ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 1969: Marochnik et al., 1969; Marochnik et al.3 1972: Mishurov Zenina 1999: Léppine et al., 1972; Mishurov Zenina 1999; Léppine et al.4 2001: Fernandez et al., 2001; Fernandez et al.5 2001: Dias Léppine 2005. etc.).," 2001; Dias Léppine 2005, etc.)."6 In the present paper. we propose a new approach to evaluation of the corotation radius in our Galaxy.," In the present paper, we propose a new approach to evaluation of the corotation radius in our Galaxy."7 The method is based on the statistical analysis of oxygen radial distribution in the galactic dise (notice that Martin Roy 1995 and Scarano et al., The method is based on the statistical analysis of oxygen radial distribution in the galactic disc (notice that Martin Roy 1995 and Scarano et al.8 2010 also mentioned the importance of the corotation effects in analysis of abundance gradient in external galaxies)., 2010 also mentioned the importance of the corotation effects in analysis of abundance gradient in external galaxies).9 Oxygen was used since it is mainly produced by SNe II which are strongly concentrated in spiral arms., Oxygen was used since it is mainly produced by SNe II which are strongly concentrated in spiral arms.10 Hence it is the most pure indicator of spiral arms influence on the formation of radial abundance pattern in the galactic disc., Hence it is the most pure indicator of spiral arms influence on the formation of radial abundance pattern in the galactic disc.11 As an observed material. we use the on oxygen derived by Andrievsky et al. (," As an observed material, we use the data on oxygen distribution derived by Andrievsky et al. ("122002ah aa.b.c) and Luck et al. distribution.(,"2002 a,b,c) and Luck et al. ("132003.ith 2006) over Cepheids.,"2003, 2006) over Cepheids."14 Being and very young objects w precise distances. these stars give reliable information about abundances of heavy elements. close to the one in interstellar medium. in the significant part of the galactic disc.," Being bright and very young objects with precise distances, these stars give reliable information about abundances of heavy elements, close to the one in interstellar medium, in the significant part of the galactic disc."15 The main finding of the above papers is that the radial distribution of metallicity in the galactic dise isbimodal. i.e. there is a rather steep gradient in the inner part of the dise at 5xr3 kpe and a plateau-like distribution for rz7 kpe and up to about 10 kpe (the solar galactocentrie distance ry=7.9 kpc).," The main finding of the above papers is that the radial distribution of metallicity in the galactic disc is, i.e. there is a rather steep gradient in the inner part of the disc at $5 \le r \le 7$ kpc and a plateau-like distribution for $r > 7$ kpc and up to about 10 kpc (the solar galactocentric distance $r_0 =7.9$ kpc)."16 Hence. there is a bending in the slope of the distribution at r7 Κρο.," Hence, there is a bending in the slope of the distribution at $r \sim7$ kpc."17 The above fine structure in the radial abundance distribution is very important., The above fine structure in the radial abundance distribution is very important.18 It indicates that in the galactic dise the distribution formation is caused by some non-trivial process., It indicates that in the galactic disc the distribution formation is caused by some non-trivial process.19 Mishurov et al. (, Mishurov et al. (202002). Acharova et αἱ. (,"2002), Acharova et al. ("212005:vail 2010) developed a theory of spiral arms influence on the distribution of oxygen in the galactic disc.,2005; 2010) developed a theory of spiral arms influence on the radial distribution of oxygen in the galactic disc.22 They show that the bending in the slope of oxygen distribution is associated with the corotation resonance., They show that the bending in the slope of oxygen distribution is associated with the corotation resonance.23 However. in our previous papers we fitted the theory to the observations “by eyes”.," However, in our previous papers we fitted the theory to the observations “by eyes”."24" Now we propose a statistical method for the deriving of the corotation resonance location by means of analysis of oxygen ""istribution along the galactic radius.", Now we propose a statistical method for the deriving of the corotation resonance location by means of analysis of oxygen distribution along the galactic radius.25" Simultaneously the so-called “constant for the rate of oxygen synthesis"" is estimated.", Simultaneously the so-called “constant for the rate of oxygen synthesis” is estimated.26 Let XHy’) be an observed distribution of any .X element along the galactic radius r (as usual X74]=logCNx/INg).(ούNx //Ng).. where Nxag is the number of .X element or hydrogen atoms in the object. the first item refers to a star located at the distance +. the second one - to the Sun).," Let $[X/H]^{ob}(r)$ be an observed distribution of any $X$ element along the galactic radius $r$ (as usual $[X/H] = log(N_X/N_H)_s - log(N_X/N_H)_{\odot}$ , where $N_{X,H}$ is the number of $X$ element or hydrogen atoms in the object, the first item refers to a star located at the distance $r$, the second one - to the Sun)."27 On the other hand. let us assume that XLO) is a theoretical distribution of the corresponding element which depends on some vector À. the coordinates of the vector being the sought-for free parameters of our theory.," On the other hand, let us assume that $[X/H]^{th}(r)$ is a theoretical distribution of the corresponding element which depends on some vector $\hat{\lambda}$, the coordinates of the vector being the sought-for free parameters of our theory."28 To fit the observations we minimize the variance o over A:, To fit the observations we minimize the variance $\sigma^2$ over $\hat{\lambda}$ :29"where is a coefficient, and Emin and Emax are the energy band boundaries.","where $C$ is a coefficient, and $E_{\rm min}$ and $E_{\rm max}$ are the energy band boundaries."30 The fluenceC sensitivity for a one year exposure is within the background-limited regime—namely within one year many background photons are expected to be detected within the point-spread-function of the detector., The fluence sensitivity for a one year exposure is within the background-limited regime—namely within one year many background photons are expected to be detected within the point-spread-function of the detector.31" In the case of GLAST-LAT, backgrounds are the EGB or Galactic foreground emissions."," In the case of -LAT, backgrounds are the EGB or Galactic foreground emissions."32" Therefore, we start our discussion from this background-limited case."," Therefore, we start our discussion from this background-limited case."33" Let us define this background rate ofGLAST by Nos.for which we assume E?! spectrum and use the energy-dependent angular resolution and on-source effective area Aeg().7 The criterion of point-source detection is where o represents significance of detection, and photon count from the source is obtained by Therefore, using equation (B1)) in equations (B4)) and (B3)), we can obtain the sensitivity to the coefficient Cj as follows: and then using equation (B2)), this can be translated into the sensitivity to the number and energy fluences, Fyjim and Fig."," Let us define this background rate of by $\dot N_{\rm bg}$,for which we assume $E^{-2.1}$ spectrum and use the energy-dependent angular resolution and on-source effective area $A_{\rm eff}(E)$ The criterion of point-source detection is where $\sigma$ represents significance of detection, and photon count from the source is obtained by Therefore, using equation \ref{eq:dNdE}) ) in equations \ref{eq:photon34count}) ) and \ref{eq:detection criterion}) ), we can obtain the sensitivity to the coefficient $C_{\rm lim}$ as follows: and then using equation \ref{eq:N}) ), this can be translated into the sensitivity to the number and energy fluences, $F_{N,{\rm lim}}$ and $F_{\rm lim}$."35" We here note that Cj, depends on {, a, Emin, and Emax, while N,jim depends only on f, Emin, and Emax."," We here note that $C_{\rm lim}$ depends on $t$, $\alpha$, $E_{\rm min}$ , and $E_{\rm36max}$, while $N_{\gamma,{\rm lim}}$ depends only on $t$, $E_{\rm37min}$, and $E_{\rm max}$."38" In this regime, the time dependence is Fimος1? from equation (B3))."," In this background-limited regime, the time dependence is $F_{\rm lim} \propto t^{1/2}$ from equation \ref{eq:detection criterion}) )."39" We confirmed that, using the EGBintensity measured EGRET and resolution of LAT, we could obtain the limit comparable to Fybyjim=2.4X10? cm”, in the case of a=2, t=70 d, energy-dependentEmin=100 angularMeV, Emax=oo, and o=5."," We confirmed that, using the EGBintensity measured by EGRET and energy-dependent angular resolution of LAT, we could obtain the limit comparable to $F_{N,{\rm lim}} = 2.4 \times 10^{-2}$ $^{-2}$ , in the case of $\alpha = 2$, $t = 70$ d, $E_{\rm min} =40100$ MeV, $E_{\rm max} = \infty$, and $\sigma = 5$."41 The results of this procedure for several values of interest of α are summarized in equation (13)) and Table 1.., The results of this procedure for several values of interest of $\alpha$ are summarized in equation \ref{eq:GLAST limit}) ) and Table \ref{table:GLAST}.42" Here, we used EGRET energy range, i.e., Emin=30 MeV and Emax=30 GeV, but we can instead adopt different values."," Here, we used EGRET energy range, i.e., $E_{\rm min} = 30$ MeV and $E_{\rm max} = 30$ GeV, but we can instead adopt different values."43" If the time scale is short such that Nyjim«1, then the above does not but the is obtained by the expected photon count from the source."," If the time scale is short such that $N_{\gamma,{\rm lim}} < 1$, then the argument above does not apply, but the sensitivity is simply obtained by the expected photon count from the source."44" In this photon-count-limitedargument regime, we apply,can evaluate the sensitivityfluence simplysensitivity by requiring to be a few; here we use N.,2 5."," In this photon-count-limited regime, we can evaluate the fluence sensitivity by requiring $N_\gamma$ to be a few; here we use $N_\gamma = 5$ ."45 One can obtain the corresponding Cjim by solving this criterion using equation (B4))., One can obtain the corresponding $C_{\rm lim}$ by solving this criterion using equation \ref{eq:photon count}) ).46" Thistime, N.,Cii, is independent of t."," Thistime, $C_{\rm lim}$ is independent of $t$ ."47" Then again using equation (B2)), one can get the fluence sensitivity in this regime asshown in Table 1.."," Then again using equation \ref{eq:N}) ), one can get the fluence sensitivity in this regime asshown in Table \ref{table:GLAST}. ."48C). and one for X-band.,"C), and one for X-band."49 All bands except X are converted to a common IE in the frequency range of 7.5-12.5 GIIz., All bands except X are converted to a common IF in the frequency range of 7.5-12.5 GHz.50 The signals from the EVLA X-band receiver. which operates at 8 to 12 Gllz. are routed directly into the main downconverters without [requency conversion.," The signals from the EVLA X-band receiver, which operates at 8 to 12 GHz, are routed directly into the main downconverters without frequency conversion."51 The RF signals [rom the hieh Ireeuency receivers are converted to IE as follows., The RF signals from the high frequency receivers are converted to IF as follows.52 The first IF conversion for signals from the Ix. Ίνα and Q-band receivers occurs in (he receivers themselves.," The first IF conversion for signals from the K, Ka and Q-band receivers occurs in the receivers themselves."53 At this stage of the IF. the frequency of the signals lies in the range of 8-18 GllIz.," At this stage of the IF, the frequency of the signals lies in the range of 8-18 GHz."54 IF conversion does not take place in the INu-band receiver. which delivers its 12-18 Gllz RF signal directly to the telescopes IF system.," IF conversion does not take place in the Ku-band receiver, which delivers its 12-18 GHz RF signal directly to the telescope's IF system."55 The signals from all four of the high frequency receivers are then routed to à broadband UX converter module., The signals from all four of the high frequency receivers are then routed to a broadband UX converter module.56 In this module. IF signals in (he frequency range of 7.5-12.5 Gllz are amplified and routed directly to the module's output.," In this module, IF signals in the frequency range of 7.5-12.5 GHz are amplified and routed directly to the module's output."57 IF sienals in the frequency range of 11.5-18 Gllz are amplified and downconverted to a 7.5-12.5 Gllz IF using LO signals [rom the svnthesizers discussed below., IF signals in the frequency range of 11.5-18 GHz are amplified and downconverted to a 7.5-12.5 GHz IF using LO signals from the synthesizers discussed below.58 Like the X and Ixu-band receivers. no frequency conversion is performed in the 4. D. L. 5. and C-band receivers.," Like the X and Ku-band receivers, no frequency conversion is performed in the 4, P, L, S, and C-band receivers."59 The 4 and P-band signals are combined and then routed to the 4P converter module where they are up-converted to the range of 1.0 to 1.4 GlIz., The 4 and P-band signals are combined and then routed to the 4P converter module where they are up-converted to the range of 1.0 to 1.4 GHz.60 These signals and those from the L. S and C-band receivers are routed to another conversion stage. in which the signals are up-converted to the 7.5 to 12.5 Gllz IF frequency range. again using LO signals from (he svuthesizers described below.," These signals and those from the L, S and C-band receivers are routed to another conversion stage, in which the signals are up-converted to the 7.5 to 12.5 GHz IF frequency range, again using LO signals from the synthesizers described below."61 Thus. signals from all receivers are converted to the 1.5-12.5 IF frequency. range.," Thus, signals from all receivers are converted to the 7.5-12.5 IF frequency range."62 In the final downconverter modules. the IE signal is bandpass filtered to 7.5-12.5 GllIz aud amplified.," In the final downconverter modules, the IF signal is bandpass filtered to 7.5-12.5 GHz and amplified."63 The amplitude of the IF signal is then leveled to a standard power by adjusting a 32-step attenuator., The amplitude of the IF signal is then leveled to a standard power by adjusting a 32-step attenuator.64 The leveled signal is then split into two paths., The leveled signal is then split into two paths.65 Each of these patlis is converted (o a range of 2048 to 4096 MIIz using LO signals from a fine-tunable frequency svithesizer., Each of these paths is converted to a range of 2048 to 4096 MHz using LO signals from a fine-tunable frequency synthesizer.66 These signals are routed into digitally controlled. 15 step. gain slope equalizers.," These signals are routed into digitally controlled, 15 step, gain slope equalizers."67 The equalizers are used to compensate for slopes in (he signal baudpass due to variations in the receivers. cables ancl upstream electronics.," The equalizers are used to compensate for slopes in the signal bandpass due to variations in the receivers, cables and upstream electronics."68 Compensating for the slope is very important because of the limited dvnamic range of the 3-bit digilizers (see below)., Compensating for the slope is very important because of the limited dynamic range of the 3-bit digitizers (see below).69 The outputs of these equalizers are passed through a second 32 step allenuator to set Che levels required by the digitizers., The outputs of these equalizers are passed through a second 32 step attenuator to set the levels required by the digitizers.70 The signals are output [rom (he module through very sharp cutoff. 2048-4096 MIIZ. anti-aliasing filters and connected to the 3-bit digitizers in the modules for the data transmission svstem (DTS) which operate on a 4096 MlIZ clock.," The signals are output from the module through very sharp cutoff, 2048-4096 MHz, anti-aliasing filters and connected to the 3-bit digitizers in the modules for the data transmission system (DTS) which operate on a 4096 MHz clock."71 Note that elsewhere in this document the IF bandwidth is referred (o as a nominal 2 Gllz band. although in fact it is 2.048 61111.," Note that elsewhere in this document the IF bandwidth is referred to as a nominal 2 GHz band, although in fact it is 2.048 GHz."72 Additionallv. one of the 2048 to 4096 MIIz paths can be routed to an additional stage where it is converted by a 4096 MIIz fixed LO signal to a range of 1024 to 2048 MIIZ.," Additionally, one of the 2048 to 4096 MHz paths can be routed to an additional stage where it is converted by a 4096 MHz fixed LO signal to a range of 1024 to 2048 MHz."73 This signal is leveled by a 32-bit step attenuator. then output from the module through a sharp," This signal is leveled by a 32-bit step attenuator, then output from the module through a sharp"74Those significant conclusions may leach us about important aspects of the formation of the two galaxies.,Those significant conclusions may teach us about important aspects of the formation of the two galaxies.75 For instance. (he comparable mean metallicities may be indicative ol similar overall chemical enrichment. suggesting that the early star formation efficiency has been similar in the (wo svstemsor perhaps in the sub-components that eventually assembled to form them.," For instance, the comparable mean metallicities may be indicative of similar overall chemical enrichment, suggesting that the early star formation efficiency has been similar in the two systems—or perhaps in the sub-components that eventually assembled to form them."76 The similar a-enhancement. assessed by measurements of Mg and Fe-sensilive absorption lines. suggests (hat either the time scale for star formation. the IMF. or a combination thereof. were similar in both galaxies.," The similar $\alpha$ -enhancement, assessed by measurements of Mg and Fe-sensitive absorption lines, suggests that either the time scale for star formation, the IMF, or a combination thereof, were similar in both galaxies."77 The dillerence in CN strength. which has been ascribed to a difference in nitrogen abundance. is difficult to interpret. owing mostly to uncertainties in the models for the nucleosvnthesis of that element.," The difference in CN strength, which has been ascribed to a difference in nitrogen abundance, is difficult to interpret, owing mostly to uncertainties in the models for the nucleosynthesis of that element."78 The issue is [further complicated by the fact thal CNO elements are seen (o present strong star-(o-star variations in Galactic GCs (e.g..Grattonetal.2004.anclreferencestherein).. which may be associated with the presence of multiple stellar populations in those GC's (Conroy&Spergel2010:Piotto2009:MartellηCannonetal. herein).. and by inference. in their M 31 counterparts.," The issue is further complicated by the fact that CNO elements are seen to present strong star-to-star variations in Galactic GCs \citep[e.g.,][and references therein]{gr04}, which may be associated with the presence of multiple stellar populations in those GCs \citep[][and references therein]{cs10,pi09,ms09,can98}, and by inference, in their M 31 counterparts."79 Reearclless. anv scenario for the formation of the MIW and M 31 haloes. and their GC svstems. will be challenged by the large nitrogen abundance differences between svstems that look otherwise very similar.," Regardless, any scenario for the formation of the MW and M 31 haloes, and their GC systems, will be challenged by the large nitrogen abundance differences between systems that look otherwise very similar."80 This is the fourth of a series of papers dedicated to analvzing the kinematics and Cchemistyy of a large sample of M31 GC's. based on high-quality integrated. spectra [or several hundred ΔΙ 31 clusters. obtained with AIAIT/Tectospec.," This is the fourth of a series of papers dedicated to analyzing the kinematics and chemistry of a large sample of M 31 GCs, based on high-quality integrated spectra for several hundred M 31 clusters, obtained with MMT/Hectospec."81 In Paper E we characterized the population of voung (S 2 Gvr) M 31 clusters in terms of their ages. metallicities. masses. and kinematics.," In Paper I \citep{ca09a} we characterized the population of young $\simless$ 2 Gyr) M 31 clusters in terms of their ages, metallicities, masses, and kinematics."82 In Paper IE (Caldwelletal.2011).. the ages and metallicities of M 31 old GCs were studied.," In Paper II \citep{ca10}, the ages and metallicities of M 31 old GCs were studied."83 In particular. we found no differences between the ages of the (wo old GC svstenis. in disagreement. with previous claims.," In particular, we found no differences between the ages of the two old GC systems, in disagreement with previous claims."84 Moreover. we found that ihe M 31 GC svstem does not have a bimodal metallicity distribution. in agreement with recent findings (Yoonetal.2006).," Moreover, we found that the M 31 GC system does not have a bimodal metallicity distribution, in agreement with recent findings \citep{yo06}."85. In Paper IHE (Morrisonetal.2010).. we suggest that the old bulee GCs in M 31 are characterized by à bar-like kinematics.," In Paper III \citep{mo10}, we suggest that the old bulge GCs in M 31 are characterized by a bar-like kinematics."86resolution better than 071 that should reveal any resolved bipolar scattered light structure.,resolution better than $0\farcs1$ that should reveal any resolved bipolar scattered light structure.87" It has been suggested that the arc-shaped filamentary structure that seems to 'connect. TMR-IC with TMR-1AB is a material tail formed during an encounter of proto-stellar disks surrounding TMR-1A and B respectively (Lin et 11998, T98)."," It has been suggested that the arc-shaped filamentary structure that seems to 'connect' TMR-1C with TMR-1AB is a material tail formed during an encounter of proto-stellar disks surrounding TMR-1A and B respectively (Lin et 1998, T98)."88" The same encounter may have caused the formation of TMR-1C from fragmentation of a part of the filament into a very low-mass object, or through ejection during the dynamical interaction."," The same encounter may have caused the formation of TMR-1C from fragmentation of a part of the filament into a very low-mass object, or through ejection during the dynamical interaction."89 As such there would be a clear physical relationship between the filament and TMR-1C. The higher spectral resolution of our ISAAC data as compared to the previous spectrum of the filament (Terebey et 22000) allows us to extract new physical information for the nature of the filament., As such there would be a clear physical relationship between the filament and TMR-1C. The higher spectral resolution of our ISAAC data as compared to the previous spectrum of the filament (Terebey et 2000) allows us to extract new physical information for the nature of the filament.90 Previous studies mainly report on scattered light emission arising from the filament., Previous studies mainly report on scattered light emission arising from the filament.91" However, in spite of a clear component of continuum emission, we believe that there is another distinct process present, that is shocks."," However, in spite of a clear component of continuum emission, we believe that there is another distinct process present, that is shocks."92" In Figure 8 we plot the spatial distribution of the intensities in the Hy 1-0SS(1) and Η2 QQ(1) emission lines, and in the continuum, along the filament."," In Figure \ref{h2exc} we plot the spatial distribution of the intensities in the $_2$ S(1) and $_2$ Q(1) emission lines, and in the continuum, along the filament."93 Obviously there are 2 locations where the emission in molecular hydrogen is significantly in excess., Obviously there are 2 locations where the emission in molecular hydrogen is significantly in excess.94" Spectra at these 2 locations along the filament have been extracted (H2 knot 1 and H» knot 2 in Figure 4,, note: the H» knot 1 location, aaperture 2, actually includes 2 peaks of H» emission which showed indistinguishable spectra and where therefore combined to improve the signal-to-noise)."," Spectra at these 2 locations along the filament have been extracted $_2$ knot 1 and $_2$ knot 2 in Figure \ref{spectra}, note: the $_2$ knot 1 location, aperture 2, actually includes 2 peaks of $_2$ emission which showed indistinguishable spectra and where therefore combined to improve the signal-to-noise)."95" Both spectra show a wealth of emission lines, which are predominantly ro-vibrational lines of molecular hydrogen."," Both spectra show a wealth of emission lines, which are predominantly ro-vibrational lines of molecular hydrogen."96 Molecular hydrogen emission mainly originates from either of the two physical processes: shock excitation or ultraviolet fluorescence., Molecular hydrogen emission mainly originates from either of the two physical processes: shock excitation or ultraviolet fluorescence.97 We use the intensity ratio of the transitions Hy vz1-0SS(1) at 2.12um and Hy v=2-1SS(1) at 2.24um to distinguish between these two cases., We use the intensity ratio of the transitions $_2$ S(1) at $\mu$ m and $_2$ S(1) at $\mu$ m to distinguish between these two cases.98" Thermal excitation via shocks should be the responsible mechanism if this ratio is >5, and gas densities are not too high, €10?cm? (Shull and Beckwith 1982)."," Thermal excitation via shocks should be the responsible mechanism if this ratio is $\gtrsim 5$, and gas densities are not too high, $\lesssim 10^5 {\rm cm}^{-3}$ (Shull and Beckwith 1982)."99" Since we measure a 2.12,m/2.24um ratio of ~8.25 and of ~5.6, for the Hz knot 1 spectrum and the H» knot 2 spectrum respectively, and we do not observe any lines from transitions of high vibrational levels, we conclude that the H5 emission in the filament is due to shock excitation."," Since we measure a $\mu$ $\mu$ m ratio of $\sim 8.25$ and of $\sim 5.6$, for the $_2$ knot 1 spectrum and the $_2$ knot 2 spectrum respectively, and we do not observe any lines from transitions of high vibrational levels, we conclude that the $_2$ emission in the filament is due to shock excitation."100 Support for the shock interpretation is also gained from Ho ortho-para ratios discussed below., Support for the shock interpretation is also gained from $_2$ ortho-para ratios discussed below.101" Slightly different is the situation for the spectrum extracted close to TMR-1AB, which does not show any detectable emission at 2.24um, suggesting the absence of molecular gas at higher temperatures (z KK)."," Slightly different is the situation for the spectrum extracted close to TMR-1AB, which does not show any detectable emission at $\mu$ m, suggesting the absence of molecular gas at higher temperatures $\gtrsim$ K)."102" The Bry recombination line of atomic hydrogen at 2.166,m, on the other hand, is one of the most prominent lines in this spectrum."," The $\gamma$ recombination line of atomic hydrogen at $\mu$ m, on the other hand, is one of the most prominent lines in this spectrum."103 This indicates that a process must be present that is capable of ionizing hydrogen., This indicates that a process must be present that is capable of ionizing hydrogen.104 Winds from the young stellar object is one of the likely responsible mechanisms., Winds from the young stellar object is one of the likely responsible mechanisms.105 But also disk accretion onto the central source may be the cause for the Bry emission., But also disk accretion onto the central source may be the cause for the $\gamma$ emission.106" Prato et (2009) present a K-band spectrum of TMR-1AB which shows similar features as our ISAAC spectrum obtained close to TMR-1AB (remember that the ISAAC slit positioning is offset by almost 1"" from the TMR-1AB peak emission).", Prato et (2009) present a K-band spectrum of TMR-1AB which shows similar features as our ISAAC spectrum obtained close to TMR-1AB (remember that the ISAAC slit positioning is offset by almost $1^{\prime\prime}$ from the TMR-1AB peak emission).107" These authors determine, from the Bry emission line luminosity, a mass accretion rate of 1.9x10-7Mo/yr for TMR-1, which is quite consistent with Bry emission being generated by accretion."," These authors determine, from the $\gamma$ emission line luminosity, a mass accretion rate of $1.9\times10^{-7} {\rm M}_\odot/{\rm yr}$ for TMR-1, which is quite consistent with $\gamma$ emission being generated by accretion."108 What causes the shocks in the filament?, What causes the shocks in the filament?109" It has been known for long, that TMR-1 is associated with a large molecular outflow (Terebey et 11990, Hogerheijde et 11998) observed aat CO (3—2)."," It has been known for long, that TMR-1 is associated with a large molecular outflow (Terebey et 1990, Hogerheijde et 1998) observed at $^{12}$ CO (3–2)."110 The direction of this outflow is in very good agreement with the direction of a jet indicated in Fell narrow-band near-infrared images (Petr-Gotzens et 22002)., The direction of this outflow is in very good agreement with the direction of a jet indicated in FeII narrow-band near-infrared images (Petr-Gotzens et 2002).111 The position angle of the filament is different by ~20° from the position angle of the outflow and jet., The position angle of the filament is different by $\sim 20^{\circ}$ from the position angle of the outflow and jet.112" A plausible scenario is that the filament is part of the edge of a cavity cleared by a lower velocity outflow, as for example observed in 2211 (Gueth Guilloteau 1999)."," A plausible scenario is that the filament is part of the edge of a cavity cleared by a lower velocity outflow, as for example observed in 211 (Gueth Guilloteau 1999)."113" The molecular hydrogen emission knots along the filament would then arise, because this lower velocity flow hits into the cavity rim, thereby creating a C-type shock (see Sec."," The molecular hydrogen emission knots along the filament would then arise, because this lower velocity flow hits into the cavity rim, thereby creating a C-type shock (see Sec."114 3.4.1)., 3.4.1).115" Or, the filament is intrinsic, pre-existing dense material being shocked by the outflow as it happens to be in its way."," Or, the filament is intrinsic, pre-existing dense material being shocked by the outflow as it happens to be in its way."116 It is unlikely that the filament is a jet by itself., It is unlikely that the filament is a jet by itself.117" While bent jets have been observed (Davis et 11994, Bally Reipurth 2001), the significant amounts of continuum emission coming from the filament, together with a high degree of polarization (Whitney et 11997), and detection of high column densities associated with the filament (Hogerheijde et 11998, Motte André 2001), exclude a jet."," While bent jets have been observed (Davis et 1994, Bally Reipurth 2001), the significant amounts of continuum emission coming from the filament, together with a high degree of polarization (Whitney et 1997), and detection of high column densities associated with the filament (Hogerheijde et 1998, Motte André 2001), exclude a jet."118‘Lo avoid of fingers-of-god elfect we used the correction factor in calculation of space distance between galaxies.,To avoid of fingers-of-god effect we used the correction factor in calculation of space distance between galaxies.119 Lf the projected. r and radial ο distances were an equivalent. we should calculate a space distance between two galaxies as Obviously we work in the space of radial velocities and under r we mean {οι," If the projected $r$ and radial $v$ distances were an equivalent, we should calculate a space distance between two galaxies as Obviously we work in the space of radial velocities and under $r$ we mean $r\cdot H_{0}$."120 We inserted. the certain factor koc loas a weight of the radial component., We inserted the certain factor $k<1$ as a weight of the radial component.121 This factor is responsible for the relative virial motion of galaxies., This factor is responsible for the relative virial motion of galaxies.122" In that case the modified distance is m=(7&72,2| ", In that case the modified distance is $m^ {2 }=v^ {2 }k^ {2 }+r^ {2 }$.123After some transformations we obtained the equation of ellipse: where m is the minor semiaxis and 4nn is the major semiaxis of the ellipse., After some transformations we obtained the equation of ellipse: where $m $ is the minor semiaxis and $ \frac {m }{k }$ is the major semiaxis of the ellipse.124 We took into account some tolerance Dy in measuringe., We took into account some tolerance $v_{p}$ in measuring$v$.125 For that we [abelled a major semiaxis as 70—d|ny where (is a distance in the space of racial velocities according to (8).," For that we labelled a major semiaxis as $ \frac {m }{k }=d+v_{p }$, where $d^ {2 }$ is a distance in the space of radial velocities according to (8)."126 So the weight of the radial component is &=47—., So the weight of the radial component is $k= \frac {m }{d+v_ {p }}$.127" Since new distance niis a part of formula for A. therefore for the simplification we used here m—d and obtained new distance In case of e,=0 the formula. (10) changes to (8)."," Since new distance $m$ is a part of formula for $k$ , therefore for the simplification we used here $m=d$ and obtained new distance In case of $v_ {p } = 0$ the formula (10) changes to (8)."128 Lf the galaxies are located at the great. distance αoocy. formula (10) also changes to (S).," If the galaxies are located at the great distance $d >> v_ {p}$, formula (10) also changes to (8)."129 Soin these cases the virial velocities have a week action on the distance measurement accuracy., So in these cases the virial velocities have a week action on the distance measurement accuracy.130 IH d~es. than 1|ELc Lobe. the weight of racial distance decreases.," If $d \sim v_ {p }$, than $1+ \frac {v_ {p }}{d }>1, $ i.e. the weight of radial distance decreases."131 In case d<<ny denominator (1|5). tends to infinity and the radial component loses significance. while projected distance r keeps it.," In case $d<<v_{p }$ denominator $\left( 1+\frac{v_{p}}{d}\right)^{2}$ tends to infinity and the radial component loses significance, while projected distance $r$ keeps it."132 For the our caleulations we used py = 300 Km + as the value of typical relativevelocities in small galaxy systems (Ceccarelli ct al., For the our calculations we used $v_ {p }$ = 300 km $^{-1}$ as the value of typical relativevelocities in small galaxy systems (Ceccarelli et al.133 2005)., 2005).134 Aloreover Ixarachentsev et al. (, Moreover Karachentsev et al. (1351989) showed that majority of physically bound. triplets have rms velocity S.<300 kms ,1989) showed that majority of physically bound triplets have rms velocity $S_{v} < 300$ km $^{-1}$ .136For the testing our method. robustnesswe compared main parameters in cases of dillerent. ον., For the testing our method robustnesswe compared main parameters in cases of different $v_{p}$ .137 Table 7 , Table \ref{tab6} 138hehtcurves.,lightcurves.139 We estimate the significance of the measured time-cdelavs through simulations., We estimate the significance of the measured time-delays through simulations.140 The intrinsic power spectrum of the source is an approximate power-law with index ~2., The intrinsic power spectrum of the source is an approximate power-law with index $\sim 2$.141 Based on this power spectral shape aud using the method proposed by Timuner&Ποσο(1995).. we simmlate 200 pais of highteurves having the same ucasured time-delay as the observed pair.," Based on this power spectral shape and using the method proposed by \cite{Tim95}, we simulate 200 pairs of lightcurves having the same measured time-delay as the observed pair."142 Measureineut errors were added to cach lishteurve aud the pairs were hen subjected to au identical aualvsis. where the cross-correlation functiou was fitted by a Camssian function.," Measurement errors were added to each lightcurve and the pairs were then subjected to an identical analysis, where the cross-correlation function was fitted by a Gaussian function."143 The root mean square deviation of the centroids of the vost fit Caussian functions. was then taken to be the L-sigima error ou the time-delay.," The root mean square deviation of the centroids of the best fit Gaussian functions, was then taken to be the 1-sigma error on the time-delay."144 The first column of Figure 1. shows the rans and the iue lag for Mrk 1010 are plotted as function of energy iu., The first column of Figure \ref{cross_comp} shows the r.m.s and the time lag for Mrk 1040 are plotted as function of energy bin.145 Below 2 keV. the time lag decreases with energy which means that the variation in the soft photons occurafter the corresponding variation in the hd ones i.c. here is a soft time lag.," Below $2$ keV, the time lag decreases with energy which means that the variation in the soft photons occur the corresponding variation in the hard ones i.e. there is a soft time lag."146 For energies 2 keV. the time ag increases with energv as in the regular case of lard aes.," For energies $> 2$ keV, the time lag increases with energy as in the regular case of hard lags."147 To validate the analvsis techuique aud to make a direct comparison with other sources. the rielt column of Figure Lo show the raus and time lag for Mk- 335. computed using auidentical analysis of its similar length observation," To validate the analysis technique and to make a direct comparison with other sources, the right column of Figure \ref{cross_comp} show the r.m.s and time lag for Mrk 335, computed using an analysis of its similar length observation."148 Although the raus varies differently with energy. the time lag for Mik 335 increases with euergv (e. hard lags}.," Although the r.m.s varies differently with energy, the time lag for Mrk 335 increases with energy (i.e. hard lags)."149 This is consistent with the more detailed analysis. iucludiug frequency depeudenuce. of this source (Arévaloetal.2008).," This is consistent with the more detailed analysis, including frequency dependence, of this source \citep{Are08}."150. Figure Lo shows that the r.urs decreases with energy for Mrk 1010. while it is nearly constaut for λα 2335.," Figure \ref{cross_comp} shows that the r.m.s decreases with energy for Mrk 1040, while it is nearly constant for Mrk 335."151 This may indicate that the variabilitv in Mik 1010 is due to variations in the absorbing mecdimm., This may indicate that the variability in Mrk 1040 is due to variations in the absorbing medium.152 Moreover. if the absorbing medium (e.g. warn absorber) reacts to a change in the hard N-vay coutimmun with a time delay. this could naturally explain the soft lags observed in the source.," Moreover, if the absorbing medium (e.g. warm absorber) reacts to a change in the hard X-ray continuum with a time delay, this could naturally explain the soft lags observed in the source."153 Hoscever. as seen in Figure 2.. the lharcducss ratio variation is on longer timescale aud unucorrelated with the lutensity variation.," However, as seen in Figure \ref{lcurve}, the hardness ratio variation is on longer timescale and uncorrelated with the intensity variation."154 Thus. such a model caunot explain the soft lags observed.," Thus, such a model cannot explain the soft lags observed."155 Frequeney dependent time lags ia X-ray binarics and AGN can be explained in terms of fluctuations propagating from the outer regions of the cisk to the inner (Lyubarskii1997)., Frequency dependent time lags in X-ray binaries and AGN can be explained in terms of fluctuations propagating from the outer regions of the disk to the inner \citep{Lyu97}.156. To reconcile soft laes. either the waves have to propagate outwards or the hard photos have to arise from outer regions. both of which secnm rather physically unrealistic.," To reconcile soft lags, either the waves have to propagate outwards or the hard photons have to arise from outer regions, both of which seem rather physically unrealistic."157" Tn the most straight forward interpretation. Comptonization naturally predicts a time lag between cherey bands to be ~Rife log(Eo/E4). where Ris the size of the region and L/L, is the ratio of the enereies."," In the most straight forward interpretation, Comptonization naturally predicts a time lag between energy bands to be $\sim R/c$ $\log(E_2/E_1)$, where $R$ is the size of the region and $E_2/E_1$ is the ratio of the energies."158 While the energy dependence is consistent witli what is observed in black hole binaries aud ACN. the Comptonization interpretation is often ruled out because it is cifficult to reconcile with the observed frequency dependence of the lags.," While the energy dependence is consistent with what is observed in black hole binaries and AGN, the Comptonization interpretation is often ruled out because it is difficult to reconcile with the observed frequency dependence of the lags."159 However. it is iuportaut to note that Comptouization lag ust exist aud should manifest at high enough frequencies when the wave propagation lag is small.," However, it is important to note that Comptonization lag must exist and should manifest at high enough frequencies when the wave propagation lag is small."160 Thus at high frequencies the lag should saturate to the Conmptonization lag values., Thus at high frequencies the lag should saturate to the Comptonization lag values.161 While. this saturation las not been detected. the observed time lags already Hupose a stringent upper lait on the size of the Comptonizing region. R for ACNs.," While, this saturation has not been detected, the observed time lags already impose a stringent upper limit on the size of the Comptonizing region, $R$ for AGNs."162 For Ark 561. the time lag variation of ~50 sec log(Eo/E4) (Arévaloetal.2006) requires that P?2«1013 Gu or <26AL/e? for at 107AZ. black hole.," For Ark 564, the time lag variation of $\sim 50$ sec $\log (E_2/E_1)$ \citep{Are06} requires that $R < 2 \times 10^{11}$ cm or $ < 2 GM/c^2$ for at $10^7 M_\odot$ black hole."163 It is nof known whether the lags in Ak 1010 are frequency depeudent aud hence a Coniptonization origin may still be viable., It is not known whether the lags in Mrk 1040 are frequency dependent and hence a Comptonization origin may still be viable.164 Soft lags due to Comptonization is indeed possible. as invoked to explain the soft lags observed for κας QPO in N-vav binaries (Leeetal. 