ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2. The hot subdwarfs have representative effective temperatures and surface gravities near 0000 K and logg~ 55.5. respectively.," The hot subdwarfs have representative effective temperatures and surface gravities near 000 K and $\log g \sim$ 5.5, respectively."3 For a general review of their observed properties. see Heber(2009).," For a general review of their observed properties, see \cite{heber09}."4 Kilkennyetal.(1997). discovered the first hot subdwarf that showed stellar oscillations (hereafter: sUBV)., \citet{kilkenny97} discovered the first hot subdwarf that showed stellar oscillations (hereafter: sdBV).5 The discovery provided the first opportunity to use asteroseismology to look inside these enigmatie stars. with many more found with similar periods in the following years.," The discovery provided the first opportunity to use asteroseismology to look inside these enigmatic stars, with many more found with similar periods in the following years."6 Now. around 50 objects of this class are known (Ostensenetal.2010b).," Now, around 50 objects of this class are known \citep{ostensen10a}."7. At the same time. independent theoretical work suggested that these stars could undergo nonradial pulsations (Charpinetetal.1996).. providing a “jump-start” to exploiting their asteroseismic potential.," At the same time, independent theoretical work suggested that these stars could undergo nonradial pulsations \citep{charp96}, providing a “jump-start” to exploiting their asteroseismic potential."8" The first pulsators showed relatively short-period pulsations (the. short-period sdBV. stars. or HHya stars. frequencies higher than about Η2): these are attributed to pressure modes (p-modes) and are driven in the outer part of the star,"," The first pulsators showed relatively short–period pulsations (the short-period sdBV stars, or Hya stars, frequencies higher than about $\mu$ Hz); these are attributed to pressure modes $p$ -modes) and are driven in the outer part of the star."9 As discovered later. sdB stars can also show variation with pulsation periods an order-of-magnitude longer (Greenetal.2003).," As discovered later, sdB stars can also show variation with pulsation periods an order-of-magnitude longer \citep{green03}."10 The variability in these long period sdBV stars. tor HHer stars) show frequencies below about 5005 Hz: this variability is caused by gravity modes (g-modes) as suggested by theoretical models (Fontaineetal.2003).," The variability in these long period sdBV stars, (or Her stars) show frequencies below about $\mu$ Hz; this variability is caused by gravity modes $g$ -modes) as suggested by theoretical models \citep{fontaine03}."11. The g-modes are established deeper in the stars than the pressure modes., The $g$ -modes are established deeper in the stars than the pressure modes.12 Hybrid stars. pulsating in both kind of modes were also found observationally (Schuhetal.2006).," Hybrid stars, pulsating in both kind of modes were also found observationally \citep{schuh06}."13. As they exhibit both types of modes. models of these stars can give better constraints on their interiors since the pulsations probe both the deeper layers as well as layers nearer the surface.," As they exhibit both types of modes, models of these stars can give better constraints on their interiors since the pulsations probe both the deeper layers as well as layers nearer the surface."14 Observations of long period sdBV stars. including detection of new pulsators. are not easy from the ground.," Observations of long period sdBV stars, including detection of new pulsators, are not easy from the ground."15 Relatively long period photometric variations (with only a few cycles per night) can be affected by variable sky transparency., Relatively long period photometric variations (with only a few cycles per night) can be affected by variable sky transparency.16 To make definitive determination of the pulsation frequency requires extended photometric campaigns. preferably at several sites widely spaced in longitude to reduce day/night aliasing.," To make definitive determination of the pulsation frequency requires extended photometric campaigns, preferably at several sites widely spaced in longitude to reduce day/night aliasing."17 However. provides long-duration continuous. homogenous. evenly spaced time-series photometry. makingit an ideal instrument for asteroseismology.," However, provides long–duration continuous, homogenous, evenly spaced time-series photometry, makingit an ideal instrument for asteroseismology."18 TheKepler science goals. mission design. and overall performance are reviewed by Boruckietal.(2010).. Kochetal.(2010). and Jenkinsetal.(2010).," The science goals, mission design, and overall performance are reviewed by \cite{borucki10}, \cite{koch10} and \cite{jenkins10}."19 Objects classitied as hot subdwarfs located in field of view of the photometer were observed during the survey phase in the first year of the mission., Objects classified as hot subdwarfs located in field of view of the photometer were observed during the survey phase in the first year of the mission.20 As the spacecraft is rolled every 3 months. the survey phase was divided into 4 quarters.," As the spacecraft is rolled every 3 months, the survey phase was divided into 4 quarters."21 Analysis of the observations of compact stars from the first half of the survey phase (QO. OI and Q2) is described in the following papers: (Ostensenetal.2010a.PaperD.. (Kawaleretal.20102.Paper ID.. (Reedetal.2010.Paper ΠΙΟ. (VanGrooteletal.2010.Paper TV). (Kawaleretal.2010b.PaperV) and Ostensenetal.(20106).," Analysis of the observations of compact stars from the first half of the survey phase (Q0, Q1 and Q2) is described in the following papers: \cite[][Paper I]{ostensen10b}, \cite[][Paper II]{kawaler10a}, \cite[][Paper III]{reed10}, \cite[][Paper IV]{vangrootel10}, \cite[][Paper V]{kawaler10b} and \cite{ostensen10c}."22. In this paper we focus on pulsating sdB stars discovered with data from the last 6 months of the survey phase (Q3 and Q4., In this paper we focus on pulsating sdB stars discovered with data from the last 6 months of the survey phase (Q3 and Q4).23 These are (ordered by quarters): 77668647. 