodynamic model of Watson et al. ( +1981).,1981). + The term F. is the stellar fux. averaged over tho whole planct surface. faldug iuto accouut both the coutribution in the 1-1000 waveleugth iuterval aud the Lymau-a fux. so that the otal coutribution Fy for an orbital separation « (in AU)," The term $F_\star$ is the stellar flux, averaged over the whole planet surface, taking into account both the contribution in the 1-1000 wavelength interval and the $\alpha$ flux, so that the total contribution $F_\star$ for an orbital separation $a$ (in AU)" +this means that ΑΣ} is given by Fig.,this means that $\Delta^{2s}_{\perp}(k)$ is given by Fig. + d for trausverse wavenumbers.," \ref{fig_lDk} + for transverse wavenumbers." + ⊀≚↴∖↴↸⊳∪∐∏≻⋜∐⋅↸∖≼↧↖↖↽↕↑∐⊟∶↴∙⊾∙↕∙∙↖↖↽," As compared with Fig. \ref{fig_lDk}," +"↸∖↸⊳⋜⋯↸⊳↕∐∖↸⊳↨↘↽ that the οσο.πο|power. Po. ⋅is ΓΡ...amplified by⋅⋅ a factor (14 |πουoO⇁⋅≻ ⋅ ⋅∩−∙↖↖⇁∐↸∖↥⋅↸∖⋜↧↴∖↴↴∖↴↑⋜⋯≼↧⋜⋯↧∐↕∶↴∙⊾↕∐∖↥⋅∪↥⋅≼∐∖↥⋅↑↸∖↥⋅⋯↴∖↴⋜∐⋅↸∖⋜⋯∏≻∐∏↸∖≼↧ ⋅⋅ bv factors+ (1t|-fF)"". see Eq.(96))."," we can check that the linear-regime power, $P^{s(1)}_{\parallel}$, is amplified by a factor $(1+f)^2$ , whereas standard higher order terms are amplified by factors $(1+f)^{2n}$, see \ref{sPstd}) )." + Even though the sale factors apply to the higher order terms of the “renormalized” perturbative expausion. see Eq.(98)). their peak height is not ercater than in Fie.," Even though the same factors apply to the higher order terms of the “renormalized” perturbative expansion, see \ref{sPsigvn}) ), their peak height is not greater than in Fig." + | for n2 because of the stronger Caussian camping prefactor «iL|fre in Eq.(97))., \ref{fig_lDk} for $n\geq 2$ because of the stronger Gaussian damping prefactor $e^{-k^2(1+f)^2\sigma_v^2}$ in \ref{sPsigv}) ). + For large » this even ends to a sinaller amplitude as compared with the associated real-xpace contribution., For large $n$ this even leads to a smaller amplitude as compared with the associated real-space contribution. +" This makes the full noulinear Zeldovich aud “sticky model"" power spectra ereater than their real-space counterparts on large scales. in the quasi-linear regine. ut snaller in the highly nonlinear regie."," This makes the full nonlinear Zeldovich and “sticky model” power spectra greater than their real-space counterparts on large scales, in the quasi-linear regime, but smaller in the highly nonlinear regime." + In particular. it is clear from Eq.(91)) that the ligh-A damping of he Zeldovich power spectrum becomes sharper because of the factor (1|f)Zu iuB the exponential+ term (even hough this only leads to a power-law decay as noticed im Sect. 3.1)).," In particular, it is clear from \ref{Psk-Iq-parallel}) ) that the $k$ damping of the Zeldovich power spectrum becomes sharper because of the factor $(1+f)^2$ in the exponential term (even though this only leads to a power-law decay as noticed in Sect. \ref{Logarithmic-power}) )." +" As well as for the real-space power Προςπι, he “renormalized” perturbative expansion (97)) Is more convenieut to distinguish the relative contributions of lugher order terms. as they are all positive aud do not slow the cancellations associated with the standard expansion (96))."," As well as for the real-space power spectrum, the “renormalized” perturbative expansion \ref{sPsigv}) ) is more convenient to distinguish the relative contributions of higher order terms, as they are all positive and do not show the cancellations associated with the standard expansion \ref{sPstd}) )." +" Since within the “sticky model” we have after shell crossing As;= 0. just as we had Ary=0 in real space, we again obtain a hk tail at hieh A for the nouperturbative term Prth). whence aasUn~Kk. as would be the case for oanar structures in redshift space."," Since within the “sticky model” we have after shell crossing $\Delta s_1=0$ , just as we had $\Delta x_1=0$ in real space, we again obtain a $k^{-2}$ tail at high $k$ for the nonperturbative term $\Pscpar(k)$, whence $\Delta^{2s}_{\parallel \rm sticky}(k) \sim k$, as would be the case for planar structures in redshift space." +" However. because the donünaut effect of redshift distortions on small scales is to decrease the power. through damping factors of the form eΕλ 775, the nonperturbative redshift-space contribution DU,(hy) is less than its reabspace counterpart."," However, because the dominant effect of redshift distortions on small scales is to decrease the power, through damping factors of the form $e^{-k^2(1+f)^2\sigma_v^2}$ , the nonperturbative redshift-space contribution $\Pscpar(k)$ is less than its real-space counterpart." + Coupled with the fasterdecay of P.(Gk). this leads to a temporary decrease of AxATsticky(hy at ko. dto Hh tat z;=.2. before. the asviuptotic tail X& becomes domiuaut.," Coupled with the faster decay of $\PZelpar(k)$, this leads to a temporary decrease of $\Delta^{2s}_{\parallel \rm sticky}(k)$ at $k\sim 1$ to $4 h$ $^{-1}$ at $z=2$, before the asymptotic tail $\propto k$ becomes dominant." +" The ""stickv model” is not inteuded here to describe the redshift-space power spectrum better han the Zeldovichapproximation.", The “sticky model” is not intended here to describe the redshift-space power spectrum better than the Zeldovichapproximation. +" hideed. on small scales setting Ac,=0Is 1ο realistic. since one should rather deseribe αι{]- and take iuto account the finite velocity"," Indeed, on small scales setting $\Delta v_1=0$is not realistic, since one should rather describe multi-streaming and take into account the finite velocity" +third. phase covered the CDES in a 16 field grid orientated at 45° to this. ie.,"third phase covered the CDFS in a 16 field grid orientated at $45{\degr}$ to this, ie." + with position angle —67.35., with position angle $-67.35{\degr}$. + The number of pixels was too great for the whole observed area to be mosaiced into à single image., The number of pixels was too great for the whole observed area to be mosaiced into a single image. + Instead. the four phases of observations were combined. into 15 frames. corresponding to the 15 field areas of the first. phase of observation.," Instead, the four phases of observations were combined into 15 frames, corresponding to the 15 field areas of the first phase of observation." + Because of the two cillerent orientations of the data. for each of these 15 frames there were typically S observed images which covered all or part of the field area.," Because of the two different orientations of the data, for each of these 15 frames there were typically 8 observed images which covered all or part of the field area." + ‘These data were combined by much the same methods as the ISAAC data above. but with an additional step of rebinning: (i) For each of the 15 frames. wesmap was used to fit transforms between the pixel grid of the phase one observation ancl that of all subsequent observations (tvpically 7) whieh cover at least part of the same area of sky.," These data were combined by much the same methods as the ISAAC data above, but with an additional step of rebinning: (i) For each of the 15 frames, `wcsmap' was used to fit transforms between the pixel grid of the phase one observation and that of all subsequent observations (typically 7) which cover at least part of the same area of sky." + ‘ecotran could then be usec to rebin these observations into the same pixel grid. as the phase one observation (which was not rebinned)., `geotran' could then be used to rebin these observations into the same pixel grid as the phase one observation (which was not rebinned). + This rebinning would allow observations taken at different position angles to be simply. aclded together. (, This rebinning would allow observations taken at different position angles to be simply added together. ( +ii) The exposure maps supplied: with cach observed image were similarly rebinned into the phase 1. pixel eric. (,ii) The exposure maps supplied with each observed image were similarly rebinned into the phase 1 pixel grid. ( +ii) For each of the 15 frames. the data images to be combined (rebinned. except for phase 1) were multiplied by their respective exposure maps and then added: together using ‘combine’.,"iii) For each of the 15 frames, the data images to be combined (rebinned, except for phase 1) were multiplied by their respective exposure maps and then added together using `combine'." + The exposure maps were similarly combined., The exposure maps were similarly combined. + Then the combined. exposure map image was divided by the combined exposure map. to produce a ‘final’ co-added image where the contribution at each pixel rom each of the input images is proportional to its weighting (from its exposure map). and the sum of the weighting actors is normalized to unity. (," Then the combined $\times$ exposure map image was divided by the combined exposure map, to produce a `final' co-added image where the contribution at each pixel from each of the input images is proportional to its weighting (from its exposure map), and the sum of the weighting factors is normalized to unity. (" +"iv) A weighting map for cach of the 15 ""final [rames was produced by multiplving the combined weighting map ον a map of the number of input images contributing at cach pixel (again. as for the ISAAC data)","iv) A weighting map for each of the 15 `final' frames was produced by multiplying the combined weighting map by a map of the number of input images contributing at each pixel (again, as for the ISAAC data)." +" Sources were detected on the ISAAC ancl ACS images using SExtractor(Bertin and Arnauts 1996). as in Paper lL. We make use of both ""total magnitudes. derived by ""SlExtractor ον fitting elliptical apertures to each detection. and aperture magnitudes. measured by “SLxtractor’ in circular apertures of fixed 2.0 aresec diameter."," Sources were detected on the ISAAC and ACS images using `SExtractor'(Bertin and Arnauts 1996), as in Paper I. We make use of both `total' magnitudes, derived by `SExtractor' by fitting elliptical apertures to each detection, and aperture magnitudes, measured by `SExtractor' in circular apertures of fixed 2.0 arcsec diameter." + The former will be used or limiting the sample anc the latter for measuring colours., The former will be used for limiting the sample and the latter for measuring colours. + Alagnitucles are given in the Vega svstem and can »* converted. to the AB system as (Avy.1...στο)=GNiEAderτων|OLSEL.1.373.0.904.0.403) ," Magnitudes are given in the Vega system and can be converted to the AB system as $(K_s,H,J,I_{775})_{AB}= (K_s,H,J,I_{775})_{Vega}+(1.841, 1.373, +0.904, 0.403)$ ." +"Source detection. was performed on the ISAAC A, mosaic (together with its weighting map). with the chosen criterion. that a source. must exceed Lm, above the background. or 22.75 AN, mag aresee7. in at least 6 contiguous pixels."," Source detection was performed on the ISAAC $K_s$ mosaic (together with its weighting map), with the chosen criterion that a source must exceed $1.4\sigma_{sky}$ above the background, or 22.75 $K_s$ mag $\rm arcsec^{-2}$, in at least 6 contiguous pixels." + In addition. a detection filter (3.0 pixel J'WIIM. Gaussian) was emploved.," In addition, a detection filter (3.0 pixel FWHM Gaussian) was employed." +. Detections on the low signal-to-noise edges of the mosaic were excluded. leaving a data area of 50.4 aremin?.," Detections on the low signal-to-noise edges of the mosaic were excluded, leaving a data area of 50.4 $\rm arcmin^2$." + The catalog of AS detections forms thesource list for our ERO sample., The catalog of $K_s$ detections forms thesource list for our ERO sample. +" Photometry of these sources in Z7 and oJ was obtained simplv bv positionally registering (to the nearest. pixel) the // and J mosaics to the A, mosaic and then running SExtractor in ‘double-image mode! to detect sources in A. as before. and then measure their Huxes on the ff and. J images."," Photometry of these sources in $H$ and $J$ was obtained simply by positionally registering (to the nearest pixel) the $H$ and $J$ mosaics to the $K_s$ mosaic and then running SExtractor in `double-image mode' to detect sources in $K_s$, as before, and then measure their fluxes on the $H$ and $J$ images." +" Sources were detected separately on the ACS £77;- band image with the criterion that they exceed 1.750, in at least 8 pixels. and a 2.5 pixel ENIM Gaussian detection filter."," Sources were detected separately on the ACS $I_{775}$ -band image with the criterion that they exceed $1.75\sigma_{sky}$ in at least 8 pixels, and a 2.5 pixel FWHM Gaussian detection filter." + As some detections. especially at brighter magnitudes. will be Galactic stars. we performed star-galaxy separation on the source list. using a plot of peak/total A. llux against magnitude.," As some detections, especially at brighter magnitudes, will be Galactic stars, we performed star-galaxy separation on the source list, using a plot of peak/total $K_s$ flux against magnitude." + This was cllective to a limit {νο=19.0. to which 30 objects were classecl as stars. and. all fainter detections were assumed to be galaxies.," This was effective to a limit $K_s=19.0$, to which 30 objects were classed as stars, and all fainter detections were assumed to be galaxies." + We estimate the resolution of the ISAAC data as the mean Gaussian EWILIM. of the non-saturateck stars. OAG aresec.," We estimate the resolution of the ISAAC data as the mean Gaussian FWHM of the non-saturated stars, 0.46 arcsec." + At this depth. the slope of the Galactic star counts is only tx~OL (e.g. Roche et al.," At this depth, the slope of the Galactic star counts is only ${dN\over dm}\simeq 0.1$, (e.g. Roche et al." + 1999) which by extrapolation would indicate the star-contamination at LO«A22 to be ~63 stars. or 4.6 per cent of the galaxy sample.," 1999) which by extrapolation would indicate the star-contamination at $1922$." +" Comparison with the two even deeper surveys suggests we are near-complete to A,c21.5 with some (20 per cent) incompleteness at 22."," Comparison with the two even deeper surveys suggests we are near-complete to $K_s\simeq 21.5$ with some $\sim +20$ per cent) incompleteness at $21.55.3 (c.g. Mannucci et al.," In Paper I they were selected on the basis of a colour $R-K>5.0$ , while some authors have used slightly stricter criteria of $I-K>4.0$ or $R-K>5.3$ (e.g. Mannucci et al." + 2002)., 2002). +" Phroughout this paper we select EROs asdv. 3.92. which corresponds to our evolving 15/80 model at 2>0.99 and is approximately equivalent (on he basis of a passive ERO model) to the BoA>5.0 of ""aper Landto 4...AS3.75 for the slightlylonger Z-band (ος."," Throughout this paper we select EROs as $I_{775}-K_s>3.92$ , which corresponds to our evolving E/S0 model at $z>0.99$ and is approximately equivalent (on the basis of a passive ERO model) to the $R-K>5.0$ of Paper I and to $I-K_s>3.75$ for the slightlylonger $I$ -band (eg." + as on the VETE FOLDSI instrument), as on the VLT FORS1 instrument). +and the p-moce spectrum (for further details see GD97).,and the -mode spectrum (for further details see GD97). + The assumption made reearcdine (he nonstandaid models is that due to the accretion of metal-rich matter. the Sun's interior. (defined here as B.« Ha). is composed of material al à lower heavy-element abundance than the Sun's surface.," The assumption made regarding the nonstandard models is that due to the accretion of metal-rich matter, the Sun's interior, (defined here as R$<$ $_{\mathrm {env}}$ ), is composed of material at a lower heavy-element abundance than the Sun's surface." + In order to produce such nonstandard solar models with low-Z interiors. the run of Z in the initial ZAMS model was mocified.," In order to produce such nonstandard solar models with low-Z interiors, the run of Z in the initial ZAMS model was modified." + The interior metal abundance was initiallv set to the homogeneous value of Zi out to (AL/AL. )=0.9. indicating a metal-poor interior.," The interior metal abundance was initially set to the homogeneous value of $_{\mathrm {int}}$ out to $_\odot$ )=0.9, indicating a metal-poor interior." + The more metal-rich exterior of the Sun. (M/M. 0.975. was setup with a metal abundance of Zia.," The more metal-rich exterior of the Sun, $_\odot$ $\ge$ 0.975, was setup with a metal abundance of $_{\mathrm {init}}$." + Zint aud Zin represent ZAMS mass fractions of all heavy. elements [or (he interior and exterior. respectively.," $_{\mathrm {int}}$ and $_{\mathrm {init}}$ represent ZAMS mass fractions of all heavy elements for the interior and exterior, respectively." + In the intermediate region. O.O<(AL/AL. )<0.975. Z linearly increases [rom Zi 0o Zinit-," In the intermediate region, $\le$ $_\odot$ ${\le}$ 0.975, Z linearly increases from $_{\mathrm {int}}$ to $_{\mathrm {init}}$." + In deciding what value Zig might be for the nonstandard solar models. it is relevant to note (hat the Sun is observed to be more metal rich than the surrounding ISM. with Zi possibly as low as of Z. (Mathis 1996).," In deciding what value $_{\mathrm {int}}$ might be for the nonstandard solar models, it is relevant to note that the Sun is observed to be more metal rich than the surrounding ISM, with $_{\mathrm {ISM}}$ possibly as low as of $_\odot$ (Mathis 1996)." + Believing the Sun formed from material typical ol the ISM. the metal-enhanced exterior could have resulted [rom the bombardiment of material in the form of comets. asteroids. planetesimals and proto-planets.," Believing the Sun formed from material typical of the ISM, the metal-enhanced exterior could have resulted from the bombardment of metal-rich material in the form of comets, asteroids, planetesimals and proto-planets." + With a long diffusion timescale. most of this material should still exist in (he upper lavers of the Sun. leaving (he interiormetal-poor. much likethe surrounding ISM.," With a long diffusion timescale, most of this material should still exist in the upper layers of the Sun, leaving the interiormetal-poor, much likethe surrounding ISM." + With this in mind. we chose a value of Zi —0.65Z..," With this in mind, we chose a value of $_{\mathrm {int}}$ $_\odot$ ." + Other values of 0.004... 0.50Z.. and 0.80Z. were also examined.," Other values of $_\odot$, $_\odot$, and $_\odot$ were also examined." + A choice ofμι = 0.80Z; corresponds to an accretion enhancement of about in iron. or about in meteoric material.," A choice of$_{\mathrm {int}}$ = $_{\mathrm {init}}$ corresponds to an accretion enhancement of about $_\oplus$ in iron, or about $_\oplus$ in meteoric material." + Similarly. Zi0.65Z4. Zin =O.50Zini. and Zim —0.30Zi4 Corresponds to about . and . respectively. in iron accretion. or about . and . respectively. in meteoric material accretion.," Similarly, $_{\mathrm {int}}$ $_{\mathrm {init}}$, $_{\mathrm {int}}$ $_{\mathrm {init}}$, and $_{\mathrm {int}}$ $_{\mathrm {init}}$ corresponds to about $_\oplus$, $_\oplus$ and $_\oplus$, respectively, in iron accretion, or about $_\oplus$, $_\oplus$ and $_\oplus$, respectively, in meteoric material accretion." + Four standard solar models were created. differing only by the value of Zi. the initial or ZAMS mass fraction value of all heavy elements in the solar exterior.," Four standard solar models were created, differing only by the value of $_{\mathrm {init}}$, the initial or ZAMS mass fraction value of all heavy elements in the solar exterior." + Without the assumption of a more metal-poor interior. Zi is assumed equivalent to Zin.," Without the assumption of a more metal-poor interior, $_{\mathrm {int}}$ is assumed equivalent to $_{\mathrm {init}}$." + Values of Zi were taken as 0.0170. 0.0188. 0.0200. and 0.0220.," Values of $_{\mathrm {init}}$ were taken as 0.0170, 0.0188, 0.0200, and 0.0220." + These standard solar models comprise models 4117-20 in Tables 1-3., These standard solar models comprise models 17-20 in Tables 1-3. + Zing was also varied in the nonstandarcl solar models. (hus along with the varving Zi. a grid was created. comprising models 411-16 in Tables 1-3.," $_{\mathrm {init}}$ was also varied in the nonstandard solar models, thus along with the varying $_{\mathrm {int}}$, a grid was created, comprising models 1-16 in Tables 1-3." + Physical characteristics of both the standard (2117-20) and nonstandard (2211-16) solar models are listed in Table 1., Physical characteristics of both the standard 17-20) and nonstandard 1-16) solar models are listed in Table 1. + Table 1 includes. from left to right: Model. the model number: Type. the twpe of model. where NS5M staads for a nonstandard solar model and SSAI stands for a standardsolar model: Ni. the initial or ZAMS mass fraction value of hvdrogen: Zi. the initial or ZAMS mass [raction value of all heavy elements in the solar exterior: Zi Ziui- the initial or ZAMS mass fraction value of all heavy. elements in the solar interior relative lo Zi: Newer the surface massfraction value of hydrogen at the evolved age: ζω. the surface mass fraction of all heavy elements at the evolved age: Ma. the fraction of the total," Table 1 includes, from left to right: Model, the model number; Type, the type of model, where NSSM stands for a nonstandard solar model and SSM stands for a standardsolar model; $_{\mathrm {init}}$, the initial or ZAMS mass fraction value of hydrogen; $_{\mathrm {init}}$, the initial or ZAMS mass fraction value of all heavy elements in the solar exterior; $_{\mathrm {int}}$ $_{\mathrm {init}}$ , the initial or ZAMS mass fraction value of all heavy elements in the solar interior relative to $_{\mathrm {init}}$ ; $_{\mathrm {surf}}$ , the surface massfraction value of hydrogen at the evolved age; $_{\mathrm {surf}}$ , the surface mass fraction of all heavy elements at the evolved age; $_{\mathrm {env}}$ , the fraction of the total" +"electromagnetic stress-euergv tensor Tu from the Faraday tensor FC’, ικαπιο €À1)). we first find where we have used &,,1,.600=24d,","electromagnetic stress-energy tensor $T^{ab}_{\rm em}$ from the Faraday tensor $F^{ab}$ , Inserting \ref{faraday1}) ), we first find where we have used $\epsilon_{abc}\epsilon^{abd} = 2 \gamma_c^{~d}$." +" With e"" . the first term in (7-5)) becomes Combining the last two equatious then vieclds the electromagnetic stress-cucrey tensor in 3|1 form This stress-enerev tensor can now be iuserted iuto (2- 10)) to (2-13)) to obtain the electromagnetic source ternis."," With $\epsilon^{abc} \epsilon_a^{~de} = \gamma^{bd} \gamma^{ce} - +\gamma^{be} \gamma^{cd}$ , the first term in \ref{Tem}) ) becomes Combining the last two equations then yields the electromagnetic stress-energy tensor in $3+1$ form This stress-energy tensor can now be inserted into \ref{rho}) ) to \ref{trS}) ) to obtain the electromagnetic source terms." +" For the mass-cucrey deusitv p, we find which is the euerey deusity of the electromagnetic fields.", For the mass-energy density $\rho_{\rm em}$ we find which is the energy density of the electromagnetic fields. + Tlle energyex flux $77ορ reducesred to the PovutiuePovutiug vectort The stress tensor .. is Its trace (2-13)). finally is equal to the miass-euergv deusity Pou The above results are not surprising: expressed in terius of the electromagnetic field compoucuts as measured by a normal observer. p. ie. an observer who is at rest with respect to the slices X. the 3|1 source terms have tle sale fori as in flat space (compare exercise 5.1 in \lisner. Thorne Wheeler 1973).," The energy flux $S_i^{\rm em}$ reduces to the Poynting vector The stress tensor $S_{ij}^{\rm em}$ is Its trace \ref{trS}) ), finally, is equal to the mass-energy density $\rho_{\rm em}$ The above results are not surprising: expressed in terms of the electromagnetic field components as measured by a normal observer, $n^a$, i.e. an observer who is at rest with respect to the slices $\Sigma$, the $3+1$ source terms have the same form as in flat space (compare exercise 5.1 in Misner, Thorne Wheeler 1973)." + Iu this section we compare our notation aud findings with those of Sloan Suuur (1985. SS). Tawley Evaus (1988. EDD: aud 1989. TIE) aud (1989. Z).," In this section we compare our notation and findings with those of Sloan Smarr (1985, SS), Hawley Evans (1988, EH; and 1989, HE) and Zhang (1989, Z)." + SS define the three-velocity coy Zhaugbv writing the velocity 4cee as aud (see equations (SS-2.1))., SS define the three-velocity $v^i_{\rm SS}$ by writing the four-velocity $u^a$ as and (see equations (SS-2.1)). + Here WV is the Loreutz factor between « and 0 as in (1-3))., Here $W$ is the Lorentz factor between $u^a$ and $n^a$ as in \ref{W}) ). +" The normalization «d,=l leads to which shows that cS is the velocity of the fuid with respect to a normal observer.", The normalization $u^a u_a = -1$ leads to which shows that $v^i_{\rm SS}$ is the velocity of the fluid with respect to a observer. + Zhang (1989) adopts the same formmlation as SS. but denotes VV with 5 (see equation (Z-2.11)).," Zhang (1989) adopts the same formulation as SS, but denotes $W$ with $\gamma$ (see equation (Z-2.11))." + IIE adopt the same definition of threc-volocitv as we do. defining the threc-velocitv οἱ to be the velocity with respect to observers. (seo equation (1-5)) above)," HE adopt the same definition of three-velocity as we do, defining the three-velocity $v^i$ to be the velocity with respect to observers, (see equation \ref{v}) ) above)." + We use the subscript W since this definition is used in Wilson's equations of relativistic hvdrodyviiuuies (see Wilson 1972: Dawley. ΦΠΑ Wilsou 1981).," We use the subscript W since this definition is used in Wilson's equations of relativistic hydrodynamics (see Wilson 1972; Hawley, Smarr Wilson 1984)." + With (8-5)). the four-velocity a! can be written Comparing (S-1)) aud (8-6)) shows that the two definitions of e! are related by We can now compare the ideal MIID equation (1-5)) oei the different treatimeuts.," With \ref{vW}) ), the four-velocity $u^a$ can be written Comparing \ref{uSS}) ) and \ref{uW}) ) shows that the two definitions of $v^i$ are related by We can now compare the ideal MHD equation \ref{MHD}) ) in the different treatments." + Since TE adopt the same definition for οἱ=ry as we do. their equations (EIT-ÀT1) and (ITE-11) should be identical to our equation [-5)).," Since HE adopt the same definition for $v^i = v^i_{\rm +W}$ as we do, their equations (EH-A14) and (HE-14) should be identical to our equation \ref{MHD}) )." + Iu their expression. however. the shift terii is abseut.," In their expression, however, the shift term is absent." + This abseut shift term can be traced back to their equation (IIE-13). which does not agree with our equation (1-1)).," This absent shift term can be traced back to their equation (HE-13), which does not agree with our equation \ref{ohm_spatial}) )." + It is likely that the shift termi: was nussed by dropping the term €j¢j. Tho aliguaacut of iudices is incorrect in S88 equation (2.9) (which they express in terms of 4! instead of c)., It is likely that the shift term was missed by dropping the term $\epsilon_{itj}$ The alignment of indices is incorrect in SS's equation (2.9) (which they express in terms of $u^i$ instead of $v^i$ ). + Fixing it and utilizing (8-2)) aud (8-7)) males their equation equivalent to (1-8))., Fixing it and utilizing \ref{ulowSS}) ) and \ref{translate_v}) ) makes their equation equivalent to \ref{MHD}) ). + To compare with Zhaue ideal MIID equation (Z-2.12). we insert (8-7)) auto (14-8)).s which iuuuediatelv vields Zhang’s result showing that our result aerees with that of Zhaug.," To compare with Zhang's ideal MHD equation (Z-2.12), we insert \ref{translate_v}) ) into \ref{MHD}) ), which immediately yields Zhang's result showing that our result agrees with that of Zhang." + We find similar errors iu the Faraday equation., We find similar errors in the Faraday equation. + We fouud that the shift terms in CI-8)) cancel all other shift terius when inserted iuto (3-10)). ultimately vieldiug expressious (1-11)) and (1-13)) which do not iuclude απ shift termes.," We found that the shift terms in \ref{MHD}) ) cancel all other shift terms when inserted into \ref{Bdot}) ), ultimately yielding expressions \ref{MHD_faraday}) ) and \ref{MHD_faraday2}) ) which do not include any shift terms." + With the shift terms beime abseut in equation (ITE-11). the corresponding terms do not cancel. leacing to the incorrect equatious (IIE-17) and (IIE-18). (see also (EIE-2.5) aud (EIIT-À17)).," With the shift terms being absent in equation (HE-14), the corresponding terms do not cancel, leading to the incorrect equations (HE-17) and (HE-18) (see also (EH-2.8) and (EH-A17))." + Zhauss expression for the Faraday equation (Z-2.13°) can be recovered by inserting (8-7)) iuto (1-13)) which can be rewritten as or This shows that our equations (I-11)) aud (1-13)) again agree with the expressiousof Zhaug., Zhang's expression for the Faraday equation (Z-2.13') can be recovered by inserting \ref{translate_v}) ) into \ref{MHD_faraday2}) ) which can be rewritten as or This shows that our equations \ref{MHD_faraday}) ) and \ref{MHD_faraday2}) ) again agree with the expressionsof Zhang. +" Tuterestinely, Zhang refers to EIL and iufact their equations look quite similar iu that they both coutain the above shift terms."," Interestingly, Zhang refers to EH, and infact their equations look quite similar in that they both contain the above shift terms." +IToscever. Zlaue uses (ha as the threc- while Hawley aud Evaus use ety.,"However, Zhang uses $v^i_{\rm SS}$ as the three-velocity, while Hawley and Evans use $v^i_{\rm W}$ ." + Therefore the, Therefore the +and Coy. suggestingOO that the model overprecdicted the abundance of acetylene.,"and $_2$ $_2$, suggesting that the model overpredicted the abundance of acetylene." + Indeed. a comparison of the model with data in the 760-780 ! yauge iniplos the need for a sealing factor of 0.5-0.6 to reproduce the observations. suggesting a Cols mole fraction of approximately 1.510* at 10 pbar. or a peak abundance of 2.2«10* at 3.1 par. though we stress that our sensitivity to Co» is limited to the wines of the cussion band at 760-790 1 ," Indeed, a comparison of the model with data in the 760-780 $^{-1}$ range implies the need for a scaling factor of 0.5-0.6 to reproduce the observations, suggesting a $_2$ $_2$ mole fraction of approximately $1.5\times10^{-7}$ at 10 $\mu$ bar, or a peak abundance of $2.2\times10^{-7}$ at 3.4 $\mu$ bar, though we stress that our sensitivity to $_2$ $_2$ is limited to the wings of the emission band at 760-790 $^{-1}$ ." +Finally. the AKARI spectruii between 900-1100 ! has a low signal-to-noise ratio (Fig. 1)).," Finally, the AKARI spectrum between 900-1100 $^{-1}$ has a low signal-to-noise ratio (Fig. \ref{spectrum}) )," + because the radiance is very weak at these wavenumbers. but shows a 1iodulatiou at 952 | (10.5 pau. the vp baud) which could be caused by ethivleue (ΟΠ).," because the radiance is very weak at these wavenumbers, but shows a modulation at 952 $^{-1}$ (10.5 $\mu$ m, the $\nu_7$ band) which could be caused by ethylene $_2$ $_4$ )." + Fig., Fig. + & indicates that ie forward model allows us to partially reproduce the -rorpholoey of this region of the spectra., \ref{c2h4} indicates that the forward model allows us to partially reproduce the morphology of this region of the spectrum. + Using the three cluperature profiles. we deteruine a scale factor for the uodel profile of 1.1! uo. equivalent to a peak abundance of 7.8!T«10 Tat 1.3 phar. or 5.0!mS10 Tat 2.8 phar. 16 peak of the contribution function in Fie. 2..," Using the three temperature profiles, we determine a scale factor for the model profile of $1.4^{+0.5}_{-0.6}$ , equivalent to a peak abundance of $7.8_{-3.4}^{+2.8}\times10^{-7}$ at 1.3 $\mu$ bar, or $5.0_{-2.1}^{+1.8}\times10^{-7}$ at 2.8 $\mu$ bar, the peak of the contribution function in Fig. \ref{cf}." + Though we ust be cautious. because the spectral iiorpliology is not oxeciselv reproduced by the forward models.," Though we must be cautious, because the spectral morphology is not precisely reproduced by the forward models." + Furthermore. 16 ISO spectrum preseuted by showe« the ΟΠΠ peak as a narrow sinele-pixel feature. whereas our modelled ethvlene emission for AIKARI is rather broad.," Furthermore, the ISO spectrum presented by showed the $_2$ $_4$ peak as a narrow single-pixel feature, whereas our modelled ethylene emission for AKARI is rather broad." + Finally. 10 region of the spectrum between 980-1100 cur1 shows excess Cluission which is not explaiued by our model. aud it may be possible that higher-order hivdrocarbous. whose spectral features are unresolved. are causing additional Cluission iu this range.," Finally, the region of the spectrum between 980-1100 $^{-1}$ shows excess emission which is not explained by our model, and it may be possible that higher-order hydrocarbons, whose spectral features are unresolved, are causing additional emission in this range." + Neptune's near-infrared spectrun in Fig., Neptune's near-infrared spectrum in Fig. +" d is douünated bv reflected suulieht. from Neptuues cloud lavers. in addition to absorption due to CIT,."," \ref{spectrum} is dominated by reflected sunlight from Neptune's cloud layers, in addition to absorption due to $_4$." + The peak at L7 jan is of particular significance. as discussed in Section [.1..," The peak at 4.7 $\mu$ m is of particular significance, as discussed in Section \ref{CO}." + At shorter wavelengths. the AIARI near-IR προ shows considerable deviations frou. VLT/ISAAC spectra between 305-11 jii obtained iun August 2005(7). sueeestive of meteorological variability discussed. iu Section 5.3..," At shorter wavelengths, the AKARI near-IR spectrum shows considerable deviations from VLT/ISAAC spectra between 3.5-4.1 $\mu$ m obtained in August 2002, suggestive of meteorological variability discussed in Section \ref{meteo}." + The enmüssiou peak at [7 pan cannot be reproduced by thermal or solar reflected LTE (local thermodvuaiuc equilibrium) radiative transfer., The emission peak at 4.7 $\mu$ m cannot be reproduced by thermal or solar reflected LTE (local thermodynamic equilibrium) radiative transfer. + Just as ou Uranus. where a siinilar cinission feature has been detected previously(7).. the feature cau be interpreted as fluorescent (non-LTE) cuuission of CO.," Just as on Uranus, where a similar emission feature has been detected previously, the feature can be interpreted as fluorescent (non-LTE) emission of CO." + The population in the upper levels of the observed. transition is bv solu absorption. mainly from the CO 1-0 aud 2-0 bauds.," The population in the upper levels of the observed transition is by solar absorption, mainly from the CO 1-0 and 2-0 bands." + However. the coutribution from the (1-0) band (resonant. fluorescence} isi strongly self-absorbed. so the (2-1) band therefore dominates the spectrum.," However, the contribution from the (1-0) band (resonant fluorescence) is strongly self-absorbed, so the (2-1) band therefore dominates the spectrum." + This explains the waveleneth shift iu the observed spectrum compared to the (1-0) band centre;, This explains the wavelength shift in the observed spectrum compared to the (1-0) band centre. + A full nou-ETE radiative model has. been adapted to Neptune with the following characteristics., A full non-LTE radiative model has been adapted to Neptune with the following characteristics. + The atmospheric structure was taken frou the iicl-IR. determinations iu Section 3..3 with a variable CO abundance vertical profile.," The atmospheric structure was taken from the mid-IR determinations in Section \ref{midir}, with a variable CO abundance vertical profile." + Two CO vertical profiles were modeled to produce the svuthetic spectra in Fie. 9:, Two CO vertical profiles were modeled to produce the synthetic spectra in Fig. \ref{akari_CO}: + The upper atinospheric abundance was modeled using an eddy. diffusion coefficient of ος10* ens. +(?).., The upper atmospheric abundance was modeled using an eddy diffusion coefficient of $2\times10^7$ $^{2}$ $^{-1}$. + The svuthetic spectra in Fig., The synthetic spectra in Fig. + 9 were calculated frou a nou-LTE radiative model inchicing solar raciation absorption. selt-absorptiou iu the resonant fluorescent (1-0) baud. aud frequeucy redistribution from vibrational CO bands.," \ref{akari_CO} were calculated from a non-LTE radiative model including solar radiation absorption, self-absorption in the resonant fluorescent (1-0) band, and frequency redistribution from vibrational CO bands." + For both profiles. we scaled the abundauce of CO to obtain the best fit to the AINART observations.," For both profiles, we scaled the abundance of CO to obtain the best fit to the AKARI observations." + The weighting function of the 2-1 fluorescent emission is found to peak around 1 bar. with much smaller contributions from the 1-0 baud at higher altitudes (O.01-0.1 imibar). therefore eiviug sensitivity to the CO distribution iu both the stratospheric and tropospheric parts of the atimosphere.," The weighting function of the 2-1 fluorescent emission is found to peak around 1 bar, with much smaller contributions from the 1-0 band at higher altitudes (0.01-0.1 mbar), therefore giving sensitivity to the CO distribution in both the stratospheric and tropospheric parts of the atmosphere." + A simile depth of cuiission was found for fluoresceuce of CO ou Urauus. as discussed iu7T).," A similar depth of emission was found for fluorescence of CO on Uranus, as discussed in." + Despite the fact that uon-LTE effects are usually doninaur oulv in the low-frequency collisional regime of the upper atmosphere. the decrease in the nou-LTE coutributiou is couuter-balauced by the imcrease in the optical depth of CO. and the non-LTE euuissiou iu the 2-1 baud is not affected by seltabsorption like the 1-0 baud.," Despite the fact that non-LTE effects are usually dominant only in the low-frequency collisional regime of the upper atmosphere, the decrease in the non-LTE contribution is counter-balanced by the increase in the optical depth of CO, and the non-LTE emission in the 2-1 band is not affected by self-absorption like the 1-0 band." + The results of the non-LTE radiative ranster imnodel are shown in Fie. 9.., The results of the non-LTE radiative transfer model are shown in Fig. \ref{akari_CO}. + A continuuu has been added to the svuthetic spectra to fit the AIKARI spectiuu outside the CO xud., A continuum has been added to the synthetic spectra to fit the AKARI spectrum outside the CO band. + The dashed line shows the effects of restricting CO o the stratosphere - its absence frou the troposphere means that the fluorescent chussioln ds insufficient to reproduce the peak in the AKARI spectrmu., The dashed line shows the effects of restricting CO to the stratosphere - its absence from the troposphere means that the fluorescent emission is insufficient to reproduce the peak in the AKARI spectrum. + The best-fitting model had CO/IL;22.5«108 in the stratosphere with a decrease in the abundance by a factor of four olov 10 iibar., The best-fitting model had $_2$ $2.5\times10^{-6}$ in the stratosphere with a decrease in the abundance by a factor of four below 10 mbar. + Oulv by including tropospheric CO do we beein to reproduce the enission feature. which would likely be inrproved via the addition of higher vibrations CO bands.," Only by including tropospheric CO do we begin to reproduce the emission feature, which would likely be improved via the addition of higher vibrations CO bands." + However. given the spectral resolution of the observed spectra (and the uncertainties m the mput atmospheric profiles discussed earlier).this wasnot deenied necessary at this stage.," However, given the spectral resolution of the observed spectra (and the uncertainties in the input atmospheric profiles discussed earlier),this wasnot deemed necessary at this stage." + The consequences of tropospheric CO are briefly discussed im Section 5.., The consequences of tropospheric CO are briefly discussed in Section \ref{discuss}. . +(SSBs) with the most evolved donors have much in common with symbiotic binaries.,(SSBs) with the most evolved donors have much in common with symbiotic binaries. + SSBs therefore form a natural bridge between CVs and symbiotics. as they comprise à natural extension of both classes. producing a unified picture of acereting WDs.," SSBs therefore form a natural bridge between CVs and symbiotics, as they comprise a natural extension of both classes, producing a unified picture of accreting WDs." + The close-binary SSS (CBSS) model was designed to explain the phenomenon of binary SSSs which. like the flagship sources CAL 83 and CAL 87. have orbital periods 1n the range of tens of hours. and estimated bolometric luminosities ~10°7—10? ergs sla (See van den Heuvel et 11992: Rappaport. Di Stefano. Smith 1994 [RDS].)," The close-binary SSS (CBSS) model was designed to explain the phenomenon of binary SSSs which, like the flagship sources CAL 83 and CAL 87, have orbital periods in the range of tens of hours, and estimated bolometric luminosities $\sim 10^{37}-10^{38}$ ergs $^{-1}.$ (See van den Heuvel et 1992; Rappaport, Di Stefano, Smith 1994 [RDS].)" + The range of observed orbital periods implies a range of Roche lobe radit compatible with the size and mass of donors that could in fact meet these requirements., The range of observed orbital periods implies a range of Roche lobe radii compatible with the size and mass of donors that could in fact meet these requirements. + The model is therefore roughly consistent with the data on the known systems., The model is therefore roughly consistent with the data on the known systems. + At present. most of the known SSSs with optical [Ds that do not place them in an already-understood-class of hot WD system are considered to be candidates for the CBSS model.," At present, most of the known SSSs with optical IDs that do not place them in an already-understood-class of hot WD system are considered to be candidates for the CBSS model." + First principles estimates based on a population synthesis study to determine how many such CBSSs should be active in à galaxy such as our own found that there are likely to be on the order of 1000 presently active CBSSs in the Milky Way with L>1077 eres s! (RDS: Yungelson 1996)., First principles estimates based on a population synthesis study to determine how many such CBSSs should be active in a galaxy such as our own found that there are likely to be on the order of $1000$ presently active CBSSs in the Milky Way with $L> 10^{37}$ ergs $^{-1}$ (RDS; Yungelson 1996). + Studies of the effect of absorption then confirmed that all but a fraction of a percent of these systems would not have been detected by ROSAT (Di Stefano Rappaport 1994)., Studies of the effect of absorption then confirmed that all but a fraction of a percent of these systems would not have been detected by ROSAT (Di Stefano Rappaport 1994). + In spite of the fact that the CBSS model ts self-consistent. it has remarkably little direct observational support.," In spite of the fact that the CBSS model is self-consistent, it has remarkably little direct observational support." + There are. however. indirect signs that some CBSS candidates may be well-described by the model.," There are, however, indirect signs that some CBSS candidates may be well-described by the model." + These signs include the following. (, These signs include the following. ( +1) There are well-defined regions in the H-R. diagram where steady nuclear burning has been predicted to occur.,1) There are well-defined regions in the H-R diagram where steady nuclear burning has been predicted to occur. + Determinations of SSS temperatures and luminosities thus far have been subject to significant uncertainties., Determinations of SSS temperatures and luminosities thus far have been subject to significant uncertainties. + Nevertheless. some (but not all) CBSS candidates seem to occupy regions of the H-R diagram consistent with quasi-steady nuclear burning.," Nevertheless, some (but not all) CBSS candidates seem to occupy regions of the H-R diagram consistent with quasi-steady nuclear burning." + At present. until Chandra’s low-energy calibration 1s. better understood and/or more XMM data become available. the uncertainties are too large to allow apparent placement in the H-R diagram to confirm or falsify the conjecture that any particular CBSS candidate contains a nuclear-burning WD. (," At present, until Chandra's low-energy calibration is better understood and/or more XMM data become available, the uncertainties are too large to allow apparent placement in the H-R diagram to confirm or falsify the conjecture that any particular CBSS candidate contains a nuclear-burning WD. (" +(2) The X-ray spectra (most of which are still fairly crude) are reasonably well-fit by WD atmosphere models (van Teeseling 11996).,2) The X-ray spectra (most of which are still fairly crude) are reasonably well-fit by WD atmosphere models (van Teeseling 1996). + Both and erating spectra of selected SSSs are beginning to be analyzed. and will allow us to test the applicability of WD atmosphere models in detail.," Both and grating spectra of selected SSSs are beginning to be analyzed, and will allow us to test the applicability of WD atmosphere models in detail." + There is published work on just one system. CAL 83 (Paerels et 22001).," There is published work on just one system, CAL 83 (Paerels et 2001)." + There are clear disagreements between the WD atmosphere models applied to the data so far and the observed grating spectra., There are clear disagreements between the WD atmosphere models applied to the data so far and the observed grating spectra. + It remains to be seen if these can be resolved. (, It remains to be seen if these can be resolved. ( +(3) Nuclear-burning WDs should have aceretion disks with distinctive features (Popham 11996).,3) Nuclear-burning WDs should have accretion disks with distinctive features (Popham 1996). + This is because the amount of energy provided by the WD in the form of heat and radiation. is ~10 times greater than the accretion energy.," This is because the amount of energy provided by the WD in the form of heat and radiation, is $\sim 10$ times greater than the accretion energy." + The inner regions of such a disk are thick and very hot. contributing to the total soft X-ray emission.," The inner regions of such a disk are thick and very hot, contributing to the total soft X-ray emission." + The disk geometry flares at large radii., The disk geometry flares at large radii. + It cools with distance from the central WD. and is the dominant source of radiation at ultraviolet and optical wavelengths.," It cools with distance from the central WD, and is the dominant source of radiation at ultraviolet and optical wavelengths." + The optical and UV observations of several CBSS candidates are consistent with the first-principles disk predictions. and this may be the strongest indication that CBSSs contain accreting objects surrounded by reprocessing-dominated disks (Popham 11996).," The optical and UV observations of several CBSS candidates are consistent with the first-principles disk predictions, and this may be the strongest indication that CBSSs contain accreting objects surrounded by reprocessing-dominated disks (Popham 1996)." + In addition. the first-principles predictions of disk geometry are in general agreement with a model of CAL 87 that was constructed to explain the eclipse profile of that system (Meyer-Hofmeister. Schandl. Meyer 1997). (," In addition, the first-principles predictions of disk geometry are in general agreement with a model of CAL 87 that was constructed to explain the eclipse profile of that system (Meyer-Hofmeister, Schandl, Meyer 1997). (" +4) Some CBSS candidates have been observed to have jets with velocities roughly compatible with the escape velocity from a WD.,4) Some CBSS candidates have been observed to have jets with velocities roughly compatible with the escape velocity from a WD. + Since. however. objects more compact than WDs can be surrounded by WD-sized photospheres. it may be possible for such winds to originate well below the photosphere. and to escape from a region around the poles.," Since, however, objects more compact than WDs can be surrounded by WD-sized photospheres, it may be possible for such winds to originate well below the photosphere, and to escape from a region around the poles." + If so. the resultingσι velocities could be comparable to those observed.," If so, the resulting velocities could be comparable to those observed." + In symbiotic systems. the donor star is very evolved.," In symbiotic systems, the donor star is very evolved." + In most cases it is thought that the donor does not fill its Roche lobe but that the WD aceretes mass by capturing a small fraction of the donors wind., In most cases it is thought that the donor does not fill its Roche lobe but that the WD accretes mass by capturing a small fraction of the donor's wind. +" Since the donor may be losing mass at 1075104M... yr7!, the WD aceretion rate can be high enough to— allow either episodic or quasi-steady nuclear burning."," Since the donor may be losing mass at $10^{-6}-10^{-4} M_\odot$ $^{-1}$, the WD accretion rate can be high enough to allow either episodic or quasi-steady nuclear burning." + Symbiotics form a well-studied class and there is evidence from several directions that the model described above is correct., Symbiotics form a well-studied class and there is evidence from several directions that the model described above is correct. + The existence of symbioties 15. therefore. one of the strongest arguments that nuclear burning may fuel high luminosities and temperatures comparable to those measured in SSS binaries.," The existence of symbiotics is, therefore, one of the strongest arguments that nuclear burning may fuel high luminosities and temperatures comparable to those measured in SSS binaries." + The effects of absorption make it difficult to discover SSSs in the disk of the Milky Way: even bright. hot SSSs in the Galactic disk can be found in surveys likeSurvey only if they are within about 1 kpe of Earth Rappaport 1994).," The effects of absorption make it difficult to discover SSSs in the disk of the Milky Way; even bright, hot SSSs in the Galactic disk can be found in surveys like only if they are within about $1$ kpc of Earth Rappaport 1994)." + Fortunately. two methods that do not depend on X-ray surveys have been able to identify previously unknown Galactic SSSs with temperatures and luminosities lower than those of any discovered via surveys.," Fortunately, two methods that do not depend on X-ray surveys have been able to identify previously unknown Galactic SSSs with temperatures and luminosities lower than those of any discovered via surveys." + The pattern of optical time variability of the SSS RX JOS13.9-6951 (Alcock et 11996. Southwell et al.," The pattern of optical time variability of the SSS RX J0513.9-6951 (Alcock et 1996, Southwell et al." + 1996). was observed by Brian Warner (private communication) to be similar to that of members of the Vy Scl subclass of nova-like variables.," 1996), was observed by Brian Warner (private communication) to be similar to that of members of the Vy Scl subclass of nova-like variables." + Because the soft X-ray emission from RX JOS13.9-695] turned on during its optical low-state. we monitored Vy Sel stars and obtained ToO time to observe one such system. V751 Cyg. during its optical low state.," Because the soft X-ray emission from RX J0513.9-6951 turned on during its optical low-state, we monitored Vy Scl stars and obtained ToO time to observe one such system, V751 Cyg, during its optical low state." +" During this occasion. it was observed to have a bolometric luminosity of 6.5«10°° eres s!(D/500pc). where D is the distance to the system. and KT=ΙΣΤ eV (Greiner et 11999, Greiner Stefano») This lumimosity is several orders of magnitude larger than expected due to accretion alone. making a strong case for nuclear burning."," During this occasion, it was observed to have a bolometric luminosity of $6.5 \times 10^{36}$ ergs $^{-1}\, (D/500 pc),$ where $D$ is the distance to the system, and $k\, T = 15^{+15}_{-10}$ eV (Greiner et 1999, Greiner ) This luminosity is several orders of magnitude larger than expected due to accretion alone, making a strong case for nuclear burning." + If a CV appears so bright that its luminosity cannot be explained by accretion alone. then it may be a candidate NBWD (Patterson et 1998. Steiner Diaz 1998).," If a CV appears so bright that its luminosity cannot be explained by accretion alone, then it may be a candidate NBWD (Patterson et 1998, Steiner Diaz 1998)." + V See has, V Sge has +in the models of ?.,in the models of . +. If the shells are created due to à two- interaction scenario. the exact details of the interaction will significantly complicate a straightforward interpretation. and it must be stressed that the above estimates are order-of-magnitude estimates.," If the shells are created due to a two-wind interaction scenario, the exact details of the interaction will significantly complicate a straightforward interpretation, and it must be stressed that the above estimates are order-of-magnitude estimates." + We conclude that our results are consistent with previous investigations and with the thermal-pulse-formation scenario., We conclude that our results are consistent with previous investigations and with the thermal-pulse-formation scenario. + We have investigated how the new imaging polarimeter and coronograph PolCor can be used to study the circumstellar dust distribution around AGB stars., We have investigated how the new imaging polarimeter and coronograph PolCor can be used to study the circumstellar dust distribution around AGB stars. + In this preliminary study. observations of the circumstellar structure around the S-type star W Aql and the two detached-shell sources. DR Ser and U Cam. were performed.," In this preliminary study, observations of the circumstellar structure around the S-type star W Aql and the two detached-shell sources, DR Ser and U Cam, were performed." + Here we summarize our results and draw the following conclusions: The main reason for the construction of PolCor was the neec for an instrument that can measure faint scattered light close to bright stars., Here we summarize our results and draw the following conclusions: The main reason for the construction of PolCor was the need for an instrument that can measure faint scattered light close to bright stars. + The instrument is optimized for both scatterec light from circumstellar dust particles as well as resonance line scattering from circumstellar gas in the following ways., The instrument is optimized for both scattered light from circumstellar dust particles as well as resonance line scattering from circumstellar gas in the following ways. + To increase the contrast between the PSF wings and polarizec scattered. light from the dust. the instrument includes a polarizing mode.," To increase the contrast between the PSF wings and polarized scattered light from the dust, the instrument includes a polarizing mode." + To further bring down the surface brightness of the wings of the stellar PSF (Point Spread Funetion) anc avoid saturation of the central star. a coronographic optical design was chosen.," To further bring down the surface brightness of the wings of the stellar PSF (Point Spread Function) and avoid saturation of the central star, a coronographic optical design was chosen." +" In addition. to cancel out the diffraction cross of the PSF. a Lyot stop blocks the image of the support blades of the secondary mirror,"," In addition, to cancel out the diffraction cross of the PSF, a Lyot stop blocks the image of the support blades of the secondary mirror." + In order to optimize the contrast ratio in the detection of resonance line scattering. the instrument is equipped with ultra-narrow band optical filters.," In order to optimize the contrast ratio in the detection of resonance line scattering, the instrument is equipped with ultra-narrow band optical filters." + Finally. to spatially resolve structures in the circumstellar environments. the instrument uses (Sects 3.2 and A.2.)). which considerably improves the sharpness of the images compared to the seeing limited case.," Finally, to spatially resolve structures in the circumstellar environments, the instrument uses (Sects \ref{ss:obsdata} and \ref{a:red}) ), which considerably improves the sharpness of the images compared to the seeing limited case." + The PolCor instrument is briefly described in the following points:, The PolCor instrument is briefly described in the following points: +covering fraction.,covering fraction. + DG. is the incomplete Gamma function in which x22./—6 +1. y)where o ts the faint-end slope of the Schechter galaxy luminosity function and ./ parameterizes a Holmbergike luminosity scaling of l..," $\Gamma(x,y)$ is the incomplete Gamma function in which $x=2\beta - +\alpha +1$ where $\alpha$ is the faint–end slope of the Schechter galaxy luminosity function and $\beta$ parameterizes a Holmberg–like luminosity scaling of Eq. \ref{eq:rl}. ." + The parameter wulanionΞ[μμLO. where Lyi. 1$ the minimumEq. luminosity of contributing to absorption.," The parameter $y=L_{min}/L^{\ast}$, where $L_{min}$ is the minimum luminosity of galaxies contributing to absorption." + The influence of v on the value of Ry becomes relatively more important as}> 0.," The influence of $y$ on the value of $R_{\rm x}$ becomes relatively more important as $\beta +\rightarrow 0$ ." +" We present our samplein Figure a. plottinsW,(2796) versus Ly/L,."," We present our samplein Figure \ref{fig:ewd}$ $a$, plotting $W_r(2796)$ versus $L_B/L^{\ast}_B$." +" The solid points have W,(2796)>0.3 and the open points are weak systems (Churchillet.al. 1999).. having W,(2796)<0.3 A. and would have been classified as non-absorbing galaxies im previous surveys (e.g..SDP94:Guillemin&Bergeron 1997)... W,(2796)dN>0.3A.paper."," The solid points have $W_r(2796)\geq +0.3$ and the open points are weak systems \citep{weakI}, having $W_r(2796)<0.3$ , and would have been classified as non–absorbing galaxies in previous surveys \citep[e.g., +SDP94;][]{gb97}. . $W_{r}(2796) \geq 0.3$,." + In Figure lavotethatbothabsorbingandnon —absorbinggalaxiesspanthesameluminosityrange., In Figure \ref{fig:ewd}$ $a$ note that both absorbing and non--absorbing galaxies span the same luminosity range. + Applying Eq. 2..," Applying Eq. \ref{eq:dndz},," +" we computed the statistical absorption radius. Ry. for W,(2796)>0.3 employing the most current Schechter luminosity function parameters and absorber redshift path density."," we computed the statistical absorption radius, $R_{\rm x}$, for $W_r(2796) \geq 0.3$ employing the most current Schechter luminosity function parameters and absorber redshift path density." + We dNfdzz0.8 (Nestor 2005). 4=L3. and 4.adopted=53.14«107? Gal Mpc? (Faberetal.2007) for the (2;20 redshift bin. where the mean redshift of our sampleis 0.58.," We adopted $dN/dz=0.8$ \citep{nestor05}, $\alpha=1.3$ , and $\Phi_{\ast}=3.14\times 10^{-3}$ Gal $^{-3}$ \citep{faber05} + for the $\left< z \right> =0.5$ redshift bin, where the mean redshift of our sample is 0.58." + Since the luminosity scaling is necessarily constr by our sample. we consider both notWe=0.2 and ./20 (Le.. no rainedscaling) for v=0.05 and y=0.01.," Since the luminosity scaling is not necessarily constrained by our sample, we consider both $\beta=0.2$ and $\beta=0$ (i.e., no scaling) for $y=0.05$ and $y=0.01$." + obtained. By of his sample. S95 empirically deduced 55 kpe and inferred f.=1. /=0.2 and v=0.05.," We obtained, By of his sample, S95 empirically deduced $R_{\ast}= 55$ kpc and inferred $f_c=1$, $\beta = 0.2$ and $y=0.05$." + Assuming f.= 1.)=0.2 and v20.05. we computed a statistical covering fraction corrected absorber halo radius of R.=88 kpe.," Assuming $f_c=1$, $\beta = 0.2$ and $y=0.05$, we computed a statistical covering fraction corrected absorber halo radius of $R_{\ast}= 88$ kpc." + The difference between the two values arises from the different methods used to determine R..: S95 applied a fit to a known sample of absorption selected galaxies. whereas. our values are directly computed from measured absorption and galaxy statistics.," The difference between the two values arises from the different methods used to determine $R_{\ast}$ ; S95 applied a fit to a known sample of absorption selected galaxies, whereas, our values are directly computed from measured absorption and galaxy statistics." + Assuming f. less than unity would increase our computed value of R.. yielding a value even less consistent with that of S95.," Assuming $f_c$ less than unity would increase our computed value of $R_{\ast}$, yielding a value even less consistent with that of S95." + In Figure Ib. the projectedquasar —galaxyseparation.D. isplottedversusLa Ly.," In Figure \ref{fig:ewd}$ $b$, the projected quasar--galaxy separation, $D$, is plotted versus $L_B/L^{\ast}_B$." + The mean impact parameter is dash-dot(D;=53.2 kpe which ts close to the S95 halo size., The mean impact parameter is $\left=53.2$ kpc which is close to the S95 halo size. + The line is the halo radius. RL). from Eq.," The dash–dot line is the halo radius, $R(L)$, from Eq." + 1. using Α.=55 kpe. f.=1. and +}=0.2 found by S95.," \ref{eq:rl} using $R_{\ast}=55$ kpc, $f_c=1$, and $\beta = 0.2$ found by S95." + Three non-absorbing galaxies reside below the ) boundary and five reside above., Three non–absorbing galaxies reside below the $R(L)$ boundary and five reside above. + This 1s not necessarily inconsistent with S95. who found two of 14 non-absorbing galaxies below the R(L) boundary.," This is not necessarily inconsistent with S95, who found two of 14 non–absorbing galaxies below the $R(L)$ boundary." +" However. we find 16 W,(2796)270.3 absorbers that are outside the A(L) boundary byas much as 60 kpe."," However, we find 16 $W_r(2796) \geq 0.3$ absorbers that are outside the $R(L)$ boundary byas much as 60 kpc." + In the standard halo model. galaxies. above the R(L) boundary are expected to not be associated with Woo>0.3 absorption.," In the standard halo model, galaxies above the $R(L)$ boundary are expected to not be associated with $W_r(2796) \geq 0.3$ absorption." + The dash-dash line is the halo radius. RCL). from Eq.," The dash–dash line is the halo radius, $R(L)$, from Eq." + | using the parameters Αι288 kpe. f£.21. and ./2 0.2.," \ref{eq:rl} using the parameters $R_{\rm x}=88$ kpc, $f_c=1$, and $\beta = 0.2$ ." + We find that five of the eight non-absorbing galaxies lie below the A(.) absorboundary., We find that five of the eight non–absorbing galaxies lie below the $R(L)$ boundary. + These five galaxies are expected tobe strong bing ealaxies if they obey the R(L) relation., These five galaxies are expected tobe strong absorbing galaxies if they obey the $R(L)$ relation. + Also. there are three absorbing galaxies above the R(GL) boundary.," Also, there are three absorbing galaxies above the $R(L)$ boundary." + From Figure Ibirwouldappecrthatthevalueof.? 1s not constrained for the B-band luminosities since non-absorbing galaxies are both above and below R(L) for both the R55 kpe deduced by S95 and our computed size of Ry=88 kpe.," From Figure \ref{fig:ewd}$ $b$ it would appear that the value of $\beta$ is not constrained for the B-band luminosities since non–absorbing galaxies are both above and below $R(L)$ for both the $R_{\ast}=55$ kpc deduced by S95 and our computed size of $R_{\rm +x}=88$ kpc." + Assumingthat there is no luminosity scaling. we explore halo cross sections with ./=0.," Assumingthat there is no luminosity scaling, we explore halo cross sections with $\beta=0$." + In Figure 2a. weplotW42790) versus D.," In Figure \ref{fig:l}$ $a$, we plot $W_r(2796)$ versus $D$ ." +" The vertical line is the statistical absorber radius.R,264 kpe (whereD/R,= 1). for}ZO and y20.05."," The vertical line is the statistical absorber radius,$R_{\rm x}=64$ kpc (where$D/R_{\rm x}=1$ ), for $\beta = 0$ and $y=0.05$." +" The top axisgives D/R,.", The top axisgives $D/R_{\rm x}$ . + Galaxies to the left of theline are consistent with the computed statistical absorber radius., Galaxies to the left of theline are consistent with the computed statistical absorber radius. + Galaxies to the right ofthe line are inconsistent: if the standard halo model applies these particular galaxies must have halos with f.< , Galaxies to the right ofthe line are inconsistent; if the standard halo model applies these particular galaxies must have halos with $f_c<1$ . +We find five of 29galaxies at D> Ry., We find five of 29galaxies at $D>R_{\rm x}$ . +" If we assume v=0.01 and J= O0. we obtain R,243 kpe andfind 16 galaxies reside atD>Ry and four non-absorbing galaxies are expected to have W,(2796)that=0.3 absorption."," If we assume $y=0.01$ and $\beta=0$ , we obtain $R_{\rm x}=43$ kpc andfind 16 galaxies reside at$D>R_{\rm x}$ and that four non–absorbing galaxies are expected to have $W_r(2796) \geq 0.3$ absorption." + Note thatRy is very, Note that$R_{\rm x}$ is very +(b) rejected doubles: those sources with 3 or fewer FIRST components. all further than 15 aresec from the optical galaxy. and with total flux greater than half of the sum of the two NVSS fluxes. were rejected. (,"(b) rejected doubles: those sources with 3 or fewer FIRST components, all further than 15 arcsec from the optical galaxy, and with total flux greater than half of the sum of the two NVSS fluxes, were rejected. (" +c) uncertain cases: any sources not satisfying either of the above conditions were classified as uncertain. and referred for visual analysis.,"c) uncertain cases: any sources not satisfying either of the above conditions were classified as uncertain, and referred for visual analysis." + The lower two plots of Figure | show the results of this classification of candidate doubles for the SDSS sources and an equivalent number of random positions., The lower two plots of Figure \ref{nvssdbls} show the results of this classification of candidate doubles for the SDSS sources and an equivalent number of random positions. + Galaxies with 3 NVSS components within 3> aremins could represent one of four possibilities: (1) a triple radio source associated with the galaxy: (G1) a double radio source associated with the galaxy. together with an unassociated VSS source: (ii) a single radio source. with two unassociated sources (or an unassociated double source): (iv) 3 unassociated VSS sources.," Galaxies with 3 NVSS components within 3 arcmins could represent one of four possibilities: (i) a triple radio source associated with the galaxy; (ii) a double radio source associated with the galaxy, together with an unassociated NVSS source; (iii) a single radio source, with two unassociated sources (or an unassociated double source); (iv) 3 unassociated NVSS sources." + It is the first two possibilities that are the concern or the multiple-source analysis., It is the first two possibilities that are the concern for the multiple–source analysis. + Comparison between the SDSS galaxies and the. random »ositions (Fig 29) suggests that a source should be classified as a potential triple if all three components are within 120 arcsec. and one of the following three conditions is also satisfied: (1) the flux weighted mean position of all three components is within [5 arcsec of the optical galaxy position: Gi) the flux weighted mean yosition of the two more distant components is within 15 aresec of the optical galaxy position [this for the case where these are the," Comparison between the SDSS galaxies and the random positions (Fig \ref{nvsstrpls}) ) suggests that a source should be classified as a potential triple if all three components are within 120 arcsec, and one of the following three conditions is also satisfied: (i) the flux weighted mean position of all three components is within 15 arcsec of the optical galaxy position; (ii) the flux weighted mean position of the two more distant components is within 15 arcsec of the optical galaxy position [this for the case where these are the" +The observations made by the Super-Namiokande [1].. the K2K. |2].. the SNO EMi| aud the KAMLAND [| experiments have brought a breastlrough iu ιο Geld of neutrino plysics.,"The observations made by the Super-Kamiokande \cite{fukuda}, the K2K \cite{ahn}, the SNO \cite{ahmad} and the KAMLAND \cite{eguchi} experiments have brought a breakthrough in the field of neutrino physics." + The lonestanding puzzles of the solar ucutrine eficit. [5Γ| and of the atinospherie anomaly have been clarified: tje expected Huxes are reduced due to the neutrino oscillation pheuo110110)1. INO the chauge oei flavour that neutrios uidergo while traveling 6].," The longstanding puzzles of the solar neutrino deficit \cite{davis} and of the atmospheric anomaly have been clarified: the expected fluxes are reduced due to the neutrino oscillation phenomenon, i.e. the change in flavour that neutrinos undergo while traveling \cite{pontecorvo}." + The overa] picture is ow also confirmed w the xcent iiini-DOONE result. |1].., The overall picture is now also confirmed by the recent mini-BOONE result \cite{AguilarArevalo:2007it}. + Neutrino oscillatious ΠΙΟv that neutriuos are massive xuticles and represeut 1ο first direct expernueuta evidence for plivsics bevon the Salcard Mocel., Neutrino oscillations imply that neutrinos are massive particles and represent the first direct experimental evidence for physics beyond the Standard Model. + Aaderstanding the nechanisin for ecnerating f1ο neutro masses and their niall values is clearly τα funciuueutal question. that needs to be understood.," Understanding the mechanism for generating the neutrino masses and their small values is clearly a fundamental question, that needs to be understood." + Ou ιο other haud. the o»yeseutv kuowi1 (as well as uukuow1) ueuTino properties lave important implications for othey doimauis oD plhyvsies as wel. among which astroplivsics. e.g. for Ol colu]οςisjon of processes like the nucleosvutlesis of heavy eleineuts. axd cosinoloey.," On the other hand, the presently known (as well as unknown) neutrino properties have important implications for other domains of physics as well, among which astrophysics, e.g. for our comprehension of processes like the nucleosynthesis of heavy elements, and cosmology." + An impressive progress las heei achieve«d 1 our knowledec of neutrino properties., An impressive progress has been achieved in our knowledge of neutrino properties. + Most of the pariuneters of he Aali-Nakagawa-Sakat:Poutecorve (AINSP) unitary marix [5|o relatie tl1e neturing flavor to the mass basis. are nowadays determined. exceot the tunc neurimo mixing anele. usually called O45.," Most of the parameters of the Maki-Nakagawa-Sakata-Pontecorvo (MNSP) unitary matrix \cite{mns}, relating the neutrino flavor to the mass basis, are nowadays determined, except the third neutrino mixing angle, usually called $\theta_{13}$." + Tlowever. this matrix might be complex. nieauine there mieit be (one or more) phases.," However, this matrix might be complex, meaning there might be (one or more) phases." + A non-zero Dirac pliase iiitroduces a diffesence between neutri1ο zud auti-neutrino oscillatiois and inpies the breakine of the CP svuuuaetry oe1 the leptou sector., A non-zero Dirac phase introduces a difference between neutrino and anti-neutrino oscillations and implies the breaking of the $\cal{CP}$ symmetry in the lepton sector. + Inowiug its valuc ασ require t1ο availaülitv of very oeitense nneutrino beams iu jext-eeneralon accelerator weitrime experlucuts. iunelv stper-beams. neutrino factories or beta-beauuis.," Knowing its value might require the availability of very intense neutrino beams in next-generation accelerator neutrino experiments, namely super-beams, neutrino factories or beta-beams." + Desides τίpreseutiug a crucial ¢iscovery. the observation of à non-zero phase wieght hep unraveling 1C asvlunetry between matter aud anti-matter in the Universe :uid have an oeupact in astrophysics. e.g. for core-colapse supernova physies |tye.," Besides representing a crucial discovery, the observation of a non-zero phase might help unraveling the asymmetry between matter and anti-matter in the Universe and have an impact in astrophysics, e.g. for core-collapse supernova physics \cite{Balantekin:2007es}." + ZuccIln has first proposed the ide vof producing electron (6uitijueutriuo CALLIN 1Lsine the heta-decay of boost«d radioactive ious: the mp)eta-bewunu 10].., Zucchelli has first proposed the idea of producing electron (anti)neutrino beams using the beta-decay of boosted radioactive ions: the “beta-beam” \cite{zucchelli}. + It js three main advantages: weLknown fluxes. purity (iu flavour) aud collimaion.," It has three main advantages: well-known fluxes, purity (in flavour) and collimation." + This simple idea exuloits iaiyor developiuenuts im the fic5d of iiclear oivsies. where radioactive ion beam facilities under study such as 10 european EURISOL project are expectec to reac 13on intensities of 1043+> per second.," This simple idea exploits major developments in the field of nuclear physics, where radioactive ion beam facilities under study such as the european EURISOL project are expected to reach ion intensities of $10^{11-13}$ per second." + A feasiην study of the original scenario is ougoiug (2005-2009) witli1 the EURISOL Desieu Study (DS) financed by the European Couuuuuty., A feasibility study of the original scenario is ongoing (2005-2009) within the EURISOL Design Study (DS) financed by the European Community. + At present. various beta-beam scenarios can be found in the literature.," At present, various beta-beam scenarios can be found in the literature, depending on the ion acceleration." + lt.," They are usually classified following the value of the Lorentz $\gamma$ boost factor, as low energy $\gamma=6-15$ ) \cite{Volpe:2003fi,McLaughlin:2003yg,Serreau:2004kx,McLaughlin:2004va,Balantekin:2005md,Balantekin:2006ga,Jachowicz:2006xx,Barranco:2007ej,Lazauskas:2007va,Lazauskas:2007bs,Amanik:2007ce,Amanik:2007ce,Amanik:2007zy,Bueno:2006yg,nathalie}, original $\gamma \approx 60-100$ ) \cite{zucchelli,maur03,maur05,bur05,gugl05,cam06,ber05}, , medium $\gamma$ of several hundreds) and high-energy $\gamma$ of the order of thousands) \cite{bur04,don05,hub06,Agarwalla:2006vf,Agarwalla:2006gz}. (" +..,For a review of all scenarios see \cite{Volpe:2006in}. .) + , An extensive investigation of the corresponding physics potential is being performed and new ideas keep being proposed. +," For example, a radioactive ion beam production method is discussed in \cite{rubbia06} and will be investigate within the new ""EuroNU"" DS." +L1.," Thanks to this method two new ions $^{8}$ B and $^{8}$ Li are being considered as candidate emitters, while the previous literature is mainly focussed on $^{6}$ He and $^{18}$ Ne." +.. ., The corresponding sensitivity is currently under study (see e.g. \cite{Coloma:2007nn}) ). +Ll1.," In the original scenario \cite{zucchelli}, the ions are produced, collected, accelerated up to several tens GeV/nucleon - after injection in the Proton Synchrotron and Super Proton Synchrotron accelerators at CERN - and stored in a storage ring of 7.5 km (2.5 km) total length (straight sections)." +:.," The neutrino beam produced by the decaying ions point to a large water Čeerenkov detector \cite{deBellefon:2006vq} (about 20 times Super-Kamiokande), located at the (upgraded) Fréjjus Underground Laboratory, in order to study $\cal{CP}$ violation, through a comparison of $\nu_e \rightarrow \nu_{\mu}$ and $\bar{\nu}_e \rightarrow \bar{\nu}_{\mu}$ oscillations." +Q., This facility is based on reasonable extrapolation of existing technologies and exploits already existing accelerator infrastructure to reduce cost. + oe 01., Other technologies are being considered for the detector as well \cite{Autiero:2007zj}. +σος1 d., A first feasibility study is performed in \cite{autin}. +11.," The choice of the candidate emitter has to meet several criteria, including a high intensity achievable at production and a not too short/long half-life." +o Ll.," The ion acceleration window is determined by a compromise between having the $\gamma$ factor as high aspossible, to profit of larger cross sections and better focusing" +done in Fig. 4..,"done in Fig. \ref{fig:PhaseInclinationN}," + we recognize a similar trend in the intensity diagram., we recognize a similar trend in the intensity diagram. + 1 the ratio Αι=5. the luminosity varies between 0.22=1/5 and 1 in normalized unities whereas for N/Ny=2. it lies between 0.54z1/2 and 1.," If the ratio $N/N_0=5$, the luminosity varies between $0.22\approx1/5$ and $1$ in normalized unities whereas for $N/N_0=2$, it lies between $0.54\approx1/2$ and 1." + Aloreover. the current sheet thickness directly impacts on the duty evele of the Leht-curve. or in other words. on the width of the gamma-ray pulses.," Moreover, the current sheet thickness directly impacts on the duty cycle of the light-curve, or in other words, on the width of the gamma-ray pulses." + This has been check by changing the parameter A. to 5 or 2 instead of the previous value of 10., This has been check by changing the parameter $\Delta_\varphi$ to 5 or 2 instead of the previous value of 10. + Results are shown in Fi , Results are shown in Fig. \ref{fig:PhaseInclinationD}. +To better assess the dillerences. we summarize all the light-curves lor X=72 degrees and ὁ=90 degrees in. two plots as depicted in Fig.6..," To better assess the differences, we summarize all the light-curves for $\chi=72$ degrees and $\zeta=90$ degrees in two plots as depicted in \ref{fig:PhaseInclinationSummary}." + Finally. there exist. two. limiting cases.," Finally, there exist two limiting cases." + First the aligned rotator showing no pulsed emission., First the aligned rotator showing no pulsed emission. + Second. the perpendicular rotator emits. pulsed. high-energy. raciation over the whole sky. and. both its polar caps are visible., Second the perpendicular rotator emits pulsed high-energy radiation over the whole sky and both its polar caps are visible. + A direct. consequence is a double peak structure in both radio and ganuna-ray light-curves. with a separation of A=0.5.," A direct consequence is a double peak structure in both radio and gamma-ray light-curves, with a separation of $\Delta=0.5$." + ο.)0020|0451 is a typical example., PSRJ0030+0451 is a typical example. + The photon Hux fy. measured by an observer located on Earth is biased. due to anisotropic emission from the wind depending on the viewing angle ¢., The photon flux $F_{\rm obs}$ measured by an observer located on Earth is biased due to anisotropic emission from the wind depending on the viewing angle $\zeta$. + This fact is clear from the aforementioned. phase-inclination. plots shown in the previous paragraphs., This fact is clear from the aforementioned phase-inclination plots shown in the previous paragraphs. + The observed. gamma-ray. [lux has to be corrected. to obtain the true gamma-ray luminosity by introducing a correction factor fe defined by Llere D is the distance of the pulsar to the observer and Fas the observed flux.," The observed gamma-ray flux has to be corrected to obtain the true gamma-ray luminosity by introducing a correction factor $f_\Omega$ defined by Here $D$ is the distance of the pulsar to the observer and $F_{\rm + obs}$ the observed flux." + As in the polar cap and outer/slot eap models (Wattersetal.2009)... the correction. implied here by a relativistic beaming elfect is given by For the striped wine model. this correction factor is shown in fie.," As in the polar cap and outer/slot gap models \citep{2009ApJ...695.1289W}, the correction implied here by a relativistic beaming effect is given by For the striped wind model, this correction factor is shown in fig." + 7 with the full dependence on obliquity y and inclination of Earth line of sight Cz., \ref{fig:FacteurCorrection} with the full dependence on obliquity $\chi$ and inclination of Earth line of sight $\zeta_E$ . + We can approximately separate the correction. [actor into two regions of constant value., We can approximately separate the correction factor into two regions of constant value. + In the first region. for an obliquity y«$/2./cr. the correction is close to be uniform. and equal roughly to 1.90.," In the first region, for an obliquity $\chi<\pi/2 - +\zeta_E$, the correction is close to be uniform and equal roughly to 1.90." + Phis case corresponds to a line of sight not crossing the current sheets in the wind. there is almost no pulsed. emission. visible.," This case corresponds to a line of sight not crossing the current sheets in the wind, there is almost no pulsed emission visible." + In the second region. where X77/2Ce. the correction is also almost uniform and equal roughly. to 0.4.," In the second region, where $\chi > \pi/2 - \zeta_E$, the correction is also almost uniform and equal roughly to 0.4." + Fhis case corresponds to a line of sight. intersecting the current sheets. leading to pulsed emission.," This case corresponds to a line of sight intersecting the current sheets, leading to pulsed emission." + This behavior is expected from the definition of the correction factor Ίσα. (412)., This behavior is expected from the definition of the correction factor Eq. \ref{eq:FacteurFocal}) ). + Indeed. for a fixed obliquity v. the numerator is à constant whereas the denominator depends on the line of sight towards the Earth.," Indeed, for a fixed obliquity $\chi$ , the numerator is a constant whereas the denominator depends on the line of sight towards the Earth." + On one side. in the first region X27πGg. the phase-averaged emission is faint ancl weakly pulsed.," On one side, in the first region $\chi > \pi/2 - \zeta_E$, the phase-averaged emission is faint and weakly pulsed." + Lt follows a small denominator therefore a large correction factor., It follows a small denominator therefore a large correction factor. + On the other side. in the second region. the situation is opposite. the emission during the pulses is strong ancl so the denominator of Eq. (41))," On the other side, in the second region, the situation is opposite, the emission during the pulses is strong and so the denominator of Eq. \ref{eq:FacteurFocal}) )" + larecr. Linally the correction factor is weakest.," larger, finally the correction factor is weakest." + Note that these bouncing values depend on the sheet thickness parameterized by A. as well as on the particle density contrast. parameterized by No and iN., Note that these bounding values depend on the sheet thickness parameterized by $\Delta_\varphi$ as well as on the particle density contrast parameterized by $N_0$ and $N$. + We conclude our study by fitting light-curves of a small sample of pulsars., We conclude our study by fitting light-curves of a small sample of pulsars. + The only relevant [ree parameters in our model are the &cometry of the wind. the particle density number and the size of the current sheets.," The only relevant free parameters in our model are the geometry of the wind, the particle density number and the size of the current sheets." + In. this last section. we specialize our results to some Fermi detected ganuna-ray pulsars and show the best parameters. fitting their high-cnerew light-curves above LOO MeV. Therefore. the knowledge of the viewing angle and the obliquity allows an estimation of the (lux correction via the beaming factor.," In this last section, we specialize our results to some Fermi detected gamma-ray pulsars and show the best parameters fitting their high-energy light-curves above 100 MeV. Therefore, the knowledge of the viewing angle and the obliquity allows an estimation of the flux correction via the beaming factor." + Eventually a true gamma-ray Luminosity versus spin-down luminosity can be plotted., Eventually a true gamma-ray luminosity versus spin-down luminosity can be plotted. + We start with an estimate of the peak separation when one radio pulse is detected., We start with an estimate of the peak separation when one radio pulse is detected. + In that case. ¢στx as explained above and the knowledge of A immediately implies a solution for ο.," In that case, $\zeta\approx\chi$ as explained above and the knowledge of $\Delta$ immediately implies a solution for $\zeta$." + This has been done for several pulsars and listed in Tab. 1., This has been done for several pulsars and listed in Tab. \ref{tab:Geometrie}. + En all the results shown below. for simplicity. we took a constant Lorentz factor of the wind equal to P.=10.," In all the results shown below, for simplicity, we took a constant Lorentz factor of the wind equal to $\Gamma_{\rm v}=10$." + Let us have a deeper look on a representative sample of L'ermi-detected gamma-ray pulsars., Let us have a deeper look on a representative sample of Fermi-detected gamma-ray pulsars. + PSR. 0020|0451 is a millisecond pulsar. 22=4.87 ms. showing a double pulse structure in the radio band.," PSR J0030+0451 is a millisecond pulsar, $P=4.87$ ms, showing a double pulse structure in the radio band." + This niw suggest that both its magnetic poles are. visible. or in other words. it is almost a perpendicular rotator with vm907.," This may suggest that both its magnetic poles are visible, or in other words, it is almost a perpendicular rotator with $\chi \approx 90^o$." + Nevertheless. the maximal intensity of both radio pulses are sensibly dillerent. this is interpreted as the line of sight passing closer to one magnetic pole than to the other.," Nevertheless, the maximal intensity of both radio pulses are sensibly different, this is interpreted as the line of sight passing closer to one magnetic pole than to the other." + An alternative would be to explain it by a process occurring in the vicinity. of the polar caps with variable. efficiency., An alternative would be to explain it by a process occurring in the vicinity of the polar caps with variable efficiency. + Llowever. polar cap emission is not the main purpose of this work so we simply assume identical shapes for both radio-," However, polar cap emission is not the main purpose of this work so we simply assume identical shapes for both radio-pulses." + Therefore. an obliquity close to 90 degrees but. less matches the right ecometry.," Therefore, an obliquity close to $90$ degrees but less matches the right geometry." +" Setting xy867"" satisfactorily agrees with the radio light-curve. see E δν,"," Setting $\chi \approx 67^o$ satisfactorily agrees with the radio light-curve, see Fig. \ref{fig:FermiCL}," + on the top eft plot., on the top left plot. + To have the right eunma-ray. peak separation. we wave to adopt ¢585°.," To have the right gamma-ray peak separation, we have to adopt $\zeta +\approx 85^o$." + Moreover. the radio-pulses are very xoad. cach of them having a duty evele of roughly 0.2 in hase.," Moreover, the radio-pulses are very broad, each of them having a duty cycle of roughly $0.2$ in phase." + Therefore. to reconcile our model with data. we have o extend the polar cap region to a sizeable fraction of the whole neutron star surface. Fig. S.," Therefore, to reconcile our model with data, we have to extend the polar cap region to a sizeable fraction of the whole neutron star surface, Fig. \ref{fig:FermiCL}," + top left plot., top left plot. + Emission starts right. after the light-cvlinder radius., Emission starts right after the light-cylinder radius. + Vhere is still a excess of 0.1 in the phase delay compared to observation., There is still a excess of 0.1 in the phase delay compared to observation. + This has to be explained by some other retardation effects of the radio pulse such as the strong eravitational field regime (which we have shown to be negligible) or bv magnetic field bending due to charges llowing within themagnetosphere ancl disturbingthe closed field lines structure taking to be an exact clipole., This has to be explained by some other retardation effects of the radio pulse such as the strong gravitational field regime (which we have shown to be negligible) or by magnetic field bending due to charges flowing within themagnetosphere and disturbingthe closed field lines structure taking to be an exact dipole. + PSR. J0218]4232 is another milliseconc pulsar. P= ms. showing a less clear double pulse structure," PSR J0218+4232 is another millisecond pulsar, $P=2.32$ ms, showing a less clear double pulse structure" +"order of the size of the X-ray source (in order to obtain complete eclipses. but without long intervals with complete obscuration. in agreement with the observations) provicle a second relation between the distance and size of the The above conditions require that the X-ray. source has ἃ size no larger than a few gravitational radii. estimated from the available black hole mass measurements (in the range 10""-10' AL. for most of the sources with measured eclipses). and that the obscuring clouds. have tangential velocities of several LO? km +. and densities in the range 10 yp ↓∪−↓∪≼⇍⊔↓⋟⊳↓↥∢⊾⊳","order of the size of the X-ray source (in order to obtain complete eclipses, but without long intervals with complete obscuration, in agreement with the observations) provide a second relation between the distance and size of the The above conditions require that the X-ray source has a size no larger than a few gravitational radii, estimated from the available black hole mass measurements (in the range $^6$ $^7$ $_\odot$ for most of the sources with measured eclipses), and that the obscuring clouds have tangential velocities of several $^3$ km $^{-1}$, and densities in the range $^{10}$ $^{11}$ $^{-3}$." +∖⋖⋅⋜⊔⋅∢⊾↿↓↥⋖⊾⇂∙∖⇁↓≻⊔⇍⋜↧↓∖⇁⋜↧↓⋯⊾⊳∖⇂∪↓⋅∐↓⋅∪⋯⇂ Boop . ⋅ Emission Line clouds. which are therefore. presumably one and the same with the X-ray eclipsing The central idea in this work is that it is possible to perform “tomography” experiments using X-ray eclipses of AGNs.," These are the typical values for Broad Emission Line clouds, which are therefore presumably one and the same with the X-ray eclipsing The central idea in this work is that it is possible to perform “tomography” experiments using X-ray eclipses of AGNs." + In particular. the experiment would. be relevant to est relativistic elfects in the inner regions around the supermassive black hole.," In particular, the experiment would be relevant to test relativistic effects in the inner regions around the supermassive black hole." + Pwo elfects are expected. on both he iron emission linc. and the continuum rellected emission.," Two effects are expected, on both the iron emission line, and the continuum reflected emission." + In the following. we first describe these elfects physically. and we then investigate them quantitatively by means ofline:: The broad iron Ka emission line is believed to be »oduced by reflection of the primary radiation olf the inner xuwts of the accretion disc (Fabian et al.," In the following, we first describe these effects physically, and we then investigate them quantitatively by means of: The broad iron $\alpha$ emission line is believed to be produced by reflection of the primary radiation off the inner parts of the accretion disc (Fabian et al." + 1989)., 1989). + To a first approximation the profile of the line does not depend. on he exact geometry of the primary X-ray emitter. (usually assumed to be a hot corona around. the aceretion esc). while it is allected by both special relativistic (Doppler shift of line frequencies. and Doppler boosting of the observed intensity) and general relativistic (gravitational recshift and licht bending) elfects (Fabian et al.," To a first approximation the profile of the line does not depend on the exact geometry of the primary X-ray emitter (usually assumed to be a hot corona around the accretion disc), while it is affected by both special relativistic (Doppler shift of line frequencies, and Doppler boosting of the observed intensity) and general relativistic (gravitational redshift and light bending) effects (Fabian et al." + 1989. Laor et al.," 1989, Laor et al." + 1990. Dovéiiak et al.," 1990, Dovčiiak et al." + 2004)., 2004). + Available models. such as Dovéiiak. ct al. (," Available models, such as Dovčiiak et al. (" +2004) allow the line profile from dillerent. clise regions to he computed. taking into account the above ellects. the disc inclination and a dependence of disc emissivity with radius.,"2004) allow the line profile from different disc regions to be computed, taking into account the above effects, the disc inclination and a dependence of disc emissivity with radius." + In particular. the approaching and receding halves of the disc are expected to. produce two markedly. different line profiles (Fig.," In particular, the approaching and receding halves of the disc are expected to produce two markedly different line profiles (Fig." + LX)., 1A). + Usually. only the total line emission can be observed. and the contributions from cdillerent regions of the disc cannot be separated.," Usually, only the total line emission can be observed, and the contributions from different regions of the disc cannot be separated." + X-ray eclipses provide a way to overcome thiscontinuum., X-ray eclipses provide a way to overcome this. +. If a hieh-EW. relativisticallv broadened iron line is observed. strong relativistic signatures on the reflection continuum are also expected.," If a high-EW, relativistically broadened iron line is observed, strong relativistic signatures on the reflection continuum are also expected." + These effects can be divided in two tvpes: (1) a mocification of the overall spectral shape. and (2) an increase of the ratio between reflected ancl primary continuum.," These effects can be divided in two types: (1) a modification of the overall spectral shape, and (2) an increase of the ratio between reflected and primary continuum." + The former effect is hard to detect observationallv. because it would require a precise knowledge of the shape of the primary continuum.," The former effect is hard to detect observationally, because it would require a precise knowledge of the shape of the primary continuum." + The latter effect. can instead. be probed. observationallv., The latter effect can instead be probed observationally. + In. the mocel proposed by Miniutti Fabian (2004). if the primary emission arises from a region close to the event horizon. the raction of the radiation illuminating the accretion disc can x much higher than the geometrical covering [actor of the disc as seen from the X-ray. source. because of gravitational vending.," In the model proposed by Miniutti Fabian (2004), if the primary emission arises from a region close to the event horizon, the fraction of the radiation illuminating the accretion disc can be much higher than the geometrical covering factor of the disc as seen from the X-ray source, because of gravitational bending." + Moreover. the iron emission line and the continuum reflection must be treated. self. consistently. because both are due to reprocessing of the same primary radiation.," Moreover, the iron emission line and the continuum reflection must be treated self consistently, because both are due to reprocessing of the same primary radiation." + Ln oactice. if à strong iron line is detected. (with a higher equivalent width than observed on average in similar GN). he ratio between reflected. ancl primary continuum should also be higher than the standard. rellection clliciency.," In practice, if a strong iron line is detected (with a higher equivalent width than observed on average in similar AGN), the ratio between reflected and primary continuum should also be higher than the standard reflection efficiency." + Εις cllect will be particularly strong in the 20-40 keV. energy range. where the contribution of the rellected. emission. is expected to be higher (e.g... Magdziarz Zeziarski 1995).," This effect will be particularly strong in the 20-40 keV energy range, where the contribution of the reflected emission is expected to be higher (e.g., Magdziarz Zdziarski 1995)." + Since the enhancement of the reflected Lux is mainly due to Doppler boosting. à strong asvnunetry in the high-energvy spectrum is expected during. a Compton-thick eclipse. oween the προς (receding) and “blue” (approaching) idves of the accretion disc.," Since the enhancement of the reflected flux is mainly due to Doppler boosting, a strong asymmetry in the high-energy spectrum is expected during a Compton-thick eclipse, between the “red” (receding) and “blue” (approaching) halves of the accretion disc." + The hieh-cnerey continuum variation should correlate with the relativistic line variation during a Compton-thick eclipse: both components should ag (Lead) the centroid of the primary continuum eclipse (in »actice. the eclipse of the 2-3 keV. continuum). according o the receding (approaching) half being obscurecl first.," The high-energy continuum variation should correlate with the relativistic line variation during a Compton-thick eclipse; both components should lag (lead) the centroid of the primary continuum eclipse (in practice, the eclipse of the 2-3 keV continuum), according to the receding (approaching) half being obscured first." + The model chosen for the simulations is based on theobserved eclipses in our best example. NGC 1365.," The model chosen for the simulations is based on the eclipses in our best example, NGC 1365." + As briellv summarized in the previous Section. and. reported extensively in several publications (Risaliti et al.," As briefly summarized in the previous Section, and reported extensively in several publications (Risaliti et al." + 1999. 2005. 2007. 2009. 2009D. Maiolino et al.," 1999, 2005, 2007, 2009A, 2009B, Maiolino et al." + 2010). we observed several eclipses in this source. both total ancl partial. and by both Compton-thin and Compton-thick clouds.," 2010), we observed several eclipses in this source, both total and partial, and by both Compton-thin and Compton-thick clouds." + Ln xwticular. eclipses by clouds with Ng~35.1075 and with covering factors Cp750-9054 are rather common. ancl are seen in almost all the observations longer than a few ens of ks.," In particular, eclipses by clouds with $_H\sim3-5\times10^{23}$ $^{-2}$, and with covering factors $_F\sim$ are rather common, and are seen in almost all the observations longer than a few tens of ks." + The duration of the eclipses is of the order of 50 ks., The duration of the eclipses is of the order of 50 ks. + Compton-thick eclipses are also common. as demonstrated » the changing status (from transmission-dominated. to rellection-dominated) among cillerent observations. and in xwiicular bx a snapshot. campaign of six 15 ks ong observations. where a complete Compton-thick eclipse iippened in a time scale shorter than two days.," Compton-thick eclipses are also common, as demonstrated by the changing status (from transmission-dominated to reflection-dominated) among different observations, and in particular by a snapshot campaign of six 15 ks long observations, where a complete Compton-thick eclipse happened in a time scale shorter than two days." + Beside he eclipses. the high-qualityNAZALNewlon anclSuzaku observations revealed two crucial spectral features: 1) a road emission feature. with a substantial equivalent width 7350 eV). and. well fitted with a relativistic iron line rom a maximally rotating black hole (Risaliti et al.," Beside the eclipses, the high-quality and observations revealed two crucial spectral features: 1) a broad emission feature, with a substantial equivalent width $\sim$ 350 eV), and well fitted with a relativistic iron line from a maximally rotating black hole (Risaliti et al." + 2009): and (2) a high-cnerey continuum excess. which cannot »* reproduced by a primary emission-plus-partial-covering model (see Risaliti οἱ al.," 2009A); and (2) a high-energy continuum excess, which cannot be reproduced by a primary emission-plus-partial-covering model (see Risaliti et al." + 200012 for a detailed: cliseussion) rut is instead well reproduced by a self-consistent relativistic rellection model (Walton et al.," 2009B for a detailed discussion), but is instead well reproduced by a self-consistent relativistic reflection model (Walton et al." + 2010)., 2010). + We used for the simulations the best fit model of and spectra of NGC 1365 outside eclipses (lüsaliti et al., We used for the simulations the best fit model of and spectra of NGC 1365 outside eclipses (Risaliti et al. + 2009.4. Walton et al.," 2009A, Walton et al." + 2010)., 2010). + We will discuss in the next Section the implications of this choice., We will discuss in the next Section the implications of this choice. + The model parameters are sunimarized in Table 1., The model parameters are summarized in Table 1. + Phe model profiles for the dilferent. eclipse phases are shown in Fig., The model profiles for the different eclipse phases are shown in Fig. + 1., 1. +"lo level with those derived from fits at 3.22, 4.42 and 5.22 days since burst (Vreeswijketal.,1999),, 1.33 days since burst (Starlingetal.,2007) and at 5.3 days since burst (Bloometal., 1998).","$\sigma$ level with those derived from fits at 3.22, 4.42 and 5.22 days since burst \citep{vreeswijk1}, 1.33 days since burst \citep{columnsI} and at 5.3 days since burst \citep{bloom}." +". At this confidence level the result is inconsistent with previous estimates at 0.94 days (Castro-Tiradoetal., 1999),, 1.22 days (Vreeswijketal.,1999) and 4.4 days (Djorgovskietal.,1998,hostgalaxy measurement).."," At this confidence level the result is inconsistent with previous estimates at 0.94 days \citep{castrotirado}, , 1.22 days \citep{vreeswijk1} and 4.4 days \citep[][host galaxy measurement]{djorg}." +" MW, LMC and SMC extinction curves are indistinguishable for these data; this is partially because we do not have data in the bluer bands where the bbump characteristic of only the MW curve would occur at this redshift."," MW, LMC and SMC extinction curves are indistinguishable for these data; this is partially because we do not have data in the bluer bands where the bump characteristic of only the MW curve would occur at this redshift." +" The SMC extinction curve is generally the best approximation to GRB host galaxy extinction laws of the three aforementioned curves, as shown in many studies and most likely following the low metallicity pattern of GRB hosts (e.g.Zeh,2006;Schadyetal.,2007;Starling 2007).."," The SMC extinction curve is generally the best approximation to GRB host galaxy extinction laws of the three aforementioned curves, as shown in many studies and most likely following the low metallicity pattern of GRB hosts \citep[e.g.][]{galwij,stratta,kann,schady,columnsI}." + At four later epochs spanning 1.2—5.2 days since burst Vreeswijketal.(1999) created nIR/optical SEDs and find a decrease in the intrinsic optical extinction of AAy=0.24—0.96., At four later epochs spanning $1.2-5.2$ days since burst \cite{vreeswijk1} created nIR/optical SEDs and find a decrease in the intrinsic optical extinction of $\Delta A_V = 0.24-0.96$. +" In order to test the possible decreasing extinction proposed by these authors we recreated the nIR/optical SEDs at the epochs 3.2, 4.4 and 5.2 days since trigger."," In order to test the possible decreasing extinction proposed by these authors we recreated the nIR/optical SEDs at the epochs 3.2, 4.4 and 5.2 days since trigger." + We do not reproduce the SED at 1.2 days because this epoch (optical data from 1.2 days extrapolated to 1.3 days) has been covered using the same SED method and models in Starlingetal.(2007) and we will use the results from that fit., We do not reproduce the SED at 1.2 days because this epoch (optical data from 1.2 days extrapolated to 1.3 days) has been covered using the same SED method and models in \cite{columnsI} and we will use the results from that fit. +" Likewise, the previously reported epochs of 5.2 and 5.3 days (Vreeswijketal.,1999;Bloomal.,1998,respectively) are close in time so are treated here with a single SED."," Likewise, the previously reported epochs of 5.2 and 5.3 days \citep[][respectively]{vreeswijk1,bloom} are close in time so are treated here with a single SED." +" We gathered all available data to create light curves in seven photometric bands, BVRIJHK (the B band was not included in the SEDs of Vreeswijketal. (1999))), interpolating from the six nearest points in time to find the magnitude per epoch."," We gathered all available data to create light curves in seven photometric bands, $BVRIJHK$ (the $B$ band was not included in the SEDs of \cite{vreeswijk1}) ), interpolating from the six nearest points in time to find the magnitude per epoch." + We corrected for the host galaxy contribution to each band using the host magnitudes from Sokolovetal.(2001) (B band) and Vreeswijketal.(1999) (VRIJH K) and errors on the host magnitude determinations were combined with the datapoint and fit errors., We corrected for the host galaxy contribution to each band using the host magnitudes from \cite{sokolov} $B$ band) and \cite{vreeswijk1} $VRIJHK$ ) and errors on the host magnitude determinations were combined with the datapoint and fit errors. + The SEDs are shown in Fig., The SEDs are shown in Fig. + 3 and fit results are presented in Table 3.., \ref{newseds} and fit results are presented in Table \ref{tab:newseds}. +" Fitting a model consisting of a power law plus fixed Galactic extinction and variable (SMC- or MW-like) host extinction, we find we cannot constrain both the power law slope and the host extinction simultaneously."," Fitting a model consisting of a power law plus fixed Galactic extinction and variable (SMC- or MW-like) host extinction, we find we cannot constrain both the power law slope and the host extinction simultaneously." +" We derive upper limits on Ay which are consistent with each other for these three epochs, and with most previous measurements."," We derive upper limits on $A_V$ which are consistent with each other for these three epochs, and with most previous measurements." +" We may hope to reproduce the decrease in Ay if we keep the power law slope fixed, as done by Vreeswijketal.(1999)."," We may hope to reproduce the decrease in $A_V$ if we keep the power law slope fixed, as done by \cite{vreeswijk1}." +". They fixed Bop,=1.013 (or I= 2.013) which they measured from a single power law fit to their optical-X-ray SED at 1.2 days since trigger.", They fixed $\beta_{\rm opt}=1.013$ (or $\Gamma=2.013$ ) which they measured from a single power law fit to their optical–X-ray SED at 1.2 days since trigger. +" At a similar time, 1.3 days, Starlingetal. measured βορι=0.87 (SMC) and 0.88 (MW)(or I= 1.87,1.88) from a broken power law fit to an"," At a similar time, 1.3 days, \cite{columnsI} + measured $\beta_{\rm opt}=0.87$ (SMC) and 0.88 (MW)(or $\Gamma=1.87,1.88$ ) from a broken power law fit to an" +wavefront compensation is active which will mean that the wavefront is flat.,wavefront compensation is active which will mean that the wavefront is flat. +" In the closed-loop operation when the SHS only measures the residual image motion after each correction, the measured values are smaller, than in open loop operation."," In the closed-loop operation when the SHS only measures the residual image motion after each correction, the measured values are smaller, than in open loop operation." +" Figure 11 shows the measured by the wavefront sensor during the open-loop procedure, the Tip-Tilt and the high order compensation procedures as a test to check the smooth performance of the reconstruction algorithms."," Figure 11 shows the measured by the wavefront sensor during the open-loop procedure, the Tip-Tilt and the high order compensation procedures as a test to check the smooth performance of the reconstruction algorithms." +" Again, the units are radians."," Again, the units are radians." + Clear differences between the three processes are appreciated., Clear differences between the three processes are appreciated. +" A natural guide star of V ~5.2 magnitude was used for this experiment, with a SHS frame rate of 420Hz and collecting a total number of 21000 for each process."," A natural guide star of V $\sim5.2$ magnitude was used for this experiment, with a SHS frame rate of 420Hz and collecting a total number of 21000 for each process." + The average seeing FWHM conditions were around 1.4”.," The average seeing FWHM conditions were around 1.4""." + An improvement of a factor ~2—3 is observed in terms of measured by the Shack-Hartman sensor when only the Tip-Tilt compensation (TT) is applied., An improvement of a factor $\sim2-3$ is observed in terms of measured by the Shack-Hartman sensor when only the Tip-Tilt compensation (TT) is applied. +" When the high order algorithm (HO) is added, a decrease of the RMS by a factor 15 is seen."," When the high order algorithm (HO) is added, a decrease of the RMS by a factor 15 is seen." +" On the other hand, a decrease in the median values of every mode's coefficient is observed."," On the other hand, a decrease in the median values of every mode's coefficient is observed." + T'he decrease for the modes from 2-10 is listed in Table 5., The decrease for the modes from 2-10 is listed in Table 5. +" Any AO system may have internal inconsistencies: i.e., the system considers that the correction is adequate, minimizing the RMS, but the wavefront is not correctly compensated."," Any AO system may have internal inconsistencies: i.e., the system considers that the correction is adequate, minimizing the RMS, but the wavefront is not correctly compensated." +" For instance, this may happen if the wavefront sensor has a systematic error."," For instance, this may happen if the wavefront sensor has a systematic error." +" Then the influence functions for the membrane would be obtained with that bias, and the global failure of the system would not be noticeable only from the analysis of the RMS."," Then the influence functions for the membrane would be obtained with that bias, and the global failure of the system would not be noticeable only from the analysis of the RMS." +" To be completely sure of the performance of our AO system, simultaneous images were taken with the scientific camera."," To be completely sure of the performance of our AO system, simultaneous images were taken with the scientific camera." + Figures 12-14 show some examples of a real-time closed-loop aberration compensation using a natural guide star., Figures 12-14 show some examples of a real-time closed-loop aberration compensation using a natural guide star. + These preliminary results were obtained during the commissioning of the instrument at the 2.2m Calar Alto telescope., These preliminary results were obtained during the commissioning of the instrument at the 2.2m Calar Alto telescope. + An observing log of the observations carried out can be found in table 6., An observing log of the observations carried out can be found in table 6. + The images are clearly improved when applying the closed loop wavefront compensation even under quite poor seeing conditions., The images are clearly improved when applying the closed loop wavefront compensation even under quite poor seeing conditions. +" Figure 12 shows a 4.6 magnitude star (SAO88071) observed under very bad turbulence conditions, with a natural seeing FWHM of about 2.5”."," Figure 12 shows a 4.6 magnitude star (SAO88071) observed under very bad turbulence conditions, with a natural seeing FWHM of about 2.5""." + The data were obtained during the campaign of May 2008., The data were obtained during the campaign of May 2008. +" Under such bad seeing, of the actuators reached their maximum values and therefore only an improvement of a factor of 2 in terms of FWHM could be achieved."," Under such bad seeing, of the actuators reached their maximum values and therefore only an improvement of a factor of 2 in terms of FWHM could be achieved." + The central wavelength of the observations was again the same as before., The central wavelength of the observations was again the same as before. + The frame rate of the reconstruction was 420Hz and 14 modes were taken into account with the KS28 lenslet array., The frame rate of the reconstruction was 420Hz and 14 modes were taken into account with the KS28 lenslet array. +" Under these poor observational conditions, observing techniques like lucky imaging are completely useless."," Under these poor observational conditions, observing techniques like lucky imaging are completely useless." + However SAOLIM was, However SAOLIM was +leads to an inversion of prior searches for planetary companions to WDs. which avoided low mass WDs as being the products of binary interactions.,"leads to an inversion of prior searches for planetary companions to WDs, which avoided low mass WDs as being the products of binary interactions." + Instead. some of these objects max be the descendants of the sort of metal-rich. stars that are known to have a high specific frequency of planet detection.," Instead, some of these objects may be the descendants of the sort of metal-rich stars that are known to have a high specific frequency of planet detection." + We would like to thank I. N. Reid for a careful reading of this manuscript., We would like to thank I. N. Reid for a careful reading of this manuscript. +" We would also like to thank the participants of the morning ""Astronomy Collee at the Department of Astronomy. The Ohio State University. for the daily aud lively astro-ph. discussion. one of which prompted us to investigate the problem described in (his paper."," We would also like to thank the participants of the morning “Astronomy Coffee” at the Department of Astronomy, The Ohio State University, for the daily and lively astro-ph discussion, one of which prompted us to investigate the problem described in this paper." +Note thattemperature.,Note that. + It is common in both numerical modelling of clusters (e.g.Dolagetal.2001). and in data analysis aiming to reconstruct magnetic-field strengths and spectra (e.g.Murgiaetal.2004:Kuchar&Enflin2009) to assume an exclusive relationship between {2 and n...," It is common in both numerical modelling of clusters \citep[e.g.][]{dsgf01} and in data analysis aiming to reconstruct magnetic-field strengths and spectra \citep[e.g.][]{mgfgdftd04,ke09} to assume an exclusive relationship between $B$ and $n_{\rm e}$." + Our arguments suggest that these models may need to be generalised to accommodate the temperature dependence., Our arguments suggest that these models may need to be generalised to accommodate the temperature dependence. +" For typical electron densities (7,~0.01 — 0.1em ) and temperatures εἰ1 — 3 keV) at the centres of cool-core clusters. equation (29)) implies central magnetic fields 1 = 10μέ. within observational constraints."," For typical electron densities $n_{\rm e}\sim 0.01$ – $0.1~{\rm cm}^{-3}$ ) and temperatures $T\sim 1$ – $3~{\rm keV}$ ) at the centres of cool-core clusters, equation \ref{eqn:Bprofile}) ) implies central magnetic fields $\sim 1$ – $10~\mu{\rm G}$, within observational constraints." +" For example. conditions near the centre of the popular Hydra A cluster (7.65 and 7;c3.11keV: Davidetal. 20011: H. Russell. private communication) imply a thermal-equilibrium magnetic-field strength Bo~12.4τμ, "," For example, conditions near the centre of the popular Hydra A cluster $n_{\rm e,c}\simeq 0.072~{\rm cm}^{-3}$ and $T_{\rm c}\simeq 3.11~{\rm keV}$; \citealt{dnmfjprw01}; ; H. Russell, private communication) imply a thermal-equilibrium magnetic-field strength $B_{\rm c}\simeq 12.4~ \xi^{-1/2}~\mu{\rm G}$." +"Farther out around 730kpe. the observed electron density »,0.02em and temperature Tox3.5keV imply P2oτεU7μα, "," Farther out around $\simeq 30~{\rm kpc}$, the observed electron density $n_{\rm e}\simeq 0.02~{\rm cm}^{-3}$ and temperature $T\simeq 3.5~{\rm keV}$ imply $B\simeq 7~ \xi^{-1/2}~\mu{\rm G}$." +These are both in good agreement with magnetic-field strength estimates in Hydra A from Faraday rotation maps (Vogt&EnBlin2003.2005).," These are both in good agreement with magnetic-field strength estimates in Hydra A from Faraday rotation maps \citep{ve03,ve05}." +". For another cluster. A2199. popular among theorists (e.g.Parrish.Quataert&Sharma2009).. a central density Ώρος20.1em* and central temperature 7;c2keV (Johnstoneetal.2002: H. Russell. private communication) imply 2.11£τμ, Eil"," For another cluster, A2199, popular among theorists \citep[e.g.][]{pqs09}, a central density $n_{\rm e,c} \simeq 0.1~{\rm cm}^{-3}$ and central temperature $T_{\rm c}\simeq 2~{\rm keV}$ \citealt{jafs02}; H. Russell, private communication) imply $B_{\rm c}\simeq 11~\xi^{-1/2}~\mu{\rm G}$." +ek&Owen(2002) inferred a central magnetic-tield strength there of 15μα by assuming that only one magnetic filament along the line of sight accounts for the observed rotation measure., \citet{eo02} inferred a central magnetic-field strength there of $15~\mu{\rm G}$ by assuming that only one magnetic filament along the line of sight accounts for the observed rotation measure. + In Table |.. we list these and other central magnetic-tield strength predictions.," In Table \ref{tab:bfields}, we list these and other central magnetic-field strength predictions." + In order to estimate the turbulent velocities in the ICM. we assume that the large-scale kinetic and magnetic energies are in overall equipartition. where (yy.=(31> is the rms flow velocity.," In order to estimate the turbulent velocities in the ICM, we assume that the large-scale kinetic and magnetic energies are in overall equipartition, where $U_{\rm rms}\equiv \langle u^2\rangle^{1/2}$ is the rms flow velocity." + This is expected to be the case for a magnetic field amplified and brought to saturation by the fluctuation dynamo (see.e.g.reviewbySchekochihin&Cowley2007.andreferences therein)..," This is expected to be the case for a magnetic field amplified and brought to saturation by the fluctuation dynamo \citep[see, e.g., review by][and references therein]{sc07}." + Then the rms turbulent velocity is equal to the Alfvénn speed and. using equation (29)). we therefore obtain in the Bremsstrahlung regime.," Then the rms turbulent velocity is equal to the Alfvénn speed and, using equation \ref{eqn:Bprofile})), we therefore obtain in the Bremsstrahlung regime." + In other words. velocities.," In other words, ." +" The corresponding Mach number is where e,=(/imi)7 is the sound speed.", The corresponding Mach number is where $c_{\rm s} = (T/m_{\rm i})^{1/2}$ is the sound speed. + Note the weak dependence of A/ on temperature., Note the weak dependence of $M$ on temperature. + For 7)=1 — 10keV. Cg. ranges from c44£L7Kms3 to 210£L7Kmsὃν so M ranges from c(0.16τσ to 0.24£4°)," For $T\simeq 1$ – $10~{\rm keV}$, $U_{\rm rms}$ ranges from $\simeq 44~\xi^{-1/2}~{\rm km~s}^{-1}$ to $210~\xi^{-1/2}~{\rm km~s}^{-1}$, so $M$ ranges from $\simeq 0.16~\xi^{-1/2}$ to $0.24~\xi^{-1/2}$." + While the turbulent velocities are not yet measured directly. theoretical (e.g.Dennis&Haugen 2006).. numerical (e.g.Norman&Bryan1999:Ricker&Sarazin2001:Sunyaev.NormanBryan2003). and indirect observational (e.g.Schueckeretal.2004:ChurazovRe- estimates suggest that the numbers we are predicting are reasonable.," While the turbulent velocities are not yet measured directly, theoretical \citep[e.g.][]{dc05,ev06,ssh06}, numerical \citep[e.g.][]{nb99,rs01,snb03} and indirect observational \citep[e.g.][]{sfmbb04,cfjsb04,rcbf05,rcbf06,gfsm06,rcsbf08,sfs10} estimates suggest that the numbers we are predicting are reasonable." + We caution here that equation (313) should be considered a lower limit on the actual turbulent velocity since (yi. is unlikely to be smaller. but could be larger. than the Alfvénn speed.," We caution here that equation \ref{eqn:Uprofile}) ) should be considered a lower limit on the actual turbulent velocity since $U_{\rm rms}$ is unlikely to be smaller, but could be larger, than the Alfvénn speed." +In magnetohydrodynamic numerical simulations. it is often larger by a factor of order unity (e.g.Schekochihinetal.2004:Haugen. 2004.,"In magnetohydrodynamic numerical simulations, it is often larger by a factor of order unity \citep[e.g.][]{sctmm04,hbd04}. ." +.. Implicit in the above discussion is the requirement that there be enough turbulent energy for the viscous heating rate mandated by the marginal stability condition(see eq. 143), Implicit in the above discussion is the requirement that there be enough turbulent energy for the viscous heating rate mandated by the marginal stability condition(see eq. \ref{eqn:heating3}) ) + to be maintained., to be maintained. + , +Thus. anv solid annulus is subject to a tensile stress. (he maximum of which occurs at its midline and is equal to Ar). where Ar=rs—rq is the width of the annulus.,"Thus, any solid annulus is subject to a tensile stress, the maximum of which occurs at its midline and is equal to x)^2, where $\Delta x\equiv x_2-x_1$ is the width of the annulus." +" If we linearize the first two of equations (4)) with respect to a state of uniform shear (ug,—0. Oro/O0x= s). and neglect perturbations in the stress tensor. (hen small disturbances are stable if and only if s>—2Q."," If we linearize the first two of equations \ref{eq:motion}) ) with respect to a state of uniform shear $u_0=0$, $\p v_0/\p x=s$ ), and neglect perturbations in the stress tensor, then small disturbances are stable if and only if $s>-2\Omega$." + This is the well-known Ravleigh eriterion for the stability of Couette flow (Chandrasekhar1961)., This is the well-known Rayleigh criterion for the stability of Couette flow \citep{cha61}. +. Equation (4.1)) for the maximum height-integrated tensile stress (Loree per unit length) in a solid annulus can be converted to an equation for the ordinary tensile stress (force per unit area) by approximating the vertical structure of (he ring as that of a homogeneous slab with thickness and densitv p—p/h (note that p is less than the density of the ring particles. by the filling factor): m 2 in which we have inserted parameters appropriate for Saturn.," Equation \ref{eq:sigmax}) ) for the maximum height-integrated tensile stress (force per unit length) in a solid annulus can be converted to an equation for the ordinary tensile stress (force per unit area) by approximating the vertical structure of the ring as that of a homogeneous slab with thickness $h$ and density $\rho=\mu/h$ (note that $\rho$ is less than the density of the ring particles, by the filling factor): = )^2, in which we have inserted parameters appropriate for Saturn." +" The maximum width of a solid annulus with a given tensile strength may be called its ""tidal width.", The maximum width of a solid annulus with a given tensile strength may be called its “tidal width”. + If we identify the tical width with half of the dominant wavelength of 100 km seen in the irregular structure (ie. Ar= 50km) then we require that a frozen assembly of ring particles have a tensile strength or vield stress Z1x10?dvncm, If we identify the tidal width with half of the dominant wavelength of 100 km seen in the irregular structure (i.e. $\Delta r=50\km$ ) then we require that a frozen assembly of ring particles have a tensile strength or yield stress $\gtrsim 1\times 10^5\hbox{ dyn cm}^{-2}$. + The strength. of rine-particle assemblies is. of course. very difficult to estimate.," The strength of ring-particle assemblies is, of course, very difficult to estimate." +" An upper limit. is. the vield. stress of. solid. ice.. which. is. aya,~10*αναcm> at teniperatures"," An upper limit is the yield stress of solid ice, which is $\sigma_{\rm max}\sim 10^7\hbox{ dyn cm}^{-2}$ at temperatures" +by the cube of eis;A0.,by the cube of $c_{disp}/10$. + We seo that the dependence on formation redshift is weak. and that higher mass halos have a progressively largerὃν critical A.," We see that the dependence on formation redshift is weak, and that higher mass halos have a progressively larger critical $\lambda$." + In Fig., In Fig. +e 4. we show the fraction of halos giving rise to luminous disks in the model. assuming a gaussian distribution forIn(A) with mean In(0.05) and dispersion 0.5 (Alo et al.," 4, we show the fraction of halos giving rise to luminous disks in the model, assuming a gaussian distribution for$\ln(\lambda)$ with mean $\ln(0.05)$ and dispersion 0.5 (Mo et al." + 1997)., 1997). +" The solid curve is lor Cais,=10 km +. the dashec curve allows a smooth niass-dependencee of Cai, von 5 to 15 kms 1 as the mass changes from 107 to1047A.."," The solid curve is for $c_{disp}= +10$ km $^{-1}$, the dashed curve allows a smooth mass-dependence of $c_{disp}$ from 5 to 15 km $^{-1}$ as the mass changes from $10^8$ to$10^{12} M_\odot$." + Phe fraction of luminous halos increases [rom at 2.10AL. το at just over 1077AL..., The fraction of luminous halos increases from at $2 \times 10^9 M_\odot$ to at just over $10^{12} M_\odot$. + Dark Dgravitational lenses of high5 mass ~107AL. apparentlv required to explain the missing lens double quasar population {1awkins 1997). are possible as the most massive examples of halos with dark rotationallv-supported clisks.," Dark gravitational lenses of high mass $\sim 10^{12} M_\odot$, apparently required to explain the missing lens double quasar population (Hawkins 1997), are possible as the most massive examples of halos with dark rotationally-supported disks." + ‘These halos always have the possibility to cause splittines of images: he singular density profile assures this. and splittings of up to about + aresce are possible from 101247. halos at 20.5.," These halos always have the possibility to cause splittings of images; the singular density profile assures this, and splittings of up to about 4 arcsec are possible from $10^{12} M_\odot$ halos at $z \sim 0.5$." +" 1n addition to he dark lensing possibility. there are many other interesting consequences of this model: the mass-dependence of the bright fraction will alter the LumiinostE function il will no longer reflect. the uncderlving halo mass function. which may be useful since. mos currently popular galaxy fortnation models over-predict the low-mass population: perhaps most interestingly. there shoulc be no spiral galaxies with total masses below abou 10""AL. (el."," In addition to the dark lensing possibility, there are many other interesting consequences of this model: the mass-dependence of the bright fraction will alter the luminosity function – it will no longer reflect the underlying halo mass function, which may be useful since most currently popular galaxy formation models over-predict the low-mass population; perhaps most interestingly, there should be no spiral galaxies with total masses below about $10^9 M_\odot$ (cf." + compilation by Roberts Llevnes 1994): low-mass or high-spin halos should lead: to short-lived brigh galaxies. allecting the interpretation of the faint blue number counts: luminous galaxies should be found in high-densiE environments.," compilation by Roberts Heynes 1994); low-mass or high-spin halos should lead to short-lived bright galaxies, affecting the interpretation of the faint blue number counts; luminous galaxies should be found in high-density environments." + Phe last two points are explored in the nex two sections., The last two points are explored in the next two sections. + Lt should be noted that the possibilities for dark galaxies are much. lower if non-barvonic dark matter contributes much less than the critical density., It should be noted that the possibilities for dark galaxies are much lower if non-baryonic dark matter contributes much less than the critical density. + In this case. the minimum. spiral mass drops substantially. to around. LOCAL. if 0.2. but the cisk selberavityC cannot be ignorede in this case.," In this case, the minimum spiral mass drops substantially, to around $10^7 M_\odot$ if $\Omega_0=0.2$ , but the disk self-gravity cannot be ignored in this case." + LDGs will not be entirely dark. as it seems impossible to oevent some fragmentation of the initial halo (Tegmark et al.," LDGs will not be entirely dark, as it seems impossible to prevent some fragmentation of the initial halo (Tegmark et al." + 1997: Padoan. Jimenez Jones 1997).," 1997; Padoan, Jimenez Jones 1997)." +" Without ongoing star formation in the disk. the galaxy will rapidly face. woducing a short-livecl bright population of ""disappearing cdwarfs'."," Without ongoing star formation in the disk, the galaxy will rapidly fade, producing a short-lived bright population of `disappearing dwarfs'." + The details of the process are not. crucial for the arguments in this paper. but for illustration we calculate he brightness of a halo of mass 1027AZ.. using the star ormation model of Padoan et al.," The details of the process are not crucial for the arguments in this paper, but for illustration we calculate the brightness of a halo of mass $10^{10} M_\odot$, using the star formation model of Padoan et al." + 1997. with formation redshifts of 0.5 and. 1 (Fig.," 1997, with formation redshifts of 0.5 and 1 (Fig." + 5)., 5). + We also show the colour evolution in Lig., We also show the colour evolution in Fig. + 6., 6. + The assumptions here are star ormation cllicicney (a prediction. of the model. but. the results may be scaled if desired). and an initial metallicity of Z-0.002. Y-0.24.," The assumptions here are star formation efficiency (a prediction of the model, but the results may be scaled if desired), and an initial metallicity of Z=0.002, Y=0.24." + The graphs use he latest. version of our svnthetic stellar population code (.imenez et al., The graphs use the latest version of our synthetic stellar population code (Jimenez et al. + 191, 1997). + These results evidently. have consequences for the number counts of galaxies since the initial bright. phase of LDCs niw account for the population of blue galaxies found at high redshifts (ef Aletcalle ct al LOOT anc references therein)., These results evidently have consequences for the number counts of galaxies since the initial bright phase of LDGs may account for the population of blue galaxies found at high redshifts (cf Metcalfe et al 1997 and references therein). + In the most extreme cases CEvson et al., In the most extreme cases (Tyson et al. + 1986) the observed limiting magnitudes for clark ⋖⋅⊔≱∖⋖⋅≱∖⋜⊔⋅⋖⋅∶∫↙⊽⇉⊥⋅↱≻⊳ Ho26 and Bo» 25.," 1986) the observed limiting magnitudes for dark lenses are: $I > 24.5$, $R > 26$ and $B > 25$ ." + And [for the surface brightness - Sos⋅ ∫⊐⋟↙⇁⇉⋀⋅≤⋗⊔↓⋜↧⋏∙≟⋜⊔⋅≼⋱∖∢⋅≼∙−⋡∐↥⋖," And for the surface brightness $R > 27.9 +\rm\, mag\, arcsec^{-2}$ ." +⋅↓⋅∢⋅⇂∩↓⋅∢⊾⊳⋖⋅∖⇁⋖⋅⊔ al a redshift of 0.5. a LDG has a magnitude below the limits found by CEvson et," Therefore, even at a redshift of 0.5, a LDG has a magnitude below the limits found by (Tyson et" + <10% 2.., $\simlt 10\%$ \ref{spectable}. +" 4? Nyy=(1.50.2) ?. (Nyz1.6«1072 2,sun0l."," $\chi^2$ $\nh = +(1.5\pm0.2) \times 10^{22}$ $^{-2}$ \citep[$\nh \approx 1.6 \times +10^{22}$ $^{-2}$." + The fitted column deusitv for the power-law model. Ny=34!uo«O7 7. ds significantly lareer than the integrated 21 cur Galactic value of 2«1072 cm? averaged over a 0.77« patch of the sky (Dickey&Lockman 1990).," The fitted column density for the power-law model, $\nh = 3.4^{+0.6}_{-0.5} \times 10^{22}$ $^{-2}$, is significantly larger than the integrated 21 cm Galactic value of $2\times 10^{22}$ $^{-2}$ averaged over a $0.\arcdeg7 \times +0.\arcdeg7$ patch of the sky \citep{dic90}." +. The best fitted blackbody model vielded a temperature of &KTpp=O.LL40.03. keV with a fit statistic of Ye=0.9 for 133 degrees of freedom (seo Fig. 3))., The best fitted blackbody model yielded a temperature of $kT_{\rm BB} = 0.44\pm0.03$ keV with a fit statistic of $\chi^2_{\nu} = 0.9$ for 133 degrees of freedom (see Fig. \ref{specfig}) ). + The bolometric huninosity at 7.1 kpe is Lpp(bol=3.7«10° ores +. corresponding to a blackbody area of zL0&100:424 cni? or z0.5% of the NS surface (see Table 3)).," The bolometric luminosity at $7.1$ kpc is $L_{BB}({\rm bol}) = 3.7\times10^{33}$ ergs $^{-1}$, corresponding to a blackbody area of $\approx 1.0 \times 10^{11}\,d_{7.1}^2$ $^2$ or $\approx 0.5\%$ of the NS surface (see Table \ref{modeltable}) )." + The addition of a secoud conrponeut to either spectral model is uncoustraimed., The addition of a second component to either spectral model is unconstrained. + Evideutly the dux has remained steady between both oobservatious aud the oone (Sewardetal.2003) in 2001., Evidently the flux has remained steady between both observations and the one \citep{sew03} in 2001. + Since the spectral fit to the blackbody mo0del inplies that only a small fraction of the NS surface is detected. we also derived an indepeudent upper lanit to the effective blackbody temperature of the eutire NS surtace.," Since the spectral fit to the blackbody model implies that only a small fraction of the NS surface is detected, we also derived an independent upper limit to the effective blackbody temperature of the entire NS surface." + Assuming d=Td kpe. Ng=1.5<107 7. and a radius at infinity of 12 lan. we compared simulated spectra of increasing blackbody temiperature with the data until the predicted spectruu exceeded the observed flix iu the lowest energy bius by 30.," Assuming $d=7.1$ kpc, $N_{\rm H} = 1.5 \times +10^{22}$ $^{-2}$, and a radius at infinity of 12 km, we compared simulated spectra of increasing blackbody temperature with the data until the predicted spectrum exceeded the observed flux in the lowest energy bins by $3\sigma$." + The resulting upper luit is logTS<6.21. which. because of the large distance aud column density. is not constraining of NS cooling theory.," The resulting upper limit is $\log +T^{\infty}_e < 6.24$, which, because of the large distance and column density, is not constraining of NS cooling theory." + Although the blackbodyv is the preferred spectral model. we note that it is uot entirelv consistent with the large pulsed. fraction o the light curve asstuned to be come from a small spot ou the surface of the NS.," Although the blackbody is the preferred spectral model, we note that it is not entirely consistent with the large pulsed fraction of the light curve assumed to be coming from a small spot on the surface of the NS." + Light bending causedby thiestrong eravitational field of the NS ecuerally preveuts he observation of such large modulation as is seen from üfthe aneular cependenceof the cmitted intensity is, Light bending causedby thestrong gravitational field of the NS generally prevents the observation of such large modulation as is seen from ifthe angular dependenceof the emitted intensity is +the presence of the plasma. the term às is the refraction dellection due to the inhomogeneity of the plasma. the term Ay isa correction to the third term.,"the presence of the plasma, the term $\hat{\alpha}_3$ is the refraction deflection due to the inhomogeneity of the plasma, the term $\hat{\alpha}_4$ is a correction to the third term." + We are interested mainly in the effects. described by the terms à. à» and As.," We are interested mainly in the effects, described by the terms $\hat{\alpha}_1$, $\hat{\alpha}_2$ and $\hat{\alpha}_3$." + For the singular isothermal sphere the projected: mass Ad(b) is:, For the singular isothermal sphere the projected mass $M(b)$ is: +Also marked in Figure 5 are intermediate-size objects ~ 5-10 ,Also marked in Figure \ref{fig:cmd} are intermediate-size objects $r_{\rm h}$ $\sim$ 5–10 pc). +"Many of these lie close to the blue color(rh sequence pc).established by the more extended objects, suggesting a close relationship."," Many of these lie close to the blue color sequence established by the more extended objects, suggesting a close relationship." + A revision of the UCD boundary to sizes smaller than ry~ 10 pc may be warranted (we will return to this point , A revision of the UCD boundary to sizes smaller than $r_{\rm h}\sim$ 10 pc may be warranted (we will return to this point later). +We also plot the data for nuclei from a later).sample of early- Virgo galaxies (Cótéetal.2006).., We also plot the data for nuclei from a sample of early-type Virgo galaxies \citep{2006ApJS..165...57C}. +" The color trend for these nuclei tracks that of the UCDs closely, including both the narrow blue locus and the sharp transition to red colors at bright magnitudes."," The color trend for these nuclei tracks that of the UCDs closely, including both the narrow blue locus and the sharp transition to red colors at bright magnitudes." +" This was noticed before (e.g., Evstigneevaetal.2008;Norris&Kannap-pan for bright objects, and we now find that the close 2011))coincidence extends to the new low-luminosity area of parameter space for UCDs."," This was noticed before (e.g., \citealt{2008AJ....136..461E,2011MNRAS.414..739N}) ) for bright objects, and we now find that the close coincidence extends to the new low-luminosity area of parameter space for UCDs." + A general implication is that the UCDs and nuclei have experienced very similar self enrichment processes., A general implication is that the UCDs and nuclei have experienced very similar self enrichment processes. +" A long-standing suggestion also becomes more probable, that UCDs have their origins as nuclei that have since been stripped by tidal forces."," A long-standing suggestion also becomes more probable, that UCDs have their origins as nuclei that have since been stripped by tidal forces." +" The bend in the UCD color distribution could then be due to a transition from dwarf early-type (dE) to giant early-type progenitors (e.g., Norris&Kannappan 2011))."," The bend in the UCD color distribution could then be due to a transition from dwarf early-type (dE) to giant early-type progenitors (e.g., \citealt{2011MNRAS.414..739N}) )." +" Note, though, that apart from one extremely red object that is very large 100 there is no particular tendency for these red objects(~ to pc),be larger than the average UCD."," Note, though, that apart from one extremely red object that is very large $\sim$ 100 pc), there is no particular tendency for these red objects to be larger than the average UCD." + A narrow color spread for the blue GCs would normally imply that they are a coeval population., A narrow color spread for the blue GCs would normally imply that they are a coeval population. +" Surprisingly, the spectroscopic age estimates for a very limited subset of these M87 UCDs and dwarf nuclei (based on Lick indices; Paudeletal.2010, suggest that both young and old objects in both2011)) categories conform to the same color-magnitude trends (Figure 5))."," Surprisingly, the spectroscopic age estimates for a very limited subset of these M87 UCDs and dwarf nuclei (based on Lick indices; \citealt{2010ApJ...724L..64P,2011MNRAS.413.1764P}) ) suggest that both young and old objects in both categories conform to the same color-magnitude trends (Figure \ref{fig:cmd}) )." + It is a puzzling coincidence that young and old nuclei can have the same colors at a given luminosity., It is a puzzling coincidence that young and old nuclei can have the same colors at a given luminosity. +" Accurate age determinations are notoriously difficult and the sample of objects with age estimates is small, but this intriguing result should motivate extending age studies to larger samples of both UCDs and dwarf nuclei."," Accurate age determinations are notoriously difficult and the sample of objects with age estimates is small, but this intriguing result should motivate extending age studies to larger samples of both UCDs and dwarf nuclei." +" Nonetheless, the color offset between the UCDs and the blue GCs underscores a distinction between these two populations and again argues against a UCD origin from star clusters, or mergers of star clusters, that were analogous to the GCs that survive today."," Nonetheless, the color offset between the UCDs and the blue GCs underscores a distinction between these two populations and again argues against a UCD origin from star clusters, or mergers of star clusters, that were analogous to the GCs that survive today." + In the right panel of Figure 5 we compare the size-luminosity parameter space for the same objects that were plotted in the left panel., In the right panel of Figure \ref{fig:cmd} we compare the size-luminosity parameter space for the same objects that were plotted in the left panel. +" Overall, the dE nuclei are systematically brighter at a given size than the UCDs."," Overall, the dE nuclei are systematically brighter at a given size than the UCDs." +" If the brighter nuclei are found to be young, this luminosity offset might be simply explained as a result of fading (by 2 mags)."," If the brighter nuclei are found to be young, this luminosity offset might be simply explained as a result of fading (by $\sim$ 2 mags)." +" This would imply that some of the compact “GCs” are really “UCDs” in the sense that they are stripped nuclei (e.g., Freeman 1993))."," This would imply that some of the compact “GCs” are really “UCDs” in the sense that they are stripped nuclei (e.g., \citealt{1993ASPC...48..608F}) )." +" An alternative way to view the data is that the UCDs are larger than nuclei at a given luminosity, which could then be interpreted as post-stripping expansion (e.g., Evstigneevaetal. "," An alternative way to view the data is that the UCDs are larger than nuclei at a given luminosity, which could then be interpreted as post-stripping expansion (e.g., \citealt{2008AJ....136..461E}) )." +"It may be that the nuclei both expand and fade after 2008)).stripping, although one might then"," It may be that the nuclei both expand and fade after stripping, although one might then" +stars.,stars. + In the case of many low-mass X-ray binaries. it is often not possible to directly observe the secondary star optically since the accretion disc dominates the observed Dux.," In the case of many low-mass X-ray binaries, it is often not possible to directly observe the secondary star optically since the accretion disc dominates the observed flux." + Hence. reliable cvnamical mass estimates are not available for many of these svstenis.," Hence, reliable dynamical mass estimates are not available for many of these systems." + Cygnus X-2. which is one of the brightest. low-mass X-rav binaries known. is one of the rare cases among the persistent low-mass X-ray. binaries where the secondary star is casily observed.," Cygnus X-2, which is one of the brightest low-mass X-ray binaries known, is one of the rare cases among the persistent low-mass X-ray binaries where the secondary star is easily observed." + (νο X-2 is known to contain a neutron star because Type E X-ray bursts have been observed (Ixahn Crindlav 1984: Ixuulkers. van der Ixlis. van Paraclijs 1995: Wijnands et 11997: Smale 1998).," Cyg X-2 is known to contain a neutron star because Type I X-ray bursts have been observed (Kahn Grindlay 1984; Kuulkers, van der Klis, van Paradijs 1995; Wijnands et 1997; Smale 1998)." + The neutron star is believed to be accreting mass from its companion al a near Eddington rate (see Smale 1908)., The neutron star is believed to be accreting mass from its companion at a near Eddington rate (see Smale 1998). + V1341 ονο. its optical counterpart (Giacconi et 11967). is relatively bright. so reasonably precise spectroscopic and photometric observations can be obtained.," V1341 Cygni, its optical counterpart (Giacconi et 1967), is relatively bright, so reasonably precise spectroscopic and photometric observations can be obtained." + The orbital period. of 2=Ü.844 days was determined by Cowley et (1979). and bv Crampton Cowley (1980) from the observed. radial velocity. variations of the companion star., The orbital period of $P=9.844$ days was determined by Cowley et (1979) and by Crampton Cowley (1980) from the observed radial velocity variations of the companion star. + Cowley et. ((1979) also reported a spectral type for the companion star in the range of AD to F2 (they attributed the change in the observed spectral type to X-ray. heating of the secondary)., Cowley et (1979) also reported a spectral type for the companion star in the range of A5 to F2 (they attributed the change in the observed spectral type to X-ray heating of the secondary). + Casares. Charles. Ixuulkers (1998. hereafter CCIX98) have recently refined the measurements of the orbital parameters.," Casares, Charles, Kuulkers (1998, hereafter CCK98) have recently refined the measurements of the orbital parameters." +" They determined. a period of P?=9.8444+0.0003 days. an optical mass function of where M, is the mass of the neutron star. AZ. is the mass of the companion star. A is the semi-amplitude of the companions radial velocity curve. and where q=MM,0.34+ 0.04."," They determined a period of $P=9.8444\pm 0.0003$ days, an optical mass function of where $M_x$ is the mass of the neutron star, $M_c$ is the mass of the companion star, $K_c$ is the semi-amplitude of the companion's radial velocity curve, and where $q=M_c/M_x=0.34\pm 0.04$ ." + C'CISO8S also determined a spectral type for the companion star of ΑΘΗ and. reported no variation of the spectral type with orbital phase. in contradiction to Cowley et ((1979).," CCK98 also determined a spectral type for the companion star of A9III and reported no variation of the spectral type with orbital phase, in contradiction to Cowley et (1979)." + One needs a measurement of the orbital inclination in order to derive mass measurements from the orbital elements ofCOWS., One needs a measurement of the orbital inclination in order to derive mass measurements from the orbital elements of CCK98. +" Models of the optical/LH light curves are the most ""direct"" method to determine the inclination AAvni Baheall 1975: Avni LOTS)", Models of the optical/IR light curves are the most “direct” method to determine the inclination Avni Bahcall 1975; Avni 1978). + We have gathered C. D. and V photometric data of ονο N-2 from the literature. with the goal of obtaining the mean light curve and. deriving the inclination.," We have gathered $U$, $B$, and $V$ photometric data of Cyg X-2 from the literature with the goal of obtaining the mean light curve and deriving the inclination." + We demonstrate. that the derived: mean orbital light curves show the familiar signature of ellipsoidal variations., We demonstrate that the derived mean orbital light curves show the familiar signature of ellipsoidal variations. + Ehe light curves are then modeled to place limits on the inclination., The light curves are then modeled to place limits on the inclination. + We also show that the photometric period is consistent. with the spectroscopic orbital period., We also show that the photometric period is consistent with the spectroscopic orbital period. + We describe below the analysis of the tabulated photometric data. period. determination. and the cllipsoical mocelling.," We describe below the analysis of the tabulated photometric data, period determination, and the ellipsoidal modelling." + We conclude with a discussion of the mass of the neutron star and the distance to the source., We conclude with a discussion of the mass of the neutron star and the distance to the source. + We used. all the photoelectric ancl photographic data as tabulated in the literature for our analysis., We used all the photoelectric and photographic data as tabulated in the literature for our analysis. + These are photoclectric CU. D. and V) data obtained between 1967 and 1984 (Ixristian et 140967: Peimbert et 11968: Miumford 1970: Chevalier. Bonazzola Ilovaisky 1976: Lyutyi SSunvaev 1976: Lovaiskv ct 11978: Wilvachkoy 1978: Jeskin οἱ 11979: Goranskii LLyutyi 1988). and photographie (2 and V) data obtained in 1974 and 1975 (Basko et 11976).," These are photoelectric $U$, $B$, and $V$ ) data obtained between 1967 and 1984 (Kristian et 1967; Peimbert et 1968; Mumford 1970; Chevalier, Bonazzola Ilovaisky 1976; Lyutyi Sunyaev 1976; Ilovaisky et 1978; Kilyachkov 1978; Beskin et 1979; Goranskii Lyutyi 1988), and photographic $B$ and $V$ ) data obtained in 1974 and 1975 (Basko et 1976)." + The uncertainties of the photoelectrie data are typically between 0.02.0.03 magnitudes inthe V and D band. and 0.050.08 magnitudes in the (C band. while the photographic data have typical uncertainties between 0.080.15 magnitudes (see Goranskii LLvutyi 1988)," The uncertainties of the photoelectric data are typically between 0.02–0.03 magnitudes in the $V$ and $B$ band, and 0.05–0.08 magnitudes in the $U$ band, while the photographic data have typical uncertainties between 0.08–0.15 magnitudes (see Goranskii Lyutyi 1988)." + Close D. and V photographicn magnitudesIn in time with £ and Y. photoclectric magnitudes show their measurements to be consistent with cach other: we therefore combined them., Close $B$ and $V$ photographic magnitudes in time with $B$ and $V$ photoelectric magnitudes show their measurements to be consistent with each other; we therefore combined them. + Phe mean C. D and V band. magnitudes (with the rms given in brackets) of €ve X-2 from our sample are 14.95 (0.31). 15.16 (0.20). and 14.70 (0.21). respectively.," The mean $U$, $B$ and $V$ band magnitudes (with the rms given in brackets) of Cyg X-2 from our sample are 14.95 (0.31), 15.16 (0.20), and 14.70 (0.21), respectively." + Although several periodicities had been reported: between ~0.25 and ~14 davs before 1979. none of them were consistent with the orbital period as determined from the spectroscopic observations by Cowley et ((1979). and Crampton CCowlev (1980) (sec also CCIxX98).," Although several periodicities had been reported between $\sim$ 0.25 and $\sim$ 14 days before 1979, none of them were consistent with the orbital period as determined from the spectroscopic observations by Cowley et (1979) and Crampton Cowley (1980) (see also CCK98)." + After 1979 it was shown that. folding the photoclectric and photographie cata on the spectroscopic period. gave an cllipsoical dedlouble-peaked) shaped Light curve (Cowley et 11979: Goranskii LLyutyi 1988)., After 1979 it was shown that folding the photoelectric and photographic data on the spectroscopic period gave an ellipsoidal double-peaked) shaped light curve (Cowley et 1979; Goranskii Lyutyi 1988). + Still up to today. no period analysis of the CveNN-2 light curves has given independent. proof of the orbital variations.," Still up to today, no period analysis of the X-2 light curves has given independent proof of the orbital variations." + We therefore subjected all the combined C (469 points). D (966 points). anc V. (572 points) band. data separately to a period analysis using various techniques (e.g... Lomb-Scargle ancl phase dispersion. minimization).," We therefore subjected all the combined $U$ (469 points), $B$ (966 points), and $V$ (572 points) band data separately to a period analysis using various techniques (e.g., Lomb-Scargle and phase dispersion minimization)." + We searched the data for periodicities between 0.1 and. 1000 claws., We searched the data for periodicities between 0.1 and 1000 days. + Plots of the Lomb-Searele periodograms can be found in the upper panels of Figure 1.., Plots of the Lomb-Scargle periodograms can be found in the upper panels of Figure \ref{scargfig}. + In the figure we also give the 3e confidence level. above which we regard signals as significant.," In the figure we also give the $\sigma$ confidence level, above which we regard signals as significant." + These confidence levels were determined from a cumulative probability. distribution appropriate for our three data sets (see Homer et 11996)., These confidence levels were determined from a cumulative probability distribution appropriate for our three data sets (see Homer et 1996). + Phe most significant. peak found in both the B and V band data were at à period of 4.92 days. whereas no significant peak near this period was found in the U band data.," The most significant peak found in both the $B$ and $V$ band data were at a period of $\sim$ 4.92 days, whereas no significant peak near this period was found in the U band data." + In the lower panels of ligure 1 we give the power spectra of the corresponding window functions in the three passbands., In the lower panels of Figure \ref{scargfig} we give the power spectra of the corresponding window functions in the three passbands. + Clearly. the most," Clearly, the most" + , +it wmatches the modeled distribution. we obtained a best-fit distance for the cluster.,"it matches the modeled distribution, we obtained a best-fit distance for the cluster." + We fud tιο data to be consistent with a distance to NGC 2261 of 913 pe., We find the data to be consistent with a distance to NGC 2264 of $913$ pc. +" Quantitative tests of our ajalvsis reveas uncertainties of LO anc 110 pe due to sailing aud svstemiatie effects. respectively,"," Quantitative tests of our analysis reveals uncertainties of 40 and 110 pc due to sampling and systematic effects, respectively." + This distance cSnate suecosts a revised age for the cluster of ~1.5 4vis. althoug1 inore detailed investigations of the full cluser moeniboersip are required to draw stroug conclisions.," This distance estimate suggests a revised age for the cluster of $\sim$ 1.5 Myrs, although more detailed investigations of the full cluster membership are required to draw strong conclusions." + The authors wish o thauk Steve Strou for a prompt and helpful referee report that muproved the analysis presented here. aud Russel White aud Jeff Burchfield for providing IDL code that formed the basis of our cross correlation pipeline.," The authors wish to thank Steve Strom for a prompt and helpful referee report that improved the analysis presented here, and Russel White and Jeff Burchfield for providing IDL code that formed the basis of our cross correlation pipeline." + EJB acknowledges the support of the SAO Suuunuer Πιο Program. made possible by a erant from the NSF.," EJB acknowledges the support of the SAO Summer Intern Program, made possible by a grant from the NSF." + NASA support was provided to Is. Covey for this work through the Spitzer Space Telescope Fellowship Program. through a contract issued by the Jet Propulsion Laboratory. California Institute of Technology under a contract with NASA.," NASA support was provided to K. Covey for this work through the Spitzer Space Telescope Fellowship Program, through a contract issued by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA." +Our goal in this paper is to cxaunine how the variations of supernova conditions as well as of nuclear data inputs iufluence the global trend of the zp-process.,Our goal in this paper is to examine how the variations of supernova conditions as well as of nuclear data inputs influence the global trend of the $\nu$ p-process. + The paper is organized as follows., The paper is organized as follows. + In 2. a basic picture of the mvp-process is outlined.," In 2, a basic picture of the $\nu$ p-process is outlined." + A senmi-analvtie neutrino-drivenu wind model and au up-to-date reaction network code are described. which are used in this study 3).," A semi-analytic neutrino-driven wind model and an up-to-date reaction network code are described, which are used in this study 3)." + We take the wind-termination radius (or temperature). the neutrino ΓΕ the neutrou-star mass. and the electron fraction as the key parameters of supernova |).," We take the wind-termination radius (or temperature), the neutrino luminosity, the neutron-star mass, and the electron fraction as the key parameters of supernova conditions 4)." + Iu previous studies (Frohlichetal.conditions2006a.b:varanictersPruetetal.2006:Wanajo 2006).. some of these were varied to test their scusitivities. but oulv for luted cases;," In previous studies \citep{Froe2006, Froe2006b, Prue2006, Wana2006}, some of these parameters were varied to test their sensitivities, but only for limited cases." +" Tn particular. the effect of wiud ermüinatiou has uot been discussed at all in previous studies,"," In particular, the effect of wind termination has not been discussed at all in previous studies." +" As the kev nuclear reactious. we take triple-n. ""Beto.5)H C. Bea. p?C (all relevant to the breakout roni the pp-chain region). aud the (ηςp) reactions on PONT YT and °' Ge 5)."," As the key nuclear reactions, we take $\alpha$, $^7$ $(\alpha, \gamma)^{11}$ C, $^{10}$ $(\alpha, p)^{13}$ C (all relevant to the breakout from the pp-chain region), and the $(n, p)$ reactions on $^{56}$ Ni, $^{60}$ Zn, and $^{64}$ Ge 5)." + Sensitivities of the masses of he nuclei alone the rp-process path are also discussed., Sensitivities of the masses of the nuclei along the$\nu$ p-process path are also discussed. + We then discuss the possible role of the rp-process as the astroplivsical origin of the p-uuclei 6)., We then discuss the possible role of the $\nu$ p-process as the astrophysical origin of the p-nuclei 6). + A sunmuuv of our results follows in 7., A summary of our results follows in 7. +" The ""rmp-process"" was first identified in Frohlich (2006a).. aud the termi: was introduced by -4(2006b) and is svnonviuous with the rp-process” in the subsequent works (PruetetWanajo 2006)."," The $\nu$ p-process” was first identified in \citet{Froe2006}, and the term was introduced by \citet{Froe2006b} and is synonymous with the ``neutrino-induced rp-process” in the subsequent works \citep{Prue2006, Wana2006}." +. Thisis a similar process to the rp-process first proposed by Wallace&Woosley (1981)., This is a similar process to the rp-process first proposed by \citet{Wall1981}. +. The rp-process is. however. essentially a new uucleosvuthetic process exhibiting a number of different aspects compared to the classical rp-process," The $\nu$ p-process is, however, essentially a new nucleosynthetic process exhibiting a number of different aspects compared to the classical rp-process." + The mp- starts with the seed uncleus 7? Ni 9!Ge. the first J! -waitine-point uncles iu the classical rp-process patlovay). assembled from free nucleons in nuclear quasi-equilibrimm (QSE) during the initial hieh teiuperature phase (Z5>LH: where T5 is the temperature im units of 10? K).," The $\nu$ p-process starts with the seed nucleus $^{56}$ Ni $^{64}$ Ge, the first $\beta^+$ -waiting-point nucleus in the classical rp-process pathway), assembled from free nucleons in nuclear quasi-equilibrium (QSE) during the initial high temperature phase $T_9 > 4$; where $T_9$ is the temperature in units of $10^9$ K)." + The rp-process is therefore a process. which needs no pre-existing seeds.," The $\nu$ p-process is therefore a process, which needs no pre-existing seeds." + When the temperature decreases below Z5=3 (clefined as the onset of à p-xocess in this study) and QSE freezes out. the p-XrOcess starts.," When the temperature decreases below $T_9 = 3$ (defined as the onset of a $\nu$ p-process in this study) and QSE freezes out, the $\nu$ p-process starts." + Neutrino capture on free protons. p(m.c!)» in a protou-crich ucutrino-driven wind gives rise to a inv amount of free neutrons (10H10+? in nass fraction).," Neutrino capture on free protons, $p(\bar{\nu}_\mathrm{e}, e^+)n$, in a proton-rich neutrino-driven wind gives rise to a tiny amount of free neutrons $10^{-11}-10^{-12}$ in mass fraction)." + These neutrous iuuuediatelv duce the exchange reaction. (69.p). and in part radiative neutron capture. (0.5). on the seed nucleus ONT and subsequeut reavier nuclei with decav timescales of a few ius. well low the expansion timescale of the wind aud well below he 3!-decay lifetimes of these πιά.," These neutrons immediately induce the exchange reaction, $(n, p)$, and in part radiative neutron capture, $(n, \gamma)$, on the seed nucleus $^{56}$ Ni and subsequent heavier nuclei with decay timescales of a few ms, well below the expansion timescale of the wind and well below the $\beta^+$ -decay lifetimes of these nuclei." + The unclear flow xoceeds with combination of radiative proton captures. (p.5). and neutron captures. the latter replacing the role ofJ! -decavs iu the classical rp-process.," The nuclear flow proceeds with combination of radiative proton captures, $(p, \gamma)$, and neutron captures, the latter replacing the role of $\beta^+$ -decays in the classical rp-process." + A laree muuber of free protons relative to that of PONT at To=3. which allows for neutron capture on the seed uuclei. is required to initiate the rp-process.," A large number of free protons relative to that of $^{56}$ Ni at $T_9 = +3$, which allows for neutron capture on the seed nuclei, is required to initiate the $\nu$ p-process." + Ilieh eutropy aud short expansion timescale of the ejecta make the triple-a process. bridging from Leht C4 12) to heavy (Ac 12) nuclei less effective and help to leave a large number of free protons at the onset of the rp-process.," High entropy and short expansion timescale of the ejecta make the $\alpha$ process, bridging from light $A < 12$ ) to heavy $A \ge 12$ ) nuclei, less effective and help to leave a large number of free protons at the onset of the $\nu$ p-process." + It should be noted. however. that proton-rich matter freezing out frou nuclear statistical equilibriuu (NSE) mainly consists of Nj and (Seitenzahletal.2008).," It should be noted, however, that proton-rich matter freezing out from nuclear statistical equilibrium (NSE) mainly consists of $^{56}$ Ni and \citep{Seit2008}." +. This is a fundamental difference from a (iioderatelv) neutron-rich NSE. where ιο free neutrons exist at freezeout.," This is a fundamental difference from a (moderately) neutron-rich NSE, where no free neutrons exist at freezeout." + This makes the requirelcuts for cutropy and expansion timescale less crucial. compared to the case of r-process. allowing for he vp-process taking place with typical wind conditions (Frohlichetal.2006a:Pruct2006:Wanajo2006).," This makes the requirements for entropy and expansion timescale less crucial, compared to the case of r-process, allowing for the $\nu$ p-process taking place with typical wind conditions \citep{Froe2006, Prue2006, Wana2006}." +. Uulike the r-process. the rp-process is not terminated x the exhaustion offree protons. but by the teniperature decrease below Fo=1.5 (defined as the cud of a mp- xocess). Where proton capture slows due to the Coulomb xuYicr.," Unlike the r-process, the $\nu$ p-process is not terminated by the exhaustion of free protons, but by the temperature decrease below $T_9 += 1.5$ (defined as the end of a $\nu$ p-process), where proton capture slows due to the Coulomb barrier." + The eud of mp-processing is thus a proton-rich freezeout., The end of $\nu$ p-processing is thus a proton-rich freezeout. +" For this reason. the protou-to-sced ratio. V/A (the umber per uucleou for free protous divided that for nuclei with Z>2) at Tyo=3 doces not jecessary serve as a ακομα]. euide for the strength of he wp-process as the neutrou-to-seed ratios are in the case of the r-process,"," For this reason, the proton-to-seed ratio, $Y_\mathrm{p}/Y_\mathrm{h}$ (the number per nucleon for free protons divided by that for nuclei with $Z > 2$ ) at $T_9 = 3$ does not necessary serve as a useful guide for the strength of the $\nu$ p-process as the neutron-to-seed ratios are in the case of the r-process." + Rather. the uunuber ratio of free jeutrons created bv pa.6!ja (for Tyx3) relative to he seed nuclei (at 75=3). Ay. can be a useful (but still crude) measure for the 7p-process as proposed. by Practettunnediatehal.(2006).," Rather, the number ratio of free neutrons created by $p(\bar{\nu}_\mathrm{e}, e^+)n$ (for $T_9 \le 3$ ) relative to the seed nuclei (at $T_9 = 3$ ), $\Delta_\mathrm{n}$, can be a useful (but still crude) measure for the $\nu$ p-process as proposed by \citet{Prue2006}." +.. Note that cach neutron capture by (n.p) is followed by one or two radiative proton captures. increasing the atomic masses by one or two units.," Note that each neutron capture by $(n, p)$ is immediately followed by one or two radiative proton captures, increasing the atomic masses by one or two units." + Similar to eq. (, Similar to eq. ( +"2) in Pruetetal.(2006)... we define whereY,ι (equal| to the mass fraction of free protons. 1 Xu) and 1jh ave the values at Z5=3.","2) in \citet{Prue2006}, we define where$Y_\mathrm{p}$ (equal to the mass fraction of free protons, $X_\mathrm{p}$ ) and $Y_\mathrm{h}$ are the values at $T_9 = 3$." +" The uet iuuber of pv captured per free proton for Ty3:23. n,. is defined as where A, ds the rate for ptsc! ya."," The net number of $\bar{\nu}_\mathrm{e}$ captured per free proton for $T_9 +\le 3$, $n_{\bar{\nu}_\mathrm{e}}$, is defined as where $\lambda_{\bar{\nu}_\mathrm{e}}$ is the rate for $p(\bar{\nu}_\mathrm{e}, e^+)n$ ." + The sed. a double nage nucleus ?9Nio reniadns the most abundant heavy micleus throughout the rp-process.," The seed, a double magic nucleus $^{56}$ Ni, remains the most abundant heavy nucleus throughout the $\nu$ p-process." + Therefore. oulv a Yactiou of Ni is consumed for the production of heavier iuclei.," Therefore, only a fraction of $^{56}$ Ni is consumed for the production of heavier nuclei." +" For this reason. A,~10 is enough for the xoduction of nuclei with A~100110. as we will see in the subsequent sections."," For this reason, $\Delta_n \sim +10$ is enough for the production of nuclei with $A \sim 100-110$, as we will see in the subsequent sections." + The vp-process flow passes through the even-eveu Πιο up to Z=N~LO aud gradually deviates toward he Z«NN region.," The $\nu$ p-process flow passes through the even-even nuclei up to $Z = +N \sim 40$ and gradually deviates toward the $Z < N$ region." + As the flow proceeds toward higher Z inclei: and as the temperature decreases. (9.5) compotes with (9. p). owing to the latter having a Coulomb barrier in its exit channel.," As the flow proceeds toward higher $Z$ nuclei, and as the temperature decreases, $(n, \gamma)$ competes with $(n, p)$ , owing to the latter having a Coulomb barrier in its exit channel." +" When A, is laree cuough. the How eventually approaches the -stability line. aud even crosses iuto the neutrounaich region."," When $\Delta_\mathrm{n}$ is large enough, the flow eventually approaches the $\beta$ -stability line, and even crosses into the neutron-rich region." +" The latter happens when the net ΠΙΟ: of 7. captured per free proton after he zp-process. defined as is nof uesligible coupared to v,.."," The latter happens when the net number of $\bar{\nu}_\mathrm{e}$ captured per free proton after the $\nu$ p-process, defined as is not negligible compared to $n_{\bar{\nu}_\mathrm{e}}$ ." + The eud point of the rp-process ds thus 1w the supernova denies. which cuters into Eq.(," The end point of the $\nu$p-process is thus determined by the supernova dynamics, which enters into Eq. (" +3) determinedratherthrough Apxà7 (i is the radius fro the center). thanby the nature of unclear plivsics as iu case of the classical rp-process.,"3) through $\lambda_{\bar{\nu}_\mathrm{e}} \propto r^{-2}$ $r$ is the radius from the center), rather than by the nature of nuclear physics as in case of the classical rp-process." +acdelitional data from the Westerbork array and thus provides a second [requeney at which the outer lobes were detected.,additional data from the Westerbork array and thus provides a second frequency at which the outer lobes were detected. + Theoretical modelling in Section 5 adds further support to these observations., Theoretical modelling in Section 5 adds further support to these observations. + We note that we cannot categorically rule out the presence of hotspots in the middle lobes sonic BCR objects have recessed hotspots. ancl structures of sizes comparable with the resolution limit have been detected in other objects (c.g. Jevaktumar Saikia 2000) — but. with no firm evidence to the contrary. we assume that they are not present in the middle or outer lobes of D0925|420.," We note that we cannot categorically rule out the presence of hotspots in the middle lobes – some 3CR objects have recessed hotspots, and structures of sizes comparable with the resolution limit have been detected in other objects (e.g. Jeyakumar Saikia 2000) – but, with no firm evidence to the contrary, we assume that they are not present in the middle or outer lobes of B0925+420." + The middle and inner lobes of D0925|042 were also detected in the linear polarisation. (LP) images mace from the 2001 VLA data in D array., The middle and inner lobes of B0925+042 were also detected in the linear polarisation (LP) images made from the 2001 VLA data in B array. + We do not have polarisation calibration available for the FIRST cata and so cannot extend this analysis to the outer lobes., We do not have polarisation calibration available for the FIRST data and so cannot extend this analysis to the outer lobes. + The LP [ux density ab 4.9- and δι] was low and/or the structure partially resolved out but the structure is clear at 1.4. Gllz and. where structure was visible. the fractional polarisation (FP) did not appear to vary significantly with frequeney.," The LP flux density at 4.9- and 8.4-GHz was low and/or the structure partially resolved out but the structure is clear at 1.4 GHz and, where structure was visible, the fractional polarisation (FP) did not appear to vary significantly with frequency." + A rotation measure (RAL) image was created. using all three frequencies.," A rotation measure (RM) image was created, using all three frequencies." + The lowest possible RAL values. were in the range LO15 27. which is consistent with the Galactic medium being the only Faraday. screen between us and the source: such a conclusion was also reached. lor DIS34|620 (Schoenmakers et al.," The lowest possible RM values were in the range 10–15 $^{-2}$, which is consistent with the Galactic medium being the only Faraday screen between us and the source; such a conclusion was also reached for B1834+620 (Schoenmakers et al." + 2000b) and any intrinsic contribution to the RM in 41453|3308 was deemed to be small (sonar et al., 2000b) and any intrinsic contribution to the RM in J1453+3308 was deemed to be small (Konar et al. + 2006)., 2006). + We show the 1.4-CLlz FP image in Fig. 3:, We show the 1.4-GHz FP image in Fig. \ref{fp}; + electric Ποιά vectors are. over-plotted. ancl include the correction (28) due to Faraday rotation., electric field vectors are over-plotted and include the correction $28^{\circ}$ ) due to Faraday rotation. + The middle lobes are clearly polarised to2054... higher in the southern lobe and towards the edges: such a FP is comparable with that measured for 1453|3308 (Ixonar et al.," The middle lobes are clearly polarised to, higher in the southern lobe and towards the edges; such a FP is comparable with that measured for J1453+3308 (Konar et al." + 2006)., 2006). + The core and/or inner lobes of 00055|480 are weakly polarised., The core and/or inner lobes of B0925+480 are weakly polarised. + Ehe. direction. of the electric. field vectors appears to change between the two pairs of lobes at the centre. the magnetic field. is apparently. aligned quasi-perpendicularlv to the position angle of the racio galaxy and direction of jet motion.," The direction of the electric field vectors appears to change between the two pairs of lobes – at the centre, the magnetic field is apparently aligned quasi-perpendicularly to the position angle of the radio galaxy and direction of jet motion." + Phe magnetic field in the middle lobes has become aligned. comparably with the radio galaxy., The magnetic field in the middle lobes has become aligned comparably with the radio galaxy. + We note that this elfect in the core/inner lobes is ambiguous since they are not Lully resolved and we may be looking at the combined. effects of an unpolarised. core ancl polarised. inner lobes., We note that this effect in the core/inner lobes is ambiguous since they are not fully resolved and we may be looking at the combined effects of an unpolarised core and polarised inner lobes. + This structure of the magnetic field in BO925|480 seems less complex than in J1453|3308.," This structure of the magnetic field in B0925+480 seems less complex than in J1453+3308," +In obtaining our theoretical estimate of (he scattered disk population. we use (he current observational estimate of the JFC population. we assume a value of (he ratio of dormant lo active comets. and we use the current estimate of JFC dvnamieal lifetimes.,"In obtaining our theoretical estimate of the scattered disk population, we use the current observational estimate of the JFC population, we assume a value of the ratio of dormant to active comets, and we use the current estimate of JFC dynamical lifetimes." + We have used conservative assumptions for the observational estimate and the ratio of dormant to aclive comets: any revisions to either of these factors would cause the theoretical estimate {ο increase. not decrease. thus worsening the discrepancy.," We have used conservative assumptions for the observational estimate and the ratio of dormant to active comets; any revisions to either of these factors would cause the theoretical estimate to increase, not decrease, thus worsening the discrepancy." + The dvnanmical lifetime estimate is based on numerical modeling and its error is undetermined. so it is unclear if this would increase or decrease the discrepancy. but the estimate would need to be too short by an order of magnitude or more to erase the gap between our theoretical prediction for the scattered disk and the current observations.," The dynamical lifetime estimate is based on numerical modeling and its error is undetermined, so it is unclear if this would increase or decrease the discrepancy, but the estimate would need to be too short by an order of magnitude or more to erase the gap between our theoretical prediction for the scattered disk and the current observations." + Therefore. other explanations for the discrepancy. nist be sought.," Therefore, other explanations for the discrepancy must be sought." + A source of uncertainty that might contribute to the cliserepaney is the conversion of magnitude (o size when comparing population estimates., A source of uncertainty that might contribute to the discrepancy is the conversion of magnitude to size when comparing population estimates. + Doing (his requires an assumption about the albedos of 5DOs., Doing this requires an assumption about the albedos of SDOs. + The standard practice has been (o assume an average albedo of 0.04., The standard practice has been to assume an average albedo of 0.04. + This value is based on the measured albedos of many short ancl long period comets (?).. and it was adopted here wherever a conversion between magnitude and size was required.," This value is based on the measured albedos of many short and long period comets \citep{lamy04}, and it was adopted here wherever a conversion between magnitude and size was required." + llowever. this albedo might not apply uniformly to CIXBOs and 5DOs: ? report on the wide range of albedos measured for KWBOs and suggest that 0.1 would be a more reasonable assumption than (he canonical 0.04.," However, this albedo might not apply uniformly to CKBOs and SDOs; \citet{grundy05} report on the wide range of albedos measured for KBOs and suggest that 0.1 would be a more reasonable assumption than the canonical 0.04." + ? similarly report a wide spread of albedos lor KBOs and Centaurs., \citet{stansberry08} similarly report a wide spread of albedos for KBOs and Centaurs. + They also report that larger objects have a tendeney. toward higher albedos. and that there are hints of a trend amongst the Centaurs for objects with smaller perihelia to have lower albedos (although these are still mostly higher than 0.04).," They also report that larger objects have a tendency toward higher albedos, and that there are hints of a trend amongst the Centaurs for objects with smaller perihelia to have lower albedos (although these are still mostly higher than 0.04)." + If these higher albedos were used to convert between magnitude and sizes. our definition ol JFC-sized SDOs would be shifted toward brighter magnitudes.," If these higher albedos were used to convert between magnitude and sizes, our definition of JFC-sized SDOs would be shifted toward brighter magnitudes." + In Fig. 6..," In Fig. \ref{f:size_dist}," +" the ""theoretical estimate"" would likewise shift to brighter magnitudes.", the “theoretical estimate” would likewise shift to brighter magnitudes. + This increases the range of magnitudes, This increases the range of magnitudes +Canuna-Rav Bursts (CRB) were discovered in 1969 (INIebesadel 1973) by the Vela satellites. deploved by USA to verify the compliance of USSR to the unclear test ban treaty.,"Gamma-Ray Bursts (GRB) were discovered in 1969 (Klebesadel 1973) by the Vela satellites, deployed by USA to verify the compliance of USSR to the nuclear test ban treaty." + In the following 28 vears thousauds of eveuts have been observed by several satellites. leading to a good characterization of the global properties of this phenomenon.," In the following 28 years thousands of events have been observed by several satellites, leading to a good characterization of the global properties of this phenomenon." + A big step in this area was achieved with BATSE (Fishman 1991) The isotropical distribution of the eveuts iu the sky (Fishman Moegau 1995) was sugeestiveOO of an extragalactic origin. but a direct measurement of the distance in a single object was not available.," A big step in this area was achieved with BATSE (Fishman 1994) The isotropical distribution of the events in the sky (Fishman Meegan 1995) was suggestive of an extragalactic origin, but a direct measurement of the distance in a single object was not available." + What was lacking was a position. where theGrail of CRB scicutists. ic. thecounterpart. could have been searched for at all wavelenghts with more chances to catch it.," What was lacking was a position, where the of GRB scientists, i.e. the, could have been searched for at all wavelenghts with more chances to catch it." + This was achieved in 1996. with observations of CRB by BeppoSAX.," This was achieved in 1996, with observations of GRB by BeppoSAX." + Before BeppoSAX (Piro 1995. Boclla 1999) CRB astronomy has proceeded on a statistical approach aud the oulv information gathered was lianited to the teus of seconds of the CRB: the subsequent evolution was completely unknown.," Before BeppoSAX (Piro 1995, Boella 1999) GRB astronomy has proceeded on a statistical approach and the only information gathered was limited to the tens of seconds of the GRB: the subsequent evolution was completely unknown." + The operations for a prompt follow up of GRBs became operative ou December 1996.," The operations for a prompt follow up of GRBs became operative on December 1996," +applied by means of the 100 ancl 240 yam DIRBE maps. up to 2= 21Ix and in low angular resolution 7).,"applied by means of the 100 and 240 $\mu$ m DIRBE maps, up to $T = 21$ K and in low angular resolution $1^{\circ}$ )." + Their values correspond to the integrated> cust column contribution throughout the Galaxy., Their values correspond to the integrated dust column contribution throughout the Galaxy. + Phe transformation rom to «νι assumed ;iy=0.11224) and Ry=AS/EQ(D1)3.1 (οανάσα et al.," The transformation from to $A_{K,FIR}$ assumed $A_K = 0.112 A_V$ and $R_V = A_V/E(B-V) = 3.1$ (Cardelli et al." + 1989)., 1989). + The 2NALASS extinction values. on the other hand. are based on he position of Bulge red. giant stars in the CMD ancl. as such. are limited in depth by opacity cllects in the emploved raniels. especially in the J band.," The 2MASS extinction values, on the other hand, are based on the position of Bulge red giant stars in the CMD and, as such, are limited in depth by opacity effects in the employed bands, especially in the J band." + In this section we compare the extinction. values derived. from dust emission. clay ley. to those. from he 2NLASS photometry. jysarass.," In this section we compare the extinction values derived from dust emission, ${\it A_{K,FIR}}$ , to those from the 2MASS photometry, $A_{K,2MASS}$." + But before. we can operlv compare these two extinction maps. we must first investigate the possible existence of systematic cllects on his comparison. such as variations in dust temperature and line of sight distribution or the presence of high clensity intervening clouds.," But before we can properly compare these two extinction maps, we must first investigate the possible existence of systematic effects on this comparison, such as variations in dust temperature and line of sight distribution or the presence of high density intervening clouds." + Such. effects. should. arise due o the widely different observational signatures from. the interstellar medium on which the two extinction values are λασος., Such effects should arise due to the widely different observational signatures from the interstellar medium on which the two extinction values are based. + In order to help interpreting the relation between οτι and Aypres we consider a simple mocel of dust. distributed exponentially along and perpendicular to the Galactic plane.," In order to help interpreting the relation between ${\it A_{K,2MASS}}$ and ${\it A_{K,FIR}}$, we consider a simple model of dust distributed exponentially along and perpendicular to the Galactic plane." + The optical depth out to some distance» from the Sun in the direction given by Galactic coordinates (£.5) is then: where Z=rsinb and Ro=Bà|rieosb.—2Ryrvcoshcost are evlindrical coordinates centred on the Galaxy.," The optical depth out to some distance from the Sun in the direction given by Galactic coordinates $\ell$ ) is then: where ${\it Z = r sin b}$ and ${\it R^2 = R_0^2 + r^2cos^2b - +2~R_0~r~cosb~cos\ell }$ are cylindrical coordinates centred on the Galaxy." + Ry and Zo are the dust horizontal and. vertical exponential scales. whose values we assume to be 2.5 kpe (Robin et al.," ${\it R_d}$ and ${\it Z_d}$ are the dust horizontal and vertical exponential scales, whose values we assume to be 2.5 kpc (Robin et al." +" 1996 and Drimmel Spergel 2001) and 110 pe (Mendez van Altena 1998). respectively,"," 1996 and Drimmel Spergel 2001) and 110 pc (Mendez van Altena 1998), respectively." + We also adopt Ry=8.5 kpe for the Sun's distance to the centre of the Galaxy., We also adopt ${\it R_0} = 8.5$ kpc for the Sun's distance to the centre of the Galaxy. + We numerically performed the integral above for the same directions. for which we have 2M1ASS and DIRBE/IRAS data., We numerically performed the integral above for the same directions for which we have 2MASS and DIRBE/IRAS data. +" For cach direction. we assume that our mocdel .pass and Aypry values are proportional to το) (hereafter 75) and T(x) (hereafter. r4). respectively,"," For each direction, we assume that our model ${\it A_{K,2MASS}}$ and ${\it A_{K,FIR}}$ values are proportional to $\tau(R_0)$ (hereafter $\tau_{8.5}$ ) and $\tau(\infty)$ (hereafter $\tau_{\infty}$ ), respectively." + To. model. the. foreground and background. distribution with respect to the Calactic Centre. we also assume that the solar position is cisplaced w Zasy=15 pe above the Galactic plane (ee. Cohen 1995): in the double exponential dust. distribution moclel. he fraction of foreground-to-total dust. distribution does not depend on whether the Sun is displaced above or below he Galactic Plane.," To model the foreground and background distribution with respect to the Galactic Centre, we also assume that the solar position is displaced by ${\it Z_{sun}} = 15$ pc above the Galactic plane (e.g. Cohen 1995); in the double exponential dust distribution model, the fraction of foreground-to-total dust distribution does not depend on whether the Sun is displaced above or below the Galactic Plane." + A full cata models comparison is currently under way., A full data models comparison is currently under way. + For now we restrict our discussion to he basic model features anc thei dilferences. relative to he cata., For now we restrict our discussion to the basic model features and their differences relative to the data. + Fig., Fig. + ? shows r as a function of distance [rom us for several directions (/.5) as predicted by our simple moclel.," 7 shows $\tau$ as a function of distance from us for several directions $(l,b)$ as predicted by our simple model." + The figure clearly shows the dependence on Galactic latitude of the expected contribution of dust. beyond Ry=8.5 kpe., The figure clearly shows the dependence on Galactic latitude of the expected contribution of dust beyond $R_0 = 8.5$ kpc. + Phe fraction of the total optical depth caused by dust bevond the Galactic centre varies [rom 50% at the Galactic Plane to only a few percent for 6=4., The fraction of the total optical depth caused by dust beyond the Galactic centre varies from 50 at the Galactic Plane to only a few percent for $b = 4^{\circ}$. + Fig., Fig. + 7 also shows that the total optical clepth itself decreased by nearly two orders of magnitude between these two Galactic latitudes., 7 also shows that the total optical depth itself decreased by nearly two orders of magnitude between these two Galactic latitudes. + The dependence on f£. on the other hand. is quite small.," The dependence on $\ell$, on the other hand, is quite small." + As we determined οντος in cells of 4° on a side. the resolution of our maps is larger than the 6.1 resolution «t the SEDOS extinction maps.," As we determined $A_{K,2MASS}$ in cells of 4' on a side, the resolution of our maps is larger than the 6.1' resolution of the SFD98 extinction maps." +" In order to place both maps on a similar angular resolution. we convolve the Ay.oaa extinction. map with. aa=4.5"" hosGaussian."," In order to place both maps on a similar angular resolution, we convolve the ${\it A_{K,2MASS}}$ extinction map with a $\sigma = 4.5^{\prime}$ Gaussian." +: Llowever. there are biases that do not depend on the resolution scale of the maps.," However, there are biases that do not depend on the resolution scale of the maps." + One important issue is that the ολοτος values require a minimum number of stars along the upper giant branch to be determined.," One important issue is that the $A_{K,2MASS}$ values require a minimum number of stars along the upper giant branch to be determined." + Regions with «ly 2μιαν be obscuredenough that only the brightest. stars will fall in the range Av.11 used to determine elysarass (sce Sect.," Regions with $A_K$ $2$may be obscuredenough that only the brightest stars will fall in the range $K_s \leq 11$ used to determine $A_{K,2MASS}$ (see Sect." + 2.1)., 2.1). + I£ the region covers the entire cell. then no," If the region covers the entire cell, then no" +The Inudamental understanding of GRB alterelows has been questioned by the mission (Gehrelsetal.2004).. which has revealed several unexpected behaviors in the X-ray alterglows (e.g..seeZhang2007.forareview)..,"The fundamental understanding of GRB afterglows has been questioned by the mission \citep{gehrels04}, which has revealed several unexpected behaviors in the X-ray afterglows \citep[e.g., see][for a review]{zhang07}." + Some bursts have an initial steep decline. followed by a shallow decline a few hundred seconds later (e.g..Tagliaferrietal.2005).," Some bursts have an initial steep decline, followed by a shallow decline a few hundred seconds later \citep[e.g.,][]{tagliaferri05}." +. Others |iive erraticrratic [la[lares withith strong spectraliral variations (e.g..Burial. 2007).," Others have erratic flares with strong spectral variations \citep[e.g.,][]{burrows05,chincarini07}." +. As a group. thev were proposed to have some canonical behaviors (Zhangοἱal.2006).," As a group, they were proposed to have some canonical behaviors \citep{zhang06,nousek06}." +. Contracdictorilv. some other bursts also show evidences for a single power-law decline (Liangetal. 2009).. which are consistent. with the observations (Costa1999).," Contradictorily, some other bursts also show evidences for a single power-law decline \citep{liang09}, , which are consistent with the observations \citep{costa99}." + With the X-ray alterglows being puzzlingly diverse. it is a great challenge to produce an applicable aud self-consistent physical understanding (e.g..seeZhang2007.forareview)..," With the X-ray afterglows being puzzlingly diverse, it is a great challenge to produce an applicable and self-consistent physical understanding \citep[e.g., see][for a review]{zhang07}." + Previous works on GRB diversity. were based on relatively restricted samples. e.g.. 27 bursts in Nouseketal.(2006).. with only 10 measured redshifts: 33 bursts in (2007).. with only 9 measured redshifts: and 19 bursts in Lianeetal.