2001).," Soft lags due to Comptonization is indeed possible, as invoked to explain the soft lags observed for kHz QPO in X-ray binaries \citep{Lee01}."165. A fluctuation in the electron temperature will lead to variations du the hard N-ravs after a σαν., A fluctuation in the electron temperature will lead to variations in the hard X-rays after a delay.166 À fraction of these hard N-ravs may impinge back ou the iuput photon producing region aud hence affect the soft photous., A fraction of these hard X-rays may impinge back on the input photon producing region and hence affect the soft photons.167 This will lead to a detectable soft lag., This will lead to a detectable soft lag.168" Alternatively, the soft lag could be due to reverberation of a complex eravitationally blurred reflection component to variations of the continu. as proposed for 11 0707-195 (Fabianetal.2009)."," Alternatively, the soft lag could be due to reverberation of a complex gravitationally blurred reflection component to variations of the continuum, as proposed for 1H 0707-495 \citep{Fab09}."169. It is interesting to note that if like for ΤΙ 0707-19. the contiuuuu in Mrk 1010 ouly dominates im the 1-2 keV baud. the time lag variation with energy observed. may be naturally explained.," It is interesting to note that if like for 1H 0707-49, the continuum in Mrk 1040 only dominates in the $1$ $2$ keV band, the time lag variation with energy observed, may be naturally explained."170 The temporal aud spectral signatures of both these models can be quantified. although. especially for the reflection scenario. the complex aud non-dutuitive effect of light. bending needs to be taken iuto account.," The temporal and spectral signatures of both these models can be quantified, although, especially for the reflection scenario, the complex and non-intuitive effect of light bending needs to be taken into account."171 Both models cau be tested and their paraicters tightly constrained. because they will ueed to sel£conusisteutlv explain the lage and raus versus enerev as well as the photon spectrum.," Both models can be tested and their parameters tightly constrained, because they will need to self-consistently explain the lag and r.m.s versus energy as well as the photon spectrum."172 Successful application of either model will provide rich divideuds imn terms of constrainime the radiative processes. ecometry and more iportautlv the size of the syste aud provide opportunity to test strong Ceneral Relativistic effects.," Successful application of either model will provide rich dividends in terms of constraining the radiative processes, geometry and more importantly the size of the system and provide opportunity to test strong General Relativistic effects."173 Note however. that for both scenarios. the time lag should not be frequency dependeut.," Note however, that for both scenarios, the time lag should not be frequency dependent."174"For over a decade now cluster gas mass fractions as inferred [ron N-rav. observations have been used as a probe of the universal ratio of barvon to total mater densities. O,/O0,, (c.g. White et 11993: David et al.","For over a decade now cluster gas mass fractions as inferred from X-ray observations have been used as a probe of the universal ratio of baryon to total matter densities, $\Omega_b/\Omega_m$ (e.g., White et 1993; David et al."175 1995: Evrarel 1997: Mohr et 11999: Roussel et 2200k Allen οἱ 22002: Lin et 22003: Ettori 2003: Allen et 22004)., 1995; Evrard 1997; Mohr et 1999; Roussel et 2000; Allen et 2002; Lin et 2003; Ettori 2003; Allen et 2004).176" Supplementing these gas mass pactions wih constraints on ©, from. c.g. cosmic microwave background. (CMD) measurements or a combination ο Dig Bang Nucleosynthesis (BBN) predictions anc D/IL measurements from high recshi 1oquasars. therefore allows one to measure the tota matter density 8."," Supplementing these gas mass fractions with constraints on $\Omega_b$ from, e.g., cosmic microwave background (CMB) measurements or a combination of Big Bang Nucleosynthesis (BBN) predictions and D/H measurements from high redshift quasars, therefore allows one to measure the total matter density $\Omega_m$."177 The reliabiliv oL this test rests on the assum.xion that clusters have been able retain the origina barvon inventory assigned to them in the carly universe., The reliability of this test rests on the assumption that clusters have been able retain the original baryon inventory assigned to them in the early universe.178" So-caled ""non-radiative Cosmoogical simulations. which include a hyerodynamic. treatment of the barvons bu neglect sources or sinks such as radiative cooling. star formation. and feedback. indeed indicate that clusters retain nearly all their barvons until the present day (e... Frenk e 11999: Way ct 22004: Crain et 22006)."," So-called “non-radiative” cosmological simulations, which include a hydrodynamic treatment of the baryons but neglect sources or sinks such as radiative cooling, star formation, and feedback, indeed indicate that clusters retain nearly all their baryons until the present day (e.g., Frenk et 1999; Kay et 2004; Crain et 2006)."179 The same is generally true for simulations with cooling and feedback., The same is generally true for simulations with cooling and feedback.180 Although t10 fraction of baryons in the hot phase depends strongly on the model. most recent. simulations predict a mild increase in the hot gas fraction with cluster mass. aud little evoluion with redsult (e... Tornatore et 22003: Ixravisov ο 22005: Ltori ct 22006).," Although the fraction of baryons in the hot phase depends strongly on the model, most recent simulations predict a mild increase in the hot gas fraction with cluster mass, and little evolution with redshift (e.g., Tornatore et 2003; Kravtsov et 2005; Ettori et 2006)."181 Although the cluster baryon fraction test. has. been examined xeviouslv in many studies. there are several good reasons for revisiing it.," Although the cluster baryon fraction test has been examined previously in many studies, there are several good reasons for revisiting it."182 First. new high-quality. data. obtained from the and telescopes now allow us lo probe both the surface brightness and temperature profiles of clusters out to large raclil," First, new high-quality data obtained from the and telescopes now allow us to probe both the surface brightness and temperature profiles of clusters out to large radii."183 As a result. both the statistical ancl svstematic observational uncertainties on the gas mass fraction are substantially improved.," As a result, both the statistical and systematic observational uncertainties on the gas mass fraction are substantially improved."184 Second. much improved. (e.g... Ix-band) measurements of the stellar content of clusters. are now available.," Second, much improved (e.g., K-band) measurements of the stellar content of clusters are now available."185" ""Third. cosmological simulations can now robustly predict. the barvon fractions within rou. which is roughly the same radius the latest X-ray measurements reliably extend out to."," Third, cosmological simulations can now robustly predict the baryon fractions within $r_{500}$, which is roughly the same radius the latest X-ray measurements reliably extend out to."186 Fourth. analyses of mock observations of realistic cosmological simulations allow us to. e.g. quantify the observational bias introduced. by assuming strict hyelrostatic equilibrium (119) in the derivation of X-ray gas mass [ractions.," Fourth, analyses of mock observations of realistic cosmological simulations allow us to, e.g., quantify the observational bias introduced by assuming strict hydrostatic equilibrium (HSE) in the derivation of X-ray gas mass fractions."187 Finally. analysis of the recently," Finally, analysis of the recently"188The physical flux F4 is related to the specific intensity through where Ηλ is the Eddington flux (the first-order moment of the radiation field).,The physical flux $F_\lambda$ is related to the specific intensity through where $H_\lambda$ is the Eddington flux (the first-order moment of the radiation field).189 The integration of eqtn., The integration of eqtn.190" 4 using an analytical limb-darkening law to represent I)(j1), with coefficients determined by least squares, will not normally recover the physical flux exactly."," \ref{eq:flux}191 using an analytical limb-darkening law to represent $I_\lambda(\mu)$, with coefficients determined by least squares, will not normally recover the physical flux exactly."192" To address this, we can impose the condition that in linear and quadratic cases, respectively."," To address this, we can impose the condition that in the linear and quadratic cases, respectively."193" Requiring theI)(j), evaluated from the limb-darkening law, to equal I)(js), evaluated from the model atmosphere, at some arbitrary 4= x, we obtain for the linear law."," Requiring $\hat{I}_\lambda(\mu)$, evaluated from the limb-darkening law, to equal $I_\lambda(\mu)$, evaluated from the model atmosphere, at some arbitrary $\mu194= x$ , we obtain for the linear law."195" Wade&Rucinski(1985) chose x= 1, whence (noting the Wade& Rucinski""s “angle-averaged” [astrophysical] flux is f/m in the nomenclature adopted here)."," \citet{Wade85} chose $x=1$ , whence (noting the \citeauthor{Wade85}' 's “angle-averaged” [astrophysical] flux is $F_\lambda/\pi$ in the nomenclature adopted here)."196" In effect, the choice of x fixes the intercept of the linear law, with the constraint of flux conservation then fixing the slope."," In effect, the choice of $x$ fixes the intercept of the linear law, with the constraint of flux conservation then fixing the slope."197" The equivalent algebra for the quadratic law follows from selecting any two values jj=21,22 at which ""RO is equal to I)(i), giving a pair of simultaneous equations that can readily be solved for u1,u2. Wade&Rucinski(1985),"," The equivalent algebra for the quadratic law follows from selecting any two values $\mu = x_1, x_2$ at which $\hat{I}_\lambda(\mu)$ is equal to $I_\lambda(\mu)$, giving a pair of simultaneous equations that can readily be solved for $u_1,198u_2$. \citet{Wade85},"199", and subsequent authors, used σι=1,20.1 (values which are also adopted here), but again these are more or less arbitrary choices."," and subsequent authors, used $x_1 = 1, x_2 = 0.1$ (values which are also adopted here), but again these are more or less arbitrary choices."200" The weakness of the standard flux-conserving approach is the lack of a compelling physical argument to select any particular x values for the normalization (other than requiring the intensities to be everywhere positive; e.g., requiring 0>u1 in the linear case)."," The weakness of the standard flux-conserving approach is the lack of a compelling physical argument to select any particular $x$ values for the normalization (other than requiring the intensities to be everywhere positive; e.g., requiring $0 \geq u \geq 1$ in the linear case)."201" Rather than making an arbitrary choice of x, we can instead introduce the more objective requirement of minimising the sum of the squares of the differences between model and fitted intensities while still requiring flux to be conserved."," Rather than making an arbitrary choice of $x$, we can instead introduce the more objective requirement of minimising the sum of the squares of the differences between model and fitted intensities while still requiring flux to be conserved."202" For a linear law it is convenient first to determine u by by minimising $7(iu)−,using standard least- techniques, where and to then evaluate Corresponding results for the quadratic law are Not surprisingly, this newly introduced approach of flux-conserving least squares generally yields numerical coefficients very close to those found using the LS2 method."," For a linear law it is convenient first to determine $u$ by by minimising $\sum{\left({\hat{I}(\mu) - I(\mu)}\right)^2}$, using standard least-squares techniques, where and to then evaluate Corresponding results for the quadratic law are Not surprisingly, this newly introduced approach of flux-conserving least squares generally yields numerical coefficients very close to those found using the LS2 method."203" 'Therefore, although it may be regarded as superior to LS2 in principle, in practice itaffords no great benefit (and turns out not to give results particularly closeto photometrically inferred LDCs)."," Therefore, although it may be regarded as superior to LS2 in principle, in practice itaffords no great benefit (and turns out not to give results particularly closeto photometrically inferred LDCs)."204We refer to this model as PNM.,We refer to this model as PNM.205 Our MCMC rapidly converges and we find a best-fit model with a reduced x? of 6.06 (x? of 30.3 with 5 degrees of freedom)., Our MCMC rapidly converges and we find a best-fit model with a reduced $\chi^2$ of 6.06 $\chi^2$ of 30.3 with 5 degrees of freedom).206 The dotted green curves in Figure 1 show this best fit., The dotted green curves in Figure \ref{fig:wpgg_Slope} show this best fit.207" It is clear that the model provides a poor fit to the data, as it deviates downward from a power law on small scales."," It is clear that the model provides a poor fit to the data, as it deviates downward from a power law on small scales."208 We therefore find that by varying the P(N|M) free parameters alone we are unable to reproduce the innermost M06 data points., We therefore find that by varying the $P(N|M)$ free parameters alone we are unable to reproduce the innermost M06 data points.209" We have essentially reproduced the discrepancy between the very small-scale M06 data and the Zhengetal. modeling, and thus shown that including the small-scale(2008) points in the fit does not repair the discrepancy."," We have essentially reproduced the discrepancy between the very small-scale M06 data and the \citet{zheng08} modeling, and thus shown that including the small-scale points in the fit does not repair the discrepancy."210" Since we cannot reproduce the small-scale LRG clustering by varying the P(N|M) distribution, we naturally set our sights next on the radial distribution of LRG satellites within their dark matter halos."," Since we cannot reproduce the small-scale LRG clustering by varying the $P(N|M)$ distribution, we naturally set our sights next on the radial distribution of LRG satellites within their dark matter halos."211" As described in ??,, we have assumed that these galaxies trace the dark matter halo density distribution, which is in turn described by an NFW density profile."," As described in \ref{HOD}, we have assumed that these galaxies trace the dark matter halo density distribution, which is in turn described by an NFW density profile."212 The simplest change we can make is to allow galaxies to have a different NFW concentration than the halos they occupy., The simplest change we can make is to allow galaxies to have a different NFW concentration than the halos they occupy.213 We thus introduce a new free parameter fea) that relates the satellite galaxy concentration cg4j to that of the dark matter halo c: In the previous 4 parameter PNM model we found that Mo was very poorly constrained., We thus introduce a new free parameter $\fgal$ that relates the satellite galaxy concentration $\Cgal$ to that of the dark matter halo $c$ : In the previous 4 parameter PNM model we found that $\Mzero$ was very poorly constrained.214" In order to keep the same number of free parameters, we fix Mo to Myin, setting the exponential cut-off for satellite galaxies to occur at Myin."," In order to keep the same number of free parameters, we fix $\Mzero$ to $\Mmin$, setting the exponential cut-off for satellite galaxies to occur at $\Mmin$."215" Therefore, we now vary the following 4 free parameters: Mmin, M1, a, and fa}."," Therefore, we now vary the following 4 free parameters: $\Mmin$, $\Mone$, $\alpha$ , and $\fgal$."216 We refer to this model as PNMC., We refer to this model as PNMC.217 We find a best-fit model with a reduced x? of 2.52 (x? of 12.6 with 5 degrees of freedom)., We find a best-fit model with a reduced $\chi^2$ of 2.52 $\chi^2$ of 12.6 with 5 degrees of freedom).218 The dashed blue curves in Figure 1 show this best fit., The dashed blue curves in Figure \ref{fig:wpgg_Slope} show this best fit.219" The PNMC model clearly does better than the PNM model in explaining the small-scale LRG clustering; however, it still provides a poor fit."," The PNMC model clearly does better than the PNM model in explaining the small-scale LRG clustering; however, it still provides a poor fit."220" We find that [ο values of ~5—10 are preferred, showing that LRGs are more concentrated than the dark matter for this PNMC model."," We find that $\fgal$ values of $\sim 5-10$ are preferred, showing that LRGs are more concentrated than the dark matter for this PNMC model."221 This makes sense because increasing cg4j means that we are adding more satellite galaxies towards the center of halos., This makes sense because increasing $\Cgal$ means that we are adding more satellite galaxies towards the center of halos.222 This forces the scale radius inwards and boosts the amplitude of the inner part of £(r)., This forces the scale radius inwards and boosts the amplitude of the inner part of $\xi(r)$.223" However, while simply moving more galaxies towards the center may aid in fitting thevery inner most 2-3 data points, this can result in a poorer fit to the outermost data points."," However, while simply moving more galaxies towards the center may aid in fitting thevery inner most 2-3 data points, this can result in a poorer fit to the outermost data points."224" In other words, varying μαι can shift wp(rp) in the ry direction, but it cannot alter its shape, which is fundamentally not a power law in the case of an NFW satellite profile (see dashed blue curve in bottom panel of Fig. 1))."," In other words, varying $\Cgal$ can shift $\wpp\rp$ in the $r_\mathrm{p}$ direction, but it cannot alter its $\emph{shape}$, which is fundamentally not a power law in the case of an NFW satellite profile (see dashed blue curve in bottom panel of Fig. \ref{fig:wpgg_Slope}) )."225" Adopting an NFW form for the density profile of satellite LRGs is not capable of reproducing the small-scale correlation function, no matter what concentration we use."," Adopting an NFW form for the density profile of satellite LRGs is not capable of reproducing the small-scale correlation function, no matter what concentration we use."226 We therefore relax the NFW assumption by allowing the inner slope of the profile to vary., We therefore relax the NFW assumption by allowing the inner slope of the profile to vary.227" Recall that the NFW profile has a logarithmic slope dlnp/dlnr of -] at scales much less than the scale radius r,, and -3 at scales muchlarger than r,."," Recall that the NFW profile has a logarithmic slope $d\ln \rho/d\ln r$ of -1 at scales much less than the scale radius $r_s$, and -3 at scales muchlarger than $r_s$."228" We assume a new density profile for satellite LRG galaxies that is similar to NFW, except that the inner slope is no longer fixed to -1, but is a new free parameter —: This reduces to NFW for y=1."," We assume a new density profile for satellite LRG galaxies that is similar to NFW, except that the inner slope is no longer fixed to -1, but is a new free parameter $-\gamma$: This reduces to NFW for $\gamma=1$."229" A model of this form has been used by papers that study the inner slope of the dark matter density profile (e.g., Fukushige 2005))."," A model of this form has been used by papers that study the inner slope of the dark matter density profile (e.g., \citealt{fukushige04,reed05}) )."230" In order to use thisnew profile in our modeling, we need tocompute the pair distributions Εος and Fys(r), as described in ??.."," In order to use thisnew profile in our modeling, we need tocompute the pair distributions $F_{\mathrm{cs}}(r)$ and $F_{\mathrm{ss}}(r)$ , as described in \ref{2pt_xigg}. ."231" While Fis(r) is the (η)profile itself, Fur) is the convolution of the profile with itself and"," While $F_{\mathrm{cs}}(r)$ is the profile itself, $F_{\mathrm{ss}}(r)$ is the convolution of the profile with itself and"232"we intercept both overdensities, resulting in a double RC.","we intercept both overdensities, resulting in a double RC."233" Interestingly, in this map the far side of the X fades faster than the near side, when moving away from the Galactic plane."," Interestingly, in this map the far side of the X fades faster than the near side, when moving away from the Galactic plane."234 In the next section we will investigate whether this is a real feature or an artifact of our data analysis., In the next section we will investigate whether this is a real feature or an artifact of our data analysis.235" Let us concentrate, here, on the 3D shape of the Galactic bulge in a qualitative way."," Let us concentrate, here, on the 3D shape of the Galactic bulge in a qualitative way."236" 'The panel at b——4? also shows the Galactic bar, as traced by Rattenburyetal.(2007) using OGLE II data for stars at a similar latitude."," The panel at $b=-4^\circ$ also shows the Galactic bar, as traced by \cite{2007MNRAS.378.1064R} using OGLE II data for stars at a similar latitude."237 In the work of Rattenbury et al., In the work of Rattenbury et al.238 the derived bar was arbitrarily shifted in distance so that its center would be at 8 kpc., the derived bar was arbitrarily shifted in distance so that its center would be at 8 kpc.239 The angle between the structure we find and the line of sight is clearly the same as that of the Rattebury's bar., The angle between the structure we find and the line of sight is clearly the same as that of the Rattebury's bar.240" The center of structure, at b=—4°, is ~7 kpc away from the Sun (see below)."," The center of structure, at $b=-4^\circ$, is $\sim 7$ kpc away from the Sun (see below)."241" In Fig. 4,,"," In Fig. \ref{xshape},"242" each panel shows a vertical section of the density map, parallel to |—0° axis, at a given longitude."," each panel shows a vertical section of the density map, parallel to $l=0^\circ$ axis, at a given longitude."243" The X—6 plane passing from |=0° is in the central, middle panel."," The $X-b$ plane passing from $l=0^{\circ}$ is in the central, middle panel."244" The Sun would be at (.X,b)=(0,0°), outside each panel, on the left."," The Sun would be at $(X,b)=(0,0^{\circ})$, outside each panel, on the left."245" Lines of sight at different latitudes are shown as horizontal color strips, in each panel."," Lines of sight at different latitudes are shown as horizontal color strips, in each panel."246" Again, the line of sight at (1,b)=(0?,4-4?) is missing due to high extinction."," Again, the line of sight at $(l,b)=(0^\circ,+4^\circ)$ is missing due to high extinction."247 Thin white lines in each panel are, Thin white lines in each panel are248svuchrotron plotous however the hard. baud is affeced first bv he svuchrotron cutoff aud this hasons a result the decreuse of the hardness ratio.,synchrotron photons – however the hard band is affected first by the synchrotron cutoff and this has as a result the decrease of the hardness ratio.249 During this phase he spectrum in X-rays is shaped by an exporential cuXE (svucliroron enüssion) and an emereig fiwv power ON colponcnt (SSC cuuission)., During this phase the spectrum in X-rays is shaped by an exponential cutoff (synchrotron emission) and an emerging flat power law component (SSC emission).250 Thus. it came(4 be simply approxirated by a single power law aud οabeled by a photon 1ides (shaded area in the insert).," Thus, it cannot be simply approximated by a single power law and `labeled' by a photon index (shaded area in the insert)."251 At later times. the SSC component starts appearing m the hard baud while the decreasing svuchrotron componeit dominates the soft onc. resulting in an increase of the larcducss ratio.," At later times, the SSC component starts appearing in the hard band while the decreasing synchrotron component dominates the soft one, resulting in an increase of the hardness ratio."252 Flualv. at even later times both lauds mὉ domiuated by t1ο SSC compoucut. whose low energy part cau be approxinated by a fat power law. and due to its eradual Scepenine the harcduess raio appears to decTease gently.," Finally, at even later times both bands are dominated by the SSC component, whose low energy part can be approximated by a flat power law, and due to its gradual steepening the hardness ratio appears to decrease gently."253 I1 cases where the N-ray flux decays as a power law with time. as in panel (d) ο Fig. 10..," In cases where the X-ray flux decays as a power law with time, as in panel (d) of Fig. \ref{sximatika2},"254 we fiud 10 slenificant hi)ectral evolution., we find no significant spectral evolution.255 The photon iudex is :»proxinatelv Constaut alnost for three or four decades in fine. as t1C )OWOY aw ποσο of the svuchrotroi1 coniponent dominates until late timesii the X-rays (sec 1isert in panel d) of Fig. 11)).," The photon index is approximately constant almost for three or four decades in time, as the power law segment of the synchrotron component dominates until late times in the X-rays (see insert in panel (d) of Fig. \ref{HR}) )."256 The other two cases presened in panels >) and (c)of Fig., The other two cases presented in panels (b) and (c)of Fig.257 11 lie somewhere inbetween the two aforroimienutined example cases., \ref{HR} lie somewhere inbetween the two aforrementioned example cases.258 Αιmel the qualitative evolution of the photon ides with time is a robust feature of our modelο its specific value depends ou the value of the other mode parameters. such as the slope of the clectrou euergv spectrum.," Although the qualitative evolution of the photon index with time is a robust feature of our model, its specific value depends on the value of the other model parameters, such as the slope of the electron energy spectrum."259 In all our runs we have used a typical value of p=? 2.3., In all our runs we have used a typical value of $p=2.3$ .260" ?tohaveappearshownin(Petropoulou.theoxoceediugsMastichiadisof25h&Piran""Texas(2011)Syinpo- 6. 10.. 8)). eq.m)))) JL.. {77).. ?2?)). (?).. (?7?T). ("," \cite{fanetal08}261 \ref{lcX} \ref{sximatika2}. \ref{lcV}) \ref{topt}) \ref{HR}. \citep{butler2007, liang07}. \cite{vaughan06, liang07}) \citep{zhang06}, \citep{ghisellini07,ghisellini08}, \citep{eichler06, granot_konigl06}, \citep{mastichiadiskazanas09},"2622?).. (?).. (?) , \citep{shao07} 263"Galaxy clusters are a potentially very powerful probe of non-linear cosmological structure formation since their abundance and its evolution depends sensitively on the matter density, the normalisation of density fluctuations and the dark energy.","Galaxy clusters are a potentially very powerful probe of non-linear cosmological structure formation since their abundance and its evolution depends sensitively on the matter density, the normalisation of density fluctuations and the dark energy."264" Conventionally, theoretical predictions of the cluster population parametrise clusters by mass."," Conventionally, theoretical predictions of the cluster population parametrise clusters by mass."265" This is potentially problematic since mass is strictly not observable and an integral quantity which, for irregularly shaped bodies without well-defined boundary, is hard to define unambiguously."," This is potentially problematic since mass is strictly not observable and an integral quantity which, for irregularly shaped bodies without well-defined boundary, is hard to define unambiguously."266" Calibration relations are needed between the mass and observable quantities such as X-ray temperature and luminosity, which are themselves prone to systematic and random uncertainties."," Calibration relations are needed between the mass and observable quantities such as X-ray temperature and luminosity, which are themselves prone to systematic and random uncertainties."267 We have proposed a different approach avoiding any reference to mass (?).., We have proposed a different approach avoiding any reference to mass \citep{Angrick2009}.268" The X-ray temperature function of the cluster population, ttheir number-density distribution with X-ray temperature, can be theoretically predicted based on the statistics of gravitational-potential fluctuations."," The X-ray temperature function of the cluster population, their number-density distribution with X-ray temperature, can be theoretically predicted based on the statistics of gravitational-potential fluctuations."269 This procedure has several advantages., This procedure has several advantages.270" First, it parametrises the cluster population directly by their temperature, which is a locally defined observable tightly related to the potential depth."," First, it parametrises the cluster population directly by their temperature, which is a locally defined observable tightly related to the potential depth."271 Ambiguities caused by the integral definition of the mass are thus avoided., Ambiguities caused by the integral definition of the mass are thus avoided.272" Second, calibration relations for the mass are circumvented, thus removing their scatter from the uncertainty of any inferences (seealso?).."," Second, calibration relations for the mass are circumvented, thus removing their scatter from the uncertainty of any inferences \citep[see also][]{Lau2011}."273" Third, the gravitational potential evolves much less than the matter density, extending the range of validity of linear structure evolution."," Third, the gravitational potential evolves much less than the matter density, extending the range of validity of linear structure evolution."274 We have shown under which conditions this potential-based temperature function reproduces the theoretical predictions based on matter density and mass., We have shown under which conditions this potential-based temperature function reproduces the theoretical predictions based on matter density and mass.275" Here, we address two subsequent questions."," Here, we address two subsequent questions."276" First, we compare the potential-based temperature function to a gas-dynamical, numerical simulation."," First, we compare the potential-based temperature function to a gas-dynamical, numerical simulation."277" While we find agreement at low redshift, there is increasing disagreement towards moderate and higher redshifts."," While we find agreement at low redshift, there is increasing disagreement towards moderate and higher redshifts."278" This brings us to the development of an analytic model for the effect of cluster mergers on the X-ray temperature function, which leads to very good agreement of our theoretical predictions based on potential statistics with the numerical results."," This brings us to the development of an analytic model for the effect of cluster mergers on the X-ray temperature function, which leads to very good agreement of our theoretical predictions based on potential statistics with the numerical results."279 Our analytic model could be considered as providing an analytic complement to the numerical study by ?.., Our analytic model could be considered as providing an analytic complement to the numerical study by \citet{Randall2002}.280" Second, we use the potential-based temperature function including the merger model to infer the cosmological parameters O49 and σᾳ from two different samples of galaxy clusters."," Second, we use the potential-based temperature function including the merger model to infer the cosmological parameters $\Omega_\mathrm{m0}$ and $\sigma_8$ from two different samples of galaxy clusters."281" The results are not conclusive yet, mainly because of tension between observationally inferred temperatures and theoretically motivated temperature definitions, but we find reasonable values for both parameters provided we use a definition of an X-ray temperature function that seems appropriate for the comparison with observational data."," The results are not conclusive yet, mainly because of tension between observationally inferred temperatures and theoretically motivated temperature definitions, but we find reasonable values for both parameters provided we use a definition of an X-ray temperature function that seems appropriate for the comparison with observational data."282 The paper is structured as follows: We first review briefly in Sect., The paper is structured as follows: We first review briefly in Sect.283" 2 the derivation of the potential-based temperature function, extending it to include ellipsoidal rather than spherical collapse."," \ref{sec:tempFunc} the derivation of the potential-based temperature function, extending it to include ellipsoidal rather than spherical collapse."284We compare it to a gas-dynamical numerical simulation in Sect.,We compare it to a gas-dynamical numerical simulation in Sect.285 3 and develop the analytic model for merger effects in Sect. 4.., \ref{sec:simulation} and develop the analytic model for merger effects in Sect. \ref{sec:mergers}.286 The inference of cosmological parameters is described in Sect. 5.., The inference of cosmological parameters is described in Sect. \ref{sec:cosmoParam}.287" Its results are discussed in Sect. 6,,"," Its results are discussed in Sect. \ref{sec:results},"288 and we conclude with a summary in Sect. 7.., and we conclude with a summary in Sect. \ref{sec:summary}.289" In the following, we use the X-ray temperature function introduced by ? and an extension thereof based on the generalisation from spherical to ellipsoidal collapse."," In the following, we use the X-ray temperature function introduced by \citet{Angrick2009} and an extension thereof based on the generalisation from spherical to ellipsoidal collapse."290" Both approaches avoid any reference to the globally defined, strictly unobservablemass,, but are directly derived from the Gaussian statistics of cosmological potential fluctuations."," Both approaches avoid any reference to the globally defined, strictly unobservable, but are directly derived from the Gaussian statistics of cosmological potential fluctuations."291 We briefly sketch the main idea and the basic steps in the derivation of an X-ray temperature function for galaxy clusters that does not invoke cluster mass., We briefly sketch the main idea and the basic steps in the derivation of an X-ray temperature function for galaxy clusters that does not invoke cluster mass.292" It is based on the number density of minima of a homogeneous and isotropic Gaussian random field, discussed in great detail by ?.."," It is based on the number density of minima of a homogeneous and isotropic Gaussian random field, discussed in great detail by \citet{Bardeen1986}."293" For further detail on the derivation, we refer to ?.."," For further detail on the derivation, we refer to \citet{Angrick2009}."294 The differential number density of potential minima with depth between ® and ®+d is, The differential number density of potential minima with depth between $\Phi$ and $\Phi+\dd\Phi$ is295Hirsch et al.).,Hirsch et al.).296 The orbital velocity in this case may well be augmented by a kick due to an impulse from the supernova shock (e.g. Marietta et 22000)., The orbital velocity in this case may well be augmented by a kick due to an impulse from the supernova shock (e.g. Marietta et 2000).297 The evolution of the WD-sdB binary system KPD 193042752 (see. e.g.. Maxted. Marsh North 2000) has been investigated by Ergma. Fedorova Yungelson (2001).," The evolution of the WD–sdB binary system KPD 1930+2752 (see, e.g., Maxted, Marsh North 2000) has been investigated by Ergma, Fedorova Yungelson (2001)."298 They conclude that this system is likely to eventually result in a merger of two WDs (see also Geter et al., They conclude that this system is likely to eventually result in a merger of two WDs (see also Geier et al.299 2007)., 2007).300 However we see no reason why similar systems could not produce a SN la via a single-degenerate channel. hence producing such objects as US 708 and then LP 400-22.," However we see no reason why similar systems could not produce a SN Ia via a single-degenerate channel, hence producing such objects as US 708 and then LP 400-22."301 We have considered the formation. of apparently single LMWDs in general. concluding that the most natural scenario for the formation of single LMWDs ts that they are the remnants of donor stars in single-denenerate SNe Ia. Indeed. lone LMWDs should be 1f some single-degenerate SNe [a do occur with giant donor stars. as inferred from the observations of Patat et ((2007). notably if the donors lose a significant fraction of their envelopes. as predicted for giant donors (Marietta et 22000).," We have considered the formation of apparently single LMWDs in general, concluding that the most natural scenario for the formation of single LMWDs is that they are the remnants of donor stars in single-denenerate SNe Ia. Indeed, lone LMWDs should be if some single-degenerate SNe Ia do occur with giant donor stars, as inferred from the observations of Patat et (2007), notably if the donors lose a significant fraction of their envelopes, as predicted for giant donors (Marietta et 2000)."302 The observations of Maxted et ((2000). van Leeuwen et ((2006) and Kilie et (2006) are all in support of the existence of a population of genuinely single LMWDs.," The observations of Maxted et (2000), van Leeuwen et (2006) and Kilic et (2006) are all in support of the existence of a population of genuinely single LMWDs."303 It seems difheult for the najority of apparently single UCWDs to posess companions. and we have adopted them as a useful sample of single LMWDs.," It seems difficult for the majority of apparently single UCWDs to posess companions, and we have adopted them as a useful sample of single LMWDs."304 We have integrated a population of SN Ia donor remnants through a simple Galactic potential and compared the results of those calculations to the known space velocities of apparently single UCWDs., We have integrated a population of SN Ia donor remnants through a simple Galactic potential and compared the results of those calculations to the known space velocities of apparently single UCWDs.305 Our results are consistent with the single low-mass UCWDs having once been red-giant donor stars at the time of a SN la explosion. as predicted for single LMWDs.," Our results are consistent with the single low-mass UCWDs having once been red-giant donor stars at the time of a SN Ia explosion, as predicted for single LMWDs."306 A unified picture emerges in which the high-velocity WDs are remnants of main-sequence donors in SNe Ia (as suggested first by Hansen. 2003). and a kinematically cooler population of single LMWDs were once giant donors in long-period SN Ia progenitors: their longer orbital periods led to a lower runaway velocity wheras their tenuous envelopes were stripped more easily by the supernova ejecta to produce LMWDs.," A unified picture emerges in which the high-velocity WDs are remnants of main-sequence donors in SNe Ia (as suggested first by Hansen, 2003), and a kinematically cooler population of single LMWDs were once giant donors in long-period SN Ia progenitors: their longer orbital periods led to a lower runaway velocity wheras their tenuous envelopes were stripped more easily by the supernova ejecta to produce LMWDs."307 Furthermore. it seems plausible that runaway LMWDs such as LP 400-22 and runaway hot subdwarf stars such as US 708 originate from donor stars in short-period (~1 h) SN Ia systems.," Furthermore, it seems plausible that runaway LMWDs such as LP 400-22 and runaway hot subdwarf stars such as US 708 originate from donor stars in short-period $\rm \sim 1~h$ ) SN Ia systems."308 We will explore this idea in more detail in a future paper., We will explore this idea in more detail in a future paper.309 We thank Uli Heber for very interesting conversations and for bringing the issue of runaway hot subdwarfs to our attention., We thank Uli Heber for very interesting conversations and for bringing the issue of runaway hot subdwarfs to our attention.310 Questions from Marten van Kerkwik helped improve the clarity of our arguments. and we thank an anonymous referee for their useful comments.," Questions from Marten van Kerkwijk helped improve the clarity of our arguments, and we thank an anonymous referee for their useful comments."311 Discussions with the stellar group at Oxford were also useful., Discussions with the stellar group at Oxford were also useful.312 SJ] has been supported by PPARC grant PPA/G/S/2003/00056 Global Jet Watch. and CW by a PPARC Advanced Fellowship.," SJ has been supported by PPARC grant PPA/G/S/2003/00056 Global Jet Watch, and CW by a PPARC Advanced Fellowship."313 ZH visited Oxford thanks. in part. to a Royal Society UK-China Joint Project Grant (Ph.," ZH visited Oxford thanks, in part, to a Royal Society UK-China Joint Project Grant (Ph."314P. and Z.H.).,P. and Z.H.).315 This work was partly supported by the National Science. Foundation of China under Grant Nos., This work was partly supported by the National Science Foundation of China under Grant Nos.316 10521001. 