88302197. 110001893. 1103553698 and 1113558725.," These are (ordered by quarters): 7668647, 8302197, 10001893, 10553698 and 11558725."24 In the Q3 data we found + sdBV of HHer class. while in the Q4 dataset we found a fifth object.," In the Q3 data we found 4 sdBV of Her class, while in the Q4 dataset we found a fifth object."25 All stars presented in this paper are spectroscopically contirmed sdB stars (see Paper VI)., All stars presented in this paper are spectroscopically confirmed sdB stars (see Paper VI).26 In Table 2 we provide their spectroscopic parameters., In Table \ref{spec_par} we provide their spectroscopic parameters.27 They were obtained by fitting spectra to model grids in order to derive effective temperature. surface gravity and photospheric helium abundance. which was an indication whether an object is a hot subdwarf or not.," They were obtained by fitting spectra to model grids in order to derive effective temperature, surface gravity and photospheric helium abundance, which was an indication whether an object is a hot subdwarf or not."28 Spectroscopic data along with fitting procedure are provided in the leading paper for the final half of the survey phase 2011.Paper VI)., Spectroscopic data along with fitting procedure are provided in the leading paper for the final half of the survey phase \citep[][Paper VI]{ostensen11}.29 Although we did not find any predominantly p-mode pulsators from Q3 or Q4. we detected many peaks in the short period regime in many targets.," Although we did not find any predominantly $p$ -mode pulsators from Q3 or Q4, we detected many peaks in the short period regime in many targets."30 However. these are few. compared with the large number of peaks identified in the longer period g-mode range.," However, these are few, compared with the large number of peaks identified in the longer period $g$ -mode range."31 Moreover.Kepler data have a variety of instrumental issues causing some artefacts to appear in the photometric data at frequencies comparable to the p-modes seen in sdBV stars.," Moreover, data have a variety of instrumental issues causing some artefacts to appear in the photometric data at frequencies comparable to the $p$ -modes seen in sdBV stars."32 Some of these artefacts are related to the long-cadence (LC) readout timings. are well-characterised. and their frequencies are known to high precision (as described in details in the Data Release Notes and Gilliland et al.," Some of these artefacts are related to the long-cadence (LC) readout timings, are well-characterised, and their frequencies are known to high precision (as described in details in the Data Release Notes and Gilliland et al."33 2010)., 2010).34 We believe. though. that some single," We believe, though, that some single"35We were able to obtain the lower state energies for the majority of the observed lines and a plot of the results in the region 740 — 2100 cm! can be seen in Figure 6..,We were able to obtain the lower state energies for the majority of the observed lines and a plot of the results in the region 740 – 2100 $^{-1}$ can be seen in Figure \ref{fig6}.36" There is good agreement with the HITRAN lower state energies for the same region displayed in Figure 7,, and the pattern of lines is similar."," There is good agreement with the HITRAN lower state energies for the same region displayed in Figure \ref{fig7}, and the pattern of lines is similar."37 Note that because of self-absorption cold NH3 in the end of the Al;O4 tube means that the strong room temperature lines are missing., Note that because of self-absorption cold $_{3}$ in the end of the $_{2}$ $_{3}$ tube means that the strong room temperature lines are missing.38 They have been added back into the final line lists from HITRAN to make each line list complete., They have been added back into the final line lists from HITRAN to make each line list complete.39M 87 is one of the nearest active galaxies (16.7Mpe:Jordinetal.2005) which exhibits relativistic outflows.,"M 87 is one of the nearest active galaxies \citep[16.7 Mpc; ][]{J05}40 which exhibits relativistic outflows."41 The mass of the central supermassive black hole (SMBH) is measured to be 3.2 10? AL.. from HST observations of the tonized gas disk (e.g...1997).," The mass of the central supermassive black hole (SMBH) is measured to be 3.2 $\times$ $^{9}$ $M_{\sun}$ from HST observations of the ionized gas disk \citep[{\em42e.g.},."43 Recent analyses of the stellar kinematics suggest a larger mass of 6.6 « 10” AL. (Gebhardtetal.2011)., Recent analyses of the stellar kinematics suggest a larger mass of 6.6 $\times$ $^{9}$ $M_{\sun}$ \citep[]{G11}.44. This larger mass gives an apparent size ~ 8 µας for the Schwarzschild radius ες., This larger mass gives an apparent size $\sim$ 8 $\mu$ as for the Schwarzschild radius $r_{s}$.45 This galaxy therefore provides a unique opportunity to study the relativistic outflow with the highest physical resolution in units of ry., This galaxy therefore provides a unique opportunity to study the relativistic outflow with the highest physical resolution in units of $_{s}$.46 Based on the VLA/VLBI observations during the past three decades. the structure of the M87 jet has been extensively examined.," Based on the VLA/VLBI observations during the past three decades, the structure of the M87 jet has been extensively examined."47 Junoretal.(1999) found a smooth variation of the jet opening angle from 60° at ~ 0.03 pe to smaller than 10° over ~ 10 pe. indicating that the jet is being collimated by the magnetohydrodynamie (MHD) process (Meier 2001).," \citet[]{J99}48 found a smooth variation of the jet opening angle from $^\circ$ at $\sim$ 0.03 pc to smaller than $^\circ$ over $\sim$ 10 pc, indicating that the jet is being collimated by the magnetohydrodynamic (MHD) process \citep[]{MKU01}."49. One of the most interesting features in the M87 Jet is the bright knot G. lying about 1” (~ 78 pe) from the core in the VLA maps (Owenetal.