(2009)... with only 12 measured redshiflts.," Previous works on GRB diversity were based on relatively restricted samples, e.g., 27 bursts in \citet{nousek06}, with only 10 measured redshifts; 33 bursts in \citet{chincarini07}, with only 9 measured redshifts; and 19 bursts in \citet{liang09}, with only 12 measured redshifts." + With more than 500 GRBs detected up to now. we realize that il is urgent to revisit the diversity issue wilh an extended sample.," With more than 500 GRBs detected up to now, we realize that it is urgent to revisit the diversity issue with an extended sample." + Using a collection of 150 GRBs with well detected: X-ray afterglows ancl known redshifts. we find that there exist some underlving global features in the rest-frame X-ray light curves. which might clarify the diversity issue and provide some strong constraints on the (heoretical models.," Using a collection of 150 GRBs with well detected X-ray afterglows and known redshifts, we find that there exist some underlying global features in the rest-frame X-ray light curves, which might clarify the diversity issue and provide some strong constraints on the theoretical models." + The structure of this Letter is as lollows: the sample aud data analysis are presented in Section 2.. the rest Game light curves are interpreted in Section 3.. and the discussions ancl conclusion are given in Section 4.. Swiffi," The structure of this Letter is as follows: the sample and data analysis are presented in Section \ref{sec:sample}, the rest frame light curves are interpreted in Section \ref{sec:ugf}, , and the discussions and conclusion are given in Section \ref{sec:discussion}." +s a multiwavelength observatory (Gehrelsetal.2004).. which carries three instruments: Burst Alert Telescope (BAT). X-Ray Telescope (XRT). and Ultraviolet/Optical Telescope (UVOT).," is a multiwavelength observatory \citep{gehrels04}, which carries three instruments: Burst Alert Telescope (BAT), X-Ray Telescope (XRT), and Ultraviolet/Optical Telescope (UVOT)." + We made extensive use of the automated BAT-XRT products provided by the UNSwift Science Data Centre (Evansetal.2010).. the online BAT GRB Event Data Processing Report provided by Taka Sakamoto and Scott D. Bartheliny. and the online big table of all well-localized GRBs provided by Jochen," We made extensive use of the automated BAT-XRT products provided by the UK Science Data Centre \citep{evans10}, the online BAT GRB Event Data Processing Report provided by Taka Sakamoto and Scott D. Barthelmy, and the online big table of all well-localized GRBs provided by Jochen." +Greiner! In Table 1.. we list the 150 bursts from GRD050126 to CRB 100425À with measured redshifts.," In Table \ref{tab:sample}, , we list the 150 bursts from GRB050126 to GRB 100425A with measured redshifts." + We find themean redshift \,\sim$ 2.14(with the median $\sim 1.93$ ), which is" + , + , +provided Sorta Wu (2003). and for NGC 4697 we used the source list of Sarazin et al. (,"provided Soria Wu (2003), and for NGC 4697 we used the source list of Sarazin et al. (" +2001).,2001). + For MIOI and M51. we set the input parameters for WAVDETECT to cover the energy range 0.1—7 keV. For galaxies in which the lower energy limit used by WAVDETECT was greater than 0.1 keV. we carried out a visual inspection to search for any sources with reliable detections but with few photons detected above 0.3 keV. Source counts in each energy band were determined via aperture photometry.," For M101 and M51, we set the input parameters for WAVDETECT to cover the energy range 0.1–7 keV. For galaxies in which the lower energy limit used by WAVDETECT was greater than 0.1 keV, we carried out a visual inspection to search for any sources with reliable detections but with few photons detected above 0.3 keV. Source counts in each energy band were determined via aperture photometry." + The radius of the aperture was varied with off-axis angle in order to match the encircled energy function., The radius of the aperture was varied with off-axis angle in order to match the encircled energy function. + Background was chosen from an annulus region centered on each source., Background was chosen from an annulus region centered on each source. + We note that. while the calibration at the lowest energies (kT<0.3 keV) will need to be refined for spectral fits. source detection algorithms should include photons with energies as low as 0.1 keV if all SSSs and QSSs are to be detected.," We note that, while the calibration at the lowest energies $k\, T < 0.3$ keV) will need to be refined for spectral fits, source detection algorithms should include photons with energies as low as $0.1$ keV if all SSSs and QSSs are to be detected." + In 3 of the galaxies. photons with energies between 0.1 keV and 0.3 keV have helped to detect a small number of SSSs and QSSs.," In $3$ of the galaxies, photons with energies between $0.1$ keV and $0.3$ keV have helped to detect a small number of SSSs and QSSs." + Because visual inspection of each source must be carried out anyway. any spurious sources detected because of background effects at low energy can be easily eliminated.," Because visual inspection of each source must be carried out anyway, any spurious sources detected because of background effects at low energy can be easily eliminated." + In addition to estimates of the number of background objects based on the Deep Field data (see the references in each of the galaxies below). we also used the ChaMP Multiwavelength Project ')) archives (P. Green. private communication) to estimate the contamination from soft X-ray sources in the foreground (X-ray active stars) and background (e.g.. soft AGN).," In addition to estimates of the number of background objects based on the Deep Field data (see the references in each of the galaxies below), we also used the ChaMP Multiwavelength Project ) archives (P. Green, private communication) to estimate the contamination from soft X-ray sources in the foreground (X-ray active stars) and background (e.g., soft AGN)." + In 5 ACIS-S observations with durations of ~10—20 ks. only 3 sources were found to be QSSs: no SSSs were identified.," In 5 ACIS-S observations with durations of $\sim 10-20$ ks, only 3 sources were found to be QSSs; no SSSs were identified." + We therefore believe that the background contribution of soft sources is small compared with the large population of SSSs in our sample galaxies., We therefore believe that the background contribution of soft sources is small compared with the large population of SSSs in our sample galaxies. + MIOI (= NGC5457) is a face-on nearby (5.4-6.7 Mpc) spiral and was observed by ACIS-S for about 100ks on 2000 March 26-27., M101 (= NGC5457) is a face-on nearby (5.4–6.7 Mpc) spiral and was observed by ACIS-S for about 100ks on 2000 March 26-27. + Detailed results of the observations have been reported by Pence et al. (, Detailed results of the observations have been reported by Pence et al. ( +2001).,2001). + We generated our own source list here with CIAO task WAVDETECT instead of CELLDETECT used by Pence et al. (, We generated our own source list here with CIAO task WAVDETECT instead of CELLDETECT used by Pence et al. ( +2001).,2001). + We also used different energy bands covering 0.1—7 keV. instead of 0.125-8 keV in Pence et al. (," We also used different energy bands covering 0.1–7 keV, instead of 0.125–8 keV in Pence et al. (" +2001).,2001). + Pence et al. (, Pence et al. ( +2001) estimated that 27 sources are possible background AGN.,2001) estimated that 27 sources are possible background AGN. + While the source lists agree with each other generally. we found 8 additional sources (118 in total) in the S3 chip.," While the source lists agree with each other generally, we found 8 additional sources (118 in total) in the S3 chip." + The list of SSSs and QSSs is shown in Table 2., The list of SSSs and QSSs is shown in Table 2. + We found a total of 53 VSSs: 32 were SSSs and 21 were QSSs., We found a total of 53 VSSs; 32 were SSSs and 21 were QSSs. + M$83 (= NGCS5236) is a barred spiral galaxy with low inclination angle (/= 24°): it has a starburst nucleus and the estimated distance ranges from 3.7 Mpe to 8.9 Mpe., M83 (= NGC5236) is a barred spiral galaxy with low inclination angle $i=24^{\circ}$ ); it has a starburst nucleus and the estimated distance ranges from 3.7 Mpc to 8.9 Mpc. + A ACIS-S observation was taken on 2000 April 29 for about S50ks., A ACIS-S observation was taken on 2000 April 29 for about 50ks. + The X-ray point source properties and the nuclear region were discussed by Soria and Wu (2002.2003).," The X-ray point source properties and the nuclear region were discussed by Soria and Wu (2002,2003)." + One hundred and twenty seven point sources were found in the S3 chip (0.3-8 keV) and approximately 10 sources are likely to be background AGN., One hundred and twenty seven point sources were found in the S3 chip (0.3–8 keV) and approximately 10 sources are likely to be background AGN. + We used this source list for our analysis., We used this source list for our analysis. +" In. addition, visual inspection from a 0.121 keV image discovered | new SSS."," In addition, visual inspection from a 0.1–1 keV image discovered 1 new SSS." + Table 3 lists M83's SSSs and QSSs., Table 3 lists M83's SSSs and QSSs. + We found a total of 54 VSSs: 28 were SSSs and 26 were QSSs., We found a total of 54 VSSs; 28 were SSSs and 26 were QSSs. + MSI (= NGC5194) is a nearby (7.7-8.4 Mpc) interacting spiral galaxy with moderate inclination (/=467)., M51 (= NGC5194) is a nearby (7.7–8.4 Mpc) interacting spiral galaxy with moderate inclination $i=46^{\circ}$ ). + A ACIS-S observation was performed on 2000 June 20 for about I5ks., A ACIS-S observation was performed on 2000 June 20 for about 15ks. + A detailed analysis of the data is given by Terashima Wilson (2003)., A detailed analysis of the data is given by Terashima Wilson (2003). + We generated our own source list with the CIAO task WAVDETECT., We generated our own source list with the CIAO task WAVDETECT. + A total of 72 sources (in 0.3-7 keV) were found in the $3 chip., A total of 72 sources (in 0.3–7 keV) were found in the S3 chip. + About 10 of the sources are expected to be background objects., About 10 of the sources are expected to be background objects. + All SSSs and QSSs are listed in Table 4., All SSSs and QSSs are listed in Table 4. + We found a total of 23 VSSs: 13 were SSSs and 10 were QSSs., We found a total of 23 VSSs; 13 were SSSs and 10 were QSSs. + NGC4697 is an elliptical galaxy at a distance of 11.7-23.3 Mpe., NGC4697 is an elliptical galaxy at a distance of 11.7–23.3 Mpc. + It was observed by ACIS-S on 2000 January 15-16 for about 40ks., It was observed by ACIS-S on 2000 January 15-16 for about 40ks. + Ninety point sources were detected in the S3 chip (0.3-10 keV: Sarazin. Irwin. Bregman 2001): about 10-15 background objects are expected in the observation.," Ninety point sources were detected in the S3 chip (0.3–10 keV; Sarazin, Irwin, Bregman 2001); about 10–15 background objects are expected in the observation." + The complete source list and results from this observation can be found in Sarazin et al. (, The complete source list and results from this observation can be found in Sarazin et al. ( +2001).,2001). + We also inspected an image from 0.1—1 keV and found | new uncatelogued SSS., We also inspected an image from 0.1–1 keV and found 1 new uncatelogued SSS. + Table 5 lists the SSSs and QSSs found with our selection procedure., Table 5 lists the SSSs and QSSs found with our selection procedure. + We found a total of 19 VSSs: 4 were SSSs and 15 were QSSs., We found a total of 19 VSSs; 4 were SSSs and 15 were QSSs. + To determine whether our algorithm selects sources that are genuinely soft. we have extracted the energy spectra of all very soft sources that provided more than ~200 counts.," To determine whether our algorithm selects sources that are genuinely soft, we have extracted the energy spectra of all very soft sources that provided more than $\sim 200$ counts." + Background counts were extracted in annulus regions centered on each source., Background counts were extracted in annulus regions centered on each source. + There are 10 such sources., There are $10$ such sources. + We have also considered the spectra of sources with more than 100 counts. although the uncertainties in spectral parameters are large.," We have also considered the spectra of sources with more than $100$ counts, although the uncertainties in spectral parameters are large." + A representative spectrum of a QSS-o source is shown in Figure |., A representative spectrum of a $\sigma$ source is shown in Figure 1. + The spectral fits are list in Table 6., The spectral fits are list in Table 6. + Because many VSSs are faint. fits of individual spectra are not possible.," Because many VSSs are faint, fits of individual spectra are not possible." + If. therefore. we found a number of sources that (1) had been identified by the same criteria. and which (2) displayed similar broadband spectra and (3) provided a total of approximately 100 counts. we extracted the composite energy spectra (see e.g.. Figure 1).," If, therefore, we found a number of sources that (1) had been identified by the same criteria, and which (2) displayed similar broadband spectra and (3) provided a total of approximately $100$ counts, we extracted the composite energy spectra (see e.g., Figure 1)." + Because the response matrices vary across the detector. a weighted RMF and ARF was generated following the thread recommended by the X-rayCenter.," Because the response matrices vary across the detector, a weighted RMF and ARF was generated following the thread recommended by the X-ray." +.. Results are presented together with the individual spectra in Table 6., Results are presented together with the individual spectra in Table 6. + The analysis ofChandra spectra of VSSs is fraught with uncertainties because the low-energy (AT<0.5 keV) calibration of ACIS-S is not yet well understood?.," The analysis of spectra of VSSs is fraught with uncertainties because the low-energy $k\, T < 0.5$ keV) calibration of ACIS-S is not yet well understood." +. It is therefore important to keep in mind that the spectral fits of SSSs. especially those that peak at energies near or below 0.5 ," It is therefore important to keep in mind that the spectral fits of SSSs, especially those that peak at energies near or below $0.5$ " +their results with characteristic SEDs of blazars.,their results with characteristic SEDs of blazars. + Here. we adopt a simplified description of the particle dynamics and radiation processes. and focus on the expected monochromatic light curves dominated by the plasmoid deceleration.," Here, we adopt a simplified description of the particle dynamics and radiation processes, and focus on the expected monochromatic light curves dominated by the plasmoid deceleration." + We review (he observational motivation from ος 279 in 32.. describe the model for the plasmoid dynamics in 33.. and outline our treatment of radiation processes in §4..," We review the observational motivation from 3C 279 in \ref{motivation}, describe the model for the plasmoid dynamics in \ref{model}, and outline our treatment of radiation processes in \ref{radiation}." + As a test of our numerical simulations. we develop an analviical solution to the plasmoid dynamics and light curves in (he self-similar deceleration phase in 85..," As a test of our numerical simulations, we develop an analytical solution to the plasmoid dynamics and light curves in the self-similar deceleration phase in \ref{deceleration}." + In 86. we present results of our simulations and fits to the observed exponential flux decay of ος 279 in January 2006., In \ref{results} we present results of our simulations and fits to the observed exponential flux decay of 3C 279 in January 2006. + We summarize in $7.., We summarize in \ref{summary}. +" Throughout this paper. we refer to a as the energy spectral index. Fy, [Jv] xv""."," Throughout this paper, we refer to $\alpha$ as the energy spectral index, $F_{\nu}$ [Jy] $\propto \nu^{-\alpha}$." +" A cosmology with Q,,=0.3. O4=0.7. and Hy=70 km ! ! is used."," A cosmology with $\Omega_m = 0.3$, $\Omega_{\Lambda} = 0.7$, and $H_0 = 70$ km $^{-1}$ $^{-1}$ is used." + In this cosmology. and using the redshift of 2=0.536. the Iuminosity distance of ος 279 is dp=3.08 Gpe.," In this cosmology, and using the redshift of $z = 0.536$, the luminosity distance of 3C 279 is $d_L = 3.08$ Gpc." + 3C 279 was observed in a WEDT campaign al radio. near-IR. aud optical frequencies. throughout the spring of 2006.," 3C 279 was observed in a WEBT campaign at radio, near-IR, and optical frequencies, throughout the spring of 2006." + Details of the observations. data analvsis. and implications of the optical variability patterns observed during that campaign have been published in Dóttcheretal.(2007b).," Details of the observations, data analysis, and implications of the optical variability patterns observed during that campaign have been published in \cite{boettcher07b}." +. Fie., Fig. + 1. shows the optical light curves of 3C 279 during spring 2006., \ref{lightcurves} shows the optical light curves of 3C 279 during spring 2006. + The light curves exhibit an exiraordinarilv clean quasi-expouential decay with a characteristic time scale of 7;~12.8 davs around JD 2453743. JD 2453760., The light curves exhibit an extraordinarily clean quasi-exponential decay with a characteristic time scale of $\tau_d \sim 12.8$ days around JD 2453743 – JD 2453760. + This light curve feature can not be interpreted as the signature of radiative cooling since the svnchrotron cooling tme scale for electrons emitting svuchrotron radiation in Cae optical Ro baud is where 5; is the magnetic field in Gauss aud D4 is the Doppler factor in units of 10., This light curve feature can not be interpreted as the signature of radiative cooling since the synchrotron cooling time scale for electrons emitting synchrotron radiation in the optical R band is where $B_G$ is the magnetic field in Gauss and $D_1$ is the Doppler factor in units of 10. + This is of (he order of at most a few hours lor (vpical values of the magnetic field strength expected in quasars (2B~1 GJ)., This is of the order of at most a few hours for typical values of the magnetic field strength expected in quasars $B \sim 1$ G). + Setüng the svnelirotron. cooling time scale equal to the observed exponential decay (ime scale. would require a magnetic field of B—7xLOο G. which is about three orders of magnitude lower than usually inferred for quasar jets.," Setting the synchrotron cooling time scale equal to the observed exponential decay time scale, would require a magnetic field of $B \sim 7 \times 10^{-4} \, D_1^{-1}$ G, which is about three orders of magnitude lower than usually inferred for quasar jets." + We therefore favor a model in which the light curve decay is associated with the dynamics of (he emission regionrather (han microscopic processes., We therefore favor a model in which the light curve decay is associated with the dynamics of the emission regionrather than microscopic processes. + We note (hat similar quasi-exponential decavs have also been observed in 3C 279 repeatedly in the 2007 observing season (Larionovetal. 2003).., We note that similar quasi-exponential decays have also been observed in 3C 279 repeatedly in the 2007 observing season \citep{larionov08}. . +obtained by SOB (see Sec.,obtained by SF03 (see Sec. + 2) for the specific emissivity Co(z). the halo eutol£ mass Miu;=ως). ancl use as the minimum redshift at which these sources contribute to the background. the value sa.=SAN (corresponding to the epoch at which metal-lree star. formation ends note that we are making the reasonable assumption that no such a source can be resolved. by current observations) then. by also making use of expressions (5)) and (6)). we can derive predictions for the contribution of the clustering of (unresolved) Popllls to the background. Ductuations at cillerent. wavelengths.," 2) for the specific emissivity $\epsilon_{\nu}(z)$, the halo cutoff mass $M_{min}\equiv +M_{min}(z)$, and use as the minimum redshift at which these sources contribute to the background the value $z_{end}=8.8$ (corresponding to the epoch at which metal-free star formation ends -- note that we are making the reasonable assumption that no such a source can be resolved by current observations), then, by also making use of expressions \ref{eq:xi}) ) and \ref{eq:beff}) ), we can derive predictions for the contribution of the clustering of (unresolved) PopIIIs to the background fluctuations at different wavelengths." + The cases for A= 1L25jm. A= 1.65pm and A=2.1 7pm. (respectively corresponding to J. LL ancl Ix. bancs) are presented in Figure 1. by the solid. dashed and dotted lines.," The cases for $\lambda=1.25 \mu$ m, $\lambda=1.65 \mu$ m and $\lambda=2.17 \mu$ m (respectively corresponding to J, H and K bands) are presented in Figure \ref{fig:cth} by the solid, dashed and dotted lines." + Since these wavelengths at the redshifts under exam are always greater than the rest-frame Lya. the contribution [rom the e.77/6 term in equation 4 can be neglected in the calculation of C'(6) (see SEQ03).," Since these wavelengths at the redshifts under exam are always greater than the rest-frame $\alpha$, the contribution from the $e^{-2\tau_{eff}}$ term in equation 4 can be neglected in the calculation of $C(\theta)$ (see SF03)." + The first feature to be noticed in the plot is the sharp drop of all the curves at @=200 aresec., The first feature to be noticed in the plot is the sharp drop of all the curves at $\theta\simeq 200$ arcsec. + This is due to the fact that such an angular scale corresponds to distances roÉONG Alpe (with the minimum. value corresponding to tone=SG dn the adopted: cosmology). where the spatial correlation Function has already. steepened. from its power-law behaviour and rapidly approaches the zero value.," This is due to the fact that such an angular scale corresponds to distances $r\simgt 8.6$ Mpc (with the minimum value corresponding to $z_{end}=8.8$ in the adopted cosmology), where the spatial correlation function has already steepened from its power-law behaviour and rapidly approaches the zero value." + As a first conclusion of this work we can then sav that the clustering of unresolved Poplll sources cannot account. [or any of the observed. Ductuations on scales 200 arcsec. which instead require. much more local objects (for. the Alatsumoto ct al.," As a first conclusion of this work we can then say that the clustering of unresolved PopIII sources cannot account for any of the observed fluctuations on scales $\simgt 200$ arcsec, which instead require much more local objects (for the Matsumoto et al." + 2003. results the maximum acceptable redshift turns out to be ze1 2)., 2003 results the maximum acceptable redshift turns out to be $z\sim 1-2$ ). + The second point to stress is the remarkably: different amplitude of the intensity. Uuctuations as evaluated at different: frequencies., The second point to stress is the remarkably different amplitude of the intensity fluctuations as evaluated at different frequencies. + More. specifically. (0) is found. to decrease. by about two orders of magnitude when going rom A=1.25 jim to A=2.17 yam. As already argued by 5100. the reason for this decrement has to be found in the extremely strong Lya nebular emission line responsible or a considerable fraction of the Poplll emissivity which. once redshifted to the present time. gives its maximum contribution in the .J band and rapidly disappears at he other two wavelengths. under exani," More specifically, $C(\theta)$ is found to decrease by about two orders of magnitude when going from $\lambda=1.25\;\mu$ m to $\lambda=2.17\;\mu$ m. As already argued by SF03, the reason for this decrement has to be found in the extremely strong ${\alpha}$ nebular emission line – responsible for a considerable fraction of the PopIII emissivity – which, once redshifted to the present time, gives its maximum contribution in the J band and rapidly disappears at the other two wavelengths under exam." + We discuss the implications of these findings in the next Section., We discuss the implications of these findings in the next Section. + lxashlinskv ct al. (, Kashlinsky et al. ( +2002) and Odenwald et al. (,2002) and Odenwald et al. ( +2003) have recently reported the first. detection of small angular scale Uuctuations in the Near Infrared. Backeround.,2003) have recently reported the first detection of small angular scale fluctuations in the Near Infrared Background. +" Their measurcments were obtained by using long integration data constructed from 2ALASS (""Two Micron Sky Survey) observations anc by then coadcing images in order to produce a 8.651° field. divided into seven square patches 512"" on the side."," Their measurements were obtained by using long integration data constructed from 2MASS (Two Micron Sky Survey) observations and by then coadding images in order to produce a $8.6^{\prime}\times 1^{\circ}$ field, divided into seven square patches $^{\prime\prime}$ on the side." + In each patch. individual stars and ealaxiecs were removed down to a magnitude limit which," In each patch, individual stars and galaxies were removed down to a magnitude limit which" +the SER was coustaut for all t>fy. the uuuber of stars evolving iuto SNe in the eiven mass interval diving the time Aft is equal to the mumber of new stars that are formed in the same mass interval.,"the SFR was constant for all $t\ge t_0$, the number of stars evolving into SNe in the given mass interval during the time $\Delta t$ is equal to the number of new stars that are formed in the same mass interval." + Thus. in this case. where £620) is assuunced to be eiven by Equation (1)) with the normalization defined by Equation (3)).," Thus, in this case, where $\xi (m)$ is assumed to be given by Equation \ref{eq:IMF}) ) with the normalization defined by Equation \ref{eq:norm2}) )." + This normalization keeps the total mass of the stars which are formed per wait time constant., This normalization keeps the total mass of the stars which are formed per unit time constant. + If Af is small compared to the time scale ou which joy changes. the uuuber of all stars that evolve during Af can be approximated as Note that the SER iu Equatious (29)) and (303) should be considered au average value over a #τμ.," If $\Delta t$ is small compared to the time scale on which $m_{\rm low}$ changes, the number of all stars that evolve during $\Delta t$ can be approximated as Note that the SFR in Equations \ref{eq:SNR1}) ) and \ref{eq:SNR2}) ) should be considered an average value over a $t-t_0$." + Variations of the SER ou wich shorter time-scales are of no importance here., Variations of the SFR on much shorter time-scales are of no importance here. + The SERof a ultva-luuinous infrared galaxy (ULIRG) can be estimated as where Ley is the fax infra-red (FIR) οςτν of the ULIRG (?).., The SFRof a ultra-luminous infra-red galaxy (ULIRG) can be estimated as where $L_{\rm FIR}$ is the far infra-red (FIR) luminosity of the ULIRG \citep{kennicutt1998a}. . + One of the nearest ULIRCGs is Arp 22|, One of the nearest ULIRGs is Arp 220. + Using Erin—1l.«1052L. for Arp 22 (23.. Equation (313) iuplies a SFR of =210M.xr+ for tha ealaxy.," Using $L_{\rm FIR}=1.41\times10^{12} \ {\rm L}_{\odot}$ for Arp 220 \citep{sanders2003a}, Equation \ref{eq:SFR}) ) implies a SFR of $\approx 240 \ {\rm M}_{\odot} \, {\rm yr}^{-1}$ for that galaxy." +" The SNe in Arp 220 have been observed in a central region with a diuueter of z1k)c. from where about 10 per cent of its FIR huuinositv originates δε,"," The SNe in Arp 220 have been observed in a central region with a diameter of $\approx 1\ {\rm kpc}$, from where about 40 per cent of its FIR luminosity originates \citep{soifer1999a}." + Equation (31)) thus implics à SER of z100M.xr+ if only this part of Arp 220 is considered.," Equation \ref{eq:SFR}) ) thus implies a SFR of $\approx 100 \ {\rm M}_{\odot} \, {\rm yr}^{-1}$ if only this part of Arp 220 is considered." + Note that this SER js consistent with the SER that has been sugeested for a fornune UCD if UCDs form ou a timescale of approximately 1 Myr (7)., Note that this SFR is consistent with the SFR that has been suggested for a forming UCD if UCDs form on a timescale of approximately 1 Myr \citep{dabringhausen2009a}. . + Also note that the observed SN in Arp 220 do not seemto distributed, Also note that the observed SN in Arp 220 do not seemto distributed +In this section we provide analytic expressions of f(z) and q(z) for the gravitational interaction potential energy of the Kuzmin disk of baryons embedded in various density distributions of dark matter halo.,In this section we provide analytic expressions of $f(z)$ and $q(z)$ for the gravitational interaction potential energy of the Kuzmin disk of baryons embedded in various density distributions of dark matter halo. + The NFW density distribution and the corresponding gravitational potential are given respectively by and Then. we obtain the total mass of dark halo and the analytic expression of the following function: For this case. we cannot obtain the exact analytic expression of q(z).," The NFW density distribution and the corresponding gravitational potential are given respectively by and Then, we obtain the total mass of dark halo and the analytic expression of the following function: For this case, we cannot obtain the exact analytic expression of $q(z)$." + Instead. we obtain an approximate expression of q(2) around >=Q0 aus follows: The homogeneous density distribution and the corresponding gravitational potential are given respectively by and Then. we obtain the total mass of dark halo and the analytic expressions of the following functions: and The 17r density distribution and the corresponding gravitational potential are given respectively by Then. we obtain the total mass of dark halo," Instead, we obtain an approximate expression of $q(z)$ around $z=0$ as follows: The homogeneous density distribution and the corresponding gravitational potential are given respectively by and Then, we obtain the total mass of dark halo and the analytic expressions of the following functions: and The $1/r$ density distribution and the corresponding gravitational potential are given respectively by and Then, we obtain the total mass of dark halo" +We carried out an extensive HST imaging survey of 110 BL Lac objects with WEPCO2. primarily in the F702W. (R-band) These were a randomly selected subset of 132 BL Lacs from six complete samples (4 N-rav-. 1 raclio-. d opticallv-selected) spanning the full range of observed BL Lac spectral properties.,"We carried out an extensive HST imaging survey of 110 BL Lac objects with WFPC2, primarily in the F702W (R-band) These were a randomly selected subset of 132 BL Lacs from six complete samples (4 X-ray-, 1 radio-, 1 optically-selected) spanning the full range of observed BL Lac spectral properties." + The complete IIST-observed subsample of 110 BL Lacs covers a redshift range of 0.027xz1.34., The complete HST-observed subsample of 110 BL Lacs covers a redshift range of $0.027 \le z \le 1.34$. + The host galaxy parameters were extracted by fitting a model galaxy. profile plus a central point spread [function (PSF) to the azimuthallvy-averaged. image profile., The host galaxy parameters were extracted by fitting a model galaxy profile plus a central point spread function (PSF) to the azimuthally-averaged image profile. + Extensive testing on simulated data. aud comparison to results from (the two-dimensional analysis of a subsample has shown that this approach allows accurate measurement of the magnitude of both the host galaxy and nucleus and of the host galaxy scale radius. as well as allowing us to distinguish between a bulge- or disk-dominated galaxy profile.," Extensive testing on simulated data, and comparison to results from the two-dimensional analysis of a subsample has shown that this approach allows accurate measurement of the magnitude of both the host galaxy and nucleus and of the host galaxy scale radius, as well as allowing us to distinguish between a bulge- or disk-dominated galaxy profile." + The excellent IST resolution proved to be vital in determination of the morphological parameters. as most of the critical inlormation was within 0.5 1 areseconds of the core.," The excellent HST resolution proved to be vital in determination of the morphological parameters, as most of the critical information was within 0.5 – 1 arcseconds of the core." + The full details of the image reduction and host galaxy fitting can be found in Scarpaοἱa£.(2000) ancl (he host galaxy results are presented in Urry.efal.(2000)., The full details of the image reduction and host galaxy fitting can be found in \citet{Scarpa} and the host galaxy results are presented in \citet{Urry}. +. Lost galaxies were resolved in 655€ of the sample. with 95% resolved for 2<0.5. and none resolved [or z>0.7.," Host galaxies were resolved in $65\%$ of the sample, with $95\%$ resolved for $z < 0.5$, and none resolved for $z>0.7$." + All resolved host galaxies with sufficient signal-to-noise ratios were well-litted by a de Vaucouleurs profile (1.e.. a bulge-«lominated host). in preference to an exponential prolile (1.e.. a cdisk-dominated host).," All resolved host galaxies with sufficient signal-to-noise ratios were well-fitted by a de Vaucouleurs profile (i.e., a bulge-dominated host), in preference to an exponential profile (i.e., a disk-dominated host)." + This strongly supports the idea that AGN reside in elliptical galaxies rather than spirals., This strongly supports the idea that radio-loud AGN reside in elliptical galaxies rather than spirals. + The average IN-corrected absolute magnitude of the host galaxies [rom the entire HST-imaged sample is Mj;=—23.7250.6 mag (RAIS dispersion)., The average K-corrected absolute magnitude of the host galaxies from the entire HST-imaged sample is $M_R=-23.7 \pm 0.6$ mag (RMS dispersion). + To minimize the number of unresolved host galaxies (while still maintaining a useful redshift range). we restrict this sample to 2<0.5 for this comparison study.," To minimize the number of unresolved host galaxies (while still maintaining a useful redshift range), we restrict this sample to $z\lesssim 0.5$ for this comparison study." + We further restrict the sample to 20.15 to match the available quasar subsample (see below)., We further restrict the sample to $z\gtrsim 0.15$ to match the available quasar subsample (see below). + The final low-power subsample consists of 40 objects with 0.150 in units of bins. where we used a=46 time bins of 500 s each as shown in Figure 3bb. lor the time interval marked by a horizontal bar in Figure ᾖος, For €« 0. D and & are interchangecl."," To quantify the relative timing of the two curves, we computed the cross correlation function as follows: for a time lag $\ell \ge 0$ in units of bins, where we used $m=46$ time bins of 500 s each as shown in Figure \ref{lightcurves}b b, for the time interval marked by a horizontal bar in Figure \ref{lightcurves}c c. For $\ell < 0$ , $D$ and $R$ are interchanged." +" Ilere. Ry is the radio [αν ancl D, is the X-ray time derivative al the grid point / (the boxcear-smoothed version was used: the result using the Chebycehev-smoothed version is in full agreement)."," Here, $R_k$ is the radio flux and $D_k$ is the X-ray time derivative at the grid point $k$ (the boxcar-smoothed version was used; the result using the Chebychev-smoothed version is in full agreement)." + The quantities 2 and D are the means of the respective variables., The quantities $\bar{R}$ and $\bar{D}$ are the means of the respective variables. + The first factor on the right-hand side of equation 2 corrects for the decreasing number of terms in the denominator of the second factor., The first factor on the right-hand side of equation \ref{cross} corrects for the decreasing number of terms in the denominator of the second factor. + To obtain identical time bius For bot curves. we linearly interpolated the radio data to the grid defined by the X-ray bins: this is sulliciently accurate eiven the short time bins compared to the intrinsic light curve variability Gime scales.," To obtain identical time bins for both curves, we linearly interpolated the radio data to the grid defined by the X-ray bins; this is sufficiently accurate given the short time bins compared to the intrinsic light curve variability time scales." + The inset in Figure 3cc shows P(6)., The inset in Figure \ref{lightcurves}c c shows $P(\ell)$. + The function sharply peaks at zero lag. indicating no significant lag between the (wo curves.," The function sharply peaks at zero lag, indicating no significant lag between the two curves." + Note (hat the units of the N-vav time derivative and the radio flux are not important for equation 1. and the fieures have been sealed arbitrarily.," Note that the units of the X-ray time derivative and the radio flux are not important for equation \ref{neupert} + and the figures have been scaled arbitrarily." + Also. the N-rav time derivative is mostly negative since the variability occurs during the gradual decline from the main peak.," Also, the X-ray time derivative is mostly negative since the variability occurs during the gradual decline from the main peak." + Again. this is of little importance as such a (rend can be subtracted from the data. shifting the derivative to larger values.," Again, this is of little importance as such a trend can be subtracted from the data, shifting the derivative to larger values." + Fieuree 3. shows compellinge evidence for the presence of a Neupert effect. i.e... a racio liehtex curve that is approximately proportional to the time derivative of the X-ray lightex curve.," Figure \ref{lightcurves} shows compelling evidence for the presence of a Neupert effect, i.e., a radio light curve that is approximately proportional to the time derivative of the X-ray light curve." +The lieht curves alone do not prove the operation of chromospheric evaporation induced by,The light curves alone do not prove the operation of chromospheric evaporation induced by +case. because acoustic waves generated in the corona are able to heat the surrounding gas directly. unlike acoustic waves produced al the photosphere.,"case, because acoustic waves generated in the corona are able to heat the surrounding gas directly, unlike acoustic waves produced at the photosphere." + ILowever. N-waves are rapidly damped. so that the heating occurs only in inner region as seen in the lower right panels of fies.) and 2..," However, N-waves are rapidly damped, so that the heating occurs only in inner region as seen in the lower right panels of \ref{fig:taudp} and \ref{fig:fwdp}." + Then. location of maximum temperature. λε. Is quite close to the surface.," Then, location of maximum temperature, $T_{\rm max}$, is quite close to the surface." + In an outside region of Z1.5/2.. heat is input only by outward thermal conduction. and the flow is accelerated mostly by thermal pressure.," In an outside region of $\gtrsim 1.5R_{\odot}$, heat is input only by outward thermal conduction, and the flow is accelerated mostly by thermal pressure." + As a result. speed of the solar wind at LAU is < 300km/s. which is slightly slower than the actual low-speed wind (300~450km/s).," As a result, speed of the solar wind at 1AU is $\lesssim 300$ km/s, which is slightly slower than the actual low-speed wind $300 \sim 450$ km/s)." + The top right panel of fie.2 interesüngly illustrates that distributions of ay. are almost identical in spite of very dillerent inputs of £i05..," The top right panel of \ref{fig:fwdp} interestingly illustrates that distributions of $\alpha_{\rm w}$ are almost identical in spite of very different inputs of $F_{\rm w,0}$." + Particularly. initial N-wawve amplitiucles. ovra). al rq. ave within a range between 0.48 and 0.49.," Particularly, initial N-wave amplitudes, $\alpha_{\rm w}(r_{\rm d})$, at $r_{\rm d}$, are within a range between 0.48 and 0.49." + This is because Fia (0pazyes: eq.(0))) mostly. owes iis variation (o change of ambient pressure (see 823.2.1)).," This is because $F_{\rm w,0}$ $\sim p \alpha_{\rm w,0}^2 c_{\rm s}$; \ref{eq:wvfx}) )) mostly owes its variation to change of ambient pressure (see \ref{sc:tmxptr}) )." + Moreover. an upper rieht panel of fie.l also inclicates Chat initial a(70.5) is almost independent ol τ and μι ," Moreover, an upper right panel of \ref{fig:taudp} also indicates that initial $\alpha_{\rm w}(\simeq 0.5)$ is almost independent of $\tau$ and $f_{\rm max}$." +We have found that 0.45«ανα)<0.52 within our parameter regions of Fug=(1-20)x10 ere 7s |. 7=60— 300s. and fii;=1—5.," We have found that $0.45 < \alpha_{\rm w}(r_{\rm d}) < 0.52$ within our parameter regions of $F_{\rm w,0}=(1-20)\times 10^5$ erg $^{-2}$ $^{-1}$, $\tau=60-300$ s, and $f_{\rm max}=1-5$." + This proves that ay<1 is fulfilled in the entire region. which justifies the assumption of weak shock.," This proves that $\alpha_{\rm w} < 1$ is fulfilled in the entire region, which justifies the assumption of weak shock." + Middle right panels of fies.l and 2 show that the dissipation length is a drastically varying function on r., Middle right panels of \ref{fig:taudp} and \ref{fig:fwdp} show that the dissipation length is a drastically varying function on $r$. + This implies that (he assumption of a constant dissipation length usually taken in previous models for the elobal corona (Withbroe1988:Sancdbak&Leer19904). is very poor for our N-wave process.," This implies that the assumption of a constant dissipation length usually taken in previous models for the global corona \citep{wtb88,sl94} is very poor for our N-wave process." + In the following discussions. we examine dependences of the wind structures on the respective input parameters.," In the following discussions, we examine dependences of the wind structures on the respective input parameters." + First. we argue dependences on wave periods.," First, we argue dependences on wave periods." + As illustrated in fie.L.. N-waves wilh smaller 7 dissipate more quickly and (he heating occurs in thinner region close to the surface.," As illustrated in \ref{fig:taudp}, N-waves with smaller $\tau$ dissipate more quickly and the heating occurs in thinner region close to the surface." + This simply leads to deposition of wave energy in denser region., This simply leads to deposition of wave energy in denser region. + Since radiative loss. qu(erg s. 1). is in proportion to f£ [or optically thin plasma. a greater fraction of energy supplied in denser region goes into radiative escape.," Since radiative loss, $q_{\rm R}$ (erg $^{-3}$ $^{-1}$ ), is in proportion to $\rho^2$ for optically thin plasma, a greater fraction of energy supplied in denser region goes into radiative escape." + Consequently. a smaller amount of energv remains to heat the corona and accelerate the flow.," Consequently, a smaller amount of energy remains to heat the corona and accelerate the flow." + The case adopting smaller 7(=G60s) gives lower temperature in (he corona. and therefore. a smaller pressure scale height and a more rapid decrease of density. as shown in fig.l..," The case adopting smaller $\tau$ (=60s) gives lower temperature in the corona, and therefore, a smaller pressure scale height and a more rapid decrease of density, as shown in \ref{fig:taudp}." + Lower temperature also lakes (he sonic point more distant [rom the solar surface. and (hen. mass flix of the solar wind becomes much smaller (han that expected from the 7= 300s case (tab.1)).," Lower temperature also takes the sonic point more distant from the solar surface, and then, mass flux of the solar wind becomes much smaller than that expected from the $\tau=300$ s case \ref{tab:mdr}) )." + second. we study effects on areal expansion of the flow tube.," Second, we study effects on areal expansion of the flow tube." +" Comparing results adopting the same £4=1.8x I0erg 7s ! and 7= 300s but different. fia,=1 and 5 in 1. one can notice significant change of density structure."," Comparing results adopting the same $F_{\rm w,0}=7.8\times 10^5$ erg $^{-2}$ $^{-1}$ and $\tau=300$ s but different $f_{\rm max}=1$ and 5 in \ref{fig:taudp}, one can notice significant change of density structure." + The model considering the non-racdial expansion eives more drastic decrease of densitv as a function of r in spite of similar initial density at the inner boundary., The model considering the non-radial expansion gives more drastic decrease of density as a function of $r$ in spite of similar initial density at the inner boundary. + Temperature in the inner corona is also lower in that model. since more traction of the input energv is lost acliabatically due to geometrical expansion," Temperature in the inner corona is also lower in that model, since more fraction of the input energy is lost adiabatically due to geometrical expansion" +"where s, is “retarded” (ime given by (he implicit equation ]t is important to understand precisely (he meaning of the expressions xX,(s,) aud vy(sy).",where $s_a$ is “retarded” time given by the implicit equation It is important to understand precisely the meaning of the expressions ${\bf x}_a(s_a)$ and ${\bf v}_a(s_a)$. +" They do not mean that x, and v, have becomefunctions of sy: they are functionsonly of the parameter 4."," They do not mean that ${\bf +x}_a$ and ${\bf v}_a$ have become of $s_a$; they are functions of the parameter $u$ ." +" Rather the expression x,(s,) means x,(u=s4). or “X,(u) evaluated at u=s, Where s, is given by evaluating Eq. (15))"," Rather the expression ${\bf x}_a(s_a)$ means ${\bf x}_a(u=s_a)$, or ${\bf x}_a (u)$ evaluated at $u=s_a$ where $s_a$ is given by evaluating Eq. \ref{retarded}) )" + for a chosen field point (/.x).," for a chosen field point $(t,{\bf x})$”." +" This will be important. lor example. when we carry out Tavlor expansions of x,(s,) and vy(s,)."," This will be important, for example, when we carry out Taylor expansions of ${\bf x}_a(s_a)$ and ${\bf v}_a(s_a)$." + These issues. are acldressed in detail in an Appendix., These issues are addressed in detail in an Appendix. + substituting Eqs. (14)), Substituting Eqs. \ref{UVLW}) ) + into Eqs. (9)), into Eqs. \ref{metric}) ) +" aud thence into (13)). we can write the time delay in the form where /, denotes (he time of reception of the rav and where ¢=a,/(2+25)."," and thence into \ref{Deltat}) ), we can write the time delay in the form where $t_r$ denotes the time of reception of the ray and where $\zeta += \alpha_1/(2+2\gamma)$." + Equation (16)) is a sum of contributions for each body in (he svstem., Equation \ref{Delta2}) ) is a sum of contributions for each body in the system. +" Since we are working to linear order in m. we can evaluate the integral lor each body separately. then multiply each by 1, and sum over the bodies."," Since we are working to linear order in $m$, we can evaluate the integral for each body separately, then multiply each by $m_a$ and sum over the bodies." +" We rewrite the unperturbed trajectory of the light rav in the more convenient form where σ is the time / modulo a constant. and £, is a vector from the barveenter to the light ταν at the moment of its closest approach to body a: the parameter σ is chosen so (hat g=O at (his point."," We rewrite the unperturbed trajectory of the light ray in the more convenient form where $\sigma$ is the time $t$ modulo a constant, and ${\bf \xi}_a$ is a vector from the barycenter to the light ray at the moment of its closest approach to body $a$; the parameter $\sigma$ is chosen so that $\sigma=0$ at this point." + Because we are working to firstorder in mi. we can ignore all effects related to the deflection of this ray.," Because we are working to firstorder in $m_a$ , we can ignore all effects related to the deflection of this ray." + We adopt the simplified notation, We adopt the simplified notation +The good level of agreement cisplaved in Fig.,The good level of agreement displayed in Fig. + 1 among three independent approaches to determining the Ly AL relation indicates that. optical ancl X-ray selection methods are finding similar populations of massive halos., \ref{fig:lm} among three independent approaches to determining the $L_X$ $M$ relation indicates that optical and X-ray selection methods are finding similar populations of massive halos. + Furthermore. the maxBCGRASS result extends to a lower mass scale than is probed. by O2 and SOG.," Furthermore, the maxBCG–RASS result extends to a lower mass scale than is probed by RB02 and S06." + In this section. we point out. elfects that could lead. to differences among the three measurements.," In this section, we point out effects that could lead to differences among the three measurements." + The discussion is aimed at raising issues to be addressed by more detailed analysis in future work., The discussion is aimed at raising issues to be addressed by more detailed analysis in future work. + Non-zero bias in hyvedrostatie mass estimates. displayed in earlv. low-resolution gas simulations1990)... is a possible source of svstematic error that would shift the 11302. result. relative to the true relation.," Non-zero bias in hydrostatic mass estimates, displayed in early, low-resolution gas simulations, is a possible source of systematic error that would shift the RB02 result relative to the true relation." + Recent studies using mock X-ray exposures of numerical simulations predict a systematic underestimate of binding mass at the level of 0.25 in Indl2007).., Recent studies using mock X-ray exposures of numerical simulations predict a systematic underestimate of binding mass at the level of $-0.25$ in ${\rm ln}M$. + Correcting the RBO2 result by this amount would. more closely align it with the maxBCCRASS relation., Correcting the RB02 result by this amount would more closely align it with the maxBCG–RASS relation. + Assuming the latter is an unbiased estimate of the underlving halo relation. the luminosity ollset between the two relations measures the Malmaquist. bias arising from the X-ray [lux limit of the LIPLUGCS sample used by 1209.," Assuming the latter is an unbiased estimate of the underlying halo relation, the luminosity offset between the two relations measures the Malmquist bias arising from the X-ray flux limit of the HIFLUGCS sample used by RB02." + Ciood agreement would signal a small bias. meaning small intrinsic scatter (ὃς 104) between luminosity and. mass.," Good agreement would signal a small bias, meaning small intrinsic scatter $\lesssim{} 10\%$ ) between luminosity and mass." + Such small scatter is considered unlikely by the analysis of SOG., Such small scatter is considered unlikely by the analysis of S06. + A separate argument can be made based. on. slope estimates., A separate argument can be made based on slope estimates. + Lf hvdrostatie mass estimates scale with true mass as CUDxML then one would expect the 02 slope to differ bv 1.5c from the maxDC€RASS value.," If hydrostatic mass estimates scale with true mass as $\langle M_{\rm est} \rangle \propto M_{\rm +true}^{1+\epsilon}$, then one would expect the RB02 slope to differ by $1.5\epsilon$ from the maxBCG–RASS value." + The measured slope cillerence. 0.15x0.15. implies «=0.1+0.1.," The measured slope difference, $0.15 +\pm 0.15$, implies $\epsilon = 0.1 \pm 0.1$." + Strongly mass dependent hyelrostatic biases are therefore ruled out., Strongly mass dependent hydrostatic biases are therefore ruled out. + One could shift. the RBO2 result to. higher. masses without requiring a major reduction in scatter. as constrained in SOG.," One could shift the RB02 result to higher masses without requiring a major reduction in scatter, $\sigma_{\mathrm{ln}M|L}$, as constrained in S06." + This would require shifting the tare.806 result by mocilvine the assumed cosmology., This would require shifting the S06 result by modifying the assumed cosmology. + The luminosity normalization is sensitive to power spectrum normalization. Lx~ay1 sw raising ex to 0.95 would shift the S06 result to lower £x and preserve the current level of Malmequist-bias for the R.BoO2 result.," The luminosity normalization is sensitive to power spectrum normalization, $L_X +\sim \sigma_8^{-4}$, so raising $\sigma_8$ to $0.95$ would shift the S06 result to lower $L_X$ and preserve the current level of Malmquist-bias for the RB02 result." + Llowever. this adjustment would ollse the SOG and maxBCCRASS relations at the 260 level.," However, this adjustment would offset the S06 and maxBCG–RASS relations at the $2 \sigma$ level." + Since it is binned by richness. the maxBCCRASS result is sensitive to covariance among Ly and Noy a κος Adoug.," Since it is binned by richness, the maxBCG–RASS result is sensitive to covariance among $L_X$ and $N_{200}$ at fixed $M_{200}$." + Simulations suggest mild anti-correlation. as a ixed mass high concentration halos have higher Ly bu ewer galaxies2006).," Simulations suggest mild anti-correlation, as at fixed mass high concentration halos have higher $L_X$ but fewer galaxies." +.. As an illustration of he elfect of covariance. consider the case of a bivariate. og-normal distribution for Ly ancl Nou with constan covariance.," As an illustration of the effect of covariance, consider the case of a bivariate, log-normal distribution for $L_X$ and $N_{200}$ with constant covariance." +" The olf-ciagonal term can be characterized. by he correlation coellicient. +ÓlitLOlNO. Where oy=(In.X—In.Y)/eo1,x are the normalized. deviations from the mean relation."," The off-diagonal term can be characterized by the correlation coefficient, $r \equiv \langle \delta_{{\rm +ln}L} \delta_{{\rm ln}N} \rangle$, where $\delta_{{\rm ln}X} = ({\rm ln}X- {\rm +ln}\bar{X}) / \sigma_{{\rm ln}X}$ are the normalized deviations from the mean relation." + Consider a mass function that is a local power-law. απαλή~AlOU=eUU. where p—InM.," Consider a mass function that is a local power-law, $dn/d{\rm ln}M \sim +M^{-\alpha} = e^{-\alpha \mu}$, where $\mu \equiv \ln M$." + Convolving this function with the bivariate log-normial. ancl using Bayes’ theorem. allows one to write the conditional likelihood Poplv). where f=InLy and v=InNowy.," Convolving this function with the bivariate log-normal, and using Bayes' theorem, allows one to write the conditional likelihood $P(\ell , \mu | \nu) $, where $\ell \equiv \ln +L_X$ and $\nu \equiv \ln N_{200}$." +" Phe result is a bivariate Gaussian with mean mass pl)=pol)ασ2ule with ο). the inverse of the input mean richnessmass relationand 0,4, the scatter in mass at fixed richness."," The result is a bivariate Gaussian with mean mass $\bar{\mu}(\nu) = \bar{\mu}_0(\nu) - \alpha \sigmn^2$, with $\bar{\mu}_0(\nu)$ the inverse of the input mean richness–mass relationand $\sigmn$ the scatter in mass at fixed richness." + The X-ray luminosity at fixed optical richness is distributed in a los-normal manner with mean and variance where p is the slope of the halo Ly Adsoy relation., The X-ray luminosity at fixed optical richness is distributed in a log-normal manner with mean and variance where $p$ is the slope of the halo $L_X-M_{200}$ relation. + When Lx and Nous are independent (e— 0). the mean luminosity reflects that of the mean mass selected. by the richness cut.," When $L_X$ and $N_{200}$ are independent $r = 0$ ), the mean luminosity reflects that of the mean mass selected by the richness cut." + When rz 0. the mean is shifted by an amount," When $r \ne 0$ , the mean is shifted by an amount" +knots. connected to the core by a much fainter low-ionization lane (Corradi ct al.,"knots, connected to the core by a much fainter low-ionization lane (Corradi et al." + 2000: see Figure 1)., 2000; see Figure 1). + Goncaalves. et al. (, Gonçaalves et al. ( +2001) have proposed that the low-ionization lanes and knots of Ix 4-47 are genuine jets.,2001) have proposed that the low-ionization lanes and knots of K 4-47 are genuine jets. + Their morphological and kinnemmatticcal properties are explainable if the jets and knots were formed by accretion disks. attaining velocities of several hundred. kilometers per second (the main properties of these models. are also summarized. in Goncaalves et al.," Their morphological and cal properties are explainable if the jets and knots were formed by accretion disks, attaining velocities of several hundred kilometers per second (the main properties of these models are also summarized in Gonçaalves et al." + 2001 and Balick Frank 2002)., 2001 and Balick Frank 2002). + These highly supersonic velocities imply that the resulting LISs are likely to be shock-excited., These highly supersonic velocities imply that the resulting LISs are likely to be shock-excited. + lx 4-47 is a poorly stucied PN. for which statistical methods provide an unrealistic wide range of distances. for instance. N.5 kpc (Cahn. Whaler Stanghellini 1992) or 26 kpe (van de Steene Zijlstra 1994).," K 4-47 is a poorly studied PN, for which statistical methods provide an unrealistic wide range of distances, for instance, 8.5 kpc (Cahn, Kaler Stanghellini 1992) or 26 kpc (van de Steene Zijlstra 1994)." + Corradi. et al. (, Corradi et al. ( +2000) computed a distance between 3 kpe and 7 kpc assuming that the object participates to the ordered rotation of the disk. of the Galaxy. but. note that the relatively aree height of IX. 4-437 on the Galactic. plane (0.54. kpe or a distance of 7 kpc) adds some further uncertainty to his determination.,"2000) computed a distance between 3 kpc and 7 kpc assuming that the object participates to the ordered rotation of the disk of the Galaxy, but note that the relatively large height of K 4-47 on the Galactic plane (0.54 kpc for a distance of 7 kpc) adds some further uncertainty to this determination." + Tajitsu Tamura (1998) estimated a distance of 5.9 kpc using the integrated. LAS fluxes under he (crude) assumption of constant dust mass for all PNe., Tajitsu Tamura (1998) estimated a distance of 5.9 kpc using the integrated IRAS fluxes under the (crude) assumption of constant dust mass for all PNe. + Lacking of anything better. we shall adopt in the following his distance of 5.9 κρο," Lacking of anything better, we shall adopt in the following this distance of 5.9 kpc." + Lumsden et al. (, Lumsden et al. ( +2001). mapped he HI» emission from Ix 4-47 finding that it is excited. by shocks.,2001) mapped the $_2$ emission from K 4-47 finding that it is excited by shocks. + The object also appears in the 6 em VLA radio survey of Aacuist Kwok (1990) showing a very compact radio core. with a diameter of 0.25 arcsec. and one of the largest brightness temperatures (Εςστο Ix) found in PNe.," The object also appears in the 6 cm VLA radio survey of Aaquist Kwok (1990) showing a very compact radio core, with a diameter of 0.25 arcsec, and one of the largest brightness temperatures $_b$ =8700 K) found in PNe." + So far. the properties (Luminosity ancl temperature) of its central star as well as its nebular (physical ancl chemical) properties are not. known.," So far, the properties (luminosity and temperature) of its central star as well as its nebular (physical and chemical) properties are not known." + 1n this work. we address the debated issue of the nature and origin of hieh-velocity LISs. through the determination of the physical parameters. excitation and chemistry of Ix 47.," In this work, we address the debated issue of the nature and origin of high-velocity LISs, through the determination of the physical parameters, excitation and chemistry of K 4-47." + Spectra of the core and the pair of knots are analyzed using two different models. which consider the gas to be either fully photoionized by the PN central star. or fully ionized by shocks.," Spectra of the core and the pair of knots are analyzed using two different models, which consider the gas to be either fully photoionized by the PN central star, or fully ionized by shocks." + We will show that Ix 4-47 is particularly: interesting for this study because. in contrast to most of the LISs studied up to now (Dopita 1997: Dwarkadas Dalick 1908: Miranda et al.," We will show that K 4-47 is particularly interesting for this study because, in contrast to most of the LISs studied up to now (Dopita 1997; Dwarkadas Balick 1998; Miranda et al." + 2000: Goncaalves 2003: Goncaalves et al., 2000; Gonçaalves 2003; Gonçaalves et al. + 2003). its pair of LISs is mainly shock excited.," 2003), its pair of LISs is mainly shock excited." + Spectra. of Ix 4-47. were obtained on 2001. August 28 at he 2.5m Isaac Newton telescope (INTE) at the Observatorio del Roque de los Muchachos on La Palma (Spain). using he Intermediate Dispersion Spectrograph (LDS).," Spectra of K 4-47 were obtained on 2001 August 28 at the 2.5m Isaac Newton telescope (INT) at the Observatorio del Roque de los Muchachos on La Palma (Spain), using the Intermediate Dispersion Spectrograph (IDS)." + The LDS was used with the 235 mm camera and the 300V. erating. oxoviding a spectral coverage from 3650 to 7000 wwith a spectral reciprocal dispersion of 3.3 pix.* anda resolution of 6.9A.," The IDS was used with the 235 mm camera and the R300V grating, providing a spectral coverage from 3650 to 7000 with a spectral reciprocal dispersion of 3.3 $^{-1}$ and a resolution of 6.9." +. Phe spatial scale of the instrument was Y'.70 pix.1 with the TEKS CCD., The spatial scale of the instrument was $''$ .70 $^{-1}$ with the TEK5 CCD. +" Seeing varied from 1"".1 o 17.2.", Seeing varied from $''$ .1 to $''$ .2. + The slit width and length were aand4... respectively.," The slit width and length were and, respectively." + The slit was positioned through the centre of the nebula at PX. = 41. passing through the knots. and the exposure times were 3. 1500. Bias frames. twilight and tungsten flat-field exposures. ares and exposures of standard stars DD]332642. Cre ODB23990. IIDIO445. and BD|254655. were. obtained.," The slit was positioned through the centre of the nebula at P.A. = $^{\circ}$, passing through the knots, and the exposure times were $\times $ 1800 s. Bias frames, twilight and tungsten flat-field exposures, arcs and exposures of standard stars BD+332642, Cyg 9, HD19445, and BD+254655, were obtained." + Spectra were reduced. and tux calibrated. usine the standard. URAL package for long-slit: spectra., Spectra were reduced and flux calibrated using the standard IRAF package for long-slit spectra. + Line Duxes were measured sepparrattellv for the three nebular regions indicated in Figure 1.. namely L.. aanclIxnot2..," Line fluxes were measured ly for the three nebular regions indicated in Figure \ref{image}, namely , and." + The observed line Utixes are given in Table 1., The observed line fluxes are given in Table 1. + Errors in the fluxes were caleulated taking into account the errors in the measurement of the fluxes. as well as systematic errors of the µας calibrations. background determination. and sky subtraction.," Errors in the fluxes were calculated taking into account the errors in the measurement of the fluxes, as well as systematic errors of the flux calibrations, background determination, and sky subtraction." + The bottom lines of ‘Table 1 give the estimated accuracy of the measured. [uxes for a range of line Uuxes (relative to 1111} in cach of the regions., The bottom lines of Table 1 give the estimated accuracy of the measured fluxes for a range of line fluxes (relative to ) in each of the regions. + Absolute fliuxes integrated alone the slit in. cach region are as follows: ΠΛ FOUL)ο Ve. =2.76: and P(e =1.64 (in units of 10.17 ere ceniτς dy ," Absolute fluxes integrated along the slit in each region are as follows: $_{\rm {Knot1}}$ =2.41; $_{\rm +{Core}}$ =2.76; and $_{\rm {Knot2}}$ =1.64 (in units of $10^{-15}$ erg $^{-2}$ $^{-1}$ )." +Figure 2 shows the spatial profiles. of low- to high-excitation oxvgen emission lines6300A.. 3729A)) anc 5007A)): we clearly sec hat the knots have a much lower excitation than the core.," Figure \ref{ratio} shows the spatial profiles of low- to high-excitation oxygen emission lines, ) and ); we clearly see that the knots have a much lower excitation than the core." + While the low-ionization proliles aand 13729A))) show local maxima at the positions of the knots. the »prolile presents its maxima in the core and does not peak at the knots.," While the low-ionization profiles and )) show local maxima at the positions of the knots, the profile presents its maxima in the core and does not peak at the knots." + The average values of aab the knots are 2.0 (Ixnot1)) and. 2.1. (Ixnot2)). much ugher than those usually found for spherical ancl elliptical Ne (c.g. Aller Czvzak 1983). although such. values are requenthy found in the Peimbert Tvpe E objects (Peimbert 978: Peimbert Torres-Peimbert 1983).," The average values of at the knots are 2.0 ) and 2.1 ), much higher than those usually found for spherical and elliptical PNe (e.g., Aller Czyzak 1983), although such values are frequently found in the Peimbert Type I objects (Peimbert 1978; Peimbert Torres-Peimbert 1983)." + Phe Core. on the," The , on the" +CXOU JOL0048-721184 which is in the SAIC. since their position in the P?P diagram is unlikely to depend on which ealaxy they reside.,"CXOU J010043-721134 which is in the SMC, since their position in the $P-\dot +{P}$ diagram is unlikely to depend on which galaxy they reside." + The predicted: number of active magnetars [rom our [avoured mocdel can be reconciled with the observed number of 5ROSAT detected sources if we assume that only ~20% of magnetars were in an active state which brought then toa high enough luminosity to be detected by this satellite., The predicted number of active magnetars from our favoured model can be reconciled with the observed number of 5 detected sources if we assume that only $\sim 20$ of magnetars were in an active state which brought them to a high enough luminosity to be detected by this satellite. + 1n this case. the actual birthrate of magnetars would be ~3510tye +. which of course depends on our. basic assumption that all stars in the mass range 20945M. produce magnetars.," In this case, the actual birthrate of magnetars would be $\sim 3\times +10^{-3}\,$ $^{-1}$, which of course depends on our basic assumption that all stars in the mass range $20-45\Msun$ produce magnetars." + However. we note that the total number of observed. magnetars in the Galaxy is only 14.," However, we note that the total number of observed magnetars in the Galaxy is only 14." + If. no additional magnetars exist in our Galaxy. that is if all magnetars have already. been discovered. this means that we have produced too many magnetars from progenitors in he mass range 20.��45M...," If no additional magnetars exist in our Galaxy, that is if all magnetars have already been discovered, this means that we have produced too many magnetars from progenitors in the mass range $20-45\Msun$." + This may suggest that. some οἱ stars in this mass range will produce black holes., This may suggest that some of stars in this mass range will produce black holes. + 1 his is the case. the birth rate of magnetars would reduce to 1.5Qv d.," If this is the case, the birth rate of magnetars would reduce to $\sim 1.5\times +10^{-3}\,$ $^{-1}$." + Studies of SCA bursts conducted by Ixouveliotouctal.(1994) indicated that there cannot be more than 7 active SGlsinthe Galaxy and Ixouveliotouetal.(1998). suggested hat magnetars are born at arate of about 0.1 per century.," Studies of SGR bursts conducted by \citet{Kouveliotou94} indicated that there cannot be more than 7 active SGRs in the Galaxy and \citet{Kouveliotou98} + suggested that magnetars are born at a rate of about $0.1$ per century." + The recent study. carried. out by Cill&τον(2007). was απο on a study of the five AXPs detected in theROSAT All-Sksy Survey. and indicated a birthrate of 0.22 per century with their progenitors being massive main sequence stars.," The recent study carried out by \citet{Gill07} was based on a study of the five AXPs detected in the All-Sky Survey, and indicated a birthrate of 0.22 per century with their progenitors being massive main sequence stars." + Both these estimates are generally consistent with the birth rate that we deduce., Both these estimates are generally consistent with the birth rate that we deduce. + Another recent study carried out by Alunoetal.(2008) who searched for magnetars in archival Chandra and. NAIAI-Newton observations of the Galactic plane. vielded a birthrate in the range 3.10%ὅ107 |.," Another recent study carried out by \citet{Muno08} who searched for magnetars in archival Chandra and XMM-Newton observations of the Galactic plane, yielded a birthrate in the range $3\times 10^{-3}-6\times 10^{-2}\,$ $^{-1}$." + The upper end of this range is exeluded by our calculations., The upper end of this range is excluded by our calculations. + On the fossil field hypothesis. the high value indicated for the magnetic Dux index > may simply rellect the intrinsic magnetic [ux distribution on the main sequence.," On the fossil field hypothesis, the high value indicated for the magnetic flux index $\gamma$ may simply reflect the intrinsic magnetic flux distribution on the main sequence." +" Observations of main sequence stars show that the maximum magnetic Uuxes observed on the main sequence map on to the magnetic Huxes of the highest field magnetic white dwarls (10710"" € ) and neutron stars (1077 1057€) rather well."," Observations of main sequence stars show that the maximum magnetic fluxes observed on the main sequence map on to the magnetic fluxes of the highest field magnetic white dwarfs $10^8-10^9$ G ) and neutron stars $10^{14}-10^{15}\,$ G) rather well." + Llowever. due to sensitivity. limitations of polarimetric observations. only the upper end. of the magnetic field. distribution of main sequence stars (the stronely magnetic stars) can be observed. so we only have a partial picture of magnetism on the main sequence.," However, due to sensitivity limitations of polarimetric observations, only the upper end of the magnetic field distribution of main sequence stars (the strongly magnetic stars) can be observed, so we only have a partial picture of magnetism on the main sequence." + Unfortunately. most stars in the mass range 820M. that give rise to radio pulsars have magnetic Iuxes well below the currently observed range on the Main Sequence so that the index 5 cannot be empiricallv estimated.," Unfortunately, most stars in the mass range $8-20\Msun$ that give rise to radio pulsars have magnetic fluxes well below the currently observed range on the Main Sequence so that the index $\gamma$ cannot be empirically estimated." + We note however mt magnetic Duxes similar to those inferred in magnetars cur in 25% of massive D and O-type stars., We note however that magnetic fluxes similar to those inferred in magnetars occur in $\sim 25$ of massive B and O-type stars. + If we somehow clismiss the close similarities between 10 magnetic [fluxes of massive main sequence stars and magnetars by putting them down to mere coincidence. dternatives to the fossil field hypothesis need to be explored.," If we somehow dismiss the close similarities between the magnetic fluxes of massive main sequence stars and magnetars by putting them down to mere coincidence, alternatives to the fossil field hypothesis need to be explored." + — is possible that the mass of the progenitor determines the μαxn of the nascent neutron star and thereby the strength of a civnamo generated field., It is possible that the mass of the progenitor determines the spin of the nascent neutron star and thereby the strength of a dynamo generated field. + Support for this hypothesis comes from the caleulations of Legeretal.(2005) which allow for angular momentum transport by magnetic fields eenerated by dillerential rotation during stellar evolution.," Support for this hypothesis comes from the calculations of \cite{Heger05} + which allow for angular momentum transport by magnetic fields generated by differential rotation during stellar evolution." + Phese show that more massive stars tend. to. produce more rapidly, These show that more massive stars tend to produce more rapidly +binaries (9=3.6 km/s may mimic a chromospheric condition similar to that of WD 179949. although our cooling function gy for the chromospheric radiation is based on the observation of (he Sun (Anderson&Athay1989)."," In this sense, the model for $B_*=5 $ G and $=3.6$ km/s may mimic a chromospheric condition similar to that of HD 179949, although our cooling function $q_R$ for the chromospheric radiation is based on the observation of the Sun \citep{AA89}." +". Having obtained the radiative [lux 10°* erg ? + from the hot chromosphere in (he case for D,— 5G and =3.6 km/s. we can estimate the Iuninosity of the hot spot."," Having obtained the radiative flux $\sim 10^{6-7}$ erg $^{-2}$ $^{-1}$ from the hot chromosphere in the case for $B_*=5$ G and $=3.6$ km/s, we can estimate the luminosity of the hot spot." + In our model. (he cross-sectional area of the converge flux tube in the chromosphere is about. 8000 (mes smaller than the planets magnetosphere.," In our model, the cross-sectional area of the converging flux tube in the chromosphere is about 8000 times smaller than the planet's magnetosphere." + In other words. the area of the hot spot in the chromosphere is given by which when multiplied by (he chromospheric fux gives the luminosity of (he chromospheric hot spot zz107*7 ere/s. This total chromospheric emission is still 2-4 orders of magnitude weaker (han the observational Ca II emissions for IID 179949.," In other words, the area of the hot spot in the chromosphere is given by which when multiplied by the chromospheric flux gives the luminosity of the chromospheric hot spot $\approx 10^{23-25}$ erg/s. This total chromospheric emission is still 2-4 orders of magnitude weaker than the observational Ca II emissions for HD 179949." + By conducting a numerical experiment. we study the thermal response of the atinosphere of a solar-ivpe star (o the dissipation of an injected electron beam αἱ the coronal base.," By conducting a numerical experiment, we study the thermal response of the atmosphere of a solar-type star to the dissipation of an injected electron beam at the coronal base." + The experiment is carried out based on Che lramework of the 1-D magnetolvedrodvnamic simulation by $105 with non-linear wave dissipation. radiative cooling. and thermal conduction.," The experiment is carried out based on the framework of the 1-D magnetohydrodynamic simulation by SI05 with non-linear wave dissipation, radiative cooling, and thermal conduction." + We asstume that the magnetic stress due to the orbital motion of the planet relative to the stellar coronal fields generates an electron beam. which in turn funnels along (he stellar open fielcl lines to the central star.," We assume that the magnetic stress due to the orbital motion of the planet relative to the stellar coronal fields generates an electron beam, which in turn funnels along the stellar open field lines to the central star." + As the beam travels inwards. the energy [τικ of the incoming electron bea is intensified bv (he areal focusing of the super-radially converging open flux tube.," As the beam travels inwards, the energy flux of the incoming electron beam is intensified by the areal focusing of the super-radially converging open flux tube." + We use (he stellar parameters of ILD 179949 as an illustrative example but ignore possible magnetic properlies arising [rom ils stellar rotation., We use the stellar parameters of HD 179949 as an illustrative example but ignore possible magnetic properties arising from its stellar rotation. +" When the average stellar field al the photosphere D, is about 1 G and the average amplilucle of the wave velocity πο> is about 1.8 km/s. the stellar atinosphere is not considerably altered. alter the beam dissipation is"," When the average stellar field at the photosphere $B_*$ is about 1 G and the average amplitude of the wave velocity $$ is about 1.8 km/s, the stellar atmosphere is not considerably altered after the beam dissipation is" +Observations of the luminosity functions of high redshift galaxies enable one to determine in situ the star formation rate density. (SFRD) as a function of redshift.,Observations of the luminosity functions of high redshift galaxies enable one to determine in situ the star formation rate density (SFRD) as a function of redshift. + A plot of these two quantiües has become known as a Madau cliagram (Lilly οἱ 11996. Macdau οἱ 11996. 1993).," A plot of these two quantities has become known as a Madau diagram (Lilly et 1996, Madau et 1996, 1998)." + Locally. we observe the results of this early evolution in the form of old," Locally, we observe the results of this early evolution in the form of old" +shape and noise of the CCF. height of its central peak. anc goodness of its Gaussian fit.,"shape and noise of the CCF, height of its central peak, and goodness of its Gaussian fit." + These procedures were designec only to reduce the errors. and the results were stable whe experimenting with different combinations of procedures and involved parameters. varying by no more than a few km s.," These procedures were designed only to reduce the errors, and the results were stable when experimenting with different combinations of procedures and involved parameters, varying by no more than a few km $^{-1}$." +" When this was not the case. the measurement was judgec unreliable and excluded. as when the results were sensitive to changes in either continuum normalization or extractior algorithm,"," When this was not the case, the measurement was judged unreliable and excluded, as when the results were sensitive to changes in either continuum normalization or extraction algorithm." + After the correction to heliocentric RVs. we verified that no systematic error was present in the results.," After the correction to heliocentric RVs, we verified that no systematic error was present in the results." + First. we checked the zero-point of each frame by averaging the RVs of the 53 brightest stars. excluding measurements with errors larger than 5 km s~!.," First, we checked the zero-point of each frame by averaging the RVs of the 53 brightest stars, excluding measurements with errors larger than 5 km $^{-1}$." + We thus derived the corrections to reduce each frame to the same zero-point. although they were lower tha 1.5 km s!. i.e. well within the typical error of the 53 starX (3.5-4 km s! y.," We thus derived the corrections to reduce each frame to the same zero-point, although they were lower than 1.5 km $^{-1}$, i.e. well within the typical error of the 53 stars (3.5-4 km $^{-1}$ )." + We then plotted. for each frame. the residual ofο each star with respect to its weighted-averaged RV as a functio of the fiber number. to check for the presence of a systematic effect that varied with position on the CCD. as done by7..," We then plotted, for each frame, the residual of each star with respect to its weighted-averaged RV as a function of the fiber number, to check for the presence of a systematic effect that varied with position on the CCD, as done by." + The plot relative to the first frame is shown 1 Figure 3 as an example., The plot relative to the first frame is shown in Figure \ref{f_syst} as an example. + The average value of these residuals was always lower than 0.1 km s7!. indicating that any offset between exposures was correctly removed in the previous step.," The average value of these residuals was always lower than 0.1 km $^{-1}$, indicating that any offset between exposures was correctly removed in the previous step." + Moreover. the linear and third-order fit never differed from zero by more than | km s'. proving that there is no residual trend in the measured RVs. and the results are free from systematics well beyond the typical random errors of 33-4 km |s.," Moreover, the linear and third-order fit never differed from zero by more than 1 km $^{-1}$, proving that there is no residual trend in the measured RVs, and the results are free from systematics well beyond the typical random errors of 3-4 km $^{-1}$." + Any search for binaries by means of multi-epoch RV measurement is based on the comparison between the observed variations and the uncertainties., Any search for binaries by means of multi-epoch RV measurement is based on the comparison between the observed variations and the uncertainties. + A precise definition of the errors Is therefore of fundamental importance for the correct interpretation of the results., A precise definition of the errors is therefore of fundamental importance for the correct interpretation of the results. +" The uncertainty associated with each measurement was defined as the quadratic sum of the error of the CC technique?).. the wle error defined in refeyata.. andtheuncertaintyintroducedwhencorrectingthezero— pointo feachframe(S refe,vstematies)."," The uncertainty associated with each measurement was defined as the quadratic sum of the error of the CC technique, the wlc error defined in \\ref{c_data}, and the uncertainty introduced when correcting the zero-point of each frame \\ref{c_systematics}) )." +T hislastquantitywasde finedasthermsofthecorrection pointo fthe frame saroundthemeanvalue.," This last quantity was defined as the rms of the corrections applied to each frame, i.e. the scatter in the zero-point of the frames around the mean value." +T heCCerrorcompletelydominat," The CC error completely dominates the error budget, being typically" +figure that the clouds do not fall in the same region as the simulations: the clouds are much more concentrated around the central galaxy in both position and velocity than the darkauatter halos.,figure that the clouds do not fall in the same region as the simulations; the clouds are much more concentrated around the central galaxy in both position and velocity than the dark-matter halos. + The results of the 2-dimensional KS-test bear this out. eiviug au average probability of 8.0 ( for WAAP3 aud 7.0 for WALAPS (across all rotations of all major halos) that the velocity distributious are consistent.," The results of the 2-dimensional KS-test bear this out, giving an average probability of 8.0 $\%$ for WMAP3 and 7.0 $\%$ for WMAP5 (across all rotations of all major halos) that the position-velocity distributions are consistent." + We observed a wide area of the nearby M8] fibuneut iu au attempt to find clouds tracingo dark matter minihalos predicted by ACDM cosinological simulations., We observed a wide area of the nearby M81 filament in an attempt to find clouds tracing dark matter minihalos predicted by $\Lambda$ CDM cosmological simulations. + We detected 5 new clouds. bringing the total to 15 clouds in the AISI Filament inchiding our previously publishec observations.," We detected 5 new clouds, bringing the total to 13 clouds in the M81 Filament including our previously published observations." + Of the 13 clouds detected in the observe region. { are likely to be part of the Milkv. Wax IIVC svsteui.," Of the 13 clouds detected in the observed region, 4 are likely to be part of the Milky Way HVC system." + We compared the properties of the remaining 9 clouds to two cosinological dark natter N-body simulations., We compared the properties of the remaining 9 clouds to two cosmological dark matter N-body simulations. + We fud that there are απ fewer clouds than simulations predict. aud hat the phase space distribution of the detected clouds does not match that of he simulated clouds.," We find that there are far fewer clouds than simulations predict, and that the phase space distribution of the detected clouds does not match that of the simulated clouds." + There are two possible explanations for his discrepancy. both of which may bo true.," There are two possible explanations for this discrepancy, both of which may be true." + First. he to dark matter mass fraction in ninibalos nav be less than 0.187," First, the to dark matter mass fraction in minihalos may be less than $\%$." + Secondly. the plase space distribution of dark matter umihalos predicted by ACDM cosimological simnlatious may be incorrect.," Secondly, the phase space distribution of dark matter minihalos predicted by $\Lambda$ CDM cosmological simulations may be incorrect." + Because our simmlatious are darkauatter only. none of the simulated clouds are tidal debris (which would coutain no dark matter).," Because our simulations are dark-matter only, none of the simulated clouds are tidal debris (which would contain no dark matter)." + With these siauulations. we cannot predict the properties1 of clouds representativo of tidal debris. mut we can confidently sav that the clouds we lave detected do NOT iatch the properties expected for dark-imatter minibalos.," With these simulations, we cannot predict the properties of clouds representative of tidal debris, but we can confidently say that the clouds we have detected do NOT match the properties expected for dark-matter minihalos." + The detected clouds are also not compatible with cold accretion. since we do not detect clouds near ion-interactiug galaxiescol accretion clouds should be detectable regardless of interactions.," The detected clouds are also not compatible with cold accretion, since we do not detect clouds near non-interacting galaxies–cold accretion clouds should be detectable regardless of interactions." + In ‘act. recent research sugeests that cold accretion clouds should be prevalent in non-interacting eroups. due to the lack of mitigating environmental effects COosterlooetal.2010).," In fact, recent research suggests that cold accretion clouds should be prevalent in non-interacting groups, due to the lack of mitigating environmental effects \citep{ost10}." +. Therefore. we conclude that the clouds we have detected are not likely to be tracers of the predicted darkanatter münibhalos iu tle Meal Fibunent.," Therefore, we conclude that the clouds we have detected are not likely to be tracers of the predicted dark-matter minihalos in the M81 Filament." + Lustead. they are most likelv eenerated through galaxy interactions.," Instead, they are most likely generated through galaxy interactions." + Iu order to understand the detailed role of galaxy interactions πι ecueratineg clouds. further simulatious inchidingo ogas physics aud deeper observatious of more filbunents are needed.," In order to understand the detailed role of galaxy interactions in generating clouds, further simulations including gas physics and deeper observations of more filaments are needed." + This study allows us to constrain the uuuber of detected clouds that may be selt-eravitatiug., This study allows us to constrain the number of detected clouds that may be self-gravitating. + Tn a study of eravitationally bound molecular clouds. Larson(1979.1981) fouud a strong correlation between velocity dispersion aud cloud size. given bv where £ is the diameter of the cloud.," In a study of gravitationally bound molecular clouds, \citet{lar79,lar81} found a strong correlation between velocity dispersion and cloud size, given by where $L$ is the diameter of the cloud." + Our survey detection threshold of σι = 10 kins + οἼνος a cloud size of 330 pe. so the angular resolution of our observations (10 kpe) is the Πιο factor in detecting sclberavitating clouds.," Our survey detection threshold of $\sigma_v$ = 10 km $^{-1}$ gives a cloud size of 330 pc, so the angular resolution of our observations (10 kpc) is the limiting factor in detecting self-gravitating clouds." + All of our clouds are unresolved in the CBT beam., All of our clouds are unresolved in the GBT beam. + Our aneular resolution limit gives a velocity dispersion of 36 kan !. so for anv of the detected clouds to be sclteravitating they must have a velocity dispersion less than or equal to this value.," Our angular resolution limit gives a velocity dispersion of 36 km $^{-1}$, so for any of the detected clouds to be self-gravitating they must have a velocity dispersion less than or equal to this value." + Ouly two of he 9 clouds that we have cetermined to reside in the M81 group satisfy this coustraint., Only two of the 9 clouds that we have determined to reside in the M81 group satisfy this constraint. + The nuplication of this constraint is that most interaction-ecnerated clouds iu our detection space are not seltberavitating., The implication of this constraint is that most interaction-generated clouds in our detection space are not self-gravitating. + On a side note. darkanatter filaments such as the M81 Fibuueut are predicted to have diffuse emission (Poppingetal. 2009).," On a side note, dark-matter filaments such as the M81 Filament are predicted to have diffuse emission \citep{popping09}." +. The enmüssiou is predicted to be approxinately 3 times fainter than our survey., The emission is predicted to be approximately 3 times fainter than our survey. + Our observations do. however. place an upper limit ou diffuse emission from the cosmic web.," Our observations do, however, place an upper limit on diffuse emission from the cosmic web." + To estimate this. we determined our column density seusitivitv usine: The average Do detection thresholkl for column denstv was Li ον 1015 cin?.," To estimate this, we determined our column density sensitivity using: The average $\sigma$ detection threshold for column density was 4.4 $\times$ $^{18}$ $^{-2}$." + This column density falls within the Desert”. where the eas in the cosnüc web is not affected bv selt-shiclding and is therefore photoionized," This column density falls within the Desert"", where the gas in the cosmic web is not affected by self-shielding and is therefore photoionized" +"A more detailed view of the metal distribution is shown in Figures 5 and 6, where we plot the enriched mass as a function of gas overdensity and metallicity.","A more detailed view of the metal distribution is shown in Figures 5 and 6, where we plot the enriched mass as a function of gas overdensity and metallicity." +" Early on, the initial ejecta have not propagated very far and the metals occupy a small region in density and metallicity space, located at the relic H11 region density of ~0.1cm7° and at supersolar metallicities."," Early on, the initial ejecta have not propagated very far and the metals occupy a small region in density and metallicity space, located at the relic H region density of $\sim 0.1~{\rm cm}^{-3}$ and at supersolar metallicities." +" Over time, the SN remnant then distributes its metals to the surrounding medium and the average metallicity decreases, while the total enriched mass increases."," Over time, the SN remnant then distributes its metals to the surrounding medium and the average metallicity decreases, while the total enriched mass increases." +" Once the potential well of the galaxy has become deep enough, a large fraction of the hot, metal-rich gas residing in the IGM has recollapsed to high densities."," Once the potential well of the galaxy has become deep enough, a large fraction of the hot, metal-rich gas residing in the IGM has recollapsed to high densities." +" By z~10, the enriched mass contained within the densest parcels of gas in the galaxy has increased to roughly 10°Mo, with a clear peak in the distribution at Z~107?Zo."," By $z\simeq 10$, the enriched mass contained within the densest parcels of gas in the galaxy has increased to roughly $10^{5}~M_{\odot}$, with a clear peak in the distribution at $Z\sim 10^{-3}~Z_{\odot}$." +" Interestingly, this exceeds any critical metallicity quoted in the literature (Bromm&Loeb2003;Schneideretal. and we expect that a stellar cluster with a normal 2006),IMF will form2009)."," Interestingly, this exceeds any critical metallicity quoted in the literature \citep{bl03a,schneider06}, and we expect that a stellar cluster with a normal IMF will form." +. It therefore appears that a single PISN is sufficient to trigger a transition from Pop HI to Pop II star formation., It therefore appears that a single PISN is sufficient to trigger a transition from Pop III to Pop II star formation. +" Finally, we note that the additional photoheating in Sim A has an interesting effect on the distribution of metals."," Finally, we note that the additional photoheating in Sim A has an interesting effect on the distribution of metals." +" As is evident from Figures 1 and 2, the enriched region is generally larger and better mixed in Sim A. In some cases, the photoheating even ejects significant amounts of enriched gas out of the potential well of the galaxy, which can be seen in the case of the metal bubble extending to the lower left of the simulation box."," As is evident from Figures 1 and 2, the enriched region is generally larger and better mixed in Sim A. In some cases, the photoheating even ejects significant amounts of enriched gas out of the potential well of the galaxy, which can be seen in the case of the metal bubble extending to the lower left of the simulation box." +" This behavior is intriguing in light of claims that the IGM is substantially enriched at high redshifts &Cowie1996;Schayeetal.2003),, although this (Songailais generally attributed to SN feedback instead of photoheating, which acts on objects with small circular velocities (Thoul&Weinberg1996;Dijkstraetal."," This behavior is intriguing in light of claims that the IGM is substantially enriched at high redshifts \citep{sc96,schaye03}, although this is generally attributed to SN feedback instead of photoheating, which acts on objects with small circular velocities \citep{tw96,dijkstra04}." +" Comparing Figures 5 and 6, we also find more quantitative2004).. evidence of this effect."," Comparing Figures 5 and 6, we also find more quantitative evidence of this effect." +" From top left to bottom right, an increasing amount of enriched gas accumulates at low densities, which then accretes onto the nascent galaxy."," From top left to bottom right, an increasing amount of enriched gas accumulates at low densities, which then accretes onto the nascent galaxy." +" In both simulations, we have included fine-structure cooling for C, O and Si at low temperatures and collisional excitation and recombination cooling at high temperatures."," In both simulations, we have included fine-structure cooling for C, O and Si at low temperatures and collisional excitation and recombination cooling at high temperatures." +" Depending on metallicity, the latter can dominate over H and He cooling at very early times."," Depending on metallicity, the latter can dominate over H and He cooling at very early times." +" Such a phase exists during the first few million years after the SN explosion, when the temperature of the SN remnant exceeds 10?K and the metallicity within the remnant is well above solar."," Such a phase exists during the first few million years after the SN explosion, when the temperature of the SN remnant exceeds $10^{5}~{\rm K}$ and the metallicity within the remnant is well above solar." +" By performing test runs with and without metal line cooling in a smaller simulation box, we have found that metals temporarily enhance the net cooling rate by a factor of a few."," By performing test runs with and without metal line cooling in a smaller simulation box, we have found that metals temporarily enhance the net cooling rate by a factor of a few." +" However, even for the case of a PISN, the influence on the dynamical evolution of the SN remnant remains small."," However, even for the case of a PISN, the influence on the dynamical evolution of the SN remnant remains small." +" At temperatures below 104K, fine-structure cooling provided by heavy elements takes over."," At temperatures below $10^{4}~{\rm K}$, fine-structure cooling provided by heavy elements takes over." +" However, we find that once the gas has cooled to the regime where"," However, we find that once the gas has cooled to the regime where" +In order to simulate the time evolution of dark matter halos and the ICM in merging clusters. we use the latest. version of GRAPE (GRavity PipE. GRAPE-7). which is the special-purpose computer for gravitational dwnamücs (Sugimoto et al.,"In order to simulate the time evolution of dark matter halos and the ICM in merging clusters, we use the latest version of GRAPE (GRavity PipE, GRAPE-7), which is the special-purpose computer for gravitational dynamics (Sugimoto et al." + 1990)., 1990). + We use our orginal GRADPE-SPII code (Bekki Chiba 2006: Dekki 2009) which combines the method of smoothed particle hvdrodyvnamies (SPII) with GRAPE for ealeulations of thiree-dimensional sell-eravitating fluids in astrophysics., We use our original GRAPE-SPH code (Bekki Chiba 2006; Bekki 2009) which combines the method of smoothed particle hydrodynamics (SPH) with GRAPE for calculations of three-dimensional self-gravitating fluids in astrophysics. + Since the models for the structures of dark matter halos and the physical properties of hot eas within the halos are already given in detail by Bekki (2009). we only brielly describe the models here.," Since the models for the structures of dark matter halos and the physical properties of hot gas within the halos are already given in detail by Bekki (2009), we only briefly describe the models here." +" The structure of each of the two clusters in a merger is modeled. using an ""NEW? profile predicted by the cold dark matter cosmology (Navarro et al.", The structure of each of the two clusters in a merger is modeled using an “NFW” profile predicted by the cold dark matter cosmology (Navarro et al. +" 1996). and (he masses and sizes of the clusters are represented by M4 aud 2,4. respectively."," 1996), and the masses and sizes of the clusters are represented by $M_{\rm cl}$ and $R_{\rm cl}$, respectively." + Henceforth. all masses and lengths are measured in units of M4 ancl τος respectively. unless otherwise specified.," Henceforth, all masses and lengths are measured in units of $M_{\rm cl}$ and $R_{\rm cl}$, respectively, unless otherwise specified." + Velocity and time are measured in units of Vy = (GMa/R4)? and lay = (RU/GMA)!7. respectivelv. where G is the gravitational constant and assumed to be 1.0 in the present studs;," Velocity and time are measured in units of $V_{\rm cl}$ = $ +(GM_{\rm cl}/R_{\rm cl})^{1/2}$ and $t_{\rm cl}$ = $(R_{\rm +cl}^{3}/GM_{\rm cl})^{1/2}$, respectively, where $G$ is the gravitational constant and assumed to be 1.0 in the present study." + These V; and /4 correspond to the circular velocity. and dvnamical (ime scale at I4. respectively.," These $V_{\rm cl}$ and $t_{\rm cl}$ correspond to the circular velocity and dynamical time scale at $R_{\rm d}$, respectively." +" The c parameter (=""μι. where ry and rj, are the scale and virial radii of the NEW profile. respectively) for a cluster with M4 (—May) is chosen according to the predicted C- May relation in the ACDM simulations (e.g.. Neto οἱ al."," The $c$ parameter $=r_{\rm s}/r_{\rm vir}$, where $r_{\rm s}$ and $r_{\rm vir}$ are the scale and virial radii of the NFW profile, respectively) for a cluster with $M_{\rm cl}$ $M_{\rm dm}$ ) is chosen according to the predicted $c$ $M_{\rm dm}$ relation in the $\Lambda$ CDM simulations (e.g., Neto et al." + 2007)., 2007). + A reasonable value of e is thus 4.7 for May=10M., A reasonable value of $c$ is thus 4.7 for $M_{\rm dm}=10^{14} {\rm M}_{\odot}$. + The larger and smaller clusters in a merger. whose mass ratio is denoted as a (0.1xma< 1). are relerred to as CLI and CL2. respectively. for convenience.," The larger and smaller clusters in a merger, whose mass ratio is denoted as $m_{\rm 2}$ $0.1 \le m_{\rm 2} \le 1$ ), are referred to as CL1 and CL2, respectively, for convenience." +" If CLI has mass M4 and radius Z4. then CL2 has mass m»M, and radius ym»fia."," If CL1 has mass $M_{\rm cl}$ and radius $R_{\rm cl}$, then CL2 has mass $m_{2} M_{\rm cl}$ and radius $\sqrt{m_2}R_{\rm cl}$." +" The ICM has mass M, and the same spatial distribution (pe) as the dark matter and is assumed to be initially in hydrostatic equilibrium.", The ICM has mass $M_{\rm g}$ and the same spatial distribution ${\rho}_{\rm g}$ ) as the dark matter and is assumed to be initially in hydrostatic equilibrium. + The initial gaseous temperature of an ICM particle is therefore determined by the gas density. total mass. and gravitational potential at the location of the particle via Eulers equation for hydrostatic equilibrium (e.g.. equation LE-8 in Binney Tremaine 1937).," The initial gaseous temperature of an ICM particle is therefore determined by the gas density, total mass, and gravitational potential at the location of the particle via Euler's equation for hydrostatic equilibrium (e.g., equation 1E-8 in Binney Tremaine 1987)." + Therefore gaseous temperature Tr) at radius r from the center of a cluster can be described as: where my. C. and Ay ave the proton mass. the gravitational constant. and the Dolizmanun constant. respectively. and. M(7) is the total mass within + determined by (he adopted mass distributions of dark matter aud. barvonic components in the cluster.," Therefore gaseous temperature $T_{g}(r)$ at radius $r$ from the center of a cluster can be described as: where $m_{\rm p}$, $G$, and $k_{\rm B}$ are the proton mass, the gravitational constant, and the Boltzmann constant, respectively, and $M(r)$ is the total mass within $r$ determined by the adopted mass distributions of dark matter and baryonic components in the cluster." + Radiative cooling is, Radiative cooling is +ootpoiuts of the Parker spiral.,footpoints of the Parker spiral. + However. dy considering ιο ETT wave as a fastanode MIID wave (which moves aster at higher altitudes due to decreasing deusitv). thev showed that the calculated wave frout at higher altitude (~ LOR.) is fast chough to connect the dare site with 1e Sup-spacecratt field line.," However, by considering the EIT wave as a fast-mode MHD wave (which moves faster at higher altitudes due to decreasing density), they showed that the calculated wave front at higher altitude $\sim$ $1.5R_\odot$ ) is fast enough to connect the flare site with the Sun-spacecraft field line." + We would like to suggest an alternative possibility., We would like to suggest an alternative possibility. + Our simulation results (Figures 6 and 12)) show rat reconnection between the core magnetic fix rope Gutimately connected with the flare region) and the overlying or surrounding maeuctic Ποια occurs at a simular height range., Our simulation results (Figures \ref{fig:f7} and \ref{fig:f8}) ) show that reconnection between the core magnetic flux rope (intimately connected with the flare region) and the overlying or surrounding magnetic field occurs at a similar height range. + The recounectiou(s) subsequently displace the flux rope connectivity out of the fare region to a distance of ~ LAR... cousisteut with observations.," The reconnection(s) subsequently displace the flux rope connectivity out of the flare region to a distance of $\sim$ $1R_\odot$, consistent with observations." + Using a combination of multiwavelength observational analysis aud a elobal MIID simulation driven by real data. we study the 13 February 2009 coronal wave CME dinuuines event observed by STEREO. in quadrature.," Using a combination of multi-wavelength observational analysis and a global MHD simulation driven by real data, we study the 13 February 2009 coronal wave – CME – dimmings event observed by STEREO, in quadrature." + We fud that the diffuse bright frout cuission is primarily due to mass density cuhanucement., We find that the diffuse bright front emission is primarily due to mass density enhancement. + This is caused by a conibination of both wave and non-wave nechauisuis. both of which are diecth-diveu bv the CATE. which expands to a considerable lateral exteut in the low (< 200 Miu) corona.," This is caused by a combination of both wave and non-wave mechanisms, both of which are directly-driven by the CME, which expands to a considerable lateral extent in the low $<$ 200 Mm) corona." +" The reorganization of the magnetic field through reconnection facilitates lateral expansion of the CME. leading to far-reaching compression aud ""opening"" of the surrounding maguetic field."," The reorganization of the magnetic field through reconnection facilitates lateral expansion of the CME, leading to far-reaching compression and “opening” of the surrounding magnetic field." + This is further evidenced by secondary dinnünugs that form across the solar disk., This is further evidenced by secondary dimmings that form across the solar disk. + We find the diffuse coronal wave frout displays a dual structure. consisting of a brighter and a weaker component.," We find the diffuse coronal wave front displays a dual structure, consisting of a brighter and a weaker component." + The brighter coumponcut. observed primarily in base difference EUVI data. is due to plasma bene conrpressed. by the expanding CATE (against both sumroundius and overbliues magnetic field).," The brighter component, observed primarily in base difference EUVI data, is due to plasma being compressed by the expanding CME (against both surrounding and overlying magnetic field)." + Some of the bright patches correspond to regions of reconnection where the Seld oricutation is favourable for this to occur., Some of the bright patches correspond to regions of reconnection where the field orientation is favourable for this to occur. + This unou-wawve component maps directly to the CME footprint at every stage of the evolution., This non-wave component maps directly to the CME footprint at every stage of the evolution. +" Thus. there is a strong coupling between the development of the coronal ""wave bright frout. CATE aud associated. dinmnuiues."," Thus, there is a strong coupling between the development of the coronal “wave” bright front, CME and associated dimmings." + The weaker component. which is most likely to be detected iun runuiug difference EUVI data is present throughout the event. aud ultimately decouples from the bright compoucut after the CATE ceases: lateral expansion late iu the event.," The weaker component, which is most likely to be detected in running difference EUVI data is present throughout the event, and ultimately decouples from the bright component after the CME ceases lateral expansion late in the event." + This suggests that the weaker conrponeut is au MIID wave. initially driven by the expanding CALE. later becoming freely propagating.," This suggests that the weaker component is an MHD wave, initially driven by the expanding CME, later becoming freely propagating." + This work demonstrates the considerable isiglt eained from advanced numerical/ simulations well constrained by observations., This work demonstrates the considerable insight gained from advanced numerical simulations well constrained by observations. + We hope that this worl can progress the coronal wave community away frou divisive. separatist theories toward a amore coliesive. holistic approach to understaudius the complexity of EUV coronal waves.," We hope that this work can progress the coronal wave community away from divisive, separatist theories toward a more cohesive, holistic approach to understanding the complexity of EUV coronal waves." + Future work should focus on the colubined analysis of other well-observed events and on what coronal “waves” can tell us both about their dviving CAIEs. aud the structure and dynamics of the surrounding corona.," Future work should focus on the combined analysis of other well-observed events and on what coronal “waves” can tell us both about their driving CMEs, and the structure and dynamics of the surrounding corona." + The potential for coronal scisinoloey can now be pursued with the coufident identification of the true wave component., The potential for coronal seismology can now be pursued with the confident identification of the true wave component. + As this study demonstrates. detailed elobal ATID siuulations are essential for firtlerine development of comprehensive physical models.," As this study demonstrates, detailed global MHD simulations are essential for furthering development of comprehensive physical models." + We must now imclude rigorous quantitative data analvsis for comparison with such imnodols, We must now include rigorous quantitative data analysis for comparison with such models. + This eoal will be forwarcdec both by the continuing development of automatec lcasurement techuiques aud by the wpcomime launch of the Atmospheric Imaging Assembly aboard the Solar Dynamics Observatory., This goal will be forwarded both by the continuing development of automated measurement techniques and by the upcoming launch of the Atmospheric Imaging Assembly aboard the Solar Dynamics Observatory. + We would like to thank an unknown referee for lisfher coments and sugecstious., We would like to thank an unknown referee for his/her comments and suggestions. + We thauk Yane Lin and Wao Thai for providing the magnuetoeram data. and Michelle Aliray for suggestions about displaviug the simulation data.," We thank Yang Liu and Hao Thai for providing the magnetogram data, and Michelle Murray for suggestions about displaying the simulation data." + We also thank Pascal Déónunouliu. Nariaki Nitta-san. Tibor Torrokks and and Veronica Outiveros for helpful discussions.," We also thank Pascal Démmoulin, Nariaki Nitta-san, Tibor Törrökk and and Veronica Ontiveros for helpful discussions." + This work. has been supported by the STINE through NSF eraut ATAL-0823592 aud the NASA eraut NNNOQABLIC-BR., This work has been supported by the SHINE through NSF grant ATM-0823592 and the NASA grant NNX09AB11G-R. + Suuulation results were obtained using the Space Weather Modeling Framework. developed by the Center for Space Environment \fodeling. at the Universitv of Michigan with funding support from NASA ESS. NASA ESTO-CT. NSF KDI. aud DoD MURI.," Simulation results were obtained using the Space Weather Modeling Framework, developed by the Center for Space Environment Modeling, at the University of Michigan with funding support from NASA ESS, NASA ESTO-CT, NSF KDI, and DoD MURI." +While long-duration GRBs have been shown to be associated with core-collapse supernovae (Galama et al.,While long-duration GRBs have been shown to be associated with core-collapse supernovae (Galama et al. + 1998: Hjorth et al., 1998; Hjorth et al. + 2003: Stanek et al., 2003; Stanek et al. + 2003). the details on how the central engine of GRBs operates remain elusive.," 2003), the details on how the central engine of GRBs operates remain elusive." + The core of the star may collapse into a few solar mass black hole accretion into which powers the GRB flow (Woosley 1993)., The core of the star may collapse into a few solar mass black hole accretion into which powers the GRB flow (Woosley 1993). + Alternatively. a millisecond period protomagnetar may form at the stellar core.," Alternatively, a millisecond period protomagnetar may form at the stellar core." + In this model. magnetic fields extract the rotational energy of the magnetar launching the GRB flow (Usov 1992: Thompson 1994).," In this model, magnetic fields extract the rotational energy of the magnetar launching the GRB flow (Usov 1992; Thompson 1994)." +" Magnetars born with dipole surface fields B,~10!—10 G are common making up around ~[0% of the neutron star population with a Galactic birth rate of ~10? | (Kouveliotou et al.", Magnetars born with dipole surface fields $B_{\rm s}\sim 10^{14}-10^{15}$ G are common making up around $\sim 10$ of the neutron star population with a Galactic birth rate of $\sim 10^{-3}$ $^{-1}$ (Kouveliotou et al. + 1998)., 1998). + This rate is 2-3 orders of magnitude higher than that of long-duration GRBs (corrected for beaming: Guetta. Piran and Waxman 2005).," This rate is 2-3 orders of magnitude higher than that of long-duration GRBs (corrected for beaming; Guetta, Piran and Waxman 2005)." + If GRBs are connected to magnetar birth. a very small fraction of magnetars power GRBs indicating that special conditions need to be satistied.," If GRBs are connected to magnetar birth, a very small fraction of magnetars power GRBs indicating that special conditions need to be satisfied." + From the theoretical perspective. fast rotation and very strong fields (even in comparison to those inferred for the Galactic magnetars) appear to be needed for a successful magnetar model for GRBs (Thompson. Chang and Quatuert 2004: Uzdensky and MacFadyen 2007: Metzger. Thompson and Quataert 2007: Bucciantini et al.," From the theoretical perspective, fast rotation and very strong fields (even in comparison to those inferred for the Galactic magnetars) appear to be needed for a successful magnetar model for GRBs (Thompson, Chang and Quataert 2004; Uzdensky and MacFadyen 2007; Metzger, Thompson and Quataert 2007; Bucciantini et al." + 2009: see also Kluznniak and Ruderman 1998: Spruit 1999)., 2009; see also Kluźnniak and Ruderman 1998; Spruit 1999). + Metzger et al. (, Metzger et al. ( +"2007) explored a variety of models for the proto-neutron star wind finding that B>3xLO"" G and P=| ms are required for a powerful wind of low baryon loading to be launched within tens of seconds as needed to explain GRBs.",2007) explored a variety of models for the proto-neutron star wind finding that $B\simmore 3\times 10^{15}$ G and $P\simeq 1$ ms are required for a powerful wind of low baryon loading to be launched within tens of seconds as needed to explain GRBs. + Galactic magnetars ean release a substantial fraction of their magnetic energy during powerful flares., Galactic magnetars can release a substantial fraction of their magnetic energy during powerful flares. +" The supergiant flare of the soft gamma-ray repeater (SGR) 1806—20 resulted in the release of E,~10” ergs on a time scale of ~0.28 (Palmer et al.", The supergiant flare of the soft gamma-ray repeater (SGR) 1806–20 resulted in the release of $E_{\rm f}\sim 10^{46}$ ergs on a time scale of $\sim 0.2$ s (Palmer et al. + 2005: Hurley et al., 2005; Hurley et al. + 2005: Frederiks et al., 2005; Frederiks et al. + 2007: for a review see Mereghetti 2008)., 2007; for a review see Mereghetti 2008). +" This energy corresponds to a fraction ~OLRΒΑ of the total magnetic energy contained in the neutron star. where R=10°R, em is the radius of the star and B=10By; G is the interior field strength."," This energy corresponds to a fraction $\sim 0.1 R_6^{-3}B_{15}^{-2}$ of the total magnetic energy contained in the neutron star, where $R=10^6R_6$ cm is the radius of the star and $B=10^{15}B_{15}$ G is the interior field strength." + Such a flare could be detected up to a distance of tens of Mpe byBATSE (Palmer et al., Such a flare could be detected up to a distance of tens of Mpc by (Palmer et al. + 2005. Hurley et al.," 2005, Hurley et al." + 2005)., 2005). + Here. I argue that SGR flares from GRB-driving magnetars are a faetor of ~100 brighter than the December 2004 flare of SGR 1806—20 because of their tenfold stronger fields.," Here, I argue that SGR flares from GRB-driving magnetars are a factor of $\sim 100$ brighter than the December 2004 flare of SGR 1806–20 because of their tenfold stronger fields." + Such flares should take place hundreds of years after the formation of the magnetar (and the associated GRB) and ean be observed out to distance of ~250 Mpe., Such flares should take place $\sim$ hundreds of years after the formation of the magnetar (and the associated GRB) and can be observed out to distance of $\sim 250$ Mpc. + L estimate that a few ofthese flares should be observed per year., I estimate that a few of these flares should be observed per year. + Radio observations at the location of the flare may be able to detect and resolve the GRB afterglow proving the GRB association., Radio observations at the location of the flare may be able to detect and resolve the GRB afterglow proving the magnetar-GRB association. + The December 27. 2004 flare from SGR 1806—20 was extremely intense on Earth.," The December 27, 2004 flare from SGR 1806–20 was extremely intense on Earth." + Saturation of the instruments makes the peak flux and spectrum of the flare hard to determine., Saturation of the instruments makes the peak flux and spectrum of the flare hard to determine. + Estimates for the peak luminosity of the flare range at Ly~0.721.7x107 ergs/s with the energy contained in the spike being £y~0.5+1.7x1079 ergs (assuming isotropic explosion and the revised distance of d. 29 kpe found in Bibby et al.," Estimates for the peak luminosity of the flare range at $L_{\rm f}\sim 0.7\div 1.7\times 10^{47}$ ergs/s with the energy contained in the spike being $E_{\rm f}\sim 0.5\div 1.7\times +10^{46}$ ergs (assuming isotropic explosion and the revised distance of $d\simeq$ 9 kpc found in Bibby et al." + 2008)., 2008). + The spectrum during the flare is described by a power-law followed by an exponential cutott slightly below ~| MeV (Palmer et al., The spectrum during the flare is described by a power-law followed by an exponential cutoff slightly below $\sim 1$ MeV (Palmer et al. + 2005: Frederiks et al., 2005; Frederiks et al. + 2007)., 2007). + SGR 1506-20 has estimated surface magnetic field of, SGR 1806–20 has estimated surface magnetic field of +"of more than 2«10.1AZ, sy+ cach.",of more than $2\times10^{-4}\;M_\odot$ $^{-1}$ each. +" Unfortunately. the temperature of the stellar winds is not well known. and so for simplicity we have assumed that all the winds are Mach 30: this corresponds to a temperature of 10! OS. Iu addition. for the sources that are used in these calculations. their location in + νο, along the liue of sight) is determined randomly with the condition that the overall distribution iu this direction matches that iu c and y."," Unfortunately, the temperature of the stellar winds is not well known, and so for simplicity we have assumed that all the winds are Mach 30; this corresponds to a temperature of $10^{4-5}$ K. In addition, for the sources that are used in these calculations, their location in $z$ (i.e., along the line of sight) is determined randomly with the condition that the overall distribution in this direction matches that in $x$ and $y$." + With this proviso. all these earbv-tvpe stars are located within the ceutral parsec surroundiue Ser A*.," With this proviso, all these early-type stars are located within the central parsec surrounding Sgr A*." + For the calculations reported here. the sources are assumed to be stationary over the duratiou of the simulation.," For the calculations reported here, the sources are assumed to be stationary over the duration of the simulation." + The stars without auv observed He I line cussion have been assigned a wind velocity of 750kus| and au equal uss loss rate eboseu such that the total mass ejected by the 11 stars used here is equal to 3«102Af. |, The stars without any observed He I line emission have been assigned a wind velocity of $750 \kms$ and an equal mass loss rate chosen such that the total mass ejected by the 14 stars used here is equal to $3\times10^{-3}\;M_\odot$ $^{-1}$. + In Figmo 1. we show the positions (relative to Ser A*) of these wind sources: the size of the circle marking cach position corresponds to the relative niass loss rate (on a linear scale) for that star.," In Figure 1, we show the positions (relative to Sgr A*) of these wind sources; the size of the circle marking each position corresponds to the relative mass loss rate (on a linear scale) for that star." + Note that although we have matched the overall mass outflow rate to the observations. we have oulv used L1 of the 25 stars in the sample.," Note that although we have matched the overall mass outflow rate to the observations, we have only used 14 of the 25 stars in the sample." + There are two principal reasons for this: (1) stars further away than 10 arcsec (i projection) from Sey A* are outside of our volume of solution aud therefore could uot be included. aud (2) due to our computational resolution limits. we needed to avoid excessively large local stellar densities.," There are two principal reasons for this: (1) stars further away than 10 arcsec (in projection) from Sgr A* are outside of our volume of solution and therefore could not be included, and (2) due to our computational resolution limits, we needed to avoid excessively large local stellar densities." + So small clusters of adjaceut stars were replaced with single wind sources., So small clusters of adjacent stars were replaced with single wind sources. + Following Waller Melia (1996). we will represeut the gravitational poteutial of the dark cluster with an πιο (Tremaine.ctal. 19919).," Following Haller Melia (1996), we will represent the gravitational potential of the dark cluster with an $\eta$ -model” \cite{T94}) )." + This function represeuts au isotropic mass distribution with a single paralcter. so that the mass euclosed within radius P (n dimensionless units) is elven by We here restrict our examination to the case jj=2.5 since this provides the closest approximation to a Ising model that is physically realizable (1.0... a nonnegative distribution function). aud we scale the mass so that 2<10°AL. are euclosed within 0.01 pe (see Fig.," This function represents an isotropic mass distribution with a single parameter, so that the mass enclosed within radius $\tilde r$ (in dimensionless units) is given by We here restrict our examination to the case $\eta=2.5$ since this provides the closest approximation to a King model that is physically realizable (i.e., a nonnegative distribution function), and we scale the mass so that $2\times10^6\;M_\odot$ are enclosed within 0.01 pc (see Fig." + 2)., 2). + With this. the total integrated mass of the dark cluster is 2.7«4109AL...," With this, the total integrated mass of the dark cluster is $2.7\times10^6\;M_\odot$." + Thus. writing P in units of Ry (6. rSsh. Ry). aud choosing s to vield the observed euclosed mass at 0.01 pe (see Fig.," Thus, writing $\tilde r$ in units of $R_A$ (i.e., $r\equiv s\tilde r\times R_A$ ), and choosing $s$ to yield the observed enclosed mass at $0.01$ pc (see Fig." + 2). we ect A inore recent assessment of the enclosed mass (Coeuzel.et.al. 1997)) places a vet more rigorous constraint ou the possibility of a distributed dark matter component.," 2), we get A more recent assessment of the enclosed mass \cite{GEOE97}) ) places a yet more rigorous constraint on the possibility of a distributed dark matter component." + These newer observations may indeed, These newer observations may indeed +The observations are done with BATC photometric svstem al Xinglong Station of National Astronomical Observatories. Chinese Academy of Sciences (NAOC).,"The observations are done with BATC photometric system at Xinglong Station of National Astronomical Observatories, Chinese Academy of Sciences (NAOC)." + The 60/90 em [/3 Schmidt telescope is used with a Ford Aerospace 2048x CCD camera at its main focus., The 60/90 cm f/3 Schmidt telescope is used with a Ford Aerospace $2048\times2048$ CCD camera at its main focus. + The field of view of the CCD is 58’x with a plate scale of 1.7 arcsec per pixel., The field of view of the CCD is $58\arcmin\times58\arcmin$ with a plate scale of 1.7 arcsec per pixel. + The filler svstem of BATC project is defined by 15 intermediate-band filters which are designed specifically to avoid most of the known bright aud variable night skv emission lines., The filter system of BATC project is defined by 15 intermediate-band filters which are designed specifically to avoid most of the known bright and variable night sky emission lines. +" The definition of magnitude for the BATC survey is in the AZ, svstem which is a monochromatic £j svstem first introduced by Oke&Gunn(1933): where F,, is (he appropriately averaged monochromatic flux. (Gueasurecl in unit οἱ ergsFem?Hz +) at the effective wavelength of the specific pass-band 1996)..", The definition of magnitude for the BATC survey is in the $AB_{\nu}$ system which is a monochromatic $F_{\nu}$ system first introduced by \citet{og}: where $F_{\nu}$ is the appropriately averaged monochromatic flux (measured in unit of $\mbox{erg}~\mbox{s}^{-1}~\mbox{cm}^{-2}~\mbox{Hz}^{-1}$ ) at the effective wavelength of the specific pass-band \citep{fuku}. +" In BATC system. the £, is defined as (Yanοἱal.2000):: which ties directly the magnitude to input πας."," In BATC system, the $F_{\nu}$ is defined as \citep{yan}: which ties directly the magnitude to input flux." +" The svstem response Z2, actually used to relate the spectrum energy distribution of the source { ancl F5. includes only (he filter (transmissions."," The system response $R_{\nu}$ actually used to relate the spectrum energy distribution of the source $f_{\nu}$ and $F_{\nu}$, includes only the filter transmissions." + Other effects. such as the quantum efficiency of the CCD. the response of the telescopes optics. the Gransamission of atmosphere. etc..," Other effects, such as the quantum efficiency of the CCD, the response of the telescope's optics, the transmission of atmosphere, etc.," + are ignored., are ignored. + This makes the BATC svstem filter-defined. and the effective wavelengths are affected only at the &GA level after takine CCD cquantum ellicieney and aluminum reflection into account (Yanetal.2000).," This makes the BATC system filter-defined, and the effective wavelengths are affected only at the $\pm 6$ Å level after taking CCD quantum efficiency and aluminum reflection into account \citep{yan}." +. The flux calibration of the BATC photometric svstem is delined by four spectrophotometric standard. stars of Oke&Gunn (1983): LID 19445. TLD 84931.," The flux calibration of the BATC photometric system is defined by four spectrophotometric standard stars of \citet{og}: : HD 19445, HD 84937," +"that the observed distribution of (3—V), colors for anv Hubble type will be Gaussian.",that the observed distribution of $(B-V)_{o}$ colors for any Hubble type will be Gaussian. +" The following ciseussion is therefore based on the median colors (2—VW)""oOE of different subgroups. rather than on their mean values <(2—V),>."," The following discussion is therefore based on the median colors $(B-V)_{o}^{*}$ of different subgroups, rather than on their mean values $<(B-V)_{o}>$." + A comparison between these median colors of normal spiral and of barred galaxies is shown in Table 1 and is plotted in Figure 1., A comparison between these median colors of normal spiral and of barred galaxies is shown in Table 1 and is plotted in Figure 1. +" Also listed in this table are the (2—WW)""oOE colors containing and of the data points ancl error estimates based on the inter-quartile range divided bv the square root of the number of galaxies.", Also listed in this table are the $(B-V)_{o}^{*}$ colors containing and of the data points and error estimates based on the inter-quartile range divided by the square root of the number of galaxies. + Inspection of the data in Table 1 shows that. within any lIubble stage. the colors of normal and barred objects are very. similiar.," Inspection of the data in Table 1 shows that, within any Hubble stage, the colors of normal and barred objects are very smiliar." + This conclusion is strengthened and confirmed by IXolomogorov-Smirnov (Ix-8) tests which show no significant differences between the color distributions of Sa and SDa. Sab and SBab. Sb and SBb. She and SBbe and Se and SBe galaxies.," This conclusion is strengthened and confirmed by Kolomogorov-Smirnov (K-S) tests which show no significant differences between the color distributions of Sa and SBa, Sab and SBab, Sb and SBb, Sbc and SBbc and Sc and SBc galaxies." + The largest difference in Table 1 occurs between the colors of Sc and SBe galaxies. with the SDc galaxies appearing. on average. slightly. bluer (han those of type Se.," The largest difference in Table 1 occurs between the colors of Sc and SBc galaxies, with the SBc galaxies appearing, on average, slightly bluer than those of type Sc." + The observed color between Sc and SBe galaxies is in the sense expected [from the fact. (see Section 3) that SDc galaxies are svstematically [ainter (ud hence are expected to be metal poorer) (han are objects of (wpe Sc., The observed color between Sc and SBc galaxies is in the sense expected from the fact (see Section 3) that SBc galaxies are systematically fainter (and hence are expected to be metal poorer) than are objects of type Sc. +" It is concluded (hat presentilv available high-quality. data do not exhibit a significant difference between the intrimsie (£2—V), colors of normal ancl barred galaxies over the range of IIubble stages a - ab - b ο,", It is concluded that presently available high-quality data do not exhibit a significant difference between the intrinsic $(B-V)_o$ colors of normal and barred galaxies over the range of Hubble stages a - ab - b - bc. + The referee has raised (he interesting question whether (he presence of bars in galaxies might have affected the IIubble stage assignments of galaxies in the catalog of Sandage Tammann (1981) in à svstematie wav., The referee has raised the interesting question whether the presence of bars in galaxies might have affected the Hubble stage assignments of galaxies in the catalog of Sandage Tammann (1981) in a systematic way. + With the passing of Allan Sandage it appears unlikely that this question will ever by answered in an entirely satisfactory [ashion., With the passing of Allan Sandage it appears unlikely that this question will ever by answered in an entirely satisfactory fashion. + The Revised Shaplev-Ames Catalog (Sandage Tammann 1981) lists the 3j; Iuminosities for all of the galaxies in their sample., The Revised Shapley-Ames Catalog (Sandage Tammann 1981) lists the $M_{B}$ luminosities for all of the galaxies in their sample. + A summary of the data on the median, A summary of the data on the median +"where v(x./)=utCr./)e,+vtCr./)e, is the velocity in the rotating frame. and fonds is the vertically integrated stress tensor (dimensions of force per unit length).","where $\bfv(\bfx,t)=u(x,t)\hat\bfe_x+v(x,t)\hat\bfe_y$ is the velocity in the rotating frame, and $\Sigma_{ik}=\int \sigma_{ik}dz$ is the vertically integrated stress tensor (dimensions of force per unit length)." + We define the tangential shear to be, We define the tangential shear to be. + In a disk with zero stress gradients. a solution of the equations of motion is ur.E)—0. —5O7r. corresponding to circular IXepleriair orbits ancl constant shear s=sy—$Q.," In a disk with zero stress gradients, a solution of the equations of motion is u(x,t)=0, x, corresponding to circular Keplerian orbits and constant shear $s=s_K\equiv +-{3\over 2}\Omega$." + In a solid disk with zero shear. a solution of the equations of motion is u(x.t)—0..," In a solid disk with zero shear, a solution of the equations of motion is u(x,t)=0, ^2x)." +" If we assume that the surface density is constant. that (he zero-shear region extends from vy lows. and that the tensile stress vanishes at the edges of the solid region (1.6. X,=0 al x4.) Chen the last of (ese equations can be integrated to vield sÉsog)rsor]."," If we assume that the surface density is constant, that the zero-shear region extends from $x_1$ to $x_2$, and that the tensile stress vanishes at the edges of the solid region (i.e. $\Sigma_{xy}=0$ at $x_1,x_2$ ) then the last of these equations can be integrated to yield ^2(x-x_1)(x_2-x), (x_1+x_2)." +[VCC 513) and VCC 1122. Benderetal.(1992) aud Pedrazetal.(2002): VOC 917. (2002)]].,"[VCC 543 and VCC 1122, \citet{BBF92} and \citet{PGCSBG02}; VCC 917, \citet{GGvM02}] ]." + The mean velocity dispersion for VCC 1122 reported in Beideretal.(1992) is larger ian the value reported here. but is consistent. with the ceutral velocity dispersion measurement.," The mean velocity dispersion for VCC 1122 reported in \citet{BBF92} + is larger than the value reported here, but is consistent with the central velocity dispersion measurement." + πι“igure | shows a direct comparison of the line shape expected for a template star broadened by je. velocity dispersion for the integrated spectrum of VCCC L122: the «erived velocity dispersion is ‘learly a good match to the [9]observed spectra., Figure \ref{fig:comp} shows a direct comparison of the line shape expected for a template star broadened by the velocity dispersion for the integrated spectrum of VCC 1122; the derived velocity dispersion is clearly a good match to the observed spectra. + The veloc‘iy clispersionrol VCC OL) reported here comparable to that of Beiderοἱal.(1992): similar good agreenmet| is found between the new ervatious of VCC 917 ancL those reported in Celiaetal.(2002).. altrough the reported systemic velocity of VCC 917 is signiicautly different than that repoted here.," The velocity dispersion of VCC 543 reported here is comparable to that of \citet{BBF92}; similar good agreement is found between the new observations of VCC 917 and those reported in \citet{GGvM02}, although the reported systemic velocity of VCC 917 is significantly different than that reported here." + The derived rotation velocities auc velocity dispersions indicate that several dwart elliptica e@alaxies in the Virgo cluster have siguificant rotation com;»onents., The derived rotation velocities and velocity dispersions indicate that several dwarf elliptical galaxies in the Virgo cluster have significant rotation components. + The ratio of the rotation velocity to velocity dispersion or the Virgo dwarf elliptical galaxies is shown in Figure 5 and tabulatec in Table L., The ratio of the rotation velocity to velocity dispersion for the Virgo dwarf elliptical galaxies is shown in Figure \ref{fig:anisotrop} and tabulated in Table \ref{tab:results}. + Note. however. that the anisotropy. paralyelers. (ν/σηῃ y*. listed in Table | all shown i Figure 5. shoud be considered represeutative lower limits for the dEs.," Note, however, that the anisotropy parameters, $\sigma_m$ )*, listed in Table \ref{tab:results} and shown in Figure \ref{fig:anisotrop} should be considered representative lower limits for the dEs." + Not ouly are the derived velocity dispersious representative upper limits. the present observatious ouly sample the kinematics aloug the 1yajor axis: if the dEs have a significant velocity gradient aloug a differeut axis. such as found iu sx)ue dl galaxies [e.g.. NGC 625. (Coté.Carignan.&Freeman2000) aud NGC 5253. (Ixobuluicky&5A.sillLrnan 1995)]]. the derived anisotropy parameters will be underestimates of their true values.," Not only are the derived velocity dispersions representative upper limits, the present observations only sampled the kinematics along the major axis; if the dEs have a significant velocity gradient along a different axis, such as found in some dI galaxies [e.g., NGC 625, \citep{CCF00} and NGC 5253, \citep{KS95}] ], the derived anisotropy parameters will be underestimates of their true values." + Also s10wi iu Figure 5 arethe anisotropy parameters [or giant elliptical galaxies from Benderetal.(1992 and the dwarf elliptical galaxies in Pedrazetal.(2009).. Gelia (2002).. Simien&Prugniel (2002).. aud DeRyekeetal.(2001.2003).," Also shown in Figure \ref{fig:anisotrop} arethe anisotropy parameters for giant elliptical galaxies from \citet{BBF92} and the dwarf elliptical galaxies in \citet{PGCSBG02}, \citet{GGvM02}, \citet{SP02}, and \citet{DDZH01,DDZH03}." +. Five of he cwarl ellipical ealaxies in the Virgo sample have a signilicaut 'otatiou component., Five of the dwarf elliptical galaxies in the Virgo sample have a significant rotation component. + These galaxies overlap the k)cus of anisotropy parameters found iu giant ellipical galaxies. wlere the lower luminosity ellipticals tend to have large anisotropy parameters.," These galaxies overlap the locus of anisotropy parameters found in giant elliptical galaxies, where the lower luminosity ellipticals tend to have large anisotropy parameters." + Eight of the reinainiug dwarf ellipical galaxies have moclest anisotropy parameters. while ouly ove. VOC 1261. |as al extremely low value.," Eight of the remaining dwarf elliptical galaxies have modest anisotropy parameters, while only one, VCC 1261, has an extremely low value." + These results are significantly different than those re»orted by €telaeal.(2002) aud the early studies of Bender&Nieto(L990) atd Benderetal.(1991) where it appeared that dwarl elliptical galaxies hac uo significant rotation component., These results are significantly different than those reported by \citet{GGvM02} and the early studies of \citet{BN90} and \citet{BPN91} where it appeared that dwarf elliptical galaxies had no significant rotation component. + However. the rec‘ent opervatious by and Celaetal.(2003)) 1revealed a Bhiaudful of dwarf elliptical galaxies with significant rotation.," However, the recent observations by \citet{PGCSBG02} and \citet{GGvM03} revealed a handful of dwarf elliptical galaxies with significant rotation." + Τιus. t appears tlal the cinematics of some cwarf elliptical galaxies are domiuatec by rotation. 110 random motions.," Thus, it appears that the kinematics of some dwarf elliptical galaxies are dominated by rotation, not random motions." + While this 'esult is cotuter to tlie results reported in earlier studies. it should uot © surprisiug.," While this result is counter to the results reported in earlier studies, it should not be surprising." + ΤΙe dwarf ellipIca £ealaxies in this sample are all located in the region of stroug overdeusity tliat chewacterizes tle Vireo Clister., The dwarf elliptical galaxies in this sample are all located in the region of strong overdensity that characterizes the Virgo Cluster. + It is well known that galaxies located near the cluser center are deicient in neutral hydrogen relative to their couuterparts in the field (e.g. 2001)..," It is well known that galaxies located near the cluster center are deficient in neutral hydrogen relative to their counterparts in the field \citep[e.g.,][]{GH83,SMGGGH01}. ." + For giant spiral galaxies. the loss of their ISM may result in modest," For giant spiral galaxies, the loss of their ISM may result in modest" +"Distances of a few tens of Mpc correspond to a volume of space spanning all varieties of nuclear activity, so it seems probable that empty regions in the upper right corner of are genuinely depopulated by luminous (Group 1) R;.,;,AGN.","Distances of a few tens of Mpc correspond to a volume of space spanning all varieties of nuclear activity, so it seems probable that empty regions in the upper right corner of $R_{ir/x}$ are genuinely depopulated by luminous (Group 1) AGN." +" Any Group 1 AGN undiscovered in the X-ray band, must lie to the left of their corresponding vertical luminosity distance detection limit (e.g. a Type 1 QSO at 100Mpc undiscovered in X-rays, must lie to the left of the vertical 100Mpc line)."," Any Group 1 AGN undiscovered in the X-ray band, must lie to the left of their corresponding vertical luminosity distance detection limit (e.g. a Type 1 QSO at 100Mpc undiscovered in X-rays, must lie to the left of the vertical 100Mpc line)." +" Similarly, any low luminosity AGN, undiscovered at 12um must lie below the corresponding horizontal luminosity distance detection limit (e.g. a Type 2 QSO at 100Mpc undiscovered at 121m must lie below the horizontal 100Mpc line)."," Similarly, any low luminosity AGN, undiscovered at $\micron$ must lie below the corresponding horizontal luminosity distance detection limit (e.g. a Type 2 QSO at 100Mpc undiscovered at $\micron$ must lie below the horizontal 100Mpc line)." +" Second, we also need to check that the dispersion of AGN is not unduly affected by picking up higher luminosity AGN at relatively higher redshifts."," Second, we also need to check that the dispersion of AGN is not unduly affected by picking up higher luminosity AGN at relatively higher redshifts." + In Fig., In Fig. +" 8 we plot the 109 AGN (56 Group 1 and 53 Group 2 AGN) in the redshift range z=[0.005,0.05] (or —[20,200|Mpc)."," \ref{fig:cz} we plot the 109 AGN (56 Group 1 and 53 Group 2 AGN) in the redshift range $z=[0.005,0.05]$ (or $\sim$ [20,200]Mpc)." + Fig., Fig. + 8 excludes the highest and lowest luminosity AGN from both Groups., \ref{fig:cz} excludes the highest and lowest luminosity AGN from both Groups. +" From Fig. 8,,"," From Fig. \ref{fig:cz}," +" 53/56 Group 1 AGN have 10.05 (47/112), we find that γε is statistically significant at 0.71 and 0.67 respectively."," When we split our Group 1 distribution into those AGN at $z<0.05$ (65/112) and $z>0.05$ (47/112), we find that $S_{rc}$ is statistically significant at $0.71$ and $0.67$ respectively." +" We also find that the mean value of R;,;, for both these z<0.05 and z>0.05 Group 1 AGN populations are consistent with each other and with the mean value of of the complete Group 1 population, within the mean Rj.;,absolute deviation of each population."," We also find that the mean value of $R_{ir/x}$ for both these $z<0.05$ and $z>0.05$ Group 1 AGN populations are consistent with each other and with the mean value of $R_{ir/x}$ of the complete Group 1 population, within the mean absolute deviation of each population." +" Furthermore, the T-statistic for these ""low' and ""high? z Group 1 AGN has a significance of 0.5, indicating that the z«0.05 and z>0.05 populations do not originate in distributions with substantially different mean valuesof R;,,,."," Furthermore, the T-statistic for these 'low' and 'high' z Group 1 AGN has a significance of 0.5, indicating that the $z<0.05$ and $z>0.05$ populations do not originate in distributions with substantially different mean valuesof $R_{ir/x}$." +" In future work, we anticipate extending our sample with a view to obtaining strong statistical constraints on the value of R;,/, in AGN."," In future work, we anticipate extending our sample with a view to obtaining strong statistical constraints on the value of $R_{ir/x}$ in AGN." +" Another way of assessing the depopulation of regions of the H;,,, plot is by considering the dispersion of complete samples of AGN.", Another way of assessing the depopulation of regions of the $R_{ir/x}$ plot is by considering the dispersion of complete samples of AGN. +" The samples of Rushetal.(1993) and Sandersetal.(2003) in Table 1 correspond to complete, flux-limited IRAS samples at 121m and 60um respectively."," The samples of \citet{b59} and \citet{b60} in Table \ref{tab:sample} correspond to complete, flux-limited IRAS samples at $\micron$ and $60\micron$ respectively." +" However, in each case, only ~15% of each sample have 10keV X-ray data."," However, in each case, only $\sim 15\%$ of each sample have 2-10keV X-ray data." +" However, the sample of Rushetal.(1993) in particular spans most of our range of Lz,L1». space, so a comparison of our sample with Rushetal.(1993) could tellus if we are under-sampling a particular region of parameter space."," However, the sample of \citet{b59} in particular spans most of our range of $L_{x},L_{12um}$ space, so a comparison of our sample with \citet{b59} could tellus if we are under-sampling a particular region of parameter space." + Fig., Fig. +" 9 is as Fig. 2,,"," \ref{fig:iras12sample} is as Fig. \ref{fig:nojets}," + except that only AGN from Rushetal.(1993) are plotted., except that only AGN from \citet{b59} are plotted. +" Clearly, the subset of the complete 12um IRAS AGN sample span the full range of Rj-/z for Group 2 AGN and most of the range of R;,;, for Group 1 AGN."," Clearly, the subset of the complete $\micron$ IRAS AGN sample span the full range of $R_{ir/x}$ for Group 2 AGN and most of the range of $R_{ir/x}$ for Group 1 AGN." +" Furthermore, the 121m sample subset does not stake out otherwise unoccupied regions of R;,/, space."," Furthermore, the $\micron$ sample subset does not stake out otherwise unoccupied regions of $R_{ir/x}$ space." +" It is possible that the remainder of the complete IRAS samples picked out AGN that live in e.g. the top-left of Fig. 2,,"," It is possible that the remainder of the complete IRAS samples picked out AGN that live in e.g. the top-left of Fig. \ref{fig:nojets}, ," + ie. low Lz and large L;.., i.e. low $L_{x}$ and large $L_{ir}$ . +" However, an additional ~20% IRAS AGN had 0.2— 4.0keV X-ray flux measurements, yielding similar values of R;,/,, to those in Fig."," However, an additional $\sim 20\%$ IRAS AGN had $0.2-4.0$ keV X-ray flux measurements, yielding similar values of $R_{ir/x}$ to those in Fig." + 9 (see also, \ref{fig:iras12sample} (see also +Iu the atinospheres of the hot EHes most of the s-process elements exist in doubly ionized state and lack spectral lines in the optical region. [,In the atmospheres of the hot EHes most of the $s$ -process elements exist in doubly ionized state and lack spectral lines in the optical region. [ +Let me add a personal noe here.,Let me add a personal note here. + Iu 1996 January. David Lambert aud I were αἱ{οπρ a conference on spectroscopy in Bomyay Where we leard a talk by Indrek Martinson discussiug the and. spectra in UV and theavallability of [alrly decent gf-values.," In 1996 January, David Lambert and I were attending a conference on spectroscopy in Bombay where we heard a talk by Indrek Martinson discussing the and spectra in UV and the availability of fairly decent $gf$ -values." + This prompted us to apply lor AST - STIS spectra in searcl oL Zr aud Y abunclauces in EHe stars.), This prompted us to apply for $HST$ - $STIS$ spectra in search of Zr and Y abundances in EHe stars.] + Fortunately. strong lines ofYULur.Cet. etc.," Fortunately, strong lines of, etc.," + «lo occur iu the UV where EHe stars have appreciable flux., do occur in the UV where EHe stars have appreciable flux. + We could obtain UV spectra of 7 EHe sars with STIS on AST., We could obtain UV spectra of 7 EHe stars with $STIS$ on $HST$. + Analyses of the spectra of two EHe stars CCve and 112[LIS cdenonstrate the similarities iu the pattern of s-process elements with RCBs., Analyses of the spectra of two EHe stars Cyg and 124448 demonstrate the similarities in the pattern of $s$ -process elements with RCBs. + The two stars have the same log Ti aud log g but show large differences in [Y/Fe] and. [Zr/Fe] (similar to RCBs) (Figure 3)., The two stars have the same log $T_{\rm eff}$ and log $g$ but show large differences in [Y/Fe] and [Zr/Fe] (similar to RCBs) (Figure 3). + V1920CCvg µας ore eulianced abuudances of Y. Zr and the range in abuncdauce variatious is also very simar to RCBs (Pandey et al.," Cyg has more enhanced abundances of Y, Zr and the range in abundance variations is also very similar to RCBs (Pandey et al." + 2001)., 2004). + Although the abundauces of heavy s-process elements could not be estimated. the upper units of the abuucdauces of Ce. Nd do demonstrate the lighter s-process element ⊳∖⋜∐∎≺↵↥∐∩∐↵≺↵∐↕⋜↕∐⊓↵≺ even in EHe stars.," Although the abundances of heavy $s$ -process elements could not be estimated, the upper limits of the abundances of Ce, Nd do demonstrate the lighter $s$ -process elements are more enhanced even in EHe stars." + It is generally acknowledged that ο ία.η) Ο is the main source of neutrons tο run the s-processing in the He-burniug shells of intermecdiate-miass AGB st:us.," It is generally acknowledged that $^{13}$ $(\alpha,n)^{16}$ O is the main source of neutrons to run the $s$ -processing in the He-burning shells of intermediate-mass AGB stars." + Sulficieut. amouus of Ha ⋅⋅ ⋅ ↓∣⊾∊↽⋜↕↓⋅≺↲↕∩∣⋈↵∑≟≺↵∐≺↵↕⋅⋜↕↕↩≼⇂∣≻⊽∖⊽⊳∖↥∩∖∖↽∐⊔⊸∖⋯∑≟∩⊓↽≻↓⋅∩↕∩∐⊳∖∐∐∩↕∐≺↵↓−⊂⊔∢∙∐∐∐≺↵ ⋅ ⋅↽≻↿⋅ ⋅rshell regious to geterate ∐↩⋯↓⋅∩∐⊳∖, Sufficient amounts of $^{13}$ C are to be generated by slow mixing of protons into the $^{12}$ C rich intershell regions to generate neutrons. +⋅⊺∐↩∐≺↵⋃⋃⋅∩∐∐⋅↓⋅⋜∥∐⋜∏↕∩∐∩∢∙∢∙⇂⊔⋅⊳∖↥∐↓⋅⋜∥∐⋜↕⋃∖⇁≺↲∢∙∩∐∐⋃∩∐, The neutron irradiation occurs in radiative conditions. +⊳∖⋅⊺∐≺↵∐≺↵⋜ wier the neutron fhx the, The heavier the neutron flux the +The dimensionless distribution function f(u) should satisfy the normalization condition and t=vN_u,The dimensionless distribution function $f(\mathbf{u})$ should satisfy the normalization condition and $\lambda=xN_{\bot}u_{\bot}$. + Using the properties of the ó-function.we can reduce three-dimensional integrals in (B5)) to one-dimensional integrals over du-: where the value 4| at every point of the resonance curve Is found from the resonance condition: ⋅≏↧⋯↿⋔⊖≣∏↾⊜∶↔⊺∣⋪∐⊓∪∏∥⋯⇈⋋∣∣⋮∥⋯↿∐⋯↿∣∣⋮⋯↼∣⋅∖⋖∖∖⇁∣↴≣∁∣↴⋯⋪⊜ dependent on the harmonie number) are the boundaries of the interval where Eq. (B8) ," Using the properties of the $\delta$ -function,we can reduce three-dimensional integrals in \ref{incr3}) ) to one-dimensional integrals over $\mathrm{d}u_z$: where the value $u_{\bot}$ at every point of the resonance curve is found from the resonance condition: and the integration limits $u_{z\min}$ and $u_{z\max}$ (which are dependent on the harmonic number) are the boundaries of the interval where Eq. \ref{un_res}) )" +has a solution., has a solution. +" For [N-]«1 (which is always satisfied for X- and O-modes). the resonance curve in the momentum space (B8)) an ellipse intersecting the axis a_= Oat two points: where u-, and we. correspond to signs 7—7 and ""47 respectively."," For $|N_z|<1$ (which is always satisfied for X- and O-modes), the resonance curve in the momentum space \ref{un_res}) ) is an ellipse intersecting the axis $u_{\bot}=0$ at two points: where $u_{z1}$ and $u_{z2}$ correspond to signs $-$ ” and $+$ ”, respectively." + In this case. u-uinUp and (Unas122.," In this case, $u_{z\min}=u_{z1}$ and $u_{z\max}=u_{z2}$." + For [N-|>1. Eq. (B8))," For $|N_z|>1$, Eq. \ref{un_res}) )" + describes a hyperbola with only one branch being physical (for which. at 4—co. the longitudinal component of the momentum 4. has the same sign as N-)," describes a hyperbola with only one branch being physical (for which, at $u\to\infty$, the longitudinal component of the momentum $u_z$ has the same sign as $N_z$ )." + Therefore the integration limits in (B7)) will be equal (note that u-j>εν dn this case): ίση=—co and τν=Uo at N.«Oi uy=Wey and μας—co at N->0., Therefore the integration limits in \ref{incr4}) ) will be equal (note that $u_{z1}>u_{z2}$ in this case): $u_{z\min}=-\infty$ and $u_{z\max}=u_{z2}$ at $N_z<0$; $u_{z\min}=u_{z1}$ and $u_{z\max}=\infty$ at $N_z>0$. + Infinite integration limits can be avoided since the electron distribution function is usually defined only in a finite range of momentums. e.g. atuXdn.," Infinite integration limits can be avoided since the electron distribution function is usually defined only in a finite range of momentums, e.g., at $u\le u_{\mathrm{high}}$." + In this case. the infinite limit (upper or lower. depending on the sign of N.) should be replaced by the coordinate of the intersection point of the resonance curve with the circle 4=tp. that is where I4 is the relativistic factor of electrons with the momentum éhich-," In this case, the infinite limit (upper or lower, depending on the sign of $N_z$ ) should be replaced by the coordinate of the intersection point of the resonance curve with the circle $u=u_{\mathrm{high}}$, that is where $\Gamma_{\mathrm{high}}$ is the relativistic factor of electrons with the momentum $u_{\mathrm{high}}$." + The above formulae for the growth rate involve infinite sums over cyclotron harmonies s., The above formulae for the growth rate involve infinite sums over cyclotron harmonics $s$. + Actually. only the harmonics in à certain range sin€sὅμως Make a contribution to the growth rate. since for the other harmonics either the resonance condition (for a given wave parameters) is never satisfied or the resonance curve lies outside the domain of the electron distribution function.," Actually, only the harmonics in a certain range $s_{\min}\le s\le s_{\max}$ make a contribution to the growth rate, since for the other harmonics either the resonance condition (for a given wave parameters) is never satisfied or the resonance curve lies outside the domain of the electron distribution function." + In this work. the interval of harmonic numbers is taken with a large excess (say. from —100 to 100). and ther we check for each harmonic whether it makes a contribution into the growth rate: this method is simple and very fast. and allows us to take into account all harmonies having an effect on the growth rate.," In this work, the interval of harmonic numbers is taken with a large excess (say, from $-100$ to 100), and then we check for each harmonic whether it makes a contribution into the growth rate; this method is simple and very fast, and allows us to take into account all harmonics having an effect on the growth rate." + The change in the electron distribution function due to diffusion on the magnetotonic waves is deseribed by the last equation of the system (1) )., The change in the electron distribution function due to diffusion on the magnetoionic waves is described by the last equation of the system \ref{evolution}) ). +" In polar coordinates (p.o). this equation takes the form (Aschwanden Benz 1988)) where D,,.pm DyasI Dap. and D,, are the componentsOp of the diffusion tensor (δρα=D,,)."," In polar coordinates $(p, \alpha)$, this equation takes the form (Aschwanden Benz \cite{asc88}) ) where $D_{pp}$, $D_{p\alpha}$, $D_{\alpha p}$ , and $D_{\alpha\alpha}$ are the components of the diffusion tensor $D_{p\alpha}=D_{\alpha p}$ )." + We note that the total diffusion tensor equals the sum of the diffusion tensors on separate modes (for simplicity. the formulae below refer only to one mode).," We note that the total diffusion tensor equals the sum of the diffusion tensors on separate modes (for simplicity, the formulae below refer only to one mode)." + If we use the dimensionless momentum u and introduce. according to Aschwanden Benz (1988)) generalized diffusion coefficients then Eq. (C1))," If we use the dimensionless momentum $\mathbf{u}$ and introduce, according to Aschwanden Benz \cite{asc88}) ), generalized diffusion coefficients then Eq. \ref{dif_eq1}) )" + can be written in a form Here the expression elements are rearranged to make the numerical calculations more convenient and accurate., can be written in a form Here the expression elements are rearranged to make the numerical calculations more convenient and accurate. +" The diffusion coefficients D, (for an individual wave mode) are (AschwandenBenz 1988:: Aschwanden 1990))", The diffusion coefficients $D_r$ (for an individual wave mode) are (AschwandenBenz \cite{asc88}; ; Aschwanden \cite{asc90}) ) +So far ourlinear parametric resonance model predicts fixed radii where the resonance conditions Eq. (1)),So far our parametric resonance model predicts fixed radii where the resonance conditions Eq. \ref{eq:Resonance}) ) + are satisfied., are satisfied. + Therefore the orbital Ireequencies remain also constant. leading to fixed kIIz-QPOs.," Therefore the orbital frequencies remain also constant, leading to fixed kHz-QPOs." + This can only be an approximation since oscillations are non-linear and gas or particles dift slowly towards the neutron star due to accretion., This can only be an approximation since oscillations are non-linear and gas or particles drift slowly towards the neutron star due to accretion. + In other words. advection increases (he orbital and vertical epicycelie frequencies and puts the svstem (particles) out of resonance.," In other words, advection increases the orbital and vertical epicyclic frequencies and puts the system (particles) out of resonance." + Actually. if non-linear terms are retained. the proper frequency of the vertical excursions depends on the amplitude of these oscillations.," Actually, if non-linear terms are retained, the proper frequency of the vertical excursions depends on the amplitude of these oscillations." + Therefore. it is possible that the excitation and proper lrequencieslhemself in such a wav [o maintain the oscillator in high amplitude motion.," Therefore, it is possible that the excitation and proper frequencies in such a way to maintain the oscillator in high amplitude motion." + We call thismechanism., We call this. + Its explanation is given in more details along the following lines., Its explanation is given in more details along the following lines. + The idea of non-linear resonance (o explain QPO observations has already. been discussed by many authors. see for instance Rebusco(2004):Ποτά(2004.2005):Abramowiezetal. (2003b)..," The idea of non-linear resonance to explain QPO observations has already been discussed by many authors, see for instance \cite{2004PASJ...56..553R, 2004ragt.meet...91H, 2005AN....326..824H, + 2003PASJ...55..467A}." + Although they considered. a resonance between oscillatory mocles different from those relevant to the model presented within this paper. their results show also how non-linear phenomena can drastically improve their models.," Although they considered a resonance between oscillatory modes different from those relevant to the model presented within this paper, their results show also how non-linear phenomena can drastically improve their models." + Let us see how parametric auto-resonance works., Let us see how parametric auto-resonance works. + Add a non-linear cubic term in the usual Mathieu equation governing the vertical displacement z(/)., Add a non-linear cubic term in the usual Mathieu equation governing the vertical displacement $z(t)$. + Note that. to first order. a quadratic term would not lead to a change in proper lvequencey. with amplitude so a cubic term is more relevant for our discussion.," Note that, to first order, a quadratic term would not lead to a change in proper frequency with amplitude so a cubic term is more relevant for our discussion." + Thus. our non-linear oscillator takes (he form below h is the strength of the excitation.," Thus, our non-linear oscillator takes the form below $h$ is the strength of the excitation." +" Now. an important new [act is thatthe vertical epievclic &4,(0) and orbital O(/) frequencies are dependent."," Now, an important new fact is thatthe vertical epicyclic $\kappa_{\rm z}(t)$ and orbital $\Omega(t)$ frequencies are ." + These variable coefficients, These variable coefficients +Coalescing svstems of stellar mass binary black holes (BBIIs) are among the most likely candidates lor the first detection of gravitational waves (GWs) (Flanagan&IIughes1993:Buonannoetal. 2003).,"Coalescing systems of stellar mass binary black holes (BBHs) are among the most likely candidates for the first detection of gravitational waves (GWs) \citep{bbh1,buo03}." +. Their enormous predicted Iuminosities ο»LOPE. would allow future eround-based interferometric GW detectors. such as Advanced LIGO (larryetal.2010) and Advanced Virgo (Acerneseetal.2009). or third generation instruments such as the Einstein Telescope (ET:Punturoetal.2010).. to probe these sources out to Gpe distances.," Their enormous predicted luminosities $\sim 10^{23}L_{\odot}$, would allow future ground-based interferometric GW detectors, such as Advanced LIGO \citep{aligo} and Advanced Virgo \citep{avirgo} or third generation instruments such as the Einstein Telescope \citep[ET;][]{et}, to probe these sources out to Gpc distances." + In (his paper. we are motivated by recent increased rate estimates (Belezvuskietal.2010b) to explore the possibility that a population of DDIIs could form a detectable stochastic GW background (SGWD) signal for these instruments.," In this paper, we are motivated by recent increased rate estimates \citep{metal} to explore the possibility that a population of BBHs could form a detectable stochastic GW background (SGWB) signal for these instruments." + SGWDs can result. [roni the superposition of populations of unresolved. primordial (Grishehuk1974) or astrophysical sources (seeReeimban2011.lorarecentreview)..., SGWBs can result from the superposition of populations of unresolved primordial \citep{Grishchuk:1974ny} or astrophysical sources \citep[see][for a recent review]{regimbau11}. + Astrophysical SGWD signals are important for at least (wo reasons., Astrophysical SGWB signals are important for at least two reasons. + Firstly. they contain rich information on the elobal properties of source populations. such as their source rate evolution. their mass ranges and (heir average energy emissions.," Firstly, they contain rich information on the global properties of source populations, such as their source rate evolution, their mass ranges and their average energy emissions." + Secondly. a dominant continuous astrophlivsical backeround could mask the relic SGWD signal from the very early Universe 2003.[or reviews)..," Secondly, a dominant continuous astrophysical background could mask the relic SGWB signal from the very early Universe \citep[see][for reviews]{Maggiore,Buonanno}." + Mergers of binary neutron stars have been suggested as sources of potentially detectable SGWDs (Regimban&deFreitasPacheco2006:RegimbanChauvinean2007).," Mergers of binary neutron stars have been suggested as sources of potentially detectable SGWBs \citep{Regimbau06,Regimbau07}." +.. Recent observations of DII-Woll-Bavet (WR) star svstems (Crowtheretal.2010) and new estimates in (he metallicity abundancees of star forming galaxies (Panterοἱal.2008) imply Chat the Galactic merger rate of DDIIs may be of a similar order to that of binary neutron stars (Belezvnskietal.2010b)., Recent observations of BH-Wolf-Rayet (WR) star systems \citep{Crowther} and new estimates in the metallicity abundances of star forming galaxies \citep{2008MNRAS.391.1117P} imply that the Galactic merger rate of BBHs may be of a similar order to that of binary neutron stars \citep{metal}. +. Therefore. a population of more huninous BBIIs could produce a dominant background signal.," Therefore, a population of more luminous BBHs could produce a dominant background signal." + Our aim is to explore upper limits lor a 5GWD from coalescing BBIIs over a range of rates and svstem masses., Our aim is to explore upper limits for a SGWB from coalescing BBHs over a range of rates and system masses. + We investigate the constraints future ground based interferometric GW detectors will be able to place on the average properties of the DDII populatioΕν, We investigate the constraints future ground based interferometric GW detectors will be able to place on the average properties of the BBH population. + The paper is organized as follows., The paper is organized as follows. + In Section 2 we discuss rate estimates of coalescing BBUs and then derive cosmic source rate evolution models [or different star formation histories and minimal delay (mes., In Section 2 we discuss rate estimates of coalescing BBHs and then derive cosmic source rate evolution models for different star formation histories and minimal delay times. + In Section 3. source energy spectra for coalescing BBIIs are obtained using the template gravitational wavelorms of Ajithοἱal.(2008) and al. (2009)..," In Section 3, source energy spectra for coalescing BBHs are obtained using the template gravitational waveforms of \citet{IMR} and \citet{spin_IMR}." + We then calculate the DBII background in Section 4 and discuss the detection reeimes. detectabilitv ancl constraints on the parameter space of the predicted background in Section 5.," We then calculate the BBH background in Section 4 and discuss the detection regimes, detectability and constraints on the parameter space of the predicted background in Section 5." + Finally. in Section 6 we present our conclusions.," Finally, in Section 6 we present our conclusions." +consistent. as expected.,"consistent, as expected." + For the purposes of this paper we use the far-infrarecl luminosities determined. from the full SIED fits using the templates from Siebenmorgen&Ixrügel(2007) and for the monochromatic luminosities we use the modified blackbock fits. although we emphasise that these are consistent between the two methods.," For the purposes of this paper we use the far-infrared luminosities determined from the full SED fits using the templates from \citet{SK07} and for the monochromatic luminosities we use the modified blackbody fits, although we emphasise that these are consistent between the two methods." + Fig., Fig. + 1. shows the distribution. of our sources on the far-infrarecl luminosity versus redshift plane. which demonstrates that we are able to sample the z<0.2 Universe sullicientlv well for individual sources to investigate the form of the FIRC with this sample.," \ref{fig:L_z} shows the distribution of our sources on the far-infrared luminosity versus redshift plane, which demonstrates that we are able to sample the $z<0.2$ Universe sufficiently well for individual sources to investigate the form of the FIRC with this sample." + We use stacking of the radio cata (Sec. ??)), We use stacking of the radio data (Sec. \ref{sec:stacking}) ) + to determine whether our finclines ab ο<0.2 are consistent with the average sources properties up to.0.5 and beyond. by comparing with previous results in the literature (e.g.Ivisonetal. 2010).," to determine whether our findings at $z<0.2$ are consistent with the average sources properties up to $z\sim 0.5$ and beyond, by comparing with previous results in the literature \citep[e.g.][]{Ivison10a,Ivison10b,Bourne10}." +. We also use the results described in Llarceastlectal.(2010) to obtain the far-infrared luminosities for those sources which are stronely detected at radio wavelengths but which fall below the 5e detection limit of ourHerschet catalogue. and thus do not make it into our sample.," We also use the results described in \citet{Hardcastle10} to obtain the far-infrared luminosities for those sources which are strongly detected at radio wavelengths but which fall below the $5\sigma$ detection limit of our catalogue, and thus do not make it into our sample." + The combination of these allows us to probe to lower and higher racio luminosities at all recshifts. thus negating some of the rlases inherent to selecting in a single band.," The combination of these allows us to probe to lower and higher radio luminosities at all redshifts, thus negating some of the biases inherent to selecting in a single band." + We show these or completeness: however. we do not use them in caleulating he FIRC.," We show these for completeness; however, we do not use them in calculating the FIRC." + In Fig., In Fig. + 2. we show the correlation. between the [ar-infrared luminosity ancl the rest-Drzume. 1.43. 1 radio uminosity., \ref{fig:Lrad_vs_Lfir} we show the correlation between the far-infrared luminosity and the rest-frame 1.4 GHz radio luminosity. + We assume a radio spectral index of à=0.87. as Found. for submillimetre galaxies by Ibarctal.(2010).. or the 104 objects (72 with spectroscopic redshifts and 32 with photometric redshifts) which lie above our flux. limit in H-VELAGS and with z5 @ detections in the radio maps.," We assume a radio spectral index of $\alpha =0.8$, as found for submillimetre galaxies by \citet{Ibar10a}, for the 104 objects (72 with spectroscopic redshifts and 32 with photometric redshifts) which lie above our flux limit in H-ATLAS and with $>5$ $\sigma$ detections in the radio maps." +" One can easily see the strong correlation between the [ar-infrared and radio emission in our sample. with the best fit relation log),Lyin=(17.S+0.7)|(0.422E0.07)logquLiu, for those sources with Liacus<10° W 5 (soe Section ??))."," One can easily see the strong correlation between the far-infrared and radio emission in our sample, with the best fit relation $\log_{10}L_{\rm FIR} = (17.8 \pm 0.7) + (0.42 \pm 0.07)\log_{10}L_{\rm 1.4GHz}$ for those sources with $L_{\rm 1.4~GHz} < 10^{23}$ W $^{-1}$ (see Section \ref{sec:firc}) )." + For those sources detected at.Hersched wavelengths but which fall below our Se threshold from the radio data. we also perform a stacking analysis on the NVSS and ELBST radio images to obtain statistical detections.," For those sources detected at wavelengths but which fall below our $\sigma$ threshold from the radio data, we also perform a stacking analysis on the NVSS and FIRST radio images to obtain statistical detections." + To do this we Followed the technique of Whiteetal.(2007)... which clips the image at 5o around the median value and then combines the individual images weighted by their variance (seealsoFalederetal. 2010).," To do this we followed the technique of \citet{White07}, which clips the image at $\sigma$ around the median value and then combines the individual images weighted by their variance \citep[see also][]{Falder10}." +. The stacked images are generated in various bins of far-inlrarect Iuminositv ane recishift to allow direct. comparisons to those sources with clirect detections., The stacked images are generated in various bins of far-infrared luminosity and redshift to allow direct comparisons to those sources with direct detections. + Again we do not use these to derive the median and mean values for the FIRC but just as a guide so the reader can judge for consistency., Again we do not use these to derive the median and mean values for the FIRC but just as a guide so the reader can judge for consistency. +" The PIRC we use here is defined as the logarithmic ratio ofthe integrated far-infrared Dux. Sip. determined [rom frame wavelengths S1000 jam (followingBell2008:Lvi-sonetal.2010a) and the rest-lrame 1.4 ας A-corrected flux density. 9i46gz such that qii=logy,(Sin/3.751015](ΦεΗν)) and is dimensionless."," The FIRC we use here is defined as the logarithmic ratio of the integrated far-infrared flux, $S_{\rm IR}$, determined from rest-frame wavelengths $8-1000$ $\mu$ m \citep[following ][]{Bell03,Ivison10a}, and the rest-frame 1.4 GHz $k$ -corrected flux density, $S_{1.4\rm GHz}$ such that $q_{\rm IR} = \log_{10}[(S_{\rm IR}/3.75 \times 10^{12})/(S_{\rm 1.4GHz})]$ and is dimensionless." + 5j; has units of Woanm 7. 3.75πο10/7? Lz is the normalising frequeney (Helou et al.," $S_{\rm IR}$ has units of W $^{-2}$ , $3.75\times10^{12}$ Hz is the normalising frequency (Helou et al." +" 1985) and S,46g; has units of Wom 7 +.", 1985) and $S_{1.4\rm GHz}$ has units of W $^{-2}$ $^{-1}$. + Following Ivisonetal.(20102) we also calculate the monochromatic relationship between the A-correctecl emission. at. 25010 (using our modified blackbody fit) and 1.4 Gllz (using a spectral index of a= 0.8). hereafter qoso.," Following \citet{Ivison10a}, we also calculate the monochromatic relationship between the $k$ -corrected emission at $250\mu$ m (using our modified blackbody fit) and 1.4 GHz (using a spectral index of $\alpha=0.8$ ), hereafter $q_{250}$." + Contamination in the sample from racdio-Iuminous ACN would preferentially decrease the value of din., Contamination in the sample from radio-luminous AGN would preferentially decrease the value of $q_{\rm IR}$. + Phe radio luminosity at which AGN beein to dominate the source population occurs around Lj46g;:1077 Wo L (c.g.Mauch&Sacer2007:Wilmanetal. 2008).," The radio luminosity at which AGN begin to dominate the source population occurs around $L_{\rm 1.4GHz} \gtsim 10^{23}$ W $^{-1}$ \citep[e.g.][]{MauchSadler07, Wilman08}." +. Inspecting the FIRST radio images we find that nine of the sources in our sample show clear signs of ACN activity. Le. jet-like phenomena.," Inspecting the FIRST radio images we find that nine of the sources in our sample show clear signs of AGN activity, i.e. jet-like phenomena." + AIL of these sources have radio Iuminosities Lacusc1077 W and dii values below the sample mean. às would be expected for an AGN dominatedsource.," All of these sources have radio luminosities $L_{\rm 1.4GHz} > 10^{23}$ W $^{-1}$ and $q_{\rm IR}$ values below the sample mean, as would be expected for an AGN dominatedsource." + We omit these nine sources from all subsequent analyses. even though the effect they would have on our results is negligible.," We omit these nine sources from all subsequent analyses, even though the effect they would have on our results is negligible." + All objects with radio luminosities Liocz Wo are represented with open svmbols in all figures., All objects with radio luminosities $L_{\rm 1.4~GHz} > 10^{23}$ W $^{-1}$ are represented with open symbols in all figures. +and conclude that this (Evershed) flow is the horizontal component of penumbral convection.,and conclude that this (Evershed) flow is the horizontal component of penumbral convection. +" Overturning convection such as seen in the movie of refoslo keeps magnetic flux separated from its environment by the mechanism of (Zel’dovich 1956, Parker 1963, Weiss 1966)."," Overturning convection such as seen in the movie of \\ref{oslo} keeps magnetic flux separated from its environment by the mechanism of dovich 1956, Parker 1963, Weiss 1966)." + It is the process whereby the small scale field on the surface remains concentrated in intergranular lanes., It is the process whereby the small scale field on the surface remains concentrated in intergranular lanes. + Diffusion of the magnetic field into its environment is matched by the convective flow advecting the field lines back into the field concentration., Diffusion of the magnetic field into its environment is matched by the convective flow advecting the field lines back into the field concentration. + The balance between the two processes determines the thickness of the boundary separating the flow from the field., The balance between the two processes determines the thickness of the boundary separating the flow from the field. +" The speed of the overturning flow inferred from the data in refperpslit,, about 2 km/s, agrees well with the velocities found in the simulations of Heinemann et al. ("," The speed of the overturning flow inferred from the data in \\ref{perpslit}, about 2 km/s, agrees well with the velocities found in the simulations of Heinemann et al. (" +2007).,2007). +" The question can be raised when convecting flows such as seen in Figs. 1,"," The question can be raised when convecting flows such as seen in Figs. \ref{stria}," +",4 are ‘field free’ as in Parker’s view of umbraldots.", \ref{oslo} are `field free' as in Parker's view of umbral. +". A convecting flow near a magnetic boundary will at some level carry stray fields with it, resulting from diffusion or hydrodynamic entrainment of the external field."," A convecting flow near a magnetic boundary will at some level carry stray fields with it, resulting from diffusion or hydrodynamic entrainment of the external field." +" This would broaden the transition between the flow-dominated interior and the surrounding magnetic field, so that observed magnetic signals could look the same as those of a fully magnetizedregion.."," This would broaden the transition between the flow-dominated interior and the surrounding magnetic field, so that observed magnetic signals could look the same as those of a fully magnetized." +" The physics of flux expulsion, however, makes the distinction between and regions conceptually unambiguous."," The physics of flux expulsion, however, makes the distinction between and regions conceptually unambiguous." +" In regions where the field is weak enough that the kinetic energy of the flow dominates over the magnetic forces, the flow behaves like convection in the absence of a field, as in the photosphere outside locations of strong field and in the classical flux expulsion calculations by Weiss (1966)."," In regions where the field is weak enough that the kinetic energy of the flow dominates over the magnetic forces, the flow behaves like convection in the absence of a field, as in the photosphere outside locations of strong field and in the classical flux expulsion calculations by Weiss (1966)." + This is the sense in which the gaps in Parker (1979) and in Papers LII are called ‘field free’.," This is the sense in which the gaps in Parker (1979) and in Papers I,II are called `field free'." +" In fact, the properties of the observed striation can be used to derive an upper limit to the strength of the magnetic field inside the main body of a bright filament; this is discussed in section 5.4.2.."," In fact, the properties of the observed striation can be used to derive an upper limit to the strength of the magnetic field inside the main body of a bright filament; this is discussed in section \ref{limfield}." + Magnetic fields have cohesion only along the field: neighboring field lines can slip parallel to each other without restoring forces., Magnetic fields have cohesion only along the field: neighboring field lines can slip parallel to each other without restoring forces. + The surface bounding a magnetic region from its surroundings is therefore easily corrugated or ‘fluted’ (like the columns of Greek temples)., The surface bounding a magnetic region from its surroundings is therefore easily corrugated or `fluted' (like the columns of Greek temples). +" In fact, a magnetic boundary will corrugate spontaneously by a if the curvature vector of the field lines points into the external medium BBateman 1980; for an analysis in the context of sunspots see Meyer, Schmidt and Weiss 1977)."," In fact, a magnetic boundary will corrugate spontaneously by a if the curvature vector of the field lines points into the external medium Bateman 1980; for an analysis in the context of sunspots see Meyer, Schmidt and Weiss 1977)." +" This is the case with the boundaries of the pores seen in refoslo, because the field fans out above the surface."," This is the case with the boundaries of the pores seen in \\ref{oslo}, because the field fans out above the surface." + Fluting is thus a likely explanation for the striation seen in the walls of small magnetic structures., Fluting is thus a likely explanation for the striation seen in the walls of small magnetic structures. +with the peri-Galactic distances of globular clusters than it does with the present Galactic distance £2...,with the peri-Galactic distances of globular clusters than it does with the present Galactic distance $R_{\rm{gc}}$. + In the present paper we use data in the recent compilation by Harris (1996) (2003 update) to study some of the properties of the globular clusters in the outer halo Rae>15 Κκρο) in an attempt to find out more about how the outer Galactic halo was assembled., In the present paper we use data in the recent compilation by Harris \shortcite{harris:96} (2003 update) to study some of the properties of the globular clusters in the outer halo $R_{\rm{gc}} > 15$ kpc) in an attempt to find out more about how the outer Galactic halo was assembled. + Not all galaxies are formed in the same way., Not all galaxies are formed in the same way. + Whereas the main body of our own Milky Way system seems to have formed via he early collapse of a single large protogalaxy the Andromeda galaxy (M3) appears to have been assembled at a later dae via the merger of at least two major ancestral fragments (Freeman1999:vanBergh2004:Brown 2004)..," Whereas the main body of our own Milky Way system seems to have formed via the early collapse of a single large protogalaxy the Andromeda galaxy (M31) appears to have been assembled at a later date via the merger of at least two major ancestral fragments \cite{freeman:99,vdb:04,brown:04}. ." + The Harris catalog contains 35 Galactic clusers with kpe., The Harris catalog contains $35$ Galactic clusters with $R_{\rm{gc}} > 15$ kpc. + Data on these clusters are listed in Table L.., Data on these clusters are listed in Table \ref{t:galactic}. + In this Table we have also included data for NGC 2808. wdich jus Moo=LLL kpe. because of its possible associaion with t18 Canis Major dwarf (see below).," In this Table we have also included data for NGC 2808, which has $R_{\rm{gc}} = 11.1$ kpc, because of its possible association with the Canis Major dwarf (see below)." + Of the 35 objects wit INL5 kpe. the following seven appear to be associated wit1 the Sagitarius dwarf galaxy: M34. Terzan 7 and 8. and Arp 2 (Ibataeta.1994:DaCostaArmandroff 1995): Pal.," Of the $35$ objects with $R_{\rm{gc}} > 15$ kpc, the following seven appear to be associated with the Sagittarius dwarf galaxy: M54, Terzan 7 and 8, and Arp 2 \cite{ibata:94,dacosta:95}; Pal." + 12 and NGC 4147 (Dineseuetal.2000:Martinez-Delgadoetal.2002:Belazzinia. 20032): and Pal.," 12 and NGC 4147 \cite{dinescu:00,md:02,bellazzini:03a}; and Pal." + 2 (Majewskietal.2004)., 2 \cite{majewski:04}. +. Also note he possible physical association of the globular clusters NGC 1851. NGC 1904. NGC 2298 anc NGC 2808. plus a number of old open clusters. with the recently discovered Canis Major dwarf (Martinetal.2004:Bellazzinieal.2003b:Frinchaboyet 2004).," Also note the possible physical association of the globular clusters NGC 1851, NGC 1904, NGC 2298 and NGC 2808, plus a number of old open clusters, with the recently discovered Canis Major dwarf \cite{martin:04,bellazzini:03b,frinchaboy:04}." +. In particular. Bellazzini et a (2003b) find strong evidence that the clusters AM 2 and Tombaugh 2 [which are no cataloged as globulars by Harris üre associated with the Canis Tajor system.," In particular, Bellazzini et al \shortcite{bellazzini:03b} find strong evidence that the clusters AM 2 and Tombaugh 2 [which are not cataloged as globulars by Harris] are associated with the Canis Major system." + In fact. these authors suggest tha Tombaugh 2 may actually represent an over-density in the CMa field itself. simiar to those observed in the Sagitarius and Ursa Minor dwarf gaaxies.," In fact, these authors suggest that Tombaugh 2 may actually represent an over-density in the CMa field itself, similar to those observed in the Sagittarius and Ursa Minor dwarf galaxies." + Finally. Carraro et al.," Finally, Carraro et al." + (2004) have shown that the cluster Berkeley 29 is associated with he Monoceros stream. which is thought (Martinetal.2004) to be part of the disrupted CMa dwarf.," \shortcite{carraro:04} have shown that the cluster Berkeley 29 is associated with the Monoceros stream, which is thought \cite{martin:04} to be part of the disrupted CMa dwarf." + However. this cluster has an age of 5 Gyr. which makes it somewhat too voung to be of interes for the present study of globular clusters.," However, this cluster has an age of $\sim 5$ Gyr, which makes it somewhat too young to be of interest for the present study of globular clusters." + Information on the globular clusters in the LIC. the SMC. and he Fornax dwarf spheroidal is collected in Table 2> using the data from Mackey Gilmore (2003a:2003b:2003c).," Information on the globular clusters in the LMC, the SMC, and the Fornax dwarf spheroidal is collected in Table \ref{t:external} using the data from Mackey Gilmore \shortcite{mackey:03a,mackey:03b,mackey:03c}." +.. The total uminosities and half-light radii in this Table have been newly derived for the present work., The total luminosities and half-light radii in this Table have been newly derived for the present work. + The total luminosiies CA) were obtained by integrating these authors’ radial brightness profiles to appropriate limiting radii €50 pe) using Eg., The total luminosities $M_V$ ) were obtained by integrating these authors' radial brightness profiles to appropriate limiting radii $\sim 50$ pc) using Eq. + 12 of Mackey Gilmore (2003a)., $12$ of Mackey Gilmore \shortcite{mackey:03a}. +. Rearranging this equation hen allows the subsequent determination of the half-Iight radii., Rearranging this equation then allows the subsequent determination of the half-light radii. + Distance moduli of 18.50. 15.90. and 20.68 have been adopted for he LMC. SMC. and Fornax systems. respectively.," Distance moduli of $18.50$, $18.90$, and $20.68$ have been adopted for the LMC, SMC, and Fornax systems, respectively." + The LMC sample of Mackey Gilmore (20032) omits four known globulars (NGC 1928. 1939. Reticulum. and ESOI2I-SCO3).," The LMC sample of Mackey Gilmore \shortcite{mackey:03a} omits four known globulars (NGC 1928, 1939, Reticulum, and ESO121-SC03)." + A recent program has obtained images of these four objects using the Advanced Camera for Surveys (e.g. Mackey Gilmore 2004).," A recent program has obtained images of these four objects using the Advanced Camera for Surveys (e.g., Mackey Gilmore 2004)." + Preliminary radial luminosity profiles (for which details will follow in a future work — Mackey Gilmore. in prep.)," Preliminary radial luminosity profiles (for which details will follow in a future work – Mackey Gilmore, in prep.)" + have allowed integrated magnitudes and half light radii to be estimated for these four clusters: however those for NGC 1928 and 1939 are very uncertain due to severe crowding in the cluster images., have allowed integrated magnitudes and half light radii to be estimated for these four clusters; however those for NGC 1928 and 1939 are very uncertain due to severe crowding in the cluster images. + Half light radii for these two objects should be considered upper limis only., Half light radii for these two objects should be considered upper limits only. + The LMC cluser sample is therefore complete. consisting of al 16 known globular clustertype objects.," The LMC cluster sample is therefore complete, consisting of all $16$ known globular cluster-type objects." + The Fornax cluster sample is also complete (5 clusers)., The Fornax cluster sample is also complete $5$ clusters). + For the SMC. we have only listed GC 121.," For the SMC, we have only listed NGC 121." + Although there are other reasonably old clusters in this galaxy (e.g.. Kron 3. Lindsay |). it is not clear that they are directly comparableto the globuar clusters in the Galactic halo.," Although there are other reasonably old clusters in this galaxy (e.g., Kron 3, Lindsay 1), it is not clear that they are directly comparableto the globular clusters in the Galactic halo." + It is the aim of the present paper to see if such data on the globular clusters in nearby dwarf galaxies can provide us with hints, It is the aim of the present paper to see if such data on the globular clusters in nearby dwarf galaxies can provide us with hints +starss demonstrate a lack of gas.,s demonstrate a lack of gas. +"in Cepheid οC diagrams (plots of the differences between Observed times of light inaxiuu and those Computed frou, a linear ephemeris) have been recognized for the past half century as evidence for the evolution of such stars through the instability strip (Parauceo1958:StruveExleksova&Lkaev 1982).","in Cepheid O–C diagrams (plots of the differences between Observed times of light maximum and those Computed from a linear ephemeris) have been recognized for the past half century as evidence for the evolution of such stars through the instability strip \citep{pa58,st59,ei82}." +" As noted bv Struve (1959).. ""It appears that studies of period chauge are by far the most sensitive test available to the astrononier for detecting ninute alterations in the physical characteristics of a star.”"," As noted by \citet{st59}, “It appears that studies of period change are by far the most sensitive test available to the astronomer for detecting minute alterations in the physical characteristics of a star.”" + Observations of period changes in Cepheids have been matched with some coufidence to evolutionary inodels of massive stars du various crossines of the instability strip (e.g.Turner1998:Turner&Derduikov2001.2001) in order to ideutifv the direction of strip crossing for individual variables.," Observations of period changes in Cepheids have been matched with some confidence to evolutionary models of massive stars in various crossings of the instability strip \citep[e.g.,][]{tu98,tb01,tb04} in order to identify the direction of strip crossing for individual variables." + When used for such purposes. the studv of Cepheid period changes becomes an iuportant tool for the characterization of individual members of he class.," When used for such purposes, the study of Cepheid period changes becomes an important tool for the characterization of individual members of the class." + Tn principle it should also be possible to use rate of period change for individual Cepheids to establish Likely location within the iustabilitv strip., In principle it should also be possible to use rate of period change for individual Cepheids to establish likely location within the instability strip. + Because strip crossings for individual Cepheids occur at different rates and at ciffereu Iuiiinosities for specific stellar masses. the observed rates of period change iust be closely related to strip crossing imode and location within the instability strip.," Because strip crossings for individual Cepheids occur at different rates and at different luminosities for specific stellar masses, the observed rates of period change must be closely related to strip crossing mode and location within the instability strip." + Poteutial constraints are imposed by variations in chemucal composition aud pulsation mode. e.2.. fundamental mode. first overtouc. ete. (Bercduilkovetal.1997:Turner1999)," Potential constraints are imposed by variations in chemical composition and pulsation mode, e.g., fundamental mode, first overtone, etc. \citep{be97,te99}," +... as well as by our limited ability to establish small rates of period change for OC data containing sizeable observational uncertainties (Szabados1983)., as well as by our limited ability to establish small rates of period change for O–C data containing sizeable observational uncertainties \citep{sz83}. +. In this paper we demoustrate the link iu more detail., In this paper we demonstrate the link in more detail. + The lnk between rate of period change iu Cepheids and location within the instability strip is Hllustrated with the aid of Fig., The link between rate of period change in Cepheids and location within the instability strip is illustrated with the aid of Fig. + 1., 1. + The diagram In a theoretical TTR diagrams that depicts the location of the Cepheid instability strip according to the parameters derived for Milkv Way Cepheids (Turner2001).. along with Geneva evolutionary tracks for stars of 1. 5. 7. and 10 AL. at Z=0.008 frou Lejeune&Schaerer(2001).," The diagram is a theoretical HR diagram that depicts the location of the Cepheid instability strip according to the parameters derived for Milky Way Cepheids \citep{tu01}, along with Geneva evolutionary tracks for stars of 4, 5, 7, and 10 $M_{\sun}$ at $Z = 0.008$ from \citet{ls01}." +. Lines of coustaut stellar radius are shown crossing various portions of the instability strip., Lines of constant stellar radius are shown crossing various portions of the instability strip. + According to the well established Cepheid period-racdius relation. they should represent ues of constant pulsation period or iudividual Cepheids.," According to the well established Cepheid period-radius relation, they should represent lines of constant pulsation period for individual Cepheids." + (From an examination of Fie., >From an examination of Fig. + 1 it is clear hat. if one cousiders only Cephlieids of a specific »eriod aud im a common crossing of the instability strip. those on the hot edge of the strip iust ve c92074 more nassive than those on the cool οσο of the strip.," 1 it is clear that, if one considers only Cepheids of a specific period and in a common crossing of the instability strip, those on the hot edge of the strip must be $\sim 20\%$ more massive than those on the cool edge of the strip." + Since rate of evolution increases in proportion to the mass of a star. Cephoeids ving on the hot edge of the strip are evolving ster. and hence changing their pulsation periods at a amore rapid rate. than Cepheids of ideutical xxiod Wing on the cool edge of the strip.," Since rate of evolution increases in proportion to the mass of a star, Cepheids lying on the hot edge of the strip are evolving faster, and hence changing their pulsation periods at a more rapid rate, than Cepheids of identical period lying on the cool edge of the strip." + Rate of period change therefore relates directly to ocation within the instability strip for individual Cepheids., Rate of period change therefore relates directly to location within the instability strip for individual Cepheids. + Differences iu strip crossing modes are oulv a minor concern., Differences in strip crossing modes are only a minor concern. + Cepheids with increasing »oiods must be in the first. third. or fifth crossing of the strip. whereas Cepheids with decreasing 2ο1ος] unust be in the second or fourth crossing of the strip.," Cepheids with increasing periods must be in the first, third, or fifth crossing of the strip, whereas Cepheids with decreasing periods must be in the second or fourth crossing of the strip." + A iuinor complication arises from restrictions ou our ability. to identify period changes in Cepheids tied solely to stellar evolution., A minor complication arises from restrictions on our ability to identify period changes in Cepheids tied solely to stellar evolution. + Some Cepheids exhibit erratic period changes that appear fo originate from raudou fluctuations in pulsation period., Some Cepheids exhibit erratic period changes that appear to originate from random fluctuations in pulsation period. + SZ Tau (Derduikov&Pas-tukhova 19905).. S Vul (Derduikov1991). and V1196 Aql (Berdnikovetal.2001) are excelleut exanrples. although in the first two cases it ds possible to ideutifv the uuderlius evolutionary modifications to pulsation period.," SZ Tau \citep{bp95}, S Vul \citep{be94}, and V1496 Aql \citep{be04} are excellent examples, although in the first two cases it is possible to identify the underlying evolutionary modifications to pulsation period." + A study by Berduikov&Iguatova(2000) av eive the iupression that stellar evolution has onlv a πο effec on Cepheid OC diagrams. sjuce it notes that parabolic trends were detected πι ouly 67 of 2530 Cepheids surveved.," A study by \citet{bi00} may give the impression that stellar evolution has only a minor effect on Cepheid O–C diagrams, since it notes that parabolic trends were detected in only 67 of 230 Cepheids surveyed." +" That uuniber is iuusleading. however. given that a previous survey by Tuner(1998) had fouud parabolic trends iu 137 Cepheids frou, a iuuch sanaller sample."," That number is misleading, however, given that a previous survey by \citet{tu98} had found parabolic trends in 137 Cepheids from a much smaller sample." + It was actually intended to indicate the poor temporal coverage and lack of extensive οC data available for πα wellstudied Calactic Cepheids. a situation that has been remedied iu recent vears by our ongoluig program to obtain archival data ou Cepheid brightness variations usine the Tarvard College Observatory Photographic Plate Collection.," It was actually intended to indicate the poor temporal coverage and lack of extensive O–C data available for many well-studied Galactic Cepheids, a situation that has been remedied in recent years by our ongoing program to obtain archival data on Cepheid brightness variations using the Harvard College Observatory Photographic Plate Collection." + At, At +doctunentation did not improve the results.),documentation did not improve the results.) + These variations iu he differential rotatio)are consistent with the effect of the Coriolis force on the inflows avl the counter-cells., These variations in the differential rotation are consistent with the effect of the Coriolis force on the in-flows and the counter-cells. + Maeral moving equatorward roni the higher latiides will spin-down and give slower flows ou the poleward sides ofthe sunspot zones while maeral moving poleward from the equator will spin-up aud give faster flows on the equatorward sides., Material moving equatorward from the higher latitudes will spin-down and give slower flows on the poleward sides of the sunspot zones while material moving poleward from the equator will spin-up and give faster flows on the equatorward sides. + This scenerio was suggested by Sprui(2003) as a response to cooling iu the sunspo zoues bv excess thermal cussion from faculac., This scenerio was suggested by \cite{Spruit03} as a response to cooling in the sunspot zones by excess thermal emission from faculae. + Earlicr. Suoderass(1981) had sugeested tha in-flows aud the torsional oscilations were par of a system of azimuthal couvectiou-rolls which nuerate equatorward diving cach sunspot eve5," Earlier, \cite{Snodgrass87} had suggested that in-flows and the torsional oscillations were part of a system of azimuthal convection-rolls which migrate equatorward during each sunspot cycle." + These convection-rols should have out-flows a sole undeteruined depth below the surface a possible source of the out-flows seen in some of t helioscisinology studies., These convection-rolls should have out-flows at some undetermined depth below the surface – a possible source of the out-flows seen in some of the helioseismology studies. + The Coroilis force acti ou the long-lasting northeru counter-cell should slowdown the rotation at the affected latitudes., The Coroilis force acting on the long-lasting northern counter-cell should slowdown the rotation at the affected latitudes. + This lav be the source of the uortlh-souli asvunuuetrv in the average differential rotation profile (Fig., This may be the source of the north-south asymmetry in the average differential rotation profile (Fig. + 2)., 2). + The maguetie elements under study here are also subject to a diffusiou-like random walk by the nonaxisvinunuetrie cellular flows supererauules iu particular (Leighton—1961)., The magnetic elements under study here are also subject to a diffusion-like random walk by the nonaxisymmetric cellular flows – supergranules in particular \citep{Leighton64}. +. This random walk transports he weak. nmüagnetic elements n both ougitude and latitude and leads to he formation of ape univolar areas from the receding and followine magnetic flux in active regions (Sunithsou]073)., This random walk transports the weak magnetic elements in both longitude and latitude and leads to the formation of large unipolar areas from the preceding and following magnetic flux in active regions \citep{Smithson73}. +. This raidonm walk nieht contribute to the mericdiola flow WO WlCAsUre Chie ο resultant changes iu nagretic pattern., This random walk might contribute to the meridional flow we measure due to resultant changes in the magnetic pattern. + Tu SET inodels (DeVoreet:1981:vanBallegooi-Schrijver&Liu.2008) tUs process is represented *oa diffusivity couple wih the Laplacian of he magnetic5 field.," In SFT models \citep{DeVore_etal84, vanBallegooijen_etal98, Wang_etal02, Wang_etal05, Wang_etal09, SchrijverLiu08} this process is represented by a diffusivity coupled with the Laplacian of the magnetic field." + We WolId expect that this uieht produce a neridiona flow signal in he onu of out-flows from he sunspot zones where he magnetic field is concentrated., We would expect that this might produce a meridional flow signal in the form of out-flows from the sunspot zones where the magnetic field is concentrated. + Although wlat we observe is actually in-flows toward the suusyot zoues. the effects of diffusion might nonoetheOSs aler the strucure and evolution of the meridional flAY We measure.," Although what we observe is actually in-flows toward the sunspot zones, the effects of diffusion might nonetheless alter the structure and evolution of the meridional flow we measure." + Caven this caveat. we uidertook au juvestigaticn of the effects of supererauule diffusiou on otr eastrements.," Given this caveat, we undertook an investigation of the effects of supergranule diffusion on our measurements." + Tathawayetal.