10433030 and 2007CB815406 (Z.H.) and a European Research Training Network on Type la Supernovae (HPRN-CT-20002-00303).," 10521001, 10433030 and 2007CB815406 (Z.H.) and a European Research Training Network on Type Ia Supernovae (HPRN-CT-20002-00303)."317particles may be absent (Sorrell1990).,particles may be absent \citep{sorrell90}.318. The estimated time-scale of eraphitization varies rom few weeks for circumstellar grains (Ilecht.1986). to ~105 vears for interstellar grains (Sorrell1990)., The estimated time-scale of graphitization varies from few weeks for circumstellar grains \citep{hecht86} to $\sim10^8 $ years for interstellar grains \citep{sorrell90}.319. Nanodiamonds can result. from annealing of the carbonaceous material by UV radiation e.g. in 4upernova ejecta (Nuth&Allen1992)., Nanodiamonds can result from annealing of the carbonaceous material by UV radiation e.g. in Supernova ejecta \citep{nuth92}.320. Observations show that the ivdrogenated. nanocdiamond features arise in the inner regions close to (he central star. wing higher UV (ix (Gotoetal.2000:VanIxerkhoven2002).," Observations show that the hydrogenated nanodiamond features arise in the inner regions close to the central star, having higher UV flux \citep{goto09, kerckhoven02}."321. Surface energy studies show that small diamonds are more stable against thermal evaporation and chemical attack compared to graphite particles (Nuth1987)., Surface energy studies show that small diamonds are more stable against thermal evaporation and chemical attack compared to graphite particles \citep{nuth87}.322. Formation of nanodiamonds has been studied in laboratory giving insight to possible routes of their formation in ISA, Formation of nanodiamonds has been studied in laboratory giving insight to possible routes of their formation in ISM.323 Nanodiamond formation is seen (o result from carbon vapour deposition (CVD) (Ugarte1995:Andersenetal.1993).. detonation of carbon based explosives (lNruegeretal.2005).. electron. inradiation of eraphitic shells (carbon onions) (Banhart&Ajavan1996;Lietal.2008) and ion beam irradiation of amorphous carbon films (Sunetal.1999).," Nanodiamond formation is seen to result from carbon vapour deposition (CVD) \citep{ugarte95, andersen98}, detonation of carbon based explosives \citep{krueger05}, electron irradiation of graphitic shells (carbon onions) \citep{banhart96, li08} and ion beam irradiation of amorphous carbon films \citep{sun99}."324. IXouchietal.(2005) on the basis ILEIZM studies suggest that diamonds and graphite lew nanometre in size are lormed by nucleation in organic ice mixture subjected to UV photolvsis., \citet{kouchi05} on the basis HRTEM studies suggest that diamonds and graphite few nanometre in size are formed by nucleation in organic ice mixture subjected to UV photolysis.325 Structural rearrangement between diamond and graphite is also possible., Structural rearrangement between diamond and graphite is also possible.326 Graphite subjected to annealingirradiation may go to shelled onion like lorm (Ugarte1993) or Gransform into nanocdiamond (Zaiser&Banhart1997)., Graphite subjected to annealing/irradiation may go to shelled onion like form \citep{ugarte93} or transform into nanodiamond \citep{zaiser97}.327. Laboratory experiments also show that the sp*/sp? ratio changes bv different doses of UV radiation (Ogmen&Dulev1988:Duley&Williams 1995).," Laboratory experiments also show that the $sp^3/sp^2 $ ratio changes by different doses of UV radiation \citep{ogmen88, duley-williams95}."328. Chemical conversion of PAIL clusters to nanodiamonds is proposed bv Dulev&Grishko(20011., Chemical conversion of PAH clusters to nanodiamonds is proposed by \citet{duley-grishko01}.329 Partial eraphilization of nanodiamond due to heat (LeGuillow&Rouzaud2007) or pressure conditions (Dayvdovοἱal.2007) is suggested on the basis of some experimental studies., Partial graphitization of nanodiamond due to heat \citep{leguilou07} or pressure conditions \citep{davydov07} is suggested on the basis of some experimental studies.330 Theoretical analysis bv. Kwonetal.(2008) show that surface graphitization of nanodiamond under strong radiation field can lead to core-mantle like shell structure with upto eraphitization., Theoretical analysis by \citet{kwon08} show that surface graphitization of nanodiamond under strong radiation field can lead to core-mantle like shell structure with upto graphitization.331 Thus nanodiamonds are possible within ISM carbonaceous matter and would modify the optical properties of dust., Thus nanodiamonds are possible within ISM carbonaceous matter and would modify the optical properties of dust.332 Graphitic mantle will make the nanodiamond crystals chemically less active and hard to detect spectroscopically., Graphitic mantle will make the nanodiamond crystals chemically less active and hard to detect spectroscopically.333 To calculate the extinction. scattering. absorption ancl polarization elliciencies the Discrete Dipole Approximation (DDA) is used," To calculate the extinction, scattering, absorption and polarization efficiencies the Discrete Dipole Approximation (DDA) is used"334Elias 29 (16:27:09.4. —24:37:18.9) with a bolometric luminosity L=26—27.5Le (Bontempsetal..2001: etal.. 2006)) is the most luminous Class I YSO in the p-Oph cloud.,"Elias 29 (16:27:09.4, $-$ 24:37:18.9) with a bolometric luminosity $L =33526-27.5~L_{\sun}$ \citealp{bak+01}; \citealp{nts06}) ) is the most luminous Class I YSO in the $\rho$ -Oph cloud."336 Muzerolleetal.(1998) used the luminosity in the Bry line to determine the objects aceretion luminosity at Lace = 15-18Lo. which makes it the source with the highest accretion luminosity 1n their sample.," \cite{mhc98} used the luminosity in the $\gamma$ line to determine the object's accretion luminosity at $L_{\rm acc}$ = $15-18 L_{\sun}$, which makes it the source with the highest accretion luminosity in their sample."337 More recently. used the luminosity of the hydrogen recombination lines to derive an accretion luminosity of 28.8 Le.," More recently, used the luminosity of the hydrogen recombination lines to derive an accretion luminosity of 28.8 $L_{\sun}$."338 Using millimeter interferometric observations. Boogertal.(2002) resolved the emission from the disk and the envelope surrounding Elias 29. showing that the disk is in a relatively face-on orientation (j< 60°). which explains many of the remarkable observational features of this source. such as its flat spectral energy distribution. its brightness in the near-infrared. the extended components found in speckle," Using millimeter interferometric observations, \citet{bhc+02} resolved the emission from the disk and the envelope surrounding Elias 29, showing that the disk is in a relatively face-on orientation $i <33960^{\circ}$ ), which explains many of the remarkable observational features of this source, such as its flat spectral energy distribution, its brightness in the near-infrared, the extended components found in speckle"340widely than the Southern. and to investigate this further we calculate the X7. values for both hemispheres. for various { ranges.,"widely than the Southern, and to investigate this further we calculate the $\chi^2$ values for both hemispheres, for various $\ell$ ranges."341 In Table 3 we show the fraction of simulations that find lower x7 values. with our simulations also using a North pole at (57.10).," In Table \ref{NSchi} we show the fraction of simulations that find lower $\chi^2$ values, with our simulations also using a North pole at (57,10)."342 The WAAR Northern 47 values are consistently high. while the Southern are low.," The WMAP Northern $\chi^2$ values are consistently high, while the Southern are low."343 For / =2-100 the Southern is low at the level., For $\ell=$ 2-100 the Southern $\chi^2$ is low at the level.344 However. the significance of this asvmmetry is not seen in these individual values from the North and the South. but in the ratio of the two: the fact that one is low the other is high.," However, the significance of this asymmetry is not seen in these individual values from the North and the South, but in the ratio of the two: the fact that one is low the other is high."345 Therefore. in Table 3 we also recordthe fraction of simulations which find a lower ratio.: A2. AS Rm).," Therefore, in Table \ref{NSchi} we also record the fraction of simulations which find a lower ratio, $\frac{\chi^2_N}{\chi^2_S}$ $\frac{\chi^2_S}{\chi^2_N}$ )."346 Our 4? asymmetry appears significant at the level for a North pole at (57.10).," Our $I^3_\ell$ asymmetry appears significant at the level for a North pole at (57,10)."347 However. we must take account of our North pole selection as we may have pre-selected the North pole that maximises this asvmmetry while we have not done the same for the simulations.," However, we must take account of our North pole selection as we may have pre-selected the North pole that maximises this asymmetry while we have not done the same for the simulations."348 As before. we vary the North pole position for the WALAD and for the simulations through a further 53 positions that are uniformly distributed in the Northern galactic hemisphere (ancl infer the results for the positions on the Southern galactic hemisphere).," As before, we vary the North pole position for the WMAP and for the simulations through a further 53 positions that are uniformly distributed in the Northern galactic hemisphere (and infer the results for the positions on the Southern galactic hemisphere)."349 At every North pole position we caleulate xS/AZ. and AZAS. and for each simulation we record the maximun chi-squared ratio result from all these values.," At every North pole position we calculate $\chi^2_N/\chi^2_S$, and $\chi^2_S/\chi^2_N$, and for each simulation we record the maximum chi-squared ratio result from all these values."350 In. Table 4. we record the North pole positions which maximise the ratio for the WALAP data. and the fraction of simulations with lower nmiximunm ratio values.," In Table \ref{NSchi1} we record the North pole positions which maximise the ratio for the WMAP data, and the fraction of simulations with lower maximum ratio values."351 We visualise this in Fig. S.., We visualise this in Fig. \ref{mark-chi}.352 The significance of our asymmetry. detection in the single-£ bispectrum has weakened greatly now that we have taken a selection ellect into account., The significance of our asymmetry detection in the $\ell$ bispectrum has weakened greatly now that we have taken a selection effect into account.353 In fact the only hint of asymmetry that survives is at. a level of944.. for the range f£ =2-50 with North pole at (70.0).," In fact the only hint of asymmetry that survives is at a level of, for the range $\ell=$ 2-50 with North pole at (70,0)."354 This result is not significant enough to rule out. Caussianity., This result is not significant enough to rule out Gaussianity.355 In Fig., In Fig.356 S. we sec, \ref{mark-chi} we see357accretion disc.,accretion disc.358 The sublxeperian injected gas can be considered to impart a negative torque on an otherwise Ixeplerian disc. in addition to the tidal torque.," The subKeperian injected gas can be considered to impart a negative torque on an otherwise Keplerian disc, in addition to the tidal torque."359 On the other hand. if much of the inllowing gas Lows over the dise before becoming entrained w the disc. then the injection radius will be smaller than the disc outer radius. as in the cases plotted in Fig. 3..," On the other hand, if much of the inflowing gas flows over the disc before becoming entrained by the disc, then the injection radius will be smaller than the disc outer radius, as in the cases plotted in Fig. \ref{evolution}."360 Aevond the details of the Low properties in. particular models. the results suggest that the dise structure is generally arecly independent of the angular momentum per unit mass of the inflowing gas. as seen in Figs.," Beyond the details of the flow properties in particular models, the results suggest that the disc structure is generally largely independent of the angular momentum per unit mass of the inflowing gas, as seen in Figs."361 3. and 6.., \ref{evolution} and \ref{jc}.362 The disc density distribution is mildly influenced by this quantity., The disc density distribution is mildly influenced by this quantity.363 The racial derivative of the surface density undergoes order unity changes al ring., The radial derivative of the surface density undergoes order unity changes at $r_{\rm inj}$.364 In the model considered this section. the logarithmic surface density gradient changes from -1/2 to -1 across riy.," In the model considered this section, the logarithmic surface density gradient changes from -1/2 to -1 across $r_{\rm inj}$."365 Also. or a fixed mass injection rate. the density in the outer parts of the disc scales as rijPune.," Also, for a fixed mass injection rate, the density in the outer parts of the disc scales as $\sqrt{r_{\rm inj}/r_{\rm trunc}}$."366 Bul such variations do not ead to strong changes in disc structure by typically plausible values of ring20.05rg., But such variations do not lead to strong changes in disc structure by typically plausible values of $r_{\rm inj} > 0.05 r_{\rm H}$.367 This is particularly true if the injection radius is near the disc outer edge., This is particularly true if the injection radius is near the disc outer edge.368 Instead. the disc structure interior to the disc tidal truncation region is dominated by the elfects of disc turbulent viscosity.," Instead, the disc structure interior to the disc tidal truncation region is dominated by the effects of disc turbulent viscosity."369 To include the cflcets of gas pressure. we modeled the disc using a two-dimensional SPLL code with 10 particles.," To include the effects of gas pressure, we modeled the disc using a two-dimensional SPH code with $10^5$ particles."370 The SPL parameter oxpg was set to unity in these simulations. while tsp was set to zero.," The SPH parameter $\alpha_{\rm SPH}$ was set to unity in these simulations, while $\beta_{\rm SPH}$ was set to zero."371" Phe disc sound speed was erudely modeled as a constant equal to 0.3ji]at,—(439,rg throughout."," The disc sound speed was crudely modeled as a constant equal to $0.3\, \mu^{1/3} a \Omega_{\rm p}372=0.43\,\Omega_{\rm p} r_{\rm H} $ throughout."373 The dise aspect ratio was 4//r20.16 at /?=OARY (in dimensionless units of these equations Ry=3. 07). where [ree particle orbit. crossings occur.," The disc aspect ratio was $H/r \simeq 0.16$ at $R = 0.4 R_{\rm H}$ (in dimensionless units of these equations $R_{\rm H} = 3^{-1/3}$ ), where free particle orbit crossings occur."374 The Duid equations were taken in the Lill approximation. following the force equation (30)).," The fluid equations were taken in the Hill approximation, following the force equation \ref{origs}) )."375 The particles were initially distributed so that surface density was initially δη8)xl/H in an annulus fy«BRcRau.," The particles were initially distributed so that surface density was initially $\Sigma(r, \theta) \propto 1/R$ in an annulus $R_{\rm376 in}<R<R_{\rm out}$."377" We chose A,=0.074 and have two moclels. one with fag=0.3424 and the second with Row=0.6/g which we plot in Fig. 7.."," We chose $R_{\rm in}=0.07 R_{\rm H}$ and have two models, one with $R_{\rm out}= 0.3 R_{\rm H}$ and the second with $R_{\rm out}= 0.6 R_{\rm H}$ which we plot in Fig. \ref{initial}. ."378" Phe initial velocities were taken to be circular rotation having angular speed f(2.O,in the corotating frame. with O given by equation (24))."," The initial velocities were taken to be circular rotation having angular speed $\Omega - \Omega_{\rm p}$in the corotating frame, with $\Omega$ given by equation \ref{angvel}) )."379 Particles are removed from the simulation if they reach the inner boundary at /?=0.07724 or the outer boundary located at /?=0.86729., Particles are removed from the simulation if they reach the inner boundary at $R=0.07 R_{\rm H}$ or the outer boundary located at $R=0.86 R_{\rm H}$.380 For cach particle removed. a particle is injected at à random anele and random radius between 2=0.22/24 and 2=036/24.," For each particle removed, a particle is injected at a random angle and random radius between $R=0.22 R_{\rm H}$ and $R=0.36 R_{\rm H}$."381 Fherefore. the number of particles is lixed at LO” at all times.," Therefore, the number of particles is fixed at $10^5$ at all times."382 lig., Fig.383 8 plots the angular momentum evolution as a function of time for the two initial disc sizes., \ref{jevolution} plots the angular momentum evolution as a function of time for the two initial disc sizes.384 Lhe smaller disc starts with much less angular momentum than the larger one., The smaller disc starts with much less angular momentum than the larger one.385 But after only about 3 planetary orbits both disces have similar values of angular momentum and approach a steady state., But after only about 3 planetary orbits both discs have similar values of angular momentum and approach a steady state.386 In Fig., In Fig.387 9 we plot the particles at a time of 6 planet orbital periods., \ref{final} we plot the particles at a time of 6 planet orbital periods.388 We see that particle distributions look very similar and the disc has reached a near steady state., We see that particle distributions look very similar and the disc has reached a near steady state.389 Phe viscous timescale of the disc can be estimated as ~r»., The viscous timescale of the disc can be estimated as $\sim r^2/\nu$.390 In SPLL we have that à2O.loupg=0.1 (eg.Actvmowiez&Lubow1994).," In SPH, we have that $\alpha \simeq 0.1 \alpha_{\rm SPH} =0.1$ \citep[e.g.,][]{artymowicz94}."391.. Phe value of the kinematic viscosity £ is estimated as 0lospg(44/rc)r7 and the viscous timescale evaluates to about S orbits at Z?20.3729., The value of the kinematic viscosity $\nu$ is estimated as $0.1 \alpha_{\rm SPH} (H/r)^2 r^2 \Omega$ and the viscous timescale evaluates to about 8 orbits at $R \simeq 0.3 R_{\rm H}$.392 The simulated. disc has therefore settled to a near equilibrium state on a timescale that is of order the estimated: viscous timescale., The simulated disc has therefore settled to a near equilibrium state on a timescale that is of order the estimated viscous timescale.393 This kinematic viscosity is a factor of ten or more larger than what is tvpically taken taken in circumplanetary disc simulations (e.g.D'Xngeloetal.2002:Avlille&Date2009).," This kinematic viscosity is a factor of ten or more larger than what is typically taken taken in circumplanetary disc simulations \citep[e.g.,][]{dangelo02, ayliffe09}."394. Consequently. in those simulations. the timescales to reach a steady state are longer than the case here by similar factor. (," Consequently, in those simulations, the timescales to reach a steady state are longer than the case here by similar factor. ("395In addition. previous simulations have generally not started with a circumplanctary disc.,"In addition, previous simulations have generally not started with a circumplanetary disc."396 Some time is required for its formation from inllowing gas.), Some time is required for its formation from inflowing gas.)397 For the simulations in Machida(2009).. the timescale would be determined by the inherent. viscosity in the code due to the finite dillerencing. since no viscous ternis were included.," For the simulations in \cite{machida09}, the timescale would be determined by the inherent viscosity in the code due to the finite differencing, since no viscous terms were included."398 The phasing of the arms determines the sign of the gravitational torque in the dillerent regions of space as shown in Fie. 10.., The phasing of the arms determines the sign of the gravitational torque in the different regions of space as shown in Fig. \ref{phase}. .399 Phe left plot shows the cumulative gravitational torque as a function of radius in asteady state disc after 6 planetary, The left plot shows the cumulative gravitational torque as a function of radius in asteady state disc after 6 planetary400We have made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet. Propulsion Laboratory. California Institute of Technology. under the contract with the National Acronautics ancl Space Administration.,"We have made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under the contract with the National Aeronautics and Space Administration."401 “Vhis work was supported by the Russian Foundation for Basie Research (project. no., This work was supported by the Russian Foundation for Basic Research (project no.402 090-02-00870)., 09-02-00870).403 AVAL is also grateful to the Dynasty Foundation., AVM is also grateful to the Dynasty Foundation.404 VPR acknowledges support from the “Bourse de Ia Ville de Paris”., VPR acknowledges support from the “Bourse de la Ville de Paris”.405 We wish to thank Victor Afanasiev for his great contribution ο spectroscopy at the 62m telescope. Timur Fatkhullin for he help in observations in August 2010. Ido Finkelman. who oovided: us with a list of new polar-ring candidates before heir publication: and an anonymous referee for constructive advice. which has helped us to improve the paper.," We wish to thank Victor Afanasiev for his great contribution to spectroscopy at the 6-m telescope, Timur Fatkhullin for the help in observations in August 2010, Ido Finkelman, who provided us with a list of new polar-ring candidates before their publication; and an anonymous referee for constructive advice, which has helped us to improve the paper."406 Funding for the SDSS has been provided hy he Alfred. PL Sloan Foundation. the Participating Institutions. the National Science. Foundation. the U.S. Department of Energy. the National Acronautics and Space Administration. the Japanese Monbukagakusho. the Max [anck Society. and the Higher Education Funding Council or England.," Funding for the SDSS has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."407 Phe SDSS Web Site is httpi/www.scdss.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.408 The Participating Institutions are “Phe University of Chicago. Fermilab. the Lnstitute for. Acvanced Study. he Japan Participation Croup. The Johns Hopkins University. Los Alamos National Laboratory. the tanck-lnstitute for Astronomy (AIPLA). the Max-DPlanck-Institute for Astrophysics (AIPA). New Mexico. State University. University of Pittsburgh. Princeton. University. he United States Naval Observatory. and the University of Washington.," The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington."409 Many thanks also to the Galaxy Zoo (http://www.galaxvzoo.org) organizers ancl participants. especially the rine galaxies forum. group.," Many thanks also to the Galaxy Zoo (http://www.galaxyzoo.org) organizers and participants, especially the ring galaxies forum group."410 Galaxy Zoo has »en supported in part by a Jim Gray research. erant. [rom Microsoft. and by a grant from The Leverhulme Trust.," Galaxy Zoo has been supported in part by a Jim Gray research grant from Microsoft, and by a grant from The Leverhulme Trust."411"Thus, a gap opens slightly inside rx,out once M near the outer edge of the dead zone becomes less than My.","Thus, a gap opens slightly inside $r_{\rm X,out}$ once $\dot{M}$ near the outer edge of the dead zone becomes less than $\dot{M}_{\rm w}$."412" For run D1, a gap opens at 48 AU roughly when the outer dead zone disappears, because M of the outer dead is larger than M,, while M in the inner dead zone is comparable to My."," For run D1, a gap opens at 48 AU roughly when the outer dead zone disappears, because $\dot{M}$ of the outer dead is larger than $\dot{M}_{\rm w}$ while $\dot{M}$ in the inner dead zone is comparable to $\dot{M}_{\rm w}$."413" Since the inner dead zone survives for a long time, M. remains high even after a gap opens."," Since the inner dead zone survives for a long time, $\dot{M}_{*}$ remains high even after a gap opens."414" The outward mass flux from the dead zone remains to be ~My after a gap opens, as long as the dead zone exists."," The outward mass flux from the dead zone remains to be $\sim \dot{M}_{\rm w}$ after a gap opens, as long as the dead zone exists."415" Once the dead zone disappears, the inner disc quickly dissipates and mass accretion onto the central star is halted."," Once the dead zone disappears, the inner disc quickly dissipates and mass accretion onto the central star is halted."416 It is possible to retain a steady state mass accretion with a finite residual viscosity in the dead zone., It is possible to retain a steady state mass accretion with a finite residual viscosity in the dead zone.417" The condition to retain a radially constant M is given from Eqs (3)), (5)), and (6)) as If the radial profile of T' is given such as irradiated discs, the above condition is fulfilled when NagZNada so that the radial profile of © is adjusted."," The condition to retain a radially constant $\dot{M}$ is given from Eqs \ref{eq:mt}) ), \ref{eq:nu}) ), and \ref{eq:ald}) ) as If the radial profile of $T$ is given such as irradiated discs, the above condition is fulfilled when $\Sigma\alpha_{\rm d} \ga \Sigma_{\rm a}\alpha_{\rm a}$ so that the radial profile of $\Sigma$ is adjusted."418" On the other hand, if viscous heating is the dominant heat source, the midplane temperature is given from Eqs. (5)), (6)), (9)), (10))"," On the other hand, if viscous heating is the dominant heat source, the midplane temperature is given from Eqs. \ref{eq:nu}) ), \ref{eq:ald}) ), \ref{eq:tveff}) ), \ref{eq:tvis}) )"419" as Thus, if X?o4>Daa, radial profiles of T and X are mutually adjusted so that theM can be independent of r."," as Thus, if $\Sigma^2\alpha_{\rm d} \ga \Sigma_{\rm a}^{2}\alpha_{\rm a} $, the radial profiles of $T$ and $\Sigma$ are mutually adjusted so that $\dot{M}$ can be independent of $r$ ."420 Figure 3 shows an example of evolution of a disc with aa=107? (run D6)., Figure 3 shows an example of evolution of a disc with $\alpha_{\rm d} = 10^{-5}$ (run D6).421" Since this case satisfies the condition X?oq>X2o,, M becomes almost independent of r (see the orange line at 2.0 Myr in Fig."," Since this case satisfies the condition $\Sigma^2\alpha_{\rm d} \ga \Sigma_{\rm a}^{2}\alpha_{\rm a} $, $\dot{M}$ becomes almost independent of $r$ (see the orange line at 2.0 Myr in Fig."422 3)., 3).423 Split into multiple dead zones is also suppressed., Split into multiple dead zones is also suppressed.424" As well as the cases with aa=0, a gap opens at a radius outside the dead zone."," As well as the cases with $\alpha_{\rm d} = 0$ , a gap opens at a radius outside the dead zone."425" Figure 4 shows the radial location of a gap rgap for various values of ag, Xcn, and Lx."," Figure 4 shows the radial location of a gap $r_{\rm gap}$ for various values of $\alpha_{\rm d}$, $\Sigma_{\rm CR}$, and $L_{\rm X}$ ."426 We define rgap as a radius where X becomes zero in the earliest time while ©>0 in outer radii., We define $r_{\rm gap}$ as a radius where $\Sigma$ becomes zero in the earliest time while $\Sigma > 0$ in outer radii.427" If M is independent of r in the dead zone region, the condition for gap opening is given by My>M,."," If $\dot{M}$ is independent of $r$ in the dead zone region, the condition for gap opening is given by $\dot{M}_{\rm w} \ga \dot{M}_{*}$."428" For small values of aq and “cr, M, can be smaller than My even when a dead zone exists."," For small values of $\alpha_{\rm d}$ and $\Sigma_{\rm CR}$, $ \dot{M}_{*}$ can be smaller than $\dot{M}_{\rm w}$ even when a dead zone exists."429" Thus, a gap opens beyond a dead zone in such a case."," Thus, a gap opens beyond a dead zone in such a case."430" On the other hand, for a case with large oa and cr, a gap opens at a small radius only after a dead zone disappears and M, becomes sufficiently small, as well as the cases with radially constant a’s shown in Section 3.1."," On the other hand, for a case with large $\alpha_{\rm d}$ and $\Sigma_{\rm CR}$ , a gap opens at a small radius only after a dead zone disappears and $\dot{M}_{*}$ becomes sufficiently small, as well as the cases with radially constant $\alpha$ 's shown in Section 3.1."431" Not surprisingly, gap opening beyond dead zones is possible even with large values of aq and Xon if My (or Lx) is large."," Not surprisingly, gap opening beyond dead zones is possible even with large values of $\alpha_{\rm d}$ and $\Sigma_{\rm CR}$ if $\dot{M}_{\rm w}$ (or $L_{\rm X}$ ) is large."432 Figure 5 shows comparison between observed transition discs and discs from our simulations., Figure 5 shows comparison between observed transition discs and discs from our simulations.433 In the upper panel of Fig., In the upper panel of Fig.434" 5, gap sizes and mass accretion rates are plotted."," 5, gap sizes and mass accretion rates are plotted."435" For simulations, we use rgap and the mass accretion rate onto the central star M.καρ at the time of gap opening (see Table 4)."," For simulations, we use $r_{\rm gap}$ and the mass accretion rate onto the central star $\dot{M}_{*, {\rm gap}}$ at the time of gap opening (see Table 4)."436 Subsequent evolution curves are also shown., Subsequent evolution curves are also shown.437" As can be seen, large gap (or hole) sizes and large accretion rates seen in observed transition discs are well reproduced in models with dead zones."," As can be seen, large gap (or hole) sizes and large accretion rates seen in observed transition discs are well reproduced in models with dead zones."438" On the other hand, models without dead zones are able to reproduce only discs with small mass accretion rates and small gap sizes."," On the other hand, models without dead zones are able to reproduce only discs with small mass accretion rates and small gap sizes."439" In runs N3 and N6, a gap opens at ~ 60 AU, butthe mass accretion rate is small(in these runs, another gapopens at ~ 1AU, and the disk outside the outergap quickly dissipates)."," In runs N3 and N6, a gap opens at $\sim$ 60 AU, butthe mass accretion rate is small(in these runs, another gapopens at $\sim$ 1AU, and the disk outside the outergap quickly dissipates)."440 In the lower panel of Fig., In the lower panel of Fig.441" 5, we compare between"," 5, we compare between"442we ciscuss the nature of the dvuameo driving the sustained turbulence. aud iu refeone we sunmnuuuize our conclusions.,"we discuss the nature of the dynamo driving the sustained turbulence, and in \\ref{conc} we summarize our conclusions."443 We use Athena (Cardiner&Stone2005.2008:etal.2008) for all caleulatious presented im this work.," We use Athena \citep{gs05,gs08,sto08} for all calculations presented in this work."444 We perform 3d MITID. simulations. adopting the local shearing box formalism and including vertical gravity.," We perform 3d MHD simulations, adopting the local shearing box formalism and including vertical gravity."445 We vefer the reader to Stone Carcdiner (2009) for a detailed discussion of the equations. algorithius. aud boundary coucitious specific to the shearing box. as well axa description of their implementation in Athena.," We refer the reader to Stone Gardiner (2009) for a detailed discussion of the equations, algorithms, and boundary conditions specific to the shearing box, as well as a description of their implementation in Athena."446 Were we just sununuize the basic equations aud the most relevaut features for our current work., Here we just summarize the basic equations and the most relevant features for our current work.447 The local shearing box approximation adopts a frame of reference located at a fiducial radius corotatiug with the disk at orbital frequency O., The local shearing box approximation adopts a frame of reference located at a fiducial radius corotating with the disk at orbital frequency $\Omega$.448 In this frame. the equations of ideal MIID are written in a Cartesian coordinate gvsten (e.g.2) that has unit vectors (2.3.Kk) as where T is the total stress tensor | is the identity matrix. p ds the gas deusitv. p is the eas pressure. B is the magnetic Bell. v is the velocity aud B-D=B-B.," In this frame, the equations of ideal MHD are written in a Cartesian coordinate system $(x,y,z)$ that has unit vectors $({\hat{\bm i}}, {\hat{\bm j}}, {\hat{\bm k}})$ as where ${\sf T}$ is the total stress tensor ${\sf I}$ is the identity matrix, $\rho$ is the gas density, $p$ is the gas pressure, ${\bm B}$ is the magnetic field, ${\bm v}$ is the velocity and $B^{2} = {\bm B} \cdot {\bm B}$."449 Thed shear parameter q is. definedd as so that for Keplerian flow g=3/2., The shear parameter $q$ is defined as so that for Keplerian flow $q=3/2$.450 We adopt an isothermal equation of state with p—cp., We adopt an isothermal equation of state with $p=c_{\rm s}^2 \rho$.451 Ins we also present simulations which Ποπιάο terms for constant scalar viscosity aud resistivity., In \\ref{dissip} we also present simulations which include terms for constant scalar viscosity and resistivity.452" The viscous term is VM with — v.) |. and the resistive te1ids Wo.GV.«B) when added to the richt-haud side of (2)) and (3)). respectively,"," The viscous term is ${\bm \nabla453 \cdot} {\sf M}$ with = - ), and the resistive term is $-{\bm \nabla} \times (\eta {\bm454 \nabla}\times{\bm B})$ when added to the right-hand side of \ref{eq:cons_momentum}) ) and \ref{eq:induction}) ), respectively."455 These sets of equatious adiit the well know solution corresponding to Cinearized) uniforii orbital motion w= qQOvj. which is used for the initial condition.," These sets of equations admit the well know solution corresponding to (linearized) uniform orbital motion = x, which is used for the initial condition."456" The initial equilibriuu density configuration is Gaussian with rlio, 3.410) where ο the scale height of the disk."," The initial equilibrium density configuration is Gaussian with _0 ), where $H=\sqrt{2} c_s/\Omega$ is the scale height of the disk."457" For consistency with previous work (Stonectal.1996).. we ake Q=107, e=5«I0.*. and py=L. yielding py—5«10* and FH—1."," For consistency with previous work \citep{sto96}, we take $\Omega=10^{-3}$, $c_s=5 \times 10^{-7}$, and $\rho_0=1$, yielding $p_0=5 \times 10^{-7}$ and $H=1$."458" All sinmlations are initialized o have a weak maenuetic field with a ratio of midplane gas pressive to imaguetie pressure 3}=2p,/507?100.", All simulations are initialized to have a weak magnetic field with a ratio of midplane gas pressure to magnetic pressure $\beta=2 P_0/B^2 =100$.459 The configuration is a vertical field with zero net magnetic flux that varies sinusoidally in the racial direction., The configuration is a vertical field with zero net magnetic flux that varies sinusoidally in the radial direction.460 We adopt boundary coucditions which are shearing oxdodie in ss and periodic in both y aud :.," We adopt boundary conditions which are shearing periodic in $x$, and periodic in both $y$ and $z$."461 Clearly. he periodic assumption du : is plysically unrealistic in a stratified box.," Clearly, the periodic assumption in $z$ is physically unrealistic in a stratified box."462 Of course. one advantage of this assunption is computational expediency. but the main notivation is to give us some level of control over the evolution of maeuetic flux in the simulation domain.," Of course, one advantage of this assumption is computational expediency, but the main motivation is to give us some level of `control' over the evolution of magnetic flux in the simulation domain."463 Vertically periodic boundary conditions are useful iu that he mean (volume averaged) toroidal field is conserved (ic. remains zero}., Vertically periodic boundary conditions are useful in that the mean (volume averaged) toroidal field is conserved (i.e. remains zero).464 Outflow boundary couditious will recessarily introduce electromotive forces (ΕΛΙΕΣ) at he vertical boundary which can drive growth of non-zero (By)., Outflow boundary conditions will necessarily introduce electromotive forces (EMFs) at the vertical boundary which can drive growth of non-zero $\langle B_y\rangle$.465 Such inca field evolution is plausible iu real disks. but we worry about spurious erowth in (By) due to the manner in which outflow boundary conditions are implemented.," Such mean field evolution is plausible in real disks, but we worry about spurious growth in $\langle B_y\rangle$ due to the manner in which outflow boundary conditions are implemented."466 These consideratious are Huportant because the presence of mean azimuthal field mnmav enhance or sustain turbulence (Tawleyetal. 1995)., These considerations are important because the presence of mean azimuthal field may enhance or sustain turbulence \citep{hgb95}.467 Since one of our primary goals ds to exanune the robustuess of MBRI turbulence iu stratified disks. this prescription. which prevents the erow of a (box integrated) mean field. represcuts a conservative approach.," Since one of our primary goals is to examine the robustness of MRI turbulence in stratified disks, this prescription, which prevents the grow of a (box integrated) mean field, represents a conservative approach."468 All sinulatious make use of Athena’s orbital advection scheme (Stone Gardiner. 2009). allowing us to consider domains with large radial extent.," All simulations make use of Athena's orbital advection scheme (Stone Gardiner, 2009), allowing us to consider domains with large radial extent."469 Orbital advection schemes (Masset2000:Jolsonetal.2008) take advantage of the fact that Equations (1-3)) can be split into two systems. one of which correspouds to near advection operator with velocity ej and another with ouly involves the fluctuations óe=eοκ.," Orbital advection schemes \citep{mas00,jgg08} take advantage of the fact that Equations \ref{eq:cons_mass}- \ref{eq:induction}) ) can be split into two systems, one of which corresponds to linear advection operator with velocity ${\bm v}_K$ and another with only involves the fluctuations $\delta470{\bm v}={\bm v}-{\bm v}_K$."471 The inteeration of linear advection operator is very simple and not subject to a Couraut-Erxiedricl-Lewy (CFL) condition., The integration of linear advection operator is very simple and not subject to a Courant-Friedrich-Lewy (CFL) condition.472 Since de«wy near the boundaries. the CFL condition in the second svstenà is much less restrictive than iu standard algorithms. particularly for comains with large radial extent.," Since $\delta {\bm v} \ll {\bm v}_K$ near the boundaries, the CFL condition in the second system is much less restrictive than in standard algorithms, particularly for domains with large radial extent."473 It also has the advantage of removing the systematic variation of truucation error introduced by the shear. which cau lead to spurious effects (Johnsonetal.2008).," It also has the advantage of removing the systematic variation of truncation error introduced by the shear, which can lead to spurious effects \citep{jgg08}."474. We utilize a nuuber of diagnostic tools to analyze the simulation output. iucludiug Fourier analysis.," We utilize a number of diagnostic tools to analyze the simulation output, including Fourier analysis."475 This is straightforward in a periodic domain. but in a shearing periodic system. the basis fuuctions are shearing waves with a time dependent wavevector.," This is straightforward in a periodic domain, but in a shearing periodic system, the basis functions are shearing waves with a time dependent wavevector."476 This complication can be haudled with simple rcmappines before aud after Fourier transforming. as outlined in Wawleyetal.(1995).," This complication can be handled with simple remappings before and after Fourier transforming, as outlined in \citet{hgb95}."477 The quantities of principal interest will be the power density spectra (PSDs) of the magnetic and kinetic energies., The quantities of principal interest will be the power density spectra (PSDs) of the magnetic and kinetic energies.478 Although the PSD is highly anisotropic in A- we still iud it useful to plot shell averaged Fourier amplitudes.," Although the PSD is highly anisotropic in $k$ -space, we still find it useful to plot shell averaged Fourier amplitudes."479 For example. we define the shell averaged power spectrum of the magnetic field as 7m beh? μα”...," For example, we define the shell averaged power spectrum of the magnetic field as B^2_k k^2 (k)|^2,"480Long-baseline optical interferometry promises high precision astrometry using modest eround-based instruments.,Long-baseline optical interferometry promises high precision astrometry using modest ground-based instruments.481 In. particular the Mark III Stellar Interferometer (Shao1983) and Navy Prototype Optical Interferometer (NPOL Armstrong et al. 1998))," In particular the Mark III Stellar Interferometer \citep{shao88} and Navy Prototype Optical Interferometer (NPOI, Armstrong et al. \nocite{arm98}) )"482 have achieved global astrometric precision al the 10 mas (1 mas = 10 arcseconds) level (Ihumineletal.1994).. while the Palomar Testbed Interferometer (PTI. Colavita et al.," have achieved global astrometric precision at the 10 mas (1 mas = $10^{-3}$ arcseconds) level \citep{hum94}, while the Palomar Testbed Interferometer (PTI, Colavita et al."483 ) hasdemonstrated an astrometric precision of LOO µας (Lys = LO° areseconds) between moclerately close (30 aresecond) pairs of bright stus (Shao&Colavila1992:1994: 2000)..," \nocite{col99} ) hasdemonstrated an astrometric precision of 100 $\mu$ as $1 \mu$ as = $10^{-6}$ arcseconds) between moderately close (30 arcsecond) pairs of bright stars \citep{shao92,col94,l00}. ."484 While interferometiric aud astrometric methods have proven very. uselul, While interferometric and astrometric methods have proven very useful485Moving to simulations that operate al globular cluster number densities will make it possible to look for orbital migration in small-period planetary. svstems.,Moving to simulations that operate at globular cluster number densities will make it possible to look for orbital migration in small-period planetary systems.486 Hence this study will have implications for future planet searches in globular clusters. especially if hot Jupiter planetary svstems cannot form directly in such an environment.," Hence this study will have implications for future planet searches in globular clusters, especially if hot Jupiter planetary systems cannot form directly in such an environment."487 We are extremely grateful to Jun Makino and the University of Tokvo for the loan of the GRAPE-G board., We are extremely grateful to Jun Makino and the University of Tokyo for the loan of the GRAPE-6 board.488 We thank David Zurek. Shigeru Ida and Rosemary Mardling for helpful discussions.," We thank David Zurek, Shigeru Ida and Rosemary Mardling for helpful discussions."489flick bouudaries. the rate of increase of the energv of the fiuid is ==k,"fluid boundaries, the rate of increase of the energy of the fluid is = =."490"r- Ehe quantities inwupa/2.mw,EA/2 may bo regarded as the enerevox density Do!aud the non ‘acvected enereyo flux associated with the forcing."," The quantities $ m\omega_p \rho_A/2 , m\omega_p {\bf F_A}/2$ may be regarded as the energy density and the non advected energy flux associated with the forcing."491° Iu ]particular when the forcing. source SA ds. localised iu. space. the rate of. change of. orbital. euergv ds. associated. with. a couserved enerev flux propagating. away to large distances⋅ from. the protoplauct.," In particular when the forcing source ${\bf S_A}$ is localised in space, the rate of change of orbital energy is associated with a conserved energy flux propagating away to large distances from the protoplanet."492 The total effect of the protoplauct is obtained by «πας the independent coutributious from differeut in. When the unperturbed coufguration is axisvnuuetric andthe perturbingpotential 9 depends ou νο aud ἕ inthe colubination οφ. the energy fluxes couvert to fluxes of the angular momentum component along the svummetry axis by dividing by the pattern speed.," The total effect of the protoplanet is obtained by summing the independent contributions from different $m.