— 1989)..," One of the most interesting features in the M87 jet is the bright knot G, lying about $\arcsec$ $\sim$ 78 pc) from the core in the VLA maps \citep[]{O89}. ."50" That region has been resolved by the HST into a structured complex known as ""HST-I"" (Birettaetal.1999).", That region has been resolved by the HST into a structured complex known as “HST-1” \citep[]{B99}.51 It is located around 0.8 - 1.0” (ος 05.78 pe) from the core., It is located around 0.8 - $\arcsec$ (or $62 - 78$ pc) from the core.52 It consists of bright knots. whose (apparent) proper motions are superluminal with a range of leGe (Birettaetal. 1999)...," It consists of bright knots, whose (apparent) proper motions are superluminal with a range of $4c - 6c$ \citep[]{B99}. ."53 A similar velocity pattern has been observed at radio frequencies using the VLBA., A similar velocity pattern has been observed at radio frequencies using the VLBA.54 The component of HST-1 which ts furthest upstream (1.e.. Id). is stationary to within the errors (< 0.25¢). and has been identified as the origin of the superluminal ejections (Cheungetal. 2007).," The component of HST-1 which is furthest upstream (i.e., HST-1d), is stationary to within the errors $<0.25c$ ), and has been identified as the origin of the superluminal ejections \citep[]{C07}."55" The structure of the jet downstream of HST-1 (1.IS"" or(.11.5 kpe) can be characterized by a conical shape with an opening angle of ~6° (Owenetal.1989).."," The structure of the jet downstream of HST-1 $1 - 18 \arcsec$ or $0.1 - 1.5$ kpc) can be characterized by a conical shape with an opening angle of $\sim566^{\circ}$ \citep[]{O89}."57 HST-1 is also a remarkable site for large flaring activity across the electromagnetic spectrum from radio through optical to X-ray bands (Madrid2009:Harrisetal.2009).," HST-1 is also a remarkable site for large flaring activity across the electromagnetic spectrum from radio through optical to X-ray bands \citep[]{M09, H09}."58. Chandra observations show that the flaring event started in 2000. and its brightness eventually increased more than 50 times.," Chandra observations show that the flaring event started in 2000, and its brightness eventually increased more than 50 times."59 Peak brightness occurred in 2005 and an adiabatic compression has been suggested as a cause of the flare (Harrisetal.2006)., Peak brightness occurred in 2005 and an adiabatic compression has been suggested as a cause of the flare \citep[]{H06}.60 It is thought to be one possible sites for TeV ~-ray emission (Harrisetal.2009)., It is thought to be one possible sites for TeV $\gamma$ -ray emission \citep[]{H09}.61. Note that all distances are in projection throughout this section., Note that all distances are in projection throughout this section.62 We conducted the EVN observations towards M 87 on 7 March 2009 at a wavelength of 18 em with Cambridge (UK). Effelsberg (Germany). Jodrell Bank (UK). Knockin (UK). Medicina (Italy). Noto (Italy). Onsala (Sweden). Torun (Poland). and Westerbork (Netherlands) stations.," We conducted the EVN observations towards M 87 on 7 March 2009 at a wavelength of 18 cm with Cambridge (UK), Effelsberg (Germany), Jodrell Bank (UK), Knockin (UK), Medicina (Italy), Noto (Italy), Onsala (Sweden), Torun (Poland), and Westerbork (Netherlands) stations."63 Both left and right circular polarization data were recorded at each telescope using 8 channels of 8 MHz bandwidth and 2 bit sampling., Both left and right circular polarization data were recorded at each telescope using 8 channels of 8 MHz bandwidth and 2 bit sampling.64 The data were correlated at the JIVE correlator., The data were correlated at the JIVE correlator.65 amplitude calibration for each station was derived from a measurement of the system temperatures during each run and the antenna gain., amplitude calibration for each station was derived from a measurement of the system temperatures during each run and the antenna gain.66 Fringe fitting was performed using AIPS., Fringe fitting was performed using AIPS.67 After delay and rate solutions were determined. the data were averaged over 12 seconds in each IF and calibrated using Difmap.," After delay and rate solutions were determined, the data were averaged over 12 seconds in each IF and self-calibrated using Difmap."68 We conducted the MERLIN observations on 9 March 2007 at a wavelength of 18 em with Defford. Cambridge. Knockin. Darnhall. Jodrell Bank and Tabley stations.," We conducted the MERLIN observations on 9 March 2007 at a wavelength of 18 cm with Defford, Cambridge, Knockin, Darnhall, Jodrell Bank and Tabley stations."69 Both left and right circular. polarization data were transferred from each telescope with 15 MHz bandwidth., Both left and right circular polarization data were transferred from each telescope with 15 MHz bandwidth.70 Initially. the data were pipelined. and a channel-by-channel flux scale derived from 3C 286 observation was applied.," Initially, the data were pipelined, and a channel-by-channel flux scale derived from 3C 286 observation was applied."71 After this amplitude calibration. we self-calibrated the data using Difmap.," After this amplitude calibration, we self-calibrated the data using Difmap."72 We also analyzed archival VLBA data of the M 87 jet (BK073)., We also analyzed archival VLBA data of the M 87 jet (BK073).73 Those observations were carried out on 22 January 2000 at 15 GHzwith allten stations of the VLBA and one station of the VLA., Those observations were carried out on 22 January 2000 at 15 GHzwith allten stations of the VLBA and one station of the VLA.74 4 IFs. each with an 8-MHz bandwidth. were recorded at each telescope.," 4 IFs, each with an 8-MHz bandwidth, were recorded at each telescope."75 