(2010) have receatly produced a model of the photospheric flows which includes he cellular ἩOWS. sUpergr:ules là paricula. observed with he SOMO MDI iusruuent.," \cite{Hathaway_etal10} have recently produced a model of the photospheric flows which includes the cellular flows, supergranules in particular, observed with the SOHO MDI instrument." +" The ος]ular flows 1n this model 1lave velocity spectra. Ποιος, and 1notions that Latei those seen iu the MDI data itself."," The cellular flows in this model have velocity spectra, lifetimes, and motions that match those seen in the MDI data itself." + We have taken the vector velocities from this m0ela id used. them Oo transport nüagnetic clemeits whose initial spatial distrition Was tken frOni all AIDI synoptic macetic map., We have taken the vector velocities from this model and used them to transport magnetic elements whose initial spatial distribution was taken from an MDI synoptic magnetic map. + We fhelise d onr anaVSIS oocedures to mcasure the axisvinuetric flows., We then used our analysis procedures to measure the axisymmetric flows. + We isolated the effects of diffusion by only Πιοπιαπας he evolving cellular flows., We isolated the effects of diffusion by only including the evolving cellular flows. + We cle) not iuclude he axisvuuuetrie meridional flow or differential rotation aud he cellular flow pattern itself does iof participate in anv axisvuuuetric meridioial flow or differeifial rotation., We do not include the axisymmetric meridional flow or differential rotation and the cellular flow pattern itself does not participate in any axisymmetric meridional flow or differential rotation. + The celllay flow simulation produced vector velocities ο ioa heloeraphic erid with 1096 ]Nw 1500 equispaced poiuts iu lougitude and latinde from an evovine velocity spectrum tlat extened to spherical wavenunibers of 1500. (supereramles have spherical Wavelbers of ~LOO )., The cellular flow simulation produced vector velocities on a heliographic grid with 4096 by 1500 equispaced points in longitude and latitude from an evolving velocity spectrum that extended to spherical wavenumbers of 1500 (supergranules have spherical wavenumbers of $\sim 100$ ). +" The iniial maenetic fied cüstrilition was taken Youn an \DI svnoptic magnetic chart for Carrineto1 rotation 2000 (iiid-200:3 just after the peak ο ‘the suuspo οποιο),", The initial magnetic field distribution was taken from an MDI synoptic magnetic chart for Carrington rotation 2000 (mid-2003 – just after the peak of the sunspot cycle). + Our maenctic fiux traisport snaulation was calculated on a erid t10 salο szea5 OU Liappetc ποασ., Our magnetic flux transport simulation was calculated on a grid the same size as our mapped magnetograms. + At each pixel in our siuulatec magnetic map we introduce a nmnunber of 1000 C maguetic elenicuts wih filling factors of uuti the average field strength iji that pixel equalec the observed feld streneth (a singIe clement iu a pixe would prodiCC a field streneth of 50 CO., At each pixel in our simulated magnetic map we introduced a number of 1000 G magnetic elements with filling factors of until the average field strength in that pixel equaled the observed field strength (a single element in a pixel would produce a field strength of 50 G). + This processs required soue 120.000 magetic clemens.," This process required some 120,000 magnetic elements." + These eleinents were then ransported explicitly bv the veocity field. from he cellular flow sunuulation iu 15auimnute fiue seps for 10 clave., These elements were then transported explicitly by the velocity field from the cellular flow simulation in 15-minute time steps for 10 days. + Exauples from f1¢ simulated magnetic maps are shown in Fie., Examples from the simulated magnetic maps are shown in Fig. + 9., 9. + The magnetic eclucuts are transported to the borders of the cels and then contine to move as the cells themselves evolve. (, The magnetic elements are transported to the borders of the cells and then continue to move as the cells themselves evolve. ( +This was shown in previous ΠΠ by Simon (2001)..),This was shown in previous simulations by \cite{Simon_etal01}. .) + The imaenetic clemenuts retain, The magnetic elements retain +where Eyer is the peak energy of the spectrmu. aud a. are the power-law indices for ploton cucreics below or above the break energy respectively.,"where $E_{\rm peak}$ is the peak energy of the spectrum, and $\alpha$, $\beta$ are the power-law indices for photon energies below or above the break energy respectively." + At last. the complete data set of all our 55 CRBs are shown in Table 1. where the error bars are la ranec.," At last, the complete data set of all our 55 GRBs are shown in Table 1, where the error bars are $1 \sigma$ range." + We investigate if an intrinsic correlation exists between the three parameters of Lx.T4 and Γιπο as following. where a.b. and e are constants to be determined from the ft to the observational data.," We investigate if an intrinsic correlation exists between the three parameters of $L_{\rm X},~T_{\rm a}$ and $E_{\gamma,\rm iso}$ as following, where $a,~b$, and $c$ are constants to be determined from the fit to the observational data." + Iu this equation. e is the constant of the intercept.," In this equation, $a$ is the constant of the intercept." +" b aud e are actually the indices of time and enerev when we approximate Lx as power-law fuuctious of T4 aud £.3.,."," $b$ and $c$ are actually the power-law indices of time and energy when we approximate $L_{\rm X}$ as power-law functions of $T_{\rm a}$ and $E_{\gamma,\rm iso}$." + Due to the complesity of CRB samplue. an intrinsic scattering parameter. Ome IS dutroduced m our analysis. as is usually done by other researchers (Reichart 2001: Chuidorzi et al.," Due to the complexity of GRB sampling, an intrinsic scattering parameter, $\sigma_{\rm int}$, is introduced in our analysis, as is usually done by other researchers (Reichart 2001; Guidorzi et al." + 2006: Amati ct al 2008)., 2006; Amati et al 2008). + This extra variable that follows a normal distribution of Α(0.02.) is engaged to represent all the contribution to Ly from other ποναι hidden variables.," This extra variable that follows a normal distribution of $N(0,~\sigma_{\rm int}^{2})$ is engaged to represent all the contribution to $L_{\rm X}$ from other unknown hidden variables." + To derive the best ft to the observational data with the above three-parameter correlation. we use the method preseuted iu D'Aeostini (2005).," To derive the best fit to the observational data with the above three-parameter correlation, we use the method presented in $'$ Agostini (2005)." + Tere. for simplify. we first define wy=lostaa). ty=lostLORyperst aud y=lost—€—10it'erg," Here, for simplify, we first define $x_{1}={\rm log}(\frac{T_{\rm a}}{10^{3}\rm s})$, $x_{2}={\rm log}(\frac{E_{\gamma,\rm iso}}{10^{53}\rm erg})$, and $y={\rm log}(\frac{L_{\rm X}}{10^{47}\rm erg/s})$." +" The joint likelihood function for the coefficieuts of a.ὃνο and og, is (D'Agostiui 2005) where / is the corresponding serial mmuberof GRBs iu our sample."," The joint likelihood function for the coefficients of $a,~b,~c$ and $\sigma_{\rm int}$ is (D'Agostini 2005) where $i$ is the corresponding serial number of GRBs in our sample." + Iu order to get the best-fit coefficients. the so called Markov chain Monte. Carlo techuignes are used in our calculations.," In order to get the best-fit coefficients, the so called Markov chain Monte Carlo techniques are used in our calculations." + For cach Markov claim. we generate 109 samples according to the likelihood function.," For each Markov chain, we generate $10^{6}$ samples according to the likelihood function." + Then we derive the the coefficients of a.b...c aud Dig according to the statistical results of tle samples.," Then we derive the the coefficients of $a,~b,~c$ and $\sigma_{\rm int}$ according to the statistical results of the samples." + Our likelihood. fuuction can also be conveniently applied to the two-parameter L-T correlation case studied by D2010. by simply taking e=0.," Our likelihood function can also be conveniently applied to the two-parameter L-T correlation case studied by D2010, by simply taking $c=0$." + We have checked our method by comparing our result for the L-T correlation with that of D2010., We have checked our method by comparing our result for the L-T correlation with that of D2010. + The results are eenerallv consistent. which proves the reliability of our codes.," The results are generally consistent, which proves the reliability of our codes." +" Iu our study. we assume a flat ACDAL cosinology with 77—69.7laus|Mpe. and Q4,=0.291 (the same values as D2010)."," In our study, we assume a flat $\Lambda \rm CDM$ cosmology with $H=69.7~\rm km\cdot s^{-1}\cdot Mpc^{-1}$ and $\Omega_{\rm M}=0.291$ (the same values as D2010)." + By using the method described iu Section 2. we fud that the best-fit correlation between Ly. T4 aud E.ο 1s Figure 1 shows the above correlation.," By using the method described in Section 2, we find that the best-fit correlation between $L_{\rm X}$, $T_{\rm a}$ and $E_{\gamma,\rm iso}$ is Figure 1 shows the above correlation." + In this figure. the solid line is plotted from Eq. (," In this figure, the solid line is plotted from Eq. (" +7). and the poiuts represent the 55 CRBs of our sample (the filled poiuts correspond to,"7), and the points represent the 55 GRBs of our sample (the filled points correspond to" +We collected images with typical exposures times from 10 to 120 seconds. covering a time interval of about 0.5 hours.,"We collected images with typical exposures times from 10 to 120 seconds, covering a time interval of about 0.5 hours." + Image reduction was carried out by following the standard procedures., Image reduction was carried out by following the standard procedures. + Astrometry was performed using the and the catalogues., Astrometry was performed using the and the catalogues. + We performed aperture photometry for the afterglow and comparison stars., We performed aperture photometry for the afterglow and comparison stars. + The afterglow was not detected in the optical., The afterglow was not detected in the optical. + In the NIR it was detected only in the // and As bands., In the NIR it was detected only in the $H$ and $Ks$ bands. + Results for the photometry are reported in reftable:optical.., Results for the photometry are reported in \\ref{table:optical}. + The GROND instrument equipping the 2.2m ESO/MPI telescope at La Silla started observation 17.1 hr after the trigger. gave a redshift limit of 2.3.5 and a best fit of intrinsic extinction of Av between 0.6 and 1.2 (Clemens.Kruehler. 2008)).," The GROND instrument equipping the 2.2m ESO/MPI telescope at La Silla started observation 17.1 hr after the trigger, gave a redshift limit of $z<3.5$ and a best fit of intrinsic extinction of Av between 0.6 and 1.2 \citealt{Clemens08}) )." +" For /« h.the temporal index ay=—1.55+0.04 and the spectral index 9,=—0.74+0.05 are related by a33/2um 0.5. being consistent with the forward-shock emission inthe FW medium as long as Mia«£A ve."," For $tt_{\rm b2}$, the temporal index $\alpha_3=-1.24\pm0.03$ and the spectral index $\beta_{3}=-1.27\pm0.10$ are related by $\alpha-3\beta/2\sim 0.5$, suggesting that the medium can be either FW or CD given $\nu_{_{\rm X}}>\max\{\nu_{\rm +m},\nu_{\rm c}\}$ \citealt{Zhang04}) )." + If the FW scenario holds from the very beginning. we have Pellis)zesa)zmας because of £p.x17.," If the FW scenario holds from the very beginning, we have $\nu_{\rm c}(t_{\rm b2})>\nu_{\rm c}(t_{\rm b1})>\nu_{_{\rm X}}$ because of $\nu_{\rm c} \propto t^{1/2}$." +" One can. of course. assume that either 21, or ej has increased abruptly and then get a ellus)< po)."," One can, of course, assume that either $A_{*}$ or $\epsilon_{\rm B}$ has increased abruptly and then get a $\nu_{\rm c}(t_{\rm b2})\ll \nu_{\rm c}(t_{\rm +b1})$ ." + However. such a treatment is lack of any solid physical background and is thus artificial.," However, such a treatment is lack of any solid physical background and is thus artificial." + On the other hand. if we assume that at /—νι there comes the FW to CD transition. the forward shock emission light curve will get flattened by a factor of (4°. roughly consistent with the data (please note that as is only poorly constrained).," On the other hand, if we assume that at $t\sim t_{\rm b1}$ there comes the FW to CD transition, the forward shock emission light curve will get flattened by a factor of $t^{1/2}$, roughly consistent with the data (please note that $\alpha_2$ is only poorly constrained)." + In this scenario. the steepening at { implies that ο{ο}2 ως. Below we present our quantitative estimates.," In this scenario, the steepening at $t\geq t_{\rm b2}$ implies that $\nu_c(t_{\rm b2})>\nu_{_{\rm X}}$ Below we present our quantitative estimates." +" In a FW; medium.: we have a,=L13p ""and,= roi: inthe case of £y,xexp."," In a FW medium, we have $\alpha_1=\frac{1-3p}{4}$ and $\beta_1=-\frac{p-1}{2}$ in the case of $\nu_{\rm m}<\nu_{\rm X}<\nu_{\rm c}$." +" Ina CD medium. we have a.= and i,=§ forexστοvo}."," In a CD medium, we have $\alpha_3=\frac{2-3p}{4}$ and $\beta_3=-\frac{p}{2}$ for $\nu_{\rm X}>\max\{\nu_{\rm m},\nu_{\rm c}\}$." +" We find that p=2.5 fits both the temporal and spectral slopes of GRB 081109A. In a FW medium. we have te.g..Chevalier&Li. 2000):: where /7i is the isotropic equivalent energy. > is the redshift of the GRB and £2, is the corresponding luminosity distance. /,4 is the time in days since trigger in the observer's frame. and C,2)/3(p 1)]."," We find that $p=2.5$ fits both the temporal and spectral slopes of GRB 081109A. In a FW medium, we have \citep[e.g.,][]{Chevalier00}: : where $E_{\rm k}$ is the isotropic equivalent energy, $z$ is the redshift of the GRB and $D_{\rm +L}$ is the corresponding luminosity distance, $t_{\rm d}$ is the time in days since trigger in the observer's frame, and $C_{p}\equiv13(p-2)/[3(p-1)]$ ." +" In our model. at /~65.6 s. £j,«O.3keV. vo10keV. and Πλ~2.6107Jv are needed."," In our model, at $t\sim 65.6$ s, $\nu_{\rm m}<0.3{\rm keV}$, $\nu_{\rm c}>10{\rm keV}$ and $F_{\rm +0.3keV}\sim2.6\times10^{-3}~{\rm Jy}$ are needed." + So we have In a CD medium. we have (e.g.Sari.Piran.&1998): At ~[us 2900s. our model suggests that ο and Ü.3keV. and ολων~5.7510.7Jy.," So we have In a CD medium, we have \citep[e.g.,][]{Sari98}: At $t\sim t_{\rm b2}\sim 2900$ s, our model suggests that $\nu_{\rm m}$ and $\nu_{\rm c}<0.3{\rm +keV}$ , and $F_{\rm 0.3keV}\sim5.7\times10^{-5}~{\rm Jy}$." +" We then have In a termination shock model. the crossing time is estimated by Chevalier.Li&Fransson(2004): For GRB 0811094, there is no self-consistent solution for Eqs.61--63.. Egs.(10--12)). and. Eq.cl4)) provided that ej is a constant in the free wind and in the CD medium."," We then have In a termination shock model, the crossing time is estimated by \cite{Chevalier04}: i.e., For GRB 081109A, there is no self-consistent solution for \ref{eq:wind,m,X}- \ref{eq:wind,FX}) ), \ref{eq:ISM,m,X}- \ref{eq:ISM,FX}) ) and \ref{eq:R_t_2}) ) provided that $\epsilon_{\rm B}$ is a constant in the free wind and in the CD medium." +" With eqs.cl+)). (Sy) and CLE». wehave εροέριω c7. where thesubscripts ""CD"" and “w"" representthe physical parameters measured in CD and FW medium. respectively."," With \ref{eq:R_t_2}) ), \ref{eq:wind,X,c}) ) and \ref{eq:ISM,X,c}) ), wehave $\epsilon_{\rm B,CD}/\epsilon_{\rm B,w}\geq 7$ , where thesubscripts ${\rm CD}$ "" and ${\rm w}$ "" representthe physical parameters measured in CD and FW medium, respectively." +A similar assumption was needed in the modelingof the afterglow data of GRB 050904 (Gendreetal. 20075) and GRBOSO319 (Kambleetal. 20075).,A similar assumption was needed in the modelingof the afterglow data of GRB 050904 \citealt{Gendre07}) ) and GRB050319 \citealt{Kamble07}) ). + The physical reasonis that the CD medium has been heated by the termination reverse shock and then may be weakly magnetized., The physical reasonis that the CD medium has been heated by the termination reverse shock and then may be weakly magnetized. +nol changed appreciably. we believe the difference is due to the higher SNR of the new cata. and to a better. more complete IRS data calibration.,"not changed appreciably, we believe the difference is due to the higher SNR of the new data, and to a better, more complete IRS data calibration." + While previously we had reported water ice at only moderate abundances in 11ID693230. the change does concern us lor the purported detections of water ice in other svstems we have studied to date.," While previously we had reported water ice at only moderate abundances in HD69830, the change does concern us for the purported detections of water ice in other systems we have studied to date." + Fieure T shows (he contributions of various particle sizes to the overall emission spectrum along with various power-laws., Figure \ref{dustsize} shows the contributions of various particle sizes to the overall emission spectrum along with various power-laws. + The steepest. α?. power-law provides the best fil to the IRS spectrum.," The steepest, $a^{-3.9}$, power-law provides the best fit to the IRS spectrum." + The distribution of grains sizes is typically assumed to follow a distribution dn/daoxa.oE77. as expected [rom a simple model [or a steady-state collisional cascade1969).," The distribution of grains sizes is typically assumed to follow a power-law distribution $dn/da \propto a^{-3.5}$, as expected from a simple model for a steady-state collisional cascade." +. However. a greater concentration of small dust can be produced if the strength of the particles against collisional disruption depends on grain size. will smaller particles being more resistant to destruction than larger ones2011).," However, a greater concentration of small dust can be produced if the strength of the particles against collisional disruption depends on grain size, with smaller particles being more resistant to destruction than larger ones." +. Observationally. a steeper power-law appears to be required to explain the combined IR and visible light emission [rom the resolved disks orbiting ILD207129 (à. 757) and IID92945 (a η)2011).," Observationally, a steeper power-law appears to be required to explain the combined IR and visible light emission from the resolved disks orbiting HD207129 $a^{-3.9}$ ) and HD92945 $a^{-3.7}$ )." +. Our model for ILD69820s disk enission suggests a comparably steep power law., Our model for HD69830's disk emission suggests a comparably steep power law. +" Consistent with our previous work we obtain a dust mass of 3x107"" ο and surface area of 12x1077 em? in 0.1-10 jam grains and. by extrapolation up to 10 m planetesimals with a e.? power law. a total mass of solid material 2x107! ο2007). Another explanation for (he particle size distribution comes from the competition between eravitational and radiation forces (Povutine-Robertson drag and blow-out by radiation pressure) which controls the small grain lifetime."," Consistent with our previous work we obtain a dust mass of $\times10^{20}$ g and surface area of $\times10^{24}$ $^2$ in 0.1-10 $\mu$ m grains and, by extrapolation up to 10 m planetesimals with a $a^{-3.9}$ power law, a total mass of solid material $\times10^{21}$ g. Another explanation for the particle size distribution comes from the competition between gravitational and radiation forces (Poynting-Robertson drag and blow-out by radiation pressure) which controls the small grain lifetime." +" The parameter 2=£,,;/F,,,. depends on physical properties of the dust grains and the stellar radiation field 2004).", The parameter $\beta= F_{rad}/F_{grav} $ depends on physical properties of the dust grains and the stellar radiation field . +. The value of ;2 as a ΠΙΟΙΟ of particle size is shown in Figure 8. [or astronomical silicate in the radiation field of IID69330., The value of $\beta$ as a function of particle size is shown in Figure \ref{betafig} for astronomical silicate in the radiation field of HD69830. + Only a narrow size range around ~ 0.4 jm diameter attains 9 20.5. so that a turnover (but not a complete truncation) in the size distribution would be expected at sizes just below | mi as observed: i.e.. the derived distribution is entirely consistent wilh that expected for dust that is being produced in steady state [rom a reservoir of larger objects.," Only a narrow size range around $\sim$ 0.4 $\micron$ diameter attains $\beta>$ 0.5, so that a turnover (but not a complete truncation) in the size distribution would be expected at sizes just below 1 $\micron$ as observed; i.e., the derived distribution is entirely consistent with that expected for dust that is being produced in steady state from a reservoir of larger objects." + For different compositions. in particular those with grains of lower densities. 3 would be higher than that in Figure 8 and a broader range of particle sizes would be removed.," For different compositions, in particular those with grains of lower densities, $\beta$ would be higher than that in Figure \ref{betafig} and a broader range of particle sizes would be removed." + Overall. the new data. particularly given the lack of a definite detection of H3O ice. leads to a straightforward conclusion that the ILD69330 debris is dominated by small grains «1 jan composed of material similar to C-class asteroids which formed in drier. interior portions of solar nebula.," Overall, the new data, particularly given the lack of a definite detection of $_2$ O ice, leads to a straightforward conclusion that the HD69830 debris is dominated by small grains $<$ 1 $\mu$ m composed of material similar to C-class asteroids which formed in drier, interior portions of solar nebula." + As suggested bv Figure 10 in(2011).. the silicates in the HLD69830 disk ave enriched in olivines relative to pvroxenes. suggestive of highlv processed material in a few Gvr-old svstem and substantially different [rom (he more primitivematerial seen in," As suggested by Figure 10 in, the silicates in the HD69830 disk are enriched in olivines relative to pyroxenes, suggestive of highly processed material in a few Gyr-old system and substantially different from the more primitivematerial seen in" +use it if the dillerence. between (16)) and. (5)) is small.,use it if the difference between \ref{11b3}) ) and \ref{11a5}) ) is small. + Mathematically it can be written as: As we have already discussed. in thendroduclion. Es»ecilie angular momentum of the majority of the dark uatter particles hardly can be larger than 900kpe- kms. LEubstituting ry= Ror=r. to the inequality. we can see iud its right part is equal to 1107.km? fs. while its left xut ds 5507rkm-.," Mathematically it can be written as: As we have already discussed in the, specific angular momentum of the majority of the dark matter particles hardly can be larger than $900\;\text{kpc}\cdot\text{km/s}$ Substituting $r_0=R$, $r=r_{\odot}$ to the inequality, we can see that its right part is equal to $110^2\; \text{km}^2/\text{s}^2$ , while its left part is $\sim 550^2\; \text{km}^2/\text{s}^2$." + Hence the inequality. asserts near 1e Solar System. the influence of the angular momentunm. on the radial dynamics is still negligible for the majority of DMPS. ancl we can use (112) up to rr. as before.," Hence the inequality asserts near the Solar System, the influence of the angular momentum on the radial dynamics is still negligible for the majority of DMPs, and we can use \ref{11a6}) ) up to $r_\odot$ as before." +" Thus 16 DALP distribution throughout 0, in this approximation ""oincides with (13)).", Thus the DMP distribution throughout $\upsilon_r$ in this approximation coincides with \ref{11b2}) ). + However. the particles have also some üstribution throughout ος.," However, the particles have also some distribution throughout $\upsilon_\rho$." + For simplicity we will suppose wt foxexp( where oy=80km/s. though the distribution can be 05/265)much narrower.," For simplicity we will suppose that $f\propto \exp(-\upsilon^2_\rho/2\sigma^2_0)$ where $\sigma_0=80$, though the distribution can be much narrower." + Then the normalized DAIP distribution near the Solar System can be closely approximated. by where ονlHChetOmer]. Cons=562km/s.," Then the normalized DMP distribution near the Solar System can be closely approximated by where $\upsilon_r\in [-\upsilon_{max};\upsilon_{max}]$, $\upsilon_{max}=562$." + Distribution (18)) is strongly anisotropic and actually describes two colliding beams of particles., Distribution \ref{11b6}) ) is strongly anisotropic and actually describes two colliding beams of particles. + Fie., Fig. + 1 represents distributions (13)) and. (1)) (solid. and dashed lines. respectively).," \ref{fig1} represents distributions \ref{11b2}) ) and \ref{11b1}) ) (solid and dashed lines, respectively)." + One can see that (13)) is much narrower and has much higher average velocity., One can see that \ref{11b2}) ) is much narrower and has much higher average velocity. + Phe physical reason of it is obvious: in the case of Maxwell distribution (1)) the particles move almost. circularly. which is why only a few of DAIPs from the edge of the halo reach the Solar orbit.," The physical reason of it is obvious: in the case of Maxwell distribution \ref{11b1}) ) the particles move almost circularly, which is why only a few of DMPs from the edge of the halo reach the Solar orbit." + On the contrary. in the case considered. in this article the majority of DAIPs comes from the halo edge ad thus are much more accelerated. by the gravitational field.," On the contrary, in the case considered in this article the majority of DMPs comes from the halo edge and thus are much more accelerated by the gravitational field." + Consequently. the question of what of the distributions. (1)) or (13)). is correct. can be reduced to whether the particles from the halo edge can reach the Solar orbit or not.," Consequently, the question of what of the distributions, \ref{11b1}) ) or \ref{11b2}) ), is correct, can be reduced to whether the particles from the halo edge can reach the Solar orbit or not." + In addition to the arguments presented. in the we note that. according to (16)). a particle falling. [rom r—dt should have a specific angular momentum fe~4000kpc:km/s. lest the particle can reach 5=8kpc.," In addition to the arguments presented in the we note that, according to \ref{11b3}) ), a particle falling from $r=R$ should have a specific angular momentum $\mu\sim 4000\; +\text{kpc}\cdot\text{km/s}$ , lest the particle can reach $r=8$." + This value is huge. it far exceed not only the characteristic momentum of halo objects. but even the momentum of the disk. and thus looks very unlikely.," This value is huge, it far exceed not only the characteristic momentum of halo objects, but even the momentum of the disk, and thus looks very unlikely." + So particles from the edge of the halo freely reach the Earth. and their spectrum should be closer to €13)).," So particles from the edge of the halo freely reach the Earth, and their spectrum should be closer to \ref{11b2}) )." + Ao similar consideration allows us to examine the dependence of velocity. distribution. (13)) on the density profile., A similar consideration allows us to examine the dependence of velocity distribution \ref{11b2}) ) on the density profile. + Our assumption of the existence of a large region with pxr7 is approximately correct. for massive spiral ealaxies. such as the Milkv-Mav (Duttonetal.2010).," Our assumption of the existence of a large region with $\rho\propto r^{-2}$ is approximately correct for massive spiral galaxies, such as the Milky-Way \citep{2010MNRAS.407....2D}." + Llowever. we obtained (13)) on the additional assumption hat the edge of the halo is more or less sharp.," However, we obtained \ref{11b2}) ) on the additional assumption that the edge of the halo is more or less sharp." + \leanwhile. he outer region of the halo can have a clensity profile steeper than r7. but not steep enough to be considered as a cutolf.," Meanwhile, the outer region of the halo can have a density profile steeper than $r^{-2}$, but not steep enough to be considered as a cutoff." + As an instance. one can consider a double power-aw halo (Lisantietal.2011)..," As an instance, one can consider a double power-law halo \citep{lisanti}." + How can it influence on the velocity profile?, How can it influence on the velocity profile? + The answer depends on the mass fraction of this steeper region with respect to the total mass of the ido., The answer depends on the mass fraction of this steeper region with respect to the total mass of the halo. + Hf the fraction is small. the distribution dillers little rom (13)). as we demonstrated with distribution (15)).," If the fraction is small, the distribution differs little from \ref{11b2}) ), as we demonstrated with distribution \ref{11g1}) )." + Let us consider the case when the fraction is significant., Let us consider the case when the fraction is significant. + We indicate the radius where the profile gets steeper than + ov Wk hereafter we will name outer halo’ the region out of 98., We indicate the radius where the profile gets steeper than $r^{-2}$ by $\mathfrak R$; hereafter we will name 'outer halo' the region out of $\mathfrak R$. + s we could see. in the model with sharp halo edge he majoritv of the particles comes from the edge of the iilo.," As we could see, in the model with sharp halo edge the majority of the particles comes from the edge of the halo." + Expressing this fact mathematically. clistribution £(ro) is small for ro<2 and goes to infinity at the edge of the iilo (11)).," Expressing this fact mathematically, distribution $\xi(r_0)$ is small for $r_0\mathfrak R$. +"According to (7)). their contribution to the halo mass in interval dr. depends on r only as v6,l3). esτς)."," According to \ref{11a8}) ), their contribution to the halo mass in interval $dr$ depends on $r$ only as $\upsilon_r^{-1}(r)$. $\upsilon_r^{-1}(r)$," + however. changes rather slowly. inside the region where rO7.since the potential there (see (2))) depends on r only logarithmically.," however, changes rather slowly inside the region where $\rho\propto r^{-2}$ , since the potential there (see \ref{11a2}) )) depends on $r$ only logarithmically." + Therefore. the particles falling from the edge of halo provide almost the same contribution to the halo mass on each radius inside the region dill=consi. which corresponds to pzzx.7.," Therefore, the particles falling from the edge of halo provide almost the same contribution to the halo mass on each radius inside the region $dM\approx \text{\it +const}$, which corresponds to $\rho\approx r^{-2}$." + Function £(r) should be chosen so that it reproduces the density profile. in particular. it should provide pxr7.," Function $\xi(r_0)$ should be chosen so that it reproduces the density profile, in particular, it should provide $\rho\propto r^{-2}$." + However. as we could see. the particles from the outer halo by themselves give a very similar profile. and we need relatively lew of particles with ry«n in order to make it exactly r7.," However, as we could see, the particles from the outer halo by themselves give a very similar profile, and we need relatively few of particles with $r_0<\mathfrak R$ in order to make it exactly $r^{-2}$." + Consequently. £69) is small for ry«WX. and a significant fraction still comes from the halo edge.," Consequently, $\xi(r_0)$ is small for $r_0<\mathfrak R$, and a significant fraction still comes from the halo edge." +Thus. thisproperty of the distribution does not depend on the exact density profile. being only a result of the assumption of strong anisotropy of the velocity distribution and of the Hatness of potential (2)).,"Thus, thisproperty of the distribution does not depend on the exact density profile, being only a result of the assumption of strong anisotropy of the velocity distribution and of the flatness of potential \ref{11a2}) )." + Function £(ro) unambiguously determines the velocity distribution of the dark matter particles. ancl the above- common properties of £(ru) directly. correspond to characteristies of fle).," Function $\xi(r_0)$ unambiguously determines the velocity distribution of the dark matter particles, and the above-mentioned common properties of $\xi(r_0)$ directly correspond to characteristics of $f(\upsilon)$ ." + For the Milkv. Way galaxy 9ὶ , For the Milky Way galaxy $\mathfrak R$ +the transient pulsar curing the 1993 August outburst. vielded the value of Ny in the range of OS1.73 1077 alonis ? (able 1: Shrader et al.,"the transient pulsar during the 1993 August outburst, yielded the value of $N_H$ in the range of 0.8–1.73 $\times$ $^{22}$ atoms $^{-2}$ (Table 1; Shrader et al." + 1999)., 1999). + In case of data obtained from the Suzaku observation of the pulsar. it is found that the Q.8-70.0. keV. broac-bancl spectra. can γα well described by three different continuum models with similar statistical parameters.," In case of data obtained from the Suzaku observation of the pulsar, it is found that the 0.8-70.0 keV broad-band spectra can be well described by three different continuum models with similar statistical parameters." + Phe high energy eutoll power-aw model and NPIZX continuum model vielded higher value ol Ny than that of the Galactic value in the direction of the pulsar., The high energy cutoff power-law model and NPEX continuum model yielded higher value of $N_H$ than that of the Galactic value in the direction of the pulsar. + Lt is interesting to note that. inspite of high value of column density. a blackbody component of temperataure Al ~0.2 keV was also requirect for these two continuum mocoels o describe the broad-band spectrum of the pulsar.," It is interesting to note that, inspite of a high value of column density, a blackbody component of temperature $kT$ $\sim$ 0.2 keV was also required for these two continuum models to describe the broad-band spectrum of the pulsar." + In these wo models. it is estimated that the absorption correc lux of the soft. XN-rav. excess (blackbody) in is about of the unabsorbed source [ux in 08-70 keV energv rouge.," In these two models, it is estimated that the absorption corrected flux of the soft X-ray excess (blackbody) in is about of the unabsorbed source flux in 0.8-70 keV energy range." + The third model ic. the partial covering moclel. however. fits the pulsar spectrum comparatively better than the previous two continuum models.," The third model i.e. the partial covering model, however, fits the pulsar spectrum comparatively better than the previous two continuum models." + Based on our results from the phase resolved: spectroscopy. the earlier two continuum models were not. preferred to describe the properties of the pulsar.," Based on our results from the phase resolved spectroscopy, the earlier two continuum models were not preferred to describe the properties of the pulsar." + In the partial covering model. μι is considered as the Galactic hydrogen column density. and Ng» is interpreted as the column density ofthe material that is local to the neutron star.," In the partial covering model, $_{H1}$ is considered as the Galactic hydrogen column density, and $_{H2}$ is interpreted as the column density of the material that is local to the neutron star." + Phe value of Ng» is maximun. during the primary dip that is interpreted: as due to the accretion column., The value of $_{H2}$ is maximum during the primary dip that is interpreted as due to the accretion column. + The high. value of Ng» and the covering fraction at 0.40.5 pulse ohase range explain the dip like feature in the pulse profile., The high value of $_{H2}$ and the covering fraction at 0.4–0.5 pulse phase range explain the dip like feature in the pulse profile. +" Phe broad-bancl spectroscopy of also shows the presence of a narrow iron lx,, emission line at 6.4 keV. The iron emission line is eenerallv interpreted as due to the Duorescent line from the cold matter in the surrounding region of the neutron star.", The broad-band spectroscopy of also shows the presence of a narrow iron $_\alpha$ emission line at 6.4 keV. The iron emission line is generally interpreted as due to the fluorescent line from the cold matter in the surrounding region of the neutron star. + We wish to thank the referee. for his/her suggestions on the paper., We wish to thank the referee for his/her suggestions on the paper. + The research work at Physical Research Laboratory ds. funded by the Department of Space. Government of India.," The research work at Physical Research Laboratory is funded by the Department of Space, Government of India." + SN thanks Zullikar Ali for useful discussion in ILEXD/€GSO cata processing., SN thanks Zulfikar Ali for useful discussion in HXD/GSO data processing. + Cle would. like to acknowledge the hospitality. provided. by the Physical ltesearch Laboratory curing his visit to carry out the present work., CK would like to acknowledge the hospitality provided by the Physical Research Laboratory during his visit to carry out the present work. + The authors would like to thank all the members of the Suzaku for their contributions in the instrument preparation. spacecraft! operation. software. development. and in-orbit instrumental calibration.," The authors would like to thank all the members of the Suzaku for their contributions in the instrument preparation, spacecraft operation, software development, and in-orbit instrumental calibration." +" ""This research has made use of data obtained through HIZASABRC Online Service. provided by the NASA/GSEC. in support of NASA Ligh Encrev Astrophysies Programs."," This research has made use of data obtained through HEASARC Online Service, provided by the NASA/GSFC, in support of NASA High Energy Astrophysics Programs." +"In the next sections we will show that £3, is often too close to 2 to be able to rely on 7, for an estimate of the true age of a MS.",In the next sections we will show that $P_0$ is often too close to $P$ to be able to rely on $\tau_c$ for an estimate of the true age of a MSP. + The very low spin-down rates of the MSIPs have so far preclucecl any direct. measurements of the braking index., The very low spin-down rates of the MSPs have so far precluded any direct measurements of the braking index. + An index of i=3 is indicated for old normal radio pulsars. but values n~152.8 have been measured in vounger pulsars (Lyne 1996: Hobbs et al.," An index of $n=3$ is indicated for old normal radio pulsars, but values $n\sim 1.5-2.8$ have been measured in younger pulsars (Lyne 1996; Hobbs et al." + 2004)., 2004). + In this work. we have adopted η=3. but it is conceivable that a clillerent value of η may be appropriate for the AISPs.," In this work, we have adopted $n=3$, but it is conceivable that a different value of $n$ may be appropriate for the MSPs." + For instance. if spin down is by multi-polar radiation. the braking inclex will be somewhat larger than 3. while if angular momentum is lost mainly by gravitational radiation. we expect n=5 (Camilo. Thorsett Wulkarni 1994).," For instance, if spin down is by multi-polar radiation, the braking index will be somewhat larger than $3$, while if angular momentum is lost mainly by gravitational radiation, we expect $n=5$ (Camilo, Thorsett Kulkarni 1994)." + In our mocdelling we adopt à?=3 but we also discuss the implications of using a larger value of n., In our modelling we adopt $n=3$ but we also discuss the implications of using a larger value of $n$. + We synthesise the properties of the AISPs using essentially που method described. in Ferrario Wickramasinghe (2006. hereafter FW).," We synthesise the properties of the MSPs using essentially the method described in Ferrario Wickramasinghe (2006, hereafter FW)." + However. in he present study there are two main cilferences.," However, in the present study there are two main differences." + Firstly. we directlv assume an initial magnetic field. clistribution or the AISPs without attempting to relate it back to the magnetic properties of the (main sequence) progenitors.," Firstly, we directly assume an initial magnetic field distribution for the MSPs without attempting to relate it back to the magnetic properties of the (main sequence) progenitors." + We herefore have as our basic input the ΑΙ birth magnetic ield. distribution. which we describe bv à Gaussian in the ogarithim. and the birth spin distribution also described by a Gaussian.," We therefore have as our basic input the MSP birth magnetic field distribution, which we describe by a Gaussian in the logarithm, and the birth spin distribution also described by a Gaussian." + We stress that here with “birth” characteristics of MSPs we refer to those characteristics that the MSPs lave as they switch on as radio emitters. regardless of their oevious history.," We stress that here with “birth” characteristics of MSPs we refer to those characteristics that the MSPs have as they switch on as radio emitters, regardless of their previous history." + Hence. the results of our calculations co not depend in any wavs on the specific route(s) leading to he formation of the MISPs.," Hence, the results of our calculations do not depend in any ways on the specific route(s) leading to the formation of the MSPs." + Secondly. we take into consideration the three Doppler accelerations effects. cited by Damour Tavlor. (1991) which alfect the observed. spin-down rate of the λος. namely. (i) the Galactic differential rotation. (ii) the vertical acceleration. A. in the Galactic potential anc (ii) the intrinsic transverse velocity of the pulsar.," Secondly, we take into consideration the three Doppler accelerations effects cited by Damour Taylor (1991) which affect the observed spin-down rate of the MSPs, namely, (i) the Galactic differential rotation, (ii) the vertical acceleration $K_z$ in the Galactic potential and (iii) the intrinsic transverse velocity of the pulsar." + “Phus. the observed spin-down rate is given by (c.g. Toscano et al.," Thus, the observed spin-down rate is given by (e.g. Toscano et al." + 1999) where 5 is the “intrinsic” spin-down rate and AP is the term due to the aforementioned acceleration effects., 1999) where $\dot P_i$ is the “intrinsic” spin-down rate and $\Delta\dot P$ is the term due to the aforementioned acceleration effects. + Llence. when we compare our models to observations. we introduce these acceleration. terms to our. synthetic population to mimic the behaviour of the observed: MSPs.," Hence, when we compare our models to observations, we introduce these acceleration terms to our synthetic population to mimic the behaviour of the observed MSPs." + We follow the motions of the stars we generate by integrating the equations of motion in the Galactic potential of Wuijken Gilmore (1989) assuming that the neutron stars are born with a kick velocity given by a Gaussian distribution with velocity dispersion m..., We follow the motions of the stars we generate by integrating the equations of motion in the Galactic potential of Kuijken Gilmore (1989) assuming that the neutron stars are born with a kick velocity given by a Gaussian distribution with velocity dispersion $\sigma_v$. + lo [it the observations. we also model the racio Iuminosity at 1400 MIIZ and compare it to the members of our list with a measured value at this frequency.," To fit the observations, we also model the radio luminosity at 1400 MHZ and compare it to the members of our list with a measured value at this frequency." + Phe studies of Wramer ct al. (, The studies of Kramer et al. ( +1998) and Ixuzmin (2002) indicate that despite the Large cdillerences in periods and magnetic fields. normal pulsars and MSPs exhibit the same flux density spectra. therefore pointing towards the same omission mechanism. although the AISPs tend to be weaker sources on average (Ixramer et al.,"1998) and Kuz'min (2002) indicate that despite the large differences in periods and magnetic fields, normal pulsars and MSPs exhibit the same flux density spectra, therefore pointing towards the same emission mechanism, although the MSPs tend to be weaker sources on average (Kramer et al." + 1998)., 1998). + Hence. similarly to many oevious investigators (e.g. PW: Naravan Ostriker 1990). we have assumed that the luminosity £a4oo at 400 MIIZ can x described by a mean luminosity of the forni llere the luminosities are in units of mJy κρο," Hence, similarly to many previous investigators (e.g. FW; Narayan Ostriker 1990), we have assumed that the luminosity $L_{400}$ at 400 MHZ can be described by a mean luminosity of the form Here the luminosities are in units of mJy $^2$." +" We jwe modelled the spread around. Lio using the dithering ""uncetion of Naravan Ostriker (1990) to take into account he various intrinsic physical variations within the sources ancl also variations caused. by different viewing geometries.", We have modelled the spread around $L_{400}$ using the dithering function of Narayan Ostriker (1990) to take into account the various intrinsic physical variations within the sources and also variations caused by different viewing geometries. + This function is given by where and e and b are constants to be determined (Llartman et al., This function is given by where and $a$ and $b$ are constants to be determined (Hartman et al. + 1997)., 1997). + I|xramer ct al. (, Kramer et al. ( +1998). find that by restricting their comparison analysis of normal radio-pulsars to λος to sources up to 1.5 kpc. the mean spectral indices of normal racio-pulsars and AISPs are essentially the same. i.e... 1.640.2 (AISPs) anc 1.7x0.1 (normal pulsars).,"1998) find that by restricting their comparison analysis of normal radio-pulsars to MSPs to sources up to 1.5 kpc, the mean spectral indices of normal radio-pulsars and MSPs are essentially the same, i.e., $-1.6\pm 0.2$ (MSPs) and $-1.7\pm 0.1$ (normal pulsars)." + Hence. our deduced radio luminosity at 400 MEI is scalec to 1400 ΧΙ using a spectral index of 1.7 (as in FW)., Hence our deduced radio luminosity at 400 MHZ is scaled to 1400 MHZ using a spectral index of $-1.7$ (as in FW). + Once all the intrinsic properties of our model MSI's are determined. we check for pulsars detectability at 1400 MIIZ by the Parkes multi-beam receiver (c.g. Manchester ct al.," Once all the intrinsic properties of our model MSPs are determined, we check for pulsars detectability at 1400 MHZ by the Parkes multi-beam receiver (e.g. Manchester et al." + 2001: Vranesevie et al., 2001; Vranesevic et al. + 2004)., 2004). + Furthermore. pulsars radio emission is anisotropic with pulsars at shorter periods exhibiting wider beams. hence we need to correct for this factor. since this will inlluence the birth rates of AISPs.," Furthermore, pulsars radio emission is anisotropic with pulsars at shorter periods exhibiting wider beams, hence we need to correct for this factor, since this will influence the birth rates of MSPs." + For example. large beams would require smaller birth rates. since the AISPs would have a greater chance to be detected.," For example, large beams would require smaller birth rates, since the MSPs would have a greater chance to be detected." + Llowever. there is as vet no agreement on the beaming fraction-period relationship. particularly for the AISPs.," However, there is as yet no agreement on the beaming fraction-period relationship, particularly for the MSPs." + Rankin (1993). Gil ct al. (," Rankin (1993), Gil et al. (" +1993) and. Ixramoer et al. (,1993) and Kramer et al. ( +1994) pointed out that observational evidence seems to suggest that the opening angles of normal raclio-pulsars (that is. the last open dipolar field line) is proportional to L/ZP.,"1994) pointed out that observational evidence seems to suggest that the opening angles of normal radio-pulsars (that is, the last open dipolar field line) is proportional to $1/\sqrt{P}$ ." + In the absence of a consensus on this issue. we use Ixramer's (1994) model at a frequency of 1.4 112 for the opening half-angle 6 (in degrees) of the pulsar beam: These values of 8 vield duty eveles of less than unity for periods down to about 1 ms.," In the absence of a consensus on this issue, we use Kramer's (1994) model at a frequency of 1.4 GHz for the opening half-angle $\theta$ (in degrees) of the pulsar beam: These values of $\theta$ yield duty cycles of less than unity for periods down to about 1 ms." + However. we would. Like to remark that our results are quite insensitive to slight modifications to the above @/—P? relationship.," However, we would like to remark that our results are quite insensitive to slight modifications to the above $\theta-P$ relationship." + Then. by assuming that the viewing angles of MSPs are randomly distributed. the fraction f of the sky swept by the radiation beam isgiven by (Emmering Chevalier 1989)," Then, by assuming that the viewing angles of MSPs are randomly distributed, the fraction $f$ of the sky swept by the radiation beam isgiven by (Emmering Chevalier 1989)" +sspectral window. the limb darkening cocllicicnt was adopted: from extensive. tables of vanLanime(1993) according to the estimated spectral type.,"spectral window, the limb darkening coefficient was adopted from extensive tables of \citet{hamme93} according to the estimated spectral type." + Precision of the RY measurements is defined bv random errors (inlluenced mainly by the S/N ratio of spectra. width and intensity of components in the extracted DES) and bv systematic effects. of spectrograph flexure which are rather hard to quantify.," Precision of the RV measurements is defined by random errors (influenced mainly by the S/N ratio of spectra, width and intensity of components in the extracted BFs) and by systematic effects of spectrograph flexure which are rather hard to quantify." + Our observations did not utilize a iodine cell and telluric spectral Lines were not present in our spectral window so no simple. external checks on the RY zero-point were available.," Our observations did not utilize a iodine cell and telluric spectral lines were not present in our spectral window so no simple, external checks on the RV zero-point were available." + We attempted to assess the stability of our RV. system by using multiple observations of bright standard. stars., We attempted to assess the stability of our RV system by using multiple observations of bright standard stars. + For such stars having at [east 5 spectra. the first spectrum. of a given star was used. as a template and the RWs were then determined. fitting the (obviously very narrow) Gaussian function to the extracted Bes for the remaining spectra.," For such stars having at least 5 spectra, the first spectrum of a given star was used as a template and the RVs were then determined fitting the (obviously very narrow) Gaussian function to the extracted BFs for the remaining spectra." + As expected. the scatter within such samples depends on the spectral type of the stancard ancl decreases for Iate-type standards with large numbers of strong lines in their spectra.," As expected, the scatter within such samples depends on the spectral type of the standard and decreases for late-type standards with large numbers of strong lines in their spectra." + Along the spectral sequence. we obtained: HD 907633. A2V. m—LIS kms . LID 128167. F2V.o0—0.91 kms 1 LED 102870. ER.5IV-V. 0—08i kn +. and LID 144579 CSV. a=0.59 kim ," Along the spectral sequence, we obtained: HD 97633 – A2V, $\sigma = 1.13$ km $^{-1}$, HD 128167 – F2V, $\sigma = 0.91$ km $^{-1}$ , HD 102870 – F8.5IV-V, $\sigma = 0.84$ km $^{-1}$ , and HD 144579 – G8V, $\sigma = 0.59$ km $^{-1}$." +llence. one can expect systematic deviations of individual RVs to be at the level of typically less than about 1.0. 1.2 km sLl.," Hence, one can expect systematic deviations of individual RVs to be at the level of typically less than about 1.0 – 1.2 km $^{-1}$." + This ellectively means that for measurements with formal stanclard errors given in Table 3. smaller than about 0.5 lLO0kms +. the systematic errors dominate in the error budget.," This effectively means that for measurements with formal standard errors given in Table \ref{rv.tab} smaller than about 0.5 – 1.0 km $^{-1}$, the systematic errors dominate in the error budget." + The resulting RVs for most observed systems are given in Table 3. (not given for binaries ancl multiples. with complicated blends of components)., The resulting RVs for most observed systems are given in Table \ref{rv.tab} (not given for binaries and multiples with complicated blends of components). + With many. targets observed just once. we cannot exclude a possibility that we missed several SBI svstems or SB2 systems observed. close to their spectroscopic conjunctions.," With many targets observed just once, we cannot exclude a possibility that we missed several SB1 systems or SB2 systems observed close to their spectroscopic conjunctions." + Spectroscopic observations showed that part of the targets are double or triple svstems (see Fig. 1))., Spectroscopic observations showed that part of the targets are double or triple systems (see Fig. \ref{bfplots}) ). + Is of individual components in these cases were determined. by the same oocedures as described in. Pribullaetal.(2006)., RVs of individual components in these cases were determined by the same procedures as described in \citet{ddo11}. +. In the case of SB2 svstems. double rotational or Gaussian profiles were fitted to the components. depending on the rotational xoadening of the lines: the fitted. functions are indicated in ‘Table 3.. ," In the case of SB2 systems, double rotational or Gaussian profiles were fitted to the components, depending on the rotational broadening of the lines; the fitted functions are indicated in Table \ref{rv.tab}. ." +For the triple svstem LS Cne. the third (slowly-rotating) component was first removed after a multi-component Gaussian model was fit to the observed DEs: the oliles of the binary components were then approximated » rotational profiles.," For the triple system ES Cnc, the third (slowly-rotating) component was first removed after a multi-component Gaussian model was fit to the observed BFs; the profiles of the binary components were then approximated by rotational profiles." + For the triple systems LID 61199 and HD715638. where components are always blended. no individual RVs could be determined.," For the triple systems HD 61199 and HD 75638, where components are always blended, no individual RVs could be determined." + The present survey has. lec το detection of 7 new LD 9014. (GSC 5276-0313). LID32704m (GSC PM4758-tAN. LD 46105 (GSC 0158-2674). ID 4 (GSC 0154-2360) where both visual components are SB2. GSC. 0814-0323. LD 345468. (CSC. 2141-0922: components always blended). and LID 345479 (GSC 1628-2407: a marginal detection).," The present survey has led to detection of 7 new spectroscopic binaries: HD 9014 (GSC 5276-0313), HD 32704 (GSC 4758-0066), HD 46105 (GSC 0158-2674), HD 46180 (GSC 0154-2360) where both visual components are SB2, GSC 0814-0323, HD 345468 (GSC 2141-0922; components always blended), and HD 345479 (GSC 1628-2407; a marginal detection)." + Prior to the present spectroscopic survey. MOST. photometry showed that LD 46180. and GSC 0814-0323. contain eclipsing binaries.," Prior to the present spectroscopic survey, MOST photometry showed that HD 46180, and GSC 0814-0323 contain eclipsing binaries." + All spectroscopic binaries in NGC 752 observed. within this survey were already. detected by Danieletal.(1994)., All spectroscopic binaries in NGC 752 observed within this survey were already detected by \citet{daniel94}. +. ‘This applies to GSC 2816-2068. GSC 2816-2176. GSC 2816-2274. and GSC) 2816-2276.," This applies to GSC 2816-2068, GSC 2816-2176, GSC 2816-2273, and GSC 2816-2276." + Unfortunately. the authors did not give any details regarding the orbital periods or preliminary spectroscopic orbits.," Unfortunately, the authors did not give any details regarding the orbital periods or preliminary spectroscopic orbits." + The most interesting and important is GSC 2816-2068. which was found to be an eclipsing binary with 2 = 15.52 days with eclipses MM 0.11 mag deep.," The most interesting and important is GSC 2816-2068, which was found to be an eclipsing binary with $P$ = 15.52 days with eclipses about 0.11 mag deep." + Four systems. GSC 0814-0323. LD 7370!he LID 46180. and HD. 75638 deserve special attention (see following subsections).," Four systems, GSC 0814-0323, HD 73709, HD 46180, and HD 75638 deserve special attention (see the following subsections)." + Notes n other svstenis are given below the main table (Tablecents 1, Notes for other systems are given below the main table (Table \ref{main.tab}) ). + The spectroscopic (case of GSC 814-323 and LID 73709) were determined. by the dillerential corrections The only newly discovered. SB2 (and à eclipsing binary discovered. by MOST) for which. we have enough n to obtain a preliminary spectroscopic orbit is GSC (ISn14-0323. ocated in the sky close to the open cluster M67.," The spectroscopic elements (case of GSC 814-323 and HD 73709) were determined by the differential corrections The only newly discovered SB2 (and a eclipsing binary discovered by MOST) for which we have enough data to obtain a preliminary spectroscopic orbit is GSC 0814-0323, located in the sky close to the open cluster M67." +" ratio of component Iuminosities. as estimated from the Bes when he components are split. is about Lo/L,~0.29."," The ratio of component luminosities, as estimated from the BFs when the components are split, is about $L_2/L_1 \sim 0.29$." +" With orbital period as long as 68 days. and with the obvious oesence of eclipses. the orbital-plane inclination must. be very close to 907 so Chat the projected masses of components. Ad,=1.3940.08 AL. and AM, = 0.9640.06 M. must be close o the true ones."," With orbital period as long as 68 days, and with the obvious presence of eclipses, the orbital-plane inclination must be very close to $90\degr$ so that the projected masses of components, $M_1 = 1.39 \pm 0.08$ $_\odot$ and $M_1$ = $\pm$ 0.06 $_\odot$ must be close to the true ones." + The predicted spectroscopic conjunction. Η. 2453547.35 40.86. occurs S days earlier than predicted w an eclipse observed by MOST and using the spectroscopic xriod.," The predicted spectroscopic conjunction, HJD $2\,453\,547.35\pm0.86$ , occurs 8 days earlier than predicted by an eclipse observed by MOST and using the spectroscopic period." + There is a single racial velocity measurement of GSC 0814-0323 at LLJD 3321.88 published by Mathieuetal (1986). giving RV=126405 km +.," There is a single radial velocity measurement of GSC 0814-0323 at HJD 321.88 published by \citet{math1986}, giving $RV = 12.6 \pm 0.5$ km $^{-1}$." + The nmieasurement. probably. refers to the brighter component of the visual pair ancl hence to the primary component of the eclipsing svstem., The measurement probably refers to the brighter component of the visual pair and hence to the primary component of the eclipsing system. + The light curve of GSC 0814-0323. was discussed in a paper dedicated to MOST photometry of M67 Ποια (Pribullaetal.2008)., The light curve of GSC 0814-0323 was discussed in a paper dedicated to MOST photometry of M67 field \citep{m67}. +. LID 73709. was found to be SBI by Abt&Willmarth(1999) who determined PO orbital elements: P=7.220401) dave. Vy34.6(01)(he kms| and A=31.202) uus +. based on 3t) RV. =measurements over 8 vears.," HD 73709 was found to be SB1 by \citet{abt1999} who determined the following orbital elements: $P = 7.2204(1)$ days, $V_0 = 34.6(1)$ km $^{-1}$ and $K = 31.2(2)$ km $^{-1}$, based on 30 RV measurements over 3 years." + MOST photometry showed that the star is an eclipsing binary with P=7.22 days. which is compatible with the spectroscopic determination.," MOST photometry showed that the star is an eclipsing binary with $P = 7.22$ days, which is compatible with the spectroscopic determination." + The system is a high-probability member ofhe Praesepe cluster., The system is a high-probability member ofthe Praesepe cluster. +Our new RVs were combined with hose of Abt&Willmarth(1999) to refine the orbital elements.,Our new RVs were combined with those of \citet{abt1999} to refine the orbital elements. + Since the orbital cecentricity was found. to. be insignificant. we assumed the circular orbit.," Since the orbital eccentricity was found to be insignificant, we assumed the circular orbit." + All RVs andhe combined solution are shown inFig. 2.., All RVs andthe combined solution are shown inFig. \ref{orbits}. . +inler (here are small-scale spatial variations in (he background (probably due to unresolved point sources).,infer there are small-scale spatial variations in the background (probably due to unresolved point sources). + We attempted (ο correct. [or these two effects bv. filing a second-order polynomial to the surface brightness profile of (he background., We attempted to correct for these two effects by fitting a second-order polynomial to the surface brightness profile of the background. + Quaclratics were the polynomials with acceptable fits to the background surface brightness profile (reduced o142. 1.70. 1.08. and 1.02. respectively. for 33. 33. 26. and 47 degrees of [reedon).," Quadratics were the lowest-order polynomials with acceptable fits to the background surface brightness profile (reduced $\chi^2 = 1.42$, $1.70$, $1.08$, and $1.02$, respectively, for 33, 33, 26, and 47 degrees of freedom)." + Observation 10529 has the least well-behaved background al small racii. and (his is partially responsible for the lower values at small radii for (his observation.," Observation 10529 has the least well-behaved background at small radii, and this is partially responsible for the lower values at small radii for this observation." + As noted above. our main conclusion that there is extended coronal emission around NGC! 1961 out to at least 40 kpe cloes not depend on (his smoothing techniques. ancl we can still get an acceptable fit to the data without any smoothing.," As noted above, our main conclusion – that there is extended coronal emission around NGC 1961 out to at least 40 kpc – does not depend on this smoothing techniques, and we can still get an acceptable fit to the data without any smoothing." + Smoothing (he background allows us to remove a principal source of error in our analvsis. however. vielding a wider and more reliable range of acceptable fits.," Smoothing the background allows us to remove a principal source of error in our analysis, however, yielding a wider and more reliable range of acceptable fits." + The data with smoothed background. as well as the acceptable fits. are shown in Figure 4.," The data with smoothed background, as well as the acceptable fits, are shown in Figure 4." + We take the fits to the smoothed data (unacceptable ab less than confidence) as the fiducial range for the rest of the paper., We take the fits to the smoothed data (unacceptable at less than confidence) as the fiducial range for the rest of the paper. + Note that this range encompasses (he entire range of acceptable fits to the unsmoothed cata., Note that this range encompasses the entire range of acceptable fits to the unsmoothed data. + We present the smoothed surface brightness profile in log-log space in Figure 5., We present the smoothed surface brightness profile in log-log space in Figure 5. + In this ligure. we have subtracted out the estimated contribution from X-ray binaries and [rom stars. as discussed in section 3.4.," In this figure, we have subtracted out the estimated contribution from X-ray binaries and from stars, as discussed in section 3.4." + For ease of visualization in log-log space. for this ligure we have not subtracted out the smoothed background: rather. we indicate the level of the smoothed background for comparison.," For ease of visualization in log-log space, for this figure we have not subtracted out the smoothed background; rather, we indicate the level of the smoothed background for comparison." + Again. we clearly detect emission above the background out to 40-50 kpe. in multiple quacdrants. ancl this emission is more extended than the emission from stars and X-ray binaries.," Again, we clearly detect emission above the background out to 40-50 kpc, in multiple quadrants, and this emission is more extended than the emission from stars and X-ray binaries." +" The parameters for the joint fit with the highest enclosed mass are (Sy)=3.85x10 counts tem 7 7. d=0.41. ry=1.00 kpe). and the parameters for the fit with the lowest enclosed mass are (Sy=1.38x107 count stem 7 7, d=0.54. ry=4.04 kpe)."," The parameters for the joint fit with the highest enclosed mass are $S_0 = 3.85\times10^{-8}$ count $^{-1}$ $^{-2}$ $^{-2}$, $\beta = 0.41$, $r_0 = 1.00$ kpc), and the parameters for the fit with the lowest enclosed mass are $S_0 =1.38\times10^{-8}$ count $^{-1}$ $^{-2}$ $^{-2}$, $\beta = 0.54$, $r_0 = 4.04$ kpc)." + We also examined the spectrum of the source photons. to verily that the emission is consistent with strong metal emission lines atop a thermal bremsstrahlung continuum as expected (and not. for example. unresolved point sources). aud to measure the temperature ol the hot emitting gas.," We also examined the spectrum of the source photons, to verify that the emission is consistent with strong metal emission lines atop a thermal bremsstrahlung continuum as expected (and not, for example, unresolved point sources), and to measure the temperature of the hot emitting gas." + We examined (he spectrum of observation 10531., We examined the spectrum of observation 10531. + We made a 0.5-6 keV image and removed point sources using WAVDETECT. then selected the inner 40 kpe (160 aresec) a," We made a 0.5-6 keV image and removed point sources using WAVDETECT, then selected the inner 40 kpc (160 arcsec) a" +12003).,). + The laboratory temperature required for the O» ices to fit the width of the bands of both isotopes is 30 Ik. close to the sublimatiou temperature (Fie.," The laboratory temperature required for the $_2$ --rich ices to fit the width of the bands of both isotopes is 30 K, close to the sublimation temperature (Fig." + lec f), \ref{f:labfit2}c c--f). +" At the low vapor pressures and large time scales in iuterstellar space these temperatures scale down to 18 Is (Nakagawa1950),", At the low vapor pressures and large time scales in interstellar space these temperatures scale down to $\sim$ 18 K \citep{naka80}. + While it is likely that these couditious occur somewhere in the envelope orIRS9.. one nav question how a these temperatures so close to the sublimation temperature the abundance of apolar ices can be so large.," While it is likely that these conditions occur somewhere in the envelope or, one may question how at these temperatures so close to the sublimation temperature the abundance of apolar ices can be so large." +" C&πομιιο, although pure CO ices are spectroscopically sheltly preferred. from an astroplivsical point of view both pure CO. aix No containing CO ices. and. less likely. processed Ov rich CO ices could be the constituents of apolar ices,"," Concluding, although pure CO ices are spectroscopically slightly preferred, from an astrophysical point of view both pure CO, and $_2$ containing CO ices, and, less likely, processed $_2$ –rich CO ices could be the constituents of apolar ices." + Tu this work. we found that the solid aabundance ratio is TLELS (3o) in the Ine of sight 3.2).," In this work, we found that the solid abundance ratio is $\pm$ 15 $\sigma$ ) in the line of sight 3.2)." + This value is in good aerecmment with the gas phase CO isotope ratio of 78 that is expected at the ealactocentric radi sof ((9.L kpe: Wilson&Rood 1991))., This value is in good agreement with the gas phase CO isotope ratio of 78 that is expected at the galactocentric radius of (9.4 kpc; \citealt{wils94}) ). + Furthermore. the isotope ratios for ooOas and solid CO are simnüluw to that found for solid staο PCOL/PCOs along the same line of sight (SOLIS: Boogertetal. 2000)).," Furthermore, the isotope ratios for gas and solid CO are similar to that found for solid state $_2$ $_2$ along the same line of sight $\pm$; \citealt{boog00}) )." + These values are expect to trace the ‘true? carbon isotope ratio at this ealacocentric radius (see below). which provides constraluts on noccls for the chemical evolution of the Galaxy (Tosi1982).," These values are expected to trace the `true' carbon isotope ratio at this galactocentric radius (see below), which provides constraints on models for the chemical evolution of the Galaxy \citep{tosi82}." +. Also. the isotope ratios provide au independent test Kx the chemical origi of interstellar CO».," Also, the isotope ratios provide an independent test for the chemical origin of interstellar $_2$." + Chemical fractionation. or isotope selective destruction. expressed in the isetopic excliauge reaction can greatly chanec he atomie 204212CCD/250010a satio. even deep within dense ckmuds.," Chemical fractionation, or isotope selective destruction, expressed in the isotopic exchange reaction can greatly change the atomic $^{12}{\rm C}^{(+)}/^{13}{\rm C}^{(+)}$ ratio even deep within dense clouds." + Species derived from atomic CU! will reflect the οthanced isotope ratio., Species derived from atomic $^{\rm (+)}$ will reflect the enhanced isotope ratio. + On the other hand. the isotope ratio of CO. aud its chemical daughter products. is not siguificautly affected bv these processes iu dense clouds. where CO is the main carbon reservoir.," On the other hand, the isotope ratio of CO, and its chemical daughter products, is not significantly affected by these processes in dense clouds, where CO is the main carbon reservoir." + Within this framework. the carbon isotope ratio of a variety of wolecules in dense clouds has been investigated in chemical models (Langer&Caraeccdel1989).," Within this framework, the carbon isotope ratio of a variety of molecules in dense clouds has been investigated in chemical models \citep{lang89}." +.. These models show isotope ratios of 120220 for II;CO. CS. and TICN compared to 73 for CO.," These models show isotope ratios of 120–220 for $_2$ CO, CS, and HCN compared to 73 for CO." + The wide range of values reflects the range of temperatures and deusities used iu the models., The wide range of values reflects the range of temperatures and densities used in the models. + The ratios increase with temperature aud density., The ratios increase with temperature and density. + Iu the case ofIRS9.. the large abundance of apolar CO ices indicates dust temperatures less than the sublimation temperature ( from the combined lit is 66.2+ 2.5km/s. although this determination is less secure since three of individual fits result in 5. values which," Our determination of the systemic velocity $\gamma$ from the combined fit is $66.2 \pm 2.5$ km/s, although this determination is less secure since three of individual fits result in $\gamma$ values which" +"frame comoving with the emitter, and the lapse function, A, which includes both the effects of gravitational time dilation (between the emitter’s radius r, and the pertinent radius r) and the Doppler shift associated with motion of the emitting particles at το: where B=v/c in terms of the emitting particle's velocity v, and 6, is the aforementioned angle between the local magnetic field vector and the outwardly pointing ray, since and are parallel in the assumed Keplerian geometry.","frame comoving with the emitter, and the lapse function, $\Lambda$, which includes both the effects of gravitational time dilation (between the emitter's radius $r_e$ and the pertinent radius $r$ ) and the Doppler shift associated with motion of the emitting particles at $r_e$: where $\beta=v/c$ in terms of the emitting particle's velocity $v$, and $\theta_e$ is the aforementioned angle between the local magnetic field vector and the outwardly pointing ray, since and are parallel in the assumed Keplerian geometry." +" At radius r, we have v(r)2v, and the intensity then follows from the relativistic invariant."," At radius $r$, we have $\nu(r)=\Lambda \nu$, and the intensity then follows from the relativistic invariant." +" For the image of the direct emission viewed at infinity, we simply set r—co, While for the scattered light, r becomes the radius r,. at which the scattering has occurred, and an additional “scattered” lapse function A,.=(1—R;/r;.)!? is introduced to incorporate the effects of gravitational time dilation between r,. and infinity. ("," For the image of the direct emission viewed at infinity, we simply set $r\rightarrow\infty$, while for the scattered light, $r$ becomes the radius $r_{sc}$ at which the scattering has occurred, and an additional “scattered"" lapse function $\Lambda_{sc}=(1-R_s/r_{sc})^{1/2}$ is introduced to incorporate the effects of gravitational time dilation between $r_{sc}$ and infinity. (" +Note that we are not including an additional Doppler shift factor into the expression for Λι. because the frequency shift associated with the scattering itself is already included in the evaluation of the Comptonized photon's energy.),Note that we are not including an additional Doppler shift factor into the expression for $\Lambda_{sc}$ because the frequency shift associated with the scattering itself is already included in the evaluation of the Comptonized photon's energy.) +" The position angle of polarized light may be calculated from a relativistic invariant related to the parallel transport of a polarization vector along the null rays (see, e.g., Connors Stark 1977)."," The position angle of polarized light may be calculated from a relativistic invariant related to the parallel transport of a polarization vector along the null rays (see, e.g., Connors Stark 1977)." + We perform the parallel transport operation quite directly by defining a reference vector at the detector and numerically propagating it along with the null ray itself., We perform the parallel transport operation quite directly by defining a reference vector at the detector and numerically propagating it along with the null ray itself. +" This allows us to consistently map a position angle from one frame to the next, an essential feature for calculating radiative transfer for the ordinary and extraordinary waves as they propagate around the black hole."," This allows us to consistently map a position angle from one frame to the next, an essential feature for calculating radiative transfer for the ordinary and extraordinary waves as they propagate around the black hole." +" Scattering introduces a significant complication to this process because it not only redirects the photon's trajectory, but also creates its own polarization."," Scattering introduces a significant complication to this process because it not only redirects the photon's trajectory, but also creates its own polarization." + We follow the method described in Connors et al. (, We follow the method described in Connors et al. ( +"1980), based on the use of normalized Stokes parameters where / is the intensity and Q, U are theStokes parameters determining the linear polarization.","1980), based on the use of normalized Stokes parameters where $I$ is the intensity and $Q$, $U$ are theStokes parameters determining the linear polarization." +" The Stokes parameters X; and Y; of the scattered beam can be determined from X; and Y,, once the scattered photon's new direction is known and a new set of reference axes have been defined from the wavevectors before and after scattering."," The Stokes parameters $X_s^\prime$ and $Y_s^\prime$ of the scattered beam can be determined from $X_s$ and $Y_s$, once the scattered photon's new direction is known and a new set of reference axes have been defined from the wavevectors before and after scattering." + Werefer the reader to this well-written paper for further details., Werefer the reader to this well-written paper for further details. + The observer is located at infinity with viewing angle i relative to the z-axis in the frame (see figure 1)., The observer is located at infinity with viewing angle $i$ relative to the $z$ -axis in the non-rotating frame (see figure 1). +" The deflection angle of a photon emitted by plasma in the transiently energized inner region of the disk is y, where cosy= cosicos¢, ϕ being the azimuthal angle"," The deflection angle of a photon emitted by plasma in the transiently energized inner region of the disk is $\psi$ , where $\cos\psi=\cos i\cos\phi$ , $\phi$ being the azimuthal angle" +physical model.,physical model. + This shows that considering the emissiou roni the cutive GC region (not just the Faraday rotation w the foreground) makes the region Faraday. thick., This shows that considering the emission from the entire GC region (not just the Faraday rotation by the foreground) makes the region Faraday thick. + Despite the Faraday thickness. the model shows that he RM at 6 «cn preserves the observed cast-west eradieut.," Despite the Faraday thickness, the model shows that the RM at 6 cm preserves the observed east-west gradient." + Figure 13 compares our observed RM at G «cm to the RAL derived— along many lines of sight hrough this model., Figure \ref{rmhist} compares our observed RM at 6 cm to the RM derived along many lines of sight through this model. + This is similar to the RAL derived roni the model iu Fieure 11.. which did not calculate he Faraday dispersion function. but instead assumed. Faraday rotation occurred in the foreground.," This is similar to the RM derived from the model in Figure \ref{fig:faraday-depth}, which did not calculate the Faraday dispersion function, but instead assumed Faraday rotation occurred in the foreground." + Figure 13 confirms that considering the emissivityv produces a wide range of RAL but that there is a clear east-west eradieut.," Figure \ref{rmhist} confirms that considering the emissivity produces a wide range of RM, but that there is a clear east-west gradient." + The qualitative agreenieut. between models with aud without cmissivity shows that the observed RM gradieut is caused by the oricutation of the magnetic Ποια in the GC region., The qualitative agreement between models with and without emissivity shows that the observed RM gradient is caused by the orientation of the magnetic field in the GC region. + Figure 12 also shows the polarization fraction expected when cousidering the cumissivity of the model., Figure \ref{fig:depolarization} also shows the polarization fraction expected when considering the emissivity of the model. + As we assunie an intrinsic polarization fraction of tle plot shows that nearly every line of sight will have siguificaut depoluizatiou.," As we assume an intrinsic polarization fraction of, the plot shows that nearly every line of sight will have significant depolarization." + Ou average. the predicted polarization fraction is at L8 GIIz and at Ll GIIz.," On average, the predicted polarization fraction is at 4.8 GHz and at 1.4 GHz." + Since the simulation docs uot inchide beam depolarization and assumes a perfectly organized magnetic field. the predictions should overestimate the polarization fraction.," Since the simulation does not include beam depolarization and assumes a perfectly organized magnetic field, the predictions should overestimate the polarization fraction." + We consider the predictions im agreement with the observed polarization fraction of 10 to at LAG GIIz and < at 1.1 GIIz., We consider the predictions in agreement with the observed polarization fraction of 10 to at 4.86 GHz and $<1$ at 1.4 GHz. + Iu sunuuary.1% considering the enmüssivitv of our best- model for the GC magnetized plasma shows that the observed RM structure has a complex counection to the actual physical properties.," In summary, considering the emissivity of our best-fit model for the GC magnetized plasma shows that the observed RM structure has a complex connection to the actual physical properties." + However. the RM trend with Calactic longitude is directly related to the magnetic field direction iu the GC region.," However, the RM trend with Galactic longitude is directly related to the magnetic field direction in the GC region." + More detailed physical modehue will require polariuetry with hundreds of channels between 2 and 8 GIIz. such as with the EVLA (Ulvestadetal.200G6).," More detailed physical modeling will require polarimetry with hundreds of channels between 2 and 8 GHz, such as with the EVLA \citep{u06}." +. Eight NRFs were detected in polarized cinission at 6 cn and seven of these have reliable RAL measurements (Lawetal.2008a)}., Eight NRFs were detected in polarized emission at 6 cm and seven of these have reliable RM measurements \citep{gcl_vla}. +. Interestingly. all but one of these have RAL consistent with their surrouncing diffuse emission.," Interestingly, all but one of these have RM consistent with their surrounding diffuse emission." + Iu other words. the RAIs toward the NRFs largely follow the longitude dependence found toward the diffuse emission.," In other words, the RMs toward the NRFs largely follow the longitude dependence found toward the diffuse emission." + It the RMs toward the filaments was unrelated to that of the diffuse ciunission. a binonual probability distribution," If the RMs toward the filaments was unrelated to that of the diffuse emission, a binomial probability distribution" +55 OTIG+TI4 is identified as à prototvpe of LBLs since its svnchrotron emission peaks in (he optical band (e.g.. Nieppola et al.,"S5 0716+714 is identified as a prototype of LBLs since its synchrotron emission peaks in the optical band (e.g., Nieppola et al." + 2006)., 2006). + The photometric detection of its host galaxy suggested. a recshilt of 0.31+0.08 (Nilsson οἱ al., The photometric detection of its host galaxy suggested a redshift of $0.31\pm0.08$ (Nilsson et al. + 2003)., 2008). + It has been intensively observed and studied in many wavelengths. especially in the optical band (e.g.. Wu et al.," It has been intensively observed and studied in many wavelengths, especially in the optical band (e.g., Wu et al." + 2007 and reference therein)., 2007 and reference therein). + It is strongly variable [rom radio to X-ray bands on different. timescales (e.g.. Wagner et al.," It is strongly variable from radio to X-ray bands on different timescales (e.g., Wagner et al." + 1996)., 1996). + The EGRET onboard the Compton Gamma-ray Observatory detected its high energy gamma-ray (27LOO MeV) emission several times [rom 1991 to 1996 (Hartman et al., The EGRET onboard the Compton Gamma-ray Observatory detected its high energy gamma-ray $>100$ MeV) emission several times from 1991 to 1996 (Hartman et al. + 1999)., 1999). + The gamma-ray fluxes varied bv à [actor of (wo on timescale of vears. but the spectral indexflux correlation was not found. (Nandikotkur et al.," The gamma-ray fluxes varied by a factor of two on timescale of years, but the spectral index–flux correlation was not found (Nandikotkur et al." + 2007)., 2007). + In. 2008. AGILE detected a variable gamma-ray flux. with a peak flux above the maximum obtained by EGRET (Chen et al.," In 2008, AGILE detected a variable gamma-ray flux, with a peak flux above the maximum obtained by EGRET (Chen et al." + 2003)., 2008). + Observations by WEGRA resulted in an upper limit of Πας αἱ very high enerey (VILE) gamma-ray energies (>1.6 TeV) (Aharonian et al., Observations by HEGRA resulted in an upper limit of flux at very high energy (VHE) gamma-ray energies $>1.6$ TeV) (Aharonian et al. + 2004)., 2004). + [1 is also in the first. Fermi-LAT bright source list (Abdo et al., It is also in the first Fermi-LAT bright source list (Abdo et al. + 2009)., 2009). + Recenth. the MAGIC collaboration reported the first detection of VUE eamima-ravs Irom the source al 5.80 level (Anderhub et al.," Recently, the MAGIC collaboration reported the first detection of VHE gamma-rays from the source at $5.8\sigma$ level (Anderhub et al." + 2009)., 2009). + The discoverv of S5 07164714 as a VILE gamma-ray LBL was triggered by ils very high optical state. suggesting a possible correlation between the VIE eanmmnma-rayv and (he optical emissions.," The discovery of S5 0716+714 as a VHE gamma-ray LBL was triggered by its very high optical state, suggesting a possible correlation between the VHE gamma-ray and the optical emissions." + 55 O716+714 is also a preferred. target (to perform simultaneous multi-wavelength observations (e.g.. Villala et al.," S5 0716+714 is also a preferred target to perform simultaneous multi-wavelength observations (e.g., Villata et al." + 2008: Giommi et al., 2008; Giommi et al. + 2003)., 2008). + Wu et al. (, Wu et al. ( +2009) reported the first detection of time lags between the variations in different optical wavelengths.,2009) reported the first detection of time lags between the variations in different optical wavelengths. + 55 0716-71 has been observed by various N-raw telescopes., S5 0716+71 has been observed by various X-ray telescopes. + The observations in 1991 Mareh with the PSPC onboard ROSAT revealed a behavior of flux-related spectral variations in (he 0.12.4 keV band., The observations in 1991 March with the PSPC onboard ROSAT revealed a behavior of flux-related spectral variations in the 0.1–2.4 keV band. + Two distinct spectral components are needed to describe the concave X-ray spectra (Cappi et al., Two distinct spectral components are needed to describe the concave X-ray spectra (Cappi et al. + 1994)., 1994). + ASCA observed the source in 1994 March and confirmed the spectral shape found by ROSAT in higher energies: the spectra flatten with increasing energies (IXubo et al., ASCA observed the source in 1994 March and confirmed the spectral shape found by ROSAT in higher energies: the spectra flatten with increasing energies (Kubo et al. + 1993)., 1998). + The three oobservations in 1996. 1998 and 2000 revealed the spectral and temporal variability of the two spectral components.," The three observations in 1996, 1998 and 2000 revealed the spectral and temporal variability of the two spectral components." + It was in faint states in the 1996 and 1993 observation (Giomumni et al., It was in faint states in the 1996 and 1998 observation (Giommi et al. + 1999)., 1999). + The spectral fits with a broken power law model resulted in concave spectra in the 0.110 keV band. breaking al ~2—3 keV. The 2000 observation caught (he source in its high state (Taglialerri et al.," The spectral fits with a broken power law model resulted in concave spectra in the 0.1–10 keV band, breaking at $\sim 2-3$ keV. The 2000 observation caught the source in its high state (Tagliaferri et al." + 2003)., 2003). + The concave spectra can be disentangled into two power law components. crossing al ~1.5 keV. The sleeper power law component dominates the soft X-ray enission. whereas the flatter one contributes more to the hard. X-ravs.," The concave spectra can be disentangled into two power law components, crossing at $\sim1.5$ keV. The steeper power law component dominates the soft X-ray emission, whereas the flatter one contributes more to the hard X-rays." + The soft X-ray spectral index is (he largest out of the three oobservations. indicating a softer-when-brighter behaviour for the soft X-ray variabilitv.," The soft X-ray spectral index is the largest out of the three observations, indicating a softer-when-brighter behaviour for the soft X-ray variability." + The oobservations also revealed large ancl rapid variations in the soft X-ray banc and the lack of, The observations also revealed large and rapid variations in the soft X-ray band and the lack of +flux between 1994 and 2000. however oobservations [rom 1996 and 1997 as well as the present data show a sharp transition between hieh and low flux over a period of 4 montlis (see Table. 1)).,"flux between 1994 and 2000, however observations from 1996 and 1997 as well as the present data show a sharp transition between high and low flux over a period of 4 months (see Table. \ref{cont}) )." + Turneretal.(2005.2008). used a varving covering factor.," \citet[]{turner05,turner08} used a varying covering factor." + However. Mehldipouretal.(2010). found that a varying covering factor did not fit the data. while. variable source continuum could.," However, \citet{mehdipour10} found that a varying covering factor did not fit the data, while, variable source continuum could." + In order to compare the absorption in 2001 and in 2006 we scaled up the 2001 spectrum to the [lux level of 2006 near specific lines., In order to compare the absorption in 2001 and in 2006 we scaled up the 2001 spectrum to the flux level of 2006 near specific lines. + Since absorption depends exponentially on optical depth. this comparison directly shows changes in optical depth. independent of continuum flax.," Since absorption depends exponentially on optical depth, this comparison directly shows changes in optical depth, independent of continuum flux." + If the absorber did not change. (he scaled-up trough should match that of the ," If the absorber did not change, the scaled-up trough should match that of the high-state." +Because (he continuum shape during (the (wo states is dillerent. this comparison is meaningful only locally.," Because the continuum shape during the two states is different, this comparison is meaningful only locally." + Indeed. we show this comparison around (he most prominent lines.," Indeed, we show this comparison around the most prominent lines." + Results for Si and Mg K à lines. and for 237! and 7! are shown in Fig. 7..," Results for Si and Mg K $\alpha$ lines, and for $^{+23}$ and $^{+21}$ are shown in Fig. \ref{ratio1}," + where the low stat spectrum is nultiplied by 4 in the upper left panel. by 4.5 in the upper right panel. by 4.3 in the lower left panel. ancl by 5.2 in the lower right panel.," where the low stat spectrum is multiplied by 4 in the upper left panel, by 4.5 in the upper right panel, by 4.3 in the lower left panel, and by 5.2 in the lower right panel." + The S/N in the low-state is worse. but it appears that component 1 (the slowest component) did not change much between the hieh ancl low states.," The S/N in the low-state is worse, but it appears that component 1 (the slowest component) did not change much between the high and low states." + On the other hand. some of component 2 and most of components 3 and 4 are absent in the 2001 low state.," On the other hand, some of component 2 and most of components 3 and 4 are absent in the 2001 low state." + In (hie next section. we discuss a possible geometrical explanation for (is result.," In the next section, we discuss a possible geometrical explanation for this result." + We [ind that apart [rom a lower continuum level. the 2001 spectrum of aalso lacks the faster absorption components.," We find that apart from a lower continuum level, the 2001 spectrum of also lacks the faster absorption components." + The appearance of high-ionization (logh£~3.5 em))xx components with. columns ofB NyEe107?>ni 7 are reminiscentn ofB the variable. covering invoked by Turneretal.(2005.2008) (o explain (he varving continuum shape.," The appearance of high-ionization $\log \xi \sim 3.5$ ) components with columns of $N_H \sim 10^{23}$ $^{-2}$ are reminiscent of the variable covering invoked by \citet[]{turner05,turner08} to explain the varying continuum shape." + We allude to three other possible explanations: - The faster components of the outflow are also more ionized., We allude to three other possible explanations: - The faster components of the outflow are also more ionized. + One possibility could be that the [ast components recombined due to the reduced Ες. and are (hus not seen in 2001.," One possibility could be that the fast components recombined due to the reduced flux, and are thus not seen in 2001." + However. one would still expect to observe the [fast components in lower charge states.," However, one would still expect to observe the fast components in lower charge states." + We could not detect the [ast components in the 2001 spectrum in any ion., We could not detect the fast components in the 2001 spectrum in any ion. + Since (he 2001 spectrum has a much lower signal to noise ralio. we can nol unambienously rule oul this possibility. -," Since the 2001 spectrum has a much lower signal to noise ratio, we can not unambiguously rule out this possibility. -" + Another possibility could be that the [ast components. while not in the line of sight in 2001. passed through our line of sight in 2006. 5 vears are plenty of time compared to the variability time scale of mouths that perhaps," Another possibility could be that the fast components, while not in the line of sight in 2001, passed through our line of sight in 2006, 5 years are plenty of time compared to the variability time scale of months that perhaps" + (<1 (Dressler& (Blakeetal.2004: al.2009)..," $< 1$ \citep{dressler83,couch87}. \citep{yang04,yang08}, \citealt{panuzzo07}) \citep{zabludoff96,poggianti99}." + (Poggianti&Wu2000)..," \citep{blake04,goto07,vergani10} \citep{duc02,saintonge08,dressler09,haines09}. \citep{poggianti00}." + 24j/m in Abell 851 imply that star formation has largely ceased in these objects., $\mu$ in Abell 851 imply that star formation has largely ceased in these objects. + Obscured star formation may also be detected via radio emission at 20 em (1.4 GHz). which is produced by synchrotron radiation from high energy cosmic rays originating m supernova shells and yields a measure of the massive star formation rate (Condon1992:Kennicutt1998).," Obscured star formation may also be detected via radio emission at 20 cm (1.4 GHz), which is produced by synchrotron radiation from high energy cosmic rays originating in supernova shells and yields a measure of the massive star formation rate \citep{condon92, +kennicutt98}." +. Although Smailetal.(1999) found evidence of recent star formation in 5 K+A galaxies. other studies find little evidence of ongoing star formation within small samples (Miller&Owen2001:Goto 2004).," Although \cite{smail99} found evidence of recent star formation in 5 K+A galaxies, other studies find little evidence of ongoing star formation within small samples \citep{miller01,goto04}." +. However. Buyleetal.(2006) found that most K+A have substantial gas reservoirs. similar to those of spirals of the same luminosity. and suggest that K+A galaxies may be observed during a hiatus in an episodic star formation history or that current star formation may be obscured.," However, \cite{buyle06} + found that most K+A have substantial gas reservoirs, similar to those of spirals of the same luminosity, and suggest that K+A galaxies may be observed during a hiatus in an episodic star formation history or that current star formation may be obscured." + In this we use a stack of radio images to further test the current star formation rate and/or AGN activity in spectroscopically selected KA galaxies., In this we use a stack of radio images to further test the current star formation rate and/or AGN activity in spectroscopically selected K+A galaxies. + A description of the data and the analysis is provided in the next section. whilewe interpret and discuss our results in section 3.," A description of the data and the analysis is provided in the next section, whilewe interpret and discuss our results in section 3." +" We adopt the latest WMAP cosmological parameters with O4,=0.27. Q4=0.73 and Hy271 kms ! !."," We adopt the latest WMAP cosmological parameters with $\Omega_{M}=0.27$, $\Omega_{\Lambda}=0.73$ and $_0=71$ km $^{-1}$ $^{-1}$." + We select a sample of 811. K+A galaxies from the Data Release 7 of the SDSS (Yorketal.2000:Abazajian2009) using an updated catalog of Goto(2007).," We select a sample of 811 K+A galaxies from the Data Release 7 of the SDSS \citep{york00,abazajian09} using an updated catalog of \cite{goto07}." +. Only objects classified as galaxies with a spectroscopic signal-to-noise »1U per pixel are considered., Only objects classified as galaxies with a spectroscopic signal-to-noise $> 10$ per pixel are considered. + The selection criteria of ΚΑ galaxies are equivalent widths of Ha>—3.0À.. Hó>5.0 and [OI] >—2.5A.. where emission lines are negative.," The selection criteria of K+A galaxies are equivalent widths of $\alpha > -3.0$, $\delta > 5.0$ and [OII] $> -2.5$, where emission lines are negative." + Galaxies of redshift 0.35<2<0.37 are excluded from the sample due to the 5577A ssky feature., Galaxies of redshift $0.35 < z < 0.37$ are excluded from the sample due to the $5577$ sky feature. + The selected sample of ΚΑ galaxies haveredshifts ranging 0.02στ« (LL , The selected sample of K+A galaxies haveredshifts ranging $0.02 < z < 0.4$ . +We then use data from the FIRST survey (Beckeretal. to derive a mean radio image of K+A galaxies., We then use data from the FIRST survey \citep{becker95} to derive a mean radio image of K+A galaxies. + Typical detection limits for a single FIRST image are ~1 mJy. which.," Typical detection limits for a single FIRST image are $\sim$ 1 mJy, which," +It is well known that classical Newtonian dynamics fails on galactic scales.,It is well known that classical Newtonian dynamics fails on galactic scales. + There is astronomical ancl Cosmological evidence for a discrepancy. between the dynamically measured mass-to-light ratio of anv svstem and (he minimum mass-to-light ratios that are compatible with our understanding of stars. of galaxies. of groups and clusters of galaxies. and of superclusters.," There is astronomical and cosmological evidence for a discrepancy between the dynamically measured mass-to-light ratio of any system and the minimum mass-to-light ratios that are compatible with our understanding of stars, of galaxies, of groups and clusters of galaxies, and of superclusters." + It turns out that on large scales most astronomical svstems have much larger mass-to-light ratios than (hie central parts., It turns out that on large scales most astronomical systems have much larger mass-to-light ratios than the central parts. + Observations on (he rotation curves have turn out that galaxies are not rotating in the same manner as the Solar Svstem., Observations on the rotation curves have turn out that galaxies are not rotating in the same manner as the Solar System. + If the orbits of the stars are governed solely by gravitational force. it was expected that stus at the outer edge of the dise would have à much lower orbital velocity than those near the middle.," If the orbits of the stars are governed solely by gravitational force, it was expected that stars at the outer edge of the disc would have a much lower orbital velocity than those near the middle." + In fact. bv the Virial theorem the total kinetic energy should be half the total gravitational binding energv of (he galaxies.," In fact, by the Virial theorem the total kinetic energy should be half the total gravitational binding energy of the galaxies." + Experimentally. however. (he total kinetic energy is found to be much greater (han predicted by the Virial theorem.," Experimentally, however, the total kinetic energy is found to be much greater than predicted by the Virial theorem." + Galactic rotation curves. which illustrate the velocity of rotation versus the distance from the galactic center. cannot be explained by only (he visible matter.," Galactic rotation curves, which illustrate the velocity of rotation versus the distance from the galactic center, cannot be explained by only the visible matter." + This suggests that either a large portion of the mass ol galaxies was contained in the relatively dark galactic halo or Newtonian dvnaimics does not apply universally., This suggests that either a large portion of the mass of galaxies was contained in the relatively dark galactic halo or Newtonian dynamics does not apply universally. + The dark matter proposal is mostly referred (ο Zwicky (1957) who gave the first empirical evidence for the existence of the unknown (tvpe of matter that takes part in the galactic scale only by. its gravitational action., The dark matter proposal is mostly referred to Zwicky (1957) who gave the first empirical evidence for the existence of the unknown type of matter that takes part in the galactic scale only by its gravitational action. + He found that the motion of the galaxies of the clusters induced by (the gravitational field of the cluster can only be explained by the assumption of dark matter in addition to the matter of the sum of the observed galaxies., He found that the motion of the galaxies of the clusters induced by the gravitational field of the cluster can only be explained by the assumption of dark matter in addition to the matter of the sum of the observed galaxies. + Later. It was demonstrated (hat dark matter is not only an exotic property of clusters but," Later, It was demonstrated that dark matter is not only an exotic property of clusters but" +The Large Magellanic Cloud (LMC). with its low foreground absorption and relative proximity of ~50 kpe (2)... offers the ideal laboratory for the detailed study of a complete sample of objects such as supernova remnants (SNRs).,"The Large Magellanic Cloud (LMC), with its low foreground absorption and relative proximity of $\sim$ 50 kpc \citep{2008MNRAS.390.1762D}, offers the ideal laboratory for the detailed study of a complete sample of objects such as supernova remnants (SNRs)." + The proximity enables detailed spatial studies of the remnants. and the accurately known distance allows for analysis of the energetics of each remnant.," The proximity enables detailed spatial studies of the remnants, and the accurately known distance allows for analysis of the energetics of each remnant." + In addition. the wealth of wide-field multiwavelength data available. from radio maps to optical emission-line images and broad-band photometry to global X-ray mosaics. provides information about the contexts and environments in which these remnants are born and evolve.," In addition, the wealth of wide-field multiwavelength data available, from radio maps to optical emission-line images and broad-band photometry to global X-ray mosaics, provides information about the contexts and environments in which these remnants are born and evolve." + It is possible to obtain a relatively complete sample of SNRs in the LMC and not only study the global properties of the sample but also study the subclasses in detail (e.g.. sorted by and radio morphology. diameter or by type of the supernova progenitor).," It is possible to obtain a relatively complete sample of SNRs in the LMC and not only study the global properties of the sample but also study the subclasses in detail (e.g., sorted by and radio morphology, diameter or by type of the supernova progenitor)." + Toward this goal. we have been studying SNRs in the Magellanic Clouds (MCs) in. greater detail using combined optical. radio. and X-ray observations.," Toward this goal, we have been studying SNRs in the Magellanic Clouds (MCs) in greater detail using combined optical, radio, and X-ray observations." + Today we know over 40 confirmed SNRs in the LMC and another 35-40 candidates (?).., Today we know over 40 confirmed SNRs in the LMC and another 35-40 candidates \citep{2008MNRAS.383.1175P}. + Here. we report on multi-frequency observations of a previously known and intriguing LMC supernova remnant.," Here, we report on multi-frequency observations of a previously known and intriguing LMC supernova remnant." + wwas initially suggested as a candidate by ?.., was initially suggested as a candidate by \citet{1984PASAu...5..537T}. + ? classified it as an SNR based on observations made with the Molonglo Radio Observatory. at 36cem (v2843 MHz). and they noted no optical counterpart.," \citet{1985ApJS...58..197M} classified it as an SNR based on observations made with the Molonglo Radio Observatory, at cm $\nu$ =843 MHz), and they noted no optical counterpart." + ? added further confirmation. with a set of radio-continuum observations. (with. the Parkes telescope) over a wide frequency range and estimated a steep spectrum with powerlaw index ? observed bbut reported no detection at. far-ultraviolet (FUV) wavelengths.," \citet{1998A&AS..130..421F} added further confirmation, with a set of radio-continuum observations (with the Parkes telescope) over a wide frequency range and estimated a steep spectrum with powerlaw index \citet{2006ApJS..165..480B} observed but reported no detection at far-ultraviolet (FUV) wavelengths." + ?— associated an X-ray counterpart to. this radio SNR fromROSAT PSPC observations., \citet{1999A&AS..139..277H} associated an X-ray counterpart to this radio SNR from PSPC observations. + According to the entry number in their catalogue. the ROSAT source Is named498.," According to the entry number in their catalogue, the ROSAT source is named." +". We observed wwith the Australia Telescope Compact Array (ATCA) on 6"" April 1997. with an array configuration EW375. at wavelengths of 6 and 3 em (v24790 and 8640 MHz)."," We observed with the Australia Telescope Compact Array (ATCA) on $^\mathrm{th}$ April 1997, with an array configuration EW375, at wavelengths of 6 and 3 cm $\nu$ =4790 and 8640 MHz)." +" The observations were done in so called ""snap-shot mode. totaling ~1 hour of integration over a 12 hour period."," The observations were done in so called “snap-shot” mode, totaling $\sim$ 1 hour of integration over a 12 hour period." + Source 1934-638 was used for primary calibration ard source 0530-727 was used for secondary calibration., Source 1934-638 was used for primary calibration and source 0530-727 was used for secondary calibration. + The (2) and (2). software packages were used for data reduction and analysis., The \citep{2006Miriad} and \citep{2006Karma} software packages were used for data reduction and analysis. + More information about the observiig procedure and other sources observed during this session can be found in ?..?? and ?..," More information about the observing procedure and other sources observed during this session can be found in \citet{2007MNRAS.378.1237B}, \citet{2008SerAJ.177...61C,2008SerAJ.176...59C} and \citet{2009SerAJ.179...55C}." +" Baselines formed with the 6"" ATCA antenna were excluded. as the other five antennas were arranged in a compact configuration."," Baselines formed with the $6^\mathrm{th}$ ATCA antenna were excluded, as the other five antennas were arranged in a compact configuration." + The cem image (Fig. 1)), The cm image (Fig. \ref{fig-6cm}) ) +" has a resolution of x3]"" aat position angle aand the r.m.s noise is estimated to be 0.4 mJy/beam.", has a resolution of $\times$ at position angle and the r.m.s noise is estimated to be 0.4 mJy/beam. + Due to the signal to noise restrictions and the size of the remnant. no reliable image could be prepared at cem.," Due to the signal to noise restrictions and the size of the remnant, no reliable image could be prepared at cm." + We also used all available radio-continuum images of the LMC., We also used all available radio-continuum images of the LMC. + These are composed of observations. at. several radio. frequencies having moderate resolution at. 36cem (v=843MHz.MOST:?) and 20cem ?)..," These are composed of observations at several radio frequencies having moderate resolution at cm \citep[$\nu$=843~MHz, MOST;][]{1991IAUS..148..114T} and cm \citep[$\nu$=1400~MHz, ATCA;][]{ 2007MNRAS.382..543H}." +" sserendipitously observed oon 28"" January 2007. for a total of about 20 ks (observation ID 0402000601) at an off-axis angle of ~6’.."," serendipitously observed on $^\mathrm{th}$ January 2007, for a total of about 20 ks (observation ID 0402000601) at an off-axis angle of $\sim$." + The observation was performed with the EPIC instruments (PNandtwoMOScameras.|2?) in imaging read out mode.," The observation was performed with the EPIC instruments \citep[PN and two MOS cameras, ][]{2001A&A...365L..18S,2001A&A...365L..27T} in imaging read out mode." + Thin optical blocking filters were used to optimise observations of the target. the supersoft X-ray source candidate JJ0529.4—6713 (?) which is associated with the planetary nebula LLO9.," Thin optical blocking filters were used to optimise observations of the target, the supersoft X-ray source candidate $-$ 6713 \citep{2008A&A...482..237K} which is associated with the planetary nebula L69." +characterized also by the patterns seen in the solar system (Lodders 2003) and. in interstellar clouds. exhibiting 'cold cloud! depletions (e.g... Savage Sembach 1996: Welty et al.,"characterized also by the patterns seen in the solar system (Lodders 2003) and in interstellar clouds exhibiting `cold cloud' depletions (e.g., Savage Sembach 1996; Welty et al." + 1999b: see Table53)., 1999b; see Table\ref{tab:depl}) ). + The first six lines ofTable τ list the predicted ratios for several representative combinations of depletion and temperature., The first six lines ofTable \ref{tab:ratios} list the predicted ratios for several representative combinations of depletion and temperature. + For Mg. Cr. and Fe for which the first ions should be dominant — the predicted ratios are given by where Ax and ὃς are the solar abundance and depletion of clement X. respectively.," For Mg, Cr, and Fe – for which the first ions should be dominant – the predicted ratios are given by where $_{\rm X}$ and $\delta_{\rm X}$ are the solar abundance and depletion of element X, respectively." + Phe calculation for caleium is slightly more complicated. as must also be considered.," The calculation for calcium is slightly more complicated, as must also be considered." + The adopted. photoionization rates (Ex) are taken in most cases from Péqquignot Aldrovandi (1986). assuming the WI radiation field. (de Boer et al.," The adopted photoionization rates $\Gamma_{\rm X}$ ) are taken in most cases from Péqquignot Aldrovandi (1986), assuming the WJ1 radiation field (de Boer et al." + 1973): the collisional ionization rates (ex) are taken from 8Iiull Van Steenberg (1982)., 1973); the collisional ionization rates $_{\rm X}$ ) are taken from Shull Van Steenberg (1982). + The total (radiative plus dielectronic) recombination rate coellicients (ax) are caleulated rom the parameters given by Aldrovandi Péqquignot (1973. 1974). Shull Van Steenberg (1982). and/or Péqquignot Aldrovandi (1986).," The total (radiative plus dielectronic) recombination rate coefficients $\alpha_{\rm X}$ ) are calculated from the parameters given by Aldrovandi Péqquignot (1973, 1974), Shull Van Steenberg (1982), and/or Péqquignot Aldrovandi (1986)." + The lower set of curves for shows the ratios predicted using the photoionization and (total) recombination rates computed by Nahar. Bautista. Pradhan (1997).," The lower set of curves for shows the ratios predicted using the photoionization and (total) recombination rates computed by Nahar, Bautista, Pradhan (1997)." +" ForCri. Do; 8o 1s twas estimated by Mever Roth (1990). and acy has been set t0 6 = 0L em?s. + (for T = 100 Is). similar to the values determined for radiative recombination to a number of other trace neutral species (Péqquignot Aldroyandi 1986): the temperature dependence of acy is assumed to be the same as for ax, (ie. with no significant contribution [rom cdielectronic recombination for 1 « 12000 lx: see comments below. however)."," For, $\Gamma_{\rm Cr}$ = 8 $\times$ $^{-10}$ $^{-1}$ was estimated by Meyer Roth (1990), and $\alpha_{\rm Cr}$ has been set to 6 $\times$ $^{-12}$ $^{3}$ $^{-1}$ (for $T$ = 100 K), similar to the values determined for radiative recombination to a number of other trace neutral species (Péqquignot Aldrovandi 1986); the temperature dependence of $\alpha_{\rm Cr}$ is assumed to be the same as for $\alpha_{\rm Na}$ (i.e., with no significant contribution from dielectronic recombination for $T$ $<$ 12000 K; see comments below, however)." + I£ the recombination is dominated instead by charge exchange with large molecules or small grains (Lep» οἱ al., If the recombination is dominated instead by charge exchange with large molecules or small grains (Lepp et al. + LOSS: Weingartner Draine 2001: Liszt 2003: Welty et al., 1988; Weingartner Draine 2001; Liszt 2003; Welty et al. + 2003). and if the resulting neutrals clo not stick to the grains (sticking parameter s = 0). then the preclictec ratios change by at most 0.1 dex.," 2003), and if the resulting neutrals do not stick to the grains (sticking parameter $s$ = 0), then the predicted ratios change by at most 0.1 dex." + The predicted raios forMei.Car. and shown in Fig.," The predicted ratios for, and shown in Fig." + 4 exhibit some common trends., \ref{fig:pred} exhibit some common trends. + At Compcratures below about 3000. Ix. the ratios rellect. primarily photoionization and radiative recombination — and are not very sensitive to the overall strength. of the radiation field. the electron density n. or the temperature.," At temperatures below about 3000 K, the ratios reflect primarily photoionization and radiative recombination – and are not very sensitive to the overall strength of the radiation field, the electron density $n_e$, or the temperature." + Because is often a trace species. however. the ratio does depend on n.," Because is often a trace species, however, the ratio does depend on $n_e$." + M somewhat higher temperatures. all the ratios increase due to dielectronic recombination (which does not significantly alect until much higher temperatures) — starting at about 4000 Ix. 3000 Ix. ancl 5000 Ix forAled.Cad. and Fer. respectively (Aldrovandi Péqquignot 1973. 1974: Shull Van Steenberg 1982).," At somewhat higher temperatures, all the ratios increase due to dielectronic recombination (which does not significantly affect until much higher temperatures) – starting at about 4000 K, 3000 K, and 5000 K for, and , respectively (Aldrovandi Péqquignot 1973, 1974; Shull Van Steenberg 1982)." + For the main clouc(s) toward ὁ Oph. the observed ratios forMeL.Car. and are in good. agreement with the predicted cold. eloud. values (consistent with the depletions derived. from the corresponding dominant. species and. the temperature inferred. from. HI». rotational excitation)," For the main cloud(s) toward $\zeta$ Oph, the observed ratios for, and are in good agreement with the predicted cold cloud values (consistent with the depletions derived from the corresponding dominant species and the temperature inferred from $_2$ rotational excitation)." + The ratio for is lower than the predicted. cold. cloud. value by more than a factor of 10. however but is not as deficient relative to the value predicted using the Nahar et al. (," The ratio for is lower than the predicted cold cloud value by more than a factor of 10, however [but is not as deficient relative to the value predicted using the Nahar et al. (" +1997) rates].,1997) rates]. + Mever Roth (1990) remarked that. the electron density estimated toward ¢ Oph from the ratio was similar to the values obtained from other neutral/first ion ratios: Welty et al. (, Meyer Roth (1990) remarked that the electron density estimated toward $\zeta$ Oph from the ratio was similar to the values obtained from other neutral/first ion ratios; Welty et al. ( +2003) noted that it is not uncommon for to be somewhat weaker than expected. relative to other trace neutral species.,"2003) noted that it is not uncommon for to be somewhat weaker than expected, relative to other trace neutral species." + For the ‘strong low-velocity’ clouds toward. 28 Ori. (where some trace neutral species are relatively strong ancl the depletions are intermediate between the representative warm and cold. cloucl values: Welty ο al., For the `strong low-velocity' clouds toward 23 Ori (where some trace neutral species are relatively strong and the depletions are intermediate between the representative warm and cold cloud values; Welty et al. + 1999b) and for the main cloud(s) toward LD 72127A (with warm cloud. depletions) the observed ratios lor and are closer to the predicted: warm ‘loucl values for 7 ~ 3000 Ix (although the gas is likely much cooler than that in both cases). but the ratios for again are low by factors of 1025.," 1999b) and for the main cloud(s) toward HD 72127A (with warm cloud depletions), the observed ratios for and are closer to the predicted warm cloud values for $T$ $\sim$ 3000 K (although the gas is likely much cooler than that in both cases), but the ratios for again are low by factors of 10–25." + For the main cloud(s) toward LID 72127D. the observed ratios for both ancl are about a factor of 10 higher than those toward LID 72127. Eehe ratio for thus is closer to the value predicted. for solar relative abundances than to that. predicted. for. warm cloud abundances (for 2 ~ 3000 I). while the ratio for is consistent with the predicted warm cloud. value at that T (io. low compared to Ca)): the observed ratio forlL. however. isvale.," For the main cloud(s) toward HD 72127B, the observed ratios for both and are about a factor of 10 higher than those toward HD 72127A. The ratio for thus is closer to the value predicted for solar relative abundances than to that predicted for warm cloud abundances (for $T$ $\sim$ 3000 K), while the ratio for is consistent with the predicted warm cloud value at that $T$ (i.e., low compared to ); the observed ratio for, however, is." + As calcium. chromium. and iron usually are much more severely. depleted into dust than is sodium. an enhancement of the neutral speciesCa.Cri. and Fer. relative toNat. could be due to much less severe depletions.," As calcium, chromium, and iron usually are much more severely depleted into dust than is sodium, an enhancement of the neutral species, and , relative to, could be due to much less severe depletions." + As noted above. dielectronic recombination can increase the abuncances ofAlger.Car. and when the temperature exceeds about 4000 Ix. 3000 Ix. and 5000 Ix. respectively.," As noted above, dielectronic recombination can increase the abundances of, and when the temperature exceeds about 4000 K, 3000 K, and 5000 K, respectively." + The cloud at 165 km s toward SNIOSTA is relatively cold. as the D lines at that velocity. exhibit resolved. hyperfine structure. with b ~ 0.3 km (Potting Cuillineham Loss: Welty Crowther. in preparation)). but the ratios of various dominant species suggest that there is essentially no depletion there (Welty et al.," The cloud at $+$ 65 km $^{-1}$ toward SN1987A is relatively cold [as the D lines at that velocity exhibit resolved hyperfine structure, with $b$ $\sim$ 0.3 km $^{-1}$ (Pettini Gillingham 1988; Welty Crowther, in preparation)], but the ratios of various dominant species suggest that there is essentially no depletion there (Welty et al." + 19992)., 1999a). + Phe observed ratio is within a factor of 2 of the predicted value for solar relative abundances at 100 Ix. (ie. a cold. cust-free cloud). though it is also consistent with the values. predicted. for somewhat warmer. eas.," The observed ratio is within a factor of 2 of the predicted value for solar relative abundances at 100 K (i.e., a cold, dust-free cloud), though it is also consistent with the values predicted for somewhat warmer gas." +" For""up the component at {932 km s1 toward ο Ori. the b-values forNar. and all 0.36-0.38 km indicate that that cloud. also is fairl cold (Welty et al."," For the component at $+$ 3 km $^{-1}$ toward $\epsilon$ Ori, the $b$ -values for, and – all 0.36-0.38 km $^{-1}$ – indicate that that cloud also is fairly cold (Welty et al." + 1994. L996. 2003).," 1994, 1996, 2003)." + The slightly elevated ratio thus may reflect. less severe depletion. of magnesium there (and not dielectronic recombination)., The slightly elevated ratio thus may reflect less severe depletion of magnesium there (and not dielectronic recombination). + The still higher. values of and/or seen in several other cases. however. would seem to imply some combination of mild (or negligible) clepletions aud clicleetronie recombination in warmer gas ο... Ginacisski Ixrogulec though the ratios generally are not unusually high.," The still higher values of and/or seen in several other cases, however, would seem to imply some combination of mild (or negligible) depletions and dielectronic recombination in warmer gas (e.g., Gnacińsski Krogulec – though the ratios generally are not unusually high." + The strong observed absorption from Car. Cri. and," The strong observed absorption from , , and" +likely due to turbulence rather than differential rotation of the galactic plane.,likely due to turbulence rather than differential rotation of the galactic plane. + In the following. we compare the chemical and kinematic properties of these two ensembles.," In the following, we compare the chemical and kinematic properties of these two ensembles." + While the thick lines in Figs., While the thick lines in Figs. + 4 and 5 result from a linear regression unweighted by the fractional errors on the fitting parameters. the values given below come from averages.," \ref{FigCorrelation1} and \ref{FigCorrelation2} result from a linear regression unweighted by the fractional errors on the fitting parameters, the values given below come from averages." + The linewidths of the Gaussian components of the HCO. CN. HCN. and HNC line profiles are close to be the same.," The linewidths of the Gaussian components of the $^{+}$, CN, HCN, and HNC line profiles are close to be the same." + We find that the CN. HCN. and HNC line profiles are systematically narrower than those of HCO™ (by a factor of 0.7 to 0.9).," We find that the CN, HCN, and HNC line profiles are systematically narrower than those of $^{+}$ (by a factor of 0.7 to 0.9)." + In Fig. 4..," In Fig. \ref{FigCorrelation1}," + the CN and HCN line profiles appear to be narrower than those of HNC (by a factor of 0.8 to 0.9) but this result is mostly due to the hyperfine structure of HNC that has not been taken into account in the decomposition., the CN and HCN line profiles appear to be narrower than those of HNC (by a factor of 0.8 to 0.9) but this result is mostly due to the hyperfine structure of HNC that has not been taken into account in the decomposition. + Once the correction discussed in Sect., Once the correction discussed in Sect. + 2 is applied. the significance of the linewidth difference disappears.," \ref{SectObs} is applied, the significance of the linewidth difference disappears." + The profiles of C:H and CiH» have been studied with a different method. and the components identified are not the same as those in the present study (Germ 2010).," The profiles of $_2$ H and $_3$ $_2$ have been studied with a different method, and the components identified are not the same as those in the present study (Gerin 2010)." + In order to be able to compare the data to chemical models. molecular abundances must be derived and column densities of hydrogen measured.," In order to be able to compare the data to chemical models, molecular abundances must be derived and column densities of hydrogen measured." + In particular. it is essential to determine whether the wide dynamic ranges over which the correlations are observed (Figs.," In particular, it is essential to determine whether the wide dynamic ranges over which the correlations are observed (Figs." + 4. and 5)) are related to variations. of the total column density of the gas sampled or/and of the physical and chemical conditions in the absorbing gas., \ref{FigCorrelation1} and \ref{FigCorrelation2}) ) are related to variations of the total column density of the gas sampled or/and of the physical and chemical conditions in the absorbing gas. + The main difficulty is to estimate the fraction of molecular hydrogen that is not directly observable., The main difficulty is to estimate the fraction of molecular hydrogen that is not directly observable. + Using 22] em observations of HL 29 em and 20.3 mm observations of CH. and the remarkable correlation between CH and H». N(CCH)/N(H:)=4.3x1077 (Liszt Lucas 2002). we evaluate the total amount of gas Ny=N(CH)+2N(H:) along the galactic lines of sight. as in Godard (2009) for the lines of sight studied by Liszt Lucas (2001).," Using $\lambda 21$ cm observations of HI, $\lambda +9$ cm and $\lambda 0.3$ mm observations of CH, and the remarkable correlation between CH and $_2$, $N({\rm CH})/N({\rm H}_2) = 4.3 \times 10^{-8}$ (Liszt Lucas 2002), we evaluate the total amount of gas $N_{\rm H} = +N({\rm H}) + 2N({\rm H}_2)$ along the galactic lines of sight, as in Godard (2009) for the lines of sight studied by Liszt Lucas (2001)." + The HI column densities are inferred from VLA 221 em absorption line observations (Koo 1997; Fish 2003)., The HI column densities are inferred from VLA $\lambda 21$ cm absorption line observations (Koo 1997; Fish 2003). + Wherever possible. we derive N(H>) from CH observations (at 9 em by Rydbeck 1976. at | THz by Germ 2010 in prep.).," Wherever possible, we derive $N({\rm H}_2)$ from CH observations (at 9 cm by Rydbeck 1976, at 1 THz by Gerin 2010 in prep.)." + An independent estimate of the total column density of gas toward the star-forming regions is inferred from the analysis of the 2MASS survey (Cutie 2003)., An independent estimate of the total column density of gas toward the star-forming regions is inferred from the analysis of the 2MASS survey (Cutie 2003). + Marshall (2006) have measured the near infrared colour excess in large areas of the inner Galaxy (]«1007. |b]<10°) to obtain the visible extinctions (Ay~10AÀ4). providing an estimate of the total hydrogen column density along the lines of sight.," Marshall (2006) have measured the near infrared colour excess in large areas of the inner Galaxy $|l|<100^{\circ}$, $|b|<10^{\circ}$ ) to obtain the visible extinctions $A_V \sim 10 A_K$ ), providing an estimate of the total hydrogen column density along the lines of sight." + Table 4. lists the HI (and Η». where available) colum densities in selected velocity intervals. as well as the total hydrogen column densities inferred from extinction.," Table \ref{TabHI} lists the HI (and $_2$, where available) column densities in selected velocity intervals, as well as the total hydrogen column densities inferred from extinction." + However the uncertainties on these estimations are large: (1) the error o the N(CH)—N(H») relation is about a factor of 3 (Liszt Lucas 2002): (2) this correlation has been established in the local diffuse medium but has never beer observed 1 the inner Galaxy material; (3) because of the low resolutio of the 2MASS survey (~15 aremin). the error on the total hydrogen column density (computed as the standard deviatio of the extinetion measured along the four closest lines of sigh= surrounding a given source) is larger than 30σος and (4) The HI column densities inferred from VLA 22] em absorptio line observations are directly proportional to the assumed spi temperature.," However the uncertainties on these estimations are large: (1) the error on the $N({\rm CH})-N({\rm H}_2)$ relation is about a factor of 3 (Liszt Lucas 2002); (2) this correlation has been established in the local diffuse medium but has never been observed in the inner Galaxy material; (3) because of the low resolution of the 2MASS survey $\sim 15$ arcmin), the error on the total hydrogen column density (computed as the standard deviation of the extinction measured along the four closest lines of sight surrounding a given source) is larger than 30; and (4) The HI column densities inferred from VLA $\lambda 21$ cm absorption line observations are directly proportional to the assumed spin temperature." + Hence. while the two determinations agree with each other within toward W51 and W49N. they differ by at least a factor of 2 toward G10.62-0.38.," Hence, while the two determinations agree with each other within toward W51 and W49N, they differ by at least a factor of 2 toward G10.62-0.38." + According to the extinction. measurements. the lines of sight sample between 1.3 (W51) and 12.5 (W49N) magnitudes of gas.," According to the extinction measurements, the lines of sight sample between 1.3 (W51) and 12.5 (W49N) magnitudes of gas." +" The total velocity coverage of the absorption features is ~lOkms""! ttoward W51 and 48 ttoward W49N. Therefore. the average hydrogen column density is only twice larger along the line of sight toward W49N than along that toward W51."," The total velocity coverage of the absorption features is $\sim 10$ toward W51 and 48 toward W49N. Therefore, the average hydrogen column density is only twice larger along the line of sight toward W49N than along that toward W51." + It is therefore possible to estimate the molecular abundances relative to the total hydrogen column density Ny for each. velocity component. assuming that Ny scales with their linewidth according to Ny/Ayv=2.2 and 4.7x107 em/km ttoward W51 and W49N respectively.," It is therefore possible to estimate the molecular abundances relative to the total hydrogen column density $N_{\rm H}$ for each velocity component, assuming that $N_{\rm H}$ scales with their linewidth according to $N_{\rm H}/\Delta v = 2.2$ and $\times +10^{20}$ $^{-2}$ toward W51 and W49N respectively." + This is equivalent to assuming a uniform HI optical depth in the gas components where we observe molecular absorption., This is equivalent to assuming a uniform HI optical depth in the gas components where we observe molecular absorption. + Such an approximation underestimates the HI column density per unit velocity by no more than a factor 2., Such an approximation underestimates the HI column density per unit velocity by no more than a factor 2. + The total hydrogen column densities estimated with this method and given in Table Α.1 for W49N and WS] are smaller by only than those inferred from IR extinction., The total hydrogen column densities estimated with this method and given in Table A.1 for W49N and W51 are smaller by only than those inferred from IR extinction. + We therefore estimate that the total H column density per velocity component on these two lines of sight does not exceed 1.5 magnitude (or about 2.5x107! cm)., We therefore estimate that the total H column density per velocity component on these two lines of sight does not exceed 1.5 magnitude (or about $2.5 \times 10^{21}$ $^{-2}$ ). +scaltering (7.e0.0020) [from Ie Η at z<3.,scattering $\tau_e \approx 0.0020$ ) from He III at $z \leq 3$. +" With this He HI contribution. equation (2) vields 7.= 0.040. 0.045. and 0.050 for z,= 6.0. 6.5. ancl 7.0. respectively."," With this He III contribution, equation (2) yields $\tau_e =$ 0.040, 0.045, and 0.050 for $z_r =$ 6.0, 6.5, and 7.0, respectively." +" For large redshifts. Q,,(1+2)'29O4. and the integral simplifies to llere. we have scaled (to a rejonization epoch z,27."," For large redshifts, $\Omega_m (1+z)^3 \gg \Omega_{\Lambda}$, and the integral simplifies to Here, we have scaled to a reionization epoch $z_r \approx 7$." +" From the approximate expression in equation (3). we see that 7.xVRSXOM""Hy 1 "," From the approximate expression in equation (3), we see that $\tau_e \propto (\rho_{\rm cr} \Omega_b \Omega_m^{-1/2} H_0^{-1}$ )." +"Thus. 7 is nearly independent of the Hubble constant. since pxh? while the combined parameters. Q5? and Q,,/?. are inferred. [rom D/II. CAIB. and large-scale galaxv motions."," Thus, $\tau_e$ is nearly independent of the Hubble constant, since $\rho_{\rm cr} \propto h^2$ while the combined parameters, $\Omega_b h^2$ and $\Omega_m h^2$, are inferred from D/H, CMB, and large-scale galaxy motions." + The scaling with therefore cancels to lowest order., The scaling with $h$ therefore cancels to lowest order. + À slight dependence remains from the small O4 term in equation (2), A slight dependence remains from the small $\Omega_{\Lambda}$ term in equation (2). +" If we invert the approximate . (3). we can estimate the recdshilt of primary (Gunn- reionization. (1+top)2(7.77)[7(cap)/t1.05]? scaled to the value. 7,=0.05. expected for full ionization back to zap27."," If we invert the approximate equation (3), we can estimate the redshift of primary (Gunn-Peterson) reionization, $(1+z_{\rm GP}) \approx (7.77) [\tau_e(z_{\rm GP})/0.05]^{2/3}$, scaled to the value, $\tau_e = 0.05$, expected for full ionization back to $z_{\rm GP} \approx 7$." +" As discussed in 2.2. (his is approximately the WAIAP-5 value of optical depth. z.=0.08440.016. reduced by Ar,80.03."," As discussed in 2.2, this is approximately the WMAP-5 value of optical depth, $\tau_e = 0.084 \pm 0.016$, reduced by $\Delta \tau_e \approx 0.03$." + This additional scattering. rz. may arise [rom high-: star formation. X-ray preionization. and residual electrons left. after incomplete recombination.," This additional scattering, $\Delta \tau_e$, may arise from $z$ star formation, X-ray preionization, and residual electrons left after incomplete recombination." +" The latter electrons are computed to have fractional ionization zr,zz(0.5—3.0)x10* between 2 = 10700 (Seager 2000).", The latter electrons are computed to have fractional ionization $x_e \approx (0.5-3.0) \times 10^{-3}$ between $z$ = 10–700 (Seager 2000). + Inaccuracies in computing (heir contribution therelore add systematic uncertaintwv. to the CA\MB-derived value of 7., Inaccuracies in computing their contribution therefore add systematic uncertainty to the CMB-derived value of $\tau_e$. + Partial ionization may also arise [rom the first stars (Venkatesan. Tunilinson. Shull 2003. herealter VTS03) and from penetrating N-ravs produced by early black holes (VGS01: Ricotti Ostriker 2004. 2005).," Partial ionization may also arise from the first stars (Venkatesan, Tumlinson, Shull 2003, hereafter VTS03) and from penetrating X-rays produced by early black holes (VGS01; Ricotti Ostriker 2004, 2005)." +" Forcomplete sudden reionization. Komatsu (2008) estimated. z,£z10.8dL4 at C.L.. bv combining WMAP-5 data with other measures (SNe. BAO)."," Forcomplete sudden reionization, Komatsu (2008) estimated $z_r \approx 10.8 \pm 1.4$ at C.L., by combining WMAP-5 data with other distance measures (SNe, BAO)." +" The WMAP-5 data alone (Dunklev 2008) imply T.=0.08Tnuc 0.017. with z,=11.041.4 C.L.)."," The WMAP-5 data alone (Dunkley 2008) imply $\tau_e = 0.087 \pm 0.017$ , with $z_r = 11.0 \pm 1.4$ C.L.)." +" Their likelihood curves allow a range (X13.0 al CLL. They also claim that WALAP-5 data exclude z,—6 at more than L The additional ionization sources αἱ z> wwill contribute electron scattering that maa bring the WALAP ancl Gunn-Peterson results into agreement for the epoch of complete reionization.", Their likelihood curves allow a range $7.5 \leq z_r \leq 13.0$ at C.L. They also claim that WMAP-5 data exclude $z_r = 6$ at more than C.L. The additional ionization sources at $z >$ will contribute electron scattering that may bring the WMAP and Gunn-Peterson results into agreement for the epoch of complete reionization. + In our calculations. described in 3.we make several kev assumptions.," In our calculations, described in 3,we make several key assumptions." + First. we assume a fully ionized IGM out to & 67. accounting for both and ionized helium.," First, we assume a fully ionized IGM out to $\approx$ 6–7, accounting for both $^+$ and ionized helium." + Second. we investigate the effects of ICM parüal ionization al z2τομ.," Second, we investigate the effects of IGM partial ionization at $z >$." + Finally. in computing the contribution of residual electrons. ad high redshifts. we adopt the concordance parameters [rom the WMAP-5 data set.," Finally, in computing the contribution of residual electrons at high redshifts, we adopt the concordance parameters from the WMAP-5 data set." +" The CMD optical depth is formally à 5o result. which may improve as WMADP refines its estimates of the matter density. ,,. and the parameters. ex ancy. that govern small-scale power."," The CMB optical depth is formally a $5 \sigma$ result, which may improve as WMAP refines its estimates of the matter density, $\Omega_m$ , and the parameters, $\sigma_8$and $n_s$ that govern small-scale power." + Both σς and, Both $\sigma_8$ and +The proximity of the Andromeda galaxy. M31. has long macle it a prime target for studies of galaxy structure and stellar populations.,"The proximity of the Andromeda galaxy, M31, has long made it a prime target for studies of galaxy structure and stellar populations." + One technique has been (o isolate particular populations: for example. studies of Iuminous stars (IIvunphlirevsοἱal.1990). showed that AI31l has a lower massive star formation rate than M22 and the LMC.," One technique has been to isolate particular populations: for example, studies of luminous stars \citep{hmf90} + showed that M31 has a lower massive star formation rate than M33 and the LMC." + Global studies of parüceular components have also been valuable: IL 1 maps provide estimates of the mass distribution (Braun&Thilker2004) and have recently revealed a population of high-velocity clouds (Thilkeretal.2004)... PHOT (IIaasetal.1998).. ASSN (Ixraemeretal.2002).," Global studies of particular components have also been valuable: H I maps provide estimates of the mass distribution \citep{bt04} and have recently revealed a population of high-velocity clouds \citep{thil04}. \citep{haas98}, \citep{kraemer02}," +. andZ5 (ILabingetal.1984). observations showed a bright ring of infrared emission with radius 10 kpe coincident with many of the II 1Iregions., and \citep{habing84} observations showed a bright ring of infrared emission with radius 10 kpc coincident with many of the H IIregions. +where d/di=O/Ol--v-V.,where $d/dt=\partial/\partial t+\mbf{v}\cdot\mbf{\nabla}$. + We seck a one-dimensional solution that satisfies thermal equilibrium at infinity: where subscripts | and 2 denote the values at. =—o and +=x. respectively.," We seek a one-dimensional solution that satisfies thermal equilibrium at infinity: where subscripts 1 and 2 denote the values at $x=-\infty$ and $x=\infty$, respectively." +" Omitting the y—.z— and time dependences of the variables, andintegrating equations 1)) and (2)) with respect to .r, we obtain the basic equations corresponding to the three conservation laws: where v is the -component of the velocity."," Omitting the $y-,\,z-$ and time dependences of the variables, andintegrating equations \ref{EOC}) ) and \ref{EOM}) ) with respect to $x$, we obtain the basic equations corresponding to the three conservation laws: where $v$ is the $x$ -component of the velocity." +" From equations (16)).(17)). and (4)), the velocity, pressure, and density can be expressed in terms of the temperature, mass flux j and total momentum A: The density p, and temperature Tj at.=—x. are obtained from the solution of equation (14)) if the pressure at c=—ox (pi) 1sgiven."," From equations \ref{SE1}) \ref{SE2}) ), and \ref{EOS}) ), the velocity, pressure, and density can be expressed in terms of the temperature, mass flux $j$ and total momentum $M$: The density $\rho_{1}$ and temperature $T_{1}$ at $x=-\infty$ are obtained from the solution of equation \ref{TE}) ) if the pressure at $x=-\infty$ $(p_{1})$ isgiven." +" Then the total momentum can be expressed as a function of the mass flux and given pressure at.= —oc, M=M(J. p). and the boundary conditions"," Then the total momentum can be expressed as a function of the mass flux and given pressure at $x=-\infty$ , $M=M(j,p_{1})$ , and the boundary conditions" +models favor values close to these.,models favor values close to these. + Typical accretion rates in the collapsar model are 0.05 - 0.1 AL.sec.! (MacFadyenfigures5and10).., Typical accretion rates in the collapsar model are 0.05 - 0.1 $\Msunsec$ \citep[their figures 5 and 10]{mac99}. + The neutron excess will be smaller in Tvpe IE collapsars powered by fall back rather than direct black hole formation (AlacFacven. 2001)., The neutron excess will be smaller in Type II collapsars powered by fall back rather than direct black hole formation \citep{mac01}. +. Considerable accretion into the hole and mass loss from the disk maa continue. al a declining rate. even alter(he main GRB producing event (720 s) is over 2002).," Considerable accretion into the hole and mass loss from the disk may continue, at a declining rate, even afterthe main GRB producing event $\sim$ 20 s) is over \citep{zha02}." +. It thus seems Likely (hat the collapsar model will be able to provide the PONT necessary (o make the supernovae that accompany GRBs (though only if az0.1)., It thus seems likely that the collapsar model will be able to provide the $^{56}$ Ni necessary to make the supernovae that accompany GRBs (though only if $\alpha \gtaprx 0.1$ ). + This is also true of the slower accreting models like helium-star black hole mergers and black hole white dwarl mergers., This is also true of the slower accreting models like helium-star black hole mergers and black hole white dwarf mergers. + However any wind from mereing compact objects. or similar moclels like (he supranova. will be neutron rich.," However any wind from merging compact objects, or similar models like the supranova, will be neutron rich." +" Though perhaps of interest lor nucleosyntliesis. they will not produce ""Ni. at least during the black hole accretion epoch."," Though perhaps of interest for nucleosynthesis, they will not produce $^{56}$ Ni, at least during the black hole accretion epoch." + For disks with highex accretion rates. and certainly for mergingexe neutron stars or black hole neutron star mergers.e the matter near the event horizon will be verv neutron rich.," For disks with high accretion rates, and certainly for merging neutron stars or black hole neutron star mergers, the matter near the event horizon will be very neutron rich." +" If (his material pollutes (he outgoing jet. the the GRB jet will itsell. at least initially, contain [ree neutrons."," If this material pollutes the outgoing jet, the the GRB jet will itself, at least initially, contain free neutrons." + The dvnamies of accelerating neutron-rich jets can differ dramatically from the dynamics ol pure proton jets., The dynamics of accelerating neutron-rich jets can differ dramatically from the dynamics of pure proton jets. + Fuller.Pruet.&Abazajian(2000) showed that a high Lorentz factor fireball (hat is neutron rich can lead (o two very distinct kinematic components. a slow neutron outflow and a fast proton outflow.," \citet{ful00} showed that a high Lorentz factor fireball that is neutron rich can lead to two very distinct kinematic components, a slow neutron outflow and a fast proton outflow." + This arises because the unchareec neutrons are weakly coupled to the radiation dominated plasma. ancl are accelerated principally via strong neutron-proton scatterings (Derishev.lxocharovsky.&Nocharovsky1999).," This arises because the uncharged neutrons are weakly coupled to the radiation dominated plasma, and are accelerated principally via strong neutron-proton scatterings \citep{der99}." +.. Strong scalterings freeze oul when thev become slow compared to the dynamic timescale ancl al (his point (he neutrons coast., Strong scatterings freeze out when they become slow compared to the dynamic timescale and at this point the neutrons coast. + If (his decoupling occurs while the jet is still accelerating. then the coulomb-coupled protons go on to have a larger Lorentz factor than the neutrons.," If this decoupling occurs while the jet is still accelerating, then the coulomb-coupled protons go on to have a larger Lorentz factor than the neutrons." + Roughly. dvnamic neutron decoupling is only expected [or last jets.," Roughly, dynamic neutron decoupling is only expected for fast jets." + Here the precise meaning of “last” depends. among other things. (he fireball source size.," Here the precise meaning of “fast” depends, among other things, the fireball source size." + For relativistic flows originating from compact objects. the dvinanmic (nmescale characterizing (he acceleration of the flow is about 1 ms and the final Lorentz factor must be greater (han ~300 in order for dynamic neutron decoupling to occur.," For relativistic flows originating from compact objects, the dynamic timescale characterizing the acceleration of the flow is about 1 ms and the final Lorentz factor must be greater than $\sim300$ in order for dynamic neutron decoupling to occur." + For jets in the collapsar model. (he timescale characterizing the acceleration is set by the surface of last interaction of the jet with the stellar envelope at ~ LOMen.," For jets in the collapsar model, the timescale characterizing the acceleration is set by the surface of last interaction of the jet with the stellar envelope at $\sim10^{11}\cm$ ." + In this case the final Lorentz factor of the jet has to be =3000 , In this case the final Lorentz factor of the jet has to be $\gtrsim3000$ +chance probability by (he number of [requencies searched.,chance probability by the number of frequencies searched. + In this case. the global sienilicance becomes9554.," In this case, the global significance becomes." +. Similar analvsis shows that the single-trial period detection is signilicant at 99.9%. confidence for.. but only in the second half of the observation (Figure Ybb).," Similar analysis shows that the single-trial period detection is significant at $99.9\%$ confidence for, but only in the second half of the observation (Figure \ref{ps1}b b)." + If the entire light curve is used. the significance of its periodic signal drops to 99.7% (Figure aa): it is clearly coming from just the second half of the observation.," If the entire light curve is used, the significance of its periodic signal drops to $99.7\%$ (Figure \ref{ps1}a a); it is clearly coming from just the second half of the observation." + The global significance corresponding to Figure ΤΡ is96%..., The global significance corresponding to Figure \ref{ps1}b b is. + Period detection in LI] 0419577 is significant al 99.6% for a single trial. but only eloballv.," Period detection in 1H 0419–577 is significant at $99.6\%$ for a single trial, but only globally." + Thus. we find that two of the three candidate periods have global significance >95%. a tantalizing if not entirely conclusive result.," Thus, we find that two of the three candidate periods have global significance $> 95\%$, a tantalizing if not entirely conclusive result." + One notable pattern among the candidate periods detected here in three objects is (heir ordering as a [function of redshift and huninositwv., One notable pattern among the candidate periods detected here in three objects is their ordering as a function of redshift and luminosity. + The flux of Ton 150 is approximately twice that of4711... and its redshift is slightly higher.," The flux of Ton S180 is approximately twice that of, and its redshift is slightly higher." + Thus. the luminosity of Ton S180 is about. 2.5 times that of4711.," Thus, the luminosity of Ton S180 is about 2.5 times that of." +". I£ the luminosity of Che source is proportional to the mass of the black hole. which in Gun is proportional to the characteristic (dynamical) time scale. (hen. one might expect the period of Ton 5180 (2.08 days) to be about 2.5 times that of ((0.89 davs). not [far [rom the ""observed"" [actor of 2.3."," If the luminosity of the source is proportional to the mass of the black hole, which in turn is proportional to the characteristic (dynamical) time scale, then one might expect the period of Ton S180 (2.08 days) to be about 2.5 times that of (0.89 days), not far from the “observed” factor of 2.3." + Also. since the fluxes detected. by [from LT 0419577 and are approximately the same. their luminosities scale as 27.," Also, since the fluxes detected by from 1H 0419–577 and are approximately the same, their luminosities scale as $z^2$." +" Then one might expect the period ol LIT 0419577 (5.8 davs) to be about 4 times that of4711.. not far from the ""observed"" [auctor of 6."," Then one might expect the period of 1H 0419–577 (5.8 days) to be about 4 times that of, not far from the “observed” factor of 6." + It is encouraging that (hese period values appear to be related to the Iuninosiües of the objects. a plivsical quantity. and not. lor example. to the length of the observation. which might have favored a more prosaic explanation im terms of the frequently deceptive properties of red noise.," It is encouraging that these period values appear to be related to the luminosities of the objects, a physical quantity, and not, for example, to the length of the observation, which might have favored a more prosaic explanation in terms of the frequently deceptive properties of red noise." + A striking property of these light curves is the large amplitude and rapid variability of some of them., A striking property of these light curves is the large amplitude and rapid variability of some of them. + Although it is eenerally (true that variability amplitude in AGNs increases with increasing photon energy. ib is now clear that EUV variability is as dramatic as anv detected at higher energies.," Although it is generally true that variability amplitude in AGNs increases with increasing photon energy, it is now clear that EUV variability is as dramatic as any detected at higher energies." + Therefore. it is of fundamental importauce (o measure variability in the EUV because of the likelihood that this component contains the bulk of the emission from the inner accretion disk. and most of the bolometric luminosity as well.," Therefore, it is of fundamental importance to measure variability in the EUV because of the likelihood that this component contains the bulk of the emission from the inner accretion disk, and most of the bolometric luminosity as well." + This is certainly (rue in the case of 4711., This is certainly true in the case of . +. Because of ils steep power-law spectrum of D22.2—2.6as measured by, Because of its steep power-law spectrum of $\Gamma = 2.2-2.6$as measured by +some examples of these disconinuities. which are of the same kind as alreacly mentioned for other CVs in Section 2.,"some examples of these discontinuities, which are of the same kind as already mentioned for other CVs in Section 2." + There are abrupt period changes at times 0.4645 and 0.4810. and phase discontinuities at 0.4600 ancl 0.4780.," There are abrupt period changes at times 0.4645 and 0.4810, and phase discontinuities at 0.4690 and 0.4780." + After 0.4810 the change in period is so large that the OC values run olf the top of the panel and “wrap around’., After 0.4810 the change in period is so large that the O–C values run off the top of the panel and `wrap around'. + The O€ variations in this example do not correlate with the general. brightness changes., The O–C variations in this example do not correlate with the general brightness changes. + A few runs have QPOs of large amplitude., A few runs have QPOs of large amplitude. + Phese are listed in Table 1. and two average profiles are shown in Fig. 13.., These are listed in Table \ref{tab1} and two average profiles are shown in Fig. \ref{avQPO}. + Although these QPOs are obvious in the light curves. their presence in VW. Livi (and. by implication. in the light curves of other CVs) has previously been ascribed to slow Ilickering.," Although these QPOs are obvious in the light curves, their presence in VW Hyi (and, by implication, in the light curves of other CVs) has previously been ascribed to slow flickering." + “Phe most extreme examples are shown in the upper panelof Fie. 12..," The most extreme examples are shown in the upper panelof Fig. \ref{lc0019}," + which shows the second run on VW Llvi made by the senior author at a time when QPOs had vet to be identified by Patterson et al. (, which shows the second run on VW Hyi made by the senior author at a time when QPOs had yet to be identified by Patterson et al. ( +1977). and. which was used merely as part of the series of runs which first clisclosedl orbital modulation in VW Livi (Warner 1975).,"1977), and which was used merely as part of the series of runs which first disclosed orbital modulation in VW Hyi (Warner 1975)." + Phe coherence of the apparent large Dares and clips in the upper panel of Fig., The coherence of the apparent large flares and dips in the upper panel of Fig. + 12. can be judged from the mean light curve (the lower profile) given in Fig. 13.., \ref{lc0019} can be judged from the mean light curve (the lower profile) given in Fig. \ref{avQPO}. + The question of coherence is an important onc., The question of coherence is an important one. + By their very nature. QPOs of short coherence are dillicult to detect in the Fourier transform.," By their very nature, QPOs of short coherence are difficult to detect in the Fourier transform." + Fig., Fig. + 14 shows the details of the 71 min of light curve obtained on 23 September 1984 near the end. of a normal outburst., \ref{dnobup} shows the details of the 71 min of light curve obtained on 23 September 1984 near the end of a normal outburst. + The QPO maxima. spaced 300 s apart. are shown by vertical bars.," The QPO maxima, spaced 300 s apart, are shown by vertical bars." + We can interpret the evolution of the QPO in this light curve as the growth ancl decay of a QPO (indicated by single vertical bars) over about 5 evcles. followed by growth. ancl decay over + - 6 eveles of another QPO (double bars) of similar period. but phase shifted relative to the first QPO by —0.4 evele.," We can interpret the evolution of the QPO in this light curve as the growth and decay of a QPO (indicated by single vertical bars) over about 5 cycles, followed by growth and decay over 4 - 6 cycles of another QPO (double bars) of similar period, but phase shifted relative to the first QPO by $\sim$ 0.4 cycle." + Such a phase shift leads to spread of power and lowering of peak amplituce in the Fourier transform., Such a phase shift leads to spread of power and lowering of peak amplitude in the Fourier transform. + A characteristic of large QPOs is that at their minima they drag the intensity well below the smooth lower envelope of the light curve., A characteristic of large QPOs is that at their minima they drag the intensity well below the smooth lower envelope of the light curve. + We illustrate in the lower part of Fig., We illustrate in the lower part of Fig. + 12) another light curve. obtained near the end of a normal outburst. in which the QPO phenomenon is very strong as judged by the dips and Lares.," \ref{lc0019} another light curve, obtained near the end of a normal outburst, in which the QPO phenomenon is very strong as judged by the dips and flares." + Phe Fourier transform of this light curve. Fig. 15..," The Fourier transform of this light curve, Fig. \ref{four5248}," + shows the fundamental. first ancl second. harmonics of a period near 2100 s. which account for the repetitive narrow dips marked in Fig. 12..," shows the fundamental, first and second harmonics of a period near 2100 s, which account for the repetitive narrow dips marked in Fig. \ref{lc0019}. ." + Phe predicted times of orbital hump, The predicted times of orbital hump +radial direction.,radial direction. +" We also find a resolution dependence in the maximum density, as expected."," We also find a resolution dependence in the maximum density, as expected." + Several other studies have been undertaken in order to investigate the influence of the numerics on the results of this work., Several other studies have been undertaken in order to investigate the influence of the numerics on the results of this work. + Changing the minimum gas temperature of the simulation changes the minimum size of the cloudlets., Changing the minimum gas temperature of the simulation changes the minimum size of the cloudlets. +" The higher we choose this threshold value, the smoother the cloud appears."," The higher we choose this threshold value, the smoother the cloud appears." + Clumps continue to form due to the converging flow., Clumps continue to form due to the converging flow. +" By increasing the density of the surrounding medium, at some point, its cooling time is small enough to form small clumps, which overcome the density threshold for radiation pressure interaction in our simulations."," By increasing the density of the surrounding medium, at some point, its cooling time is small enough to form small clumps, which overcome the density threshold for radiation pressure interaction in our simulations." +" With their ram pressure, they lead to a faster formation of filaments in the cloud."," With their ram pressure, they lead to a faster formation of filaments in the cloud." +" In this paper, we investigated the radiation pressure interaction of infalling dusty gas clouds with the active nucleus of a Seyfert galaxy, exemplified for the physical parameters of 11068."," In this paper, we investigated the radiation pressure interaction of infalling dusty gas clouds with the active nucleus of a Seyfert galaxy, exemplified for the physical parameters of 1068." +" Dictated by the gas column density, clouds will be accreted or expelled from the central region."," Dictated by the gas column density, clouds will be accreted or expelled from the central region." +" Outward accelerated clouds will interact and merge with clouds and filaments further out, until the critical column density is reached."," Outward accelerated clouds will interact and merge with clouds and filaments further out, until the critical column density is reached." + Fig., Fig. + 19 shows the column density distribution in radial direction for the 3D model of the 22 galaxy 11068 as discussed in ?.., \ref{fig:coldens_3d} shows the column density distribution in radial direction for the 3D model of the 2 galaxy 1068 as discussed in \citet{Schartmann_10}. +" It is shown for all polar angles, each of them averaged over the azimuthal angle."," It is shown for all polar angles, each of them averaged over the azimuthal angle." +" Clearly visible is the two-component structure — the geometrically thin, but high-column density disc and the extended low-column density torus on tens of parsec scale."," Clearly visible is the two-component structure – the geometrically thin, but high-column density disc and the extended low-column density torus on tens of parsec scale." + 'The dark blue dotted line denotes the transition between in- and outflow motion as derived in this article., The dark blue dotted line denotes the transition between in- and outflow motion as derived in this article. +" The latter is only a rough estimate, as it neglects the radius dependence given by the extended potential of the nuclear star cluster."," The latter is only a rough estimate, as it neglects the radius dependence given by the extended potential of the nuclear star cluster." +" The light blue dashed line shows the same column density threshold, but assuming a radiation characteristic of the source proportional to |cos(#)|. 19,, (?).. ?)"," The light blue dashed line shows the same column density threshold, but assuming a radiation characteristic of the source proportional to $|cos(\vartheta)|$ \ref{fig:coldens_3d}, \citep{Larson_05}. \citealp{Scoville_95})" +"). ? (?),, ? "," \citealp{Gomez_09} \citep{Blackman_01}, \citet{Rees_87} " +Afoute Carlo simulatious of the substellar mass funcetiou have been presented. viekliug LF and Τι distributions that can be directly compared to observations.,"Monte Carlo simulations of the substellar mass function have been presented, yielding LF and $_{eff}$ distributions that can be directly compared to observations." +" A few salicut points are worth reviewing: The results presented here are qualitatively in agreeinent with those of Allenetal.(200L).. who construct a two-dimensional grid of mass aud age distributions to derive L aud T,.y¢¢ distributious for comparison via Bavesian analysis."," A few salient points are worth reviewing: The results presented here are qualitatively in agreement with those of \citet{all04}, who construct a two-dimensional grid of mass and age distributions to derive L and $_{eff}$ distributions for comparison via Bayesian analysis." + Iu particular. many of the features in the LF ideutified iu their simulations also appear here. despite differences in technique.," In particular, many of the features in the LF identified in their simulations also appear here, despite differences in technique." + Both studies therefore provide useful tools for coustrainiug the substellar AIF in the field., Both studies therefore provide useful tools for constraining the substellar MF in the field. + Paper H iu this series will apply the simulations presented here to the local T dwarf LF derived from the 2MASS survey of Durgasseretal.(2003a).. improving upon earlier estimates by. Durgasser(2001). that were hiudered bv snall number statistics.," Paper II in this series will apply the simulations presented here to the local T dwarf LF derived from the 2MASS survey of \citet{me03a}, improving upon earlier estimates by \citet{me01} that were hindered by small number statistics." + The simulations cau also be used for a wide variety of Imagine survers. both as a predictive tool and as a means of probing the shape aud scale of the substellar ME. the age distribution of cool halo chwarfs. the uininuua “stellar” formation mass. aud the vertical distribution of brown dwarts in the Galaxy.," The simulations can also be used for a wide variety of imaging surveys, both as a predictive tool and as a means of probing the shape and scale of the substellar MF, the age distribution of cool halo dwarfs, the minimum “stellar” formation mass, and the vertical distribution of brown dwarfs in the Galaxy." + aacknowledges usoful discussions with AÀIeu. CChabrier. CCruz. KIxirkpatrick. and MMoustakas during the preparation of the manuscript. and thanks the referee RReid for extensive conuuents that ereatlv improved this article.," acknowledges useful discussions with Allen, Chabrier, Cruz, Kirkpatrick, and Moustakas during the preparation of the manuscript, and thanks the referee Reid for extensive comments that greatly improved this article." + Financial support for this work was provided iu, Financial support for this work was provided in +problem.,problem. + Iu couclusion. the detexiuiation of a small subset of initial couditions allows for à 1iucli more efficient survey of the parameter space.," In conclusion, the determination of a small subset of initial conditions allows for a much more efficient survey of the parameter space." + In this work. we lave taken a step in this direction.," In this work, we have taken a step in this direction." + We must keep iu miud that the system at hand is highly chaotic. aud iust in the eud )o studied wmmerically.," We must keep in mind that the system at hand is highly chaotic, and must in the end be studied numerically." + The resulting determinations are often probabilistic rather than couclusive. however the results are certainly bound to gain statistical weight as he number of completed simulations increascs.," The resulting determinations are often probabilistic rather than conclusive, however the results are certainly bound to gain statistical weight as the number of completed simulations increases." + Thus. while muuch progress is wot to be mace. additional research carries great value since a solid understanding of initial conditions plavs au unavoidably important role iu further development of a comprehensive model for solar svsteni's formation.," Thus, while much progress is yet to be made, additional research carries great value since a solid understanding of initial conditions plays an unavoidably important role in further development of a comprehensive model for solar system's formation." + We thaux Πα] Levisou. Alessandro Morbidelli: Ramo Drasser. Creegory Laughlin aud Darin Ragozzine for useful discussions.," We thank Hal Levison, Alessandro Morbidelli, Ramon Brasser, Gregory Laughlin and Darin Ragozzine for useful discussions." +with PA the position angle.,with PA the position angle. + All photometric parameters were fitted by cubic splines as functions of semi-major axis distance., All photometric parameters were fitted by cubic splines as functions of semi-major axis distance. + The galaxy nucleus (i.e. the brightest. pixel) was used. as zeropoint for both e and 6. the semi-minor axis distance.," The galaxy nucleus (i.e. the brightest pixel) was used as zeropoint for both $a$ and $b$, the semi-minor axis distance." + This allowed to reconstruct the surface brightness al a given point on the sky and to construct color. profiles (c.g. IU as a function of radius), This allowed to reconstruct the surface brightness at a given point on the sky and to construct color profiles (e.g. $-$ R as a function of radius). +" FCC207 has de-reddened: magnitudes mz,=14.39 mae. mg=ld4s86 mag and mg=16.19 mag (hence OR=1.33 mag. 1=07 mag)."," FCC207 has de-reddened magnitudes $m_I=14.39$ mag, $m_R = 14.86$ mag and $m_B = 16.19$ mag (hence $-{\rm R}=1.33$ mag, $-{\rm +I}=0.47$ mag)." + lis nucleus has a distorted shape: it is more elongated. than the bulk of the galaxy (123. versus 122) and is somewhat kidnev-shaped., Its nucleus has a distorted shape: it is more elongated than the bulk of the galaxy (E3 versus E2) and is somewhat kidney-shaped. + This is probably due to dust-absorptionto the north of the nucleus. noticeable in the It color map (Figure 4)) as a patch that is £:0.2 mag redder than its surroundings.," This is probably due to dust-absorptionto the north of the nucleus, noticeable in the $-$ R color map (Figure \ref{FCC207_BR}) ) as a patch that is $\approx 0.2$ mag redder than its surroundings." + Phe nucleus lt=0.90 mag) is significantly bluer than the bull of the galaxy —1.25 mag)., The nucleus $-{\rm R}=0.90$ mag) is significantly bluer than the bulk of the galaxy $-{\rm R}=1.25$ mag). + his behavior is similar to what c.g. Bremnes (1998). find in clwarl galaxies in nearby groups.," This behavior is similar to what e.g. Bremnes \cite{brem1} + find in dwarf galaxies in nearby groups." + A small. slightly. east-west. elongated: blue object 1t=1.10 mag) can be seen to the west of the nucleus.," A small, slightly east-west elongated blue object $-{\rm R}=1.10$ mag) can be seen to the west of the nucleus." + It is also visible in the Lla image., It is also visible in the $\alpha$ image. + Its elongation rules out the possibility that it is a faint foreground star., Its elongation rules out the possibility that it is a faint foreground star. + As can be seen in Figure 5.. the BOR. Land ROL colors stay essentially. constant outside the nucleus.," As can be seen in Figure \ref{FCC207_cm}, the $-{\rm R}$, $-{\rm I}$ and $-{\rm I}$ colors stay essentially constant outside the nucleus." + Loa voung stellar population is present outside the nuclear region of ECC207 (the inner 2”) then these stars are apparently well mixed with the older population., If a young stellar population is present outside the nuclear region of FCC207 (the inner $2''$ ) then these stars are apparently well mixed with the older population. + FCCO46 is a rather. blue object. with de-reddened magnitudes m;=14.43 mag. mj=14.58 mag and mg=15.00 mag (hence ]t=LII mag. 1=0.45mag).," FCC046 is a rather blue object, with de-reddened magnitudes $m_I=14.43$ mag, $m_R = 14.88$ mag and $m_B = 15.99$ mag (hence $-{\rm R}=1.11$ mag, $-{\rm I}=0.45$mag)." + The nucleus. a round. (E0) and blue Ro=0.10 mag) object. (see. Figure 6)). is olfset by L to the south-west of the center of the outer isophotes (see Figure 3)). ," The nucleus, a round (E0) and blue $-{\rm R}=0.10$ mag) object (see Figure \ref{FCC046_BR}) ), is offset by $''$ to the south-west of the center of the outer isophotes (see Figure \ref{surf_207}) ). $-{\rm R}$," +It. Land E color profiles are presented in Figure 7. and show a very cilferent behavior than those of ECC207., $-{\rm I}$ and $-{\rm I}$ color profiles are presented in Figure \ref{FCC046_cm} and show a very different behavior than those of FCC207. + The colors of the stellar population become redder towards larger radi., The colors of the stellar population become redder towards larger radii. + The nucleus of ECC046 is much bluer than those of nucleated cwarfs presented by Bremnes (e.g. (1998)))., The nucleus of FCC046 is much bluer than those of nucleated dwarfs presented by Bremnes (e.g. \cite{brem1}) ). + These authors typically find Bo2z0.5 for the nucleus., These authors typically find $B-R \approx 0.5$ for the nucleus. + The nucleus is resolved in the B-banc image., The nucleus is resolved in the B-band image. + Εις implies tha 10 nucleus is much larger than would be expected for a tvpical dl. Even with the superior resolving power olHST. Lauer (1995). could not resolve the nuclei of 5 nucleated Virgo cles.," This implies that the nucleus is much larger than would be expected for a typical dE. Even with the superior resolving power of, Lauer \cite{lau} could not resolve the nuclei of 5 nucleated Virgo dEs." +" The diameter (PWILAT) of the nucleus was estimated using the relation with EWA the true. dimension. ΕΛΑΤεν, its observed ENIM and FEWIDALay the average ENIM of the stars in the image."," The diameter (FWHM) of the nucleus was estimated using the relation with ${\rm FWHM}_{\rm true}$ the true dimension, ${\rm FWHM}_{\rm +obs}$ its observed FWHM and ${\rm FWHM}_{\rm star}$ the average FWHM of the stars in the image." +" Phe seeing. estimated from 10 stars in the D-band image. was 0.82""+0.04""."," The seeing, estimated from 10 stars in the B-band image, was $0.82''\pm 0.04''$." +" The measured PWIA of the nucleus is ΕΝΑΕΔΕ=11"" or FWA&65 pe (for fly=75 km/s/Mpc and a Fornax systemic velocity eo.=1379 km/s)."," The measured FWHM of the nucleus is ${\rm FWHM}_{\rm obs}=1.1''$ or ${\rm FWHM}_{\rm true}\approx +65$ pc (for $H_0=75$ km/s/Mpc and a Fornax systemic velocity $v_{\rm +sys} = 1379$ km/s)." + We fitted a two-component mocel to the B-barnc surface brightness of FCCOLG: an axisvmmetric componen centered on the outer isophotes that represents the light of the underlving stellar population and a round componen centered on the position of the nucleus., We fitted a two-component model to the B-band surface brightness of FCC046: an axisymmetric component centered on the outer isophotes that represents the light of the underlying stellar population and a round component centered on the position of the nucleus. + The results of this decomposition are presented in Figure S.., The results of this decomposition are presented in Figure \ref{2comp}. + The nucleus has a blue magnitude mg=18.55 mag (Mg=12.77) anc comprises about of the total B-band luminosity of the ealaxy., The nucleus has a blue magnitude $m_B = 18.55$ mag $M_B=-12.77$ ) and comprises about of the total B-band luminosity of the galaxy. + IH. should be noted that the nucleus of ECCOA6 was apparently not visible on the photographic plates on which Ferguson's catalog (1980). was based. since it is classified as a dl (Le. as à non-nucleatecd cdwarl).," It should be noted that the nucleus of FCC046 was apparently not visible on the photographic plates on which Ferguson's catalog \cite{fer} was based, since it is classified as a dE4 (i.e. as a non-nucleated dwarf)." +" The underlving stellar envelope deviates from an axisvmnmetric mass model and shows a pronounced. lopsidedness. visible in Figure 3 as the bump in Ae in the region ναῦ=2H12""."," The underlying stellar envelope deviates from an axisymmetric mass model and shows a pronounced lopsidedness, visible in Figure \ref{surf_207} as the bump in $\Delta \alpha$ in the region $\sqrt{ab} \approx 2'' - 12''$." +" ""phis asvmumetry may be due to an asvmamoetrie distribution of few but bright voung stars.", This asymmetry may be due to an asymmetric distribution of few but bright young stars. + This appears to be. plausible since the dynamical time scale. estimated as for tvpical values 7zz0.5 kpe and Ar)τεLOCAL.. is of the order of the life-time of the voungest stars so these would not have had. time to disperse all over the face of he galaxy.," This appears to be plausible since the dynamical time scale, estimated as for typical values $r \approx 0.5$ kpc and $M(r) \approx 10^9 +M_\odot$, is of the order of the life-time of the youngest stars so these would not have had time to disperse all over the face of the galaxy." + The cause of persistent m=1 perturbations. hat involve a sizable fraction of a galaxys mass. is still poorly understood.," The cause of persistent $m=1$ perturbations, that involve a sizable fraction of a galaxy's mass, is still poorly understood." + Interactions are often invoked. especially in bright galaxies. but examples of isolated Iopsided galaxies are know (particularly inH1. Baldwin (1980))).," Interactions are often invoked, especially in bright galaxies, but examples of isolated lopsided galaxies are know (particularly in, Baldwin \cite{bal}) )." + Since here is no galaxy detected within a 20°.20 square centered on FCCOAG. it seems unlikely that an encounter with another galaxy has caused the Iopsidedness.," Since there is no galaxy detected within a $20'\times 20'$ square centered on FCC046, it seems unlikely that an encounter with another galaxy has caused the lopsidedness." + Dynamical instabilities ave also been invoked (Alerritt (1999). ancl references herein) but it remains unclear whether such a hypothesis may work for all galaxies., Dynamical instabilities have also been invoked (Merritt \cite{mer} and references therein) but it remains unclear whether such a hypothesis may work for all galaxies. + Drinkwater (2001) jwe measured La EWs of LOS confirmed. Fornax cluster members. including FCCO4G and FCC?O07 with the spectrograph on the Ulx Schmidt Telescope.," Drinkwater \cite{dri} have measured $\alpha$ EWs of 108 confirmed Fornax cluster members, including FCC046 and FCC207 with the spectrograph on the UK Schmidt Telescope." +" Ehe elective aperture diameter of this system is at least 6.7"" (the fibre diameter) and could be as large as "" (because of -image movements due to tracking. errors and cillerential atmospheric refraction).", The effective aperture diameter of this system is at least $''$ (the fibre diameter) and could be as large as $''$ (because of image movements due to tracking errors and differential atmospheric refraction). + They. find : For comparison. we calculated. the EA inside some aperture radius r from our images as :," They find : For comparison, we calculated the EW inside some aperture radius $r$ from our images as :" +From our 2-D numerical simulations. we synthesized the absorbed focal plane spectra to be compared with observations by using the following procedure.,"From our 2-D numerical simulations, we synthesized the absorbed focal plane spectra to be compared with observations by using the following procedure." + As a first step. from the integration of the hydrodynamic equations 2.. 3 and 4.. we derive the temperature and density 2-D distributions in the computational domain.," As a first step, from the integration of the hydrodynamic equations \ref{eq:massa-1}, , \ref{eq:momento-1} and \ref{eq:en+r+c-1}, we derive the temperature and density 2-D distributions in the computational domain." + We reconstruct the 3-D spatial distribution of these physical quantities by rotating the 2-D slabs around the symmetry axis., We reconstruct the 3-D spatial distribution of these physical quantities by rotating the 2-D slabs around the symmetry axis. + Then we derive the emission measure. defined as LAL={nongedV. (where η and iq are the electron and hydrogen densities. respectively. and W is the volume of emitting plasma).," Then we derive the emission measure, defined as $EM = \int n_{e} n_{\rm H} dV$ (where $n_{e}$ and $n_{\rm H}$ are the electron and hydrogen densities, respectively, and $V$ is the volume of emitting plasma)." + From the 3-D spatial distributions of T and EAL. we derive the distribution of emission measure A(T) for the computational domain as a whole or for part of it: we consider the temperature range [10%—1(| K. divided into 71 bins equispaced in log7; the total EAL in each temperature bin is obtained summing the emission measure of all the fluid elements corresponding to the same bin.," From the 3-D spatial distributions of $T$ and $EM$, we derive the distribution of emission measure $EM(T)$ for the computational domain as a whole or for part of it: we consider the temperature range $[10^{3}-10^{8}]$ K, divided into $74$ bins equispaced in $\log T$; the total $EM$ in each temperature bin is obtained summing the emission measure of all the fluid elements corresponding to the same bin." + From the EA/(T). using the MEKAL spectral code (2)) for optically thin plasma. we derive the number of photons in the 1-th energy bin às where D is the distance of the object. 7; is the energy in the i-th bin. P(7).E) describes the radiative losses as a function of the energy and of the temperature in the k-th bin.," From the $EM(T)$, using the MEKAL spectral code \citealt{mgv85}) ) for optically thin plasma, we derive the number of photons in the i-th energy bin as where $D$ is the distance of the object, $E_{i}$ is the energy in the i-th bin, $P(T_{k}, E)$ describes the radiative losses as a function of the energy and of the temperature in the k-th bin." +" To compare our model results with observations. we synthesize the focal plane spectrum. (C. as predicted to be observed with the CAhiandra//ACIS-I or XMM-Newton//EPIC-pn X-ray imaging spectrometers taking into account the spectral instrumental response: where £..,.,, is the exposure time. A(£) is the effective area and AZ(/.E) is the instrumental response."," To compare our model results with observations, we synthesize the focal plane spectrum, $C_{i}$ , as predicted to be observed with the /ACIS-I or /EPIC-pn X-ray imaging spectrometers taking into account the spectral instrumental response: where $t_{exp}$ is the exposure time, $A(E)$ is the effective area and $M(i,E)$ is the instrumental response." + Finally we take into account the interstellar medium absorption column density. Nyy (2)). and we analyze the absorbed focal planespectrum with XSPEC V11.2 inorder to compare our findings with published," Finally we take into account the interstellar medium absorption column density, $N_{\rm H}$ \citealt{mm83}) ), and we analyze the absorbed focal planespectrum with XSPEC V11.2 inorder to compare our findings with published" +used to show an error iu the (Stone&Norman1992) solution.,used to show an error in the \citep{1992ApJS...80..791S} solution. + The initial states are sted in Table as test F6 aud the problemi was run in a domain of πα1. units with A=0.25.," The initial states are listed in Table \ref{tabshocktubes} as test F6 and the problem was run in a domain of $64 +\times 1 \times 1$ units with $\lambda=0.25$." + Fixed boundaries were used in the .c direction aud periodic boundaries in the y aud > directions., Fixed boundaries were used in the $x$ direction and periodic boundaries in the $y$ and $z$ directions. +" Compared to the uoucouscrvative result shown in Falle(2002). the slow shock is captured more accurately,", Compared to the nonconservative result shown in \cite{2002ApJ...577L.123F} the slow shock is captured more accurately. + At this resolution. the slow shock aud the contact discoutiuuitv directly behind it have uot vet separated. and the bulk viscosity of the «οποιο is," At this resolution, the slow shock and the contact discontinuity directly behind it have not yet separated, and the bulk viscosity of the scheme is" +within nearly isothermal haloes (Dubinski Carlberg 1991: avarro. Frenk White 1996. 1997).,"within nearly isothermal haloes (Dubinski Carlberg 1991; Navarro, Frenk White 1996, 1997)." + Lt is therefore useful to examine the consequences of dark haloes on the formation and evolution of barred galaxies to seek consistency with the xevailing world moclel and the observable universe., It is therefore useful to examine the consequences of dark haloes on the formation and evolution of barred galaxies to seek consistency with the prevailing world model and the observable universe. + The pattern speed of the bar is an important although cillieult to measure indicator of disc dvnamices and. dark malo structure., The pattern speed of the bar is an important although difficult to measure indicator of disc dynamics and dark halo structure. + Observations of carly-type barred: galaxies (Moerrifield WKuijken 1995 (M&IxIx): Gerssen et al., Observations of early-type barred galaxies (Merrifield Kuijken 1995 K); Gerssen et al. + 1999) hrough the application of the Tremaine-Meinberg moethoc (Tremaine Weinberg 195480) NN) have shown the xutern speed to be fast. since the bars end near corotation.," 1999) through the application of the Tremaine-Weinberg method (Tremaine Weinberg 1984b) W) have shown the pattern speed to be `fast', since the bars end near corotation." + rocky models of disc dvnamies with static backerounc yaloes (summarized in Selbvood LOST) have shown the xutern speed also to be fast., N-body models of disc dynamics with static background haloes (summarized in Sellwood 1981) have shown the pattern speed also to be fast. + Llowever. soon alterware it was recognized (Tremaine Weinbere 1984a: Weinberg 1985) that rotating bars would spin down significantly due o dynamical friction from the dark halo.," However, soon afterward it was recognized (Tremaine Weinberg 1984a; Weinberg 1985) that rotating bars would spin down significantly due to dynamical friction from the dark halo." + More. recen simulations with self-consistent disc and halo clistributions clearly showed this effect: angular momentum is transferre rom the bar to the halo through torques due to geravitationa wakes in the halo. which result in surprisingly low pattern speeds for simulated: bars. (Debattista ροήνους 2000 (DSS): Mrisiriotis Athanassoula 2000).," More recent simulations with self-consistent disc and halo distributions clearly showed this effect: angular momentum is transferred from the bar to the halo through torques due to gravitational wakes in the halo, which result in surprisingly low pattern speeds for simulated bars (Debattista Sellwood 2000 S); Misiriotis Athanassoula 2000)." + SS conductec xwametric studies by varying the halo to disc mass ratio of their models. and. found that a maximal cise vields je least pattern speed slow down., S conducted parametric studies by varying the halo to disc mass ratio of their models and found that a maximal disc yields the least pattern speed slow down. + They argued that the observational evidence of fast bars implies a maximum: disc in all barred. galaxies., They argued that the observational evidence of fast bars implies a maximum disc in all barred galaxies. + Dar structure ane dynamics can also be examined. in edge-on systems., Bar structure and dynamics can also be examined in edge-on systems. + The thin bars that form in clises are subject oa buckling instability which causes a bar to bend vertically and thicken into a bulge-like object within a few dvnanical imes. as was shown numerically by Raha ct al. (," The thin bars that form in discs are subject to a buckling instability which causes a bar to bend vertically and thicken into a bulge-like object within a few dynamical times, as was shown numerically by Raha et al. (" +1991). fenniecr Eriedli (L991). and Combes Sanders (1981).,"1991), Pfenniger Friedli (1991), and Combes Sanders (1981)." + Ixuijken Alerrifielel (1995). MM). have. shown that the kinematics of peanut-shaped bulges of NGC 5746 and NGC 5965 are consistent with orbits in a bar potential. the theory of which was confirmed by Bureau Athanassoula (1999) VA).," Kuijken Merrifield (1995) M) have shown that the kinematics of peanut-shaped bulges of NGC 5746 and NGC 5965 are consistent with orbits in a bar potential, the theory of which was confirmed by Bureau Athanassoula (1999) A)." + The observational test described by MM can also be applied to simulations. which can be viewed at any angle for more complete results.," The observational test described by M can also be applied to simulations, which can be viewed at any angle for more complete results." + Through5 B and LE band observations of 15 5galaxies. IElmesgSlmeereen Elmeg Elmegreen. (1085)(1985) 1have shown| that carly-| (SBO. SBa) and| late-t[ate-tvpe |bars Ihave significantly.enilthy dillerenclill[ properties.," Through B and I band observations of 15 galaxies, Elmegreen Elmegreen (1985) have shown that early- (SB0, SBa) and late-type bars have significantly different properties." + Although resonance positions and bar lengths are hard to quantify observationally. there is evidence to suggest that earlyv-tvpe bars are longer. out to the corotation radius. have a flat surface brightness profile along their length. and end beyond the turnover radius of the rotation curve.," Although resonance positions and bar lengths are hard to quantify observationally, there is evidence to suggest that early-type bars are longer, out to the corotation radius, have a flat surface brightness profile along their length, and end beyond the turnover radius of the rotation curve." + The late-tvpe bars on the other hand. are much shorter. with exponential surface brightness profiles.," The late-type bars on the other hand are much shorter, with exponential surface brightness profiles." + In this paper. we revisit the problem of the bar ancl buckling instabilities in self-consistent disc galaxy models with live haloes.," In this paper, we revisit the problem of the bar and buckling instabilities in self-consistent disc galaxy models with live haloes." + Our goal is to study the pattern speed evolution of numerical bars as well as quantily the structural ancl kinematic properties for comparison with observed. facc-on ane edge-on barred. galaxies., Our goal is to study the pattern speed evolution of numerical bars as well as quantify the structural and kinematic properties for comparison with observed face-on and edge-on barred galaxies. + We have taken care to re-seale our models to observed. svstems Lor comparison., We have taken care to re-scale our models to observed systems for comparison. + We extend. previous work by introducing a new. more realistic mass model anc going to much higher resolution with a simulation containing N—20M particles. a actor of 20 times larger than most work on the subject.," We extend previous work by introducing a new, more realistic mass model and going to much higher resolution with a simulation containing N=20M particles, a factor of 20 times larger than most work on the subject." + Our motivation for using high resolution is to examine he numerical convergence of results. since subtleties of dvnanmical interactions between disces and haloes may not »' captured. correctly even with haloes with more than zIAL particles (e.g. Weinberg 2001).," Our motivation for using high resolution is to examine the numerical convergence of results, since subtleties of dynamical interactions between discs and haloes may not be captured correctly even with haloes with more than $\approx +1$ M particles (e.g. Weinberg 2001)." + Phe disc of our large simulation contains LOAL particles. taking us well out. of he regime where cise self-heating contaminates results.," The disc of our large simulation contains 10M particles, taking us well out of the regime where disc self-heating contaminates results." + We are confident. that the dynamics of these models reliably represents the gravitational behaviour of real galaxies., We are confident that the dynamics of these models reliably represents the gravitational behaviour of real galaxies. + There are also disagreements between various simulations of bars in the literature which use. different N-bods codes. and initial conditions., There are also disagreements between various simulations of bars in the literature which use different N-body codes and initial conditions. + We attempt here to achieve convergence by comparing three of our simulations with those of other eroups. as well as to observations. by examining the bar structure. pattern speed. and edge-on kinematics.," We attempt here to achieve convergence by comparing three of our simulations with those of other groups, as well as to observations, by examining the bar structure, pattern speed, and edge-on kinematics." + We simulate bars by setting up an initially axisvmmoetric system including a disc and dark halo which is formally in equilibrium but unstable., We simulate bars by setting up an initially axisymmetric system including a disc and dark halo which is formally in equilibrium but unstable. + Models with rotation curves which are disc-dominated. approaching the maximal disc as defined bv van Albaca Sancisi (1986). usually form a bar within a few dvnanmical times. and the Ostriker Peebles (1973) empirical criterion is still a useful indicator of the instability.," Models with rotation curves which are disc-dominated, approaching the maximal disc as defined by van Albada Sancisi (1986), usually form a bar within a few dynamical times, and the Ostriker Peebles (1973) empirical criterion is still a useful indicator of the instability." + We use the method of Ixuijken Dubinski (IXD) (1905) to generate. sell-consisten disc|halo models. with a nearly [lat rotation curve., We use the method of Kuijken Dubinski (KD) (1995) to generate self-consistent disc+halo models with a nearly flat rotation curve. + We consider models with cisc-dominatecl rotation curves with and without a central bulge., We consider models with disc-dominated rotation curves with and without a central bulge. + The KD models are gencratec rom a distribution function (DE) that is the sum of up to 3 unctions: a threc-integral disk DE. à bulge DE modelled as Ixing model with an energy cut-oll ££«0 and a halo DE tha isa llattened King model DE (or lowered Evans model) with he usual truncation at a tidal racius at £=0.," The KD models are generated from a distribution function (DF) that is the sum of up to 3 functions: a three-integral disk DF, a bulge DF modelled as King model with an energy cut-off $E < 0$ and a halo DF that is a flattened King model DF (or lowered Evans model) with the usual truncation at a tidal radius at $E=0$." + We examine models with and without a bulge as described below., We examine models with and without a bulge as described below. + The disk DE is a function of E. z-angular momentum. £L. and a hird approximate integral. the z energy. fe.=27/2|(2).," The disk DF is a function of E, $z$ -angular momentum, $L_z$ and a third approximate integral, the $z$ energy, $E_z = \dot{z}^2/2 + \Phi(z)$." + The disk. DEF is constructed assuming a exponential racial surface density. profile and an approximately sech-z eclec-on profile with fixed. vertical scale length: z;., The disk DF is constructed assuming a exponential radial surface density profile and an approximately $\rm{sech}^2 z$ edge-on profile with fixed vertical scale length $z_d$. +" The disk squared racial velocity dispersion. a7, is assumed to decline exponentially with the same scale-leneth as the disk. like real galaxies."," The disk squared radial velocity dispersion, $\sigma_R^2$ is assumed to decline exponentially with the same scale-length as the disk like real galaxies." + We can generate N-body realizations of these models and they are formally in equilibrium with an initial virial ratio 27710., We can generate N-body realizations of these models and they are formally in equilibrium with an initial virial ratio $2T/W=-1.0$. + The bulgeless model is nearly a formal maximal disc model. with the rotation curve rising to a roughly Lat profile within two scale lengths (Figure 1).," The bulgeless model is nearly a formal maximal disc model, with the rotation curve rising to a roughly flat profile within two scale lengths (Figure 1)." + Although the, Although the +"Synchrotron emissivity is calculated from the formula 1986}[Moderskietal J2003):: isyn(v))= v. where R(x)=2?[K1/3()Kay3(x)—0.62(Kay3(x)” K1/3(a))|, ug=B?