$ When the unperturbed configuration is axisymmetric andthe perturbingpotential $\Phi'$ depends on $\varphi$ and $t$ in the combination $ \omega_p t -\varphi,$ the energy fluxes convert to fluxes of the angular momentum component along the symmetry axis by dividing by the pattern speed."493" Thentorque acting on the ean be written — LIE,uhthetotal—pukτε..When.Eb fluidas for the characteristic situations cousidered here. the wave fluxes produce au enerev and angular momentum loss from the svstem. the orbit: decays or dE,HEmdEguufdt<0. We comment that the fact that the οποιον changes in the orbit can be measured through cucrey fluxes at distant: boundaries∙ eeneralises∙ a corresponding. result for; lyvdvodvuaiic disk forcing (see Papaloizou Terquem 2006) to the general MIID case."," Then the total torque acting on the fluid can be written as ${\cal T} = d J_{fluid}/ dt =\omega_p^{-1} dE_{fluid}/dt.$ When, as for the situations considered here, the wave fluxes produce an energy and angular momentum loss from the system, the orbit decays or $dE_{orb}/dt = -dE_{fluid}/dt < 0.$ We comment that the fact that the energy changes in the orbit can be measured through energy fluxes at distant boundaries generalises a corresponding result for hydrodynamic disk forcing (see Papaloizou Terquem 2006) to the general MHD case."494 In particular if there are no excited waves or advected disturbances. there are no induced changes to the orbit.," In particular if there are no excited waves or advected disturbances, there are no induced changes to the orbit."495" The scaling of the rate of eucrev change given by must the physical parameters of the problemi can be hound quite generally,"," The scaling of the rate of energy change given by equation \ref{bint}) ), that was obtained from the local analysis, with the physical parameters of the problem can be obtained quite generally."496" The leugth scale appropriate aeererion to the maguetosphere and the orbit- is. expeced to be The muit of time is O,!. aud the pattern speed is expected. to be uy,)~Q.. SEESgivingo a characteristic] relative velocity. ryQ.. Thisde velocity: would be expected to he characteristic of both the fow velocity along field lines and the relative velocity between the orbiting protoplauet and the magnetosphere."," The length scale appropriate to the magnetosphere and the orbit is expeced to be $r_0.$ The unit of time is $\Omega_*^{-1},$ and the pattern speed is expected to be $\omega_p \sim \Omega_* ,$ giving a characteristic relative velocity $r_0\Omega_*.$ This velocity would be expected to be characteristic of both the flow velocity along field lines and the relative velocity between the orbiting protoplanet and the magnetosphere."497" For a characteristic density iu the neighbourhood of the protoplanet. p. we fud natural scaliues from equations (7. - 11)) aud (31)) for the response displacement aud torque such that €Xro9M,/M. aud TxpGM,(Q254). Thus we write =ΓΕ FplGAgyr2 ου.d«σαE, f includes dependence on softeniug or the siall scale cut off as well as the existence of propagating waves."," For a characteristic density in the neighbourhood of the protoplanet, $\rho,$ we find natural scalings from equations \ref{Lagp} - \ref{indp}) ) and \ref{AEM}) ) for the response displacement and torque such that $\boldxi \propto r_0 M_p/M_*$ and ${\cal T} \propto \rho (GM_p)^2/(\Omega_*^2 r_0).$ Thus we write = (GM_p)^2/ _*^2 where $f$ includes dependence on softening or the small scale cut off as well as the existence of propagating waves."498" is equivalent το quation (25)) if f=liry§lshlGuohinin)D(vΌως) From equation. (32)) a characteristic⋅⋅ rate of. evolution. of. protoplanet in. circular. orbit. at radius. rj, cam be estimated. from. = |~""E For the maguctically dominated region (sec eg."," This is equivalent to quation \ref{bint}) ) if $f = 4\pi r_0\Omega_*^2 499 \ln\left ({k_{max}/ k_{min}}\right){\cal D}/(|{\bf v-U}|\omega_p )$ From equation \ref{TN2}) ) a characteristic rate of evolution of protoplanet in circular orbit at radius $r_{orb}$ can be estimated from = | - For the magnetically dominated region (see eg."500 Douvier et al., Bouvier et al.501" 2006) we set p=Ar(LarpO). Then for AL.=LAL...AL,=10PALrapO.5ry eivine a location slightly iuterior to the 2:1 conunenusurabilitv with © aud a characteristic accretion rate for a protostellar disk AL=3<LOSALoy+ e.g. Muzerolle et al."," 2006) we set $\rho = {\dot M}/(4\pi r_0^3\Omega_*).$ Then for $M_* = 1M_{\odot}, M_p = 10^{-3}M_*, r_{orb} =0.5 r_0 $ giving a location slightly interior to the 2:1 commensurability with $\Omega_*,$ and a characteristic accretion rate for a protostellar disk ${\dot M} = 3\times 10^{-8}M_{\odot} y^{-1}$ ( e.g. Muzerolle et al."502 2003. ). we obtain fj4~2«10Hy. Thus the expected evolution of sucha protoplanet orbit is expected to be very small over a protostellar∙∙ disk lifetimeGEM ~ LO'y.≓−∙Note too Gr that this result is not chaneed if the orbital decay. ra5 is| Chhanced by a factor. f£)—50. correspondiug. to use of. equationon (253) with. D=1 correspondiusgcorresponcdiug to effectiveffective wavewax propagation. |v||.U]=(r9Q.)/2 aud ονρα~100. Tt also indicates that no additional mechanism. such as special torques acting near the imuer disk edge (Masset et ὲal.," 2003 ), we obtain $t_{orb} \sim 2\times 10^{11} y.$ Thus the expected evolution of such a protoplanet orbit is expected to be very small over a characteristic protostellar disk lifetime $\sim 10^{7} y.$ Note too that this result is not changed if the orbital decay rate is enhanced by a factor $f\sim 50,$ corresponding to use of equation \ref{bint}) ) with ${\cal D} =1$ corresponding to effective wave propagation, $|{\bf v-U}| = (r_0\Omega_*)/2$ and $k_{max}/ k_{min}\sim 100.$ It also indicates that no additional mechanism, such as special torques acting near the inner disk edge (Masset et al."503 2006) is needed to halt the inward mieration of pro eiut plancts., 2006) is needed to halt the inward migration of proto giant planets.504 It inv also be argued that the expected accretion outo the ]protoplanetps is neglieible while it is iuside the magnetosphere., It may also be argued that the expected accretion onto the protoplanet is negligible while it is inside the magnetosphere.505 Iu order that accretion can take place an amount of energv comparable to the orbital binding be dissipated in⋅⋅ order⋅ for material⋅ to⋂≀∏↙↕↾↕↭∐≼⋟⋟∏↓↙↕↾∖⋯∖⊲⋔↾↙↕⋯⋂∐⋯⋯↾↕↕⋠∖↕⊲≽≼↙↕↕⋠↕↕↕⋠↕↕↖∖↕⊴∙↸∖∐↸∖↥⋅∶↴∙⊾⋅↖⇁ become with the protoplanet., In order that accretion can take place an amount of energy comparable to the orbital binding energy must be dissipated in order for material to become bound to the protoplanet.506" Thus LE estimate of the obtained ovate onto The protoplauet is given bi - AM,----- which ∙∙iuplicsLuv that the accretion. time. scale is. the same ἃas that .for orbital. evoevolution.", Thus an estimate of the accretion rate onto the protoplanet is given by M_p which implies that the accretion time scale is the same as that for orbital evolution.507ou. We here consider other effects that may lead to orbital decay of the protoplanet., We here consider other effects that may lead to orbital decay of the protoplanet.508 First we derive an effective drag cocficicnt characterising the ανασα friction acting through the gravitational torques calculated above., First we derive an effective drag coefficient characterising the dynamical friction acting through the gravitational torques calculated above.509" To do this we write _ -CpsRp|U,2 C Landau Lifshitz 1903). where the expression is applied locally and Cp is the drag cocfficicut."," To do this we write = R_p^2 ( Landau Lifshitz 1993), where the expression is applied locally and $C_D$ is the drag coefficient."510" f Adopting r/R,=200. we find that tho larger estimate of £4, given above corresponds to Cp0.1 while the smaller estimate"," f Adopting $r_0/R_p = 200,$ we find that the larger estimate of $t_{orb}$ given above corresponds to $C_D \sim 0.1$ while the smaller estimate"511channels for the formation of κά] stars considered by Han et C(20C22. 2003) objects which resemble Le-rich πο stars.,"channels for the formation of sdB stars considered by Han et (2002, 2003) objects which resemble He-rich sdO stars."512" ‘This subset of sdO stars ""cannot. be explained with nonien single star evolutionary models? (Strocer et 22007).", This subset of sdO stars `cannot be explained with canonical single star evolutionary models' (Stroeer et 2007).513D. Xn extension of this model could include mergers of He W with other low-mass CO WDs: however. massive sdD stars which leave remnants resembling normal-mass CO WDs probably do not produce Lle-sdOs (see Saio Jelfery 2002).," An extension of this model could include mergers of He WDs with other low-mass CO WDs; however, massive sdB stars which leave remnants resembling normal-mass CO WDs probably do not produce He-sdOs (see Saio Jeffery 2002)."514 Le-sclOs produced: by this scenario have relatively high luminositites compared to sd stars. which may help to distinguish between this ancl alternative scenarios. (c.g. Salo Jelfery 2000: Miller Bertolami et 22008).," He-sdOs produced by this scenario have relatively high luminositites compared to sdB stars, which may help to distinguish between this and alternative scenarios (e.g. Saio Jeffery 2000; Miller Bertolami et 2008)."515 More speculatively. we have also argued that svstenis containing two hot subchwarls(ος. DG 1544]488. Ahmad eb Y): LE 0301-3039. Lisker et 22004) could [orm me double-core/| comamon-envelope evolution.," More speculatively, we have also argued that systems containing two hot subdwarfs (e.g., PG 1544+488, Ahmad et 2004; HE 0301-3039, Lisker et 2004) could form through double-core common-envelope evolution."516 This generally requires. that the subdwarfs have| similar masses and favours intermediate-niass progenitors., This generally requires that the subdwarfs have similar masses and favours intermediate-mass progenitors.517 Since intermediate-mass giants have a rather cdillerent. chemical profile. this may also naturally explain why hot κανατς in these svstems are preferentially Le-rich.," Since intermediate-mass giants have a rather different chemical profile, this may also naturally explain why hot subdwarfs in these systems are preferentially He-rich."518 We thank the participants at the Bamberg Shanghai Lot) Subdwarl conferences. for. enjovable discussions. in particular Stephan Ceier. Uli Heber. Simon Jellery. Cjs Nelemans Rov Ostensen.," We thank the participants at the Bamberg Shanghai Hot Subdwarf conferences for enjoyable discussions, in particular Stephan Geier, Uli Heber, Simon Jeffery, Gijs Nelemans Roy stensen."519 We also thank Simon Jelferv as the referee: his insightful comments helped improve this work., We also thank Simon Jeffery as the referee; his insightful comments helped improve this work.520 SJ has been partially supported. by PPARC erant DDPA/OG/S/2003/00056. China National Postdoc Fund Grant 220090450005 and the National Science. Foundation of China Grants 1109501122 and 10903001.," SJ has been partially supported by PPARC grant PPA/G/S/2003/00056, China National Postdoc Fund Grant 20090450005 and the National Science Foundation of China Grants 10950110322 and 10903001."521 111 is supported. by theNatural Science Foundation of China under Grant 110821061 and the Chinese Academy. of Sciences under Grant IXIxJCXN2-YW-T24., ZH is supported by the Natural Science Foundation of China under Grant 10821061 and the Chinese Academy of Sciences under Grant KJCX2-YW-T24.522 Some of this research was done during the IKEEP programme “Formation and Evolution of Globular Clusters’. and so was partially supported by the National Science Foundation under Grant No.," Some of this research was done during the KITP programme `Formation and Evolution of Globular Clusters', and so was partially supported by the National Science Foundation under Grant No."523 NSE PIIYO5-51164., NSF PHY05-51164.524accretion rate is independeut of τι and is given simply by Tn particulary. at the sublimation radius given by equation (1)) this accretion rate is equal to = (Ry)= (254) (9) ~T vies:oT. 17.,"accretion rate is independent of $\tau_\parallel$ and is given simply by 1)= In particular, at the sublimation radius given by equation \ref{eq:R_S}) ) this accretion rate is equal to = (R_s)= ( )^2 10^7 )^2."52510) R11 has shown this uunerical estimate to be cousisteut with the lower euvelope of the Mz values interred for the metalrich WDs exhibiting detectable IR ciission associated with their debris disks., R11 has shown this numerical estimate to be consistent with the lower envelope of the $\dot M_Z$ values inferred for the metal-rich WDs exhibiting detectable IR emission associated with their debris disks.526 Iu the opposite lint of a disk. which is optically thin to incident stellar radiation. τεςI. oue fluids Tt is easv to show that this expression coincides with A that one would calculate bv ΝΗΣΙ assunüug disk particles to be directly ilhuninated by starlight (i.c. unobscired by other particles) aud considerimg cach of them as independent from others.," In the opposite limit of a disk, which is optically thin to incident stellar radiation, $\tau_{\parallel} \ll 1$, one finds = It is easy to show that this expression coincides with $\dot M$ that one would calculate by simply assuming disk particles to be directly illuminated by starlight (i.e. unobscured by other particles) and considering each of them as independent from others."527 Azimuthal PR drag force acting on a single. perfectly absorbing particle of luass np=(lz3)pa? 1s Given by where O4 is dxeplerian angular velocity.," Azimuthal PR drag force acting on a single, perfectly absorbing particle of mass $m=(4\pi/3)\rho a^3$ is given by = a^2 where $\Omega_K$ is Keplerian angular velocity."528" This force eives rise to radial dift velocity M—— auc results in mass aceretion rate M=2zr0,X. which is casily shown to reduce to equation (11))."," This force gives rise to radial drift velocity v_r == and results in mass accretion rate $\dot M=2\pi r v_r\Sigma$, which is easily shown to reduce to equation \ref{eq:mdot_de}) )."529 Evolution of the debris disk is described bw the coutiuuitv equation ü with AL given by equation (5)).," Evolution of the debris disk is described by the continuity equation - = 0, with $\dot M$ given by equation \ref{eq:mdot}) )."530 We introduce new dimensionless time aud space variables LI where 0 is the characteristic timescale of the problem., We introduce new dimensionless time and space variables x T where t_0 is the characteristic timescale of the problem.531" If R5, coincides with the sublimation radius P, defined im (1)) then ,ποστ =- zh5.10! . where we took p—HN ο om "," If $R_{in}$ coincides with the sublimation radius $R_s$ defined in \ref{eq:R_S}) ) then t_0 = 5 10^4, where we took $\rho = 3$ g $^{-3}$."532Using equations (3))-(6)) and definitious (15)). (16) we can bring the continuity equation (11)) to a scale-free fori: ( jt.," Using equations \ref{eq:alpha}) \ref{eq:phi}) ) and definitions \ref{eq:dim}) ), \ref{eq:t_0}) ) we can bring the continuity equation \ref{eq:cont}) ) to a scale-free form: - ( ) = 0."533 A notable fact about equation (18)) is that it does not contain any free parameters., A notable fact about equation \ref{eq:1}) ) is that it does not contain any free parameters.534 Once τις.T) is obtained by solving this equation. oue can casily infer mass accretion rate at any point iu the disk slice where Af. is) defined by equation (9)).," Once $\tpar(x,T)$ is obtained by solving this equation, one can easily infer mass accretion rate at any point in the disk since M(x,T) where $\dot M_{\infty}$ is defined by equation \ref{eq:mdot_PR}) )."535 Because the viscous timescale of the eas produced by debris sublimation is very short compared to the disk evolution time (RIL). the metal accretion rate onto the WD surface Afy is eiven simply bx right].," Because the viscous timescale of the gas produced by debris sublimation is very short compared to the disk evolution time (R11), the metal accretion rate onto the WD surface $\dot M_Z$ is given simply by ]."536 Iu the following we will use Az(T) aud Mv=1.7) interchanginely.," In the following we will use $\dot M_Z(T)$ and $\dot M(x=1,T)$ interchangingly."537 Analysis of equation (18)) may be simplified if we introduce a new function yor2)—AfterT)/M4=(Looe7) fe. which is just the mass accretion rate through the debris disk normalized by M4.," Analysis of equation \ref{eq:1}) ) may be simplified if we introduce a new function $y(x,T)\equiv 538\dot M(x,T)/\dot M_{\infty}=\left(1-e^{-\tau_\parallel}\right)/x$ , which is just the mass accretion rate through the debris disk normalized by $\dot M_{\infty}$ ."539 Then equation (18)) transforms to | (uy —}j— --υ., Then equation \ref{eq:1}) ) transforms to + ( y - ) = 0.540 It has an implicit solution y= fry wl| lathsy).," It has an implicit solution y = f(xy - y^2 T + (1-xy)),"541"in which (he compact star of mass M, moves around a Be star of mass M, and radius. A, in an orbit of eecentricity ο, exerting resonant torques 744, on the Be decretion disk.","in which the compact star of mass $\Mx$ moves around a Be star of mass $M_{\ast}$ and radius $R_{\ast}$ in an orbit of eccentricity $e$ , exerting resonant torques $\Tres$ on the Be decretion disk."542 As first approximation. (he disc is assumed to be coplanner.," As first approximation, the disc is assumed to be coplanner."543" The criterion for the dise truncation al agiven resonance radius ο 15 where Z4, can be easily shown to be dominated by the torque of the inner Lindblad resonance Ti,7$5(Tuin"," The criterion for the disc truncation at agiven resonance radius $\rtrunc$ is where $\Tres$ can be easily shown to be dominated by the torque of the inner Lindblad resonance $\Tres\simeq \sum_{ml}(\Tml)_{\rm544ILR}$."545" For neur-INeplerian discs. given the expression of viscosity and resonance toreues as Eqs.(G) and (8) in Negueruela&Okazaki(2001).. the above truncation criterion can be approximated as where the radius of the inner Lindblad resonance is r=(an—1)//)?7(14-qu).|a. 0 is the Shakura-Sunvaev viscosity parameter. à is (he semmimajor axis of the binary orbit. aud (qs,=άνΑν."," For near-Keplerian discs, given the expression of viscosity and resonance torques as Eqs.(6) and (8) in \citet{neg01}, the above truncation criterion can be approximated as where the radius of the inner Lindblad resonance is $r=((m-1)/l)^{2/3}(1+\qx)^{-1/3}a$, $\alpha$ is the Shakura-Sunyaev viscosity parameter, $a$ is the semmimajor axis of the binary orbit, and $\qx\equiv \Mx/M_{\ast}$."546 The Reynolds number fe is determined by (he thermal structure of the disk., The Reynolds number $Re$ is determined by the thermal structure of the disk.547" In our calculation. an isothermal dise with e,/Vi(GR)~4.1ΜΜ ds assumed as in Okazaki&Negueruela(2001).. where c, is the sound. speed of the disk. Vi is the Keplerian velocity. ancl the disk temperature 74 is about. 1/2 of the effective temperature Tay of the Be star."," In our calculation, an isothermal disc with $\cs/\vk(R_{\ast})\sim5484.1\times 10^{-2}(\Td/\Teff)^{1/2}$ is assumed as in \citet{oka01}, where $\cs$ is the sound speed of the disk, $\vk$ is the Keplerian velocity, and the disk temperature $\Td$ is about $1/2$ of the effective temperature $\Teff$ of the Be star."549" For a Weplerian disk. the scale height // of the disk is then We adopt R,/R.z(M,/M.)""? to get the corresponding radius of the donor star."," For a Keplerian disk, the scale height $H$ of the disk is then We adopt $R_{\ast}/R_{\sun}\approx (M_{\ast}/M_{\sun})^{0.8}$ to get the corresponding radius of the donor star."550" The Κον [function in the criterion (2)) is the potential component ὤμῃ. which can be expressed as ""AME is the Laplace coefficient with argument©= r/ro. and rs=a(l—e7)/(1+ecos()) is the distance of the compact star from the donor star."," The key function in the criterion \ref{alpha}) ) is the potential component $\phiml$, which can be expressed as where is the Laplace coefficient with argument$x=r/r_2$ , and $r_2=a(1-e^2)/(1+e\cos (f))$ is the distance of the compact star from the donor star."551 To make it convenient to solve the, To make it convenient to solve the552The time delay of light. also known as the Shapiro effect. is one of the observational cornerstones of general relativity.,"The time delay of light, also known as the Shapiro effect, is one of the observational cornerstones of general relativity."553" For a light ray passing; a body of mass m, at location x,. and received by an observer at Xj. (he excess delay is given by. (modulo a constant)"," For a light ray passing a body of mass $m_a$ at location ${\bf x}_a$, and received by an observer at ${\bf x}_r$, the excess delay is given by (modulo a constant)"554Let (7.9) be the position of the lens relative to the source in units of the Einstein ring.,"Let $(\tau,\beta)$ be the position of the lens relative to the source in units of the Einstein ring."555 Explicitly. where ἐν ds the Einstein crossing (me. and vy is Che lens-source separation at /y.," Explicitly, where $t_\e$ is the Einstein crossing time, and $u_0$ is the lens-source separation at $t_0$."556" More explicitly. (07.09)=[s,(E)ggvSU)Ep.δρπιο+5-(jaa]."," More explicitly, $(\delta\tau,\delta\beta)=557[s_n(t)\pi_{\e,N} + s_e(t)\pi_{\e,E},- s_n(t)\pi_{\e,E} + s_e(t)\pi_{\e,N}]$."558 I define (7.9) to be also handed. so that if 45>0 then the lens is passing the source on ils right as seen [rom the Earth.," I define $(\tau,\beta)$ to be also right-handed, so that if $u_0>0$ then the lens is passing the source on its right as seen from the Earth."559" These equations serve to define (he ""vector microlens parallax” πι=(πιv.8i). whose magnitude zj=πι gives the projected size of the Einstein ring. ὃν=ΑΙ.πμ. and whose direction gives the direction of the lens relative to (he source as seen in the adopted frame."," These equations serve to define the “vector microlens parallax” $\bpi_\e = (\pi_{\e,N},\pi_{\e,E})$, whose magnitude $\pi_\e = |\bpi_\e|$ gives the projected size of the Einstein ring, $\tilde r_\e = {\rm AU}/\pi_\e$, and whose direction gives the direction of the lens relative to the source as seen in the adopted frame."560 That is. at /=fy. d(r.3)/dl=(1.0)/le.," That is, at $t=t_p$, $d(\tau,\beta)/dt=(1,0)/t_\e$."561" So if the lens is going due north ime=(s.0)].the parallax deviation (07.02)=(54.5,)5j. while if it is going due east. (07.09)=(s,.—s,)ape. which. since both (τ.ο) and (5,.5.) ave right-handed. are (he proper behaviors."," So if the lens is going due north $[\bpi_\e = (\pi_{\e,N},0)]$,the parallax deviation $(\delta\tau,\delta\beta)=(s_n,s_e)\pi_\e$, while if it is going due east, $(\delta\tau,\delta\beta)=(s_e,-s_n)\pi_\e$, which, since both $(\tau,\beta)$ and $(s_n,s_e)$ are right-handed, are the proper behaviors."562 There are several advantages (ο using these variables., There are several advantages to using these variables.563 Most significantly. when (he event is fit including the parallax effect. the parameters fy. uy. ancl fy. will come out to be very similar (o their values when it is fit. without parallax.," Most significantly, when the event is fit including the parallax effect, the parameters $t_0$, $u_0$, and $t_\e$, will come out to be very similar to their values when it is fit without parallax."564 That is. these parameters are given directly by the data ancl do not depend on Che parallax model.," That is, these parameters are given directly by the data and do not depend on the parallax model."565 This can be very important [ου cases In which the parallax is not strongly. constrained., This can be very important for cases in which the parallax is not strongly constrained.566 In such cases. the trajectory relative to the Sun will also not be well constrained. so tlie errors in fy. uy. and {ἐς in the heliocentric frame will be huge.," In such cases, the trajectory relative to the Sun will also not be well constrained, so the errors in $t_0$, $u_0$, and $t_\e$ in the heliocentric frame will be huge."567 But these errors will also be extremely correlated. since whatever values one adopts. thev must conspire to produce exactly the right peak amplitude at exactly the right (ime. ancl passing al exactly the right rate as seen from the Earth.," But these errors will also be extremely correlated, since whatever values one adopts, they must conspire to produce exactly the right peak amplitude at exactly the right time, and passing at exactly the right rate as seen from the Earth."568 The downside is (hat ab the end of the day. one must still convert to heliocentric coordinates in order to extract some of (he parameters.," The downside is that at the end of the day, one must still convert to heliocentric coordinates in order to extract some of the parameters."569 However. it is actually better to perlorm (his step separately so as to be able to understand the various sources of uncertaintv in the final measurement.," However, it is actually better to perform this step separately so as to be able to understand the various sources of uncertainty in the final measurement."570 Also. note that I am fitting& lor πι.[b rather than rp[b=AU/apFE or vzm(Pe/lkg)tmpe/my).afasπ," Also, note that I am fitting for $\bpi_\e$ rather than $\tilde r_\e\equiv \au/\pi_\e$ or $\tilde \bv\equiv(\tilde r_\e/\tilde t_\e)(\bpi_\e/\pi_\e)$."571"ι, As with (trigonometric parallaxes. microlens parallaxes are much better behaved than their inverse quantiües. parlicularly when (Πεν are near zero."," As with trigonometric parallaxes, microlens parallaxes are much better behaved than their inverse quantities, particularly when they are near zero."572 See also Gould (2000).., See also \citet{natural}. .573 I begin with the data set obtained from the MACIIO web site (http://www.macho.memaster.ca)., I begin with the data set obtained from the MACHO web site (http://www.macho.mcmaster.ca).574current total ass of SC stars still iu clusters. Leeree.,"current total mass of SG stars still in clusters, $M_{SG,GCS}^{now}$."575 A systematic observational sticky of SCO stars in Galactic globular clusters is still lacking. aud will require sieuificaut effort.," A systematic observational study of SG stars in Galactic globular clusters is still lacking, and will require significant effort."576 Currently the only study. affording au estimate of the fraction of SCO stars in a significant uunber of Galactic clusters. as well as exploration of possible trends of the SC. fraction with other cluster properties. is the spectroscopic survey of ~2000 stars iu 19 Galactic elobular clusters carried out by Carretta (2009a.).," Currently the only study affording an estimate of the fraction of SG stars in a significant number of Galactic clusters, as well as exploration of possible trends of the SG fraction with other cluster properties, is the spectroscopic survey of $\sim2000$ stars in 19 Galactic globular clusters carried out by Carretta (2009a,b)."577 They fined that all clusters studied host SC stars. and that the fraction of individual cluster masses in SC stars ranges from about to more than.," They find that all clusters studied host SG stars, and that the fraction of individual cluster masses in SG stars ranges from about to more than."578. ence we define the current cluster SCC ass fraction Peerpopes by where Ale 24107ALL is the current total mass of halo Galactic globular clusters (assmuiug M/L=2: Mackey van den Bergh 2005).," Hence we define the current cluster SG mass fraction $\fsgcse$ by where $M_{GCS}^{now}\sim 2\times57910^{7} M_{\odot}$ is the current total mass of halo Galactic globular clusters (assuming $M/L=2$; Mackey van den Bergh 2005)."580 Most of the clusters studied are more massive than ~LAL. and it is nof known whether such a huge SC fraction is conunon to all Galactic elobular clusters or onlv to those currently more massive than some threshold.," Most of the clusters studied are more massive than $\sim 10^5581M_{\odot}$, and it is not known whether such a large SG fraction is common to all Galactic globular clusters or only to those currently more massive than some threshold."582 For purposes of this Letter we simply assume as a reference value FAeuzm0.5., For purposes of this Letter we simply assume as a reference value $\fsgcse \simeq 0.5$.583 Results for diticreut values of Fee cu bo very casily derived from those shown iu this Letter., Results for different values of $\fsgcse$ can be very easily derived from those shown in this Letter.584 To complete our calculation we need an estimate of Agi. the initial total mass of all stars in globular clusters.," To complete our calculation we need an estimate of $M_{GCS}^{init}$, the initial total mass of all stars in globular clusters."585 This is not easily determined from observations of the current Galactic globular cluster system., This is not easily determined from observations of the current Galactic globular cluster system.586 Here again. we simplyparaiuctrize the normalization of refequusgü or 1. bw defining the parameter @= Where we take Aj=109AZ... (seo ce. Freeman Blaud-Uawthorn 2002).," Here again, we simplyparametrize the normalization of \\ref{eq:msg0} or \ref{eq:msg2} by defining the parameter $\phihalo=M_{GCS}^{init}/M_{halo}$ where we take $M_{halo}=10^9587M_{\odot}$ (see e.g. Freeman Bland-Hawthorn 2002)."588" The current fraction of SG stars in the stellar halo. ο. then is Finally. if we define j as the ratio of the total initial lass of SC stars iu the Galactic globular cluster system to the total tuitial mass of the cluster svstem aud use the definition of PaceGey ta refequusguow aloug with the values of Mp4, and ALEC adopted above. we can rewrite rofeqifsg as The form of refeqifsgb allows to casily ddentiv the differcut theoretical aud observational iugredients needed for the determination of faci μ. We sunuuiaize them here."," The current fraction of SG stars in the stellar halo, $\fsge$, then is Finally, if we define $\eta$ as the ratio of the total initial mass of SG stars in the Galactic globular cluster system to the total initial mass of the cluster system and use the definition of $\fsgcse$ in \\ref{eq:msgnow} along with the values of $M_{halo}$ and $M_{GCS}^{now}$ adopted above, we can rewrite \\ref{eq:fsg} as The form of \\ref{eq:fsgb} allows to easily identify the different theoretical and observational ingredients needed for the determination of $\fsge$ We summarize them here."589 Tn reffig:fsel we show the depeudence of jj ou the power- index o of the IGCAIF., In \\ref{fig:fsg1} we show the dependence of $\eta$ on the power-law index $\alpha$ of the IGCMF.590" Differeut lines correspond to different pairs of values of Ry, aud FR. a I&93 or à IKOL IME and differeut values for tlhe of the IGC'ME (Aer and Mii: Ay, is fixed parametersat 105AM)."," Different lines correspond to different pairs of values of $R_h$ and $R$, a K93 or a K01 IMF and different values for the parameters of the IGCMF $M_C$ and $M_{low}$; $M_{up}$ is fixed at $10^7~M_{\odot}$ )."591 Comparison of the results for models with differeut values of R shows no siguificant differences., Comparison of the results for models with different values of $R$ shows no significant differences.592" An increase in Ave) and/or Mj, imereases the fraction of the total initial mass in clusters massive chough to Ότι SG stars (M21058107: κος Fie. 1))."," An increase in $M_C$ and/or $M_{low}$ increases the fraction of the total initial mass in clusters massive enough to form SG stars $M\simgt 10^{4.8}-10^{5}$; see Fig. \ref{fig:hydrofig}) ),"593 and heuce increases jj., and hence increases $\eta$.594" Similarly. as a decreases the fraction of total nass dn luassive clusters increases, aud so does j."," Similarly, as $\alpha$ decreases the fraction of total mass in massive clusters increases, and so does $\eta$."595" For a fixed value of AR. decreasing the value of Ry, adopted has the obvious cousequence of increasing the action of AGB cjecta retained aud the amount of SC stars formed iu lower-mass clusters."," For a fixed value of $R$, decreasing the value of $R_h$ adopted has the obvious consequence of increasing the fraction of AGB ejecta retained and the amount of SG stars formed in lower-mass clusters."596 The absolute upper lait Cpa.20.08 for a W983 TTF and jiu&4.125 for a νο IME) would be attained by assuming Quurealistically) that all clusters Gucluding the low-mass ones) were compact enough at the time of SC formation (0545100 Myr) to retain all the ACB ejecta and reach a fraction of SCC stars formed ©20.08 or &20.125 for a IW93 and a νο IMPE respectively., The absolute upper limit $\eta_{max} \simeq 0.08$ for a K93 IMF and $\eta_{max} \simeq 0.125$ for a K01 IMF) would be attained by assuming (unrealistically) that all clusters (including the low-mass ones) were compact enough at the time of SG formation $30\simlt t \simlt 100$ Myr) to retain all the AGB ejecta and reach a fraction of SG stars formed $\xi\simeq 0.08$ or $\xi\simeq 0.125$ for a K93 and a K01 IMF respectively.597" From the results shown in Fig.2 one can casily calculate as a function of 9 aud for any of the combinations of IGCMPE, cluster structura parameters aud IAIF explored."," From the results shown in \ref{fig:fsg1} one can easily calculate as a function of $\phihalo$ and for any of the combinations of IGCMF, cluster structural parameters and IMF explored."598" For example. refiie:tse2.. shows the dependence of ou @& for a power-law IGCMPE with a=L8. for various values of Misa RoR, and for either a I&93 or a IWOL IME. (αμα. as discussed above. we have adopted Feeeg= 0.5)."," For example, \\ref{fig:fsg2}, shows the dependence of on $\phihalo$ for a power-law IGCMF with $\alpha=1.8$, for various values of $M_{low}$, $R$, $R_h$ and for either a K93 or a K01 IMF (and, as discussed above, we have adopted $\fsgcse=0.5$ )."599" If clusters were at the time of SC formation (30242100 Abvr) amore compact than assumed here. the lines of vs ® would fall between those shown in vefiie:tse2 aud that correspondiug to the absolute upper Iit casily obtained using Eq.9 and the maxi value Of Cina,&0.08 for a 893 INE and Εν20.125 for a ΟΙ IMF).Figs."," If clusters were at the time of SG formation $30\simlt t \simlt 100$ Myr) more compact than assumed here, the lines of vs $\phihalo$ would fall between those shown in \\ref{fig:fsg2} and that corresponding to the absolute upper limit easily obtained using \ref{eq:fsgb} and the maximum value of $\eta$ $\eta_{max}\simeq 0.08$ for a K93 IMF and $\eta_{max}\simeq 0.125$ for a K01 IMF).Figs."600 2 and 3 demonstrate that. for the broad rauge of values of the ICCAIF parameters considered. the predicted fraction of SC stars iu the halo is always sinall. fsca<|6% for a K93 IME aud fscaOT9( for a OL IME .," \ref{fig:fsg1} and \ref{fig:fsg2} demonstrate that, for the broad range of values of the IGCMF parameters considered, the predicted fraction of SG stars in the halo is always small, $\fsge<4-6\%$ for a K93 IMF and $\fsge<7-9\%$ for a K01 IMF ."601 This result is consistent with the simall fraction (~1.5-2.5% )) of halo stars ideutified as SC stars, This result is consistent with the small fraction $\sim$ ) of halo stars identified as SG stars602emission area.,emission area.603" This higher excitation zone is centered on star ,11145 but cut by the dust lane.", This higher excitation zone is centered on star 1145 but cut by the dust lane.604" The eastern lobe has a smaller mean value of ,33.5 and rises to ,33.8 toward the north-eastern part of the lobe.", The eastern lobe has a smaller mean value of 3.5 and rises to 3.8 toward the north-eastern part of the lobe.605" Although it was known that Sk-71°51 is not a single star but a compact cluster (?),, its attributed luminosity was based on low-resolution observations obtained using a 61 cm telescope with an aperture in size (?).."," Although it was known that $-71^{\circ}51$ is not a single star but a compact cluster \citep{garmany87}, its attributed luminosity was based on low-resolution observations obtained using a 61 cm telescope with an aperture in size \citep{isser75}."606" Apart from the fact that Sk-71°51 is a tight cluster, the presence of a relatively bright star ,99), detached from the main cluster but possibly present in the aperture, leads to an overstimation of the magnitude."," Apart from the fact that $-71^{\circ}51$ is a tight cluster, the presence of a relatively bright star 9), detached from the main cluster but possibly present in the aperture, leads to an overstimation of the magnitude."607" The result of the image restoration by deconvolution, as explained in Sect."," The result of the image restoration by deconvolution, as explained in Sect."608" 2.2, for a 256? pixels field, corresponding to 21"".8? on the sky, centered on -71?51, is presented in reffig:deconvolution and listed in reftab:deconvolution which also gives the astrometry and photometry of the stars."," 2.2, for a $^{2}$ pixels field, corresponding to $^{2}$ on the sky, centered on $-71^{\circ}51$ , is presented in \\ref{fig:deconvolution} and listed in \\ref{tab:deconvolution}609 which also gives the astrometry and photometry of the stars."610" The tight core of the Sk-71°51 cluster, covering a area, is made up of at least 6 components, stars ,117, 14, 21, 19, 13, and 12."," The tight core of the $-71^{\circ}51$ cluster, covering a area, is made up of at least 6 components, stars 17, 14, 21, 19, 13, and 12."611" The brightest component, ,117 with V=12.85, B-V= —0.15, and V-R=—0.06 mag, is separated by from the second brightest star, ,114 with V=16.60, B-V=—0.09, and V-R=—0.06 mag."," The brightest component, 17 with $V=12.85$, $B-V=-0.15$ , and $V-R=-0.06$ mag, is separated by from the second brightest star, 14 with $V=16.60$, $B-V=-0.09$, and $V-R=-0.06$ mag."612" Interestingly, the V and B—V magnitudes for star agree well with ?’’s results."," Interestingly, the $V$ and $B-V$ magnitudes for star agree well with \citet{oey}' 's results."613" We notice that the present higher resolution data reduce the brightness of -71°51 by 0.14 mag with respect to (2):: V=12.71, B-V=-0.09, U-B=--Ι.00 mag."," We notice that the present higher resolution data reduce the brightness of $-71^{\circ}51$ by 0.14 mag with respect to \citep{isser75}: : $V=12.71$, $B-V=-0.09$, $U-B=-1.00$ mag."614" The stars for which the spectroscopy was obtained are indicated in reffig:schema,, while the spectrograms are displayed in and 10.."," The stars for which the spectroscopy was obtained are indicated in \\ref{fig:schema}, while the spectrograms are displayed in \\ref{fig:otypes} and \ref{fig:btypes}."615" The spectral classification was performed without knowledge of the stellar identifications or locations, with reference to the criteria and atlas of ?.."," The spectral classification was performed without knowledge of the stellar identifications or locations, with reference to the criteria and atlas of \citet{wal-fitz}."616 The results are summarized in reftab:classification which also gives the corresponding photometric and astrometric information., The results are summarized in \\ref{tab:classification} which also gives the corresponding photometric and astrometric information.617 In the following some details of the two most interesting cases are given., In the following some details of the two most interesting cases are given.618 Star #117 isthe brightest component of the Sk-71°51 cluster reftab:deconvolution)).The spectral classification of -71?51 has changed severaltimes as a function of the quality of the, Star 17 isthe brightest component of the $-71^{\circ}51$ cluster \\ref{tab:deconvolution}) ).The spectral classification of $-71^{\circ}51$ has changed severaltimes as a function of the quality of the619be driven to high e values and v~0.,be driven to high $e$ values and $\nu\simeq 0$.620" Starting from a population of planetesimals with negligible eccentricities, we end up after a certain delay with many highly eccentric planetesimals with their lines of apsides more or less aligned with that of the planet y50."," Starting from a population of planetesimals with negligible eccentricities, we end up after a certain delay with many highly eccentric planetesimals with their lines of apsides more or less aligned with that of the planet $\nu\simeq 0$."621" This naturally generates a clump of planetesimals close to the apoastron of their orbits, as due to Kepler's second law, the planetesimals spend most of their time near apoastron."," This naturally generates a clump of planetesimals close to the apoastron of their orbits, as due to Kepler's second law, the planetesimals spend most of their time near apoastron."622 This is the origin of the clumps we obtain in our simulations with low-mass planets (Fig. 9))., This is the origin of the clumps we obtain in our simulations with low-mass planets (Fig. \ref{nonResonantStructure}) ).623" So, why does this not hold for more massive planets?"," So, why does this not hold for more massive planets?"624 The secular dynamics described above is valid as long as the planetesimal does not undergo any close encounter with the planet., The secular dynamics described above is valid as long as the planetesimal does not undergo any close encounter with the planet.625" In the case of a close encounter, the orbit of the planetesimal is suddenly changed, and it is often ejected."," In the case of a close encounter, the orbit of the planetesimal is suddenly changed, and it is often ejected."626 Many regions in Fig., Many regions in Fig.627 8 correspond to a planet crossing orbit., \ref{hsec} correspond to a planet crossing orbit.628 The probability of having a close encounter with the planet within a given timespan is higher if the planet is more massive., The probability of having a close encounter with the planet within a given timespan is higher if the planet is more massive.629" It scales as m3, because the Hill radius ry of the planet scales as mj3, and the encounter cross-section is expected to scale as rh."," It scales as $m_p^{2/3}$, because the Hill radius $r_\mathrm{H}$ of the planet scales as $m_p^{1/3}$, and the encounter cross-section is expected to scale as $r_\mathrm{H}^2$."630 The mass ratio between a 3 Jupiter mass planet and an Earth-sized planet is ~1000.," The mass ratio between a $3$ Jupiter mass planet and an Earth-sized planet is $\sim 1\,000$."631 We thus expect a planetesimal to undergo 100 times more encounters with the first planet than with the second., We thus expect a planetesimal to undergo $100$ times more encounters with the first planet than with the second.632" Finally, with massive planets, most of the planetesimals are subject to a close encounter with the planet"," Finally, with massive planets, most of the planetesimals are subject to a close encounter with the planet"633Lastly. in relsect:Discussion.. we analvze our results. and compare aud contrast the information obtned from polarization studies to that from phase-resolvecl spectroscopy.,"Lastly, in \\ref{sect:Discussion}, we analyze our results, and compare and contrast the information obtained from polarization studies to that from phase-resolved spectroscopy."634" In (he canonical pulsar model. (he magnetospheres of highlv magnetized NSs contain tenuous plasma whose density is approximated by the Goldreich-Julian formula. no;=f[D/(ce)x * where fy=f/(1Iz) and By,=DB/(10!G) are the NS rotation frequency and magnetic field strength (e.e..?).."," In the canonical pulsar model, the magnetospheres of highly magnetized NSs contain tenuous plasma whose density is approximated by the Goldreich-Julian formula, $n_{\rm GJ} = f B/(c e) \approx 6.9\times 10^{12} f_1 B_{14} \mbox{ cm}^{-3}$ , where $f_1=f/(\mbox{1 Hz})$ and $B_{14} = B/(10^{14}\mbox{ G})$ are the NS rotation frequency and magnetic field strength \citep[e.g.,][]{ShapiroTeukolsky86a}."635 The magnetar model contains a more complicated magnetic field süiructure compared to the standard dipole case., The magnetar model contains a more complicated magnetic field structure compared to the standard dipole case.636 The presence ol twisted magnetic fields (e.g.. due to erustal motion and magnetic reconfiguration) leads {ο significant magnetospheric currents. which can. in principle. maintain electron-positron densities (hat are orders of magnitude larger (han ne) (e.g..?)