Data, Data76are long-lived. this could lead to localized GI.,"are long-lived, this could lead to localized GI."77 As discussed above. when dust settles toward the midplane. both (de-stabilizing) shear and (stabilizing) buovaancey increase.," As discussed above, when dust settles toward the midplane, both (de-stabilizing) shear and (stabilizing) cy increase."78 In the situation where dust and gas are well-enough coupled. (μον may be considered a single fluid.," In the situation where dust and gas are well-enough coupled, they may be considered a single fluid."79 For a stratified flow. competition between the opposing shear aud buovaney effects is (racilionally described by the Richardson number. where ος) is the equilibrium shear velocity in (he plane perpenclicular to é..," For a stratified flow, competition between the opposing shear and buoyancy effects is traditionally described by the Richardson number, where $v(z)$ is the equilibrium shear velocity in the plane perpendicular to $\vect{\hat e}_z$ ."80 Miles(1961) and Howard(1961). proved (or incompressible flow in the Doussinesque approximation) that Ri«1/4 somewhere in the laver is a necessary (but not sufficient) condition Lor instability (see also Drazin leid 1981. p. 325: a review of the proof is presented in the Appendix D of Li. Goodman Naravan 2003).," \citet{mil61} and \citet{how61} proved (for incompressible flow in the Boussinesque approximation) that $\Ri<1/4$ somewhere in the layer is a necessary (but not sufficient) condition for instability (see also Drazin Reid 1981, p. 325; a review of the proof is presented in the Appendix B of Li, Goodman Narayan 2003)."81 As Garaud&Lin(2004) argue. however. some of the assumptions in this prool while acceptable in other physical regimes. are not applicable to the problem at hand.," As \citet{gar04} argue, however, some of the assumptions in this proof, while acceptable in other physical regimes, are not applicable to the problem at hand."82 In this paper. we explore the influence of an effect not considered in arriving al the “his L/£ stability criterion. namely (he Coriolis force.," In this paper, we explore the influence of an effect not considered in arriving at the $\Ri > 1/4$ ” stability criterion, namely the Coriolis force."83 In 82. we present the basic equations of the model problem we have defined., In \ref{linear_sec} we present the basic equations of the model problem we have defined.84 In 83. we perform a linear stability analysis of a discrete thiree-Iaver. configuration. consisting of a dust-rich laver surrounded: by dusi-Dree eas.," In \ref{threelayer_sec} we perform a linear stability analysis of a discrete three-layer configuration, consisting of a dust-rich layer surrounded by dust-free gas."85 This analvsis relaxes some of the assumptions made by previous work. compares modes ol instability with even and odd svimmetry. and assesses the effect of the Coriolis force.," This analysis relaxes some of the assumptions made by previous work, compares modes of instability with even and odd symmetry, and assesses the effect of the Coriolis force."86 In we present the results of our numerical experiments. focusing on (he effect the Coriolis force has on the stability of model disks with two different (continuous) initial dust distributions.," In \ref{numerics_sec} we present the results of our numerical experiments, focusing on the effect the Coriolis force has on the stability of model disks with two different (continuous) initial dust distributions."87 Finally. in 85 we present our conclusions.," Finally, in \ref{conclusions_sec} we present our conclusions."88" Consider the reference [frame of a fIuid orbiting a central star at a distance Γη. with angular velocity £2,"," Consider the reference frame of a fluid orbiting a central star at a distance $R_0$, with angular velocity $\vect{\Omega}_F$."89 For adiabatic flow of a ganmuna-law gas. the equations ofhydrocdvuamics in this frame reac," For adiabatic flow of a gamma-law gas, the equations ofhydrodynamics in this frame read"90 For adiabatic flow of a ganmuna-law gas. the equations ofhydrocdvuamics in this frame reacl," For adiabatic flow of a gamma-law gas, the equations ofhydrodynamics in this frame read"91We have analvsed the first vear WAITAP data using a spherical mexican hat wavelet.,We have analysed the first year WMAP data using a spherical mexican hat wavelet.92 We detect non-Ganssianily at e significance. consistent with that reported by Vielva et al. (," We detect non-Gaussianity at $\sim$ significance, consistent with that reported by Vielva et al. ("932003).,2003).94 This detection corresponds to a positive kurtosis and to the presence of a larger than expected umber of cold pixels (wavelet coefficients) in (he southern Galactic hemisphere on scales 3—5°., This detection corresponds to a positive kurtosis and to the presence of a larger than expected number of cold pixels (wavelet coefficients) in the southern Galactic hemisphere on scales $3-5^\circ$.95 We have tested for changes in the sienilicance of the signal with the (vpe of mask usec., We have tested for changes in the significance of the signal with the type of mask used.96 The signal is found to be robust. and is found in the LLC map as well.," The signal is found to be robust, and is found in the ILC map as well."97 We have also compared confidence contours obtained for the kurtosis spectra using the full noise simulation maps provided by the WMAP team. containing 1//f noise and other ellects [rom data processing. to those obtained from using simulations that contain just white noise.," We have also compared confidence contours obtained for the kurtosis spectra using the full noise simulation maps provided by the WMAP team, containing $1/f$ noise and other effects from data processing, to those obtained from using simulations that contain just white noise."98 We find very good agreement., We find very good agreement.99 We have also applied another test statistic. the scale-scale correlations