/(8x) and vp=eB/(21m.c).","Synchrotron emissivity is calculated from the formula \citep{1986A&A...164L..16C,2003A&A...406..855M}: )= , where $\mathcal{R}(x)=x^2[K_{1/3}(x)K_{4/3}(x)-0.6x({K_{4/3}(x)}^2-{K_{1/3}(x)}^2)]$ , $u_B=B^2/(8\pi)$ and $\nu_B=eB/(2\pi m_ec)$." +" Since fR(a)de=4V31/81, one finds that the frequency-integrated formula is-"," Since $\int\mathcal{R}(x)dx=4\sqrt{3}\pi/81$, one finds that the frequency-integrated formula is." +" The IC radiation emissivity is calculated from Atoyan|1981j|Moderskiet al.|2005):: ,H))-=Ter (A8) where eo “0,is the energy of the incident photon (in units of 2 πιες”). € is. the energy of the scattered photon, α1ο(εο) is. the energy density spectrum of incident radiation and js is the cosine of the scattering angle, w=ε/γ. ὂμ=2εογ(1—2)."," The IC radiation emissivity is calculated from \citep{1981Ap&SS..79..321A,2005MNRAS.363..954M}: ) = , where $\epsilon_0$ is the energy of the incident photon (in units of $m_ec^2$ ), $\epsilon$ is the energy of the scattered photon, $u_0(\epsilon_0)$ is the energy density spectrum of incident radiation and $\mu$ is the cosine of the scattering angle, $w=\epsilon/\gamma$, $b_\mu=2\epsilon_0\gamma(1-\mu)$." +" For the f,, function see Eq. (B2)).", For the $f_\mu$ function see Eq. \ref{eq_f}) ). + The frequency-integrated formula is: ο(μ)) = ο where (bu) —3=-C," The frequency-integrated formula is: ) = , where ) = ." +"AL5) In the Thomson limit (b,<1) {κν.μ(μ)~1, thusω"," In the Thomson limit $b_\mu\ll 1$ ) $f_{\rm KN,\mu}(b_\mu)\sim 1$, thus." +"ρα-- When the incident radiation field is isotropic, we can average the above formulae over the scattering angle: (v)) =jc""n =(422) gammarn,where b=4εργ. f(w,b) = fxn(b) = ."," When the incident radiation field is isotropic, we can average the above formulae over the scattering angle: ) = = , where $b=4\epsilon_0\gamma$, f(w,b) = (b) = ." +".(A25) In the ((8Thomson limit,2)) jic/jsyn~2Lis(—5)]]uo/unp."," In the Thomson limit, $j_{\rm IC}/j_{\rm SYN} \sim u_0/u_{\rm B}$." + Radiative cooling of electrons is calculated from = ," Radiative cooling of electrons is calculated from \citep{2003A&A...406..855M,2005MNRAS.363..954M}: = ." +"The pair-production deouo(€o)absorption ..(429)coefficientfrom a directed beam of ambient photons of energy eo=hvo/(mec?) and energy density uo is (Gould&Schréder[1967) (6,u)) =2 where = left((2-)](A35) and8= \/1—1/z."," The pair-production absorption coefficientfrom a directed beam of ambient photons of energy $\epsilon_0=h\nu_0/(m_ec^2)$ and energy density $u_0$ is \citep{1967PhRv..155.1404G} + ) =, where = ] and $\beta=\sqrt{1-1/x}$ ." +requires inconceivably high temperatures. above LO°T...,"requires inconceivably high temperatures, above $10^6 ~T_c$." + We conclude that the interaction of the plasma in the region of interest here. up to some LO 7... must definitely require some non-perturbative features.," We conclude that the interaction of the plasma in the region of interest here, up to some 10 $T_c$, must definitely require some non-perturbative features." + This situation has triggered numerous efforts to modilv the perturbative approach to include such features., This situation has triggered numerous efforts to modify the perturbative approach to include such features. +" In one approach [10].. the O(g"") term in the pressure is evaluated bv a non-perturbative scale determination. using lattice results for magnetic screening."," In one approach \cite{Laine}, the $O(g^6)$ term in the pressure is evaluated by a non-perturbative scale determination, using lattice results for magnetic screening." + This leads (o à systematic effective field theory. For which in principle all orders can be calculated.," This leads to a systematic effective field theory, for which in principle all orders can be calculated." + Another possibility is given by including sums over certain graph classes. thus effectively shifting the point about which the perturbation expansion is performed. [11]..," Another possibility is given by including sums over certain graph classes, thus effectively shifting the point about which the perturbation expansion is performed \cite{Patkos}." + In particular. (his is studied for the terms dominating at high temperature (hard thermal loops. IVTL) [12.13]. and leads to an improved convergence of the perturbation series of the pressure.," In particular, this is studied for the terms dominating at high temperature (hard thermal loops, HTL) \cite{HTL,resum} and leads to an improved convergence of the perturbation series of the pressure." +" Both approaches have in common To illustrate this. we show in relTrace. (left) the behavior obtained with the help of a partially non-perturbative O(g) [10].. and in Trace. (right) corresponding results from modified ΗΤΙ, caleulations||12].. in both cases compared to the form obtained in $U(3) lattice QCD."," Both approaches have in common To illustrate this, we show in \\ref{Trace} (left) the behavior obtained with the help of a partially non-perturbative $O(g^6)$ \cite{Laine}, , and in \\ref{Trace} (right) corresponding results from modified HTL calculations \cite{HTL}, in both cases compared to the form obtained in $SU(3)$ lattice QCD." + The latter show for e—242 a decrease as L/T?. so that T?.N(T) becomes approximately constant above 7).," The latter show for $\e - 3P$ a decrease as $1/T^2$, so that $T^2 \Delta(T)$ becomes approximately constant above $T_c$." + We see in (right) that in leading (LO) and next-to-leading order (NLO) the breakdown of perturbation theory persists also in a IITL approach. and even the inclusion of a partially non-perturbative NNLO contribution cannot reproduce the lattice result. neither in size nor in functional form.," We see in \\ref{Trace} (right) that in leading (LO) and next-to-leading order (NLO) the breakdown of perturbation theory persists also in a HTL approach, and even the inclusion of a partially non-perturbative NNLO contribution cannot reproduce the lattice result, neither in size nor in functional form." + Such a conclusion had been reached belore. see citeL-Z..," Such a conclusion had been reached before, see \\cite{L-Z}." + Recent studies [15]. have shown that in the case of full QCD with light quark flavors. the cliscrepancy between Lattice data ancl weak-coupling results is reduced. with quite good agreement down to about 2 - 3 T: however. neither the approximate T7 behavior of ACT) in the range Irom T; to about 5 7... nor the sudden drop in the eritical region can be thus obtained.," Recent studies \cite{Strick2} have shown that in the case of full QCD with light quark flavors, the discrepancy between lattice data and weak-coupling results is reduced, with quite good agreement down to about 2 - 3 $T_c$; however, neither the approximate $T^{-2}$ behavior of $\Delta(T)$ in the range from $T_c$ to about 5 $T_c$, nor the sudden drop in the critical region can be thus obtained." + In general. (he breakdown observed in any perturbative treatment as we enter the transition reelon is of course not surprising.," In general, the breakdown observed in any perturbative treatment as we enter the transition region is of course not surprising." + Critical or even pseucdo-critical behavior wilh an increasing correlation range is simply not a perturbative phenomenon., Critical or even pseudo-critical behavior with an increasing correlation range is simply not a perturbative phenomenon. + We therefore have (ο find a non-perturbative approach toaddress (he behavior of (he plasma in (his region., We therefore have to find a non-perturbative approach toaddress the behavior of the plasma in this region. +A multiwavelength color-composite image of the NGC 1512/1510 system is shown in Vie.,A multi-wavelength color-composite image of the NGC 1512/1510 system is shown in Fig. + 11., 11. + The combination of the large-scale delistribution with deep optical ancl CY emission maps is an excellent way to highlight the locations of star formation within the gaseous disk., The combination of the large-scale distribution with deep optical and $UV$ emission maps is an excellent way to highlight the locations of star formation within the gaseous disk. + NGC 1512's cenvelope is four times larger than its ος optical size (sec ‘Table 1) anc about twice as large as the stellar extent measured from. Malin's deep. optical image and from the GALEN CV images., NGC 1512's envelope is four times larger than its $B_{\rm 25}$ optical size (see Table 1) and about twice as large as the stellar extent measured from Malin's deep optical image and from the GALEX $UV$ images. + Calibrated £UCV. 1750A)) and. NEV 2150A)) images are provided by Gil de Paz et al. (, Calibrated $FUV$ ) and $NUV$ ) images are provided by Gil de Paz et al. ( +2007a) as part of theGatlaries.,2007a) as part of the. +. Phe data were obtained on the 29th of December 2003. with an exposure time in both bands of 2380 seconds.," The data were obtained on the 29th of December 2003, with an exposure time in both bands of 2380 seconds." + The CALIEN full of-view is ~1°22 in diuneter. and the pixel size is 1/755.," The GALEX full field-of-view is $\sim$ 2 in diameter, and the pixel size is 5." +" The GALES point-spreacd function in the central 0755 has a EWIIM of —5""..", The GALEX point-spread function in the central 5 has a FWHM of $\sim$. + Figure 12 gives à multi-wavelength view of the GC 1512/1510 svstenmi. shown with high resolution == 700 pc) over the main star-forming disk (similar in size o Fig.," Figure 12 gives a multi-wavelength view of the NGC 1512/1510 system, shown with high resolution = 700 pc) over the main star-forming disk (similar in size to Fig." + 1)., 1). + Our main purpose here is to emphasize how the observed extent ancl distribution of stars and gas depend on 1e tracer., Our main purpose here is to emphasize how the observed extent and distribution of stars and gas depend on the tracer. + The cistribution is by far the largest and extends well bevond 1f area shown here., The distribution is by far the largest and extends well beyond the area shown here. + The GALEN £UCV. and NOV images. ⊳∖↥∪∖∖⊽⊔↓↥⋖⊾↓⋅∢⋅⊳∖⊔↓∪∪↿↓↥⋯⇂∣∪⋜⋯⋜⋯⋏∙≟⊔↓⋜⊔⋅↓⋅∢⊾⊳∖∪↓⋯↓∪⊔∪⇂↓⋅↱≻↦↿↓⋅⋯⇍⋖⊾ . ⋅∕∕ ⊳∖⋜⊔⋅⇂⋅∪↓⋅⊔↓⊲↓⊔⋏∙≟↓⋅⋖⋅⋏∙≟⊀↓∪⊔⊳∖⋯∐↿∪⋜↧↓⋅⋯⇂⊲," The GALEX $FUV$ and $NUV$ images, shown here smoothed to an angular resolution of, trace star forming regions out to a radius of $\sim$." +⋯⊳∖∪⇂⋅∿↓∪↙↦↳∖↓⋜↧∐⊔↼⊳∖∠⇂∢⊾⋖⋅↓≻ ∪≻↿⊲⊔∼⋜↧↓, Malin's deep optical image (see Fig. +⊀↓⊔↓⋜↧⋏∙≟⋖⋅↿∖⊳∖∢⊾⋖⋅↓⊲↝↓⋏∙≟⊳↓⊐⊳∖↓↥∪∖∖⊽⊳, 1) shows a very similar distribution. +∖⋜↧∖⇁∢⊾↓⋅∙∖⇁≻↕↓↥↓↕↓⋜↧↓⋅∠⇂⊲↓⊳∖∣↓⋰↓∣∥∐⊲⊓⋟⊔⋡ We expect that a deep mmosaic would also match this. as hinted at by the faint chains of rregions seen in the rather limited ολα image.," We expect that a deep mosaic would also match this, as hinted at by the faint chains of regions seen in the rather limited SINGG image." + The Spitzer Sjii image allows us to see the inner spiral arms as they connect to the bar. but. detects. no emission in the outer disk.," The Spitzer $\mu$ m image allows us to see the inner spiral arms as they connect to the bar, but detects no emission in the outer disk." + Most obviously missing is à map of the molecular gas in the svstem (e.g. as traced by," Most obviously missing is a map of the molecular gas in the system (e.g., as traced by" +line and again the computed values of the density agree with the constraints inferred. from the line parameters.,line and again the computed values of the density agree with the constraints inferred from the line parameters. + Taken together. these facts strengthen the interpretation of the low state emission in term of an extended source and open the exciting possibility to monitor spectroscopically the clillerent atmospheric components of the disk during the transition [rom the low to the high state.," Taken together, these facts strengthen the interpretation of the low state emission in term of an extended source and open the exciting possibility to monitor spectroscopically the different atmospheric components of the disk during the transition from the low to the high state." + We would like to thank the referee. Arvind Parmar. for a careful reading of the manuscript.," We would like to thank the referee, Arvind Parmar, for a careful reading of the manuscript." + Based. on observations obtained with NMM-Newton. an ESA science mission with instruments and contributions directly. funded. by LSA Alember States and the USA (NASA).," Based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA)." + This paper makes use of quick-Iook results provided by the ASM/BRAXTE team whom we thank., This paper makes use of quick-look results provided by the ASM/RXTE team whom we thank. +trajectories across a sulflicient range of epochs: ii) are located at a larger projected separation from the inner shell boundary. so as to minimize (he possible impact of strong; anisotropic punpineg effects: and. iii) have compact structure and hish SNR.,"trajectories across a sufficient range of epochs; ii) are located at a larger projected separation from the inner shell boundary, so as to minimize the possible impact of strong anisotropic pumping effects; and, iii) have compact structure and high SNR." + In Figure ll we show (his analvsis for a prominent infalline component al the center north of the projected shell. that is visible over epochs," In Figure \ref{fig-pcntr-n} we show this analysis for a prominent infalling component at the center north of the projected shell, that is visible over epochs." +{SS-AIL}.. In Figure 11.. the linear polarization structure of this northern component is shown at the twelve epochs spaced along the trajectory over (nme. using the same composite representation of emission as used in Figures 3. to 9.. but with a more finely-samplec total intensity contour scale. described in further detail in the ligure caption.," In Figure \ref{fig-pcntr-n}, the linear polarization structure of this northern component is shown at the twelve epochs spaced along the trajectory over time, using the same composite representation of linearly-polarized emission as used in Figures \ref{fig-pcntr-3} to \ref{fig-pcntr-9}, but with a more finely-sampled total intensity contour scale, described in further detail in the figure caption." + The outermost epochs of the component trajectory are omitted due to the low SNR. when the component appears and disappears., The outermost epochs of the component trajectory are omitted due to the low SNR when the component appears and disappears. + In common with Figures 3. (0 9.. each panel in Figure 11:38 a zeroth-moment inge over [requency: the pronounced component elongation visible in (hese zeroth-monment component images al several epochs along the trajectory is most readily explained in terms of a velocity gradient along (he elongation major axis.," In common with Figures \ref{fig-pcntr-3} to \ref{fig-pcntr-9}, each panel in Figure \ref{fig-pcntr-n} is a zeroth-moment image over frequency; the pronounced component elongation visible in these zeroth-moment component images at several epochs along the trajectory is most readily explained in terms of a velocity gradient along the elongation major axis." + These velocity gradients are most directly assumed to arise [rom linear acceleration along a three-dimensional component irajectory inclined to the line of sight to the observer., These velocity gradients are most directly assumed to arise from linear acceleration along a three-dimensional component trajectory inclined to the line of sight to the observer. + The weighted-mean component positions. with associated error bars. ave plotted in Figure 12. lor each epoch along the trajectory.," The weighted-mean component positions, with associated error bars, are plotted in Figure \ref{fig-traj-n} for each epoch along the trajectory." + At each component position in this figure. a bold vector of uniform length (over epoch) is drawn at the orientation of the integrated component EVPA.," At each component position in this figure, a bold vector of uniform length (over epoch) is drawn at the orientation of the integrated component EVPA." + A least-squares fit to the component positions. incorporating x- ancl v-errors. was performed using software described by (2006).," A least-squares fit to the component positions, incorporating x- and y-errors, was performed using software described by \citet{weiner06}." +. The fitted mean projected trajectory is extrapolated in Figure 14 across the full diameter of the SiO maser shell at epoch{ZZ}.. here chosen as an epoch near the mid-point of the northern component trajectory shown in Figure 12..," The fitted mean projected trajectory is extrapolated in Figure \ref{fig-nr-n} across the full diameter of the SiO maser shell at epoch, here chosen as an epoch near the mid-point of the northern component trajectory shown in Figure \ref{fig-traj-n}." + Figure 14 shows that the projected component trajectory is non-radial with respect to the likely stellar position relative to the SiO shell distribution: this qualitative asserüion remains valid within the statistical errors of the projected linear [it parameters., Figure \ref{fig-nr-n} shows that the projected component trajectory is non-radial with respect to the likely stellar position relative to the SiO shell distribution; this qualitative assertion remains valid within the statistical errors of the projected linear fit parameters. + If dyvnamicallv-sienifieant eas pressure gradients are 100 present. (hen purely gravitational infall would be radial toward the central star.," If dynamically-significant gas pressure gradients are not present, then purely gravitational infall would be radial toward the central star." + We ote that this component has an EVPA oriented predominantly orthogonal to the projected proper motion vector., We note that this component has an EVPA oriented predominantly orthogonal to the projected proper motion vector. + As noted above. the location of this component is at a significantly arger radius than the inner shell boundary. ancl therefore minimizes the possibility of strong anisotropic pumping ellects.," As noted above, the location of this component is at a significantly larger radius than the inner shell boundary, and therefore minimizes the possibility of strong anisotropic pumping effects." + Over parts of the earlier epoch range(CC-N].. a component is visible approximately 3.25 mas (o the east of the northern component considered here.," Over parts of the earlier epoch range, a component is visible approximately 3.25 mas to the east of the northern component considered here." + This north-eastern component is al a significantly lower SNR. and is not clearly detected in inear polarization at epochs as a result.," This north-eastern component is at a significantly lower SNR, and is not clearly detected in linear polarization at epochs as a result." + Given the proximinity to (he northern component. however. we plot the counterpart of Figure 12. [or this component as Figure 13..," Given the proximinity to the northern component, however, we plot the counterpart of Figure \ref{fig-traj-n} + for this component as Figure \ref{fig-traj-ne}." + This shows the north-eastern component moving outward over these epochs with an EVPA again predominantly orthogonal to the projected proper motion vector., This shows the north-eastern component moving outward over these epochs with an EVPA again predominantly orthogonal to the projected proper motion vector. +(Laming2001α) where @ is (he angle between B and f. Uy=vhg;fmi and Afq*/M is the product of the element abundance. ionization lraction aud charge squared of the particular ious (hat excite (he wave. divided by (their mass in atomic mass units.,"\citep{laming01a} + where $\theta$ is the angle between $\vec{B}$ and $\vec{k}$, $v_{th\perp}=\sqrt{k_{\rm B}T_{i\perp}/m_i}$ and $Afq^2/M$ is the product of the element abundance, ionization fraction and charge squared of the particular ions that excite the wave, divided by their mass in atomic mass units." + Protons are expected to have insulliciently large gvroradii to excite lower-hvbrid waves. and so the [actor Aq?/AL favors a-parlicles over otherminor ions in (lie wave generation.," Protons are expected to have insufficiently large gyroradii to excite lower-hybrid waves, and so the factor $Afq^2/M$ favors $\alpha$ -particles over otherminor ions in the wave generation." + The term —1 in the square brackets represents the ion Landau damping given bv the imaginary part of the expression for v in equation 2., The term $-1$ in the square brackets represents the ion Landau damping given by the imaginary part of the expression for $\omega$ in equation 2. +" Equation 4 is similar to equation (3.20) in Degelnan&Chiueh(1938).. with the identification of their diit velocity vy;=ος,ΩΙ. and in their case w/h<<ο."," Equation 4 is similar to equation (3.20) in \citet{begelman88}, with the identification of their drift velocity $v_{di}= +-v_{th\perp}^2/\Omega _iL$, and in their case $\omega /k << v_{th\perp}$." + Their trealiment vields waves at much higher / (han ours does. since thev consider a single ion distribution drifGne with velocity. vj; producing waves al 72c/c. whereas we (real the effect αἱ a single point of a continuum of different Maxwellians with differing densities (bul otherwise the same) producing waves al &2(weis)(r4/L).," Their treatment yields waves at much higher $k$ than ours does, since they consider a single ion distribution drifting with velocity $v_{di}$ producing waves at $k\simeq\omega/v_{di}$, whereas we treat the effect at a single point of a continuum of different Maxwellians with differing densities (but otherwise the same) producing waves at $k\simeq\left(\omega/v_{th\perp}\right)\left(r_g/L\right)$." + This difference is appropriate in view of the [act that they are interested in plasmas with ion pressure >>> magnetic pressure D electron pressure where (he plasma itself amplifies (he magnetic field.while here we are concerned with magnetic pressure >> ion and electron pressures where (he magnetic field is imposed externally.," This difference is appropriate in view of the fact that they are interested in plasmas with ion pressure $>>$ magnetic pressure $>>$ electron pressure where the plasma itself amplifies the magnetic field,while here we are concerned with magnetic pressure $>>$ ion and electron pressures where the magnetic field is imposed externally." + Degelman&Chiueh(1988) also considered the effects of magnetic curvature., \citet{begelman88} also considered the effects of magnetic curvature. + We assume that the necessary gradients in magnetic field are much less likely (o exist in the low 3 plasma of the solar coronal hole., We assume that the necessary gradients in magnetic field are much less likely to exist in the low $\beta$ plasma of the solar coronal hole. + We find the wavevector fygy. where the growth rate is maximized in the direction perpendicular to. 2 (i.e. 0= 7/2).and the maximum growth rate itself. which is plotted in units of wxAf/q7/M inFigure 2.," We find the wavevector $k_{max}$ where the growth rate is maximized in the direction perpendicular to $\vec{B}$ (i.e. $\theta =\pi /2$ ),and the maximum growth rate itself, which is plotted in units of $\omega\times Afq^2/M$ inFigure 2." +" If the waves are driven to marginal stability ΑνoO,f/o wrg/Lvj. where vj is the perpendicular ion velocity. equation 1 can be written "," If the waves are driven to marginal stability $k_{max}\simeq\Omega_e/v_{e\perp}\simeq\omega r_g/Lv_{i\perp}$ , where $v_{i\perp}$ is the perpendicular ion velocity, equation 1 can be written At saturation where $k_{\perp}v_{e\perp}/\Omega_e\simeq 1$ $I\simeq 1/2$ , and putting $k_{||}/k=\cos\theta$ " +and BOD regions.,and BGD regions. + The correction factor fLE) is the enerey-cdependeut cffective-arca ratio between the SRC and BOD regions., The correction factor $f(E)$ is the energy-dependent effective-area ratio between the SRC and BGD regions. + Using software. we estimated the FCEZ) values for cach NRT as given in Figure L.," Using software, we estimated the $f(E)$ values for each XRT as given in Figure \ref{fig:n11_ratio}." + This estimation also takes iuto account the contaminating material built up on the optical blocking filters of the NIS (Ixoviuua et 22007)., This estimation also takes into account the contaminating material built up on the optical blocking filters of the XIS (Koyama et 2007). + The differences iu the results αλλος the telescopes are mainly due to the scattering of the optical axes of the NRTs (see Figure 8 of Serlomitsos et 22007)., The differences in the results among the telescopes are mainly due to the scattering of the optical axes of the XRTs (see Figure 8 of Serlemitsos et 2007). + The DGD-subtracted. SRC Spectra are shown iu Figure 5., The BGD-subtracted SRC spectra are shown in Figure \ref{fig:n11_diffuse}. + The data from three FIs were combined because thei response characteristics are alinost identical., The data from three FIs were combined because their response characteristics are almost identical. + No significant signal was detected in the euergv baud above ~3 keV. which is cousisteut with the m in Section 3.," No significant signal was detected in the energy band above $\sim$ 3 keV, which is consistent with the result in Section \ref{sssec:n11_suzaku1}." +"3.0,ο ΕΙ μα T QO VIII (70.65 dekeV). Ne EIN (0.91 keV). and Me XI DI keV) were arly separate. indicating a thermal origin of t1ο soft N-ravs."," K-shell emission lines of O VIII $\sim$ 0.65 keV), Ne IX $\sim$ 0.91 keV), and Mg XI $\sim$ 1.34 keV) were clearly separate, indicating a thermal origin of the soft X-rays." + Thus. we fitteLthe spectra with an opticalv thin thermal plasima model (APEC: Suuith et 2200]|.," Thus, we fitted the spectra with an optically thin thermal plasma model (APEC: Smith et 2001)." + The electron (kT) aud emission mecastre (a.V. wherefemmperatins ie. unitingE and Vie the electron aud proton deusities. and the volune. respectively) were treated as free parameters.," The electron temperature $kT_e$ ) and emission measure $n_e n_p V$, where $n_e$, $n_p$, and $V$ are the electron and proton densities, and the emitting volume, respectively) were treated as free parameters." + The clemental abuudances relative to solar values (Anders&Crevesse1989) were fixed to the mean LAIC values of Russell&Dopita(1992).. but the Mg and Si abundances were assumed. to be those of IIuches et (C1998) since the values from RussellDopita(1992) were more uncertain.," The elemental abundances relative to solar values \citep{angr} + were fixed to the mean LMC values of \cite{rd}, but the Mg and Si abundances were assumed to be those of Hughes et (1998) since the values from \cite{rd} were more uncertain." + The iuterstellar extinction iu the Galaxy aud LAIC were separately considered., The interstellar extinction in the Galaxy and LMC were separately considered. +" The Galactic absorption column density with the solar abuudauces was fixed to he Jm"" = [3«TP! ? (Dickey&Lockman1990)...", The Galactic absorption column density with the solar abundances was fixed to be $N_{\rm H}^{\rm G}$ = $4.3\times 10^{20}$ $^{-2}$ \citep{dl}. + The other component jwas a free parameter. with the asstuuption of theNGM LMC inetal abundances.," The other component $N_{\rm H}^{\rm LMC}$ ) was a free parameter, with the assumption of the LMC metal abundances." + In addition. the poiut source model derived in Section ut3.2. was eiven as a fixed component (ith an indepencde absorption coluun).," In addition, the point source model derived in Section \ref{ssec:n11_xmm} was given as a fixed component (with an independent absorption column)." +" This model eave a best fit with AZ, = 0.18 (0.170.19) keV aud = |11/109.", This model gave a best fit with $kT_e$ = 0.18 (0.17–0.19) keV and = 144/109. +" We next allowed the abuudauces of ο, Ne. Meg. and Fe to vary freely (oy using a VAPEC model)."," We next allowed the abundances of O, Ne, Mg, and Fe to vary freely (by using a VAPEC model)." + Then. we obtained a significantly improved fit with 99/105.," Then, we obtained a significantly improved fit with = 99/105." + The best-fit paramecters are eiven in Table 3.., The best-fit parameters are given in Table \ref{tab:fit_n11}. + The Fe abuudance was found to be sliebtlv lower than the mean LAIC value (~0.3 solar: Russell Dopita 1992: IIughes ot 11998)., The Fe abundance was found to be slightly lower than the mean LMC value $\sim$ 0.3 solar: Russell Dopita 1992; Hughes et 1998). + The observed fiux of L9«10DP (in the 0.52.0 keV band) is comparable with the result |ONazóéóetal.(2001). but inconsistent with that of Maddoxetal.(2009) (92.5«100S8 1) though the same data were analvzed.," The observed flux of $4.9 \times 10^{-13}$ (in the 0.5–2.0 keV band) is comparable with the result of \cite{naze04} but inconsistent with that of \cite{m09} $\sim$$2.5 \times 10^{-13}$ ), although the same data were analyzed." + The derived clectron temperature was slightly hüeher than the values in previous reports (~0.2 keV: Dine ot 22001: Nazé et 22001: Maddox et 22009)., The derived electron temperature was slightly higher than the values in previous reports $\sim$ 0.2 keV: Dunne et 2001; Nazé et 2004; Maddox et 2009). + We chmud. however. that the fit with a fixed AT; of 0.2 keV so vielded au acceptable vvalue of 111/106.," We found, however, that the fit with a fixed $kT_e$ of 0.2 keV also yielded an acceptable value of 111/106." + This temperature difference does not severely affect the flux in the hard (2 keV) X-ray baud., This temperature difference does not severely affect the flux in the hard $>$ 2 keV) X-ray band. + A-rav nuages of the N51D region are shown in Figure 6 for the NIS soft N-rav baud(a). the NIS hard N-rav baud (b). aud the EPIC hard X-ray baud (c).," X-ray images of the N51D region are shown in Figure \ref{fig:n51d_image} for the XIS soft X-ray band (a), the XIS hard X-ray band (b), and the EPIC hard X-ray band (c)." + The binuine factors and sinoothing Caussian kernels are same as those used in Figure 1.., The binning factors and smoothing Gaussian kernels are same as those used in Figure \ref{fig:n11_image}. + Similarly to N11. the diffuse structure was ouly observed iu the soft-baud image.," Similarly to N11, the diffuse structure was only observed in the soft-band image." + The bright soft enission is coincident with the OB association LIDS1aud is surrounded by the N51D sshell (see also Figure 1 of Cooper et 22001)., The bright soft emission is coincident with the OB association LH54and is surrounded by the N51D shell (see also Figure 1 of Cooper et 2004). + The SRC region was selectedto be the same as that in Cooperetal.(200 D: an ellipse with major aud minor radi of 5/8 aud Ll. respectively. aud ai s l'-quare.," The SRC region was selectedto be the same as that in \cite{c04}: : an ellipse with major and minor radii of $5.\!'8$ and $4'$ , respectively, and a $4'$$\times$$4'$ -square," +fixed rank.,fixed rank. +" In the case of the clusters, the flux limit forces a changing luminosity limit with redshift, so the ranks will be changing at fixed mass."," In the case of the clusters, the flux limit forces a changing luminosity limit with redshift, so the ranks will be changing at fixed mass." +" If this is not taken into account, a massive cluster at high-z (z~1) will get a much lower rank than a massive cluster at low-z (z~ 0.1)."," If this is not taken into account, a massive cluster at high-z $z\sim1$ ) will get a much lower rank than a massive cluster at low-z $z\sim0.1$ )." +" After ranking, the first step is to fit a rank-mass relation R(M) to the cluster catalog, provided rank, and the matched halo catalog provided mass."," After ranking, the first step is to fit a rank-mass relation $R(M)$ to the cluster catalog, provided rank, and the matched halo catalog provided mass." +" We use the fitting formula This relation has no motivation other than a global fitting function, valid at all redshifts provided that the ranking is performed as described above."," We use the fitting formula This relation has no motivation other than a global fitting function, valid at all redshifts provided that the ranking is performed as described above." +" For our mock catalogs, the best fit parameters for this fitting functionare M,=2.26x 1011, M.=1.40x104, Μο=1.85x 1015. M,=1.85x1014 and a=—1.15."," For our mock catalogs, the best fit parameters for this fitting functionare $M_p=2.26 \times 10^{17}$ , $M_e=1.40 \times 10^{14}$, $M_0=1.85 \times 10^{13}$ , $M_1=1.85 \times 10^{14}$ and $\alpha=-1.15$." + We then invert the relation above to compute an “observed mass” for each cluster and proceed to the matching., We then invert the relation above to compute an “observed mass” for each cluster and proceed to the matching. +" If the proxy used to rank the clusters has a tight correlation with mass, the ranking will be accurate and the observed mass will show a tight correlation with the true mass for the matched pairs."," If the proxy used to rank the clusters has a tight correlation with mass, the ranking will be accurate and the observed mass will show a tight correlation with the true mass for the matched pairs." +" It is important to notice, that the use of ranking instead of observed mass, does not require the mass-observable relation to be calibrated."," It is important to notice, that the use of ranking instead of observed mass, does not require the mass-observable relation to be calibrated." +" Moreover, neither mass information nor the ranking is used in the matching process, which is membership-based."," Moreover, neither mass information nor the ranking is used in the matching process, which is membership-based." + A match takes place if a fraction of member galaxies is shared by a halo-cluster pair., A match takes place if a fraction of member galaxies is shared by a halo-cluster pair. + The best match is the object sharing the largest fraction of galaxies., The best match is the object sharing the largest fraction of galaxies. +" We require unique matching, in which a given halo/cluster is not allowed to be associated with more than one "," We require unique matching, in which a given halo/cluster is not allowed to be associated with more than one cluster/halo." +"As both lists are ranked by number of galaxies, cluster/halo.uniqueness is imposed by eliminating a matched object from the list of available objects for future matches down the list."," As both lists are ranked by number of galaxies, uniqueness is imposed by eliminating a matched object from the list of available objects for future matches down the list." +" We also require two-way matching, where the best matching pair is found when the matching is performed in both directions, halos-to-clusters and clusters-to-halos."," We also require two-way matching, where the best matching pair is found when the matching is performed in both directions, halos-to-clusters and clusters-to-halos." + We note that this approach to cluster-halo matching is quite general and can be applied to any cluster-finding algorithm that produces a list of cluster members., We note that this approach to cluster-halo matching is quite general and can be applied to any cluster-finding algorithm that produces a list of cluster members. + It will be developed in more detail as a framework for comparing different algorithms establishing their usefulness for cosmological tests(?).., It will be developed in more detail as a framework for comparing different algorithms establishing their usefulness for cosmological tests. + Completeness is defined as the fraction of halos having a counterpart in the cluster catalog., Completeness is defined as the fraction of halos having a counterpart in the cluster catalog. + Purity in turn is defined as the fraction of objects in the cluster catalog that correspond to a true halo., Purity in turn is defined as the fraction of objects in the cluster catalog that correspond to a true halo. +" In both cases, only unique two-way matches are considered."," In both cases, only unique two-way matches are considered." +" Allowing for non-unique matching, where each cluster may have more than one matching halo and vice-versa, would be a more permissive approach."," Allowing for non-unique matching, where each cluster may have more than one matching halo and vice-versa, would be a more permissive approach." +" For instance, purity would not be affected by a halo being split in two components and completeness would not be affected by two halos appearing as a single cluster."," For instance, purity would not be affected by a halo being split in two components and completeness would not be affected by two halos appearing as a single cluster." + We count the number of matched objects in bins of mass and redshift., We count the number of matched objects in bins of mass and redshift. +" Therefore, Note that C(M,z) can be computed using the true mass of the halos, being totally independent of the mass proxy used to rank the clusters."," Therefore, Note that $C(M,z)$ can be computed using the true mass of the halos, being totally independent of the mass proxy used to rank the clusters." +" T'he true mass of the clusters, however, is available only for the matched objects."," The true mass of the clusters, however, is available only for the matched objects." +" Therefore P(M,z) has to be computed using the observed mass and does depend on the ranking."," Therefore $P(M,z)$ has to be computed using the observed mass and does depend on the ranking." +" We fit a power law to the Mops—Mierelation from the matched objects and use it to transform the scale in the P(M,z) plots and show both completeness and purity as a function of Mie."," We fit a power law to the $M_{\mathrm{obs}}-M_{\mathrm{true}}$relation from the matched objects and use it to transform the scale in the $P(M,z)$ plots and show both completeness and purity as a function of $M_{\mathrm{true}}$." +" This cannot be performed before the rank-mass relation fitting step, which is part of the matching process."," This cannot be performed before the rank-mass relation fitting step, which is part of the matching process." +" This method allow us to evaluate the efficiency of any cluster finder imposing minimum requirements, namely a list of members for each cluster."," This method allow us to evaluate the efficiency of any cluster finder imposing minimum requirements, namely a list of members for each cluster." + T'he selection function can be defined in terms of completeness and purity as 'This is a simplified definition., The selection function can be defined in terms of completeness and purity as This is a simplified definition. +" For cosmological studies with real data, f(M,z) should be defined and evaluated in likelihood analysis that includes the scatter in the mass-observablea relation after calibration."," For cosmological studies with real data, $f(M,z)$ should be defined and evaluated in a likelihood analysis that includes the scatter in the mass-observable relation after calibration." +" Here, however, we simply want to compare the observed cluster number counts Λους(Μ,2) to the predictions from the ACDM cosmological model "," Here, however, we simply want to compare the observed cluster number counts $N_{obs}(M,z)$ to the predictions from the $\Lambda$ CDM cosmological model $N_{\Lambda{\mathrm{CDM}}}(M,z)$." +"In this case, the selection function is easilyNacpm(M,z). taken into account: 'This comparison allows us to develop a feel for how well we can recover the true cluster number counts using the VT catalog and our ability to perform a cosmological test using VT clusters as a probe."," In this case, the selection function is easily taken into account: This comparison allows us to develop a feel for how well we can recover the true cluster number counts using the VT catalog and our ability to perform a cosmological test using VT clusters as a probe." + The method described above is very simplified with respect to the procedures involved in an actual measurement of the mass function., The method described above is very simplified with respect to the procedures involved in an actual measurement of the mass function. + This would require a measurement of the mass-observable relation and its scatter., This would require a measurement of the mass-observable relation and its scatter. +" We do not perform this because the V'T cluster catalog provides only Ngals, the number of galaxies on the membership list, as a mass proxy."," We do not perform this because the VT cluster catalog provides only Ngals, the number of galaxies on the membership list, as a mass proxy." +" This Ngals was not optimized to have a tight relation with mass, as for example the A estimator of?."," This Ngals was not optimized to have a tight relation with mass, as for example the $\lambda$ estimator of." +. Measuring and optimizing a mass proxy is a necessary step if the VT is to be used in performing cosmological tests., Measuring and optimizing a mass proxy is a necessary step if the VT is to be used in performing cosmological tests. +" But this problem is better addressed by a separate algorithm, specifically designed to provide a calibrated mass proxy including the mean relation and the scatter."," But this problem is better addressed by a separate algorithm, specifically designed to provide a calibrated mass proxy including the mean relation and the scatter." + In Fig., In Fig. + B] we show the completeness and purity as 8 function of mass and redshift for different Gaussian oz values., \ref{comp_pur1} we show the completeness and purity as a function of mass and redshift for different Gaussian $\sigma_z$ values. + The photometric redshift errors have a strong impact on both completeness and purity., The photometric redshift errors have a strong impact on both completeness and purity. +"For oc;= 0.015, completeness lies above for all redshift bins and masses above ~10!*? M.","For $\sigma_z=0.015$ , completeness lies above for all redshift bins and masses above $\sim 10^{13.5}M_{\odot}$ ." +" Purity however, drops"," Purity however, drops" +Based on the scientific aud techuical motivation outlined iu the previous section. the Max-Plauck-Iustitut. fir extraterrestrische Physik (MPEjin Garching. Germany. started in the late 90s the development ο| SPIFFI(SPoectrometer or Iufrared Faiut Ficld huaeiuce). a state of the art adaptive optics assisted near infrared intceral field spectrometer.,"Based on the scientific and technical motivation outlined in the previous section, the Max-Planck-Institut fürr extraterrestrische Physik (MPE) in Garching, Germany, started in the late 90's the development of SPIFFI ectrometer for nfrared aint ield maging), a state of the art adaptive optics assisted near infrared integral field spectrometer." + Because of the ereat success «ff SPIFETs precursor 3D ||... SPIFFI was hought as a travelling mstruneut for several telescopes. includiue the> Calar Alto Observatory. the European Southeru Observatory (ESO) aud he Large Dinocular Telescope (LBT).," Because of the great success of SPIFFI's precursor 3D \cite{weitzel96}, SPIFFI was thought as a travelling instrument for several telescopes, including the Calar Alto Observatory, the European Southern Observatory (ESO) and the Large Binocular Telescope (LBT)." + Iu «xder to keep SPIFFTs dimensions aud weight to its absolute niniiun. we started the evelopiueut of a new image slicor based on flaved fibers 2.," In order to keep SPIFFI's dimensions and weight to its absolute minimum, we started the development of a new image slicer based on flared fibers \cite{tecza98}." + However. given tie very Good collaboration witi ESO on xevious mmstrumoeut projects (SITARP Laud SHARP I)... MPE decked to nuld a VET specific instrumen SPIFFI. ο be assisted with ESO's adaptive optics system NACAO.," However, given the very good collaboration with ESO on previous instrument projects (SHARP I and SHARP II) \cite{hofmann95}, MPE decided to build a VLT specific instrument SPIFFI, to be assisted with ESO's adaptive optics system MACAO." +", This combination of au adaptive ofies system and an oeiteeral field spectrometer is jointlv refered to as SINFONI ! (SINele Faiit Object Near Infrared. Investigation).", This combination of an adaptive optics system and an integral field spectrometer is jointly refered to as SINFONI \cite{thatte98} gle aint bject ear nfrared nvestigation). + From the very beginning. SINFONT was thought to be a fast track iustruneut.," From the very beginning, SINFONI was thought to be a fast track instrument." + First lielit is foreseen in 2002 on VLT T«Τ, First light is foreseen in 2002 on VLT UT3. +ο Since SPIEFI will remain at the VLT. the constraints ou size aud weight have been relaxed. aud a iiürror based inage slicer could be cousidered for SPIEFI again.," Since SPIFFI will remain at the VLT, the constraints on size and weight have been relaxed, and a mirror based image slicer could be considered for SPIFFI again." + Civeu the superior performance of a ΗΤΟΙ based miaege slicer. tje fieht schedule for SPIFFT. aud unexpected delays in the development of the fiber based image slicer. we decided to equip SPIFFI with à mirror slicer. )," Given the superior performance of a mirror based image slicer, the tight schedule for SPIFFI, and unexpected delays in the development of the fiber based image slicer, we decided to equip SPIFFI with a mirror slicer \cite{tecza00}." + SPIFFI records simultaneously the spectra of all 32 x 32 iuage points of a two-dinieusioiil feld of view., SPIFFI records simultaneously the spectra of all 32 x 32 image points of a two-dimensional field of view. + It thus allows spectroscopy of objects with a complex spatial structure. aud will make the most cfBcieu use of observing time compared to alternative 1aging spectroeraphs.," It thus allows spectroscopy of objects with a complex spatial structure, and will make the most efficient use of observing time compared to alternative imaging spectrographs." + Caven the relevance of near iufrarecL spectroscopv for may areas of modern astronomy. SPIEFI will cover the wavelengths of the three atinosplieric bards {1.1 jn - 1.1 n). IL (1.15 jun - 1.55 gr}. and K (195 gan - 2.15 pau). ie. frou 1.1 pan - 2.15 gan. The imstrumeut is ftlly crvogenic. aud will be equipped with zi Us x Us WAWAIL® array from Rockwell.," Given the relevance of near infrared spectroscopy for many areas of modern astronomy, SPIFFI will cover the wavelengths of the three atmospheric bands J (1.1 $\mu$ m - 1.4 $\mu$ m), H (1.45 $\mu$ m - 1.85 $\mu$ m), and K (1.95 $\mu$ m - 2.45 $\mu$ m), i.e. from 1.1 $\mu$ m - 2.45 $\mu$ m. The instrument is fully cryogenic, and will be equipped with an 1k x 1k HAWAII \cite{hodapp96} array from Rockwell." + The image scale of SPIEFI allows both Nyist siuupled imagine at the ditfraction limit of the telescope ( 0.025 arcsec/pixcl). aud sccing lanited observations (0.25 arcsec/pixel).," The image scale of SPIFFI allows both Nyquist sampled imaging at the diffraction limit of the telescope ( 0.025 arcsec/pixel), and seeing limited observations (0.25 arcsec/pixel)." + Au intermediate uaee scale provides a compromise of field size and spatial resolution., An intermediate image scale provides a compromise of field size and spatial resolution. + The spectral resolution of the spectrometer In about LOOO for all three waveleneth bands J. IT. and Wh. which allows detailed kinematic study of galaxies. aud at he same time an effective OIT-avoidauce of the atmospheric emission lines in the NIR.," The spectral resolution of the spectrometer is about 4000 for all three wavelength bands J, H, and K, which allows detailed kinematic study of galaxies, and at the same time an effective OH-avoidance of the atmospheric emission lines in the NIR." + A inore moderate resolution R ~-- 2000 is implemented. too. for objects that are too faint for Ligh resolution spectroscopy. covering IT I& sinitaucouslv.," A more moderate resolution R $\approx$ 2000 is implemented, too, for objects that are too faint for high resolution spectroscopy, covering H K simultaneously." + The optics is desigued for eratines with a resolution of up to 1000. which may be inteerated in future 1peraces of SPIFFI.," The optics is designed for gratings with a resolution of up to 10000, which may be integrated in future upgrades of SPIFFI." + Figure 1. shows a perspective view of the main componcits of SPIFFI., Figure \ref{assembly_perspective_bw} shows a perspective view of the main components of SPIFFI. + The SPIFFT iuteeral ek spectrometer will cousist of three basic components: (a) Preoptics: The Preoptics reimage the object plane from the adaptive optics outo the inage slicer. providing the differeut pixel scales.," The SPIFFI integral field spectrometer will consist of three basic components: (a) Preoptics: The Preoptics reimage the object plane from the adaptive optics onto the image slicer, providing the different pixel scales." + In addijou. a cold stop at the interiiediate 1pil position will allow efficieut suppression of the thermal backerouucd.," In addition, a cold stop at the intermediate pupil position will allow efficient suppression of the thermal background." + The pre optics will also lost broad bau filters for selecting the wavelength range. (, The pre optics will also host broad band filters for selecting the wavelength range. ( +b) Tnage slicer: The iuage slicer cuts tjo two dimensional field iuto a set of 32 individual slitlets. and rearranges them to a one-dimensional pseudo long sli.,"b) Image slicer: The image slicer cuts the two dimensional field into a set of 32 individual slitlets, and rearranges them to a one-dimensional pseudo long slit." + This nage slicing is done by a set ο: 61 plane mirrors. (, This image slicing is done by a set of 64 plane mirrors. ( +ο) Spectrometer: The spectrometer reinages the pseudo loue slit from the image slicer ono the detector.,c) Spectrometer: The spectrometer reimages the pseudo long slit from the image slicer onto the detector. + The gratiugs are located at the iuteriuediate pupil position., The gratings are located at the intermediate pupil position. + Iu. addition. aso called Ποας (sky spider) at the cutrance of the iustruinent will allow the observation of tjo sky backerouud simultaneous with he astronomical target.," In addition, a so called ""Himmelsspinne"" (sky spider) at the entrance of the instrument will allow the observation of the sky background simultaneous with the astronomical target." + Figure 2 shows a schematic view of the SPIFFI optics., Figure \ref{assembly_top} shows a schematic view of the SPIFFI optics. + The preoptics reiiiage the foca plane of the adaptive optics outo the image slicer., The preoptics reimage the focal plane of the adaptive optics onto the image slicer. + It consists of a fixed. collimator. a filter wheel. aud an optic wheel.," It consists of a fixed collimator, a filter wheel, and an optic wheel." + The preoptics provide three differcut magnifications (17.5 x. Ls x. 1.78 x) with equivalent pixel scales of 0.025 :wesecpixel. 0.1 arcsecpixel. and 0.25 arcesec/pixel.," The preoptics provide three different magnifications (17.8 x, 4.45 x, 1.78 x) with equivalent pixel scales of 0.025 arcsec/pixel, 0.1 arcsec/pixel, and 0.25 arcsec/pixel." + Tu addition. a pupil inagiug lens will allow for an accurate aliguucut of SPIFFIs optical axis with the telescope / adaptive optics.," In addition, a pupil imaging lens will allow for an accurate alignment of SPIFFI's optical axis with the telescope / adaptive optics." + Figure 3. shows the preoptics with the three imaging lenses., Figure \ref{preoptic} shows the preoptics with the three imaging lenses. +"Vs=500GeV near y= +1, AZ(W*)~Au/u and Ar""(W-)~Ad/d, evaluated at x= 0.435.","$\sqrt s = 500\mbox{GeV}$ near $y=+1$ , $A_{L}^{PV}(W^+) \sim \Delta u /u$ and $A_{L}^{PV}(W^-) \sim \Delta d /d$, evaluated at $x=0.435$ ." +" Similarly for near y=—1, AZ""(W*)~—Ad/d and AZ""(W-)e—Aa/a, evaluated at x—0.059. 'The features appear clearly on the left hand side of Fig."," Similarly for near $y=-1$, $A_{L}^{PV}(W^+) \sim -\Delta \bar d /\bar d$ and $A_{L}^{PV}(W^-) \sim -\Delta \bar u /\bar u$, evaluated at $x=0.059$ The features appear clearly on the left hand side of Fig." +" 4, where the calculations were done at two different energies."," 4, where the calculations were done at two different energies." + For completeness we also show the predicted AP’(2) on the right hand side of Fig., For completeness we also show the predicted $A_{L}^{PV}(Z)$ on the right hand side of Fig. +" 4, but in this case the interpretation is not so straightforward."," 4, but in this case the interpretation is not so straightforward." + Moreover the production rateof Z'sis much lower than Ws. , Moreover the production rateof $Z$ 'sis much lower than $W$ +into account. their total stellar ages could be made consistent with the age of the halo.,"into account, their total stellar ages could be made consistent with the age of the halo." + This stresses (he importance of reducing the size of the parallax measurements through the use of modern CCD techniques. such as those currently being obtained at the USNO.," This stresses the importance of reducing the size of the parallax measurements through the use of modern CCD techniques, such as those currently being obtained at the USNO." + If the values of the trigonometric parallax measurements for LIIS 147 and LIIS 542 are confirmed. these (wo white dwarls could indeed be verv voung according to our results.," If the values of the trigonometric parallax measurements for LHS 147 and LHS 542 are confirmed, these two white dwarfs could indeed be very young according to our results." + This conclusion seems to be independent of the particular choice of the initial-Dfinal mass relation adopted here since both stars have inferred masses nearly 0.1. aabove the upper limit of 0.55 {for the white dwarls currently being formed in globular clusters. and presumably in the ealactic halo as well.," This conclusion seems to be independent of the particular choice of the initial-final mass relation adopted here since both stars have inferred masses nearly 0.1 above the upper limit of 0.55 for the white dwarfs currently being formed in globular clusters, and presumably in the galactic halo as well." + In (his paper. we have demonstrated the importance of determining{οἱ stellar ages in order to associate anv white dwarf with a given population.," In this paper, we have demonstrated the importance of determining stellar ages in order to associate any white dwarf with a given population." + This can only be accomplished through a precise mass determination. which for cool white dwarls require accurate Wigonomelric parallax measurements.," This can only be accomplished through a precise mass determination, which for cool white dwarfs require accurate trigonometric parallax measurements." + Even though it is not possible to conclude at Chis stage that any white cwarf in the OILDIIS sample is too voung to belong to the halo population. with the elarine exception of LIIS 4033. modern parallax measurements for al least. two white dwarfs. LIIS 147 and LIIS 542. seem to indicate that voung white dwarls with halo kinematics do exist.," Even though it is not possible to conclude at this stage that any white dwarf in the OHDHS sample is too young to belong to the halo population, with the glaring exception of LHS 4033, modern parallax measurements for at least two white dwarfs, LHS 147 and LHS 542, seem to indicate that young white dwarfs with halo kinematics do exist." + The possibility that that voung high velocity white dwarfs. most likely associated with the voung disk. might exist is intriguing.," The possibility that that young high velocity white dwarfs, most likely associated with the young disk, might exist is intriguing." + Dergeron(2003) summarized some physical mechanisms proposed in the literature that could produce these voune high-velocity white dwarls., \citet{ber03} summarized some physical mechanisms proposed in the literature that could produce these young high-velocity white dwarfs. + These include remnants of donor stars from close mass-transfer binaries (hat produced (vpe Ia supernovae via (he single degenerate channel (Hansen2002).. or other alternative mechanisnis by which stars can be ejected from the thin disk into the galactic halo with the required hieh velocities.," These include remnants of donor stars from close mass-transfer binaries that produced type Ia supernovae via the single degenerate channel \citep{hansen02}, or other alternative mechanisms by which stars can be ejected from the thin disk into the galactic halo with the required high velocities." + The other white dwarl stars in the OIIDIIS sample are fairly wari. and the onlv wav they could be associated with the halo population is to have stellar masses near ~0.51M... in which case they. can indeed be very old.," The other white dwarf stars in the OHDHS sample are fairly warm, and the only way they could be associated with the halo population is to have stellar masses near $\sim 0.51$, in which case they can indeed be very old." + Trigonometric parallaxes will hopefully become available lor all stars from this sample in (he near future., Trigonometric parallaxes will hopefully become available for all stars from this sample in the near future. + The two most likely halo candidates in the OIIDIIS sample are F351—50 and WD 0351—564 (the two objects at the bottom of Fig., The two most likely halo candidates in the OHDHS sample are $-$ 50 and WD $-$ 564 (the two objects at the bottom of Fig. + 6 and also labeled in Fig. 8))., \ref{fg:f6} and also labeled in Fig. \ref{fg:f8}) ). +" They correspond to the (vo coolest objects in Figure 9 with Cia,200 ((the (wo rightmost filled circles at the bottom of the figure).", They correspond to the two coolest objects in Figure \ref{fg:f9} with $\vtan>200$ (the two rightmost filled circles at the bottom of the figure). + Masses below 0.6 wwould vield total stellar ages above 11 Gyr., Masses below 0.6 would yield total stellar ages above 11 Gyr. +ionization parameter. the ability for shocked σας to cool would be compromised.,"ionization parameter, the ability for shocked gas to cool would be compromised." + This is shown in Fig. 9..," This is shown in Fig. \ref{fig:nw6_highip}," + where a rellant is expanding iuto a stationary medium with =z1500 E is LOs higher than in Fies., where a remnant is expanding into a stationary medium with $\Xi \approx 1500$ $\Xi$ is 10x higher than in Figs. + 2. aud 3))., \ref{fig:nw6_rho} and \ref{fig:nw6_temp}) ). + The iicreased: photon fiux. from the AGN increases the rate of Compton heating. aud leads to a reduction iu the uet coolLBic rate.," The increased photon flux from the AGN increases the rate of Compton heating, and leads to a reduction in the net cooling rate." + While the radius of the roiinaut is largely ποσαreed. its inorphology is affected: the shocked eas is not coupressec as mach. aud cool clouds do not form.," While the radius of the remnant is largely unchanged, its morphology is affected: the shocked gas is not compressed as much, and cool clouds do not form." + This behaviour is consistent with the earlier work prescuted iu Dittird (2001))., This behaviour is consistent with the earlier work presented in Pittard \cite{PDFH2001}) ). + To investigate whether cool clouds could form in a remnant frou a type Ian SN explosion. we have computed an additional model with appropriate parameters: E=10 eve. M.=LAA... aud à=7 Chevalier 1982)).," To investigate whether cool clouds could form in a remnant from a type Ia SN explosion, we have computed an additional model with appropriate parameters: $E = 10^{51} \erg$ , $M = 1.4 \Msol$, and $n = 7$ Chevalier \cite{C1982}) )." + The main difference with this model is that the increased, The main difference with this model is that the increased +the possible recvcling mechanisms.,the possible recycling mechanisms. + In the case of GCs. it also represents a crucial (ool for quanlilvine the occurrence of dynamical interactions. understanding the effects of crowded stellar environments on the evolution of binaries. determining (he shape of the GC potential well. and estimating the mass-to-light ratio in the GC cores (e.g.. Phinney 1992: Possenti el al.," In the case of GCs, it also represents a crucial tool for quantifying the occurrence of dynamical interactions, understanding the effects of crowded stellar environments on the evolution of binaries, determining the shape of the GC potential well, and estimating the mass-to-light ratio in the GC cores (e.g., Phinney 1992; Possenti et al." + 2003: Ferraro et al., 2003; Ferraro et al. + 20032)., 2003a). + Despite their importance. up lo now only six optical counterparts to MSP companions have been identified in five GCs.," Despite their importance, up to now only six optical counterparts to MSP companions have been identified in five GCs." + In the colour-magnitude diagram (CAID) three of them have positions consistent wilh the cooling sequences of helium. WDs. in agreement with the expectations of the MSP recvcling scenario.," In the colour-magnitude diagram (CMD) three of them have positions consistent with the cooling sequences of helium WDs, in agreement with the expectations of the MSP recycling scenario." + These are (he companions to. MSP-U in 47 Tucanae (Edmonds et al., These are the companions to MSP-U in 47 Tucanae (Edmonds et al. + 2001): MSP-À in NGC 6752 (Ferraro et al., 2001); MSP-A in NGC 6752 (Ferraro et al. + 20035). and PSR B1620-26 in M4 (Sigurdsson et al.," 2003b), and PSR B1620-26 in M4 (Sigurdsson et al." + 2003)., 2003). + The other identified companions show. instead. quite peculiar properties.," The other identified companions show, instead, quite peculiar properties." + The luminosity and colours of the optical companion to MSP-À in NGC 6397 are totally incompatible with those of a WD., The luminosity and colours of the optical companion to MSP-A in NGC 6397 are totally incompatible with those of a WD. + This is a relatively bright. tidally deformed star. suggesting that the svstem either harbours a newly born MSP. or is the result of an exchange interaction (Ferraro et al.," This is a relatively bright, tidally deformed star, suggesting that the system either harbours a newly born MSP, or is the result of an exchange interaction (Ferraro et al." + 2001b)., 2001b). + The companion star to MSP-D in NGC 6266 is a similarly bright object. with Iuninositv comparable to the cluster main sequence (AIS) (urn-olf. an anomalous red colour and optical variability suggestive of a tidallv. deformed star which filled its Roche Lobe (Cocozza et al.," The companion star to MSP-B in NGC 6266 is a similarly bright object, with luminosity comparable to the cluster main sequence (MS) turn-off, an anomalous red colour and optical variability suggestive of a tidally deformed star which filled its Roche Lobe (Cocozza et al." + 2008)., 2008). + This object is also a Chandra: X-ray source. (hus supporting the hypothesis that some interaction is occurring between (he pulsar wind and the eas streaming olf the companion.," This object is also a Chandra X-ray source, thus supporting the hypothesis that some interaction is occurring between the pulsar wind and the gas streaming off the companion." + Finally the companion to MSP-W in 47 Tuc has been identified to be a [aint MIS star. showing large-anplitude. sinusoidal huminosity variations probably due to the heating effect of the pulsar (Edmonds et al.," Finally the companion to MSP-W in 47 Tuc has been identified to be a faint MS star, showing large-amplitude, sinusoidal luminosity variations probably due to the heating effect of the pulsar (Edmonds et al." + 2002)., 2002). + As à part of a project aimed to perform a svstematie search for optical companions to binary AISPs in GCs (see Ferraro et al., As a part of a project aimed to perform a systematic search for optical companions to binary MSPs in GCs (see Ferraro et al. + 2001b. Ferraro et al.," 2001b, Ferraro et al." + 2003b. Cocozza et al.," 2003b, Cocozza et al." + 2003). here we focus our attention on M28 (NGC 6626).," 2008), here we focus our attention on M28 (NGC 6626)." + M23 is a Galactic GC with intermediate central density (logpj=4.9 in units of AZ. /pc*: Prvor Mevlan 1993)., M28 is a Galactic GC with intermediate central density $\log \rho_0=4.9$ in units of $M_\odot/$ $^3$; Pryor Meylan 1993). + It is the first GC where a MSP was discovered (Lvne et al., It is the first GC where a MSP was discovered (Lyne et al. + 1937) and to date it is known (to harbour a total of twelve pulsars (Béeein 2006)., 1987) and to date it is known to harbour a total of twelve pulsars (Béggin 2006). + This is the third largest population of known pulsars in GC's. alter (hat of Terzan 5 (with 33 objects: Ransom et al.," This is the third largest population of known pulsars in GCs, after that of Terzan 5 (with 33 objects; Ransom et al." + 2005. but see the recent results by Ferraro et al.," 2005, but see the recent results by Ferraro et al." + 2009b ancl Lanzoni et al., 2009b and Lanzoni et al. + 2010. suggesting that Terzan 5 is not a genuine GC) and that of 47 Tue (with 23 MSPs: Camilo et al.," 2010, suggesting that Terzan 5 is not a genuine GC) and that of 47 Tuc (with 23 MSPs; Camilo et al." + 2000: Freire οἱ al., 2000; Freire et al. +" Among the binary MSPs harboured in M28. J1824-24521I (hereafter. M28II) deserves special attention since il is an eclipsing svstem showing a number of timing, irregularities. possibly due to the tidal elfect on the companion star (Bégein 2006: Stairs et. al."," Among the binary MSPs harboured in M28, J1824-2452H (hereafter M28H) deserves special attention since it is an eclipsing system showing a number of timing irregularities, possibly due to the tidal effect on the companion star (Béggin 2006; Stairs et al." + 2006)., 2006). + I1, It +between the maximum (367 for Sr) and a tenth of that is indicated in yellow with the medium marked by a dotted line.,between the maximum (367 for Sr) and a tenth of that is indicated in yellow with the medium marked by a dotted line. + The total ejecta mass is taken to be the sum of the ejected mass from the core and the outer H/He-envelope (=8.8M—1.38Mo+0.01147.43 Mo).," The total ejecta mass is taken to be the sum of the ejected mass from the core and the outer H/He-envelope $= 8.8\,M_\odot - 1.38\,M_\odot + 0.0114\,M_\odot= +7.43\,M_\odot$ )." +" Note that the N=50 species, factors*9Kr, ®’Rb, isotopesΜο*5Sr,= and °°Zr, valueshave the largest production for with of 610, 414, 442, and 564, respectively."," Note that the $N=50$ species, $^{86}$ Kr, $^{87}$ Rb, $^{88}$ Sr, and $^{90}$ Zr, have the largest production factors for with values of 610, 414, 442, and 564, respectively." +" As discussed by Wanajoetal.(2009),, in the 1D case only Zn and Zr are on the normalization band, although some light p-nuclei (up to ??Mo) can be sizably produced."," As discussed by \citet{Wana2009}, in the 1D case only Zn and Zr are on the normalization band, although some light p-nuclei (up to $^{92}$ Mo) can be sizably produced." +" In contrast, we find that all elements between Zn and Zr, except for Ga, fall into this band in the 2D case (Ge is marginal), although all others are almost equally produced in 1D and 2D. This suggests ECSNe to be likely sources of Zn, Ge, As, Se, Br, Kr, Rb, Sr, Y, and Zr, in the Galaxy."," In contrast, we find that all elements between Zn and Zr, except for Ga, fall into this band in the 2D case (Ge is marginal), although all others are almost equally produced in 1D and 2D. This suggests ECSNe to be likely sources of Zn, Ge, As, Se, Br, Kr, Rb, Sr, Y, and Zr, in the Galaxy." +" Note that the origin of these elements is not fully understood, although Sr, Y, and Zr in the solar system are considered to be dominantly made by the s-process."," Note that the origin of these elements is not fully understood, although Sr, Y, and Zr in the solar system are considered to be dominantly made by the s-process." + The ejected masses of °°Ni 3.0x107? Mo) and all Fe (3.1x107? Ma) are the (—?9Fe;same as in the 1D case (2.5x107?2009).," The ejected masses of $^{56}$ Ni $\to ^{56}$ Fe; $3.0 \times 10^{-3}\,M_\odot$ ) and all Fe $3.1 \times 10^{-3}\,M_\odot$ ) are the same as in the 1D case \citep[$2.5 \times 10^{-3}." +" The fact that oxygen is absent in ECSN ejecta but a dominant product of more massive CCSNe, can pose a constraint on the frequency of ECSNe (Wanajoetal. 2009)."," The fact that oxygen is absent in ECSN ejecta but a dominant product of more massive CCSNe, can pose a constraint on the frequency of ECSNe \citep{Wana2009}." +". Considering the isotope 99Kr with its largest production factor in our 2D model and assuming f to be the fraction of ECSNe relative to all CCSNe, one gets where Xo(®°Kr)=2.4x107? and X$(1$0) are the mass fractions in the solar system (Lodders 2003), M(®6Kr)=1.1x107Ms is our ejecta mass of 6Kr, and Masgc(1$O)=1.5Μα the production of 160) by all other CCSNe, averaged over the stellar initial mass function between 13Mc, and 40Me (seeWanajoetal.2009;Nomoto 2006)."," Considering the isotope $^{86}$ Kr with its largest production factor in our 2D model and assuming $f$ to be the fraction of ECSNe relative to all CCSNe, one gets where $X_\odot(^{86}\mathrm{Kr}) = 2.4 \times 10^{-8}$ and $X_\odot(^{16}\mathrm{O}) = 6.6 \times 10^{-3}$ are the mass fractions in the solar system \citep{Lodd2003}, $M(^{86}\mathrm{Kr}) = 1.1 \times +10^{-4}\,M_\odot$ is our ejecta mass of $^{86}$ Kr, and $M_\mathrm{noEC}(^{16}\mathrm{O}) = 1.5\,M_\odot$ the production of $^{16}$ O by all other CCSNe, averaged over the stellar initial mass function between $13\,M_\odot$ and $40\,M_\odot$ \citep[see][]{Wana2009, +Nomo2006}." +. Equation (1) leads to f—0.048., Equation (1) leads to $f = 0.048$. +" The frequency of ECSNe relative to all CCSNe is thus ~4%,, assuming that all Kr in the solar system except for a possible contribution from the s-process (18%,Arlandinietal.1999),, originates from ECSNe."," The frequency of ECSNe relative to all CCSNe is thus $\sim$, assuming that all $^{86}$ Kr in the solar system except for a possible contribution from the s-process \citep[18\%,][]{Arla1999}, originates from ECSNe." +" This is in good agreement with the prediction from a recent synthetic model of SAGB stars (forsolarmetallicitymodels,Poelarendsetal. 2008).."," This is in good agreement with the prediction from a recent synthetic model of SAGB stars \citep[for solar +metallicity models,][]{Poel2008}." + The remarkable difference between the 1D and 2D cases (Fig. 3)), The remarkable difference between the 1D and 2D cases (Fig. \ref{fig:ECSNyields}) ) + can be understood by the element formation in nuclear (quasi-)eqilibrium., can be understood by the element formation in nuclear (quasi-)eqilibrium. +" Representative for all elements in the normalization band of Fig. 3,,"," Representative for all elements in the normalization band of Fig. \ref{fig:ECSNyields}," +" the final mass fractions of the isotopes 9Zn, “Ge, ®°Se, 84Kr, 558r, and 9?Zr (accountingfordominantfractionsof49%,ementsinthesolarsystem,Lodders2003) are displayed for all tracer trajectories in Fig. 4.."," the final mass fractions of the isotopes $^{64}$ Zn, $^{74}$ Ge, $^{80}$ Se, $^{84}$ Kr, $^{88}$ Sr, and $^{90}$ Zr \citep[accounting for dominant fractions of +49\%, 36\%, 50\%, 57\%, 82\%, and 51\%, respectively, of their +elements in the solar system,][]{Lodd2003} are displayed for all tracer trajectories in Fig. \ref{fig:massfractions}." + Nuclear quasi-equilibrium (QSE) makes nuclei heavier than the Fe-group up to A~90 (Meyeretal..1998)., Nuclear quasi-equilibrium (QSE) makes nuclei heavier than the Fe-group up to $A \sim 90$ \citep{Meye1998}. +". 9475, where888r, and 9°Zr are thus produced at Y,=0.43- calculations) the a-concentration (at the end of the is X(4He)= 0.001-0.1."," $^{64}$ Zn, $^{88}$ Sr, and $^{90}$ Zr are thus produced at $Y_\mathrm{e} = 0.43$ --0.49, where the $\alpha$ -concentration (at the end of the calculations) is $X(^4\mathrm{He}) = 0.001$ –0.1." +" The QSE with abundant a particles, however, is known to leave a deep trough in the abundance curve between A ~60 and 90 because of the strong binding at N—28 and 50."," The QSE with abundant $\alpha$ particles, however, is known to leave a deep trough in the abundance curve between $A\sim$ 60 and 90 because of the strong binding at $N = +28$ and 50." +" This explains the substantial underproduction of elements around Z «33-37 in the 1D case (Fig. 3,,"," This explains the substantial underproduction of elements around $Z \sim$ 33–37 in the 1D case (Fig. \ref{fig:ECSNyields}," + blue line)., blue line). +" As the a-concentration becomes small, QSE asymptotes to nuclear statistical equilibrium (NSE)."," As the $\alpha$ -concentration becomes small, QSE asymptotes to nuclear statistical equilibrium (NSE)." +" Since NSE with neutron excess (Y.ην~ 0.4) leads to nuclei heavier than the Fe-group up to 84 (Hartmannetal. 1985),, the trough can be filled by NSE-abundances assembledin the n-rich ejecta lumps."," Since NSE with neutron excess $Y_\mathrm{e} \sim 0.4$ ) leads to nuclei heavier than the Fe-group up to $A \approx 84$ \citep{Hart1985}, the trough can be filled by NSE-abundances assembled in the n-rich ejecta lumps." +" The small X(*He) (< 107?) at Y,~ 0.40-0.42 (Fig. 4))", The small $X(^4{\mathrm{He}})$ $< 10^{-5}$ ) at $Y_\mathrm{e} \sim 0.40$ –0.42 (Fig. \ref{fig:massfractions}) ) + is indicative of the consumption of almost all o-particles before freeze-out from NSE., is indicative of the consumption of almost all $\alpha$ -particles before freeze-out from NSE. +" Accordingly, QSE asymptotes to NSE in this Y.-range and yields substantial amounts of Ge, ®°Se, and 9Kr (made as “Zn, ®°Ge, and 5496), nuclei that cannot be created in a-rich QSE."," Accordingly, QSE asymptotes to NSE in this $Y_\mathrm{e}$ -range and yields substantial amounts of $^{74}$ Ge, $^{80}$ Se, and $^{84}$ Kr (made as $^{74}$ Zn, $^{80}$ Ge, and $^{84}$ Se), nuclei that cannot be created in $\alpha$ -rich QSE." + A similar result can be seen in the QSE study by Meyeretal.(1998) with entropies and Y;-values close to ours here (see Fig., A similar result can be seen in the QSE study by \citet{Meye1998} with entropies and $Y_\mathrm{e}$ -values close to ours here (see Fig. + 14 in their In the, 14 in their paper). + paper).n-rich ejecta lumps NSE a-deficient QSE) conditions are established for several (orreasons., In the n-rich ejecta lumps NSE (or $\alpha$ -deficient QSE) conditions are established for several reasons. + They have smaller entropies (s~ 13-15kg per baryon) than the," They have smaller entropies $s +\approx 13$ $15\,k_\mathrm{B}$ per baryon) than the" +and for £27rs defined as in $3.1: Not only is the shape (A) different in the two domains. their evolution with «à is also different.,"and for $R > r_{-2}$ defined as in 3.1: Not only is the shape $\lambda$ ) different in the two domains, their evolution with $\alpha$ is also different." + Nevertheless. this result can be useful in obtaining an estimate of the shape of projected Einasto profile in these two domains demarcated by +».," Nevertheless, this result can be useful in obtaining an estimate of the shape of projected Einasto profile in these two domains demarcated by $r_{-2}$." + The X model. with errors <0.5'4 does not face any of the above issues.," The $\Sigma_E$ model, with errors $< 0.5 \%$ does not face any of the above issues." + Further. unlike the Sersie profile. the Xe model can predict the central density with almost 0% errors due to the existence of an analytical solution.," Further, unlike the Sersic profile, the $\Sigma_E$ model can predict the central density with almost $0 \%$ errors due to the existence of an analytical solution." + Thus. if the underlying 3D distribution is Einasto-like. the 2D distribution should be modeled with Xe.," Thus, if the underlying 3D distribution is Einasto-like, the 2D distribution should be modeled with $\Sigma_E$." + The “ie model is not just a good description of the projected Einasto profile but is also expressed in terms of the 3D Einasto profile parameters., The $\Sigma_E$ model is not just a good description of the projected Einasto profile but is also expressed in terms of the 3D Einasto profile parameters. +" It should thus be possible to recover the 3D parameters (a.r.».p. 2) from fits to 2D distributions that subscribe to an underlying 3D Einasto-like system,"," It should thus be possible to recover the 3D parameters $\alpha, r_{-2}, \rho_{-2}$ ) from fits to 2D distributions that subscribe to an underlying 3D Einasto-like system." + For the wide family of numerically projected Einasto profiles Mv deseribed in this paper. we could recover the 3D parameters for all of them with an accuracy of ~10. ου better. by fitting Xv with and the parametrizations of and through a non-linear least squares Levenberg-Marquardt algorithm.," For the wide family of numerically projected Einasto profiles $\Sigma_N$ described in this paper, we could recover the 3D parameters for all of them with an accuracy of $\sim 10^{-3}$ or better, by fitting $\Sigma_N$ with and the parametrizations of and through a non-linear least squares Levenberg-Marquardt algorithm." + Given that. as of now robust data (within virialized regions) from N-body simulations are in the domain tie to Pou. the fits were performed in this domain.," Given that, as of now robust data (within virialized regions) from N-body simulations are in the domain $r_{conv}$ to $r_{200}$, the fits were performed in this domain." + In passing. we note that our results are even better," In passing, we note that our results are even better" +ab which the magnetic field may be very strong (Rosenau&FrankenthalPohl2004).,"at which the magnetic field may be very strong \citep{Rosenau76,lp04}." +. It is well known that the contact discontinuity is hyelrocwuamically unstable (e.g.Dlondin&Ellison2001).. and so in projection it will appear as an extended feature with a turbulent field structure.," It is well known that the contact discontinuity is hydrodynamically unstable \citep[e.g.][]{be01}, and so in projection it will appear as an extended feature with a turbulent field structure." + Also. if the SNR efficiently accelerates cosmic rays. the contact cliscontinuity will be closer to the Forward shock (han in a purely hydrodvnamical SNR.," Also, if the SNR efficiently accelerates cosmic rays, the contact discontinuity will be closer to the forward shock than in a purely hydrodynamical SNR." + Using X-ray measurements. Warrenetal.(2005) on average find traces of the contact discontinuitv in Tvcho's SNR out to of the projected radius of the forward shock.," Using X-ray measurements, \citet{warren} on average find traces of the contact discontinuity in Tycho's SNR out to of the projected radius of the forward shock." + use the same technique on data of the remnant of SN 1006 and find Chat in the regions of bright non-thermal X-ray emission the contact discontinuitv extends all the wav to the Forward shock., \citet{cc08} use the same technique on data of the remnant of SN 1006 and find that in the regions of bright non-thermal X-ray emission the contact discontinuity extends all the way to the forward shock. + In both remnants the proximity of forward shock and the contact discontinuitv presumably arises from a combination of hydrodynamical instabilities of the contact discontinity and structural modifications on account of cosmic-ray acceleration., In both remnants the proximity of forward shock and the contact discontinuity presumably arises from a combination of hydrodynamical instabilities of the contact discontinuity and structural modifications on account of cosmic-ray acceleration. + In anv case. in SN 1006 we may not find a line of sight that is clearly inside the forward shock but outside the contact discontinuityv.," In any case, in SN 1006 we may not find a line of sight that is clearly inside the forward shock but outside the contact discontinuity." + For Tvchos SNR. radio-polarimetry data are required wilh an angular resolution around of the angular radius. so the forward shock and the contact discontinuityv areal least a lew beamwidth apart.," For Tycho's SNR radio-polarimetry data are required with an angular resolution around of the angular radius, so the forward shock and the contact discontinuity areat least a few beamwidth apart." + DeLanevetal.(2002) observed the polarized svuchrotron emission from Keplers SNR αἱ 6 em and 20 em wavelength., \citet{del02} observed the polarized synchrotron emission from Kepler's SNR at 6 cm and 20 cm wavelength. + After rotating the measured electric polarization by 90°. they found predominantly radial magnetic polarization in the outer regions of the remnant. where the degree of polarization was a few per cent at 6 cm and less (han that at 20 cm.," After rotating the measured electric polarization by $90^\circ$, they found predominantly radial magnetic polarization in the outer regions of the remnant, where the degree of polarization was a few per cent at 6 cm and less than that at 20 cm." + The angular resolution is moderate. though. and the beam size is about of the projected radius of the forward shock.," The angular resolution is moderate, though, and the beam size is about of the projected radius of the forward shock." + This is a factor of 100 worse than the beamsize assumed [or the figures in this paper. and a direct comparison is therefore diffieult.," This is a factor of 100 worse than the beamsize assumed for the figures in this paper, and a direct comparison is therefore difficult." + Also. the contact cliscontinuity and the forward shock are not clearly separated at this resolution. ancl so any inferred. field orientation and turbulence level cannot be unambiguously associated with the magnetic-field structure directly behind the forward shock.," Also, the contact discontinuity and the forward shock are not clearly separated at this resolution, and so any inferred field orientation and turbulence level cannot be unambiguously associated with the magnetic-field structure directly behind the forward shock." + Dickeletal.(1991) presented radio polarimetry data of Tvchos SNB. at 6 cm and 20 em wavelength., \citet{di91} presented radio polarimetry data of Tycho's SNR at 6 cm and 20 cm wavelength. + The spatial resolution is about 0.7% of the forward-shock radius. roughly comparable to. 300 cells in our magnelic-lield model.," The spatial resolution is about $0.7\%$ of the forward-shock radius, roughly comparable to 300 cells in our magnetic-field model." + The radio morphologv can be well described by an outer rim and an inner shell of outer radius 0.92 SNR. radii 2000)., The radio morphology can be well described by an outer rim and an inner shell of outer radius 0.92 SNR radii \citep{ks00}. +. The outer rim is positionallv coincident with (he outer periphery of the X-ray emission. suggesting that the inner shell marks the location of the contact discontinuity ancl (he reverse shock.," The outer rim is positionally coincident with the outer periphery of the X-ray emission, suggesting that the inner shell marks the location of the contact discontinuity and the reverse shock." + We conclude that our model is applicable to polarized radio emission [rom ihe outer rim., We conclude that our model is applicable to polarized radio emission from the outer rim. + In the outer rims. the percentage polarization at 6 cm wavelength is twpically in the range 20% to 30%. and the field orientation is radial (c£.Fig.5aofDickeletal. 1991).," In the outer rims, the percentage polarization at 6 cm wavelength is typically in the range $20\%$ to $30\%$ , and the field orientation is radial \citep[cf. Fig.5a of][]{di91}. ." +which means lower M/L ratios as redshift increase.,which means lower $M/L$ ratios as redshift increase. +" In order to observe this evolution, we fit a line (y=ag+ a,x) to the zo and z3 redshift samples (see Fig."," In order to observe this evolution, we fit a line $y=a_0+a_1x$ ) to the $z_0$ and $z_3$ redshift samples (see Fig." +" 10), obtaining ao=—0.924 and a,=—0.544 for zo, and dy=—18.686 and a,=—1.304 for z3."," 10), obtaining $a_0=-0.924$ and $a_1=-0.544$ for $z_0$, and $a_0=-18.686$ and $a_1=-1.304$ for $z_3$." + The variation in M/L at a given rest frame optical luminosity can be as much as a factor of ~70 (Shapley et al., The variation in $M/L$ at a given rest frame optical luminosity can be as much as a factor of $\sim$ 70 (Shapley et al. +" 2005), which means that for any range in luminosity there exist an extended range of stellar masses."," 2005), which means that for any range in luminosity there exist an extended range of stellar masses." + This large variation in M/L explains the lack of correlation in the L—Z relation for the z3 sample compared to the local relation., This large variation in $M/L$ explains the lack of correlation in the $L-Z$ relation for the $z_3$ sample compared to the local relation. +" For a small range of absolute magnitudes in the z3 sample, we have a widely range"," For a small range of absolute magnitudes in the $z_3$ sample, we have a widely range" +,1. + Lorentz and SU(3) gr, Many fundamental properties of matter at the quantum level can be announced without mentioning the space-time realm. +oups derived fromc," The Pauli exclusion principle, symmetry between particles and anti-particles, electric charge and baryonic number conservation belong to this category." +ubic quark algebra," Quantum mechanics itself can be formulated without any mention of space, as was shown by Born, Jordan and Heisenberg \cite{BornJH} in their version of matrix mechanics, or in J. von Neumann's \cite{JvNeumann} formulation of quantum theory in terms of the $C^*$ algebras." + Richar, The non-commutative geometry \cite{MDVRKJM} gives another example of interpreting the space-time relationships in pure algebraic terms. +"d Ixerner* April 8,2023 We showthat the "," Einstein's dream was to be able to derive the properties of matter, and perhaps its very existence, from the singularities of fields defined on the space-time, and if possible, from the geometry and topology of the space-time itself." +Lorentz andthe SU(3) groups c," A follower of Maxwell and Faraday, he believed in the primary role of fields and tried to derive the equations of motion as characteristic behavior of field singularities, or the singularities of the space-time (see e.g. \cite{EinsteinInfeld}) )." +an bederived [romthe co- variauce pri, But one can defend an alternative point of view supposing that the existence of matter is primary with respect to that of the space-time. +nciple couserviug a Za-graded thr," In this light, the idea to derive the geometric properties of space-time, and perhaps its very existence, from fundamental symmetries and interactions proper to matter's most fundamental building blocks seems quite natural." +ee-form oua Za-graded cu," If the the space-time is to be derived from the interactions of fundamental constituents of matter, then it seems reasonable to choose the strongest ineractions available, which are the interactions between quarks." +bic algebra represe," The difficulty resides in the fact that we should define these “quarks"" (or their states) without any mention of space-time." +uting quarks endowed with non-staudard comaiuutatiou laws.," The minimal requirements for the definition of quarks at the initial stage of model building are the following: 0.5cm ) The mathematical entities representing quarks should form a linear space over complex numbers, so that we could produce their linear combinations with complex coefficients." + ™ Laboratoirede Physique Théoriquede la Matiére Condensée. Université ," 0.5cm ) They should also form an associative algebra, so that we could consider their multilinear combinations; 0.5cm ) There should exist two isomorphic algebras of this type corresponding to quarks and anti-quarks, and the conjugation transformation that maps one of these algebras onto another, ${\cal{A}} \rightarrow {\bar{\cal{A}}}$." +Pierre-et-Marie-Curie-CNRS Tow22. Léme étage. Bo," 0.5cm ) The three quark (or three anti-quark) and the quark-anti-quark combinations should be distinguished in a certain way, for example, they should form a subalgebra in the algebra spanned by the generators." +ite 121. I. Place Jussieu.75005 Paris. France," With this in mind we can start to explore the algebraic properties of quarks that would lead to more general symmetries, that of space and time, appearing as a consequence of" +Observing the outskirts of galaxy clusters is nuportaut for nuderstanding the ornation processes of larec-scale structures;,Observing the outskirts of galaxy clusters is important for understanding the formation processes of large-scale structures. + For instance. studyius the intracluster eas around the virial radius gives an opportunity to nmueasure the transition beween the eravitationally-hound eas of clusters and the intalline material from larec-scale structures.," For instance, studying the intracluster gas around the virial radius gives an opportunity to measure the transition between the gravitationally-bound gas of clusters and the infalling material from large-scale structures." + Tracing the eas out to the virial radius ds also Huportaut for calibrating the N-rav niass measurements. which are important to cosmology (ο2h. Ilo," Tracing the gas out to the virial radius is also important for calibrating the X-ray mass measurements, which are important to cosmology \citep[e.g.,][]{voit}." +wever. nieasuring the xopertes of the iutracluster iiedium in chster outskirts is difficult because of the low surface brightuess of these regious.," However, measuring the properties of the intracluster medium in cluster outskirts is difficult because of the low surface brightness of these regions." + Au iustruiment wit ra low dternal background is required fo 1ueasture the source clussion at lieh racii., An instrument with a low internal background is required to measure the source emission at high radii. + Iu the past few years. the satelite achieved a breakthrous 11i this domain. performing measurements of the thermodynamical properties of tre ICAL out to the virial radius TUUM.," In the past few years, the satellite achieved a breakthrough in this domain, performing measurements of the thermodynamical properties of the ICM out to the virial radius \citep{bautz,reip09,hoshino,kawa}." + PISS 075-191 (2 0.1028) is a verv lines (Ly~ὃνP 10ergss 3 dn the 2-10 keV??). cool-core chster located iu the vicinity of the Calactic plaue (5 L7).," PKS 0745-191 $z=0.1028$ ) is a very luminous \citep[$L_X\sim3\times 10^{45}$ ergs $^{-1}$ in the 2-10 keV, cool-core cluster located in the vicinity of the Galactic plane $b=+3^\circ$ )." +" From, a /NIS. observation of the cluster. ? (hereafter. C09) measured the cluster enidssion onu to ~L.5rouy- aud cetermined a value of M200l.T Mpc (15.2 arcinin) for the virial radius."," From a /XIS observation of the cluster, \citet{george} (hereafter, G09) measured the cluster emission out to $\sim1.5r_{200}$, and determined a value of $r_{200}=1.7$ Mpc (15.2 arcmin) for the virial radius." + Surprisingly. the authors noted a flatteniug of the density and cutropy profiles around rogo. at variance with results from cosinological simulations (6.8. 7T.," Surprisingly, the authors noted a flattening of the density and entropy profiles around $r_{200}$, at variance with results from cosmological simulations \citep[e.g.,][]{roncarelli,tozzi}." + This and similar results frou other authors inspired a large amount of theoretical work (e.9..?7).. invoking several mechanisms (ο nou-thermal pressure support. eas clumping) to reconcile siuulations aud oservations.," This and similar results from other authors inspired a large amount of theoretical work \citep[e.g.,][]{lapi,nagai}, invoking several mechanisms (e.g., non-thermal pressure support, gas clumping) to reconcile simulations and observations." + An iudepenudoeut confirmation of this result would therefore be very nuportaut to our uudoerstaucine of cluster outskirts., An independent confirmation of this result would therefore be very important to our understanding of cluster outskirts. + Iu this Oper. we presen the analysis of an archival Position Scusitive Proportioua Counter (PSPC) observation of PINS 0715-191. with the aim of coufiriuine the result o: C09.," In this paper, we present the analysis of an archival Position Sensitive Proportional Counter (PSPC) observation of PKS 0745-191, with the aim of confirming the result of G09." +" Although he PSPC could not measure temperatures because of its limited vandpass (0.1-2.1 σον), its low iustrunental background aud large field of view (~2 square deerees) made it au excellent. tool or the study ο[low surface-brightuess regious such as he outer regions of galaxv clusters (seeeos27)."," Although the PSPC could not measure temperatures because of its limited bandpass (0.1-2.4 keV), its low instrumental background and large field of view $\sim$ 2 square degrees) made it an excellent tool for the study of low surface-brightness regions such as the outer regions of galaxy clusters \citep[see e.g.,][]{vikhlinin99,neumann05}." + We also perform a niass analysis using the PSPC cleusity xofile aud the clupcrature lueasureluents froni various other X-rav satelites. aud coire f10 XCsults with the neasurenients of C09.," We also perform a mass analysis using the PSPC density profile and the temperature measurements from various other X-ray satellites, and compare the results with the measurements of G09." + The paper is organized as follows., The paper is organized as follows. + Iu Sect. 2..," In Sect. \ref{data}," + we describe the data analysis procedure., we describe the data analysis procedure. + We esent our results for the deusiv profile of the cluster iu Sect. 3.. ," We present our results for the density profile of the cluster in Sect.\ref{results}, ," +and discuss them iu Sect. £L., and discuss them in Sect. \ref{discussion}. +" Throughout 16 paper. we asstune a ACDM cosinology with Q,,=0.3. Q4=0.7. and fy=7Hans |: |l."," Throughout the paper, we assume a $\Lambda$ CDM cosmology with $\Omega_m=0.3$, $\Omega_\Lambda=0.7$, and $H_0=70$ km $^{-1}$ $^{-1}$." + PISS 0715-19) was the tarect ofa pointed OSAT//PSPC observation on October 15. 1993 (olervation ID RPSOOG23NOO). for a total of 10.5 ksecο," PKS 0745-191 was the target of a pointed /PSPC observation on October 15, 1993 (observation ID RP800623N00) for a total of 10.5 ksec." + We reduce the data usiug the Extended 8nrce Analysis Software (ESAS.?)..," We reduced the data using the Extended Source Analysis Software \citep[ESAS,][]{esas}." +" To climinate flaring periods. we extracted a helt curve from the raw event files am rejected all ti11ο xeriods where the Master Veto count rate was above 220 counts |,"," To eliminate flaring periods, we extracted a light curve from the raw event files and rejected all time periods where the Master Veto count rate was above 220 counts $^{-1}$." + We then used the ESAS task ο create a iode of the scattered solar X-rav backeroun (SSN.T). axd generated a particle background. iode using the executable (27)..," We then used the ESAS task to create a model of the scattered solar X-ray background \citep[SSX,][]{solarxrb}, and generated a particle background model using the executable \citep{partback,plucinsky}." + The total model for he nou A-rav backgroundC» (NNB) aud the SSN was then interred., The total model for the non X-ray background (NXB) and the SSX was then inferred. + À counts nuage in the 0.62.0 Κον baud was hen extracted from the cleaned event file and the correspondiug exposure map was created using the taskcast_ecp., A counts image in the 0.4-2.0 keV band was then extracted from the cleaned event file and the corresponding exposure map was created using the task. +. Point sources were then detected roni the iuaee (using the program detect}) aud a poiut soUurce ask was eenerated to excise the correspoudiug regio1s, Point sources were then detected from the image (using the program ) and a point source mask was generated to excise the corresponding regions. + As a result. a backerouncd-subtracted. exposure-correced image was created and adaptively simoothed.," As a result, a background-subtracted, exposure-corrected image was created and adaptively smoothed." + In Fig. 1.. ," In Fig. \ref{image}, ," +"we showthe resulting nuage together with the ]xsition of rogo estimated by (100,Point sources have hee1 niasked from the image.", we showthe resulting image together with the position of $r_{200}$ estimated by G09.Point sources have been masked from the image. +Ideally. the next step would be to perform the same type of calculation as in?) for different initial conditions. including descriptions for radiative and mechanical feedback.fields. and varying the sink particle radius.,"Ideally, the next step would be to perform the same type of calculation as in \citet{bonnell08} for different initial conditions, including descriptions for radiative and mechanical feedback, and varying the sink particle radius." + Ihe dynamical analysis of such simulations would provide a good verification of our conclusions. and would improve the current understanding of the dependence on initial conditions and input physics.," The dynamical analysis of such simulations would provide a good verification of our conclusions, and would improve the current understanding of the dependence on initial conditions and input physics." + The order-of-magnitude extension of our results from subcluster to actual star cluster scales should be investigated further., The order-of-magnitude extension of our results from subcluster to actual star cluster scales should be investigated further. + With the continuously improving computational facilities. it will be possible to simulate systems on the scales needed to cover the formation of star clusters.," With the continuously improving computational facilities, it will be possible to simulate systems on the scales needed to cover the formation of star clusters." + The key ingredients of such an effort will be larger particle numbers and smaller sink particle radii., The key ingredients of such an effort will be larger particle numbers and smaller sink particle radii. + Additionally. infraredspectroscopic observations can be used to verify the length scales on which star-forming regions are gas-poor prior to the onset ofremoval.," Additionally, infrared observations can be used to verify the length scales on which star-forming regions are gas-poor prior to the onset of." + The current and upcoming generation of telescopes will provide excellent opportunities for this., The current and upcoming generation of telescopes will provide excellent opportunities for this. + If gas expulsion indeed only weakly affects the survival chances of stellar structure. it will need to be verified in which regimes infant mortality still plays a role.," If gas expulsion indeed only weakly affects the survival chances of stellar structure, it will need to be verified in which regimes infant mortality still plays a role." + In order to understand the relation between the CFE and the local environment. the relative contributions to early star cluster disruption of infant mortality and the cruel cradle effect will need to be quantified.," In order to understand the relation between the CFE and the local environment, the relative contributions to early star cluster disruption of infant mortality and the cruel cradle effect will need to be quantified." + Possible ways in which this could be done observationally include searching for young clusters that are currently going through gas expulsion and mapping the radial velocities of the stars. or tracing the velocity dispersion profiles of young. gas-poor clusters in dense regions.," Possible ways in which this could be done observationally include searching for young clusters that are currently going through gas expulsion and mapping the radial velocities of the stars, or tracing the velocity dispersion profiles of young, gas-poor clusters in dense regions." + To aid this effort. the differences between the kinematic signatures of energy injection into a star cluster by gas expulsion or tidal shocks have to be established theoretically.," To aid this effort, the differences between the kinematic signatures of energy injection into a star cluster by gas expulsion or tidal shocks have to be established theoretically." + The combination of these approaches should provide a conclusive picture of the mechanisms that determine which fraction of star formation results in bound star clusters., The combination of these approaches should provide a conclusive picture of the mechanisms that determine which fraction of star formation results in bound star clusters. + We thank the anonymous referee for thoughtful comments., We thank the anonymous referee for thoughtful comments. + JMDK is grateful to Eli Bressert for helpful discussions and acknowledges the kind hospitality of the Institute of Astronomy in Cambridge. where a large part of this work took place.," JMDK is grateful to Eli Bressert for helpful discussions and acknowledges the kind hospitality of the Institute of Astronomy in Cambridge, where a large part of this work took place." + ThM acknowledges funding byCONSTELLATION.. a European Commission FP6 Marie Curie Research Training Network.," ThM acknowledges funding by, a European Commission FP6 Marie Curie Research Training Network." + This research is supported by the Leids Kerkhoven-Bosscha Fonds (LKBF) and the Netherlands Organisation for Scientic Research (NWO). grant 021.001.038.," This research is supported by the Leids Kerkhoven-Bosscha Fonds (LKBF) and the Netherlands Organisation for ScientiÞc Research (NWO), grant 021.001.038." + In this appendix we verify that the resolution of SPH simulation is not playing an important role in the evolution theof the stellar-to-gas mass ratio of the subclusters., In this appendix we verify that the resolution of the SPH simulation is not playing an important role in the evolution of the stellar-to-gas mass ratio of the subclusters. + We accomplish this via a series of controlled. idealised tests in which a cluster of 10 sink particles üccretes from an envelope of gas.," We accomplish this via a series of controlled, idealised tests in which a cluster of 10 sink particles accretes from an envelope of gas." + The total mass of the system is I. divided equally between the sinks and the gas.," The total mass of the system is 1, divided equally between the sinks and the gas." + The sinks are initially of equal mass. thus each has mass 0.05.," The sinks are initially of equal mass, thus each has mass 0.05." +" They are placed randomly in a Plummer model of virial radius rji,=|. and we use the same initial configuration of the stars in each test."," They are placed randomly in a Plummer model of virial radius $r_{\rm sinks} = 1$, and we use the same initial configuration of the stars in each test." + The median nearest neighbour separation of the sinks is 0.43., The median nearest neighbour separation of the sinks is 0.43. + The gas is likewise in a Plummer sphere spatially. although with a larger radius than the sinks.," The gas is likewise in a Plummer sphere spatially, although with a larger radius than the sinks." + The gas has zero initial kinetic energy and minimal thermal support. so that the gas falls onto the sink cluster and is accreted.," The gas has zero initial kinetic energy and minimal thermal support, so that the gas falls onto the sink cluster and is accreted." + We run two sets of tests. one in which the gas sphere's virial radius is ten times rau. Le. ra.=10. and one in which faa=3.," We run two sets of tests, one in which the gas sphere's virial radius is ten times $r_{\rm sinks}$, i.e. $r_{\rm gas} = 10$, and one in which $r_{\rm gas} = 3$." + The two numerical scales we are concerned with are the accretion radius of the sinks noc. and the smoothing length of the gas particles.," The two numerical scales we are concerned with are the accretion radius of the sinks $r_{\rm acc}$, and the smoothing length of the gas particles." + For the sink radii. we use the set rna= [0.125.0.0625.0.03125].," For the sink radii, we use the set $r_{\rm acc} = \{0.125, 0.0625, +0.03125\}$ ." + The middle value yields approximately the ratio of the neighbour distance to the accretion radius seen in the clusters in the simulation., The middle value yields approximately the ratio of the neighbour distance to the accretion radius seen in the clusters in the simulation. + The smoothing length of the gas is determined by the number of gas particles., The smoothing length of the gas is determined by the number of gas particles. + To roughly mateh the simulated value. suppose the sinks have masses |M...," To roughly match the simulated value, suppose the sinks have masses $1~\msun$." + The total gas mass is then 10M... and 510+ sas particles approximates the resolution of the large-scale simulation.," The total gas mass is then $10~\msun$, and $5\times10^4$ gas particles approximates the resolution of the large-scale simulation." + We run the 0.0625 accretion radius cases with four times more and fewer gas particles. Le. 2IO and 1.25 10.In Fig.," We run the 0.0625 accretion radius cases with four times more and fewer gas particles, i.e. $2\times10^5$ and $1.25\times10^4$ .In Fig." + Al we show the gas mass as a function of time for, \ref{fig:AppendixFigure} we show the gas mass as a function of time for +where 1 represents the identity matrix in 3.N-dimensions.,where $1$ represents the identity matrix in $3N$ -dimensions. + Using a generalization of the algorithm for explicitly computing derivatives of computational algorithms. we can compile the Jacobian matrix for the evolution mapping defined by any integration scheme.," Using a generalization of the algorithm for explicitly computing derivatives of computational algorithms, we can compute the Jacobian matrix for the evolution mapping defined by any integration scheme." + Wedenote by α the relative change in the sum of the absolute values of the diagonal from lower left to upper right between J and ο., Wedenote by $dI$ the relative change in the sum of the absolute values of the diagonal from lower left to upper right between $J^TSJ$ and $S$. + If equation holds. d]=0.," If equation holds, $dI = +0$." + We compare dI [rom the individual ancl adaptive timestep integrator described in (his paper to di from a standard individual and adaptive timestep Lermite integrator (2).., We compare $dI$ from the individual and adaptive timestep integrator described in this paper to $dI$ from a standard individual and adaptive timestep Hermite integrator \citep{Makino1991}. + It is difficult to precisely control the stepsizes chosen in an adaptive timestep scheme. so we measure df as a [function of the total number of steps taken for the evolution. rao.," It is difficult to precisely control the stepsizes chosen in an adaptive timestep scheme, so we measure $dI$ as a function of the total number of steps taken for the evolution, $n_{\rm{steps}}$." + An error which scales as A should scale as nsleps*p, An error which scales as $h^r$ should scale as $n_{\rm{steps}}^{-r}$. + Based on the discussion in Section 2.1.2.. we expect that dI from (he variational integrator will be fifth order (that is. it scales as Dac.) while d/ from the Ilermite integrator will be fourth order (exactly the same order as the integrators (rajectory error).," Based on the discussion in Section \ref{ThreePointIntegrator}, we expect that $dI$ from the variational integrator will be fifth order (that is, it scales as $n_{\rm{steps}}^{-5}$ ), while $dI$ from the Hermite integrator will be fourth order (exactly the same order as the integrator's trajectory error)." + Figure 6 demonstrates that this is exactly the ease for simulations of a Plummer initial condition with N=25 bodies and varying numbers of steps over a total time interval of Z/=1.0 by both algorithms., Figure \ref{hermiteVariationalSymplecticError} demonstrates that this is exactly the case for simulations of a Plummer initial condition with $N = 25$ bodies and varying numbers of steps over a total time interval of $T = 1.0$ by both algorithms. + Because thev both depend on the accuracy. of the solution to the implicit equation(16a).. we expect that svinplectieitv and angulare momentum conservation error would scale similarly in a long-term simulation.," Because they both depend on the accuracy of the solution to the implicit equation, we expect that symplecticity and angular momentum conservation error would scale similarly in a long-term simulation." + Results in the next section show that angular momentum error in a long-running simulation is about one order of magnitude better than the energy conservalion error (Figure 7)) using our algorithm. while the Hermite algorithm. produces angular momentum errors Commensurate with its energv conservation error.," Results in the next section show that angular momentum error in a long-running simulation is about one order of magnitude better than the energy conservation error (Figure \ref{ManyBodyDeltaEAndL}) ) using our algorithm, while the Hermite algorithm produces angular momentum errors commensurate with its energy conservation error." + Our algorithm appears to have the advantage in angular momentum conservation and svmplecticitv in large-/N. long-time simulations.," Our algorithm appears to have the advantage in angular momentum conservation and symplecticity in $N$, long-time simulations." + llere we compare a 1000-body. cluster. simulation run using our variational inleerator with another such simulation using the NDODY?2h code (7).., Here we compare a 1000-body cluster simulation run using our variational integrator with another such simulation using the NBODY2h code \citep{Aarseth2001}. + NBODY2h is not the in cluster simulations: it js an appropriate comparison to our code because il uses (he state-of-the-art Hermite integration algorithm but uses softening instead of treating close encounters specially., NBODY2h is not the state-of-the-art in cluster simulations; it is an appropriate comparison to our code because it uses the state-of-the-art Hermite integration algorithm but uses softening instead of treating close encounters specially. + We have run many such simulations(he one described here is (vpical., We have run many such simulations—the one described here is typical. + Recall we use the standard units: the total svstem mass is M=1. G=1. and the total energv f=—1/4 (2)..," Recall we use the standard units: the total system mass is $M = 1$, $G += 1$, and the total energy $E = - 1/4$ \citep{Heggie1986}. ." + In stanclared units. (he virial radius of the svstem is 1.," In standard units, the virial radius of the system is 1." + Initial conditions for both runs are a randomly sampled Plummer model shilted into a coordinate, Initial conditions for both runs are a randomly sampled Plummer model shifted into a coordinate +a more detailed examination of cluster atmospheres reveals striking differences.,a more detailed examination of cluster atmospheres reveals striking differences. +" Even with the relatively low resolution of our simulation, and the resulting inability to fully reproduce correct structures in the cluster atmospheres, we can identify gross differences in the projected maps."," Even with the relatively low resolution of our simulation, and the resulting inability to fully reproduce correct structures in the cluster atmospheres, we can identify gross differences in the projected maps." + shows projections of mass and turbulent pressure for two clusters., shows projections of mass and turbulent pressure for two clusters. +" The mass projections of both clusters are roughly spherical, as expected."," The mass projections of both clusters are roughly spherical, as expected." +" However, the turbulent pressure maps show more varying morphology."," However, the turbulent pressure maps show more varying morphology." +" While the halos are roughly equal in mass 8x101457! Mo), one shows much greater turbulent (structure, indicating recent merger activity, which may explain the scatter in2."," While the halos are roughly equal in mass $\sim 8 \times 10^{14} \hmsol$ ), one shows much greater turbulent structure, indicating recent merger activity, which may explain the scatter in." +". Thus, even though different mechanisms of CR generation may produce similar cluster counts (as we will see below), high-resolution radio and X-ray imaging of clusters may help to determine which mechanism dominates."," Thus, even though different mechanisms of CR generation may produce similar cluster counts (as we will see below), high-resolution radio and X-ray imaging of clusters may help to determine which mechanism dominates." +" Since we do not include in our simulations any detailed CR generation mechanisms, and because we want to keep our model as general as possible, we must fix the scaling parameter C, by using observations."," Since we do not include in our simulations any detailed CR generation mechanisms, and because we want to keep our model as general as possible, we must fix the scaling parameter $C_s$ by using observations." + This scaling will then combine any extra constants and parameters not included in our analysis., This scaling will then combine any extra constants and parameters not included in our analysis. +" For a given set of model parameters, we set C, by assigning a radio luminosity to the most massive cluster in our simulation."," For a given set of model parameters, we set $C_s$ by assigning a radio luminosity to the most massive cluster in our simulation." +" This cluster has a mass ~2x1015h-!Mo, which fits within the observed radio halo mass range of 2x1015—6x10!ΛΙ Mg."," This cluster has a mass $\sim 2\times 10^{15} \hmsol$, which fits within the observed radio halo mass range of $2 \times 10^{15} - 6 \times 10^{15} \hmsol$ ." +" We do this with the Pj4—M, relation found in CBS06, which is based on combining the observed correlation of radio halo power and X-ray luminosity with the correlation between X-ray luminosity and mass: We then apply this same constant scaling to all remaining high-resolution halos in the sample."," We do this with the $P_{1.4} - M_v$ relation found in CBS06, which is based on combining the observed correlation of radio halo power and X-ray luminosity with the correlation between X-ray luminosity and mass: We then apply this same constant scaling to all remaining high-resolution halos in the sample." +" While the scaling may contain some additional dependence on mass or turbulent pressure not accounted for in our parameterization, this can easily be accommodated in our study by adding to (or subtracting from) the parameters a and c."," While the scaling may contain some additional dependence on mass or turbulent pressure not accounted for in our parameterization, this can easily be accommodated in our study by adding to (or subtracting from) the parameters $a$ and $c$." + An example of a particular model compared against the observed relation is shown in4., An example of a particular model compared against the observed relation is shown in. +. Our best-fit relation in this plot and throughout this paper uses only the clusters within the observed mass range., Our best-fit relation in this plot and throughout this paper uses only the clusters within the observed mass range. +" Since very few radio halos have been observed beyond a redshift of ~0.4, and available statistics do not strongly constrain evolution in this relation,we will fix the scaling at z=0 and apply the same scaling to higher-redshift clusters."," Since very few radio halos have been observed beyond a redshift of $\sim 0.4$, and available statistics do not strongly constrain evolution in this relation,we will fix the scaling at $z=0$ and apply the same scaling to higher-redshift clusters." +" We will also assume power-law energy spectra with a spectral index of 1.2, consistent with low-redshift observations (?).."," We will also assume power-law energy spectra with a spectral index of 1.2, consistent with low-redshift observations \citep{Feretti2004}." +" Finally, we do not include in our model the relationship between synchrotron break frequency and the presence of a radio halo, which can be used to calibrate models to the observed fraction of clusters hosting radio halos (CBS06)."," Finally, we do not include in our model the relationship between synchrotron break frequency and the presence of a radio halo, which can be used to calibrate models to the observed fraction of clusters hosting radio halos (CBS06)." + We will discuss the potential impacts of this assumption in the conclusion., We will discuss the potential impacts of this assumption in the conclusion. +" To constrain our model choices we make selections for the model parameters, assign radio powers to the clusters using the procedure described above, find the best-fit line to our derived P;.4—M, data above a mass threshold of 1015h-!Mo, and compare the best-fit slope and normalization to the observed values."," To constrain our model choices we make selections for the model parameters, assign radio powers to the clusters using the procedure described above, find the best-fit line to our derived $P_{1.4}-M_v$ data above a mass threshold of $10^{15}~\hmsol$, and compare the best-fit slope and normalization to the observed values." + We only accept model choices that produce fits that lie within 1o of the observed relation., We only accept model choices that produce fits that lie within $1\sigma$ of the observed relation. + This is a strategy similar to the one employed by CBS06: except that we are applying a test by enforcing the known relation to somewhat lower radio powers than they consider., This is a strategy similar to the one employed by CBS06: except that we are applying a test by enforcing the known relation to somewhat lower radio powers than they consider. + We do this so that we can capture enough halos (~10) to generate sufficient statistics for our best-fit lines., We do this so that we can capture enough halos $\sim 10$ ) to generate sufficient statistics for our best-fit lines. +" Obviously, we could just select two models that span the valid range and analyze their difference, but we wish to explore the relationships among the various model parameters and the separate consequences of varying each one."," Obviously, we could just select two models that span the valid range and analyze their difference, but we wish to explore the relationships among the various model parameters and the separate consequences of varying each one." + shows colormap plots of allowable models., shows colormap plots of allowable models. +" We vary (B) from 0.2 to 6.0wG, b from 0.5 to 1.5, a from 0.0 to 5.0, and finally c from 0.0 to 3.0."," We vary $\aveb$ from $0.2$ to $6.0 \mg$, $b$ from $0.5$ to $1.5$ , $a$ from $0.0$ to $5.0$, and finally $c$ from $0.0$ to $3.0$." +" We could explore even larger values of a and c, but as we will discuss below lo uncertainties in the measured Βι46Η,—My relation place upper limits on the scaling of a and c at these chosen maximum values."," We could explore even larger values of $a$ and $c$ , but as we will discuss below $1\sigma$ uncertainties in the measured $\pmvir$ relation place upper limits on the scaling of $a$ and $c$ at these chosen maximum values." +" We also assume a positive correlation between radio power and M, and T',.", We also assume a positive correlation between radio power and $M_v$ and $\Gamma_v$. +" While we allow the mass and turbulent pressure scaling parameters to vary all the way to 0, we constrain the scalings associated with magnetic fields."," While we allow the mass and turbulent pressure scaling parameters to vary all the way to $0$ , we constrain the scalings associated with magnetic fields." +" We constrain the average cluster magnetic field strength from 0.2µία, which is set by observed upper limits on hard X-ray emission (CBS06), to 6.0uG, which is a reasonable upper limit from rotation measure observations (e.g. ?).."," We constrain the average cluster magnetic field strength from $0.2 \mg$, which is set by observed upper limits on hard X-ray emission (CBS06), to $6.0 \mg$, which is a reasonable upper limit from rotation measure observations \citep[e.g.][]{Bonafede2011}." +" The restrictions on b come from the simulations of ?,, which followed the adiabatic compression of seed magnetic fields as clusters formed."," The restrictions on $b$ come from the simulations of \citet{Dolag2002}, which followed the adiabatic compression of seed magnetic fields as clusters formed." +" They found a scaling B«M'9?,", They found a scaling $B \propto M^{1.33}$. +" We allow some uncertainty in this value, but do not allow a compete lack of scaling of magnetic field with cluster mass."," We allow some uncertainty in this value, but do not allow a compete lack of scaling of magnetic field with cluster mass." +" For simplicity, we have combined the mass and turbulent pressure values as a+c, so a+c is varied from 0.0 to 9.0. The contours for each individual parameter show structures similar to those for this combined parameter."," For simplicity, we have combined the mass and turbulent pressure values as $a+c$, so $a+c$ is varied from $0.0$ to $9.0$ The contours for each individual parameter show structures similar to those for this combined parameter." + In these plots we are showing the allowed value for a given point on each contour plot., In these plots we are showing the allowed value for a given point on each contour plot. + All values less than the plotted value are also allowed., All values less than the plotted value are also allowed. +" For example, for b=1.0 and (B)=3.0uG the allowable values for a4-c are from 0.0 to ~1.5."," For example, for $b=1.0$ and $\aveb=3.0 \mg$ the allowable values for $a+c$ are from $0.0$ to $\sim 1.5$." + We find that very strong magnetic fields are only allowed if the scalings with virial mass and turbulent pressure are very steep., We find that very strong magnetic fields are only allowed if the scalings with virial mass and turbulent pressure are very steep. +" In these cases strong radio power in low mass objects due to high (B) is offset by significantly lower radio power associated with M, or Ty.", In these cases strong radio power in low mass objects due to high $\aveb$ is offset by significantly lower radio power associated with $M_v$ or $\Gamma_v$. +" If the scaling of magnetic field strength with cluster mass is above unity, then it is difficult to fit strong magnetic fields at high mass within the observed relations."," If the scaling of magnetic field strength with cluster mass is above unity, then it is difficult to fit strong magnetic fields at high mass within the observed relations." +" We find several regions forbidden in our models: strong magnetic fields coupled with low a--c, and very low or very high à4-c and 6 values."," We find several regions forbidden in our models: strong magnetic fields coupled with low $a+c$, and very low or very high $a+c$ and $b$ values." +" We see interesting structures in the contours: steps and wiggles in the a+ plots, and striations in the others."," We see interesting structures in the contours: steps and wiggles in the $a+c$ plots, and striations in the others." +" These are due to the scatter that develops in the P14—M, relations and the resulting variations of the best-fit lines.", These are due to the scatter that develops in the $P_{1.4}-M_v$ relations and the resulting variations of the best-fit lines. +" Because of thisvariation, we do notsee monotonically increasing (or decreasing) behavior in the contour plots, especially at extreme values."," Because of thisvariation, we do notsee monotonically increasing (or decreasing) behavior in the contour plots, especially at extreme values." +"Surprisingly, we find that a—c0.0 is allowed, but only at low (B) and high b.","Surprisingly, we find that $a=c=0.0$ is allowed, but only at low $\aveb$ and high $b$ ." + This is because of the implicitmass, This is because of the implicitmass +The core of coronal mass ejection (ΟΛΠ) clouds occasionally exposes very bright coucentrated patches in white-lelt coronagrapls.,The core of coronal mass ejection (CME) clouds occasionally exposes very bright concentrated patches in white-light coronagraphs. + They are interpreted as cool plasma material from a prominence that was embedded inside the streamer environment of the CALE before the eruption., They are interpreted as cool plasma material from a prominence that was embedded inside the streamer environment of the CME before the eruption. + During the eruption process. the promunence is then expelled along with the sirrounding streamer plasiua.," During the eruption process, the prominence is then expelled along with the surrounding streamer plasma." + Polaud aud Munro (1976) report one such observation made on 21 August 1973. 15:11 UT with the Skvlab white-helt coronagraph aud its Well 30.1 nia spectrolicloeraph.," Poland and Munro (1976) report one such observation made on 21 August 1973, 15:11 UT with the Skylab white-light coronagraph and its HeII 30.4 nm spectroheliograph." + About Ls nun before. an Πα nage1 taken at the Sacramento Peak Observatory had shown bright patches extending out to 1.12 .. but facing in iuteusitv with time.," About 18 min before, an $\alpha$ image taken at the Sacramento Peak Observatory had shown bright patches extending out to 1.42 $_{\odot}$ but fading in intensity with time." + Even though the coronagrapl field-ofview was limited to above 1.5 R.. it was conclude that IIa racdiatiou contributed to the white-light image because its signal was less polarised iu some bright patches than in the surrounding region.," Even though the coronagraph field-of-view was limited to above 1.5 $_{\odot}$ , it was concluded that $\alpha$ radiation contributed to the white-light image because its signal was less polarised in some bright patches than in the surrounding region." + Πα radiation is the result of the electronic j=3 } 15535 transition of the hvdrosgen atom., $\alpha$ radiation is the result of the electronic $j$ =3 $\rightarrow$ $j$ =2 transition of the hydrogen atom. + In equilibrium at an electron temperature below 50.000 Ik. the j=3 level is populated iuuceh more by absorption of the ubieut Lv.) radiation than bv absorption «: photospherie Ho.," In equilibrium at an electron temperature below 50,000 K, the $j$ =3 level is populated much more by absorption of the ambient $\beta$ radiation than by absorption of photospheric $\alpha$." + This causes a substantial decrease m polarisation of the enütted Πα radiation below the theoretica Waa value of for pure resonant scattering (Poland aud Miro 1976)., This causes a substantial decrease in polarisation of the emitted $\alpha$ radiation below the theoretical maximum value of for pure resonant scattering (Poland and Munro 1976). + Besides. the Παπ]ο effect caused by the coronal maguctic field (Salial-Brechot et al.," Besides, the Hanle effect caused by the coronal magnetic field (Sahal-Brechot et al." + 1977. Heiuzel et al.," 1977, Heinzel et al." + 1996) and collisional depolarisation (οΙΟ ct al., 1996) and collisional depolarisation (Bommier et al. + 1986) reduce the amount of polarisation even further., 1986) reduce the amount of polarisation even further. + As a result. the linear polarisation of Ta radiation observed in proniuenuces well above the limb ranges from a fraction of a percent (Candorfer. 2000: Wiehr and Diauda. 2003) to a few percent (Leroy et al.," As a result, the linear polarisation of $\alpha$ radiation observed in prominences well above the limb ranges from a fraction of a percent (Gandorfer, 2000; Wiehr and Bianda, 2003) to a few percent (Leroy et al.," + 1981)., 1984). + The white-light oendssion of the solar Ik-corona originates im Thomsou-scatteriuge of plotospheric light by free electrons., The white-light emission of the solar K-corona originates in Thomson-scattering of photospheric light by free electrons. + Detailed. description of the Thomsou-scattering theory cau be found iu various papers(6.8... Alunuaert 1930: vau de IHulst 1950: Billmes 1966).," Detailed description of the Thomson-scattering theory can be found in various papers, Minnaert 1930; van de Hulst 1950; Billings 1966)." + The anisotropy of the incident light causes the observed scattered radiation to exhibit a polarisation parallel to the visible lub., The anisotropy of the incident light causes the observed scattered radiation to exhibit a polarisation parallel to the visible limb. + The deeree ofpolarisation depends on the distance from the solar surface and on the scattering angle to the observer., The degree of polarisation depends on the distance from the solar surface and on the scattering angle to the observer. + Indeed. it has been proposed to use the observed degree of polarisation to estimate tlic distance of the coronal scattering volume off the plane of the «kv (POS:ce... Moran aud Davila 2001. Deve et al.," Indeed, it has been proposed to use the observed degree of polarisation to estimate the distance of the coronal scattering volume off the plane of the sky (POS;, Moran and Davila 2004, Dere et al." + 2005. Vourlidas aud Howard 2006).," 2005, Vourlidas and Howard 2006)." + ence. a reduction of polarisation of a wlhüte-lieht signal from the corona cau in principle also be explained by a geometric effect. ik Poland aud Muuro's conclusion oulv holds if it is assume that the Πα material is well eiibedded in the CALE clo of enhanced electron deusitv and is located close to the POS of the observer.," Hence, a reduction of polarisation of a white-light signal from the corona can in principle also be explained by a geometric effect, and Poland and Munro's conclusion only holds if it is assumed that the $\alpha$ material is well embedded in the CME cloud of enhanced electron density and is located close to the POS of the observer." + Tn this letter. we report the observation of a simular incidence with the CORLL coronagraph ou board the two STEREO spacecraft A and D. In additiou to the polarisation mieasurements from which we determine the azuuauthal barvceeutre position of the CATE plasina. a stereoscopic triangulation of the low-polarisation patch proves that the prominence material is well embedded inside the CAIE.," In this letter, we report the observation of a similar incidence with the COR1 coronagraph on board the two STEREO spacecraft A and B. In addition to the polarisation measurements from which we determine the azimuthal barycentre position of the CME plasma, a stereoscopic triangulation of the low-polarisation patch proves that the prominence material is well embedded inside the CME." + EUVI and CORI are the multi-waveloneth EUV telescope and the iunermniost coronaeraph of the Sin Earth Connection Coronal and Ueliospheric Iuivestigation(SECCTID instrument suite (Woward ct al., EUVI and COR1 are the multi-wavelength EUV telescope and the innermost coronagraph of the Sun Earth Connection Coronal and Heliospheric Investigation(SECCHI) instrument suite (Howard et al. + 2008) aboard the twin Solar Terrestrial Relations Observatory, 2008) aboard the twin Solar Terrestrial Relations Observatory + Ax-band.,$K$ -band. + Xssuming that the aceretion disc contributes loss than of the A-band light. the jet component must be less than polarised.," Assuming that the accretion disc contributes less than of the $K$ -band light, the jet component must be less than polarised." + The corresponding magnetic field ordering is f«0.38.J1118+480:, The corresponding magnetic field ordering is $f < 0.38$.: +: The polarisation spectrum of this source. including optical data from Schultz.Hakala&Luovelin(2004) is shown in the centre panel of Fig.," The polarisation spectrum of this source, including optical data from \cite*{schuet04} is shown in the centre panel of Fig." + 4., 4. + Schultzetal. claim the LP is variable (with a positive detection in some optical bands but not in others) and their strongest detection (2.60) is in the /-band: LP = 0.57., \citeauthor{schuet04} claim the LP is variable (with a positive detection in some optical bands but not in others) and their strongest detection $\sigma$ ) is in the $I$ -band; LP = $\pm$. + There is no apparent increase at higher frequencies. with a L-band upper limit of (30) so the positive detection is unlikely to be due to interstellar dust. (the extinction. is very low: see Table 2).," There is no apparent increase at higher frequencies, with a $B$ -band upper limit of $\sigma$ ) so the positive detection is unlikely to be due to interstellar dust (the extinction is very low; see Table 2)." + We find 3m upper limits on the order of LP in J and A., We find $\sigma$ upper limits on the order of LP in $J$ and $K$. + According to a recent study of the broadband: quiescent spectrum of NPE J1118|480.2007).. the jet could. make a significant contribution to the mic-LRoptical spectrum.," According to a recent study of the broadband quiescent spectrum of XTE J1118+480, the jet could make a significant contribution to the mid-IR–optical spectrum." + In their model (middle right panel of their Fig., In their model (middle right panel of their Fig. + 3). the jet. contributes approximatelyA5'A.. and of the Hux in A. J and £. respectively.," 3), the jet contributes approximately, and of the flux in $K$, $J$ and $I$, respectively." + From the polarisation measuremoents. this would correspond to a jet LP of 1Jy transient sources with ~ 1 day time-scales at a range of Galactic latitudes., \citet{Matsumura09} have discovered a number of $>1\unit{Jy}$ transient sources with $\sim$ 1 day time-scales at a range of Galactic latitudes. +" ? discovered a 30 Jy transient source at 1.4 GHz with a 5 ms time-scale, but there is evidence this may be atmospheric (?).."," \citet{lorimer2007bmr} discovered a 30 Jy transient source at 1.4 GHz with a 5 ms time-scale, but there is evidence this may be atmospheric \citep{BurkeSpolaor10lg}." +" ? found a ~100mJy transient at 330 MHz during deep Very Long Baseline Interferometer (VLBI) observations, and ? found 39 variable sources in the Galactic Plane with 3 epochs of 5 GHz Very Large Array (VLA) observations, most of which had no known counterparts at other wavelengths."," \citet{lec2008deep} found a $\sim 100 \unit{mJy}$ transient at 330 MHz during deep Very Long Baseline Interferometer (VLBI) observations, and \citet{Becker10} found 39 variable sources in the Galactic Plane with 3 epochs of 5 GHz Very Large Array (VLA) observations, most of which had no known counterparts at other wavelengths." + In this paper we present a survey for transient and variable sources at 843 MHz with characteristic time-scales from days to years., In this paper we present a survey for transient and variable sources at 843 MHz with characteristic time-scales from days to years. +" We aim to characterise the variable and transient radio sky at this frequency, enumerate the most extreme variable sources, find transient sources and develop techniques suitable for upcoming radio surveys."," We aim to characterise the variable and transient radio sky at this frequency, enumerate the most extreme variable sources, find transient sources and develop techniques suitable for upcoming radio surveys." + For our analysis we are using the Molonglo Observatory Synthesis Telescope (MOST)., For our analysis we are using the Molonglo Observatory Synthesis Telescope (MOST). +" The MOST and its predecessor the Molonglo Cross, have been at the forefront of research in this area over several decades."," The MOST and its predecessor the Molonglo Cross, have been at the forefront of research in this area over several decades." +" Using the Molonglo Cross, ? was the first to observe low frequency variability at 408 MHz."," Using the Molonglo Cross, \citet{Hunstead72} was the first to observe low frequency variability at 408 MHz." +" In an archival survey of calibrator measurements, ? found that one-third of the bright point sources at 843 MHz were variable, and a weak Galactic latitude dependence was demonstrated, indicating that interstellar scintillation was at least partly responsible."," In an archival survey of calibrator measurements, \citet{gaensler2000most} found that one-third of the bright point sources at 843 MHz were variable, and a weak Galactic latitude dependence was demonstrated, indicating that interstellar scintillation was at least partly responsible." +" The MOST has been used to discover several hundred pulsars in a number of surveys (?),, and a survey for short-duration transients has been performed by ? but with a null result."," The MOST has been used to discover several hundred pulsars in a number of surveys \citep{Manchester85}, and a survey for short-duration transients has been performed by \citet{Amy89} but with a null result." +" As a follow-up instrument, the MOST was the first telescope to detect prompt radio emission from SN1987A (? ?)), and it has been used to monitor a number of Galactic accreting systems (?),, a brightening supernova remnant (7) and a magnetar flare (7).."," As a follow-up instrument, the MOST was the first telescope to detect prompt radio emission from SN1987A \citeauthor{Turtle87} \citeyear{Turtle87}) ), and it has been used to monitor a number of Galactic accreting systems \citep{Hannikainen98}, a brightening supernova remnant \citep{Murphy08} and a magnetar flare \citep{Gaensler05}." +" The MOST archive is a unique resource which is able to address the limitations of sky coverage, sensitivity and cadence that have accompanied other blind surveys."," The MOST archive is a unique resource which is able to address the limitations of sky coverage, sensitivity and cadence that have accompanied other blind surveys." +" In addition, the experience gained from analysing wide field-of-view images provides an opportunity to develop techniques suitable for upcoming wide-field transient and variability surveys such as the Variables And Slow ‘Transients (VAST) survey for the Australian Square Kilometre Array Pathfinder (ASKAP) (?) and the LOFAR Transients Key Project (?).."," In addition, the experience gained from analysing wide field-of-view images provides an opportunity to develop techniques suitable for upcoming wide-field transient and variability surveys such as the Variables And Slow Transients (VAST) survey for the Australian Square Kilometre Array Pathfinder (ASKAP) \citep{Chatterjee10} and the LOFAR Transients Key Project \citep{Fender08}." + In 82 we describe the MOST and its image archive., In $\S$ 2 we describe the MOST and its image archive. +" In 83 we describe our method of extracting light curves from this archive and in §4 we present the results of applying our method, including quality checks and selected sources."," In $\S$ 3 we describe our method of extracting light curves from this archive and in $\S$ 4 we present the results of applying our method, including quality checks and selected sources." +" In § 5 we discuss our results, The Molonglo Observatory Synthesis Telescope (MOST) is located near Canberra, Australia and was constructed by modification of the East-West arm of the former One-Mile Mills Cross telescope."," In $\S$ 5 we discuss our results, The Molonglo Observatory Synthesis Telescope (MOST) is located near Canberra, Australia and was constructed by modification of the East-West arm of the former One-Mile Mills Cross telescope." + The MOST is an east-west synthesis array comprising two cylindrical paraboloids each of dimension 778 m x 12 m separated by 15 m. Radio waves are received by a line feed system of 7744 circular dipoles., The MOST is an east-west synthesis array comprising two cylindrical paraboloids each of dimension 778 m $\times$ 12 m separated by 15 m. Radio waves are received by a line feed system of 7744 circular dipoles. +" The telescope is steered in the North-South axis by mechanical rotation of the paraboloids about their long axis, and in the East-West axis by phasing the feed elements along the arms."," The telescope is steered in the North-South axis by mechanical rotation of the paraboloids about their long axis, and in the East-West axis by phasing the feed elements along the arms." +" By tracking the field over 12 h, a full synthesis image can be formed."," By tracking the field over 12 h, a full synthesis image can be formed." + The near-continuous UV coverage from 15 m to 1.6 km results in good response to complex structure and low sidelobe levels., The near-continuous UV coverage from 15 m to 1.6 km results in good response to complex structure and low sidelobe levels. + Technical specifications are shown in Table [Il., Technical specifications are shown in Table \ref{tab:mostspecs}. + The MOST has been described in detail by ? and ?.., The MOST has been described in detail by \citet{Mills81} and \citet{robertson1991themost}. + Since 1986 the MOST has observed a single field for a 12 h synthesis almost every week night and often during the day on weekends., Since 1986 the MOST has observed a single field for a 12 h synthesis almost every week night and often during the day on weekends. +" At the beginning and end of each 12 h synthesis, a set of up to 8 different calibrator sources is observed."," At the beginning and end of each 12 h synthesis, a set of up to 8 different calibrator sources is observed." +" Calibrator measurements are discarded if they do not pass a number of checks, and the remaining measurements are averaged to obtain gain and pointing solutions for the beginning and end of the observation."," Calibrator measurements are discarded if they do not pass a number of checks, and the remaining measurements are averaged to obtain gain and pointing solutions for the beginning and end of the observation." + The gain and pointing solutions are linearly interpolated over the synthesis time between two calibratorobservations., The gain and pointing solutions are linearly interpolated over the synthesis time between two calibratorobservations. + The full list of calibrators is described by ?.., The full list of calibrators is described by \citet{CambellWillson94}. + Known variable calibrators were removed from the list following the analysis of ?.., Known variable calibrators were removed from the list following the analysis of \citet{gaensler2000most}. + Our present analysis is performed on the final images processed according the procedure described by ? and ?.., Our present analysis is performed on the final images processed according the procedure described by \citet{Green1999MGPS1} and \citet{Bock99}. . +" The MOST is capable of observing in a number of different modes depending on the desired signal-to-noise ratio and field size, as summarised in Table Bl."," The MOST is capable of observing in a number of different modes depending on the desired signal-to-noise ratio and field size, as summarised in Table \ref{tab:imagetypes}. ." + The MOST field of, The MOST field of +οσοι dnverse-Compton aud svuchrotron enission. which is roughly eiven by the ratio of radiation aud naguetie field energy deusities. C./(B?/sz).,"between inverse-Compton and synchrotron emission, which is roughly given by the ratio of radiation and magnetic field energy densities, $U_\gamma/(B^2/8\pi)$." + In order o account for the z-rav cussion. the magnetic field energv density needs to be close to equipartition with the hermal enerey of the plasma.," In order to account for the $\gamma$ -ray emission, the magnetic field energy density needs to be close to equipartition with the thermal energy of the plasma." + Since a significant fraction of this thermal energy is eundtted as 5-ays. we estimate Beἀπ~ UL.," Since a significant fraction of this thermal energy is emitted as $\gamma$ -rays, we estimate $B^2/8\pi\sim U_\gamma$ ." +" Using U.cL./AxcRZI?e this eives D—LLο Go aud f2~10?Tas/DBae[2| as. where Le5,=L-/literes+. Bs=B/lo’ CG. aud =104? Πε is the observed frequency. 5=Tyme=ΓΡ OTe."," Using $U_\gamma\simeq L_{\gamma}/4\pi +R_\gamma^2\Gamma^2c$ this gives $B\sim10^5L_{\gamma,51}^{1/2}\Gamma_{2.5}^{-1}R_{13}^{-1}$ G and $t_c\sim10^{-2}\Gamma_{2.5}/B_5\nu'_{15}(1+y)$ s, where $L_{\gamma,51}=L_\gamma/10^{51}\rm +erg\,s^{-1}$, $B_5=B/10^5$ G, and $\nu'_{15}=\nu'/10^{15}$ Hz is the observed frequency, $\nu'=\Gamma\nu=\Gamma\gamma^2_\nu eB/2\pi m_ec$ ." +" Since tv);=1)«f, the electrons. which were initially accelerated to high energy at which their svuchrotrou emission peaks at 1 MeV. rapidly cool down to energies at which their svuchrotrou cluission peaks well below the optical baud."," Since $t_c(\nu'_{15}=1)\ll t_d$, the electrons, which were initially accelerated to high energy at which their synchrotron emission peaks at $\sim1$ MeV, rapidly cool down to energies at which their synchrotron emission peaks well below the optical band." +" Neelecting svuchrotron selfabsorption. this would have lead to a synchrotron spectrum of E,xp.7? exteudiug from the s-ray band to below the optical band (CE, stands for the flux per unit frequency)."," Neglecting synchrotron self-absorption, this would have lead to a synchrotron spectrum of $F_\nu\propto \nu^{-1/2}$ extending from the $\gamma$ -ray band to below the optical band $F_\nu$ stands for the flux per unit frequency)." +" Self-absorption of photons of frequency v is dominated bv electrons with Lorenz factor 5,. which constitute a fraction £.(5,)/f4 of the clectron population."," Self-absorption of photons of frequency $\nu$ is dominated by electrons with Lorenz factor $\gamma_\nu$, which constitute a fraction $t_c(\gamma_\nu)/t_d$ of the electron population." +" We lay therefore approximate the (volume averaged) absorption coefficient by a,zn[ftGiMfalP.9BGnew). where the electron density is giveu οςΞi,PRPine. with L, the kinetic Ilunünositv of the CRB 1x17?outflow."," We may therefore approximate the (volume averaged) absorption coefficient by $\alpha_\nu\approx +n_e[t_c(\gamma_\nu)/t_d] e^3B /2\gamma_\nu(m_ec\nu)^2$, where the electron density is given by $n_e=L_k/4\pi \Gamma^2R^2m_pc^3$, with $L_k$ the kinetic luminosity of the GRB outflow." +" The self-absorption frequency. where the optical depth a,2/T equals unity. is independent oof B. aud. tho correspondiug electron Lorenz factor is >,=—Ava)zm2016Dlp.1nτα|y)πο Tere Liu=Γιloeres |."," The self-absorption frequency, where the optical depth $\alpha_\nu R/\Gamma$ equals unity, is independent of $B$, and the corresponding electron Lorenz factor is $ + \gamma_a\equiv\gamma_\nu(\nu_a)\approx30L_{k,52}^{1/6}\Gamma_{2.5}^{-1/3}B_5^{-1/2}R_{13}^{-1/3}(1+y)^{-1/6}. +$ Here $L_{k,52}=L_k/10^{52}\rm erg\,s^{-1}$ ." +" Note. that the electron. cooling rate is modified below 5,. and f£. becomes larger thin that used for deriving eq. (13)."," Note, that the electron cooling rate is modified below $\gamma_a$, and $t_c$ becomes larger than that used for deriving eq. \ref{eq:absorp_nu}) )," + due to the absorption of radiation., due to the absorption of radiation. + Towever this modification is not large for yo~1. in which cease cooling by inverse-Comptou cinission i:4. comparable to svuchrotrou cooling.," However this modification is not large for $y\sim1$, in which case cooling by inverse-Compton emission is comparable to synchrotron cooling." + Examining eq. (1)).," Examining eq. \ref{eq:absorp_nu}) )," + we expect a large optical depth below the A-vav band aud hence a strong suppression of the optical tux., we expect a large optical depth below the X-ray band and hence a strong suppression of the optical flux. +" This appears to be incousisteut with observations. which typically show FL,2 Fi(eg.Yostetal. 2007)."," This appears to be inconsistent with observations, which typically show $F_{\nu_{\rm op}}\ga F_{\nu_\gamma}$ \citep[e.g.,][]{Yost07}." +. It should be mentioned here that. within the context of the current model. the coustraint A.<104! em. which implies variability1%o>1 eV. is obtained uot ouly from the observed time. fay.but also from the requirement that the svuchrotron euission peaks in the MeV band.," It should be mentioned here that, within the context of the current model, the constraint $R_\gamma<10^{14}$ cm, which implies $\nu'_a\gg1$ eV, is obtained not only from the observed variability time, $t_{\rm var}$, but also from the requirement that the synchrotron emission peaks in the MeV band." +" The characteristic (plasma frame) Lorentz factor of the >-ray cutting electrous i8 540myfin, που 3.2)). leading to svuchrotron emission peaking at hi5~1 MeV implies therefore Π.τς1035 cm."," The characteristic (plasma frame) Lorentz factor of the $\gamma$ -ray emitting electrons is $\gamma_e\sim +m_p/m_e$ (see \ref{sec:rad}) ), leading to synchrotron emission peaking at $h\nu'_p\sim1$ MeV implies therefore $R_\gamma\lesssim10^{13}$ cm." +" This coustraint iuav be avoided. for bursts where HR.X1055 cnm can not be inferred from fy, in a model where 5-ray enmuüssion is assumed to be produced bv iuverse-Compton scattering of TIAM1 MeV svuchrotron plotous (assunnuiue magnetic field well below equipartition)."," This constraint may be avoided, for bursts where $R_\gamma\lesssim10^{13}$ cm can not be inferred from $t_{\rm var}$ , in a model where $\gamma$ -ray emission is assumed to be produced by inverse-Compton scattering of $h\nu'_p\ll1$ MeV synchrotron photons (assuming magnetic field well below equipartition)." + Iu such a iodel the inverse-Comptou spectrum is expected to be lard. Foxv7. at low frequencies. fie’c1 MeV. due to selfabsorptiou of the svuchrotron spectriun (0.2.Panaitescu& Mészáros2000).," In such a model the inverse-Compton spectrum is expected to be hard, $F_\nu\propto\nu^2$, at low frequencies, $h\nu'<1$ MeV, due to self-absorption of the synchrotron spectrum \citep[e.g.][]{Pana00}." +. The observed ρουται is softer for most bursts., The observed spectrum is softer for most bursts. + The optical depth for optical photons drops below unity at radi A8=>loben (see eq. 1: , The optical depth for optical photons drops below unity at radii $R\ga10^{15}$ cm (see eq. \ref{eq:absorp_nu}; ; +note (114)xREY see refsecózad))," note $(1+y)\propto R^{2/3}$, see \\ref{sec:rad}) )." + We show here that the optical ciissiou could be produced by “residual” collisions at such large radi," We show here that the optical emission could be produced by ""residual"" collisions at such large radii." + Note. that the time delay between x-ray aud optical Cluission inthis inodel. is expected to be shorter than the characteristic temporal resolution of the optical observations. which is a few seconds.," Note, that the time delay between $\gamma$ -ray and optical emission inthis model, is expected to be shorter than the characteristic temporal resolution of the optical observations, which is a few seconds." + Thus. optical and οταν cussion nav appear to be sinultaneous.," Thus, optical and $\gamma$ -ray emission may appear to be simultaneous." + However. better temporal resolution niav allow oue to detect a systematic time delay between the two wave bands.," However, better temporal resolution may allow one to detect a systematic time delay between the two wave bands." + In addition. one would expect larger observed variability timescales at ouger wavelengths. Tdelay: ," In addition, one would expect larger observed variability timescales at longer wavelengths, $t_{\rm var, op}\sim\tau_{\rm +delay}$ ." +We approsimate thefioi outflow by a sequence of |o91 equal mass shells (/=1...eeVW) separated by au initial fixed distance efq and expanding with Guitial) Lorenz actors Ευ drawn from a random distribution with au ⋜↧↖↽↸∖↥⋅⋜↧∶↴∙⊾↸∖↕⇁⋜⋯≼⊔∐↑↕⋜↧↕↖⇁⋜∐⋅↕⋜∐⊔⊳↸∖⊼⊺↕−−⊳⋃ ⋅⋅⋅ ⋅ ⋅≻cI7.," We approximate the outflow by a sequence of $N\gg1$ equal mass shells $i=1,\ldots,N$ ) separated by an initial fixed distance $ct_{\rm var}$ and expanding with (initial) Lorenz factors $\Gamma_{i,0}$ drawn from a random distribution with an average $\Gamma$ and initial variance $\sigma^2_{\Gamma,0}<\Gamma^2$." +" We asstune that he radial extent of the outflow /Nefz, is much sinaller han the collision radii Ro>I?efa. ie. N«I?. which is reasonable eiven the observed variability (e.gFish-nan&Aecean 1995)."," We assume that the radial extent of the outflow $Nct_{\rm var}$ is much smaller than the collision radii $R>\Gamma^2 ct_{\rm +var}$, i.e. $N\ll\Gamma^2$, which is reasonable given the observed variability \citep[e.g][]{fm95}." +. The model max. of course. be coniplicated. ee. by adding several variability times or o allowing variable mass shells," The model may, of course, be complicated, e.g. by adding several variability times or by allowing variable mass shells." + Adding such deerees of freedom may allow one to coutrol the details of the xedieted. lone wave leneth cussion., Adding such degrees of freedom may allow one to control the details of the predicted long wave length emission. + Our main goal is o demonstrate that the simplest model cousidered here nav naturally account for the observed optical emission., Our main goal is to demonstrate that the simplest model considered here may naturally account for the observed optical emission. + The dynamics of late residual collisions is discussed iu X1.. aud the radiation they are expected to eeucrate is discussed in$8 3.2..," The dynamics of late residual collisions is discussed in \ref{sec:dynamics}, and the radiation they are expected to generate is discussed in \ref{sec:rad}." + Let us first cousider the evolution of the outflow using the simplifving assumption that shells merece after collisions., Let us first consider the evolution of the outflow using the simplifying assumption that shells merge after collisions. + This assuuptiou would be approximately valid if all the iuterual energy. generated by a collision of two shells is raciated away., This assumption would be approximately valid if all the internal energy generated by a collision of two shells is radiated away. +" As the flow radius increases. the typical nuuber (2) of initial shells that merge iuto one suele shell increases, aud the variance of the Lorenz factors of the resulting shells decreases."," As the flow radius increases, the typical number $n(R)$ of initial shells that merge into one single shell increases, and the variance of the Lorenz factors of the resulting shells decreases." + For a group of shells with a simall Lorenz factor variance. the velocities e; of the shells iu the shells ceuter of momentum frame are not highlv relativistic.," For a group of shells with a small Lorenz factor variance, the velocities $v_i$ of the shells in the shells' center of momentum frame are not highly relativistic." +" In this case. conservation of moment Προς that the velocity of a merged group of shells is given by the average of merged shells! velocities. c=(1n)3774ei aud that the variance of the velocities of inerged. eroups of shells is oa.)=eof where 0,9 is the initial variance."," In this case, conservation of momentum implies that the velocity of a merged group of shells is given by the average of merged shells' velocities, $\bar v=(1/n)\sum_{i=1}^n +v_i$, and that the variance of the velocities of merged groups of shells is $\sigma_v(n)=\sigma_{v,0}/\sqrt{n}$ where $\sigma_{v,0}$ is the initial variance." +" This. inturn. naplies Vnthat the variance of(observer frame) Lorenz factors. στ)x a,(ajfe. evolves like στη)=op.ψη."," This, inturn, implies that the variance of (observer frame) Lorenz factors, $\sigma_\Gamma(n)/\Gamma\approx\sigma_{v}(n)/c$ , evolves like $\sigma_\Gamma(n)=\sigma_{\Gamma,0}/\sqrt{n}$." + Collisionsof, Collisionsof +QSO Iuminosity function is drawn [rom Pei (1995).,QSO luminosity function is drawn from Pei (1995). +" The opacity of the intergalactic medium is computed from the observed redshift ancl column density distributions of Ly-a absorbers eiven bx μι, 2..", The opacity of the intergalactic medium is computed from the observed redshift and column density distributions of $\alpha$ absorbers given by Equ. \ref{eq:dndzdnh1}. + The effects of attenuation ancl reemission of radiation by hvdrogen ancl helium in Ly-a absorbers ave included in (hese models., The effects of attenuation and reemission of radiation by hydrogen and helium in $\alpha$ absorbers are included in these models. +" Their result [or gq,=0.5 and ας=1.8 ab z= Ois (n)—L6x107 ergss 1! ? Du. d", Their result for $q_{0}=0.5$ and $\alpha_{s}=1.8$ at $z=0$ is $J(\nu_{0}) = 1.6 \times 10^{-23}$ ergs $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$. + Fardal et ((1998) compute opacity models for the intergalactic medium (IGM) based on high resolution observations of the high redshift Ly-a forest [rom several authors., Fardal et (1998) compute opacity models for the intergalactic medium (IGM) based on high resolution observations of the high redshift $\alpha$ forest from several authors. + Shull et ((1999) extend the models of Fardal et ((1998) to 2=0. treating opacity of low reclshilt Ly-a forest [rom observations made with HIST/GIIBS (Penton et 22000a.b) and with IIST/FOS (Wevinann οἱ 11993).," Shull et (1999) extend the models of Fardal et (1998) to $z=0$, treating opacity of low redshift $\alpha$ forest from observations made with HST/GHRS (Penton et 2000a,b) and with HST/FOS (Weymann et 1998)." + Like Haardt Madan (1996). thev also incorporate the observed vedshilt distribution of Lviman limit svstems with Ny.) >17 (Stengler-Larrea et 11995. Storrie-Lombardi et 11994).," Like Haardt Madau (1996), they also incorporate the observed redshift distribution of Lyman limit systems with $_{{\rm HI}}$ ) $ > 17$ (Stengler-Larrea et 1995, Storrie-Lombardi et 1994)." +" Their models also allow for a contribution from star formation in galaxies in addition to AGN,", Their models also allow for a contribution from star formation in galaxies in addition to AGN. +" The QSO Iuminosity finetion again is taken to follow the form given by Pei (1995) with upper/lower cutoffs at 0.01/10 L,.", The QSO luminosity function again is taken to follow the form given by Pei (1995) with upper/lower cutoffs at 0.01/10 $_{*}$. +" QSO UV spectral inclicies are assumed (o equal 0.56. while (he ionizing spectrum al v>vy has a,=1.5."," QSO UV spectral indicies are assumed to equal 0.86, while the ionizing spectrum at $\nu > \nu_{0}$ has $\alpha_{s}=1.8$." + The contribution to the background. [rom stars was normalized to the Ha luminosity [function observed by Gallego et ((1995) and the escape fraction of photons of all energies from ealaxies was taken to be =0.05., The contribution to the background from stars was normalized to the $\alpha$ luminosity function observed by Gallego et (1995) and the escape fraction of photons of all energies from galaxies was taken to be $ =0.05$. + The full radiative transfer model described in Fardal et ((1998) was used to caleulate the contribution to the mean intensity by AGN. but not the contribution [rom stars. as (hey were assumed (ο contribute no fInx above 4 Rc. (he energies al which the ellects of IGM reprocessing become important.," The full radiative transfer model described in Fardal et (1998) was used to calculate the contribution to the mean intensity by AGN, but not the contribution from stars, as they were assumed to contribute no flux above 4 Ryd, the energies at which the effects of IGM reprocessing become important." + These authors [ind J(m)—2x10 “eress bem ? Fsr tat 2~0. with approximately equal contributions from AGN and stars. a value somewhat lower than our result for z«1. but which is allowed within the errors.," These authors find $J(\nu_{0})=2.4 \times 10^{-23}$ ergs $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$ at $z\sim 0$, with approximately equal contributions from AGN and stars, a value somewhat lower than our result for $z < 1$, but which is allowed within the errors." + We estimate the contribution to the UV backgrounde from star-forminge 0galaxies usinee the ealaxv Iuminositv [unetion of the Canada-France Redshilt Survey (Lilly et 11995)., We estimate the contribution to the UV background from star-forming galaxies using the galaxy luminosity function of the Canada-France Redshift Survey (Lilly et 1995). + At 2o 0.5. we derive J7(54)=1.5x107 eres ? !sr | assuming =1.," At $z \sim 0.5$ , we derive $J^{\rm gal}(\nu_{0})= 1.5 \times 10^{-22}$ ergs $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$, assuming $=1$." +" The IIM96 models for the QSO contribution give 7979(5,)25.2x107 ergss bem ?Iz ! ! al z00.5.", The HM96 models for the QSO contribution give $J^{\rm QSO}(\nu_{0}) = 5.2 \times 10^{-23}$ ergs $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$ at $z \sim 0.5$. + These estimates. and the range of measured (14) in this paper. ~5—16xLO77 s 7 >Hz sr imply an− escape fraction of⋅MEM UV .photons from galaxies. between/ 1% TO.," These estimates, and the range of measured $J(\nu_{0})$ in this paper, $\sim 5-16 \times 10^{-23}$ ergs $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$ imply an escape fraction of UV photons from galaxies between and." +..The J(n) inferred from 4 /dzin Section 7.3. implies escape fractions well over 1004., The $J(\nu_{0})$ inferred from $d{\cal N}/dz$ in Section \ref{sec-dndz} implies escape fractions well over. +.. Bianchi et ((2001) make updated estimates of the mean intensity of the backeround with contributions from both QSOs and star-forming galaxies., Bianchi et (2001) make updated estimates of the mean intensity of the background with contributions from both QSOs and star-forming galaxies. + Their models incorporate various values of the escape Iraction of Lyman conünuum photons trom galaxies which are constant with redshilt and wavelength., Their models incorporate various values of the escape fraction of Lyman continuum photons from galaxies which are constant with redshift and wavelength. + Our new results alz«1.7 are most consistent with, Our new results at$z < 1.7$ are most consistent with +(Ny= 1 I0! em?) for source UIO (the blue source in Fig.,= 1 $^{21}$ ) for source U10 (the blue source in Fig. + Ib) as well as most of the other CVs but not for the BY candidate U18 (see below)., 1b) as well as most of the other CVs but not for the BY candidate U18 (see below). + Source U24 is similar in x-ray color (Fig., Source U24 is similar in x-ray color (Fig. + 2) and spectral shape to the quiescent low-mass x-ray binaries (or soft x-ray transients in quiescence) in v Centauri (Rutledge et al., 2) and spectral shape to the quiescent low-mass x-ray binaries (or soft x-ray transients in quiescence) in $\omega$ Centauri (Rutledge et al. + 2001) and in 47 Tue (GHEM. and Heinke et al.," 2001) and in 47 Tuc (GHEM, and Heinke et al." + 2001: hereafter HGLE)., 2001; hereafter HGLE). + A BB spectral fit is acceptable (kT=0.19+0.02 keV. Ny=S+5«107 em7). as are power law fits (with a steep unrealistic photon index of 641 and high Nj. sh«107! em) and thermal bremsstrahlung fits (with. kT=0.33--0.05 keV. Ny=2.241«107! env).," A BB spectral fit is acceptable $\pm0.02$ keV, $N_H$ $5\pm5\times10^{20}$ $^{-2}$ ), as are power law fits (with a steep unrealistic photon index of $\pm1$ and high $N_H$ , $5^{+2}_{-1}\times10^{21}$ $^{-2}$ ) and thermal bremsstrahlung fits (with $\pm0.05$ keV, $N_H$ $2.2\pm1\times10^{21}$ $^{-2}$ )." + None of these are physically realistic models. and we turn to hydrogen or helium atmosphere neutron star models (Zavlin. Pavlov. Shibanov 1996; Rajagopal Romani 1996) physically motivated by radiation of heat accumulated in the core of an accreting neutron star during transient episodes and reradiated during quiescence (Brown. Bildsten. Rutledge 1998).," None of these are physically realistic models, and we turn to hydrogen or helium atmosphere neutron star models (Zavlin, Pavlov, Shibanov 1996; Rajagopal Romani 1996) physically motivated by radiation of heat accumulated in the core of an accreting neutron star during transient episodes and reradiated during quiescence (Brown, Bildsten, Rutledge 1998)." + This model has been fit successfully to the qLMXBs Cen X-4. Aql X-1. CXOU 132619.7-472910.8 in x Cen: and X5 and X7 in 47 Tuc (Rutledge et al.," This model has been fit successfully to the qLMXBs Cen X-4, Aql X-1, CXOU 132619.7-472910.8 in $\omega$ Cen; and X5 and X7 in 47 Tuc (Rutledge et al." + 2001 and references therein: HGLE)., 2001 and references therein; HGLE). + 5.5truecm We fit the unmagnetized models of Lloyd Hernquist (2001. in preparation). which assume a completely tonized atmosphere and opacity due to coherent electron scattering and free-free absorption.," 8.5truecm We fit the unmagnetized models of Lloyd Hernquist (2001, in preparation), which assume a completely ionized atmosphere and opacity due to coherent electron scattering and free-free absorption." +" A neutron star surface gravity of log e,214.38 was assumed. yielding a gravitational redshift of 0.306."," A neutron star surface gravity of log $g_s$ =14.38 was assumed, yielding a gravitational redshift of 0.306." + Either a hydrogen or helium atmosphere gives a good fit (see Table | for Το). with implied radii of the neutron star (R4. as seen at infinity) of 4.9*H km for a hydrogen atmosphere. and 12.053 km for a helium atmosphere.," Either a hydrogen or helium atmosphere gives a good fit (see Table 1 for $_{eff}$ ), with implied radii of the neutron star $_{\infty}$, as seen at infinity) of $^{+14}_{-1}$ km for a hydrogen atmosphere, and $^{+3}_{-7}$ km for a helium atmosphere." + These are consistent with theoretical predictions for R4. which span the range 10 to 18 km (Lattimer Prakash. 2001). and the similarity of the fits to better-constrained fits on X5 and X7 in 47Tuc suggests that we are indeed seeing thermal emission from the whole surface of the neutron star.," These are consistent with theoretical predictions for $_{\infty}$ which span the range 10 to 18 km (Lattimer Prakash, 2001), and the similarity of the fits to better-constrained fits on X5 and X7 in 47Tuc suggests that we are indeed seeing thermal emission from the whole surface of the neutron star." + No power law component is seen. with only of the total emission above 2.5 keV and only one photon above3.3 keV. A marginal 1) emission feature is seen in the spectrum at 0.9 keV. similar to the more significant features seen in X5 and X7 in 47 Tuc.," No power law component is seen, with only of the total emission above 2.5 keV and only one photon above 3.3 keV. A marginal $\sigma$ ) emission feature is seen in the spectrum at 0.9 keV, similar to the more significant features seen in X5 and X7 in 47 Tuc." + The lack of variability and complete lack of a power law component suggest that no aceretion onto the neutron star surface is currently taking place (see HGLE)., The lack of variability and complete lack of a power law component suggest that no accretion onto the neutron star surface is currently taking place (see HGLE). + 9.3truecm A dramatic eclipse (duration —-00.5hour) for source U23 (ΟΝΕ is seen midway through the 49ksee observation. consistent with the 11.3 hour period discovered for this eclipsing CV (GTEC).," 9.4truecm A dramatic eclipse (duration 0.5hour) for source U23 (CV1) is seen midway through the 49ksec observation, consistent with the 11.3 hour period discovered for this eclipsing CV (GTEC)." + Similarly. U17 (CV3) shows smooth variations.," Similarly, U17 (CV3) shows smooth variations." + Pulsation analysis for the CVs reveals. several candidate periods.but longer observations (to be conducted in Chandra cycle 3) are required.," Pulsation analysis for the CVs reveals several candidate periods, but longer observations (to be conducted in Chandra cycle 3) are required." + The BY candidate U20 is clearly flaring whereas the surprisingly hard spectrum BY (or possible RS CVn) UI$8 appears constant as do U[5 and U43., The BY candidate U20 is clearly flaring whereas the surprisingly hard spectrum BY (or possible RS CVn) U18 appears constant as do U15 and U43. + Source U12 shows a smooth sinusoidal like variation (discussed below) over the Chandra observation., Source U12 shows a smooth sinusoidal like variation (discussed below) over the Chandra observation. + The x-ray spectral results suggest 9 CVs. all with moderately hard TB spectra and internal self-absorption.," The x-ray spectral results suggest 9 CVs, all with moderately hard TB spectra and internal self-absorption." + The intrinsicNj;.. particularly for UIO (CV6). suggests these systems may be dominated by magnetic CVs which show internal absorption from their “accretion curtains” (cf.," The intrinsic, particularly for U10 (CV6), suggests these systems may be dominated by magnetic CVs which show internal absorption from their “accretion curtains” (cf." + GHEM and references therein)., GHEM and references therein). + Three of these CVs (CVs 1-3) were originally identified as such in our initial HST survey (Cool et al 1995)., Three of these CVs (CVs 1-3) were originally identified as such in our initial HST survey (Cool et al 1995). + Two others (CVs 4-5) were found via variability or as counterparts to ROSAT HRI sources (Cool et al 1998: Grindlay 1999)., Two others (CVs 4-5) were found via variability or as counterparts to ROSAT HRI sources (Cool et al 1998; Grindlay 1999). + CVs 6-8 were discovered in our deeper followup HST survey (GTEC)., CVs 6-8 were discovered in our deeper followup HST survey (GTEC). + The 9th (= ROSAT source A) we identify as à CV on the basis of its Chandra spectrum. which closely resembles that of U21 (CV4): it lies outside the HST field of view.," The 9th $=$ ROSAT source A) we identify as a CV on the basis of its Chandra spectrum, which closely resembles that of U21 (CV4); it lies outside the HST field of view." + Using the very likely identifications with CVs 1-8. the required shifts in RA. Dee between HST and Chandra are..their.. due (primarily) to the difference in absolute astrometry of respective guide star systems (all positions in Table | are on the Chandra reference frame. currently accurate to (lo) (Alderoft et al 2000).," Using the very likely identifications with CVs 1-8, the required shifts in RA, Dec between HST and Chandra are, due (primarily) to the difference in absolute astrometry of their respective guide star systems (all positions in Table 1 are on the Chandra reference frame, currently accurate to $\sigma$ ) (Aldcroft et al 2000)." + This solution Ντ Mito nal seaera ERADE iBYe Dre &tasradentidied CB from; Tt; igtasl franksebenqiantanadly psn," This solution allows precise ) positional searches for the BY Dra stars identified (2 from TGEC, and 2 from subsequent analysis)." + OHSΠΕΝtei DV DandiBAKs &(o ΡΟΗ δρprm So NSESoul , The HST detected CVs and BYs are marked in the CMDs of Figure 3. +Dui tonRUNSn hp TUOor WHdk |TIRE (JIRENT hid cr wesetamoin (Q or companion ofat My>1H., No star is seen at the position of the likely qLXMB and we set a limit for the optical companion of $M_V > 11$. + TAPER mit 5d the ween nas Source U12. optically identified by TGEC with a BY star (WF4-1). is in fact the eclipsing binary MSP (PSRJ1740-5340) previously discovered in NGC 6397 (D'Amico et al 2001a) for which the pulsar timing position (D'Amico et al 2001b) suggests the same optical counterpart (Ferraro et al 2001).," 12.5truecm ol and Bolton 2001) are shown as dots.} Source U12, optically identified by TGEC with a BY star (WF4-1), is in fact the eclipsing binary MSP (PSRJ1740-5340) previously discovered in NGC 6397 (D'Amico et al 2001a) for which the pulsar timing position (D'Amico et al 2001b) suggests the same optical counterpart (Ferraro et al 2001)." +" The offset in position. (radio-x-ray) A(RA.Dec)=..., is consistent with the Chandra astrometric uncertainties."," The offset in position, (radio-x-ray) $\delta$ (RA,Dec)=, is consistent with the Chandra astrometric uncertainties." + The BY signatures (main sequence like binary: weak emission) are likely due to MSP heating (or shock excitation) of the main sequence companion in this unusual long-period (1.35d) binary system. which ts evident in the x-ray variation of UI2: the smooth rise in x-ray flux is consistent with the phase of egress from radio eclipse.," The BY signatures (main sequence like binary; weak emission) are likely due to MSP heating (or shock excitation) of the main sequence companion in this unusual long-period (1.35d) binary system, which is evident in the x-ray variation of U12: the smooth rise in x-ray flux is consistent with the phase of egress from radio eclipse." + Further details. and comparison with the MSPs detected by Chandra in 47Tuc (GHEM). are given in Grindlay et al. in preparation.," Further details, and comparison with the MSPs detected by Chandra in 47Tuc (GHEM), are given in Grindlay et al, in preparation." +" Surprisingly. none of the ""non-flickerers"" (Cool et al 1998. TGEC) which we have identified as containing He White Dwarfs (Edmonds et al 1999). are detected with Chandra."," Surprisingly, none of the “non-flickerers” (Cool et al 1998, TGEC) which we have identified as containing He White Dwarfs (Edmonds et al 1999), are detected with Chandra." + The suspected ROSAT detection of NF3 (Verbunt and Johnston 2000) is in fact 118. identified here with a neighboring BY Dra candidate aaway. and similar to the MSP UI2 in its position in the CMD (Fig.," The suspected ROSAT detection of NF3 (Verbunt and Johnston 2000) is in fact U18, identified here with a neighboring BY Dra candidate away, and similar to the MSP U12 in its position in the CMD (Fig." + dis, 3). +"tributionThis suggests the HeWDs in NGC 6397. with radial 3). indicatingthey contain""dark"" binary companions (TGEC). do not contain neutron stars which would likely"," This suggests the HeWDs in NGC 6397, with radial distribution indicatingthey contain “dark” binary companions (TGEC), do not contain neutron stars which would likely" +driven away by (he energy released by stars in the star particle.,driven away by the energy released by stars in the star particle. + The metal enriched particles mix with metal-free gas particles. but do not enrich them since (here is no diffusion [rom gas particles.," The metal enriched particles mix with metal-free gas particles, but do not enrich them since there is no diffusion from gas particles." + Therefore the metal distribution is not evenly smoothed. but concentrated in the [ew gas particles that have been directly enriched by star-forming particles.," Therefore the metal distribution is not evenly smoothed, but concentrated in the few gas particles that have been directly enriched by star-forming particles." + As a result most of the WIIIM is poor in metals and its emission is underestimated., As a result most of the WHIM is poor in metals and its emission is underestimated. + This can be avoided if a model of diffusion of metals Grom one particle to the others is included in the simulation. which is not the ease of the simulation we used.," This can be avoided if a model of diffusion of metals from one particle to the others is included in the simulation, which is not the case of the simulation we used." + In addition to the metallicity extracted from the Borgani model. we used three analytical models based on relations between metallicity and densitv (see Fig. 6)).," In addition to the metallicity extracted from the Borgani model, we used three analytical models based on relations between metallicity and density (see Fig. \ref{metallicity-vs-density}) )." +" The first analvtical model (defined as ""Croft model) links the metallicity directly to the eas density. using the relation Zx(p/p)!?."," The first analytical model (defined as “Croft model”) links the metallicity directly to the gas density, using the relation $Z\propto(\rho/\overline{\rho})^{1/2}$." + Metallicity is normalized to Z=0.005 Z:- ab p=p. so that it matches the measured metallicity of the Ly-a forest. while an upper limit of Z=0.3 Z. fits well with data on clusters Fangetal.(2005).," Metallicity is normalized to $Z=0.005$ $Z\odot$ at $\rho=\overline\rho$, so that it matches the measured metallicity of the $\alpha$ forest, while an upper limit of $Z=0.3$ $Z_\odot$ fits well with data on clusters \cite{Fang05}." +. This model is in agreement with (he metallicity predicted by Cen Ostriker (1999a) at 2=3 and is about a factor 5 lower than the IGM metallicity at more recent times., This model is in agreement with the metallicity predicted by Cen Ostriker (1999a) at $z=3$ and is about a factor 5 lower than the IGM metallicity at more recent times. + Nevertheless we adopted this model as comparison since il has also been used by other authors (2005).," Nevertheless we adopted this model as comparison since it has also been used by other authors \cite{Croft01, Fang05}." +. The second analvtical metallicity model (which we called the “Scatter model”) is based on the distribution function of metallicity [rom Cen and Ostriker (1999b) at recdshift -=0., The second analytical metallicity model (which we called the “Scatter model”) is based on the distribution function of metallicity from Cen and Ostriker (1999b) at redshift $z=0$ . +" Part of the output of that simulation consists of three boxes of 512% cells with values of temperature. density. ancl metallicity,"," Part of the output of that simulation consists of three boxes of $512^3$ cells with values of temperature, density, and metallicity." + Using the three boxes we generated the probability distribution function of metallicity as a function of density. where metallicity is divided in 110 intervals from 10.* to 10! Z. and density is divided in 70 intervals from 10.? to 107 py.," Using the three boxes we generated the probability distribution function of metallicity as a function of density, where metallicity is divided in 110 intervals from $10^{-7}$ to $10^4$ $Z_\odot$ and density is divided in 70 intervals from $10^{-3}$ to $10^4$ $\rho_b$." + When (his model is selected. the code reads the density of each particle and assigns a random metallicitv based on the probability distribution function at the corresponding density.," When this model is selected, the code reads the density of each particle and assigns a random metallicity based on the probability distribution function at the corresponding density." + The average distribution of metallicity for this model is represented by the black curve in Fie. 6.., The average distribution of metallicity for this model is represented by the black curve in Fig. \ref{metallicity-vs-density}. + This model has the highest metallicity among the four models (a [actor 2—3 for overdensities between LO and 1000) and. since at first order (he intensity of the lines depends linearly on metalliitv. we use the emission with (he scatter model as an upper limit for our set of simulations.," This model has the highest metallicity among the four models (a factor $2-3$ for overdensities between 10 and 1000) and, since at first order the intensity of the lines depends linearly on metallicity, we use the emission with the scatter model as an upper limit for our set of simulations." +" The third analvtical metallicity model. labeled ""Cen model”. is an improved version of (he scatter model. where we also include redshift dependence evaluated Irom Fig."," The third analytical metallicity model, labeled “Cen model”, is an improved version of the scatter model, where we also include redshift dependence evaluated from Fig." + 2 of Cen Ostriker (1999b)., 2 of Cen Ostriker (1999b). +" A ""random"" metallicity is initially evaluated following the same procedure used for the scatter model. then it is modified according to redshift of the particle."," A “random” metallicity is initially evaluated following the same procedure used for the scatter model, then it is modified according to redshift of the particle." + We note that the redshift dependence of the metallicity is optimized for WIIIM particles aud would overestimate (hemetallicity of clusters aud groups., We note that the redshift dependence of the metallicity is optimized for WHIM particles and would overestimate themetallicity of clusters and groups. + By definition the average values of the, By definition the average values of the + (e.g..seeRempel2006)... (Leighton1959).," \citep[e.g., see][]{rem06}. \citep{lei59}." +. Wilson(1978) (~0.5 μΗΖ) (Libbrecht&Wo," \cite{wil78} \citep{bro89,sch98}." +odard1990;Salabertetal.2004).. al.2003).. (Baglinetal.2006)..2010).," $\sim$ $\mu$ \citep{lw90,sal04}. \citep{wal03}, \citep{bag06},," +. as well as ground-based networks like the Stellar Observations Network Group (SONG:Grundahletal.2008).. are now allowing additional tests of dynamo models using other solar-type stars (e.g..seeChaplinetal.2007:etal.2007)..," as well as ground-based networks like the Stellar Observations Network Group \citep[SONG;][]{gru08}, are now allowing additional tests of dynamo models using other solar-type stars \citep[e.g., see][]{cha07,met07}. ." +" The F8V star ; Horologii ( Hor = 117051 = 8810. Vz54. B-Vz0.57) hosts a non-transiting 2 M, exoplanet with an orbital period of 311. days (Kürsteretal.2000:Naefetal. 2001)."," The F8V star $\iota$ Horologii $\iota$ Hor $\equiv$ 17051 $\equiv$ 810, V=5.4, $-$ V=0.57) hosts a non-transiting 2 $M_J$ exoplanet with an orbital period of 311 days \citep{kur00,nae01}." +. Although 1t is currently situated in the southern hemisphere. kinematic considerations have led to the suggestion that it could be an evaporated member of the Hyades cluster (Montesetal.20010.," Although it is currently situated in the southern hemisphere, kinematic considerations have led to the suggestion that it could be an evaporated member of the Hyades cluster \citep{mon01}." +.. Asteroseismic observations support this conclusion. since the acoustic oscillation frequencies of the star are best reproduced with models that have the same metallicity. heltum abundance. and stellar age as other Hyades members (Vauclairetal.2005).," Asteroseismic observations support this conclusion, since the acoustic oscillation frequencies of the star are best reproduced with models that have the same metallicity, helium abundance, and stellar age as other Hyades members \citep{vau08}." + We report the discovery of a l.6-year magnetic activity cycle in. ; Hor from synoptic Ca HK measurements obtained with the Small and Moderate Aperture Research Telescope System (SMARTS) 1.5-m telescope at Cerro Tololo Interamerican Observatory (CTIO) since 2008., We report the discovery of a 1.6-year magnetic activity cycle in $\iota$ Hor from synoptic Ca HK measurements obtained with the Small and Moderate Aperture Research Telescope System (SMARTS) 1.5-m telescope at Cerro Tololo Interamerican Observatory (CTIO) since 2008. + We provide an overview of the survey methodology and analysis methods in refSEC2.. and we present the stellar activity measurements and other derived properties in refSEC3..," We provide an overview of the survey methodology and analysis methods in \\ref{SEC2}, and we present the stellar activity measurements and other derived properties in \\ref{SEC3}." + We conclude with a discussion of the broader implications of this discovery for stellar dynamo modeling and future observations in refSECA.., We conclude with a discussion of the broader implications of this discovery for stellar dynamo modeling and future observations in \\ref{SEC4}. + The chromospheric activity survey of Henryetal.(1996) contained a total of 1016 observations of 815 individual stars with visual magnitudes between 0.0 and about 9.0. which were observed using the instrument on theCTIO1.5-m telescope.," The chromospheric activity survey of \cite{hen96} contained a total of 1016 observations of 815 individual stars with visual magnitudes between 0.0 and about 9.0, which were observed using the instrument on theCTIO1.5-m telescope." +" Several sub-samples were defined.including the “Best Brightest” (B) and ""Nearby"" (N) samples. which together contain 92 individual stars with visual magnitudes between 0.0 and 7.9. and B-V colors"," Several sub-samples were defined,including the “Best Brightest” (B) and “Nearby” (N) samples, which together contain 92 individual stars with visual magnitudes between 0.0 and 7.9, and $-$ V colors" +constraint on its soution.,constraint on its solution. + The discovery that there is a plausible solution argues for tle model. aud nay be astep towad the more challenging. and perhaps workable. problem of determiuine whetler the o»erved mass concentrations outside the LG could have been arranged at high 'eclshift so as to act as the third uassive |od.," The discovery that there is a plausible solution argues for the model, and may be a step toward the more challenging, and perhaps workable, problem of determining whether the observed mass concentrations outside the LG could have been arranged at high redshift so as to act as the third massive body." + Even with all tie simuplifving assumptions tle solution required the lengthy nuiuerical approach outLied in Section ??.., Even with all the simplifying assumptions the solution required the lengthy numerical approach outlined in Section \ref{sec:sec2}. + 1 do not iiagiue this methoc will linc applicatious to problems outside the Local Group aid its more inunediate neighbors. but I believe the opportunity o explore in Austally close detail what happeed in our iminediate extragalactic neighborhood justilies the tanelecd procedure.," I do not imagine this method will find applications to problems outside the Local Group and its more immediate neighbors, but I believe the opportunity to explore in unusually close detail what happened in our immediate extragalactic neighborhood justifies the tangled procedure." + The main focus of this paper is the analysis of the past |istory of the LMC in Section ??.., The main focus of this paper is the analysis of the past history of the LMC in Section \ref{sec:sec3}. + Iu this compulation the mass of tve LMC is a parameter to je adjusted. along wih the other Inasses {ο fi ο the measured velociies of the LMC and M:M., In this computation the mass of the LMC is a parameter to be adjusted along with the other masses to fit to the measured velocities of the LMC and M31. +T at leads to an LMC mass of about Lx10!AL., That leads to an LMC mass of about $4\times 10^{10}M_\odot$. + OGD point out that at this mass. and within the uucertaiuty of the measwed relative velocity of le Clouds. the SMC cau be bouud to the LMC. te reasonable sitation eiven their similar positions and motious.," K06b point out that at this mass, and within the uncertainty of the measured relative velocity of the Clouds, the SMC can be bound to the LMC, the reasonable situation given their similar positions and motions." + Section ?? presents examples of hec ousisteucy of this sItuation in the solution or the motion of the LMC., Section \ref{sec:sec4} presents examples of the consistency of this situation in the solution for the motion of the LMC. + Section ?? reviews tle arguuments for plausibility of the history of tre Clouds obtained here., Section \ref{sec:sec5} reviews the arguments for plausibility of the history of the Clouds obtained here. + The stinplifving approxiuations iu this calculation rectIre sonne e«inments., The simplifying approximations in this calculation require some comments. + The first assumptio[un is that. back to redshift σι10. the momentum aud cener of ruass of a protogalaxy are uselully approximated by the rnometrtun amd position of a single 1lass lracer. in ai N-body problem witl stnall ;N.," The first assumption is that, back to redshift $z_{\rm init}\sim 10$, the momentum and center of mass of a protogalaxy are usefully approximated by the momentum and position of a single mass tracer, in an $N$ -body problem with small $N$." + This need. not. be inconsisteut with the hierarcical growh of galaxies by merging of substructures: each body is ueaut to represent the mean 110tiou of tje collection of substructures hat in the course of time 1jerge to form the galaxy., This need not be inconsistent with the hierarchical growth of galaxies by merging of substructures: each body is meant to represent the mean motion of the collection of substructures that in the course of time merge to form the galaxy. + Lu he solution obtained here the pliysica separatious of the protogalaxles at Zini160 are comparable to their present massive halo radil. ueaning the couditiou for tle mass trace: iioclel is that at tyyi the bulk of each protogalaxy already is within its present halo radius.," In the solution obtained here the physical separations of the protogalaxies at $z_{\rm init}\sim 10$ are comparable to their present massive halo radii, meaning the condition for the mass tracer model is that at $z_{\rm init}$ the bulk of each protogalaxy already is within its present halo radius." + In. parti—lar. the LNIC could be i pieces at tin. provided the yleces are scattered over less than about 1JO kpe.," In particular, the LMC could be in pieces at $z_{\rm init}$, provided the pieces are scattered over less than about 100 kpc." + The model fails if the LMC forms at z«10 by he merger of pieces that οςne together toug quite differeut paths., The model fails if the LMC forms at $z<10$ by the merger of pieces that come together along quite different paths. + But different paths suggest ‘elative velocities well above motious wittu ithe LMC. which sugeMODests tlie pieces are not likely to neree.," But different paths suggest relative velocities well above motions within the LMC, which suggests the pieces are not likely to merge." + The initial condition in the model is tlat the peculiar velocities of the protoClouds satisfy, The initial condition in the model is that the peculiar velocities of the protoClouds satisfy +At the present epoch barvous in stars and ealaxies coustitute onlv a small fraction of the total barvon deusitv predicted by the Bie Bang uucleosvuthesis model (?)