..," The presence of twisted magnetic fields (e.g., due to crustal motion and magnetic reconfiguration) leads to significant magnetospheric currents, which can, in principle, maintain electron-positron densities that are orders of magnitude larger than $n_{\rm GJ}$ \citep[e.g.,][]{Thompsonetal02a}."637 This suggests the possibility that resonant evclotron. scattering in the magnetosphere distorts some of the radiation emerging from the NS surface. producing a NT component al energies £~1—10 keV. Alodeling (his emission requires sophisticated scattering calculations Chat depend on the maenelic geomet(ryv and magnetosphere structure: sienilicant progress has been mace in several recent works (??7)..," This suggests the possibility that resonant cyclotron scattering in the magnetosphere distorts some of the radiation emerging from the NS surface, producing a NT component at energies $E\sim 1-10$ keV. Modeling this emission requires sophisticated scattering calculations that depend on the magnetic geometry and magnetosphere structure; significant progress has been made in several recent works \citep[][]{LyutikovGavriil06a,FernandezThompson07a,Reaetal08a}."638 In this paper. we focus on thermal photons that emerge directly from the NS surface. uncdistorted by scattering processes in (he magnetosphere.," In this paper, we focus on thermal photons that emerge directly from the NS surface, undistorted by scattering processes in the magnetosphere."639 In addition. we make the simplifving assumption (hat the NS has a pure dipole magnetic field.," In addition, we make the simplifying assumption that the NS has a pure dipole magnetic field."640 While the actual magnetar field structure is likely to be more complicated. it is unlikely to distort the polarization signal. which depends on the field structure at distances much greater than (he star radius: [ar from the star. the field is dominated by the dipole component.," While the actual magnetar field structure is likely to be more complicated, it is unlikely to distort the polarization signal, which depends on the field structure at distances much greater than the star radius; far from the star, the field is dominated by the dipole component."641 If the emitted polarization is instead determined exclusively by processes at the NS surface or scattering. the vacuum polarization signature is destroved.," If the emitted polarization is instead determined exclusively by processes at the NS surface or scattering, the vacuum polarization signature is destroyed."642 In the work below. we assume that. N-rav. photons are emitted Irom a hot region with Tap~5x105 Ix. centered around the magnetic pole.," In the work below, we assume that X-ray photons are emitted from a hot region with $T_{\rm eff}\sim 5\times 10^6$ K, centered around the magnetic pole."643 The bulk emission [rom the rest of the star is taken (o be al à lower temperature and to contribute negligiblv to the observed signal., The bulk emission from the rest of the star is taken to be at a lower temperature and to contribute negligibly to the observed signal.644 We also assume that the size of the X-ray emission region is much smaller than the NS radius. AR. with an approximately constant magnetic field normal to the NS surface.," We also assume that the size of the X-ray emission region is much smaller than the NS radius, $R$, with an approximately constant magnetic field normal to the NS surface."645 The opening angular radius of the polar capis defined to be o< 2z., The opening angular radius of the polar capis defined to be $\beta < 2\pi$ .646 This geometry is consistent with, This geometry is consistent with647excess originates [rom (he same population as the Ix ancl M stars.,excess originates from the same population as the K and M stars.648 More specifically. the MIR excess originales [rom the dust in the cireumstellar shells of the subset of the Ix and M stus that are currently going through their AGB phase.," More specifically, the MIR excess originates from the dust in the circumstellar shells of the subset of the K and M stars that are currently going through their AGB phase."649 Nine elliptical galaxies were observed with CAM on ISO in six narrow bands between Gpmun and μη. From Ganm to 9am the emission is consistent with the combined stellar emission [from the IX and M-type stars that dominate elliptical galaxys integrated light., Nine elliptical galaxies were observed with CAM on ISO in six narrow bands between m and m. From m to m the emission is consistent with the combined stellar emission from the K and M-type stars that dominate elliptical galaxy's integrated light.650 In eight of these galaxies we detected excess over stellar photospheric emission from 9jmm to mun. For one galaxy. NGC 1404. ISOCAA CVF data. with its finer spectral resolution. shows the excess emission is consistent with the known μη oxvgen-rich AGB silicate feature.," In eight of these galaxies we detected excess over stellar photospheric emission from m to m. For one galaxy, NGC 1404, ISOCAM CVF data, with its finer spectral resolution, shows the excess emission is consistent with the known m oxygen-rich AGB silicate feature."651 We used Galactic and LAIC AGB stars to calibrate a sealing relation. revealing galactic-wide mass loss rates for these galaxies.," We used Galactic and LMC AGB stars to calibrate a scaling relation, revealing galactic-wide mass loss rates for these galaxies."652 These observed rates mostly agree wilh theoretical predictions., These observed rates mostly agree with theoretical predictions.653 The observed rates do not scale with Iuminositv (o a universal rate and (hus suggests physical differences between these populations., The observed rates do not scale with luminosity to a universal rate and thus suggests physical differences between these populations.654 We also show that emission at all wavelengths is consistent with a de Vaucouleurs’ law., We also show that emission at all wavelengths is consistent with a de Vaucouleurs' law.655 Now that it is possible to observe the signatures of mass loss. it would be valuable {ο revisit (he predicted mass loss characteristics of cluster anc galaxy. sized. populations.," Now that it is possible to observe the signatures of mass loss, it would be valuable to revisit the predicted mass loss characteristics of cluster and galaxy sized populations."656 Tracking (he populations total mass loss through (ime in a quantitative manner would be a valuable contribution to the field., Tracking the population's total mass loss through time in a quantitative manner would be a valuable contribution to the field.657 Also the calibration of the relationship between mass loss and mid IR excess needs further investigation with additional studies of individual AGB stars., Also the calibration of the relationship between mass loss and mid IR excess needs further investigation with additional studies of individual AGB stars.658 In particular. the effects of different metallicites should be investigated. as it is known to play a role. but the exact nature is not vel determined.," In particular, the effects of different metallicites should be investigated, as it is known to play a role, but the exact nature is not yet determined."659 An exciting avenue of research that will surely develop once the calibrations of these AGB [features is accurately known. is the color-color diagnostics.," An exciting avenue of research that will surely develop once the calibrations of these AGB features is accurately known, is the Visual-MIR color-color diagnostics."660 This observational tool was recently explored in a theoretical study by Bressanetal.(1998)... which shows that for certain populations these (tvpes of relations could potentially break the age-anetallidty degeneracy (hat has long plagued optical color-color relations.," This observational tool was recently explored in a theoretical study by \citet{Bressan98}, which shows that for certain populations these types of relations could potentially break the age-metallicity degeneracy that has long plagued optical color-color relations."661 With SOFIA. SIRTIF and other upcoming IR. missions. in addition to the continuing work though high alütude erounc-based windows. it should be possible to continue (o investigate these issues.," With SOFIA, SIRTIF and other upcoming IR missions, in addition to the continuing work though high altitude ground-based windows, it should be possible to continue to investigate these issues."662 We thank the ISO discretionary time committee for generously granting time for NGC 1404 with the CVF as follow-up to our CAM data., We thank the ISO discretionary time committee for generously granting time for NGC 1404 with the CVF as follow-up to our CAM data.663 We would also like to thank the IPAC support team. especially Ken Ganga who guided us through the initial reductions of the tricky," We would also like to thank the IPAC support team, especially Ken Ganga who guided us through the initial reductions of the tricky"664"In our previous studies of NPs (Gonthieretal.2002.2004.2007).. we adopted the intrinsic radio luminosity moclel given bv the general form from Arzoumanian.Chernolf&Cordes(2002) (ACC) with MIIZ. a=—1.3 and 3=0.4. but reduced the luminosity £, by a factor of GO (Gonthier and by 73 (Gonthieretal.2007) to obtain adequate agreement between the simulated birth rate. flux. and distance distributions and those detected. parücularly by the Parkes Multibeam Pulsar survev (PAIBPS) (see Gonthieretal. (2004))).","In our previous studies of NPs \citep{Gon02, Gon04, Gon07}, we adopted the intrinsic radio luminosity model given by the general form from \citet{Arz02} (ACC) with $L_o=2.1\times 10^{12} {\rm{ mJy}} \cdot {\rm{kpc}}^{\rm{2}} \cdot {\rm{MHz}}$ , $\alpha = -1.3$ and $\beta = 0.4$, but reduced the luminosity $L_o$ by a factor of 60 \citep{Gon04} and by 73 \citep{Gon07}665 to obtain adequate agreement between the simulated birth rate, flux, and distance distributions and those detected, particularly by the Parkes Multibeam Pulsar survey (PMBPS) (see \citet{Gon04}) )."666 In ACC. the predicted birth rate was 0.13 neutron stars per century.," In ACC, the predicted birth rate was 0.13 neutron stars per century."667 In order (ο obtain a birth rate near 2 neutron stars per century. we had to decrease the luminosity constant. Z4.," In order to obtain a birth rate near 2 neutron stars per century, we had to decrease the luminosity constant $L_o$."668 The assumed radio Iuminosity is directly related to the simulated neutron star birth rate., The assumed radio luminosity is directly related to the simulated neutron star birth rate.669 Various studies propose neutron star birt rates that span somewhat of a range., Various studies propose neutron star birth rates that span somewhat of a range.670 For example. the a range of birth rates from 0.9 to 1.9 per century was obtained Irom (he analysis of PAIBPS by Vranesevicοἱal.(2004).," For example, the a range of birth rates from 0.9 to 1.9 per century was obtained from the analysis of PMBPS by \citet{Vran04}."671. In a recent. population svnthesis. Faucher-Giguére&Ixaspi(2006). estimate a Larger birth rate of about 2.8 per century. whereas Lorimeretal.(2006). [ind 1.42:0.2 per century from their analvsis.," In a recent population synthesis, \citet{Fauch06} estimate a larger birth rate of about 2.8 per century, whereas \citet{Lorimer06} find $1.4 \pm 0.2$ per century from their analysis."672" More recently Gonthieretal.(2007) determined the reduction [actor of the radio luminosity bv normalizing the simulated neutron star birth rate {ο rate of Type II supernovae of 2.1 per century. lollowing the work of Tamuimann.Lólfer&Schroder (1994).. using only the Parkes Multibeani survey. as we max have the best description of the flux threshold 5,4, for that survey (Crawlorel. private communication)."," More recently \citet{Gon07} determined the reduction factor of the radio luminosity by normalizing the simulated neutron star birth rate to rate of Type II supernovae of 2.1 per century, following the work of \citet{Tamm94}, , using only the Parkes Multibeam survey, as we may have the best description of the flux threshold $S_{min}$ for that survey (Crawford, private communication)."673 While the neutron star birth rate of 2.1 per century provides a constraint on the luminosity of NPs. MSPs appear in a very different region in the P— diagram. requiring careful consideration of the period and period derivative dependence of (he radio Iuminosity used by the population svnthesis study.," While the neutron star birth rate of 2.1 per century provides a constraint on the luminosity of NPs, MSPs appear in a very different region in the $\dot P-P$ diagram, requiring careful consideration of the period and period derivative dependence of the radio luminosity used by the population synthesis study."674 Often. radio astronomers refer to the radio Iuminosity in terms of a opseudoluminositv (547) determined from the radio flux S observed at a specific Irequency and (he pulsar distance d.," Often, radio astronomers refer to the radio luminosity in terms of a “pseudoluminosity"" $Sd^2$ ) determined from the radio flux $S$ observed at a specific frequency and the pulsar distance $d$."675 One cannot generally determine the intrinsic radio huminosity of a given pulsar [rom the Sd?. even at a given frequency. as the detected average [lux is stronglv dependent on the viewing eeomelry.," One cannot generally determine the intrinsic radio luminosity of a given pulsar from the $Sd^2$, even at a given frequency, as the detected average flux is strongly dependent on the viewing geometry."676 However. if the number of detected pulsars in a group is large. one might be justified in assuming that (he emission region ol the eroup of pulsars is completely saanpled in a random fashion.," However, if the number of detected pulsars in a group is large, one might be justified in assuming that the emission region of the group of pulsars is completely sampled in a random fashion."677 Therefore. the detected Sd? would be proportional to the intrinsic luminosity of the group of pulsars if the survevs represented. an unbiased sample of the true flux distribution.," Therefore, the detected $Sd^2$ would be proportional to the intrinsic luminosity of the group of pulsars if the surveys represented an unbiased sample of the true flux distribution."678 However. since racio survevs necessarily sample the hieh end of the flixdistribution. inferring the intrinsic luminosities of pulsars is diflieult at best.," However, since radio surveys necessarily sample the high end of the fluxdistribution, inferring the intrinsic luminosities of pulsars is difficult at best."679 In. addition. selection effects of the radio surveys," In addition, selection effects of the radio surveys"680where +—rrg and rg is the position of the center of the shearing sheet box.,where $x=r-r_0$ and $r_0$ is the position of the center of the shearing sheet box.681 The term 2007.7 represents the tidal force (difference of the gravitational and inertial force): q is the parameter introduced in the previous subsection ancl measures (he steepness of the rotation profile., The term $2q\Omega^2x$ represents the tidal force (difference of the gravitational and inertial force); $q$ is the parameter introduced in the previous subsection and measures the steepness of the rotation profile.682 Note (hat the pressure term contains only [fluctuations related (o the presence of turbulence. which is not the case in Couette-Tavlor flows.," Note that the pressure term contains only fluctuations related to the presence of turbulence, which is not the case in Couette-Taylor flows."683 It is interesting to note that this equation shares features with both Eqs. (4)), It is interesting to note that this equation shares features with both Eqs. \ref{NSR}) )684 aud (8)): in particular. linear stability is ensured for q«2. e. 5«—1 for the laminar linear profile.," and \ref{NSCT}) ); in particular, linear stability is ensured for $q<2$, i.e. $S<-1$ for the laminar linear profile."685 This makes the loss of turbulence in the simulations of Balbusefa£(1996) and ILawlev.efa£.(1999). [or values of q s1nmdler (han 2 bv a few percents only. all (he more intriguing.," This makes the loss of turbulence in the simulations of \citet{BHS96} and \citet{HBW99}, for values of $q$ smaller than 2 by a few percents only, all the more intriguing."686 In fact. all available pieces of evidence strongly suggest that numerical simulations of rotating Couette flows and of σαν driven shearecl motions in the shearing sheet limit should display turbulence. as I argue now.," In fact, all available pieces of evidence strongly suggest that numerical simulations of rotating Couette flows and of tidally driven sheared motions in the shearing sheet limit should display turbulence, as I argue now."687 Fist. plane Couette flows. rotating. Couette flows. and tidallv driven. shearing sheet flows have similar linear stability properties.," First, plane Couette flows, rotating Couette flows, and tidally driven shearing sheet flows have similar linear stability properties."688 For all three (vpes of (lows. the viscously relaxed laminar solution is a simple linear shear. which is always linearly stable for (he plane Couette[low*.. and stable for the other two flows once $<—1 (which is the only case of interest here).," For all three types of flows, the viscously relaxed laminar solution is a simple linear shear, which is always linearly stable for the plane Couette, and stable for the other two flows once $S< -1$ (which is the only case of interest here)."689 Plane Couette [lows are subject to finite amplitude instabilities (see. e.g.. Lerner 1998.. DubrulleandZahn 1991... and references therein).," Plane Couette flows are subject to finite amplitude instabilities (see, e.g., \citealt{LK88}, \citealt{DZ91}, and references therein)."690 The same is true of rotating Couette flows (Johnson1963).. and of shearing sheet flows (Dubrulle1993).," The same is true of rotating Couette flows \citep{John63}, and of shearing sheet flows \citep{Bulle93}."691. As finite amplitude instabiliües are considered {ο trigger the turbulence seen both in experimental and numerical investigations of plane Couette flow. one would expect the same to be (rue of ihe other two flows.," As finite amplitude instabilities are considered to trigger the turbulence seen both in experimental and numerical investigations of plane Couette flow, one would expect the same to be true of the other two flows."692 secondlv. let us reexamine (he differences. between rotating Couette flows and the shearing sheet [lows with the other flows discussed previously.," Secondly, let us reexamine the differences between rotating Couette flows and the shearing sheet flows with the other flows discussed previously."693 They amount to differences in boundary conditions. of mean force terms. and of geometry.," They amount to differences in boundary conditions, of mean force terms, and of geometry."694 The shearing sheet boundary conditions are in a wav intermediate between rigid ancl free boundary conditions. as they imply that (he mean flow obevs rigid boundary conditions. whereas the fluctuating part obevs periodic boundary. conditions: rotating Couette Low," The shearing sheet boundary conditions are in a way intermediate between rigid and free boundary conditions, as they imply that the mean flow obeys rigid boundary conditions, whereas the fluctuating part obeys periodic boundary conditions; rotating Couette flow"695in the lensing galaxy is also a possibility.,in the lensing galaxy is also a possibility.696 The lensing crosssection of massive spiral galaxies may have been unclerestimated. or carlytyx0 galaxies at redshifts 0.9<<LO could be substantially dustier than those seen locally.," The lensing cross–section of massive spiral galaxies may have been underestimated, or early–type galaxies at redshifts $0.5<z<1.0$ could be substantially dustier than those seen locally."697 In. either. case if a population of clusty galaxies contributes significantly to the lensing cross section at these redshifts. Chen samples of gravitational lenses drawn from optical samples of quasars would be significantly incomplete. producing an unclerestimate of the value of Oy.," In either case if a population of dusty galaxies contributes significantly to the lensing cross section at these redshifts, then samples of gravitational lenses drawn from optical samples of quasars would be significantly incomplete, producing an underestimate of the value of $\Omega_{\Lambda}$."698 The uncertainty over the elfect of dust on the lensing statistics could be greatly reduced by searching lor gravitational lenses in à Ix.band. Εανlimited sample of quasars.," The uncertainty over the effect of dust on the lensing statistics could be greatly reduced by searching for gravitational lenses in a K–band, flux–limited sample of quasars."699 Quasars have been detected at all wavelengths from gammaravs to radio waves and they produce a significant fraction of their energv output. over many decades in. frequency., Quasars have been detected at all wavelengths from gamma--rays to radio waves and they produce a significant fraction of their energy output over many decades in frequency.700 Furthermore. the proportion of the total energy radiated a different frequencies varies substantiallly among the quasar population.," Furthermore, the proportion of the total energy radiated at different frequencies varies substantiallly among the quasar population."701 A deep survey at. sav. optical wavelengths could miss quasars where the bulk of the energy is emittec in. sav. the farinfrared. and.," A deep survey at, say, optical wavelengths could miss quasars where the bulk of the energy is emitted in, say, the far–infrared, and."702versa. To characterise the bolometric energy. output of the quasar population i is necessary to undertake surveys at several wavelengths that include significant contributions from the cilleren components that make up the quasar spectrum. (Llewet and Foltz. 1994).," To characterise the bolometric energy output of the quasar population it is necessary to undertake surveys at several wavelengths that include significant contributions from the different components that make up the quasar spectrum (Hewett and Foltz, 1994)."703 Phe importance of undertaking surveys a multiple Frequencies is illustrated by. Webster et al (1995). who claim that. due to the ellects of extinction. the bulk otre quasar population has gone undetected. in optica surveys.," The importance of undertaking surveys at multiple frequencies is illustrated by Webster et al (1995), who claim that, due to the effects of extinction, the bulk of the quasar population has gone undetected in optical surveys."704 This conclusion is nevertheless controversial (c.g. enn et al 1998) and surveys for quasars in the Ix. hanc would. provide a direct test of the hypothesis by establishing the raction of reddened quasars that are underrepresente in optical samples., This conclusion is nevertheless controversial (e.g. Benn et al 1998) and surveys for quasars in the K band would provide a direct test of the hypothesis by establishing the fraction of reddened quasars that are under–represented in optical samples.705 The IXXN method exploits the fact that. by comparison with a star with the same V-J colour. quasars are οσους in J-Ix. so the two populations separate in the twocolour diagram [or point sources.," The KX method exploits the fact that, by comparison with a star with the same V-J colour, quasars are redder in J-K so the two populations separate in the two–colour diagram for point sources."706 T1e upper plot in Figure 1 shows the spectrum of a quasar of redshift 2=3 and the V. J and Ix filter transmission curves.," The upper plot in Figure 1 shows the spectrum of a quasar of redshift $z=3$ and the V, J and K filter transmission curves."707 Overplotted is the spectrum of an early Ix.star. chosen because its V-J colour is similar to the quasar.," Overplotted is the spectrum of an early K–star, chosen because its V-J colour is similar to the quasar."708 The excess Dux of the quasar in the Ix. band. amounting to 0.5 mag. is evident.," The excess flux of the quasar in the K band, amounting to $\sim 0.5\,$ mag, is evident."709 The lower plot in Figure 1 shows the ellectiveness of the KX method in detecting also reddened quasars., The lower plot in Figure 1 shows the effectiveness of the KX method in detecting also reddened quasars.710 Ehe quasar spectrum of the upper plot has been reddened as appropriate for an absorbing cloud at 2.5 with rest.[rame L(V)=0.3., The quasar spectrum of the upper plot has been reddened as appropriate for an absorbing cloud at $z=2.5$ with rest–frame $E(B-V)=0.3$.711 Overplotted is the spectrum of an Alstar. chosen for the mach in V-J colour.," Overplotted is the spectrum of an M–star, chosen for the match in V-J colour."712 The excess Dux of the quasar in the Ix band is again clearly visible., The excess flux of the quasar in the K band is again clearly visible.713 The KN method in practice is illustrated in Figure 2 which isa VJIx twocolour ciagraum showing the location of Galactic stars ) and quasars (e)., The KX method in practice is illustrated in Figure 2 which is a VJK two–colour diagram showing the location of Galactic stars $\times$ ) and quasars $\bullet$ ).714 The stellar photometry was taken from the list of bright UIXIICE. standards [or which the quoted. photometric errors are 0.015 in J-Ix. aux 0.05 in V-J. The VJIx quasar photometry (Llewett et. al. in preparation) Consists of 152 quasars. 0.2<2.«34. [rom the Large Bright Quasar Survey (Llewett. Foltz aux Chaltlee 1995) ancl 20 quasars. 2.40<234. 16.5κ|«19.5. used. in studies of DLA absorbers (e.g. Pei. Fall and. Bechtold 1991: ‘Table 1).," The stellar photometry was taken from the list of bright UKIRT standards for which the quoted photometric errors are $0.015$ in J-K and $0.05$ in V-J. The VJK quasar photometry (Hewett et al, in preparation) consists of 152 quasars, $0.2 < z <7153.4$, from the Large Bright Quasar Survey (Hewett, Foltz and Chaffee 1995) and 20 quasars, $2.0 < z < 3.4$, $16.5 < V < 19.5$ , used in studies of DLA absorbers (e.g. Pei, Fall and Bechtold 1991; Table 1)."716 For clarity. ineliviclua error bars are not plotted. bu the photometric errors are nearly all <0.15 mag in each colour.," For clarity, individual error bars are not plotted but the photometric errors are nearly all $\le 0.15\,$ mag in each colour."717 Phe V photometry was not in gencral acquired a the same epoch as the infrare magnitudes and an additlona scatter of ~Ol mae. clue o intrinsic photometric variability in the quasars. will be esent in the V-] colour or many of the objects.," The V photometry was not in general acquired at the same epoch as the infrared magnitudes and an additional scatter of $\sim 0.1\,$ mag, due to intrinsic photometric variability in the quasars, will be present in the V-J colour for many of the objects."718 A possible selecion boundary. Joh036(V.J) LIS. cliscriminating the quasars from the sequence of stars is shown by the ashec line.," A possible selection boundary, ${\mathrm J-K}>0.36\,({\mathrm719V-J})+0.18$ , discriminating the quasars from the sequence of stars is shown by the dashed line."720 All but one of the 172 quasars plotted. z.<3.4. lie o the right of the selection ine shown.," All but one of the 172 quasars plotted, $z <7213.4$, lie to the right of the selection line shown."722 Tre quasar to the left of the selection line is LDOS1212|1415. a »oad absorption line object at recishift >=1.638.," The quasar to the left of the selection line is LBQS1212+1445, a broad absorption line object at redshift $z=1.63$."723 The ]x.photometry for this object in the UIXLICE dataset. that orovides Dany of the infrared. magnitudes shown in Figure 1 is O4mae fainter than an observation mace with the Alultiple Mirror Telescope (MNUE).," The K–photometry for this object in the UKIRT dataset that provides many of the infrared magnitudes shown in Figure 1 is $0.4\,$ mag fainter than an observation made with the Multiple Mirror Telescope (MMT)."724 While the use of the MÀ TRmagnitude would move the object. 0.4 mag rightward into the well populated. portion of the plot there is no inlication of anvthing amiss with the UIXIICE Ix-band magniuce and or Consisteney we have plotted the J-Ix. colour from the UALR observations.," While the use of the MMT K–magnitude would move the object $0.4\,$ mag rightward into the well populated portion of the plot there is no indication of anything amiss with the UKIRT K-band magnitude and for consistency we have plotted the J-K colour from the UKIRT observations."725 Also shown In Lig., Also shown In Fig.726 2 are the reddening vectors for an intervening absorber wit van LAIC extinction curve. of restframe EK(D1) 0l. at five cilferent recshifts.," 2 are the reddening vectors for an intervening absorber with an LMC extinction curve, of rest--frame $E(B-V)=0.1$ , at five different redshifts."727. Lach vector rubs approximat«‘ly parallel to the stellar locus. so reddened quasars can aso be detected. by this methoct.," Each vector runs approximately parallel to the stellar locus, so reddened quasars can also be detected by this method."728 Given adequate signalotonoise ratio. 10. in the estimate of the object colours the KN method should identify nearly all quasars found. in optical samples. whether reddenecl or not. above the Ix.band Dux limit.," Given adequate signal–to–noise ratio, $\sim 10$, in the estimate of the object colours the KX method should identify nearly all quasars found in optical samples, whether reddened or not, above the K–band flux limit."729 Application of the WN method in practice will require σου quality images in order to separate point sources from galaxies. because the colour distribution of faint. galaxies overlaps that of quasars (this is also true. of the UWS method).," Application of the KX method in practice will require good quality images in order to separate point sources from galaxies, because the colour distribution of faint galaxies overlaps that of quasars (this is also true of the UVX method)."730 X potential οΠοεν which we have not adcdressed is the brightness of the quasar host galaxy., A potential difficulty which we have not addressed is the brightness of the quasar host galaxy.731 Phe contribution to the total lux of the host galaxy. will in general be Iarger in the Ix band than in the optical so lower luminosity quasars might be excluded from a catalogue of point sources., The contribution to the total flux of the host galaxy will in general be larger in the K band than in the optical so lower luminosity quasars might be excluded from a catalogue of point sources.732 l]lowever. this is notan issue for the bright Hux levels considered in 833.," However, this is notan issue for the bright flux levels considered in 3."733lt ds now well established that the centre of almost every ealaxy contains a supermassive black hole (SALBLD). and that in many cases the mass of this hole is closely connected with properties of the host galaxy bulge through the Af0 and AMAlinuae relations (Ferrarese Merritt. 2000: Cobhardt οἱ al.,"It is now well established that the centre of almost every galaxy contains a supermassive black hole (SMBH), and that in many cases the mass of this hole is closely connected with properties of the host galaxy bulge through the $M - \sigma$ and $M -M_{\rm bulge}$ relations (Ferrarese Merritt, 2000; Gebhardt et al."734 2000: LLàrring Itix 2004)., 2000; Härring Rix 2004).735" Phe connection is physically reasonable. since the black bole binding energv Ale"" considerably exceeds the bulge binding energy ~Misuasetr"" (Ixing. 2003) (here η0.1 is the aceretion elliciency. and 0 the velocity dispersion of the bulge)."," The connection is physically reasonable, since the black hole binding energy $\eta Mc^2$ considerably exceeds the bulge binding energy $\sim M_{\rm bulge}\sigma^2$ (King, 2003) (here $\eta\sim 0.1$ is the accretion efficiency and $\sigma$ the velocity dispersion of the bulge)."736 The black hole communicates its presence to the host by driving powerful outflows when it is fed matter at superIExldington rates., The black hole communicates its presence to the host by driving powerful outflows when it is fed matter at super–Eddington rates.737 If these outllows are momentumdriven. ic. communicate only their ram pressure to the surrounding interstellar gas. the Mσ΄ relation emerges naturally as specifving the black hole mass at which an Edcington outllow can drive a significant bubble into the bulge σας (xing. 2003: 2005).," If these outflows are momentum–driven, i.e. communicate only their ram pressure to the surrounding interstellar gas, the $M -738\sigma$ relation emerges naturally as specifying the black hole mass at which an Eddington outflow can drive a significant bubble into the bulge gas (King, 2003; 2005)."739 At smaller masses. the black hole can onlv drive bubbles which recollapse. and evidently do not interrupt the gas supply to the black hole which ultimately powers its growth.," At smaller masses, the black hole can only drive bubbles which recollapse, and evidently do not interrupt the gas supply to the black hole which ultimately powers its growth."740 This argument implicitly. suggests that the Alσ relation Is an upper limit to the black hole mass. rather than a tight relation.," This argument implicitly suggests that the $M - \sigma$ relation is an upper limit to the black hole mass, rather than a tight relation."741 Ht is now clear (Datcheldor. 2010) that this is probably so. as observational selection makes it. dilficult to measure black hole masses below the relation (cf Section 3).," It is now clear (Batcheldor, 2010) that this is probably so, as observational selection makes it difficult to measure black hole masses below the relation (cf Section 3)."742 The obvious question then is how far below this limit the majority of SMDBLL lic., The obvious question then is how far below this limit the majority of SMBH lie.743 New insight into this question comes from recent X.rav observations by Tomboesi et al. (, New insight into this question comes from recent X–ray observations by Tombesi et al. (7442010a. b) of Fast (eo~ 0.160) outllows in a Large fraction of local AGN.,"2010a, b) of fast $v \sim 0.1c$ ) outflows in a large fraction of local AGN."745 ] shall argue here that this means that most. local AGN contain black holes wing below the ALc limit. and that most of these systems. undergo superEddington episodes which switch olf only for relatively short intervals.," I shall argue here that this means that most local AGN contain black holes lying below the $M746- \sigma$ limit, and that most of these systems undergo super–Eddington episodes which switch off only for relatively short intervals."747 The hole masses are probably not very far below the AL(0 value.," The hole masses are probably not very far below the $M -748\sigma$ value."749 Εν show that Ededington outflows at masses significantly below this are RavleighTaylor unstable and therefore inellicient in suppressing accretion., I will show that Eddington outflows at masses significantly below this are Rayleigh–Taylor unstable and therefore inefficient in suppressing accretion.750 The argument by Soltan (1982) relates the mass density of black holes in the local universe to the total background radiation they produced. while growing., The argument by Soltan (1982) relates the mass density of black holes in the local universe to the total background radiation they produced while growing.751 It suggeststhat the average mediumtolarge galaxy hosts a black hole of mass ZOOM..., It suggeststhat the average medium–to–large galaxy hosts a black hole of mass $\ga 10^8\msun$.752 Et is reasonable to suppose that the growth phases of these SALBLI are observable as AGN., It is reasonable to suppose that the growth phases of these SMBH are observable as AGN.753 But since the incidence of AGN among all galaxies is relatively low. this must mean that the holes spend much of their time growing ab the maximum. possible rate. ie. that. specified by the I5ddington limit.," But since the incidence of AGN among all galaxies is relatively low, this must mean that the holes spend much of their time growing at the maximum possible rate, i.e. that specified by the Eddington limit."754 In this case the ÀJ.@ relation constrains their growth. and we should expect the black hole masses in AGN to lie the relation. with a galaxy nucleus ceasing to be active once its SMDII reaches this mass.," In this case the $M-\sigma$ relation constrains their growth, and we should expect the black hole masses in AGN to lie the relation, with a galaxy nucleus ceasing to be active once its SMBH reaches this mass."755 We are thus led to the conclusions that ((a) and, We are thus led to the conclusions that (a) and756stars rarely had Roche lobe-filling factors over 0.6. whereas the latter author notes that symbiotic stars exhibit ellipsoidal variability despite their moderate Roche lobe-filling factors.,"stars rarely had Roche lobe-filling factors over 0.6, whereas the latter author notes that symbiotic stars exhibit ellipsoidal variability despite their moderate Roche lobe-filling factors."757 A possible explanation for this discrepancy could be that the usual expression for the Roche radius overestimates it due to neglecting radiation pressure and other factors countering stellar gravity. which can both shrink the effective Roche-lobe and make surface ellipsoidal distortions important at smaller radii (22).," A possible explanation for this discrepancy could be that the usual expression for the Roche radius overestimates it due to neglecting radiation pressure and other factors countering stellar gravity, which can both shrink the effective Roche-lobe and make surface ellipsoidal distortions important at smaller radii ."758. This possibility ts explored further by ?., This possibility is explored further by .759. The observed limit on the giant's Roche-lobe would be explained by a reduction of the effective gravity on the stellar surface to 0.15-0.35 of its Newtonian value (??)