between wavelet coe[licients.," We have also applied another test statistic, the scale-scale correlations between wavelet coefficients."100 Significant scale-scale correlations are seen amongst the coefficients over the range of seales that indicate the above non-Gaussianily., Significant scale-scale correlations are seen amongst the coefficients over the range of scales that indicate the above non-Gaussianity.101 We (hen use the skewness statistic on the different scales to place constraints on the non-linear coupling parameter [νε the motivation being to see how much non-Gaussianily of this particular form is allowed by current data.," We then use the skewness statistic on the different scales to place constraints on the non-linear coupling parameter $f_{NL}$, the motivation being to see how much non-Gaussianity of this particular form is allowed by current data."102 It is also a way to compare the sensitivity of different test statistics to (his parameter., It is also a way to compare the sensitivity of different test statistics to this parameter.103 Constraints obtained are closely consistent with those obtained by IXomatsu et al. (, Constraints obtained are closely consistent with those obtained by Komatsu et al. (1042003) using the eubie statistic and Minkowski fhunctionals on the same data.,2003) using the cubic statistic and Minkowski functionals on the same data.105" The constraints on fay, derived here could possibly be made more stringent if we used spherical wavelets on (he Wiener filtered map of primordial perturbations as discussed in Ixomatsu. Spergel Wandelt (2003)."," The constraints on $f_{NL}$ derived here could possibly be made more stringent if we used spherical wavelets on the Wiener filtered map of primordial perturbations as discussed in Komatsu, Spergel Wandelt (2003)."106 We will explore this in a future paper., We will explore this in a future paper.107 The kurlosis statistic is not sensitive to this form of non-Gaussianityv., The kurtosis statistic is not sensitive to this form of non-Gaussianity.108 We will present constraints on other forms of non-Gaussianity implied bv the kurtosis statistic of the WAIAP data elsewhere., We will present constraints on other forms of non-Gaussianity implied by the kurtosis statistic of the WMAP data elsewhere.109 We acknowledge the use of non-Gaussian simulations from Ixomatsu οἱ al. (, We acknowledge the use of non-Gaussian simulations from Komatsu et al. (1102003) [WALAP paper].,2003) [WMAP paper].111 It is a pleasure to thank Eiichiro Ixomatsu for beneficial discussions and comments on the manuscript., It is a pleasure to thank Eiichiro Komatsu for beneficial discussions and comments on the manuscript.112 PM (thanks Gang Chen for useful discussions., PM thanks Gang Chen for useful discussions.113 We acknowledge the use of OSCER supercomputing faciliües at the University of Oklahoma., We acknowledge the use of OSCER supercomputing facilities at the University of Oklahoma.114 This work is supported in part by NSF CAREER erant. AST-0091335., This work is supported in part by NSF CAREER grant AST-0094335.115seen from Fig. 3.. sinal,"seen from Fig. \ref{fig:critical_core_mass},"116ler core accretion rate vields smaller critical core mass. which implies core isolation triggers the WH gas accretion.," smaller core accretion rate yields smaller critical core mass, which implies core isolation triggers the KH gas accretion."117 For a core of M. not to be isolated. that is. Ale<Mi. ↓∖⊽≺↵⊸∖↕⋅∖∖↽↩∢∙∩∐⊳∖↥≺⇂≺↵↕⋅↕∐≺↵∢∙∩∐≺∐⋃∩∐↥∎∩↕⋅⋜↕∢∙∩↕⋅≺↵↕∩⋜↕∖⊽∩↥≺⇂↕∐≺↵⊾⊁∐∑≟⋜↕⊳∖⋜∥∙∢∙↥⋅≺↵∏∩∐⋯∐↥⊔↕⊳∖↥⊳∖∩↥⋜↕∏∩∐⋅ ⊡∑∸⇂⊔⋅≺↵∙⋅," For a core of $M_{\rm c}$ not to be isolated, that is, $M_{\rm c} < M_{\rm c, iso}$, Next, we consider the condition for a core to avoid the KH gas accretion until its isolation."118⋝⋟∖∐∪∖∖↽⊳∖↕∐⋜∐⋀⊔∙∷∙⊲⊥−↥↿↥↜∖≺↵⊸∖↥↽≻↓⋅≺↲↜∖↜∖≺↲≺⇂⋜≹↥↽≻↥↽∐⋅∩⊸∖∐∐⋜∏≺↵↥⊽∖⊽∣≽⊽∖⇁ except for fully convective cases.," Figure 3 shows that $M_{\rm c,crit}$ is expressed approximately by except for fully convective cases."119 Note that cousideration of fully. convective cases does uot change our couclusiou (see below)., Note that consideration of fully convective cases does not change our conclusion (see below).120 The couditiou for a core to avoid the NH gas. accretion is Me<Mouas ," The condition for a core to avoid the KH gas accretion is $M_{\rm c} < M_{\rm c, crit}$."121"sug Tease=MM, aud Eq. (9))."," Using $\tau_{\rm c,acc} \equiv M_{\rm c}/\dot{M}_{\rm c}$ and Eq. \ref{eq:m_crit}) ),"122 this couditiou is rewritten by (see Fig. 5)), this condition is rewritten by (see Fig. \ref{fig:KH}) )123 For cores of 30. 15 and 70M.. τις must be shorter than 1x109 years. 2x10? years. aud 3x10! vears. respectively.," For cores of 30, 45 and $70 {\rm M}_{\oplus}$, $\tau_{\rm c,acc}$ must be shorter than $1 \times 10^{6}$ years, $2 \times 10^5$ years, and $3 \times 10^4$ years, respectively."124 The core growth timescale due to planetesimal accretion is given by where ii is the mass of a plauetesimal.," The core growth timescale due to planetesimal accretion is given by \citep{IL04a}125 where $m$ is the mass of a planetesimal."126 The dependence on f; appears because damping of velocity dispersiou of plauetesimals due to aerocdyuamical drag is taken into account., The dependence on $f_{\rm g}$ appears because damping of velocity dispersion of planetesimals due to aerodynamical drag is taken into account.127 Substituting Eq. (11)), Substituting Eq. \ref{eq:tau_c_acc}) )128 into Eq. (10)).," into Eq. \ref{eq:m_crit_time}) ),"129 we have This inequality iudicates that large. fy is needed to keep core accretion rate high enough to avoid the WH gas accretion., we have This inequality indicates that large $f_{\rm d}$ is needed to keep core accretion rate high enough to avoid the KH gas accretion.130 For subcritical core accretion. both Eqs. (8))," For subcritical core accretion, both Eqs. \ref{eq:f_iso}) )"131 aud (12)) must be satisfied., and \ref{eq:f_tau}) ) must be satisfied.132" For AZ,=L.3M.. aud (Fe/H]—0.36 (fa/f;= 2.3). which