..,At the present epoch baryons in stars and galaxies constitute only a small fraction of the total baryon density predicted by the Big Bang nucleosynthesis model \citep*{fukugita_etal98}. + This is iu agreement with the Cold Dark Matter (CDAD) models of structure formation which predict that a larec Taction of barvons at zz0 is located in filaments and iuterealactie πουπα of groups aud clusters. where it is shock-heated to teniperatures of T—10—107 K (T7).," This is in agreement with the Cold Dark Matter (CDM) models of structure formation which predict that a large fraction of baryons at $z\approx 0$ is located in filaments and intergalactic medium of groups and clusters, where it is shock-heated to temperatures of $T\sim 10^5-10^7$ K \citep{cen_ostriker99,dave_etal99}." + The detection of the παπαο intergalactic ποτα (ΝΠΙΔ aud studies of its proporties represent a challenge., The detection of the warm/hot intergalactic medium (WHIM) and studies of its properties represent a challenge. + The iutegrated soft N-rav cluission of this eas may contribute significantly o the observed extragalactic N-vav backerouud (XRB:e.g..??7)..," The integrated soft X-ray emission of this gas may contribute significantly to the observed extragalactic X-ray background \citep[XRB; +e.g.,][]{croft_etal01,phillips_etal01,voit_bryan01}." + The best prospects for direct detection are. however. through absorption or," The best prospects for direct detection are, however, through absorption or" +the degeneracy between. lens distance. mass and velocity (Gould.1992).,"the degeneracy between lens distance, mass and velocity \cite{gould92}." +. We follow Gould (1998) and define the quantity OL. which measures the ratio of the earth's acceleration along P 2he projected lens velocity vector) during the event and n —self.," We follow Gould (1998) and define the quantity =, which measures the ratio of the earth's acceleration along $\tilde{v}$ (the projected lens velocity vector) during the event and $\abs{\tilde{v}}$ itself." + This gives us an approximate measure of the streneth ‘the parallax effect of an event., This gives us an approximate measure of the strength of the parallax effect of an event. + For a given event curation 10 elfe ct inereases as the observer-lens distance and the vpical lens velocity decrease., For a given event duration the effe ct increases as the observer-lens distance and the typical lens velocity decrease. + “Phus. a typical halo (6ezm l/4) event will have >z0.05 whereas if ιο MACTIIOs are arranged in a thick disk configuration (\approx 200 {\rm km/s}, +=1/4$ ) event will have $\gamma\approx 0.05$ whereas if the MACHOs are arranged in a thick disk configuration $\approx 100 {\rm km/s}, +=1/10$ ) then typically $\gamma \approx 0.11$." + We lus expect an increase in the number of observed parallax events for lenses in a fat disk configuration., We thus expect an increase in the number of observed parallax events for lenses in a fat disk configuration. + In order to more carefully estimate the increase in expected. parallax events. we have performed a Monte Carlo analysis of lensing events for lenses in a fat disk and a halo distribution.," In order to more carefully estimate the increase in expected parallax events, we have performed a Monte Carlo analysis of lensing events for lenses in a fat disk and a halo distribution." + We sample the light curve for cach event in à manner chosen to correspond. roughly to the present surveys: daily measurements. photometry. and. 5r vear baseline. in order to generate the data.," We sample the light curve for each event in a manner chosen to correspond roughly to the present surveys: daily measurements, photometry, and 5 year baseline, in order to generate the data." + We also consider an experiment with photometry for comparison., We also consider an experiment with photometry for comparison. + We then fit a first order parallax light-curve to the data and determine CGould's ~ parameter (Gould1998) as a measure of the strength of the parallax effects., We then fit a first order parallax light-curve to the data and determine Gould's $\gamma$ parameter \cite{newgould} as a measure of the strength of the parallax effects. + The distribution of measured ος can then be used to distinguish between very thick disk and halo lens distributions., The distribution of measured $\gamma$ 's can then be used to distinguish between very thick disk and halo lens distributions. + In Figure 7 we present the cumulative probability distributions for * for a thick disk ancl a halo., In Figure 7 we present the cumulative probability distributions for $\gamma$ for a thick disk and a halo. + The ability of an experiment to distinguish between these lens distributions will depend. on the number of events and photometry., The ability of an experiment to distinguish between these lens distributions will depend on the number of events and photometry. + We find that an experiment with photometry and 15 events can distinguish between a very thick disk and a halo with a significance of about5%.. while an experiment with photometry is unable to do so.," We find that an experiment with photometry and 15 events can distinguish between a very thick disk and a halo with a significance of about, while an experiment with photometry is unable to do so." + With shotometry at least 75 events are required., With photometry at least 75 events are required. + We no that these estimates do not. include. backgrounds. from binary source and lens events. whose light curves can mimic parallax effects.," We note that these estimates do not include backgrounds from binary source and lens events, whose light curves can mimic parallax effects." + Llowever. future observations are likely to include more finely sampled light curves from followup claI on alerted events.," However, future observations are likely to include more finely sampled light curves from followup data on alerted events." + Such detailed light curves will increase the ability to discriminate between parallax ancl binary lens or source effects in at least some of the cases., Such detailed light curves will increase the ability to discriminate between parallax and binary lens or source effects in at least some of the cases. + Microlensing studies have vielded much exciting data in the vast few vears and are continuing to survey dilferent. lines of sight through the Galaxy in order to probe the Galactic ido., Microlensing studies have yielded much exciting data in the past few years and are continuing to survey different lines of sight through the Galaxy in order to probe the Galactic halo. + However. the conclusions that can be drawn from the data to date are very model dependent assumptions abou he distribution of the lenses and their velocity structure lve a strong impact on their interpretation.," However, the conclusions that can be drawn from the data to date are very model dependent – assumptions about the distribution of the lenses and their velocity structure have a strong impact on their interpretation." + Thus we nee ο examine a wide range of reasonable lens clistributions., Thus we need to examine a wide range of reasonable lens distributions. + Very thick disks present a reasonable alternative to a wilo population of lenses., Very thick disks present a reasonable alternative to a halo population of lenses. + Lo the lenses are stellar remnants. i seems likely that their configuration will be more condensec han that of a standard non-barvonic halo.," If the lenses are stellar remnants, it seems likely that their configuration will be more condensed than that of a standard non-baryonic halo." + While we have ound that very thick disks cannot lower the lens mass estimate to the brown clwarl regime. they have the advantage hat their total mass in NLACIIOs is somewhat less than hat for a standard halo that is truncated. at SOkpe (and much less than a NLACTIO halo which traces the extended," While we have found that very thick disks cannot lower the lens mass estimate to the brown dwarf regime, they have the advantage that their total mass in MACHOs is somewhat less than that for a standard halo that is truncated at $50\kpc$ (and much less than a MACHO halo which traces the extended" +In the model-5. the non-uniform excitation of MBI is realized by non-uniform resistivity while the magnetic field is set uniform.,"In the $\eta$, the non-uniform excitation of MRI is realized by non-uniform resistivity while the magnetic field is set uniform." + The result of model nicely illustrates our scenario for dust accumulation., The result of $\eta$ nicely illustrates our scenario for dust accumulation. + Figure 3aa shows the evolution of MRI., Figure \ref{fig:eta-3D}a a shows the evolution of MRI. + The black lines depict the magnetic field lines and the gray scale shows the gas radial velocity., The black lines depict the magnetic field lines and the gray scale shows the gas radial velocity. + The unstable region lies between two white lines (JrH|= 0.18)., The unstable region lies between two white lines $\left|x/H\right|=0.18$ ). + MB is first excited only in the initially unstable region (see the plot al /Q= 19) and significant angular momentum and mass are transported there., MRI is first excited only in the initially unstable region (see the plot at $t\Omega=19$ ) and significant angular momentum and mass are transported there. + The MBI (turbulence intrudes into the stable region (/Q=30)., The MRI turbulence intrudes into the stable region $t\Omega=30$ ). + Deep inside the stable region. however. is always undisturbed. (Lr/1/|2 0.5) because of the rapid. dissipation by the enhanced resistivity.," Deep inside the stable region, however, is always undisturbed $\left|x/H\right| \gtrsim 0.5$ ) because of the rapid dissipation by the enhanced resistivity." + Figures daa and 4bb show the radial profiles of (he pressure and the angular velocity of the gas. respectively.," Figures \ref{fig:eta-puy}a a and \ref{fig:eta-puy}b b show the radial profiles of the pressure and the angular velocity of the gas, respectively." + The quantities have been averaged azimuthally ancl vertically., The quantities have been averaged azimuthally and vertically. + The sampling limes are /Q= 0. 40. and 70.," The sampling times are $t\Omega=$ 0, 40, and 70." + The zone between the two vertical dotted lines is the unstable region., The zone between the two vertical dotted lines is the unstable region. + The inhomogeneous MBRI growth creates (he rigid rotation pattern in the middle of the simulation box (|.r/I|< 0.15)., The inhomogeneous MRI growth creates the rigid rotation pattern in the middle of the simulation box $\left|x/H\right| \lesssim 0.15$ ). + The pressure distribution is considerably mocdified such that the resultant. pressure gracient force balances with the modified Coriolis force., The pressure distribution is considerably modified such that the resultant pressure gradient force balances with the modified Coriolis force. + The flattened rotation prolile cannot sustain the excitation of MIRI in the unstable zone., The flattened rotation profile cannot sustain the excitation of MRI in the unstable zone. + Indeed. the turbulence weakens extremely al /Q=10 in Figure 3aa. The profiles of pressure or angular velocity in Figures daa and 4bb depict the quasi-steady state sel up by (he non-uniform: MRI activity.," Indeed, the turbulence weakens extremely at $t\Omega=70$ in Figure \ref{fig:eta-3D}a a. The profiles of pressure or angular velocity in Figures \ref{fig:eta-puy}a a and \ref{fig:eta-puy}b b depict the quasi-steady state set up by the non-uniform MRI activity." + Most of what we see here is quite similar to the results of the two-dimensional simulations described in Paper I even though the initial settings for seed magnetic field and resistivity distribution are totally different., Most of what we see here is quite similar to the results of the two-dimensional simulations described in Paper I even though the initial settings for seed magnetic field and resistivity distribution are totally different. + The rigidex rotation causes egas to rotate faster than Iweplerian velocity in (Figure fbb)., The rigid rotation causes gas to rotate faster than Keplerian velocity in $0.0\lesssim x/H\lesssim 0.4$ (Figure \ref{fig:eta-puy}b b). + This can change the particle migration drastically., This can change the particle migration drastically. + Figure 3bb shows the temporal evolution of the particle densitv., Figure \ref{fig:eta-3D}b b shows the temporal evolution of the particle density. + The color eode is set such that the maximun is ien times the initial value., The color code is set such that the maximum is ten times the initial value. + After the particles are swept out of the unstable region bv the MRI flow. they. accumulate (o the location al ο70.4 (note that particles leaving the simulation box from the left hand boundary reenter [rom the right hand boundary alter the shearing box correction is Caken into account).," After the particles are swept out of the unstable region by the MRI flow, they accumulate to the location at $x/H\simeq0.4$ (note that particles leaving the simulation box from the left hand boundary reenter from the right hand boundary after the shearing box correction is taken into account)." + Though not visible in the panels. the particles initiallv in (he stable zone are swept likewise towards (he same location.," Though not visible in the panels, the particles initially in the stable zone are swept likewise towards the same location." + The accumulation of particles is most clearly shown in Figure 4cc in which the radial distribution of (he number of particles that is averaged azimuthally aud vertically and is normalized by the initial value., The accumulation of particles is most clearly shown in Figure \ref{fig:eta-puy}c c in which the radial distribution of the number of particles that is averaged azimuthally and vertically and is normalized by the initial value. + To analvze the particle concentration dvnamies in more details. in Figure tld. we plot ihe maximum (the solid line) and the minimum (the dashed line) values of ry al a given," To analyze the particle concentration dynamics in more details, in Figure \ref{fig:eta-puy}d d, we plot the maximum (the solid line) and the minimum (the dashed line) values of $v_{\rm f}$ at a given" +isochrones are significantly older than the input ones for |Fe/Il]7 ~—2. the difference increasing with metallicitv.,"isochrones are significantly older than the input ones for $\ge$ $\sim-2$, the difference increasing with metallicity." + In the hieh metallicity regime. retrieved relative ages are up to e» 0.3 (or ~ 4 Gyr) older (han (he input value.," In the high metallicity regime, retrieved relative ages are up to $\sim$ 0.3 (or $\sim$ 4 Gyr) older than the input value." + In summary. (he horizontal and especially verlical-amethod derived ages are largely dependent on the initial He value and. CNONa mixture.," In summary, the horizontal- and especially vertical-method derived ages are largely dependent on the initial He value and CNONa mixture." + In other words. if the relative age of a GGC is measured using these methods. undetected differences in the He content and/or CNONa abundance translates in an unreal age determination.," In other words, if the relative age of a GGC is measured using these methods, undetected differences in the He content and/or CNONa abundance translates in an unreal age determination." + The difference between the measured relative age and the actual one can be of the order of ~ 0.4-0.3 (which correspond to several Gyr in absolute age). especially for high metallicity clusters.," The difference between the measured relative age and the actual one can be of the order of $\sim$ 0.4-0.8 (which correspond to several Gyr in absolute age), especially for high metallicity clusters." + It is clear that the vertical method more sensitive to variations in Y and/or CNONa chemical abundances., It is clear that the vertical method more sensitive to variations in Y and/or CNONa chemical abundances. + We note (hat. while for the 11ο content a wide interval has been explored. for the case of the extreme CNONa mixture. we have investigated ouly (he case of an enhancement factor equal io 2in the CNO elements abundance.," We note that, while for the He content a wide interval has been explored, for the case of the extreme CNONa mixture, we have investigated only the case of an enhancement factor equal to 2 in the CNO elements abundance." + His evident that. in case of larger CNO enhancement factors. the expected difference between the input age ancl the retrieved one woulcl be «quite larger.," It is evident that, in case of larger CNO enhancement factors, the expected difference between the input age and the retrieved one would be quite larger." + The rMSFE-method ages were also measured [or our set of isochrones. erouping them in subsets with the same iron content.," The rMSF-method ages were also measured for our set of isochrones, grouping them in subsets with the same iron content." + In (his case. a larger age interval was considered.," In this case, a larger age interval was considered." + Results are shown in Figure6., Results are shown in Figure. + Error bars represent the relative age uncertainty derived from the rMSFE. procedure (σοι. described in.," Error bars represent the relative age uncertainty derived from the rMSF procedure $\sigma_{MSF}$, described in." +2009). If He enhanced isochrones are considered. il is apparent that the measured rMSE-method relative ages tend to be slightly older (han the input ones. especially for hieh metallicity isochrones.," If He enhanced isochrones are considered, it is apparent that the measured rMSF-method relative ages tend to be slightly older than the input ones, especially for high metallicity isochrones." + Η all values of Y and input ages are considered. the mean determined relative age is 20.03 (or 0.4 Gyr if expressed in absolute age) older than the input one. showing an rms dispersion around (his mean of also ~ 0.03 (or 0.4 Gyr).," If all values of Y and input ages are considered, the mean determined relative age is $\sim$ 0.03 (or 0.4 Gyr if expressed in absolute age) older than the input one, showing an rms dispersion around this mean of also $\sim$ 0.03 (or 0.4 Gyr)." + Ht is noticeable that. this result is also independent of the Y value. that is. even extreme Y values translate into a ~0.0340.08 relative age difference between the input ancl rMSE-method derived ages.," It is noticeable that this result is also independent of the Y value, that is, even extreme Y values translate into a $\sim$ $\pm$ 0.03 relative age difference between the input and rMSF-method derived ages." + In the case of the extreme CNONa mixture. the results ave shown in Figure7.," In the case of the extreme CNONa mixture, the results are shown in Figure." + In this case. 10 appears (hat rMSE-method derived relative ages are ~0. 1040.02 (or ~1£0.3 Gr in terms of absolute age) older than the actual ages.," In this case, it appears that rMSF-method derived relative ages are $\sim$ $\pm$ 0.02 (or $\sim$ $\pm$ 0.3 Gyr in terms of absolute age) older than the actual ages." + No significant trend with |Fe/1I] is found., No significant trend with [Fe/H] is found. + thee framework of massive star formation in the Magellanic Clouds., e framework of massive star formation in the Magellanic Clouds. +TMR-1 (IRAS 04361-2547) is a class I young stellar object located in the Taurus molecular cloud. that was actually resolved into a binary source with a measured components’ separation of 0.31°(Terebey et al.,"TMR-1 (IRAS 04361+2547) is a class I young stellar object located in the Taurus molecular cloud, that was actually resolved into a binary source with a measured components' separation of (Terebey et al." + 1998. hereafter T98).," 1998, hereafter T98)." + We will therefore refer to it as TMR-IAB in the following., We will therefore refer to it as TMR-1AB in the following. + The total bolometric luminosity of TMR-1AB had been estimated to ~2.8L.. indicative for a low-mass protostellar system (Kenyon et 1993).," The total bolometric luminosity of TMR-1AB had been estimated to $\sim 2.8{\rm L}_\odot$, indicative for a low-mass protostellar system (Kenyon et 1993)." + The circumstellar environment of TMR-IAB ts characterized by extended emission from a dusty proto-stellar envelope and from patches of molecular cloud material left over from the proto-stellar collapse., The circumstellar environment of TMR-1AB is characterized by extended emission from a dusty proto-stellar envelope and from patches of molecular cloud material left over from the proto-stellar collapse. + In their sensitive HST/NICMOS observations. T98 detected a faint compact object. named TMR-1C. at a projected distance of ~ ffrom TMR-IAB. which corresponds to ~ AAU at the distance of the Taurus molecular cloud.," In their sensitive HST/NICMOS observations, T98 detected a faint compact object, named TMR-1C, at a projected distance of $\sim$ from TMR-1AB, which corresponds to $\sim$ AU at the distance of the Taurus molecular cloud." + The physical association of TMR-IC with TMR-IAB was suggested on the basis of the presence of a striking filament structure that arises from TMR-1 and points directly towards TMR-1C. T98 further suggested that TMRI-C was catapulted to its current location due to dynamical interactions with the proto-binary TMRI-AB and that the are-shaped filament could trace the ejection path of TMR-IC through the gaseous infalling circumstellar envelope of ΤΜΕ-Ι., The physical association of TMR-1C with TMR-1AB was suggested on the basis of the presence of a striking filament structure that arises from TMR-1 and points directly towards TMR-1C. T98 further suggested that TMR1-C was catapulted to its current location due to dynamical interactions with the proto-binary TMR1-AB and that the arc-shaped filament could trace the ejection path of TMR-1C through the gaseous infalling circumstellar envelope of TMR-1. + The very low luminosity suggested for TMR-IC indicated that it should be a substellar object. maybe even a planetary mass object.," The very low luminosity suggested for TMR-1C indicated that it should be a substellar object, maybe even a planetary mass object." + However. the physical association of TMR-IC with TMR-I. and hence its nature as à substellar object. was strongly debated during the years after its discovery.," However, the physical association of TMR-1C with TMR-1, and hence its nature as a substellar object, was strongly debated during the years after its discovery." + In an attempt to clarify the evolutionary status of TMR-IC. Terebey et ((2000) carried out near-infrared spectroscopy using the Keck telescope.," In an attempt to clarify the evolutionary status of TMR-1C, Terebey et (2000) carried out near-infrared spectroscopy using the Keck telescope." + The result of these observations showed that the spectrum of TMR-IC. at the signal-to-noise level that could be reached. is consistent with an extincted background dwarf star spectrum. but still room was left for an interpretation within the extremely low-mass object ejection hypothesis.," The result of these observations showed that the spectrum of TMR-1C, at the signal-to-noise level that could be reached, is consistent with an extincted background dwarf star spectrum, but still room was left for an interpretation within the extremely low-mass object ejection hypothesis." + In this paper we use ESO (VULT) data obtained with the (ISAAC). as well as Spitzer/IRAC observations in. order to revisit the TMR-] system.," In this paper we use ESO (VLT) data obtained with the (ISAAC), as well as /IRAC observations in order to revisit the TMR-1 system." + After the description of the observations and the data reduction 22). we discuss n1 3.1 the morphology of the circumstellar dusty environment of TMR-1 and report on the detection of new features anc objects identified i our sensitive ISAAC images.," After the description of the observations and the data reduction 2), we discuss in 3.1 the morphology of the circumstellar dusty environment of TMR-1 and report on the detection of new features and objects identified in our sensitive ISAAC images." + We ther use our K-band low-resolution spectroscopy together with the spectral energy distribution of TMR-1C. which we construct from the photometry presented in this paper and collectec from the literature. in order to analyze the nature of TMR-IC in 33.2 and 3.3.," We then use our K-band low-resolution spectroscopy together with the spectral energy distribution of TMR-1C, which we construct from the photometry presented in this paper and collected from the literature, in order to analyze the nature of TMR-1C in 3.2 and 3.3." + Our K-band spectroscopy was also performed on a significant part of the filament structure “connecting” TMR-IC with TMR-IAB., Our K-band spectroscopy was also performed on a significant part of the filament structure ”connecting” TMR-1C with TMR-1AB. + Since the spectral resolution is almost 4 times higher than in previous spectroscopic observations we are able to resolve numerous emission-line features arising from the filament., Since the spectral resolution is almost 4 times higher than in previous spectroscopic observations we are able to resolve numerous emission-line features arising from the filament. + In 3.4 we analyze the filament spectrum in detail. which leads us to conclude that a significant part of its emission is characterized by shock-exeited emission.," In 3.4 we analyze the filament spectrum in detail, which leads us to conclude that a significant part of its emission is characterized by shock-excited emission." + In 44 we present scenarios that could possibly explain the symmetry of the circumstellar nebulosities. the filamentary structures. and the existence of a par of very low-mass objects. as a physical entity.," In 4 we present scenarios that could possibly explain the symmetry of the circumstellar nebulosities, the filamentary structures, and the existence of a pair of very low-mass objects, as a physical entity." + Finally. we summarize our results and conclusions in 55.," Finally, we summarize our results and conclusions in 5." + A first set of images of TMR-1 was obtained at Ks-band (Cl.= 2.16um. A4= 0.27um) with ISAAC at the VLT-ANTU(UTI) telescope as part of commissioning of the instrument.," A first set of images of TMR-1 was obtained at Ks-band $\lambda_c=2.16\mu$ m, $\Delta \lambda=0.27\mu$ m) with ISAAC at the VLT-ANTU(UT1) telescope as part of commissioning of the instrument." + These data were taken during the night December 04-05. 1998. immediately before the spectroscopic observations. providing also a flux calibration for these (Sec. 2.3).," These data were taken during the night December 04-05, 1998, immediately before the spectroscopic observations, providing also a flux calibration for these (Sec. \ref{Obs_Spec}) )." + The data are, The data are +we calculate the Iuuinositv of these discrete features iu xlveonal apertures containius the features. and using adjoining regions to determine the local backgrouud for accurate backeround subtraction.,"we calculate the luminosity of these discrete features in polygonal apertures containing the features, and using adjoining regions to determine the local background for accurate background subtraction." + The subtraction of a ocally-defined backerouud from the Iuninuositv of each cature ensures that simall-scale backeround uucertaiutyv due to spatial variation of the subtracted galaxy model is uiininized., The subtraction of a locally-defined background from the luminosity of each feature ensures that small-scale background uncertainty due to spatial variation of the subtracted galaxy model is minimized. + Even so. the backerouud subtraction renuainus he biggest source of uncertaintv du mcasuring the fiux in cach region.," Even so, the background subtraction remains the biggest source of uncertainty in measuring the flux in each region." + We quantity this error by making small adjustinents to the backeround regious to quantity the resulting backeround flux (see Ruclick 2010 for more details)., We quantify this error by making small adjustments to the background regions to quantify the resulting background flux (see Rudick 2010 for more details). + We find this variation to be —c 0.25 ADU. which we propagate to uncertainties in the derived huminosities.," We find this variation to be $\sim \pm$ 0.25 ADU, which we propagate to uncertainties in the derived luminosities." + As an independent check of the robustuess of the derived substructure luminosities. we also reduced a colpletely independent dataset imaging M9 in 2005. and compared it to the results for the 2006 ALLO dataset described here.," As an independent check of the robustness of the derived substructure luminosities, we also reduced a completely independent dataset imaging M49 in 2005, and compared it to the results for the 2006 M49 dataset described here." + We find the derived. luminosities of the features agree to ~5-105., We find the derived luminosities of the features agree to $\sim$. +". Iu addition to caleulatiug the total Iuninositv of each απο, we also compute the peak surface brightuess."," In addition to calculating the total luminosity of each feature, we also compute the peak surface brightness." +" We quantify this bv constructing a subtracted 77x37"". (0.5x0.5 spc) median smoothed. model Πμαρσο, aud exanuning the pixel iutensitics in cach feature."," We quantify this by constructing a $7\arcsec$ $7\arcsec$ (0.5x0.5 kpc) median smoothed, model subtracted image, and examining the pixel intensities in each feature." + To avoid statistical fluctuations associated with ideutifviug the xiehtest binned pixcl. we define peak surface brightucss | he the 90th percentile of the iuteusitv distribution.," To avoid statistical fluctuations associated with identifying the brightest binned pixel, we define peak surface brightness to be the 90th percentile of the intensity distribution." + A visual examination of the images shows this to be robust against contauunation from unsubtracted backerowund objects and stars., A visual examination of the images shows this to be robust against contamination from unsubtracted background objects and stars. + We beein with briehtest Vigo elliptical. M9. ocated in the Virgo Southern Extension. four degrees south of Ms7.," We begin with brightest Virgo elliptical, M49, located in the Virgo Southern Extension, four degrees south of M87." + The final mask for MIO iuchudes all of he bright stars im the field. as well as uearby faint galaxies(e.g. NGCLL92. NGCLISS).," The final mask for M49 includes all of the bright stars in the field, as well as nearby faint galaxies (e.g. NGC4492, NGC4488)." + We fit theisephotal nodel using IRAF’s ELLIPSE task. as described in 822.2. using fixed center (at a= 12:20:16.8. ὃ= Ps:d0Q:01.8 J2000).," We fit the isophotal model using IRAF's ELLIPSE task, as described in 2.2, using fixed center (at $\alpha =$ 12:29:46.8, $\delta =$ +8:00:01.8 J2000)." +" Our extracted surface brightness xofle never reaches our limiting magnitude of = 29: the fitstopsconcergingpastRsy.y,=232,8. 27. yd. wheretoomuchofthegalacyortoudsof "," Our extracted surface brightness profile never reaches our limiting magnitude of $ = 29$ ; the fit stops converging past $\rsma = 32.8'$ $ = +27.5$ ) where too much of the galaxy extends off the edges of our image." +Tossatle fynebe," The best fit profiles for surface brightness, position angle, and ellipticity are shown in Figure \ref{allfits}." +cdoowitbetiangle. andel aud the composite V. baud. profile of 109.," We compare our results to Peletier (1990) with CCD surface photometry in $BR$ bands, Kim (2000) who used a CCD in Washington $CT_{1}$ bands, and the composite $V$ band profile of K09." + As can be see in Figure 2.. the ellipticitv aud position anele profiles are in very good agreement between these studies.," As can be see in Figure \ref{allfits}, the ellipticity and position angle profiles are in very good agreement between these studies." + The isophotal fits to Sévrsic aud 2dV profiles are shown in Fieure 2 aud Tablereasonably 2.., The isophotal fits to Sérrsic and 2dV profiles are shown in Figure \ref{allfits} and Table \ref{sbfits}. + For the S@rsic fit our extracted parameters agree well (within 26) with those measured by IEK09., For the Sérrsic fit our extracted parameters agree reasonably well (within $2\sigma$ ) with those measured by K09. + There is uo siguificaut difference im the qualitv of ft between the Séórsic and 2dV models: extracting a total huninositv for the galaxies from the fitted profiles vields Ly=1.6aud1.5«101. for the Sérrsic aud 2dV fits. respectively.," There is no significant difference in the quality of fit between the Sérrsic and 2dV models; extracting a total luminosity for the galaxies from the fitted profiles yields $L_V = 1.6 +{\rm\ and\ } 1.5\times 10^{11} L_\sun$ for the Sérrsic and 2dV fits, respectively." + In the 20V fit. the outer coniponent carries of the total ealaxy luuwinosity.," In the 2dV fit, the outer component carries of the total galaxy luminosity." + We subtract the extracted profile from the original inage of M9 to vield our residual image. shown in Figure 3.," We subtract the extracted profile from the original image of M49 to yield our residual image, shown in Figure \ref{subtract_m49m87}." + Strikinely visible iu the residual miage is a complex systel of diffuse shells., Strikingly visible in the residual image is a complex system of diffuse shells. + A lee shell sits ((90 kpc) to the northwest (Reeiou 1). while a double-edeed shell (Region 3) sits ou the opposite side of MI9. ((60 kpe) to the southeast.," A large shell sits (90 kpc) to the northwest (Region 1), while a double-edged shell (Region 3) sits on the opposite side of M49, (60 kpc) to the southeast." + There is also a complex iuner structure (Region 2) ((30 kpe) to the nortlnvest of M9. which appears to be the overlapping of several discrete shells.," There is also a complex inner structure (Region 2) (30 kpc) to the northwest of M49, which appears to be the overlapping of several discrete shells." + We also sec a phune south of ALLO center (Region 1). which partially overlaps the SE shell (Region 5).," We also see a plume south of M49 center (Region 4), which partially overlaps the SE shell (Region 5)." + Finally. we ideutifv a faint pluie to the northeast (Region 6). runing through the galaxy VCC 1251. and perhaps connecting with the inner shell structure.," Finally, we identify a faint plume to the northeast (Region 6), running through the galaxy VCC 1254, and perhaps connecting with the inner shell structure." + The peak surface brightuesses aud total huninosities of these features are given in Table 3.., The peak surface brightnesses and total luminosities of these features are given in Table \ref{m49tab}. + While these shells were not seen in the recent Tal (2009) study of tidal features around nearby ellipticals. it is Likely due to the extended nature of the shells: the field of view of the Tal nuages was too siall to reach most ofthese outer features.," While these shells were not seen in the recent Tal (2009) study of tidal features around nearby ellipticals, it is likely due to the extended nature of the shells; the field of view of the Tal images was too small to reach most of these outer features." + We also note at even fainter surface Yishtuesses a lint of a phuue παπα ο the northeast of N19. but this (Cuunarked) pluie is oulv mareially detected. aud we do not photometer it.," We also note at even fainter surface brightnesses a hint of a plume running to the northeast of M49, but this (unmarked) plume is only marginally detected, and we do not photometer it." + We note iu the context of these shells that if the isophotal model has spurious features init (due to rapidly changing ellipticity and position angle iu the derived ELLIPSE model). the subtraction process can imprint shell-like artifacts into the residual inage.," We note in the context of these shells that if the isophotal model has spurious features in it (due to rapidly changing ellipticity and position angle in the derived ELLIPSE model), the subtraction process can imprint shell-like artifacts into the residual image." + We have becu very careful iu the fitting process to avoid these types of features., We have been very careful in the fitting process to avoid these types of features. + The fitted isophotal parameters vary siootlily with radius. aud we have checked that the best-fit model did not have auy structure that would be inpriuted ou the image. aud we have also verifiedthat all these residual nu bash The ο fthecedgesofourinntimcpDle," The fitted isophotal parameters vary smoothly with radius, and we have checked that the best-fit model did not have any structure that would be imprinted on the residual image, and we have also verified that all these structures can be recovered in the unsubtracted images." +orPhuue APAS)(Regious L| 5) also Tes very near the tidally disturbed dwarf irreguka UCC 7636 Gu our iuage. UGC 7636 itself lies under the circular," The S Plume (Regions 4 5) also lies very near the tidally disturbed dwarf irregular UGC 7636 (in our image, UGC 7636 itself lies under the circular" +"Collisions with He introduce a small correction to. the expression of the friction coefficient a;, defined by eq. (7)).",Collisions with He introduce a small correction to the expression of the friction coefficient $\alpha_{in}$ defined by eq. \ref{frict}) ). + For a neutral component made of H» and He. eq. (20))," For a neutral component made of $_2$ and He, eq. \ref{he_lan}) )" + gives with gg. |., gives with c_i= ). + For example. for a cosmic(cs) He abundance of O.l. the He correction factors based on the Langevin approximation are cy=L12. cu=013. and ¢cHyco!=1.15. (see also Mouschovias 1996).," For example, for a cosmic He abundance of 0.1, the He correction factors based on the Langevin approximation are $c_{{\rm H}^+}=1.12$, $c_{{\rm H}_3^+}=1.13$, and $c_{{\rm HCO}^+}=1.15$ (see also Mouschovias 1996)." + Similarly. for collisions with atomic hydrogen. the He correction for the Η-Η rate coefficient is CH)—1.08.," Similarly, for collisions with atomic hydrogen, the He correction for the $^+$ rate coefficient is $c_{{\rm +H}^+}=1.08$." +" Figure 16. shows the momentum transfer cross section for -He collisions computed by Krstié Schultz (1999) with a semi-classical treatment in the energy range 0.1eV.0.3 (based also on optical magnitudes). although Che true eas temperature is probably significantly lower (han the 25 keV fit here.," We therefore tentatively identify this object as CXOU J033912.0-352609, a likely hot, massive cluster of galaxies at $z>0.3$ (based also on optical magnitudes), although the true gas temperature is probably significantly lower than the 25 keV fit here." + We have described (he aquisition aud initial analysis of (he most detailed wide-field X-ray data on the Fornax cluster to date., We have described the aquisition and initial analysis of the most detailed wide-field X-ray data on the Fornax cluster to date. + In presenting some of the initial results of the CFS here we have attempted to illustrate several kev aspects of the Fornax cluster environment which are now accessible for further investigation., In presenting some of the initial results of the CFS here we have attempted to illustrate several key aspects of the Fornax cluster environment which are now accessible for further investigation. + Namelv: (1) there is clear evidence of interaction between al least 2 galaxies (NGC 1404 and NGC 1387) and the Fornax ICM., Namely: (1) there is clear evidence of interaction between at least 2 galaxies (NGC 1404 and NGC 1387) and the Fornax ICM. + In (he case of NGC! 1404 we have obtained the first quantitative constraint on its motion perpendicular to our line-ol-sight. opening the wav (o constraining its orbital configuration when combined wilh existing redshift information. (," In the case of NGC 1404 we have obtained the first quantitative constraint on it's motion perpendicular to our line-of-sight, opening the way to constraining it's orbital configuration when combined with existing redshift information. (" +2) the Fornax ICM has a clearly asymmetric morphology which we suggest may be related to the larger scale dynamics of this region. in which we are perhaps wilnessine the coalescence of Fornax with an intalline group along a 1 Alpe filamentary structure. (,"2) the Fornax ICM has a clearly asymmetric morphology which we suggest may be related to the larger scale dynamics of this region, in which we are perhaps witnessing the coalescence of Fornax with an infalling group along a 1 Mpc filamentary structure. (" +3) possibly related (o this ongoing growth. ancl almost certainty related (ο the local ICAL density environment we find that the majoritw of N-rav. active Fornax galaxies are distributed. away [rom the bulk of the ICM. and between the Fornax,"3) possibly related to this ongoing growth, and almost certainly related to the local ICM density environment we find that the majority of X-ray active Fornax galaxies are distributed away from the bulk of the ICM, and between the Fornax" +elliptical fts. these features show wp as positive and uceative residuals in the subtracted muiage.,"elliptical fits, these features show up as positive and negative residuals in the subtracted image." + We restrict our discussion of the substructure around ALS6 to regions outside the area where these terms dominate the residual liebt profile., We restrict our discussion of the substructure around M86 to regions outside the area where these terms dominate the residual light profile. + Around λος we find several stall radial streams. iucluding oues to the north (Region 1). south (Region 1). southeast (Region 5). aud east (Region 6).," Around M86, we find several small radial streams, including ones to the north (Region 1), south (Region 4), southeast (Region 5), and east (Region 6)." +" These sill are1 vers iili lv1to be fitting artifacts,⋅⋅ thes 5S colerent aud consistent across may isophotesas of the 6"," These small features are very unlikely to be fitting artifacts, as they are coherent and consistent across many isophotes of the galaxies." + We also find a few simall pluies between M86 Total MSIE (ReeionsH 2n nand 3)., We also find a few small plumes between M86 and M84 (Regions 2 and 3). +" We7 have∙⋅ verified that""| all Lotal features can be seen in the uusubtracted image. Nove. are therefore not artifacts of the subtraction process,"," We have verified that all these features can be seen in the unsubtracted image, and are therefore not artifacts of the subtraction process." + The is telmpting to link up features 1 and Ll. aud features 2 and 6. into continuous streams that cross the face of MBS6. as would be expected from tidal stripping of ↴∖↴↓↓⋮↥∐∩↥⋅↴⋝↕↾↕∐⋮↴⋁↴∖↴⋮↧↑," It is tempting to link up features 1 and 4, and features 2 and 6, into continuous streams that cross the face of M86, as would be expected from tidal stripping of small orbiting satellites." +≼∖∐↕↑≼∖↴∖↴∙↽∏∐∖↕⋯⊔↕∐∩↴∖↴↕↾⋮↖↽∩↕⊳↾∐≼∖↴∖↴≼∖↕⊳≼∖≘⋔∐⋅≼∖↴∖↴ iscunall typically 20038LOTL.. (Table 5)).," The luminosity of these features is small, typically $2-3 \times 10^7 +L_{\sun}$ (Table \ref{m84m86tab}) )." + A dogles stream of light (Reegious A aud B) also extends from the nearby interacting pair of galaxies NGC L135/8., A dogleg stream of light (Regions A and B) also extends from the nearby interacting pair of galaxies NGC 4435/8. + This nature of this feature. first identified by Malin (1991). remains i doubt: optically it is πο than other tidal streams in Virgo (Iudick 2010). and inultiwavelougth observations suggest that it may iu fact be avery unfortunate projection of galactic erus across the ealaxy pair (Cortese 2010).," This nature of this feature, first identified by Malin (1994), remains in doubt; optically it is bluer than other tidal streams in Virgo (Rudick 2010), and multiwavelength observations suggest that it may in fact be a very unfortunate projection of galactic cirrus across the galaxy pair (Cortese 2010)." + We have also compared our deep optical πμασο to the narrowband Ho image of Kenney (2008). who found a very coniplex system of Wa filaments connecting M86 with NGC 1138.," We have also compared our deep optical image to the narrowband $\alpha$ image of Kenney (2008), who found a very complex system of $\alpha$ filaments connecting M86 with NGC 4438." + I&euney proposed a collision between the ISAL of the two galaxies as the source of the filaments., Kenney proposed a collision between the ISM of the two galaxies as the source of the filaments. + Tf these galaxies are in collision. we see no strong evidence of it iu our nunaging.," If these galaxies are in collision, we see no strong evidence of it in our imaging." + We find no correlation between that Πα imap and our deep imaging. and the few tidal features we see between the galaxies (Regions 5 and 6) are simall and narrow. sugeestive of sinall stripping of low velocity dispersion dwarf galaxies.," We find no correlation between that $\alpha$ map and our deep imaging, and the few tidal features we see between the galaxies (Regions 5 and 6) are small and narrow, suggestive of small stripping of low velocity dispersion dwarf galaxies." + However this docs uot rule out an encounter the hieh relative velocitiesof M86 and NGC Liss (Ae—=1379 lans) would suppress the formation of strong tidal features. but still drive the strong response in the ISM/ICGM eiviug rise to the ionized Πα filaments seca by Ixeunexal.," However this does not rule out an encounter – the high relative velocitiesof M86 and NGC 4438 $\Delta v=1379$ km/s) would suppress the formation of strong tidal features, but still drive the strong response in the ISM/IGM giving rise to the ionized $\alpha$ filaments seen by Kenney." +.. Ou sinaller scales. Ehuecerecn (2000) used optical iuaegiug to ideutify a number of dust streamers 10-20 kpe from the center of M86. which they attributed to dust stripping from the chvart elliptical VCC 882.," On smaller scales, Elmegreen (2000) used optical imaging to identify a number of dust streamers 10-20 kpc from the center of M86, which they attributed to dust stripping from the dwarf elliptical VCC 882." + Other evidence for dust stripping from galaxies orbiting κου comes frou far infrared ISOPIIOT imaging (Stickel 2003) which revealed a number of iufrared sources with spectra consistent with cold dust cussion Wing within 35 kpc from M86., Other evidence for dust stripping from galaxies orbiting M86 comes from far infrared ISOPHOT imaging (Stickel 2003) which revealed a number of infrared sources with spectra consistent with cold dust emission lying within 35 kpc from M86. + These features are all close enough to AISG that they le within the region where our cllipse subtraction is confused bv the AL conipoueuts im the ealaxy profiles. and so we have uot tried to Xlentifv features here (although we do see the optical dust lanes identified by Ehucercen 2000).," These features are all close enough to M86 that they lie within the region where our ellipse subtraction is confused by the $A4$ components in the galaxy profiles, and so we have not tried to identify features here (although we do see the optical dust lanes identified by Elmegreen 2000)." + Nonetheless. the general inference that ALS6 is accreting and stripping a population of dwarf galaxies is consistent with the optical streamers we ideutifv at larger radius.," Nonetheless, the general inference that M86 is accreting and stripping a population of dwarf galaxies is consistent with the optical streamers we identify at larger radius." + As we did with M8ST. we have compared our residual nage with the far infrared maps to guard against ↸⊳∪∐↕∏↴∖↴↕∪∐↖↖↽↕↑∐∶↴∙⊾⋜↧↕⋜↧↸⊳↑↕," As we did with M87, we have compared our residual image with the far infrared maps to guard against confusion with galactic cirrus." +↸⊳↸⊳∐⋅↥⋅∏↴∖↴∙↽∕∏∐∖≯∙ . ∙∙ infrared∙∙ Maps show dust contamination to the west of ALS1: some ofsignificant this enrus can be seen as the (labeled) diffuse feature seen in the upper right edge of our image., The infrared maps show significant dust contamination to the west of M84; some of this cirrus can be seen as the (unlabeled) diffuse feature seen in the upper right edge of our image. + There is also infrared cuuission associated with the dogleg phuue near NGC 1135/8. one of the arguients for its identification as galactic eirrus (Cortese 2010).," There is also infrared emission associated with the dogleg plume near NGC 4435/8, one of the arguments for its identification as galactic cirrus (Cortese 2010)." +" Other than these features, we see no clear between the dust. cussion aud correspondencethe diffuse streamers we haveinfrared identified near M81 and ALS6"," Other than these features, we see no clear correspondence between the infrared dust emission and the diffuse streamers we have identified near M84 and M86." + The elliptical galaxy M89 has the lowest luninosity iu our sample. and resides one degree cast of AIST.," The elliptical galaxy M89 has the lowest luminosity in our sample, and resides one degree east of M87." + M8SO's final mask eliminates all of the bright stars aud small ealaxics in the field of view. and we also mask the sight shell to the south and the strong Πο feature o the west. both identified first bv Malin (1979).," M89's final mask eliminates all of the bright stars and small galaxies in the field of view, and we also mask the bright shell to the south and the strong “jet” feature to the west, both identified first by Malin (1979)." + Since hese features are obvious substructures distinct frou he smooth galaxy light. we waut to exclude them from contributing to the elliptical isophotal Hr.," Since these features are obvious substructures distinct from the smooth galaxy light, we want to exclude them from contributing to the elliptical isophotal fit." +" We aeain USE a fixed center (ofa =12:35:39.8. 6= |sities12:3oe2 J2000) for our fit. aud ourbest-fit surface DrieES reaches our linitiue magnitude of = 29«fRayj4 =23"".."," We again use a fixed center (of $\alpha=$ 12:35:39.8, $\delta=$ +12:33:23.2 J2000) for our fit, and our best-fit surface brightness profile reaches our limiting magnitude of $ = 29$ at $\rsma$." +" Our vest ft elliptical model is shown in Figure 2.. where we also compare our surface brightuess profile with that of 00, who combined original observations with published data to construct a composite V-baud profile for M89."," Our best fit elliptical model is shown in Figure \ref{allfits}, where we also compare our surface brightness profile with that of K09, who combined original observations with published data to construct a composite $V$ -band profile for M89." + The comparison shows an excellent match in ellipticity aud position angle., The comparison shows an excellent match in ellipticity and position angle. + Oi best-fit Sérrsie aud 2dV fits to the luminosity profile are shown in Figure 2. and the parameters ire elven in Table 2.., Our best-fit Sérrsic and 2dV fits to the luminosity profile are shown in Figure \ref{allfits} and the parameters are given in Table \ref{sbfits}. + Our fitted Sérrsic model has an lüeh index of 7=11.6. similar to the value of n=(199:13.9 extremely foundby Caon 3). but higher than the η=9.2 reported by I&09.," Our fitted Sérrsic model has an extremely high index of $n=14.6$, similar to the value of $n=13.9$ found by Caon (1993), but higher than the $n=9.2$ reported by K09." + Again. however. the radial range of the fit is important: in a fit with a radial range that more closely matches ours. X09 derive a larger value of &=13.75 (see Figure 56 of S09).," Again, however, the radial range of the fit is important; in a fit with a radial range that more closely matches ours, K09 derive a larger value of $n=13.75$ (see Figure 56 of K09)." + Tn our fits. the 2d model viclds a somewhat better fit than the Sérrsic model.V with the outer componcut contributing of the total Iuminositv of £y-=3.9&LOM EL.," In our fits, the 2dV model yields a somewhat better fit than the Sérrsic model, with the outer component contributing of the total luminosity of $L_V=3.9 \times 10^{10} +L_{\sun}$ ." + The Sérsicgives a higher total Iuninosity. of Ly=19 «1019...," The Sérrsicgives a higher total luminosity of $L_V=4.9 +\times 10^{10} L_{\sun}$ ." + Subtracting our isophotal model from the raw iuage vields the residual image shown in Figure L. , Subtracting our isophotal model from the raw image yields the residual image shown in Figure \ref{subtract_m84m86m89}. . +As, As in +"ol t10 Others scalar. parameters in the model is performed. the edietabilitv P. landscape variance e, and P-weighted lanescape variance ayο should be higher than the values quoted in this paper.","of the others scalar parameters in the model is performed, the predictability $P$, landscape variance $\sigma_{\lambda_i}$ and $P$ -weighted landscape variance $\sigma_{\lambda_i P}$ should be higher than the values quoted in this paper." + It is very unlikely that the variations ofoher parameters could cancel out exactly the intluence oltjo elliciencies à €., It is very unlikely that the variations of other parameters could cancel out exactly the influence of the efficiencies $\alpha$ $\epsilon$. + Vhere is a hierarchy of causes for this behavior that mus be explored., There is a hierarchy of causes for this behavior that must be explored. + First of all. might this be a signature ol t1e hierarchical build of galaxies?," First of all, might this be a signature of the hierarchical build of galaxies?" + In such a picture it is easy to imagine that mild perturbations a carly times might add up to finally vield very clilfercnt values for very similar initial conditions., In such a picture it is easy to imagine that mild perturbations at early times might add up to finally yield very different values for very similar initial conditions. + This would account for the relatively larec values of the variance over the ào-c plane compared to the intrinsic variances over the whole population of similar halos in the cosmological volume., This would account for the relatively large values of the variance over the $\alpha$ $\epsilon$ plane compared to the intrinsic variances over the whole population of similar halos in the cosmological volume. + But. probably not for the low predictability. values., But probably not for the low predictability values. + Could this be an artifact coming [rom the semi-analytic models of galaxy formation?, Could this be an artifact coming from the semi-analytic models of galaxy formation? + In these moclels. generally. the distinction between what is to be considered as the central ealaxy depend on which galaxy is the most massive.," In these models, generally the distinction between what is to be considered as the central galaxy depend on which galaxy is the most massive." + This is ambiguous when various galaxies inside à dark matter halo have similar masses. in that case the selection of the central galaxy might be subject to noise.," This is ambiguous when various galaxies inside a dark matter halo have similar masses, in that case the selection of the central galaxy might be subject to noise." + This could explain in part the seemingly random landscapes for high mass haloes., This could explain in part the seemingly random landscapes for high mass haloes. + On he last level of the hierarchy. could this. be coming [romcode?," On the last level of the hierarchy, could this be coming from?" +? This is impossible to. confirm without performing the same kind of experiment with another fully Ledged semi-analvtic model., This is impossible to confirm without performing the same kind of experiment with another fully fledged semi-analytic model. + Which take us to the issue of comparison between semi-analytie models of galaxy formation., Which take us to the issue of comparison between semi-analytic models of galaxy formation. + The predictability. as à meaningful scalar objective function. opens the possibility to measure. the biases from cülferent. semi-analvtie codes.," The predictability, as a meaningful scalar objective function, opens the possibility to measure the biases from different semi-analytic codes." + This could allow the comparison. of dillerent. codes based. on its numerical performance. going bevond. the rather ill-posecl strategy of comparison based on astrophysical perlormance. Lc. reproducing Observations.," This could allow the comparison of different codes based on its numerical performance, going beyond the rather ill-posed strategy of comparison based on astrophysical performance, i.e. reproducing observations." + Finally. the small perturbations we niade on the scalar parameters were constructed to not have any ellect on the mean properties of the galaxies such as the luminosity function.," Finally, the small perturbations we made on the scalar parameters were constructed to not have any effect on the mean properties of the galaxies such as the luminosity function." + lt nieans hat formally the galaxies we have produced ab every perturbation are consistent with the overall galaxy. population., It means that formally the galaxies we have produced at every perturbation are consistent with the overall galaxy population. + As a consequence of all this. studies making use of selected subpopulations from a wider population generated using semi-analvtic models. should bear in mind that this smaller population might not be unique.," As a consequence of all this, studies making use of selected subpopulations from a wider population generated using semi-analytic models, should bear in mind that this smaller population might not be unique." + The dispersion on this subsample of galaxies. coming from the perturbations that can be induced on every parameter in the model. should be explicitly stated.," The dispersion on this subsample of galaxies, coming from the perturbations that can be induced on every parameter in the model, should be explicitly stated." + Including that dispersion (in the form of error. bars. lor instance) seems a necessary condition to make a of semi-analvtic models. acknowledging in an explicit manner its limitations on predictabilitv.," Including that dispersion (in the form of error bars, for instance) seems a necessary condition to make a of semi-analytic models, acknowledging in an explicit manner its limitations on predictability." +"The observations presented here were obtained with NAOS-CONICA (NACO), the AO system at the Very Large Telescope (VLT), and SAM (?) in two different campaigns.","The observations presented here were obtained with NAOS-CONICA (NACO), the AO system at the Very Large Telescope (VLT), and SAM \citep{Tuthill2010} in two different campaigns." +" TheL’ observations were obtained in March 2010 under excellent atmospheric conditions (average coherent time of 77>=8mms, and average seeing of 066), while the K, data were obtained in July 2010 under moderate atmospheric conditions (70—4 mms, and seeing of 1""00)."," The observations were obtained in March 2010 under excellent atmospheric conditions (average coherent time of $\tau_0$ ms, and average seeing of 6), while the $K_s$ data were obtained in July 2010 under moderate atmospheric conditions $\tau_0$ ms, and seeing of 0)." +" In March 2010, T Cha was observed with the L27 objective, the seven-hole mask and the L’ filter (A.— 3.80um, A\=00.62 ym)."," In March 2010, T Cha was observed with the L27 objective, the seven-hole mask and the $L'$ filter $\lambda_c$ = $\mu$ m, $\Delta\lambda$ 0.62 $\mu$ m)." + The target and a calibrator star 1102260) were observed during 10 minutes each., The target and a calibrator star 102260) were observed during 10 minutes each. +" We repeated the sequence star+calibrator nine times, integrating a total of 48 minutes on-source."," We repeated the sequence star+calibrator nine times, integrating a total of 48 minutes on-source." + The observational procedure included a dithering pattern that placed the target in the four quadrants of the detector., The observational procedure included a dithering pattern that placed the target in the four quadrants of the detector. + We acquired datacubes of 100 frames of ssec integration time in each offset position., We acquired datacubes of 100 frames of sec integration time in each offset position. +" The plate scale, 27.10+0.10 mmas/pix, and true north orientation of the detector, -0.48+0.25 degrees, were derived using the astrometric calibrator ϐ Ori! C observed in April 2010."," The plate scale, $\pm$ mas/pix, and true north orientation of the detector, $\pm$ 0.25 degrees, were derived using the astrometric calibrator $\theta$ $^1$ C observed in April 2010." +" For the K,-band data we used the $27 objective and the same strategy, but integrating in datacubes of 100 frames with ssec of individual exposure time."," For the $K_s$ -band data we used the S27 objective and the same strategy, but integrating in datacubes of 100 frames with sec of individual exposure time." +" We spent a total of 20 minutes on-source, and we used two stars, 1102260 and 1101251, as calibrators."," We spent a total of 20 minutes on-source, and we used two stars, 102260 and 101251, as calibrators." + All data were reduced using a custom pipeline detailed in Lacour et al. (, All data were reduced using a custom pipeline detailed in Lacour et al. ( +in preparation).,in preparation). +" In brief, each frame is flat-fielded, dark-subtracted, and bad-pixel-corrected."," In brief, each frame is flat-fielded, dark-subtracted, and bad-pixel-corrected." +" The complex amplitudes of each one of the 7x6/2—21 fringe spatial frequencies were then used to calculate the bispectrum, from which the argument is taken to derive the closure phase."," The complex amplitudes of each one of the $7\times6/2=21$ fringe spatial frequencies were then used to calculate the bispectrum, from which the argument is taken to derive the closure phase." +" Lastly, the closure phases were fitted to a model of a binary source."," Lastly, the closure phases were fitted to a model of a binary source." +" The three free parameters of the fit are the flux ratio, the separation, and the position angle of the companion candidate."," The three free parameters of the fit are the flux ratio, the separation, and the position angle of the companion candidate." + The upper left panel of Fig., The upper left panel of Fig. + 1 depicts the minimum x? as a function of position angle and separation., \ref{fig1} depicts the minimum $\chi^2$ as a function of position angle and separation. +" For an arbitrary fit, χ is high (reduced x? of e 9), but the map shows a clear minimum for a companion to the west of the star."," For an arbitrary fit, $\chi^2$ is high (reduced $\chi^2$ of $\approx 9$ ), but the map shows a clear minimum for a companion to the west of the star." + The phase corresponding to the best-fit model is shown in the right panel of the same figure., The phase corresponding to the best-fit model is shown in the right panel of the same figure. +" It consists of a sinusoidal curve with a specific angular direction, and a period of half the resolution of the 8.2 meter telescope."," It consists of a sinusoidal curve with a specific angular direction, and a period of half the resolution of the 8.2 meter telescope." + In the same figure we plotted the deconvolved phases from the measured closure phases that were projected onto the orientation of the best-fit binary., In the same figure we plotted the deconvolved phases from the measured closure phases that were projected onto the orientation of the best-fit binary. +" The best-fitting companion parameters for the L-band data are a separation of 61.8+7.4 mmas, a position angle of 78.5+1.2 degrees, and a fractional flux with respect to the central object of 0.92+0.20%."," The best-fitting companion parameters for the L-band data are a separation of $61.8 \pm 7.4$ mas, a position angle of $78.5\pm 1.2$ degrees, and a fractional flux with respect to the central object of $0.92 \pm 0.20$." +". To confirm the validity of the detection, each one of the nine star--calibrator data pairs was also analyzed separately."," To confirm the validity of the detection, each one of the nine star+calibrator data pairs was also analyzed separately." +" Because the observations were taken in ‘pupil tracking mode’, all optical and electronic aberrations should remain at frozen orientation on the detector, while a real structure on the sky willrotate with the azimuth pointing of the telescope (close to the sidereal rate)."," Because the observations were taken in `pupil tracking mode', all optical and electronic aberrations should remain at frozen orientation on the detector, while a real structure on the sky willrotate with the azimuth pointing of the telescope (close to the sidereal rate)." +" This expected rotation of the detection is illustrated in Fig. 1,,"," This expected rotation of the detection is illustrated in Fig. \ref{fig1}," + which strongly argues against an instrumental artifact., which strongly argues against an instrumental artifact. +" The detection error bars reported above are 1-c, but owing to the low separation, there is a strong degeneracy between separation and flux ratio."," The detection error bars reported above are $\sigma$, but owing to the low separation, there is a strong degeneracy between separation and flux ratio." + This is highlighted in the contours shown in Fig. 2.., This is highlighted in the contours shown in Fig. \ref{fig2}. +" The limits of the 3 c contours correspondto a spread of parameters between flux ratio of at mmas, and at mmas."," The limits of the 3 $\sigma$ contours correspondto a spread of parameters between flux ratio of at mas, and at mas." +" We did not detect any source around T Cha in the K,- data.", We did not detect any source around T Cha in the $K_s$ -band data. +" Figure 3 shows the 1-c, 2-c, and 3-o sensitivity"," Figure \ref{fig3} shows the $\sigma$ , $\sigma$ , and $\sigma$ sensitivity" +be able to liit the contribution of VAIS to Z1X of the total star formation rate density out to a redshift of 2. uuless both mixing and 7?Ni production are abseut for allPPSNe.,"be able to limit the contribution of VMS to $\lsim 1\,$ of the total star formation rate density out to a redshift of 2, unless both mixing and $^{56}$ Ni production are absent for all." +. Such constraints already place meanimeful limits ou the cosmological propagation of metals., Such constraints already place meaningful limits on the cosmological propagation of metals. + The nupact of future NIR searches is even more xonisneg. as the majoritv of the PPSN liebt is emitted at restframe wavelengths loueward of —σοςΑ..," The impact of future NIR searches is even more promising, as the majority of the PPSN light is emitted at restframe wavelengths longward of $\sim 8000$." + Thus alanued NIR satellite mussious such as/DEAL would be over two orders of maguitudes more sensitive to han preseut optical survevs. aud able to probe redshifts )ovond z26.," Thus planned NIR satellite missions such as would be over two orders of magnitudes more sensitive to than present optical surveys, and able to probe redshifts beyond $z \approx 6$." + Iu this case. even the dinniest would o detectable out to zzΙ.," In this case, even the dimmest would be detectable out to $z \approx 4$." + Although the peak of the metal-free star forination density almost certaimlv occurred at extremely carly times. here is mich to be learned frou: PPSN searches at more uoderate redshifts.," Although the peak of the metal-free star formation density almost certainly occurred at extremely early times, there is much to be learned from PPSN searches at more moderate redshifts." + Iu fact. due to volume aud tuuc-dilation effects. the peak in the number of per dee? per d: per vear is likely to lie well below :=10. Furthenuore. the data sets necessary for such analvses are already being plauued for and collected.," In fact, due to volume and time-dilation effects, the peak in the number of per $^2$ per $z$ per year is likely to lie well below $z=10.$ Furthermore, the data sets necessary for such analyses are already being planned for and collected." + While the properties are diverse. a singular couclusion cau be drawn from our modcling.," While the properties are diverse, a singular conclusion can be drawn from our modeling." + Searches for pair-production SNe at zzzG will dramatically increase our uuderstanding of the history of cosniüc eurichiment. the nature of metal-free stars. and the evolution of gaseous matter in the universe.," Searches for pair-production SNe at $z \lesssim 6$ will dramatically increase our understanding of the history of cosmic enrichment, the nature of metal-free stars, and the evolution of gaseous matter in the universe." + We thank Brian O'Shea Zoltan Waiman for helpfiσι discussious about primordial star formation. Avishayv CaYan. Peter Carnavich. Weidong Li. Dovi Pozuauski. Tony Spadafora. aud Yun Wane. for iuformation o- current and wpcoming supernova surveys. aud Nick Scoville for iufoxiuation ou the COSMOS surver.," We thank Brian O'Shea Zoltan Haiman for helpful discussions about primordial star formation, Avishay Gal-Yam, Peter Garnavich, Weidong Li, Dovi Poznanski, Tony Spadafora, and Yun Wang, for information on current and upcoming supernova surveys, and Nick Scoville for information on the COSMOS survey." + We are also erateful to the anomvinous referee for helpful sugecstions that ereatlv improved the manuscript., We are also grateful to the anonymous referee for helpful suggestions that greatly improved the manuscript. + This work was supported by the National Science Foundation under erants PITY99-07919. ASTO2-06111. aud ASTO2-05738. bv NASA erants NACS-11513. NACH5-12036 and NNGOLICGIXS5C. aud by the DOE Program for Scientific Discovery through Advanced Computing (SciDAC: DE-FCO2-01ER11176).," This work was supported by the National Science Foundation under grants PHY99-07949, AST02-06111, and AST02-05738, by NASA grants NAG5-11513, NAG5-12036 and NNG04GK85G, and by the DOE Program for Scientific Discovery through Advanced Computing (SciDAC; DE-FC02-01ER41176)." + PM. acknowledges support from the Alexander von Huiubokd Foundation., PM acknowledges support from the Alexander von Humbold Foundation. + ΑΠ was also funded bv DOE contract. W-7105-ENC-36 to the Los Alamos National Laboratory. by NASA erauts SWIF03-0017-0037 and NACG5-13700. aud under NASA/STSci HST-CGO-," AH was also funded by DOE contract W-7405-ENG-36 to the Los Alamos National Laboratory, by NASA grants SWIF03-0047-0037 and NAG5-13700, and under NASA/STSci HST-GO-09437.08-A." +particular its high n]] luminosity (vanBoekeletal..2009).. this uncertainty will not eritically influence our results.,"particular its high ] luminosity \citep{boekel09}, this uncertainty will not critically influence our results." + The X-ray luminosity is in rough agreement with an estimated X-ray luminosity corresponding to the marginal excess flux seen in the HRC image (Güdeletal..2007¢)., The X-ray luminosity is in rough agreement with an estimated X-ray luminosity corresponding to the marginal excess flux seen in the HRC image \citep{guedel07c}. +. DG Tau. DP Tau. and HN Tau show peculiar X-ray spectra with two components subject to different absorbing gas column densities (Giideletal..2007b.2009b).," DG Tau, DP Tau, and HN Tau show peculiar X-ray spectra with two components subject to different absorbing gas column densities \citep{guedel07b, guedel09b}." +. We considered only the hard. coronal component for the X-ray flux. while the soft component is probably associated with the jets.," We considered only the hard, coronal component for the X-ray flux, while the soft component is probably associated with the jets." +" In Sz 102 (= TH 28. or ""Krautter's Star”). the entire observed X-ray flux may be related to jets (Güdeletal..2009b)."," In Sz 102 (= TH 28, or “Krautter's Star”), the entire observed X-ray flux may be related to jets \citep{guedel09b}." +. Its X-ray spectrum is very soft. while the expected near-edge-on geometry should absorb essentially all stellar X-rays or transmit only the hardest portion of the spectrum.," Its X-ray spectrum is very soft, while the expected near-edge-on geometry should absorb essentially all stellar X-rays or transmit only the hardest portion of the spectrum." + We will therefore not consider this star for statistical studies involving Lx., We will therefore not consider this star for statistical studies involving $L_{\rm X}$. + Table 5 summarizes sample statistics., Table \ref{table5} summarizes sample statistics. + In total. our sample contains 92 objects. for all of which we derived [Net]] fluxes or upper limits or found corresponding information in the literature (58 detections and 34 upper limits).," In total, our sample contains 92 objects, for all of which we derived ] fluxes or upper limits or found corresponding information in the literature (58 detections and 34 upper limits)." + X-ray information is available for 67 of these objects. 64 of which were detected.," X-ray information is available for 67 of these objects, 64 of which were detected." + Both [Neu]] and X-ray detections are available for 40 objects., Both ] and X-ray detections are available for 40 objects. + Obviously. ancillary data are far from complete for our sample. and therefore smaller subsets had to be used for specific correlation studies.," Obviously, ancillary data are far from complete for our sample, and therefore smaller subsets had to be used for specific correlation studies." + For à summary of the analysis strategies for the largest u]] subsample discussed in our paper. see Lahuisetal.(2007).," For a summary of the analysis strategies for the largest ] subsample discussed in our paper, see \citet{lahuis07}." +. The objects from Spitzer GO program 2030 (AORs 145XXXXX in Table 2)) were all reduced according to the procedure described in Carr&Najita(2008)., The objects from Spitzer GO program 2030 (AORs 145XXXXX in Table \ref{table2}) ) were all reduced according to the procedure described in \citet{carr08}. +. X-ray data are available from different satellite observatories., X-ray data are available from different satellite observatories. + We confined our X-ray analysis to data from the CCD detectors on board (Jansenetal..2001) and the hencetorth: Weisskopfetal. 1996)., We confined our X-ray analysis to data from the CCD detectors on board \citep{jansen01} and the henceforth; \citealt{weisskopf96}) ). + AlthoughROSAT observed many of our targets as well. its rather soft bandpass (0.1—2 keV) and its very low spectral resolving power (E/AEx 2) make a reliable modeling of relatively faint CTTS subject to considerable absorption difficult and uncertain.," Although observed many of our targets as well, its rather soft bandpass (0.1–2 keV) and its very low spectral resolving power $E/\Delta E \approx 2$ ) make a reliable modeling of relatively faint CTTS subject to considerable absorption difficult and uncertain." + All and data were consistently reduced and analyzed., All and data were consistently reduced and analyzed. + The data reduction procedures for data are identical to those deseribed in Giideletal.(2007a)for objects in Taurus., The data reduction procedures for data are identical to those described in \citet{guedel07a} for objects in Taurus. + Whenever possible. we extracted the X-ray spectra from the pn-type (EPIC-pn: Strüderetal. 2001)): if this camera did not provide useful data (e.g. if the target fell into a CCD gap). we used the two spectra extracted from the MOS-type EPIC cameras (Turneretal.. 2001).," Whenever possible, we extracted the X-ray spectra from the pn-type (EPIC-pn; \citealt{strueder01}) ); if this camera did not provide useful data (e.g., if the target fell into a CCD gap), we used the two spectra extracted from the MOS-type EPIC cameras \citep{turner01}." + The few spectra were extracted. from theSpectrometer (ACIS). using the so- events? files from the archive.," The few spectra were extracted from the (ACIS), using the so-called events2 files from the archive." + Both for andChandra. counts were extracted from circular areas around the source position. and background spectra were defined from nearby. source-free areas on the same CCD chip.," Both for and, counts were extracted from circular areas around the source position, and background spectra were defined from nearby, source-free areas on the same CCD chip." + The X-ray spectral interpretation. was performed in the XSPEC vers., The X-ray spectral interpretation was performed in the XSPEC vers. + 11.3.1 software (Arnaud.1996)— using simple one- or two-component (in exceptional cases. three-component) optically thin. collistonal-equilibrium plasma models. each component being defined by its temperature (7) and emission measure (EM).," 11.3.1 software \citep{arnaud96} using simple one- or two-component (in exceptional cases, three-component) optically thin, collisional-equilibrium plasma models, each component being defined by its temperature $T$ ) and emission measure (EM)." + The element abundances of the plasma were held fixed at values commonly found in pre-main sequence or young active stars (see Güdeletal.2007a))., The element abundances of the plasma were held fixed at values commonly found in pre-main sequence or young active stars (see \citealt{guedel07a}) ). + The spectral model was further subject to photoelectric absorption described by the absorbing gas (equivalent hydrogen) column density. Ny.," The spectral model was further subject to photoelectric absorption described by the absorbing gas (equivalent hydrogen) column density, $N_{\rm H}$ ." + Fit parameters therefore were 7 and EM for each component. and Ny in common to all components.," Fit parameters therefore were $T$ and EM for each component, and $N_{\rm H}$ in common to all components." + We will report only the total X-ray fluxes of our targets and Ny. as these are the most Important parameters for theories of t]] emission.," We will report only the total X-ray fluxes of our targets and $N_{\rm H}$, as these are the most important parameters for theories of ] emission." + Fitted EMs roughly scale with Lx. and temperatures were usually found in the range typical for T Tauri stars (1.e.. a few tenths to a few keV. see Güdeletal.2007a for the Taurus objects reported here).," Fitted EMs roughly scale with $L_{\rm X}$, and temperatures were usually found in the range typical for T Tauri stars (i.e., a few tenths to a few keV, see \citealt{guedel07a} for the Taurus objects reported here)." + We start the presentation of our results by reviewing the range of evolutionary stages and circumstellar environments of our targets., We start the presentation of our results by reviewing the range of evolutionary stages and circumstellar environments of our targets. + This consideration is motivated by our finding that jets and outflows appear to be important contributors to the u]] emission from young stars., This consideration is motivated by our finding that jets and outflows appear to be important contributors to the ] emission from young stars. + We have identified. 14. objects with some evidence of spatially resolved jets or outflows. defining the subelass ofsources.," We have identified 14 objects with some evidence of spatially resolved jets or outflows, defining the subclass of." + This classificatior is purely qualitative (e.g.. based on imaging in forbidden lines. or evidence of Herbig-Haro objects) as no effort was nade to quantify mass loss rates. shock speeds. or shock excitation in the jets.," This classification is purely qualitative (e.g., based on imaging in forbidden lines, or evidence of Herbig-Haro objects) as no effort was made to quantify mass loss rates, shock speeds, or shock excitation in the jets." + We do. at this stage. not include objects with indirect evidence for jets. such as strong but spatially unresolved |Or]] emission.," We do, at this stage, not include objects with indirect evidence for jets, such as strong but spatially unresolved ] emission." + We will discuss such more quantitative parameters that may be related to outflows in a later step., We will discuss such more quantitative parameters that may be related to outflows in a later step. + Our sample also contains 13 which we study separately., Our sample also contains 13 which we study separately. + Note that we include different types of transition disks (e.g.. ΝαΠίαetal. 20071).," Note that we include different types of transition disks (e.g., \citealt{najita07}) )." + Some of them have low disk masses and are optically thin (at UV and infrared wavelengths) throughout the disk., Some of them have low disk masses and are optically thin (at UV and infrared wavelengths) throughout the disk. + They are sometimes also called “anemic” disks (Ladaetal..2006)., They are sometimes also called “anemic” disks \citep{lada06}. +".. Another class of transition disks are those with a gap or hole in the dust distribution in the mner disk but with a massive optically thick outer disk. sometimes also called ""cold"" disks (Brownetal.. 2007)."," Another class of transition disks are those with a gap or hole in the dust distribution in the inner disk but with a massive optically thick outer disk, sometimes also called “cold” disks \citep{brown07}." +. Several cold disks are now known to have residual gas present inside the dust gap (e.g.. Pontoppidanetal.20058:Salyketal. 2009)).," Several cold disks are now known to have residual gas present inside the dust gap (e.g., \citealt{pontoppidan08, salyk09}) )." + Transition disks rarely show jets. making them a relatively homogeneous group without much [Neu] contamination from jets and outflows. although the level of disk elearance willobviously vary among the objects.," Transition disks rarely show jets, making them a relatively homogeneous group without much ] contamination from jets and outflows, although the level of disk clearance willobviously vary among the objects." +CS Cha is exceptional in this group. showing both a transition disk (Espaillatetal..2007) and signatures of a jet (Takamietal.. 2003)..,"CS Cha is exceptional in this group, showing both a transition disk \citep{espaillat07} and signatures of a jet \citep{takami03}. ." + We will address this case separately although we will, We will address this case separately although we will +rotalion axis change is noted with radius. and a in velocity dispersion is found with radius. possibly indicating a dillerence in orbital anisotropy compared with the GC's.,"rotation axis change is noted with radius, and a in velocity dispersion is found with radius, possibly indicating a difference in orbital anisotropy compared with the GCs." + A very similar effect has been noted for the Leo elliptical NGC 3379. although with a much smaller data sample (Romanowskyetal.2003:Dergond2006:Pierce2006).," A very similar effect has been noted for the Leo elliptical NGC 3379, although with a much smaller data sample \citep[][]{romanowsky03,bergond06,pierce06}." +. We also determine (he total dynamical mass using both the GC's and the PNe by separately calculating the pressure supported mass with (he (racer mass estimator and the rotationally supported mass using the spherical component of the Jeans equation., We also determine the total dynamical mass using both the GCs and the PNe by separately calculating the pressure supported mass with the tracer mass estimator and the rotationally supported mass using the spherical component of the Jeans equation. + The total mass is (1.3.2:0.5)xLOY AL. from the GC population out to a projected radius of 50 kpe. or (1.0280.2)x107 AL. out to 90 kpe from the PNe.," The total mass is $(1.3\pm0.5) \times 10^{12}$ $M_{\odot}$ from the GC population out to a projected radius of 50 kpc, or $(1.0\pm0.2) \times 10^{12}$ $M_{\odot}$ out to 90 kpc from the PNe." + Overall. we have enough evidence to cautiously conclude Chat a major episode of star omnation occurred about 8—10 Gyr ago (corresponding (o a redshift z= 1.2 - 1.3) and this nav have been when the bulk of the visible galaxv was built.," Overall, we have enough evidence to cautiously conclude that a major episode of star formation occurred about $8-10$ Gyr ago (corresponding to a redshift z = 1.2 - 1.8) and this may have been when the bulk of the visible galaxy was built." + We still do not know just why (he most metal-poor clusters show up in such relatively large numbers and appear to have ages ol 10—12 Gyr. but this is a common issue in all big galaxies.," We still do not know just why the most metal-poor clusters show up in such relatively large numbers and appear to have ages of $10-12$ Gyr, but this is a common issue in all big galaxies." + This kinematic study and the age study of Beasleyοἱal.(2006) on the NGC 5128 cluster svstem indicate that additional spectroscopic studies to. build up both the radial velocily database and. age distribution can lead to rich dividends., This kinematic study and the age study of \cite{beasley06} on the NGC 5128 cluster system indicate that additional spectroscopic studies to build up both the radial velocity database and age distribution can lead to rich dividends. + Large. GC samples are Clearly needed (o remove the current sample biases ancl (o fully understand. (he complex kinematics and history of (his giant. elliptical galaxy., Large GC samples are clearly needed to remove the current sample biases and to fully understand the complex kinematics and history of this giant elliptical galaxy. + It seems clear as well that each galaxy needs to be individually studied to filly understand the different galaxy formation histories., It seems clear as well that each galaxy needs to be individually studied to fully understand the different galaxy formation histories. + We are continuing these studies particularly for NGC 5128. with the eventual aim of al least doubling the total GC! sample size in (this unique svstem.," We are continuing these studies particularly for NGC 5128, with the eventual aim of at least doubling the total GC sample size in this unique system." + Acknowledgements: WEL aad GLILLI acknowledge financial support from NSERC through operating research grants., Acknowledgements: WEH and GLHH acknowledge financial support from NSERC through operating research grants. + DAF thanks the ARC for financial support., DAF thanks the ARC for financial support. +selected radio galaxy population (there are none in our sample).,selected radio galaxy population (there are none in our sample). + Flat integrated. radio spectra are produced when he [lat spectrum radio core dominates over the steep spectrum lobes in the frequency region of interest. and consequenthy such sources have high values of the parameter. £2.," Flat integrated radio spectra are produced when the flat spectrum radio core dominates over the steep spectrum lobes in the frequency region of interest, and consequently such sources have high values of the core-to-lobe parameter, $R$." + Fig., Fig. + 19 showed the strong anti-correlation between ely and 2. which we interpreted in erms of the geometry of the obscuring material.," \ref{fig:correl} showed the strong anti-correlation between $A_V$ and $R$, which we interpreted in terms of the geometry of the obscuring material." + We should herefore expect the nuclei of E96's radio galaxies to be Less reavily obsceured than those of our sample members., We should therefore expect the nuclei of T96's radio galaxies to be less heavily obscured than those of our sample members. + This should result in brighter (ancl hence more readily detectable) nuclei and a tendency for their sources to lie below obe brighter than) the A. z relation., This should result in brighter (and hence more readily detectable) nuclei and a tendency for their sources to lie below be brighter than) the $K$ $z$ relation. + Indeed. an ollset of Vildtmmae to brighter magnitudes needs to be applied to he relation of Lilly ct ((1995b) in order to obtain the rest fit to their raw data.," Indeed, an offset of mag to brighter magnitudes needs to be applied to the relation of Lilly et (1995b) in order to obtain the best fit to their raw data." + The single-filter imaging of 196 does not permit the detailed. method. of extinction. determination we employed in Section 4.1.., The single-filter imaging of T96 does not permit the detailed method of extinction determination we employed in Section \ref{sec:extinction}. +" Instead. we estimate the average extinction [or ""96's radio galaxy sample as a whole. by comparing the luminosities of the nuclei detected in the radio galaxies with those detected in the racio-Ioud. quasars."," Instead we estimate the average extinction for T96's radio galaxy sample as a whole, by comparing the luminosities of the nuclei detected in the radio galaxies with those detected in the radio-loud quasars." + Due to the wav the samples were matched. the intrinsic Iuminosities of the active nuclei should. be the same.," Due to the way the samples were matched, the intrinsic luminosities of the active nuclei should be the same." + Pheir Tables 4 and 5 indicate that the mean observed. luminosity of the radio galaxy nuclei is mmage fainter than that of the raclio-loud quasar nuclei., Their Tables 4 and 5 indicate that the mean observed luminosity of the radio galaxy nuclei is mag fainter than that of the radio-loud quasar nuclei. + A similar result. is found. when the LanefLusat ratios are compared.," A similar result is found when the $L_{\rm +nuc}/L_{\rm host}$ ratios are compared." + For a tvpical redshift 2om 0.2. this corresponds to chyπε137.," For a typical redshift $z +\approx 0.2$ , this corresponds to $A_V \approx 13^m$." +" By contrast. our sample has an average extinction zl:223""."," By contrast, our sample has an average extinction $A_V > 23^m$." + Our estimate appears to be more in line with the aclmittedlIy very Lint previous study in this field., Our estimate appears to be more in line with the admittedly very limited previous study in this field. + Simpson (1994a) studied a small. but complete. sample of nearby radio galaxies from the MS4 survey (Burgess Llunsteac 1994) which included three Class A (Line Longair 1979) objects.," Simpson (1994a) studied a small, but complete, sample of nearby radio galaxies from the MS4 survey (Burgess Hunstead 1994) which included three Class A (Hine Longair 1979) objects." +" A nuclear source was detecte in one object. which further study. revealed: to. sulfer. an extinction. ely=30c4"" (PIS 205: Simpson e 11995)."," A nuclear source was detected in one object, which further study revealed to suffer an extinction $A_V = 30 \pm +4^m$ (PKS $-$ 205; Simpson et 1995)." + The lower limits determined for the other two Class A sources implied an average Ayo217.," The lower limits determined for the other two Class A sources implied an average $A_V > +21^m$." + Ehe powerfu radio galaxy Cyvenus A has also had its quasar nucleus detected in the near-inlrared (Djorgovski et 11991). ane he most recent extinction estimates indicate very heavy obscuration (elyz1507: Simpson 1994a. Ward. 1996).," The powerful radio galaxy Cygnus A has also had its quasar nucleus detected in the near-infrared (Djorgovski et 1991), and the most recent extinction estimates indicate very heavy obscuration $A_V \approx 150^m$; Simpson 1994a, Ward 1996)." + We also note that two of T96's radio galaxies. 3€ 219 (L94: Hill et 110996) and 3€ 287.1 (IE2racleous Llalpern 1994) ‘learly show broad. Ha in their optical spectra.," We also note that two of T96's radio galaxies, 3C 219 (L94; Hill et 1996) and 3C 287.1 (Eracleous Halpern 1994) clearly show broad $\alpha$ in their optical spectra." + 1 is therefore to be expected that these two objects. possess xieht nuclear sources in the near-infrared., It is therefore to be expected that these two objects possess bright nuclear sources in the near-infrared. + We conclude that LOG's sample is predisposed towards sources with relatively ow nuclear obscuration. and believe that our sample. being cllectively complete and free from. selection. biases. is more representative of the radio galaxy population at large.," We conclude that T96's sample is predisposed towards sources with relatively low nuclear obscuration, and believe that our sample, being effectively complete and free from selection biases, is more representative of the radio galaxy population at large." + Even though Ες sample of radio galaxies appears to be biased. towards objects with low nuclear obscuration. the host galaxies should not be alfected.," Even though T96's sample of radio galaxies appears to be biased towards objects with low nuclear obscuration, the host galaxies should not be affected." +" Our multiwavelength images allow us to compute robust upper limits to the stellar Hux at ἐν (and hence an upper limit to the shift of the AN 2 relation reeuired) in a relatively simple manner which does not involve a ""black box” routine such as the two-dimensional fitting procedure.", Our multi-wavelength images allow us to compute robust upper limits to the non-stellar flux at $K$ (and hence an upper limit to the shift of the $K$ $z$ relation required) in a relatively simple manner which does not involve a “black box” routine such as the two-dimensional fitting procedure. + First. we assume that all the L'] flux in. a 3-areseeκ aperture arises. ⋅from the nucleus SI.nce here be some starlight present. this will overestimate he true nuclear flux.," First, we assume that all the $L'$ flux in a 3-arcsec aperture arises from the nucleus – since there be some starlight present, this will overestimate the true nuclear flux." + In the three instances where no detection. was made at Lo.∕ we use the 370⋅ upper limit⋠⋠ (again.. overestimating the true Dux).," In the three instances where no detection was made at $L'$ , we use the $3\sigma$ upper limit (again, overestimating the true flux)." + We then determine an upper imit to the A-band flux by assuming that the spectrum is an unredcdened a=1.3 power law., We then determine an upper limit to the $K$ -band flux by assuming that the spectrum is an unreddened $\alpha = 1.3$ power law. + Although there will »* variations in the near-intrarecl spectral indices of the objects in our sample. these should average oul among the en galaxies.," Although there will be variations in the near-infrared spectral indices of the objects in our sample, these should average out among the ten galaxies." + We compute the faintest possible host. galaxy ἐνρα magnitude by subtracting this nuclear flux. from he observed. 12-aresec aperture Dux., We compute the faintest possible host galaxy $K$ -band magnitude by subtracting this nuclear flux from the observed 12-arcsec aperture flux. + When this analysis is applied to 3Cλ 234. the maximum nuclear strength we derive exceeds the observed. L2-aresee magnitude. which indicates he conservative nature of our. approach.," When this analysis is applied to 3C 234, the maximum nuclear strength we derive exceeds the observed 12-arcsec magnitude, which indicates the conservative nature of our approach." + Obviously. we cannot merely exclude ος 234 [rom the analvsis. since it is the most strongly. contaminated: source in Our sample. so we assume the host has Av=14.2. as determined. by our moclel-fitting (POG obtain a very similar result).," Obviously, we cannot merely exclude 3C 234 from the analysis, since it is the most strongly contaminated source in our sample, so we assume the host has $K = 14.2$, as determined by our model-fitting (T96 obtain a very similar result)." + Even with these gross overestimates of the nuclear Ηχος (and hence underestimates of the host galaxy. brightnesses). the olfset from the A z relation is only A=0.35. somewhat less than the mmae found by “POG.," Even with these gross overestimates of the nuclear fluxes (and hence underestimates of the host galaxy brightnesses), the offset from the $K$ $z$ relation is only $\Delta = 0.35$, somewhat less than the mag found by T96." + More realistic estimates. such as assuming that the nucleus sullers at least mmag of extinction. (just. enough. to obseure. broad. Ho). imply nw27.," More realistic estimates, such as assuming that the nucleus suffers at least mag of extinction (just enough to obscure broad $\alpha$ ), imply $\Delta < 0.27$." + The A. z relation followed by the host galaxies in our sample cannot therefore be the same as that found. by 'T96 for the galaxies in their sample. unless the nuclei of our radio ealaxies have intrinsic near-infrared spectral indices of ax0.2.," The $K$ $z$ relation followed by the host galaxies in our sample cannot therefore be the same as that found by T96 for the galaxies in their sample, unless the nuclei of our radio galaxies have intrinsic near-infrared spectral indices of $\alpha < 0.2$." + This is obviously. incompatible with unification models which claim that the nuclei of radio galaxies are identical to those of quasars., This is obviously incompatible with unification models which claim that the nuclei of radio galaxies are identical to those of quasars. + llow then did “POG find such a large shift in the A relation?, How then did T96 find such a large shift in the $K$ $z$ relation? + We first rule out the possibility that the galaxies in T96's sample are genuinely fainter than ours., We first rule out the possibility that the galaxies in T96's sample are genuinely fainter than ours. + Although ος sample is generally of lower radio luminosity than ours. Lill Lilly (1991) have shown that there is no iference in the optical magnitudes of radio galaxies over wee orders of magnitude in radio luminosity. and the opticalinfrared. colours of the two samples cannot. cüller » half à magnitude.," Although T96's sample is generally of lower radio luminosity than ours, Hill Lilly (1991) have shown that there is no difference in the optical magnitudes of radio galaxies over three orders of magnitude in radio luminosity, and the optical–infrared colours of the two samples cannot differ by half a magnitude." + In addition. Eales ct ((1997) have gaiown that the A magnitudes of radio galaxies [rom the LnC and 6€ samples (6C is selected at à ~5 times fainter ux level) are similar at low redshift.," In addition, Eales et (1997) have shown that the $K$ magnitudes of radio galaxies from the 3C and 6C samples (6C is selected at a $\sim 5$ times fainter flux level) are similar at low redshift." + Finally. if we exclude rose radio galaxies [rom Εθν sample which do not meet je 3CTIU flux. limit. their result.is virtually unchanged.," Finally, if we exclude those radio galaxies from T96's sample which do not meet the 3CRR flux limit, their resultis virtually unchanged." + Similarly. i£. we consider only FRILL galaxies from “LOG. oronly those galaxies with a steep radio spectrum. we find no significant change to their result.," Similarly, if we consider only II galaxies from T96, oronly those galaxies with a steep radio spectrum, we find no significant change to their result." + We consider two likely explanations for the cillerent, We consider two likely explanations for the different +Valle 2007; Liang et 22007; Virgili et 22009).,Valle 2007; Liang et 2007; Virgili et 2009). + Although we model it as a power-law. it could be the tail of a Gaussian component.," Although we model it as a power-law, it could be the tail of a Gaussian component." +" At the high Iuminosity range. the measured slope dN/dLxLot—"""" is close to the prediction of the ~quasi-universal Gaussian jet” GLN/dLxLot. Zhang οἱ 22004)."," At the high luminosity range, the measured slope $dN/dL \propto L^{-1.27\pm0.06}$ is close to the prediction of the “quasi-universal Gaussian jet” $dN/dL \propto L^{-1}$, Zhang et 2004)." + At the very high Iuminosity end ο...1ῤῤίοιος1). the ~quasi-universal Gaussian jet” predicts dN/dLxL? (Llovd-Ronning οἱ 22004: Dai Zhang 2004). which cannot be tested with the current data.," At the very high luminosity end $L_{peak} > 10^{51}\lumin$ ), the “quasi-universal Gaussian jet” predicts $dN/dL \propto L^{-2}$ (Lloyd-Ronning et 2004; Dai Zhang 2004), which cannot be tested with the current data." + Unlike many of the previous studies. we do not make anv assumption on the GRB rate. since there are recent studies suggesting that the GRB rate does not follow the star formation rate (e.g.. Stanek et 22006).," Unlike many of the previous studies, we do not make any assumption on the GRB rate, since there are recent studies suggesting that the GRB rate does not follow the star formation rate (e.g., Stanek et 2006)." + Instead. we measure the average GRB luminosity [uniction in a large redshift bin.," Instead, we measure the average GRB luminosity function in a large redshift bin." + We compare the LEs in (wo Iuminosity bins., We compare the LFs in two luminosity bins. + The :>1 LF shows a drop at wo low luminosity data points., The $z\ge1$ LF shows a drop at two low luminosity data points. + This result can be affected by (he uncertainties in the ((vigger efliciency close to the ddetection limit., This result can be affected by the uncertainties in the trigger efficiency close to the detection limit. + Η we neglect these two data points. the LFs for the two redshilt bins are consistent.," If we neglect these two data points, the LFs for the two redshift bins are consistent." + However. the large measurement uncertainties in the z<1 LF make it difficult io test whether the GRB rate follows the star formation rate.," However, the large measurement uncertainties in the $z<1$ LF make it difficult to test whether the GRB rate follows the star formation rate." + We thank D. Zhang. C. ο. Nochanek. R. Salvaterra. ancl (he anonvmous referee. [or helpful discussion.," We thank B. Zhang, C. S. Kochanek, R. Salvaterra, and the anonymous referee for helpful discussion." +have high contrasts (AH>>10). putting them below the 5c NACO-SDI threshold.,"have high contrasts $\Delta$ $>>$ 10), putting them below the $\sigma$ NACO-SDI threshold." +" However. two companions have larger separations 70.3"". approaching the separations of the already discovered objects of 2.. 2.. ? and ? and. combined with a AH«13.5. they could be amenable to SDI imaging."," However, two companions have larger separations $>$ $''$, approaching the separations of the already discovered objects of \citet{marois08}, \citet{mccaughrean03}, \citet{chauvin} and \citet{neuhauser} and, combined with a $\Delta$ $<$ 13.5, they could be amenable to SDI imaging." + Note that another secure AO detection is Fomalhaut 5 but this 1s located far off the plot scale with an angular separation of ~ 14.9”., Note that another secure AO detection is Fomalhaut $b$ but this is located far off the plot scale with an angular separation of $\sim$ $''$. + The NACO-SDI (?)) and NICI (http://www.gemini.edu/sciops/imstruments/nici) sensitivities are highlighted on Fig., The NACO-SDI \citealp{mugrauer}) ) and NICI (http://www.gemini.edu/sciops/instruments/nici) sensitivities are highlighted on Fig. + 2. by dotted and dashed lines respectively., \ref{cont_sep} by dotted and dashed lines respectively. + Note that we can not be sure if the Mugrauer Neuhauser detectability limits are actual 5c limits or some lower threshold limit., Note that we can not be sure if the Mugrauer Neuhauser detectability limits are actual $\sigma$ limits or some lower threshold limit. + Once the masses and semimajor axes are more precisely defined. the companion magnitudes and separations will most likely increase giving lower contrasts and more viable targets.," Once the masses and semimajor axes are more precisely defined, the companion magnitudes and separations will most likely increase giving lower contrasts and more viable targets." + This has been highlighted on the plot by the error bars which represent the direction in which all companions are expected to move once inclination and eccentricity effects are considered and more RV data points acquired., This has been highlighted on the plot by the error bars which represent the direction in which all companions are expected to move once inclination and eccentricity effects are considered and more RV data points acquired. + Another major source of uncertainty is age., Another major source of uncertainty is age. + For example. a typical Io age uncertainty for these types of objects is ~+2 Gyr. which translates to a ~+2 magnitude error in AH with the primary.," For example, a typical $\sigma$ age uncertainty for these types of objects is $\sim$$\pm$ 2 Gyr, which translates to a $\sim$$\pm$ 2 magnitude error in $\Delta$ H with the primary." + Due to the high contrast ratios and extremely small separations the majority of these companions are out of reach of current instruments., Due to the high contrast ratios and extremely small separations the majority of these companions are out of reach of current instruments. + However. future Extreme-AO systems which are proposing to reach 215 magnitudes of contrast may be able to bridge this gap.," However, future Extreme-AO systems which are proposing to reach $>$ 15 magnitudes of contrast may be able to bridge this gap." +" All companions with Ty,> 2000K (triangles in Fig.", All companions with $_{\rm{EFF}}~>~$ 2000K (triangles in Fig. + and taken from ? and ?)) have H-band magnitudes less than 15. allowing direct imaging using normal AO techniques.," \ref{cont_sep} and taken from \citealp{nidever} and \citealp{jenkins10}) ) have $H$ -band magnitudes less than 15, allowing direct imaging using normal AO techniques." +" Four of these objects have separations larger than 0.35"" and AH less than 8. making excellent coronographie targets."," Four of these objects have separations larger than $''$ and $\Delta$ H less than 8, making excellent coronographic targets." + All planetary-mass companions are off the Fig., All planetary-mass companions are off the Fig. + 2 plot scale since they have much larger H-band contrasts., \ref{cont_sep} plot scale since they have much larger $H$ -band contrasts. +" The star in this figure shows the position of a 6M, planet in a Jupiter-like orbit as à companion to à 0.2 Gyr. KO star at Spe."," The star in this figure shows the position of a $_{\rm{J}}$ planet in a Jupiter-like orbit as a companion to a 0.2 Gyr, K0 star at 5pc." + The age and spectral type were chosen since they relate to the best case scenario for one of our objects HD120780., The age and spectral type were chosen since they relate to the best case scenario for one of our objects HD120780. + It shows that by adopting the lower limit to the large errors on the age of this system that the potential exists to detect planetary-mass objects around such stars., It shows that by adopting the lower limit to the large errors on the age of this system that the potential exists to detect planetary-mass objects around such stars. + Even still. these types of objects reside extremely close to the plotted instrument thresholds. highlighting just how difficult it is to obtain a direct Image of any planetary-mass object with the current suite of instruments available.," Even still, these types of objects reside extremely close to the plotted instrument thresholds, highlighting just how difficult it is to obtain a direct image of any planetary-mass object with the current suite of instruments available." + However. radial-velocity studies have revealed a high number (>28% of planet hosting stars) of multiple planet systems (?)). therefore imaging planet-host stàrs can provide useful constraints on any longer period. massive companions not yet revealed in the radial-velocity dataset (e.g. 2:: ?)).," However, radial-velocity studies have revealed a high number $\ge$ of planet hosting stars) of multiple planet systems \citealp{wright09}) ), therefore imaging planet-host stars can provide useful constraints on any longer period, massive companions not yet revealed in the radial-velocity dataset (e.g. \citealp{mugrauer06}; ; \citealp{mugrauer07}) )." + AM radial-velocity data in. this section were generated using the AAPS and Keck pipelines., All radial-velocity data in this section were generated using the AAPS and Keck pipelines. + These pipelines are still undergoing development following the procedures and techniques deseribed in ? and ???..," These pipelines are still undergoing development following the procedures and techniques described in \citet{marcy92} and \citet{butler,butler01,butler06}." + The Keplerian fits shown in Figs. 3.. 4..," The Keplerian fits shown in Figs. \ref{rv_25874}, \ref{rv_32778}, \ref{rv_91204}," + 5.. 6 and 7 are performed using the Systemic algorithm (2)). however we note that most are not very well constrained using the current radial-velocity data.," \ref{rv_120780}~ and \ref{rv_145825} are performed using the Systemic algorithm \citealp{meschiari09}) ), however we note that most are not very well constrained using the current radial-velocity data." + Table | lists some relevant information for each object relating to both the radial-velocityand photometric analysis in this work., Table \ref{tab:stars} lists some relevant information for each object relating to both the radial-velocityand photometric analysis in this work. + The parameters and their analysis methods can be found in ?.. ?.. 2.. 2..2..? and ?..," The parameters and their analysis methods can be found in \citet{vanleeuwen05}, \citet{henry}, \citet{valenti05}, \citet{wright05}, \citet{jenkins06c}, \citet{takeda07} and \citet{jenkins08}." + Tables 2.. 3.. 4.. 5 and 6 list all radial-velocity data.," Tables \ref{tab:rv1}, \ref{tab:rv2}, \ref{tab:rv3}, \ref{tab:rv4}~ and \ref{tab:rv5} list all radial-velocity data." + The AAPS has obtained 11 radial-velocity data points over a period of 4.4 years (Fig., The AAPS has obtained 11 radial-velocity data points over a period of 4.4 years (Fig. + 3. data taken from ?)), \ref{rv_25874} data taken from \citealp{jenkins10}) ). + The minimum best-fit Keplerian orbit to this data has an amplitude of »1000ms! relating to a companion period of 6.5 years. eccentricity 0.43 and à minimum mass of 66M.," The minimum best-fit Keplerian orbit to this data has an amplitude of $>$ $^{-1}$ relating to a companion period of 6.5 years, eccentricity 0.43 and a minimum mass of $_{\rm{J}}$." + However. the curvature of the fit has been generated by the algorithm itself as within the uncertainties all the data points lie in a straight line. known as a liner.," However, the curvature of the fit has been generated by the algorithm itself as within the uncertainties all the data points lie in a straight line, known as a liner." + Therefore. the orbital solutions to this data series are lower limits.," Therefore, the orbital solutions to this data series are lower limits." +" For comparison the best-fit Keplerian with twice the orbital period would relate to a companion minimum mass of ~190M, and similar y of 2.5.", For comparison the best-fit Keplerian with twice the orbital period would relate to a companion minimum mass of $\sim$ $_{\rm{J}}$ and similar $\chi$$^{2}$ of 2.5. + From experience we estimate the lower limit of the period of the orbit to be around four times larger than currently estimated., From experience we estimate the lower limit of the period of the orbit to be around four times larger than currently estimated. + If we take the period range 6.4-25.8 years and the Hippareos distance of 25.9]pe. the projected separation will be in the range 0.13-0.," If we take the period range 6.4-25.8 years and the Hipparcos distance of 25.91pc, the projected separation will be in the range $''$." +"34"". The absolute H-band magnitude is 3.20 magnitudes and our estimation for the absolute H-band magnitude of the companion using the technique in Section 3.1 is 15.3] magnitudes. giving a best estimate for the contrast ratio upperlimit of 12.11 magnitudes."," The absolute H-band magnitude is 3.20 magnitudes and our estimation for the absolute H-band magnitude of the companion using the technique in Section 3.1 is 15.31 magnitudes, giving a best estimate for the contrast ratio upperlimit of 12.11 magnitudes." + Five radial-velocities over a period of 2.25 years for this object (Fig. 4)), Five radial-velocities over a period of 2.25 years for this object (Fig. \ref{rv_32778}) ) + and the best-fit Keplerian orbit has a semi-amplitude of ~750ms~!., and the best-fit Keplerian orbit has a semi-amplitude of $\sim$ $^{-1}$ . + This is consistent with a companion with a, This is consistent with a companion with a +Brightest cluster galaxies (BCGs) are large and luminous galaxies located in the centers of galaxy clusters.,Brightest cluster galaxies (BCGs) are large and luminous galaxies located in the centers of galaxy clusters. + The formation history of BCGs and their halos 1s connected to the formation of the cluster itself (?)) and to the presence of diffuse intra- light (??)).," The formation history of BCGs and their halos is connected to the formation of the cluster itself \citealt{Dubinski98}) ) and to the presence of diffuse intra-cluster light \citealt{Gonzalez+05, Murante+07}) )." + The formation of BCG and their halos can be investigated by the combined study of the stellar kinematics and the population content of their halos., The formation of BCG and their halos can be investigated by the combined study of the stellar kinematics and the population content of their halos. + Dynamical timescales in the halos are on the order of 1 Gyr approaching a significant fraction of the age of the universe. and therefore the fingerprints of the formation processes may still be preserved there.," Dynamical timescales in the halos are on the order of 1 Gyr, approaching a significant fraction of the age of the universe, and therefore the fingerprints of the formation processes may still be preserved there." + So far. the studies that provide both stellar kinematics and line strength mdices in BCGs have been limited to within one effective radius (e.g ?:; 2:: 27; 22:; 22)). therefore measurements over a wider radial range are highly desirable.," So far, the studies that provide both stellar kinematics and line strength indices in BCGs have been limited to within one effective radius (e.g \citealt{Carter+99}; \citealt{Fisher+95}; \citealt{Brough+07}; \citealt{Spolaor+08a, Spolaor+08b}; \citealt{Loubser+08, Loubser+09}) ), therefore measurements over a wider radial range are highly desirable." + This work ts the first of a series aimed at studying the formatior history of BCGs by probing the stellar kinematics and populations of their outer halos. covering regions at 3 effective radii or larger.," This work is the first of a series aimed at studying the formation history of BCGs by probing the stellar kinematics and populations of their outer halos, covering regions at 3 effective radii or larger." + As first targets. we selected NGC 4874 and NGC 4889. the two BCGs in the Coma cluster (Abell 1656).," As first targets, we selected NGC 4874 and NGC 4889, the two BCGs in the Coma cluster (Abell 1656)." + The inner parts of these galaxies have been studied with photometric. kinematic and stellar populations data documented and available in the literature (e.g. ????)).," The inner parts of these galaxies have been studied with photometric, kinematic and stellar populations data documented and available in the literature (e.g. \citealt{Mehlert+00, Gavazzi+03, Gerhard+07, + Trager+08}) )." + In this paper we describe the data acquisition. reduction. and the measurements of the long slit stellar kinematies. for both galaxies. and the line strength indices for NGC 4889.," In this paper we describe the data acquisition, reduction, and the measurements of the long slit stellar kinematics for both galaxies, and the line strength indices for NGC 4889." + The data set in NGC 4889 extends out to 65 kpe (which correspond to ~4.3 effective radii. 2)). providing the most radially extended measurements of absorption line kinematics line strength indices in the outer halo of a BCG.," The data set in NGC 4889 extends out to 65 kpc (which correspond to $\sim 4.3$ effective radii, \citealt{Jorgensen+95}) ), providing the most radially extended measurements of absorption line kinematics line strength indices in the outer halo of a BCG." + These data are the basis of forthcoming papers investigating the formation history and evolution of the galaxies in the Coma cluster core., These data are the basis of forthcoming papers investigating the formation history and evolution of the galaxies in the Coma cluster core. + The paper is organized as follows., The paper is organized as follows. + Spectroscopic observations and data reduction are discussed in Section 2.., Spectroscopic observations and data reduction are discussed in Section \ref{sec:observations}. + The sky subtraction and the radial binning of the spectra we described in Sections 3 and 4.. respectively.," The sky subtraction and the radial binning of the spectra are described in Sections \ref{sec:sky} and \ref{sec:radial_binning}, respectively." + Section 5 describes the measurements of the stellar kinematics. while Section 6 describes the measurements of the line strength indices.," Section \ref{sec:stellar_kinematics} describes the measurements of the stellar kinematics, while Section \ref{sec:indices} describes the measurements of the line strength indices." + Finally. the results are discussed in Section 7..," Finally, the results are discussed in Section \ref{sec:discussion}. ." +" In this paper. we adopt a distance to NGC 4784 of D= Mpe and an effective radius of R,=7077935.21 kpe: for NGC 4889 we adopt D=92.7 Mpe and R,=33/788=15.23 kpe."," In this paper, we adopt a distance to NGC 4784 of $D=102.6$ Mpc and an effective radius of $R_e = 70\farcs79 = 35.21$ kpc; for NGC 4889 we adopt $D=92.7$ Mpc and $R_e = 33\farcs88 = 15.23$ kpc." + Distances are taken from the NASA/IPAC Extragalactic Database (NED) and the effective radii from ?.., Distances are taken from the NASA/IPAC Extragalactic Database (NED) and the effective radii from \citet{Jorgensen+95}. +" Long slit spectra were acquired with the Faint Object Camera And Spectrograph (FOCAS. ?)) at the SUBARU telescope of the National Astronomical Observatory of Japan (NAOJ). on Mauna Kea (Hawaii, USA)."," Long slit spectra were acquired with the Faint Object Camera And Spectrograph (FOCAS, \citealt{Kashikawa+02}) ) at the SUBARU telescope of the National Astronomical Observatory of Japan (NAOJ), on Mauna Kea (Hawaii, USA)." + Data were collected during two runs: in run #11 (April 2007) we obtained 8 hours integration long shit data on the West side of the NGC 4889 major axis. in the region m between NGC 4874 and NGC 4889. with a spectral resolution of 76s'.," Data were collected during two runs; in run 1 (April 2007) we obtained 8 hours integration long slit data on the West side of the NGC 4889 major axis, in the region in between NGC 4874 and NGC 4889, with a spectral resolution of 76." +. In run #22 (May 2008) we obtained 5.5 hours integration of long slit data for the NGC 4889 minor axis. with a spectral resolution of 96s7!.," In run 2 (May 2008) we obtained 5.5 hours integration of long slit data for the NGC 4889 minor axis, with a spectral resolution of 96." +. In Figure | the observed field and slits locations are shown.," In Figure \ref{fig:field} + the observed field and slits locations are shown." + In Table 1 we provide a summary of the observing log and instrumental set up., In Table \ref{tab:setup} we provide a summary of the observing log and instrumental set up. + During these runs. we observed a set of kinematic. template stars and. Lick. spectrophotometric standard stars for calibration to the Lick system.," During these runs, we observed a set of kinematic template stars and Lick spectrophotometric standard stars for calibration to the Lick system." + Long slit spectra on blank fields of the COMA cluster were also obtained for the sky background evaluation and to correct for large-scale illumination. patterns due to slit vignetting., Long slit spectra on blank fields of the COMA cluster were also obtained for the sky background evaluation and to correct for large-scale illumination patterns due to slit vignetting. + In addition. we observed at leastone flux standard star per night. to flux calibrate the spectra.," In addition, we observed at leastone flux standard star per night, to flux calibrate the spectra." + Standard data reduction (bias subtraction. flat fielding to correct for pixel to pixel chip sensitivity fluctuations) were," Standard data reduction (bias subtraction, flat fielding to correct for pixel to pixel chip sensitivity fluctuations) were" +companions to monitored main-sequence.,companions to monitored main-sequence. + We compute that those with orbital periods larger than e4 days producing transits of Aeplermonitored stars may be ~20 (mes less common than (the dwarls which transit. (largels (see Figure 5)., We compute that those with orbital periods larger than $\sim 4$ days producing transits of -monitored stars may be $\sim 20$ times less common than the s which transit targets (see Figure 5). + These will produce transits with no evidence of lensing., These will produce transits with no evidence of lensing. + The disk of a small object must directly overlap the disk of its stellar companion to decrease (he amount of light we receive from it., The disk of a small object must directly overlap the disk of its stellar companion to decrease the amount of light we receive from it. + Detectable lensing can occur. however. even without overlap between the object aud its companion.," Detectable lensing can occur, however, even without overlap between the object and its companion." + Thus. the cross section for lensing events is higher. and the lensing events caused by transiting white cdwarfs will be supplemented by lensing events caused by the cwarls making more clistant approaches.," Thus, the cross section for lensing events is higher, and the lensing events caused by transiting white dwarfs will be supplemented by lensing events caused by the dwarfs making more distant approaches." + The rate of pure lensing events depends on finite source size effects. so 10 nisl be computed in each case.," The rate of pure lensing events depends on finite source size effects, so it must be computed in each case." + The enhancement of a factor will be modest., The enhancement of a factor will be modest. + For objects more compact and more massive (han white dwarls. lensing is by far the dominant effect. and finite-lens effects are not important. (," For objects more compact and more massive than white dwarfs, lensing is by far the dominant effect, and finite-lens effects are not important. (" +See below.),See below.) + We included more massive stars in our simulation. ancl kept (rack of those binaries in which a neutron star or black hole orbits a main sequence star within roughly 0.5 AU.," We included more massive stars in our simulation, and kept track of those binaries in which a neutron star or black hole orbits a main sequence star within roughly $0.5$ AU." + The evolutionary patliwaws that produce such orbits are far less certam than the evolutionary channels producing close whlite-dwarf/main-sequence binaries., The evolutionary pathways that produce such orbits are far less certain than the evolutionary channels producing close white-dwarf/main-sequence binaries. + Nevertheless. we know that svstems with main sequence stars wilh mass in the range orbit neutron stars and black holes.," Nevertheless, we know that systems with main sequence stars with mass in the range $0.8-2\, M_\odot$ orbit neutron stars and black holes." + When the orbits are close enough (with semimajor axis of a few solar radii) such binaries are detected as low-mass x-ray binaries.," When the orbits are close enough (with semimajor axis of a few solar radii), such binaries are detected as low-mass x-ray binaries." + In. our simulation we considered all binaries with primary mass larger than 8.5... (the lowest mass star producing a neutron star renman() and secondary mass between 0.8M. and 2A/.. We (hen assumed that 1/6—1/5 of the initial orbital separations could be compatible with evolutionary channels (hat produce close neutron-star/11ain-sequence pairs (see. e.g. ]|xalogera Webbink 1998: Kiel Ibulev 2006).," In our simulation we considered all binaries with primary mass larger than $8.5\, M_\odot$ (the lowest mass star producing a neutron star remnant) and secondary mass between $0.8\, M_\odot$ and $2\, M_\odot.$ We then assumed that $\sim 1/6-1/5$ of the initial orbital separations could be compatible with evolutionary channels that produce close neutron-star/main-sequence pairs (see, e.g., Kalogera Webbink 1998; Kiel Hurley 2006)." +" Although we did not follow the detailed evolution of individual svstems. our approach vielded a binary fraction of neutron stars in close orbits with main-sequence stars or their remnants of (<0.5 AU) of 5x10.7. We found thatAepler could detect 1—2 lensing ""events"" by neutron stars or black holes corresponding {ο approaches close enough that the compact object (üransits the companion star."," Although we did not follow the detailed evolution of individual systems, our approach yielded a binary fraction of neutron stars in close orbits with main-sequence stars or their remnants of $< 0.5\, AU$ ) of $5\times 10^{-5}.$ We found that could detect $1-2$ lensing “events” by neutron stars or black holes corresponding to approaches close enough that the compact object transits the companion star." + In most cases. (he neutron star or black hole would be too dim for eclipses of it to be detected.," In most cases, the neutron star or black hole would be too dim for eclipses of it to be detected." + We started by considering evolutionary models for INOI-T4 and INOI-81., We started by considering evolutionary models for KOI-74 and KOI-81. + Our results agree, Our results agree +such edges whose crossings with the image contour line detine its entry to and exit from the respective square.,such edges whose crossings with the image contour line define its entry to and exit from the respective square. + Usually contour plot algorithms determine the cut of the contour line with the edge by linear interpolation using the values of /y(a:).p] at the corners.," Usually contour plot algorithms determine the cut of the contour line with the edge by linear interpolation using the values of $F[\vec y(\vec x),\vec p]$ at the corners." + However. since the images are dominated by convex contours. this choice systematically leads to an underestimation of the enclosed area.," However, since the images are dominated by convex contours, this choice systematically leads to an underestimation of the enclosed area." + From practice. it has emerged that simply using the midpoint between the corners provides an estimate that on average deviates less from the true image area for moderate precisions.," From practice, it has emerged that simply using the midpoint between the corners provides an estimate that on average deviates less from the true image area for moderate precisions." + It might happen that the image contour line runs through squares of different depth., It might happen that the image contour line runs through squares of different depth. + For adjacent squares of different depth joining at an edge. the contour line has to be put through the edge of the square with larger depth. tthe smaller one.," For adjacent squares of different depth joining at an edge, the contour line has to be put through the edge of the square with larger depth, the smaller one." +" Let us consider a circular source with angular radius p,8p whose center is at y"". so that p= (g'"".p,) constitutes the respective parameter vector."," Let us consider a circular source with angular radius $\rho_\star\,\theta_\rmn{E}$ whose center is at ${\vec y}^{(0)}$ , so that $\vec p = ({\vec y}^{(0)}, \rho_\star)$ constitutes the respective parameter vector." + For the square denoted by the ∏⋯⋯⋂∙⋮↾⋯↲∁⋅∖∣⋅∣∁⊓∖⊽≀⋅⊥⊔↘⊔⊐⋡∙⋯↳⊓∖⊽≀⋅⊥∣↴⋡⊽≀⋅⊐∣↴⊐∣↴∁↾∣↧∁⋡∙∣↲∩⇂⇈∁↲↘ ↘ ↘⊥↘⊥ intersections of the edges with the contour line.," For the square denoted by the running index $i$, let $(x_1^{(i)},x_2^{(i)})$ and $(x_1^{(i+1)},x_2^{(i+1)})$ be the adopted intersections of the edges with the contour line." + A symmetric discretization of Eq. (9)), A symmetric discretization of Eq. \ref{eq:maguniform}) ) + then yields The absolute error in the area cannot exceed the sum of the area of all squares through which the contour line runs. but it can be expected to be much smaller than that.," then yields The absolute error in the area cannot exceed the sum of the area of all squares through which the contour line runs, but it can be expected to be much smaller than that." + While the ratio 5 between these squares and the approximated enclosed area gives some measure for the quality of the approximation. it vastly overestimates the typical error.," While the ratio $\varepsilon$ between these squares and the approximated enclosed area gives some measure for the quality of the approximation, it vastly overestimates the typical error." + However. a suitable value for = can be chosen from testing how its variation affects the final result.," However, a suitable value for $\varepsilon$ can be chosen from testing how its variation affects the final result." +" For a general surface brightness /g(a):gy"".p,]. one finds where and thebrightness of the source. centered at 3 reads"," For a general surface brightness $I[{\vec y}(\vec x); {\vec y}^{(0)}, \rho_\star]$, one finds where and thebrightness of the source, centered at ${\vec y}^{(0)}$ reads" +in the observed. spectra with one exception.,in the observed spectra with one exception. +" In the case of Q1122 we decrease Doi by in order to reproduce the evel of apparent 70, at low mH).", In the case of Q1122 we decrease $\bar D_{\rmn{O\textsc{VI}}}$ by in order to reproduce the level of apparent $\tau_{\rmn{O\textsc{vi}}}$ at low $\tau_{\rmn{H\textsc{i}}}$. + Ehe need for this is most ikely clue to a deficit of saturated regions in our svnthetic spectra., The need for this is most likely due to a deficit of saturated regions in our synthetic spectra. + The contribution of saturated regions to the mean lux decrement is high at low redshift’ and the failure to adequately reproduce the high incidence of these svstenis eads to a bias in the mean Ilux decremoent (?).., The contribution of saturated regions to the mean flux decrement is high at low redshift and the failure to adequately reproduce the high incidence of these systems leads to a bias in the mean flux decrement \citep{2003astro.ph..8078V}. + The triangles in the left panel of Fig., The triangles in the left panel of Fig. + 6 show he relation for the four observed. spectra., \ref{searchplots} show the relation for the four observed spectra. + For the synthetic spectra we assume as before. that. the distribution. takes the form. described. in. equations (S)) and (9)., For the synthetic spectra we assume as before that the distribution takes the form described in equations \ref{delcutrangezero}) ) and \ref{delcutrangeconst}) ). + We have varied. the density and he overdensitv threshold. for. addition. of over. the range movi/?ui=00.3 and (n/n)aa—0 100., We have varied the density and the overdensity threshold for addition of over the range $n_{\rmn{O\textsc{VI}}}/n_{\rmn{H\textsc{I}}} = 0-0.3$ and $(n/\bar n)_{\rmn {cut}} = 0-100$ . + We have produced. samples. of 40. synthetic. spectra or each set of values., We have produced samples of 40 synthetic spectra for each set of values. + We have then calculated: the relation for cach sample. ancl assessed. the agreement with the observed relation by calculating X7., We have then calculated the relation for each sample and assessed the agreement with the observed relation by calculating $\chi^2$. + ote. however. that there may be additional sources of error such inhomogeneities in the metal distribution which our Monte Carlo technique does not take into account.," Note, however, that there may be additional sources of error such inhomogeneities in the metal distribution which our Monte Carlo technique does not take into account." + The crosses and squares in the left panels of Fig., The crosses and squares in the left panels of Fig. + 6. show the relation with no and the best litting values for DONIMHI =O). respectively," \ref{searchplots} show the relation with no and the best fitting values for $n_{\rmn{O\textsc{VI}}}/n_{\rmn{H\textsc{I}}}$ $=0$ ), respectively." + Lhebest fFillingealucbasareduced yz close to or somewhat smaller than one., The best fitting value has a reduced $\chi^2_{\rmn{r}}$ close to or somewhat smaller than one. + There is thus good agreement between the relation for our best fitting simulations and the real data., There is thus good agreement between the relation for our best fitting simulations and the real data. + In the right panels of Fig., In the right panels of Fig. + 6 we use the relation of svnthetie and observed. spectra for QIIOT to provide an example of the cilliculty in constraining, \ref{searchplots} we use the relation of synthetic and observed spectra for Q1107 to provide an example of the difficulty in constraining. + The top panel of Eig., The top panel of Fig. + 7. shows the reduced X7 as a function of moyi/mgi for the four observed: QSOs., \ref{rcutchisq} shows the reduced $\chi^2_{\rmn{r}}$ as a function of $n_{\rmn{O\textsc{VI}}}/n_{\rmn{H\textsc{I}}}$ for the four observed QSOs. + In Q1442 there is à marginal detection ofOvi. in. Q1107 lis detected. with a poorly constrained density (novi£mgi8 0.08) while in Q1122 is clearly. detected with novisnap70.06.," In Q1442 there is a marginal detection of, in Q1107 is detected with a poorly constrained density $n_{\rmn{O\textsc{VI}}}/n_{\rmn{H\textsc{I}}} +\approx 0.08$ ) while in Q1122 is clearly detected with $n_{\rmn{O\textsc{VI}}}/n_{\rmn{H\textsc{I}}} \approx 0.06$." + In Q1422 no is detected., In Q1422 no is detected. + Indeed. we find that the spectrum. of QIJ22 is inconsistent with absorption at the same level as detected in Q1122 and QII07 with a confidence of greater than 99%.. In the bottom panel of Fig.," Indeed, we find that the spectrum of Q1422 is inconsistent with absorption at the same level as detected in Q1122 and Q1107 with a confidence of greater than In the bottom panel of Fig." + 7. we show how the reduced AI varies as a [function of (η η].λλο have assumed. that moving and are independent in the caleulation of the confidence level., \ref{rcutchisq} we show how the reduced $\chi^2_{\rmn{r}}$ varies as a function of $(n/\bar{n})_{\rmn{cut}}$ .We have assumed that $n_{\rmn{O\textsc{VI}}}/n_{\rmn{H\textsc{I}}}$ and are independent in the calculation of the confidence level. + of greater than 4 for Q1122. 7 lor QII07 and 4 for Ql442 are ruled out. with confidence.," of greater than 4 for Q1122, 7 for Q1107 and 4 for Q1442 are ruled out with confidence." +There is thus no significant detection of at overcensitics <5.,There is thus no significant detection of at overdensities $\la 5$ . +result.,result. + Tere. we report new. deeper optical observations with the heck telescope. which show a possible counterpart to the ssvstcli.," Here, we report new, deeper optical observations with the Keck telescope, which show a possible counterpart to the system." +" We miaeed the field containiug wwith the Low Resolution Imagine 5ctroeraphi (Oke ct citeokea:5)) at the Weck TI telesco]20, on the nights of November 28 aud 29. 1997 (UT)."," We imaged the field containing with the Low Resolution Imaging Spectrograph (Oke et \\cite{oke&a:95}) ) at the Keck II telescope, on the nights of November 28 and 29, 1997 (UT)." + On the 2Sth. three 00-5 exposures were obained in the R baud. aud two KI-s exposures iu D. O ithe 29th. ore L50-s and four 0-8 in BR. three 900-5 in D. and five 600-5 exposures in V were taken.," On the 28th, three 600-s exposures were obtained in the R band, and two 900-s exposures in B. On the 29th, one 450-s and four 600-s in R, three 900-s in B, and five 600-s exposures in V were taken." + All images were ake at alrniass <1.1., All images were taken at airmass $<\!1.4$. + The skies were cear on the second night. but the first night was plagued by eimls.," The skies were clear on the second night, but the first night was plagued by cirrus." + The reductioi was clone as descrilved by Iulkuwnuli& van Kerkwijk 1998 ) for the field o£ RX 3125. which was observed ou the παλιο uights.," The reduction was done as described by Kulkarni van Kerkwijk \cite{kulkvk:98}) ) for the field of RX $-$ 3125, which was observed on the same nights." + For the photometric caliMalon. we used Laudolt fields: D aud R. the fmr listed in Table of the above reference: in V. the first two ouly.," For the photometric calibration, we used Landolt fields: in B and R, the four listed in Table 1 of the above reference; in V, the first two only." + We estimate uncertaimtics of xü.021nag in the zero points., We estimate uncertainties of $\simlt\!0.02\un{mag}{}$ in the zero points. + For the astrometry. we selected from the 3.0 cataoeue (Monet et citemionea: 5)) a] 163 stars that overlapped with a 10-5 R-baid inage.," For the astrometry, we selected from the USNO-A2.0 catalogue (Monet et \\cite{mone&a:98}) ) all 163 stars that overlapped with a 10-s R-band image." +" We measured treir centroids. anc corrected for mstruienutal distorticn using a bicubic Aunctiou determined by Cohen (priv ""teconmnmunication)."," We measured their centroids, and corrected for instrumental distortion using a bi-cubic function determined by Cohen (private communication)." + With the plate scale known accuraolv. we fitted oulv or the zero-poiuts in cach coordinae aud the positiou anee on he sky.," With the plate scale known accurately, we fitted only for the zero-points in each coordinate and the position angle on the sky." + After rejecting 7 outliers (residual arecr than 55). the root-mea-sqnare residuals were y/22( i reach coordinate.," After rejecting 7 outliers (residual larger than 8), the root-mean-square residuals were 20 in each coordinate." + The astronetry was transferred otιο stacked B. V.. and. & images using 2S transfer stars οose to the pulsar position. solving again for rotation aud zero-poiuts.," The astrometry was transferred to the stacked $B$, $V$, and $R$ images using 28 transfer stars close to the pulsar position, solving again for rotation and zero-points." + The rims residuals were 7 profile. as usually assunec.," In particular, the forward shock rapidly moves into prior phases of mass loss from the progenitor which need not be distributed in a smooth $r^{-2}$ profile as usually assumed." + Numerical calculations become necessary. including radiative losses. particularly for tle reverse sliock.," Numerical calculations become necessary, including radiative losses, particularly for the reverse shock." + We uote the preseuation of Nyiuark&PFrausson(2003) demonstrating that uitiple tem»eratures exist in the shocsed gas in coutrast to the considerably simpler moclels adopted or the present analysis., We note the presentation of \cite{NF03} demonstrating that multiple temperatures exist in the shocked gas in contrast to the considerably simpler models adopted for the present analysis. + We conclude that the aud observations detected the [first hiuts of increasing transj»areucy of the matter surrounding SNI9T8k. The iucreasiig transparency signals the staA ol its «eciue in the X-ray. baud., We conclude that the and observations detected the first hints of increasing transparency of the matter surrounding SN1978K. The increasing transparency signals the start of its decline in the X-ray band. + ΤΙe low-tetiperature spectral coiipouents remaiu essentially unehaugec from the epochs except or the addiion oL the detected Si., The low-temperature spectral components remain essentially unchanged from the epochs except for the addition of the detected Si. +" Within the errors. the higbi-tempe""ature COLLyonents lave also no changed: --- “we restrict our ateition solely to the aud. observations of 2000 and. 2002 then we see a deciLe of a factor of 71.5. consistent with au interpretation of Increas]he talSyarency."," Within the errors, the high-temperature components have also not changed; if we restrict our attention solely to the and observations of 2000 and 2002, then we see a decline of a factor of $\sim$ 1.5, consistent with an interpretation of increasing transparency." + Additional X-ray observations will conlirm or refute our interpretation., Additional X-ray observations will confirm or refute our interpretation. + If N-ray ine enmüssion is becomiiD>oO increasingly visible. line emission in other Dauds tay be expected t«> chauge depeucdiug upou he atomic cascades.," If X-ray line emission is becoming increasingly visible, line emission in other bands may be expected to change depending upon the atomic cascades." + An observation with teHST STI Spectrograp1 is Clearly warranted: sucl t1 observation would also aid iu sorting out he emission reglon ai de‘ifvine the nature of the Ine einisslou uncovered with the FOS observation (S99)., An observation with the STI Spectrograph is clearly warranted; such an observation would also aid in sorting out the emission region and clarifying the nature of the line emission uncovered with the FOS observation (S99). + Additional X-ray. olBELValious over he coming years are iuportaut to investigateH possible variations lu ile wind as well as detectiug je expectecd developing line emission., Additional X-ray observations over the coming years are important to investigate possible variations in the wind as well as detecting the expected developing line emission. + [Pour iuterpretation Is correct. 1ren the decline plase comanenced just. within the past few vears ane jyovides au opportutity o observe tlie decliue.," If our interpretation is correct, then the decline phase commenced just within the past few years and provides an opportunity to observe the decline." + Compason wlth SNIO87TÀ will reveal dillerences lisely attribitable to the clilferine densities of the circumstelar uela., Comparison with SN1987A will reveal differences likely attributable to the differing densities of the circumstellar media. + At least two radio-eiittiD>oO supernovae have shown hesitations aud increases o1 the decli," At least two radio-emitting supernovae have shown hesitations and increases on the decline," +Compression by the spiral shock is least near the radius at which the spiral pattern corotates with the disk orbital motion.,Compression by the spiral shock is least near the radius at which the spiral pattern corotates with the disk orbital motion. + At significant distances [rom CR. shock compression will be strong and will suppress fragmentation.," At significant distances from CR, shock compression will be strong and will suppress fragmentation." + A major aim of this section is to estimate (he minimum distance away from the CHR. at which (Bis suppression is elfective., A major aim of this section is to estimate the minimum distance away from the CR at which this suppression is effective. +" We first examine criterion (1) by noting that If the shock is strong and isothermal. then where ey, is the ó-direction speed of (he spiral shock Iront relative to the pre-shock malerial and (is the angle to (he normal of the spiral shock front made by the fluid streamlines coming into the shock."," We first examine criterion (1) by noting that If the shock is strong and isothermal, then where $v_{\rm sh}$ is the $\phi$ -direction speed of the spiral shock front relative to the pre-shock material and $\psi$ is the angle to the normal of the spiral shock front made by the fluid streamlines coming into the shock." + At a distance 9r from the CR of the spiral mode. where ór/r1 and © is the clisk’s undisturbed angular frequency. of rotation.," At a distance $\delta r$ from the CR of the spiral mode, where $\delta r/r \ll 1$ and $\Omega$ is the disk's undisturbed angular frequency of rotation." + The factor ay—1 [ον a disk in Weplerian rotation but may differ from unity for disks with significant sell-2ravilv or pressure support., The factor $\alpha_3 = 1$ for a disk in Keplerian rotation but may differ from unity for disks with significant self-gravity or pressure support. +" We define a, such (hat Using (6) through (9). we find that the thin-sheet condition (1) is satisfied if Now let us consider criterion (3) for compression-induced suppression of fragmentation."," We define $\alpha_4$ such that Using (6) through (9), we find that the thin-sheet condition (1) is satisfied if Now let us consider criterion (3) for compression-induced suppression of fragmentation." + For disk eas that is strictly isothermal. (he Toomre(1964). stability parameter Q; is," For disk gas that is strictly isothermal, the \citet{toomre64} stability parameter $Q_{\rm i}$ is" +data were obtained. of which we have selected the best 50 davs in terms of atmospheric quality in order to generate a first set of maps.,"data were obtained, of which we have selected the best $\sim$ 50 days in terms of atmospheric quality in order to generate a first set of maps." + Most of the observation time was devoted to the two high declination regions 22.46° while at the low declination region 16°36J) only 8 days of good observations were obtained., Most of the observation time was devoted to the two high declination regions $22^{\circ}-46^{\circ}$ while at the low declination region $16^{\circ}-36^{\circ}$ only 8 days of good observations were obtained. + The individual scans are reconstructed from. the stored harmonics via an EET using LDL routines on à workstation., The individual scans are reconstructed from the stored harmonics via an FFT using IDL routines on a workstation. + A scan consists of 212 points which represent fixed positions in hour angle (LLX) and declination (DEC)., A scan consists of 212 points which represent fixed positions in hour angle (HA) and declination (DEC). + The top diagram of Figure 4 represents a typical COSALOSOALAS scan containing the point source Tau A. The main modulation observed. is due mostly to the change in air masses ancl eround pickup as the instrument scans a circle on the sky., The top diagram of Figure 4 represents a typical COSMOSOMAS scan containing the point source Tau A. The main modulation observed is due mostly to the change in air masses and ground pickup as the instrument scans a circle on the sky. + To reduce the dominant ground pick-up elfect. we have covered he eround surrounding the instrument with aluminum dates and have increased. the size of the spinning mirror hat is currently heavily uncder-illiuminated.," To reduce the dominant ground pick-up effect, we have covered the ground surrounding the instrument with aluminum plates and have increased the size of the spinning mirror that is currently heavily under-illuminated." + Data alfected ον the Sun or Moon were removed., Data affected by the Sun or Moon were removed. + To remove these spurious signals. we use Fourier series o subtract low Fourier components from the data.," To remove these spurious signals, we use Fourier series to subtract low Fourier components from the data." + Firstly. we reduce the ellect of changes in the gain of the instrument wv dividing the data by the calibration signal.," Firstly, we reduce the effect of changes in the gain of the instrument by dividing the data by the calibration signal." + Secondly. we it each of the scans to a Fourier series of 11. coellicients. which means five sines ancl cosines plus a total power level and subtract the fit from the cata.," Secondly, we fit each of the scans to a Fourier series of 11 coefficients, which means five sines and cosines plus a total power level and subtract the fit from the data." +" Therefore. angular scales arger than 5 degrees are removed from the data. limiting he angular resolution range to 15"". but most of the atmospheric contribution is also removed."," Therefore, angular scales larger than 5 degrees are removed from the data, limiting the angular resolution range to $1^{\circ}-5^{\circ}$, but most of the atmospheric contribution is also removed." + This procedure works very well but needs to be repeated: iteratively so hat strong astronomical features such as the Galaxy are preserved and no extra baseline is introduced around them., This procedure works very well but needs to be repeated iteratively so that strong astronomical features such as the Galaxy are preserved and no extra baseline is introduced around them. + At cach fitting step a re-weighting of the data is performed so that data three sigma away [rom the best fit are zero-weighted for the next step., At each fitting step a re-weighting of the data is performed so that data three sigma away from the best fit are zero-weighted for the next step. + After three or four iterations. contributions from strong astronomical sources are weighted to zero and the atmospheric shape is accurately reproduced by the fit.," After three or four iterations, contributions from strong astronomical sources are weighted to zero and the atmospheric shape is accurately reproduced by the fit." + The upper diagram of Figure 4 also displays such alit to the scan. while the lower diagram shows the residuals after baseline subtraction.," The upper diagram of Figure 4 also displays such a fit to the scan, while the lower diagram shows the residuals after baseline subtraction." + Long drift) baselines possibly due. to changes in atmospheric conditions throughout the day are still present in the data., Long drift baselines possibly due to changes in atmospheric conditions throughout the day are still present in the data. + To reduce these. we perform a second Π to the data.," To reduce these, we perform a second fit to the data." + Each of the positions in the scans throughout the day are fitted to Fourier series of seven coellicients and the fit is subtracted from the data., Each of the positions in the scans throughout the day are fitted to Fourier series of seven coefficients and the fit is subtracted from the data. + This fitting procedure only removes from the data features at angular scales larger than 20° and therefore it does not allect the 1°ο structure we are able to observe., This fitting procedure only removes from the data features at angular scales larger than $20^{\circ}$ and therefore it does not affect the $1^{\circ}-5^{\circ}$ structure we are able to observe. + Note that in this case we also perform an iterative procedure to reduce the effect of Galaxy on the xseline fit., Note that in this case we also perform an iterative procedure to reduce the effect of Galaxy on the baseline fit. + Once the fitting procedure is finished the clean scans are saved as LDL FILS files along with the Julian date., Once the fitting procedure is finished the clean scans are saved as IDL FITS files along with the Julian date. + For each clean scan we reproduce the instrumental »)nting on the sky and derive out RA anc DEC for each position in the scan., For each clean scan we reproduce the instrumental pointing on the sky and derive out RA and DEC for each position in the scan. + A simple projection scheme is used. so that cach RA and DEC position is converted into γκο positions in the map., A simple projection scheme is used so that each RA and DEC position is converted into pixel positions in the map. + For each pixel in the map we calculate an average contribution from all the scan positions ving within that pixel., For each pixel in the map we calculate an average contribution from all the scan positions lying within that pixel. + Phe mean temperature. value and dispersion are calculated for cach pixel., The mean temperature value and dispersion are calculated for each pixel. + Points within the xxel three sigma away from the mean value are excluded rom the final result ancl the map-making process is repeated iteratively., Points within the pixel three sigma away from the mean value are excluded from the final result and the map-making process is repeated iteratively. + The final map is composed of a mean value map. an error map anc a number of points per pixel map that are stored in a single LOL ΕΤ file.," The final map is composed of a mean value map, an error map and a number of points per pixel map that are stored in a single IDL FITS file." + Pixels of 1/3 degrees in RA and DEC are used: because they sample. properly the beam response and minimize the noise contribution per beam area., Pixels of $1/3\times 1/3$ degrees in RA and DEC are used because they sample properly the beam response and minimize the noise contribution per beam area. +" The first region observed covers the range from 16° to 36 in declination and the second one covers the range from. 25"" to 45°.", The first region observed covers the range from $16^{\circ}$ to $36^{\circ}$ in declination and the second one covers the range from $25^{\circ}$ to $45^{\circ}$. + Both have complete WA coverage., Both have complete RA coverage. + The latter region is of special interest because it overlaps that observed by the raciometers of the Tenerife Experiment (Gutierrez et al., The latter region is of special interest because it overlaps that observed by the radiometers of the Tenerife Experiment (Gutiérrrez et al. + 2000) and the 33 Cllz interferometer (Dicker et al., 2000) and the 33 GHz interferometer (Dicker et al. + 1999. Larrison et al.," 1999, Harrison et al." + 2000) ancl will allow for a future comparison., 2000) and will allow for a future comparison. + Our primacy calibration sources are the supernova remnant Tau A for the low declination observations anc Cvg A for the higher declinations., Our primary calibration sources are the supernova remnant Tau A for the low declination observations and Cyg A for the higher declinations. + We measure the beam of the instrument using these two sources., We measure the beam of the instrument using these two sources. + Each beam was fitted as an elliptical Gaussian to the main lobe., Each beam was fitted as an elliptical Gaussian to the main lobe. + The sidelobes are 40 dB below the main beam., The sidelobes are 40 dB below the main beam. + Figure 5r shows the observations of Tau A. and the two-climensional fit of the beam.," Figure 5 shows the observations of Tau A, and the two-dimensional fit of the beam." +" From this analysis we conclude that the main beam is described by a circular Gaussian with EWILMs of 1.08720.077 at 13 Cillz. 1.04720.07"" at 15 Cillz and 0.94740.05"" at 17 Cillz."," From this analysis we conclude that the main beam is described by a circular Gaussian with FWHMs of $^\circ \pm 0.07^\circ$ at 13 GHz, $^\circ \pm 0.07^\circ$ at 15 GHz and $^\circ \pm +0.05^\circ$ at 17 GHz." + Vhe Ilux, The flux +of To~10—15x10? determined from the flux curvature method applied to high resolution data (?)..,of $T_0\sim10-15\times10^3$ determined from the flux curvature method applied to high resolution data \citep{2011MNRAS.410.1096B}. + The discrepancy may be due to an inadequate simulation model for calibrating the statistic used to estimate the gas temperature., The discrepancy may be due to an inadequate simulation model for calibrating the statistic used to estimate the gas temperature. +" Alternatively, it may indicate that either wwas reionized too late in the simulation here, or that the Heur--ionizing source was too hard."," Alternatively, it may indicate that either was reionized too late in the simulation here, or that the -ionizing source was too hard." +" A temperature inversion occurs for p/(p)>5, as is expected for thermal balance between photoionization heating and atomic line and radiative recombination cooling in dense structures."," A temperature inversion occurs for $\rho/\langle\rho\rangle>5$, as is expected for thermal balance between photoionization heating and atomic line and radiative recombination cooling in dense structures." + Only such high density gas is able to achieve thermal balance; the time scale to achieve equilibrium is too long in underdense gas (??)..," Only such high density gas is able to achieve thermal balance; the time scale to achieve equilibrium is too long in underdense gas \citep{Meiksin94, MR94}." + A similar trend between temperature and density is found for a pure dark matter simulation with radiative transfer (?).., A similar trend between temperature and density is found for a pure dark matter simulation with radiative transfer \citep{2007MNRAS.380.1369T}. +" Compared with optically thin reionization, the excess temperature boost allowing for radiative transfer occurs primarily for underdense gas, as shown in Fig."," Compared with optically thin reionization, the excess temperature boost allowing for radiative transfer occurs primarily for underdense gas, as shown in Fig." + 6 (right panel)., \ref{fig:dT_rho_contours} (right panel). +" Most of the gas with ϱ/(ϱ)>3 experiences very little boost at all, as it is able to quickly recover thermal balance."," Most of the gas with $\rho/\langle\rho\rangle > 3$ experiences very little boost at all, as it is able to quickly recover thermal balance." + A map of the difference in the temperatures is shown in Fig. 7.., A map of the difference in the temperatures is shown in Fig. \ref{fig:dT_map}. + Boosts of AT>15x10? K are visible downstream of very dense structures which act to filter, Boosts of $\Delta T>15\times10^3$ K are visible downstream of very dense structures which act to filter +The solar abundance of indium is controversial because ils generally accepted value significantly exceeds. the meteoritic value.,The solar abundance of indium is controversial because its generally accepted value significantly exceeds the meteoritic value. + At a factor of six cdillerence. this remains the largest unexplained diserepaney between meteoritie and solar abundance values.," At a factor of six difference, this remains the largest unexplained discrepancy between meteoritic and solar abundance values." + In this paper we address. this problem by considering the nucleosynthesis of indium and through indium line svnthesis for the quiet solar photosphere and sunspot umbrae including hyperfine structure in detail., In this paper we address this problem by considering the nucleosynthesis of indium and through indium line synthesis for the quiet solar photosphere and sunspot umbrae including hyperfine structure in detail. +" The meteoritic indium abundance is (? and references therein) where Aj,=log(tpi/ng)|12 with ny, and ng the incdium and hydrogen particle densities. respectively."," The meteoritic indium abundance is \citealt{2003ApJ...591.1220L} and references therein) where $A_{\rm +In} \equiv \log(n_{\rm In}/n_{\rm H}) + 12$ with $n_{\rm In}$ and $n_{\rm H}$ the indium and hydrogen particle densities, respectively." + Fable 1 summarises the determinations of the solar indium abundance in the literature., Table \ref{tab:abundances} summarises the determinations of the solar indium abundance in the literature. + ALL measurements are based on a single. very weak feature in the quict-sun spectrum at A=451.1307 nm which is commonly identified as one of the rresonance lines.," All measurements are based on a single, very weak feature in the quiet-sun spectrum at $\lambda = 451.1307$ nm which is commonly identified as one of the resonance lines." + “Phe initial result of 2? was. based on an erroneous oscillator strength., The initial result of \citet{1960ApJS....5....1G} was based on an erroneous oscillator strength. +" The other three determinations scatter around. ol),= 1.6. the value listed in the compilation of. ον,"," The other three determinations scatter around $\AInS = +1.6$ , the value listed in the compilation of \citet{2005ASPC..336...25A}." + The 0.5 dex. discrepancy with the meteoritic value cannot. be explained. by the usual uncertainties of abundance determination such as line strength measurement. imprecise atomic data ancl solar modeling ceficiencies.," The 0.8 dex discrepancy with the meteoritic value cannot be explained by the usual uncertainties of abundance determination such as line strength measurement, imprecise atomic data and solar modeling deficiencies." + The origin of elements. heavier than is mostly attributed to. neutron-capture processes. (see.?.[orareview) ," The origin of elements heavier than is mostly attributed to neutron-capture processes \citep[see][for a +review]{1994ARA&A..32..153M}. ." +Sfow neutron capture (the s process) occurs for relatively low neutron densities (10* em 7). while repid neutron capture (the r process) occurs for relatively high neutron densities (2107 em ?).," $Slow$ neutron capture (the $s$ process) occurs for relatively low neutron densities $\simeq 10^7 +$ $^{-3}$ ), while $rapid$ neutron capture (the $r$ process) occurs for relatively high neutron densities $> 10^{20}$ $^{-3}$ )." + ?. analvsed the Sn/In abundance ratio., \citet{1978ApJ...219..307A} analysed the Sn/In abundance ratio. + Hle found that no combination of r- Op s-process products even remotely resembling those which generally predict the solar svstem abundances very successfully can give Sn/In as low as 1.4. (which results from taking Ay)=1.71)., He found that `no combination of $r$ - or $s$ -process products even remotely resembling those which generally predict the solar system abundances very successfully can give Sn/In as low as 1.4' (which results from taking $\AInS = 1.71$). + ltecentlv. 7? sugeested that because. of. its. low condensation temperature.(536 Ix... 2)). indium may have," Recently, \citet{2006MNRAS.370L..90G} suggested that because of its low condensation temperature(536 K, \citealt{2003ApJ...591.1220L}) ), indium may have" +find a restricted range for the bulge-to-disk ratios at the probability level.,find a restricted range for the bulge-to-disk ratios at the probability level. + The correlation between band disk and bulge scale length is shown in Fig., The correlation between band disk and bulge scale length is shown in Fig. + 5 and ts consistent with other studies (4105: Courteau et al. 1996))., \ref{bdcorrel} and is consistent with other studies (dJ95; Courteau et al. \cite{courteau}) ). + However. the trend could be partly due to the selection criteria used. because we are discriminating against large bulge. small disk galaxies.," However, the trend could be partly due to the selection criteria used, because we are discriminating against large bulge, small disk galaxies." + Galaxies with compact. bright bulges and faint extended disks would comply to the criteria. but we do not have them in our sample.," Galaxies with compact, bright bulges and faint extended disks would comply to the criteria, but we do not have them in our sample." + Furthermore. there are no large. pure disk. LSB galaxies known till now. so it is likely that only the area below the plotted trend is affected by selection effects.," Furthermore, there are no large, pure disk, LSB galaxies known till now, so it is likely that only the area below the plotted trend is affected by selection effects." + A correlation between disk and bulge scale length suggests that the formation of bulge and disk is coupled., A correlation between disk and bulge scale length suggests that the formation of bulge and disk is coupled. + The ratio of disk-to-bulge scale length for both HSB and LSB galaxies has large scatter around ~10 and is illustrated in Fig. 6.., The ratio of disk-to-bulge scale length for both HSB and LSB galaxies has large scatter around $\sim 10$ and is illustrated in Fig. \ref{sclratios}. + The LSB galaxies continue the trend defined by HSB galaxies towards lower surface brightnesses., The LSB galaxies continue the trend defined by HSB galaxies towards lower surface brightnesses. + In Fig., In Fig. + 7. we plot the distribution of disk central surface brightness with disk scale length for the samples of dJ95. dB95. Sprayberry and the current sample.," \ref{hmu} we plot the distribution of disk central surface brightness with disk scale length for the samples of dJ95, dB95, Sprayberry and the current sample." + All samples fit in. with the general trend that there are no galaxies with high central surface brightnesses and large disk scale lengths., All samples fit in with the general trend that there are no galaxies with high central surface brightnesses and large disk scale lengths. + Some of the galaxies in our sample have such large disk scale lengths that they are found in the region of giant LSB galaxies and therefore could be classified as such., Some of the galaxies in our sample have such large disk scale lengths that they are found in the region of giant LSB galaxies and therefore could be classified as such. + To investigate whether disk and bulge central surface brightnesses are related we plot these parameters in Fig., To investigate whether disk and bulge central surface brightnesses are related we plot these parameters in Fig. + 8 for the samples of dJ95 and our sample., \ref{mumu} for the samples of dJ95 and our sample. +" The figure clearly shows how the LSB galaxies fill the low surface brightness region. but split into two groups; one near jfy,1, = 20 mag ? and one near j/4, = 22 mag 7."," The figure clearly shows how the LSB galaxies fill the low surface brightness region, but split into two groups; one near $\mu_{0,\rm b}$ = 20 mag $^{-2}$ and one near $\mu_{0,\rm b}$ = 22 mag $^{-2}$." + These groups do not correspond to the two types of bulge LSB galaxies mentioned in Section 2. but the groups are a mixture of both these types.," These groups do not correspond to the two types of bulge LSB galaxies mentioned in Section 2, but the groups are a mixture of both these types." + There seems to be a very broad general tendency for both HSB and LSB, There seems to be a very broad general tendency for both HSB and LSB +Since the eas is dispersed later. the mass distribution of heavy clemeuts of the planets should reflect the surface density.,"Since the gas is dispersed later, the mass distribution of heavy elements of the planets should reflect the surface density." + The well-known inuünnuui mass solar rebula iuodel (Ibwashi 1981) is constructed as follows: he material in each planet is recovered to the solar conrposition and spread over au annulus reaching Παπαν o the orbits of its neighbors., The well-known minimum mass solar nebula model (Hayashi 1981) is constructed as follows: the material in each planet is recovered to the solar composition and spread over an annulus reaching halfway to the orbits of its neighbors. +" By using the ""annulus approach. the surface deusitv X from anv node can be conipared o the masses of the planets"," By using the “annulus"" approach, the surface density $\Sigma$ from any model can be compared to the masses of the planets." + Maux nebula nodels have been built. based on a constent o viscosity (uniform AMT) where the viscous stress is scaled with oessure Pas oP., Many nebula models have been built based on a $constant$ $\alpha$ viscosity (uniform AMT) where the viscous stress is scaled with pressure $P$ as $\alpha P$. + For example. the similarity solution by Iartmanun et al. (," For example, the similarity solution by Hartmann et al. (" +1998) shows that X varies as ~rPb at s1uall radii and falls sharply at large distances (where + is he helioceutric radius).,1998) shows that $\Sigma$ varies as $\sim r^{-1}$ at small radii and falls sharply at large distances (where $r$ is the heliocentric radius). + Notice that X decreases outward with r., Notice that $\Sigma$ decreases outward with $r$. + I list. in Table 1 (iu units of the earth mass. AM. M. caleulated heavy eleimieut masses with X—rE and νι measured masses of the terrestrial plauets or masses of heavy eleiients of the Jovian planets interred from current planet model (Caullot 1999).," I list, in Table 1 (in units of the earth mass, $M_\oplus$ ), $M_\alpha$, calculated heavy element masses with $\Sigma \sim r^{-1}$ and $M_h$, measured masses of the terrestrial planets or masses of heavy elements of the Jovian planets inferred from current planet model (Guillot 1999)." +" AL, is scaled with the heavy clement mass of Uranus.", $M_\alpha$ is scaled with the heavy element mass of Uranus. + From this table. by comparing heavy clement masses of the planets with those obtained from X—++. E discover that audenhanced.," From this table, by comparing heavy element masses of the planets with those obtained from $\Sigma \sim r^{-1}$, I discover that and." +" Notice that by ""the mass euliaucemoeut? throughout this letter. T1nean the cuhancement compared with the nebula model of constant o."," Notice that by “the mass enhancement"" throughout this letter, I mean the enhancement compared with the nebula model of $constant$ $\alpha$." + The terrestrial planets also have some cuhancement except the famous Mars drop aud low Mercury mass., The terrestrial planets also have some enhancement except the famous Mars drop and low Mercury mass. + I will discuss these together later., I will discuss these together later. + I use the widely accepted approach for a values (Papaloizou Lin 1995: Stone et al., I use the widely accepted approach for $\alpha$ values (Papaloizou Lin 1995; Stone et al. + 2000: Balbus 2003)., 2000; Balbus 2003). + For the case of the solar uchula. see the review bv Stone et al. (," For the case of the solar nebula, see the review by Stone et al. (" +2000) aud references therein.,2000) and references therein. + Tt seems that ποντουςπας turbulence is ineffective as an AAMT aechanisia., It seems that hydrodynamic turbulence is ineffective as an AMT mechanism. + Cravitational iustabilitv cau transport anenlar momentum when the nebula is 11assive (Laughlin Bodenheiuner 1991: Papaloizou Lin 1995)., Gravitational instability can transport angular momentum when the nebula is massive (Laughlin Bodenheimer 1994; Papaloizou Lin 1995). + The effective value of à is ~0.030.1.," The effective value of $\alpha$ is $\sim +0.03-0.1$." + This cal dominate the AMT during the early stage., This can dominate the AMT during the early stage. + Much of the stellar inass av be eained this way., Much of the stellar mass may be gained this way. + As the nebula mass drops. less offiieut AMT processes take over.," As the nebula mass drops, less efficient AMT processes take over." + The MIID Gnagnuetolbydrodvuamic) turbulence driven bx the maenetorotational instability (MBRI) is a very likely mechanism (Stone et al., The MHD (magnetohydrodynamic) turbulence driven by the magnetorotational instability (MRI) is a very likely mechanism (Stone et al. + 2000)., 2000). + The viscosity is high (low) when the MBI can (uot) survive., The viscosity is high (low) when the MRI can (not) survive. + The ideal MID sinulatious give values ofà raneine rods«10.? to ~0.6.," The $ideal$ MHD simulations give values of $\alpha$ ranging from $5 +\times 10^{-3}$ to $\sim 0.6$." + The high value is reached when there is a net vertical field., The high value is reached when there is a net vertical field. + A typical value for à is 2., A typical value for $\alpha$ is $^{-2}$. + The solar maguctic field way provide such a net vertical field inside Mercury if lC SOR dynamo starts that early., The solar magnetic field may provide such a net vertical field inside Mercury if the solar dynamo starts that early. + Wave propagation alone is a less effective AMT than the ANID turbulence., Wave propagation alone is a less effective AMT than the MHD turbulence. + The excitation is most powerful iu the outer reeion of the nebula., The excitation is most powerful in the outer region of the nebula. + This lav favor hieh a iu the outer region., This may favor high $\alpha$ in the outer region. + The value used to fi observations of accretion rates (Πα. ct al., The value used to fit observations of accretion rates (Hartmann et al. + 1998) is a~107., 1998) is $\alpha \sim 10^{-2}$. + The age cousideration also indicates ac10107., The age consideration also indicates $\alpha \sim 10^{-3}-10^{-2}$. + Jin (1996) considered the effect of clue diffusion ou the MRI and showed that the MBRI is damped when the diffusion rate is greater than the MBI growth rate., Jin (1996) considered the effect of ohmic diffusion on the MRI and showed that the MRI is damped when the diffusion rate is greater than the MRI growth rate. + The, The +We say that a property P(r) holds for 7-almost all: €JR ΠΕ PCr) is valid for all :c€IRXC provided that Ü€|J.,We say that a property ${\cal P}(x)$ holds for $\id$ -almost all $x \in \R$ iff ${\cal P}(x)$ is valid for all $x \in \R \setminus U$ provided that $U\in\id$. + For a subset À/CΙσ32 andr €—JEqm we define5 a Motivated by Fubini's Theorem we define the family and reler the reader to the paper of Ger (1975) or to the monograph of Kuczma (2009) |Ch., For a subset $M\subset \R^2$ and $x\in \R$ we define a Motivated by Fubini's Theorem we define the family and refer the reader to the paper of Ger (1975) or to the monograph of Kuczma (2009) [Ch. +" XVII, $5]) for further details."," XVII, 5]) for further details." + In the sequel we will need the following We proceed with proving the following result., In the sequel we will need the following We proceed with proving the following result. +important part of the interface dynamo mocdel originally. proposed bv Parker(Parker(1993))).,important part of the interface dynamo model originally proposed by Parker\cite{Parker}) ). + Such overshooting behaviour will naturally occur at other similar interfaces., Such overshooting behaviour will naturally occur at other similar interfaces. + When there are multiple convection zones such overshooting leads to enhanced communication and transport between the unstable Lavers., When there are multiple convection zones such overshooting leads to enhanced communication and transport between the unstable layers. + H is of importance to understand the nature ofthis interaction., It is of importance to understand the nature of this interaction. + In A-type stars in particular. with two convection zones that are in quite close proximity. fascinating dvnamies aud mixing may occur.," In A-type stars in particular, with two convection zones that are in quite close proximity, fascinating dynamics and mixing may occur." + Overshooting plumes from an upper convection zone and a lower convection zone can interact in the convectively stable region separating them., Overshooting plumes from an upper convection zone and a lower convection zone can interact in the convectively stable region separating them. + Furthermore if conditions are right it is possible for plumes to overshoot completely and. pierce the other convection zone. which would lead to transportation of ‘contaminants’ directly from one convectively unstable region into the other.," Furthermore if conditions are right it is possible for plumes to overshoot completely and pierce the other convection zone, which would lead to transportation of `contaminants' directly from one convectively unstable region into the other." + Therefore. he two fundamental questions are: How far apart do these avers need to be before they can be considered as clisjoint: and how close must they be for direct. penetration from one aver to the other to occur.," Therefore, the two fundamental questions are: How far apart do these layers need to be before they can be considered as disjoint; and how close must they be for direct penetration from one layer to the other to occur." +" Earlier analytic work (CLFoonmreefa£,(1976): Latour.‘Toomre&Zahn (1976))) on this problem adopted a mean- approach. which gives a highly simplified view of he nonlinear interactions but allows the reduction of the oblem to a relatively simple set of ODIZs. and it serves as a guide for the fully compressible simulations that are he subject of this paper."," Earlier analytic work \cite{TZLS}; \cite{LTZ}) ) on this problem adopted a mean-field approach, which gives a highly simplified view of the nonlinear interactions but allows the reduction of the problem to a relatively simple set of ODE's, and it serves as a guide for the fully compressible simulations that are the subject of this paper." + Latour concluded that the wo convectively unstable lavers need to be separated by a distance of at least. two pressure scale heights for there to »» no interaction between the lavers., Latour concluded that the two convectively unstable layers need to be separated by a distance of at least two pressure scale heights for there to be no interaction between the layers. + Such a condition can » achieved. in a number of ways via the variation of the different parameters that naturally occur in the model., Such a condition can be achieved in a number of ways via the variation of the different parameters that naturally occur in the model. + One wav ds to increase the vertical extent of the domain aud so increase the width of the intermediate laver., One way is to increase the vertical extent of the domain and so increase the width of the intermediate layer. + Another wav is to vary the conductivity of the mid laver., Another way is to vary the conductivity of the mid layer. + In this paper we choose to explore the elfeets of both of these changes given that the separation of the two zones as well as their relative concluetivitics can be different in cdilferent stars., In this paper we choose to explore the effects of both of these changes given that the separation of the two zones as well as their relative conductivities can be different in different stars. + For simplicity we choose to focus on convective lavers of fixed width but we note that one could alternatively fix the domain height and decrease the width of the convection zones and so increase the width of the convectively stable region: this was the approach adopted in a preliminary investigation by Muthsam. Wolfgang. Friedrich. & Lichich Muthsamefa£ (1999))).," For simplicity we choose to focus on convective layers of fixed width but we note that one could alternatively fix the domain height and decrease the width of the convection zones and so increase the width of the convectively stable region; this was the approach adopted in a preliminary investigation by Muthsam, Wolfgang, Friedrich $\&$ Liebich \cite{MWFL}) )." + Aluthsam examined three cases in a three dimensional model in a Cartesian geometry with a small aspect ratio., Muthsam examined three cases in a three dimensional model in a Cartesian geometry with a small aspect ratio. + In this simple study they showed that bringing he two convection zones closer together. bv shrinking he width of the convectively unstable region. led to the convection lavers merging as the interaction between the avers inereased.," In this simple study they showed that bringing the two convection zones closer together, by shrinking the width of the convectively unstable region, led to the convection layers merging as the interaction between the layers increased." + However. their. preliminary investigation warrants a more detailed: study. for a number of reasons.," However, their preliminary investigation warrants a more detailed study for a number of reasons." + First. while they did make a passing remark as to the oessure scale height change across the box they. did: not comment on how the pressure scale height changes across the mid-lIaver. which Toonuwe indicated was the important actor.," First, while they did make a passing remark as to the pressure scale height change across the box they did not comment on how the pressure scale height changes across the mid-layer, which Toomre indicated was the important factor." + Further. while they acknowledge the earlier work hy 'Toomre they did not relate their numerical calculation directly o that work.," Further, while they acknowledge the earlier work by Toomre they did not relate their numerical calculation directly to that work." + This paper is organised as follows: In the next section we provide a detailed discussion of our model. the numerical methocl used to solve the equations and the parameters that we select.," This paper is organised as follows: In the next section we provide a detailed discussion of our model, the numerical method used to solve the equations and the parameters that we select." + In section 3 we examine the cllect of varving the mid-laver thickness ancl stilfness of the convectively stable region before concluding in section 4., In section 3 we examine the effect of varying the mid-layer thickness and stiffness of the convectively stable region before concluding in section 4. + We consider the evolution of a compressible Uuiel in a laver and consider a model that is in the spirit. of earlier papers on penetrative convection (Tobiasefαἱ(1998):: Tobiasefaf(2001))): these in turn represent a simple extension of studies of convection in a single Cartesian laver., We consider the evolution of a compressible fluid in a layer and consider a model that is in the spirit of earlier papers on penetrative convection \cite{TBCT1}; \cite{TBC2}) ); these in turn represent a simple extension of studies of convection in a single Cartesian layer. + The following scalings are used to express the equations in dimensionless form (Matthews.Proctor.&Weiss(1995))): lengths are sealed with the laver depth d. times with the isothermal sound travel time dAHu. density with its value at the top of the laver po. temperature with its value at the top of the laver T5.," The following scalings are used to express the equations in dimensionless form \cite{MPW}) ): lengths are scaled with the layer depth $d$, times with the isothermal sound travel time $d/\sqrt{R_*T_0}$, density with its value at the top of the layer $\rho_0$, temperature with its value at the top of the layer $T_0$." + The governing equations can then be expressed as: where z is taken downward. @ is the cimensionless temperature clilferenee across the laver. ἐν ids the gas constant. m is. the polvtropic. index.. &=fy-dpucpyyi(RI)ope is the dimensionless thermal dillusivitv. « is the ratio of specific heats. 7 is the stress tensor given by: P—p anda is the Prandtl number.," The governing equations can then be expressed as: where $z$ is taken downward, $\theta$ is the dimensionless temperature difference across the layer, $R_*$ is the gas constant, $m $ is the polytropic index, $\kappa=K/d \rho_{0} c_{P} \sqrt(R_{*} T_{0})$ is the dimensionless thermal diffusivity, $\gamma$ is the ratio of specific heats, $\mathbf{\tau}$ is the stress tensor given by: $P = \rho T$ and $\sigma$ is the Prandtl number." + In order to achieve the required basic state we allow the thermal profile to be non-linear ancl we take where A is the characteristic size of the transition region between cach of the lavers., In order to achieve the required basic state we allow the thermal profile to be non-linear and we take where $\Delta$ is the characteristic size of the transition region between each of the layers. + In this work the characteristic sizes of the transition regions are taken to be the same for simplicity., In this work the characteristic sizes of the transition regions are taken to be the same for simplicity. + The static density and temperature profiles are found. by solving the equations of hyelrostatic balance., The static density and temperature profiles are found by solving the equations of hydrostatic balance. + To this static state. throughout the. domain. random perturbations are introduced. with amplitudes. which lie within the interval -0.05.0.05].," To this static state, throughout the domain, random perturbations are introduced, with amplitudes which lie within the interval [-0.05,0.05]." + The aspect ratio for the computational domain in this study is ΕΕ. where D is the total depth of the box. and the domain is assumed to be periodic in and y.," The aspect ratio for the computational domain in this study is $\mathcal{D}$, where $\mathcal{D}$ is the total depth of the box, and the domain is assumed to be periodic in and ." +. Ehe conditions on the upper and lower boundaries are:, The conditions on the upper and lower boundaries are: +redsdüft accompanied. bv absorption ancl enission features at the redshift of the radio galaxy. z-0.0177 (see Fig. 5)).,"redshift accompanied by absorption and emission features at the redshift of the radio galaxy, z=0.0177 (see Fig. \ref{3c386}) )." + Dofore modcling the stellar population of this galaxy. we removed the contribution of the foreground star.," Before modeling the stellar population of this galaxy, we removed the contribution of the foreground star." +" We obtain the best match of the absorption lines of the star using a PSV stellar template (from Pickles1998)). with ie παλιο reddening of the galaxy, E(B-VWj= 0.335."," We obtain the best match of the absorption lines of the star using a F5V stellar template (from \citealt{pickles98}) ), with the same reddening of the galaxy, E(B-V)= 0.335." + The ow resolution spectruni resulting from subtracting the oreground star is shown in Fig., The low resolution spectrum resulting from subtracting the foreground star is shown in Fig. + 5 where we also prescut 1¢ Πα spectral region from the high resolution spectrum. with a well visible Ho |[N II| triplet and [S IH] doublet.," \ref{3c386} where we also present the $\alpha$ spectral region from the high resolution spectrum, with a well visible $\alpha$ +[N II] triplet and [S II] doublet." + No broad Wea line is visible in this spectrum iu contrast to je result of Simpsonctal.(1996)., No broad $\alpha$ line is visible in this spectrum in contrast to the result of \citet{simpson96}. +. The next step of our analysis consists of the measurement of the enüssiou line intensities for which we used thespecfit package in IRAF., The next step of our analysis consists of the measurement of the emission line intensities for which we used the package in IRAF. + We measured line iuteusities fitting Gaussian profiles to Πο. [O HIJAA 1959.5007. O I[AAG300.61. Πα. [N TYAAGSbss Land [S H]AAGT16.31.," We measured line intensities fitting Gaussian profiles to $\beta$, [O $\lambda\lambda$ 4959,5007, [O $\lambda\lambda$ 6300,64, $\alpha$, [N $\lambda\lambda$ 6548,84, and [S $\lambda\lambda$ 6716,31." + Some constraints were adopted to reduce the nmuuber of ree parameters: we required the EWIIM and the velocity o be the same for all the lines., Some constraints were adopted to reduce the number of free parameters: we required the FWHM and the velocity to be the same for all the lines. + The integrated fluxes of cach line were free to vary except for those with shown ratios from atomic plivsics: ic. the [O TAAG300.6L. O AA (959.5007 aud [N TYAAGS5Ls.8L doublets.," The integrated fluxes of each line were free to vary except for those with known ratios from atomic physics: i.e. the [O $\lambda\lambda$ 6300,64, [O $\lambda\lambda$ 4959,5007 and [N $\lambda\lambda$ 6548,84 doublets." + Where required. we sert a linear continuum.," Where required, we insert a linear continuum." + Table 7 snnnidzes the intensities of the nain CLUSSION lues (clereddened for Galactic absorption) relative to the intensity of the uarrow component of Ila. for which we Ooeive fiux and huuimositv.," Table \ref{bigtable} summarizes the intensities of the main emission lines (dereddened for Galactic absorption) relative to the intensity of the narrow component of $\alpha$, for which we give flux and luminosity." + To each line we associated its relative error. as a oercentage.," To each line we associated its relative error, as a percentage." + We placed upper lnuits at a 36 level to the nucdetected. but diagnostically portant. cussion lines by measuring the noise level in the reeious suroundiusg the expected positions of the lines. and adopting as hne width the iustruinental resolution.," We placed upper limits at a $\sigma$ level to the undetected, but diagnostically important, emission lines by measuring the noise level in the regions surrounding the expected positions of the lines, and adopting as line width the instrumental resolution." + When no cnussion lines are visible. we only report the upper limit forIIo.," When no emission lines are visible, we only report the upper limit for." +.. The missing values in Table 7 correspond to lines outside the coverage of the spectra or severely affected by telluric bauds., The missing values in Table \ref{bigtable} correspond to lines outside the coverage of the spectra or severely affected by telluric bands. + For the galaxies with a broad-line componcut we first attempted to reproduce the DER. cunission with a gaussian xofile. allowing for velocity shifts with respect to the marrow lines and also for Hue asviunietry.," For the galaxies with a broad-line component we first attempted to reproduce the BLR emission with a gaussian profile, allowing for velocity shifts with respect to the narrow lines and also for line asymmetry." + Most line profiles were well reproduced. but in some cases (e.g. 3€ 332) wo eaussiaus had to be included.," Most line profiles were well reproduced, but in some cases (e.g. 3C 332) two gaussians had to be included." + Nouctheless. iu 3€ 111 and iu 3€ 115 the broad line profile is so complex. and he prominence of the broad component with respect Oo narrow lines is so large. it precludes any attempt to neasure the [N IH] doublet aud the narrow component of IIo (or / iu the blue region of the spectrum).," Nonetheless, in 3C 111 and in 3C 445 the broad line profile is so complex, and the prominence of the broad component with respect to narrow lines is so large, it precludes any attempt to measure the [N II] doublet and the narrow component of $\alpha$ (or $\beta$ in the blue region of the spectrum)." + For these objects we use the [O TH] line as reference instead of the iurow cconiponenut., For these objects we use the [O III] line as reference instead of the narrow component. + No narrow lines are visible iu 3€ 273 and we ouly report its broad flux., No narrow lines are visible in 3C 273 and we only report its broad flux. + For all 18 galaxies with a broad cconiponent we also give its fux iu Table 7.., For all 18 galaxies with a broad component we also give its flux in Table \ref{bigtable}. + These objects will be discussed iu more detail in Sect. 13.., These objects will be discussed in more detail in Sect. \ref{broad}. + An important issue related to the subtraction of the stellar coniponent is the effect of the template mis-imatch for the mueastrements of the cussion lines., An important issue related to the subtraction of the stellar component is the effect of the template mis-match for the measurements of the emission lines. + This is particularly 2iurportaut for the estimate of IL/ in the galaxies showing quuission lines of relatively low equivalent width., This is particularly important for the estimate of $\beta$ in the galaxies showing emission lines of relatively low equivalent width. + In fact they can be strongly affected by the level of the absorption features associated to the stellar population., In fact they can be strongly affected by the level of the absorption features associated to the stellar population. + We consider as an example the case of 3€ 310., We consider as an example the case of 3C 310. + Its spectrunn is of average quality in our dataset and it shows only weak cussion hes. while the Τ line is. at most. mmarelually detected iu its spectrum.," Its spectrum is of average quality in our dataset and it shows only weak emission lines, while the $\beta$ line is, at most, marginally detected in its spectrum." + The best fitting stellar. population has an age of 5 Gyr and a imetalicitv of Z=0.05 and it is shown in red iu the middle panel of Fig., The best fitting stellar population has an age of 5 Gyr and a metalicity of Z=0.05 and it is shown in red in the middle panel of Fig. + 6 superposed on the original spectrun., \ref{3c310} superposed on the original spectrum. + Iu the residual spectrum a well defined IL) line eiierges là enuission. caused by the removal of a substantial absorption associated with the stellar cinission.," In the residual spectrum a well defined $\beta$ line emerges in emission, caused by the removal of a substantial absorption associated with the stellar emission." + This indicates that its intensity is stronely influenced by the choice of the stellar template., This indicates that its intensity is strongly influenced by the choice of the stellar template. + To associate a proper error to this procedure it is necessary. to establish the range of acceptable stellar models (in terms of age aud metalicity) and the resulting uncertainty in the Lue measurement., To associate a proper error to this procedure it is necessary to establish the range of acceptable stellar models (in terms of age and metalicity) and the resulting uncertainty in the line measurement. + As a forma error propagation across all steps of the ata reduction is clearly unfeasible. we estimated the vpical error of our spectra by measuring the rms flux in contiuuun dominated spectral regions.," As a formal error propagation across all steps of the data reduction is clearly unfeasible, we estimated the typical error of our spectra by measuring the rms flux in continuum dominated spectral regions." + Even with this pproach. the value of ⋟⋅⋅miuiuuu reduced 422 obtained. roni the best fitting stellar population is often lareer iui the value indicative of à £ooc fit (A 1) and Us is du contrast with the fact tha the stellar nodels seein to trace in general the spectra rather well.," Even with this approach, the value of minimum reduced $\chi^2_{\rm r}$ obtained from the best fitting stellar population is often larger than the value indicative of a good fit $\chi^2_{\rm r} \sim 1$ ) and this is in contrast with the fact that the stellar models seem to trace in general the spectra rather well." + There are several reasons for. this+ discrepancy:. i)H the AZD is nof xoperlv normalized (e.g. because not all data poiuts are independent) 8) our estimate of the signal-to-noise ratio does not include the uncertaimties iu e.g. the wavelength and flux calibration. ii) there are rea Πο between data aud models. iu part caused by the use of a discrete erid of stellar 1nodols.," There are several reasons for this discrepancy: i) the $\chi^2_{\rm r}$ is not properly normalized (e.g. because not all data points are independent) ii) our estimate of the signal-to-noise ratio does not include the uncertainties in e.g. the wavelength and flux calibration, iii) there are real mismatches between data and models, in part caused by the use of a discrete grid of stellar models." + We then decided. when necessary. to rescale our error bars such that the overall best fitting model provides \7/do.f.," We then decided, when necessary, to rescale our error bars such that the overall best fitting model provides $\chi^2$ /d.o.f." + = 1. following the approach propose by Barthetal.