., The observed limit on the giant's Roche-lobe would be explained by a reduction of the effective gravity on the stellar surface to 0.15-0.35 of its Newtonian value .760. From the above discussion one may conclude that the frequency of binaries must be expected to be lower among M giants than among K giants. because the larger radii of the former forbid them from being located to the left of the dashed line in the e — logP diagram of Fig. 6..," From the above discussion one may conclude that the frequency of binaries must be expected to be lower among M giants than among K giants, because the larger radii of the former forbid them from being located to the left of the dashed line in the $e$ – $\log P$ diagram of Fig. \ref{Fig:elogP-SB9},"761 whereas this restriction does not apply to K giants., whereas this restriction does not apply to K giants.762 This statement will be quantified in Sect. 2.6.., This statement will be quantified in Sect. \ref{Sect:K}.763 Not many estimates of the binary frequency among K giants exist in the literature., Not many estimates of the binary frequency among K giants exist in the literature.764 An early study by of 40 K giants in the field resulted in a frequency of 15 to spectroscopic binaries (over a 3 yr time span and with a radial-velocity internal error of 0.40 1)., An early study by of 40 K giants in the field resulted in a frequency of 15 to spectroscopic binaries (over a 3 yr time span and with a radial-velocity internal error of 0.40 ).765 In open clusters. Mermilliod Mayor (2008. in prep.)," In open clusters, Mermilliod Mayor (2008, in prep.)"766 find a much higher frequency of 30.8+1.76€ (= 217/704) for G and K giants under similar observing conditions (similar time span with 3 measurements per star)., find a much higher frequency of $30.8\pm1.7$ (= 217/704) for G and K giants under similar observing conditions (similar time span with 3 measurements per star).767 Surprisingly. for the giants that are not cluster members. the same authors derive a much lower binary frequency. namely 1642% (= 46/285).," Surprisingly, for the giants that are not cluster members, the same authors derive a much lower binary frequency, namely $16\pm2$ (= 46/285)."768 A binary frequency may also be derived for the sample of Hipparcos K giants monitored with CORAVEL and studied by?., A binary frequency may also be derived for the sample of Hipparcos K giants monitored with CORAVEL and studied by.769. Table 4. lists the binary frequency among that sample of K giants., Table \ref{Tab:frequency} lists the binary frequency among that sample of K giants.770 To compare binary frequencies among K and M giants. one should try to avoid systematic and selection effects as much as possible.," To compare binary frequencies among K and M giants, one should try to avoid systematic and selection effects as much as possible."771 Most importantly. the comparison should involve binary frequencies derived from the same number of measurements covering approximately the same time span.," Most importantly, the comparison should involve binary frequencies derived from the same number of measurements covering approximately the same time span."772 For M giants. Table + reveals that not respecting this condition may cause the binary frequency estimate to vary by about a factor of two (from in sample I to in samples II. HII. IV. after excluding the Miras).," For M giants, Table \ref{Tab:frequency} reveals that not respecting this condition may cause the binary frequency estimate to vary by about a factor of two (from in sample I to in samples II, III, IV, after excluding the Miras)."773 Therefore. the binary frequencies among sample | of M giants and among K giants were re-assessed based on the radial-velocity standard deviations computed only from 2 datapoints (the first and the last available).," Therefore, the binary frequencies among sample I of M giants and among K giants were re-assessed based on the radial-velocity standard deviations computed only from 2 datapoints (the first and the last available)."774 The stars flagged as binaries in a given sample may then change., The stars flagged as binaries in a given sample may then change.775 However. it is found that the of binaries remains the same (to within 2 units). both for K and M giants.," However, it is found that the of binaries remains the same (to within 2 units), both for K and M giants."776 Therefore. we may conclude that the fraction of spectroscopic binaries among M giants (after correcting for the difficulty of finding binaries among Mira variables) is less than among K giants by à factor 6.3/14.5= 0.43.," Therefore, we may conclude that the fraction of spectroscopic binaries among M giants (after correcting for the difficulty of finding binaries among Mira variables) is less than among K giants by a factor 6.3/14.5= 0.43."777 What could be the origin of such a difference in the binary frequencies among K and M giants?, What could be the origin of such a difference in the binary frequencies among K and M giants?778 Part of it probably comes from the greater difficulty of finding binaries among M giants because of their smaller orbital velocity amplitudes and larger intrinsic jitter (Fig. 5)).," Part of it probably comes from the greater difficulty of finding binaries among M giants because of their smaller orbital velocity amplitudes and larger intrinsic jitter (Fig. \ref{Fig:jit_vs_R}) ),"779 which prevents a small velocity difference from being ascribed to the orbital motion as it is for K giants., which prevents a small velocity difference from being ascribed to the orbital motion as it is for K giants.780 This is especially true for a small number of measurements. as 1n our sample I. Another possibility may reside in the different distributions of K and M giants in the eccentricity — period diagram. as shown in Fig. 6..," This is especially true for a small number of measurements, as in our sample I. Another possibility may reside in the different distributions of K and M giants in the eccentricity – period diagram, as shown in Fig. \ref{Fig:elogP-SB9}."781 It must be stressed that this figure refers to samples offield giants. 1.e.. orbits for K giants being retrieved from the Ninth Catalogue of Spectroscopic Binary Orbits(?).. explicitely excluding the orbits for K giants in clusters derived by (Fig. 7)).," It must be stressed that this figure refers to samples of giants, i.e., orbits for K giants being retrieved from the Ninth Catalogue of Spectroscopic Binary Orbits, explicitely excluding the orbits for K giants in clusters derived by (Fig. \ref{Fig:elogP_cluster_mass}) )."782 This allows for a direct comparison of this sample with the sample of M giants without worrying about differences between field and cluster populations., This allows for a direct comparison of this sample with the sample of M giants without worrying about differences between field and cluster populations.783 For stars evolving on the first-ascent giant branch. the radii of K giants are on average smaller than those of M giants. so that the minimum orbital period observed for M giants is expected to be somewhat longer than for K giants. as confirmed by Fig. 6..," For stars evolving on the first-ascent giant branch, the radii of K giants are on average smaller than those of M giants, so that the minimum orbital period observed for M giants is expected to be somewhat longer than for K giants, as confirmed by Fig. \ref{Fig:elogP-SB9}."784 The resulting decrease in binary frequency may be estimated by computing the ratio between the number of K giants to the right of the solid line to the total number of K giants. or 118/164 2 0.72.," The resulting decrease in binary frequency may be estimated by computing the ratio between the number of K giants to the right of the solid line to the total number of K giants, or 118/164 = 0.72."785 Applying this factor to the frequency of M giant binaries thus yields 6.3 / 0.72 = 8.8%.. closer to the binary frequency among field K giants. but still well below it. and this result is robust.," Applying this factor to the frequency of M giant binaries thus yields 6.3 / 0.72 = 8.8, closer to the binary frequency among field K giants, but still well below it, and this result is robust."786 For example. if the long-dashed line from Fig.," For example, if the long-dashed line from Fig."787 6 is used as the limit. the correction factor would be 126/164 = 0.77 instead of 0.72.," \ref{Fig:elogP-SB9} is used as the limit, the correction factor would be 126/164 = 0.77 instead of 0.72."788 Still another bias. which may alter the factor 0.72 used above. should be taken into consideration.," Still another bias, which may alter the factor 0.72 used above, should be taken into consideration."789 This bias is related to the evolutionary status of the K giant. which may either be the first-ascent giant branch or the core-He burning.," This bias is related to the evolutionary status of the K giant, which may either be the first-ascent giant branch or the core-He burning."790 For low-mass stars. the latter phase implies that stars have gone through the tip of the RGB where they reached a very large radius (similar to that of M giants).," For low-mass stars, the latter phase implies that stars have gone through the tip of the RGB where they reached a very large radius (similar to that of M giants)."791 Therefore. core-He-burning K giants are expected to have an eccentricity — period distribution similar to that of M giants.," Therefore, core-He-burning K giants are expected to have an eccentricity – period distribution similar to that of M giants."792 Thus the eccentricity — period diagram. of K giants must be expected to mix such K giants with orbital properties similar to M giants with K giants having orbital parameters more typical of less evolved (first-ascent giant branch) stars (1e.. short periods and possibly high eccentricities).," Thus the eccentricity – period diagram of K giants must be expected to mix such K giants with orbital properties similar to M giants with K giants having orbital parameters more typical of less evolved (first-ascent giant branch) stars (i.e., short periods and possibly high eccentricities)."793 Since stars spend more time in the He-burning clump. the former should be more numerous. however.," Since stars spend more time in the He-burning clump, the former should be more numerous, however."794 For intermediate-mass. K giants. this segregation does not occur since they never went through a stage with large radii.," For intermediate-mass K giants, this segregation does not occur since they never went through a stage with large radii."795 This may be checked by using the sample of K giant binaries in open clusters non-members).. where the K-giant mass may be identified with the cluster turnoff mass.," This may be checked by using the sample of K giant binaries in open clusters , where the K-giant mass may be identified with the cluster turnoff mass."796 Figure 7 reveals that. as expected. the K giants in clusters with turnoff masses lower than 1.75 aare mostly found in the region occupied by M giants. with only two short-period circular orbits (out of 9). in accordance with the masses of M giants estimated to fall in the range1.2 —," Figure \ref{Fig:elogP_cluster_mass} reveals that, as expected, the K giants in clusters with turnoff masses lower than 1.75 are mostly found in the region occupied by M giants, with only two short-period circular orbits (out of 9), in accordance with the masses of M giants estimated to fall in the range1.2 –"797for separately. see Section 3)).,"for separately, see Section \ref{transit}) )."798 The full normalised light curve is shown in Figure 2.., The full normalised light curve is shown in Figure \ref{fulllc}.799 We evaluate the actual noise level per 5|25ss by measuring the dispersion about hh (7 exposures) bins and scaling it by V7. giving 8.9x107+. compared to a photon noise level of 5.6x1077.," We evaluate the actual noise level per s by measuring the dispersion about h (7 exposures) bins and scaling it by $\sqrt{7}$, giving $8.9 \times 10^{-4}$, compared to a photon noise level of $5.6\times 10^{-4}$."800 Possible factors contributing to the difference include residual instrumental effects and the intrinsic variability of the star., Possible factors contributing to the difference include residual instrumental effects and the intrinsic variability of the star.801 A preliminary ephemeris (orbital period P. and epoch 70) was obtained by least-squares fitting of periodic. trapezoidal transits to the ight curve after filtering out the out-of-transit variations using a ]-day baseline iterative non-linear filter.," A preliminary ephemeris (orbital period $P$ and epoch $T_0$ ) was obtained by least-squares fitting of periodic, trapezoidal transits to the light curve after filtering out the out-of-transit variations using a 1-day baseline iterative non-linear filter."802 A more careful removal of the variability was then carried out by fitting a straight line to a light curve section. lasting a little over one transit duration before and after each transit., A more careful removal of the variability was then carried out by fitting a straight line to a light curve section lasting a little over one transit duration before and after each transit.803 We also experimented with higher order polynomials. but they did not improve the dispersion of the residuals. and do not change the results of the subsequent analysis.," We also experimented with higher order polynomials, but they did not improve the dispersion of the residuals, and do not change the results of the subsequent analysis."804" We folded the corrected segments of ight curve using the preliminary period ephemeris. rebinned them in bins of 0.0003 in phase. and fitted the result to obtain preliminary estimates of the system scale a/R,. the radius ratio A,/R,. the inclination ; and the linear limb-darkening coefficient uv. where R, is the star radius. Ry the planet radius and « the semi-major axis."," We folded the corrected segments of light curve using the preliminary period ephemeris, rebinned them in bins of 0.0003 in phase, and fitted the result to obtain preliminary estimates of the system scale $a/R_{\rm s}$, the radius ratio $R_{\rm p}/R_{\rm s}$, the inclination $i$ and the linear limb-darkening coefficient $u$, where $R_{\rm s}$ is the star radius, $R_{\rm p}$ the planet radius and $a$ the semi-major axis."805 We opted to fit for it rather than fix it because reliable theoretical limb-darkening coefficients are not currently available for the CoRoT bandpass., We opted to fit for $u$ rather than fix it because reliable theoretical limb-darkening coefficients are not currently available for the CoRoT bandpass.806" The ephemeris was then refined by fitting for the time of transit centre 7c for each individual transit event (fixing all other parameters) and fitting a linear relation to the Το. Finally. the light curve was folded again at the refined ephemeris and rebinned to perform a final fit for a/R,. R;/R.. i and a."," The ephemeris was then refined by fitting for the time of transit centre $T_{\rm C}$ for each individual transit event (fixing all other parameters) and fitting a linear relation to the $T_C$ 's. Finally, the light curve was folded again at the refined ephemeris and rebinned to perform a final fit for $a/R_{\rm s}$, $R_{\rm p}/R_{\rm s}$, $i$ and $u$."807 At each stage. we use the formalism of ?. with quadratic limb darkening to generate model transit light curves and the implementation of the Levenberg-Marquart fitting algorithm. kindly provided by MMarkwart. to perform the fit.," At each stage, we use the formalism of \citet{ma02} with quadratic limb darkening to generate model transit light curves and the implementation of the Levenberg-Marquart fitting algorithm, kindly provided by Markwart, to perform the fit."808 The period was fixed at the ephemeris value. and the epoch was also fixed except when fitting individual transits.," The period was fixed at the ephemeris value, and the epoch was also fixed except when fitting individual transits."809 The eccentricity was assumed to be zero (the best fit to the radial velocity data is a circular orbit with an eccentricity uncertainty of 0.1. see Paper V).," The eccentricity was assumed to be zero (the best fit to the radial velocity data is a circular orbit with an eccentricity uncertainty of 0.1, see Paper V)."810 We also tried fitting the transits with a quadratic limb-darkening prescription. but this did not improve the fit. and therefore we reverted to linear limb-darkening.," We also tried fitting the transits with a quadratic limb-darkening prescription, but this did not improve the fit, and therefore we reverted to linear limb-darkening."811 To evaluate the noise-induced uncertainties on the transit parameters. includingσι the effect. of red. noise. we used a ‘correlated bootstrap’ approach.," To evaluate the noise-induced uncertainties on the transit parameters, including the effect of red noise, we used a `correlated bootstrap' approach."812" The residuals from the global best fit were divided into bins lasting hh (2/3 of the transit ""Suration. or 1/4 of the duration of the light curve segments used to calibrate the out-of-transit variations around each transit). randomly shuffled. and added back to the fit before fitting the ndividual transits."," The residuals from the global best fit were divided into bins lasting h $2/3$ of the transit duration, or $1/4$ of the duration of the light curve segments used to calibrate the out-of-transit variations around each transit), randomly shuffled, and added back to the fit before fitting the individual transits."813 Over-sampled and non over-sampled bins were shuffled separately., Over-sampled and non over-sampled bins were shuffled separately.814" Each bin is shuffled whole. preserving the detailed time sampling of individual bins. so the procedure ""Soes not account for the effect of small data gaps. but it does account for correlated noise on hour timescales. including the effect of star spots crossed by the planet."," Each bin is shuffled whole, preserving the detailed time sampling of individual bins, so the procedure does not account for the effect of small data gaps, but it does account for correlated noise on hour timescales, including the effect of star spots crossed by the planet."815 We used 100 realisations when fitting individual transits and 1000. when fitting the folded light curve., We used 100 realisations when fitting individual transits and 1000 when fitting the folded light curve.816 At each realisation. we also added a constant drawn from a Gaussian distribution with zero mean and standard deviation 0.001 to the data. to account for the," At each realisation, we also added a constant drawn from a Gaussian distribution with zero mean and standard deviation 0.001 to the data, to account for the"817measurements of CAIB optical depth from future missions. there is hope that more stringent constraints on high-: star formation and black-hole accretion will be possible.,"measurements of CMB optical depth from future missions, there is hope that more stringent constraints on $z$ star formation and black-hole accretion will be possible."818 These data include additional vears of WALAP observations. as well as thePlanch mission.," These data include additional years of WMAP observations, as well as the mission."819 We are grateful to David Spergel. Licia Verde. Rachel Bean. and Nick Gnedin for useful discussions regarding the interpretation of WMAP data and numerical simulations.," We are grateful to David Spergel, Licia Verde, Rachel Bean, and Nick Gnedin for useful discussions regarding the interpretation of WMAP data and numerical simulations."820 We thank Douglas Scott and. Wan Yan Wong for providing their calculations of recombination history., We thank Douglas Scott and Wan Yan Wong for providing their calculations of recombination history.821 This research at the University of Colorado was supported by astrophysical theory. grants from NASA (NNNOT-AGYTTG) and NSF (ASTOT-07474)., This research at the University of Colorado was supported by astrophysical theory grants from NASA (NNX07-AG77G) and NSF (AST07-07474).822[rom the PSF wines. giving 286+29 source counts. a detection siguificauce of 9.90.,"from the PSF wings, giving $286\pm 29$ source counts, a detection significance of $9.9 \sigma$."823" In the raclii range—120"".. here are 1766 «routs. of which 1278 should be background aud 32 from the PSF wines. giving 156d251 source couus. a detection siguificance of about δ.0σ."," In the radii range, there are 1766 counts, of which 1278 should be background and 32 from the PSF wings, giving $456\pm 51$ source counts, a detection significance of about $8.9\sigma$."824" To analyze the spectrum of the extended emission. we extracted counts from the two annular regions. r— 20""-60""and r=1'-2/.. using he CLAO taskspecextract."," To analyze the spectrum of the extended emission, we extracted counts from the two annular regions, $r=20\arcsec$ and $r=1\arcmin$, using the CIAO task."825 The background regions were the same as for the point source above (see Figure 1))., The background regions were the same as for the point source above (see Figure \ref{im}) ).826 The spectra were ouce more grouped to at least 25 counts per bin. aud fitted witl ab absorbe PL model in the enerey rauge kkeV. The coltunu cleusity was kept fixed at the yest-Lit value obtained fromthe fit to the point source spectrum (Nyy=6.110? 2).," The spectra were once more grouped to at least 25 counts per bin, and fitted with an absorbed PL model in the energy range keV. The column density was kept fixed at the best-fit value obtained fromthe fit to the point source spectrum $N_H=6.4\times10^{21}$ $^{-2}$ )."827 For tje ier aiiulus. ilthere is considerable contaiination [rom the PSF wings. which may have a difTerent. spectunm L'om the point. source because oft euergv dependeuce of the the PSF.," For the inner annulus, there is considerable contamination from the PSF wings, which may have a different spectrum from the point source because of the energy dependence of the the PSF."828 To aecoun for this. we fit the counts extracted [rom t simlated PSF events in the same annulus. auc t1en incl«le tlis as an additional frozen component (UU0.50. N—3.83x10puss 1 >“καν Lis LEkeV) when fittiug the exteuded emissiou.," To account for this, we fit the counts extracted from the simulated PSF events in the same annulus, and then include this as an additional frozen component $\Gamma=0.59$, $N=3.83\times10^{-7}$ $^{-1}$ $^{-2}$ $^{-1}$ is keV) when fitting the extended emission."829 T LestIts of the fits are shown in Table 2.. while the correspoudiug fluxed spectra ancl coifidlence COLours are shown in Figur es2 and )3.. respectively.," The results of the fits are shown in Table \ref{fit}, while the corresponding fluxed spectra and confidence contours are shown in Figures \ref{fluxed} and \ref{contour}, respectively."830" The obse""ved energy [flux was fo5skev 5ἂν 4 (inner)» ac (7.5c1.9)x10!  1 (outer)."," The observed energy flux was $F_{\rm 0.5-8\,keV}=(8.8\pm1.9)\times10^{-14}$ $^{-2}$ $^{-1}$ (inner) and $(7.5\pm1.9)\times10^{-14}$ $^{-2}$ $^{-1}$ (outer)."831 Using t ‘optimal’ energy range as defiued above gives very similar fit parameters., Using the `optimal' energy range as defined above gives very similar fit parameters.832 We fiud that the inner anuulus spectrum is only sliguly softer than tle point source. whie the outer annulus is significautly softer.," We find that the inner annulus spectrum is only slightly softer than the point source, while the outer annulus is significantly softer."833 To better see the morptology of the exeuded emissiou. we subtracted tLe model PSF fro the original image.," To better see the morphology of the extended emission, we subtracted the model PSF from the original image."834 The relaive positions of the simulated ancl observed sources were acljustec [9] iiniunize the residuals., The relative positions of the simulated and observed sources were adjusted to minimize the residuals.835 The 'esiult is show i Figure 5.., The result is shown in Figure \ref{subtract}.836 Some exteuded structu'e Is apparent. such as wisps to the north and east.," Some extended structure is apparent, such as wisps to the north and east."837 With the relatively low S/N it is hard to say more. but. interestingly. sinilar structure is visible ii the short on-axis Chandra observation of 2005 Àoil 13 (Figure 1)).," With the relatively low S/N it is hard to say more, but, interestingly, similar structure is visible in the short on-axis Chandra observation of 2005 April 13 (Figure \ref{im}) )."838 To quantify any auisotropy. we considered the clistributio 10[ the extended emission over azimulthal anges about the point source.," To quantify any anisotropy, we considered the distribution of the extended emission over azimuthal angles about the point source."839 Figure 6. stows a net histoeram of backgrouud- aud PSF-subtraced COUus for the inner annulus., Figure \ref{quad} shows a net histogram of background- and PSF-subtracted counts for the inner annulus.840 The distribullon appears o be non-uniform.m with. X>15.9 for 5 deg‘ees ol [freedom for a constant value (1ull hypothesis srobability of )).," The distribution appears to be non-uniform, with $\chi^2=15.9$ for 5 degrees of freedom for a constant value (null hypothesis probability of )."841 The difference between the simulatec| and. point source images shows residuals up to r—oat 23. altiough the two agree well in the racial slot (Figure 1) .," The difference between the simulated and point source images shows residuals up to $r=3\arcsec$ , although the two agree well in the radial plot (Figure \ref{rad}) )."842 This suggests some imperfections in the PSF model ou sinall scales., This suggests some imperfections in the PSF model on small scales.843We provide a sample 3-D relaxiug TVD code written in Fortran 90.,We provide a sample 3-D relaxing TVD code written in Fortran 90.844 The code is implemented using OpeuMP directives to run in parallel on shared memory machines., The code is implemented using OpenMP directives to run in parallel on shared memory machines.845 The code is fast and memory fricudly., The code is fast and memory friendly.846" The array stores the five conserved hydro quautities a=(p.poy.pe,pe.ο) for cach cell in the Cartesian cubical lattice with side lenethnc."," The array stores the five conserved hydro quantities ${\sf a}=(\rho,\rho v_x,\rho v_y,\rho v_z,e)$ for each cell in the Cartesian cubical lattice with side length."847 For cach sweep. we first call the suxouti1e to determine the appropriate time step which satisfies the CFL condition.," For each sweep, we first call the subroutine to determine the appropriate time step which satisfies the CFL condition."848 The updating of 1v including the flux in thex direction is performed by tiesweepx «ΙΙοιtine., The updating of by including the flux in the direction is performed by the subroutine.849 The data array is divided iuto 1-D array sections which are operated ou by the subroutine., The data array is divided into 1-D array sections which are operated on by the subroutine.850 The independeif columns are distributed aποιος multiple processors ou a shared memory machine the OpeudIP directives., The independent columns are distributed amongst multiple processors on a shared memory machine by the OpenMP directives.851 The relaxiie TVD subroutine in this sample code is written for ease of readability aud therefore. is not fulv optimized.," The relaxing TVD subroutine in this sample code is written for ease of readability and therefore, is not fully optimized."852 A the begiuniis of each parial step in f1ο Ruice-Ixutta time inteeration scheme. the coll-averaged variables defired at exid ccJl centres are caleulated by theaverageflux subroutine.," At the beginning of each partial step in the Runge-Kutta time integration scheme, the cell-averaged variables defined at grid cell centres are calculated by the subroutine."853" The fluxes at cell boundaries Or the rieht-iuoviugOoC» aud le7uoving waves are stored infr arcfl. respectively,"," The fluxes at cell boundaries for the right-moving and left-moving waves are stored in and, respectively."854 We have implemented the mime. superbee. arc Van Leer fx limuters aud he user of the code can easily switch between them.," We have implemented the minmod, superbee, and Van Leer flux limiters and the user of the code can easily switch between them."855 We have pr'ovided sonie initial conditions for the Sedov-Taxor blast wave test., We have provided some initial conditions for the Sedov-Taylor blast wave test.856 The reader is encouraged to test the code aud compare how tje various flux Liniters do at resolving strong shocks., The reader is encouraged to test the code and compare how the various flux limiters do at resolving strong shocks.857 This sample code docs not implement the modified relaxing TD scheme descrijd at the eud of 55.2. which las been found worl very well with the Vau Leer flux limiter but unsable with superbee for the 3-D Sedov Taylor test.," This sample code does not implement the modified relaxing TVD scheme described at the end of $\S\ref{sec:1dscl}$, which has been found work very well with the Van Leer flux limiter but unstable with superbee for the 3-D Sedov Taylor test."858 We have found that the superbee niter is often unstaldle for 3-D Huid sinmlatious., We have found that the superbee limiter is often unstable for 3-D fluid simulations.859 Please contact the authors regarding any questions ou the iiplementation of the relaxing TVD algoritlun., Please contact the authors regarding any questions on the implementation of the relaxing TVD algorithm.860"To fit the observed Fe/H value we required to adopt, again, Apin = 0.01, Fig.","To fit the observed Fe/H value we required to adopt, again, $_{bin}$ = 0.01, Fig."861" 5 shows the time evolution of the element abundances (O, C, N, Ne, S, Cl, Ar, and Fe) relative to H as predicted by model MIR. The thick lines in every panel represent our model results and the symbols are equal to those in Fig."," \ref{xivstrl} shows the time evolution of the element abundances (O, C, N, Ne, S, Cl, Ar, and Fe) relative to H as predicted by model M1R. The thick lines in every panel represent our model results and the symbols are equal to those in Fig."862 3., 3.863 In this model the computed C/H value agrees well with the observational value obtained from RLs., In this model the computed C/H value agrees well with the observational value obtained from RLs.864" The predicted N/H ratio is slightly closer to the observational constraint than in the model MAC, but it is still 3.6 c higher than the observed value, again indicating that the N yields for LIMS have to be revised."," The predicted N/H ratio is slightly closer to the observational constraint than in the model M4C, but it is still 3.6 $\sigma$ higher than the observed value, again indicating that the N yields for LIMS have to be revised."865 The predicted evolution of Ne/H shows relatively good agreement with observed values of old PNe but not so good for young PNe and regions., The predicted evolution of Ne/H shows relatively good agreement with observed values of old PNe but not so good for young PNe and regions.866" In the case of S/H, the predicted evolution is in a good agreement with the PNe observed values but not with observations of regions."," In the case of S/H, the predicted evolution is in a good agreement with the PNe observed values but not with observations of regions."867" The predictions for CI/H and Ar/H are significantly lower than the observed values, in all the cases."," The predictions for Cl/H and Ar/H are significantly lower than the observed values, in all the cases."868 The described behaviors are clearly noticed in Fig., The described behaviors are clearly noticed in Fig.869" 6 where we present the predicted evolution of the C/O, N/O, Ne/O, S/O, CI/O, Ar/O and Fe/O abundance ratios as a function of 12+log O/H and the individual values of the best observed objects (see $4.3)."," \ref{xivsorls} where we present the predicted evolution of the C/O, N/O, Ne/O, S/O, Cl/O, Ar/O and Fe/O abundance ratios as a function of 12+log O/H and the individual values of the best observed objects (see 4.3)."870" In this figure, many of the Ne/O observed values (in particular those of young PNe and regions) lie above the predictions, the S/O for regions isit well predicted within lc level."," In this figure, many of the Ne/O observed values (in particular those of young PNe and regions) lie above the predictions, the S/O for regions is well predicted within $\sigma$ level."871 The predicted CI/O and Ar/O values are ~ 2 o lower than the observed values., The predicted Cl/O and Ar/O values are $\sim$ 2 $\sigma$ lower than the observed values.872 This latter problem is due to the flat extrapolation assumed for the SN yields for m>40 (see $33)., This latter problem is due to the flat extrapolation assumed for the SN yields for $m > 40 $ (see 3).873" According to Woosley Weaver (1995), Cl and Ar yields for m=40 aare lower than for m=35 aand therefore very massive stars would contribute less than massive stars to the ISM enrichment of those elements."," According to Woosley Weaver (1995), Cl and Ar yields for $m = 40 $ are lower than for $m = 35 $ and therefore very massive stars would contribute less than massive stars to the ISM enrichment of those elements."874 We consider that to make a better comparison between models and observations SN yields for m>40 aare necessary., We consider that to make a better comparison between models and observations SN yields for $m > 40 $ are necessary.875 Recall that the yields in this paper for m>40 wwere extrapolated from the m=40 yyields and this extrapolation seems not adequate., Recall that the yields in this paper for $m > 40 $ were extrapolated from the $m = 40 $ yields and this extrapolation seems not adequate.876fromJES imaging of such svstems and hence the relative importance of different excitation mechanisms with radius from the centre of the galaxy.,from imaging of such systems and hence the relative importance of different excitation mechanisms with radius from the centre of the galaxy.877 Two of the galaxies in this study also show significant velocity structure (A2204 and ZwS193)., Two of the galaxies in this study also show significant velocity structure (A2204 and Zw8193).878 Figure 6 shows the reduced 2-D frames of these objects., Figure 6 shows the reduced 2-D frames of these objects.879 The velocity shear is present in both the ionized and molecular gas lines in A2204 but is most o»onounced in the 1-0 8(3) line., The velocity shear is present in both the ionized and molecular gas lines in A2204 but is most pronounced in the 1-0 S(3) line.880 In Zws193 the molecular> [ines are weak compared to Pao so a direct comparison o “the (wo phases is not possible., In Zw8193 the molecular lines are weak compared to $\alpha$ so a direct comparison of the two phases is not possible.881 The amplitudes of these velocity shifts (2300) kms 1) are at the imit of the resolution provided. by CGS4 ancl higher resolution integral field. spectroscopy has the potential to reveal more about the properties of these, The amplitudes of these velocity shifts $>$ 300 km $^{-1}$ ) are at the limit of the resolution provided by CGS4 and higher resolution integral field spectroscopy has the potential to reveal more about the properties of these882Several nore curves are shown in the ligure: The constant one is the line one ges neelectiug the doppler effect. which has bee1 doue iu ilost publications computing the maeetic field iu X-Ray binaries so far.,"Several more curves are shown in the figure: The constant one is the line one gets neglecting the doppler effect, which has been done in most publications computing the magnetic field in X-Ray binaries so far."883 The clottec ines are without gravitatioal redshift or graviational ligit deflection: tle crosses are the restlts of a Moite-Carlo-Simulatjou that uses a realisic geometry and nonrelativistic cold cross sections., The dotted lines are without gravitational redshift or gravitational light deflection; the crosses are the results of a Monte-Carlo-Simulation that uses a realistic geometry and nonrelativistic cold cross sections.884 Details of this moclel wil be publislec| elsewlere (Weth et al..," Details of this model will be published elsewhere (Weth et al.,"885 in preparedion)., in preparation).886 These line euergles are Svseimatically lower han the oues of the simple moclel: the reason fo ‘that is that scatteriig takes plac‘e also above the 101 spot. Wwjere the 1magnetic fiek drops steeper than rp72 (?)..," These line energies are systematically lower than the ones of the simple model; the reason for that is that scattering takes place also above the hot spot, where the magnetic field drops steeper than $r^{-3}$ \citep{wasserman83}."887 The «illerence iu he plot correspoids to a height of abouw 1201n. Iu real systems. there are tw) accreting polar caps. so what the obse“Vel sees is the sum of two spectra a| different angles. wl16 hare Oy aid 05=LSO°—04 in the simjest case.," The difference in the plot corresponds to a height of about 150m. In real systems, there are two accreting polar caps, so what the observer sees is the sum of two spectra at different angles, which are $\theta_{1}$ and $\theta_2=180^\circ-\theta_1$ in the simplest case."888 Because the luminosity depends on the direction. too. at some angles the line feature of one cap will be µίακει in the background of the other one.," Because the luminosity depends on the direction, too, at some angles the line feature of one cap will be hidden in the background of the other one."889 Iu most cases however. these two lines will be too close to eacl other to be resolved.," In most cases however, these two lines will be too close to each other to be resolved."890" A quantity which cau be measured is EUNHs) = [ts value is always smaller than the theoretical μιανΤὰ which ean ye OXalned by taking the cyclotron energies seen at Oj,=0 and 0,4;=1505.", A quantity which can be measured is ) = Its value is always smaller than the theoretical maximum which can be obtained by taking the cyclotron energies seen at $\theta_{\mathrm{obs}}=0$ and $\theta_{\mathrm{obs}}=180^\circ$.891 It depends only ou tle neutron star raclius and on 4j., It depends only on the neutron star radius and on $\eta$.892 However. this does not constrain the parameter Ry/His significantM7 ULless £>2. which has not been fourxl vet in any system.," However, this does not constrain the parameter $R_{\mathrm{N}}/R_{\mathrm{S}}$ significantly unless $\xi \ge 2$, which has not been found yet in any system."893 Iu the case of Her X-1 the geometry (1. e. inclination of the rotatio laxis aud position o ‘the magnetic poles) is known (?).. so a model value of£ can be computed NN ding the appropriate augles.," In the case of Her X-1 the geometry (i. e. inclination of the rotation axis and position of the magnetic poles) is known \citep{blum00}, so a model value of $\xi$ can be computed by using the appropriate angles."894 Unfortunately Her X-1 is not ideal for our purpose because oL its li ich|uuinuisitv of £47=2.0 (?).. so|lat radiation pressuὁ cannot be neglected here.," Unfortunately Her X-1 is not ideal for our purpose because of its high luminisity of $L_{37}=2.0$ \citep{nagase89}, so that radiation pressure cannot be neglected here."895 In cousequence. there are three wksOWL parameters (2x. 8. aud 4). nuit only. two quantities that cai be measured (Eqs aud Εμμ).," In consequence, there are three unknown parameters $R_{\mathrm{N}}$, $B$, and $\eta$ ), but only two quantities that can be measured $E_{c, \mathrm{max}}$ and $E_{c,\mathrm{min}}$ )."896 In order to compute the parameters. au acditioual assumption is needed.," In order to compute the parameters, an additional assumption is needed."897 Two approaches will be tried: Firs tyfRey is fixe toa specific value. in 11e second one radiation presstre is completely neglected by setting jj—1.," Two approaches will be tried: First $R_{\mathrm{N}}/R_{\mathrm{S}}$ is fixed toa specific value, in the second one radiation pressure is completely neglected by setting $\eta=1$."898" Acoting Ba,=30.920.3 keV. Ey,=30.3+1.0 keV (?) aud ;-—NETYE and +10° (?).. aud further assuming a neutron star radius of Ry=3.0404. equation » )) vields y=0.9c0.5. which is consistent. with no radiation pressure."," Adopting $E_{\mathrm{max}}=36.9\pm0.3$ keV, $E_{\mathrm{min}}=30.3\pm1.0$ keV \citep{soong90} and $i=83^\circ\pm4^\circ$ and $\theta_{\mathrm{pole}}=20^\circ\pm10^{\circ}$ \citep{blum00}, and further assuming a neutron star radius of $R_{\mathrm{N}}=3.0 R_{\mathrm{S}}$, equation \ref{ecobs}) ) yields $\eta=0.9\pm0.5$, which is consistent with no radiation pressure."899 Most of the error is due to the large uncertainty iu θρως. the positions of the magnetic poles relative to the rotation axis.," Most of the error is due to the large uncertainty in $\theta_{\mathrm{pole}}$ , the positions of the magnetic poles relative to the rotation axis."900has just collapsed and undergone major mergers. as confirmed by the structured features around the main galaxies NGC4874 and NGC4889 and by the ongoing fall of the NGC4839 galaxy group into the main body of the cluster (Adami et al.,"has just collapsed and undergone major mergers, as confirmed by the structured features around the main galaxies NGC4874 and NGC4889 and by the ongoing fall of the NGC4839 galaxy group into the main body of the cluster (Adami et al."901 2005)., 2005).902 Al656 also exhibits extended radio emissions. including a young radio halo close to center and an outer radio relic located in the SW direction beyond the NGC4839 galaxy group (Giovannini et al.," A1656 also exhibits extended radio emissions, including a young radio halo close to center and an outer radio relic located in the SW direction beyond the NGC4839 galaxy group (Giovannini et al."903 199]. and references therein).," 1991, and references therein)."904 From Eq. (, From Eq. (9058) we derive an overall massMy=ων.N10 M... in agreement with the value of 9.7?!.10M. obtained by Gavazzi et al. (,"8) we derive an overall mass$M_R=9061.24^{+0.44}_{-0.66}\times 10^{15}\,M_{\odot}$ , in agreement with the value of $9.7^{+6.1}_{-3.5}\times 10^{14}\, M_{\odot}$ obtained by Gavazzi et al. ("9072009) from gravitational lensing.,2009) from gravitational lensing.908 A2256 at z0.06 Is à cluster. as highlighted by several studies in various spectral bands; it is à strong X-ray emitter with luminosity Lyz-107? erg s7!.," A2256 at $z\approx 0.06$ is a cluster, as highlighted by several studies in various spectral bands; it is a strong X-ray emitter with luminosity $L_X \approx 10^{45}$ erg $^{-1}$."909 We have used the SM to fit the brightness distribution by Mohr et al. (, We have used the SM to fit the brightness distribution by Mohr et al. (9101999) and the temperature profile observed with. by Snowden et al. (,1999) and the temperature profile observed with by Snowden et al. (9112008). on using the entropy profiles given by Eqs. (,"2008), on using the entropy profiles given by Eqs. ("9125) or by Eqs. (,5) or by Eqs. (9136) and (7): our results are illustrated in Fig.,6) and (7); our results are illustrated in Fig.914 8 and 9., 8 and 9.915 From the SM. we find the virial radius R=2.2753 Mpe. and the halo concentration parameter c=2.7*. ," From the SM, we find the virial radius $R = 2.2^{+0.3}_{-0.3}$ Mpc, and the halo concentration parameter $c=2.7^{+1.7}$ ."916"In the inner ICP regions we find &,=6.27%HCi«107.", In the inner ICP regions we find $\bar{k}_c=6.2^{+3.9}_{-3.1}\times 10^{-2}$.917 Throughout the cluster body we derive the entropy slope «=1.487235. ," Throughout the cluster body we derive the entropy slope $a =9181.48^{+0.35}_{-0.29}$ ."919In the outskirts we obtain: kyTy=4.4755) keV and ng23.6475534«10?E em.3 yielding ky=4000*1727 keV οι”.," In the outskirts we obtain $k_B T_R =9204.4^{+0.9}_{-0.9}$ keV and $n_R=3.64^{+0.04}_{-0.22}\times92110^{-5}$ $^{-3}$, yielding $k_R=4000^{+1097}_{-980}$ keV $^{2}$."922 Correspondingly. we find k=24845 keV em.," Correspondingly, we find $k_c=248^{+224}_{-185}$ keV $^2$."923 Both the brightness and temperature distributions call for an entropy floor: basing on Eqs. (, Both the brightness and temperature distributions call for an entropy floor; basing on Eqs. (924"6) and (7) we derive a floor radius rp2264410"" kpe from the brightness. an evidence reinforced by the value ry=265*15, kpe we obtain from the temperature profile.","6) and (7) we derive a floor radius $r_f=264^{+102}_{-80}$ kpc from the brightness, an evidence reinforced by the value $r_{f}=265^{+80}_{-170}$ kpc we obtain from the temperature profile."925 Its introduction allows the SM to fit well the structured temperature profile of A2256: this features a temperature decrement similar to a CC cluster (e.g.. Piffaretti et al.," Its introduction allows the SM to fit well the structured temperature profile of A2256; this features a temperature decrement similar to a CC cluster (e.g., Piffaretti et al."926 2005: Leccardi Molendi 2009). but at small radii T(r) reverses its trend and increases toward the center.," 2005; Leccardi Molendi 2009), but at small radii $T(r)$ reverses its trend and increases toward the center."927 Such a behavior is understood from the relation TU)xkUays in the inner region where the entropy is constant. the temperature is expected to decrease outwards following the density. while for r>ry the entropy starts to increase and to dominate the density decrement. so raising the temperature out to à peak at r2:380 kpe (about 5); beyond the peak the density steepens and offsets the entropy rise.," Such a behavior is understood from the relation $T(r)\propto k(r)\, n(r)^{2/3}$; in the inner region where the entropy is constant, the temperature is expected to decrease outwards following the density, while for $r>r_f$ the entropy starts to increase and to dominate the density decrement, so raising the temperature out to a peak at $r\approx 350$ kpc (about $5'$ ); beyond the peak the density steepens and offsets the entropy rise."928 The central temperature behavior suggests that the energy delivered by a merger has remolded the whole inner structure. and hence that the ICP is itself thermodynamically young within a dynamically young DM halo.," The central temperature behavior suggests that the energy delivered by a merger has remolded the whole inner structure, and hence that the ICP is itself thermodynamically young within a dynamically young DM halo."929 The halo’s young age is supported by the low values cz4 of the DM concentration. as expected in clusters with à recent transition from fast collapse to slow accretion (see 1).," The halo's young age is supported by the low values $c\approx9304$ of the DM concentration, as expected in clusters with a recent transition from fast collapse to slow accretion (see 1)."931 It isalso indicated by the recentand intense merger activity that characterize A2256. as pinned down by ROSAT.. and," It isalso indicated by the recentand intense merger activity that characterize A2256, as pinned down by , and"932of this paper.,of this paper.933 Although we sugecst motivations for our extrapolatious of au NRB to early epochs. the three cases below inerely provide a theoretical framework in which to study the effects of au NRD at hieh redshifts.," Although we suggest motivations for our extrapolations of an XRB to early epochs, the three cases below merely provide a theoretical framework in which to study the effects of an XRB at high redshifts."934 We adopt two basic forms for the hieh-: NRB. one that is more directly tied to carly QSOs. aud the other. a modified version of the NRB eiven in Madau&Efstathiou(1999).," We adopt two basic forms for the $z$ XRB, one that is more directly tied to early QSOs, and the other, a modified version of the XRB given in \citet{me99}."935" Iu the first case. the specific intensity of cach QSO is taken o have a broken power-law form. Jf,Xνον where a = l.5 for hr = 13.6300 eV (Zheugctal.1997) and a = hs for fv = 300 60V - 10 keV. AVashburnctal. 