correspond to ΗΡΙ19026. the conditions are plotted in Fig. 9.."," For $M_* = 1.3 {\rm M}_\odot$ and [Fe/H]=0.36 $f_{\rm d}/f_{\rm g} = 2.3$ ), which correspond to HD149026, the conditions are plotted in Fig. \ref{fig:condition}."133 Subcritical core accretion could be possible far [rom the pareut star in relatively massive disks lor 30M. cores., Subcritical core accretion could be possible far from the parent star in relatively massive disks for $30{\rm M}_{\oplus}$ cores.134 However. for 15 aud TOM cores. extremely massive or extremely metal-rich disks with fa>30—50 are required.," However, for $45$ and $70{\rm M}_{\oplus}$ cores, extremely massive or extremely metal-rich disks with $f_{\rm d} > 30-50$ are required."135 Even for those large values of fy. since the critical core mass reaches its tnaNximal value in cases of high core accretion rate. subcritical formation of 15 aud 70 NM... is impossible in some cases (see Fie. 3)).," Even for those large values of $f\sub{d}$ , since the critical core mass reaches its maximal value in cases of high core accretion rate, subcritical formation of 45 and 70 $\mearth$ is impossible in some cases (see Fig. \ref{fig:critical_core_mass}) )."136 Although formation of a 30NL. core may not be very clifIicult iu relatively metal-rich disks. 30M. is the lowest estimated value lor 37 of HD119026b in the cold storage model: 20—80ML is most likely.," Although formation of a $30{\rm M}_{\oplus}$ core may not be very difficult in relatively metal-rich disks, $30{\rm M}_{\oplus}$ is the lowest estimated value for $M_Z$ of HD149026b in the cold storage model; $50$ $80{\rm M}_{\oplus}$ is most likely."137 Therefore. heavy elemeuts must be supplied alter substautial accretion of the envelope.," Therefore, heavy elements must be supplied after substantial accretion of the envelope."138 This issue is discussed iusection [.1.., This issue is discussed insection \ref{sec:Z_supply}. .139The cosmic star formation rate in the universe is shaped by the physical conditions that govern the growth of galaxies.,The cosmic star formation rate in the universe is shaped by the physical conditions that govern the growth of galaxies.140 An initial. probably short-lived. /~LO? vr. episode of population Lb-clominatecl star formation at z15 (e.g.Maioetal.2010) is followed. by a steady increase in cosmic population L/L star formation activity that reaches a peak around z~2 (Llopkins&Beacom2006).. coinciding with a peak in the merger activity of galaxies (c.g.Ixhochfar 2009a)..," An initial, probably short-lived, $t \sim 10^6$ yr, episode of population III-dominated star formation at $z \sim 15$ \citep[e.g.][]{2010MNRAS.tmp..905M} is followed by a steady increase in cosmic population II/I star formation activity that reaches a peak around $z \sim 2$ \citep{2006ApJ...651..142H}, coinciding with a peak in the merger activity of galaxies \citep[e.g.][]{2001ApJ...561..517K,2008MNRAS.386..909C,2009MNRAS.397..506K}."141 The steady decline at lower redshifts is quite strong. however. allowing for 50% of thepresent-day stellar mass to have been formed between z=0 and 1 (Pérez-CGonzálezetαἱ. 2008).," The steady decline at lower redshifts is quite strong, however, allowing for $\sim 50 \%$ of thepresent-day stellar mass to have been formed between $z= 0$ and $1$ \citep{2008ApJ...675..234P}."142. Within the hierarchical ACDAL framework. the initial increase in the cosmic star formation is closely linked. to the growth of the hosting dark matter haloes.," Within the hierarchical $\Lambda$ CDM framework, the initial increase in the cosmic star formation is closely linked to the growth of the hosting dark matter haloes."143 The short cooling time-scale of halo gas favours etlicient Cuclling of star formation in galaxies. in particular at high. redshifts and in dark matter haloes with A4;%1017 M. (e.g.Binney1977:Silk1977:Rees&OstrikerDirnboimDekel 2003)..," The short cooling time-scale of halo gas favours efficient fuelling of star formation in galaxies, in particular at high redshifts and in dark matter haloes with $M_{vir} \ltsim 10^{12}$ $_{\odot}$ \citep[e.g.][]{1977ApJ...215..483B,1977ApJ...211..638S,1977MNRAS.179..541R,2003MNRAS.345..349B}."144 Alore massive haloes at z2 however. reveal elficient feeding of their central galaxies as well.," More massive haloes at $z > 2$ however, reveal efficient feeding of their central galaxies as well."145 Cold streams of gas that enter the virial radius along cosmic filaments penetrate through the diffuse hot halo eas ancl reach the potential minimum ofthe halo (Ixeresetal.2005:Ocvirk2008:Dekeletal. 2009)..," Cold streams of gas that enter the virial radius along cosmic filaments penetrate through the diffuse hot halo gas and reach the potential minimum of the halo \citep{2005MNRAS.363....2K,2008MNRAS.390.1326O,2009Natur.457..451D}."146 Massive galaxies at z2 show gas-to- mass ratios of order unity suggesting that cold Lows could. indeed be a very ellicient means of providing gas to ealaxies (Daclelietal.2010a:Tacconi 2010)..," Massive galaxies at $z \sim 2$ show gas-to-stellar mass ratios of order unity suggesting that cold flows could indeed be a very efficient means of providing gas to galaxies \citep{2010ApJ...713..686D,2010Natur.463..781T}. ."147 Atos<2. cold streams in massive haloes cease to exist and feedback ellects control the cosmic star formation (e.g.Schaveetal.2010.scehoweverBouchect 2009)..," At $z<2$, cold streams in massive haloes cease to exist and feedback effects control the cosmic star formation \citep[e.g.][see however Bouche et al. 2009]{2010MNRAS.402.1536S}. ."1487T assumed that their svstems were isothermal. and so were unable to measure the extra energy in the GM which gives rise to this excess entropy.,"\scite{ponman98a} assumed that their systems were isothermal, and so were unable to measure the extra energy in the IGM which gives rise to this excess entropy."149 Their analysis was therefore owed. on a rough estimate of the likely energy. injection owed. on the that it was caused. by supernova-driven galactic winds., Their analysis was therefore based on a rough estimate of the likely energy injection based on the that it was caused by supernova-driven galactic winds.150 Here. because of our spatially resolved emperature profiles. we can actually attempt to the injected energy and then compare it to the energy expected rom galactic winds or other heating mechanisms.," Here, because of our spatially resolved temperature profiles, we can actually attempt to the injected energy and then compare it to the energy expected from galactic winds or other heating mechanisms."151 The excess energy is composed. of two parts: extra hermal energy. and reduced. gravitational binding energy.," The excess energy is composed of two parts: extra thermal energy, and reduced gravitational binding energy."152 Due to the fact that our data do not extend beyond. 