(2001) in a different context.," = 1, following the approach proposed by \citet{barth01} in a different context." + This is a conservative approach since it has the effect of increasing the range of the acceptable templates with respect to what would have been obtained ouly using the measured rms of cach spectrum., This is a conservative approach since it has the effect of increasing the range of the acceptable templates with respect to what would have been obtained only using the measured rms of each spectrum. +relable. aud do not iuclude these RV data iu the analyses uch follow.,"reliable, and do not include these RV data in the analyses which follow." + On all nights a Li ine was detected from the primary star (Figure 2 ))., On all nights a Li line was detected from the primary star (Figure \ref{fig_lithium}) ). + 1ο equivalent widths were computed using direct ceration over the lines relative to the combined COutinua from the two stars., The equivalent widths were computed using direct integration over the lines relative to the combined continua from the two stars. + Uncertamties from the pldine reduction were used to cive the statistical uucertaity., Uncertainties from the pipeline reduction were used to give the statistical uncertainty. + Au additional svstematic uncertaintv was OSiuated by choosing different methods of finding the COΠΠ aud recomputiug the equivalent widths., An additional systematic uncertainty was estimated by choosing different methods of finding the continuum and recomputing the equivalent widths. + A ὖσ upper luit οi the secoudarvs Li line was placed using the data from 2007 October 25. when the two stars were separated by 89 kins1 (2 AJ).," A $\sigma$ upper limit on the secondary's Li line was placed using the data from 2007 October 25, when the two stars were separated by 89 km $\rm s^{-1}$ (2 )." + These equivalent widths are given iu the first two columns of Table 3.., These equivalent widths are given in the first two columns of Table \ref{tab_Li_eqw}. + The continuum normalized spectrum ou 2007 October 25. which has the maxiuuni separation of the two stars. was fit with a combination of svuthetic spectra calculated with SPECTRUAL from Castelli-Ikuruez model atinospheres with solar metalicitv.," The continuum normalized spectrum on 2007 October 25, which has the maximum separation of the two stars, was fit with a combination of synthetic spectra calculated with SPECTRUM from Castelli-Kurucz model atmospheres with solar metalicity." + Free paralucters were two cjfective temperatures. a single CSiu a sinele loe(e). and two normalizations.," Free parameters were two effective temperatures, a single $v {\rm sin} i$, a single log(g), and two normalizations." + One blue and one red region of the spectrum were fit 10991360 aand 6282-6519A., One blue and one red region of the spectrum were fit – 4099–4360 and 6282-6549. + The best fit in both cases had To =6500 I& and 6250 I& for the primary aud secondary stars. respectively aud log(e)25.0.," The best fit in both cases had $_{\rm eff}$ =6500 K and 6250 K for the primary and secondary stars, respectively and log(g)=5.0." + Cotours οf chi-square iudicate the uucertainty is within 250 I (the exiddiug of the models) in Tyg.," Contours of chi-square indicate the uncertainty is within 250 K (the gridding of the models) in $_{\rm + eff}$." + The lines are mieasuraldv broader than the ThÀr calibration lamp nes at the same wavelengths., The lines are measurably broader than the ThAr calibration lamp lines at the same wavelengths. +" The best fit models hac esum=LO+1 kin ""E"," The best fit models had $v {\rm sin} +i = 10 \pm 1$ km $^{-1}$." + To compute the stars” Li equivaleu widths relative to heir own stellar coutiuua. the flux ratio of tljo two stars uust be obtained aGTÜTA.," To compute the stars' Li equivalent widths relative to their own stellar continua, the flux ratio of the two stars must be obtained at." +. Svutheic spectra were fit as above to the region at 6615 6835À., Synthetic spectra were fit as above to the region at 6645 –. +. The st fit flux ratio was 1.397 E 0.007., The best fit flux ratio was 1.397 $\pm$ 0.007. + ILowever. this statistical uncertainty. probabv uunderestinuates the svsteiuatics Toni how the modes are calculated.," However, this statistical uncertainty probably underestimates the systematics from how the models are calculated." +" Applying tus flux ratio to the mcasured equivalent widths makes the wimary sud seco1eluv equivalent widths increase by actors of L.709 anc 2.587. respectively,"," Applying this flux ratio to the measured equivalent widths makes the primary and secondary equivalent widths increase by factors of 1.709 and 2.387, respectively." + The couputed equivalent widths are given in the last two cohnius of Table MiD, The computed equivalent widths are given in the last two columns of Table \ref{tab_Li_eqw}. + The Spectra Were exanuued for evide1ος of chromospheric activity., The spectra were examined for evidence of chromospheric activity. + Bot1 stars show weal central YCVOYSals ou heir Ca Π ane LIN lines (Figure 3)) that change in veocity along with the stars., Both stars show weak central reversals on their Ca H and K lines (Figure \ref{fig_calcium}) ) that change in velocity along with the stars. + The Balmer lines show 10 centra reversaD», The Balmer lines show no central reversals. + The velocilos were fit for the stellar lass ratio (secondaryrjuiuv) vielding 0.91 + 0.02 aud the line of sigit ractia velociv ovieldi1ο ΞSSο”..., The velocities were fit for the stellar mass ratio (secondary/primary) yielding 0.91 $\pm$ 0.02 and the line of sight radial velocity yielding $\rm \gamma = -8.8 \pm 0.6\ km\ s^{-1}$. + Altrough t10 sunall umber of observatious prohi the calculan)1i of the full binary orbit. I tested whether a circular oryt CotId fit tjo. velocities.," Although the small number of observations prohibit the calculation of the full binary orbit, I tested whether a circular orbit could fit the velocities." +" The best prodiced reasonable residuaS (clkmns 5) Or ala or with a period of 3LIS davs. —BNddus1. consistent with he fit a)ove, ald lass ratio 0.03. agail1 consistent with he fit a))»ve."," The best fit produced reasonable residuals $<$ 1 km $\rm +s^{-1}$ ) for an orbit with a period of 3.448 days, $\gamma$ =-8.4 km $\rm +s^{-1}$, consistent with the fit above, and mass ratio 0.93, again consistent with the fit above." + This orbi. shown in Fietre lo vields nsu for each star ο σα1d 0.12 for the primary aud secondary stars respectively.," This orbit, shown in Figure \ref{fig_binaryvel} yields $m {\rm sin^3}i$ for each star – 0.13 and 0.12 for the primary and secondary stars respectively." + I estimate the TUO Lhasses of the stars as 1.3 and 1.2 M. based ou the effective temperatures (6500 and 6250 IX) obtaiued iu he spectral fit described in 3 aud the ME spectral-type calibration, I estimate the true masses of the stars as 1.3 and 1.2 $_\odot$ based on the effective temperatures (6500 and 6250 K) obtained in the spectral fit described in 3 and the MK spectral-type calibration +motions.,motions. +" This is obtained by projecting the two-dimensional point correlation function €(rp,7) along the where Τρ and π are the components of the galaxy-galaxy separation vector respectively perpendicular and parallel to the line-of-sight (??).."," This is obtained by projecting the two-dimensional two-point correlation function $\xi(r_p,\pi)$ along the where $r_p$ and $\pi$ are the components of the galaxy-galaxy separation vector respectively perpendicular and parallel to the line-of-sight \citep{peebles80,fisher94}." +" €(rp,π) is measured using the ? estimator and properly accounting for the survey selection function and various incompleteness effects, as thoroughly described in ?.."," $\xi(r_p,\pi)$ is measured using the \citet{landy93} estimator and properly accounting for the survey selection function and various incompleteness effects, as thoroughly described in \citet{delatorre09}." + Error bars are estimated through the blockwise bootstrap method (e.g.??)..," Error bars are estimated through the blockwise bootstrap method \citep[e.g.][]{porciani02,norberg09}." + This is discussed in detail and compared to results from mock samples in ? and ?.., This is discussed in detail and compared to results from mock samples in \citet[][]{meneux09} and \citet{porciani09}. + All clustering codes and methods used here have been extensively tested against independent programs in the course of the latter analyses., All clustering codes and methods used here have been extensively tested against independent programs in the course of the latter analyses. + In Fig., In Fig. +" 2 we show the projected correlation function computed for the 10k sample in the redshift range 0.6G.," These luminosity indicators have been used to identify specific bursts \citep{frr00} that are at redshifts of $z \sim 10$ as well as to show that the star formation rate of the Universe is rising steadily \citep{frr00,sdb01,lfr01} from $z \sim 2$ to $z>6$." +" ThisLetter reports on the construction of a Hubble diagram (a plot of Iuminosity distance. D,. versus redshilt) as a means of measuring (he expansion history of our Universe."," This reports on the construction of a Hubble diagram (a plot of luminosity distance, $D_L$, versus redshift) as a means of measuring the expansion history of our Universe." + Only nine GRBs have the required information of red shift (2). peak flux (11. lag time (Tag). aid variability (V).," Only nine GRBs have the required information of red shift $z$ ), peak flux $P$ ), lag time $\tau_{lag}$ ), and variability $V$ )." + These data are collected in Table 1. along with the characteristic photon energy (ρω) and the observed huninosity (Lu).," These data are collected in Table 1, along with the characteristic photon energy $E_{peak}$ ) and the observed luminosity $L_{obs}$ )." + These nine bursts were all detected by BATSE with redshifls measured [from optical spectra of either the alterglow or the host galaxy., These nine bursts were all detected by BATSE with redshifts measured from optical spectra of either the afterglow or the host galaxy. + The hiehly unusual GID950425 (associated with supernova SN1998bw) is nol included because it is likely to be qualitatively different from (he classical GRBs., The highly unusual GRB980425 (associated with supernova SN1998bw) is not included because it is likely to be qualitatively different from the classical GRBs. + Bursts with red shifts that were not recorded by BATSE cannot (vet) have their observed. parameters converted (o energies and fluxes that are comparable with DATSE data., Bursts with red shifts that were not recorded by BATSE cannot (yet) have their observed parameters converted to energies and fluxes that are comparable with BATSE data. +" Sinplisticallv. plots of Lop. versus 7, and Lop. versus V. can calibrate the luminosity indicators. which then can vield luminosity distances to each burst lor plotting on a Hubble"," Simplistically, plots of $L_{obs}$ versus $\tau_{lag}$ and $L_{obs}$ versus $V$ can calibrate the luminosity indicators, which then can yield luminosity distances to each burst for plotting on a Hubble" +Recent observations of the Virgo cluster and its vicinity permit a better understanding of the plivsies behind the visible structure aud kinematics of the svstoi.,Recent observations of the Virgo cluster and its vicinity permit a better understanding of the physics behind the visible structure and kinematics of the system. + The most complete list of data ou the Virgo Cluster aud the Vireoceutric flow has been collected by Eauacheutsev Nasonova (2010)., The most complete list of data on the Virgo Cluster and the Virgocentric flow has been collected by Karachentsev Nasonova (2010). + These include distance moduli of ealaxies from the Catalogue of the Neighbouring Galaxies (= CNG. ISuacheutsev et al.," These include distance moduli of galaxies from the Catalogue of the Neighbouring Galaxies (= CNG, Karachentsev et al." + 2005) aud also from the literature with the best measurements prefered., 2005) and also from the literature with the best measurements prefered. + Distances from the Tip of the Red Caant Brauch (TRCOB) aud the Cepheids are used from the CNC together with new TRGD distances (INaracheutsey et al., Distances from the Tip of the Red Giant Branch (TRGB) and the Cepheids are used from the CNG together with new TRGB distances (Karachentsev et al. + 2006. Tully et al.," 2006, Tully et al." + 2006. Me et al.," 2006, Mei et al." + 2007)., 2007). + For ealaxy images m two or more photometric bands obtained with WFPC2 or ACS cameras at the OST. the TRGB method vields distances with an accuracy of about (Rizzi oet al.," For galaxy images in two or more photometric bands obtained with WFPC2 or ACS cameras at the HST, the TRGB method yields distances with an accuracy of about (Rizzi et al." + 2007)., 2007). + The database includes also data on 300 E and $0 ealaxics from the Surfac| Drightuess Fhictuation (SBF) method by Toury ct al. (, The database includes also data on 300 E and S0 galaxies from the Surface Brightness Fluctuation (SBF) method by Tonry et al. ( +2000) with a typical distance error of,2000) with a typical distance error of. + The total sample coutaius the velocities aud distauces of 1371 Oogalaxies within 30 Mpce from the VireoOo cluster center., The total sample contains the velocities and distances of 1371 galaxies within $30$ Mpc from the Virgo cluster center. + Especially interestingC» is the sample of 761 [m]ealaxies selected to avoid the effect of unknown taugeutial (to the liue of sieht) velocity coniponeuts., Especially interesting is the sample of 761 galaxies selected to avoid the effect of unknown tangential (to the line of sight) velocity components. + The velocity-distance diagram for this sample taken from dEaracheutsev Nasonova (2010) is given in Fig.l., The velocity-distance diagram for this sample taken from Karachentsev Nasonova (2010) is given in Fig.1. + The zero-velocity radius within the retarded expausion field around a point-lise mass concentration nieans the distance where the radial velocity relative to the οςiceutration is zero., The zero-velocity radius within the retarded expansion field around a point-like mass concentration means the distance where the radial velocity relative to the concentration is zero. + In the ideal case of the Lass concentration at rest within the expanding PFriediuauu universe this is the distance where the radial peculiar velocity towards the concentration is equal to the IIubble velocity for the same distance., In the ideal case of the mass concentration at rest within the expanding Friedmann universe this is the distance where the radial peculiar velocity towards the concentration is equal to the Hubble velocity for the same distance. + Using Tulls-Fisher distances in the Dubble diagram. Teerikorpi et al. (," Using Tully-Fisher distances in the Hubble diagram, Teerikorpi et al. (" +1992) could for the first time see the location of the zero-velocity radius Ry for the Virgo system. so that Πομουzm0.15 or RyzzT.E Apc.,"1992) could for the first time see the location of the zero-velocity radius $R_0$ for the Virgo system, so that $R_0/R_{\rm Virgo} \approx 0.45$ or $R_0 \approx 7.4$ Mpc." + The work by Iaracheutsev Nasouova (2010) puts the zero-velocitvradius at Ry=5.407.5 Moc., The work by Karachentsev Nasonova (2010) puts the zero-velocityradius at $R_0 = 5.0 - 7.5$ Mpc. + For R«Ry. positive aud negative velocities appear in practically equal nuubers: for R7Ry. the velocities are positive with a few exceptions likely due to errors in distances.," For $R < R_0$, positive and negative velocities appear in practically equal numbers; for $R > +R_0$, the velocities are positive with a few exceptions likely due to errors in distances." + The zero-velocity radius eives the upper luit of the size of the eravitationally bound cluster. aud the diagram shows that the Virgoceutric How starts at R>Ry and extends at least up to 30 Mpc.," The zero-velocity radius gives the upper limit of the size of the gravitationally bound cluster, and the diagram shows that the Virgocentric flow starts at $R \ge R_0$ and extends at least up to 30 Mpc." + The zero-velocity radius has been often used for estimating the total mass My of a eravitationally bound svsteni., The zero-velocity radius has been often used for estimating the total mass $M_0$ of a gravitationally bound system. + According to Lvudeu-Bell. (1981). and Saudage (1986). the spherical model with A=0 leads to the estimator RR(1)My=(UO With the age of the universe fip=13.7 Gyr (Sperecl et al.," According to Lynden-Bell (1981) and Sandage (1986), the spherical model with $\Lambda =0$ leads to the estimator M_0 = ^2/8G) } With the age of the universe $t_U = 13.7$ Gyr (Spergel et al." + 2007). Naracheutsey Nasonova (2010) find the Vireo cluster mass Ay=(6.32.0)«101 AZ.," 2007), Karachentsev Nasonova (2010) find the Virgo cluster mass $M_0 = (6.3 \pm 2.0) \times +10^{14} M_{\odot}$ ." + This result agrees with the virial mass ο...6sT1014ΗΕ estimated by Woffinan Salpeter (1982) aud ~LxLothar. of Valtonen et al. (, This result agrees with the virial mass $M_{\rm vir} = 6 \times 10^{14} M_{\odot}$ estimated by Hoffman Salpeter (1982) and $ \sim 4 \times 10^{14} M_{\odot}$ of Valtonen et al. ( +1985) and Saarinen Valtoucn (1985).,1985) and Saarinen Valtonen (1985). + Teerikorpi et al. (, Teerikorpi et al. ( +1992) and Ekholu et al. (,1992) and Ekholm et al. ( +1999. 2000) found that the real cluster mass might be from 1 to 2 the virial mass. or (0.61.2)4ΤΟ AZ...,"1999, 2000) found that the real cluster mass might be from 1 to 2 the virial mass, or $(0.6-1.2) \times +10^{15} M_{\odot}$ ." +" Tully Mohavace (2001) derived the mass 1.2«&1055AZ. withthe ""umunerical action” iiethod."," Tully Mohayaee (2004) derived the mass $1.2 \times 10^{15} M_{\odot}$ withthe ""numerical action"" method." +Recent observations with high spatial resolution ancl polarimetric sensitivity revealed that quiel photospheric regions contain a large amount of horizontal magnetic field (Orozcoal.2007a.b:Liteset 2008).,"Recent observations with high spatial resolution and polarimetric sensitivity revealed that quiet photospheric regions contain a large amount of horizontal magnetic field \citep{Orozco:etal:2007a,Orozco:etal:2007b,Lites:etal:2008}." +. The size of the horizontal field patches varies from less than one (o a few arcsec (Litesetal.1996:DePontieu2002:MartinezGonzálezelal.2007:ILarvev.etIshikawa2008:Jin 2009).," The size of the horizontal field patches varies from less than one to a few arcsec \citep{Lites:etal:1996,DePontieu:2002,Marian:etal:2007,Harvey:etal:2007,Ishikawa:etal:2008,Jin:etal:2009}." +. Those with sizes comparable to the average size of (he eranular pattern are verv dynamic (Ishikawaetal.&Tsuneta.2009:Jinetal. 2009).," Those with sizes comparable to the average size of the granular pattern are very dynamic \citep{Ishikawa:etal:2008,Ishikawa:Tsuneta:2009,Jin:etal:2009}." +. Such Horizontal Internetwork Fields (IHE) appear in internetwork as well as in plage regions with no sienificant difference in the rate of occurrence., Such Horizontal Internetwork Fields (HIF) appear in internetwork as well as in plage regions with no significant difference in the rate of occurrence. + Their lifetimes range from a minute to about ten minutes. comparable to the lifetime of granules.," Their lifetimes range from a minute to about ten minutes, comparable to the lifetime of granules." + Some of them are recognized to be loop-like, Some of them are recognized to be loop-like +"For any numbers 9;. j=1.....;N, assumingvalues 0 or 1 we have Therefore, if (e4.....€x) is a random vector valued in {0.11 and 9$=ude; then Comparing this lormula with (22). we conclude that factorial moments of 5 have the form","For any numbers $\delta_j$ , $j=1,\ldots,N$, assumingvalues $0$ or $1$ we have Therefore, if $(\eps_1,\ldots,\eps_N)$ is a random vector valued in $\{0,1\}^N$ and $S=\sum_{i=1}^N\;\eps_i$ then Comparing this formula with , we conclude that factorial moments of $S$ have the form." +" IF; in addiüon. the random variables (e4.....εν) are exchangeable, then the above formula simplifies to"," If, in addition, the random variables $(\eps_1,\ldots,\eps_N)$ are exchangeable, then the above formula simplifies to." +" As we will see in Section ??,, our sufficient condition for asymptotie normality will work well for several set-ups falling within such a scheme."," As we will see in Section \ref{sec:appl}, our sufficient condition for asymptotic normality will work well for several set–ups falling within such a scheme." +" This will be preceded by a derivation of new identities [or integer partitions, which will give a major enhancement of the tools we will use to prove limit theorems."," This will be preceded by a derivation of new identities for integer partitions, which will give a major enhancement of the tools we will use to prove limit theorems." +" Recall that if b.=(5,) isa cumulant sequence for a sequence of numbersα= (αμ) that 1s, b=f(a) withf given by (22), then lor J>1 "," Recall that if $\b=(b_n)$ isa cumulant sequence for a sequence of numbers$\a=(a_n)$ , that is, $\b=f(\a)$ with$f$ given by , then for $J\ge1$ " +to minimize the number of false detections.,to minimize the number of false detections. + Correction for eharge-trausler efficiency loss has been doue according to the prescriptious of Dolphin(2002)., Correction for charge-transfer efficiency loss has been done according to the prescriptions of \citet{Do02}. +.. Figure 2. shows the distribution of photometric errors as a function of V and J maguitudes as determined by DAODPHOT., Figure \ref{Fig2} shows the distribution of photometric errors as a function of $V$ and $I$ magnitudes as determined by DAOPHOT. + It is seen that errors areabout 0.2 mag at V. — 27 mae aud { = 26 mae for both PC aud WE (rames., It is seen that errors areabout 0.2 mag at $V$ = 27 mag and $I$ = 26 mag for both PC and WF frames. + They increase to about 0.l maee at. V. — 28 maee aud / = 27 mage., They increase to about 0.4 mag at $V$ = 28 mag and $I$ = 27 mag. +e The total numbers of recovered stars in both PC aud WF frames are respectively 51632. 332561 aud 22121 inthe V. baud. the / baud aud in both bauds. adoptiug a matching radius of 1 pixel.," The total numbers of recovered stars in both PC and WF frames are respectively 51632, 33564 and 22121 in the $V$ band, the $I$ band and in both bands, adopting a matching radius of 1 pixel." + The correspouding numbers of recovered stars in the PC [rame ouly are 9888. SOLS aud 3115.," The corresponding numbers of recovered stars in the PC frame only are 9888, 5918 and 3415." + That more than a third of the stars are not matched is due to the combination of incompleteness effects aud an increasing number of false detectious at faint umaguitudes., That more than a third of the stars are not matched is due to the combination of incompleteness effects and an increasing number of false detections at faint magnitudes. + The trausformation of imstrumeutal magnitudes to the Joliusou-Cousius CBVRL photometric system as defiued by Landolt(1992) was performed according to the prescriptions of Holtzmanetal.(1995b)., The transformation of instrumental magnitudes to the Johnson-Cousins $UBVRI$ photometric system as defined by \citet{La92} was performed according to the prescriptions of \citet{Ho95b}. +. The maguitudes and colors of poiut sources were corrected for Galactic interstellar extinction adoptiug Ay = 0.12 mae aud A; = 0.07 mae (Schlegeletal.1998)., The magnitudes and colors of point sources were corrected for Galactic interstellar extinction adopting $A_V$ = 0.12 mag and $A_I$ = 0.07 mag \citep{S98}. + We have carried out a completeness analysis for each of the frames usiug the DAOPHOT routine ADDSTAR., We have carried out a completeness analysis for each of the frames using the DAOPHOT routine ADDSTAR. + For each maguitucle biu listed in Table 1.. we have aclclecl artificial stars amounting to ~ of the total number of real stars elected iu each (rame.," For each magnitude bin listed in Table \ref{Tab1}, we have added artificial stars amounting to $\sim$ of the total number of real stars detected in each frame." + We then performed a new photometric reduction usiug the same procedure as the one applied to the original frame. aud checked low many added stars were recovered in this maguitude bin.," We then performed a new photometric reduction using the same procedure as the one applied to the original frame, and checked how many added stars were recovered in this magnitude bin." + This operation was repeated 10 times [or each [rame auc for each inaguitude bin aud the results were averaged., This operation was repeated 10 times for each frame and for each magnitude bin and the results were averaged. + The completeness factor in each magnitude bin defiued as the percentage of recovered artificial stars is shown in Table 1., The completeness factor in each magnitude bin defined as the percentage of recovered artificial stars is shown in Table 1. + The completeness limit of the PC image is acceptable in the 25 — 26 mag ranee. aud ~ respectively in V and £. but drops to ~ and ~ in the 27 — 28 mag range.," The completeness limit of the PC image is acceptable in the 25 – 26 mag range, $\sim$ and $\sim$ respectively in $V$ and $I$, but drops to $\sim$ and $\sim$ in the 27 – 28 mag range." + The completeness limits of the ΛΕΣ and WF1 images are comparable to that of the PC image., The completeness limits of the WF2 and WF4 images are comparable to that of the PC image. + However. because of the larger crowding. the completeness limits of the WES image are worse. being in V aud ~ in J in the 25 — 26 mage range.," However, because of the larger crowding, the completeness limits of the WF3 image are worse, being $\sim$ in $V$ and $\sim$ in $I$ in the 25 – 26 mag range." + Fig., Fig. + 3 shows the / vs V—/ CMD of NGC 2366 derived (rom all frames., \ref{Fig3} shows the $I$ vs $V-I$ CMD of NGC 2366 derived from all frames. + Tt can be seen that NGC 2366 contains diverse stellar populations iu a variety of evolutionary stages: maiu-sedqueuce (M5). blue loop (BL). red supereiant (RSC). asymptotic giant branch (AGB). and red giant branch (RGB) stars.," It can be seen that NGC 2366 contains diverse stellar populations in a variety of evolutionary stages: main-sequence (MS), blue loop (BL), red supergiant (RSG), asymptotic giant branch (AGB), and red giant branch (RGB) stars." + The detection of RGB stars allows to derive the distance to NGC 2366 using theobserved magnitude £ of the tip of RGB stars (ERGB)., The detection of RGB stars allows to derive the distance to NGC 2366 using theobserved magnitude $I$ of the tip of RGB stars (TRGB). + This technique is based on the observed coustaucy ol the absolute maguituce A; zz —1.05 mag of TRGB stars in old globular stellar clusters 1990).., This technique is based on the observed constancy of the absolute magnitude $M_{I}$ $\approx$ –4.05 mag of TRGB stars in old globular stellar clusters \citep{Da90}. . + In the CMD. the TRGB is sigualed by a sharp drop in the number of RGB stars toward brighter J maguituces.," In the CMD, the TRGB is signaled by a sharp drop in the number of RGB stars toward brighter $I$ magnitudes." + This drop cau be seen distinctly in the CMD of Fig. 3.., This drop can be seen distinctly in the CMD of Fig. \ref{Fig3}. . + To, To +"present at the ""true"" value of the parameter.",present at the “true” value of the parameter. + Indeed. because of the stochastic nature of the power spectrum and because we have only one data set (the time series is one). the local minimum associated with the “true” value does not exist.," Indeed, because of the stochastic nature of the power spectrum and because we have only one data set (the time series is one), the local minimum associated with the “true” value does not exist." + The “true” value is only the mean value obtained on a large set of experiments., The “true” value is only the mean value obtained on a large set of experiments. + Thus. 1) the use of MAP has to be performed with a reliable prior (1.9. solar splitting frequeney ~0.4 μΗΖ) 11) the MAP has to be used only to prevent the fit from converging towards an incorrect solution (1.9. negative splitting).," Thus, i) the use of MAP has to be performed with a reliable prior (i.e. solar splitting frequency $\sim 0.4\ \mu$ Hz) ii) the MAP has to be used only to prevent the fit from converging towards an incorrect solution (i.e. negative splitting)." +" The most common problem met with fiting the CoRoT solar-like oscillation spectra is the ""Dirac-Itke"" convergence (Sect. 3 L2) ", The most common problem met with fitting the CoRoT solar-like oscillation spectra is the “Dirac-like” convergence (Sect. \ref{sect_struggle}) ). +According to the Bayesian approach. we must use all the information that may be deduced through reliable complementary observations or physical arguments.," According to the Bayesian approach, we must use all the information that may be deduced through reliable complementary observations or physical arguments." + A proxy of the splitting frequency often can be deduced from the power spectrum itself., A proxy of the splitting frequency often can be deduced from the power spectrum itself. + Indeed. on the power spectra of the 3 CoRoT targets HD 49933. HD 181420 and HD 181906. an excess power at very low frequency (<10 μΗΖ) is observed (Fig.," Indeed, on the power spectra of the 3 CoRoT targets HD 49933, HD 181420 and HD 181906, an excess power at very low frequency $< 10\ \mu$ Hz) is observed (Fig." + 3 in AOS and 809. Fig.," 3 in A08 and B09, Fig." + 4 in Garcia et al., 4 in Garcia et al. + 2009)., 2009). + This feature ts associated with the rotational frequency. which appears directly in the power spectrum thanks to the motion of stellar spots.," This feature is associated with the rotational frequency, which appears directly in the power spectrum thanks to the motion of stellar spots." + It corresponds to the star surface rotation., It corresponds to the star surface rotation. + For physical reasons it is clear that the internal stellar rotation does not differ strongly with respect to the surface rotation. otherwise the star would not stay in state of equilibrium (all are main sequence stars).," For physical reasons it is clear that the internal stellar rotation does not differ strongly with respect to the surface rotation, otherwise the star would not stay in state of equilibrium (all are main sequence stars)." + Hence. the splitting prior is determined by this low frequency excess power. with a confidence interval that has to be chosen ad-hoc. as a function of the width of the low-frequency peak (e. g. 10% confidence for Benomar et al.," Hence, the splitting prior is determined by this low frequency excess power, with a confidence interval that has to be chosen ad-hoc, as a function of the width of the low-frequency peak (e. g. $\pm 10$ confidence for Benomar et al." + 2009)., 2009). + The second prior addresses the original purpose of the paper., The second prior addresses the original purpose of the paper. + We started by considering that the mode amplitude varies as a continuous function of the frequency., We started by considering that the mode amplitude varies as a continuous function of the frequency. + This is justified by theoretical studies (?.. ? and ?)) and has been observed in solar seismological data (e.g. 2)).," This is justified by theoretical studies \citealt{Houdek_99}, \citealt{Samadi_01} and \citealt{Samadi_07}) ) and has been observed in solar seismological data (e.g. \citealt{Chaplin_98}) )." + The mode amplitude of a single is defined by its integral A=ΥπΓΗ., The mode amplitude of a single p-mode is defined by its integral $A=\sqrt{\pi \Gamma H}$. + As shown in ?.. the mode height and width determinations are strictly correlated.," As shown in \citet{Toutain_Appourchaux_94}, the mode height and width determinations are strictly correlated." + So. constraining one of them is sufficient to constrain the amplitude.," So, constraining one of them is sufficient to constrain the amplitude." +" In solar seismological data (e.g. GOLF). the height presents à ""bell"" shaped dependence as a function of the frequency (Fig. 3))."," In solar seismological data (e.g. GOLF), the height presents a “bell” shaped dependence as a function of the frequency (Fig. \ref{fig_golf_1}) )," + while the width presents a more complex behavior: 2 slopes and a plateau (Fig. 4))., while the width presents a more complex behavior: 2 slopes and a plateau (Fig. \ref{fig_golf_2}) ). + On CoRoT data (e.g. HD 49933 in A08) the smoothed power spectrum shows that the height mainly follows a bell shaped profile. as for the Sun.," On CoRoT data (e.g. HD 49933 in A08) the smoothed power spectrum shows that the height mainly follows a bell shaped profile, as for the Sun." + It reflects the fact that the oscillation spectrum presents a beginning. an ending and a maximum in between.," It reflects the fact that the oscillation spectrum presents a beginning, an ending and a maximum in between." + On the other hand. contrarily to the GOLF solar data in which the mode width is measurable with the naked eye. in the CoRoT data it is impossible to give an estimate of the width trend. because of the SNR.," On the other hand, contrarily to the GOLF solar data in which the mode width is measurable with the naked eye, in the CoRoT data it is impossible to give an estimate of the width trend, because of the SNR." + It appeared logical to take such information into account., It appeared logical to take such information into account. + The difficulty is to find a simple mathematical anc computational translation of it., The difficulty is to find a simple mathematical and computational translation of it. + The first idea is to fix the height close to a bell shaped profile., The first idea is to fix the height close to a bell shaped profile. + The drawback of such αἱ approach is to introduce several hyper parameters to describe the bell shaped profile in the fitting process. which goes against the aim of reducing both the total number of parameters anc the computational time.," The drawback of such an approach is to introduce several hyper parameters to describe the bell shaped profile in the fitting process, which goes against the aim of reducing both the total number of parameters and the computational time." + Therefore. we propose to replace the one height per overtone estimate by a continuous analytical function of the frequency. whose parameters are determined 1 the fitting process.," Therefore, we propose to replace the one height per overtone estimate by a continuous analytical function of the frequency, whose parameters are determined in the fitting process." + Figure 3. presents the solar mode heights as measured in 3 years of GOLF data. corresponding to a period of solar minimum activity.," Figure \ref{fig_golf_1} presents the solar mode heights as measured in 3 years of GOLF data, corresponding to a period of solar minimum activity." + We have estimated the mode parameters by fitting the power spectrum with the MLE in groups of 4 overtones: 27 modes were fitted in the frequency range [1650.5000] «Hz.," We have estimated the mode parameters by fitting the power spectrum with the MLE in groups of 4 overtones: 27 modes were fitted in the frequency range $[1650,5000]\ \mu$ Hz." + The purpose of the plot is to show that, The purpose of the plot is to show that +"velocity vector). i, is the frequeney of the scattered photon (measured in the comoving frame of the shocked material).","velocity vector), $\nu_s$ is the frequency of the scattered photon (measured in the comoving frame of the shocked material)." + As shown in eq. (12)), As shown in eq. \ref{eq:j}) ) +" the scattered. power has a maximum al 8,=x and goes to zero for small scattering angles.", the scattered power has a maximum at $\theta_s=\pi$ and goes to zero for small scattering angles. + The shocked medium moves toward us with a bulk Lorentz [actor about tens., The shocked medium moves toward us with a bulk Lorentz factor about tens. +" The photons scattered in the comoving frame at an angle 8,—z/2 from the velocity vector are those making an angle 6—L/P with the line of sight in the observer frame CosB,=(cosNf160540)."," The photons scattered in the comoving frame at an angle $\theta_s\sim \pi/2$ from the velocity vector are those making an angle $\theta \sim +1/\Gamma$ with the line of sight in the observer frame $\cos +\theta_s=(\cos\theta-\beta)/(1-\beta \cos \theta)$." + So the received: power is depressed. (relative to the isotropic seed. photon case) but not significantly. as shown below.," So the received power is depressed (relative to the isotropic seed photon case) but not significantly, as shown below." + Η the seed. photons are also isotropic (so are the scattered ones). integrating eq. (12))," If the seed photons are also isotropic (so are the scattered ones), integrating eq. \ref{eq:j}) )" +" vields the well known result (e.g. Blumenthal Could. 1970) What we care about is the cdivergeney of receiving number of scattered. photons at vain.=Ὦtv. between the photon beam case and the isotropic photon case (D=rajcos08) is the Doppler factor). which is represented bv fi, and can be estimated as (e.g. Rabicki Lightman 1979) where 8; is the jet half-opening angle of the ejecta."," yields the well known result (e.g. Blumenthal Gould 1970) What we care about is the divergency of receiving number of scattered photons at $\nu_{\rm obs}={\cal D}^{-1}\nu_s$ between the photon beam case and the isotropic photon case ${\cal +D}=\Gamma (1-\beta \cos \theta)$ is the Doppler factor), which is represented by $f_{\rm cor}$ and can be estimated as (e.g. Rybicki Lightman 1979) where $\theta_j$ is the jet half-opening angle of the ejecta." +" We have fi,20.4 ford~2.3 and 6;z9L/L.", We have $f_{\rm cor}\simeq 0.4$ for $\delta \sim 2.3$ and $\theta_j\gg 1/\Gamma$. + 1n the ISM case. sub-GeV photons can be collected by GLAST. where Cu=61ἐν)νι:," In the ISM case, sub-GeV photons can be collected by GLAST, where $C_\beta \equiv +6(1-\beta_{_{XRT}})/\beta_{_{XRT}}$." + Usually at least five photos are needed to claim a detection (Zhang Mésszárros 2001). so we need à—10em7. whichis typical (Panaiteseu Ixumar 2002).," Usually at least five photos are needed to claim a detection (Zhang Mésszárros 2001), so we need $n\sim 10~{\rm cm^{-3}}$, whichis typical (Panaitescu Kumar 2002)." + The cllective area of EGRET onboard Compton Gamma Rav Observatory (CORO) is 5borerv1500rem.y., The effective area of EGRET onboard Compton Gamma Ray Observatory (CGRO) is $S_{\rm _{EGRET}}\sim 1500~{\rm cm^2}$. + A rather high circumburst density of p~100cm is needed. to. get 5. sub-GeV photons., A rather high circumburst density of $n\sim 100~{\rm cm^{-3}}$ is needed to get 5 sub-GeV photons. + Afterglow moceling (Panaitescu & Ixumar 2002) suggests that such a high density is uncommon around GRB progenitors., Afterglow modeling (Panaitescu $\&$ Kumar 2002) suggests that such a high density is uncommon around GRB progenitors. +" Thev may be the reasons for the rare detections of delavecl sub-CGeV photon ashes by EGRET (see refsec:MIG,ase fordetaits),"," They may be the reasons for the rare detections of delayed sub-GeV photon flashes by EGRET (see \\ref{sec:MG_case} + for details)." + 3elore turning to a comparison with observations we ask (wo questions., Before turning to a comparison with observations we ask two questions. + First we ask whether SSC process of the electrons accounting for the EUM Uares can produce sub-GeV photons., First we ask whether SSC process of the electrons accounting for the FUV flares can produce sub-GeV photons. + We then ask what are the implications of the cooling due to the IC process on the forward shock emission., We then ask what are the implications of the cooling due to the IC process on the forward shock emission. + The answer to the first. question. can these sub-CGeV photons be attributed to the SSC radiation of the electrons accounting for the FUY [lares is. very likely negative.," The answer to the first question, can these sub-GeV photons be attributed to the SSC radiation of the electrons accounting for the FUV flares is very likely negative." + Firsth. the outllow powering the EUM. fares. may. be highly magnetized. (Usov. 1992: Thompson 1994: Lyutikov Blandford 2003: Spruit. Daigne Drenkhahn 2001: Fan et al.," Firstly, the outflow powering the FUV flares may be highly magnetized (Usov 1992; Thompson 1994; Lyutikov Blandford 2003; Spruit, Daigne Drenkhahn 2001; Fan et al." + 20052: Proga Zhang 2006) in which case the svnchrotron sel-Compton radiation. is too weak to be detectable., 2005a; Proga Zhang 2006) in which case the synchrotron self-Compton radiation is too weak to be detectable. +" Secondly. if the late barvonic internal shock emission. peaks in the FUV bancl (ice. Vac). the typical SSC frequency should. be ~oFie100keV+7),GA/0.01keV)tensMeV. where 5,544100 is the minimum Lorentz factor of electrons accelerated in the late internal shocks (see also Wei et al."," Secondly, if the late baryonic internal shock emission peaks in the FUV band (i.e., $\nu_{\rm uv}$ ), the typical SSC frequency should be $\sim \gamma_{e,m}^2 \nu_{\rm uv}\sim 100 +~{\rm keV}~\gamma_{e,m,2}^2(\nu_{\rm uv}/0.01{\rm keV})\ll {\rm +tens~MeV}$ , where $\gamma_{e,m}\sim 100$ is the minimum Lorentz factor of electrons accelerated in the late internal shocks (see also Wei et al." + 2006)., 2006). + Ls contribution to sub-GeV emission. [lux is unimportant., Its contribution to sub-GeV emission flux is unimportant. + Lf the typical svnehrotron radiation frequency of late internal shocks is in X-ray band. the SSC radiation may peak in tens AeV band (Wang et al.," If the typical synchrotron radiation frequency of late internal shocks is in X-ray band, the SSC radiation may peak in tens MeV band (Wang et al." + 2006)., 2006). +" Llowever. as we have already mentioned in section 1. for most. ""X-ray Lares” detected. so far. the peak energy may be lower than 0.2 keV. So the tens AleV emission from the SSC process may be infrequent."," However, as we have already mentioned in section 1, for most “X-ray flares"" detected so far, the peak energy may be lower than 0.2 keV. So the tens MeV emission from the SSC process may be infrequent." + We need to verify that the sub-CGeV. photons won't be absorbed by the high energy tail of the FUY Ilare photons., We need to verify that the sub-GeV photons won't be absorbed by the high energy tail of the FUV flare photons. +" The pair production optical depth for photons with energy ~1] GeV (absorbed by the Dare photons with energy cias2}2] 771) ean be estimated as (οι. Svensson LOST) Ns... =.AE∣⊳(;boesurποστςASL""iecbewheretotal the ""n [lare photon number satisfvingm fy 2cons."," The pair production optical depth for photons with energy $\sim 1$ GeV (absorbed by the flare photons with energy $\epsilon_{a,{\rm obs}}\sim 2(\Gamma +m_e c^2)^2/[(1+z)^2 {\rm GeV}]\sim 0.2 {\rm +MeV}~E_{k,53}^{1/4}n_0^{-1/4}t_3^{-3/4}[(1+z)/2]^{-5/4}$ ) can be estimated as (e.g., Svensson 1987) where $N_{>\epsilon_{a,{\rm obs}}}= {\beta_{_{ XRT}}-1 \over +\beta_{_{ XRT}}} ({ h\nu_{\rm uv} \over \epsilon_{a,{\rm obs}} +})^{\beta_{_{XRT}}}{4\pi D_L^2{\cal F}\over (1+z)^2 h\nu_{\rm +uv}}$ is the total flare photon number satisfying $h +\nu>\epsilon_{a,{\rm obs}}$." +Clearly such a small optical depth won't allect the sub-GeV ας., Clearly such a small optical depth won't affect the sub-GeV flux. + FUY dares may. play an additional role., FUV flares may play an additional role. + C'onsider the possibility. that after the cease of the >ray burst. the central engine does not turn olf and gives rise to long term but sharply decaying soft. radiation component (mainly in far-ultraviolet. band).," Consider the possibility that after the cease of the $\gamma-ray$ burst, the central engine does not turn off and gives rise to long term but sharply decaying soft radiation component (mainly in far-ultraviolet band)." + The LC process of these FUY photons cools the forward. shock electrons. and. the IC parameter Y may be dominated: by. Yvee, The IC process of these FUV photons cools the forward shock electrons and the IC parameter $Y$ may be dominated by $Y_{_{EIC}}$. + dhis will reduce the carly X-ray (lux emitted. by these electrons since the X-ray (lux recorded. by NICE. is x(1|Y)+ (e.g. eq. (," This will reduce the early X-ray flux emitted by these electrons since the X-ray flux recorded by XRT is $\propto (1+Y)^{-1}$ (e.g., eq. (" +6) of Fan Piran 2006).,6) of Fan Piran 2006). +" For illustration. with Lin~6LOMoreseg,obi/400).2122] for 400s«F<104s. we have Y,PEEο400)""8T (we have used Eq. 5] "," For illustration, with $L_{ph}\sim +6\times 10^{49}~{\rm ergs}~\epsilon_{B,-2} +E_{k,53}(t/400)^{-1.7}[(1+z)/2]^{1.7}$ for $400 {\rm s}instability ⋡⋯∐↓⋡∖↿∩↓⋅⊔⇍⋜↧∐∙∖⇁↓⋯⊳∖↓↥⋯⇂∠⊔∐∐∼⊔∐⊓⋅⊳∖⇂∪↓⋅↿∖∖⊽∪↓⋅⋖⋅⋜↧≱∖∪⊔≱∖∶↿⇂↥∢⋅. . planet of the≽− ΕΙ 8799 ⋅system could have formed by⋅ irst instability⊀ as"". the cooling timescales. are. likely o⋅ o be small enough. such. that. fragmentation⊀ is⊀ possible.", \cite{Nero_Bjorkman_GI_analysis} have argued analytically that Fomalhaut b and at least the outer planet of the HR 8799 system could have formed by gravitational instability as the cooling timescales are likely to be small enough such that fragmentation is possible. + Aloreover. disces. in. their. earlv stages are thought to be massive. (7)ο suggesting. that gravitationalDN instability.κ. must xav a role in the evolution of a disc in the late Class Land early. .Class HE stages.," Moreover, discs in their early stages are thought to be massive \citep{Eisner_Carpenter_massive_discs} suggesting that gravitational instability must play a role in the evolution of a disc in the late Class I and early Class II stages." +" It has also been proposed that. core accretion. may be a method by which. planets may form⋅ at small radii"" (~O(. 10).AU) whilst. eravitationalEN instability."" may be the mechanism. by which. planets may form⋅ at larger raclii↔ (2O(100). AU) (e.g.:72) though a hybrid. scenario. of ⋅⋅forming. eas giants. in. the same system by both core accretion. and eravitational instability has vet to be modelled.", It has also been proposed that core accretion may be a method by which planets may form at small radii $\sim \rm{O}(10) \rm{AU}$ ) whilst gravitational instability may be the mechanism by which planets may form at larger radii $\gtrsim \rm{O}(100) \rm{AU}$ ) \citep[e.g.][]{Boley_CA_and_GI} though a hybrid scenario of forming gas giants in the same system by both core accretion and gravitational instability has yet to be modelled. + There are two quantities that have historically been used to determine whether a disc is likely to fragment., There are two quantities that have historically been used to determine whether a disc is likely to fragment. +" The first. is. the stability"" parameter >(?).. where c. is the sound speed in the disc. Bj, ds the epievclic freequeney. which for. Ixeplerian clises is"," The first is the stability parameter \citep{Toomre_stability1964}, where $c_{\rm s}$ is the sound speed in the disc, $\kappa_{\rm ep}$ is the epicyclic frequency, which for Keplerian discs is" +central star.,central star. + For Haro 6-10 S we found an emission withii 1.0 AU from the central star with a temperature of 900K anc à second colder emission at 100K. originating within 7 AL from the central star.," For Haro 6-10 S we found an emission within 1.0 AU from the central star with a temperature of $K$ and a second colder emission at $K$, originating within 7 AU from the central star." +" The disc of Haro 6-10 N is seen close to edge-on (/= 80°). while Haro 6-10 S is almost seen face-o1 (i= 10"")."," The disc of Haro 6-10 N is seen close to edge-on $i = 80^o$ ), while Haro 6-10 S is almost seen face-on $i = 10^o$ )." + The derived inclinations of the binary components are consistent with the fact that the central star of Haro 6-10 S is visible in the optical. while the star of Haro 6-10 N is obscurec by an additional extinction. represented by the circumstellar disc and is only barely visible in the optical.," The derived inclinations of the binary components are consistent with the fact that the central star of Haro 6-10 S is visible in the optical, while the star of Haro 6-10 N is obscured by an additional extinction represented by the circumstellar disc and is only barely visible in the optical." + These results are also consistent with the general appearance of the binary system described in Section 4.].., These results are also consistent with the general appearance of the binary system described in Section \ref{optical-nir}. + In the case of Haro 6-10 N. the model fits the observations very well. while for Haro 6-10 S the model fitting is less accurate; the model reproduces the mid-infrared spectrum. the correlated spectra. and the absolute value of the visibilities. but does not fit their shape.," In the case of Haro 6-10 N, the model fits the observations very well, while for Haro 6-10 S the model fitting is less accurate; the model reproduces the mid-infrared spectrum, the correlated spectra, and the absolute value of the visibilities, but does not fit their shape." + We thus additionally tested. the robustness of our results to be sure that the Monte Carlo simulations did not only find a local minimum in the parameter space instead of the absolute minimum., We thus additionally tested the robustness of our results to be sure that the Monte Carlo simulations did not only find a local minimum in the parameter space instead of the absolute minimum. + Since the best defined parameters are the disc inclinations. we changed their initial values. for Haro 6-10 N to a face-on dise (/= 3°) and for Haro 6-10 S to an edge-on disc 6= 80).," Since the best defined parameters are the disc inclinations, we changed their initial values, for Haro 6-10 N to a face-on disc $i = 3^o$ ) and for Haro 6-10 S to an edge-on disc $i = 80^o$ )." + Also in this case the Monte Carlo simulations converge to the results previously obtained., Also in this case the Monte Carlo simulations converge to the results previously obtained. + We also run the whole modelling with the position angles as additional free parameters., We also run the whole modelling with the position angles as additional free parameters. + Although the derived position angles differ from the observed ones by ~70° for Haro 6-10 N and ~50° for Haro 6-10 S. the results for the remaining parameters are almost identical to the above given values.," Although the derived position angles differ from the observed ones by $\sim70^o$ for Haro 6-10 N and $\sim50^o$ for Haro 6-10 S, the results for the remaining parameters are almost identical to the above given values." + Given the higher uncertainties of the measurements for the southern component and the poorer fits (Fig. 2)).," Given the higher uncertainties of the measurements for the southern component and the poorer fits (Fig. \ref{BBG_S}) )," + the formal errors derived. for its dise. parameters are most probably a lower limit., the formal errors derived for its disc parameters are most probably a lower limit. + The simple size estimates derived in Section 4.3.1 are also consistent with higher inclinations (Table 5)., The simple size estimates derived in Section \ref{gbd} are also consistent with higher inclinations (Table \ref{Gaussian}) ). + We further want to emphasise. that our approach strongly relies on the assumption that the components of Haro 6-10 can be described by a superposition of two Gaussian brightness distributions.," We further want to emphasise, that our approach strongly relies on the assumption that the components of Haro 6-10 can be described by a superposition of two Gaussian brightness distributions." + If the true brightness distribution would show significant deviations. our results would be biased.," If the true brightness distribution would show significant deviations, our results would be biased." + Also the interpretation of the value found for the inclination (defined as the elongation of the Gaussians) then would be no longer straightforward., Also the interpretation of the value found for the inclination (defined as the elongation of the Gaussians) then would be no longer straightforward. + Unfortunately. such deviations can not be ruled out with the limited number of measurements at hand.," Unfortunately, such deviations can not be ruled out with the limited number of measurements at hand." + However. Gaussian brightness distributions have proven to be à reasonable assumption for a wide variety of centrally heated objects.," However, Gaussian brightness distributions have proven to be a reasonable assumption for a wide variety of centrally heated objects." + In this section we compare our results with previous works and discuss which mechanism might have formed the binary system Haro 6-10., In this section we compare our results with previous works and discuss which mechanism might have formed the binary system Haro 6-10. + The optical images of Haro 6-10 highlight some filamentary structures (as described in Section 4.1)) which might have the following explanations: 1) it is circumstellar material with an are-like shape simply illuminated by the central star. or 2) it is the projection of the scattered light of a cavity in the circumbinary envelope. or 3) it represents the circumstellar material shocked by an outflow.," The optical images of Haro 6-10 highlight some filamentary structures (as described in Section \ref{optical-nir}) ) which might have the following explanations: 1) it is circumstellar material with an arc-like shape simply illuminated by the central star, or 2) it is the projection of the scattered light of a cavity in the circumbinary envelope, or 3) it represents the circumstellar material shocked by an outflow." + The existence of a cavity in an envelope has been suggested around a similar system. T Tau N. by ? and ?..," The existence of a cavity in an envelope has been suggested around a similar system, T Tau N, by \cite{Momoseetal1996} and \cite{Stapelfeldtetal1998}." + In this picture. a wide-angle wind creates oblique shocks when interacting with the molecular environment.," In this picture, a wide-angle wind creates oblique shocks when interacting with the molecular environment." +" On the other hand. the existence of an outflow is supported by the resolved extended emission of H» at 6.5""in the south direction and is consistent with the filament structure (2).."," On the other hand, the existence of an outflow is supported by the resolved extended emission of $_2$ at in the south direction and is consistent with the filament structure \citep[][]{Doppmannetal2008}." + ? already identified three outflow systems in their narrow-band optical images., \cite{Devineetal1999} already identified three outflow systems in their narrow-band optical images. + In addition to the large-scale structure two separate outflows closer to Haro 6-10 were found., In addition to the large-scale structure two separate outflows closer to Haro 6-10 were found. + This suggests that both components are producing outflows., This suggests that both components are producing outflows. + Based on integral-field spectroscopy and polarimetry ? suggest the northern source as the origin of a jet with a length of superimposed on the bright reflection nebula., Based on integral-field spectroscopy and polarimetry \cite{MovsessianMagakian1999} suggest the northern source as the origin of a jet with a length of superimposed on the bright reflection nebula. + They propose that the dise around this component is seen edge-on. while the southert component is surrounded by a less inclined disc.," They propose that the disc around this component is seen edge-on, while the southern component is surrounded by a less inclined disc." + ? report on a parsec-scale Herbig Haro flow with clumpy redshifted gas pointing to the north-east., \cite{Stojimirovicetal2007} report on a parsec-scale Herbig Haro flow with clumpy redshifted gas pointing to the north-east. + The blueshifted south-western part of the flow is contaminated by an unrelated foreground cloud., The blueshifted south-western part of the flow is contaminated by an unrelated foreground cloud. + ?. found à bulk of Bry emission from the two sources together with an extended. fainter emission from the southeri component.," \cite{Becketal2010} found a bulk of $\gamma$ emission from the two sources together with an extended, fainter emission from the southern component." + The same extended emission was measured also in the HT] line and is thus clearly determining the direction of an outflow originating from this source., The same extended emission was measured also in the II] line and is thus clearly determining the direction of an outflow originating from this source. + At 1.2 nm the emission was again resolved with the PdBI (?) and the millimetre flux is almost the same for the two components., At 1.2 mm the emission was again resolved with the PdBI \citep[][]{Guilloteauetal2011} and the millimetre flux is almost the same for the two components. + Under the assumption that the disc i5 optically thin at these wavelengths. the mass of the disces can be directly derived from the fluxes.," Under the assumption that the disc is optically thin at these wavelengths, the mass of the discs can be directly derived from the fluxes." + The measured fluxes thus imply that the dises of Haro 6-10 N and S have almost the same mass., The measured fluxes thus imply that the discs of Haro 6-10 N and S have almost the same mass. + The measured large extinction. associated by ? to à foreground cloud is also in agreement with the envelope we introduced to explain the mid-infrared absorption spectrum through both components of the binary system., The measured large extinction associated by \cite{Stojimirovicetal2007} to a foreground cloud is also in agreement with the envelope we introduced to explain the mid-infrared absorption spectrum through both components of the binary system. + Our findings on the circumstellar discs around the two sources of the binary system are consistent with the picture drawn by the above studies., Our findings on the circumstellar discs around the two sources of the binary system are consistent with the picture drawn by the above studies. + Also the misalignment of the disces and the suggested, Also the misalignment of the discs and the suggested +a Gaussian best-fit distribution.,a Gaussian best-fit distribution. + Similar behavior is seen in the eurent. PDFs initially Gaussian distributed tending to strongly non-Gaussian statistics with long tails for later limes., Similar behavior is seen in the current PDFs – initially Gaussian distributed tending to strongly non-Gaussian statistics with long tails for later times. + relfig:eur-PDF is the current PDF at an advanced time into the numerical solution., \\ref{fig:cur-PDF} is the current PDF at an advanced time into the numerical solution. + It is to be noted that the density gradient PDF has longer tails at higher sunplitude than does the current PDF., It is to be noted that the density gradient PDF has longer tails at higher amplitude than does the current PDF. + One would expect (hese to be in rough agreement. since (he underlying density and magnetic fields have comparable PDFs that remain Gaussian distributed throughout ihe numerical solution.," One would expect these to be in rough agreement, since the underlying density and magnetic fields have comparable PDFs that remain Gaussian distributed throughout the numerical solution." + The discrepaucy. between the density eracient and. current PDFs suggests a process (hat enhances density derivatives above magnetic field derivatives., The discrepancy between the density gradient and current PDFs suggests a process that enhances density derivatives above magnetic field derivatives. + Future work is required to explore causes of this enhancement., Future work is required to explore causes of this enhancement. + This result is significant for pulsar scintillation. which is most sensitive to density gradients.," This result is significant for pulsar scintillation, which is most sensitive to density gradients." + Although interstellar turbulence is magnetic in nature. the KAW regime has the benelit of Hactuation equipartilion between n and D.," Although interstellar turbulence is magnetic in nature, the KAW regime has the benefit of fluctuation equipartition between $n$ and $B$." + The densitv gradient. however. is more non-Gaussian (han (he magnetic component. sugeesting that this type of turbulence is specially endowed to produce the tvpe of scintillation scaling observed with pulsar signals.," The density gradient, however, is more non-Gaussian than the magnetic component, suggesting that this type of turbulence is specially endowed to produce the type of scintillation scaling observed with pulsar signals." + Ensemble runs for the 5/50«1 regime vield distributions similar to the j/5(o1 regime in all fields., Ensemble runs for the $\eta / \mu \ll 1$ regime yield distributions similar to the $\eta / \mu \sim 1$ regime in all fields. + The ensemble PDF for two times is shown in rellig:dgx-PDF-zero-mu.., The ensemble PDF for two times is shown in \\ref{fig:dgx-PDF-zero-mu}. + The initial density gradient PDF is Gaussian distributed., The initial density gradient PDF is Gaussian distributed. + For later times lone tails are evident ancl consistent with the kurtosis excess measurements as presented above for the yp=0 case., For later times long tails are evident and consistent with the kurtosis excess measurements as presented above for the $\mu = 0$ case. + The density eracdient. distribution has longer tails at higher amplitude than the current. distribution: the overall distributions are similar to those [or the 2/10| regime. despite the absence of filamentary structures and the presence of sheets.," The density gradient distribution has longer tails at higher amplitude than the current distribution; the overall distributions are similar to those for the $\eta / \mu \sim 1$ regime, despite the absence of filamentary structures and the presence of sheets." + The strongly. non-Gaussian statistics are insensitive to (he damping regime. provided that (he diffusion coefficient is small enough to allow density gradients to persist.," The strongly non-Gaussian statistics are insensitive to the damping regime, provided that the diffusion coefficient is small enough to allow density gradients to persist." +" Using the normalizations for ((3)) and (4)) and using B= L4G. n=0.08 oE and T;=1 eV. 5. the normalized Spitzer resistivity. is 2.41x10.* and 5,4. the normalized collisional diffusivity. is 1.9x10.*."," Using the normalizations for \ref{psi-eqn}) ) and \ref{den-eqn}) ) and using $B=1.4 \mu$ G, $n=0.08$ $^{-3}$ and $T_e=1$ eV, $\eta_{norm}$, the normalized Spitzer resistivity, is $2.4 \times 10^{-7}$ and $\mu_{norm}$, the normalized collisional diffusivity, is $1.9 \times 10^{-7}$." + For a resolution of 512°. these damping values are unable to keep the svstem numerically stable.," For a resolution of $512^2$, these damping values are unable to keep the system numerically stable." + The threshold for stability. requires the simulation to be greater than 5x10.5. which is almost within an order of magnitude of the ISAT value.," The threshold for stability requires the simulation $\eta$ to be greater than $5 \times 10^{-6}$, which is almost within an order of magnitude of the ISM value." + The numerical solutions presented here. while motivated by the pulsar signal width scalings. more generally characterize the current and densitv gradient PDFs when the damping parameters are varied.," The numerical solutions presented here, while motivated by the pulsar signal width scalings, more generally characterize the current and density gradient PDFs when the damping parameters are varied." + We would expect the density gradients to be non-Gaussian when using parameters that correspond to the ISM., We would expect the density gradients to be non-Gaussian when using parameters that correspond to the ISM. + Future work will address (he pulsar, Future work will address the pulsar +in nearby giant elliptical galaxies. the photometric data of 553W0091 indicate up to a factor of two larger ages when metallicity mixtures are adopted.,"in nearby giant elliptical galaxies, the photometric data of 53W091 indicate up to a factor of two larger ages when metallicity mixtures are adopted." + The UV continua of young galaxies. such as LBDS 53W09]. are not sensitive to OS.," The UV continua of young galaxies, such as LBDS 53W091, are not sensitive to OS." + In addition. solar abundance models reasonably approximate them.," In addition, solar abundance models reasonably approximate them." + This relative immunity of the UV data against such complexities makes the UV spectrum of a distant galaxy a very useful age indicator., This relative immunity of the UV data against such complexities makes the UV spectrum of a distant galaxy a very useful age indicator. + Our UV-based estimate is approximately 2.0+0.2 Gyr and apparently inconsistent with that of Spinrad et al..," Our UV-based estimate is approximately $2.0 \pm 0.2$ Gyr and apparently inconsistent with that of Spinrad et al.," + 3.5 Gyr. but consistent with the age estimates we obtained using the new Jimenez models.," 3.5 Gyr, but consistent with the age estimates we obtained using the new Jimenez models." + The photometric data of 553W09] indicate 1.5+0.2 Gyr., The photometric data of 53W091 indicate $1.5 \pm 0.2$ Gyr. + The slightly larger estimates from the UV continuum fit would be consistent with this photometry-based one if we include a small amount of reddening and/or if the core of this galaxy is somewhat older or more metal-rich than its outskirt. all of which are quite plausible.," The slightly larger estimates from the UV continuum fit would be consistent with this photometry-based one if we include a small amount of reddening and/or if the core of this galaxy is somewhat older or more metal-rich than its outskirt, all of which are quite plausible." + It may also indicate that there is no substantial age spread among the stars in LBDS S53WO91., It may also indicate that there is no substantial age spread among the stars in LBDS 53W091. + The age estimates of Spinrad and his collaborators were heavily based on selected UV spectral breaks., The age estimates of Spinrad and his collaborators were heavily based on selected UV spectral breaks. + This was because UV spectral breaks were believed to be less sensitive to the uncertainties in reddening., This was because UV spectral breaks were believed to be less sensitive to the uncertainties in reddening. + If this is true and if we are ignoring the possible reddening effects. our age estimates should be systematically larger than theirs because reddening makes the continuum look older. which is opposite to what we have found.," If this is true and if we are ignoring the possible reddening effects, our age estimates should be systematically larger than theirs because reddening makes the continuum look older, which is opposite to what we have found." + Thus the difference between Spinrad et al, Thus the difference between Spinrad et al. +s estimate and ours cannot be reconciled by adopting any conventional reddening law.,'s estimate and ours cannot be reconciled by adopting any conventional reddening law. + Our results on LBDS 53W09] are vulnerable to the uncertainties in the spectral library in matching the F-type stellar spectra in the UV., Our results on LBDS 53W091 are vulnerable to the uncertainties in the spectral library in matching the F-type stellar spectra in the UV. + Such uncertainties may exist not only in the detailed spectral features. such as those studied by Spinrad et al. (," Such uncertainties may exist not only in the detailed spectral features, such as those studied by Spinrad et al. (" +1997) and Heap et al. (,1997) and Heap et al. ( +1998). but also in the continuum.,"1998), but also in the continuum." + The same authors of Heap et al. (, The same authors of Heap et al. ( +1998) are currently obtaining the UV spectra of F-type stars using HST/STIS.,1998) are currently obtaining the UV spectra of F-type stars using HST/STIS. + When the project is complete. a more accurate analysis both on the spectral breaks and the continuum will be possible.," When the project is complete, a more accurate analysis both on the spectral breaks and the continuum will be possible." + There is no doubt that precise age estimates of high-z galaxies would be very useful for constraining cosmology., There is no doubt that precise age estimates of $z$ galaxies would be very useful for constraining cosmology. + In order to fully take advantage of the power of this technique. however. we first need to understand the details of the population synthesis. which are currently creating a substantial disagreement in age estimate.," In order to fully take advantage of the power of this technique, however, we first need to understand the details of the population synthesis, which are currently creating a substantial disagreement in age estimate." + We propose to carry out à comprehensive investigation on the various population synthesis models through a series of standard tests on the objects whose ages have been independently determined., We propose to carry out a comprehensive investigation on the various population synthesis models through a series of standard tests on the objects whose ages have been independently determined. + Such objects may include the sun. M32. and Galactic globular clusters.," Such objects may include the sun, M32, and Galactic globular clusters." + Our models (the Y1 models) currently pass these tests reasonably., Our models (the Yi models) currently pass these tests reasonably. + Our age estimates indicate that LBDS 53W091 formed approximately at z22-—3., Our age estimates indicate that LBDS 53W091 formed approximately at $z = 2$ – 3. + However. our smaller age estimate for this galaxy does not contradict work that suggests galaxies generally formed at high redshifts. regardless of the rarity of massive ellipticals at z51.5.," However, our smaller age estimate for this galaxy does not contradict work that suggests galaxies generally formed at high redshifts, regardless of the rarity of massive ellipticals at $z \approx 1.5$." + Furthermore. we are just beginning to expand our observations of galaxies to high redshift. and so the existence of a few old galaxies at high redshifts does yet prove any galaxy formation scenario. although it can potentially constrain cosmological parameters (in the sense that the ages of a few objects can provide lower limits on the age of the Universe at that redshift).," Furthermore, we are just beginning to expand our observations of galaxies to high redshift, and so the existence of a few old galaxies at high redshifts does yet prove any galaxy formation scenario, although it can potentially constrain cosmological parameters (in the sense that the ages of a few objects can provide lower limits on the age of the Universe at that redshift)." + Finding no old galaxies at high redshift would support a low z; for the general population., Finding no old galaxies at high redshift would support a low $z_f$ for the general population. + Building a larger database of observations is therefore crucial to achieve a unique and statistically significant solution., Building a larger database of observations is therefore crucial to achieve a unique and statistically significant solution. + Dunlop (1998) reported a discovery| of another galaxy 553W069) whose UV spectrum looks even redder than that of 553W09]. although its redshift is only slightly smaller (z=1.43).," Dunlop (1998) reported a discovery of another galaxy 53W069) whose UV spectrum looks even redder than that of 53W091, although its redshift is only slightly smaller $z=1.43$ )." + This would be a stronger sign of large ages of high-z galaxies., This would be a stronger sign of large ages of $z$ galaxies. + As more data are collected. our vision to the high-z universe will be clearer.," As more data are collected, our vision to the $z$ universe will be clearer." + This work was encouraged by the open-minded response of Hyron Spinrad to our initial interest in. the work on LBDS553W09]| done by him and his collaborators., This work was encouraged by the open-minded response of Hyron Spinrad to our initial interest in the work on 53W091 done by him and his collaborators. + We thank his group. in. particular Daniel. Stern. for providing the spectrum of 553W091.," We thank his group, in particular Daniel Stern, for providing the spectrum of 53W091." + We are grateful to Taddy Kodama for providing his metallicity distribution models and to Gustavo Bruzual for providing the spectrum of M32., We are grateful to Taddy Kodama for providing his metallicity distribution models and to Gustavo Bruzual for providing the spectrum of M32. + The constructive eriticisms and comments of Raul Jimenez. Hyron Spinrad. Gustavo Bruzual. Sydney Barnes and Pierre Demarque improved the manuscript significantly.," The constructive criticisms and comments of Raul Jimenez, Hyron Spinrad, Gustavo Bruzual, Sydney Barnes and Pierre Demarque improved the manuscript significantly." + We owe special thanks to Raul Jimenez and Gustavo Bruzual for making their models available to us., We owe special thanks to Raul Jimenez and Gustavo Bruzual for making their models available to us. + This work was supported by the Creative Research Initiative Program of the Korean Ministry of Science Technology grant., This work was supported by the Creative Research Initiative Program of the Korean Ministry of Science Technology grant. + Part of this work was performed while 5.Υ. held a National Research Council-(NASA Goddard Space Flight Center) Research Associateship., Part of this work was performed while S.Y. held a National Research Council-(NASA Goddard Space Flight Center) Research Associateship. +streamlines corresponding to these orbits may lead to non-lincar phenomena such as shocks.,streamlines corresponding to these orbits may lead to non-linear phenomena such as shocks. + The residual. velocity Ποιά produced by our simulation is intencded to show the deviations from circular motion expected. for the elliptica stellar orbits of a barred. potential (Figure. 2((5))., The residual velocity field produced by our simulation is intended to show the deviations from circular motion expected for the elliptical stellar orbits of a barred potential (Figure \ref{resids}( (b)). +. “hese deviations appear as inflow and outflow. but there is nonel How either way in this non-dissipative mocel.," These deviations appear as inflow and outflow, but there is no flow either way in this non-dissipative model." + Thus it shoul be noted that observations of streaming motions in galactic bars do not necessarily imply net inflow: these may simply be the radial components of non-cireular motion expectec in à non-axisvmmetric bar potential., Thus it should be noted that observations of streaming motions in galactic bars do not necessarily imply net inflow; these may simply be the radial components of non-circular motion expected in a non-axisymmetric bar potential. + Sophisticated simulations which include σας dynamical elfects have been conducted: by several authors (c.g. Sanders “Tubbs. 1980: Van Albada Roberts. 1981: Schwarz. 1981. 1984: Combes Gerin. 1985: Athanassoula. 1992a.b: Sellwood. Wilkinson. 1993. and references herein) to explain features. such as shocks. in barred ealaxies in ternis of the interaction between various families of periodic orbits in the bar.," Sophisticated simulations which include gas dynamical effects have been conducted by several authors (e.g. Sanders Tubbs, 1980; Van Albada Roberts, 1981; Schwarz, 1981, 1984; Combes Gerin, 1985; Athanassoula, 1992a,b; Sellwood Wilkinson, 1993, and references therein) to explain features, such as shocks, in barred galaxies in terms of the interaction between various families of periodic orbits in the bar." + The existence of such orbits hen allow various physical. parameters of the bar. such as he presence of possible resonances. to be inferred.," The existence of such orbits then allow various physical parameters of the bar, such as the presence of possible resonances, to be inferred." +high-inass region. the IME has a relatively steep slope of — 1.7. while it flattens iu the low-mass range (Qe = 1.2 for O5AL.San< 7$ hours and well beyond the observed concentration of nova-like system orbital periods between three and four hours, it is interesting to explore any differences these three long period systems might exhibit." + The known orbital ancl physical parameters [rom (he literature on the three svstems are presented in Table 1 along with the relerences., The known orbital and physical parameters from the literature on the three systems are presented in Table 1 along with the references. + We list [or these three systems. by row: (1) the NL subtivpe(s): (2) average apparent V-magnitude: (3) the orbital period in hours: (4) the interstellar reddening —V [E(J)|: (5) mass of the white dwarf in solar masses: (6) mass of the red dwarf in solar masses: (7) the orbital inclination i and: (8) the distance in parsecs.," We list for these three systems, by row: (1) the NL subtype(s); (2) average apparent V-magnitude; (3) the orbital period in hours; (4) the interstellar reddening $\bv$ )]; (5) mass of the white dwarf in solar masses; (6) mass of the red dwarf in solar masses; (7) the orbital inclination i and; (8) the distance in parsecs." + The listed. values of white dwarl mass. orbital inclination. and the reddening E(D-V) were adopted as initial values in the model filling.," The listed values of white dwarf mass, orbital inclination, and the reddening E(B-V) were adopted as initial values in the model fitting." + The wide range of published distance determinations for V363 Aur as well as the single distance estimates published for RZ Gru and AC Cne allow a useful comparison with the model-derived distances [rom this work., The wide range of published distance determinations for V363 Aur as well as the single distance estimates published for RZ Gru and AC Cnc allow a useful comparison with the model-derived distances from this work. +solution to Equation (10)) satisfying the boundary conditions ats=+L/2 1s where Αι). As(r) and As(r) are time-dependent coefficients. ó(fj) is a time-dependent phase. and z. and denote the locations of the interfaces between the prominence thread and the evacuated regions. namely The locations of the interfaces change as the dense thread moves along the magentic tube.,"solution to Equation \ref{eq:kinkQ}) ) satisfying the boundary conditions at $z = \pm L/2$ is where $A_1( t_1 )$ , $A_2(t_1)$, and $A_3(t_1)$ are time-dependent coefficients, $\phi( t_1 )$ is a time-dependent phase, and $z_-$ and $z_+$ denote the locations of the interfaces between the prominence thread and the evacuated regions, namely The locations of the interfaces change as the dense thread moves along the magentic tube." + Qj must satisfy appropriate boundary conditions at z=z-., $Q_1$ must satisfy appropriate boundary conditions at $z=z_\pm$. + Since the interfaces correspond to contact discontinuities (seeGoedbloed&Poedts2004).. the boundary conditions are where [{X]] stands for the jump of the quantity X at z=ce.," Since the interfaces correspond to contact discontinuities \citep[see][]{goedbloed}, the boundary conditions are where $[[X]]$ stands for the jump of the quantity $X$ at $z = z_{\pm}$." + Applying the conditions of Equation (13)) on the solutions given by Equation (11)). we arrive at the following equation Equation (14)) is the time-dependent dispersion relation.," Applying the conditions of Equation \ref{eq:boundary}) ) on the solutions given by Equation \ref{eq:solgen}) ), we arrive at the following equation Equation \ref{eq:disper}) ) is the time-dependent dispersion relation." + For fixed rj. the solution of Equation (14)) ts c(fi).," For fixed $t_1$, the solution of Equation \ref{eq:disper}) ) is $\omega \left( t_1 \right)$." + Note that. although Equation (14)) is written in à more compact form. it is consistent with dispersion relations previously obtained for normal modes in the static case. Le. vo=0.," Note that, although Equation \ref{eq:disper}) ) is written in a more compact form, it is consistent with dispersion relations previously obtained for normal modes in the static case, i.e., $v_0 = 0$." + Equation (14)) with vo= O15 equivalent to Equation (11) of Soleretal.(2010) if the substitutions Ly—Lsots and {ς-LMe.ny are performed in their expression., Equation \ref{eq:disper}) ) with $v_0 = 0$ is equivalent to Equation (11) of \citet{solerstatic} if the substitutions $L_{\rm e}^+ \to \frac{L-\lp}{2} - z_0$ and $L_{\rm e}^- \to \frac{L-\lp}{2} + z_0$ are performed in their expression. + Also for vo=0. Equation (14)) is similar to Equation (17) of Joarder&Roberts(1992) and Equation (A5) of Oliveretal.(1993) obtained in Cartesian geometry.," Also for $v_0 = 0$, Equation \ref{eq:disper}) ) is similar to Equation (17) of \citet{joarder} and Equation (A5) of \citet{oliverslab} obtained in Cartesian geometry." + We have solved Equation (14)) by standard numerical techniques., We have solved Equation \ref{eq:disper}) ) by standard numerical techniques. + The frequencies of the fundamental mode and of the lowest seven harmonics with respect to z are displayed as functions of time in Figure 2 for a particular set of parameters., The frequencies of the fundamental mode and of the lowest seven harmonics with respect to $z$ are displayed as functions of time in Figure \ref{fig:disper} for a particular set of parameters. + We find that the dispersion diagram is symmetric with the time when the thread is located at the center of the magnetic tube (denoted by a vertical dotted line in Fig. 2)), We find that the dispersion diagram is symmetric with the time when the thread is located at the center of the magnetic tube (denoted by a vertical dotted line in Fig. \ref{fig:disper}) ) + as point of symmetry., as point of symmetry. + The fundamental mode and the first harmonic are smooth functions of time., The fundamental mode and the first harmonic are smooth functions of time. + The other harmonics displayed in Figure 2 show a complicated set of couplings and avoided crossings., The other harmonics displayed in Figure \ref{fig:disper} show a complicated set of couplings and avoided crossings. + The reason for this behavior ts that the fundamental mode and the first harmonie correspond to oscillations of the flux tube because both the prominence and the evacuated parts of the tube are disturbed., The reason for this behavior is that the fundamental mode and the first harmonic correspond to oscillations of the flux tube because both the prominence and the evacuated parts of the tube are disturbed. + On the contrary. high harmonies correspond to modes more confined within one of these regions.," On the contrary, high harmonics correspond to modes more confined within one of these regions." + Thus. thecollection of modes and their properties are similar to those studied by Joarder(1992) and Oliveretal.(1993) in slab geometry.," Thus, thecollection of modes and their properties are similar to those studied by \citet{joarder} and \citet{oliverslab} in slab geometry." +" From hereon we restrict our analysis to the fundamental mode of oscillation, whose frequency 1s the lowest order solution to Equation (149)."," From hereon we restrict our analysis to the fundamental mode of oscillation, whose frequency is the lowest order solution to Equation \ref{eq:disper}) )." + To obtain an approximation to the frequency. we perform a Taylor expansion of Equation (14)) and neglect terms with O(ur) and higher orders in c.," To obtain an approximation to the frequency, we perform a Taylor expansion of Equation \ref{eq:disper}) ) and neglect terms with $\mathcal{O} \left( \omega^4 \right)$ and higher orders in $\omega$." + The following expression is obtained The effect of the flow is contained in the denominator of the right-hand side of Equation (15))., The following expression is obtained The effect of the flow is contained in the denominator of the right-hand side of Equation \ref{eq:freq}) ). + We see that the effect of the flow on the frequency is more complicated than a simple Doppler shift., We see that the effect of the flow on the frequency is more complicated than a simple Doppler shift. + There are two reasons that cause this dependence., There are two reasons that cause this dependence. + On the one hand. our model is à complicated structure in the sense that only the dense prominence material is moving.," On the one hand, our model is a complicated structure in the sense that only the dense prominence material is moving." + It is well known that à wave propagating in a uniform magnetic tube with a constant siphon flow ts affected by a constant Doppler shift of the frequency due to the flow., It is well known that a wave propagating in a uniform magnetic tube with a constant siphon flow is affected by a constant Doppler shift of the frequency due to the flow. + However. the effect of the flow Is not so simple in. more complicated configurations.," However, the effect of the flow is not so simple in more complicated configurations." + Even in the case of a flux tube with a constantflow within the tube but no flow in the exterior of the tube the wave frequencies suffer corrections due to the flow that are not simple frequency shifts (see.e.g..Nakartakov& 2003)..," Even in the case of a flux tube with a constantflow within the tube but no flow in the exterior of the tube the wave frequencies suffer corrections due to the flow that are not simple frequency shifts \citep[see, e.g.,][]{nakaroberts,terra}. ." + Our configuration is very different from the typical uniform magnetic flux tube, Our configuration is very different from the typical uniform magnetic flux tube +Iu a uniform deusitv sphere. the scale height 77=x and the rght-haud side of equation vanishes.,"In a uniform density sphere, the scale height $H = \infty$ and the right-hand side of equation vanishes." + Its left-hand side (eq [18]|] can benefit from the following decomposition.," Its left-hand side (eq \ref{eq:seperatepsi}] ]) can benefit from the following decomposition, = _1 (x_1) _2(x_2), with $\psi_i$ satisfying _i _i + K^2 _i = 0." + and dy is a constant introduced when we separate variables.," Here the differential operator ${\cal D}_i$ is _i = ] -, and $K$ is a constant introduced when we separate variables." + This result was first obtained by aud its solutions ire called “Bryan's inodes', This result was first obtained by and its solutions are called 'Bryan's modes'. + Iu fact. the solutions to ey and c» are the associated Legendre polvuouials.," In fact, the solutions to $\psi_1$ and $\psi_2$ are the associated Legendre polynomials." + Requiring ce to be finite at the rotation axis Gey= 1). we fud ey aud c»tobe the same spherical harmonic of the first kind1972): (4= with ( being an integer. K?=(((|1) and the Poe)variable wv taken over the ranges 44C[yl]. andorC|prqr]. respectively.," Requiring $\psi$ to be finite at the rotation axis $x_1 = 1$ ), we find $\psi_1$ and $\psi_2$tobe the same spherical harmonic of the first kind: $\psi_1 = +\psi_2 = P_\ell^m(x)$ with $\ell$ being an integer, $K^2 = +\ell(\ell+1)$, and the variable $x$ taken over the ranges $x_1 \in +[\mu,1]$, and $x_2 \in [-\mu,\mu]$, respectively." +" We explicitly require that eye,=gi)CoGcoqi) so the cigceutunction needs ouly one normalization coustaut."," We explicitly require that $\psi_1 (x_1 = +\mu) = \psi_2 (x_2 = \mu)$ so the eigenfunction needs only one normalization constant." + The following boundary conditions apply., The following boundary conditions apply. + First. at the equator (te= 0). even-parity modes satisfv ," First, at the equator $x_2 = 0$ ), even-parity modes satisfy = 0, while odd-parity modes satisfy = 0." +Properties of the Legendre polynomials require that (6|av) to be an even integer in the former case. and odd iu the latter.," Properties of the Legendre polynomials require that $(\ell+m)$ to be an even integer in the former case, and odd in the latter." + Second. c4 is finite at the polar axis (ry= 1).," Second, $\psi_1$ is finite at the polar axis $x_1 =1$ )." + The munerical equivalent to this statement is best realized by introducing a variable g; which is related to c; as , The numerical equivalent to this statement is best realized by introducing a variable $g_i$ which is related to $\psi_i$ as _i (x_i) = g_i (x_i). +This variable satisfies (eq. [20)) (, This variable satisfies (eq. \ref{eq:psii}) ) ( +1-4 iadig E| 52| A6 92epu| Reeularity,"1- x_i^2) - 2x_i (|m|+1) + ^2 g_i = 0, where $\lambda^2 = K^2 - |m|(|m|+1) = \ell(\ell+1)-|m|(|m|+1)$." + 52.∣∣↽↽ of the cigeufuuction atay =1then translates iuto a boundary coucditiou, Regularity of the eigenfunctionat $x_1 = 1$ then translates into a boundary condition. +" mΠω""", = g_1. + Oi solutious show that near the rotation axis. gy approaches a constant. while c4 approaches zero (f [n]> 0).," Our solutions show that near the rotation axis, $g_1$ approaches a constant, while $\psi_1$ approaches zero (if $|m| > 0$ )." + Tn this problem. the ceieeufunction can be solved iudepeudeutlv of the cigeuvalue µ.," In this problem, the eigenfunction can be solved independently of the eigenvalue $\mu$." + So to determine H. we need one more boundary condition.," So to determine $\mu$, we need one more boundary condition." + We euforce the physical condition that there is vacumun outside the planetary surface (r= 1) and therefore pressure perturbation at the surface las to bezero.," We enforce the physical condition that there is vacuum outside the planetary surface $r=1$ ), and therefore pressure perturbation at the surface has to bezero." +Written in a convenient form of óp/p=ο1989). this corresponds to (using eq.|12]],"Written in a convenient form of $\delta p/\rho = 0$, this corresponds to (using eq.\ref{eq:xi2}] ]" +| audignoring the colmpressional terni). bep r- Piven = S6," andignoring the compressional term), = _1 = - _1 ) = - g _r = 0." +" We relate £. to c using equation (15).. as well as relations prescuted in Appeudix A.. So requiringo £,,=0 at the surface (ry= μον ο)= μ) is equivalent to requiring that _ ΚΙΝ"," We relate $\xi_r$ to $\psi$ using equation , as well as relations presented in Appendix \ref{sec:coordinate}, , So requiring $\xi_r = 0$ at the surface $x_1 = \mu$ or $|x_2| = \mu$ ) is equivalent to requiring that = - , = - [x_2] . ." +" We relate £. to c using equation (15).. as well as relations prescuted in Appeudix A.. So requiringo £,,=0 at the surface (ry= μον ο)= μ) is equivalent to requiring that _ ΚΙΝ)"," We relate $\xi_r$ to $\psi$ using equation , as well as relations presented in Appendix \ref{sec:coordinate}, , So requiring $\xi_r = 0$ at the surface $x_1 = \mu$ or $|x_2| = \mu$ ) is equivalent to requiring that = - , = - [x_2] . ." +"efficient winding up and amplification of the magnetic field frozen into the gas via the kinematic dynamo In order to better quantify the amplification of the field, we also plot the distribution of the magnetic field along the line passing through the cluster center.","efficient winding up and amplification of the magnetic field frozen into the gas via the kinematic dynamo In order to better quantify the amplification of the field, we also plot the distribution of the magnetic field along the line passing through the cluster center." + This is shown in the left panel of Figure 8., This is shown in the left panel of Figure 8. + The color coding of the curves is the same as in Figure 2., The color coding of the curves is the same as in Figure 2. + The runs with cooling boost the field by over two orders of magnitude beyond the amplification seen in the non-radiative cases., The runs with cooling boost the field by over two orders of magnitude beyond the amplification seen in the non-radiative cases. + The top horizontal line denotes the physical field at the initial redshift (2= 20) and the bottom one is for the value of the field that would result from cosmological expansion down to z=0 without any structure formation effects., The top horizontal line denotes the physical field at the initial redshift $z=20$ ) and the bottom one is for the value of the field that would result from cosmological expansion down to $z=0$ without any structure formation effects. + These reference levels show that the magnetic field in clusters is boosted beyond the initial physical field by over an order of magnitude., These reference levels show that the magnetic field in clusters is boosted beyond the initial physical field by over an order of magnitude. + The boost in the strength of the magnetic field in the adiabatic case is ~103 compared to the value a uniform magnetic field would have at z=0., The boost in the strength of the magnetic field in the adiabatic case is $\sim 10^4$ compared to the value a uniform magnetic field would have at $z=0$. +" The magnitude of this amplification is consistent with that obtained by ?,, ? and in our earlier work where the numerical resolution was higher."," The magnitude of this amplification is consistent with that obtained by \citet{dolag99}, \citet{dolag02} and in our earlier work \citep{bruggen05b} where the numerical resolution was higher." + Simple (?)scaling arguments show that this field strength exceeds the field expected from the magnetic flux freezing arguments., Simple scaling arguments show that this field strength exceeds the field expected from the magnetic flux freezing arguments. +" Specifically, for"," Specifically, for" +We have elected. to select our sample based. on ον in the rest-frame of the radio source.,We have elected to select our sample based on $\nu S_{\nu}$ in the rest-frame of the radio source. + HE we select with a [lux limit of (7iLimi at a selection frequency. i. in the rest-frame of the radio source. this is equivalent to a limit of in the observed frame.," If we select with a flux limit of $(\nu_{\rm s} S_{\nu_{\rm s}})_{\rm Limit}$ at a selection frequency $\nu_{\rm s}$ in the rest-frame of the radio source, this is equivalent to a limit of in the observed frame." +" We work out 55,54,.y using a fit to the racio spectrum described below.", We work out $S_{[ \nu_{\rm s}/(1+z) ]}$ using a fit to the radio spectrum described below. + Cancelling out f£ our selection then reduces to imposing a redshift-dependent flux density limit: We argue that this is a more physically useful way of defining a sample as the selection. is based. directly on power emitted at low frequency rather than on. [lux received per unit frequency., Cancelling out $\nu_{\rm s}$ our selection then reduces to imposing a redshift-dependent flux density limit: We argue that this is a more physically useful way of defining a sample as the selection is based directly on power emitted at low frequency rather than on flux received per unit frequency. + There are of course many allernative selection methods. one could. think of (for example integrating the spectrum in the rest. [rame over some larger frequeney range). but. this criterion has the advantage of being simple to implement.," There are of course many alternative selection methods one could think of (for example integrating the spectrum in the rest frame over some larger frequency range), but this criterion has the advantage of being simple to implement." + For the NEC samples we have used a selection criterion of, For the NEC samples we have used a selection criterion of +and Fy remains finite. we can confirm the increase of A? in logarithmic seale of Z and the paraboloidal shape of field lines similar with equation (57)) in (he asymptotic region.,"and $F_{2}$ remains finite, we can confirm the increase of $\mm^{2}$ in logarithmic scale of $Z$ and the paraboloidal shape of field lines similar with equation \ref{par}) ) in the asymptotic region." + llowever. il is clear [rom equation (53)) that AP decreases as P increases under a fixed Z.," However, it is clear from equation \ref{constb}) ) that $\mm^{2}$ decreases as $\y$ increases under a fixed $Z$." + The energy. conversion becomes less efficient on outer flux surfaces., The energy conversion becomes less efficient on outer flux surfaces. + Further we note that the solution (53)) fails to give a real value οἱ AFP in the range 0«| under a fixecl Z., Further we note that the solution \ref{constb}) ) fails to give a real value of $\mm^2$ in the range $\y \ll 1$ under a fixed $Z$. + such a region should be covered by inner [lux surfaces corresponding to small V. aud the previous solution (54)) with /xV should be used there.," Such a region should be covered by inner flux surfaces corresponding to small $\Psi$, and the previous solution \ref{model}) )with $k\propto\Psi$ should be used there." + One mav consider a more realistic dependence of & on V., One may consider a more realistic dependence of $k$ on $\Psi$. + Then. a smooth change of M7 from equation (54)) to equation (53)) will be allowed as V increases in the range 0«VWp. It is sure (hat according (o a choice of the integrals of motion as functions of V we can obtain various evolutionary models of energy conversion in jet flows. which may show more complicated behaviors dillerent from the simplest solution (54)).," Then, a smooth change of $\mm^2$ from equation \ref{model}) ) to equation \ref{constb}) ) will be allowed as $\Psi$ increases in the range $0 < \Psi < \Psi_{0}$, It is sure that according to a choice of the integrals of motion as functions of $\Psi$ we can obtain various evolutionary models of energy conversion in jet flows, which may show more complicated behaviors different from the simplest solution \ref{model}) )." + ILIowever. we would like to emphasize (he kev result obtained here that a rough ecquipartition between magnetic ancl kinetic energies is realized at the radius £2—RLF [ar bevond the light evlincler radius Ry. and the subsequent logaritlimic increase of kinetic energy goes on al larger radii >RE.," However, we would like to emphasize the key result obtained here that a rough equipartition between magnetic and kinetic energies is realized at the radius $R \sim R_{\rm L}E$ far beyond the light cylinder radius $R_{\rm L}$, and the subsequent logarithmic increase of kinetic energy goes on at larger radii $R \gg R_{\rm L}E$." + This potentiality of MIID acceleration will be robust at least under the boundary condition for inner Παν surfaces V.—0 such that the rest-mass energy loading rate is given by fhxWY to keep (he total specilic enerey 7 very huge., This potentiality of MHD acceleration will be robust at least under the boundary condition for inner flux surfaces $\Psi \rightarrow 0$ such that the rest-mass energy loading rate is given by $k \propto \Psi$ to keep the total specific energy $E$ very large. + 1 so. we can claim that there exists the critical scale given by 2=REE lor conversion of Povnting flux injected in jet flows. whichis important for discussing a prompt emission of radiation owing to dissipation of kinetic energv of bulk motion.," If so, we can claim that there exists the critical scale given by $R = R_{\rm L}E$ for conversion of Poynting flux injected in jet flows, whichis important for discussing a prompt emission of radiation owing to dissipation of kinetic energy of bulk motion." + We have presented a parametric representation of Alfvénn Mach number ÀJ by the ratio € of poloidal electric to toroidal magnetic field strength. to avoid the troublesome analvsis of the critical condition at the [ast-inagnetosonic point.," We have presented a parametric representation of Alfvénn Mach number $M$ by the ratio $\xi$ of poloidal electric to toroidal magnetic field strength, to avoid the troublesome analysis of the critical condition at the fast-magnetosonic point." + Then. from the poloidal wind equation we have easily derived. (rans-Las(-maenetosonic solutions including (le parameter € defined as a smooth function along a fiekd line.," Then, from the poloidal wind equation we have easily derived trans-fast-magnetosonic solutions including the parameter $\xi$ defined as a smooth function along a field line." + If the parametric function € is asvimptotically larger than the eritical value £.. the flux surface have been shown to be confined within a finite radius .=re.," If the parametric function $\xi$ is asymptotically larger than the critical value $\xi_{\rm c}$, the flux surface have been shown to be confined within a finite radius $x=x_{\rm c}$." + Otherwise. (he dvnamical fine-tuning of£ have been required for acceleration to highly relativistic bulk speeds.," Otherwise, the dynamical fine-tuning of $\xi$ have been required for acceleration to highly relativistic bulk speeds." + To determine the parametric function €. we have also given the approximated form of the Grad-Shalranov. equation applied to jets ejected with a very large total specific energy. £ and confined within a very sinall opening angle of order of 17 £.," To determine the parametric function $\xi$, we have also given the approximated form of the Grad-Shafranov equation applied to jets ejected with a very large total specific energy $E$ and confined within a very small opening angle of order of $1/E$ ." + Acceleration of outflows in generic models with the integrals of motion E. Oy and / variously dependent on V has not been analvzed in this paper.," Acceleration of outflows in generic models with the integrals of motion $E$ , $\Omega_{F}$ and $k$ variously dependent on $\Psi$ has not been analyzed in this paper." + The comparison of the two, The comparison of the two +"when the MACHO alert system was running were the events 4, 13, 14, and 15 which have the follow-up photometry, which has been used to confirm the microlensing interpretation of these events.","when the MACHO alert system was running were the events 4, 13, 14, and 15 which have the follow-up photometry, which has been used to confirm the microlensing interpretation of these events." +" Thus, it is [air to consider these 4 events as a randomly selected sub-sample of the events passing criteria A. My final sub-category of ""confirmed"" events are those event with red clump giant source stars with achromatic light curves, and events 1 and 25 fall in this category."," Thus, it is fair to consider these 4 events as a randomly selected sub-sample of the events passing criteria A. My final sub-category of “confirmed"" events are those event with red clump giant source stars with achromatic light curves, and events 1 and 25 fall in this category." +" Event 1, of course, was the first event published by MACHO (Alcocketal.1993)., and its light curve was observed with a high enough S/N to be convincing to most astronomers, as well as to the MACHO team itself; which referred to it as the “gold plated event.”"," Event 1, of course, was the first event published by MACHO \citep{macho-nat93}, and its light curve was observed with a high enough S/N to be convincing to most astronomers, as well as to the MACHO team itself, which referred to it as the “gold plated .""" +" This event does show a significant deviation [rom the standard light curve, which is explained by a binary lens model (DominikAlcocketal. 2000a).."," This event does show a significant deviation from the standard light curve, which is explained by a binary lens model \citep{dominik94,rhie_dm96,macho-binaries}." +" Event 25 is less dramatic, but it is classified as confirmed event because of its position on the red clump giant region of the color magnitude diagram and the fact that brightening is achromatic. ("," Event 25 is less dramatic, but it is classified as confirmed event because of its position on the red clump giant region of the color magnitude diagram and the fact that brightening is achromatic. (" +The chromatic brightening of a red clump star could be due to blending with a variable main sequence star.),The chromatic brightening of a red clump star could be due to blending with a variable main sequence star.) +" High confidence in the microlensing interpretation of the events with red clump giant source stars is jusufied MACHO results for Galactic bulge microlensing, where of ~lO red clump giant source stars that triggered the MACHO alert system with an apparently achromatic brightening in a single image were later classified as microlensing events based upon excellent fits to microlensing models using the MACHO survey data as well as follow-up observations from GMAN (Alcocketal.1997c) and MPS 1999)."," High confidence in the microlensing interpretation of the events with red clump giant source stars is justified MACHO results for Galactic bulge microlensing, where of $\sim 40$ red clump giant source stars that triggered the MACHO alert system with an apparently achromatic brightening in a single image were later classified as microlensing events based upon excellent fits to microlensing models using the MACHO survey data as well as follow-up observations from GMAN \citep{macho-95blg30} and MPS \citep{mps-98smc1}." +", The situation is quite dillerent [or main sequence source stars.", The situation is quite different for main sequence source stars. +" It has long been noüced that there is a class of main sequence stars in the LMC, sometimes referred to as “bumpers”, with variability characterisucs that are similar to microlensing (Aubourgetal.1995;Beaulieu1996;Alcock1996a).."," It has long been noticed that there is a class of main sequence stars in the LMC, sometimes referred to as “bumpers"", with variability characteristics that are similar to microlensing \citep{eros-lowmass, eros-lmc-Be, macho-lmc1}." +" That is. they exhibit relatively brief brightening episodes, but spend most of the üme at a constant brightness."," That is, they exhibit relatively brief brightening episodes, but spend most of the time at a constant brightness." +" MACHO and EROS attempted to prevent these variable stars [rom contaminating their microlensing samples by applying cuts to the color-magnitude diagrams of the source stars (Aubourgetal.1995:Lasserre2000;Afonsoetal.2003a;Alcock1996a,1997b, 2000b).. but the evidence indicates that variable stars that have contaminated previous LMC microlensing candidate samples have properues similar to the brighter main sequence stars that are removed [rom the microlensing search analysis (Beaulieuetal.1996;Keller2002)."," MACHO and EROS attempted to prevent these variable stars from contaminating their microlensing samples by applying cuts to the color-magnitude diagrams of the source stars \citep{eros-lowmass,eros-lmc-tau,eros-smc-tau, +macho-lmc1,macho-lmc2,macho-lmc5.7}, but the evidence indicates that variable stars that have contaminated previous LMC microlensing candidate samples \citep{eros12-spec,eros2-var} have properties similar to the brighter main sequence stars that are removed from the microlensing search analysis \citep{eros-lmc-Be,blue-var}." +. So. it appears that the contamination of microlensing event samples by variable stars is only a serious problem for source stars on or near the main sequence.," So, it appears that the contamination of microlensing event samples by variable stars is only a serious problem for source stars on or near the main sequence." + With the classification of microlensing event candidates listed in Table 5 and described in Sec. 2.1..," With the classification of microlensing event candidates listed in Table \ref{tab-that} and described in Sec. \ref{sec-confirm}," +" it is possible to estimate the probability that the events classified as unconfirmed (events 6, 7, 8, 18, and 21) are actually microlensing events,"," it is possible to estimate the probability that the events classified as unconfirmed (events 6, 7, 8, 18, and 21) are actually microlensing events." +" Of 13 microlensing candidates, candidates, + have been observed in follow-up mode with much higher precision photometry, which confirms the microlensing interpretation."," Of 13 microlensing candidates, candidates, 4 have been observed in follow-up mode with much higher precision photometry, which confirms the microlensing interpretation." +" Since the selection of these 4 events was independent any other factor that might relate to event classification, these 4 events are a [air sub-sample of the full sample of 13 events."," Since the selection of these 4 events was independent any other factor that might relate to event classification, these 4 events are a fair sub-sample of the full sample of 13 events." + This is not the case for the two red clump giant, This is not the case for the two red clump giant +Another potentially important contamination elfect is due to the presence of background: ancl foreground. field: stars that contaminate the binary region. of the CMD.,Another potentially important contamination effect is due to the presence of background and foreground field stars that contaminate the binary region of the CMD. +. This is particularly important in OC's which contains à small number of stars and are generally located: closer to the Galactic plane with respect to GC's., This is particularly important in OCs which contains a small number of stars and are generally located closer to the Galactic plane with respect to GCs. + Fortunately. our observations cover in most cases the entire cluster extension. providing a good sampling of the field population surrounding cach cluster.," Fortunately, our observations cover in most cases the entire cluster extension, providing a good sampling of the field population surrounding each cluster." + As ai further check. we used the Galactic model of Robin et al. (," As a further check, we used the Galactic model of Robin et al. (" +2003).,2003). + A catalog covering an area of 1 square degree around each cluster center has been retrived., A catalog covering an area of 1 square degree around each cluster center has been retrived. + After scaling for the different field. of view. the number of field stars estimated bv the two approaches turns out to be very similar (ANpaaNN<10 )).," After scaling for the different field of view, the number of field stars estimated by the two approaches turns out to be very similar $\Delta +N_{field}/N_{field}<10$ )." + According to both methods the number of field stars in the core of all the OC's of our sample never exceeds. 10., According to both methods the number of field stars in the core of all the OCs of our sample never exceeds 10. + Therefore. whenever possible. we used as reference field CMD the one obtained in the external region. of our images.," Therefore, whenever possible, we used as reference field CMD the one obtained in the external region of our images." + For NGC2243.. whose observations covers only a small fraction of the cluster extent. the Galactic mocdel of Robin et al. (," For NGC2243, whose observations covers only a small fraction of the cluster extent, the Galactic model of Robin et al. (" +2003) has been used.,2003) has been used. + In this last case. each synthetic field star has been added as an artificial star to the original 2 and V. frames and the photometric analysis has been performed.," In this last case, each synthetic field star has been added as an artificial star to the original $B$ and $V$ frames and the photometric analysis has been performed." + This task accounts for the cllects of incompleteness. photometric errors ancl blending.," This task accounts for the effects of incompleteness, photometric errors and blending." + In this section we describe the adopted a»proach to estimate the fraction of binaries with gq>@sie., In this section we describe the adopted approach to estimate the fraction of binaries with $q>q_{min}$. + Lhis quantity represents a lower limit to the cluster. binary [raction., This quantity represents a lower limit to the cluster binary fraction. + To derive an accurate estimate ο this quantity we simply assumed thataff the objects ofthe ALSsample are single MS stars ancl ondy the objects of the binarysample are binary stars., To derive an accurate estimate of this quantity we simply assumed that the objects of the $MS~sample$ are single MS stars and the objects of the $binary~sample$ are binary stars. + This assumption is equivalent to assume that all binary systems in the cluster have q2(uis., This assumption is equivalent to assume that all binary systems in the cluster have $q>q_{min}$. + Since the selection boxes defined above cover two different regions of the CALD with different: completeness levels. we assigned. to cach star [ing in the ALS)semple and in the binarysample a completeness factor e; according to its magnitude (Bailvn et al.," Since the selection boxes defined above cover two different regions of the CMD with different completeness levels, we assigned to each star lying in the $MS~sample$ and in the $binary~sample$ a completeness factor $c_{i}$ according to its magnitude (Bailyn et al." + 1992)., 1992). +" Then. the corrected number ofη stars in. cach sample CN372;reales and NHbinoles ) has been calculated as We repeated the same procedure for the samples of artificial single stars and field stars. obtaining the quantities Nipsm"" and Αιunbbin Doroe the artificialpstarssample and NiField and NIAbin for the fieldstarssample: Then. we caleulated the normalization factor 5 for the artificialstarssample by comparing the number ofstars in the AIS selection box The minimum binary fraction. corrected for field stars"," Then, the corrected number of stars in each sample $N_{MS}^{obs}$ and $N_{bin}^{obs}$ ) has been calculated as We repeated the same procedure for the samples of artificial single stars and field stars, obtaining the quantities $N_{MS}^{art}$ and $N_{bin}^{art}$ for the $artificial~stars~sample$ and $N_{MS}^{field}$ and $N_{bin}^{field}$ for the $field~stars~sample$; Then, we calculated the normalization factor $\eta$ for the $artificial~stars~sample$ by comparing the number ofstars in the MS selection box The minimum binary fraction, corrected for field stars" +"model, the merger dynamics, the star formation during the interaction, and the properties of the merger remnant.","model, the merger dynamics, the star formation during the interaction, and the properties of the merger remnant." +" Although our model for the Local Group presents its past, current, and future evolution, the only way to test its validity is by comparing it to the empirical data on its present-day state."," Although our model for the Local Group presents its past, current, and future evolution, the only way to test its validity is by comparing it to the empirical data on its present-day state." +" As we focus primarily on the evolution of the two largest galaxies in the Local Group, the Milky Way and Andromeda, it is only the relative separation and motion of these two galaxies that can be compared to data."," As we focus primarily on the evolution of the two largest galaxies in the Local Group, the Milky Way and Andromeda, it is only the relative separation and motion of these two galaxies that can be compared to data." +" As mentioned in both and §refsec:results,, the separation and line-of-sight velocity of the Milky Way and Andromeda are currently measured to be 780 kpc (??,andreferencestherein),, and -120 !(?), respectively."," As mentioned in both \\ref{sec:intro} and \\ref{sec:results}, the separation and line–of–sight velocity of the Milky Way and Andromeda are currently measured to be 780 kpc \citep[][and references therein]{McC05, Rib05}, and -120 \citep{BT}, respectively." +" The proper motion of Andromeda perpendicular to our line of sight is less well constrained, but current estimates suggest that it is 200 (??).."," The proper motion of Andromeda perpendicular to our line of sight is less well constrained, but current estimates suggest that it is $<200$ \citep{P01,Loeb05}." +" Figures 5 and 6 present the direct comparisons between the observational constraints and our model, and clearly demonstrate that it is viable."," Figures \ref{fig:csep} and \ref{fig:crelvel} present the direct comparisons between the observational constraints and our model, and clearly demonstrate that it is viable." +" In particular, at a time of 4.7 Gyr after the start of the simulation (close to the present cosmic time) the separation between the Milky Way and Andromeda is 780 kpc, while the relative radial velocity is 135 and the tangential velocity is 132s!."," In particular, at a time of $4.7$ Gyr after the start of the simulation (close to the present cosmic time) the separation between the Milky Way and Andromeda is 780 kpc, while the relative radial velocity is 135 and the tangential velocity is 132." +". While the tangentials velocity is well within the limits currently favored, the line-of-sight velocity is slightly larger than (but within 2.0 c of) the observations."," While the tangential velocity is well within the limits currently favored, the line–of–sight velocity is slightly larger than (but within 2.0 $\sigma$ of) the observations." +" Even though a number of our model assumptions can be manipulated to reduce these values, e.g., the initial separation and eccentricity of the fiducial orbit, we note that our model is a good fit to the velocity when the separation between the Milky Way and Andromeda is larger than 780 kpc."," Even though a number of our model assumptions can be manipulated to reduce these values, e.g., the initial separation and eccentricity of the fiducial orbit, we note that our model is a good fit to the velocity when the separation between the Milky Way and Andromeda is larger than 780 kpc." + Given the observational uncertainties in these values we feel that there are likely to be a large number of models that can simultaneously fit all the data within its 2c error bars., Given the observational uncertainties in these values we feel that there are likely to be a large number of models that can simultaneously fit all the data within its $\sigma$ error bars. +" As mentioned in refssec:other,, the model described up to this point is one of twenty Local Group models that we have simulated."," As mentioned in \\ref{ssec:other}, the model described up to this point is one of twenty Local Group models that we have simulated." +" Since the primary conclusion of this paper, involving the timescale for the eventual merger between the Milky Way and Andromeda, may be influenced by any number of our model assumptions, we explicitly show the separation between the Milky Way and Andromeda and therefore the time of the merger, for all of our models in Figure 7.."," Since the primary conclusion of this paper, involving the timescale for the eventual merger between the Milky Way and Andromeda, may be influenced by any number of our model assumptions, we explicitly show the separation between the Milky Way and Andromeda and therefore the time of the merger, for all of our models in Figure \ref{fig:csep_ensemble}." + Figure 7 demonstrates several interesting features., Figure \ref{fig:csep_ensemble} demonstrates several interesting features. + Nearly all of the models provide a similar outcome for time when the two galaxies make their first passage (ensemble average and standard deviation are T=2.8+0.5 Gyr)., Nearly all of the models provide a similar outcome for time when the two galaxies make their first passage (ensemble average and standard deviation are $T=2.8\pm0.5$ Gyr). + The same holds true for the final merger time (T=5.4+0.4 Gyr)., The same holds true for the final merger time $T=5.4\pm0.4$ Gyr). + We also note that these average values are slightly larger than one provided by the model described up to this point., We also note that these average values are slightly larger than one provided by the model described up to this point. +" This highlights a general trend, namely the mergers that start with a larger separation and have to traverse a longer path through the intragroup medium, usually (but not always) have a quicker merger dynamics."," This highlights a general trend, namely the mergers that start with a larger separation and have to traverse a longer path through the intragroup medium, usually (but not always) have a quicker merger dynamics." +" Regardless of the relatively small differences between merger times in these models, they are all completely coalesced by 6.2 Gyr from today."," Regardless of the relatively small differences between merger times in these models, they are all completely coalesced by 6.2 Gyr from today." + In the following section we will argue that this result is a direct byproduct of our inclusion of an intragroup medium., In the following section we will argue that this result is a direct byproduct of our inclusion of an intragroup medium. +both low and high latitudes.,both low and high latitudes. +" An explanation of such quasi-biennial behavior has been put forward in terms of two different types of dynamo operating at different depths (Benevolonskaya1998a,b)."," An explanation of such quasi-biennial behavior has been put forward in terms of two different types of dynamo operating at different depths \citep{Benevolonskaya1998a, Benevolonskaya1998b}." +". Elsewhere (Saar&Brandenburg 2002),, it has been possible to identify shorter secondary periods in the activity cycles of some stars and it is conceivable that asteroseismology may be able to detect such effects in data sets which will become available, for example, from the recently launched Kepler satellite (Christensen-Dalsgaardal. 2008)."," Elsewhere \citep{Saar2002}, it has been possible to identify shorter secondary periods in the activity cycles of some stars and it is conceivable that asteroseismology may be able to detect such effects in data sets which will become available, for example, from the recently launched $Kepler$ satellite \citep{Christensen2008}." +". In spite of the known behavior of the proxies, this is the first time that the quasi-biennial variability has been noted in seismic data."," In spite of the known behavior of the proxies, this is the first time that the quasi-biennial variability has been noted in seismic data." +" Furthermore, the signature of the two-year signal in the activity index was previously restricted to times of moderate to high solar activity."," Furthermore, the signature of the two-year signal in the activity index was previously restricted to times of moderate to high solar activity." +" For the first time, we are seeing this short-term variability at low solar activity."," For the first time, we are seeing this short-term variability at low solar activity." +" To investigate this further, a sine wave was fitted to the frequency shifts observed after 1985 April (see Figure 1))."," To investigate this further, a sine wave was fitted to the frequency shifts observed after 1985 April (see Figure \ref{figure[flux shifts]}) )." +" The sine wave took the form where δ is the time in years after 1985 April 22, which is the start date of the first dd time series."," The sine wave took the form where $\delta t$ is the time in years after 1985 April 22, which is the start date of the first d time series." + The A; coefficients are given in Table 1.., The $A_i$ coefficients are given in Table \ref{table[A coefficients]}. + The sine wave was calculated using a weighted least-squares fit to the unsmoothed frequency shifts., The sine wave was calculated using a weighted least-squares fit to the unsmoothed frequency shifts. +" In equation 1,, the first collection of terms accounts for the sine wave structure of the frequency shifts."," In equation \ref{equation[sine wave]}, the first collection of terms accounts for the sine wave structure of the frequency shifts." + The second and third terms account for an offset which linearly decreases with time., The second and third terms account for an offset which linearly decreases with time. + We have determined the residuals between the best-fitting sine wave and the observed frequency shifts and the results are plotted in Figure 3.., We have determined the residuals between the best-fitting sine wave and the observed frequency shifts and the results are plotted in Figure \ref{figure[residuals]}. +" Flux residuals were also determined between a sine wave, which was scaled in amplitude using the linear fit between the flux and the frequency shifts, and the F107."," Flux residuals were also determined between a sine wave, which was scaled in amplitude using the linear fit between the flux and the frequency shifts, and the $\rm +F_{10.7}$." +" Clearly, there is a lot of structure in both sets of observed residuals and since ~2002 the frequency-shift residuals are quite substantial in size."," Clearly, there is a lot of structure in both sets of observed residuals and since $\sim2002$ the frequency-shift residuals are quite substantial in size." + Large discrepancies between the two sets of residuals are clearly evident., Large discrepancies between the two sets of residuals are clearly evident. +" A periodogram of the data from the last two cycles shows significant periods of about two and three years with greater than confidence, but the phase of the signal is not locked to that of the"," A periodogram of the data from the last two cycles shows significant periods of about two and three years with greater than confidence, but the phase of the signal is not locked to that of the" +cooling rather than heating through the intermediate temperatures.,cooling rather than heating through the intermediate temperatures. +" The current simplified implementation of clump heating does not permit a proper comparison, which is left for future work."," The current simplified implementation of clump heating does not permit a proper comparison, which is left for future work." +" Additionally, three-dimensional simulations are required for a detailed analysis of the shape of the clumps as they are stretched perhaps leading to morphologies resembling filaments (?)."," Additionally, three-dimensional simulations are required for a detailed analysis of the shape of the clumps as they are stretched perhaps leading to morphologies resembling filaments \citep{murray04}." +" This emission, in H4 and line and continuum emission of the intermittent X-ray temperature gas, may allow more accurate comparisons of this model with the observed profiles in cluster cores."," This emission, in $H_\alpha$ and line and continuum emission of the intermittent X-ray temperature gas, may allow more accurate comparisons of this model with the observed profiles in cluster cores." + Observations in the Perseus cluster (NGC 1275) (??) show a complicated structure of Πα filaments and blobs.," Observations in the Perseus cluster (NGC 1275) \citep{conselice01,fabian08} show a complicated structure of $H_\alpha$ filaments and blobs." +" The typical masses of these features are 109—105Ms, consistent with the allowed mass range for clumps in DBO08, and with the distribution predicted by our model 6))."," The typical masses of these features are $10^6-10^8\msun$, consistent with the allowed mass range for clumps in DB08, and with the distribution predicted by our model )." + We note that this result depends on the initial mass of the clumps - a free parameter here., We note that this result depends on the initial mass of the clumps - a free parameter here. + The consistency of this prediction with observation is an indication that our choice of initial mass of 1095M is reasonable., The consistency of this prediction with observation is an indication that our choice of initial mass of $10^8\msun$ is reasonable. +" ? invoked strong magnetic fields to stabilize the filaments for cosmological times, such that their age can match that of the observed radio bubbles."," \citet{fabian08} invoked strong magnetic fields to stabilize the filaments for cosmological times, such that their age can match that of the observed radio bubbles." +" Our heating model suggests instead that these filaments are constantly being destroyed, as new clumps enter the cluster core, get stretched and destroyed, and create new filaments."," Our heating model suggests instead that these filaments are constantly being destroyed, as new clumps enter the cluster core, get stretched and destroyed, and create new filaments." + The projected filling factor of these structures approaches unity within the innermost 10kpc and it drops outwards (?).., The projected filling factor of these structures approaches unity within the innermost $10\kpc$ and it drops outwards \citep{conselice01}. + Such a behaviour is predicted by our model ϐ))., Such a behaviour is predicted by our model ). +" Πα emission in other clusters have been reported by ?,, who found that the cold gas has velocities at random directions rather than a coherent radial cooling-flow pattern."," $H_\alpha$ emission in other clusters have been reported by \citet{heckman89}, who found that the cold gas has velocities at random directions rather than a coherent radial cooling-flow pattern." + This kinematics could be interpreted as clumps oscillating in and out at the vicinity of the BCG., This kinematics could be interpreted as clumps oscillating in and out at the vicinity of the BCG. +" Structures of neutral gas are also seen in the Virgo Cluster by the ALFALFA 21cm survey (??) showing evidence for neutral gas arranged in clumps, with masses as low as the detection limit of 2x10’Mo, sometimes with no optical counterparts."," Structures of neutral gas are also seen in the Virgo Cluster by the ALFALFA 21cm survey \citep{giovanelli07,kent07} showing evidence for neutral gas arranged in clumps, with masses as low as the detection limit of $2\times 10^7\msun$, sometimes with no optical counterparts." + Another prediction of this model is the power of turbulence that is produced in the ICM., Another prediction of this model is the power of turbulence that is produced in the ICM. + When the clump velocities are subsonic with respect to, When the clump velocities are subsonic with respect to +we treated cach quadrant as a separate image and made a esky level matching” at the end of the basic data reduction.,we treated each quadrant as a separate image and made a “sky level matching” at the end of the basic data reduction. +" As mentioned before. due to our observational strategy. we have two tvpes of images: science images. which are the Con-group"" ones. and night ον Mats. which are the other three ""oll-group"" images. in cach exposure."," As mentioned before, due to our observational strategy, we have two types of images: science images, which are the “on-group” ones, and night sky flats, which are the other three “off-group” images, in each exposure." +" Each science and sky Hat image was cut in four quadrants and the BLAS correction was applied to cach of the new ""quadrant images”.", Each science and sky flat image was cut in four quadrants and the BIAS correction was applied to each of the new “quadrant images”. +" Due to the non photometric conditions. some of the ""olf-Eroup images presented sky. patterns and could not be used to produce the night sky Latfields."," Due to the non photometric conditions, some of the “off-group” images presented sky patterns and could not be used to produce the night sky flatfields." +" Those sky. patterns were sometimes also present in the 7on-group"" images which could not be corrected by the Datfields and could not be used to produce our final image.", Those sky patterns were sometimes also present in the “on-group” images which could not be corrected by the flatfields and could not be used to produce our final image. + After selecting the useful images. a combination of night sky Mat. to correct for the large scale CCD response and for CCD illumination. and twilight flat. to correct for the individual pixel sensitivity was applied to the science frames.," After selecting the useful images, a combination of night sky flat, to correct for the large scale CCD response and for CCD illumination, and twilight flat, to correct for the individual pixel sensitivity was applied to the science frames." + The quacrants were rejoined in a single image with matched sky levels., The quadrants were rejoined in a single image with matched sky levels. + Ehe sky matching consists in measuring the dillerence in sky level along both sides of the matching region and correcting the sky level by a constant. so that no sky level dillerence is left and πο step- structure is present in the image.," The sky matching consists in measuring the difference in sky level along both sides of the matching region and correcting the sky level by a constant, so that no sky level difference is left and no step-like structure is present in the image." + Fhis correction was at the order of a few counts. while the sky. level is of the order of some thousands of counts.," This correction was at the order of a few counts, while the sky level is of the order of some thousands of counts." + However. this small variation would have an important ellect in our analysis.," However, this small variation would have an important effect in our analysis." + Images were registered. and. combined producing a final image for each eroup in cach filter., Images were registered and combined producing a final image for each group in each filter. + Since the nights when the data were taken were not photometric. we need to calibrate our images hy comparing them to published data by 2..," Since the nights when the data were taken were not photometric, we need to calibrate our images by comparing them to published data by \citet{men92}." + But because the ? image sizes are quite small (272 3/5). we could not measure a useful number of stars in common for the calibration (the few ones available in these fields were. in most cases. saturated. in our images).," But because the \citet{men92} image sizes are quite small $2\farcs2~\times~3\farcs5$ ), we could not measure a useful number of stars in common for the calibration (the few ones available in these fields were, in most cases, saturated in our images)." + We. therefore. decided to use the calibrated profiles of the galaxies themselves. in order to find the zero points for the images.," We, therefore, decided to use the calibrated profiles of the galaxies themselves, in order to find the zero points for the images." + We mached the instrumental profiles we obtained for cach galaxy with those presented. in. ?.. excluding the central parts. which are usually contaminated by seeing effects. and the outer parts of the galaxy. which are allected by the sky subtraction.," We matched the instrumental profiles we obtained for each galaxy with those presented in \citet{men92}, excluding the central parts, which are usually contaminated by seeing effects, and the outer parts of the galaxy, which are affected by the sky subtraction." + Even with the excluded regions. several arescconds of the surface brightness profiles where used in the fit.," Even with the excluded regions, several arcseconds of the surface brightness profiles where used in the fit." + The RAIS of the fitting was quite small (tvpical IMS = 0.05 magnitudes) but realistic errors are larger (ol the order of 0.1 to 0.2 magnitudes) since they depend on the reliability ofthe zero point for the literature data., The RMS of the fitting was quite small (typical RMS = 0.05 magnitudes) but realistic errors are larger (of the order of 0.1 to 0.2 magnitudes) since they depend on the reliability of the zero point for the literature data. + Since the IGL is an extended. very low surface brightness structure (usually less than above the night sky level) many instrumental effects like Uatlelding. scattered. light and CCD bleeding. among others. can contaminate the signal.," Since the IGL is an extended, very low surface brightness structure (usually less than above the night sky level) many instrumental effects like flatfielding, scattered light and CCD bleeding, among others, can contaminate the signal." + Therefore. very. good illumination corrections ancl short exposure times to avoid bleeding are necessary.," Therefore, very good illumination corrections and short exposure times to avoid bleeding are necessary." + Aosides the instrumental effects. some astronomical ones are important in this kind of analysis.," Besides the instrumental effects, some astronomical ones are important in this kind of analysis." + The dimming of the IGL bv the lisht from the objects in the image. like member ealaxies and stars. which need to be mocelec and subtracted from the image. is one major “problem” for this kind of study.," The dimming of the IGL by the light from the objects in the image, like member galaxies and stars, which need to be modeled and subtracted from the image, is one major “problem” for this kind of study." + Also a very accurate sky subtraction is needed for the detection and analysis of the LOL., Also a very accurate sky subtraction is needed for the detection and analysis of the IGL. + To deal with this kind of requirement. we applied a wavelet-basecl technique. the OV.WAV. package (?).. in our analysis. as shown in ?..," To deal with this kind of requirement, we applied a wavelet-based technique, the WAV package \citep{epi03}, , in our analysis, as shown in \citet{dar05}." + ThisNT technique does a multiscale analysis that uses the wavelet transform. ancl is able to separate the structures in the image by their characteristic sizes with no information (?7)..," This technique does a multiscale analysis that uses the wavelet transform, and is able to separate the structures in the image by their characteristic sizes with no information \citep{bij95,sta98}." + Since the information in astronomical images is organized hicrarchically (stars projected onto galaxies. that are projected onto a larger structure like the LGL and all projected. onto the sky. brightness level). this technique is very well suited. for our goals.," Since the information in astronomical images is organized hierarchically (stars projected onto galaxies, that are projected onto a larger structure like the IGL and all projected onto the sky brightness level), this technique is very well suited for our goals." + This method. was already applied by other authors to the same kind. of studs (0.9.1)," This method was already applied by other authors to the same kind of study \citep[{\em e.g.} +." + The main procedure is the following., The main procedure is the following. +" The images are deconvolved. into wavelet. coellicients.. which will contain information of a given size (2"" pixels. where n is the index of the wavelet coellicient - 7)—0.1.2.3....)."," The images are deconvolved into wavelet coefficients, which will contain information of a given size $2^n$ pixels, where $n$ is the index of the wavelet coefficient - $n=0, 1, 2, 3, ...$ )." + A source in the image. when deconvolve in wavelet coellicients. has a representation in each of the' coelflicients that depends on the shape and size of this object.," A source in the image, when deconvolved in wavelet coefficients, has a representation in each of the coefficients that depends on the shape and size of this object." + Also the noise. present in the image. has a represenation in the cdilferent wavelet coellicients.," Also the noise present in the image, has a representation in the different wavelet coefficients." + The representation of the noise is analvzed and the representation of t1ο signal is detected. in each cocllicient., The representation of the noise is analyzed and the representation of the signal is detected in each coefficient. + These. detections in cdillerent cocllicients are interconnected. defining. the detected. objects and each detected object is reconstrucec and separately analyzed.," These detections in different coefficients are interconnected, defining the detected objects and each detected object is reconstructed and separately analyzed." + The noise present in astronomical images is mostly dominated by small scale components., The noise present in astronomical images is mostly dominated by small scale components. + As the characteristic size of the wavelet coefTicients increases. the representation of the noise looses intensity.," As the characteristic size of the wavelet coefficients increases, the representation of the noise looses intensity." + With this behaviour of the noise representation. working in wavelet space. we are able to detect large structures. with very low surface brightness. with high confidence levels.," With this behaviour of the noise representation, working in wavelet space, we are able to detect large structures, with very low surface brightness, with high confidence levels." + Our simulations have shown that we are able to detect at a S-a-cletection level in. wavelet space. large. low surface brightness structures. that have only S/N=0.1 in real space (?)..," Our simulations have shown that we are able to detect at a$\sigma$ -detection level in wavelet space, large, low surface brightness structures, that have only $S/N = 0.1$ in real space \citep{dar05}." + After the reconstruction of each object. in an iterative process that. models anc subtracts the detected: sources from the image. we are able to recompose the IGL component and the galaxies component for each. group. in each band independently. ancl perform our analysis. which will be described below.," After the reconstruction of each object, in an iterative process that models and subtracts the detected sources from the image, we are able to recompose the IGL component and the galaxies component for each group, in each band independently, and perform our analysis, which will be described below." + A more detailed. description of the ΛΑΑλ and the simulations on the detection of IGL can be found in ?.., A more detailed description of the WAV and the simulations on the detection of IGL can be found in \citet{dar05}. +" We have re-calculated the group crossing time (/,.) and mass to light ratio (AL/L). previously calculated in ?.. using the concordance Cosmology parameters. since the originalones were calculated using 44)=100kms4Mpe+ and 1.0."," We have re-calculated the group crossing time $t_c$ ) and mass to light ratio $M/L$ ), previously calculated in \citet{hic92}, , using the concordance cosmology parameters, since the originalones were calculated using $H_0 = 100~{\rm km~s^{-1}~Mpc^{-1}}$ and $\Omega_M=1.0$ ." +embecddings in the parabolic framework (see [6.7] for similar type inequalities. and [1.2.3.8.9.10.12] for. various. elliptic. versions).,"embeddings in the parabolic framework (see \cite{IJM08, IM09} for similar type inequalities, and \cite{BG80, +BW80, Engler, KOT02, KOT03, KT00, Og03} for various elliptic versions)." +". By cousicdering. functions. /""E€W3-2m.m(Ov)+ defined: on the bounded domaiu. we have thefollowing estimate (see [5.Theorem1.2])): The differeut uorms of f appearing in inequalities (1.1)) aud (1.2)) are fiuite since where C7/7yO” Dp.is the parabolien Hólklera. space that willn be defined. later."," By considering functions $f\in W^{2m,m}_{2}(\O_{T})$ defined on the bounded domain we have thefollowing estimate (see \cite[Theorem +1.2]{Ibrahim09}) ): The different norms of $f$ appearing in inequalities \ref{Ib:eq1}) ) and \ref{Ib:eq2}) ) are finite since where $C^{\g,\g/2}$ is the parabolic Höllder space that will be defined later." + Moreover. itn isn easy to check that g bounded aud contiuuous.," Moreover, it is easy to check that $g$ bounded and continuous." +" The purpose of. this⋅ paper to show that the condition⋅⋅ f⋅=Vg€_WSunam, (vector-valued. case). or [€W377 (scalar-valued case) can be relaxed."," The purpose of this paper to show that the condition $f = \nabla g\in +W^{2m,m}_{2}$ (vector-valued case), or $f\in W^{2m,m}_{2}$ (scalar-valued case) can be relaxed." + Indeed. inequalities (1.1)) aud (1.2)) can be applied ∙≓⋉−−⋅↽≻∣⋅⋅⋅ ⋅ ⋅ .DE ↕∩⋜≹∖∖↽∐⇂≺↵↥⋅∢∙↥⋜↕⊳∖⊳∖∩↥∐∩∐≼⇂≺↵↕⋅∢∙∩∐↕⊔⋯∩⋃⊳∖↥⋯∐∙⋃∩∐⊳∖∙∕∶⊽⋅↙∕∕⊂∁⊽−⋅∩∕∖↸∕∖↥↸↜∖⇁≺↵∢∙↕∩↥⋅−∖⊽⋜↕∐∐↵≺⇂∢∙⋜≹↜∖≺↵⋝⋅∩↕⋅ ↓∎∐⋅⊳∖↕↕∐≺↵∩∐↵⋯↥⊳∖↕∐≺↲↥∎∩∐∩∖∖↽↥∐∑≟," Indeed, inequalities \ref{Ib:eq1}) ) and \ref{Ib:eq2}) ) can be applied to a wider class of Höllder continuous functions $f = \nabla g\in C^{\g,\g/2}$, $0<\g<1$ (vector-valued case), or $f\in C^{\g,\g/2}$ (scalar-valued case)." +∶⋅ ⋅ ⋅ ⋅ ∙∕∕⊂∁⊽⋯−↸↜⊳∖∢∙⋜↕↥⋜⋃⋅−∖⊽⋜↕∐∐↵≺⇂∢∙⋜↕↜∖↩⋝⋅↽⋡⊏∩∣⋈↵⋯∩↓⋅≺↲↥↽≻↓⋅≺," To be more precise, we now state the main results of this paper." +↵∢∙↥⊳∖≺↵⋅∖∖↽≺↵∐∩∖∖↽⊳∖↕⋜↕↕≺↵↕∐≺↵⋯⋜↕∐⊔⋅≺↵⊳∖⋃∐⊳∖∩↥↕↥∐⊳∖↥↽≻⋜↕↥↽≻≺↵↕⋅⋅⋃⇂⊔⋅ The second theorem deals with functions defined ou the bounded domain Qy., Ourfirst theorem is the following:The second theorem deals with functions defined on the bounded domain $\O_T$ . + We notice that inequalities (1. 1)) aud (1.5)) directly imply with the akl of the embecdiugs (1.3))) (1.1)) aud (1.2))., We notice that inequalities \ref{Ib:eq4}) ) and \ref{Ib:eq5}) ) directly imply (with the aid of the embeddings \ref{Ib:eq3}) )) \ref{Ib:eq1}) ) and \ref{Ib:eq2}) ). + Thisjs paper is isorgauizedorganized as follfollows., This paper is organized as follows. + InSection ????.. we eive the definitious of some basic fuuctioualfunctiona spaces used throughout this paper.," In Section \ref{sec2}, we give the definitions of some basic functional spaces used throughout this paper." + Section ?? is devoted to the proofs of the main results., Section \ref{sec3} is devoted to the proofs of the main results. + Let O be an open subset of Ε 1; , Let $\mathcal{O}$ be an open subset of $\R^{n+1}$ . +"A generic element z€E+ has the form 2=(r./) with rer4)€ E""."," A generic element $z\in \R^{n+1}$ has the form $z=(x,t)$ with $x=(x_{1},\ldots, +x_{n})\in \R^{n}$ ." + We begiu bydefiniug parabolic Hóllder spaces C> 77.," We begin bydefining parabolic Höllder spaces $C^{\g,\g/2}$ ." +"rom defined as in Li, Mo Gao (2008) effect).","from $z_{1/2,t_1}$ defined as in Li, Mo Gao (2008) $1.14\sigma$ effect)." + Stellar and 21/21halo ages are indistinguishable between (1.140random and parent samples for higher local densities., Stellar and halo ages are indistinguishable between random and parent samples for higher local densities. +" Furthermore, the mass-weighted stellar ages show different degrees of correlation with the ormation time of the DM halo at different global environments."," Furthermore, the mass-weighted stellar ages show different degrees of correlation with the formation time of the DM halo at different global environments." + Fig., Fig. +" 11 depicts the coherence as a function of DM halo age colours indicate a higher density of galaxies in the age vs. coherence(darker plane) for the two subsamples Ry; and Ryo for low ocal densities, ow."," \ref{fig:fig2co} depicts the coherence as a function of DM halo age (darker colours indicate a higher density of galaxies in the age vs. coherence plane) for the two subsamples $R_{V1}$ and $R_{V2}$ for low local densities, $\rho_{LOW}$." +" The solid line shows the average coherence, with its correspondingpt error bars shown in red dashed lines."," The solid line shows the average coherence, with its corresponding error bars shown in red dashed lines." +" The bottom panels show the normalised distributions of DM halo assembly and stellar mass weighted ages corresponding to the samples shown in the upper panels (black solid and red dotted lines, respectively), and DM halo assembly ages for the random counterpart samples (long-dashed lines)."," The bottom panels show the normalised distributions of DM halo assembly and stellar mass weighted ages corresponding to the samples shown in the upper panels (black solid and red dotted lines, respectively), and DM halo assembly ages for the random counterpart samples (long-dashed lines)." +" As can be seen, the DM halo assembly ages in both subsamples tend to be slightly older than in their corresponding random for and 0.760 for Ry2)."," As can be seen, the DM halo assembly ages in both subsamples tend to be slightly older than in their corresponding random subsamples $1.14\sigma$ for $R_{V1}$, and $0.76\sigma$ for $R_{V2}$ )." +" Haloes in void subsampleswalls do (1.140not show Ry, differences in their residingwith to haloes inside significant the stellar ages in respectvoid walls do show a voids;slightly however,clearer tendency towards populationso"," Haloes residing in void walls do not show significant differences in their ages with respect to haloes inside voids; however, the stellar populations in void walls do show a slightly clearer tendency towards older ages." +"lder ages. when the samples are restricted to fixed local and Finally,densities, the vs. coherence correlation is apparently global erased ageleast there is no significant detection of a completely"," Finally, when the samples are restricted to fixed local and global densities, the age vs. coherence correlation is apparently completely erased (at least there is no significant detection of a correlation)." + This (atwould indicate that the origin of the age-coherence correlation).correlation observed for the full sample of is mostly due to an underlying DM halo mass vs. coherence galaxiesrelation., This would indicate that the origin of the age-coherence correlation observed for the full sample of galaxies is mostly due to an underlying DM halo mass vs. coherence relation. +" In this paper we have studied modulations of galaxy colours and SF rates at different fixed large-scalelocal environments, within the framework of a ACDM model."," In this paper we have studied large-scale modulations of galaxy colours and SF rates at different fixed local density environments, within the framework of a $\Lambda$ CDM model." + In order densityto parameterise a global large-scale environment we used distances to landmarks given by massive haloes and large-scale voids in the simulation., In order to parameterise a global large-scale environment we used distances to landmarks given by massive haloes and large-scale voids in the simulation. +" Also, given the advantage of the knowledge of the underlying properties of galaxies and their host DM haloes, we were able to study the cause for such modulations."," Also, given the advantage of the knowledge of the underlying properties of galaxies and their host DM haloes, we were able to study the cause for such modulations." + We now summarise the main results of this study., We now summarise the main results of this study. + Our main conclusion is that the large-scale environment affects the galaxy mostly via variations in the mass function., Our main conclusion is that the large-scale environment affects the galaxy population mostly via variations in the mass function. +" there population to be a slight correlation between However,and appearsstructure, an effect that could be tested using assembly large-scaleobservational datasets providing a new, innovative way to largeplace further constraints on our current"," However, there appears to be a slight correlation between assembly and large-scale structure, an effect that could be tested using large observational datasets providing a new, innovative way to place further constraints on our current" +"This group includes the objects with well-defined decontaminated CMD sequences (Figs. 6,, 7,,","This group includes the objects with well-defined decontaminated CMD sequences (Figs. \ref{fig:6}, , \ref{fig:7}, ," +" and 8)) with relatively high values of the parameter Nj,, as well as King-like RDPs (Fig. 11))."," and \ref{fig:8}) ) with relatively high values of the parameter $N_{1\sigma}$, as well as King-like RDPs (Fig. \ref{fig:11}) )." + For young OCs we also built colour-colour diagrams (Fig. 9))., For young OCs we also built colour-colour diagrams (Fig. \ref{fig:9}) ). + The astrophysical parameters could be measured for these objects (Tables 4 and 5))., The astrophysical parameters could be measured for these objects (Tables \ref{tab4} and \ref{tab5}) ). +" The previously unknown OCs are FSR 735, FSR 807, FSR 812, FSR 826, FSR 852, FSR 904, FSR 941, FSR 953, and FSR 955."," The previously unknown OCs are FSR 735, FSR 807, FSR 812, FSR 826, FSR 852, FSR 904, FSR 941, FSR 953, and FSR 955." + We also derived parameters for the previously catalogued OCs Cz 22 and NGC2234., We also derived parameters for the previously catalogued OCs Cz 22 and NGC2234. +" KKC1 was confirmed as an OC, but the parameters of this object will be analysed in a forthcoming paper."," KKC1 was confirmed as an OC, but the parameters of this object will be analysed in a forthcoming paper." + In Fig., In Fig. + 6 we present the Jx(J—H) and Jx(J—Ks) CMDs extracted from a region R=5’ centred on the optimised coordinates of the confirmed OC FSR 953 (top-panel)., \ref{fig:6} we present the $J\times(J-H)$ and $J\times(J-K_s)$ CMDs extracted from a region $R=5'$ centred on the optimised coordinates of the confirmed OC FSR 953 (top-panel). + In the middle panels we show the comparison field corresponding to a ring with the same area as the central region., In the middle panels we show the comparison field corresponding to a ring with the same area as the central region. + In the bottom panels we show the decontaminated CMDs with the 500 Myr Padova isochrones fitted., In the bottom panels we show the decontaminated CMDs with the 500 Myr Padova isochrones fitted. +" Figure 7 show Jx(J—Κε) CMDs for the confirmed young OCs FSR 812, FSR 826, FSR 807, FSR 904, and FSR 955."," Figure \ref{fig:7} show $J\times(J-K_s)$ CMDs for the confirmed young OCs FSR 812, FSR 826, FSR 807, FSR 904, and FSR 955." +" These objects present important populations of PMS stars and, therefore, we also use isochrones of Siess,Dufour&Forestini (2000)."," These objects present important populations of PMS stars and, therefore, we also use isochrones of \citet{Siess00}." +". To examine differential reddening, we include reddening vectors computed with the 2MASS ratios for visual absorptions in the range Ay=0 to 5."," To examine differential reddening, we include reddening vectors computed with the 2MASS ratios for visual absorptions in the range $A_V=0$ to $5$." + We present in Fig., We present in Fig. +" 8 the Jx(J—H) CMDs for the remaining confirmed OCs FSR. 735, FSR 852, NGC2234, Cz 22 and FSR 941."," \ref{fig:8} the $J\times(J-H)$ CMDs for the remaining confirmed OCs FSR 735, FSR 852, NGC2234, Cz 22 and FSR 941." +" In Fig. 11,,"," In Fig. \ref{fig:11}," +" we present the RDPs of these objects, and in Table 5 we show the derived structural parameters."," we present the RDPs of these objects, and in Table \ref{tab5} we show the derived structural parameters." + We show in Table 6 integrated colours and magnitudes for confirmed OCs., We show in Table \ref{tab6} integrated colours and magnitudes for confirmed OCs. + Both FSR 904 and FSR 941 present a conspicuous excess over the King-like profile in the innermost RDP bin., Both FSR 904 and FSR 941 present a conspicuous excess over the King-like profile in the innermost RDP bin. +" This cusp has been detected in post-core collapse globular clusters (Trager,King&Djorgovski,1995) and some Gyr-old OCs, such as NGC3960 (Bonatto&Bica,2006) and LK 10 (Bonatto&Bica,2009a)."," This cusp has been detected in post-core collapse globular clusters \citep{Trager95} and some Gyr-old OCs, such as NGC3960 \citep{Bonatto06} and LK 10 \citep{Bonatto09a}." +. It has been attributed to advanced dynamical evolution., It has been attributed to advanced dynamical evolution. +" With ~500 Myr of age, FSR 941 is probably a core- OC."," With $\sim500$ Myr of age, FSR 941 is probably a core-collapsed OC." +" However, some very young OCs also present a cusp, probably as a consequence of molecular cloud fragmentation and/or star formation effects."," However, some very young OCs also present a cusp, probably as a consequence of molecular cloud fragmentation and/or star formation effects." +" In this context, we can mention NGC2244 (Bonatto&Bica, 2009b),, NGC6823 (Bica,Bonatto&Dutra,2008),, Pismis 5 and NGC1931 (Bonatto&Bica,2009c),, and FSR, 198 (Camargo,Bonatto&Bica,2009) as examples of young OCs with a central cusp."," In this context, we can mention NGC2244 \citep{Bonatto09b}, NGC6823 \citep{Bica08b}, Pismis 5 and NGC1931 \citep{Bonatto09c}, and FSR 198 \citep{Camargo09} as examples of young OCs with a central cusp." + FSR 904 presents a similar effect., FSR 904 presents a similar effect. + Withametal.(2008) presented the INT/WFC Photometric Ha Survey of the Northern Galactic Plane (IPHAS)., \citet{Witham08} presented the INT/WFC Photometric $H\alpha$ Survey of the Northern Galactic Plane (IPHAS). +" This catalogue contains positions and photometry for 4853 sources with Ha excess (seealso,Drewetal., 2005)."," This catalogue contains positions and photometry for $4853$ sources with $H\alpha$ excess \citep[see also,][]{Drew05}." +". The Ha emission is linked to several events in star clusters as stellar winds, T Tauri stars, Herbig-Haro objects, planetary nebulae and HII region associations."," The $H\alpha$ emission is linked to several events in star clusters as stellar winds, T Tauri stars, Herbig-Haro objects, planetary nebulae and HII region associations." +" FSR 807 presents 2 Ha-excess sources within the cluster radius and 3 in the neighbourhood field (J053635.21+31503.0 at 1.3’ of the cluster centre, J053631.98+314939.6 at 1.7’, J053641.46+314627.8 at 5.1’, J053619.82+314356.2 at 8.0’, and J053619.58+314353.6 at 8.06’) and FSR 812 presents 1 object (J053817.88+ 313934.8) at 4.5’ of the cluster centre."," FSR 807 presents 2 $H\alpha$ -excess sources within the cluster radius and 3 in the neighbourhood field $J053635.21+31503.0$ at 1.3' of the cluster centre, $J053631.98+314939.6$ at 1.7', $J053641.46+314627.8$ at 5.1', $J053619.82+314356.2$ at 8.0', and $J053619.58+314353.6$ at 8.06') and FSR 812 presents 1 object $J053817.88+313934.8$ ) at $4.5'$ of the cluster centre." + All objects are also present in the emission-line star catalogue of Kohoutek&Wehmeyer(1999)., All objects are also present in the emission-line star catalogue of \citet{Kohoutek99}. +. We indicate the 2 Ha emitters in FSR 807 CMD Fig. 7.., We indicate the $2$ $H\alpha$ emitters in FSR $807$ CMD Fig. \ref{fig:7}. +" The objects in this group have, in general, less defined decontaminated CMD sequences than those of the confirmed OCs, which is consistent with the lower level of the integrated N,, parameter."," The objects in this group have, in general, less defined decontaminated CMD sequences than those of the confirmed OCs, which is consistent with the lower level of the integrated $N_{1\sigma}$ parameter." + The irregular RDPs make difficult King’s law fits., The irregular RDPs make difficult King's law fits. +"By“uncertain cluster”, we mean those objects with a CMD that may suggest a cluster, but not the RDP (or the contrary).","By“uncertain cluster”, we mean those objects with a CMD that may suggest a cluster, but not the RDP (or the contrary)." +" We suggest that deeper photometry, proper motions and other methods be"," We suggest that deeper photometry, proper motions and other methods be" +but when galaxies do cross the η=2 threshold. it is always [rom m«2 to mz2. i.e. [from spheroid-like to clisk-like.,"but when galaxies do cross the $n = 2$ threshold, it is always from $n < 2$ to $n > 2$, i.e., from spheroid-like to disk-like." + ‘The results are Listed in the third and fourth columns of‘Table 3, The results are listed in the third and fourth columns ofTable \ref{tab:stack_results}. +" At 2tiun. wemeasureadislinetsiqnal fromboth populations. wilh σ and 3-0 detections [rom the clisk-like ancl spheroid-like sources. respectively,"," At $\micro$ m, we measure a distinct signal from both populations, with $\sigma$ and $\sigma$ detections from the disk-like and spheroid-like sources, respectively." + At longer wavelengths. for the disk-like population we detect signals with ercater significance than that of the combined catalog. between 25-07 and. 6.5-o. in cach FIRsubmim band: whereas for the spheroid-like population we find a much weaker signal. with four bands consistent with While the error on the stacks is Gaussian. the uncertainty associated with the average rest-frame Lyin is dominated by. the width of the redshift cstribution. which is not Gaussian.," At longer wavelengths, for the disk-like population we detect signals with greater significance than that of the combined catalog, between $\sigma$ and $\sigma$, in each FIR/submm band; whereas for the spheroid-like population we find a much weaker signal, with four bands consistent with While the error on the stacks is Gaussian, the uncertainty associated with the average rest-frame $L_{\rm FIR}$ is dominated by the width of the redshift distribution, which is not Gaussian." + Thus. for estimating 7. Lyin. and SER (Section ??)). we choose to adopt the median value and interquartile range. as they best reflect. the asvmmetric shape of the redshift cstribution. which ultimately determines the uncertainty of our measurement.," Thus, for estimating $T$, $L_{\rm FIR}$, and SFR (Section \ref{sec:SEDs_and_SFRs}) ), we choose to adopt the median value and interquartile range, as they best reflect the asymmetric shape of the redshift distribution, which ultimately determines the uncertainty of our measurement." + For reference we also quote the Gaussian uncertainties., For reference we also quote the Gaussian uncertainties. + We anticipate that the lower Gaussian errors on T. Lyin. and SER. for the spheroid-like subset exceed. the lower bound of the interquartile range. and rellect the elevated. level of uncertainty in our measurement.," We anticipate that the lower Gaussian errors on $T$, $L_{\rm FIR}$, and SFR for the spheroid-like subset exceed the lower bound of the interquartile range, and reflect the elevated level of uncertainty in our measurement." + Mo.~—243 the observed qunibandprobesrest framewarclengthso qum. which in addition to PALL emission. is where the {6Iavleigh-Jeans tail of stellar emission lies.," At $z\sim2.3$ the observed $\micro$ m band probes rest-frame wavelengths of $\micro$ m, which in addition to PAH emission, is where the Rayleigh-Jeans tail of stellar emission lies." + Ht is then plausible that the emission. we find in this band may be entirely attributed to stellar emission., It is then plausible that the emission we find in this band may be entirely attributed to stellar emission. + Since our detection o£ PATI and dust emission. particularly for the spheroid population. is supported strongly by this data point (eiven its high signal-to-noise). in this section. we investigate the contribution of pure stellar emission to the observed unbeand.," Since our detection of PAH and dust emission, particularly for the spheroid population, is supported strongly by this data point (given its high signal-to-noise), in this section, we investigate the contribution of pure stellar emission to the observed $\micro$ m band." + Any additional emission. not attributed (ο stellar emission is likely associated with PALL emission. which in turn is accompanied by longer wavelength dust. emission wt we have inferred. our SERS from.," Any additional emission not attributed to stellar emission is likely associated with PAH emission, which in turn is accompanied by longer wavelength dust emission that we have inferred our SFRs from." + We note that this emission mav be associated with either star forming regions or evolving main sequence stars (such as AGB and TP-ACD stars)., We note that this emission may be associated with either star forming regions or evolving main sequence stars (such as AGB and TP-AGB stars). +" Typically. emission. associated with star formation clominates in most galaxies (even those with moclerate SERS) as the infrared lis£ht-to-mass ratio is up to three orders of magnitude larger for a simple stellar population (SSP) of 10'7vrs compared to an SSP""n of. 10Goves(2).. where sFEP-ACGD' emission would be most significant."," Typically, emission associated with star formation dominates in most galaxies (even those with moderate SFRs) as the infrared light-to-mass ratio is up to three orders of magnitude larger for a simple stellar population (SSP) of $10^7\, \rm yrs$ compared to an SSP of $10^9\, \rm yrs$ where TP-AGB emission would be most significant." + To investigate the contribution of pure stellar emission in our sample. we calculate the predicted unobserved flnrdensities Ομ ΟΠ μηοου 22))," To investigate the contribution of pure stellar emission in our sample, we calculate the predicted $\micro$ m observed flux densities from stellar population synthesis models using redshifts and stellar massesas per our catalog (see Section \ref{sec:mass_selected_catalog}) )." + M cop foldinglimeo ALyr. IET sle," We opt to use a galaxy template with solar metallicity and an exponentially declining SFR with an e-folding time of Myr, generated with the stellar population synthesis code PEGASE.2." +llaremissionorevolvingmain sequencestarsisnolinceluded. asthesourccofnon stellaremissional jum is assumed to be the same as that of the FIR. emission.," Output from non-stellar emission or evolving main-sequence stars is not included, as the source of non-stellar emission at $\micro$ m is assumed to be the same as that of the FIR emission." + Assuming a formation redshift of z=9. the galaxy ages range from 1.5 to Gyr and the predicted un f licedensitiesduetostellaremissionrangefrom lA o]y. depending primarily on the galaxy redshift.," Assuming a formation redshift of $z=9$, the galaxy ages range from 1.5 to Gyr and the predicted $\micro$m flux densities due to stellar emission range from 1.3 to $\micro$ Jy, depending primarily on the galaxy's redshift." + For eacho8.[8 stacked sample. we find. the predicted.s. contamination per galaxy from stellar emission is 3.0. 2.9. and LJ yfortheentiresample. thedish likeandspheroid likepopulal ions. respectively.," For each stacked sample, we find the predicted contamination per galaxy from stellar emission is 3.0, 2.9, and $\micro$ Jy for the entire sample, the disk-like and spheroid-like populations, respectively." + Contribulingal mostly (see ‘Table 3)) to the observed qun f'icedenaitiesofthespherotdpopulationandlessthanb'Xtolheobscrved2- lux densities of the clisk-like and total sample. we conclude that. the mic-infrared observations (rest[rame pum )ineludedinouranalysisarcdominaledbynon sicllaremission(i.c.. dustand DALLemission )," Contributing at most (see Table \ref{tab:stack_results}) ) to the observed $\micro$ m flux densities of the spheroid population and less than to the observed $\micro$ m flux densities of the disk-like and total sample, we conclude that the mid-infrared observations (restframe $\micro$ m) included in our analysis are dominated by non-stellar emission (i.e., dust and PAH emission)." + The best-fit SED and interquartile range to the stacked values of the complete catalog are shown in the left panel of Figure5 3.. corresponding5 to a median (plus/minus Gaussian) interquartile} temperature of 7—29.131.6] II. luminosity of Ley;=6.2HA.8.0]10 L... and 63H4S.81] M. Fl," The best-fit SED and interquartile range to the stacked values of the complete catalog are shown in the left panel of Figure \ref{fig:sed}, corresponding to a median (plus/minus Gaussian) [interquartile] temperature of $T= +29.4^{+1.4}_{-0.8}~[27.3, 31.6]$ K, luminosity of $L_{\rm +FIR}=6.2^{+1.1}_{-1.0}~[4.7, 8.0]\times 10^{11}$ $\rm L_{\sun}$, and ${\rm SFR}=63^{+11}_{-11}~[48, 81]$ $\rm M_{\sun}$ $^{-1}$." + As a sanity check. we compare our modified blackbocdvy approximation to the best-fit template ofCIEO1.," As a sanity check, we compare our modified blackbody approximation to the best-fit template of." +. The purpose of this is simply to reassure ourselves that an exponential approximation on the Wien side of the thermal SED is not an unreasonable way to estimate the contribution to the bolometric luminosity short. of the SED peak. rather han an attempt to derive. SERs from fitting SED templates.," The purpose of this is simply to reassure ourselves that an exponential approximation on the Wien side of the thermal SED is not an unreasonable way to estimate the contribution to the bolometric luminosity short of the SED peak, rather than an attempt to derive SFRs from fitting SED templates." + Thus. for cach of the 101 templates. we approximate the stacked SED by taking the average of templates shifted to the redshift of cach galaxy in the catalog: this acts to smear out the otherwise highly- PALL region of the rest-frame SED probed. by the qunibend.," Thus, for each of the 101 templates, we approximate the stacked SED by taking the average of templates shifted to the redshift of each galaxy in the catalog; this acts to smear out the otherwise highly-variable PAH region of the rest-frame SED probed by the $\micro$ m band." +M'efitheresullinglemplatetoourpholomcetricpoiniswilhoulacco fill," We fit the resulting template to our photometric points without accounting for calibration uncertainties, color corrections, or correlations among bands." +emplaleisshownasa3 dol dashedlineinl'igure 3. andfallswellinsideourerrorregion.," The best-fit template is shown as a 3-dot-dashed line in Figure \ref{fig:sed}, and falls well inside our error region." + Llowerer thesk [illemplaleisspu SYM Jor 88% larger than our moclified blackbocdv estimate.," However, the SFR of the best-fit template is ${\rm SFR}= 87$ $\rm M_{\sun}$ $^{-1}$, or $\sim38$ larger than our modified blackbody estimate." + This overestimate likely arises because the fi with the CLEOL template does not. include the substantial correlations among bands (see Section ??)) which reduce the significance. of the combination of individual photometric points.," This overestimate likely arises because the fit with the CE01 template does not include the substantial correlations among bands (see Section \ref{sec:fitting}) ), which reduce the significance of the combination of individual photometric points." + We then separately fit the stacked. flux densities measurecl for clisk-like and spheroid-like galaxies., We then separately fit the stacked flux densities measured for disk-like and spheroid-like galaxies. + The best-fit’ moclifieck blackbody SED for the clisk-like population is shown in the center panel of Figure 3. ancl results in a median (plus/minus Gaussian) interquartile] temperature of Z7—32.(oy32.6(1oαιLU30:5.34.6] kts. luminosity of Lim=120[198Les)loth... and SER=122!?100.150] AL. .," The best-fit modified blackbody SED for the disk-like population is shown in the center panel of Figure \ref{fig:sed}, and results in a median (plus/minus Gaussian) [interquartile] temperature of $T = 32.6^{+1.0}_{-0.4}~[30.8, 34.6]$ K, luminosity of $L_{\rm +FIR}=12.0^{+1.4}_{-1.5}~[9.8, 14.8]\times 10^{11} \rm L_{\sun}$, and ${\rm SFR}= 122^{+15}_{-15}~[100, 150]$ $\rm +M_{\sun}$ $^{-1}$." + The best-fit CLOL template is also shown. and corresponds to a SE1tNE=142κ AL. Lο ," The best-fit CE01 template is also shown, and corresponds to a ${\rm SFR}= 142$ $\rm M_{\sun}$ $^{-1}$." +Likewise. the best-fit modified. blackbodsy SED for the spheroid-like population is shown in he right) panel of Figure 3.. and results in à median (plus/minus Caussian) ος Πο μμescepe generatedwiththestellarpopulationsqyisueeake 1η(2)JOmEpuüftranü]onLO Le.and SER=1429.20] AL. ὃν ," Likewise, the best-fit modified blackbody SED for the spheroid-like population is shown in the right panel of Figure \ref{fig:sed}, , and results in a median (plus/minus Gaussian) [interquartile] temperature of $T = +27.6^{+0.3}_{-7.6}~[24.2, 30.8]$ K, luminosity of $L_{\rm +FIR}=1.4^{+0.2}_{-0.8}~[0.9,2.0]\times 10^{11}~\rm L_{\sun}$ ,and ${\rm SFR}= 14^{+2}_{-8}~[9, 20]$ $\rm M_{\sun}$ $^{-1}$ ." +Note that the lower Gaussian errors exceed. the lower bound. of the interquartile range. thus rellecting the elevated level of uncertainty in our measurement.," Note that the lower Gaussian errors exceed the lower bound of the interquartile range, thus reflecting the elevated level of uncertainty in our measurement." + Once again. the best-fit CEOL template is shown. which corresponds to a SER= 16M; wef.," Once again, the best-fit CE01 template is shown, which corresponds to a ${\rm SFR}= 16$ $\rm +M_{\sun}$ $^{-1}$ ." + Finally. to check that contributions to the rest-frame SED from PALIs. which are hiehly variable. are not significantly inlluencing the best-fit result. we re-fit the," Finally, to check that contributions to the rest-frame SED from PAHs, which are highly variable, are not significantly influencing the best-fit result, we re-fit the" +also belongs to the category of highly polarized. quasars.,also belongs to the category of highly polarized quasars. + Significant optical Εαν variations in the source were first reported. by Lit (1972) over à time span of 5 vears., Significant optical flux variations in the source were first reported by Lü (1972) over a time span of $\sim$ 5 years. + The historical light curve of PISS 089 shows a large variation of AB — 5.4 mag during an outburst in 1948 after which it [aded by —2.2 mag within 9 davs (Liller Liller 1975)., The historical light curve of PKS $-$ 089 shows a large variation of $\Delta$ B = 5.4 mag during an outburst in 1948 after which it faded by $\sim$ 2.2 mag within 9 days (Liller Liller 1975). + Strong variations on LDV time m also have been reported for PINS UA eg.[20 AR = o) mag within 13 min. (," Strong variations on IDV time scales also have been reported for PKS $-$ 089; e.g., $\Delta$ R = 0.65 mag within 13 min. (" +"Xie οἱ ""ο AR = mae in nmn. ","Xie et 2001), $\Delta$ R = 2.0 mag in 42 min. (" +n el 22001). AVY = 1.68 mag in 60 min. (,"Dai et 2001), $\Delta$ V = 1.68 mag in 60 min. (" +Nie et m22002a).,Xie et 2002a). + In the optical LCs of this source. deep minima been observed. on dillerent. clays(e.g... Nic ct Ol: Dai et 22001: Nie et al.," In the optical LCs of this source, deep minima have been observed on different days (e.g., Xie et 2001; Dai et 2001; Xie et al." + 2002b) that nominally correspond. to a time scale of ~42 min. though no more than 3 such dips were ever seen in a single night so the evidence for a real periodicity is slight.," 2002b) that nominally correspond to a time scale of $\sim$ 42 min, though no more than 3 such dips were ever seen in a single night so the evidence for a real periodicity is slight." + Nonetheless. an eclipsing binary. black hole mocdel was to explain the occurrence of these minima (Wu et MM22005a).," Nonetheless, an eclipsing binary black hole model was proposed to explain the occurrence of these minima (Wu et 2005a)." +M This group has also claimed time sc between minima of 59 min (Nic et anotherEB22004)., This group has also claimed another possible time scale between minima of $\sim$ 89 min (Xie et 2004). + PNVery. recently. while it was being monitored by 1)Ammanco et ((209) reported detecting à rapid ganuna-ray [lare from PIs 1510. 089 in March. 2008 using the XGILE satellite.," Very recently, while it was being monitored by WEBT, D'Ammando et (2009) reported detecting a rapid gamma-ray flare from PKS $-$ 089 in March 2008 using the AGILE satellite." + We found significantD variations in the brightness5 of PKS 080 over a three month period of observations 110)., We found significant variations in the brightness of PKS $-$ 089 over a three month period of observations 10). + Even though there is not much cdillerence in the percentage variation in the magnitude of the source. (see ‘Table 4) in different bands. the colour variations are still significant (except for I).," Even though there is not much difference in the percentage variation in the magnitude of the source (see Table 4) in different bands, the colour variations are still significant (except for $-$ R)." + PISS 089 decayed from 16.1 to 17 magnitude in the B band during our observations. which is only —0.8 magnitude brighter than the faintest magnitude (Di; = reported in the historic LC of Liller Liller (1975): Ihence. we observed. the source in à [aint phase.," PKS $-$ 089 decayed from 16.1 to 17 magnitude in the B band during our observations, which is only $\sim$ 0.8 magnitude brighter than the faintest magnitude $_{mag}$ = 17.8) reported in the historic LC of Liller Liller (1975); hence, we observed the source in a faint phase." + The object BL Lac is the archetype of its class., The object BL Lac is the archetype of its class. + Observations over the past few decades have showed that its optical ancl radio emissions are highly variable and polarize and the polarization at. those widelv. separated. [requencies is found to be strongly: correlated.(e.g.. Sitko Schmid 1985)," Observations over the past few decades have showed that its optical and radio emissions are highly variable and polarized and the polarization at those widely separated frequencies is found to be strongly correlated (e.g., Sitko Schmidt 1985)." +" Lac is among the very lew sources for which more han 100 ur""mvears of optical datais availablein the literature (Shen Webb et 112988: Fan et 11998).", BL Lac is among the very few sources for which more than 100 years of optical data is available in the literature (Shen 1970; Webb et 1988; Fan et 1998). + An optica variation of AB — 5.3 mag and a possible periocicity of 14 vears has been reported for BL Lae bv ban et al. (, An optical variation of $\Delta$ B = 5.3 mag and a possible periodicity of $\sim$ 14 years has been reported for BL Lac by Fan et al. ( +19982).,1998a). + Very recently. Nieppola et ((2009) have studiec he long term variability of the source at radio frequencies and generalized a shock model that can explain it.," Very recently, Nieppola et (2009) have studied the long term variability of the source at radio frequencies and generalized a shock model that can explain it." + We found that BL Lac was variable in all the observec xwsbancds: during our observations 111)., We found that BL Lac was variable in all the observed passbands during our observations 11). + As the per centage variation is nearby equal in all the four passbancds (although a little higher in B band). we find no significan colour variations (except perhaps DB... V).," As the per centage variation is nearly equal in all the four passbands (although a little higher in B band), we find no significant colour variations (except perhaps $-$ V)." + The average lh rand magnitude of the source during our observing run is 13.95 (15.8. 14.1) which is ~1.0 magnitude brighter than he faintest magnitude reported for the source by Fan ct (2000)., The average R band magnitude of the source during our observing run is 13.95 (13.8 –14.1) which is $\sim$ 1.0 magnitude brighter than the faintest magnitude reported for the source by Fan et (2000). + This FSI is among the most intense and variable sources., This FSRQ is among the most intense and variable sources. + Phe source has been detected in the Daring state in July 2007 ancl July 2008 at. 5-rav. frequencies and those [lares have been found. to be well correlated. with optical and wavelength ares (Chisellini et 22007: ltaiteri et sOs: Villata ct , The source has been detected in the flaring state in July 2007 and July 2008 at $\gamma$ -ray frequencies and those flares have been found to be well correlated with optical and longer wavelength flares (Ghisellini et 2007; Raiteri et 2008; Villata et 2007). +The long term observational properties of 3€ 454.3 at optical ancl radio frequencies have been well studied NS multiwaveleneth campaigns (c.g.. Villata et 2200. m.," The long term observational properties of 3C 454.3 at optical and radio frequencies have been well studied through multiwavelength campaigns (e.g., Villata et 2006, 2007)." +" The "" D the source has been recently studied et ((2008c) who reported that the amplitude varied by ~5 17 per cent during their observations.", The IDV of the source has been recently studied by Gupta et (2008c) who reported that the amplitude varied by $\sim$ 5–17 per cent during their observations. + The source 3€ 454.3 showed large [ux variations in all the passbands curing our observations and the per centage variation dilfers significantlv. which leads to significant variations in the colour of source 112).," The source 3C 454.3 showed large flux variations in all the passbands during our observations and the per centage variation differs significantly, which leads to significant variations in the colour of source 12)." +" The source decavecl significantly from. R=l4.5 to 15.5. Le. AR = 1 magnitude during our observing run of 50 claws: this is 73.5 magnitudes fainter than the brightest. magnitude (15,44 = 12) but —1.5 magnitudes brighter than the faintest magnitude (16, 17) reported in the source by Villata et ((2006)."," The source decayed significantly from R=14.5 to 15.5, i.e., $\Delta$ R = 1 magnitude during our observing run of 50 days; this is $\sim$ 3.5 magnitudes fainter than the brightest magnitude $_{mag}$ = 12) but $\sim$ 1.5 magnitudes brighter than the faintest magnitude $_{mag}$ = 17) reported in the source by Villata et (2006)." + Lt is very likely that we have observed. this ISI in a post-outburst state., It is very likely that we have observed this FSRQ in a post-outburst state. + Any relationships between the variations in. brightness of each of these 12 blazars and the corresponding variations in their V. 1t EP and E colour indices are worth examining.," Any relationships between the variations in brightness of each of these 12 blazars and the corresponding variations in their $-$ V, $-$ R, $-$ I and $-$ I colour indices are worth examining." + Such colour-magnitude plots of the individual sources are clisplaved in 113, Such colour-magnitude plots of the individual sources are displayed in 13 – 15. + We cisplay colour indices that are calculated by only considering data taken » the same instrument within a time interval of no more han 20 minutes: still. the possibility of a rapid variation in overall fux within that interval sullicient to confounel our measurements must be noted.," We display colour indices that are calculated by only considering data taken by the same instrument within a time interval of no more than 20 minutes; still, the possibility of a rapid variation in overall flux within that interval sufficient to confound our measurements must be noted." + The individual panels show he DB V. h.l Land E colours plotted (in sequence ronibottom to top with arbitrary olfsets) with respect to V magnitude.," The individual panels show the $-$ V, $-$ R, $-$ I and $-$ I colours plotted (in sequence frombottom to top with arbitrary offsets) with respect to V magnitude." + The straight lines shown are the best linear it for each of the colour indices. C7. against magnitude. V. for each of the sources: CL=nV.|c.," The straight lines shown are the best linear fit for each of the colour indices, $CI$, against magnitude, $V$, for each of the sources: $CI = m V + c$." + Those fitted values for the slopes of the curves. m. and the constants. c. are listed. in Table 5.," Those fitted values for the slopes of the curves, $m$, and the constants, $c$, are listed in Table 5." + Table 5 also gives the linear Pearson correlation coefficients. r. and the corresponding null hypothesis probability values. p.," Table 5 also gives the linear Pearson correlation coefficients, $r$, and the corresponding null hypothesis probability values, $p$." + Llere a positive. slope means a positive correlation tween the colour index and apparent magnitude of the dazar. which physically means that the source tends to be xuer when it brightens or redder when it dims.," Here a positive slope means a positive correlation between the colour index and apparent magnitude of the blazar, which physically means that the source tends to be bluer when it brightens or redder when it dims." + A negative slope implies the opposite correlation. between brightness and colour so that the source exhibits a redder when brighter xhaviour., A negative slope implies the opposite correlation between brightness and colour so that the source exhibits a redder when brighter behaviour. + We found significant negative correlations (p: 1.05) between the V. magnitudes and at least some colour indices for the following blazars: PAS 0420 014 V. dV and RL): OJ 287 (B. V): 4€ 20.45 V): 3€ 273 V and D: PISS 1510. 089 V and BR) and 3€ 454.8(V. ROL Land D.," We found significant negative correlations $p \leq 0.05$ ) between the V magnitudes and at least some colour indices for the following blazars: PKS $-$ 014 $-$ V, $-$ R, and $-$ I); OJ 287 $-$ V); 4C 29.45 $-$ V); 3C 273 $-$ V and $-$ I); PKS $-$ 089 $-$ V and $-$ R) and 3C 454.3 $-$ R, $-$ I and $-$ I)." + Significant Due correlations (px; 0.05) are found. for: 3€ 66X It and D: $85 X161 712 V. HR. Land B 5 BC 273 1: BC 279 Reand RL) and. DL Lac V and D) while he correlations among the rest have significance less than 95%. 0," Significant positive correlations $p \leq 0.05$ ) are found for: 3C 66A $-$ R and $-$ I); S5 $+$ 714 $-$ V, $-$ R, $-$ I and $-$ I); 3C 273 $-$ R); 3C 279 $-$ R and $-$ I) and BL Lac $-$ V and $-$ I) while the correlations among the rest have significance less than $\%$ ." +"235""Phe two sources lacking any such correlations were AOt | 164 and PIS | 178.", The two sources lacking any such correlations were AO $+$ 164 and PKS $+$ 178. + The only blazar in our sample to show both positive ancl negative. correlations. depending upon the bands considered. was 3C 273," The only blazar in our sample to show both positive and negative correlations, depending upon the bands considered, was 3C 273." +analysis difficult.,analysis difficult. + Phe implementation we used. (Numerical ltecipes. see 2)) utilises a version of the periodogram with mocifications hy Searele (1982) anc Horne and Daliunas (1986).," The implementation we used (Numerical Recipes, see \citet{pftv86}) ) utilises a version of the periodogram with modifications by Scargle (1982) and Horne and Baliunas (1986)." + Applications of this test to radio pulsar cata can be found in ? and ?.., Applications of this test to radio pulsar data can be found in \citet{bjb+97} and \citet{klo+06}. + The LombScargle test reveals signals in the power spectral density cistribution of a source. with the presence ofa sinusoid of certain frequency indicated by a peak in the spectrum at that particular frequeney.," The Lomb–Scargle test reveals signals in the power spectral density distribution of a source, with the presence of a sinusoid of certain frequency indicated by a peak in the spectrum at that particular frequency." + The trial frequencies at which the periodogram is evaluated. are chosen to be a finite evenly spaced. set., The trial frequencies at which the periodogram is evaluated are chosen to be a finite evenly spaced set. + For a time series V(t) with No number of elements where i = 1.2....Ny. the Scargle angular frequencies range [rom w=2z/1 to w=πο) (or periods from 7 to 2777 No). where is the total time interval.," For a time series $X(\rm t_{i})$ with $N_{\rm 0}$ number of elements where $\rm i$ = $N_{\rm 0}$ , the Scargle angular frequencies range from $\omega = 2\pi/T$ to $\omega = \pi N_{\rm 0}/T$ (or periods from $T$ to $2T$ $N_{\rm 0}$ ), where is the total time interval." + The searched frequencies therefore range up to the Nyquist frequeney., The searched frequencies therefore range up to the Nyquist frequency. + Lhe number of frequencies searched. is obtained from the empirical formula (Llorne and. Daliunas 1956) The likelihood of the existence of a signal or the level of significance is calculated as a detection threshold Zi (Scarele 1952). The false alarm. probability po is the probability that a peak of power Zu will occur in the absence of a periodic signal.," The number of frequencies searched is obtained from the empirical formula (Horne and Baliunas 1986) The likelihood of the existence of a signal or the level of significance is calculated as a detection threshold $Z_{\rm 0}$ (Scargle 1982), The false alarm probability $p_0$ is the probability that a peak of power $Z_{\rm 0}$ will occur in the absence of a periodic signal." + We have searched for periodicities in the pulse arrival times., We have searched for periodicities in the pulse arrival times. + In order to do this. we have ereated a time series by accounting for all rotations of the pulsar during cach observation and assigning a delta function (i.e one for cach detection and zero for cach non-detection).," In order to do this, we have created a time series by accounting for all rotations of the pulsar during each observation and assigning a delta function (i.e one for each detection and zero for each non-detection)." + We performed this search on the entire time span of observations., We performed this search on the entire time span of observations. + In the time series for the entire. time span of observations. we searched. over ~ 1.000.000 periocis spaced. as outlined at the beginning of section. 3.1. ranging [rom ~25 minutes to 2300 cays.," In the time series for the entire time span of observations, we searched over $\sim$ 1,000,000 periods spaced as outlined at the beginning of section 3.1, ranging from $\sim$ 25 minutes to 2300 days." + Six LIRATS PSRs JOS4? 4316. 5759. 90. 1455. JIS26 1419. and 1913| 1330. show significant periodicities in the arrival times on these timescales.," Six RRATs PSRs $-$ 4316, $-$ 5759, $-$ 30, $-$ 1458, $-$ 1419, and $+$ 1330, show significant periodicities in the arrival times on these timescales." + The peaks of highest significance lor PSRs JOSLT 4316. 5759. J1754 30. JI826 1419. and 1913] 1330 are at 3.8. 1.6. 1.4. 3.6 and 11.3 hours respectively. while PSR JISIO. 1458 shows a long term periodicity of 2102 davs.," The peaks of highest significance for PSRs $-$ 4316, $-$ 5759, $-$ 30, $-$ 1419, and $+$ 1330 are at 3.8, 1.6, 1.4, 3.6 and 11.3 hours respectively, while PSR $-$ 1458 shows a long term periodicity of 2102 days." + Phere are many other significant periods and harmonics for these RRATs. with eight. three. one. thirteen. fifteen. ancl eight. independent (i.e. non-harmonically related) periodicities with significance ereater than 99% (2.50) for PSRs 4316. 5759. J1754 30. JISIO9. 1458. 1419. and 1913] 1330. respectively (See Table 2).," There are many other significant periods and harmonics for these RRATs, with eight, three, one, thirteen, fifteen, and eight independent (i.e. non-harmonically related) periodicities with significance greater than $99\%$ $\sigma$ ) for PSRs $-$ 4316, $-$ 5759, $-$ 30, $-$ 1458, $-$ 1419, and $+$ 1330, respectively (See Table 2)." + These periodicities range [rom hours to vears., These periodicities range from hours to years. + Because of the large number of detected periodicities. we do not list them all here.," Because of the large number of detected periodicities, we do not list them all here." + In order to determine the time dependence of the periodicities. we divided the time series to halves and quarters ancl performed the search again.," In order to determine the time dependence of the periodicities, we divided the time series to halves and quarters and performed the search again." +" For every ΠΛΗ, all periodicities detected in the full series were re.detected in at least one quarter subsection with lower significances."," For every RRAT, all periodicities detected in the full series were re–detected in at least one quarter subsection with lower significances." + None of the periodicities were re.detected in every. quarter. though seven out of the eight. nonharmonically related periodicities of PSR | 1330 were re.detected in three of the quarter datasets.," None of the periodicities were re–detected in every quarter, though seven out of the eight non–harmonically related periodicities of PSR $+$ 1330 were re–detected in three of the quarter datasets." + Similarly. five out of the 13 nonharmonically related periodicities of PSR «1519 1458 were re-detected in three quarters with significances greater than 95%., Similarly five out of the 13 non--harmonically related periodicities of PSR $-$ 1458 were re-detected in three quarters with significances greater than $\%$ . + The rest were re.detected in only one or two quadrants., The rest were re–detected in only one or two quadrants. + All detectable (io. within the searched. range) nonxuwmonically related: periodicities of PSR JLO18| 1330 were redetected in both halves of the dataset., All detectable (i.e. within the searched range) non--harmonically related periodicities of PSR $+$ 1330 were re–detected in both halves of the dataset. + For the rest. of he RRATVs only about five (for. PSR 1458) to two (lor PSR J1913] 1330) independent periodicities were detected in both halves., For the rest of the RRATs only about five (for PSR $-$ 1458) to two (for PSR $+$ 1330) independent periodicities were re--detected in both halves. + However every. periodicity was redetected. in at least one half section of the dataset with ower significance., However every periodicity was re--detected in at least one half section of the dataset with lower significance. + These results in general show that the »eriodicities. persist. throughout the entire. time span of observations., These results in general show that the periodicities persist throughout the entire time span of observations. + In order to gauge the reality of the. periodicities. we randomised the time series of detections and nondetections by placing the pulses randomly within the observation windows and repeating the analysis.," In order to gauge the reality of the periodicities, we randomised the time series of detections and non--detections by placing the pulses randomly within the observation windows and repeating the analysis." + We found no periodicities with significance greater. than 304 in any of these randomised. time series. which suggests the periodicities found. are real.," We found no periodicities with significance greater than $30\%$ in any of these randomised time series, which suggests the periodicities found are real." + Figure 1 shows the power spectra for the pulse arrival times from the randomised time series For the eight. 1ΑΕ»., Figure 1 shows the power spectra for the pulse arrival times from the randomised time series for the eight RRATs. + We have also applied this method to look for periodicities in he daily pulse detection rates., We have also applied this method to look for periodicities in the daily pulse detection rates. + For each cay. the observation eneth and the number of detected: pulses were used. to calculate the rate of pulse detection.," For each day, the observation length and the number of detected pulses were used to calculate the rate of pulse detection." +" Figure 2 shows how his rate varies for the eight Αν,", Figure 2 shows how this rate varies for the eight RRATs. + We then applied the LombScarele analysis to these rates. with the results of his analysis shown in Figure 3.," We then applied the Lomb–Scargle analysis to these rates, with the results of this analysis shown in Figure 3." + We list the most significant »eriod in Table 1 along with its significance., We list the most significant period in Table 1 along with its significance. + We have performed. white noise simulations and Alonte Carlo simulations to verify the significance of| the »eriodicities., We have performed white noise simulations and Monte Carlo simulations to verify the significance of the periodicities. + La white noise simulations. the cdailv rates were replaced by random. Gaussian noise.," In white noise simulations, the daily rates were replaced by random Gaussian noise." + We could then calculate the power spectrum amplitude corresponding to he desired. false alarm probability., We could then calculate the power spectrum amplitude corresponding to the desired false alarm probability. + La the second. method. Alonte Carlo simulations were used to generate spectra from. random time series which have the same sampling and he cumulative probability distribution of their maximum amplitude is calculated., In the second method Monte Carlo simulations were used to generate spectra from random time series which have the same sampling and the cumulative probability distribution of their maximum amplitude is calculated. + We then fit this distribution to Equation 2. minimizing X7 to determine an ellective value for Aj as this determines the false alarm probability for à given power spectral density.," We then fit this distribution to Equation 2, minimizing $\chi^2$ to determine an effective value for ${\it N_i}$ as this determines the false alarm probability for a given power spectral density." + Phese tests verified the significances that we have quoted., These tests verified the significances that we have quoted. + PSRs 145s and 30 have perioclicitics with greater than 2a significance at 1260 anc 994. days respectively. while PSRs 1510 0257 and 4316 have periodicitieswith greater than lo significance at 135 and 1040 days respectively.," PSRs $-$ 1458 and $-$ 30 have periodicities with greater than $\sigma$ significance at 1260 and 994 days respectively, while PSRs $-$ 0257 and $-$ 4316 have periodicitieswith greater than $\sigma$ significance at 135 and 1040 days respectively." + Phe remaining four RRATs do not show a periodicitv of significance ercater than the lo level., The remaining four RRATs do not show a periodicity of significance greater than the $\sigma$ level. + The significances obtained for the peak powerspectral density for PSRs 1458 and 30 from white noise simulations are and respectively., The significances obtained for the peak powerspectral density for PSRs $-$ 1458 and $-$ 30 from white noise simulations are and respectively. + The significances calculated. from. Monte Carlo simulations are and SOM..., The significances calculated from Monte Carlo simulations are and . +bright red variable and is. indeed. a nova.,"bright red variable and is, indeed, a nova." + This variable presented more of a challenge., This variable presented more of a challenge. + Its faintness precluded spectral observations with the MIDAI 2.4 m. In this case. theLST observations were examined in an attempt to bolster the nova classification by constraining the outburst amplitude.," Its faintness precluded spectral observations with the MDM 2.4 m. In this case, the observations were examined in an attempt to bolster the nova classification by constraining the outburst amplitude." + We were fortunate that the ACS WFC observations of this area included. 