2001)."," In the first case, the specific intensity of each QSO is taken to have a broken power-law form, $I_\nu \propto936\nu^{-\alpha}$, where $\alpha$ = 1.8 for $h \nu$ = 13.6–300 eV \citep{zheng} and $\alpha$ = 0.8 for $h \nu$ = 300 eV - 10 keV \citep{wash}. ."937. We asstune that only those plotous with energies 2 1 τον permeate the ICAL uniforiuily. while the less energetic Xiotous are absorbed in the individual host halos.," We assume that only those photons with energies $\ga$ 1 keV permeate the IGM uniformly, while the less energetic photons are absorbed in the individual host halos."938 Each QSO' spectrum is further attenuated by absorption by ivdroseus or helium iu the IGAL, Each QSO's spectrum is further attenuated by absorption by hydrogen or helium in the IGM.939 If we take the comoving munber deusity of QSOs to have a peak abundance of Poso = 105 AIpe at:3 aud FosoPoso at earlier epochs. then the mean plivsical (not comoving) separation vetween QSOs at a given i is: We assume then that the cumulative specific iuteusitv . 2 ⋅ ⋅ ∐↕↑∐↸∖↕≼∶⋀∖↕↸∖↖↽∪↕↖↽↸∖↴∖↴⋜↕↴∖↴↙∕≺−⋝↴∖↴⋃∙↖∏↑∐↑∐↸∖↸∖↖↽∪↕∏⊓∪∐∪↕↑∐↸∖ ↴∖↴≺∏∐⋅↸⊳↸∖≼∐∖∐↴∖↴↕↑⋅↖⇁⋜↕∐⋅↸∖⋜∥↧⋅↖⇁↕⋟⋜↧↸⊳↑∪↥⋅↸∖≼↧↕," If we take the comoving number density of QSOs to have a peak abundance of $\Phi_{\rm QSO}$ = $^{-6}$ $^{-3}$ at $z = 3$ and $f_{\rm QSO} \Phi_{\rm QSO}$ at earlier epochs, then the mean physical (not comoving) separation between QSOs at a given $z$ is: We assume then that the cumulative specific intensity in the IGM evolves as $d_{\rm QSO}^2$, with the evolution of the source density already factored in through $f_{\rm QSO}$."940∐↑∐⋅∪∏∶↴∙⊾∐⋅↗↳⊽≺⊒↔∪∙↖↖⊽↸∖ ∐∪↥⋅⋯⋜↧∐∑↸∖↑∐↸∖∏∐⋜↧↑↑↸∖∐∏⋜↧↑↸∖≼⇂↕⊔↸∖⋜⋯↕∐↑↸∖∐↴∖↴↕↑⋅↖⇁∫↗∕↴∖↴⋯⊳∐↑∐⋜↧↑⋜⋯ extrapolation down to 13.6 eV. usiug the QSO's intrinsic spectral shape. is fy = 7! cre emὃς 1 1 x! at +=3. consistent with observational constraints (sec. e.g. Taardt&Madau(1996):Fardaletal. (L998).. ancl references therein).," We normalize the unattenuated mean intensity $I_\nu$ such that an extrapolation down to 13.6 eV, using the QSO's intrinsic spectral shape, is $I_0$ = $^{-21}$ erg $^{-2}$ $^{-1}$ $^{-1}$ $^{-1}$ at $z = 3$, consistent with observational constraints (see, e.g., \citet{hm96,fard}, , and references therein)."941 Realistically. this uuderestimates the correspouding X-ray contribution because the radiation at 13.6 eV is subject to some attenuation from the IGAL even abr=3.," Realistically, this underestimates the corresponding X-ray contribution because the radiation at 13.6 eV is subject to some attenuation from the IGM, even at $z = 3$."942" Combining the above factors. we may paramctrize the evolution of the IGALfiltered specific intensity for 5>3 as where we adopt LO92US frau the SDSS collaboration —foso(Fanetal.2001a). aud rz,=dosoliyet(IP)|oye,Te"")oyoe!) is the IGAL optical depth. with o, being the appropriate photoionization cross section for cach species."," Combining the above factors, we may parametrize the evolution of the IGM-filtered specific intensity for $z \geq 3$ as: where we adopt $f_{\rm QSO}$ = $10^{- 0.5(z - 3)}$ from the SDSS collaboration \citep{fan2}, and $\tau_\nu = d_{\rm QSO} [n_{\rm943H^0} \sigma_\nu ({\rm H^0}) + n_{\rm He^0} \sigma_\nu ({\rm He^0}) +944n_{\rm He^+} \sigma_\nu ({\rm He^+})]$ is the IGM optical depth, with $\sigma_\nu$ being the appropriate photoionization cross section for each species."945 Heuceforth. we refer to the above NRB as case S (for the Sloan survey).," Henceforth, we refer to the above XRB as case S (for the Sloan survey)."946 An alternate prescription for the hieh-: NRB is eiven in Madau&Efstathiou (1999).. in which the present-day NRB evolves as (11:)7. weighted by an exponential cutoff factor to account for the decreasing source deusity at hieli redshift.," An alternate prescription for the $z$ XRB is given in \citet{me99}, , in which the present-day XRB evolves as $(1 + z)^3$, weighted by an exponential cutoff factor to account for the decreasing source density at high redshift."947 The specific intensity of this NRB is eiven by equ. [, The specific intensity of this XRB is given by eqn. [948"6] of Madan&Efstathiou(1999). in units of keV 2 s tsy twhich. over the enerev range 110 keV. we take to be: We will consider two cases of this NRB: case 1 with :, =. asin Madau&Efstathiou(1999).. and case 2 without the exponcutial cutoff factor. as in Collin-Souffiu(1991) where the NRB evolves cosmologically as a radiation field.","6] of \citet{me99} in units of keV $^{-2}$ $^{-1}$ $^{-1}$ $^{-1}$, which, over the energy range 1–10 keV, we take to be: We will consider two cases of this XRB: case 1 with $z_c$ = 5, as in \citet{me99}, and case 2 without the exponential cutoff factor, as in \citet{coll91} where the XRB evolves cosmologically as a radiation field."949 The asstuned specific intensity of cach NRB increases from case S through cases Laud 2., The assumed specific intensity of each XRB increases from case S through cases 1 and 2.950 At .=9. for example. their respective values at 2 keV are L1 «10.75. 1.6 <1074. and E10 ere 2s 1I 1m 4 ," At $ z = 9$, for example, their respective values at 2 keV are 4.4 $\times 10^{-26}$, 1.6 $\times 10^{-24}$, and 4 $\times 10^{-23}$ erg $^{-2}$ $^{-1}$ $^{-1}$ $^{-1}$ ."951The evolution of the temperature and ionization fractions is calculated as follows., The evolution of the temperature and ionization fractions is calculated as follows.952" We take the backerouud cosmolosv to be described bw. O04, = 0.3. O4 = 07. h—QT. Ou? = (0.019. Tesipy = 2.728 IS. aud Yn. = 0.21."," We take the background cosmology to be described by, $\Omega_{\rm953m}$ = 0.3, $\Omega_\Lambda$ = 0.7, $h = 0.7$, $\Omega_{\rm b} h^2$ = 0.019, $T_{\rm CMB,0}$ = 2.728 K, and $Y_{\rm He}$ = 0.24."954 The calculation is begun at :=12. with aES initial IGME teiiperature of 20 IK aud residual ionizatioFPorARE fractions of μι=10| aud igi=10ὃν," The calculation is begun at $z=12$, with an initial IGM temperature of 20 K and residual ionization fractions of $x_{\rm H^+} = 10^{-4}$ and $x_{\rm He^+} =95510^{-9}$."956 We conside NRBs in the redshift rauge Y «i< 12: the lower limi is roughly the latest epoch from observational limits (Faetal.20010:Beckerct2001). that cau be considere as being prior to reionization. while at ;=12 horizo effects begin to attenuate the NRD.," We consider XRBs in the redshift range 7 $< z <$ 12; the lower limit is roughly the latest epoch from observational limits \citep{fan3,957becker} that can be considered as being prior to reionization, while at $z958= 12$ horizon effects begin to attenuate the XRB."959 We demonstrate the latter by equating the lelt-crossing time for half the mean physical source separation(given by equ., We demonstrate the latter by equating the light-crossing time for half the mean physical source separation(given by eqn.960 1) with the age of the universe for NRB case S. accounting for the finite time needed for the N-rav photous from individual sources to permeate the IGAL," 1) with the age of the universe for XRB case S, accounting for the finite time needed for the X-ray photons from individual sources to permeate the IGM."961 As case S is the weakest NRB considered here. with the lowest source deusitv. this vields a couscrvative lower lint to the redshift at which horizon effects become important.," As case S is the weakest XRB considered here, with the lowest source density, this yields a conservative lower limit to the redshift at which horizon effects become important."962 Furthermore. the Eddiugton accretion timescale is ~ 15 «10* vr. assuming an average QSO radiative efficiency of," Furthermore, the Eddington accretion timescale is $\sim$ 4.5 $\times 10^7$ yr, assuming an average QSO radiative efficiency of."963 Since this corresponds to Do450 dn our adopted cosmology. by 2=12. sources have vad d 105 vr (may times their Eddiustonu timescale} o form and gcucrate an NRB (sec. however. Waimanu&Loch(2001).. on how this may not prove sufficient for the ormation of the most massive black holes that likely power he brightest QSOs).," Since this corresponds to $z \sim96450$ in our adopted cosmology, by $z = 12$, sources have had $\sim$ 4 $\times 10^8$ yr (many times their Eddington timescale) to form and generate an XRB (see, however, \citet{hl01}, on how this may not prove sufficient for the formation of the most massive black holes that likely power the brightest QSOs)."965 Our nuuerical solution for the evolving thermodvuamic xoperties of the ICAL solves the uonequilibrimm rate equations and enerev equation for the expanding ICAL cf. Giroux&Shapiro(1996).," Our numerical solution for the evolving thermodynamic properties of the IGM solves the nonequilibrium rate equations and energy equation for the expanding IGM [cf. \citet{gs96},"966.. equs. (, eqns. (9672.1)-(2.D].,2.1)-(2.4)].968 We do rot follow the nonequilibrium formation and destruction of IT». aud we do not consider detailed radiative transfer.," We do not follow the nonequilibrium formation and destruction of $_2$, and we do not consider detailed radiative transfer."969 The equations are iuteerated with a fourth-order Runec-atta scheme with the tine steps set to be less than of the shortest relevant thermal or ionization timescale., The equations are integrated with a fourth-order Runge-Kutta scheme with the time steps set to be less than of the shortest relevant thermal or ionization timescale.970 Iu Figures d3. we show the temperature. aud livdrosenu and οήτα ionization fractions of the IGAL as a function of redshift for NRD cases 1 aud 2.," In Figures 1–3, we show the temperature, and hydrogen and helium ionization fractions of the IGM as a function of redshift for XRB cases 1 and 2."971 Case S was found to have negligible effects on the thermal auc ionization properties of the IGAL and did not alter them appreciably. over the redshifts that we cousider. from their values i- an expanding ICAL without any N-ravs.," Case S was found to have negligible effects on the thermal and ionization properties of the IGM, and did not alter them appreciably, over the redshifts that we consider, from their values in an expanding IGM without any X-rays."972 We therefore do uot include case S in the Heures. but emphasize that our first result is thatthere will be no significant effects on the evolving ICM for a conservative estimate of tle NRB.," We therefore do not include case S in the figures, but emphasize that our first result is thatthere will be no significant effects on the evolving IGM for a conservative estimate of the pre-reionizationXRB."973 The plots show that. depending on the choice of the NEB. the IGAL teiiperatine ranges frou  100 K to ~ Lo! Ik. with μιvarving from to ~ 20%..," The plots show that, depending on the choice of the XRB, the IGM temperature ranges from $\sim$ 100 K to $\sim$ $^4$ K, with $x_{\rm974H^+}$varying from to $\sim$ ."975 For each case. the solutions inchiding aud exchiding adiabatie cooling are almost identical. aud are practically overlaidiu the figures.," For each case, the solutions including and excluding adiabatic cooling are almost identical, and are practically overlaidin the figures."976 As μιαν be expected. the stronger the XRD. the greater," As may be expected, the stronger the XRB, the greater"977The long wavelength emissivity of dust in the difuse medium has been modeled and tabulated by ?..,The long wavelength emissivity of dust in the difuse medium has been modeled and tabulated by \citet{LiD01}.978 At 850m. they glve kyson O.decm-/g. However. this value may not be representative of the dust properties in. molecular clouds.," At $\mu$ m, they give $\kappa_{850\mu m}=0.4$ $^2/$ g. However, this value may not be representative of the dust properties in molecular clouds."979 In particular. coagulation processes can occur between grains.," In particular, coagulation processes can occur between grains."980 The large fluffy aggregates created that way have different absorption/emission properties than those in. the diffuse medium., The large fluffy aggregates created that way have different absorption/emission properties than those in the diffuse medium.981 Enhancements of the dust emissivity can be attributed to coagulation processes., Enhancements of the dust emissivity can be attributed to coagulation processes.982 Such an emissivity enhancement is observed in our galaxy (22?) and for giant molecular clouds. the dust emissivity in the (sub-)millimeter regime is enhanced by a factor 2-3 with respect to the diffuse medium.," Such an emissivity enhancement is observed in our galaxy \citep{CBL+01,SAB+03,Bot:2007yq} and for giant molecular clouds, the dust emissivity in the (sub-)millimeter regime is enhanced by a factor 2-3 with respect to the diffuse medium."983 In order to determine the dust opacity appropriate for the GMCs probed by our observations. we chose to estimate it directly from. sub-millimeter observations in. à. Galactic molecular environment.," In order to determine the dust opacity appropriate for the GMCs probed by our observations, we chose to estimate it directly from sub-millimeter observations in a Galactic molecular environment."984 Without further knowledge. we make the assumption that the molecular ring in our Galaxy can be used as a reference for the giant molecular clouds of the SMC.," Without further knowledge, we make the assumption that the molecular ring in our Galaxy can be used as a reference for the giant molecular clouds of the SMC."985 In particular. this assumes that dust evolution (like coagulation) occur in the same way in SMC GMCs as in our galaxy.," In particular, this assumes that dust evolution (like coagulation) occur in the same way in SMC GMCs as in our galaxy."986 The method used ts similar to the one by ?:: a map of the dust emission in our Galaxy at 870um ts created using FIRAS data., The method used is similar to the one by \citet{Bot:2007yq}: a map of the dust emission in our Galaxy at $\mu$ m is created using FIRAS data.987 In the molecular ring. the 870;m dust emission correlated with is substracted from the observed emission using the correlation observed at high galactic latitude.," In the molecular ring, the $\mu$ m dust emission correlated with is substracted from the observed emission using the correlation observed at high galactic latitude."988 The remaining emission correlates with the CO intensity (?) and a linear fit on the correlation gives: We checked that in individual GMCs in our solar neighbourhood. this ratio is similar (~0.26+ 0.18- the uncertainty here reflects the dispersion between clouds) and is therefore characteristic of the dust emission in GMCs in the Milky Way.," The remaining emission correlates with the CO intensity \citep{DHT01} and a linear fit on the correlation gives: We checked that in individual GMCs in our solar neighbourhood, this ratio is similar $\sim 0.26\pm 0.18$ – the uncertainty here reflects the dispersion between clouds) and is therefore characteristic of the dust emission in GMCs in the Milky Way."989 Assuming a standard conversion factor between the CO intensity and the molecular gas column densities (Χου=ΝΗΣΙWeo1.8- km/s)! 10°°molem™ (?2))). a dust temperature in galactic GMCs of 15 K (K.as in ?.. we can deduce a dust emissivity at 870m for the molecular ring.," Assuming a standard conversion factor between the CO intensity and the molecular gas column densities $X_{CO}=N(H_2)/W_{CO}=1.8\cdot 10^{20}$ $^{-2}$ (K. $^{-1}$ \citep{DHT01,GCT05}) ), a dust temperature in galactic GMCs of 15 K as in \citet{Bot:2007yq}, we can deduce a dust emissivity at $\mu$ m for the molecular ring."990 By multiplying this value with the SMC dust to gas ratio. we obtain a dust emissivity suitable for SMC GMCs: This emissivity of dust in molecular regions corresponds to an opacity &x;o=1.26€0.021jg.," By multiplying this value with the SMC dust to gas ratio, we obtain a dust emissivity suitable for SMC GMCs: This emissivity of dust in molecular regions corresponds to an opacity $\kappa_{870}=1.26\pm0.02 cm^2/g$."991 The uncertunties quoted above for the different. values correspond to formal uncertainties from the fitting procedures and do not reflect the intrinsic. scatter in. the S70jm- Woo correlation. nor the systematic uncertainty due to the assumptions which are by far the dominant source of error.," The uncertainties quoted above for the different values correspond to formal uncertainties from the fitting procedures and do not reflect the intrinsic scatter in the $\mu$ $_{CO}$ correlation, nor the systematic uncertainty due to the assumptions which are by far the dominant source of error."992" For example. it is unclear whether ""coagulation"" of dust grains occurs in the SMC and this will be discussed further in Sec. 4.2.."," For example, it is unclear whether ""coagulation"" of dust grains occurs in the SMC and this will be discussed further in Sec. \ref{sec:discusdust}. ."993 However. within our current knowledge. most systematic effects will increase the mass estimated from the dust emission.," However, within our current knowledge, most systematic effects will increase the mass estimated from the dust emission."994 Using eq., Using eq.995 + and a dust temperature between 12 and 19 K. we can therefore determine gas masses directly from the observed 870m dust emission continuum in the CO detected GMCs of the SMC.," \ref{eqepsi} and a dust temperature between 12 and 19 K, we can therefore determine gas masses directly from the observed $\mu$ m dust emission continuum in the CO detected GMCs of the SMC."996 Gas masses for all the GMCs of the south west region of the SMC observed in CO are deduced from the LABOCA sub-millimeter emission and are summarized in Tab. 3., Gas masses for all the GMCs of the south west region of the SMC observed in CO are deduced from the LABOCA sub-millimeter emission and are summarized in Tab. \ref{tab3}.997 These masses are compared to the masses deduced from theapplication of the virial theorem on the CO line width and radii (c.f., These masses are compared to the masses deduced from theapplication of the virial theorem on the CO line width and radii (c.f.998 Tab 3 and Fig. 3))., Tab \ref{tab3} and Fig. \ref{fig3}) ).999 For comparison purposes. we took from ? the masses determined from dust millimeter emission and the virial masses for a reference sample of similar molecular clouds in the solar neighbourhood.," For comparison purposes, we took from \citet{Bot:2007yq} the masses determined from dust millimeter emission and the virial masses for a reference sample of similar molecular clouds in the solar neighbourhood."1000 For self-gravitating clouds. the velocity dispersion of the CO clumps balances the gravitational pressure and the virial masses should be similar to the cloud masses deduced from dust emission.," For self-gravitating clouds, the velocity dispersion of the CO clumps balances the gravitational pressure and the virial masses should be similar to the cloud masses deduced from dust emission."1001 However. we observe that the masses of the GMCs as deduced from dust emission are systematically larger than the virial masses determined for the same clouds.," However, we observe that the masses of the GMCs as deduced from dust emission are systematically larger than the virial masses determined for the same clouds."1002 Our study with LABOCA data at 870m therefore confirms the results obtained by ? and ?) with SIMBA data., Our study with LABOCA data at $\mu$ m therefore confirms the results obtained by \citet{RBR+04} and \citet{Bot:2007yq} with SIMBA data.1003" We find a median mass ratio My,/M7""=0.21 (0.41 for the upper limit on the dust temperature). contrasting with the mass ratio obtained for equivalent clouds in the Milky Way. which ts always above I."," We find a median mass ratio $M_{vir}/M_H^{mm}=0.21$ (0.41 for the upper limit on the dust temperature), contrasting with the mass ratio obtained for equivalent clouds in the Milky Way, which is always above 1."1004 The most straightforward interpretation of the mass discrepancy we observe in the SMC is then that the CO linewidth do not measure the full velocity distribution of the gas., The most straightforward interpretation of the mass discrepancy we observe in the SMC is then that the CO linewidth do not measure the full velocity distribution of the gas.1005 There are two independent reasons for why this could be true., There are two independent reasons for why this could be true.1006 The CO emitting regions may be present only in the interior of the molecular clouds. in regions shielded from the UV radiation field (??)..," The CO emitting regions may be present only in the interior of the molecular clouds, in regions shielded from the UV radiation field \citep{LLD+94,Glover:2010uq}."1007 If the (unresolved) CO emitting clumps are not evenly distributed in the region detected by the CO observations. the observed line width might not reflect the full velocity dispersion in the cloud.," If the (unresolved) CO emitting clumps are not evenly distributed in the region detected by the CO observations, the observed line width might not reflect the full velocity dispersion in the cloud."1008 The CO line could come from the densestregions created by shocks in a turbulent medium (?).., The CO line could come from the densestregions created by shocks in a turbulent medium \citep{Klessen:2009jt}. .1009 Simulations in a turbulent, Simulations in a turbulent1010"in this range, there was (in general) only one peak present at the time.","in this range, there was (in general) only one peak present at the time."1011" However, during one observing night, three peaks were seen simultaneously at approximately these frequencies (Figure 4))."," However, during one observing night, three peaks were seen simultaneously at approximately these frequencies (Figure \ref{fig:pow320}) )."1012" The nightly mean error for any peak appearing at 135 cdd! — 148 cdd""!, is about 0.8 dd""!."," The nightly mean error for any peak appearing at 135 $^{-1}$ – 148 $^{-1}$, is about 0.8 $^{-1}$."1013 The upper two frames in Figure 5 show the combined power spectra of the six nights of best quality., The upper two frames in Figure \ref{fig:s_pow_best2} show the combined power spectra of the six nights of best quality.1014" The bottom two panels show model power-spectra constructed from sine waves at the peak frequencies found in the combined night dataset, at 18.48 ! (wo), 36.97 cdd! (2w.), 71.9 dd!, 135.2 dd!, 144.3 cdd""! and 147.9 cdd!, using the same sampling pattern as the data."," The bottom two panels show model power-spectra constructed from sine waves at the peak frequencies found in the combined six-night dataset, at 18.48 $^{-1}$ $\omega_{\text{o}}$ ), 36.97 $^{-1}$ $2\omega_{\text{o}}$ ), 71.9 $^{-1}$, 135.2 $^{-1}$, 144.3 $^{-1}$ and 147.9 $^{-1}$, using the same sampling pattern as the data."1015" The model is able to re-construct the overall appearance and widths of the signals seen in the data reasonably well, indicating that there is power excess at these frequencies."," The model is able to re-construct the overall appearance and widths of the signals seen in the data reasonably well, indicating that there is power excess at these frequencies."1016" If excluding any of the frequencies from the model, the data power spectrum cannot be reproduced."," If excluding any of the frequencies from the model, the data power spectrum cannot be reproduced."1017" We note that 71.9 dd! is about half that of 144.3 dd, but not exactly in a 2:1 ratio, indicating that the signals are not constant in amplitude and phase (see Section 3.4 for the case of BW Sculptoris)."," We note that 71.9 $^{-1}$ is about half that of 144.3 $^{-1}$, but not exactly in a 2:1 ratio, indicating that the signals are not constant in amplitude and phase (see Section \ref{2009} for the case of BW Sculptoris)."1018" For a complete summary of the frequency analysis, see Table 2.."," For a complete summary of the frequency analysis, see Table \ref{tab:freq}."1019" BW Sculptoris (hereafter BW Scl) is a 16th magnitude blue star which was found to coincide with RXJ2353-0-3852 in the Rosat bright-source catalogue, and then identified as a cataclysmic variable by ?.."," BW Sculptoris (hereafter BW Scl) is a 16th magnitude blue star which was found to coincide with RXJ2353-0-3852 in the Rosat bright-source catalogue, and then identified as a cataclysmic variable by \cite{1997A&A...318..134A}."1020 ? independently discovered the star as a blue object in the Hamburg/ESO survey for bright QSOs., \cite{1997A&A...324L..57A} independently discovered the star as a blue object in the Hamburg/ESO survey for bright QSOs.1021 These two studies established the very short orbital period of 78 minutes., These two studies established the very short orbital period of 78 minutes.1022" In addition to broad and doubled H and He emission lines, BW Scl also shows very broad Balmer and Lyman absorptions, signifying the presence of a white dwarf of modest temperature (~15000 K; ?))."," In addition to broad and doubled H and He emission lines, BW Scl also shows very broad Balmer and Lyman absorptions, signifying the presence of a white dwarf of modest temperature $\sim 15000$ K; \citealt{2005ApJ...629..451G}) )."1023" If roughly half of the visual light comes from such a white dwarf, then the white dwarf has V=17.3 and Mv~12, implying a distance of only ~110 pc."," If roughly half of the visual light comes from such a white dwarf, then the white dwarf has $V=17.3$ and $M_{V}\sim 12$, implying a distance of only $\sim 110$ pc."1024" This also agrees with the large proper motion found in the USNO catalogue (105 ms yr!, ?))."," This also agrees with the large proper motion found in the USNO catalogue (105 $\,$ $^{-1}$, \citealt{2004AJ....127.3060G}) )."1025" These considerations (a nearby star of very short Porb), and the possibility to study the underlying white dwarf, motivated us to carry out campaigns of series photometry nearly every year since 1999."," These considerations (a nearby star of very short $P_{\textbf{orb}}$ ), and the possibility to study the underlying white dwarf, motivated us to carry out campaigns of time-series photometry nearly every year since 1999."1026" In total, BW Scl was observed for about 1000 hours spread over about 200 nights, mainly using the globally distributed telescopes of the Center for Backyard Astrophysics (CBA: ?7))."," In total, BW Scl was observed for about 1000 hours spread over about 200 nights, mainly using the globally distributed telescopes of the Center for Backyard Astrophysics (CBA: \citealt{1993ApJ...417..298S, patterson_1998}) )."1027 A summary observing log is presented in Table 3.., A summary observing log is presented in Table \ref{tab:obs2}.1028" To maximise the signal and optimise the search for periodic features, usually no filter or a very broad filter, ,wwas used."," To maximise the signal and optimise the search for periodic features, usually no filter or a very broad filter, was used."1029" Occasional runs were obtained in V and I bandpasses to provide a rough calibration, and to verify that the periodic features in the light curve are indeed broadband signals."," Occasional runs were obtained in V and I bandpasses to provide a rough calibration, and to verify that the periodic features in the light curve are indeed broadband signals."1030" The smaller (25 cm — 35 cm) telescopes generally used the star GSC 8015-671 as a comparison, while the larger (91 cm) telescopes used USNO 0450-40780391, a nearby 16th magnitude star."," The smaller (25 cm – 35 cm) telescopes generally used the star GSC 8015-671 as a comparison, while the larger (91 cm) telescopes used USNO 0450-40780391, a nearby 16th magnitude star."1031 These comparison stars can be considered to be constant., These comparison stars can be considered to be constant.1032" The clear and broadband filters permit only a rough calibration, but BW Scl remained within ~0.3 mag of V=16.6 throughout the campaign."," The clear and broadband filters permit only a rough calibration, but BW Scl remained within $\sim 0.3$ mag of $V=16.6 $ throughout the campaign."1033" In terms of instrumental magnitude, limits on night-to-night variability within each season are more stringent: typically «0.05 mag, and always «0.1 mag."," In terms of instrumental magnitude, limits on night-to-night variability within each season are more stringent: typically $< 0.05$ mag, and always $< 0.1$ mag."1034" This degree of constancy is remarkable for a cataclysmic variable, and is probably due to the WD's large contribution to the light in the optical."," This degree of constancy is remarkable for a cataclysmic variable, and is probably due to the WD's large contribution to the light in the optical."1035" In order to study the periodic behaviour, we always tried to obtain photometry densely distributed in time, preferably with contribution from telescopes widely spaced in longitude (in order to solve problems associated with daily aliases)."," In order to study the periodic behaviour, we always tried to obtain photometry densely distributed in time, preferably with contribution from telescopes widely spaced in longitude (in order to solve problems associated with daily aliases)."1036" Most of the analysis below is based on long time series from stations in New Zealand, South Africa, and Chile, and hence not afflicted by aliasing problems."," Most of the analysis below is based on long time series from stations in New Zealand, South Africa, and Chile, and hence not afflicted by aliasing problems."1037 The upper frame of Figure 6 shows the light curve from, The upper frame of Figure \ref{fig:1} shows the light curve from1038Fie.5(b) is the same as Fig.5(a). except with Εμ} given by Eq.(2)). with the empty and full beam distances. D4(à=0z)and D4(aà—12). computed by integrating the equation.,"Fig.5(b) is the same as Fig.5(a), except with $\tilde{\kappa}_{min}(z)$ given by \ref{eq:kapdef}) ), with the empty and full beam distances, $D_A(\tilde{\alpha}=0|z)$ and $D_A(\tilde{\alpha}=1|z)$, computed by integrating the Dyer-Roeder equation."1039 Comparison ol Fies.3-4 with Fig.5 shows that the errors in estimated distances using analvtical approximations of Eqs.(A))-(A12)) are much smaller than the errors in Αμ) and Ag(z2).," Comparison of Figs.3-4 with Fig.5 shows that the errors in estimated distances using analytical approximations of \ref{eq:B0,C0,D0}) \ref{eq:openA0}) ) are much smaller than the errors in $\tilde{\kappa}_{min}(z)$ and $A_0(z)$."1040 This is becauseNEHMEN m The last inequality arises [rom (he fact that D4(à=1ο} and D(à2) differ by less than ~ for a<2.," This is because | -1 | The last inequality arises from the fact that $D_A(\tilde{\alpha}=1|z)$ and $D_A(\tilde{\alpha}|z)$ differ by less than $\sim\,$ for $\tilde{\alpha}\la 2$."1041 For all practical purposes in the weak lensing of standard candles. (he local smootliness parameter àοX 2. since the probability for Aο>2 is vanishinely small for all cosmological models at all redshifts (Wane1999).," For all practical purposes in the weak lensing of standard candles, the local smoothness parameter $\tilde{\alpha}\la 2$ , since the probability for $\tilde{\alpha}\ga 2$ is vanishingly small for all cosmological models at all redshifts \citep{Wang99}."1042. Note that the probability distribution of à becomes narrower aid peaked closer to à=1 as redshift 2 increases. as (he universe is smoother on the average al high z (Wang1999).," Note that the probability distribution of $\tilde{\alpha}$ becomes and peaked closer to $\tilde{\alpha}=1$ as redshift $z$ increases, as the universe is smoother on the average at high $z$ \citep{Wang99}."1043. Our analvtical approximations. given by Eqs.(2)). (A))-CÀ12)). give an aceuraey. of better than about in all cosmological for à.<2 (see Fig.5(a)).," Our analytical approximations, given by \ref{eq:exp}) ), \ref{eq:B0,C0,D0}) \ref{eq:openA0}) ), give an accuracy of better than about in all cosmological for $\tilde{\alpha}\la 2$ (see Fig.5(a))."1044 If the exact expression for ρωσ) (see Eq.(2))). instead of Eqs.