0.2 IH dor the lowest mass svstenis. i was not possible to calculate the total binding energy of the gas within the virial racius for the entire sample. and since energy injection will change the gas distribution. considering the binding energy of the gas within a fixed.fraction of the virial radius. will be misleading.," Due to the fact that our data do not extend beyond 0.2 $R_{v}$ for the lowest mass systems, it was not possible to calculate the total binding energy of the gas within the virial radius for the entire sample, and since energy injection will change the gas distribution, considering the binding energy of the gas within a fixed of the virial radius will be misleading."153 Instead. we investigate the binding energv of eas constituting a fixed fraction of the virial mass of each system.," Instead, we investigate the binding energy of gas constituting a fixed fraction of the virial mass of each system."154 Lf the gas distributions of the svstems were self-similar. this would translate into gas within a fixed fraction of the virial racius. but it can be seen from Fig.," If the gas distributions of the systems were self-similar, this would translate into gas within a fixed fraction of the virial radius, but it can be seen from Fig."155 1. the gas cistributions of the systems are not self-similar., \ref{fig:plot0} the gas distributions of the systems are not self-similar.156 In order to calculate the virial masses of the systems from their mean temperatures the formula was used (?).. which is derived. from numerical simulations.," In order to calculate the virial masses of the systems from their mean temperatures the formula was used \cite{navarro95a}, which is derived from numerical simulations."157 A fixed fractional gas mass of 0.004. Alou was used. which was found to correspond. to a fraction of the virial raciius between 0.064 and 0.226 for the svstenis in the sample.," A fixed fractional gas mass of 0.004 $M_{200}$ was used, which was found to correspond to a fraction of the virial radius between 0.064 and 0.226 for the systems in the sample."158 The mean binding energy per particle of the central 0.004. A/oo5 of gas for the sample is plottec against temperature in Fig. 9.., The mean binding energy per particle of the central 0.004 $M_{200}$ of gas for the sample is plotted against temperature in Fig. \ref{fig:plot6}.159 LE the svstems. were self-similar then the binding energy per particle would. be. directly proportional to the temperature. ancl this relation. fitted to systems with mean leniperatures greater than 4 keV. is shown by the dashed. line.," If the systems were self-similar then the binding energy per particle would be directly proportional to the temperature, and this relation, fitted to systems with mean temperatures greater than 4 keV, is shown by the dashed line."160 “Phe uniform injection of a constant amount of excess energv per unit syvsteni mass will result in a relation of the form where {ο is the binding energy per particle. 7 is the mean gas temperature. Af is the injected. energy per xwticle and A is a constant.," The uniform injection of a constant amount of excess energy per unit system mass will result in a relation of the form where $E$ is the binding energy per particle, $T$ is the mean gas temperature, $\Delta{E}$ is the injected energy per particle and A is a constant."161 Using the function in Equation 9 results in a best it value AL = keV per particle. shown in Fig.," Using the function in Equation \ref{eq:phi} results in a best fit value $\Delta E$ = 2.2 keV per particle, shown in Fig."162 9 as a cot-clash line., \ref{fig:plot6} as a dot-dash line.163 This result. is clearly unreasonably arge. as it would. preclude the presence of significant hot eas in systems with virial temperatures less than ~ 1.5 kV. lt can be seen from Fig.," This result is clearly unreasonably large, as it would preclude the presence of significant hot gas in systems with virial temperatures less than $\sim$ 1.5 keV. It can be seen from Fig."164 9 that this model line underestimates the observed binding energy in almost all the cooler svstems., \ref{fig:plot6} that this model line underestimates the observed binding energy in almost all the cooler systems.165 This result is being driven by one system. Abell 400. which has an exceptionally small eas binding energv. with a small statistical error.," This result is being driven by one system, Abell 400, which has an exceptionally small gas binding energy, with a small statistical error."166 However. 