19 to 21 stars that could be used to directly register the Tenagra images., We were fortunate that the ACS WFC observations of this area included 19 to 21 stars that could be used to directly register the Tenagra images. + We chose 5 of these images. in which the candidate was well observed. (to register to the ACS image.," We chose 5 of these images, in which the candidate was well observed, to register to the ACS image." + Defore centroiding objects in the ACS image. we convolved it with a Gaussian of appropriate width to bring the ACS resolution down to the resolution of the Tenagra images.," Before centroiding objects in the ACS image, we convolved it with a Gaussian of appropriate width to bring the ACS resolution down to the resolution of the Tenagra images." + The IRAF task geomap was used to caleulate (he (ransformatious using a 21d order polynomial including cross teris., The IRAF task geomap was used to calculate the transformations using a 2nd order polynomial including cross terms. + The average RAIS for the 5 transformations was 2 ACS pixels in x and v. We used these transformations to place the candidate in the ACS WFC image., The average RMS for the 5 transformations was 2 ACS pixels in x and y. We used these transformations to place the candidate in the ACS WFC image. + We then calenlated the error-weighted average position for the candidate ACS position which had an RAIS of 6.4 ACS pixels., We then calculated the error-weighted average position for the candidate ACS position which had an RMS of 6.4 ACS pixels. + To check for local offsets we used two stus within 25 of the candidate (hat were visible in both the Tenagra and the ACS image.," To check for local offsets we used two stars within 25"" of the candidate that were visible in both the Tenagra and the ACS image." + We checked (he transformed positions of (hese stars and computed their error weighted average position. which had an RAIS of 2.0 ACS pixels.," We checked the transformed positions of these stars and computed their error weighted average position, which had an RMS of 2.0 ACS pixels." + These average positions showed no local offset with respect to the ACS to 0.5 ACS pixels., These average positions showed no local offset with respect to the ACS to 0.5 ACS pixels. + The larger scatter in (he candidate positions is due to the faintness of the candidate compared with the stars we used for registration., The larger scatter in the candidate positions is due to the faintness of the candidate compared with the stars we used for registration. + Figure 8 shows the position of the candidate nova in the ACS WFC V (F606W) image. wilh a 5 arcsecond field of view.," Figure \ref{n205n1hst} shows the position of the candidate nova in the ACS WFC V (F606W) image, with a 5 arcsecond field of view." + The crosses mark the live transformed candidate positions and (he smallest circle marks (he error-weiehted centroid of these positions., The crosses mark the five transformed candidate positions and the smallest circle marks the error-weighted centroid of these positions. + The next larger circle shows the RAIS error circle for (he nova candidate positions and the largest circle is 1, The next larger circle shows the RMS error circle for the nova candidate positions and the largest circle is 1 +If we would have shifted bv zx |0.2 mag the AV99? values of the isochrones used in BCP (see their Fig.,If we would have shifted by $\approx$ +0.2 mag the $\triangle V^{0.05}$ values of the isochrones used in BCP (see their Fig. + 5) iu such a wav that the average age of the coeval clusters is around 11 Cr. we would have excluded the most metal poor ones from the coeval sample. thus recovering the result obtained with the SW98 isochrones.," 8) in such a way that the average age of the coeval clusters is around 11 Gyr, we would have excluded the most metal poor ones from the coeval sample, thus recovering the result obtained with the SW98 isochrones." + Another effect of the lower absolute age of the GC is that now we find included in the coeval sample two clusters. Pal 5 and Arp 2. considered as voung by BCP.," Another effect of the lower absolute age of the GC is that now we find included in the coeval sample two clusters, Pal 5 and Arp 2, considered as young by BCP." + The first step to evaluate GC relative ages following the technique by BCP is the calibration of a relation between ΑΗΤΟΝ aud iuctallicity for the subset of coeval clusters., The first step to evaluate GC relative ages following the technique by BCP is the calibration of a relation between $\triangle (B-V)_{\rm TO}^{\rm RGB}$ and metallicity for the subset of coeval clusters. + A linear fit to the data (taking iuto account the ACBVYXSP emor given in Tab., A linear fit to the data (taking into account the $\triangle (B-V)_{\rm TO}^{\rm RGB}$ error given in Tab. + 1 and a typical error of £0.15 dex in metallicity) provides The next step is the evaluation of the ratio 6/Aty. where à is the difference between the observed A(Bο. and the oneexpected ou the basis of Eq. (," \ref{t:1} and a typical error of $\pm$ 0.15 dex in metallicity) provides The next step is the evaluation of the ratio $\delta / \Delta t_9$, where $\delta$ is the difference between the observed $\triangle (B-V)_{\rm +TO}^{\rm RGB}$ and the one on the basis of Eq. (" +"1). aud As is the relative age Gin Cor) with respect to the coeval clusters. as determined from V5,","1), and $\Delta t_9$ is the relative age (in Gyr) with respect to the coeval clusters, as determined from $\triangle V^{0.05}$." +" We determined this ratio for the four vouneger clusters NGC 1851. Pal 12. Rup 106 aud Ter 7. (sco BCP. for a discussion). then averaged these four values (having checked that they are uot significantly correlated with metallicity) aud ect: This quantity is smaller than that of BCP (-0.0093). iuplviug a larger seusitivitv of A(BTRES to age aud therefore smaller age differences for an observed A((B Γον, B"," We determined this ratio for the four younger clusters NGC 1851, Pal 12, Rup 106 and Ter 7, (see BCP for a discussion), then averaged these four values (having checked that they are not significantly correlated with metallicity) and get: This quantity is smaller than that of BCP (-0.0093), implying a larger sensitivity of $\triangle (B-V)_{\rm TO}^{\rm RGB}$ to age and therefore smaller age differences for an observed $\triangle +(B-V)_{\rm TO}^{\rm RGB}$ ." +y combining Eq. (, By combining Eq. ( +1) and Eq. (,1) and Eq. ( +2) we obtain the final relation between ACBΤΟΝ. [Fe/H]] and Ato: This equation allows the proper calculation of the error in Afy by standard error propagation.,"2) we obtain the final relation between $\triangle (B-V)_{\rm TO}^{\rm RGB}$, [Fe/H] and $\Delta t_9$: This equation allows the proper calculation of the error in $\Delta t_9$ by standard error propagation." + Taking iuto accouut the errors in A(Byes and [FeT] as well. oue ects errors of the order of 42.0 Cr in the derived values of Afy (see the vertical error bars in Fig. 3)).," Taking into account the errors in $\triangle (B-V)_{\rm TO}^{\rm RGB}$ and [Fe/H] as well, one gets errors of the order of $\pm$ 2.0 Gyr in the derived values of $\Delta t_9$ (see the vertical error bars in Fig. \ref{f:3}) )." + Without the errors Eq. (, Without the errors Eq. ( +3a) can be simplified to The coefficieuts depend of course ou the absolute age of the coeval sample: for the sake of comparison we recall here that the corresponding values obtained by BCP were (-107.5. L3. 33.5).,"3a) can be simplified to The coefficients depend of course on the absolute age of the coeval sample; for the sake of comparison we recall here that the corresponding values obtained by BCP were (-107.5, 4.3, 33.3)." + Tn Sect., In Sect. + 1 we recalled that BCP found an incousisteucy in the theoretical isochroucs by comparing the empirical relation Eq. (, 1 we recalled that BCP found an inconsistency in the theoretical isochrones by comparing the empirical relation Eq. ( +1) with them.,1) with them. + In Fig., In Fig. + 2. we show the same comparison aud. in the consicered range of metallicity. we did not fud the same problem: the empirical relation crosses a 2-Covr range in the isochroues. between 10 aud 12 Car. which is identical to the variation of ages determined from AVV (Fig. 1)).," \ref{f:2} we show the same comparison and, in the considered range of metallicity, we did not find the same problem: the empirical relation crosses a 2-Gyr range in the isochrones, between 10 and 12 Gyr, which is identical to the variation of ages determined from $\triangle V^{0.05}$ (Fig. \ref{f:1}) )." + It is also evident that the spread of the observational poiuts aud the errors associated to them (see Table 1) is large enoush to make the 1] Cyr isochrone fully compatible with the empirical relation., It is also evident that the spread of the observational points and the errors associated to them (see Table 1) is large enough to make the 11 Gyr isochrone fully compatible with the empirical relation. + To further substantiate our claim that the SW9s οποιος and therefore the semi-empirical relation derived in the previous section are trustworthy. we slow πι Fie.," To further substantiate our claim that the SW98 chrones – and therefore the semi-empirical relation derived in the previous section – are trustworthy, we show in Fig." + 3 the comparison between the differential ages , \ref{f:3} the comparison between the differential ages +a small kink in the function at the transition between the data and the extrapolation. but we find this to be quite small.,"a small kink in the function at the transition between the data and the extrapolation, but we find this to be quite small." + In the ? datafor z=2.1 there is a eut-olf at about [i—8. where the PDE stops decreasing and reaches a near constant. plateau.," In the \citet{Hilbert07} datafor $z=2.1$ there is a cut-off at about $\mu=0.8$, where the PDF stops decreasing and reaches a near constant plateau." + In this paper we are not interested in the deamplification clleets from the jp}\,S)$ with units of $^{-2}$." +Currently. there are not enough high flux (8S720mm.) sources to prefer one function over the other., Currently there are not enough high flux $S>20$ mJy) sources to prefer one function over the other. + We have chosen to use the Schechter function as our primary estimate of the source counts., We have chosen to use the Schechter function as our primary estimate of the source counts. + The power-Iaw drops olf much slower than the exponential part of the Schechter function. allowing for many more intrinsically bright objects.," The power-law drops off much slower than the exponential part of the Schechter function, allowing for many more intrinsically bright objects." + As such. the most. gradual. power-law consistent with the data can be used as an upper estimate to the counts. which results in a far more conservative estimate of the strong ensing probabilities.," As such, the most gradual power-law consistent with the data can be used as an upper estimate to the counts, which results in a far more conservative estimate of the strong lensing probabilities." + Lower limit to the source counts is ess helpful. as the corresponding uncertainty in the upper imit of lensing probabilities is unknown.," A lower limit to the source counts is less helpful, as the corresponding uncertainty in the upper limit of lensing probabilities is unknown." + The Schechter function. parameters that we adopt. are. in parallel with 7.. N’=1600. S —3.3. anda =2.," The Schechter function parameters that we adopt are, in parallel with \citet{Coppin06}, $N^\prime=1600$ , $S^\prime=3.3$, and $\alpha=-2$." + For he maximal broken power-law we use AN.=58. ο)=9. a=—22.and 7=42.," For the maximal broken power-law we use $N^\prime=58$, $S^\prime=9$, $\alpha=-2.2$, and $\beta=-4.2$." + The contribution to the overall xikeround {SQUNfdS)d S) from a power-law number counts distribution diverges at the faint end. if the slope a:2 (in equation (7))).," The contribution to the overall background $\int S(dN/dS)dS$ ) from a power-law number counts distribution diverges at the faint end if the slope $\alpha\,{\le}\,-2$ (in equation \ref{eqn:bpl}) ))." + To prevent. overproducing the submum background. we therefore set a limit on the broken power-law of 5Sο0.2 mv.," To prevent overproducing the submm background, we therefore set a limit on the broken power-law of $S\ge0.2\,$ mJy." + 2 used a phenomenological approach to model. galaxy evolution and. predict number counts at a variety of wavelengths. including 850 jim. and corrected this to include constraints from. data in ?..," \citet{Lagache03} used a phenomenological approach to model galaxy evolution and predict number counts at a variety of wavelengths, including $850\,\mu$ m, and corrected this to include constraints from data in \citeyear{Lagache04}." + Their standard. model is roughly consistent with ? in the range where data from SILADES exist. but decreases much more slowly above about 50mm.v.," Their standard model is roughly consistent with \citet{Coppin06} in the range where data from SHADES exist, but decreases much more slowly above about mJy." + This is due entirely to local bright. Euclidean counts. for which dN/dSxS.77.," This is due entirely to local bright Euclidean counts, for which $\d N/\d S +\propto S^{-5/2}$." + 2 similarly have a model or the source counts that has been adjusted to include the data., \citet{Chary01} similarly have a model for the source counts that has been adjusted to include the data. + The results of their model at S50 pr is very similar o ?.. including the bright Euclidean part as well.," The results of their model at $850\,\mu$ m is very similar to \citet{Lagache04}, including the bright Euclidean part as well." + Normalising a [Euclidean source count estimate to the SCUBA Local Universe Galaxy Survey (SLUGS:?).. ind agreement with the high Ες behaviour in both the 7 and ? models.," Normalising a Euclidean source count estimate to the SCUBA Local Universe Galaxy Survey \citep[SLUGS;][]{Dunne00}, we find agreement with the high flux behaviour in both the \citet{Lagache04} and \citet{Chary01} models." + Since the Euclidean part of the source counts comes from low redshift sources. we do not expect here to be any significant lensing here.," Since the Euclidean part of the source counts comes from low redshift sources, we do not expect there to be any significant lensing here." + Subtracting the S77 part [rom either of these models to estimate the high redshift population. we find that the high flux Fall-olf is very similar to a Schechter function.," Subtracting the $S^{-5/2}$ part from either of these models to estimate the high redshift population, we find that the high flux fall-off is very similar to a Schechter function." + This is only a first-order approximation. as in principle the source counts change for each redshift slice.," This is only a first-order approximation, as in principle the source counts change for each redshift slice." + We will investigate redshift dependence in section 4.2. and the change in the shape of the counts with redshift in 5.2.., We will investigate redshift dependence in section \ref{sec:Comparing} and the change in the shape of the counts with redshift in \ref{sec:UncCounts}. + We will also compare with the results from an evolutionary model in section 6.., We will also compare with the results from an evolutionary model in section \ref{sec:evolution}. . + But for now we will assume a single screenof sources with counts independent of redshift., But for now we will assume a single screenof sources with counts independent of redshift. + Between the low [ux limit of the models at. about μον and the knee at several mJ. both mocels predict intermediate counts between the Schechter and broken power-law fits.," Between the low flux limit of the models at about $1\,\mu$ Jy and the knee at several mJy, both models predict intermediate counts between the Schechter and broken power-law fits." + Fig., Fig. + 2 compares these functional fits to the," \ref{fig:compare-counts} + compares these functional fits to the" +can be described using three parameters: the fractional filling factor of the hieh deusity dust (ff). the density ratio between the low aud high density dust (hoΑλ). aud the size of a exid cell iu comparison to the system size (LAN. where [IN ds the ΠΙΟ: of eid cells on au axis).,"can be described using three parameters: the fractional filling factor of the high density dust $ff$ ), the density ratio between the low and high density dust $k_2/k_1$ ), and the size of a grid cell in comparison to the system size $1/N$, where $N$ is the number of grid cells on an axis)." + The differences in the radiative transter between homogeneous and two-phase dust distributions is discussed at leugth by Witt&Cordon(1996)., The differences in the radiative transfer between homogeneous and two-phase dust distributions is discussed at length by \citet{wit96}. +. The tracking of the photous through the 3-climensional exid is simple auc quite efficient., The tracking of the photons through the 3-dimensional grid is simple and quite efficient. + A photou’s location aud direction of travel is uniquely defined by its x. v. aud z yositions and the wv. e. and « direction cosines.," A photon's location and direction of travel is uniquely defined by its x, y, and z positions and the $u$, $v$, and $w$ direction cosines." + When a Xioton enters a grid cell the side through which it exits can be quickly computed in the following manner.," When a photon enters a grid cell, the side through which it exits can be quickly computed in the following manner." + Using rex. v. and 2 dimensions of the cell aud the direction cosines of the photon. the distance the photon would have o travel iu each of the x. v. and z directious to exit ie cell through a plane parallel to the wall of the cell in those directions can be computed.," Using the x, y, and z dimensions of the cell and the direction cosines of the photon, the distance the photon would have to travel in each of the x, y, and z directions to exit the cell through a plane parallel to the wall of the cell in those directions can be computed." + The photou exits hrough the side which results in the shortest distance raveled., The photon exits through the side which results in the shortest distance traveled. + The photou's position can be stepped by this distance and ancillary information updated (e... optical depth traveled).," The photon's position can be stepped by this distance and ancillary information updated (e.g., optical depth traveled)." + Just as our model permits the use of arbitrary dust distributions. it also allows photous to be cinitted from arbitrary source distributions.," Just as our model permits the use of arbitrary dust distributions, it also allows photons to be emitted from arbitrary source distributions." + These cau be a single star. a distribution of stars. or any definable surface (6.8.. au accretion disk).," These can be a single star, a distribution of stars, or any definable surface (e.g., an accretion disk)." + The sources cau enit isotropically or ouly in specific directions., The sources can emit isotropically or only in specific directions. +" We use the “ran2” pseudo-random uuuber eeuerator Which is described by Press.Teukolsksx.Vetterling.&Flannery(1992) and has a period ereater than 2«1015,"," We use the “ran2” pseudo-random number generator which is described by \citet{pre92} and has a period greater than $2 +\times 10^{18}$." + The transfer of plotous through dust using Aloute Carlo techniques is historically based on following a sinele photon through a distribution of dust., The transfer of photons through dust using Monte Carlo techniques is historically based on following a single photon through a distribution of dust. + Iu this paracigui. the chance of the photon being absorbed or scattered is deteriuned using a raudoni nuniber generator with the results dictating the life of that photon.," In this paradigm, the chance of the photon being absorbed or scattered is determined using a random number generator with the results dictating the life of that photon." + Therefore. a particular photon might exit the svsteii without interacting with a dust eram. be absorbed on its first scattering (or subsequent scatterings). or scatter one or more times before exitiug the svsteni.," Therefore, a particular photon might exit the system without interacting with a dust grain, be absorbed on its first scattering (or subsequent scatterings), or scatter one or more times before exiting the system." + This is not a particularly effiiieut method of computing the direct. scattered. or absorbed light frou a system as cach photon can contribute to only one of these quantities.," This is not a particularly efficient method of computing the direct, scattered, or absorbed light from a system as each photon can contribute to only one of these quantities." + In addition. cach photon exits the svsteni im a particular direction which is not necessarily the direction from which oue wants to observe the svstem.," In addition, each photon exits the system in a particular direction which is not necessarily the direction from which one wants to observe the system." + The efficiency of the Monte. Carlo method can be increased ereathy by assigning the plotou a weight which allows every photon to coutribute to the absorbed cuerey. the direct light. aud the scattered light for a particular luec-ofsight (WittLOTT:YusetZadch.Morris.&White 1981).," The efficiency of the Monte Carlo method can be increased greatly by assigning the photon a weight which allows every photon to contribute to the absorbed energy, the direct light, and the scattered light for a particular line-of-sight \citep{wit77, yus84}." + The algorithi we use for the radiative transfer in the DIRTY model is based on the svork of Witt(1977).. Zadeh.Morris.&White (1981). aud Code&Whitney (1995).," The algorithm we use for the radiative transfer in the DIRTY model is based on the work of \citet{wit77}, \citet{yus84}, and \citet{cod95}." +. Iu the following description of our aleorithiu. we will use the concept of the life of a photon.," In the following description of our algorithm, we will use the concept of the life of a photon." + To track each photo's state. we tabulate its position. direction of travel (via direction cosines 4. c. aud ie). weight. aud polarization (via Stokes I. OQ. U. aud. V values).," To track each photon's state, we tabulate its position, direction of travel (via direction cosines $u$, $v$, and $w$ ), weight, and polarization (via Stokes I, Q, U, and V values)." + A photon is born according to an input source distribution aud its iitial direction is usually chosen frou an isotropic distribution (c.g.. 55-7 of Witt.(1977))).," A photon is born according to an input source distribution and its initial direction is usually chosen from an isotropic distribution (e.g., 5-7 of \citet{wit77}) )." + The assuuption of isotropic cussion can be modified according to the particular problem beime studied., The assumption of isotropic emission can be modified according to the particular problem being studied. + For example. a nmiask with different sized holes at specific locations was applied in the DIRTY iodel to the central star of the nebula surrounding the R Corona Borealis star UW Cen (Clavtouetal.1999).," For example, a mask with different sized holes at specific locations was applied in the DIRTY model to the central star of the nebula surrounding the R Corona Borealis star UW Cen \citep{cla99}." +.. In. this case. only the photons ciitted in the direction of the holes iu the mask were allowed to move to the next step.," In this case, only the photons emitted in the direction of the holes in the mask were allowed to move to the next step." + The initial weight of the photon is usually where £° is the hunuinositv associated with the ath photon aud o runs from 1 to δν , The initial weight of the photon is usually where $L^\alpha$ is the luminosity associated with the $\alpha$ th photon and $\alpha$ runs from 1 to $N$ . +Usually £°=LN where £ is the luminosity of the source distribution at the modeled waveleneth aud NV is the uunnuber of photous iu the iodel zuu., Usually $L^\alpha = L/N$ where $L$ is the luminosity of the source distribution at the modeled wavelength and $N$ is the number of photons in the model run. + The value of £° caube varied depending on the particular problemi being studied to optimize the model ruunnine time (YusefZadeh.Alorris.&White1981)., The value of $L^\alpha$ can be varied depending on the particular problem being studied to optimize the model running time \citep{yus84}. +" The photon is initially assuned to be unpolarized (i.c. —Wy)= (1.0.0.0), S"," The photon is initially assumed to be unpolarized (i.e. $S_0^\alpha = +(I_0^\alpha, Q_0^\alpha, U_0^\alpha, V_0^\alpha) = (1, 0, 0, 0)$ )." +yThe(S fluxQu correspoudingUy to the part of the photon which escapes from the syste in the direction of the observer is where r(obs)y is the optical depth aloug the path frou the birth position of the photou to the surface of the system in the direction of the observer aud d is the distance to the svstoii being modeled., The flux corresponding to the part of the photon which escapes from the system in the direction of the observer is where $\tau(obs)_0^\alpha$ is the optical depth along the path from the birth position of the photon to the surface of the system in the direction of the observer and $d$ is the distance to the system being modeled. + Iu general. z(obs)g is different for cach photon emitted uuless the system being modeled has a single central poiut source emibedded m a spherical. homogeneous dust distribution.," In general, $\tau(obs)_0^\alpha$ is different for each photon emitted unless the system being modeled has a single central point source embedded in a spherical, homogeneous dust distribution." + The first scattering of the photon is forced to insure that every photon coutributes to the scattered ποτ (Cashwell&Everett 1959)., The first scattering of the photon is forced to insure that every photon contributes to the scattered light \citep{cas59}. +. The optical depth to the first scattering site Is where © is a random nuuber between 0 and 1 aud τι is the optical depth to the surface of the nebula in the direction the ath photon is traveling., The optical depth to the first scattering site is where $\xi$ is a random number between 0 and 1 and $\tau_s^\alpha$ is the optical depth to the surface of the nebula in the direction the $\alpha$ th photon is traveling. + The weight of the photon after the first scattering is theu where e is the dust albedo., The weight of the photon after the first scattering is then where $a$ is the dust albedo. + The fraction of the photou which is absorbed at the scattering site is The dux corresponding to the fraction of the photon which is scattered at the first scattering toward the observer is where r(obs)! is the optical depth from the first scattering site along the direction towards the observer. (7) is the scattering phase fuuctiou. aud ((obsy! is the anelebetween the direction the photon was traveling before the scattering aud the direction towards the observer.," The fraction of the photon which is absorbed at the scattering site is The flux corresponding to the fraction of the photon which is scattered at the first scattering toward the observer is where $\tau(obs)_1^\alpha$ is the optical depth from the first scattering site along the direction towards the observer, $\Phi(\theta)$ is the scattering phase function, and $\theta(obs)_1^\alpha$ is the anglebetween the direction the photon was traveling before the scattering and the direction towards the observer." + This angle is easily calculated for the th scattering usine, This angle is easily calculated for the $n$ th scattering using +(he temperature which in (urn define (he structure of the ISM.,the temperature which in turn define the structure of the ISM. + Such structures include dense cores (e.g.. Lee. Myers. Talalla 1999). filamentary clouds (e.g.. Schneider Elmeereen 1979; ILarjunpaa et al.," Such structures include dense cores (e.g., Lee, Myers, Tafalla 1999), filamentary clouds (e.g., Schneider Elmegreen 1979; Harjunpaa et al." + 1999). and even disks (e.g.. Padgett et al.," 1999), and even disks (e.g., Padgett et al." + 1999)., 1999). + Inpressive theoretical progress has been made on (he properties ancl evolution of these structures during last vears under simplibing assumptions (e.e.. Li 1998: Fiege Pudritz 2000: Tsuribe 1999).," Impressive theoretical progress has been made on the properties and evolution of these structures during last years under simplifying assumptions (e.g., Li 1998; Fiege Pudritz 2000; Tsuribe 1999)." + Most of the theoretical models of interstellar clouds and clumps assume static or stationary configurations. in which there is an equilibrium between the sell-eravitv. centrifugal force and some forms of internal energy in the cloud (e.g.. Dertoldi Melxee 1992: Chieze 1987: Vazquez-Semadeni Gazol 1995: Galli et al.," Most of the theoretical models of interstellar clouds and clumps assume static or stationary configurations, in which there is an equilibrium between the self-gravity, centrifugal force and some forms of internal energy in the cloud (e.g., Bertoldi McKee 1992; Chieze 1987; Vazquez-Semadeni Gazol 1995; Galli et al." +" 2001: Tomisaka. Ikeuchi. Nakamura. 1933: Φαπιο] Ghanbari 2001),"," 2001; Tomisaka, Ikeuchi, Nakamura 1988; Shadmehri Ghanbari 2001a)." + Shu. Adams. Lizano (1937) proposed a four stage scenario lor the formation of an isolated low-mass star: (a) quasistatic formation and evolution of a molecular cloud core by ambipolar diffusion: (b) dynamical collapse of the core to a protostar and circumstellar disk: (c) breakout of à powerful bipolar outflow: ancl (d) clearing of the circumstellar envelope to reveal a pre-nain-sequence star.," Shu, Adams, Lizano (1987) proposed a four stage scenario for the formation of an isolated low-mass star: (a) quasi-static formation and evolution of a molecular cloud core by ambipolar diffusion; (b) dynamical collapse of the core to a protostar and circumstellar disk; (c) breakout of a powerful bipolar outflow; and (d) clearing of the circumstellar envelope to reveal a pre-main-sequence star." + Such theories of isolated star formation assert that eravitational collapse occurs onto a thermally supported core and motions are quasi-hvedrostatic until verv late times (e.g.. Shu. Adams. Lizano 1937: Li 1993).," Such theories of isolated star formation assert that gravitational collapse occurs onto a thermally supported core and motions are quasi-hydrostatic until very late times (e.g., Shu, Adams, Lizano 1987; Li 1998)." + Nevertheless. recent work has lead to doubts as to whether (heir initial condition is a reasonable starting point.," Nevertheless, recent work has lead to doubts as to whether their initial condition is a reasonable starting point." + Rather than being quasi-static. the hierarchical and ehumpxy structures of ISM have been proposed to result [rom turbulence (e.g.. Falgarone. Phillips. Walker 1991: Elueereen 1999).," Rather than being quasi-static, the hierarchical and clumpy structures of ISM have been proposed to result from turbulence (e.g., Falgarone, Phillips, Walker 1991; Elmegreen 1999)." + Some authors examine the idea that ISAT may not be best visualized as a system of discrete clouds and conclude that the structures in the ISM may form as density fInctuations induced by large-scale interstellar turbulence (e.g. Ballesteros-Parecles. Vazquez-Semaceni. Scalo 1999).," Some authors examine the idea that ISM may not be best visualized as a system of discrete clouds and conclude that the structures in the ISM may form as density fluctuations induced by large-scale interstellar turbulence (e.g., Ballesteros-Paredes, Vazquez-Semadeni, Scalo 1999)." + However. observations of infall at small scales in isolated cores show that quasi-static course do in fact exist (Williams et al.," However, observations of infall at small scales in isolated cores show that quasi-static course do in fact exist (Williams et al." + 1999). although it seems that lor explaining large-scale motions we need an alternative explanation (e.g.. Myers Lazarian 1998).," 1999), although it seems that for explaining large-scale motions we need an alternative explanation (e.g., Myers Lazarian 1998)." + Recently. we presented a non-Jeans scenario for star formation in sell-gravitating lilamentary clouds (Shadmehri Ghanbari 2001b: hereafter SG). extending the work of Meerson. Megegec. Tajima (1996) on spherical clouds.," Recently, we presented a non-Jeans scenario for star formation in self-gravitating filamentary clouds (Shadmehri Ghanbari 2001b; hereafter SG), extending the work of Meerson, Megged, Tajima (1996) on spherical clouds." + We studied. quasi-hyvedrostatic cooling flows in these filamentary clouds., We studied quasi-hydrostatic cooling flows in these filamentary clouds. + We parameterized the cooling function as a power-law in temperature (Xx(PT ). and showed that the filament experiences radiative condensation.," We parameterized the cooling function as a power-law in temperature $\Lambda\propto\rho^{2}T^{\epsilon}$ ), and showed that the filament experiences radiative condensation." + Furthermore. since (he exponent in temperature is a [ree parameter. this cooling function ean also qualitatively represents turbulent energy dissipation.," Furthermore, since the exponent in temperature is a free parameter, this cooling function can also qualitatively represents turbulent energy dissipation." + That is we can use this cooling function to represent the dissipation rate of turbulent οποιον by identibving the velocity dispersion. with the temperature (see. e.e.. Mac Low 1999).," That is we can use this cooling function to represent the dissipation rate of turbulent energy by identifying the velocity dispersion with the temperature (see, e.g., Mac Low 1999)." + Thus. our results also apply to à turbulent filament. alihough we did not investigate (his explicitly.," Thus, our results also apply to a turbulent filament, although we did not investigate this explicitly." +since the two WEPC? data-sets have been obtained in (wo different epochs with a time baseline of more than 10 vears. ancl given (he relative small distance of M28. (d=5.6 Ixpe: Ilarris 1996). we have been able to perform a proper-motion analvsis.,"Since the two WFPC2 data-sets have been obtained in two different epochs with a time baseline of more than 10 years, and given the relative small distance of M28 (d=5.6 Kpc; Harris 1996), we have been able to perform a proper-motion analysis." +" As shown in Figure δι, the bulk of stars lie around the position (j4,c0s(0)=0. jj=0) [mas/vr]. within a radius a,1."," As shown in Figure \ref{Fig:proper_motion}, the bulk of stars lie around the position $\mu_\alpha cos(\delta)=0$, $\mu_\delta=0$ ) [mas/yr], within a radius $\sigma_{\mu} \sim1$." + These most likely are members of the cluster. while field stars are clearly separated (ihe position in the CAID of these two classes of stars further confirms such a conclusion: Dalessandro et al.," These most likely are members of the cluster, while field stars are clearly separated (the position in the CMD of these two classes of stars further confirms such a conclusion; Dalessandro et al." + 2010)., 2010). + Since no extra-galactic source can be identified in the FOV adopted for this analysis. no absolute proper motion determination can be obtained.," Since no extra-galactic source can be identified in the FOV adopted for this analysis, no absolute proper motion determination can be obtained." +" However a rough estimate can be derived by averaging the positions offield stars: we obtain ji,cos(0)=—1.40 and ο= 3.50) [mas/vr]. in agreement with previous results (Cudworth Hanson 1993)."," However a rough estimate can be derived by averaging the positions offield stars: we obtain $\mu_\alpha cos(\delta)=-1.40$ and $\mu_\delta=3.50$ ) [mas/yr], in agreement with previous results (Cudworth Hanson 1993)." +" COMM-M2S8IT lies at (jn,00s(0)=—0.0920.15. ji=0.090.15) [masvr]. thus fully behaving as à member of the cluster."," COM-M28H lies at $\mu_\alpha cos(\delta)=-0.09 \pm 0.15$, $\mu_\delta=0.09 \pm +0.15$ ) [mas/yr], thus fully behaving as a member of the cluster." + The observed light curve of COM-M?28IT (Fig. 6)), The observed light curve of COM-M28H (Fig. \ref{Fig:lc_combined}) ) + clearly shows (wo distinct aud asvimmetric minima. al phases ὁ~0.25 and ó~0.75. quite similar to what is observed lor (wo other MSP companions (Ferraro et al.," clearly shows two distinct and asymmetric minima, at phases $\phi\sim +0.25$ and $\phi\sim 0.75$, quite similar to what is observed for two other MSP companions (Ferraro et al." + 2001b: Cocozza et al., 2001b; Cocozza et al. + 2008)., 2008). + Such a shape is a clear signature of ellipsoidal variations imduced by the NS tidal field on a highly perturbed. bloated star.," Such a shape is a clear signature of ellipsoidal variations induced by the NS tidal field on a highly perturbed, bloated star." + Moreover. the relative cleepness of (he two minima (consistent wilh a light curve purely due to ellipsoidal variations) suggests that only a marginal (if any) over-heating is allecting the side of the companion facing the pulsar.," Moreover, the relative deepness of the two minima (consistent with a light curve purely due to ellipsoidal variations) suggests that only a marginal (if any) over-heating is affecting the side of the companion facing the pulsar." +" This is also supported by the non-detection of Lf, enission from the svstem (see the right panel of Fie.", This is also supported by the non-detection of $H_\alpha$ emission from the system (see the right panel of Fig. + 4)., 4). + Given the mass function derived [rom the radio observations (fj=0.002112T17M.: Dégein 2006). and assuming 1.4A7. [or the AISP mass and 0.68AZ.. [or the mass of (as derived. [rom the cluster best-fit isochrone). the resulting orbital inclination of the svstem would be /~18°.," Given the mass function derived from the radio observations $f_1=0.00211277 M_\odot$; Béggin 2006), and assuming $1.4 M_\odot$ for the MSP mass and $0.68 M_\odot$ for the mass of COM-M28H (as derived from the cluster best-fit isochrone), the resulting orbital inclination of the system would be $i\sim 18\arcdeg$." + Such a low value for the inclination angle would not produce anv optical modulation., Such a low value for the inclination angle would not produce any optical modulation. + Indeed both the light curve shape and the occurrence of eclipses in the radio signal point toward a significantly higher value of the orbital inclination (which corresponds (o a lower companion nass for a given mass function)., Indeed both the light curve shape and the occurrence of eclipses in the radio signal point toward a significantly higher value of the orbital inclination (which corresponds to a lower companion mass for a given mass function). + By assuming ;/=60 (ihe median of all possible inclination angles) a companion mass of ~0.2AM. is obtained.," By assuming $i=60\arcdeg$ (the median of all possible inclination angles) a companion mass of $\sim +0.2 M_\odot$ is obtained." + In this configuration the corresponding total mass of (he svstem would be M4=1.01. and the physical orbital separation of the system is a 2.84..., In this configuration the corresponding total mass of the system would be $M_{\rm T}=1.6 M_\odot$ and the physical orbital separation of the system is $a\sim 2.8 R_\odot$ . + In order to check whether such a configuration reproduces the observed light curve. we emploved the publicly available," In order to check whether such a configuration reproduces the observed light curve, we employed the publicly available" +inclicates that tie self-calibration cau scatter about a quarter of the real differeuce into calibration parameters.,indicates that the self-calibration can scatter about a quarter of the real difference into calibration parameters. + Noὁ that a spatialy iuvarient spectral line would jist appear as a galu offset in the allected chanues and would no appear iu the clifference images., Note that a spatially invarient spectral line would just appear as a gain offset in the affected channels and would not appear in the difference images. + In αστοι to processing he data as described above. we uade clilference images based o a more tradioual baucpass calibration using 05284-13[.," In addition to processing the data as described above, we made difference images based on a more tradional bandpass calibration using 0528+134." + The ony Channel dependent calibratio[un derived from {1e 3C sil data iself was the reuxoval of linear plase slopes with a fringe fit., The only channel dependent calibration derived from the 3C 84 data itself was the removal of linear phase slopes with a fringe fit. + Th dillereuce images derived iu this way for all channels we'e indistiuguishiable [rom uoise. but wit[un noise levels about twice as high as in the channel images basedonc manuel by channel self-calibration.," The difference images derived in this way for all channels were indistinguishable from noise, but with noise levels about twice as high as in the channel images based on channel by channel self-calibration." + This exercise adds coulicleuce hat we have not self-calibratedili :way a line aud that there is uo spatially invarieut line covering the whole source., This exercise adds confidence that we have not self-calibrated away a line and that there is no spatially invarient line covering the whole source. + Bu lower liiits on liue strength. even giveu the reductions we estimate due to the self-calibration. :'e provided by the images based ou of each channel.," But lower limits on line strength, even given the reductions we estimate due to the self-calibration, are provided by the images based on self-calibration of each channel." + Basically the bandpass calilalion p'ovided by self-calibration on the source itself is significantly better than that provided by the data on the calibrator., Basically the bandpass calibration provided by self-calibration on the source itself is significantly better than that provided by the data on the calibrator. + No recombination liue was detected in any of the images in either emission or absorption., No recombination line was detected in any of the images in either emission or absorption. + TIe limits presented bere are from the dillereie image cube based ou data witreach channel separaten sell-calibrated., The limits presented here are from the difference image cube based on data with each channel separately self-calibrated. + The ruis uoise in the differelce image is 2.3.0 with 0.5 MHz spectre resolution essentially iudepeucdent of posilion., The rms noise in the difference image is 3.0 with 0.5 MHz spectral resolution essentially independent of position. + For lower spectral or spatia resollion. up to factor: ol a lew. the noise decreases about as expecec.," For lower spectral or spatial resolution, up to factors of a few, the noise decreases about as expected." + Two example spectra from the clierence iuage cube are shown i Fietre 3.., Two example spectra from the difference image cube are shown in Figure \ref{spnoise}. + Each is the spatially integrated cifference {lis deusi vsj)ecirun for oue of two regions of the northern feature whose locations are shown iu the inset., Each is the spatially integrated difference flux density spectrum for one of two regions of the northern feature whose locations are shown in the inset. + Region A iucludes the peak of the norhern feature while Reeion B is closer to the core where a st‘oneer Lite might be expected base O1 the racial gradient of the free-[ree abs{1ο Inuiid by WalkeretaI.(2000)., Region A includes the peak of the northern feature while Region B is closer to the core where a stronger line might be expected based on the radial gradient of the free-free absorption found by \citet{W00}. +. For Regions A aud B. the integrated Παν densities iu the coutitUULi mage are 121 anc 207 mJy respectively while the spectra have one sIgnia Lolse levels of Ld aud 8.5 αν.," For Regions A and B, the integrated flux densities in the continuum image are 121 and 207 mJy respectively while the spectra have one sigma noise levels of 4.1 and 8.5 mJy." + The three siguia upper limits to the Iine-to-continuunm ratio are Q.10 :uid 0.12., The three sigma upper limits to the line-to-continuum ratio are 0.10 and 0.12. + Acdjustiug or the possible deg‘acation of {lus due to self-calibration. discussed earlier. 11ese results suggest thiab ay line is less tlan about of the continuum.," Adjusting for the possible degradation of flux due to self-calibration, discussed earlier, these results suggest that any line is less than about of the continuum." + This is the value that will be used iu the ¢Inclssion below., This is the value that will be used in the discussion below. + Note that this limit required some spatial iutegration., Note that this limit required some spatial integration. + On a poiit by poi basis. the three sigma limit o the line-to-contiuuum ratio is not much better thau 0.5.," On a point by point basis, the three sigma limit to the line-to-continuum ratio is not much better than 0.5." + Note that tlie «illerence imagenoise level is about 2x10.! of the total coitinuum [μπιν deusity., Note that the difference imagenoise level is about $2 \times 10^{-4}$ of the total continuum flux density. +" Auy attempt to mase an equivalently sensitive search for the recombination liue with a siugle clish or au interferometer that could not resolve the northern feature would have requred. baudpass calibration to bette ""than a part in 107. a difficult limit to achieve."," Any attempt to make an equivalently sensitive search for the recombination line with a single dish or an interferometer that could not resolve the northern feature would have required bandpass calibration to better than a part in $10^4$ , a difficult limit to achieve." +"post-shock conditions are virtually independent of the Mach number and the so-called. ""Mach sealing” is obtained.",post-shock conditions are virtually independent of the Mach number and the so-called “Mach scaling” is obtained. + Mach scaling appears to hold also when using the &-c turbulence niocel., Mach scaling appears to hold also when using the $k$ $\epsilon$ turbulence model. + Lor weak shocks (4 2.76) the interaction is much milder and the following dillerences are observed: i) the postshock Uow is subsonic with respect to the cloud. so a bowwave rather than a bowshock forms ahead of the cloud. ii) the compression of the cloud is more isotropic. iii) a weaker vortex ring is produced. iv) the smaller. velocity dillerence at the slip surface around the cloud limits the WL and IUE. instabilities and reduces the peak turbulent energy raction of the How. v) it takes much longer for the cloud {κ » mixed into the surrounding Dow and for it to accelerate t he intercloucl postshock speed. and vi) mass stripped from he cloud. does not as readily. form a lone tail (the set-up ime is longer).," For weak shocks $M < 2.76$ ) the interaction is much milder and the following differences are observed: i) the postshock flow is subsonic with respect to the cloud, so a bowwave rather than a bowshock forms ahead of the cloud, ii) the compression of the cloud is more isotropic, iii) a weaker vortex ring is produced, iv) the smaller velocity difference at the slip surface around the cloud limits the KH and RT instabilities and reduces the peak turbulent energy fraction of the flow, v) it takes much longer for the cloud to be mixed into the surrounding flow and for it to accelerate to the intercloud postshock speed, and vi) mass stripped from the cloud does not as readily form a long tail (the set-up time is longer)." + We further find that a prominent tail only forms if x2107., We further find that a prominent tail only forms if $\chi \gtsimm 10^{3}$. + Our most important [finding is that the analytical owescription in. Llartquistctal.(1986). for the ablative miass-loss rate of a cloud in an external [low predicts cloud. lifetimes which are in disagreement with numerically determined values., Our most important finding is that the analytical prescription in \citet{Hartquist:1986} for the ablative mass-loss rate of a cloud in an external flow predicts cloud lifetimes which are in disagreement with numerically determined values. + For instance. the predicted Lifetimes are à actor of25 times too long for clouds with LO«x107 hit ον a Mach 40 shock. while they are about 4 times too short or clouds with y=I0 hit by an AZ=3 shock.," For instance, the predicted lifetimes are a factor of $2-5$ times too long for clouds with $10 < +\chi < 10^{3}$ hit by a Mach 40 shock, while they are about 4 times too short for clouds with $\chi=10$ hit by an $M=3$ shock." + The reason for hese discrepancies appears to be due to the assumption in Llartquistetal.(1986). that the mass-loss is mostIy ciriven by oressure gradients around the cloud., The reason for these discrepancies appears to be due to the assumption in \citet{Hartquist:1986} that the mass-loss is mostly driven by pressure gradients around the cloud. + Instead. we show that he cloud. lifetime is more closely related. to the timescale or large scale Wil instabilities. though it is about 6 times onger than the latter.," Instead, we show that the cloud lifetime is more closely related to the timescale for large scale KH instabilities, though it is about 6 times longer than the latter." + We argue. however. that the rapid reduction in the Mach. number of hypersonic Lows subject o mass-loading means that previous work in the literature is unlikely to greatly change if repeated using a more accurate niass-loss rate prescription.," We argue, however, that the rapid reduction in the Mach number of hypersonic flows subject to mass-loading means that previous work in the literature is unlikely to greatly change if repeated using a more accurate mass-loss rate prescription." + In future work we will extend. our investigation to three dimensions. examine the interaction of a dense shell with a cloud. and will compare svnthetie signatures of the interaction to the tvpes of dill'use sources mentioned in the introduction.," In future work we will extend our investigation to three dimensions, examine the interaction of a dense shell with a cloud, and will compare synthetic signatures of the interaction to the types of diffuse sources mentioned in the introduction." + We would like to thank the referee for a helpful report which improved this paper., We would like to thank the referee for a helpful report which improved this paper. + JALP would also like to thank the Roval Society for funding a University Rescarch Fellowship. and is &erateful for useful discussions with John Dyson on some of this work.," JMP would also like to thank the Royal Society for funding a University Research Fellowship, and is grateful for useful discussions with John Dyson on some of this work." +"and blackbody emission from the whole surface of a 13 km radius neutron star, the 3c upper limits on the is 2.3x10° K (kT=20 eV).","and blackbody emission from the whole surface of a 13 km radius neutron star, the $\sigma$ upper limits on the is $2.3\times10^5$ K $kT=20$ eV)." +" However, the neutron star temperature is not expected to be uniform, with the magnetic poles hotter than the rest of the surface."," However, the neutron star temperature is not expected to be uniform, with the magnetic poles hotter than the rest of the surface." +" The radius of the polar cap can be estimated as Ry,=(27R?/cP)!/?~50 m, where R=10 km is the neutron star radius and P=8.51 s is the pulse period."," The radius of the polar cap can be estimated as $R_{\rm pc}=(2\pi R^3/cP)^{1/2}\sim 50$ m, where $R=10$ km is the neutron star radius and $P=8.51$ s is the pulse period." +" Significantly smaller emitting regions are expected, e.g., in the partially screened gap model (Giletal.2008) and possibly Observed in the thermal emission of old pulsars (e.g., 2009))."," Significantly smaller emitting regions are expected, e.g., in the partially screened gap model \citep{gil08} and possibly observed in the thermal emission of old pulsars (e.g., \citealt{pavolv09}) )." +" Assuming a 10 m radius polar cap, we obtain a temperature upper limit of 1.9x105 K (kT=165 eV) and a bolometric luminosity L «10?5 erg/s. Our non-detection therefore implies a polar cap efficiency L/Exot<0.4, not particularly constraining considering that efficiencies <1 per cent are typically observed in rotation-powered pulsars."," Assuming a 10 m radius polar cap, we obtain a temperature upper limit of $1.9\times10^6$ K $kT=165$ eV) and a bolometric luminosity $L<$ $^{28}$ erg/s. Our non-detection therefore implies a polar cap efficiency $L/\dot{E}_{\rm rot}<0.4$, not particularly constraining considering that efficiencies $<$ 1 per cent are typically observed in rotation-powered pulsars." +" On the other hand, much larger hot spots are inferred from the X-ray spectra of isolated neutron stars possibly heated by magnetic field decay 2009),, which might be related to ((see below)."," On the other hand, much larger hot spots are inferred from the X-ray spectra of isolated neutron stars possibly heated by magnetic field decay \citep{kaplan09}, which might be related to (see below)." +" Assuming a 500 m radius hot spot, we obtain a blackbody temperature upper limit of 4.4x10° K (kT=38 eV) and a bolometric luminosity L<7x107° erg/s. wwas not detected in the extreme UV in a deep 20 ks observation with (Korpela&Bowyer1998)."," Assuming a 500 m radius hot spot, we obtain a blackbody temperature upper limit of $4.4\times10^5$ K $kT=38$ eV) and a bolometric luminosity $L<7\times10^{28}$ erg/s. was not detected in the extreme UV in a deep 20 ks observation with \citep{korpela98}." +". The flux upper limit of 0.023 uJy at 100 is below the extrapolation to the extreme UV of the T=2.3x10? K blackbody spectrum from the whole neutron star surface, if Nu=10? cm~? is assumed."," The flux upper limit of 0.023 $\mu$ Jy at 100 is below the extrapolation to the extreme UV of the $T=2.3 \times 10^{5}$ K blackbody spectrum from the whole neutron star surface, if $N_{\rm H}=10^{20}$ $^{-2}$ is assumed." +" However, Fig."," However, Fig." +" 3 shows how the constraints derived from theEUVE data strongly depend on the interstellar absorption, while the presumably low absorption and extinction towards this nearby pulsar has no impact in the X-ray and optical band."," \ref{sed} shows how the constraints derived from the data strongly depend on the interstellar absorption, while the presumably low absorption and extinction towards this nearby pulsar has no impact in the X-ray and optical band." + We also compared the extrapolation in the optical of the same blackbody spectrum with ourVLT flux upper limits., We also compared the extrapolation in the optical of the same blackbody spectrum with our flux upper limits. +" Our deepest limit, obtained through the B filter, is a factor of zz2 above the Rayleigh-Jeans tail of the X-ray blackbody spectrum, absorbed by an interstellar reddening E(B—V)=0.02.° Thus, it does not constrain the neutron star surface temperature."," Our deepest limit, obtained through the $B$ filter, is a factor of $\approx 2$ above the Rayleigh-Jeans tail of the X-ray blackbody spectrum, absorbed by an interstellar reddening $E(B-V)=0.02$ Thus, it does not constrain the neutron star surface temperature." +" (Martinetal.2005) 3,, Yakovlev&Pethick2004 (Mignanietal.2008;Pavlov2009;Deller"," \citep{martin05short} \ref{sed}, \citealt{yakovlev04} \citep{mignani08,pavolv09,deller09}." + Mereghetti2008 (Arrasetal.2004) Mirallesetal.1998)) (Ponsetal.2009).. (Reaetal.2010)., \citealt{mereghetti08} \citep{arras04} \citealt{miralles98}) \citep{pons09}. \citep{rea2010}. +. Haberl2007 , \citealt{haberl07} +and is assumed to fill all space.,and is assumed to fill all space. + In order to ensure thal V-DB=0. we choose magnet components of the form (Giacalone&Jokipii1994:NiemiecOstrowski2006) where the c; terms denote rancomly generated phase shifts.," In order to ensure that ${\bf \nabla\cdot B}=0$, we choose magnetic-field components of the form \citep{gj94,no06} + where the $\sigma_i$ terms denote randomly generated phase shifts." +The projections of the waveveclor k are: where the angles @ and 5 are randomly selected to generate isotropic turbulence.,The projections of the wavevector ${\bf k}$ are: where the angles $\theta$ and $\eta$ are randomly selected to generate isotropic turbulence. + The wavenumber / is randomly generated with uniform distribution in Inf. such that inverse cell units.," The wavenumber $k$ is randomly generated with uniform distribution in $\ln k$, such that $2\pi\times 10^{-3}\le k \le 4\pi\times 10^{-1}$ inverse cell units." + This allows a range of wavelengths between 5 ancl 1000 cell units. or 20—4000 periods along the line of sight.," This allows a range of wavelengths between 5 and 1000 cell units, or $20-4000$ periods along the line of sight." + The amplitude of the magnetic wave follows we consider (wo possible values lor the power-law index. q.," The amplitude of the magnetic wave follows where we consider two possible values for the power-law index, $q$." + For a lxolmogorov spectrum q=5/3 and for a flat spectrum q=1., For a Kolmogorov spectrum $q=5/3$ and for a flat spectrum $q=1$. +" For a model with a IXolmogorov spectrum. (he rms magnetic amplitude is 07=/BfD,+D2)£ LOG. while a flat-spectrum model results in 0B2 μα. The flat-spectrum models involve more small-scale fInctuations than do the Ixolnogorov models."," For a model with a Kolmogorov spectrum, the rms magnetic amplitude is $\delta B=\sqrt{\langle B_{x'}^2 + B_{y'}^2 +B_{z'}^2\rangle} +\approx 10\mu$ G, while a flat-spectrum model results in $\delta B\approx 20\mu$ G. The flat-spectrum models involve more small-scale fluctuations than do the Kolmogorov models." + We do not know the (rue shape of the turbulence spectrum in SNRs. but comparing the results for the (wo magnetic-field models permits al least a qualitative estimate of the expected results for arbitrary spectra.," We do not know the true shape of the turbulence spectrum in SNRs, but comparing the results for the two magnetic-field models permits at least a qualitative estimate of the expected results for arbitrary spectra." + The projections of the magnetic-fiekl vector are determined in (he same wav as for k: except that ¢ and £ are new angles. still randomly generated such that land 0x€< 27. Ht is straightforward to develop a turbulent. magnetic field [rom the superposition of 1000 waves by summing each component as follows," The projections of the magnetic-field vector are determined in the same way as for ${\bf k}$: except that $\zeta$ and $\xi$ are new angles, still randomly generated such that $-1\le\cos{\zeta}\le 1$ and $0\le\xi\le 2\pi$ It is straightforward to develop a turbulent magnetic field from the superposition of 1000 waves by summing each component as follows" +oor souseful flor comparison with and constraining models.,or so—useful for comparison with and constraining models. + Unlortunatelv. assessment of photospheric N abundances is not so precise and usually has to rely on similar CN features.," Unfortunately, assessment of photospheric N abundances is not so precise and usually has to rely on similar CN features." + The N abundance then also depends on the derived C abundance (hrough molecular equilibrium. and the resulting uncertainties in the C/N ratio can be quite large ancl rarely below 0.2 dex.," The N abundance then also depends on the derived C abundance through molecular equilibrium, and the resulting uncertainties in the C/N ratio can be quite large and rarely below 0.2 dex." + The use of field RGB stars for conlronting model predictions is also hampered bv their uncertain masses and evolutionarv phases. especially near spectral type IxXO where the evolutionary tracks of clump stars of different mass overlap with those of first ascent stars.," The use of field RGB stars for confronting model predictions is also hampered by their uncertain masses and evolutionary phases, especially near spectral type K0 where the evolutionary tracks of clump stars of different mass overlap with those of first ascent stars." + llere. we draw attention to nearby evolved. active binary stars. whose masses and evolutionary phases can generally be much better constrained than for field stars. as offering potentially valuable laboratories for further study of dredge-up aud. post dredge-up mixing.," Here, we draw attention to nearby evolved active binary stars, whose masses and evolutionary phases can generally be much better constrained than for field stars, as offering potentially valuable laboratories for further study of dredge-up and post dredge-up mixing." + Denissenkovetal.(2006) have also piqued interest in these stars through theoretical modelling that indicates extra mixing on the RGD might be induced by tidal spin-up., \citet{Denissenkov.etal:06b} have also piqued interest in these stars through theoretical modelling that indicates extra mixing on the RGB might be induced by tidal spin-up. + In this context. the nearby (26 pe) old disk οἵαπί A And presents an interesting case: it is a mildly mmelal-poor first-ascent G3 ILI-IV star at an evolutionary phase in which CN-evcle products should have just appeared at ils surface due (o first dredge-up (Savanov&Bercdvugina1994:etal.1995:Ottmann1905:Tautvaisiene 2010a:: further characteristics are listed in Table 1)).," In this context, the nearby (26 pc) old disk giant $\lambda$ And presents an interesting case: it is a mildly metal-poor first-ascent G8 III-IV star at an evolutionary phase in which CN-cycle products should have just appeared at its surface due to first dredge-up \citealt{Savanov.Berdyugina:94,Donati.etal:95,Ottmann.etal:98,Tautvaisiene.etal:10}; further characteristics are listed in Table \ref{t:params}) )." + Other than its close binarity. it is similar to members of the sample of mildly metal-poor ([Fe/II]o- —0.5) disk giants that Cottrell&Sneden(1986). found to have unevolved (approximately solar) C/N ratios. but lower ο 11Ο ratios of ~10 30 than predicted by canonical models and reminiscent some of those seen in earlier studies of field giants toward solar metallicity (Lambert&Ries1981:IXjaergaardοἱal.1932).," Other than its close binarity, it is similar to members of the sample of mildly metal-poor $\sim -0.5$ ) disk giants that \citet{Cottrell.Sneden:86} found to have (approximately solar) C/N ratios, but lower $^{12}$ $^{13}$ C ratios of $\sim 10$ –30 than predicted by canonical models and reminiscent some of those seen in earlier studies of field giants toward solar metallicity \citep{Lambert.Ries:81,Kjaergaard.etal:82}." +. The unevolved C/N ratios contrasted with the study ofslightly more massive giants in the solar metallicity cluster M67 by Brown(1937).. which found a palpable decline of C/N on the ascent of the ejant branch.," The unevolved C/N ratios contrasted with the study ofslightly more massive giants in the solar metallicity cluster M67 by \citet{Brown:87}, which found a palpable decline of C/N on the ascent of the giant branch." +" Cottvell Sneden noted that the C/N ratios in the old disk giants. ""lave probably remained unchanged since their formation”.", Cottrell Sneden noted that the C/N ratios in the old disk giants “have probably remained unchanged since their formation”. + Standard. drecdee-up predictions [or red giants of mass 4 times the average background of the pre-whitened residuals (Bregeret 1993)..," For stars in which variability was confirmed, frequencies continued to be selected so long as their amplitude was $>4$ times the average background of the pre-whitened residuals \citep{1993A&A...271..482B}. ." + Formal uncertainties on frequencies andamplitudes, Formal uncertainties on frequencies andamplitudes +observations made with ESO Telescopes at the La Silla and Paranal Observatories under programme IDs 078.B-0623A and OSO.B-0409A. Funding for the DEEP? Galaxy Redshift Survey has been provided in part by NSF grants AST95-09798.. AST-0071048. AST-0071198.. AST-0507428.. and AST-0507483 as well as NASA LTSA grant NNGO4GC89G.. Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred P. Sloan Foundation. the Participating Institutions. the National Aeronautics and Space Administration. the National Science Foundation. the U.S. Department of Energy. the Japanese Monbukagakusho. and the Max Planck Society.,"observations made with ESO Telescopes at the La Silla and Paranal Observatories under programme IDs 078.B-0623A and 080.B-0409A. Funding for the DEEP2 Galaxy Redshift Survey has been provided in part by NSF grants AST95-09298, AST-0071048, AST-0071198, AST-0507428, and AST-0507483 as well as NASA LTSA grant NNG04GC89G. Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society." + The SDSS Web site is httpz//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 University of, The Participating Institutions are The University of +Cambridge Astronomical Survey Unit (CASU) and are distributed via the WFCAM Science Archive (WSA!)).,Cambridge Astronomical Survey Unit (CASU) and are distributed via the WFCAM Science Archive ). +" The GPS data sensitivity is comparable (ο our observations (A —18 mag). albeit with a relatively poor seeing (1"")) and a coarse pixel scale of0."," The GPS data sensitivity is comparable to our observations $K$ =18 mag), albeit with a relatively poor seeing ) and a coarse pixel scale of." +"2""... Fig.", Fig. + 2 shows the neayest-neighbour (NN) density map (Schimeja.Kumar&Ferreira2008.. and relerences (herein) of the UNIDSS A-band source counts.," 2 shows the $^{th}$ nearest-neighbour (NN) density map \citealt*{sch08}, and references therein) of the UKIDSS $K$ -band source counts." + From this figure the cluster center was found to be at Aap)=19536931.03944+203303.," From this figure the cluster center was found to be at $\alpha_{2000} = 19^{\rm h}36^{\rm m}31^{\rm s}, \delta_{2000} = ++20^{\rm \deg}33^{\rm '}03^{\rm ''}$." +" For the purpose of evaluating the [oreground/backeground contamination. we have chosen a “control region"" ~ 2' North of the cluster center at ogg,=195369325,dann,4-203448"" (see Fig."," For the purpose of evaluating the foreground/background contamination, we have chosen a “control region” $\sim$ $\arcmin$ North of the cluster center at $\alpha_{2000} = 19^{\rm h}36^{\rm m}32^{\rm s}, +\delta_{2000} = +20^{\rm \deg}34^{\rm '}48^{\rm ''}$ (see Fig." + 2)., 2). + We utilised tasks available in the Image Reduction and Analysis Facility (RAF) package for our photometric analvsis., We utilised tasks available in the Image Reduction and Analysis Facility ) package for our photometric analysis. + was used to identify sources in each image., was used to identify sources in each image. + A point spread function (PSF) model was computed by choosing stars of different brightness pac, A point spread function (PSF) model was computed by choosing stars of different brightness that were well spaced out in our images. +kage., Photometry was performed using the package. + Aperture corrections were determined bv performing multi-aperture photometry on the PSF stars., Aperture corrections were determined by performing multi-aperture photometry on the PSF stars. + The instrumental magnitudes were calibrated to the absolute scale using observations of UIXIRT faint standard stars; FS 29. FS 35 FS 140 (lawardenetal.2001)..," The instrumental magnitudes were calibrated to the absolute scale using observations of UKIRT faint standard stars; FS 29, FS 35 FS 140 \citep{haw01}." + These standards were observed over a range in airmass (1.05 - 1.79) that was comparable to the target observations., These standards were observed over a range in airmass (1.05 - 1.79) that was comparable to the target observations. + The resulting photometric data are in (he natural svstem of the Manna Kea Consortium Fillers (Simons&Tokunaga2002)., The resulting photometric data are in the natural system of the Mauna Kea Consortium Filters \citep{st02}. +. For the purpose of plotting these data. we converted magnitudes to the Bessell&Brett(1983). (hereafter BB) svstem. since (he main-sequence references are in (he DD svstem.," For the purpose of plotting these data, we converted magnitudes to the \citet{bb88} (hereafter BB) system, since the main-sequence references are in the BB system." + To do this. we first converted the Manna Ixea svstem to the CITsystem and (hen to the DD system using equations given bv Tlawarclenetal.(2001).," To do this, we first converted the Mauna Kea system to the CITsystem and then to the BB system using equations given by \citet{haw01}." +. Representative sub-images consisting of stars and uebulosity were chosen to determine the completeness limits., Representative sub-images consisting of stars and nebulosity were chosen to determine the completeness limits. + Limits were established by manually adding and (then detecting artificial stars of differing magnitudes., Limits were established by manually adding and then detecting artificial stars of differing magnitudes. +" By determining the fraction of stars recovered in each magnitude bin. we have deduced completeness limits of 19.3. 19.0 and 17.5 magnitudes in the J. H. and A bands. respectively,"," By determining the fraction of stars recovered in each magnitude bin, we have deduced completeness limits of 19.3, 19.0 and 17.5 magnitudes in the $J$, $H$ and $K$ bands, respectively." + Our observations are absolutely complete (10054) to the levels of 17.3. 17.2 and 16.2 magnitudes in J. //. and A. respectively.," Our observations are absolutely complete ) to the levels of 17.3, 17.2 and 16.2 magnitudes in $J$, $H$ and $K$, respectively." + Photometric analvsis was carried out using data with photometric errors of less than mmag., Photometric analysis was carried out using data with photometric errors of less than mag. + Absolute position calibration was achieved using the coordinates of a number of stars from the 2\TASS catalog., Absolute position calibration was achieved using the coordinates of a number of stars from the 2MASS catalog. + The astrometric accuracy of the data presented in this work is better than 0.5”., The astrometric accuracy of the data presented in this work is better than . +Ikqo we preseut a new dataset of sizes aud ήπιοics for stellar svstenis of a broad ra1ος of types in the nearby Unisrorse. from tiny star clusters and dwarf salaxies. o giaut elliptical galaxies.,"Here we present a new dataset of sizes and luminosities for stellar systems of a broad range of types in the nearby Universe, from tiny star clusters and dwarf galaxies, to giant elliptical galaxies." + Maux. of he datasets assembled iu τουςit vears have been oricuted around the inclusion of velocity dispersion esinates (c.e.. 2011.. but focusing on the simple parameters of size and Iuninosityv pernits the assedv of a larger sample that also includes πας fainter objects.," Many of the datasets assembled in recent years have been oriented around the inclusion of velocity dispersion estimates (e.g., \citealt{2008A&A...487..921M,2011ApJ...726..108T}, but focusing on the simple parameters of size and luminosity permits the assembly of a larger sample that also includes many fainter objects." + Such a database was published by Misged&Illker(2¢HI). aud serves as one of our uajor sources of data.," Such a database was published by \citet{2011MNRAS.414.3699M}, and serves as one of our major sources of data." + We| update it as described low. both by incorp¢wating additiowl data and by excluding objects with uncertain properlos.," We update it as described below, both by incorporating additional data and by excluding objects with uncertain properties." + Because of our iutercst in rare objects with uuusual properties. if is iu)ortant to iucude only data with measurements.," Because of our interest in rare objects with unusual properties, it is important to include only data with well-constrained measurements." + The basic parameters are t1ο V-band absoute niaenitude My. aud the haltlieht radius Hn plvsical units. which meais that an objects distance must be fairly we] established.," The basic parameters are the $V$ -band absolute magnitude $M_V$, and the half-light radius in physical units, which means that an object's distance must be fairly well established." + Otherwise. a fuzzy object that appears compact ou the sky might be a relatively ucarby GC or a dwarf ealaxy. or alternatively a iore distant ela ealaxy," Otherwise, a fuzzy object that appears compact on the sky might be a relatively nearby GC or a dwarf galaxy, or alternatively a more distant giant galaxy." +" Th any cases, ¢istances are established via spectroscopic redslufts. while the most nearby objects may be recognized because they can be resolved. at cast partially. iuto iuividual stars."," In many cases, distances are established via spectroscopic redshifts, while the most nearby objects may be recognized because they can be resolved, at least partially, into individual stars." + Arclated concern is to avoid objects with larec. and potentially uncerain. cleerees of reddening from dust οscuration.," A related concern is to avoid objects with large, and potentially uncertain, degrees of reddening from dust obscuration." + This applies to the A\ilky Way and to ND. wrere we nmclude oulv hose ojects with inferred extinctioj values of AyS Limag.," This applies to the Milky Way and to M31, where we include only those objects with inferred extinction values of $A_V \la 1$ mag." + Where possible. we also restrict «nr saunple te» those ojects with overall ages of z 5 Cyr in ordY to winimize thο scat erdiuluuimnositv hat can result from stellar luass-to-ight raio variations.," Where possible, we also restrict our sample to those objects with overall ages of $\ga$ 5 Gyr in order to minimize the scatter in luminosity that can result from stellar mass-to-light ratio variations." + This means onüttiug spiral ealaxies a iuteresting extended «objects like Ikxlee Laud W3. while we also exclude sub-coimpoueuts of galaxies like nulees and iclei.," This means omitting spiral galaxies and interesting extended objects like Hodge 4 and W3, while we also exclude sub-components of galaxies like bulges and nuclei." + We beein with he AIST GCs ane UCDs presented here aux iu Straorota.(2011)... and add in objects culled Yolu je Literatur ‘otha lect our criteriv," We begin with the M87 GCs and UCDs presented here and in \citet{Strader11}, and add in objects culled from the literature that meet our criteria." + Two of our largest sources of data are the catalog of Milky Way GCs from POLO)... ane the ¢onmpilation of eaaxies aud star clusters frou Miseeld&Thker(2011)...," Two of our largest sources of data are the catalog of Milky Way GCs from \citet{2010arXiv1012.3224H}, and the compilation of galaxies and star clusters from \citet{2011MNRAS.414.3699M}." +" The other sources are listed ""m1i the Table notes: ln sole cases fjese are not the original s¢mirces for the measurements. but provide compilatiois of xevious daa from the literature."," The other sources are listed in the Table notes; in some cases these are not the original sources for the measurements, but provide compilations of previous data from the literature." + I1 general. we have not atteniped to correct for variatiois dn distance scales between differcut studies.," In general, we have not attempted to correct for variations in distance scales between different studies." + Mau of Le objects did not have W-baud magnitudes reported. aud we have had to estimate these through approximate color raisforlmatious.," Many of the objects did not have $V$ -band magnitudes reported, and we have had to estimate these through approximate color transformations." +" For oue dataset (Celaetal.2003).. WO COuverted the tabulated semi-major axis effective racH to cunc""larized half-light radii based ou the ellipticities: the dSp1 catalog of Brasseurctal.(2011) ought to be corrected inthe same way. but we do not have the cllipticities available."," For one dataset \citep{2003AJ....126.1794G}, we converted the tabulated semi-major axis effective radii to circularized half-light radii based on the ellipticities; the dSph catalog of \citet{2011arXiv1106.5500B} ought to be corrected in the same way, but we do not have the ellipticities available." + Ii order to avoid biasing the categorization of these objects (as star clusters. dwarf galaxies. etce.).," In order to avoid biasing the categorization of these objects (as star clusters, dwarf galaxies, etc.)," + we have not aced any such classifiers. but only applied some suggestive labels to broad areas of paraicter space in Figure 8..," we have not added any such classifiers, but only applied some suggestive labels to broad areas of parameter space in Figure \ref{fig:uber}." + Verv roughly. usimg preliminary classifications as discussed in this paper. the extended database of 970 objects includes 00 CCS. ~ 100 ECS. ~ 50 intermediate objects. ~ LOOUCDs. ~ 50 dSphs. ~ 100 dEs aud cEs. aud ~ 100 &Es.," Very roughly, using preliminary classifications as discussed in this paper, the extended database of 970 objects includes $\sim$ 400 GCs, $\sim$ 100 ECs, $\sim$ 50 intermediate objects, $~\sim$ 100 UCDs, $\sim$ 50 dSphs, $\sim$ 100 dEs and cEs, and $\sim$ 100 gEs." + The datatable is also available on the SACES webpage:, The datatable is also available on the SAGES webpage: . +"For (8)). we need to consider the intersections of 0D,(x.|z—κ) with L as well. represented by the outer shell in Figure 2..","For \ref{eqn:w}) ), we need to consider the intersections of $\delta +B_{du}(\mathbf{x}, |\mathbf{z}-\mathbf{x}|)$ with $L$ as well, represented by the outer shell in Figure \ref{fig:triplet}." + Like in (1)). Ay=0Bo(x./yx)L where d)Bolx.|y—x[) is the sphere centered at x with radius |y—κι.," Like in \ref{eqn:2ndorderwt}) ), $I_{\mathbf{x},\mathbf{y}} = \delta +B_0(\mathbf{x},|\mathbf{y}-\mathbf{x}|) \cap L$ where $\delta B_0(\mathbf{x},|\mathbf{y}-\mathbf{x}|)$ is the sphere centered at $\mathbf{x}$ with radius $|\mathbf{y}-\mathbf{x}|$." + The delinition for [ον is similar.," The definition for $I_{\mathbf{x},\mathbf{z}}$ is similar." +" With respect to Figure 2.. Z,y contains the locations b and y. while 74,2 contains the locations c and z."," With respect to Figure \ref{fig:triplet}, , $I_{\mathbf{x}, \mathbf{y}}$ contains the locations $\mathbf{b}$ and $\mathbf{y}$, while $I_{\mathbf{x}, \mathbf{z}}$ contains the locations $\mathbf{c}$ and $\mathbf{z}$." +" To get the denominator on the right-hand side of (3)). we consider pairs of cvlinders. one on the outer shell ancl one on the inner shell. aa cvlinder associated with a point q in κα and another associated. with a point p in /4,."," To get the denominator on the right-hand side of \ref{eqn:w}) ), we consider pairs of cylinders, one on the outer shell and one on the inner shell, a cylinder associated with a point $\mathbf{q}$ in $I_{\mathbf{x},\mathbf{z}}$ and another associated with a point $\mathbf{p}$ in $I_{\mathbf{x},\mathbf{y}}$." + Each product of the volumes of these pairs of cylinders. equal to z(du)/cos8pxzdcos&q. is included in the sum onlv if the angle subtended at x by the centers of the cvlinder pair is in (he range specified by QO. if lo(Zpxq)=1.," Each product of the volumes of these pairs of cylinders, equal to $\pi d^2 +(du) /\cos\theta_\mathbf{p} \times \pi d^2 (du) +/\cos\theta_\mathbf{q}$, is included in the sum only if the angle subtended at $\mathbf{x}$ by the centers of the cylinder pair is in the range specified by $\Omega$, if $1_\Omega +(\mathbf{\angle pxq})=1$." + In Figure 2.. these pairs are highlighted by rectangles (hat are similarly shaded.," In Figure \ref{fig:triplet}, these pairs are highlighted by rectangles that are similarly shaded." + Note that the (du)? term cancels because there is a corresponding term in ihe numerator of (3))., Note that the $(du)^2$ term cancels because there is a corresponding term in the numerator of \ref{eqn:w}) ). + It is also worth noting that the numerator of (8)) has a form similar to the right-hand side of (6))., It is also worth noting that the numerator of \ref{eqn:w}) ) has a form similar to the right-hand side of \ref{eqn:dK}) ). + There may be locations in £ that cannot be a possible location for the absorber x of a triplet y.x.z ol the desired configuration.," There may be locations in $L$ that cannot be a possible location for the absorber $\mathbf{x}$ of a triplet $\mathbf{y},\mathbf{x}, +\mathbf{z}$ of the desired configuration." + Which locations these are depend on Che actual positions and lengths of the lines of sieht in L., Which locations these are depend on the actual positions and lengths of the lines of sight in $L$. + The quantütv. V. in (9)) accounts for Chis., The quantity $V$ in \ref{eqn:V}) ) accounts for this. + Each location a€L is in the set L(|ly—x|.|zx|.OQ) if there are points b.c€L such that b-a|-l|ly-x.|c-a|-|lz-x and the angle subtended by b and ς αἱ a. Zbac. is in 2. L(lyx|.|z2x].Q) is just the set (aeL:db.ceLz—x|.Zbac€ OQ].," Each location $\mathbf{a} \in L$ is in the set $L(|\mathbf{y}-\mathbf{x}|, |\mathbf{z}-\mathbf{x}|, \Omega)$ if there are points $\mathbf{b},\mathbf{c} \in L$ such that $|\mathbf{b}-\mathbf{a}| = |\mathbf{y}-\mathbf{x}|$, $|\mathbf{c}-\mathbf{a}|=|\mathbf{z}-\mathbf{x}|$ and the angle subtended by $\mathbf{b}$ and $\mathbf{c}$ at $\mathbf{a}$, $\angle \mathbf{bac}$, is in $\Omega$, $L(|\mathbf{y}-\mathbf{x}|, |\mathbf{z}-\mathbf{x}|, \Omega)$ is just the set $\{ \mathbf{a}\in L: \exists +\mathbf{b}, \mathbf{c}\in L \mbox{ with } |\mathbf{b}-\mathbf{a}| = +|\mathbf{y}-\mathbf{x}|, +|\mathbf{c}-\mathbf{a}|=|\mathbf{z}-\mathbf{x}|, \angle +\mathbf{bac}\in\Omega\}$ ." + So. by delinition. x of Figure 2 has to be in L(jy—x].jzxi.Q).," So, by definition, $\mathbf{x}$ of Figure \ref{fig:triplet} has to be in $L(|\mathbf{y}-\mathbf{x}|, |\mathbf{z}-\mathbf{x}|, \Omega)$." + To get an estimate of AK. we divide the estimator (7)) bv an estimate of ATL. NYAA=|ONU)?EP.," To get an estimate of $\mathcal{K}$, we divide the estimator \ref{eqn:estimator}) ) by an estimate of $\lambda^3A$, $(N^3/A^3)A = N^3/(\pi d^2)^2|L|^2$." + Thus. although the expression for «x includes a (zd7)?) term. the value of d need not be specified when estimating AC since il gets cancelled away by the sane term in the estimate of A?.4.," Thus, although the expression for $\omega_\mathbf{x}$ includes a $(\pi d^2)^2$ term, the value of $d$ need not be specified when estimating $\mathcal{K}$ since it gets cancelled away by the same term in the estimate of $\lambda^3A$." + The proof of unbiasedness is provided in the Appendix., The proof of unbiasedness is provided in the Appendix. +Note that it is the estimator of A*AK that isunbiased.,Note that it is the estimator of $\lambda^3A\mathcal{K}$ that isunbiased. + The estimate AC that is obtained bv dividing bv an estimate of AA may be slightly biased., The estimate $\hat{\mathcal{K}}$ that is obtained by dividing by an estimate of $\lambda^3A$ may be slightly biased. + Such a property is called ratio-unbiasedness. and is a feature of estimators of the seconc-order A [unction as well.," Such a property is called ratio-unbiasedness, and is a feature of estimators of the second-order $K$ function as well." + We ran a simulation study to explore the performance of the estimator given in (7)). with," We ran a simulation study to explore the performance of the estimator given in \ref{eqn:estimator}) ), with" +"extra-galactic fields (totaling 70 deg?) at various depths, primarily using the Spectral and Photometric Imaging Receiver (SPIRE) instrument (Griffin et al.","extra-galactic fields (totaling 70 $^2$ ) at various depths, primarily using the Spectral and Photometric Imaging Receiver (SPIRE) instrument (Griffin et al." + 2010)., 2010). +" In thisLetter, we focus on the clustering of these sources from 0.5 to 30 arcminute angular scales by making use of source catalogues in the two widest HerMES fields, Lockman-SWIRE and theSpitzer First Look Survey (FLS) observed during the Science Demonstration Phase (Oliver et al."," In this, we focus on the clustering of these sources from 0.5 to 30 arcminute angular scales by making use of source catalogues in the two widest HerMES fields, Lockman-SWIRE and the First Look Survey (FLS) observed during the Science Demonstration Phase (Oliver et al." + 2010)., 2010). +" Previous studies on the spatial correlations of sub-mm galaxies was limited to at most 100 sources, leading either to a limit on the clustering amplitude (Blain et al."," Previous studies on the spatial correlations of sub-mm galaxies was limited to at most 100 sources, leading either to a limit on the clustering amplitude (Blain et al." + 2004) or a marginal detection (Scott et al., 2004) or a marginal detection (Scott et al. + 2006)., 2006). +" While theBLAST source catalog was not used for a measurement of the angular correlation function, clustered fluctuations were detected in a power spectrum analysis of all three bands (Viero et al."," While the source catalog was not used for a measurement of the angular correlation function, clustered fluctuations were detected in a power spectrum analysis of all three bands (Viero et al." + 2009)., 2009). +" In the Lockman-SWIRE field we have detected 8154, 4899, and 1680 sources with flux densities above 30 mJy at 250, 350, and 500 um, respectively, in an area of 218’x (Oliver et al."," In the Lockman-SWIRE field we have detected 8154, 4899, and 1680 sources with flux densities above 30 mJy at 250, 350, and $500\,\mu$ m, respectively, in an area of $218'\times218'$ (Oliver et al." + 2010)., 2010). +" These counts are supplemented by 3592, 2207, and 1016 sources detected in the FLS field over an area of 135’, again down to the same flux density in each of the three bands."," These counts are supplemented by 3592, 2207, and 1016 sources detected in the FLS field over an area of $155'\times135'$ , again down to the same flux density in each of the three bands." +" These numbers allow clustering estimates at the same precision level as the first-generation of clustering studies at shorter IR wavelengths with source samples fromSpitzer data (e.g., Farrah et al."," These numbers allow clustering estimates at the same precision level as the first-generation of clustering studies at shorter IR wavelengths with source samples from data (e.g., Farrah et al." + 2006; Magliocchetti et al., 2006; Magliocchetti et al. + 2007; Waddington et al., 2007; Waddington et al. + 2007; Brodwin et al., 2007; Brodwin et al. + 2008)., 2008). +" Instead of simple power-law models, the correlation functions of HerMES sources have high enough signal-to-noise ratios that we are also able to constrain parameters of a halo model (e.g. Cooray Sheth 2002)."," Instead of simple power-law models, the correlation functions of HerMES sources have high enough signal-to-noise ratios that we are also able to constrain parameters of a halo model (e.g. Cooray Sheth 2002)." +" The angular correlation function, w(0), is a measure of the probability above Poisson fluctuations of finding two galaxies with a separation 0, ΡάΩιάΩ»=N[1+w(@)]dQ)dQ2, where N is the surface density of galaxies and dQ, are solid angles for each galaxy, corresponding to angle @."," The angular correlation function, $w(\theta)$, is a measure of the probability above Poisson fluctuations of finding two galaxies with a separation $\theta$, $Pd\Omega_1d\Omega_2 =N[1+w(\theta)]d\Omega_1d\Omega_2$, where $N$ is the surface density of galaxies and $d\Omega_i$ are solid angles for each galaxy, corresponding to angle $\theta$." + The angular correlation function is of great interest in cosmology as sources are expected to trace the underlying dark matter distribution and the clustering of sources can be related to that of the dark matter halos., The angular correlation function is of great interest in cosmology as sources are expected to trace the underlying dark matter distribution and the clustering of sources can be related to that of the dark matter halos. + For clustering measurements we make use of the HerMES source catalogues (Oliver et al., For clustering measurements we make use of the HerMES source catalogues (Oliver et al. +" 2010), based on maps made with calibrated timelines with optimized internal astrometry."," 2010), based on maps made with calibrated timelines with optimized internal astrometry." + The maps were produced using the standard SPIRE pipeline after undergoing calibration and other reduction procedures (Swinyard et al., The maps were produced using the standard SPIRE pipeline after undergoing calibration and other reduction procedures (Swinyard et al. + 2010)., 2010). +" In the FLS and Lockman-SWIRE fields, a small number of individual scans have been removed due to artifacts arising from the temperature drift correction."," In the FLS and Lockman-SWIRE fields, a small number of individual scans have been removed due to artifacts arising from the temperature drift correction." +" Catalogues were generated using the SUSSEXtractor source extractor in HIPE version 3.0, using a Gaussian PSF with FWHM of 18.15"", 25.15"", and 36.3"" at 250, 350, and 500 pm, respectively."," Catalogues were generated using the SUSSEXtractor source extractor in version 3.0, using a Gaussian PSF with FWHM of $''$, $''$, and $''$ at 250, 350, and 500 $\mu$ m, respectively." + Two independent maps were also produced by dividing the data in time., Two independent maps were also produced by dividing the data in time. + The sources that do not appear in both sub-maps are flagged as spurious sources and removed from the catalogues., The sources that do not appear in both sub-maps are flagged as spurious sources and removed from the catalogues. + The overall astrometry has been adjusted by comparing with radio positions., The overall astrometry has been adjusted by comparing with radio positions. + We also apply a Wiener filter optimized for unresolved point sources to the maps in the wide fields to remove contamination from cirrus and then we correct source fluxes through simulations., We also apply a Wiener filter optimized for unresolved point sources to the maps in the wide fields to remove contamination from cirrus and then we correct source fluxes through simulations. + The two fields chosen for this study are largely free from cirrus and the clustering measured with two source samples with and without the Wiener filter applied agree with each other within the errors., The two fields chosen for this study are largely free from cirrus and the clustering measured with two source samples with and without the Wiener filter applied agree with each other within the errors. +" Moreover, the source sample used here is restricted to sources detected with an overall significance higher than 5c, including confusion noise."," Moreover, the source sample used here is restricted to sources detected with an overall significance higher than $5\sigma$, including confusion noise." +" Once the catalogues are generated, we use the Landy-Szalay estimator to measure the correlation function with W(0)=[DD(0)—2DR(0)+RR(0)]/RR(0), where DD(6) is the number of unique pairs of real sources with separation 0, DR(0) is the number of unique pairs between the real catalogue and a mock sample of sources with random positions, and RR(0) is the number of unique pairs in the random source catalogues (Landy Szalay 1993)."," Once the catalogues are generated, we use the Landy-Szalay estimator to measure the correlation function with $\hat{w}(\theta) = [DD(\theta) - 2DR(\theta) + RR(\theta)]/RR(\theta)$, where $DD(\theta)$ is the number of unique pairs of real sources with separation $\theta$, $DR(\theta)$ is the number of unique pairs between the real catalogue and a mock sample of sources with random positions, and $RR(\theta)$ is the number of unique pairs in the random source catalogues (Landy Szalay 1993)." +" We employ 10? random mocks with 10? sources in each, a larger number of sources than in real data to reduce shot-noise in the random pair counts."," We employ $10^3$ random mocks with $10^5$ sources in each, a larger number of sources than in real data to reduce shot-noise in the random pair counts." +" Since the measured w(@) does not automatically satisfy the integral constraint (Infante 1994), we estimate the constant necessary to correct w(0) following Adelberger et al. ("," Since the measured $w(\theta)$ does not automatically satisfy the integral constraint (Infante 1994), we estimate the constant necessary to correct $w(\theta)$ following Adelberger et al. (" +2005).,2005). +" With a size of 10 deg? for each of our two fields, we find a required value of ~(2+0.2)x10? between 30’ and 40’."," With a size of 10 $^2$ for each of our two fields, we find a required value of $\sim (2 \pm 0.2)\times10^{-3}$ between $'$ and $'$." + This correction is small compared to w(0~30’)=102., This correction is small compared to $w(\theta \sim 30')\gtrsim10^{-2}$. +" We calculate the covariance matrix C;; of the correlation function involving measurements at two different angular scales 0; and 6;, using a bootstrap method similar to the one employed by Scranton et al. ("," We calculate the covariance matrix $C_{ij}$ of the correlation function involving measurements at two different angular scales $\theta_i$ and $\theta_j$, using a bootstrap method similar to the one employed by Scranton et al. (" +2002) for measurements of angular clustering in SDSS DRI.,2002) for measurements of angular clustering in SDSS DR1. + We also calculate the same covariance analytically following the prescription ofEisenstein Zaldarriaga (2001) and find to smaller off-diagonal correlations than obtained by bootstrapping the data., We also calculate the same covariance analytically following the prescription ofEisenstein Zaldarriaga (2001) and find to smaller off-diagonal correlations than obtained by bootstrapping the data. + We compute the usual Poisson errors by taking the square, We compute the usual Poisson errors by taking the square +"Since their discovery by. American miliary satellites (Vela project) iu 1967. GRBs have evoked intense interest iu the scientific σολτν, because they are the ios energetic explosions m the universe.","Since their discovery by American military satellites (Vela project) in 1967, GRBs have evoked intense interest in the scientific community, because they are the most energetic explosions in the universe." +" Typical GRBs detected by the satellite borne detectors are cousitued by keV to MeV. photons aud hev have cuerey fluxes between 1095 to tafergci, varving ii iuteusity over tiue scales roni nmillisecouds to several tens of seconds."," Typical GRBs detected by the satellite borne detectors are constituted by keV to MeV photons and they have energy fluxes between $10^{-6}$ to $10^{-4}\; erg\;cm^2$, varying in intensity over time scales from milliseconds to several tens of seconds." + The EGRET iustruneut installed ou board of the Compton (παπα Rav Observatory (CGBRO). showed that the lüeh enerev CMeV-GeV) GRB euissio1 lasts longer than the keV. cimission.," The EGRET instrument installed on board of the Compton Gamma Ray Observatory (CGRO), showed that the high energy (MeV-GeV) GRB emission lasts longer than the keV emission." + Tiere were at least five long ECRET GRBs detected simultancously with the bright DATSE sub-MeV. e1issious (Sonuneretal.1991:Dingusal.1992:Ihulevet 1991).," There were at least five long EGRET GRBs detected simultaneously with the bright BATSE sub-MeV emissions \citep{sommer94,dingus95,schneid92,hurley94}." +.. These AMeV-GeWV lone duration EGRET enissbons arrive at the detector discretly. in frageieuts.," These MeV-GeV long duration EGRET emissions arrive at the detector discretly, in fragments." + They are delaved (or aificipated to ο delaved) with the reset to the keV-MeV. BATSE bursts., They are delayed (or anticipated to be delayed) with the respect to the keV-MeV BATSE bursts. + At preseut it is uot known vet. what is the ταoper energyo limit for this long dureon component.," At present it is not known yet, what is the upper energy limit for this long duration component." + Various models predict a flucuce iu he GeWV-TeV¥ rauge conrxwable to that in the keV-MeV interval.," Various models \citep{totani99,dermer00,pilla98} predict a fluence in the GeV-TeV range comparable to that in the keV-MeV interval." + For mstauce. im case of CRB 910217 (Diigus1995).. the Mev-CrieV. emissin persisted for at least 51005. while the duration of the low-energyv (keV) eiission lasted for oulv 1808.," For instance, in case of GRB 940217 \citep{dingus95}, the Mev-GeV emission persisted for at least $5400s$, while the duration of the low-energy (keV) emission lasted for only 180s." + Fig., Fig. + preseuts the overview of this situation., \ref{fig1} presents the overview of this situation. + The long duration CRD event detected xw EGRET. tiat shows large 1.tine ¢ifferences in comparison with the BATSE sigual. can be interpreted as a result of the shock frout hitting an interstellar ποια. leading to subsequent generation of sub-TeV and TeV eanuna ravs which iu turi interact with the iufrared aud microwave backeround radiation iu the interstellar space.," The long duration GRB event detected by EGRET, that shows large time differences in comparison with the BATSE signal, can be interpreted as a result of the shock front hitting an interstellar medium, leading to subsequent generation of sub-TeV and TeV gamma rays which in turn interact with the infrared and microwave background radiation in the interstellar space." + As a result. there is a dispersio iin the observed arrival thue to the detector. because of the differences in the path leneths from the source to the observer.," As a result, there is a dispersion in the observed arrival time to the detector, because of the differences in the path lengths from the source to the observer." + There is another example of the detection ο! heh energy CRB euissious., There is another example of the detection of high energy GRB emissions. + CRB 080511D was detected by the AGILE σαΜΜΑ satellite (Caulianictal.2008)., GRB 080514B was detected by the AGILE gamma-ray satellite \citep{giuliani08}. +. This was tie first CRB. after EGRET. where photons above several te1s MeV were ΑΝdetected.," This was the first GRB, after EGRET, where photons above several tens MeV were detected." + Recently. the Fermi LAT instrunieit detected δ GRBs at energies above 100 MeV. 2009).. includiug extremely energetic GRDOS3916€ (CCN Circular 8216). with the analysis available at 20093).," Recently, the Fermi LAT instrument detected 8 GRBs at energies above 100 MeV \citep{omodei09}, including extremely energetic GRB080916C (GCN Circular 8246), with the analysis available at \citep{abdo09}) )." + This GRD shows that the emission above 100 MeV lasted 20 müuutes longer than the emission ποσα bv f1ο Feri €(BAL in the low euerev region., This GRB shows that the emission above 100 MeV lasted 20 minutes longer than the emission seen by the Fermi GBM in the low energy region. + Iu adcition to fus. the GRD LAT shows that the emission was delaved wihi respect to the CDM enission.," In addition to this, the GRB LAT shows that the emission was delayed with respect to the GBM emission." + This signature of the long duration GRBs oserved by EGRET aud LAT. ic. the lavee time difference in comparison with BATSE and CBAI. res»ectivelv. sugecsts that the bulk of the Ce euissiou arises from an exterual shock afterglow (saumar&Duran2009:Clhiselliuietab.2x0).," This signature of the long duration GRBs observed by EGRET and LAT, i.e. the large time difference in comparison with BATSE and GBM, respectively, suggests that the bulk of the GeV emission arises from an external shock afterglow \citep{kumar09,ghisellini10}." +.. I£ correct. even thisV. scenario is limited to photons with euergies below 10 GeV. due to the nuit on the maxinmii of svuchrotron cussion. when it is combined with the shock wave evolution (Piran&Nalkar2010).," If correct, even this scenario is limited to photons with energies below 10 GeV, due to the limit on the maximum of synchrotron emission, when it is combined with the shock wave evolution \citep{piran10}." +. At the eround level. with he exception of the reported TeV emissiou from BATSE GRB 970170 observed by Milagrito (a water Cherenkoy experiment aud a prototype of Milagro experiment) (atkinsetal.2000).. there were no reports of the detected signal iu the οἱwrev region above 100 GeV for auy single GRD.," At the ground level, with the exception of the reported TeV emission from BATSE GRB 970470 observed by Milagrito (a water Cherenkov experiment and a prototype of Milagro experiment) \citep{atkins00}, there were no reports of the detected signal in the energy region above 100 GeV for any single GRB." + For instance. there were approximately 12 satellite-trigecred GRBs wihin the field of view of MILACGRO.," For instance, there were approximately 42 satellite-triggered GRBs within the field of view of MILAGRO." + No significant ciission was detected from any of these, No significant emission was detected from any of these +(Werneretal.1994:Sion&Downes1992:1997).,"\citep{Werner.etal:94,Sion.Downes:92,Sion.etal:97}." +. More recently. ODwverοἱal.(2003) ancl (seealsoChuοἱal.2004). have reported a detection of weak X-ray. emission ab 1 keV based on a re-analvsis of deeper ROSAT PSPC observations of00054-5106. while Olleetal.(2004) have presented the discovery of an ο VlI-emitting nebula associated with the object.," More recently, \citet{O'Dwyer.etal:03} and \citep[see also][]{Chu.etal:04b} have reported a detection of weak X-ray emission at 1 keV based on a re-analysis of deeper ROSAT PSPC observations of, while \citet{Otte.etal:04} have presented the discovery of an O VI-emitting nebula associated with the object." + In this paper. however. we show that the Low Energy Transmission Grating spectrograph and High Resolution Camera Spectroscopic detector (LETG+IRC-S) spectrum ol ccan be qualitatively modelled as photospheric emission. and does not require a coronal explanation.," In this paper, however, we show that the Low Energy Transmission Grating Spectrograph and High Resolution Camera Spectroscopic detector (LETG+HRC-S) spectrum of can be qualitatively modelled as photospheric emission, and does not require a coronal explanation." + The excess flux [found by Flemingetal.(1993) in the 0.2-0.3 keV range arises [rom deeper alinospheric lavers revealed by a lower continuous opacily in (his region., The excess flux found by \citet{Fleming.etal:93} in the 0.2-0.3 keV range arises from deeper atmospheric layers revealed by a lower continuous opacity in this region. + Difficulties with earlier photospheric modelling attempts are shown (o have arisen because ol the neglect of (race heavier elements such as Fe., Difficulties with earlier photospheric modelling attempts are shown to have arisen because of the neglect of trace heavier elements such as Fe. + The 1 keV emission lound by lies below our detection threshold. but cannot be explained by photospheric models.," The 1 keV emission found by \citet{O'Dwyer.etal:03} lies below our detection threshold, but cannot be explained by photospheric models." +" wwas observed byChandra using the LETG+IRC-S in its standard configuration on 2000 October 25 between UT 05:16 and 10:58 for a total of LOL1ds. after correction for instrument deacltime and bad event Ποιο,"," was observed by using the LETG+HRC-S in its standard configuration on 2000 October 25 between UT 05:16 and 10:58 for a total of 19114s, after correction for instrument deadtime and bad event filtering." + ]nitial reduction of satellite (elemetry was performed by the Nh-ray Center Standard Data Processing software. but was completely reprocessed by us using CIAO 3.1.," Initial reduction of satellite telemetry was performed by the X-ray Center Standard Data Processing software, but was completely reprocessed by us using CIAO 3.1." + The analvsis described here is based on the Level 2 products of this reprocessing., The analysis described here is based on the Level 2 products of this reprocessing. + The scientific analvsis was undertaken using the software suite (Ixashyvap&Drake2000)., The scientific analysis was undertaken using the software suite \citep{Kashyap.Drake:00}. +".. The spectrum of wwas extracted by summing the events within a window 3.6"" in width in the cross-dispersion direction. and background was estimated in two strips of width 15"" each located on either side of the spectral trace."," The spectrum of was extracted by summing the events within a window $3.6\arcsec$ in width in the cross-dispersion direction, and background was estimated in two strips of width $18\arcsec$ each located on either side of the spectral trace." + The final extracted spectrum. binned at 5," The final extracted spectrum, binned at 5" +The RA/s in the Amiga-field are plotted as circles in Fig. 5..,The $RM$ s in the Auriga-field are plotted as circles in Fig. \ref{f4:rmmap}. + Filled circles denote positive values. open circles neeative. and the ciameters of the circles are proportional to RAL.," Filled circles denote positive values, open circles negative, and the diameters of the circles are proportional to $RM$." + For clarity. we oulv show the As for one iu four independent beams.," For clarity, we only show the $RM$ s for one in four independent beams." + Iu addition. RALSs are only shown when they were relably determined. ffor the average polarized intensity (P5>So. aud for reduced \? of the fit c2," In addition, $RM$ s are only shown when they were reliably determined, for the average polarized intensity $\left +> 5\sigma$, and for reduced $\chi^2$ of the fit $< 2$." + The left pauel shows RAL as determined from the observations., The left panel shows $RM$ as determined from the observations. +" Most RALS are reeative: the few positive values occur for àὃς527., while the largest negative values occur for à2557."," Most $RM$ s are negative; the few positive values occur for $\delta \la +52$, while the largest negative values occur for $\delta \ga +55$." +" We modele this systematic variation by a laree-scale linear eradicut. aud fud a eracdicut of about E1 pper degree. with the steepest slope along position augle (from north through east) of 905,"," We modeled this systematic variation by a large-scale linear gradient, and find a gradient of about 1 per degree, with the steepest slope along position angle (from north through east) of $-20\dg$." +" The average RAL. tthe RAL value iu. the ceuter of the fitted ARAZ-plaue. over the field is RA,mἉνδν, "," The average $RM$ , the $RM$ value in the center of the fitted $RM$ -plane, over the field is $RM_0 \approx -3.4$." +Subtracting the best-fit eracdicut from the RAL distribution vields the RASS shown iu the vielt-hand panel in Fie., Subtracting the best-fit gradient from the $RM$ distribution yields the $RM$ s shown in the right-hand panel in Fig. + 5 with onlv sinall-sale structive du RA., \ref{f4:rmmap} with only small-sale structure in $RM$. + The distribution of snall-scale ΠΛ. πμ... scalegeadicitissubtracted)issigni ficantlgnarrowerthaunthetotalB: l.l A insteadof2.3 IK). andisimoresgnanctrical.asisshowninFig. 6," The distribution of small-scale $RM$ s $RM$ where the gradient is subtracted) is significantly narrower than the total $RM$ distribution = 1.4 K instead of 2.3 K), and is more symmetrical, as is shown in Fig. \ref{f4:rmhist}," + , where the two histograms are compared. +The decomposition of the AM-distribution iuto a constant component. a gradient. and a small-scale coniponent is not physical. as there is probably structure on all scales.," The decomposition of the $RM$ -distribution into a constant component, a gradient, and a small-scale component is not physical, as there is probably structure on all scales." + Wowever. for our purpose it is a good approxination. aud it allows us to estimate the large-scale and random componcuts of the Galactic magnetic field. see Sect. 7..," However, for our purpose it is a good approximation, and it allows us to estimate the large-scale and random components of the Galactic magnetic field, see Sect. \ref{s4:disc}." +" Although the RAJ-distribution shows structure on many scales. the most intriguing changes occur on the scale of the beam. as illustrated in Fig. τν,"," Although the $RM$ -distribution shows structure on many scales, the most intriguing changes occur on the scale of the beam, as illustrated in Fig. \ref{f4:RRfield}." + Iu the figure. we display a « 7 array of of7 )-plots. overlaid on a exev scale representation of P at 319 MIIz.," In the figure, we display a $\times$ 7 array of $\phi(\lambda^2)$ -plots, overlaid on a grey scale representation of $P$ at 349 MHz." + Although RAL varics quite smoothly over nost of the area. there are also abrupt changes. which frequently involve a change of the sigu of RM (e.g. at (6.8)= (91.60. oor (91.68. .," Although $RM$ varies quite smoothly over most of the area, there are also abrupt changes, which frequently involve a change of the sign of $RM$ (e.g. at $(\alpha, \delta) =$ (94.60, or (94.68, )." + Abrupt RALchaugesOo over one beu with the right magnitude to cause zn angle chauge of πω|1/2)ISO ceause depolarization canals;, Abrupt $RM$changes over one beam with the right magnitude to cause an angle change of $\pm (n+1/2)\;180$ cause depolarization canals. + As RA is au iutegral over, As $RM$ is an integral over +between clusters. the presence of magnetic fields is evidenced by svuchrotron cussion but the streneth aud structure are vet to be determined.,"between clusters, the presence of magnetic fields is evidenced by synchrotron emission but the strength and structure are yet to be determined." + Ou the largest scales. limits can be imposed by the observed isotropy of the CMDB and by a statistical interpretation of Faraday rotation measures of light. frou distant quasars.," On the largest scales, limits can be imposed by the observed isotropy of the CMB and by a statistical interpretation of Faraday rotation measures of light from distant quasars." +" The isotropy of the CAIB can coustrain the preseut horizon scale fields By,τςὃν109 QU Although the distribution of Faraday rotation measures have ,lavee non-gaussiau tails. a reasonable limit cau be derived using the median of the distribution in au iuhomiogenueous universe: for fields assumed to be constant ou the preset horizou scale. By,1109 G: for fields with 50 Mpe coherence leugth. P3oxtZG6s109 C: while for 1 Mpe colereuce leusth. DyA07 022 These limits apply to à Ομ)=0.02 universe aud use quasars up to redshift +=2.5."," The isotropy of the CMB can constrain the present horizon scale fields $B_{H_0^{-1}} \la \, 3 \times 10^{-9}$ \cite{BFS97} Although the distribution of Faraday rotation measures have large non-gaussian tails, a reasonable limit can be derived using the median of the distribution in an inhomogeneous universe: for fields assumed to be constant on the present horizon scale, $B_{H_0^{-1}} \la \, 10^{-9}$ G; for fields with 50 Mpc coherence length, $B_{50 {\rm Mpc}} +\la \, 6 \times 10^{-9}$ G; while for 1 Mpc coherence length, $B_{Mpc} +\la \, 10^{-8}$ \cite{BBO99} These limits apply to a $\Omega_b h^2 = +0.02$ universe and use quasars up to redshift $z=2.5$." + Localsructures can have fields above these upper linüts as long as they are not comuπι along random Hines of site between : = 0 and 15.12 Of particular interest is f1e field in the local LO Mpc volume around us.," Local structures can have fields above these upper limits as long as they are not common along random lines of site between $z$ = 0 and \cite{RKB98,BBO99} + Of particular interest is the field in the local 10 Mpc volume around us." + Tf the Local Supercluster has fieds of about 10.7 C or larger. the propagation of ultra high euergv protous could become diffusive aud the spectrum aud augular distribution at the hiehest e: ⋅⋅⋅ ∐∖↥⋅∶↴∙⊾↕↸∖↴∖↴∖↖↽∪∏↕≺↴⋝↸∖↴∖↴↕∶↴∙⊾⋯∏↸⊳⋜⋯↑↕⋅↖⇁⋯∪≼∐∏↸∖≺↧⋅⊥⇝⊳−∖⊳⋟− For example. in∙ Figure∙ ↼⋅≻↴↴727. a source with: spectral index: 2Z2a that cau reach Eine1079 eV ds constraiue by the overproduction of lower energy events around d to LO EeV (EeV =10IS ---OV).," If the Local Supercluster has fields of about $10^{-8}$ G or larger, the propagation of ultra high energy protons could become diffusive and the spectrum and angular distribution at the highest energies would be significantly \cite{RKB98,BO99,WW79GWW80BGD89} For example, in Figure \cite{BO99} a source with spectral index $\gamma\ga 2$ that can reach $E_{max} \ga 10^{20}$ eV is constrained by the overproduction of lower energy events around 1 to 10 EeV (EeV $\equiv +10^{18}$ eV)." +" Furthermore. the structure and inagnuitude. of magnetic fields iu the Caactic: Lalo???""25.3 oy in: a possible: Galactic: wind: can also affect the observed UIIECRs."," Furthermore, the structure and magnitude of magnetic fields in the Galactic \cite{S97,HMR99} or in a possible Galactic wind can also affect the observed UHECRs." + Iu particular. if our Galaxy las a strong magnetized wind. what appears to be au isotropic distribution i arrival directions nav have originated on a small region of the sky such as the Vireo cluster? In the future. as sources of UITECTs are identified. huge scale," In particular, if our Galaxy has a strong magnetized wind, what appears to be an isotropic distribution in arrival directions may have originated on a small region of the sky such as the Virgo \cite{ABMS99} In the future, as sources of UHECRs are identified, large scale" +"where / is the time since disk formation. which we assume formed. 12 Gyr before the present clay,","where $t$ is the time since disk formation, which we assume formed $12$ Gyr before the present day." + These two radiation fields combine to heat ancl ionize the cold gas (hat is present in the dwarl galaxy., These two radiation fields combine to heat and ionize the cold gas that is present in the dwarf galaxy. + The gas is ionized according to the absorbed radiation field. for which a racial radiation field vields with ay the radial size of the cold gas in the dwarf and (r.i.z) is the combined raciation field of the Galaxy. and the extragalactic UV field at a distance 7. [requencey ν ancl redshilt : in eres 1| 7 1," The gas is ionized according to the absorbed radiation field, for which a radial radiation field yields with $R_{\rm dw}$ the radial size of the cold gas in the dwarf and $J(r,\nu,z)$ is the combined radiation field of the Galaxy and the extragalactic UV field at a distance $r$, frequency $\nu$ and redshift $z$ in ergs $^{-1}$ $^{-2}$ $^{-1}$." + These radiation fields will also heat the gas. with the heating (considering only II and lle) given by (Wolfireetal.1995) where £j is (he heating per primary electron given by Wollireetal.(1995).," These radiation fields will also heat the gas, with the heating (considering only H and He) given by \citep{Wolfire1995b} + where $E_h$ is the heating per primary electron given by \citet{Wolfire1995b}." + The cooling. A(1.Z). is calculated by metal line cooling at à metallicity of 0.1Z. with the fits provided by Schureetal.(2009). and He collision cooling by (1972).," The cooling, $\Lambda(T,Z)$, is calculated by metal line cooling at a metallicity of $0.1Z_\odot$ with the fits provided by \citet{Schure2009} and He collision cooling by \citet{Dalgarno1972}." +. As more particles are ionized than can be warmed. anv excess ionizations (aller recombination) are converted to heating with all 13.6 eV going to heat the gas.," As more particles are ionized than can be warmed, any excess ionizations (after recombination) are converted to heating with all $13.6$ eV going to heat the gas." + The transfer from cold neutral eas lo warm lonized gas. is (hen given bv," The transfer from cold neutral gas to warm ionized gas, is then given by" +he 15 to 20 per cent level. a larger range of orientations or impact parameters than for a smaller source would have created on observable signal.,"the 15 to 20 per cent level, a larger range of orientations or impact parameters than for a smaller source would have created on observable signal." + Moreover. the duration of the planetary deviation is dominated by the source star moving by its angular size. giving a rather comfortable timespan. which would still have been ~12h for an Earth-mass planet.," Moreover, the duration of the planetary deviation is dominated by the source star moving by its angular size, giving a rather comfortable timespan, which would still have been $\sim 12~\mbox{h}$ for an Earth-mass planet." + While a main-sequence star could have provided a signal with larger amplitude. the probability to observe it would have been smaller and it would not have lasted for that long.," While a main-sequence star could have provided a signal with larger amplitude, the probability to observe it would have been smaller and it would not have lasted for that long." + If one replaces the source star of OGLE 2005-BLG-390 with an 8 times smaller version. an Earth-mass planet in the same spot as OGLE 2005-BLG-390Lb would become undetectable since the smaller source would not enter a region for which significant deviations result.," If one replaces the source star of OGLE 2005-BLG-390 with an 8 times smaller version, an Earth-mass planet in the same spot as OGLE 2005-BLG-390Lb would become undetectable since the smaller source would not enter a region for which significant deviations result." + For the configuration shown in Fig. 3.," For the configuration shown in Fig. \ref{fig:OB05390simuMS}," + the angle of the source trajectory relative to the planet-star axis has therefore been slightly adjusted. resulting in à 5 per cent deviation.," the angle of the source trajectory relative to the planet-star axis has therefore been slightly adjusted, resulting in a 5 per cent deviation." + Achieving good photometry on the fainter target is more difficult and requires longer exposure times., Achieving good photometry on the fainter target is more difficult and requires longer exposure times. + Nevertheless. PLANET has demonstrated a photometric accuracy of even less than 0.5 per cent on a main-sequence star is possible provided that it is fairly isolated rather than in a crowded area.," Nevertheless, PLANET has demonstrated a photometric accuracy of even less than 0.5 per cent on a main-sequence star is possible provided that it is fairly isolated rather than in a crowded area." + While for the previously discussed case involving a giant source star. signal amplitudes significantly exceeding 3 per cent cannot result. the shown 3 per cent deviation is not even near the limit for main-sequence stars. for which very strong signatures become possible should the source happen to cross a caustic.," While for the previously discussed case involving a giant source star, signal amplitudes significantly exceeding 3 per cent cannot result, the shown 5 per cent deviation is not even near the limit for main-sequence stars, for which very strong signatures become possible should the source happen to cross a caustic." + One also sees that the duration of the planetary deviation has not decreased by a factor of 8 as the source size did., One also sees that the duration of the planetary deviation has not decreased by a factor of 8 as the source size did. + Contrary to the giant source star case. the signal duration is now roughly given by the time in which a point source passes the region of angular positions that lead to significant deviations. and remains ~Sh for the prominent peak.," Contrary to the giant source star case, the signal duration is now roughly given by the time in which a point source passes the region of angular positions that lead to significant deviations, and remains $\sim 8~\mbox{h}$ for the prominent peak." + The angular size of the source star itself is reflected in the small peak within the timespan over which the brightness in presence of the planet is smaller than without., The angular size of the source star itself is reflected in the small peak within the timespan over which the brightness in presence of the planet is smaller than without. + As before with a giant source star. the proper characterization of the planetary anomaly is not possible with the standard 2 sampling. while high-cadence sampling after having suspected or detected an anomaly will solve the problem. provided that telescopes are available to observe the target.," As before with a giant source star, the proper characterization of the planetary anomaly is not possible with the standard 2 sampling, while high-cadence sampling after having suspected or detected an anomaly will solve the problem, provided that telescopes are available to observe the target." + Interestingly. in à very early stage of the anomaly. one of the data points appears to be higher just by chance.," Interestingly, in a very early stage of the anomaly, one of the data points appears to be higher just by chance." + Further data taken at the sampling interval of 10 min however do not confirm a significant deviation. so that only after the next data point taken with the standard sampling rate the cadence anomaly monitoring remains active.," Further data taken at the sampling interval of 10 min however do not confirm a significant deviation, so that only after the next data point taken with the standard sampling rate the high-cadence anomaly monitoring remains active." + After having found that the discovery of Earth-mass planets does not constitute the limit of what can be achieved with microlensing survey/follow-up campaigns equipped with an automated anomaly detector. let us look into how far one can go.," After having found that the discovery of Earth-mass planets does not constitute the limit of what can be achieved with microlensing survey/follow-up campaigns equipped with an automated anomaly detector, let us look into how far one can go." + In fact. the rather large separation d.~1.6 of OGLE 390Lb from its host star did not offer a very fortunate configuration.," In fact, the rather large separation $d \sim 1.6$ of OGLE 2005-BLG-390Lb from its host star did not offer a very fortunate configuration." + Let us therefore also consider d.~1.25 and see how the signal amplitude and duration are affected., Let us therefore also consider $d \sim 1.25$ and see how the signal amplitude and duration are affected. + As Fig., As Fig. +" 4 shows. even for a planet with mass nm=0.1AZ, located at 1.256e. from its host in an OGLE 2005-BLG-390-like event. a signal of 10 per"," \ref{fig:OB05390subsimu} shows, even for a planet with mass $m = 0.1~M_{\oplus}$ located at $1.25\,\theta_\rmn{E}$ from its host in an OGLE 2005-BLG-390-like event, a signal of 10 per" +factor is shown in Fig. 7..,factor is shown in Fig. \ref{relecc}. + The values of the growth rate achieved in the interaction of the trapped wave with the eccentric mode are. in general. similar to the values obtained in the interaction with the warp. if the inner inclination and eccentricity are similar.," The values of the growth rate achieved in the interaction of the trapped wave with the eccentric mode are, in general, similar to the values obtained in the interaction with the warp, if the inner inclination and eccentricity are similar." + In this section we discuss the results shown in Figs 4. and 7.. where the dependence of the /=0 r mode growth rate with several parameters is represented.," In this section we discuss the results shown in Figs \ref{relwarp} and \ref{relecc}, where the dependence of the $l=0$ r mode growth rate with several parameters is represented." + In the variation of the growth rate with the dissipation factor. two regimes can be considered: weak dissipation (οx 0.05). where the variation is approximately linear. ancl strong clissipation (3 0.05). where the growth rate remains approximately constant when ο) varies (Fig.," In the variation of the growth rate with the dissipation factor, two regimes can be considered: weak dissipation $\beta \lesssim 0.05$ ), where the variation is approximately linear, and strong dissipation $\beta \gtrsim 0.05$ ), where the growth rate remains approximately constant when $\beta$ varies (Fig." + 4. (a))., \ref{relwarp} (a)). + In the former case. the »=0 intermediate mode is launched. at its inner Lindblad resonance ancl propagates. being slightly attentuated. until it reaches the inner boundary where it is rellected.," In the former case, the $n=0$ intermediate mode is launched at its inner Lindblad resonance and propagates, being slightly attentuated, until it reaches the inner boundary where it is reflected." + Owing to the attenuation. the rellected wave amplitude is smaller than the incident one. ancl therefore the intermediate mode does not cancel. itself. leaving a small amount of οποίον available for the r mode to he excited.," Owing to the attenuation, the reflected wave amplitude is smaller than the incident one, and therefore the intermediate mode does not cancel itself, leaving a small amount of energy available for the r mode to be excited." + In the strong clissipation regime. the η=0 nioele is clissipatecl before reaching the marginally stable orbit.," In the strong dissipation regime, the $n=0$ mode is dissipated before reaching the marginally stable orbit." + 1n this case. all the energy carried by this wave becomes available to excite the trapped. mode.," In this case, all the energy carried by this wave becomes available to excite the trapped mode." + As for the n=2 intermediate mode. in the strong dissipation regime. the wave is completely dissipated before reaching the corotation resonance.," As for the $n=2$ intermediate mode, in the strong dissipation regime, the wave is completely dissipated before reaching the corotation resonance." + Physically we would expect no dissipation tern to be necessary in this case., Physically we would expect no dissipation term to be necessary in this case. + An arbitrarily small amount of dissipation should lead in principle to the complete absorption of the wave at the corotation resonance., An arbitrarily small amount of dissipation should lead in principle to the complete absorption of the wave at the corotation resonance. + HLowever. this cannot be verified numerically because of the dillicultv in resolving the wavelength of the intermediate mode as the singularity at the corotation resonance is approached.," However, this cannot be verified numerically because of the difficulty in resolving the wavelength of the intermediate mode as the singularity at the corotation resonance is approached." + For small warp amplitudes. ic. before the coupling erms start alfecting the structure of the eigenfunctions. the erowth rate grows with the square of the warp amplitude at he inner boundary (Fig.," For small warp amplitudes, i.e., before the coupling terms start affecting the structure of the eigenfunctions, the growth rate grows with the square of the warp amplitude at the inner boundary (Fig." + 4. (b))., \ref{relwarp} (b)). + This is expected since the coupling mechanism relics on the suse’ of the warp twi irst on the interaction with the r mode to give rise to the intermediate modes. and then again on the interaction with he latter to feed back on the former (Fig. 3)).," This is expected since the coupling mechanism relies on the `use' of the warp twice: first on the interaction with the r mode to give rise to the intermediate modes, and then again on the interaction with the latter to feed back on the former (Fig. \ref{diagram}) )." + The excitation mechanism cliscussecl here is similar to he well known parametric instability. in the case where one of the modes is strongly damped.," The excitation mechanism discussed here is similar to the well known parametric instability, in the case where one of the modes is strongly damped." + The parametric instability is a type of resonant coupling between three modes satisfving £y7war|wae. where the subscripts p and d refer to parent ancl daughter modes. respectively.," The parametric instability is a type of resonant coupling between three modes satisfying $\omega_\textrm{p}\approx\omega_{\textrm{d}1}+\omega_{\textrm{d}2}$, where the subscripts p and d refer to parent and daughter modes, respectively." + The parametric instability results in the transfer of energy. [rom the former to the latter. when the daughter modes have small amplitude.," The parametric instability results in the transfer of energy from the former to the latter, when the daughter modes have small amplitude." + The equations describing the evolution of the mode amplitudes read. [rom ).. where 5;20 is the linear amplitude growth/damping rate of mode j and σ is the non-linear coupling constant.," The equations describing the evolution of the mode amplitudes read \citep[adapted from]{wugoldreich2001}, where $\gamma_j>0$ is the linear amplitude growth/damping rate of mode $j$ and $\sigma$ is the non-linear coupling constant." + Let us consider a simplified case where the amplitude of the parent mode is approximately constant in time (because the daughter modes are of small amplitude). and iij=ων ονται0 and 54»=>.," Let us consider a simplified case where the amplitude of the parent mode is approximately constant in time (because the daughter modes are of small amplitude), and $\omega_{\textrm{d}1}=-\omega_{\textrm{d}2}=\omega$ , $\gamma_{\textrm{p}}=\gamma_{\textrm{d}1}=0$ and $\gamma_{\textrm{d}2}=\gamma$." + In this case. the parent mode can be compared to the warp while the daughter modes 1 and 2 can be compared with the r and intermediate modes. respectively.," In this case, the parent mode can be compared to the warp while the daughter modes 1 and 2 can be compared with the r and intermediate modes, respectively." +" Assuming zl,xexp(sf). the growth rate is If -Aplow. Refs)&LAj|ow—$. ie. the growth rate is linearly related to the amplitude of the parent modo."," Assuming $A_{\textrm{d}1}\propto\exp{(st)}$, the growth rate is If $\gamma\ll|A_\mathrm{p}|\sigma\omega$, $\textrm{Re}(s)\approx|A_{\textrm{p}}|\sigma\omega-\frac{\gamma}{2}$, i.e., the growth rate is linearly related to the amplitude of the parent mode." + On the other hand. if 7Aplow. Bets)zLAPaterf ie. the growth rate is »xoportional to the square of the amplitude of the parent mode.," On the other hand, if $\gamma\gg|A_\mathrm{p}|\sigma\omega$, $\textrm{Re}(s)\approx|A_\mathrm{p}|^2\sigma^2\omega^2/\gamma$, i.e., the growth rate is proportional to the square of the amplitude of the parent mode." + The latter case is the one similar to the excitation mechanism we are discussing here., The latter case is the one similar to the excitation mechanism we are discussing here. + Lt should be noted that his parametric instability analysis gives a dependence of ti0 growth rate in 5 which is not in agreement with the numerical results (considering to be equivalent to 3). because the dependence of the spatial structure of the intermediate mode on the dissipation is not considered in this simplistic analvsis.," It should be noted that this parametric instability analysis gives a dependence of the growth rate in $\gamma$ which is not in agreement with the numerical results (considering $\gamma$ to be equivalent to $\beta$ ), because the dependence of the spatial structure of the intermediate mode on the dissipation is not considered in this simplistic analysis." + Also. the parametric instability analysis suggests that the daughter modes gain energv from the parent mode. which is not what happens in the coupling mechanism we are considering. since here the differential rotation of the disc. and not the warp. is the ultimate source of energy for the r mode.," Also, the parametric instability analysis suggests that the daughter modes gain energy from the parent mode, which is not what happens in the coupling mechanism we are considering, since here the differential rotation of the disc, and not the warp, is the ultimate source of energy for the r mode." + Although the parametric instability analysis gives a dependence of the erowth rate on the disturbance amplitude in agreement with our numerical results. it is simplistic and does not consider all the details of the coupling mechanism.," Although the parametric instability analysis gives a dependence of the growth rate on the disturbance amplitude in agreement with our numerical results, it is simplistic and does not consider all the details of the coupling mechanism." + A parallel between le parametric instability and our excitation mechanism is jerefore not. straightforward., A parallel between the parametric instability and our excitation mechanism is therefore not straightforward. + In the strong dissipation regime. the intermediate mode issipates completely. and does not inlluence the variation of rer mode growth rate with both the sound speed of the disc ux the spin of the black hole.," In the strong dissipation regime, the intermediate mode dissipates completely, and does not influence the variation of the r mode growth rate with both the sound speed of the disc and the spin of the black hole." + In this regime. the growth rate decreases with increasing ὃς. as expected.," In this regime, the growth rate decreases with increasing $c_\mathrm{s}$, as expected." + The hotter 1e disc is. the wider the modes get. which means that if the sound speed is high. the modes are not as well trapped.," The hotter the disc is, the wider the modes get, which means that if the sound speed is high, the modes are not as well trapped." + More importantly. the shape of the warp changes when the sound μαος. changes since its wavelength: (Ay) is proportional ο €.," More importantly, the shape of the warp changes when the sound speed changes since its wavelength $\lambda_\textrm{W}$ ) is proportional to $c_\textrm{s}$." + The interaction relies on the use of the warp twice. rerclore we can argue that the growth rate is proportional o |dW/dr|? (since M represents the inclination and dWfdr re actual warp).," The interaction relies on the use of the warp twice, therefore we can argue that the growth rate is proportional to $|dW/dr|^2$ (since $W$ represents the inclination and $dW/dr$ the actual warp)." + Since [dMάνMAxMj2fe Lo. or fixed sound speed the growth rate is proportional to the square of the inner warp amplitude (Fig.," Since $|dW/dr|^2\propto W_0^2/\lambda_\textrm{W}^2\propto W_0^2/c_\textrm{s}^2$, i.e., for fixed sound speed the growth rate is proportional to the square of the inner warp amplitude (Fig." + 4 (b)) and for ixed Wo. the growth rate varies with {ο (Fig.," \ref{relwarp} (b)) and for fixed $W_0$, the growth rate varies with $1/c_\textrm{s}^2$ (Fig." + 4. (c))., \ref{relwarp} (c)). + The small changes to the 1οà law are justified by the fact that. or large sound speed. the decay rate due to the ‘leakage’ at Mou is considerable.," The small changes to the $1/c_\mathrm{s}^2$ law are justified by the fact that, for large sound speed, the decay rate due to the `leakage' at $r_\textrm{out}$ is considerable." + As for the variation of the growth rate with the spin of the black hole. an important conclusion is that. in fact. as argued in the beginning of this section. there is no mode," As for the variation of the growth rate with the spin of the black hole, an important conclusion is that, in fact, as argued in the beginning of this section, there is no mode" +rreflected in the varietv. of determinations. the best fit value is likely to depend somewhat on the choice of interpolation function.,"reflected in the variety of determinations, the best fit value is likely to depend somewhat on the choice of interpolation function." + As noted by Milgrom (1983a) and Felten (1984). equation 1. does not conserve momentum.," As noted by Milgrom (1983a) and Felten (1984), equation \ref{mondeqn} does not conserve momentum." + This was addressed by Bekenstein Milgrom (1934). who wrote the moclifiecdl Poisson equation This form of modified gravity obevs the conservation laws.," This was addressed by Bekenstein Milgrom (1984), who wrote the modified Poisson equation This form of modified gravity obeys the conservation laws." + Milgrom (1994. 1999) also provides a conservative albeit non-local formalism for modified inertia rather than modified gravilv.," Milgrom (1994, 1999) also provides a conservative albeit non-local formalism for modified inertia rather than modified gravity." + Application of equation 1. has been highly successful in fitting rotation curves., Application of equation \ref{mondeqn} has been highly successful in fitting rotation curves. + It is exact for circular orbits in (he modified inertia theory., It is exact for circular orbits in the modified inertia theory. + For modified gravity as il applies in spiral galaxies. equation l is an approximation to equation 2. (hat is usually correct (o e15% (Brada Milgrom 1995).," For modified gravity as it applies in spiral galaxies, equation \ref{mondeqn} is an approximation to equation \ref{AQUAL} + that is usually correct to $\sim 15\%$ (Brada Milgrom 1995)." + For our considerations here (his suífices: il is not necessary to invoke (he aquadratic Lagrangian theory of Bekenstein Milgrom (1984). much less the generally covariant theories of Bekenstein (2004) or Sanders (2005).," For our considerations here this suffices; it is not necessary to invoke the aquadratic Lagrangian theory of Bekenstein Milgrom (1984), much less the generally covariant theories of Bekenstein (2004) or Sanders (2005)." + Indeed. for our purposes here. we merely need (he empirically proven formula connecting surface density and rotation velocity (AleGangh 2004).," Indeed, for our purposes here, we merely need the empirically proven formula connecting surface density and rotation velocity (McGaugh 2004)." + MOND is formulated in terms of the actual acceleration. as appropriate for a dynamical theory.," MOND is formulated in terms of the actual acceleration, as appropriate for a dynamical theory." + However. in the \lilky Way we have a better hancle on the surlace densities that predict the Newtonian acceleration.," However, in the Milky Way we have a better handle on the surface densities that predict the Newtonian acceleration." + Therefore. it is convenient to make the substitution v(y)=p.16r). where y=gxαμ.," Therefore, it is convenient to make the substitution $\nu(y) = \mu^{-1}(x)$, where $y = \gn/\anot$." + While not appropriate as the basis for a theory. this is functionally equivalent when using the empirical approximation of equation 1..," While not appropriate as the basis for a theory, this is functionally equivalent when using the empirical approximation of equation \ref{mondeqn}." + Replacing j/Cr) with vyHy) has the advantage that gxGR) can be clirectly computed from XA) with purely Newtonian dynamics., Replacing $\mu(x)$ with $\nu^{-1}(y)$ has the advantage that $\gn(R)$ can be directly computed from $\Sigma(R)$ with purely Newtonian dynamics. + Assuming circular. motionB (a=V7/T R).4 we then have where iis (he Newlonian rotation velocity expected for the barvons.," Assuming circular motion $a = \Vc^2/R$ ), we then have where is the Newtonian rotation velocity expected for the baryons." + The Newtonian velocity Ἐν ancl acceleralion aare computed for appropriate mass distributions (see 82)): nosimplibving assumption like a ‘spherical disk’ is made., The Newtonian velocity $\Vb$ and acceleration are computed for appropriate mass distributions (see \ref{MWmass}) ): nosimplifying assumption like a `spherical disk' is made. + Moreover. (he right hand side of equation 3. depends onlv on surface densitv. making il possible to. predict the rotation curve without reference (o il through 7=V2/ (a).," Moreover, the right hand side of equation \ref{nunotmu} depends only on surface density, making it possible to predict the rotation curve without reference to it through $x = \Vc^2/(\anot R)$ ." +Fieure l shows a three panel equatorial plane mass density contour map at three different times in the simulation.,Figure 1 shows a three panel equatorial plane mass density contour map at three different times in the simulation. +" In each case. the clensily contours span about 7 orders of magnitude. with each contour level representing a factor of 2 change in density: filled contours indicate regions of the highest density (p7 1! 7, following the convention ol BOT)."," In each case, the density contours span about 7 orders of magnitude, with each contour level representing a factor of 2 change in density; filled contours indicate regions of the highest density $\rho \geq$ $^{-10}$ $^{-3}$, following the convention of B07)." + The box for each image has dimensions of 40 AU x 40 AU., The box for each image has dimensions of 40 AU $\times$ 40 AU. + The top panel shows ihe model at the time nonaxisvmmetric structure reaches its maximum strength. around t = 0.25 ORD.," The top panel shows the model at the time nonaxisymmetric structure reaches its maximum strength, around t = 0.25 ORP." + Note the strong low-order spiral disturbance (primarily four-armed) near the inner boundary. which is a result. of the initial perturbation.," Note the strong low-order spiral disturbance (primarily four-armed) near the inner boundary, which is a result of the initial perturbation." + In the middle panel. after 3.7 ORP's. only a remnant of nonaxisvmnmeltrie structure is seen in the bulk of the disk.," In the middle panel, after 3.7 ORP's, only a remnant of nonaxisymmetric structure is seen in the bulk of the disk." + The hiehest density regions and largest amplitude disturbances are both located near the inner boundary of the grid. though some spiral features can be traced lightly in the outer regions.," The highest density regions and largest amplitude disturbances are both located near the inner boundary of the grid, though some spiral features can be traced lightly in the outer regions." + This is completely different [rom what is shown at the same evolutionary. (me for models Il and TZ in Figures 2 and 3 of DOT. namely. dense clumps and/or nascent clumping near 10 AU.," This is completely different from what is shown at the same evolutionary time for models H and TZ in Figures 2 and 3 of B07, namely, dense clumps and/or nascent clumping near 10 AU." + Over the final two ORP’s of our simulation. as shown in the bottom panel of Figure 1. our disk has evidently settled into a quasi-steady configuration. consisting primarily of a dense ring of material near (he inner hole and a large but low-zimplitude (vo-armed spiral. paris of which extend beyond the original 20 AU edge of the disk.," Over the final two ORP's of our simulation, as shown in the bottom panel of Figure 1, our disk has evidently settled into a quasi-steady configuration, consisting primarily of a dense ring of material near the inner hole and a large but low-amplitude two-armed spiral, parts of which extend beyond the original 20 AU edge of the disk." + Overall. the primary effect of the Gls is racial (rausport of mass.," Overall, the primary effect of the GIs is radial transport of mass." + Unlike some of our previous simulations. in which an unstable disk fragments into short-lived clumps (Pickettοἱal.2003:Mejia2005;Durisen2003).. no clumps ever form during the course of this simulation.," Unlike some of our previous simulations, in which an unstable disk fragments into short-lived clumps \citep{pickett03, mejia05, durisen08}, no clumps ever form during the course of this simulation." + Instead. the initial 2-. 3- ancl 4-armed perturbations grow brielly and then decay.," Instead, the initial 2-, 3- and 4-armed perturbations grow briefly and then decay." + Although the nonaxisvmmeltrie structure reaches a modest nonlinear level. with amplitudes in 9p/pc 0.1 for m = 2. 3 and 4 at about 0.25 ORP. no clumps form.," Although the nonaxisymmetric structure reaches a modest nonlinear level, with amplitudes in $\delta \rho/ \rho \sim$ 0.1 for $m$ = 2, 3 and 4 at about 0.25 ORP, no clumps form." + Local cooling times μι for vertical columnis through the disk in, Local cooling times $t_{\rm cool}$ for vertical columns through the disk in +is ongoing.,is ongoing. + ln this case. we observe increasingly large vertical age gradients at. progessively greater galactocentric distances. while the metallicity gradients might remain approximately similar.," In this case, we observe increasingly large vertical age gradients at progessively greater galactocentric distances, while the metallicity gradients might remain approximately similar." + Onlv in a [ew cases we observe à general blueing with height. for all of the colour. profiles of a given galaxy.," Only in a few cases we observe a general blueing with height, for all of the colour profiles of a given galaxy." + We will now investigate whether these eracients correlate with global galaxy parameters., We will now investigate whether these gradients correlate with global galaxy parameters. + Initial visual examination of the panels in Fig., Initial visual examination of the panels in Fig. + 1. hints at a possible dependence of the magnitude ancl scatter in the vertical colour gradients on galaxy type.," \ref{totgrads.fig} + hints at a possible dependence of the magnitude and scatter in the vertical colour gradients on galaxy type." + Therefore. we determined the average vertical colour gradient. ancl its," Therefore, we determined the average vertical colour gradient and its" +contributing region of the jet away from the jet edge and closer to the center front of the jet.,contributing region of the jet away from the jet edge and closer to the center front of the jet. + T'his effect is illustrated in figure 7.., This effect is illustrated in figure \ref{emission_coefficients_figure}. +" In these figures we have plotted ring-integrated, absorption corrected local emission coefficients for various frequencies at ten days observer time."," In these figures we have plotted ring-integrated, absorption corrected local emission coefficients for various frequencies at ten days observer time." +" The highlighted areas are the areas that, for the given frequency, contribute the most to the observed signal."," The highlighted areas are the areas that, for the given frequency, contribute the most to the observed signal." +" All emission coefficients j, are multiplied by 27h (where h is the distance to the jet axis), such that the plots show the proper relative contributions from the different angles."," All emission coefficients $j_\nu$ are multiplied by $2 \pi h$ (where $h$ is the distance to the jet axis), such that the plots show the proper relative contributions from the different angles." +" The emission coefficients are also corrected for optical depth (Tr), so the quantity that is plotted is j,27hexp[—7]."," The emission coefficients are also corrected for optical depth $\tau$ ), so the quantity that is plotted is $j_\nu 2 \pi h \exp[ - \tau ]$." +" The diagonal lines denote jet half opening angles of 20, 15 and 10 degrees from left to right (the shape of lines along a fixed angle is not affected by the transition from emission to observer frame, this only introduces a transformation the radial lines)."," The diagonal lines denote jet half opening angles of 20, 15 and 10 degrees from left to right (the shape of lines along a fixed angle is not affected by the transition from emission to observer frame, this only introduces a transformation the radial lines)." +" For a given opening angle in the hard-edged jet case, everything above the diagonal is excluded."," For a given opening angle in the hard-edged jet case, everything above the diagonal is excluded." + The plots immediately show why the jet break is postponed in the radio and differs in shape for different frequencies., The plots immediately show why the jet break is postponed in the radio and differs in shape for different frequencies. +" Aside from showing the origin of the delay in the jet break for radio frequencies, the images also show us that for higher frequencies, we look at earlier emission times in general."," Aside from showing the origin of the delay in the jet break for radio frequencies, the images also show us that for higher frequencies, we look at earlier emission times in general." +" From this it also follows that not just the jet break, but any variability resulting from changes in the fluid conditions, will likely manifest themselves in a chromatic fashion."," From this it also follows that not just the jet break, but any variability resulting from changes in the fluid conditions, will likely manifest themselves in a chromatic fashion." +" The blast wave size is smaller at earlier times, and at early times, fluid perturbations will be less smeared out."," The blast wave size is smaller at earlier times, and at early times, fluid perturbations will be less smeared out." + Thus it follows that variability will be most clearly observed in the X-ray light curve., Thus it follows that variability will be most clearly observed in the X-ray light curve. +" As the bottom plots in figures 4 and 5 show, the fractional difference between spherical and collimated outflow is not entirely independent of frequency even above the self-absorption break."," As the bottom plots in figures \ref{jetbreak_spectra_figure} and \ref{jetbreak_spectra_xi01_figure} show, the fractional difference between spherical and collimated outflow is not entirely independent of frequency even above the self-absorption break." +" Both for £y=0.1 and £x=1.0, the collimated outflow flux over the spherical outflow flux reaches a minimum in the spectral region between 1, and the cooling break νε."," Both for $\xi_N = 0.1$ and $\xi_N = 1.0$, the collimated outflow flux over the spherical outflow flux reaches a minimum in the spectral region between $\nu_m$ and the cooling break $\nu_c$." +" This leaves open the possibility that for certain physics parameters and opening angles the jet break as inferred from observational data may differ between optical and X-ray, albeit with a difference that is far less pronounced than that across the self-absorption break that we have discussed above."," This leaves open the possibility that for certain physics parameters and opening angles the jet break as inferred from observational data may differ between optical and X-ray, albeit with a difference that is far less pronounced than that across the self-absorption break that we have discussed above." +" À quantitative assessment of this effect can be made by including the observational biases and errors of measurements for the different frequencies as well, but lies outside the scope of this paper."," A quantitative assessment of this effect can be made by including the observational biases and errors of measurements for the different frequencies as well, but lies outside the scope of this paper." +" Judging purely from the simulated light curves while assuming perfect coverage of the data, a strong distinction between optical and X-ray jet breaks is not obvious."," Judging purely from the simulated light curves while assuming perfect coverage of the data, a strong distinction between optical and X-ray jet breaks is not obvious." + In order to confirm the chromaticity of the jet break in two dimensions we have run a simulation in 2D as well., In order to confirm the chromaticity of the jet break in two dimensions we have run a simulation in 2D as well. +" We have used a similar set up as in the 1D case, starting with a hard-edged jet at Lorentz factor 15 with half opening angle of 20 degrees."," We have used a similar set up as in the 1D case, starting with a hard-edged jet at Lorentz factor 15 with half opening angle of 20 degrees." + In the angular direction we have used 1 base level block instead of ten (as in the radial direction)., In the angular direction we have used 1 base level block instead of ten (as in the radial direction). + The maximum half opening angle covered for the jet is 45 degrees., The maximum half opening angle covered for the jet is 45 degrees. +" For numerical reasons, the maximum refinement"," For numerical reasons, the maximum refinement" + One of the froutiers of cueut. astronomical research is the observation of superuovae at hiel-vedshift., One of the frontiers of current astronomical research is the observation of supernovae at high-redshift. + In fact it is expected that by using SNe In as distance imdicators it will be possible to constrain the geometry of the Universe within a few vears., In fact it is expected that by using SNe Ia as distance indicators it will be possible to constrain the geometry of the Universe within a few years. + Equally naportaut and difficult. is to determine the rate of the different types of SNe as a function of redshift.," Equally important and difficult, is to determine the rate of the different types of SNe as a function of redshift." + The rationale is that the various types of SNe have progenitors of different ages: in particular core-collapse SN ITΠοο result from youug. massive stars and SN Ta originate from intermediate to old population stars (eg.," The rationale is that the various types of SNe have progenitors of different ages; in particular core-collapse SN II+Ib/c result from young, massive stars and SN Ia originate from intermediate to old population stars (eg." + Brauch et al. 199133., Branch et al. \cite{bnf}) ). + Therefore. the evolution of 1 relative SN rates with redshift can be used to probe re average SFR rate history in galaxies aud. in turn. constrain scenarios for galaxy formation aud evolution.," Therefore, the evolution of the relative SN rates with redshift can be used to probe the average SFR rate history in galaxies and, in turn, constrain scenarios for galaxy formation and evolution." + So £u. there have been onlv exploratory atteiupts iu us direction. (Joreeusen et al. 1997:," So far, there have been only exploratory attempts in this direction rgensen et al. \cite{jorg};" + Sadat et al. 1998:: Ala, Sadat et al. \cite{sadat}; +dau et al. 1998).," Madau et al. \cite{madau}) )," + which however have demonstrated i6. potential of tjs approach aud motivated. new observational efforts., which however have demonstrated the potential of this approach and motivated new observational efforts. + The accurate determination of the present time SN rates is the beuclunark. crucial to exploiting these efforts to the full.," The accurate determination of the present time SN rates is the benchmark, crucial to exploiting these efforts to the full." + Another iuportaut factor is to compare the rates of various SN vpes with different iudicators of the stellar population coiteut of galaxies in the local Universe., Another important factor is to compare the rates of various SN types with different indicators of the stellar population content of galaxies in the local Universe. + One problem wih these rates is that local SNe are rare and therefore it requires several vers or decades to collect sufficient statistics., One problem with these rates is that local SNe are rare and therefore it requires several years or decades to collect sufficient statistics. + Ta addition. in order to obtain accurate estimates of the SN rate. it is necessary to know: ‘) the sample of galaxies which have been searched for SNe. H) the frequeney aud limiting magnitude of observations and 7) the iistrumniceuts/techiniques which are used for cletectio iin order to assess scarcl biases.," In addition, in order to obtain accurate estimates of the SN rate, it is necessary to know: $i)$ the sample of galaxies which have been searched for SNe, $ii)$ the frequency and limiting magnitude of observations and $iii)$ the instruments/techniques which are used for detection in order to assess search biases." + Very few eroups of professional astronomers have had the perseverance and force to carry out a SN search program loug enough to be really useful for this purpose(cf Cappellaro ct al., Very few groups of professional astronomers have had the perseverance and force to carry out a SN search program long enough to be really useful for this purpose Cappellaro et al. + 1997. hereafter. C97).," \cite{stat95} + hereafter C97)." + Among the ainateurs in this field. an outstanding case is the visual SN search which has been conducted by Evans since 1980 (Evaus 1997)).," Among the amateurs in this field, an outstanding case is the visual SN search which has been conducted by Evans since 1980 (Evans \cite{ev:97}) )." + Theced. estimates of the SN rate based on he first 10 vears of Evans’ SN search have already beeu iblishied (Evans et al. 1989::," Indeed, estimates of the SN rate based on the first 10 years of Evans' SN search have already been published (Evans et al. \cite{ev:89};" + vau den Bereh Me Claire L199 1))., van den Bergh Mc Clure \cite{vdbmc}) ). + In this paoer we will analyze the updated log of lis survey which doubles the statistics with respect to xeviouxlv published estimates (Sec. 7273)., In this paper we will analyze the updated log of this survey which doubles the statistics with respect to previously published estimates (Sec. \ref{evans}) ). + Following the xotocol described im a previous paper (C97). we pooled together Evans’ log aud those of Xiotographüc searches and used the improved statistical wis to test a different approach for the correction of selection effects (Sec. ?7)].," Following the protocol described in a previous paper (C97), we pooled together Evans' log and those of photographic searches and used the improved statistical basis to test a different approach for the correction of selection effects (Sec. \ref{sec_hatano}) )." +Among the most unexpected discoveries brought forth by a continually growing collection of extra-solar planets has been the realization that giant planets can have near-parabolie orbits.,Among the most unexpected discoveries brought forth by a continually growing collection of extra-solar planets has been the realization that giant planets can have near-parabolic orbits. + Since the seminal discovery of Il6Cygni B (Cochranetal. 1997).. followed by HD80606 (Naefetal.2001). much effort has been dedicated to understanding the dynamical origin and evolution of systems with highly eccentric planets.," Since the seminal discovery of 16Cygni B \citep{1997ApJ...483..457C}, followed by HD80606 \citep{2001A&A...375L..27N}, much effort has been dedicated to understanding the dynamical origin and evolution of systems with highly eccentric planets." + In particular. it has been understood that in presence of a companion star on a inclined orbital plane. the most likely pathway to productio of such extreme planet eccentricities is via Kozai resonance (EggletonandKiseleva-Eggleton.2001)..," In particular, it has been understood that in presence of a companion star on an inclined orbital plane, the most likely pathway to production of such extreme planet eccentricities is via Kozai resonance \citep{2001ApJ...562.1012E}." + The Kozai resonance was first discovered 1n the context of orbital dynamies of highly-inclined asteroids forced. by Jupiter. and has been subsequently recognized as an important process in sculpting the asteroid belt (Kozai.1962) às well as being the primary mechanism by which long-period comets become Sun-grazing (Baileyetal..1992;ThomasandMor-bidelli. 1996).," The Kozai resonance was first discovered in the context of orbital dynamics of highly-inclined asteroids forced by Jupiter, and has been subsequently recognized as an important process in sculpting the asteroid belt \citep{1962AJ.....67..591K} as well as being the primary mechanism by which long-period comets become Sun-grazing \citep{1992A&A...257..315B, 1996CeMDA..64..209T}." +. Physically. the Kozai resonance corresponds to extensive excursions in eccentricity and inclination. of a test particle forced by a massive perturber. subject to conservation of the third Delaunay momentum H=VI—e?costi) (where e is the eccentricity and / is the inclination). and libration of its argument of perihelion «o» around +90°.," Physically, the Kozai resonance corresponds to extensive excursions in eccentricity and inclination of a test particle forced by a massive perturber, subject to conservation of the third Delaunay momentum $H = \sqrt{1-e^2} \cos(i)$ (where $e$ is the eccentricity and $i$ is the inclination), and libration of its argument of perihelion $\omega$ around $\pm 90^\circ$ ." + A necessary criterion for the resonance is a sufficiently large inclination (i>arecos 3/5) relative to the massive perturber's orbital plane. during the part of the cycle where the test-particle's orbit is circular.," A necessary criterion for the resonance is a sufficiently large inclination $i > \arccos \sqrt{3/5}$ ) relative to the massive perturber's orbital plane, during the part of the cycle where the test-particle's orbit is circular." + By direct analogy with the Sun-Jupiter-asteroid picture. the Kozai resoance can give rise to variation in orbital eccentricity and inclination of an extra-solar planet. whose orbit. at the time of formation. is inclined with respect to a stellar companion of the planet's host star (WuandMurray.2003).," By direct analogy with the Sun-Jupiter-asteroid picture, the Kozai resonance can give rise to variation in orbital eccentricity and inclination of an extra-solar planet, whose orbit, at the time of formation, is inclined with respect to a stellar companion of the planet's host star \citep{2003ApJ...589..605W}." + In the systems mentioned above (I6Cygni B. HD80606) the stellar companions! (e.g. loCyent A. HD80607) proper motion has been verified to be consistent with a binary solution.," In the systems mentioned above (16Cygni B, HD80606) the stellar companions' (e.g. 16Cygni A, HD80607) proper motion has been verified to be consistent with a binary solution." + Other examples of planets in binary stellar systems are now plentiful (e.g. y Cephei (Hatzesetal..2003).. HD 196885 (Correiaetal.. 2008).. ete) with binary separation spanning a wide range (à~10—1000 AU).," Other examples of planets in binary stellar systems are now plentiful (e.g. $\gamma$ Cephei \citep{2003ApJ...599.1383H}, HD 196885 \citep{2008A&A...479..271C}, etc) with binary separation spanning a wide range $\tilde{a} \sim 10 - 1000$ AU)." + However. all planets whose eccentricities are expected to have been excited by the Kozai resonance with the companion star are in wide binaries.," However, all planets whose eccentricities are expected to have been excited by the Kozai resonance with the companion star are in wide binaries." + If a Kozai cycle is characterized by à sufficiently small perihelion distance. the eccentricity of the planet may subsequently decay tidally. yielding a pathway to production of hot Jupiters. whose orbital angular momentum vector 1s mis-aligned with respect to the stellar rotation axis (FabryckyandTremaine. 2007).," If a Kozai cycle is characterized by a sufficiently small perihelion distance, the eccentricity of the planet may subsequently decay tidally, yielding a pathway to production of hot Jupiters, whose orbital angular momentum vector is mis-aligned with respect to the stellar rotation axis \citep{2007ApJ...669.1298F}." +. The presence of such objects has been confirmed via observations of the Rossiter-McLaughlin effect (McLaughlin.1924).. leading to à notion that Kozat cycles with tidal friction are responsible for generating at least some misaligned systems (Winnetal..2010:MortonandJohnson.201 D).," The presence of such objects has been confirmed via observations of the Rossiter-McLaughlin effect \citep{1924ApJ....60...22M}, leading to a notion that Kozai cycles with tidal friction are responsible for generating at least some misaligned systems \citep{2010ApJ...718L.145W, 2011ApJ...729..138M}." + Kozai cycles may have also played an important role in systems where a stellar companion is not currently observed., Kozai cycles may have also played an important role in systems where a stellar companion is not currently observed. + Indeed. one can envision an evolutionary history where the binary companion gets stripped away as the birth cluster disperses.," Indeed, one can envision an evolutionary history where the binary companion gets stripped away as the birth cluster disperses." + In fact. such a scenario may be rather likely. às the majority of stars are born in binary systems (DuquennoyandMayor. 1991).," In fact, such a scenario may be rather likely, as the majority of stars are born in binary systems \citep{1991A&A...248..485D}." + In this case. a Kozai cycle can be suddenly interrupted. causing the planets eccentricity to become “frozen-in.”," In this case, a Kozai cycle can be suddenly interrupted, causing the planet's eccentricity to become ""frozen-in.""" + In face of the observationally suggested importance of Kozai cycles during early epochs of planetary systems? dynamical evolution. the of planets in presence of a massive. inclined perturber poses a significant theoretical challenge (Larwoodetal..1996:Marzari2000:Thébaultetal.. 2010).," In face of the observationally suggested importance of Kozai cycles during early epochs of planetary systems' dynamical evolution, the of planets in presence of a massive, inclined perturber poses a significant theoretical challenge \citep{1996MNRAS.282..597L, 2009A&A...507..505M, 2010A&A...524A..13T}." + After all. in the context of the restricted problem (where only the stars are treated as massive perturbers). one would expect the protoplanetary disk to undergo significant excursions in eccentricity and inclination. due to the Kozai resonance. with different temporal phases at different radial distances. resulting in an meoherent structure.," After all, in the context of the restricted problem (where only the stars are treated as massive perturbers), one would expect the protoplanetary disk to undergo significant excursions in eccentricity and inclination due to the Kozai resonance, with different temporal phases at different radial distances, resulting in an incoherent structure." + Such a disk would be characterized by high-velocity impacts among newly-formed planetesimals. strongly inhibiting formation of more massive objects (planetaryembryos) (Lissauer. 1903).," Such a disk would be characterized by high-velocity impacts among newly-formed planetesimals, strongly inhibiting formation of more massive objects (planetaryembryos) \citep{1993ARA&A..31..129L}. ." +" Damping of eccentricities due to gas-drag has been considered as an orbital stabilization process,", Damping of eccentricities due to gas-drag has been considered as an orbital stabilization process. + However. excitation of mutual inclination among neighboring annuli," However, excitation of mutual inclination among neighboring annuli" +"two orbits, one prograde aud one retrograde.","two orbits, one prograde and one retrograde." + After the satellite completes its mereine/disruption process. we identify stars at distance larger than 15 kpc from the disk plane and simply analyze their rotation velocities.," After the satellite completes its merging/disruption process, we identify stars at distance larger than 15 kpc from the disk plane and simply analyze their rotation velocities." + Our main finding is that a counter-rotating stellar halo naturally arises when minor mergers happen on orbits with a low inclination with respect to the disk plane., Our main finding is that a counter-rotating stellar halo naturally arises when minor mergers happen on orbits with a low inclination with respect to the disk plane. + The plan of the Letter is the following., The plan of the Letter is the following. + In Section 2.. we describe our simulations: im Section 3.. we give our results on counter-rotating outer halo stars. and in Section | we draw our conclusions.," In Section \ref{sec:sim}, we describe our simulations; in Section \ref{sec:res}, we give our results on counter-rotating outer halo stars, and in Section \ref{sec:concl} we draw our conclusions." + We use a prinury Dark Matter (DM) halo containing a stellar. rotating exponential disk.," We use a primary Dark Matter (DM) halo containing a stellar, rotating exponential disk." + The DM halo has a NEW (Navarroctal.1997) racial density profile. aud a lnass. radius aud concentration appropriate for a Milky Wav like DAL halo at redshift 2=0.," The DM halo has a NFW \citep{NFW97} radial density profile, and a mass, radius and concentration appropriate for a Milky Way like DM halo at redshift $z=0$." + DM particles have velocities given by the local equilibrinm approximation (IIeruquist.1993)., DM particles have velocities given by the local equilibrium approximation \citep{Hernquist93}. +. Tuto our halo. we embed a truncated stellar disk. having an cxponcutial surface deusity kav: (rfr) where is the disk scale length. and is the surface ceutral density.," Into our halo, we embed a truncated stellar disk, having an exponential surface density law: ) where is the disk scale length, and is the surface central density." + We obtain cach disk particle’s position using the rejection method by Pressetal. (1986): the disk is iu eravitational equilibrium with the DM halo (see Cini&Mazzei(1999). for further details)., We obtain each disk particle's position using the rejection method by \cite{Press86}; the disk is in gravitational equilibrium with the DM halo (see \cite{Curir99} for further details). + We choose for the minor merecr satellite a 1ass ratio of zLO. simular to the estimated mass ratio of the LMC to the Milkv. Wav halo.," We choose for the minor merger satellite a mass ratio of $\approx 40$, similar to the estimated mass ratio of the LMC to the Milky Way halo." + The satellite coutaius a stellar bulge. with a Ieruquist radial density profile.," The satellite contains a stellar bulge, with a Hernquist radial density profile." + We realized our DM|bulge satellite configuration as in Villalobos&Πο(2008)., We realized our DM+bulge satellite configuration as in \cite{Alvaro08}. +. All the physical parameters of our inerger are listed im Table 1.., All the physical parameters of our merger are listed in Table \ref{table:ic}. + We simulated prograde mergers. iu which a satellite co-rotates with respect to the disk spin. aud retrograde oues with a counterrotating satellite.," We simulated prograde mergers, in which a satellite co-rotates with respect to the disk spin, and retrograde ones with a counter-rotating satellite." + We chose two orbits used in Readetal.(2008). for studving the thickening of the disk due to the same kiud of minor merecr: a low-inclination once. with a 10 degree angle with the disk plane. anda high inclination one with a 60 degree angle.," We chose two orbits used in \cite{Read08} for studying the thickening of the disk due to the same kind of minor merger: a low-inclination one, with a 10 degree angle with the disk plane, and a high inclination one with a 60 degree angle." + Tuitially. the ceuter of the primary halo stavs in the origi of our coordinate svsteii aud the satellite is iu (x.wz) = (80.0. 0.27. -15.2) kpe for the low-inchnation orbit aud (15.0. 0.12. -26.0) kpc for the lieh-inclination one.," Initially, the center of the primary halo stays in the origin of our coordinate system and the satellite is in (x,y,z) = (80.0, 0.27, -15.2) kpc for the low-inclination orbit and (15.0, 0.12, -26.0) kpc for the high-inclination one." + The (x.vz)] coniponuenuts of the velocity of the satellite are. in the proerade case. ( 6.3. -62.5. 0.35) Καινής for the low-iuclinatiou orbit aud (-1.2. 80.1. 2.0) kms for the lugh-inchunation one.," The (x,y,z) components of the velocity of the satellite are, in the prograde case, ( 6.3, -62.5, 0.35) km/s for the low-inclination orbit and (-1.2, 80.1, 2.0) km/s for the high-inclination one." + The retrograde orbits have the conrponeut of the velocity iuverted., The retrograde orbits have the y-component of the velocity inverted. + The secondary has always a spin parameter A= 0. where we define A=Jf(2A/V with AL being the mass iuside a radius Rand VWo=R).GAL/R the circular velocity. as in Bullocketal.(2001).," The secondary has always a spin parameter $\lambda=0$ , where we define $\lambda=J/ (\surd{2}MVR)$, with $M$ being the mass inside a radius $R$ and $V=GM/R$ the circular velocity, as in \cite{Bullock01}." +".. We use simulations with a primary halo with a spin paramcter A=1 (simulations ""À) and A0 (simulations ""D).", We use simulations with a primary halo with a spin parameter $\lambda=1$ (simulations “A”) and $\lambda=0$ (simulations “B”). + We assien the aneular momentum to DAL particles using a rigid body rotation profile., We assign the angular momentum to DM particles using a rigid body rotation profile. + The angular momentum of DAL particles is always aligned with that of the stellar clisk., The angular momentum of DM particles is always aligned with that of the stellar disk. +" Our primary Lalo has 10° DM particles inside the virial radius C2.5-10° iu total) and one million star particles in the exponential disk. with mass Afyy=109 M. and AL,=5.97«10! AL. vespectively."," Our primary halo has $10^6$ DM particles inside the virial radius $\sim +2.5\cdot 10^6$ in total) and one million star particles in the exponential disk, with mass $M_{\rm DM}=10^6$ $_\odot$ and $M_*=5.97 \times10^4$ $_\odot$ respectively." + Our DM1Bulge secondary halo has LL.10* DAL particles and 10° bulge star particles. with masses Mas=1.95<107 ML. aud Miles=2.398x104 ML...," Our DM+Bulge secondary halo has $1.1 \cdot 10^5$ DM particles and $10^5$ bulge star particles, with masses $M_{\rm sat}=1.95 +\times 10^5$ $_\odot$ and $M_{\rm bulge}=2.38 \times 10^4$ $_\odot$." + We use a Plunuuicer-equivaleut. eravitatioual softeniug leugth 5=0.5 kpe. and 5=0.25 kpc for bulee star particles.," We use a Plummer-equivalent gravitational softening length $\varepsilon= 0.5$ kpc, and $\varepsilon=0.25$ kpc for bulge star particles." + We run all our simulation using the public parallel Treecode GADGET? (Springel2005)., We run all our simulation using the public parallel Treecode GADGET2 \citep{Springel05}. +". To test the convergence of our results with resolution. we renun our set ""AT with ten times more particles iu the satellite halo."," To test the convergence of our results with resolution, we re-run our set “A” with ten times more particles in the satellite halo." + We also changed the spin parameter of primary and secondary halos. its racial distribution using the profile frou Bullock (Bullocketal.2001).. and their coupling.," We also changed the spin parameter of primary and secondary halos, its radial distribution using the profile from Bullock \citep{Bullock01}, and their coupling." + We analyze positions aud kincmatic of the bulge stars. ouce the satellite completes it iiergiug with the primary haloἘ," We analyze positions and kinematic of the bulge stars, once the satellite completes it merging with the primary halo." +"ν, We run all our simmlatious for f=1.63 Civis. corresponding to ~16 dyinauical timescales of the main halo."," We run all our simulations for $t=4.63$ Gyrs, corresponding to $\sim 16$ dynamical timescales of the main halo." + Iu all cases. iu our sinulatious the satellite is slowed down bv dynamical friction exerted on dt bv both disk and halo particles.," In all cases, in our simulations the satellite is slowed down by dynamical friction exerted on it by both disk and halo particles." + At the first periceuter. tidal forces deform: the satellite. redistributing its particles enerev (violent relaxation). and strips away some stellar particles (tidal stripping).," At the first pericenter, tidal forces deform the satellite, redistributing its particle's energy (violent relaxation), and strips away some stellar particles (tidal stripping)." + The process continues at cach subsequent passage to the periceuter. until no recognizable selferavitatins structure ds present anviuore.," The process continues at each subsequent passage to the pericenter, until no recognizable self-gravitating structure is present anymore." + Stripped star particles tracks the orbital pattern of the satellite., Stripped star particles tracks the orbital pattern of the satellite. + The spatial distribution of stars depends upon the dynamical history of the satellite to which they belonged. 1.0. how quickly it loses its orbital enerev. how strongly it ects disrupted by tidal forces. and how these effects modify the orbit itself during the ΠΙΟΓΟΟΥ process.," The spatial distribution of stars depends upon the dynamical history of the satellite to which they belonged, i.e., how quickly it loses its orbital energy, how strongly it gets disrupted by tidal forces, and how these effects modify the orbit itself during the merger process." + We rotate our coordinate svstei so that the stellar disk. lies in the N-Y plane., We rotate our coordinate system so that the stellar disk lies in the X-Y plane. + The origin is in the disk ceuter of mass., The origin is in the disk center of mass. + To detect a rotation signal in the outer halo stars. we snnplv took all the star particles initially belongiug to our satellite. and having a coordinate Z>15 kpc or Z< Wipe.," To detect a rotation signal in the outer halo stars, we simply took all the star particles initially belonging to our satellite, and having a coordinate $Z>15$ kpc or $Z<-15$ kpc." + We then calculate the rotation velocity of such particles in the disk plaue., We then calculate the rotation velocity of such particles in the disk plane. + In Figue l1. we show histograms of the rotation velocity obtained in the four simulatious of the set A: the satellite is either co-vrotating or counter-rotating witli respect to the disk. aud the orbit has either a low or a high inclination with respect to the disk plane.," In Figure \ref{fig:spin1}, we show histograms of the rotation velocity obtained in the four simulations of the set A: the satellite is either co-rotating or counter-rotating with respect to the disk, and the orbit has either a low or a high inclination with respect to the disk plane." + Iu the upper panels. we show histograms at the final time of our simulations: iu the lower ones; we performed au average over five consecutive snapshots. (~100 My) to get rid of possible sampling effect on the particle orbits which can rise using a particular ustant of time.," In the upper panels, we show histograms at the final time of our simulations; in the lower ones, we performed an average over five consecutive snapshots, $\sim 100$ Myr) to get rid of possible sampling effect on the particle orbits which can rise using a particular instant of time." + We show both the distribution of stars from single simulations. and the one resulting from taking together star particles from proerade aud retrograde orbits having the same initial inclination.," We show both the distribution of stars from single simulations, and the one resulting from taking together star particles from prograde and retrograde orbits having the same initial inclination." + The latter gives us a lint ou the possible rotation signal origin iu the case a siilar uuniber of prograde and retrograde minor accretion eventshappen during the formation history of a galaxy.," The latter gives us a hint on the possible rotation signal origin in the case a similar number of prograde and retrograde minor accretion eventshappen during the formation history of a galaxy," +We thank the referee. Y. Wu for useful suggestions.,"We thank the referee, Y. Wu for useful suggestions." +Phe studs of. the binary star. population in stellar ⋠ ⋅ ⋅ ≱∖∙∖⇁≱∖↿⋖⋅⊔↓≱∖↓⋅∢⊾↓≻↓⋅⋖⊾⊳∖∢⋅⊔↿⊳∖⋜⋯↓⊔↓↓≻∪↓⋅↿⋜⋯⇂↓⊓⋅↓∠⇂∪⇂↓⋅⋖⋅⊳∖⋖⊾⋜⊔⋅≼⇍↓↕∪⇂⊳∖∩⊾∐⋜⊔⋅ ⋅ astrophysics.,The study of the binary star population in stellar systems represents an important field of research of stellar astrophysics. +. ybinary stars are a unique. tool to determine: crucial Vaninformation: about a variety.. of. stellar properties., Binary stars are a unique tool to determine crucial information about a variety of stellar properties. +: Aloreover. they play a key role in ⊲⋅the dynamical. evolution. of⋅ stellar svstems. ancl stellar populations.. studies.," Moreover, they play a key role in the dynamical evolution of stellar systems and stellar populations studies." +. In collisionalD. systems (like. stellar clusters) binaries.. provide. the DTeravitational| fuel that PEcan delay Mand eventuallyt stop p:and reverse the process of gravitational collapse (see Hut et al., In collisional systems (like stellar clusters) binaries provide the gravitational fuel that can delay and eventually stop and reverse the process of gravitational collapse (see Hut et al. + 1992 and references therein)., 1992 and references therein). + Furthermore. the evolution of binaries in star clusters can produce. peculiar. objects of astrophwsie interest. like blue. stragelers. cataclysmic variables. low-mass X-ray binaries. millisecond. pulsars. etc. (," Furthermore, the evolution of binaries in star clusters can produce peculiar objects of astrophysic interest like blue stragglers, cataclysmic variables, low-mass X-ray binaries, millisecond pulsars, etc. (" +sce Dailvn 1995 and reference therein).,see Bailyn 1995 and reference therein). + Finally. the binary fraction is a key ingredient in dynamical models to study the evolution of galaxies and stellar svstems in general (Zhang et al.," Finally, the binary fraction is a key ingredient in dynamical models to study the evolution of galaxies and stellar systems in general (Zhang et al." + 2005)., 2005). + At odds. with the Galactic field. several processes etermine the relative frequeney of binary svstems in stellar ⋅ ≼∙⊔⋡∖⊓⊾," At odds with the Galactic field, several processes determine the relative frequency of binary systems in stellar clusters." +"↓⋅⊳∖⊳↓⊔⇂⋯∙∣⊳∣⋡↓⊔⋜⊔⋅⊓⊾⊳∖⋜⊔⋅⋖⋅≼↛∪⊔∣↓⊔⊔∪⊔⊳∖⇂⋅∖⇁⇂∪↓⋅⊔↓⋯⇂⋜⋯∠""M . ⋅ destroved.∙⊽ during, the evolution]. of⋅ the cluster∙ as a result∙ ο the ever continuing⊀⋠ interactions⊀ between binaries⊀ and single⊀ stars."," In fact, binaries are continuously formed and destroyed during the evolution of the cluster as a result of the ever continuing interactions between binaries and single stars." + opsPhe scenarioD is lopfurther complicated. by the dvnamica. evolution of the cluster (mass segregation. evaporation. etc.)," The scenario is further complicated by the dynamical evolution of the cluster (mass segregation, evaporation, etc.)" + that acts on binary. and single. stars in. a cdillerent- wav ane produces radial. &radients. in. the frequeney.⋅ of p.binaries., that acts on binary and single stars in a different way and produces radial gradients in the frequency of binaries. +. For. these reasons. the theoretical. modelling: of the dynamics. o . ≱∖⋖⊾↓⋜⊔⋅⊳∖∙∖⇁⊳∖↿⋖⋅⊔↓⊳∖↓⊔≼∼⇂⋯⊔⊔⋏∙≟↿↓↕∢⋅⋖⋅∐⋯∙↥∩⇂∣⋡↓⊔⋜⊔⋅⊓⋅⊳∖↓⊳∖⊳∖⊔∐⋜⋯ ⋅ ⋅∢⊀∢ ⊀ open challenge (Portegies Zwart. MeMillan Makino 2007: Ivanova et al.," For these reasons, the theoretical modelling of the dynamics of stellar systems including the effect of binaries is still an open challenge (Portegies Zwart, McMillan Makino 2007; Ivanova et al." + 2005: Llurley. Aarseth Shara 2007: Sollima 2008).," 2005; Hurley, Aarseth Shara 2007; Sollima 2008)." + From the observational point of view. until recent vears. the binary. fraction⋅. has been estimated. only in few ⊀⋅∢⊀⊀individual elobular clusters (οκ) (Romani Weinberg 1991: Bolte 1992: Rubenstein Bailvn 1997: Bellazzini et al.," From the observational point of view, until recent years, the binary fraction has been estimated only in few individual globular clusters (GCs) (Romani Weinberg 1991; Bolte 1992; Rubenstein Bailyn 1997; Bellazzini et al." + 2002: Clark. Sandquist Bolte 2004: Zhao Bailyn 2005).," 2002; Clark, Sandquist Bolte 2004; Zhao Bailyn 2005)." + These studies argued for a celicieney of binary stars in. GC's compared to the field (Pryor et al., These studies argued for a deficiency of binary stars in GCs compared to the field (Pryor et al. + 1989: Lut 1992: Cote et al., 1989; Hut 1992; Cote et al. + 1996)., 1996). + More recently. we investigated the fraction of binaries in a sample of thirteen. low-density GC's (Sollima," More recently, we investigated the fraction of binaries in a sample of thirteen low-density GCs (Sollima" +"temporally varying component of the angular velocity, were used (together with the means) to calculate the variations with epoch in the kinetic energy and angular momentum in different regions of the Sun.","temporally varying component of the angular velocity, were used (together with the means) to calculate the variations with epoch in the kinetic energy and angular momentum in different regions of the Sun." +" For example, the change in angular momentum of the Sun between spherical surfaces at radii γι and r» can be written as where p(r) is the density in the Sun."," For example, the change in angular momentum of the Sun between spherical surfaces at radii $r_1$ and $r_2$ can be written as where $\rho(r)$ is the density in the Sun." +" The integrand in the outer integral defines the contribution to the angular momentum per unit radius from an infinitesimal spherical shell around radius r, namely 06J/0r:=O06J/Or2|,,=,."," The integrand in the outer integral defines the contribution to the angular momentum per unit radius from an infinitesimal spherical shell around radius $r$, namely ${\partial}\delta J/{\partial} r := {\partial}\delta J/{\partial} r_2|_{r_2=r}$." +" Similarly, we can also calculate the temporal variation in the kinetic energy of rotation from the expression In evaluatingΤι expressions (2) and (3) we have used the density p(r) from a standard solar model."," Similarly, we can also calculate the temporal variation in the kinetic energy of rotation from the expression In evaluating expressions (2) and (3) we have used the density $\rho (r)$ from a standard solar model." + In addition to integrating over the entire latitude range we can consider also contributions from different latitude intervals., In addition to integrating over the entire latitude range we can consider also contributions from different latitude intervals. + The observed variation in angular velocity exhibits different behaviour in the low- and high-latitude regions., The observed variation in angular velocity exhibits different behaviour in the low- and high-latitude regions. +" At low latitudes the bands of more rapidly and more slowly rotating fluid migrate towards the equator, while at high latitudes the bands move polewards (Antia Basu 2001; Vorontsov et al."," At low latitudes the bands of more rapidly and more slowly rotating fluid migrate towards the equator, while at high latitudes the bands move polewards (Antia Basu 2001; Vorontsov et al." + 2002; Howe et al., 2002; Howe et al. + 2005; Basu Antia 2006)., 2005; Basu Antia 2006). + We therefore consider the contribution to the integral separately over the low latitudes (€ 7/4) and high latitudes (> 7/4) to see how they compare with the corresponding global quantities., We therefore consider the contribution to the integral separately over the low latitudes $\le\pi/4$ ) and high latitudes $\ge\pi/4$ ) to see how they compare with the corresponding global quantities. +" The integrands in equations (2) and (3) are essentially the same, save for the factor Qo in equation (3)."," The integrands in equations (2) and (3) are essentially the same, save for the factor $\Omega_0$ in equation (3)." +" Therefore because the angular variation of Ωρ is substantial only in the polar regions where the factor sin°@ is quite small, the temporal variations ὃν and óT are very similar."," Therefore because the angular variation of $\Omega_0$ is substantial only in the polar regions where the factor ${\rm sin}^3\theta$ is quite small, the temporal variations $\delta J$ and $\delta T$ are very similar." + Consequently in most of the following discussion we consider explicitly only the temporal variation in the kinetic energy., Consequently in most of the following discussion we consider explicitly only the temporal variation in the kinetic energy. +" We compare it with a solar activity index, for which we use the radio flux at 10.7 cm as a proxy."," We compare it with a solar activity index, for which we use the radio flux at 10.7 cm as a proxy." +" Apart from kinetic energy and angular momentum, it is possible to compute the gravitational quadrupole and higher-order multipole moments of the Sun resulting from the centrifugal force (e.g. Schwarzschild 1947; Sweet 1950; Gough 1981, 1982; Ulrich Hawkins 1981; Pijpers 1998; Antia et al."," Apart from kinetic energy and angular momentum, it is possible to compute the gravitational quadrupole and higher-order multipole moments of the Sun resulting from the centrifugal force (e.g. Schwarzschild 1947; Sweet 1950; Gough 1981, 1982; Ulrich Hawkins 1981; Pijpers 1998; Antia et al." + 2000; Roxburgh 2001; Mecheri et al., 2000; Roxburgh 2001; Mecheri et al. + 2004)., 2004). +" The gravitational potential Φ(Υ,60) outside the Sun can be written as where J, are the dimensionless multipole moments and P», are Legendre polynomials of degree 2k."," The gravitational potential $\Phi(r,\theta)$ outside the Sun can be written as where $J_{2k}$ are the dimensionless multipole moments and $P_{2k}$ are Legendre polynomials of degree $2k$." + We attempt to study the temporal variations in these quantities., We attempt to study the temporal variations in these quantities. +" We show in Figure | the temporal variation of the rotational kinetic energy of the entire convection zone, together with the contributions from the high- and low-latitude regions."," We show in Figure 1 the temporal variation of the rotational kinetic energy of the entire convection zone, together with the contributions from the high- and low-latitude regions." +" The upper panel was obtained from the MDI data, the lower panel from GONG."," The upper panel was obtained from the MDI data, the lower panel from GONG." +" An oscillatory variation with about an 11-year period is evident, although there is some difference between the values inferred from the MDI and the GONG data."," An oscillatory variation with about an 11-year period is evident, although there is some difference between the values inferred from the MDI and the GONG data." + Figure 2 depicts the temporal variation in rotational kinetic energy in different regions of the Sun obtained using the GONG data., Figure 2 depicts the temporal variation in rotational kinetic energy in different regions of the Sun obtained using the GONG data. +" The magnitude of the absolute variation increases with depth, largely on account of increasing mass density."," The magnitude of the absolute variation increases with depth, largely on account of increasing mass density." +" In order to get a more uniform comparison amongst different depths, the variation relative to the mean value of the kinetic energy in each layer is plotted; then the amplitudes are rather similar."," In order to get a more uniform comparison amongst different depths, the variation relative to the mean value of the kinetic energy in each layer is plotted; then the amplitudes are rather similar." + The contributions from low latitudes (0>2/4) and high latitudes (9«7/4) are also plotted., The contributions from low latitudes $(\theta > \pi/4)$ and high latitudes $(\theta < \pi/4)$ are also plotted. + The relative magnitude of these variations is also taken with respect to the mean kinetic energy in the entire latitude range., The relative magnitude of these variations is also taken with respect to the mean kinetic energy in the entire latitude range. + In all cases these variations are similar in magnitude., In all cases these variations are similar in magnitude. + We note that the variation in angular velocity is substantially greater at high latitudes than it is near the equator., We note that the variation in angular velocity is substantially greater at high latitudes than it is near the equator. +" The effect of that on the variation of the rotational kinetic energy and angular momentum is partly compensated by the fact that the high-latitude regions are closer to the rotation axis, and contribute less to the moment of inertia, a property which is reflected by the factor sin?0 in the integrands in equations (2) and (3), which on its own integrates to 5/6V2~0.589 and 2/3—5/6N2=0.077 in the low- and high-latitude regions respectively."," The effect of that on the variation of the rotational kinetic energy and angular momentum is partly compensated by the fact that the high-latitude regions are closer to the rotation axis, and contribute less to the moment of inertia, a property which is reflected by the factor $\sin^3\theta$ in the integrands in equations (2) and (3), which on its own integrates to $5/6 \sqrt{2} \approx 0.589$ and $2/3-5/6 \sqrt{2} = 0.077$ in the low- and high-latitude regions respectively." +" At the bottom of Figure 2 is plotted the 10.7 cm radio flux, which is an indicator of solar activity."," At the bottom of Figure 2 is plotted the 10.7 cm radio flux, which is an indicator of solar activity." + It is evident, It is evident +"where w(z,y,z) is the weight quantity at that location and v(z,y,z) is the value of the projected quantity.","where $w(x,y,z)$ is the weight quantity at that location and $v(x,y,z)$ is the value of the projected quantity." +" To evaluate this integral in our AMR setting, the integral traverses the box along cells that are at the highest refinement for a given point in space, and ignores cells that are covered by more highly refined regions."," To evaluate this integral in our AMR setting, the integral traverses the box along cells that are at the highest refinement for a given point in space, and ignores cells that are covered by more highly refined regions." +" This, like the bulk of our analysis, is done using yt, detailed above."," This, like the bulk of our analysis, is done using $yt$, detailed above." +" In Figures 2--3,, we see that in general the radio emission traces out the large scale structure seen in the density projection."," In Figures \ref{full-box-64}- \ref{zoom-box-64}, we see that in general the radio emission traces out the large scale structure seen in the density projection." +" Additionally, the emission is also highly correlated with the temperature structure."," Additionally, the emission is also highly correlated with the temperature structure." +" However, the correlation with Mach number is more interesting."," However, the correlation with Mach number is more interesting." +" In the projection of Mach number, we see shocks with strengths up to M~10—100 throughout the volume in filaments and cluster edges, whereas the peak radio emission only shows up in small, curved arcs within clusters."," In the projection of Mach number, we see shocks with strengths up to $\Mach \sim10-100$ throughout the volume in filaments and cluster edges, whereas the peak radio emission only shows up in small, curved arcs within clusters." +" At the location of these arcs, the value of the Mach number projection drops to values between M~3— 10."," At the location of these arcs, the value of the Mach number projection drops to values between $\Mach \sim3-10$ ." +" This shows that the strongest shocks which are most likely external, accretion, shocks are not responsible for the bright radio emission, and that it is instead the interior shocks (??),, as was found by ? with moderate strengths, that shine in the radio."," This shows that the strongest shocks which are most likely external, accretion, shocks are not responsible for the bright radio emission, and that it is instead the interior shocks \citep{Ryu:2003aa, Skillman:2008aa}, as was found by \citet{Hoeft:2008aa} with moderate strengths, that shine in the radio." + T'his can be understood by the fact that it is the mass flux of gas through shocks that is most important since that determines the number of electrons that can be accelerated., This can be understood by the fact that it is the mass flux of gas through shocks that is most important since that determines the number of electrons that can be accelerated. +" Therefore, while the Mach number is much lower for the interior shocks, the shock velocity stays roughly constant while the pre-shock density is much higher, yielding more accelerated electrons."," Therefore, while the Mach number is much lower for the interior shocks, the shock velocity stays roughly constant while the pre-shock density is much higher, yielding more accelerated electrons." +" In the projection of Mach number, this results in the appearance of “veins” lining the interior of the filaments, “arcs” in the periphery of the clusters, and “holes” in the centers of the clusters."," In the projection of Mach number, this results in the appearance of “veins” lining the interior of the filaments, “arcs” in the periphery of the clusters, and “holes” in the centers of the clusters." +" While they are decrements in the projection of Mach number, they are the bright areas in the radio emission."," While they are decrements in the projection of Mach number, they are the bright areas in the radio emission." +" 'The lack of strong emission in the accretion shocks suggests that having a hot, dense plasma is more important than the Mach number of the shock."," The lack of strong emission in the accretion shocks suggests that having a hot, dense plasma is more important than the Mach number of the shock." + This can be understood by Equation 3.., This can be understood by Equation \ref{eq:2}. +" Since aοςAn€vT3/2Bits/2p+B? and in most cluster situations Beyp>B? Bi.and s=2a+13, we have that aοςneB/?xne(n2!?)5/2n&/?