(AG)) and CALI)). is used. the accuracy in the estimated distance is better than for all cosmological models forAS2(see Fig.5(b)).," If the exact expression for $\tilde{\kappa}_{min}(z)$ (see \ref{eq:kapdef}) )), instead of \ref{eq:flatkap}) ) and \ref{eq:openkap}) ), is used, the accuracy in the estimated distance is better than for all cosmological models for$\tilde{\alpha}\la 2$(see Fig.5(b))."1045"The relationship between gas, metals and dust that defines the interstellar medium (ISM), plays a central role in the properties of star-formation, and in the appearance, evolution and ultimate fate of galaxies.","The relationship between gas, metals and dust that defines the interstellar medium (ISM), plays a central role in the properties of star-formation, and in the appearance, evolution and ultimate fate of galaxies."1046" However the basic quantitative relationship between gas, metals and dust is still not well-defined even for our own galaxy."," However the basic quantitative relationship between gas, metals and dust is still not well-defined even for our own galaxy."1047 Many studies have been made over the years examining the dust-to-gas ratio in the Galaxy and more recently at cosmological distances., Many studies have been made over the years examining the dust-to-gas ratio in the Galaxy and more recently at cosmological distances.1048" Two methods dominate these analyses: a) comparing hydrogen absorption to dust extinction or reddening, using the Lya line in the UV (and sometimes Hz UV lines) to get the total gas column and pairs of stars to obtain the total extinction, and b) soft X-ray photoelectric absorption that measures the total metal column density in the foreground of bright X-ray sources, and converting this to a gas column assuming a metallicity, and comparing this to a dust extinction obtained from methods like the Balmer decrement, the deviation in the optical/infrared from a blackbody spectrum or even measuring the dust column using the halo made by small angle scattering of X-rays off the dust."," Two methods dominate these analyses: a) comparing hydrogen absorption to dust extinction or reddening, using the $\alpha$ line in the UV (and sometimes $_2$ UV lines) to get the total gas column and pairs of stars to obtain the total extinction, and b) soft X-ray photoelectric absorption that measures the total metal column density in the foreground of bright X-ray sources, and converting this to a gas column assuming a metallicity, and comparing this to a dust extinction obtained from methods like the Balmer decrement, the deviation in the optical/infrared from a blackbody spectrum or even measuring the dust column using the halo made by small angle scattering of X-rays off the dust."1049" The first method provides a genuine gas-to-dust ratio, in the sense that it measures the bulk of the gas directly."," The first method provides a genuine gas-to-dust ratio, in the sense that it measures the bulk of the gas directly."1050" However, it suffers from the deficiency that it is insensitive to ionised gas and unless the molecular lines are measured, also to H2, where the fraction of hydrogen in Hy may be ~0.5 for Ay20.5 (?).."," However, it suffers from the deficiency that it is insensitive to ionised gas and unless the molecular lines are measured, also to $_2$, where the fraction of hydrogen in $_2$ may be $\sim 0.5$ for $A_V\gtrsim0.5$ \citep{2009ApJS..180..125R}."1051 Furthermore it only works along relatively low extinction lines of sight (Ay<2— 3) since it requires spectroscopy in the UV where the extinction is far higher and stars are often too faint to observe in Lya or H»., Furthermore it only works along relatively low extinction lines of sight $A_V\lesssim2-3$ ) since it requires spectroscopy in the UV where the extinction is far higher and stars are often too faint to observe in $\alpha$ or $_2$.1052" The X-ray absorption method works to very high extinctions (Ay~30 or more) and measures essentially all metals whether they are ionised or even in the solid phase, providing a census of the total column density in metals."," The X-ray absorption method works to very high extinctions $A_V\sim30$ or more) and measures essentially all metals whether they are ionised or even in the solid phase, providing a census of the total column density in metals."1053" However, it is a measurement of the metal column, not the gas column since the X-ray absorption is almost insensitive to hydrogen absorption and depends only weakly on helium."," However, it is a measurement of the metal column, not the gas column since the X-ray absorption is almost insensitive to hydrogen absorption and depends only weakly on helium."1054 Therefore the X-ray absorption requires a metallicity conversion to move from a dust-to-metals to a to-gas ratio., Therefore the X-ray absorption requires a metallicity conversion to move from a dust-to-metals to a dust-to-gas ratio.1055 It is perhaps worth noting that most studies to date in the Galaxy have either focussed on relatively nearby sets of objects or provided a small number (between 3 and about 20 for the studies) of lines of sight to locations within a few kpc of the Sun., It is perhaps worth noting that most studies to date in the Galaxy have either focussed on relatively nearby sets of objects or provided a small number (between 3 and about 20 for the studies) of lines of sight to locations within a few kpc of the Sun.1056 Most studies in the Galaxy have therefore not probed the ISM of the Milky Way in either a complete or unbiased way., Most studies in the Galaxy have therefore not probed the ISM of the Milky Way in either a complete or unbiased way.1057 These studies have consistently found a dust-to-gas ratio," These studies have consistently found a dust-to-gas ratio at a level of $N_H/A_V \sim 2\times10^{21}$ $^{-2}$ $^{-1}$ \citep{1978ApJ...224..132B,1981MNRAS.196..469W,1994ApJ...427..274D,1996Ap&SS.236..285R,1973A&A....26..257R,1975ApJ...198...95G,1975ApJ...198..103R,1995A&A...293..889P,2003A&A...408..581V,2009MNRAS.400.2050G,2009ApJS..180..125R}."1058" The statistical errors quoted for some studies have been as small as a few 10? ccm? mmag™!, however the variation from study to study is closer to a few parts in 1020 ccm? mmag™! This discrepancy may be related to an underestimate of the uncertainties or to an intrinsic scatter in the relation."," The statistical errors quoted for some studies have been as small as a few $10^{19}$ $^{-2}$ $^{-1}$, however the variation from study to study is closer to a few parts in $10^{20}$ $^{-2}$ $^{-1}$ This discrepancy may be related to an underestimate of the uncertainties or to an intrinsic scatter in the relation."1059" Gamma-ray bursts (GRBs), while found at cosmological distances, are extremely bright."," Gamma-ray bursts (GRBs), while found at cosmological distances, are extremely bright."1060 In this paper we use the large homogeneous sample of GRB X-ray afterglows to determine upper limits to the metal column densities to several hundred lines of sight through the Galaxy., In this paper we use the large homogeneous sample of GRB X-ray afterglows to determine upper limits to the metal column densities to several hundred lines of sight through the Galaxy.1061 We compare these metal column densities to all-sky hydrogen and dust surveys to obtain a new dust-to-metals ratio and metallicity value for the Galaxy., We compare these metal column densities to all-sky hydrogen and dust surveys to obtain a new dust-to-metals ratio and metallicity value for the Galaxy.1062" The GRB afterglows are subject to absorption by their hosts, with a minor contribution from intervening objects, so we use a 2D 2-sided Kolmogorov-Smirnov (KS) test to overcome this limitation to define the Galactic lower envelope to their absorbing column densities."," The GRB afterglows are subject to absorption by their hosts, with a minor contribution from intervening objects, so we use a 2D 2-sided Kolmogorov-Smirnov (KS) test to overcome this limitation to define the Galactic lower envelope to their absorbing column densities."1063" Since it is X-ray selected, the sample is not afflicted by observational bias as UV studies are."," Since it is X-ray selected, the sample is not afflicted by observational bias as UV studies are."1064" However, its greatest benefit over previous samples is that this sample passes lines of sight at random through the Galaxy, and passes through the entire Galaxy in every direction, providing a set of sightlines less affected by the relatively local nature of some previous studies."," However, its greatest benefit over previous samples is that this sample passes lines of sight at random through the Galaxy, and passes through the entire Galaxy in every direction, providing a set of sightlines less affected by the relatively local nature of some previous studies."1065" In the next section I describe the sample, data reduction and analysis techniques."," In the next section I describe the sample, data reduction and analysis techniques."1066 In section I present the results of the study.," In section \ref{sec:results}, I present the results of the study."1067 Section] contains an analysisBl. of the relevance of the results and a comparison to previous efforts inside and outside our Galaxy., Section \ref{sec:discussion} contains an analysis of the relevance of the results and a comparison to previous efforts inside and outside our Galaxy.1068" In section B], I offer my conclusions."," In section \ref{sec:conclusions}, I offer my conclusions."1069 All errors quoted are statistical uncertainties at the confidence level for one parameter of interest unless stated otherwise., All errors quoted are statistical uncertainties at the confidence level for one parameter of interest unless stated otherwise.1070" The aim of the work is to obtain equivalent hydrogen column densities (in essence the metal column density, Nu,) for a large number of sightlines through the Galaxy from the soft X- photoelectric absorption of GRB afterglows."," The aim of the work is to obtain equivalent hydrogen column densities (in essence the metal column density, $N_{\rm H_{\rm X}}$ ) for a large number of sightlines through the Galaxy from the soft X-ray photoelectric absorption of GRB afterglows."1071 These column, These column1072where jg=0.6 is the mean molecular weight of the ICM.,where $\mu=0.6$ is the mean molecular weight of the ICM.1073 Almost all of the cluster mass resides in dark matter and the ICAL aud therefore the dark matter mass distribution cau be determined through Aspyr)=ἐν) Mica).," Almost all of the cluster mass resides in dark matter and the ICM, and therefore the dark matter mass distribution can be determined through $M_\mathrm{DM}(r)=M_\mathrm{tot}(r)-M_\mathrm{ICM}(r)$ ."1074 The ICM. amass profile is given straight-forwardly by the density pies=pgp., The ICM mass profile is given straight-forwardly by the density $\rho_\mathrm{ICM}=\mu m_H n_e$.1075 We calculate ον). of cach radial bin through a Monte Carlo (MC) analysis in order το propagate nucertaimtics accurately., We calculate $M_\mathrm{DM}(r_i)$ of each radial bin through a Monte Carlo (MC) analysis in order to propagate uncertainties accurately.1076" In detail. the prescription for cach MC realization is as follows: In each bin ; the best estimates of T; and 0,,; are added to random uunnubers drawn frou Gaussian distributions represcutative of the uncertainties 07; aud ρω,"," In detail, the prescription for each MC realization is as follows: In each bin $i$ the best estimates of $T_i$ and $n_{e,i}$ are added to random numbers drawn from Gaussian distributions representative of the uncertainties $\delta T_i$ and $\delta n_{e,i}$."1077 Tn order to apply Equation(3).. we estimate the logarithiaie derivative of. e... T at he bincadius r; by the slope of the unique parabola hat passes through (lur;q1.1nZ;4). παεναι Z;). aud (lur;i4.1nT;4).," In order to apply Equation, we estimate the logarithmic derivative of, e.g., $T$ at the bin-radius $r_i$ by the slope of the unique parabola that passes through $(\ln r_{i-1},\ln T_{i-1})$, $(\ln r_i,\ln T_i)$ , and $(\ln r_{i+1},\ln T_{i+1})$."1078 In this way we can caleulate the total nass interior to +; for that data realization., In this way we can calculate the total mass interior to $r_i$ for that data realization.1079 We subtract he gas mass. estimated through a five-point Newton-Cotes integration formula applied to the same realization of the deusity data. aud we arrive at the dark matter nass Afar.," We subtract the gas mass, estimated through a five-point Newton-Cotes integration formula applied to the same realization of the density data, and we arrive at the dark matter mass $M_{\mathrm{DM},i}$."1080 We mipose a umber of checks to determine if the derived data realization is plivsically seusible: the ICAL temperature and density mst be ereater than zero in all bins. the total mass profile nist be increasing with radius. and the dark matter mass profile aud derived density profile iust also be evervwhere positive.," We impose a number of checks to determine if the derived data realization is physically sensible: the ICM temperature and density must be greater than zero in all bins, the total mass profile must be increasing with radius, and the dark matter mass profile and derived density profile must also be everywhere positive."1081 If these conditions are not met the cutive realization is discarded., If these conditions are not met the entire realization is discarded.1082 This process is repeated until Vo=5000 realizatious have been accepted., This process is repeated until $N=5000$ realizations have been accepted.1083 From these the sample mean of IuM; iu cach bin is determined. as well as the sample covariance matrix with elements where Nis the nuniber of Monte Carlo realizations.," From these the sample mean of $\ln M_i$ in each bin is determined, as well as the sample covariance matrix with elements where $N$ is the number of Monte Carlo realizations."1084 Even though we sample the ICAL temperature and density iu cach bin iudepenudeutly. the covariance matrix is not diagonal since the derivatives and physical consistency checks induce biu-to-bin correlations i the accepted sample.," Even though we sample the ICM temperature and density in each bin independently, the covariance matrix is not diagonal since the derivatives and physical consistency checks induce bin-to-bin correlations in the accepted sample."1085 We use the mean and covariance of InM rather than AY since. by iuspection. the former is closer to being Gaussian distributed.," We use the mean and covariance of $\ln M$ rather than $M$ since, by inspection, the former is closer to being Gaussian distributed."1086 We take a Bavesian approach to the statistical analysis and the usual starting poiut is the likelihood function. which we calculate in the following mamner.," We take a Bayesian approach to the statistical analysis and the usual starting point is the likelihood function, which we calculate in the following manner."1087 It requires less manipulation of the data to calculate he mass profile from the observations than to calculate he density profile., It requires less manipulation of the data to calculate the mass profile from the observations than to calculate the density profile.1088 Therefore we iuteerate the density xofile analytically or nmunericallv for cach model to obtain the amass distribution aud compare with the data i nas space. uot deusitv space.," Therefore we integrate the density profile analytically or numerically for each model to obtain the mass distribution and compare with the data in mass space, not density space."1089 Further. as nentioned above. we have found in the ALC analysis hat the mass samplines in cach bin are close to being oge-normallv distributed.," Further, as mentioned above, we have found in the MC analysis that the mass samplings in each bin are close to being log-normally distributed."1090 Therefore we coustruct the ikclihood £CM;)=exptu2) from the u function. where Ασε) is the model mass profile at the radial ceutre c; of biu 7. aud lnM; aud C;; are determined by he MC analvsis.," Therefore we construct the likelihood $\mathcal{L}(M_i)=\exp(-\chi^2/2)$ from the $\chi^2$ function, where $M(r_i)$ is the model mass profile at the radial centre $r_i$ of bin $i$, and $\ln M_i$ and $C_{ij}$ are determined by the MC analysis."1091 The main goal is fo decide which model is the etter representation of the data., The main goal is to decide which model is the better representation of the data.1092 We do this bv calculating the Bayesian evidence of cach model. which is a quautitative measure of the agreement between nodel aud data (Trotta2008)..," We do this by calculating the Bayesian evidence of each model, which is a quantitative measure of the agreement between model and data \citep{2008ConPh..49...71T}."1093 First we calculate the ikelihoods of cach model ou a erid iu the parameter space 0=(logr».logp2).," First we calculate the likelihoods of each model on a grid in the parameter space $\theta=(\log r_{-2},\log\rho_{-2})$."1094 Next. we construct the osterior probability distribution by combining the ischhood function with a prior probability distribution m(@) τονο our knowledge of logy2 and logp» vefore taking the data into account.," Next, we construct the posterior probability distribution by combining the likelihood function with a prior probability distribution $\pi(\theta)$ resembling our knowledge of $\log r_{-2}$ and $\log \rho_{-2}$ before taking the data into account."1095 We discuss the choice of prior below., We discuss the choice of prior below.1096 We then integrate the posterior to obtain he Bayesian evideuce. which ds oessentidlv the weighted average of the likehhood over the prior volune.," We then integrate the posterior to obtain the Bayesian evidence, which is essentially the weighted average of the likelihood over the prior volume."1097 The evidence of a model. given the data and a prior. quantifies how well that model explains the data.," The evidence of a model, given the data and a prior, quantifies how well that model explains the data."1098 It is portant to stress that the comparison is madeover all of the prior volume. uot just at the best fitting set of paranucters.," It is important to stress that the comparison is madeover all of the prior volume, not just at the best fitting set of parameters."1099 When conrpariue models the Baves factor P415»=E4/E» shows, When comparing models the Bayes factor $B_{12}=E_1/E_2$ shows1100accrelion rales. we can estimate (heir average value as 0.036.,"accretion rates, we can estimate their average value as 0.036."1101 This value predicted by the disk evaporation model (0.03) is well consistent with the observational result., This value predicted by the disk evaporation model $\sim 0.03$ ) is well consistent with the observational result.1102 In the hard state of black hole X-ray. binaries. the accretion rate in the disk is lower (han the maximal evaporation rate. and (he (hin disk will be truncated al a radius where the accretion rate in the disk equals to Che evaporation rate.," In the hard state of black hole X-ray binaries, the accretion rate in the disk is lower than the maximal evaporation rate, and the thin disk will be truncated at a radius where the accretion rate in the disk equals to the evaporation rate."1103 So the i»—r relation can be tested by (he truncation radius of the disk and the corresponding accretion rate estimated from the observational data., So the $ \dot{m}-r $ relation can be tested by the truncation radius of the disk and the corresponding accretion rate estimated from the observational data.1104 For such a purpose. we collect some data from. black hole N-rav. binaries (see Table 3)).," For such a purpose, we collect some data from black hole X-ray binaries (see Table \ref{truncation}) )."1105 These data are based on the spectral fitting with the ADAF + disk model (Naravan. Barret MeClintock 1997).," These data are based on the spectral fitting with the ADAF + disk model (Narayan, Barret McClintock 1997)."1106 The accretion rates in Table 3. are the Eddington-scaled values Qn=0.1M2/ Ly). which areconverted [vom the Eddington ratios (L/Lyiqa)( Zdziarski et al.," The accretion rates in Table \ref{truncation} are the Eddington-scaled values $\dot m=0.1 \dot M c^2/L_{\rm Edd}$ ), which areconverted from the Eddington ratios $L/L_{\rm Edd}$ )(Zdziarski et al."1107 2004). or [rom the rates scaled by the critical accretion rate Gin=M7Lu. Wilms et al.," 2004), or from the rates scaled by the critical accretion rate $ \dot{m}\equiv \dot{M}c^2/L_{Edd} $ , Wilms et al."1108 1999). or [rom M (in the unit of solar mass per vear) (Poutanen et al.," 1999), or from $\dot M$ (in the unit of solar mass per year) (Poutanen et al."1109 1997)., 1997).1110 The data listed in Table 3. can then be compared with the theoretical results [rom our moclel., The data listed in Table \ref{truncation} can then be compared with the theoretical results from our model.1111 Fie., Fig.1112 7 shows the observational data together with our model predictions for different strength of magnetic pressure and heat conduction., \ref{2T_observe} shows the observational data together with our model predictions for different strength of magnetic pressure and heat conduction.1113 One can see that the enhanced magnetic pressure and reduced heat conduction bring (he model predictions much closer to the observations., One can see that the enhanced magnetic pressure and reduced heat conduction bring the model predictions much closer to the observations.1114 We expect that. theoretical results with stronger magnetic fiekl or further reduced heat conduction or both will predict more consistent results. will observations., We expect that theoretical results with stronger magnetic field or further reduced heat conduction or both will predict more consistent results with observations.1115 Here we don't eive such an example not only because we don't know the accurate strength of magnetic [ield in individual objects. but also cue to the large uncertainties in the observational data.," Here we don't give such an example not only because we don't know the accurate strength of magnetic field in individual objects, but also due to the large uncertainties in the observational data."1116 Caution should be taken here (hat (here are several sets of data given in the original papers. we just listed the best fitted ones here.," Caution should be taken here that there are several sets of data given in the original papers, we just listed the best fitted ones here."1117 We also noticed that 0.97. which corresponds(o 4=32 is this work.," We also noticed that , which correspondsto $\beta=32$ is this work."111810“sem  the barotropic equation of state underestimates the maximum temperature by about a factor of two.,$10^{-8}$g $^{-3}$ the barotropic equation of state underestimates the maximum temperature by about a factor of two.1119 The only exception © this is the most rapidly-rotating calculation with 3=0.04., The only exception to this is the most rapidly-rotating calculation with $\beta=0.04$.1120 Here the maximum temperature at a given density is lower than in he other radiation hydrodynamical calculations and more similar o the barotropic equation of state., Here the maximum temperature at a given density is lower than in the other radiation hydrodynamical calculations and more similar to the barotropic equation of state.1121 This is because in this case he tirst core is actually a torus and. therefore. the gas can cool more effectively.," This is because in this case the first core is actually a torus and, therefore, the gas can cool more effectively."1122 Returning to Fig. 5..," Returning to Fig. \ref{first_core_time},"1123 we also see that it is the J>=0.04 case (rightmost panels) where the timescales between tirst and stellar core formation are most similar for the barotropic and radiation hydrodynamical calculations (differing only by about rather than a factor of 1.5 9)., we also see that it is the $\beta=0.04$ case (rightmost panels) where the timescales between first and stellar core formation are most similar for the barotropic and radiation hydrodynamical calculations (differing only by about rather than a factor of $1.5-3$ ).1124 One possible reason that the radiation hydrodynamical calculations give greater temperatures during the first core phase than the barotropic calculations is that there may be considerable shock heating which is not taken into account with a barotropic equation of state., One possible reason that the radiation hydrodynamical calculations give greater temperatures during the first core phase than the barotropic calculations is that there may be considerable shock heating which is not taken into account with a barotropic equation of state.1125 However. computing the entropy of the gas before the first core forms and in the bulk of the first core as it forms and evolves. we find it monotonically decreases in the radiation hydrodynamical calculations.," However, computing the entropy of the gas before the first core forms and in the bulk of the first core as it forms and evolves, we find it monotonically decreases in the radiation hydrodynamical calculations."1126 The rate of decrease is rapid before the first core forms (when it is cooling rapidly and almost isothermal). but even after the first core forms the gas is loosing energy due to radiation.," The rate of decrease is rapid before the first core forms (when it is cooling rapidly and almost isothermal), but even after the first core forms the gas is loosing energy due to radiation."1127 Only at the surface of the first core (around the accretion shock) does the entropy briefly increase before it radiatively cools., Only at the surface of the first core (around the accretion shock) does the entropy briefly increase before it radiatively cools.1128 This is consistent with the recent calculations of who find that essentially all of the energy liberated in the accretion shock is radiated away., This is consistent with the recent calculations of \cite{Commerconetal2011b} who find that essentially all of the energy liberated in the accretion shock is radiated away.1129 Instead. the reason the barotropic equation of state consistently underestimates the temperature in this density range is due to the approximation that η=7/5 in this part of the evolution.," Instead, the reason the barotropic equation of state consistently underestimates the temperature in this density range is due to the approximation that $\eta=7/5$ in this part of the evolution."1130 In fact. molecular hydrogen (the dominant constituent) has a ratio of specitic heat capacities of .=5/3 until it reaches ~[00 K. Only then are the rotational degrees of freedom. which lower  to 7/5. excited.," In fact, molecular hydrogen (the dominant constituent) has a ratio of specific heat capacities of $\gamma=5/3$ until it reaches $\sim 100$ K. Only then are the rotational degrees of freedom, which lower $\gamma$ to 7/5, excited."1131 Again. this is apparent in Fig.," Again, this is apparent in Fig."1132 6 where it can be seen that the lines from the radiation hydrodynamical calculations are steeper than the barotropic line in the temperature range zz20—150., \ref{temp_vs_density} where it can be seen that the lines from the radiation hydrodynamical calculations are steeper than the barotropic line in the temperature range $\approx 20-150$.1133 Above this temperature. the lines are almost parallel 5.27/5 for both). but the temperature offset (that originates in the 20.150 K range) persists.," Above this temperature, the lines are almost parallel $\gamma \approx 7/5$ for both), but the temperature offset (that originates in the $20-150$ K range) persists."1134 The barotropic equation of state could be improved for this part of the evolution by including a smooth transition from =1 to 5/3 and then a transition from 5/3 to 7/5., The barotropic equation of state could be improved for this part of the evolution by including a smooth transition from $\gamma=1$ to $5/3$ and then a transition from $5/3$ to $7/5$ .1135 However. this would still not capture all of the detail present in the radiation hydrodynamical equations (see below).," However, this would still not capture all of the detail present in the radiation hydrodynamical equations (see below)."1136The notation +) is the energy of electrons at time {μ.,The notation $\gamma_{0}$ is the energy of electrons at time $t_{0}$.1137 This solution ean be rewritten as: ul The cutoff energy is delined by setting 50=x al lime /y in equation (8)) and can be expressed as: In our models. the relativistic electrons are asstuned to be injected by merger shocks.," This solution can be rewritten as: where The cutoff energy is defined by setting $\gamma_{0}=\infty$ at time $t_{0}$ in equation \ref{Eengt2}) ) and can be expressed as: In our models, the relativistic electrons are assumed to be injected by merger shocks."1138 A power-law spectrum of relativistic electrons is expected from ditfuse shock acceleration., A power-law spectrum of relativistic electrons is expected from diffuse shock acceleration.1139" We assume that the injected spectrum has the form: where f.(r) is assumed to be proportional to the gas distribution ancl is normalized {ο be equal to. fj,(r) as described in equation (2)). ie. fer)=fü(r)."," We assume that the injected spectrum has the form: where $f_{e}(r)$ is assumed to be proportional to the gas distribution and is normalized to be equal to $f_{gas}(r)$ as described in equation \ref{Egas}) ), i.e., $f_{e}(r)=f_{gas}(r)$."1140" The parameter Ly, can be determined by normalizing the theoretical radio spectrum to the observed data.", The parameter $K_{e}$ can be determined by normalizing the theoretical radio spectrum to the observed data.1141 The power-law index s is related to the Mach number M of the merger shocks by (he expression: s=20M?+D)/CMP—1) (e.g...Gabici&Blasi2003).," The power-law index $s$ is related to the Mach number $\mathcal{M}$ of the merger shocks by the expression: $s=2(\mathcal{M}^{2}+1)/(\mathcal{M}^{2}-1)$ \citep[e.g.,][]{gab03}."1142". For studying the effects of the Mach nunmbers of merger shocks on (he non-thermal emission in galaxy. clusters. we adopt cifferent values for the power-law index s: 2.5. 3.3. 4.0. and 4.7 corresponding to Mach numbers: 3. 2. 1.73. and 1.58. respectively,"," For studying the effects of the Mach numbers of merger shocks on the non-thermal emission in galaxy clusters, we adopt different values for the power-law index $s$: 2.5, 3.3, 4.0, and 4.7 corresponding to Mach numbers: 3, 2, 1.73, and 1.58, respectively."1143 Without loss of generality. we ignore (he initial variation of the power-law index in the cluster for simplicity.," Without loss of generality, we ignore the initial variation of the power-law index in the cluster for simplicity."1144 Cosniic-ray protons can also generate secondary electrons., Cosmic-ray protons can also generate secondary electrons.1145 Nonetheless. it is still unclear about the contribution of the secondary electrons (ο the relativistic electrons in galaxy clusters.," Nonetheless, it is still unclear about the contribution of the secondary electrons to the relativistic electrons in galaxy clusters."1146 In our caleulation. we consideronly the electrons injected by merger shocks. and assume that the secondary electrons are negligible (Ixuo.Hwang.&Ip 2003)..," In our calculation, we consideronly the electrons injected by merger shocks, and assume that the secondary electrons are negligible \citep*{kuo03}. ."1147Spectra from both Obsid 2942 and Obsid 4174 were fit simultaneously with XSPEC 11.2 over the 0.3— 5kkeV energy range using APEC emission models for collisionally-ionized diffuse gas (Smith 2001) corrected for absorption using Wisconsin photo-electric cross-sections (Morrison McCammon 1983).,Spectra from both Obsid 2942 and Obsid 4174 were fit simultaneously with XSPEC $11.2$ over the $0.3 - 5$ keV energy range using APEC emission models for collisionally-ionized diffuse gas (Smith 2001) corrected for absorption using Wisconsin photo-electric cross-sections (Morrison McCammon 1983).1148 Obsid 319 was not used in the spectral analysis due to calibration uncertainties for Period B observations., Obsid 319 was not used in the spectral analysis due to calibration uncertainties for Period B observations.1149 Counts were grouped with a pre-defined grouping resulting in channels of approximately constant logarithmic width., Counts were grouped with a pre-defined grouping resulting in channels of approximately constant logarithmic width.1150" The hydrogen column density was initially fixed at its Galactic value 1.45x1030 (see http://heasarc.gsfc.nasa.gov/, Archives Software, nH:Column Density) with the gas temperature and abundance taken as free parameters."," The hydrogen column density was initially fixed at its Galactic value $1.45 \times 10^{20}$ (see http://heasarc.gsfc.nasa.gov/, Archives Software, nH:Column Density) with the gas temperature and abundance taken as free parameters."1151 The hydrogen absorbing column was then allowed to vary to check the stability of the fit., The hydrogen absorbing column was then allowed to vary to check the stability of the fit.1152 The data showed no need for increased absorption either in the cluster gas or in the outer elliptical region E, The data showed no need for increased absorption either in the cluster gas or in the outer elliptical region E1153curves presented here. more detailed observations are required to distinguish between these two,"curves presented here, more detailed observations are required to distinguish between these two"1154abundance of heavy elements is present in the atmosphere of NLTT 10480.,abundance of heavy elements is present in the atmosphere of NLTT 10480.1155 Figure5. shows the predicted location of the strongest lines ofFel.Sil. and in the X-shooter spectrum.," Figure\ref{fig-other} shows the predicted location of the strongest lines of, and in the X-shooter spectrum."1156 We calculated the position of the Zeeman-split lines. for these elements assuming a magnetic field of 0.519 MG., We calculated the position of the Zeeman-split lines for these elements assuming a magnetic field of 0.519 MG.1157 For aluminium. some weak lines appear to match the predicted positions.," For aluminium, some weak lines appear to match the predicted positions."1158" However. the putative ÀAl1L13967.8532 component should be accompanied by stronger ,13957.7353 and ,13960.2458 components that are not clearly identified."," However, the putative $\lambda$ 3967.8532 component should be accompanied by stronger $\lambda$ 3957.7353 and $\lambda$ 3960.2458 components that are not clearly identified."1159 Another possible identification for this feature is an interstellar Ca H line. although Ca K is not detected in the spectrum.," Another possible identification for this feature is an interstellar Ca H line, although Ca K is not detected in the spectrum."1160 Spectra with higher signal-to-noise ratios and better resolution are needed to clarify this identification., Spectra with higher signal-to-noise ratios and better resolution are needed to clarify this identification.1161 We estimated sodium. aluminium. silicon. and. iron abundance upper limits using the spectral ranges covered in Figure 5...," We estimated sodium, aluminium, silicon and iron abundance upper limits using the spectral ranges covered in Figure \ref{fig-other}. ."1162 We found logn(Na)/n(H).&(AD/n(H). and logi(Fe)/itH)<-9.3. while logΗΡΙ)ΜΗ)€ —-8.7.," We found $\log{n{\rm (Na)}/n{\rm (H)}},\,\log{n{\rm (Al)}/n{\rm (H)}}$, and $\log{n{\rm (Fe)}/n{\rm (H)}} \la -9.3$, while $\log{n{\rm (Si)}/n{\rm (H)}}\la -8.7$ ."1163 The abundances relative to solar range from 2x107 to 3x1077 times solar. or a few orders of magnitude below the level required to significantly increase the electron density and alter the calcium ionization balance.," The abundances relative to solar range from $2\times10^{-5}$ to $3\times10^{-4}$ times solar, or a few orders of magnitude below the level required to significantly increase the electron density and alter the calcium ionization balance."1164 We found that the high proper-motion star NLTT 10480 is a rare example of cool white dwarfs with trace heavy elements and a weak magnetic field revealed in both the He circular polarization spectrum and Zeeman line-splitting., We found that the high proper-motion star NLTT 10480 is a rare example of cool white dwarfs with trace heavy elements and a weak magnetic field revealed in both the $\alpha$ circular polarization spectrum and Zeeman line-splitting.1165 Other examples of this class of white dwarfs are the DZ white dwarfs LHS 2534 (Reidetal..2001) and G 165-7 2006).. the DAZ white dwarfs G 77-50 (Farihietal..2011) and possibly LTT 8381 (Koesteretal..2009)..," Other examples of this class of white dwarfs are the DZ white dwarfs LHS 2534 \citep{rei2001} and G 165-7 \citep{duf2006}, the DAZ white dwarfs G 77-50 \citep{far2011} and possibly LTT 8381 \citep{koe2009b}."1166 Based on independent diagnostics (Table 5)). we estimated à temperature of Ty=5200€200 K and a surface gravity close to loge= 8.," Based on independent diagnostics (Table \ref{tbl-prop}) ), we estimated a temperature of $T_{\rm eff}=5\,200\pm200$ K and a surface gravity close to $\log{g}=8$ ."1167 However. we noted systematic differences in. temperature measurements based on the calcium ionization ratio. the colour index. and the Balmer line profiles amounting to ~400 K. The weaker lines favour a lower temperature than estimated using Balmer lines alone.," However, we noted systematic differences in temperature measurements based on the calcium ionization ratio, the colour index, and the Balmer line profiles amounting to $\sim$ 400 K. The weaker lines favour a lower temperature than estimated using Balmer lines alone."1168 The temperature measured with the V-J colour index also favours a lower temperature., The temperature measured with the $V-J$ colour index also favours a lower temperature.1169 We found that increasing the heavy-element contribution to the electron density helps restore the calcium tonization balance. but we also found that the required abundance exceeds upper limits on the abundance of Na. Al. Si. and Fe by a few orders of nagnitude.," We found that increasing the heavy-element contribution to the electron density helps restore the calcium ionization balance, but we also found that the required abundance exceeds upper limits on the abundance of Na, Al, Si, and Fe by a few orders of magnitude."1170 We are left with the possibility that subtle effects on line formation (broadening parameters. magnetic-optical. ..) caused by the magnetic field may influence temperature neasurements based on Balmer line profiles.," We are left with the possibility that subtle effects on line formation (broadening parameters, magnetic-optical, ...) caused by the magnetic field may influence temperature measurements based on Balmer line profiles."1171 Although our modelling of the hydrogen line profiles takes into account the effect of inclination. we neglected the nagneto-optical effects and only approximated the full solution of the radiative transfer equations thatought toinclude all Stokes parameters (seeMartin&Wickramasinghe. 1981)..," Although our modelling of the hydrogen line profiles takes into account the effect of inclination, we neglected the magneto-optical effects and only approximated the full solution of the radiative transfer equations thatought toinclude all Stokes parameters \citep[see][]{mar1981}. ."1172 The effect of this approximation on the determination of the stellar, The effect of this approximation on the determination of the stellar1173"arguments that at the redshifts of interest, i.e. z~1000, probably the majority of energy released in p and d channels is directly converted into heat by the cosmic medium.","arguments that at the redshifts of interest, i.e. $z\sim 1000$, probably the majority of energy released in $p$ and $d$ channels is directly converted into heat by the cosmic medium."1174" Thus, we only need a detailed treatment for the photons: (A) the energetic ones originating directly from the annihilation event (prompt photons), (B) the softer ICphotons created by e~ upscattering CMB photons."," Thus, we only need a detailed treatment for the photons: (A) the energetic ones originating directly from the annihilation event (prompt photons), (B) the softer ICphotons created by $e^{\pm}$ upscattering CMB photons."1175 The processes and the corresponding cross sections relevant to the propagation of photons through the cosmic medium were taken from ?.., The processes and the corresponding cross sections relevant to the propagation of photons through the cosmic medium were taken from \citet{1989ApJ...344..551Z}.1176" Starting from the lowest of energies these include (i) photoionization, (ii) Compton losses (on both bound and free electrons), (iii) pair production on matter, (iv) photon-photon scattering, and (v) pair production on ambient photon fields."," Starting from the lowest of energies these include (i) photoionization, (ii) Compton losses (on both bound and free electrons), (iii) pair production on matter, (iv) photon-photon scattering, and (v) pair production on ambient photon fields."1177 In Fig., In Fig.1178" [l| we show the redshifts z’ where the optical depth r(z,z)=1 for various redshifts of the observer: z=0,10,500,1000."," \ref{fig1} we show the redshifts $z^{'}$ where the optical depth $\tau(z,z^{'})=1$ for various redshifts of the observer: $z=0,10,500,1000$."1179" As can be seen, for intermediate photon energies (depending on the redshift) there is a well-known X-ray/gamma-ray energy window where the photons can propagate freely over cosmologically large distances (e.g.,see?).."," As can be seen, for intermediate photon energies (depending on the redshift) there is a well-known X-ray/gamma-ray energy window where the photons can propagate freely over cosmologically large distances \citep[e.g., see][]{2004PhRvD..70d3502C}."1180 For the cosmological radiation transfer it is crucial that this ‘transparency window’ is properly modeled., For the cosmological radiation transfer it is crucial that this `transparency window' is properly modeled.1181 Once the photon gets outside of this window (we take it to happen after the first interaction) we assume that the following cascade will be locally absorbed in a very short time., Once the photon gets outside of this window (we take it to happen after the first interaction) we assume that the following cascade will be locally absorbed in a very short time.1182" Moreover, the fractions (1—fion)/3 and (1+2fion)/3 of the total absorbed energy, are assumed to be going for ionization and heating, respectively."," Moreover, the fractions $(1-f_{{\rm ion}})/3$ and $(1+2f_{{\rm ion}})/3$ of the total absorbed energy, are assumed to be going for ionization and heating, respectively."1183" Here fion is the fraction of ionized hydrogen atoms, and a similar expression for helium can beused."," Here $f_{{\rm ion}}$ is the fraction of ionized hydrogen atoms, and a similar expression for helium can beused."1184 Excitations of atoms are neglected., Excitations of atoms are neglected.1185" This approximation, motivated by the work of ?,, has been widely used in several subsequent papers, e.g. ?????.."," This approximation, motivated by the work of \citet{1985ApJ...298..268S}, has been widely used in several subsequent papers, e.g. \citet{2004PhRvD..70d3502C,2005PhRvD..72b3508P,2006MNRAS.369.1719M,2006PhRvD..74j3519Z,2009PhRvD..80d3529N}."1186" However, it is clear that these simple expressions only provide a rough estimate for the correct energy deposition efficiencies."," However, it is clear that these simple expressions only provide a rough estimate for the correct energy deposition efficiencies."1187" As mentioned by ?,, the precise redshift dependence of the efficiency factors and the fraction of energy that goes into excitations of hydrogen and helium atoms need more careful consideration of the radiative transfer processes, including secondary low-energy photons and their feedback."," As mentioned by \citet{2010MNRAS.402.1195C}, the precise redshift dependence of the efficiency factors and the fraction of energy that goes into excitations of hydrogen and helium atoms need more careful consideration of the radiative transfer processes, including secondary low-energy photons and their feedback."1188" These extra photons have the potential of further delaying recombination, hence affect the last scattering surface and CMB anisotropies (?).."," These extra photons have the potential of further delaying recombination, hence affect the last scattering surface and CMB anisotropies \citep{2000ApJ...539L...1P}."1189" We leave a more detailed investigation of these ambiguities to a future paper; however, later on in Section ?? we briefly comment on how much the omission of excitations using the rough prescription of ? changes our final results."," We leave a more detailed investigation of these ambiguities to a future paper; however, later on in Section \ref{sec4} we briefly comment on how much the omission of excitations using the rough prescription of \citet{2004PhRvD..70d3502C} changes our final results."1190 In Fig., In Fig.1191" Π] we also see that at high redshifts, as the density of the environment becomes much higher, the X-ray/gamma-ray transparency window starts to close."," \ref{fig1} we also see that at high redshifts, as the density of the environment becomes much higher, the X-ray/gamma-ray transparency window starts to close."1192" Thus at sufficiently high z, we would expect all the produced annihilation energy (excluding the energy stored in neutrinos, since these can freely leak out)to be absorbed locally."," Thus at sufficiently high $z$, we would expect all the produced annihilation energy (excluding the energy stored in neutrinos, since these can freely leak out)to be absorbed locally."1193 In the following we call the ratio of the locally produced to the locally absorbed energy the f-parameter., In the following we call the ratio of the locally produced to the locally absorbed energy the $f$ -parameter.1194" At high redshifts (but well after the neutrino decoupling) we expect the f-parameter to asymptote to the value given by (1—f,), where f, is the fraction of energy carried away by neutrinos."," At high redshifts (but well after the neutrino decoupling) we expect the $f$ -parameter to asymptote to the value given by $(1-f_{\nu})$, where $f_{\nu}$ is the fraction of energy carried away by neutrinos."1195 An example for the f-parameters in the case of p annihilation channel are shown in the upper lefthand panel of Fig. D]., An example for the $f$ -parameters in the case of $\mu$ annihilation channel are shown in the upper lefthand panel of Fig. \ref{fig2}.1196" Since ~60% of the energy is carried away by neutrinos in the u-channel the expected asymptotic high-redshift f- parameter should be ~0.4, which is indeed the case."," Since $\sim 60\%$ of the energy is carried away by neutrinos in the $\mu$ -channel the expected asymptotic high-redshift $f$ -parameter should be $\sim 0.4$, which is indeed the case."1197" With this in mind, we see that robust model-independent results from the CMB analyses can be obtained for the DM masses below ~100 GeV. This is the reason we concentrate on light WIMPS in this work."," With this in mind, we see that robust model-independent results from the CMB analyses can be obtained for the DM masses below $\sim 100$ GeV. This is the reason we concentrate on light WIMPS in this work."1198" For heavier WIMPs, the computation depends on more complicated details for energy absorption."," For heavier WIMPs, the computation depends on more complicated details for energy absorption."1199" Because we are able to calculate f-parameters, we can go on to calculate the effect on cosmological recombination."," Because we are able to calculate $f$ -parameters, we can go on to calculate the effect on cosmological recombination."1200 To this end we modify the cosmological recombination code RECFAST (?) along the lines presented in ?.., To this end we modify the cosmological recombination code RECFAST \citep{1999ApJ...523L...1S} along the lines presented in \citet{2005PhRvD..72b3508P}.

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