_"," Since $\frac{dP}{d\nu}\propto A\ n_e \xi \nu T^{3/2} +\frac{B^{1+s/2}}{B_{CMB}^2 + B^2}$ and in most cluster situations $B_{CMB}^2 > B^2$ and $s = 2\alpha + 1 ~= 3$, we have that $\frac{dP}{d\nu}\propto n_e B^{5/2} \propto n_e (n_e^{2/3})^{5/2} +\propto n_e^{8/3}$." +" This implies that since the density in the accretion shocks is zz10?— times lower than that in a merger shock, the power emitted will be down by a factor of ~2x105—105."," This implies that since the density in the accretion shocks is $\approx 10^2 - 10^3$ times lower than that in a merger shock, the power emitted will be down by a factor of $\approx +2\times 10^3 - 10^5$." + Therefore the features we see observationally are more likely to be related to merger shocks than accretion shocks., Therefore the features we see observationally are more likely to be related to merger shocks than accretion shocks. + The second method we use to study the bulk properties of the radio emitting plasma is phase diagrams., The second method we use to study the bulk properties of the radio emitting plasma is phase diagrams. + Such diagrams are the equivalent of a two-dimensional histogram., Such diagrams are the equivalent of a two-dimensional histogram. + Here we use them to study the gas properties of the radio emitting regions., Here we use them to study the gas properties of the radio emitting regions. + The structure of these diagrams is as follows., The structure of these diagrams is as follows. +" For a given simulation output, we construct x and y-axis bins that are equally spaced logarithmically in two fields."," For a given simulation output, we construct x and y-axis bins that are equally spaced logarithmically in two fields." +" Within each of these 2D bins, we integrate the total amount of a given quantity such as radio emission."," Within each of these 2D bins, we integrate the total amount of a given quantity such as radio emission." + This integrated value is normalized by the comoving volume of the simulation in order to give a comparable value between different physical size simulations., This integrated value is normalized by the comoving volume of the simulation in order to give a comparable value between different physical size simulations. +" We have found three particularly insightful quantities to examine in a range of permutions: temperature, overdensity, and Mach number."," We have found three particularly insightful quantities to examine in a range of permutions: temperature, overdensity, and Mach number." +" We have constructed one such phase diagram, seen in Figure 4,, in which the x-axis is the Mach number, the y- is temperature, and the bins are colored by the total radio emission in that bin."," We have constructed one such phase diagram, seen in Figure \ref{fig:mach-temp-radio}, in which the x-axis is the Mach number, the y-axis is temperature, and the bins are colored by the total radio emission in that bin." + The total integrated emission is normalized by the volume of the simulation and the size of the bins., The total integrated emission is normalized by the volume of the simulation and the size of the bins. +" As such, one reads this figure as “At"," As such, one reads this figure as “At" +upturn region.,upturn region. + On the tail side no such eradicut has becu found., On the tail side no such gradient has been found. + Iu this article we preseut new CO(2-1) and 6 cm radio continmuni enission observations of NGC 1330., In this article we present new CO(2-1) and 6 cm radio continuum emission observations of NGC 4330. + The available multiwavelength observations (UV. IIo.Ir. CO. 6 cn total power radio continuum. 6 em polarized radio contiuuun) are compared to a dyvuauical model including] rai pressure stripping au. for the firs tine. star formation.," The available multiwavelength observations (UV, $\alpha$, CO, 6 cm total power radio continuum, 6 cm polarized radio continuum) are compared to a dynamical model including ram pressure stripping and, for the first time, star formation." + The distribution of molecular gas iu the ealactic disk is more extended towards the upturn region., The distribution of molecular gas in the galactic disk is more extended towards the upturn region. + The upturn itself is visible iu CO and radio continuuu chussion., The upturn itself is visible in CO and radio continuum emission. + No CO nor radio continua emission is detected in the gas tail., No CO nor radio continuum emission is detected in the gas tail. + As the cinission. the 6 ci total power radio continuuni ορίου. is less extende along the uinor axis on the windward side.," As the emission, the 6 cm total power radio continuum emission is less extended along the minor axis on the windward side." + There is a secoud radio coutimmun upturn region on the tail side., There is a second radio continuum upturn region on the tail side. + This second upturn is only visible iu radio continu euission., This second upturn is only visible in radio continuum emission. + The polarized radio continuuni oenüsson ids relatively sviunietrie and. in coutrast to other Virgo spirals affectcc wera pressure. does not show an asvuuuetric ridge in 1ο outer disk.," The polarized radio continuum emission is relatively symmetric and, in contrast to other Virgo spirals affected by ram pressure, does not show an asymmetric ridge in the outer disk." +" The best ft model has been chosen from, a sexies of siuulatious with differen (1) inchnation angles between je rann pressure wind :id the disk plane. (41) values of 10 mnaxinmun rani pressure. and Gi) durations of the rai oessure strippius event."," The best fit model has been chosen from a series of simulations with different (i) inclination angles between the ram pressure wind and the disk plane, (ii) values of the maximum ram pressure, and (iii) durations of the ram pressure stripping event." + The bes fit model is cousisteu with 1ο salaxys projected position aud radial velocity oei the Virgo[m] cluster aud. the model C»gas distribution aud velocity field. reproduce he observations., The best fit model is consistent with the galaxy's projected position and radial velocity in the Virgo cluster and the model gas distribution and velocity field reproduce the observations. +" NGC 1330 experieuces a rani pressure of pa,=2500 ""(li 12 and the anele between the rani pressure wind aud the ealactic plane is 757."," NGC 4330 experiences a ram pressure of $p_{\rm rps}= +2500$ $^{-3}$ $^{-1}$ $^{2}$ and the angle between the ram pressure wind and the galactic plane is $75^{\circ}$." + Based ou the orbital segineut eiveon iun. Vollmer (2009) a WANA ral pressure of ~5000 ? 1y? will occur in ~LOO Myz., Based on the orbital segment given in Vollmer (2009) a maximum ram pressure of $\sim 5000$ $^{-3}$ $^{-1}$ $^{2}$ will occur in $\sim 100$ Myr. +"It is casily verified that this corrected redistribution ""unctiou satisfies the detailed balance relation (15)).",It is easily verified that this corrected redistribution function satisfies the detailed balance relation ). +" We prefer this method to that of DW. because it introduces no new ¢iscontinuities of slope atv =1"" aud is more amenable to the kind of analytic manipulations employed iu this paper."," We prefer this method to that of DW, because it introduces no new discontinuities of slope at $\nu =\nu'$ and is more amenable to the kind of analytic manipulations employed in this paper." + The correction proceedure eiven i equation (3)) czui be used in any formulation of the redistribution problem., The correction proceedure given in equation ) can be used in any formulation of the redistribution problem. + For this paper. however. we shall apply it to the Fokker-Planck equation (8)).," For this paper, however, we shall apply it to the Fokker-Planck equation )." + In Appendix A. it is shown thatthe Πιν) inplied bv equation (8)) satisfies the svuuuetry condijon (3)). so that equation (3)) may be used to define a corrected redistribution function.," In Appendix A, it is shown thatthe $R(\nu,\nu')$ implied by equation ) satisfies the symmetry condition ), so that equation ) may be used to define a corrected redistribution function." + Using this. we straightforwar¢Uy derive our new corrected Fokker-Plauck equation that obeys detailed: balance. namely. dt= | Pd J rbracc.. (," Using this, we straightforwardly derive our new corrected Fokker-Planck equation that obeys detailed balance, namely, = + ) J + ]. (" +sce Appendix B for the mathematical details of this derivation.),see Appendix B for the mathematical details of this derivation.) + We now identify the plavsical significance of the terus in the inner set of brackets of this corrected F-P equation., We now identify the physical significance of the terms in the inner set of brackets of this corrected F-P equation. + The first term. 0/0». 1s easily understood. since it is the sale diffusion term as in the uncorrected equation (8)).," The first term, $\partial J/\partial\nu$, is easily understood, since it is the same diffusion term as in the uncorrected equation )." + The last term. involvingthe square of J. clearly describes the stimulated scattering: let us ignore this term for the moment. since we want to make comparisons with other F-P equatiois that have also ignored this process: we shall return to it in reflNompanccts..," The last term, involvingthe square of $J$, clearly describes the stimulated scattering; let us ignore this term for the moment, since we want to make comparisons with other F-P equations that have also ignored this process; we shall return to it in \\ref{Kompaneets}. ." + There are two remaining terms. PJ/kT and ου.," There are two remaining terms, $hJ/kT$ and $-J/2\nu$." + The first of these is precisely the Basko recoil terii. as in equation 1).," The first of these is precisely the Basko recoil term, as in equation )." + This may seem remarkable. since the F-P eqation in its uicorrected form (8)) does not include recoil at all.," This may seem remarkable, since the F-P equation in its uncorrected form ) does not include recoil at all." + However. there is a simple physical explanation for tus seening coincidence.," However, there is a simple physical explanation for this seeming coincidence." +" In the theory of Brownian motion. which is also described by a F-P equation. Eiustein fouud hat thermal ο«quilibriuni required a certain relations between the cocficients of “diffusion” and “drift” (other terms for dift are ""unoημίν or “dynamical fiction)."," In the theory of Brownian motion, which is also described by a F-P equation, Einstein found that thermal equilibrium required a certain relations between the coefficients of “diffusion” and “drift” (other terms for drift are “mobility” or “dynamical friction”)." + Iu the present case. the nucorrected equation (8)) describes ouly the diffdon part of the process.," In the present case, the uncorrected equation ) describes only the “diffusion” part of the process." +" huposing detailed balance through our correction procedure has automatically eeucrated the proper ""dift? term. here eiven by the recoil ter."," Imposing detailed balance through our correction procedure has automatically generated the proper “drift” term, here given by the recoil term." + The remaining tenu 19 can be explained as follows., The remaining term $-J/2\nu$ can be explained as follows. + With jus the diffusion term aud the Dasko recoil terii. as in equaion (11)). the equilibrium solution (setting the bracket to zero) would eive JXexphifKD).," With just the diffusion term and the Basko recoil term, as in equation ), the equilibrium solution (setting the bracket to zero) would give $J \propto \exp(-h\nu/kT)$." + In fact. Dasko(C1981).. (followingField 1959).. claimed that his treatineut of recoil led totieriual equilibrium because the equilibriun solutiou of his equation was proportional to exphifKD).," In fact, \citet{Basko81}, \citep[following][]{Field59}, claimed that his treatment of recoil led tothermal equilibrium because the equilibrium solution of his equation was proportional to $\exp(-h\nu/kT)$." + However. to be 13eorouslv thermal (without stimulated processes). 7 shoud be proportional to the Wien law. 7?expthrKT). not jus exp(fvfh).," However, to be rigorously thermal (without stimulated processes), $J$ should be proportional to the Wien law, $\nu^2 \exp(-h\nu/kT)$, not just $\exp(-h\nu/kT)$." + The extra term 27/v in the F-P equaion (20)) is just what is needed to account for the missiug factor of v7., The extra term $-2J/\nu$ in the F-P equation ) is just what is needed to account for the missing factor of $\nu^2$. + Iu many applications this additional slowly varving factor nav be uiuportaut., In many applications this additional slowly varying factor may be unimportant. + However. since the goal here is to account for thermal equilibrium as precisely. as possible. this ται shiould be included as a matter of principle.," However, since the goal here is to account for thermal equilibrium as precisely as possible, this term should be included as a matter of principle." + For further investigation of the corrected equatiou (20)). especially the stimulated scattering process. it is useful to write it in terms of the photon occupation uuuber n. pdernt= ?pD E ο)rbraecc.," For further investigation of the corrected equation ), especially the stimulated scattering process, it is useful to write it in terms of the photon occupation number $n$, = ^2 + n(1+n) ]." +". This is reminiscent of the I&ompanects equation (I&oimipaneets1957:Rybicki&Lightiuan1979).. which can be written. -— 1""ed nilln ῃ rbracc.. where AV is the electron density aud op is the Thomson cross section."," This is reminiscent of the Kompaneets equation \citep{Kompaneets57,RL79}, which can be written, = ^4+ n(1+n) ] , where $N_{\rm e}$ is the electron density and $\sigma_{\rm T}$ is the Thomson cross section." +at ς20.3.,at $z>0.3$. + Based on sources detected in the Rónntgen Satellit (ROSAT) All-Sky Survey (RASS. Voges et al.," Based on sources detected in the Rönntgen Satellit (ROSAT) All-Sky Survey (RASS, Voges et al." + 1999). MACS covers 22.735 deg of extragalactic sky P.20 deg): the present MACS sample. estimated to be at least complete. comprises 124 clusters all of which have spectroscopic redshifts.," 1999), MACS covers 22,735 $^2$ of extragalactic sky $|b|>20$ deg); the present MACS sample, estimated to be at least complete, comprises 124 clusters all of which have spectroscopic redshifts." + Owing to the high X-ray flux limit of the RASS and the lower redshift limit of z=0.3. MACS clusters feature X-ray luminosities of. typically. 5—10x10H erg | in the 0.12.4 keV band (Ebeling et 22007).," Owing to the high X-ray flux limit of the RASS and the lower redshift limit of $z=0.3$, MACS clusters feature X-ray luminosities of, typically, $\times 10^{44}$ erg $^{-1}$ in the 0.1–2.4 keV band (Ebeling et 2007)." + MACS thus probes the high end of the cluster mass function. including some of the most powerful gravitational lenses (Smith et 22009: Zitrin et 22009): see also Smail et al. (," MACS thus probes the high end of the cluster mass function, including some of the most powerful gravitational lenses (Smith et 2009; Zitrin et 2009); see also Smail et al. (" +2007) for a spectacular case of galaxy-galaxy lensing in the field of a MACS cluster.,2007) for a spectacular case of galaxy-galaxy lensing in the field of a MACS cluster. + MACS clusters have been used for a wide range of cosmological and astrophysical applications. e.g.. in cosmological studies (Allen et al.," MACS clusters have been used for a wide range of cosmological and astrophysical applications, e.g., in cosmological studies (Allen et al." + 2008: Mantz et al., 2008; Mantz et al. + 2008.1 20092. by. investigations of large-scale structure (Ebeling. Barrett.," 2008, 2009a, b), investigations of large-scale structure (Ebeling, Barrett," +"Throughout this paper. we assume a A-dominatect cosmology with My= 70 kan s+ Mpe+. O4,= 0.3. and O94= 0.7.","Throughout this paper, we assume a $\Lambda$ -dominated cosmology with $H_{\rm 0} =$ 70 km $^{-1}$ $^{-1}$, $\Omega_{\rm m} =$ 0.3, and $\Omega_{\rm \Lambda} =$ 0.7." + For this cosmology. 1” corresponds to zz δι kpe at. = 2.2.," For this cosmology, $\arcsec$ corresponds to $\approx$ 8.2 kpc at $z =$ 2.2." + Tu the context of the SINS program. 80.2 =1 2 svstenis were observed im Ccluission lines iu tle infrared (rest-frame optical) with VLT/SINFONT for an average of 3.5 hours per baud aud pixel scale on cach target20001.," In the context of the SINS program, 80 $z = $ $-$ 3 systems were observed in emission lines in the infrared (rest-frame optical) with VLT/SINFONI for an average of 3.5 hours per band and pixel scale on each target." + These galaxies were larecly (62/80) taken from the (vest-frame}) UV-sclected samples of and the (rest-frame) optically-sclected samples of(2001)...(2001b)..(2006).. (2007).. aud. Ixurk et al. G," These galaxies were largely (62/80) taken from the (rest-frame) UV-selected samples of and the (rest-frame) optically-selected samples of, and Kurk et al. (" +in prep).,in prep). + From these maenitude- and color-defined samples. suitable SINS targets were culled. with the main sclection crtera being a combination of target visibility during the observing runs. night sky Line avoidance in the cnussion lines of interest. aud au estimated integrated elmission line fux 2 5 «4 ere À 7. such that high quality data could be obtained in reasonable iuteeration times.," From these magnitude- and color-defined samples, suitable SINS targets were culled, with the main selection criteria being a combination of target visibility during the observing runs, night sky line avoidance in the emission lines of interest, and an estimated integrated emission line flux $\gtrsim$ 5 $\times$ $^{-17}$ erg $^{-1}$ $^{-2}$, such that high quality data could be obtained in reasonable integration times." + Of the 62 rest-frame UV/optically-selected galaxies chosen im this manner. 52 were well detected in iiu our SINFONT observations.," Of the 62 rest-frame UV/optically-selected galaxies chosen in this manner, 52 were well detected in in our SINFONI observations." + discuss the selection of this szuuple in detail and show that the SINS ealaxies are representative of the sstar-formung galaxy population. with some bias towards the more rapidly star-formine (and therefore more huninous iu eenission) svstenis.," discuss the selection of this sample in detail and show that the SINS galaxies are representative of the star-forming galaxy population, with some bias towards the more rapidly star-forming (and therefore more luminous in emission) systems." + They also note that the SINS sample (and some of the parent samples) selects agaiust kuowu AGN and quasars. iu the interest of studviug the cvnamuc aud evolutionary state of sstar-forming galaxies.," They also note that the SINS sample (and some of the parent samples) selects against known AGN and quasars, in the interest of studying the dynamic and evolutionary state of star-forming galaxies." +" Ποπονο, a stall nuniber of previously known AGN were in fact observed in the SINS program: in the UV/optically-sclected part of the sample. there are 5 such systems. as originallv identified with the UVoptical spectroscopy of the parent surveys."," However, a small number of previously known AGN were in fact observed in the SINS program; in the UV/optically-selected part of the sample, there are 5 such systems, as originally identified with the UV/optical spectroscopy of the parent surveys." + For further details about the SINS sample. observations. aud data reduction. we refer interested readers to(2009).," For further details about the SINS sample, observations, and data reduction, we refer interested readers to." +. Tere. we analyze our SINS observations of the galaxies that were UV/optically-identified and that are welldetected in in individual spatial clemeuts: this population (totalling oof 52 sources detected inΠαν. including 1/5 of the previously known ACN) comprises the majority of the SINS sample.," Here, we analyze our SINS observations of the galaxies that were UV/optically-identified and that are well-detected in in individual spatial elements; this population (totalling of 52 sources detected in, including 4/5 of the previously known AGN) comprises the majority of the SINS sample." + To study the average properties of these sstar-forniug galaxies. we generated stacked. hieli-sigual-to-noise (S/N) spectra representative of the population as a whole.," To study the average properties of these star-forming galaxies, we generated stacked, high-signal-to-noise (S/N) spectra representative of the population as a whole." + From our inteeral field data. we first created a spatially-inteerated one-dimensional spectrum for each ealaxy by shifting each spectrmm within the galaxy datacube by its measured (Taj) velocity. and then collapsing the datacube into a single spatially-intcerated spectrum.," From our integral field data, we first created a spatially-integrated one-dimensional spectrum for each galaxy by shifting each spectrum within the galaxy datacube by its measured ) velocity and then collapsing the datacube into a single spatially-integrated spectrum." + In this manner. the spatially-intcerated spectrum contains no systematic velocity broacenineg (e.g. by large-scale rotation) ou scales larger than the PSF (EWIIN ~ | kpc).," In this manner, the spatially-integrated spectrum contains no systematic velocity broadening (e.g. by large-scale rotation) on scales larger than the PSF (FWHM $\sim$ 4 kpc)." + Testing confirmed that this approach did not affect the properties of the broad cconiponent (see below) but did improve the signalto-noise (S/N) of the detection., Testing confirmed that this approach did not affect the properties of the broad component (see below) but did improve the signal-to-noise (S/N) of the detection. + This technique has the additional benefit of randomizing ΟΠ atmospleric cluission lines in the rest-frame and therefore effectively elininatius residuals from the ΟΠ line removal., This technique has the additional benefit of randomizing OH atmospheric emission lines in the rest-frame and therefore effectively eliminating residuals from the OH line removal. + The remaining residuals from this process were inspected aud masked out by haud., The remaining residuals from this process were inspected and masked out by hand. + The sspatially-inteerated spectra were then combined iuto a single spectrum (with equivalent iuteeration time of 195 hours) by interpolating all spectra outo a common wavelength axis. converting them measured fluxes to lIumuinosities using their huuinositv distances. weighting cach spectrum by the S/N of the ecluission line. and averaging the resulting spectra.," The spatially-integrated spectra were then combined into a single spectrum (with equivalent integration time of 195 hours) by interpolating all spectra onto a common wavelength axis, converting their measured fluxes to luminosities using their luminosity distances, weighting each spectrum by the S/N of the emission line, and averaging the resulting spectra." + During this process. we do uot correct for extinction (but see rofDiscussion)).," During this process, we do not correct for extinction (but see \\ref{Discussion}) )." + Typical extinctions our sample galaxies have been measured to be y~ 12009:: see also e.g. 2006601). which trauslates to au tuclerestimation of our Ihuninosities bv at most a factor of — 2.," Typical extinctions our sample galaxies have been measured to be $A_V \sim$ 1; see also e.g. ), which translates to an underestimation of our luminosities by at most a factor of $\sim$ 2." + The average spectrum for the SINS sstar-fornüug ealaxics is presented iu the top panel of Figure 1.., The average spectrum for the SINS star-forming galaxies is presented in the top panel of Figure \ref{agn}. + We also created average spectra of subsets of the SINS ealaxy sample. iu order to test the depeudeuce of spectral properties ou other known galaxy properties.," We also created average spectra of subsets of the SINS galaxy sample, in order to test the dependence of spectral properties on other known galaxy properties." + Our average spectra reveal ai broad ciissiou component underneath the bright narrow lines., Our average spectra reveal a broad emission component underneath the bright narrow lines. + We quantify this feature iu cach average spectrüni by sSiuultaneouslv fitting a combination of a coustant continuum offset. narrow lines(Παν[NU 151) of identical kinematics (velocity auc velocity dispersion). and a single broad component. whosekimematies are allowed to vary.," We quantify this feature in each average spectrum by simultaneously fitting a combination of a constant continuum offset, narrow lines, ) of identical kinematics (velocity and velocity dispersion), and a single broad component, whosekinematics are allowed to vary." + All lines are assumed to be well-described by a single Gaussian: the validitv of this assuuption is confirmed by a reduced 47 of close to unity (Guy 1.9) for all fits (see Table 1))., All lines are assumed to be well-described by a single Gaussian; the validity of this assumption is confirmed by a reduced $\chi^2$ of close to unity $\chi_{dof}^2 \sim$ $-$ 1.9) for all fits (see Table \ref{tab:results}) ). + Our data can also be well ft bx fitting a combination of a constant continui offset. narrow lines with shared kineniaties. and broad forbidden and permitted lines with shared kinematics. with the irafio identical in the narrow and broad componcut.," Our data can also be well fit by fitting a combination of a constant continuum offset, narrow lines with shared kinematics, and broad forbidden and permitted lines with shared kinematics, with the ratio identical in the narrow and broad component." + All lines are assuned to be wellkdescribed bv this colubination of two Caussians (dotted ereen dine in Figure 1: V= 1.1). which has the same uumnber of free paralucters as the previous fit.," All lines are assumed to be well-described by this combination of two Gaussians (dotted green line in Figure \ref{agn}; $\chi_{dof}^2 =$ 1.4), which has the same number of free parameters as the previous fit." + In the limut of the S/N of our data. we cannot add additional free parameters to the fits. nor can we identify a preferred model.," In the limit of the S/N of our data, we cannot add additional free parameters to the fits, nor can we identify a preferred model." +" For clarity. we refer throughout to the former (sinele broad Gaussian under the cconiplex) as ""broad lines” and the latter (double Gaussians for both aaud as ""broad wings.”"," For clarity, we refer throughout to the former (single broad Gaussian under the complex) as “broad lines"" and the latter (double Gaussians for both and ) as “broad wings.""" + For simplicity aud for conrparison [NII[))with the literature. we primarily quantity the observed high-velocity feature with a single broad Hine in refResults..," For simplicity and for comparison with the literature, we primarily quantify the observed high-velocity feature with a single broad line in \\ref{Results}. ." + IHTowever. we also discuss the implications of the broad wines scenario on the derived propertics of the," However, we also discuss the implications of the broad wings scenario on the derived properties of the" +[or MECO-GDBLIIC/AGN. which was based on ωνxM! without accitional multipliers. suggests that MISCOAGN most likely are in a state of slow spin equilibrium.,"for MECO-GBHC/AGN, which was based on $\omega_s \propto M^{-1}$ without additional multipliers, suggests that MECO/AGN most likely are in a state of slow spin equilibrium." + In a previous paper (RLO2) we found that the spectra state switch and other spectral properties of low mass x-ray unaries. including both NS and GDBLIC. could be explaine » a magnetic propeller effect that requires an intrinsically magnetized central object.," In a previous paper (RL02) we found that the spectral state switch and other spectral properties of low mass x-ray binaries, including both NS and GBHC, could be explained by a magnetic propeller effect that requires an intrinsically magnetized central object." + Subsequently (I0L03) we appliec he Einstein field equations of Gencral Relativity to the case of a highly compact. Ixldington limited. pair dominate asma with an intrinsic equipartition magnetic field.," Subsequently (RL03) we applied the Einstein field equations of General Relativity to the case of a highly compact, Eddington limited, pair dominated plasma with an intrinsic equipartition magnetic field." + We ound that the Einstein equations permit the existence of intrinsically magnetic. highly red. shifted. extremely. long ived. collapsing. radiating MECO objects that can produce re required propeller. ellects.," We found that the Einstein equations permit the existence of intrinsically magnetic, highly red shifted, extremely long lived, collapsing, radiating MECO objects that can produce the required propeller effects." +" In addition to accounting or the strong spectral similarities of NS and CDIIC. the =lagnetospherc-accretion disk interaction associated with 16 ALECO moclel has provided explanations for radio / x-ray luminosity correlations. the mass scale invariant spectral state switch phenomenon with its suppression of the radio jet outflow. in the high/ soft state. the ""ultrasoft thermal »ealkk and hard spectral tail of the high state. and. finally. re quiescient luminosities described as spin-down driven racdiations."," In addition to accounting for the strong spectral similarities of NS and GBHC, the magnetosphere-accretion disk interaction associated with the MECO model has provided explanations for radio / x-ray luminosity correlations, the mass scale invariant spectral state switch phenomenon with its suppression of the radio jet outflow in the high/ soft state, the ""ultrasoft"" thermal peak and hard spectral tail of the high state, and, finally, the quiescient luminosities described as spin-down driven radiations." + In conclusion. we have shown here how a standard. lin. gas pressure dominated accretion disk. ancl corona can interact with the central intrinsic magnetic monients of MECO-GDBLICZAGN and NS in x-ray biniaries to clrive ow state jets.," In conclusion, we have shown here how a standard, thin, gas pressure dominated accretion disk and corona can interact with the central intrinsic magnetic moments of MECO-GBHC/AGN and NS in x-ray biniaries to drive low state jets." + In. the case of the MECO-CGDLIICZAGN he racio-infrarecl emissions of the jets have been found ο correlate with the x-ray luminosity up to a mass scale invariant cutoll L./Lg; at the spectral state switch., In the case of the MECO-GBHC/AGN the radio-infrared emissions of the jets have been found to correlate with the x-ray luminosity up to a mass scale invariant cutoff $L_c / L_{Edd}$ at the spectral state switch. + 1n this context we obtained. racio-intrared luniinositics or MECO that vary as A7- consistent with observations of GBIIC and AGN. ancl correctly predicted he observed relative radio luminosities of NS. GBIIC. and AGN.," In this context we obtained radio-infrared luminosities for MECO that vary as $M^{0.75-0.92}L_x^{2/3}$, consistent with observations of GBHC and AGN, and correctly predicted the observed relative radio luminosities of NS, GBHC, and AGN." + While much detailed: work remains to be cone. he successful comparison of the ALECO model predictions with observations stronely suggests that GBIIC and AGN may have observable intrinsic magnetic moments anchored within them and hence they do not have event We thank the anonymous referee for many. comments ancl suggestions that have substantially improved this paper.," While much detailed work remains to be done, the successful comparison of the MECO model predictions with observations strongly suggests that GBHC and AGN may have observable intrinsic magnetic moments anchored within them and hence they do not have event We thank the anonymous referee for many comments and suggestions that have substantially improved this paper." + We thank Elena Gallo for providing data for Figure 1., We thank Elena Gallo for providing data for Figure 1. + Useful information has been generously. provided by Mike Church. Leino Falcke and Thomas Maccarone.," Useful information has been generously provided by Mike Church, Heino Falcke and Thomas Maccarone." + We are very grateful to Abhas Mitra for many helpful discussions of gravitational collapse ancl pertinent astrophysical observations., We are very grateful to Abhas Mitra for many helpful discussions of gravitational collapse and pertinent astrophysical observations. +is dillicult to prove that this is the case (but note that the deficit of BCRR sources is most marked at 2<0.3. where the llo line is covered by optical spectra and the expected broad llo fluxes are high).,"is difficult to prove that this is the case (but note that the deficit of 3CRR sources is most marked at $z<0.3$, where the $\alpha$ line is covered by optical spectra and the expected broad $\alpha$ fluxes are high)." + However. in the 7€ sample. similar exposure times have been attained for the spectra at. low redshift to those at high redshift.," However, in the 7C sample, similar exposure times have been attained for the spectra at low redshift to those at high redshift." + Pherefore we are confident that in the absence of significant reddening of the BL. an insignificant number of sources would be mis-classified.," Therefore we are confident that in the absence of significant reddening of the BLR, an insignificant number of sources would be mis-classified." + A further problem is whether a weak quasar spectrum can be discerned against a stronger host galaxy spectrum., A further problem is whether a weak quasar spectrum can be discerned against a stronger host galaxy spectrum. + To determine if this could cause broad line selection problems. synthetic spectra of quasars and. galaxies were created and combined.," To determine if this could cause broad line selection problems, synthetic spectra of quasars and galaxies were created and combined." + “Phe model used for the galaxy spectra was a 1 Gyr old. stellar population synthesis model of Bruzual Charlot (1993)., The model used for the galaxy spectra was a 1 Gyr old stellar population synthesis model of Bruzual Charlot (1993). + For the quasar spectra. the LIOS composite of Francis et al. (," For the quasar spectra, the LBQS composite of Francis et al. (" +1991) was used.,1991) was used. + Poisson noise was added and it was found that broad Ila or Alell should. still be clearly visible for à quasar 2 magnitudes (in D-band) fainter than the galaxy. (Fig. 3))., Poisson noise was added and it was found that broad $\alpha$ or MgII should still be clearly visible for a quasar $2$ magnitudes (in $B$ -band) fainter than the galaxy (Fig. \ref{fig:onespec}) ). + Broad. 112. however. is more cüllicult to detect.," Broad $\beta$, however, is more difficult to detect." + Spectra with poor blue wavelength coverage (e.g. no data below 5000 X)) of sources at 0.3O.S would not include Ho or Mgll. in which case LL? is the brightest line.," Spectra with poor blue wavelength coverage (e.g. no data below $5000$ ) of sources at $0.3OL GeV by (Abdo et 22009). with a double-peaked lieht-curvoe.," Recently, these were clearly detected at $\ge 0.1$ GeV by (Abdo et 2009), with a double-peaked light-curve." + Tere. we report on the results of an archival ssurvey for pulsars.," Here, we report on the results of an archival survey for pulsars." + This paper is organised as follows: observations. data reduction and analysis are described in Sect.," This paper is organised as follows: observations, data reduction and analysis are described in Sect." + 2. while results are presented aud discussed in Sect.," 2, while results are presented and discussed in Sect." + 3 and L respectively.," 3 and 4, respectively." + Conclusions follow., Conclusions follow. + Optical images of the 6129 and 5832 fields were obtained with the AAutu telescope at the ESO Paranal observatory between April 2009 and February 2010 (see Tab., Optical images of the $-$ 6429 and $-$ 5832 fields were obtained with the Antu telescope at the ESO Paranal observatory between April 2009 and February 2010 (see Tab. + 1 for a sunniuv of the observations) and are available in the public ESOarchivel., 1 for a summary of the observations) and are available in the public ESO. +. Observatious were performed in service mode with the(FORS2: Appenzeller et 11998). a multi-mode camera for imaging and. long-slit/nulti-object spectroscopy (MOS).," Observations were performed in service mode with the; Appenzeller et 1998), a multi-mode camera for imaging and long-slit/multi-object spectroscopy (MOS)." + was equipped with its red-sensitive MIT detector. a mosaic of two « Us CCDs optimised for wavelengths longer than 6000.," was equipped with its red-sensitive MIT detector, a mosaic of two $\times$ 4k CCDs optimised for wavelengths longer than 6000." +A.. Iu its standard resolution mode. the detector las a pixel size of 07225 (242 binning) which corresponds to a projected fieldofview of 8/3\ over he CCD mosaic.," In its standard resolution mode, the detector has a pixel size of 25 $\times$ 2 binning) which corresponds to a projected field–of–view of $\farcm3 \times 8\farcm3$ over the CCD mosaic." + Towever. due to vienettiug. the effective sky coverage of the two detectors is smaller than the projected detector fieldofview and it is lavecr for the upper CCD chip.," However, due to vignetting, the effective sky coverage of the two detectors is smaller than the projected detector field–of–view and it is larger for the upper CCD chip." + Observations were performed with the standard low eun. fast read-out mode aud in high-resolution mode (1125/pixel) for 6129 aud iu standard resolution mode (07225/pixel) for 5832.," Observations were performed with the standard low gain, fast read-out mode and in high-resolution mode 125/pixel) for $-$ 6429 and in standard resolution mode 25/pixel) for $-$ 5832." + Iu both cases. the target was positioned iu the upper CCD ‘hip.," In both cases, the target was positioned in the upper CCD chip." + For 6129. xieht stars close to the pulsar position have been masked using the AIMOS slitlets as occulting bars.," For $-$ 6429, bright stars close to the pulsar position have been masked using the MOS slitlets as occulting bars." + Differeut filters were used: egyppeup (A=5570As AA=1235A)). Reprc: (A=6550As; AA=1650À)). and Zppas (A=7T6S0Au AX= D380À)).," Different filters were used: $v_{\rm HIGH}$ $\lambda=5570$; $\Delta \lambda=1235$ ), $R_{\rm SPEC}$ $\lambda=6550$; $\Delta \lambda=1650$ ), and $I_{\rm BESS}$ $\lambda=7680$; $\Delta \lambda=1380$ )." + To allow for cosmic rav removal aud nuuinise saturation of bright stars in the field. sequences of short exposures (from 200 to 750 s) were obtained per each target aud per cach filter.," To allow for cosmic ray removal and minimise saturation of bright stars in the field, sequences of short exposures (from 200 to 750 s) were obtained per each target and per each filter." + The total iutegratiou time was LLT00 s (Conca). SRUU s (Rspre:). and 1600 s (πως) for 6129 and of 21000 x (oumedr) for 5832.," The total integration time was 14700 s $v_{\rm HIGH}$ ), 8800 s $R_{\rm SPEC}$ ), and 1600 s $I_{\rm BESS}$ ) for $-$ 6429 and of 24000 s $v_{\rm HIGH}$ ) for $-$ 5832." + Exposures were taken in dark tine aud under photometriccouditious?.. with πα mostly below 1.5 aud sub-arcsecond miage quality. as measured directly on the images by fitting the full-width at half masini (FWIHIAD) of uusaturated field stars.," Exposures were taken in dark time and under photometric, with an airmass mostly below 1.3 and sub-arcsecond image quality, as measured directly on the images by fitting the full-width at half maximum (FWHM) of unsaturated field stars." + We reduced the data through standard packages inIRAF for bias subtraction. and fatfield correction using the closestiutime bias and twilight flatfields frames available in the ESO archive.," We reduced the data through standard packages in for bias subtraction, and flat–field correction using the closest–in–time bias and twilight flat–fields frames available in the ESO archive." + Per each baud. we aligned and average-stacked the reduced scicuce dmaees using theIRAF task applving a 3c filter ou the sinele Ἠποι average to filter out residual hot aud cold pixels aud cosniüc rav hits.," Per each band, we aligned and average-stacked the reduced science images using the task applying a $3 \sigma$ filter on the single pixel average to filter out residual hot and cold pixels and cosmic ray hits." + Since all exposures have been taken with sub-arcesec image qualitv. we did not apply anv selection xior to the unage stacking.," Since all exposures have been taken with sub-arcsec image quality, we did not apply any selection prior to the image stacking." + We applied the photometric calibration by using the extinctiou-corrected might zero »oiuts computed by the ypipehue and available through the instrument data quality control database?., We applied the photometric calibration by using the extinction-corrected night zero points computed by the pipeline and available through the instrument data quality control . +. To register the pulsar positions on the Tranies as xeciselv as possible. we re-conaputed their astrometric solution which is. by default. based on the coordinates of the euide star used for the telescope »oiutiug.," To register the pulsar positions on the frames as precisely as possible, we re-computed their astrometric solution which is, by default, based on the coordinates of the guide star used for the telescope pointing." + Since iiost stars from the Cauce Star Catalogue, Since most stars from the Guide Star Catalogue +We moclel the evolution of debris disks using an N-body integrator that iucludes the effects of radiation pressure. aalid solar wind drag.,"We model the evolution of debris disks using an N-body integrator that includes the effects of radiation pressure, and solar wind drag." + In this section we discuss the modifications made to a syimplectic integrator to account for the additional forces. as well as our nunerical techniques lor creating debris disks aud recording particle positions.," In this section we discuss the modifications made to a symplectic integrator to account for the additional forces, as well as our numerical techniques for creating debris disks and recording particle positions." + Siuce the general problem ofa particle moving uuder the iullueuce of gravitational aud racdiatiou Orces is nonlinear. It is uecessary to numerically integrate the orbits of all particles.," Since the general problem of a particle moving under the influence of gravitational and radiation forces is nonlinear, it is necessary to numerically integrate the orbits of all particles." + Conmunonly ied integrators include Runge-Ixutter.. Burlisch-Stoer aud. Mixed. Variable Syvimplectic (MVS) algorithius.," Commonly used integrators include Runge-Kutter, Burlisch-Stoer and Mixed Variable Symplectic (MVS) algorithms." + The MVS integrator developed by Wisdom&Holman(1991). is normally the fastest. out has the disadvantage of being unable to follow close encounters between particles aud planets. which are crucial to debris disk evolution.," The MVS integrator developed by \citet{wisdom91} is normally the fastest, but has the disadvantage of being unable to follow close encounters between particles and planets, which are crucial to debris disk evolution." + This drawback has been overcome with the use of integrators such as RMVS3 (Levison&Duncan1991). and SyMBA (Duncanetal.1998)... which are based on the Wisdom&Holman(1901) scheme but cau integrate close encounters.," This drawback has been overcome with the use of integrators such as RMVS3 \citep{ld94} and SyMBA \citep{dll98}, which are based on the \citet{wisdom91} scheme but can integrate close encounters." + Iu this work we have modified RAIVS3 to iuclude raciation and solar wind forces which affect debris disk particles., In this work we have modified RMVS3 to include radiation and solar wind forces which affect debris disk particles. + Such an approach was used by Moro-Martin&Malhotra(2002).. who moclily a variant of SVMBA. (," Such an approach was used by \citet{mm02}, who modify a variant of SyMBA. (" +Note that SyMBA and RAIVS3 handle close encounters between particles aud. planets iu differeut ways.),Note that SyMBA and RMVS3 handle close encounters between particles and planets in different ways.) + RMVSS assumes that test particles are both massless aud. collisionless — the problem of dust collisions is discussed in Section L1.., RMVS3 assumes that test particles are both massless and collisionless – the problem of dust collisions is discussed in Section \ref{subsec:collisionalproc}. +" The code requires units such that the gravitational coustaut CJ=-1 and so we have chosen clistauce.. time. auc mass units"" to be -1 AU.- -1. year aud. AL.""nΕπ)> respectively."," The code requires units such that the gravitational constant $G = 1$ and so we have chosen distance, time and mass units to be 1 AU, 1 year and $M_{\odot}/(4\pi^{2})$ respectively." + Throughout this paper we shall use « for the semi-major axis. € for eccentricity. aud ὁ for inclination. with the subscripts /p. pb aud pl relerriug to a test particle. parent body and planet respectively.," Throughout this paper we shall use $a$ for the semi-major axis, $e$ for eccentricity, and $i$ for inclination, with the subscripts ${tp}$, ${pb}$ and ${pl}$ referring to a test particle, parent body and planet respectively." +" As developed in Wisdom&Holman(1991) aud described in Levison&Duncan (1991). RAMWVS3 expands the Hamiltonian of a test particle into two integrable Components given by where HH, represents the Ixeplerian motion aruxcd the central star. aud Ayjs; represeuts the perturbances on a test particle resulting from the planet(s)."," As developed in \citet{wisdom91} and described in \citet{ld94}, , RMVS3 expands the Hamiltonian of a test particle into two integrable components given by where $H_{kep}$ represents the Keplerian motion around the central star, and $H_{dist}$ represents the perturbances on a test particle resulting from the planet(s)." + Using a timestepA/.. the second order approximation implemented in RMWVS3 cousists of applying the disturbance Hamiltonian for .N//2. applyiug the Ixeplerian Hamiltonian forA’.. and then applying the disturbance Hamiltonian again for //2.," Using a timestep, the second order approximation implemented in RMVS3 consists of applying the disturbance Hamiltonian for /2, applying the Keplerian Hamiltonian for, and then applying the disturbance Hamiltonian again for /2." + The approximation is accurate as long as the planetary disturbances are simmall compared to the Ixepleriau evolutiou., The approximation is accurate as long as the planetary disturbances are small compared to the Keplerian evolution. + This assumptionof small disturbances does not hokl when a particle, This assumptionof small disturbances does not hold when a particle +normalised to the radius of curvature al the nose of the CAIE (fo) is shown in Figure 4((e).,normalised to the radius of curvature at the nose of the CME $R_{O}$ ) is shown in Figure \ref{f4}( (e). + The curvature could only be derived from the front fitting. as such only hollow data points are shown.," The curvature could only be derived from the front fitting, as such only hollow data points are shown." + Figure 4(f) then shows the magnetosonie Mach number (A/4;5) derived. using: ) the CME speed in conjunction with the coronal model (filled svanbols) and (ii) the shock front fitted using Equation 5 (hollow svanbols)., Figure \ref{f4}( (f) then shows the magnetosonic Mach number $M_{MS}$ ) derived using: (i) the CME speed in conjunction with the coronal model (filled symbols) and (ii) the shock front fitted using Equation 5 (hollow symbols). + The mean Mach. number from (he coronal model was 3.82:0.6. while a value of 4.425 1.6 was found using the front [itting method.," The mean Mach number from the coronal model was $\pm$ 0.6, while a value of $\pm$ 1.6 was found using the front fitting method." + The mean Mach number from both methods was 4.11.2., The mean Mach number from both methods was $\pm$ 1.2. + Figure 5(a) shows the relationship between the normalised standoll distance (N/ Do) and Mach number (V 3;4) for a number of models., Figure 5(a) shows the relationship between the normalised standoff distance $\Delta$ $D_{O}$ ) and Mach number $M_{MS}$ ) for a number of models. + The Mach numbers were ealeulated using the coronal moclel (filled svaubols) and front fitting (open symbols)., The Mach numbers were calculated using the coronal model (filled symbols) and front fitting (open symbols). + The normalised stancoll distances were caleulated using measured. values of De and Ds (fillel symbols) and fits to the CAIE and shock fronts (hollow svinbols)., The normalised standoff distances were calculated using measured values of $D_{O}$ and $D_{S}$ (filled symbols) and fits to the CME and shock fronts (hollow symbols). + Both show good general agreement between our observations and the models (2056)., Both show good general agreement between our observations and the models $<$ $\%$ ). + The model of Seiff(1962) shows the poorest agreement. although this is not unexpected as it was derived lor a circular obstacle ancl the CME is «uite blunt compared (o a circle.," The model of \citet{Sieff:1962p19} shows the poorest agreement, although this is not unexpected as it was derived for a circular obstacle and the CME is quite blunt compared to a circle." + Figure 5(b) shows the relationship between the standolf distance normalised by the radius of curvature of the CME GN/ Ho) and Mach number for a number ol models., Figure 5(b) shows the relationship between the standoff distance normalised by the radius of curvature of the CME $\Delta/R_{O}$ ) and Mach number for a number of models. + In this case. Ro can only be derived from the front fitting.," In this case, $R_{O}$ can only be derived from the front fitting." +" These values are then plotted. as a function of the Mach numbers derived. using both: methods described above (hence. each value of A/Do appears twice),"," These values are then plotted as a function of the Mach numbers derived using both methods described above (hence, each value of $\Delta/D_{O}$ appears twice)." + Our results do not agree with the expected relation (Equation (4))) and indicate the the radius of curvature Jo is underestimate bv a [actor of 223.8., Our results do not agree with the expected relation (Equation \ref{Eq5}) )) and indicate the the radius of curvature $R_{O}$ is underestimate by a factor of $\approx$ 3–8. + One possible reason for this is Chat we have not considered the effect of the magnetic field of the CME and solar wind effects on the shock., One possible reason for this is that we have not considered the effect of the magnetic field of the CME and solar wind effects on the shock. + However. one would expect if this had a significant effect it would also affect the other relation.," However, one would expect if this had a significant effect it would also affect the other relation." + It should be noted that the fast magnetosonie velocity and sonic velocity caleulatecl [rom our model differ bv. less than alter excluding the first three data points as mentioned earlier., It should be noted that the fast magnetosonic velocity and sonic velocity calculated from our model differ by less than after excluding the first three data points as mentioned earlier. + This also suggests that the magnetic field should not plav a major role., This also suggests that the magnetic field should not play a major role. + A more likely reason is due to an observational affect similar to that suggested by Russell&Mulligan(2002).. where only one racius of curvature of the CME is observed.," A more likely reason is due to an observational affect similar to that suggested by \cite{Russell:2002p8853}, where only one radius of curvature of the CME is observed." + The observations provide a cross-sectional view of the CME along one of its axes., The observations provide a cross-sectional view of the CME along one of its axes. + As a result. we have no information on the curvature along other CME axes.," As a result, we have no information on the curvature along other CME axes." + For the first (ime. we have imaged a CAIE-driven shock in white light at large distances [rom the Sun.," For the first time, we have imaged a CME-driven shock in white light at large distances from the Sun." + The shoek was tracked from RR. to 19201. AAU) before it became too faint to be identify unambiguously., The shock was tracked from $_{\odot}$ to $_{\odot}$ AU) before it became too faint to be identify unambiguously. + The CATE was measured to have a velocity of, The CME was measured to have a velocity of +While the resultant [it is statistically adequate. there are clear residuals left around the iron Ix line (see Figure 2).,"While the resultant fit is statistically adequate, there are clear residuals left around the iron K line (see Figure 2)." + Adding a narrow Gaussian line gives a reduction in X7 to 1363/1268 (signilicant at greater than 99.9 confidence) for E—639οἱ keV and equivalent. width S635 eV. This additional line component. iszrconsis/en! with being at 6.7 keV. as postulatec by IWallman ct al. (," Adding a narrow Gaussian line gives a reduction in $\chi^2_\nu$ to $1363/1268$ (significant at greater than $99.9$ confidence) for $E=6.39_{-0.04}^{+0.03}$ keV and equivalent width $86^{+36}_{-26}$ eV. This additional line component is with being at 6.7 keV, as postulated by Kallman et al. (" +1996).,1996). + A (nearly) neutral iron. Uuoreseenee line is expected. [rom reflection of the intrinsic spectrum from the white dwarf surface., A (nearly) neutral iron fluorescence line is expected from reflection of the intrinsic spectrum from the white dwarf surface. + Fixing the line energy at 6.4 keV and including a neutral Compton reflection continuum that must accompany any reflected. line. emission. leads to ο=1360/1268. for an amount of rellection &DoanoU. (where H8—1 denotes the normalisation of the rellectecl continuuunm expected. from an isotropically illuminated slab covering a solid angle of 2x) assuming the abunclances in the rellector are the same as those in the hot plasma. with maximum temperature ALi=38a keV. While the detection of the reflected continuum is only marginally significant. its level is consistent with that expected from the strength of the cole iron Uuoreseence line.," Fixing the line energy at 6.4 keV and including a neutral Compton reflection continuum that must accompany any reflected line emission leads to $\chi^2_\nu=1360/1268$ , for an amount of reflection $R=1.5_{-1.3}^{+0.6}$ (where $R=1$ denotes the normalisation of the reflected continuuum expected from an isotropically illuminated slab covering a solid angle of $2\pi$ ) assuming the abundances in the reflector are the same as those in the hot plasma, with maximum temperature $kT_{max}=38^{+34}_{-13}$ keV. While the detection of the reflected continuum is only marginally significant, its level is consistent with that expected from the strength of the cold iron fluorescence line." + The line equivalent width and amount of rellection continuum are anticorrelated in the fitting. so à self consistent. rellection model (including both line anc continuum) would be much better constrained.," The line equivalent width and amount of reflection continuum are anti–correlated in the fitting, so a self consistent reflection model (including both line and continuum) would be much better constrained." + This [it is detailed in Table 1. and shown in Figure 3.," This fit is detailed in Table 1, and shown in Figure 3." + ‘The abundances of the elements in the hot plasma nee not all scale together. especially as BY Cam is proposed to have abundance anomalies to explain the enhanced NV line emission observed. in its UV. spectrum (BonnetDidaud AMouchet 1987).," The abundances of the elements in the hot plasma need not all scale together, especially as BY Cam is proposed to have abundance anomalies to explain the enhanced NV line emission observed in its UV spectrum (Bonnet–Bidaud Mouchet 1987)." + Phe N Xrav lines are below the 0.6 keV. well calibrated low energy limit of the ASC'A detectors. but can be investigated by including the less reliable data down to 0.4 keV. Phe soft excess is then also apparent (allman et al 1996). so a blackbody is needed: to model this.," The N X–ray lines are below the 0.6 keV well calibrated low energy limit of the ASCA detectors, but can be investigated by including the less reliable data down to 0.4 keV. The soft excess is then also apparent (Kallman et al 1996), so a blackbody is needed to model this." + The derived limit on the N abundance is then x15. solar. which is not restrictive.," The derived limit on the N abundance is then $\le 15\times $ solar, which is not restrictive." +" Going back to the standard bandpass. the strongest lines expected at these plasma temperatures are Io. 81. S and O. Letting the abundances of all these be free gives cle,=OALDU. ode;=0.60PS chs=0.39Qs. Ao20""7"" and Aw=O38PO with xz=1353/1264. i.c. there is no significant improvement in the fit as the inclusion of 4 extra [ree parameters gives a reduction of only AND=7."," Going back to the standard bandpass, the strongest lines expected at these plasma temperatures are Fe, Si, S and O. Letting the abundances of all these be free gives $A_{Fe}=0.41_{-0.12}^{+0.43}$, $A_{Si}=0.69_{-0.31}^{+0.30}$, $A_{S}=0.39_{-0.39}^{+0.47}$, $A_{O}=0^{+0.29}$ and $A_{rest}=0.38_{-0.38}^{+0.51}$ with $\chi^2_\nu=1353/1264$, i.e. there is no significant improvement in the fit as the inclusion of 4 extra free parameters gives a reduction of only $\Delta\chi^2=7$." + Thus there is no strong evidence for nonsolar abundance of the elements. although © is mareinally lower than expected.," Thus there is no strong evidence for non–solar abundance of the elements, although O is marginally lower than expected." + The intrinsic multitemperature plasma emission. can also be investigated in more detail., The intrinsic multi–temperature plasma emission can also be investigated in more detail. + We have so far assumed that the plasma cools from the shock temperature to the white dwarf photosphere at 1077 Ix z27 eV. and that all these cooler components contribute to the spectrum.," We have so far assumed that the plasma cools from the shock temperature to the white dwarf photosphere at $\sim 10^{5.5}$ K $\approx 27$ eV, and that all these cooler components contribute to the spectrum." + However. this is not necessarily the case since the cooling plasma may be dense enough to become optically thick. so giving an apparent minimum temperature to the cooling radiation which is rather higher than that of the white dwarf.," However, this is not necessarily the case since the cooling plasma may be dense enough to become optically thick, so giving an apparent minimum temperature to the cooling radiation which is rather higher than that of the white dwarf." +" We modify the plasma emission mocel to include the minimum temperature as a free parameter of the fit. and lind that this converges to an identical fit as before. with kl,27 eV. The limits on the O abundance are also unchanged. with slo=0""7"" (AZ= 1353/1266). showing that incomplete cooling is not responsible for any potential deficit ofO line emission."," We modify the plasma emission model to include the minimum temperature as a free parameter of the fit, and find that this converges to an identical fit as before, with $kT_{min}=27$ eV. The limits on the O abundance are also unchanged, with $A_{O}=0^{+0.29}$ $\chi^2_\nu=1353/1266$ ), showing that incomplete cooling is not responsible for any potential deficit of O line emission." + Similarly. the temperature distribution. need. not. be given by the a=1 power law model expected from pure Xray line ancl continuum cooling as the assumptions of bremsstrahlung only cooling at constant. pressure. and eravitational field may. not be accurate.," Similarly, the temperature distribution need not be given by the $\alpha=1$ power law model expected from pure X–ray line and continuum cooling as the assumptions of bremsstrahlung only cooling at constant pressure and gravitational field may not be accurate." + Letting a be free gives a significant decrease in AZ to 1354/1267 for a=0.6 and A544=55 keV. Thus the data are consistent with multi.temperature emission. from. complete cooling behind. the shock. where the accreting material is 0.5. solar abundance in all theelements.," Letting $\alpha$ be free gives a significant decrease in $\chi^2_\nu$ to $1354/1267$ for $\alpha=0.6$ and $kT_{max}=55$ keV. Thus the data are consistent with multi–temperature emission from complete cooling behind the shock, where the accreting material is $\sim 0.5\times$ solar abundance in all theelements." + This intrinsic spectrum is then modified. by rellection [from the white dwarl surface. producing both reflected continuum and associated 6.4 keV iron [uorescence," This intrinsic spectrum is then modified by reflection from the white dwarf surface, producing both reflected continuum and associated 6.4 keV iron fluorescence" +Ίου» transmission curves.,filters' transmission curves. + I£ the πιο) is a very accurate representation of the real SED of an object. this convolution will load. to more accurate results.," If the model is a very accurate representation of the real SED of an object, this convolution will lead to more accurate results." + In. our case. however. he optical/UV. part of the model is simply a power law. as already mentioned in Section 3.1.. while the SDSS ohotometry. that corresponds to the same part of the SED is quite sensitive to the presence of broad. emission lines or he presence of the small bluebump?.," In our case, however, the optical/UV part of the model is simply a power law, as already mentioned in Section \ref{sec:tori}, while the SDSS photometry, that corresponds to the same part of the SED is quite sensitive to the presence of broad emission lines or the presence of the small blue." +. Also. as a goneral remark. the photometric errors are very. small (twpically of he order of lew percent. as seen in Tables 1 and 2)) for xh. SDSS and SWIRL datapoints.," Also, as a general remark, the photometric errors are very small (typically of the order of few percent, as seen in Tables \ref{tab:ugriz} and \ref{tab:jhkspitzer}) ) for both SDSS and SWIRE datapoints." + nd even though we use the errors in the catalogues to properly weight the fits. in many cases the computed. values of the reduced x78 are very high due to the small photometric errors.," And even though we use the errors in the catalogues to properly weight the fits, in many cases the computed values of the reduced $\chi^2$ s are very high due to the small photometric errors." + In order to avoid excessively high weighting and high X7 values. many SIED fitting codes impose minimum flux errors (e.g. HvperZ. Bolzoncllaetal.2000: ImpZ. Babbedgeetal. 20042). here however we chose not to adopt this approach.," In order to avoid excessively high weighting and high $\chi^2$ values, many SED fitting codes impose minimum flux errors (e.g. HyperZ, \citealt{bolzonella00}; ImpZ, \citealt{babbedge04}) ), here however we chose not to adopt this approach." +" Based on the best-fit. model parameters à number of other physical parameters can be derived: We also address the issue of lowoptical depth tori. namely ork with equatorial 70,71.0. equivalent to Ay x22."," Based on the best-fit model parameters a number of other physical parameters can be derived: We also address the issue of lowoptical depth tori, namely tori with equatorial ${\rm \tau}_{9.7} \le 1.0$, equivalent to Av $\le 22$." + The obscuring medium (torus) is usually considered to be optically thick but there are no physical arguments against he existence of optically thin tori., The obscuring medium (torus) is usually considered to be optically thick but there are no physical arguments against the existence of optically thin tori. + We therefore test. the »xossibilitv. of quasars seen also through low optical depth orl. as opposed to the “traditional” picture of them. seen uniquely on lines of sight not intercept by the torus.," We therefore test the possibility of quasars seen also through low optical depth tori, as opposed to the “traditional” picture of them seen uniquely on lines of sight not intercept by the torus." + In order o do so. we run the SED [fitting twice. once allowing for all optical depths. and once allowing only for models with (70.7= 1.0). and compared the results.," In order to do so, we run the SED fitting twice, once allowing for all optical depths, and once allowing only for models with ${\rm \tau}_{9.7} \ge 1.0$ ), and compared the results." + From the 278 quasars comprising the sample. 247 have IRAC coverage. SG of which have additional J44A. data from 2ALASS (of a total of OF quasars of our. sample detected. by 2MLASS) and a total of 268 has a 24 datapoint.," From the 278 quasars comprising the sample, 247 have IRAC coverage, 86 of which have additional $JHK$ data from 2MASS (of a total of 97 quasars of our sample detected by 2MASS) and a total of 268 has a 24 datapoint." + If one requires a good sampling of the SEDs. one might require detections in at least S bands: i.q.Εςντι two out of four URAC bands (due to slight dillerences in the rastering. objects that lic at the edees of the fields might escape detection in 2 of the 4 bands) ancl MIPS 24 jum..," If one requires a good sampling of the SEDs, one might require detections in at least 8 bands: $u,g,r,i,z$, two out of four IRAC bands (due to slight differences in the rastering, objects that lie at the edges of the fields might escape detection in 2 of the 4 bands) and MIPS 24 ." + Similar considerations apply in that the objects that were, Similar considerations apply in that the objects that were +To study how galaxies form and evolve. in their. hosting dark matter haloes. a lot of efforts have been mace to link galaxy properties with the properties of dark matter haloes which they reside in.,"To study how galaxies form and evolve in their hosting dark matter haloes, a lot of efforts have been made to link galaxy properties with the properties of dark matter haloes which they reside in." + Phe usual methods used include galaxy kinematies(?) and galaxy lensing(??7).. which measure the mass of hosting dark matter haloes directly.," The usual methods used include galaxy \citep{erickson1987} and galaxy \citep{mandelbaum2005,mandelbaum2006}, which measure the mass of hosting dark matter haloes directly." +" Semi-analytic models trace the gas cooling. star formation. ancl feedback processes ""ab initio to get the properties of galaxiesof present dav(??).."," Semi-analytic models trace the gas cooling, star formation, and feedback processes `ab initio' to get the properties of galaxiesof present \citep{lucia2006,bower2006}." + Lalo occupation distribution mocels stuch the galaxv-halo. connection empiricallv. to. model galaxy properties using certain assumed ormula to describe the ealaxv-halo relation(?22777).," Halo occupation distribution models study the galaxy-halo connection empirically, to model galaxy properties using certain assumed formula to describe the galaxy-halo \citep{jing1998,berlind2002,yang2003,vale2004,conroy2006,wang2006}." +. For the models that describe. the formation and evolution history of galaxies. the statistics that are commonly used to constrain these models include: number statistics such as number censitv. uminositv function and stellar mass. function(22?) spated clustering. properties describedby correlation. Cunctions( ?).. void. probability distribution(?).. pairwise velocity ispersion(? ).. the," For the models that describe the formation and evolution history of galaxies, the statistics that are commonly used to constrain these models include: number statistics such as number density, luminosity function and stellar mass \citep{bullock2002,zehavi2005,moster2009}, spatial clustering properties describedby correlation \citep{jing1998, + yang2003, zehavi2005}, , void probability \citep{vale2004}, , pairwise velocity \citep{jing1998}, , the" +et al.,et al. + 1997)., 1997). + We have collected a sample of Sevferts which both slow N-rayv (cold) absorption aud whose optical or IR broad lines are rot completely μιppressed., We have collected a sample of Seyferts which both show X-ray (cold) absorption and whose optical or IR broad lines are not completely suppressed. + The ratios between the broad lines provide information ou the dust redching towards the nucleus: however. the broad cussion liies luus be used with mich care. siice the extreme couditions of the broad liue clouds ca1 affect the intriic line ratios through radiative transport effects;," The ratios between the broad lines provide information on the dust reddening towards the nucleus; however, the broad emission lines must be used with much care, since the extreme conditions of the broad line clouds can affect the intrinsic line ratios through radiative transport effects." + By assimune the standard extinction curve we cal estimate the visual extinction., By assuming the standard extinction curve we can estimate the visual extinction. + The resIting distribution for the AyNu ratio. relative to the Galactic stavdard value. is show 1 Fig.," The resulting distribution for the $\rm A_V/N_H$ ratio, relative to the Galactic standard value, is shown in Fig." + 3., 3. +" Most of he AGNs in our salple :we characterized by a deficit o [dust asorption with respect to what expected from the Nj; measured iu the N-ravs. in agreement with carly claius,"," Most of the AGNs in our sample are characterized by a deficit of dust absorption with respect to what expected from the $_H$ measured in the X-rays, in agreement with early claims." + At higher. ¢Πο hDuudjosities there are evCll nore extrele exauples of this effect: objecs that. althoug1 absorbed in tie N-ravs. do not show significant dust absorption i the optical aud appear as type L. broad line ACONS have con. recently discovered 1i hard X-ray aud radio surveys (Sambruna et al.," At higher, quasar-like luminosities there are even more extreme examples of this effect: objects that, although absorbed in the X-rays, do not show significant dust absorption in the optical and appear as type 1, broad line AGNs have been recently discovered in hard X-ray and radio surveys (Sambruna et al." + 1999. Asivama et al.," 1999, Akiyama et al." + 2000. Reeves et al.," 2000, Reeves et al." + 1997)., 1997). + Puzzling enough. the early Chandra surveys preseuted to date inve femud only a few type 1: QSOs absorbed in the hard N-ravs: this issue will be shorlv discussed in Sect.," Puzzling enough, the early Chandra surveys presented to date have found only a few type 1 QSOs absorbed in the hard X-rays; this issue will be shortly discussed in Sect." + 7., 7. + T16 origin of the reduced Ay/Ny ratio is not clear., The origin of the reduced $\rm A_V/N_H$ ratio is not clear. + An obvious explanation is hat the dust-to-gas ratio is uch lower than Caactic or that iu the immer part of the obsctving torus the cust is sublinated by the str‘one UV radiation fied., An obvious explanation is that the dust-to-gas ratio is much lower than Galactic or that in the inner part of the obscuring torus the dust is sublimated by the strong UV radiation field. + However. if he dust content im t16 absorbing wedi is significantly reducel. especially at the inner face. then mos of the UV ionizing photojs are absorbed bv f1ο atone gas.," However, if the dust content in the absorbing medium is significantly reduced, especially at the inner face, then most of the UV ionizing photons are absorbed by the atomic gas." + This should create a mec TTT reeion. which woud emit stroug (~ narrow) hydrogen ines corresponding t oa large covering factor. 1.e. nuch brighter tha1i the emission ines from the NLR {see also Netzer Laor. 19:)3).," This should create a huge HII region, which would emit strong $\sim$ narrow) hydrogen lines corresponding to a large covering factor, i.e. much brighter than the emission lines from the NLR (see also Netzer Laor, 1993)." +" Also. a sinipe shortage of dust eras with respect to the gas mass would uo explain other pecujar properties of the «ust in Ανα, such as the absence of the silicate absorplon feature iu the uid-IR specra of niost Sy2s (Clavel et al."," Also, a simple shortage of dust grains with respect to the gas mass would not explain other peculiar properties of the dust in AGNs, such as the absence of the silicate absorption feature in the mid-IR spectra of most Sy2s (Clavel et al." + 2000) and the absence of the carbon dip in the U Vos]vectra of some reddened Svs., 2000) and the absence of the carbon dip in the UV spectra of some reddened Sy1s. + Anoher interesting possibility is that the dust extinction curve is much flater han the staidard Galactic., Another interesting possibility is that the dust extinction curve is much flatter than the standard Galactic. + The high density of the eas in the eirciununuclear reeojon of AGNs is lisely to favor the erowth of large exaius (probably through coaetlation) which. i itur1. should fatten the extinction curve aud make it featureless.," The high density of the gas in the circumnuclear region of AGNs is likely to favor the growth of large grains (probably through coagulation) which, in turn, should flatten the extinction curve and make it featureless." + This effect is directlv oserved m the deuse clouds of our Galaxy. (Draine 1995)., This effect is directly observed in the dense clouds of our Galaxy (Draine 1995). + Witin the context of the optical versus X-ray. absorption. the effect of a flat extinctio 101rve (due to erai1i coagulation) is twofold: 1) given the same dust mass. the οfiecive visual extiucion is lower. aud 2) the broad lines ratio gives a deceiviug (low) measure of the extiucion.," Within the context of the optical versus X-ray absorption, the effect of a flat extinction curve (due to grain coagulation) is twofold: 1) given the same dust mass, the effective visual extinction is lower, and 2) the broad lines ratio gives a deceiving (low) measure of the extinction." + A more thorough discussion of the whole issue is eiveu in àidolino et al. (, A more thorough discussion of the whole issue is given in Maiolino et al. ( +2000|.,2000b). + So far I have discussed) X-ray. absorption iu AGNs which were discovered and classified in the optical., So far I have discussed X-ray absorption in AGNs which were discovered and classified in the optical. + However. an increasing Πο of obscured powerful ACONs has heen discovered by meaus of ατα N-ray observations iu galaxies which are optically classified as starburst or LINER.," However, an increasing number of obscured powerful AGNs has been discovered by means of hard X-ray observations in galaxies which are optically classified as starburst or LINER." + Probably. in these objects the obscuring," Probably, in these objects the obscuring" +high energy. pile-up) formed at the boundary shear laver and the complex beaming pattern.,high energy pile-up) formed at the boundary shear layer and the complex beaming pattern. + The observed limb brightened structure seen in the radio maps of AINNSOL jet can be explained if we consider the shear acceleration. of particles at. the boundary. due to velocity stratification. and. their dilfusion into the jet medium., The observed limb brightened structure seen in the radio maps of MKN501 jet can be explained if we consider the shear acceleration of particles at the boundary due to velocity stratification and their diffusion into the jet medium. + This inference does not demand large viewing angle which is required otherwise for the explanation. via differential Doppler boosting of the jet spine and boundary., This inference does not demand large viewing angle which is required otherwise for the explanation via differential Doppler boosting of the jet spine and boundary. + We have shown that shear acceleration dominates over turbulent acceleration at the boundary if we consider thin shear laver or a sharp velocity gradient., We have shown that shear acceleration dominates over turbulent acceleration at the boundary if we consider thin shear layer or a sharp velocity gradient. + Also [for the estimated set of parameters. shear acceleration timescale is much smaller than svnchrotron cooling timescale allowing acceleration of electrons to be possible.," Also for the estimated set of parameters, shear acceleration timescale is much smaller than synchrotron cooling timescale allowing acceleration of electrons to be possible." + The thickness of the limb brightened. structure will be decided. bythe distance electrons have cilfusecl into the radiation.jet medium before loosing its energy via svnchrotron Llo, The thickness of the limb brightened structure will be decided by the distance electrons have diffused into the jet medium before loosing its energy via synchrotron radiation. +wever the estimated thickness is beyond the resolution of present cay telescopes., However the estimated thickness is beyond the resolution of present day telescopes. + Simple analytical solution of the steady state cillusion equation considering mono-energetic injection ancl particle escape. indicates à steep. particle spectra for the electrons accelerated at the shear laver in comparison with turbulent acceleration.," Simple analytical solution of the steady state diffusion equation considering mono-energetic injection and particle escape, indicates a steep particle spectra for the electrons accelerated at the shear layer in comparison with turbulent acceleration." + “Phe radio spectral index map of MINN501 jet is also observed to have steep. spectra at. the boundary supporting the presence of shear acceleration., The radio spectral index map of MKN501 jet is also observed to have steep spectra at the boundary supporting the presence of shear acceleration. + The author is grateful to the anonvmous referee. for his useful comments which helped in clearing many of the ignorances and a better understanding., The author is grateful to the anonymous referee for his useful comments which helped in clearing many of the ignorances and a better understanding. + Phe author acknowledges the useful discussions with S. Bhattacharyya. N. Bhatt. M.Choucdhury ancl A-Alitra.," The author acknowledges the useful discussions with S. Bhattacharyya, N. Bhatt, M.Choudhury and A.Mitra." + Phe author is grateful to L. Stawarz and E. M. Rieger for enlightening information on various topics related to shear acceleration., The author is grateful to L. Stawarz and F. M. Rieger for enlightening information on various topics related to shear acceleration. +llydrodynamie simulations suggest that large-scale bars can lead to the formation of erand design nuclear spirals (Patsis&Athanassoula2000:EnelmaierShlosman2000).. and several observational studies support thishypothesis etal.2003b).,"Hydrodynamic simulations suggest that large-scale bars can lead to the formation of grand design nuclear spirals \citep{patsis00, englmaier00}, and several observational studies support thishypothesis \citep{pogge02, martini03b}." +. With our focus on the very central regions of nuclear spirals. we lind (hat this is in fact not the case: the grand design nuclear spirals described in are preferentially Found in strongly barred. galaxies.," With our focus on the very central regions of nuclear spirals, we find that this is in fact not the case: the grand design nuclear spirals described in \\ref{sec:nuc} are preferentially found in strongly barred galaxies." + We find. however. (hat svimnmelirc (wo-arl spiral structure is Common al larger scales in strongly barred. galaxies.," We find, however, that symmetric two-arm spiral structure is common at larger scales in strongly barred galaxies." + To differentiate between circummnuclear grand design spirals found at dilferent scales. we hereafter refer to grand design structure at small radii. defined as GD in relsec:nuc.. as SGD structure (small erancl design). and prominent erancl design structure al larger radii (within of Das. as shown in Figure 7)) as LGD structure (large grand design).," To differentiate between circumnuclear grand design spirals found at different scales, we hereafter refer to grand design structure at small radii, defined as GD in \\ref{sec:nuc}, as SGD structure (small grand design), and prominent grand design structure at larger radii (within of $D_{25}$, as shown in Figure \ref{fig:gd}) ) as LGD structure (large grand design)." + Figure 7 shows four examples of galaxies for which grand design structure is evident at larger scales. but is not present al smaller scales.," Figure \ref{fig:gd} shows four examples of galaxies for which grand design structure is evident at larger scales, but is not present at smaller scales." + Seven galaxies of the entire sample) have SGD structure. while (wenty )) have LGD structure.," Seven galaxies of the entire sample) have SGD structure, while twenty ) have LGD structure." + This larger-scale GD structure extends to the center of the galaxy in only (wo (10%)) of these twenty galaxies., This larger-scale GD structure extends to the center of the galaxy in only two ) of these twenty galaxies. + As can be seen in Figure 8.. LGD galaxies are preferentially more strongly barred than SGD galaxies.," As can be seen in Figure \ref{fig:lgdvsgd}, LGD galaxies are preferentially more strongly barred than SGD galaxies." + A Ίντο test excluding the two shared galaxies reveals a probability that SGD and LGD barstrengths are drawn from the same parent distribution., A K-S test excluding the two shared galaxies reveals a probability that SGD and LGD barstrengths are drawn from the same parent distribution. +" We further find a probability that LOD galaxies have (he same underlving distribution of Q, as the other 59 galaxies in the sample: galaxies with LGD nuclear spirals are more stronely barred (han other galaxies.", We further find a probability that LGD galaxies have the same underlying distribution of $Q_b$ as the other 59 galaxies in the sample; galaxies with LGD nuclear spirals are more strongly barred than other galaxies. + It is interesting to note that the two LGD ealaxies wilh the smallest Quy (NGCL941 and NGCI317) also have an obvious nuclear bar within the grand design structure (Erwin2004 and Greusardοἱal. 2000... respectively).," It is interesting to note that the two LGD galaxies with the smallest $Q_b$ (NGC4941 and NGC1317) also have an obvious nuclear bar within the grand design structure \citealp{erwin04} and \citealp{greusard00}, , respectively)." +Vhe thermal Sunvaev Zeldovich. (SZ) οσο (2)) is a spectral distortion. of the Cosmic Microwave. Background (CAIB) radiation due to inverse Compton scattering by the hot gas in galaxy clusters.,The thermal Sunyaev Zel'dovich (SZ) effect \citealp{SZ}) ) is a spectral distortion of the Cosmic Microwave Background (CMB) radiation due to inverse Compton scattering by the hot gas in galaxy clusters. + Lt has long been exploited in cosmological anc cluster studies in order to derive. for exaniple. the Lubble constant(e.g. ?.. 7.. 7.. ?.. 7))," It has long been exploited in cosmological and cluster studies in order to derive, for example, the Hubble constant(e.g. \citealp{Hughes1998}, \citealp{Mason_obs}, \citealp{Reese2002}, \citealp{Saunders2003}, \citealp{Bonamente2006}) )" + and the gas mass fraction (e.g. 7. 7.. ?)).," and the gas mass fraction (e.g. \citealp{Grego2001}, \citealp{Lancaster2005}, \citealp{LaRoque2006}) )." + Thanks to well developed techniques. detections are becoming routine although signaltonoise remains quite poor.," Thanks to well developed techniques, detections are becoming routine although signal–to–noise remains quite poor." + However. we are entering an era of purposebuilt instruments so this is set to improve dramatically. enabling SZ research to reach ils evident. potential.," However, we are entering an era of purpose–built instruments so this is set to improve dramatically, enabling SZ research to reach its evident potential." +" Mmain focus ⊀⋅of the SZ community⊀ at.⇀∙↗↦⇀∙↗∩⊳↾↓∖∪⊔↓⊳↧↥⊳⋖⊾⇂⋅⊔↓⋅↿↓∐⋅↓⋅⊳⊔⇂∖⇁⊳⋯⊓⊾⊳∖⊳↓⋅∢⊾∐⊳↧∣⋡⇂∢⋅∪∣⋡≱∖⋖⊾↓⋅∖⇁⊳∐⊲↓∪⊔≱∖∪⇂∎ present l to""M utilise theae redshift’ independence.of their SZ surface. Anse.aree. brightness in order to perform. blind surveys for galaxy clusters.", The main focus of the SZ community at present is to utilise the redshift–independence of the SZ surface brightness in order to perform blind surveys for galaxy clusters. + While other techniques suller from larec intrinsic biases anc complex selection cllects. SZ. surveys will produce almost catalogues ancl thus far superior datasets for constraining cosmological models.," While other techniques suffer from large intrinsic biases and complex selection effects, SZ surveys will produce almost catalogues and thus far superior datasets for constraining cosmological models." + The dedicated SZ surveys. for example Planck (2)). SPT (?.. 2). ACT (2. 2)) and the SZA (2). are now generating results.," The dedicated SZ surveys, for example Planck \citealp{Ade2011}) ), SPT \citealp{Stan2009}, \citealp{Vanderlinde2010s}) ), ACT \citealp{Menanteau2010}, \citealp{Marriage2010}) ) and the SZA \citep{Muchovej2011} are now generating results." + Alany more are expected in the near future. c.g. from AMI (2)..," Many more are expected in the near future, e.g. from AMI \citep{Zwart2008s}." + In order to Lully exploit the results of these surveys. it will be necessary to improve understanding of both the ‘selection οσο due to the presence of unsubtractecl radio sources. and also the scalings between cluster SZ observables ancl various physical quantities. especially the cluster mass.," In order to fully exploit the results of these surveys, it will be necessary to improve understanding of both the `selection effect' due to the presence of unsubtracted radio sources, and also the scalings between cluster SZ observables and various physical quantities, especially the cluster mass." +" Various groups have undertaken similar studies (c.g. 2.. ?.. "" , ‘. Phe| . diSNWe MBPselectecΙseY "," Various groups have undertaken similar studies (e.g. \citealp{Benson2004}, , \citealp{Morandi2007}, \citealp{Bonamente2008}, \citealp{Huang2010}) )." +OSsLeSarearo POULLOC κ...4is," To make further advances, reliable observations of large, well–selected samples are required." +in the upper right corner of the diagrams of Fig.,in the upper right corner of the diagrams of Fig. + 6bb-d consists of the out-of-dip cata. where the colors remain constant and the column density is at its lowest value.," \ref{fig:ccd}b b–d consists of the out-of-dip data, where the colors remain constant and the column density is at its lowest value." + As noted above. the early turn of the observed tracks in the color-color diagram suggests the presence of ar unabsorbed spectral component in the data.," As noted above, the early turn of the observed tracks in the color-color diagram suggests the presence of an unabsorbed spectral component in the data." + To quantify this €laim. we compare theoretical tracks from the partial covering model to the data.," To quantify this claim, we compare theoretical tracks from the partial covering model to the data." + This is done by varying the relative contributions of 74 and 7i. to the total spectrum such that the total normalization of the incident spectrum. fy|7p. Is kept at its pre-dip value.," This is done by varying the relative contributions of $I_\mathrm{A}$ and $I_\mathrm{U}$ to the total spectrum such that the total normalization of the incident spectrum, $I_\mathrm{A}+I_\mathrm{U}$, is kept at its pre-dip value." + Except for the normalizations. all other spectral parameters are fixed at their pre-dip values SSect. ??)).," Except for the normalizations, all other spectral parameters are fixed at their pre-dip values Sect. \ref{subsec:specfits}) )." + We define the best fit model to be the model in which the root mean square distance between the track and the data is minimal FFig. 6))., We define the best fit model to be the model in which the root mean square distance between the track and the data is minimal Fig. \ref{fig:ccd}) ). + Not surprisingly. the ratio," Not surprisingly, the ratio" +only show a weak correlation. this stucly is the first definitive campaign to probe this tvpe of behaviour.,"only show a weak correlation, this study is the first definitive campaign to probe this type of behaviour." + We have shown that NGC 7213 sits well on. the owedieted: fandamoental plane of black hole activity plot when compared with the ΔΗΛ sample., We have shown that NGC 7213 sits well on the predicted fundamental plane of black hole activity plot when compared with the MHdM03 sample. + However. we rave shown that when comparing NGC 7213 with a revised BUARB and LLAGN sample that the data points are above he expected correlation: which is however consistent with he calculated: radio ancl X-ray. loudness parameters., However we have shown that when comparing NGC 7213 with a revised BHXRB and LLAGN sample that the data points are above the expected correlation; which is however consistent with the calculated radio and X-ray loudness parameters. + We iive also shown some support that by correcting for the ime lag between events in N-ray. and radio the gradient. of data points agree better with the best fit derived from the ALIGOMOS sample on the fundamental plane., We have also shown some support that by correcting for the time lag between events in X-ray and radio the gradient of data points agree better with the best fit derived from the MHdM03 sample on the fundamental plane. + ALEBell would. like to thank Sera. Markoll.. Anthony Rushton and Sadie Jones for their useful comments. and discussion.," M.E.Bell would like to thank Sera Markoff, Anthony Rushton and Sadie Jones for their useful comments and discussion." + “The Australia Telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO., The Australia Telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. + This research has made use of the Tartarus (Version 3.1) database. created by Paul ONeill and Wirpal Nandra at Imperial College London. and Jane ‘Turner at NASA/GSEC.," This research has made use of the Tartarus (Version 3.1) database, created by Paul O'Neill and Kirpal Nandra at Imperial College London, and Jane Turner at NASA/GSFC." + Tartarus is supported by funding from PPABC. anc NASA grants NAGS5S-7385 and. NACH-," Tartarus is supported by funding from PPARC, and NASA grants NAG5-7385 and NAG5-7067." +To estimate the size of the dust belt. a series of MCFOST models were run with a range of outer disk radi.,"To estimate the size of the dust belt, a series of MCFOST models were run with a range of outer disk radii." +" All models simultaneously matched the 350,m flux and previously measured fluxes reported in Su et al. (", All models simultaneously matched the $\mu$ m flux and previously measured fluxes reported in Su et al. ( +2009) or compiled by Reidemeister et al. (,2009) or compiled by Reidemeister et al. ( +2009). plotted in Figure 2.,"2009), plotted in Figure 2." + Although the map resolution and sensitivity are limited. the disk outer radius is consistent with ~300 AU. and this radius is marked on Figure I. along with the assumed inner radius.," Although the map resolution and sensitivity are limited, the disk outer radius is consistent with $\sim$ 300 AU, and this radius is marked on Figure 1, along with the assumed inner radius." + The 350um emission is largely confined within a radius of 300 AU., The 350 $\mu$ m emission is largely confined within a radius of 300 AU. + Further details on the set of simulated 3504m images from MCFOST are given in Figure 3., Further details on the set of simulated $\mu$ m images from MCFOST are given in Figure 3. + A radius of 200 AU results in à more compact structure inconsistent. with the data. though higher sensitivity maps will be required to rule out disks much larger than 300 AU. since the surface brightness of the most extended emission is beyond the dynamic range of the CSO data.," A radius of 200 AU results in a more compact structure inconsistent with the data, though higher sensitivity maps will be required to rule out disks much larger than 300 AU, since the surface brightness of the most extended emission is beyond the dynamic range of the CSO data." + The observed disk morphology is compared with two types of models of the disk structure — a symmetric dust distributio simulated with MCFOST and an asymmetric dust distributio governed by gravitational interactions and radiation pressure., The observed disk morphology is compared with two types of models of the disk structure – a symmetric dust distribution simulated with MCFOST and an asymmetric dust distribution governed by gravitational interactions and radiation pressure. + Assuming a symmetric circular ring for the disk described 1 Table |. the effect of changing the inclination ts explored 1 Figure 3.," Assuming a symmetric circular ring for the disk described in Table 1, the effect of changing the inclination is explored in Figure 3." + As the emission ts optically thin at 3505 (unlike scattered light images at shorter wavelengths). the disk patter remains symmetric as the inclination increases.," As the emission is optically thin at $\mu$ m (unlike scattered light images at shorter wavelengths), the disk pattern remains symmetric as the inclination increases." + Since the observed map is not well matched by these symmetric patterns. it is not possible to place a strong constraint on the disk inclination to compare with estimates from planet astrometry (Lafreniérre et al.," Since the observed map is not well matched by these symmetric patterns, it is not possible to place a strong constraint on the disk inclination to compare with estimates from planet astrometry (Lafrenièrre et al." + 2009). 701m emission (Su et al.," 2009), $\mu$ m emission (Su et al." + 2009). and stability (Moro-Martínn et al.," 2009), and stability (Moro-Martínn et al." + 2010)., 2010). + The CSO map is also compared with numerical models resulting in an. asymmetric dust distribution., The CSO map is also compared with numerical models resulting in an asymmetric dust distribution. + In. addition to the extended structure. the HR 8799 disk emission at 350um is slightly offset from the coordinates of the host star.," In addition to the extended structure, the HR 8799 disk emission at $\mu$ m is slightly offset from the coordinates of the host star." + The distance from the star to the brightest point in the disk is 271 + 077. or 84 + 28AU.," The distance from the star to the brightest point in the disk is $\farcs$ 1 $\pm$ $\farcs$ 7, or 84 $\pm$ 28AU." + While the uncertainty is too large to assign à specific value to the radius of the brightest region of the disk. an estimate can be compared with the distance to the peak in surface density of the numerical simulation in Figure I.," While the uncertainty is too large to assign a specific value to the radius of the brightest region of the disk, an estimate can be compared with the distance to the peak in surface density of the numerical simulation in Figure 1." +" A dominant one-sided are of higher surface density describes the distribution of grains with f values on the order of 0.005 or less. as they become trapped in the 2:1 mean motion resonance (Wyatt 2006). based on previously published simulations of migrating planets with masses up to 1 Mj, (Wyatt 2006)."," A dominant one-sided arc of higher surface density describes the distribution of grains with $\beta$ values on the order of 0.005 or less, as they become trapped in the 2:1 mean motion resonance (Wyatt 2006), based on previously published simulations of migrating planets with masses up to 1 $_\mathrm{Jup}$ (Wyatt 2006)." + Our simulation of a planetesimal belt is a test case extending to include two higher mass planets: a similar asymmetric pattern is evident in our dust surface density map in Figure 1., Our simulation of a planetesimal belt is a test case extending to include two higher mass planets; a similar asymmetric pattern is evident in our dust surface density map in Figure 1. + The CSO map of the debris disk shows a structure suggestive of a single bright clump like the pattern produced by dust grains trapped in the 2:] mean motion resonance with a planet. while the map does not reveal two distinet clumps separated by 180 degrees. as expected for material trapped in the 3:2 resonance (Wyatt 2006).," The CSO map of the debris disk shows a structure suggestive of a single bright clump like the pattern produced by dust grains trapped in the 2:1 mean motion resonance with a planet, while the map does not reveal two distinct clumps separated by 180 degrees, as expected for material trapped in the 3:2 resonance (Wyatt 2006)." + Within the uncertainty of the measurement. the radius of the brightest region of the disk is consistent with the peak in the surface density image in our simulation; a convolution of the simulated map with the CSO beam showing a similar offset is given in Figure |.," Within the uncertainty of the measurement, the radius of the brightest region of the disk is consistent with the peak in the surface density image in our simulation; a convolution of the simulated map with the CSO beam showing a similar offset is given in Figure 1." + Based on previous simulations. resonant trapping cannot easily explain that the brightest clump leads rather than lags the planet position. since the libration point lagging position has a higher probability to be filled for an outward migration with a planet with eccentricity greater than 0.03 (Wyatt 2006).," Based on previous simulations, resonant trapping cannot easily explain that the brightest clump leads rather than lags the planet position, since the libration point lagging position has a higher probability to be filled for an outward migration with a planet with eccentricity greater than 0.03 (Wyatt 2006)." + In our simulation of a planetesimal belt surrounding two massive planets with slow outward migration. the azimuthal angle of the bulge is subject to large scale oscillations over the course of several orbits. moving between a leading and a trailing position in a continuous manner. without crossing in front of the planet.," In our simulation of a planetesimal belt surrounding two massive planets with slow outward migration, the azimuthal angle of the bulge is subject to large scale oscillations over the course of several orbits, moving between a leading and a trailing position in a continuous manner, without crossing in front of the planet." + Such an oscillating structure can be produced if the orbits of the planets become eccentric as they migrate (due to mutual iteractios) and. once formed. the structure can persist even if the eccentricities of the planetary orbits are later damped.," Such an oscillating structure can be produced if the orbits of the planets become eccentric as they migrate (due to mutual interactions) and, once formed, the structure can persist even if the eccentricities of the planetary orbits are later damped." +" If dynamical interactions are governing the particle spatial ""Sistribution such that the 350j/m-emitting. grains are trapped in à 2:1 mean motion resonance with the outermost planet. then there are important implications for the orbital history of HR 8799b."," If dynamical interactions are governing the particle spatial distribution such that the $\mu$ m-emitting grains are trapped in a 2:1 mean motion resonance with the outermost planet, then there are important implications for the orbital history of HR 8799b." + To enhance the population of planetesimals in the resonance. orbital migratior is required. although the rate of migration cannot be too high. or the trapping probability will decrease (Reche et al.," To enhance the population of planetesimals in the resonance, orbital migration is required, although the rate of migration cannot be too high, or the trapping probability will decrease (Reche et al." + 2008)., 2008). + Planet migration may have strongly influenced the timing and mass flux of the Late Heavy Bombardment of the terrestrial planets in the Solar System (Gomes et al., Planet migration may have strongly influenced the timing and mass flux of the Late Heavy Bombardment of the terrestrial planets in the Solar System (Gomes et al. + 2005). so evidence of orbital migration may be an important factor for the conditions in the as-yet unexplored terrestrial planet region in the HR 8799 system.," 2005), so evidence of orbital migration may be an important factor for the conditions in the as-yet unexplored terrestrial planet region in the HR 8799 system." + Theoretical arguments favouring Currie et al. (, Theoretical arguments favouring Currie et al. ( +2011) and rejecting Dodson-Robinson et al. (,2011) and rejecting Dodson-Robinson et al. ( +2009) orbital migration for the HR 8799 system have also been proposed.,2009) orbital migration for the HR 8799 system have also been proposed. + For a resonant pattern to persist. the eccentricity of the orbit of the planet needs to be low. since the libration amplitude of the planetesimals in resonance is Increased as eccentricity increases. causing the distribution to become smooth (Reche et al.," For a resonant pattern to persist, the eccentricity of the orbit of the planet needs to be low, since the libration amplitude of the planetesimals in resonance is increased as eccentricity increases, causing the distribution to become smooth (Reche et al." + 2008)., 2008). + Numerical simulations of the HR 8799 planet system (prior to the, Numerical simulations of the HR 8799 planet system (prior to the +Iu the standard A cold dark matter paradigm of structure formation. more massive Galaxies are asseibled from smaller ones in a series of merger events;,"In the standard $\Lambda$ cold dark matter paradigm of structure formation, more massive galaxies are assembled from smaller ones in a series of merger events." + Nearly every galaxw hosts a central supermassive black hole (SMDBII) (?7).. which iuplies that a imereer between two galaxies nearly always results in a merecr-remmaut ealaxy containing two SAIBIs.," Nearly every galaxy hosts a central supermassive black hole (SMBH) \citep{KO95.1}, which implies that a merger between two galaxies nearly always results in a merger-remnant galaxy containing two SMBHs." + Drag from ανασα] friction causes the two SMDIIS to inspiral toward the center of the imerecr-remuaut., Drag from dynamical friction causes the two SMBHs to inspiral toward the center of the merger-remnant. + The SMDIIS spend ~ Myr at separations ο1 προ (??).. then form a parsec-scale binary aud ultimately coalesce into a suele ceutral SMDIT in the imerecrremnant galaxy.," The SMBHs spend $\sim 100$ Myr at separations $\gtrsim +1$ kpc \citep{BE80.1, MI01.1}, then form a parsec-scale binary and ultimately coalesce into a single central SMBH in the merger-remnant galaxy." + This final coalescence is necessary to preserve the tight observational correlation between the mass of the black hole aud the velocity dispersion. or total mass. of the host galaxy stellar bulge (?)..," This final coalescence is necessary to preserve the tight observational correlation between the mass of the black hole and the velocity dispersion, or total mass, of the host galaxy stellar bulge \citep{FE00.1}." + Although SMDII pairs are a natural consequence of galaxy mergers. there have been few unanmibieuous detections of galaxies hosting SMDIT pairs.," Although SMBH pairs are a natural consequence of galaxy mergers, there have been few unambiguous detections of galaxies hosting SMBH pairs." + If suficicut eas accretes onto both SMDIIs. they may each be visible as an active galactic nucleus (AGN).," If sufficient gas accretes onto both SMBHs, they may each be visible as an active galactic nucleus (AGN)." + To date. there have been definitive detections of oulv four galaxies hosting such AGN pairs.," To date, there have been definitive detections of only four galaxies hosting such AGN pairs." + First. radio signatures of ACN activity in the +=0.055 elliptical galaxy 01021379 show that it hosts binary SMBIIs separated by 5 lt pe (???)..," First, radio signatures of AGN activity in the $z=0.055$ elliptical galaxy 0402+379 show that it hosts binary SMBHs separated by 5 $^{-1}$ pc \citep{XU94.1,MA04.2,RO06.1}." + Iu addition. N-rav detections of a dual AGN in the 2=0.02 ultraluminous infrared ealaxy NGC 6210 indicate it hosts1 two SMDIIS separated by 0.5 1 kpe (2).," In addition, X-ray detections of a dual AGN in the $z=0.024$ ultraluminous infrared galaxy NGC 6240 indicate it hosts two SMBHs separated by 0.5 $h^{-1}$ kpc \citep{KO03.1}." + Finally. optical spectroscopic signatures of dual AGN in the red galaxies ECGSD2 J112033.6|525917 at 2=0.71 and EGSD2 J111550.5]1520929 at ;=0.62 show these galaxies host dual SMDIIS at separations of OSL ft kpe aud 1.6 hf+ kpe. respectively (27)...," Finally, optical spectroscopic signatures of dual AGN in the red galaxies EGSD2 J142033.6+525917 at $z=0.71$ and EGSD2 J141550.8+520929 at $z=0.62$ show these galaxies host dual SMBHs at separations of 0.84 $h^{-1}$ kpc and 1.6 $h^{-1}$ kpc, respectively \citep{GE07.2,CO09.2}." + A fifth possible exaniple has been proposed by ?.. though it is likely to be an object of a different nature (e.g... 27???2)).," A fifth possible example has been proposed by \cite{BO09.2}, though it is likely to be an object of a different nature (e.g., \citealt{CH09.3,CH09.4,GA09.1,LA09.1,WR09.1}) )." + Here we present evidence for a 1.75 + 0.03 53 kpe projected spatial separation and 150 + 140 lau + line-ofsight velocity separation SMIBIT pair. visible as the +=0.36 dual AGN system COSMOS. JLO0013.15|020637.2 in the COSMOS field (?)..," Here we present evidence for a 1.75 $\pm$ 0.03 $h^{-1}$ kpc projected spatial separation and 150 $\pm$ 40 km $^{-1}$ line-of-sight velocity separation SMBH pair, visible as the $z=0.36$ dual AGN system COSMOS J100043.15+020637.2 in the COSMOS field \citep{SC07.6}." + The candidate was found serendipitouslv while visually iuspecting postage stamp images of COSAIOS ealaxies with high Sévrsic iudices iu the ACS-CGC catalog (Caifith et al..," The candidate was found serendipitously while visually inspecting postage stamp images of COSMOS galaxies with high Sérrsic indices in the ACS-GC catalog (Griffith et al.," + in preparation). which inchides morphology measurements for over half a iullion sources from five large Advanced Camera for SurveysGIST ACS) imagine datasets.," in preparation), which includes morphology measurements for over half a million sources from five large Advanced Camera for Surveys ACS) imaging datasets." + In addition. the candidate has been previously classified ax an AGN by both COSMOS (7). and the Sloan Digital Sky Survey (SDSS) (??)..," In addition, the candidate has been previously classified as an AGN by both COSMOS \citep{GA09.3} and the Sloan Digital Sky Survey (SDSS) \citep{YO00.2, RI02.2}." +" We asstue a Ubtbble constant Hy=100h lau ! Mpe1. Q,,=0.3. and O94=0.7 throughout. aud all distances are eiven iu physical (not comoving) units."," We assume a Hubble constant $H_0 =100 \, h$ km $^{-1}$ $^{-1}$, $\Omega_m=0.3$, and $\Omega_\Lambda=0.7$ throughout, and all distances are given in physical (not comoving) units." + We originally identified COSMOS JLO0013.15|020637.2. as a. dual ACN candidate foin itsST ESLIN ACS nuage taken for COSMOS (ανν , We originally identified COSMOS J100043.15+020637.2 as a dual AGN candidate from its F814W ACS image taken for COSMOS \citep{SC07.7}. . +This imaee. shown in Figure L.. shows a disturbed ealaxy with a long tidal tail that suggests the galaxy has recently undergone a merger.," This image, shown in Figure \ref{fig:cosmos}, shows a disturbed galaxy with a long tidal tail that suggests the galaxy has recently undergone a merger." +" The nucleus of the ealaxy contains two bright point sources, andwe use 0725 (0.88 lt kpe) radius apertures to measte the inaenitudeaud bhuuinositv of each source with Source EXtractor (?).."," The nucleus of the galaxy contains two bright point sources, andwe use $0\farcs25$ $0.88$ $^{-1}$ kpc) radius apertures to measure the magnitudeand luminosity of each source with Source EXtractor \citep{BE96.1}. ." +Visible Multi-Object Spectrograph (VIMOS) (Lillyetal.2007) and the I&eck Deep Extragalactic Tagine Multi- Spectrograph. (DETMOS).,Visible Multi-Object Spectrograph (VIMOS) \citep{Lilly:2007} and the Keck Deep Extragalactic Imaging Multi-Object Spectrograph (DEIMOS). + The r.nis., The r.m.s. + dispersion in the offset 04. between photometric aud spectroscopic redshift is 0.00701|2) at ip<22.5 and O.02(1|2) at ip—2| aud :<1.3 (tor (0.0601|:) for il~2[ aud D: 1.3)., dispersion in the offset $\sigma_{\Delta z}$ between photometric and spectroscopic redshift is $0.007(1+z)$ at $i^{+}_{AB}<22.5$ and $0.02(1+z)$ at $i^{+}_{AB} \sim 24$ and $z<1.3$ (or $0.06(1+z)$ for $i^{+}_{AB} \sim 24$ and $z\ge 1.3$ ). + To mitigate against catastrophic failure in estimated photo-:s. for example due to confusion between the Lyman aud Ι000Α breaks. we reject from the sample all source galaxies with a secondary peak in the redshift probability distribution function Coco»eealaxies where the parameter is ercater than zero in the Ibertetal.2009 catalog).," To mitigate against catastrophic failure in estimated $z$ s, for example due to confusion between the Lyman and $4000$ breaks, we reject from the sample all source galaxies with a secondary peak in the redshift probability distribution function galaxies where the parameter is greater than zero in the \citealt{Ilbert:2009} catalog)." + The rejected ealaxy population is expected to contain a large fraction of catastrophic errors (roughlv10565014Ilbertetal.2006:Ibert 2009)..," The rejected galaxy population is expected to contain a large fraction of catastrophic errors \citep[roughly 40\%--50\%\ --][]{Ilbert:2006,Ilbert:2009}. ." + For the purposes of cosinological constramts. we further exclude frou the sample objects with relative redshift uncertainties Ac|2)=0.05. taking the average redshift eror to be A.=(zu68_gal gal)/2.0. where and are the cconfidence Πιν on the redshift. based ou the photo- probability distribution (bertetal.2009).," For the purposes of cosmological constraints, we further exclude from the sample objects with relative redshift uncertainties $\Delta z/(1+ z) \ge 0.05$, taking the average redshift error to be $\Delta z \equiv ({\text{\tt zu68\_gal}} - $ $)/2.0$, where and are the confidence limits on the redshift, based on the photo-z probability distribution \citep{Ilbert:2009}." +. Our final source salple consists of all galaxies passing these cuts that lie within 6 of a eroup center., Our final source sample consists of all galaxies passing these cuts that lie within $\arcmin$ of a group center. + Individual ealaxies may cuter iuto the final sample multiple times if they lie within 6 of more than one peak., Individual galaxies may enter into the final sample multiple times if they lie within $\arcmin$ of more than one peak. + The photo-z quality cuts reduce the umuber deusity of source galaxies to 26 ealaxies/arciuinute. for a total of 3.7«10° galaxies (3.1<10° in the restrictec pAauple).," The photo-z quality cuts reduce the number density of source galaxies to $26$ $^{2}$, for a total of $3.7\times 10^5$ galaxies $3.1\times 10^5$ in the restricted sample)." + The mean redshift of the final sample is (2)=0.95 aud the mean relative error in redshift is τό|2)= 0.018. while the mean magnitude is (Igaiiw)~2," The mean redshift of the final sample is $\langle z \rangle = 0.95$ and the mean relative error in redshift is $\Delta z/(1+ z) = 0.018$ , while the mean magnitude is $\langle \rm{I}_{F814W} \rangle \sim 24$." + If we consider a source galaxy (or source hereafter) at redshift τς beime lensed by a foreground eroup (or “leas? hereafter) at redshift τε aud observed at te. m the weak Πιτ the tangential shear iuduced by the Ieus will be: where S(1 for sources chosen to be behind the leus: we will consider objects with both «>1 ande x1 below., Note that $x > 1$ for sources chosen to be behind the lens; we will consider objects with both $x > 1$ and $x \le 1$ below. + In terms of ιο. We can also write this in terms of M4. the value of the critical deusitv in the limit ο>x where depends oulv ou the lens properties not on the properties of the source galaxy.," In terms of $x$, We can also write this in terms of $\Sigma_{c,\infty}$, the value of the critical density in the limit $x \rightarrow \infty$: where depends only on the lens properties, not on the properties of the source galaxy." + From Equ. 1..," From Eqn. \ref{eqn:basicshear}," + the geometry of all source-Iens pairs now takes on a universal form Por} correspouds. eg. to the lensing efficicney E defined bv. Colseetal.(2002).," the geometry of all source-lens pairs now takes on a universal form $\Gamma(x)$ corresponds, e.g., to the lensing efficiency $E$ defined by \citet{Golse02}." +.. Iun. às much as the niecasured tangential ellipticitv 2; of cach source galaxy is an estimator 5; of the true tangential shear σε. we can construct a weighted sui of estimates from individual source galaxies j with respect to lensing centers / to recover the universal geometric dependence: with weights chosento maximize the sigual-to- ratio or sensitivity«5; to cosmological parameters. as ciscussecl below.," In as much as the measured tangential ellipticity $\varepsilon_t$ of each source galaxy is an estimator $\tilde{\gamma}_t$ of the true tangential shear $\gamma_t$, we can construct a weighted sum of estimates from individual source galaxies $j$ with respect to lensing centers $i$ to recover the universal geometric dependence: with weights $w_{ij}$ chosento maximize the signal-to-noise ratio or sensitivity to cosmological parameters, as discussed below." +Since we are just fitting the data to a fixed function. cosinoloey appears to have disappeared from Equ. (12)).,"Since we are just fitting the data to a fixed function, cosmology appears to have disappeared from Eqn. \ref{eqn:gamma}) )." + Tn fact. it is hidden iu the couversion frou measured source and lens redshifts to inferred source aud lens distances.," In fact, it is hidden in the conversion from measured source and lens redshifts to inferred source and lens distances." + For a given cosmology we convert redshifts to, For a given cosmology we convert redshifts to +Ascension and Declination then other stars in the vicinity of Achernar would show this trend.,Ascension and Declination then other stars in the vicinity of Achernar would show this trend. + Three stars in the vicinity of Achernar were analysed: HD. 32249. LID 12311. and. LID 3980. none of which showed the increase in amplitude.," Three stars in the vicinity of Achernar were analysed: HD 32249, HD 12311 and HD 3980, none of which showed the increase in amplitude." + Another possibility is that the increase in amplitude may only be obvious in very bright stars CXchernar being the 9th brightest star in the sky)., Another possibility is that the increase in amplitude may only be obvious in very bright stars (Achernar being the 9th brightest star in the sky). + Arcturus. Vega ancl Capella (all stars brighter than Achernar) were analysed but no similar patterns were found.," Arcturus, Vega and Capella (all stars brighter than Achernar) were analysed but no similar patterns were found." + Three stars of photometric reference were also analysed: HD. 168151. LED 155410 and LD 136064 (7).. and they also showed null results.," Three stars of photometric reference were also analysed: HD 168151, HD 155410 and HD 136064 \citep{NeilTarrant:2010}, and they also showed null results." + Variations in De stars can be ascribed to either rotation or non-radial oscillations., Variations in Be stars can be ascribed to either rotation or non-radial oscillations. + It is generally assumed that the oscillations will have constant [requeney and. phase whereas rotationally modulated variations will have a transient nature and thus non-constant frequency and. phase ic. they will be non-coherent., It is generally assumed that the oscillations will have constant frequency and phase whereas rotationally modulated variations will have a transient nature and thus non-constant frequency and phase i.e. they will be non-coherent. + Both the frequency ancl phase of what are believed to be rotationally modulated: variations can change due to outbursts from the central star to the surrounding disc (see? for a discussion of this)., Both the frequency and phase of what are believed to be rotationally modulated variations can change due to outbursts from the central star to the surrounding disc (see \citet{2003A&A...411..167S} for a discussion of this). + On the, On the +"where a;=1—(4+)/[[,(5—8)] and a?=2/(9Γι::2--).",where $a_1=1-(4+\beta)/[\Gamma_{\rm_c}(5-\beta)]$ and $a_2=2/(3\Gamma_{\rm l}+2-\beta)$ . +" Equation (2)) may be integrated to yield: where and The integral in A(t,t;) (equation (23))) has an analytic form as the integrand is proportional to a power of t for ttj."," Equation \ref{eq:loss}) ) may be integrated to yield: where and The integral in $A(t,t_{\rm i})$ (equation \ref{eq:An2}) )) has an analytic form as the integrand is proportional to a power of $t$ for $tt_{\rm j}$." +" Thus fort;€t< and for £j2 [J]birth function (see ?2)) Az— 1, [K] jet-power power-law—2.6— —3.0, and [L] jet-power power-law --2.6— —2.0."," Other sets of model parameters we investigate \ref{sec:params}) ) are: [B] $t_{\rm j}\to 5\times10^7~{\rm yr}$ , [C] $t_{\rm j}\to 5\times10^8~{\rm yr}$ , [D] $p\to 3$ , [E] $\gamma_{\rm min}\to 2000$ [F] $p\to 3$ and $\gamma_{\rm min}\to 2000$ ,[G] $p$ correlated with $Q_{\rm j}$ (see \ref{sec:params}) ), [H] $\rho_0\to 1.67\times 10^{-24}~{\rm kg}~{\rm m}^{-3}$ , [I] $\beta\to 2$ [J]birth function (see\ref{sec:BF}) ) $\Delta z\to 1$ , [K] jet-power power-law$-2.6\to -3.0$ , and [L] jet-power power-law $-2.6\to -2.0$ ." +Yp. ho. (Spergeletal.2007).,$Y_{\rm P}$ $\eta_{10}$ \citep{wmap:2007}. +. (Larsonetal.2010) Yp=0.2486+0.0006 Steigman2001. yp yo). Yp. AY/AZ Peimbertetal.2007 Peimbertetal.(2007). Yp=0.2477c0.0029. Izotov&Thuan2010)). Yp=0.256540.0010(stat)0.0050(syst). Y». AY/.XAZ. NY/.XZ. ," \citep{wmap:2010} $Y_{\rm P}=0.2486 \pm 0.0006$ \citealt{steigman:2007} $Y_{\rm P}$ $\eta_{10}$ $Y_{\rm P}$ $\Delta Y / \Delta Z$ \citealt{peimbert:2007} \citet{peimbert:2007} $Y_{\rm P}=0.2477 \pm 0.0029$ \citealt{izotov:2010}) $Y_{\rm P}=0.2565 \pm +0.0010 \, \mathrm{(stat)}\pm 0.0050 \, \mathrm{(syst)}$ $Y_{\rm P}$ $\Delta Y / \Delta Z$ $\Delta Y / \Delta Z$ " +The structure of the inner regions (sub-parsec scale) of active galactic nuclei (AGN). as probed by UV and X-ray observations. seems to be very complex. and certainly it is still not understood well.,"The structure of the inner regions (sub-parsec scale) of active galactic nuclei (AGN), as probed by UV and X-ray observations, seems to be very complex, and certainly it is still not understood well." + The optical/UV continuum emission 1s most probably due to the thermal emission from an optically thick. geometrically thin accretion disk (2).," The optical/UV continuum emission is most probably due to the thermal emission from an optically thick, geometrically thin accretion disk ." +". The disk surrounds the central supermassive black hole (SMBH). spanning radii from a few up to several hundreds of gravitational radit (p,= GMyy/c-). ie. possibly from the innermost stable circular orbit around the SMBH up to the disk self-fragmentation radius2)."," The disk surrounds the central supermassive black hole (SMBH), spanning radii from a few up to several hundreds of gravitational radii $r_g\equiv GM_{\rm{BH}}/c^2$ ), i.e. possibly from the innermost stable circular orbit around the SMBH up to the disk self-fragmentation radius." +". The origin of the X-ray continuum emission is less clearly understood and is thought to be the result of the Comptonization of accretion disk UV seed photons into a ""cloud"" of very hot electrons. the so-called X-ray corona(??)."," The origin of the X-ray continuum emission is less clearly understood and is thought to be the result of the Comptonization of accretion disk UV seed photons into a “cloud” of very hot electrons, the so-called X-ray corona." +. What is clear both from variability and microlensing studies is that the X-ray emission region is much smaller than the UV one. and it spans only a few up to tens of gravitational radii222).," What is clear both from variability and microlensing studies is that the X-ray emission region is much smaller than the UV one, and it spans only a few up to tens of gravitational radii." +" An extensive X-ray monitoring of the inner regions of the nearby Seyfert 1.8 NGC 1365 has made it possible to constrain the size of the X-ray emitting region to agam be a few r,. using a totally independent technique(?)."," An extensive X-ray monitoring of the inner regions of the nearby Seyfert 1.8 NGC 1365 has made it possible to constrain the size of the X-ray emitting region to again be a few $r_g$, using a totally independent technique." +. The UV and X-ray continuum photons are observed to be reprocessed (absorbed. re-emitted. scattered. reflected) by gas and dust in the inner regions of AGN. so that we almost never observe just the primary continuum emission of these objects1365).," The UV and X-ray continuum photons are observed to be reprocessed (absorbed, re-emitted, scattered, reflected) by gas and dust in the inner regions of AGN, so that we almost never observe just the primary continuum emission of these objects." +. Conversely. observing the reprocessing features in the UV and X-ray bands can put strong contraints on the geometry. the physical characteristics. and the dynamics of the gas hosted in the inner regions of AGN.," Conversely, observing the reprocessing features in the UV and X-ray bands can put strong contraints on the geometry, the physical characteristics, and the dynamics of the gas hosted in the inner regions of AGN." + In the past few decades. spectroscopy m the UV and X-ray band have revealed the presence of substantial column densities of ionized gas from the mner regions of AGN.," In the past few decades, spectroscopy in the UV and X-ray band have revealed the presence of substantial column densities of ionized gas from the inner regions of AGN." + In the UV band we observe blueshifted spectral absorption lines due to resonant transitions of tonized metals such as Me IL Al HI. Sr IV. C IV. N V. O VI.," In the UV band we observe blueshifted spectral absorption lines due to resonant transitions of ionized metals such as Mg II, Al III, Si IV, C IV, N V, O VI." + Depending on the width of the absorption troughs. quasars hosting such features are classified as broad absorption line quasarss.e.g.???) mini-broad absorption line quasars (mini-BAL QSOs. 500 km s!< FWHM 2000 km s) and narrow absorption line quasarss'isee93).," Depending on the width of the absorption troughs, quasars hosting such features are classified as broad absorption line quasars, mini-broad absorption line quasars (mini-BAL QSOs, $500$ km $^{-1}<$ FWHM $<2000$ km $^{-1}$ ), and narrow absorption line quasars;." + BALs features are observed in -15% of optically selected QSOs2222)., BALs features are observed in $\sim 15\%$ of optically selected QSOs. + Mini-BALs and NALs are together observed in ~12—30% of optically selected QSOs(?)., Mini-BALs and NALs are together observed in $\sim 12-30\%$ of optically selected QSOs. +. Despite the very different absorption trough widths observed. BAL. mini-BAL. and NAL QSOs share the same velocity ranges. reachingUVterminal velocities u! from a few 107 km s! upto several 107 km s!222).," Despite the very different absorption trough widths observed, BAL, mini-BAL, and NAL QSOs share the same velocity ranges, reachingUVterminal velocities $\upsilon_{out}^{UV}$ from a few $^2$ km $^{-1}$ upto several $^4$ km $^{-1}$." + Furthermore. uV is known to correlate with the continuum luminosity Loy(22)... meaning that the highest terminal velocities are observed in the objects with the highest UV continuum luminosity. suggesting an important role of the AGN UV radiation pressure in the acceleration of such winds.," Furthermore, $\upsilon_{out}^{UV}$ is known to correlate with the continuum luminosity $L_{UV}$, meaning that the highest terminal velocities are observed in the objects with the highest UV continuum luminosity, suggesting an important role of the AGN UV radiation pressure in the acceleration of such winds." + In the X-ray band absorption due to ironized species. such as N VI-VIL O VII-VIIL. Mg ΧΙ-ΧΙΗ. ΑΙ XII-XIIL. Si XUXVI. as well as L-shell transitions of Fe XVII-XXIV. are observed to be blueshifted by à few hundred to a few thousand km s! in ~50% of type | AGN???).," In the X-ray band absorption due to ionized species, such as N VI-VII, O VII-VIII, Mg XI-XII, Al XII-XIII, Si XIII-XVI, as well as L-shell transitions of Fe XVII-XXIV, are observed to be blueshifted by a few hundred to a few thousand km $^{-1}$ in $\sim 50\%$ of type 1 AGN." +. Moreover. in recent years. thanks to the high collecting area of X-ray satellites such as XMM-WNewton.. Chandra.. and Suzaku.. blueshifted absorption lines due to highly ionized gas," Moreover, in recent years, thanks to the high collecting area of X-ray satellites such as , , and , blueshifted absorption lines due to highly ionized gas" +shown that i=1 is dominant for photon energy below 30 MeV in the nuclei rest system (?)..,shown that $i=1$ is dominant for photon energy below $30$ MeV in the nuclei rest system \citep{1976ApJ...205..638P}. +" For pion production the average inelasticity is adopted as &=i(1+sii) with m4,mA the masses of pion meson and nuclei, and s the center-of-moment system energy ?.."," For pion production the average inelasticity is adopted as $\kappa= +\frac{1}{2}\left(1+\frac{m_{\pi}^2-m_A^2}{s}\right)$ with $m_{\pi},\, m_A$ the masses of pion meson and nuclei, and $s$ the center-of-moment system energy \cite{1968PhDT.........3S}." + We can see from Fig., We can see from Fig. +" 1 that for energies lower than several PeV, the pair production dominates the energy losses for proton and Helium."," \ref{cross_sec} that for energies lower than several PeV, the pair production dominates the energy losses for proton and Helium." + The photodisintegration process of Helium become important above ~4 PeV. Pion production is only important for energies higher than several tens PeV. We use MC method to simulate the interactions between CR nuclei and ambient photons., The photodisintegration process of Helium become important above $\sim 4$ PeV. Pion production is only important for energies higher than several tens PeV. We use MC method to simulate the interactions between CR nuclei and ambient photons. + The acceleration processes and interactions are decoupled for simplicity., The acceleration processes and interactions are decoupled for simplicity. + The CR. nuclei are assumed to inject into the radiation field with power-law spectra and proper relative abundance according to the measurements (??)..," The CR nuclei are assumed to inject into the radiation field with power-law spectra and proper relative abundance according to the measurements \citep{2003APh....19..193H,2008JPhCS.120f2023B}." +" Note here we adopt a correction of the measured spectra to the source spectra, taking into account the propagation effect (see below)."," Note here we adopt a correction of the measured spectra to the source spectra, taking into account the propagation effect (see below)." +" After interactions the CRs together with the e*e"" products enter the interstellar environment and propagate diffusively in the Galaxy.", After interactions the CRs together with the $^+$ $^-$ products enter the interstellar environment and propagate diffusively in the Galaxy. +" For the propagation of CR. nuclei we simply use the leaky-box model with escape time Tesc(R)ez2x105(A)"" yr (?).."," For the propagation of CR nuclei we simply use the leaky-box model with escape time $\tau_{\rm esc}(R)\approx2\times10^8\left(\frac{R}{1{\rm +GV}}\right)^{-0.6}$ yr \citep{2009A&A...497..991P}." +" The propagation of ete” is a bit complicated since the dominant effect is energy loss due to synchrotron radiation and inverse-Compton scattering, instead of diffusion (or to say escape)."," The propagation of $^+$ $^-$ is a bit complicated since the dominant effect is energy loss due to synchrotron radiation and inverse-Compton scattering, instead of diffusion (or to say escape)." + We adopt GALPROP code to calculate the propagation of electrons and positrons., We adopt GALPROP code to calculate the propagation of electrons and positrons. +our best estimate of the underlying MDF for the inner halo of M87. corrected for photometric incompleteness and color measurement bias.,"our best estimate of the underlying MDF for the inner halo of M87, corrected for photometric incompleteness and color measurement bias." + Even this corrected MDF can be relied on only for [m/H] €-0.3: any stars more metal-rich than that are almost totally cut off from our data and thus no correction factors are useful., Even this corrected MDF can be relied on only for [m/H] $\lesssim -0.3$; any stars more metal-rich than that are almost totally cut off from our data and thus no correction factors are useful. + At the opposite end. the MDF shape for [m/H] x—1.7 is very poorly determined and we can say only that there are very few stars present in that range.," At the opposite end, the MDF shape for [m/H] $\lesssim -1.7$ is very poorly determined and we can say only that there are very few stars present in that range." + At the opposite end. the MDF shape for [m/H] x—1.7 is very poorly determined and we can say only that there are very few stars present in that range.i," At the opposite end, the MDF shape for [m/H] $\lesssim -1.7$ is very poorly determined and we can say only that there are very few stars present in that range." + At the opposite end. the MDF shape for [m/H] x—1.7 is very poorly determined and we can say only that there are very few stars present in that range.i]," At the opposite end, the MDF shape for [m/H] $\lesssim -1.7$ is very poorly determined and we can say only that there are very few stars present in that range." +larger heights than in the reference mocel.,larger heights than in the reference model. + In fact. in the non rotating mocel the fountain resembles à column. and. the SNe LH located at its bottom can push the gas upward more elfectivelv.," In fact, in the non rotating model the fountain resembles a column, and the SNe II located at its bottom can push the gas upward more effectively." + In the rotating model. instead. the eas at larger 2 (ejected at. former times) lags systematically behind. the freshly expelled. gas along the circular trajectory (because of the drag bv the gaseous halo): the fountain is thus less ellicient at driving the gas to larger heights.," In the rotating model, instead, the gas at larger $z$ (ejected at former times) lags systematically behind the freshly expelled gas along the circular trajectory (because of the drag by the gaseous halo); the fountain is thus less efficient at driving the gas to larger heights." + The cilferences in the distribution of the ejecta between RAL and the non rotating model are illustrated in the lower panel of Fig. 12.., The differences in the distribution of the ejecta between RM and the non rotating model are illustrated in the lower panel of Fig. \ref{fig:vrot0}. + Contrary to the previous cases. we now do not separate ideally the disk in an inner and an outer region: instead. we consider a evlindrical volume extending vertically and. intersecting the disk with a circle with a diameter of 1 kpe and centred on the cluster located at kpe.," Contrary to the previous cases, we now do not separate ideally the disk in an inner and an outer region; instead, we consider a cylindrical volume extending vertically and intersecting the disk with a circle with a diameter of 1 kpc and centred on the cluster located at $R=8.4$ kpc." + At carly times the ejecta in the non rotating model is mostly located. inside the cvlinder. but then strageles outside while falling back.," At early times the ejecta in the non rotating model is mostly located inside the cylinder, but then straggles outside while falling back." + The ejecta in the RAL shows the same qualitative behaviour. but the mass fraction inside the cylinder remains always higher than in the non rotating case.," The ejecta in the RM shows the same qualitative behaviour, but the mass fraction inside the cylinder remains always higher than in the non rotating case." + The larger the heights reached by the ejecta. the Iarger its diffusion: the fraction left behind in RAL along a bow shaped tail (ef.," The larger the heights reached by the ejecta, the larger its diffusion: the fraction left behind in RM along a bow shaped tail (cf." + Fig. 3)), Fig. \ref{fig:colden}) ) + is negligible and does not play a substantial role in this analysis., is negligible and does not play a substantial role in this analysis. + We studied. in detail the development of the Galactic fountains in order to understand their dvnamical evolution. their role in building intermediate. velocity clouds. and condensations up to few kpe over the disk. their interaction with the hot halo and their inlluence in the redistribution of the freshly delivered metals over the disk.," We studied in detail the development of the Galactic fountains in order to understand their dynamical evolution, their role in building intermediate velocity clouds and condensations up to few kpc over the disk, their interaction with the hot halo and their influence in the redistribution of the freshly delivered metals over the disk." + In this paper we describe the evolution of a single fountain. Le. a fountain powered by SNe LL belonging to a single stellar cluster.," In this paper we describe the evolution of a single fountain, i.e. a fountain powered by SNe II belonging to a single stellar cluster." + In a companion paper we will present the results of simulations of multiple fountains fuelled by SNe IL of dilferent OB associations of various richness. occurring stochastically in space and. timo.," In a companion paper we will present the results of simulations of multiple fountains fuelled by SNe II of different OB associations of various richness, occurring stochastically in space and time." + Not all the SNe LL contribute to build galactic fountains., Not all the SNe II contribute to build galactic fountains. + Only bubbles powered by a luminosity a few times larger than the critical luminosity Li break out of the. disk pushing the ambient gas some kpc above the Galactic plane (cf. 2.2.1))., Only bubbles powered by a luminosity a few times larger than the critical luminosity $L_{\rm b}$ break out of the disk pushing the ambient gas some kpc above the Galactic plane (cf. \ref{subsubsec:singlesnexp}) ). + As shown in Fig. 9..," As shown in Fig. \ref{fig:lcr}," + this critical. luminosity decreases exponentially with the Galactocentric distance., this critical luminosity decreases exponentially with the Galactocentric distance. + In the next paper we will show how. combining this behaviour with the cumulative probability for the occurrence of Nex clustered supernovae (2)... it turns out that only ~60% of all SNe LE occurring on the disk can give rise to Galactic fountains.," In the next paper we will show how, combining this behaviour with the cumulative probability for the occurrence of $N_{\rm SN}$ clustered supernovae \citep{hili05}, it turns out that only $\sim 60$ of all SNe II occurring on the disk can give rise to Galactic fountains." + This fraction reduces almost linearly with radius: or instance. it becomes ~40% within &=4 kpc.," This fraction reduces almost linearly with radius; for instance, it becomes $\sim 40$ within $R=4$ kpc." + lt is likely that. in the case of multiple. fountains. also weaker superbubbles may reach larger. heights above the rylane finding their wav through breaks and tunnels carved »w previous. adjacent ancl more powerful superbubbles.," It is likely that, in the case of multiple fountains, also weaker superbubbles may reach larger heights above the plane finding their way through breaks and tunnels carved by previous, adjacent and more powerful superbubbles." + A discussion. on this point is postponed in the companion ?»aper., A discussion on this point is postponed in the companion paper. + In any case. a non-negligible fraction of superbubbles seems to remain contained by the thickened Galactic. clisk and do not participate to a large scale gas circulation.," In any case, a non-negligible fraction of superbubbles seems to remain contained by the thickened Galactic disk and do not participate to a large scale gas circulation." + The fate of such superbubbles has been envisaged hy ο who suggests that the superbubble stops its expansion stalling at an height z~I1 κρο, The fate of such superbubbles has been envisaged by \citet{teno96} who suggests that the superbubble stops its expansion stalling at an height $z\sim 1$ kpc. + The hot. low-clensity. metal-rich eas of its interior waits for the onset of radiative cooling.," The hot, low-density, metal-rich gas of its interior waits for the onset of radiative cooling." + Small overdense inhomosgeneities cool faster increasing their density and forming droplets which start to fall toward the disk., Small overdense inhomogeneities cool faster increasing their density and forming droplets which start to fall toward the disk. + This rain of small (—0.1 pc). metal-rich cloucets occurs over a kpe-seale volume of the galaxy.," This rain of small $\sim 0.1$ pc), metal-rich cloudets occurs over a kpc-scale volume of the galaxy." + “These cloudets will be successively photo-evaporated by the stellar radiation. eventually mixing with the ISM.," These cloudets will be successively photo-evaporated by the stellar radiation, eventually mixing with the ISM." + Although some objection mav be raised. about the details of this scheme (?).. there is no doubt that a stalled bubble must. dellate as à consequence of the depressurization of its interior due to radiative losses.," Although some objection may be raised about the details of this scheme \citep{recchi01}, there is no doubt that a stalled bubble must deflate as a consequence of the depressurization of its interior due to radiative losses." + Lt is also possible that the turbulences of the local medium cistort and. destroy the superbubble. anticipating its disappearance.," It is also possible that the turbulences of the local medium distort and destroy the superbubble, anticipating its disappearance." + In conclusion. weak bubbles do not allect much the general distribution of the ambient medium.," In conclusion, weak bubbles do not affect much the general distribution of the ambient medium." + Their size can be rather small. of the order of 100 pe (οἱ.," Their size can be rather small, of the order of 100 pc (cf." + the left panel of Fie. 2?)).," the left panel of Fig. \ref{fig:rir2}) )," + and their metal content remains strongly localized., and their metal content remains strongly localized. + On the contrary. powerful. superbubbles οἶνο rise. to Galactic fountains. anc are expected. to. drive a gas circulation on large scale (??)..," On the contrary, powerful superbubbles give rise to Galactic fountains, and are expected to drive a gas circulation on large scale \citep{shafi76, breg80}." + Simple ballistic simulations described in the Appendix (seealso2).. where the clouds are treated as bullets ejected into the halo from the Galactic midplane. actually show that the clouds fall back on the disk at clistances that can be as large as several kpe from the starting point. depending on the modulus and clireetion of he initial velocity (cf.," Simple ballistic simulations described in the Appendix \citep[see also][]{frbi06}, where the clouds are treated as bullets ejected into the halo from the Galactic midplane, actually show that the clouds fall back on the disk at distances that can be as large as several kpc from the starting point, depending on the modulus and direction of the initial velocity (cf." + the Appendix)., the Appendix). + Our hvdrodsnamical simulations. however. show that the majority of the eas ifted up by the fountains falls back on the clisk remaining within a racial clistance AR=0.5 kpe from the place where he fountain originated.," Our hydrodynamical simulations, however, show that the majority of the gas lifted up by the fountains falls back on the disk remaining within a radial distance $\Delta R=0.5$ kpc from the place where the fountain originated." + Our reference. moclel. a fountain »»vered. by LOO SNe Lh occurring at 2=8.5 kpc. may eject material up to 2 kpe which than collapses back mostly in form of dense. cold clouds and Glaments.," Our reference model, a fountain powered by 100 SNe II occurring at $R=8.5$ kpc, may eject material up to $\sim 2$ kpc which than collapses back mostly in form of dense, cold clouds and filaments." + Although he simple ballistic model indicates that these cloud should move mostly outward. (cf., Although the simple ballistic model indicates that these cloud should move mostly outward (cf. + the Appendix). our simulations show instead that they have the tendeney to drift toward the Galactic centre as they approach the disk.," the Appendix), our simulations show instead that they have the tendency to drift toward the Galactic centre as they approach the disk." + This effect is due to the interaction between the fountain and the gaseous halo above the disk., This effect is due to the interaction between the fountain and the gaseous halo above the disk. + This halo is at rest and exerts a drag force on the rotating fountain gas which looses part of its angular momentum and is pulled inward by the gravitational force., This halo is at rest and exerts a drag force on the rotating fountain gas which looses part of its angular momentum and is pulled inward by the gravitational force. + Nearly of the metals delivered by the SNe LL remains in re radial range SN«AR9 προ while the rest is dispersed on à larger range. mostly inward rather than outward (c.f.," Nearly of the metals delivered by the SNe II remains in the radial range $8 0$, which indicates that more spectral components must be acting." + From nine OM detections reported in PII (the two possible variations are excluded). our metiod can deerniüiue that three events are consisteut with a thermia variation. aud three with a nou-thermia Origin.," From nine OM detections reported in PII (the two possible variations are excluded), our method can determine that three events are consistent with a thermal variation, and three with a non-thermal origin." + The other που variations are uudetermiued. Le. lav he associaed with cit101) thermal or non-thermal processes (the cases of PEKS 0003|15. MIC3 1750|175. alc US 3172). ut with partial characteristics of thermal variatio1s.," The other three variations are undetermined, i.e., may be associated with either thermal or non-thermal processes (the cases of PKS 0003+15, MC3 1750+175, and US 3472), but with partial characteristics of thermal variations." + Iu agreenien with deDiegoetal.(1998) :ud Ramirezctal.(2009).. the resuls presente iu Secjon 7? show that nücrovariailitv. does iot depend on radio properties of quasars.," In agreement with \citet{de98} and \citet{Ram09}, the results presented in Section \ref{results} show that microvariability does not depend on radio properties of quasars." +" Moreover. our study shows that OM related to nou-thernal processes night be detectable not oulv iu racloud quasars (RLQ)((ο,ο, 3C 281/2000/ALar/ but also in RQQ{eo. Abk 830/2001/Απο] and that OM relateL to ther"" processes nnmn )e detected iu both Isinds of ¢PESjects. ΠΟ {(Ce.Yo 1628.5|3808) aud RLO (e.g.. 1510-08)."," Moreover, our study shows that OM related to non-thermal processes might be detectable not only in radio-loud quasars (RLQ) (e.g., 3C 281/2000/Mar/04) but also in RQQ (e.g., Mrk 830/2001/Aug/18), and that OM related to thermal processes might be detected in both kinds of objects, RQQ (e.g., 1628.5+3808) and RLQ (e.g., PKS 1510-08)." +" There are several explajafions to acc""OM for spectral variabilitv originating either iu tlre jet or the accretion disk.", There are several explanations to account for spectral variability originating either in the jet or the accretion disk. +" Ou the one liaud. uicrovariabilitv cal be exlaned by the Je )ecause of its physical conditions. ud lec""ALSO ine scales of OM coincide wih jet dynamics (e... Tineayetal.200]DW lita2006))."," On the one hand, microvariability can be explained by the jet because of its physical conditions, and because time scales of OM coincide with jet dynamics (e.g., \citealt{Tingay01}; \citealt{Wiita06}) )." + If all quia's can generate a reativisic jet. as suggested by the observational reports (Blundell&Rawlings2001: Blundelletal.2003 k: Gliselliuietal.2001)}. at is not surprising to fii the manifestation of non-thermal uicrovariabilitv in ROQQ.," If all quasars can generate a relativistic jet, as suggested by the observational reports \citealt{Blundell01}; \citealt{Blundell03}; \citealt{Ghisellini04}) ), it is not surprising to find the manifestation of non-thermal microvariability in RQQ." +" However. in t case of a jet. brightness temiperatures exccedà the critic‘al temperaue. T~013 R.arereqi ured references(ο,ο,. Tijgavotal.2001: Wita20060. aud therein: Fulrmiunctal.20 IN"," However, in the case of a jet, brightness temperatures exceeding the critical temperature, $T\sim 10^{12}$ K, are required (e.g., \citealt{Tingay01}; \citealt{Wiita06}, ,and references therein; \citealt{Fuhrmann08}) )." +I Although this problei iuav be overcome if irge Doppler ACTOLS ALC considered (e.g..οeοἱ Tiugav¢tal.2001: Filuiuaunetal. 2008)).," Although this problem may be overcome if large Doppler factors are considered (e.g., \citealt{Tingay01}; \citealt{Fuhrmann08}) )." + The correlation between baids represents an additional prodoni for the jet thesis. ])ecause correlated varia10119 between opticTY and higher frequencies should be observed (e.g... Nandractal.2000: Petersnetal. 2000:: Shemuneretal. 2001: Gaskell20 6)). which is no the genera rule (e.g. Edelsonetal. 20003).," The correlation between bands represents an additional problem for the jet thesis, because correlated variations between optic/UV and higher frequencies should be observed (e.g., \citealt{Nandra00}; \citealt{Peterson00}; \citealt{Shemmer01}; \citealt{Gaskell06}) ), which is not the general rule (e.g., \citealt{Edelson00}) )." + On the other haud. variatious of diverse tine scales. including OM. Ca rhe produced im accretion disks (Webb&Aalkan2000 Trevese&Vaenoetti 2001: Trevese&Vagnetti 2002:: Pereyra 2006:: see also Manealam&Wita1993: Func 2003: Wiita 2006: Caretal. 2006)).," On the other hand, variations of diverse time scales, including OM, can be produced in accretion disks \citealt{Webb00}; \citealt{Treve01}; \citealt{Treve02}; ; \citealt{Pereyra06}; see also \citealt{Mangalam93}; \citealt{Fukue03}; \citealt{Wiita06}; \citealt{Gu06}) )." + Some of these variations may be associated with disk cavnaues. or time scales associated with thermal éid sound crossing time phenomena (ήπατος and hours: e.g. ονπα 20063).," Some of these variations may be associated with disk dynamics, or time scales associated with thermal and sound crossing time phenomena (minutes and hours; e.g., \citealt{Wiita06}) )." +" Changes iu the accretio- rate can inodifv the temperature of the disk. terius the flux level aud producing short-term. variations{(ο,ο,. Weldy&Mali2000:: Perοντὰ(al.2006: : Wiita 20063)."," Changes in the accretion rate can modify the temperature of the disk, altering the flux level and producing short-term variations (e.g., \citealt{Webb00}; \citealt{Pereyra06}; \citealt{Wiita06}) )." + Perturbations ou 1C accretion (isk can also produce variations with time scales of weeks. davs. ancl even lows (e. Webb&Malkan 20001: Wiita 2006)).," Perturbations on the accretion disk can also produce variations with time scales of weeks, days, and even hours (e.g., \citealt{Webb00}; ; \citealt{Wiita06}) )." + Receutly. Chandetal.(2010) have sueeestedOO that whetd theOM is produced]* processes related to jet. then it ISexpe‘ted a smaller FWIOIAD of 1C cnussion lije dn quasars with positive detection," Recently, \citet{Chand09} have suggested that whether theOM is produced by processes related to the jet, then it isexpected a smaller FWHM of the emission lines in quasars with positive detection" +Iu the contest of cosmologicalrecoustructiou?.. a comparison with W-body simulations (?) shows that the Mouge-Aiperre-Nautorovich method is able to recover the nonlinear displaccinent field down to ~3h+ Mpe ato.=Q0. which corresponds roughly to hk~2h |.,"In the context of cosmological, a comparison with $N$ -body simulations \citep{Mohayaee2006} shows that the Monge-Ampèrre-Kantorovich method is able to recover the nonlinear displacement field down to $\sim 3 h^{-1}$ Mpc at $z=0$, which corresponds roughly to $k \sim 2 h$ $^{-1}$ ." + We can see from Table 1. that this is a very good result. as eolue to smaller scales requires taking shell crossing iuto account (in fact. at k=2h nouperturbative corrections have already started to dominate).," We can see from Table \ref{Table_range} that this is a very good result, as going to smaller scales requires taking shell crossing into account (in fact, at $k=2 h$ $^{-1}$ nonperturbative corrections have already started to dominate)." + Thus. the \ouge-Aiperre-RKautorovich uecthod appears to be close to optimal at +=0. because i goes as far as any scheme that cdisreeardsOo shell-crossingC» effects can be expected to Ooeo.," Thus, the Monge-Ampèrre-Kantorovich method appears to be close to optimal at $z=0$, because it goes as far as any scheme that disregards shell-crossing effects can be expected to go." + This can be understood partly from the fact that relatively few orders of perturbations theory are relevant at 2=0 (since νο= 9). so that it uav not help uch to explicitly include the effects of higher order terius.," This can be understood partly from the fact that relatively few orders of perturbations theory are relevant at $z=0$ (since $n_{\rm s.c.}=9$ ), so that it may not help much to explicitly include the effects of higher order terms." + Reconstruction. techniques. are also used to sharpen the acoustic peak of the real-space correlation function or to restore the harmonics of the oscillations of the power spectrin. in order to improve cosmological distance mcasurements and constraints on dark enerey (2?)..," Reconstruction techniques are also used to sharpen the acoustic peak of the real-space correlation function or to restore the harmonics of the oscillations of the power spectrum, in order to improve cosmological distance measurements and constraints on dark energy \citep{Eisenstein2007,Seo2010}." + Theon. one can read in Table 1 the wavenumber Ay. up to which one can hope to recover these baryon acoustic oscillations.," Then, one can read in Table \ref{Table_range} the wavenumber $k_{\rm s.c.}$ up to which one can hope to recover these baryon acoustic oscillations." + At 50 we can see that present sclicuies. which are based on the Luear displacement field ane nanage to reach ~0.25 + (not uecessarily for tle amplitude but at least for the shape and position of he oscillations) are not far from he upper bound. as could be expected from only a few orders of perturbation heory being relevaut (9.= 9).," At $z=0$ we can see that present schemes, which are based on the linear displacement field and manage to reach $\sim 0.2 h$ $^{-1}$ (not necessarily for the amplitude but at least for the shape and position of the oscillations) are not far from the upper bound, as could be expected from only a few orders of perturbation theory being relevant $n_{\rm s.c.}=9$ )." + At :=3 it sees tha one could eo mmch bevoud presen schemes (which do iof eo much farther than 0.255 1) In agreenen with no.=66. which means that higher orders of yerturbation theory are relevant.," At $z=3$ it seems that one could go much beyond present schemes (which do not go much farther than $0.25 h$ $^{-1}$ ), in agreement with $n_{\rm s.c.}=66$, which means that higher orders of perturbation theory are relevant." + However. for he specific o»rpose of measunus cosmological clistances from the xuvon acoustic oscillations. the poteutial is luuited by the relative amplitude of the oscillatious of the linear power spectrum itself decreasing at higher &. so that even a very eood reconstruction would not ercatlv enliance the sigual-to-noise ratio.," However, for the specific purpose of measuring cosmological distances from the baryon acoustic oscillations, the potential is limited by the relative amplitude of the oscillations of the linear power spectrum itself decreasing at higher $k$, so that even a very good reconstruction would not greatly enhance the signal-to-noise ratio." + Nevertheless. pushing to higher orders (e.9.. through resununiation schemes) remains useful for other purposes. ππο as sveak-Ieusiug studies.," Nevertheless, pushing to higher orders (e.g., through resummation schemes) remains useful for other purposes, such as weak-lensing studies." + The inerease of power ou the transition scale to nonlinearity shown in Fie., The increase of power on the transition scale to nonlinearity shown in Fig. + d. (especially iu the left panel at 2=0) is reminiscent of a similar feature observed for the gravitational dynamics (77)..," \ref{fig_lDk} + (especially in the left panel at $z=0$ ) is reminiscent of a similar feature observed for the gravitational dynamics \citep{Hamilton1991,Peacock1996}." + This is usually interpreted from a Lagrangian point of view inspired bv the spherical collapse dynamics., This is usually interpreted from a Lagrangian point of view inspired by the spherical collapse dynamics. + Thus. ? argues that. on these intermediate scales. one has £6e)X£5(4)* iu real space with 4?=2?(1|©).," Thus, \citet{Padmanabhan1996} argues that, on these intermediate scales, one has $\xib(x) \propto \xib_L(q)^3$ in real space with $q^3=x^3(1+\xib)$." +" More eenerally. in Fourier space onewrites for the nonliuear power per logarithuic iuterval of wavemunber. Αλ), the parametric svstena (7) kp = ΑΟ 174 πμ 2n with a function f to be determined."," More generally, in Fourier space onewrites for the nonlinear power per logarithmic interval of wavenumber, $\Delta^2(k)$, the parametric system \citep{Peacock1996} + k_L = ^2(k) } k, ^2(k) = f[ _L^2(k_L) ], with a function $f$ to be determined." + These relations express the conservation of matter. since the Lagrangian scale yo~ky collapses down to the Eulerian scale soLik.," These relations express the conservation of matter, since the Lagrangian scale $q\sim 1/k_L$ collapses down to the Eulerian scale $x\sim 1/k$." + The linear reginae implies that fr)226 for cc|. whereas in the highly noulinear reginae the stable-chistering ausatz (2?) eives the scaling f(r)~0? for vosLL ," The linear regime implies that $f(x) \simeq x$ for $x \ll 1$, whereas in the highly nonlinear regime the stable-clustering ansatz \citep{Peebles1982} gives the scaling $f(x) \sim x^{3/2}$ for $x \gg 1$." +At the transition one observes a sharper erowth. which ds οςstent with fle)~247 (T).," At the transition one observes a sharper growth, which is consistent with $f(x) \sim x^3$ \citep{Padmanabhan1996}." + Iu practice. oue builds a fitting formula for f(r) to match munerical siuulatious and to account for the depeucdence on the shape of the linear power spectra.," In practice, one builds a fitting formula for $f(x)$ to match numerical simulations and to account for the dependence on the shape of the linear power spectrum." + Iu any case. such models usually estimate the shape of the nonlinear two-point correlation fiction or of the nonlinear power spectrum by considering the collapse of a “typical” overdensity (77) (or merely obtainiug flr) froma sinulatious without further interpretation).," In any case, such models usually estimate the shape of the nonlinear two-point correlation function or of the nonlinear power spectrum by considering the collapse of a “typical” overdensity \citep{Padmanabhan1996,Valageas1997} (or merely obtaining $f(x)$ from simulations without further interpretation)." + It is interesting fo note that this collapse also takes place within the Zeldovich dyaiunuies studied here., It is interesting to note that this collapse also takes place within the Zeldovich dynamics studied here. + Iu particular. the function 6=F(àp) that describes the spherical collapse is no longer given bv cvcloids (7) but by the shuple expression F(dp)=αιδε91)l (77). (," In particular, the function $\delta=\cF(\delta_L)$ that describes the spherical collapse is no longer given by cycloids \citep{Peebles1980} + but by the simple expression $\cF(\delta_L)= 1/(1-\delta_L/3)^3-1$ \citep{Bernardeau1995,Valageas2009b}. . (" +"Collapse to a point is delaved from à,21.686 to à,=3. since the motion does rot accelerate as the eravitational potential well becomes deeper.)","Collapse to a point is delayed from $\delta_c \simeq 1.686$ to $\delta_c =3$, since the motion does not accelerate as the gravitational potential well becomes deeper.)" + We show in Fie., We show in Fig. +" 3 the functions A?(A)=PAGee) defined by the system (78)j}-(79)) for the Zeldovich cynics and the “sticky πιο,", \ref{fig_lfDk} the functions $\Delta^2(k) = f[ \Delta_L^2(k_L) ]$ defined by the system \ref{kL}) \ref{f-def}) ) for the Zeldovich dynamics and the “sticky model”. + Iudeed. from the knowledge of the uonlincar power ZA?(k) we obtain the Lagrangian wavemuber Ap from Eq.(78)} and next ASrp)," Indeed, from the knowledge of the nonlinear power $\Delta^2(k)$ we obtain the Lagrangian wavenumber $k_L$ from \ref{kL}) ) and next $\Delta_L^2(k_L)$." + For a eiven Eulerian wavenuuuber fk. the Lagraugiui waveuunibers Ay obtained for both models. Zeldovich dvuanues aud “sticky model”. are different.," For a given Eulerian wavenumber $k$ , the Lagrangian wavenumbers $k_L$ obtained for both models, Zeldovich dynamics and “sticky model”, are different." + Then.Fig.," Then,Fig." + 3. shows that.within the Zeldovich dyuunics. this erowth of the noulinear density coutrast through the spherical collapse is not sufficient to build up the increase," \ref{fig_lfDk} shows that,within the Zeldovich dynamics, this growth of the nonlinear density contrast through the spherical collapse is not sufficient to build up the increase" +As a rotating molecular cloud core collapses to form a star it must shed vast amounts of angular momentum to explain the observed differences between the specific. angular momentum of molecular cloud cores and stars on the main-sequence (Dodenheimer1995).,As a rotating molecular cloud core collapses to form a star it must shed vast amounts of angular momentum to explain the observed differences between the specific angular momentum of molecular cloud cores and stars on the main-sequence \citep{bod95}. +". Various plwsical processes. which serve as solutions to (his ""angular momentum problem” are thought to occur as an object transitions from a cloud core to à Zero-Age Main Sequence (ZAMS) star."," Various physical processes, which serve as solutions to this “angular momentum problem” are thought to occur as an object transitions from a cloud core to a Zero-Age Main Sequence (ZAMS) star." + For low-mass stars in the pre-main sequence stage (T Tauri stus) the regulation ol stellar rotational angular momentum is thought to be [acilitated bv the formation of and subsequent interaction wilh a circumstellar disk., For low-mass stars in the pre-main sequence stage (T Tauri stars) the regulation of stellar rotational angular momentum is thought to be facilitated by the formation of and subsequent interaction with a circumstellar disk. + Cireumstellar disks are thought to be common by-products of the star formation process (Beckwith&Sargent.1996)., Circumstellar disks are thought to be common by-products of the star formation process \citep{BS96}. +. Thev are easily identified by peculiar features like infrared and ultraviolet excesses. and in some rare circumstances ean also be detected through direct imaging (ODell.1993:MeCaughreanO'Dell 1996).," They are easily identified by peculiar features like infrared and ultraviolet excesses, and in some rare circumstances can also be detected through direct imaging \citep{Odell93,MO96}." +. Nenvon&Hartmann(1995) estimate >50% of stars in the star forming region have circumstellar disks. while Hillenbrandetal.(1998) estimate that >80% of stars in the Trapezium cluster possess circumstellar accretion disks &Lada 2001).," \citet{KH95} estimate $> 50\% $ of stars in the star forming region have circumstellar disks, while \citet{hillenbrand98} estimate that $> 80\%$ of stars in the Trapezium cluster possess circumstellar accretion disks \citep[see also][]{haisch01}." +. The IR excesses [rom these disks are (he result of heating cireumstellar eas and dust by radiation from the central star and (through. viscous aceretion., The IR excesses from these disks are the result of heating circumstellar gas and dust by radiation from the central star and through viscous accretion. + The disk temperature distribution is often modeled as a power-law., The disk temperature distribution is often modeled as a power-law. + Hf the disk is optically thick it will radiate as à blackbody with the shortest wavelengths dominated by higher temperature material in the inner disk and the longer wavelengths dominated by cooler material in the outer regions (Beckwith1999)., If the disk is optically thick it will radiate as a blackbody with the shortest wavelengths dominated by higher temperature material in the inner disk and the longer wavelengths dominated by cooler material in the outer regions \citep{beckwith99}. +. Thus. enission at different wavelengths can be used to probe different regions in the disk.," Thus, emission at different wavelengths can be used to probe different regions in the disk." +" The pioneering study by Edwardsetal.(1993) [or a set of stars from the Taurus. Auriga. Chameleon, Orion ancl Lupus star.forming regions. compared stellar rotation periods with the (44—I) color index."," The pioneering study by \citet{edwards93} for a set of stars from the Taurus, Auriga, Chameleon, Orion and Lupus star–forming regions, compared stellar rotation periods with the $(H-K)$ color index." + This color index probes a region in the disk (hat lies within a few stellar radii (~104.)., This color index probes a region in the disk that lies within a few stellar radii $(\sim 10R_{\sun})$. + They found stars whose (Jf—fv) colors indicated (he presence of an accretion disk were rotating more slowly than stars whose (//—AN) colors indicated the absence of an accretion disk., They found stars whose $(H-K)$ colors indicated the presence of an accretion disk were rotating more slowly than stars whose $(H-K)$ colors indicated the absence of an accretion disk. +" A similar study by Bouvieretal.(1993). suggested a bimodal distribution of slowly rotating classical T Tauri stars (οΤο, showing evidence of active accretion [rom a circumstellar disk) and [ast rotating weak T Tauri stars (WwTTS. //a emission-line stars with no signs of accretion)."," A similar study by \citet{bouvier93} suggested a bimodal distribution of slowly rotating classical T Tauri stars (cTTS, showing evidence of active accretion from a circumstellar disk) and fast rotating weak T Tauri stars (wTTS, weak-lined $H\alpha$ emission-line stars with no signs of accretion)." + Studies of the (ONC) have vielded mixed results., Studies of the (ONC) have yielded mixed results. + Choi&Herbst(1996) report a bimodal distribution in photometric periods of T Tauri stars in Orion as evidence for the disk-locking phenomena (seealsoHerbstοἱal.2002)., \citet{CH96} report a bimodal distribution in photometric periods of T Tauri stars in Orion as evidence for the disk-locking phenomena \citep[see also][]{herbst02}. +. Theoretical models have always relied heavily on some form ol direct or indirect angular momentum (ansfer between stars and their disks to explain the redistribution of rotational angular momentum during the transition [rom the Pre-Main Sequence (PAIS) stage to the ZAMS stage., Theoretical models have always relied heavily on some form of direct or indirect angular momentum transfer between stars and their disks to explain the redistribution of rotational angular momentum during the transition from the Pre-Main Sequence (PMS) stage to the ZAMS stage. + ILowever. an extensive study conducted by," However, an extensive study conducted by" +Since the discoveiv of the first exoplauet by Alavor Queoz (1995). planet luuters have been discovering planets with πιο: auc siualler asses.,"Since the discovery of the first exoplanet by Mayor Queloz (1995), planet hunters have been discovering planets with smaller and smaller masses." +" With the discovery of objects in the rauge of 10-20 AD). ie. 0,03- AZ, (Butler« tal."," With the discovery of objects in the range of 10-20 $\mearth$, i.e. 0.03-0.06 $\mjup$ (Butler et al." + 2001: McArthur et al., 2004; McArthur et al. + 2001: Sautos et al., 2004; Santos et al. + 200D). à new step in the quest for Earth-like planets las been taken.," 2004), a new step in the quest for Earth-like planets has been taken." + While represcuting an extraordinary achievement from. the oervatioual side. theorists still strugele to uuderstaad the structure and the origin of hese ight eiaut plaucts.," While representing an extraordinary achievement from the observational side, theorists still struggle to understand the structure and the origin of these light giant planets." + Are they essentially composed of Ices aid rocks. with vossibly a thin atmosphere. like our ice giants Urauus aud Neptune?," Are they essentially composed of ices and rocks, with possibly a thin atmosphere, like our ice giants Uranus and Neptune?" + Or do they originate from arecr eascous planets; with a large gaseous euvelope aud arelatively siuall cOLral rocky core?," Or do they originate from larger gaseous planets, with a large gaseous envelope and a relatively small central rocky core?" + The answer to these questions requires an understaudius of their formation X€FOCOsS., The answer to these questions requires an understanding of their formation process. +" C1irent planet foriuation scenarios. based either on he core accretion model or ou gravitational mstabilitv. can iore or less explain the presence of relatively massive olanets with masses zLOOMI, (or even larecr in the case of the eravitalonal instability scenario) at various orbital separations nut they do not necessarily predict the ornuation of a large nuniber of hehter planets (Boss 2001: Ida Liu 2005: Paxioizou Nelson 2005)."," Current planet formation scenarios, based either on the core accretion model or on gravitational instability, can more or less explain the presence of relatively massive planets with masses $\simgr \, 100 \, \mearth$ (or even larger in the case of the gravitational instability scenario) at various orbital separations but they do not necessarily predict the formation of a large number of lighter planets (Boss 2001; Ida Lin 2005; Papaloizou Nelson 2005)." + Iu the framework of the core accretion model (Pollack et al., In the framework of the core accretion model (Pollack et al. + 1996). the general expectation was to fud xefereutially planes either less massive or niore ninssive han the newly discovered Neptune-like planets. for tLOSC atter lie within the domain of critical mass (~10 20M.) above which runaway acerction of gas begins.," 1996), the general expectation was to find preferentially planets either less massive or more massive than the newly discovered Neptune-like planets, for these latter lie within the domain of critical mass $\sim 10-20 \mearth$ ) above which runaway accretion of gas begins." + Similarly. Ida Lin (2001) sugecs a possible deficit of intermediate uass planets (~10.1OAL. no. ον0.03. ΟΕ) with orbital separation aκ3 AU.," Similarly, Ida Lin (2004) suggest a possible deficit of intermediate mass planets $\sim 10-100 \mearth$, i.e. $\sim 0.03-0.3 \mjup$ ) with orbital separation $a<3$ AU." + Ou the opposite. using N-ο snaulatious of coliding cores in a protoplanctary disk. Druni Ciouco (2005) fud that Noptuuc-like anets close to them host-star can form easily as a by-xoduct of planetary fornation.," On the opposite, using N-body simulations of colliding cores in a protoplanetary disk, Brunini Cionco (2005) find that Neptune-like planets close to their host-star can form easily as a by-product of planetary formation." + If their scenario is correct. hese planets should be of icearock composition with only a thin atmosphere.," If their scenario is correct, these planets should be of ice-rock composition with only a thin atmosphere." + They also predict that a large population of these “hot cores” should be discovered in a near future.," They also predict that a large population of these ""hot cores"" should be discovered in a near future." + As an alternative to this coliding core scenario. aud elven he close orbital distance ο‘the Nepture-like plaucts discovered up to now. one caunot exclude he possibility that trev formed initially as larger giaut planets wich have undergone atinosplierie evaporaion durius their lifetime (Baraffe ct al.," As an alternative to this colliding core scenario, and given the close orbital distance of the Neptune-like planets discovered up to now, one cannot exclude the possibility that they formed initially as larger giant planets wich have undergone atmospheric evaporation during their lifetime (Baraffe et al." + 2005)., 2005). + Wilin this picture. formation aud evolution are strongly correlated: a correct undoerstaudiug of light planet properties thus requies a —c«sistent description of t16 planet orlmation aud evolution in order to interpret prescut-day observations.," Within this picture, formation and evolution are strongly correlated: a correct understanding of light planet properties thus requires a consistent description of the planet formation and evolution in order to interpret present-day observations." + This paper is a first atclup to derive such a consisteut pictire from the planet formation to its subsequeut ονοιion., This paper is a first attempt to derive such a consistent picture from the planet formation to its subsequent evolution. + We apply the core accretion models (cf., We apply the core accretion models (cf. + 82) developed recently by Alibert et al. (, 2) developed recently by Alibert et al. ( +2005a) to the LL Mj (0.014 375) planet (100dulo sin /) orbiting around the G- p Ara at an orbital distance e=0.09 AU (Santos et al.,2005a) to the 14 $\mearth$ (0.044 $\mjup$ ) planet (modulo sin $i$ ) orbiting around the G-star $\mu$ Ara at an orbital distance $a=0.09$ AU (Santos et al. + 20VL)., 2004). + We focus on jj Ara-like planets because it is still lO0$sSO0rable to apply the Alibert et al. (, We focus on $\mu$ Ara-like planets because it is still reasonable to apply the Alibert et al. ( +2005a) formation iode at this orbital distance. whereas it is no lonecr the case at the location of the two other Neptune-like plaucts which are located at ο<0.05 AU from their parent star (Butler et al.,"2005a) formation model at this orbital distance, whereas it is no longer the case at the location of the two other Neptune-like planets which are located at $a \, < \, 0.05$ AU from their parent star (Butler et al." + 2001: McArthur et al., 2004; McArthur et al. + 2001)., 2004). + Indeed. for a0.4 AU. the description of the inner art of the disk. incluine tidal and maenetic interactions with the star. is too crude to provide a reliable formation scenario.," Indeed, for $a \simle 0.1$ AU, the description of the inner part of the disk, including tidal and magnetic interactions with the star, is too crude to provide a reliable formation scenario." + Adopting the main characteristics of the newly born planets as predicted by the Alibert. et al... (, Adopting the main characteristics of the newly born planets as predicted by the Alibert et al. ( +2005a) formation model (core nass. heavy clement couteut). we follow the later evolution of these planets. according to Daraffe et al. (,"2005a) formation model (core mass, heavy element content), we follow the later evolution of these planets, according to Baraffe et al. (" +20YL. 2005). takiug iuto account irracliation and evaporation effects due to the vicinity of the parcut star.,"2004, 2005), taking into account irradiation and evaporation effects due to the vicinity of the parent star." + We exinudne the sensitivity of the results ou the evaporation rate by exploring a range of different rates aud present our results in &1., We examine the sensitivity of the results on the evaporation rate by exploring a range of different rates and present our results in 4. + Predictions aud uncertainties of our scenario are discussed in &5., Predictions and uncertainties of our scenario are discussed in 5. + The adopted formation model is an extension of the core accretion model for giaut gaseous plauets developed by, The adopted formation model is an extension of the core accretion model for giant gaseous planets developed by +therefore relatively hieh uitrogen abunudances).,therefore relatively high nitrogen abundances). + Daud-streugth variations were first observed in spectra of red eqjauts in globular clusters (e.g... Norris Freeman 1979.. Suutzeff 19813). but are also found iu subgiauts aud on the main sequence (ee. Briley et al. 2001))," Band-strength variations were first observed in spectra of red giants in globular clusters (e.g., Norris Freeman , Suntzeff ), but are also found in subgiants and on the main sequence (e.g., Briley et al. )," +. iudicatiug that they are a result of primordial eurichiueut rather than an evolutionary effect., indicating that they are a result of primordial enrichment rather than an evolutionary effect. +" Variations in the broad CN aud CII features are just the inost readily observed. part of a larger light-clemeut abundance pattern. a division of globular cluster stars into one eroup with typical Population II abuudances and another that is relatively cuhanced im nitrogen. ποσοπα, aud aluminum. and depleted iu carbon. oxvecn. and maenesimm."," Variations in the broad CN and CH features are just the most readily observed part of a larger light-element abundance pattern, a division of globular cluster stars into one group with typical Population II abundances and another that is relatively enhanced in nitrogen, sodium, and aluminum, and depleted in carbon, oxygen, and magnesium." + These abuudance divisious are usally studied iu the auticorrelated pairs of carbon and uitrogen or oxveen and sodiu (see. ee. Kraft1991: Gratton et al.2," These abundance divisions are usually studied in the anticorrelated pairs of carbon and nitrogen or oxygen and sodium (see, e.g., Kraft; Gratton et al.;" +001: Curetta et al. 20093)., Carretta et al. ). + The imagnuesiuni-alumi auticorrelation is more murky: although some researchers find Mg-Àl auticorrelations in individual elobular clusters (e.g.. Shetroue 1996: Gratton et al. 20013).," The magnesium-aluminum anticorrelation is more murky: although some researchers find Mg-Al anticorrelations in individual globular clusters (e.g., Shetrone ; Gratton et al. )," +" the abundance distributions are not as clearly bimodal as in the case of nitrogen. aud the origin of Me- ALrich stars is more difficult to fit into the eeucral fraanework of euricluneut. by iuoderate-anass ACB stars (οιο,, D'Ercole et al. 2008))."," the abundance distributions are not as clearly bimodal as in the case of nitrogen, and the origin of Mg-poor, Al-rich stars is more difficult to fit into the general framework of enrichment by moderate-mass AGB stars (e.g., D'Ercole et al. )." + This paper prescuts a study of the behavior of CN and CIT band strengths and |C/Fe| abundances iwoe red eant stars in the low-metallicity globular cluste NGC 5166. which has ~2.2 (aris 1996. 200: revision)).," This paper presents a study of the behavior of CN and CH band strengths and [C/Fe] abundances in red giant stars in the low-metallicity globular cluster NGC 5466, which has [Fe/H] $\simeq 2.2$ (Harris 1996, 2003 )." + Studies based on |Fe/II|CN aud CTD baud strenet[um are more difficult im low-metallicity clusters. where tlie CN variation visible in the spectra can be quite sinall despite variations iu abundance as large as iu lieherauetallicitv. globular [N/Fe|chlusters (0.9... M53. Martell et al.2," Studies based on CN and CH band strength are more difficult in low-metallicity clusters, where the CN variation visible in the spectra can be quite small despite variations in [N/Fe] abundance as large as in higher-metallicity globular clusters (e.g., M53, Martell et al.;" +008a:: M55. Briley ot al. 1993)).," M55, Briley et al. )." + The elobulaY clusters with moetallicities similar to NGC 5166 1n whic1 heht-clement abundance iuhomogeneities have been most extensively studied are M92 and MID., The globular clusters with metallicities similar to NGC 5466 in which light-element abundance inhomogeneities have been most extensively studied are M92 and M15. + The red eiauts iu both objects exhibit a progressive decline iu. |C/Fe| with advancing evolution above the magnitude level of the horizontal branch GIB: Carbon ct al.1, The red giants in both objects exhibit a progressive decline in [C/Fe] with advancing evolution above the magnitude level of the horizontal branch (HB; Carbon et al.; +982: Trefzecr et al.1, Trefzger et al.; +983: Langer et al.1, Langer et al.; +986: Delhinan ct al. 200133., Bellman et al. ). + Cüants iu both clusters typically exhibit weak. ABSS83 CN bands (Carbon et ab19, Giants in both clusters typically exhibit weak $\lambda$ 3883 CN bands (Carbon et al.; +82: Tretzecr ot al. 10501).," Trefzger et al. )," + aud do not exhibit bimodal CN distributions like those in more metalrich chisters although a handful of stars with cuhanced CN have been discovered im MIS (Langer. Suutzeff. Iraft1992: Lee 2000)).," and do not exhibit bimodal CN distributions like those in more metal-rich clusters although a handful of stars with enhanced CN have been discovered in M15 (Langer, Suntzeff, Kraft; Lee )." + Despite their lack of CN-strong giants. both M92 and MIS exhibit auticorrelated O-N. O-Na or O-AL variations. or correlated N-Na. of the type that are commouplace iu elobular clusters (Norris PilachowskiL985:: Sueden et al.1991.. τ," Despite their lack of CN-strong giants, both M92 and M15 exhibit anticorrelated O-N, O-Na or O-Al variations, or correlated N-Na, of the type that are commonplace in globular clusters (Norris Pilachowski; Sneden et al., ;" +ους Shetrone 1996))., Shetrone ). + Tn additiou. Cohen. Briley Stetson discovered that star-to-star differences iu aud abuudances exist among stars near the base [C/Fo]of the red Τοgiant brauch (ROB) in MI5. and the C aud N abundances tend to be auticorrelated.," In addition, Cohen, Briley Stetson discovered that star-to-star differences in [C/Fe] and [N/Fe] abundances exist among stars near the base of the red giant branch (RGB) in M15, and the C and N abundances tend to be anticorrelated." + These efforts have shown that for very icetal-poor stars the use of CN to cletermine which stars carry the anticorrelated light-clement abundance patter can be problematic. aud that anticorrelated. variations im light-clement abundances do exist in low-1etallicity elobular clusters despite their lack of obvious CN band streneth variation.," These efforts have shown that for very metal-poor stars the use of CN to determine which stars carry the anticorrelated light-element abundance pattern can be problematic, and that anticorrelated variations in light-element abundances do exist in low-metallicity globular clusters despite their lack of obvious CN band strength variation." + If NGC 5166 does contain the same primorcial variatious in light-clement abundances as are found in hieherauctallicity. elobular clusters. the resulting rauge in CN and CID band streusth will be mated by the low overall metallicitv of the cluster. perhaps to a degree where it is difficult to distinguish a bimodal but closely spaced CN band strength distribution from a broad but nuitmodal distribution.," If NGC 5466 does contain the same primordial variations in light-element abundances as are found in higher-metallicity globular clusters, the resulting range in CN and CH band strength will be muted by the low overall metallicity of the cluster, perhaps to a degree where it is difficult to distinguish a bimodal but closely spaced CN band strength distribution from a broad but unimodal distribution." + If NOC 5166 does not contain primordial abundance variations. that would imply that primordial eurichiuneut is not a universal process iu metallicity elobular clusters the way it is in highermetallicity clusters.," If NGC 5466 does not contain primordial abundance variations, that would imply that primordial enrichment is not a universal process in low-metallicity globular clusters the way it is in higher-metallicity clusters." +" A inetallicitv limit on primordial heht-clemeut curichinent offers some insight iuto the primordial curichiment process. aud iuto the larger aud stil-developing picture of chemical complexity within individual globular clusters ίσιο, Piotto 2008))."," A metallicity limit on primordial light-element enrichment offers some insight into the primordial enrichment process, and into the larger and still-developing picture of chemical complexity within individual globular clusters (e.g., Piotto )." + We determined photometry for πιοσος of NGC 5166 based on CCD frames obtained by IIED with the Ixitt Peak National Observatory 0.9 1 telescope on L997 May 9., We determined photometry for members of NGC 5466 based on CCD frames obtained by HEB with the Kitt Peak National Observatory 0.9 m telescope on 1997 May 9. +" The T2kKÀ chip at the Ritchey-Clocticn focus provides a 23, field. which encloses most ofthe cluster. which has a tidal radius of 31/. according to Harris(1996)."," The T2KA chip at the Ritchey-Chretien focus provides a $23'\times23'$ field, which encloses most ofthe cluster, which has a tidal radius of $34'$, according to Harris." +. We used 45V filters. as defined by Doud(2005).. with exposure times of 600. 15. [5. and 60 s. respectively. uder photometric conditions.," We used $uBVI$ filters, as defined by Bond, with exposure times of 600, 45, 45, and 60 s, respectively, under photometric conditions." + Wo calibrated the photometry to the network of uDBVI standard stars established by Siegel Bond(20053., We calibrated the photometry to the network of $uBVI$ standard stars established by Siegel Bond. +. Data were reduced using the IRAF CCDPROC pipeline aud plotometry was ineasurved with DAOPIIOT/ALLSTAR (Stetsou 19sT. tikzimarkinainBodyCitationStartsso)).," Data were reduced using the IRAF CCDPROC pipeline and photometry was measured with DAOPHOT/ALLSTAR (Stetson 1987, )." + DAOGROW (Stetson 1990)) was used to perform curve-oferowth fitting for aperture correction on both program aud standard stars., DAOGROW (Stetson ) was used to perform curve-of-growth fitting for aperture correction on both program and standard stars. + The raw plotometry was calibrated using the iterative matrix inversion technique described in Siegel ct al., The raw photometry was calibrated using the iterative matrix inversion technique described in Siegel et al. + to translate the photometry to the standard system of Laucdolt and Siegel DBoud(2005)., to translate the photometry to the standard system of Landolt and Siegel Bond. +. Table 1. lists identification nunbers. positions. and photometry for the stars observed with VIRUS-P. The star identification numbers aud coordinates are from an unpublished photometric catalog developed by ALILS. from the analysis described above.," Table \ref{t1} lists identification numbers, positions, and photometry for the stars observed with VIRUS-P. The star identification numbers and coordinates are from an unpublished photometric catalog developed by M.H.S. from the analysis described above." + The typical errors on the D. V. and I photometry are 0.030. 0.022 and 0.032 mag. respectively.," The typical errors on the B, V, and I photometry are 0.030, 0.022 and 0.032 mag, respectively." + On 2009 March 235 aud July 2829. we observed four fields i NGC 5166 for a total of 22 hr with the visible inteeral-field replicable unit spectrograph prototype (VIRUS-P. Tall et al. 2008)," On 2009 March 3–5 and July 28–29, we observed four fields in NGC 5466 for a total of 22 hr with the visible integral-field replicable unit spectrograph prototype (VIRUS-P, Hill et al. )" +) on the 2.71 Varlan J. Sith Telescope at McDonald Observatory., on the 2.7m Harlan J. Smith Telescope at McDonald Observatory. + VIRUS-P is a spectrograph with an inteeral field) unit (IFU) of 216 fibers in a hexagonal. one third fill factor. close pack pattern.," VIRUS-P is a spectrograph with an integral field unit (IFU) of 246 fibers in a hexagonal, one third fill factor, close pack pattern." +" The fibers have a projected diameter of L1"" aud have centers astrometyrically calibrated to L7"" velative to a fixed. offset euidiug camera via open cluster observations."," The fibers have a projected diameter of $4.1\arcsec$ and have centers astrometrically calibrated to $0.7\arcsec$ relative to a fixed, offset guiding camera via open cluster observations." + The field of view for the IPU is 2.89 square arcnun and with a set of three 7.117 dithers the filling factor is10054.," The field of view for the IFU is 2.89 square arcmin and with a set of three 7.14"" dithers the filling factor is." +.. The VPI erating was used. giving an instrmuental FWD between 5 aud GA over the waveleugth range of 35005800À.," The VP1 grating was used, giving an instrumental FWHM between 5 and $6\hbox{\AA}$ over the wavelength range of $3500-5800\hbox{\AA}$." + Arc lamp calibration xoduced a wavelength solution with au ris accuracy of H05À., Arc lamp calibration produced a wavelength solution with an rms accuracy of $0.05\hbox{\AA}$ . + Our procedure duriug observing was to dither the clescope and take three 1200 s exposures per field to fill, Our procedure during observing was to dither the telescope and take three 1200 s exposures per field to fill +lower and (he radial widths are wider.,lower and the radial widths are wider. + Furthermore. more particles stav outside the peaks and are scattered in the stable region.," Furthermore, more particles stay outside the peaks and are scattered in the stable region."