7. have studied the galaxy distribution in Abell 400 in detail. and concluded that it is highly subelustered. with two major subcelusters essentially superposed on the plane of the sky.," However, \scite{beers92a} have studied the galaxy distribution in Abell 400 in detail, and concluded that it is highly subclustered, with two major subclusters essentially superposed on the plane of the sky."167 llence the apparently relaxed: X-ray morphology. in. this system is probably misleading. ancl our derived energy. ancl entropy values for the cluster are unsafe.," Hence the apparently relaxed X-ray morphology in this system is probably misleading, and our derived energy and entropy values for the cluster are unsafe."168 Excluding Abell 400 from our analvsis. gives a much lower value for the fitted value of excess energy: Af = 0.44 keV per particle. corresponding to a preheating temperature of 1—0.320.2 keV. The fit is shown as a solid line in Fig. 9..," Excluding Abell 400 from our analysis, gives a much lower value for the fitted value of excess energy: $\Delta{E}$ = 0.44 keV per particle, corresponding to a preheating temperature of $T = 0.3 \pm 0.2$ keV. The fit is shown as a solid line in Fig. \ref{fig:plot6},"169 along with a formal le confidence interval., along with a formal $\sigma$ confidence interval.170 Clearly. this estimate of the excess energy is subject to large statistical and systematic errors at present. and à more accurate result should. be available in due course from. studies with the new generation of X-ray observatories.," Clearly this estimate of the excess energy is subject to large statistical and systematic errors at present, and a more accurate result should be available in due course from studies with the new generation of X-ray observatories."171 However. as we will discuss below. a value of 0.4 keV per particle agrees well with recently developed. preheating models. anc with estimates based on the metallicity of the ΑΔ.," However, as we will discuss below, a value of $\sim 0.4$ keV per particle agrees well with recently developed preheating models, and with estimates based on the metallicity of the IGM."172 To investigate whether this measured injection energv shows any radial dependence. the above procedure. was repeated for a number of dillerent. fractional gas masses.," To investigate whether this measured injection energy shows any radial dependence, the above procedure was repeated for a number of different fractional gas masses."173 The results ave plotted in Fig. 10., The results are plotted in Fig. \ref{fig:plot7}.174 At small radii. the nieasured excess energy in the eas is allected by the presence of cooling Hows. which elfectively scales up the whole of the right hand side of Equation 9 due to the increased central concentration of the gas. resulting in a higher inferred. value for AZ.," At small radii, the measured excess energy in the gas is affected by the presence of cooling flows, which effectively scales up the whole of the right hand side of Equation \ref{eq:phi} due to the increased central concentration of the gas, resulting in a higher inferred value for $\Delta{E}$ ."175" However. it can be seen that the effects. of this distortion are confined to A,<0002ους. and that the asvmptotic value of excess energy outside the cooling region is  0.4 keV. Extrapolation of the mocels to larger fractional eas masses is hiehly uncertain and would result. in. large systematic errors as it would encompass gas well bevond the data in the low mass svstenis."," However, it can be seen that the effects of this distortion are confined to $M_{\rm gas}<0.003 M_{200}$, and that the asymptotic value of excess energy outside the cooling region is $\sim$ 0.4 keV. Extrapolation of the models to larger fractional gas masses is highly uncertain and would result in large systematic errors as it would encompass gas well beyond the data in the low mass systems."176 Since PA work and shock heating can move energy around within the IGM. the exeess energy. per. particle evaluated within a subset of the total gas mass will not necessarily equal thevalue which would. be obtained. if we could extend our analysis to cover the whole of the," Since $P d\!V$ work and shock heating can move energy around within the IGM, the excess energy per particle evaluated within a subset of the total gas mass will not necessarily equal thevalue which would be obtained if we could extend our analysis to cover the whole of the"177"taken dp=1/2""Gyr and ε=O.1kpe. respectively and the tolerance parameter for gyrfaleON was set 6,= 0.9.","taken $dt=1 / 2^{10} \; \rm Gyr$ and $\epsilon=0.1 \;\rm kpc$, respectively and the tolerance parameter for gyrfalcON was set $\theta_t=0.9$ ."178 Here we can use relatively low precision because each iteration is short and errors do not accumulate (RASO9)., Here we can use relatively low precision because each iteration is short and errors do not accumulate (RAS09).179" In order to fix the c4(R) profile we applied the algorithm described in RASO9, section 2.3.1. with ng,=200 layers."," In order to fix the $\sigma_R(R)$ profile we applied the algorithm described in RAS09, section 2.3.1, with $n_{\rm div}=200$ layers."180 We used the “transvel_ceyl” modification of the algorithm of velocity transfer (see RASO9)., We used the cyl” modification of the algorithm of velocity transfer (see RAS09).181 This algorithm was also used for constructing the halo., This algorithm was also used for constructing the halo.182 For constructing the halo we also made 50 iterations., For constructing the halo we also made $50$ iterations.183" The other parameters for this construction were t;=0.5Gyr. dt=1/2? Gyr. e=0.1kpe and 6,=0.9."," The other parameters for this construction were $t_i=0.5 \; \rm Gyr$, $dt=1 / 2^{10} \; \rm Gyr$ , $\epsilon=0.1 \;\rm kpc$ and $\theta_t=0.9$."184 Our initial model was a cold model with velocities equal to zero., Our initial model was a cold model with velocities equal to zero.185" During the first 10 iterations we fixed a condition of velocity isotropy (RASO9, 2.3.4). and we did not set any kinematic constraints during the last 40 iterations."," During the first $10$ iterations we fixed a condition of velocity isotropy (RAS09, 2.3.4), and we did not set any kinematic constraints during the last $40$ iterations."186 Once all three components of our model were constructed. we simply stacked them to obtain the complete system.," Once all three components of our model were constructed, we simply stacked them to obtain the complete system."187 To check whether this was indeed near equilibrium. as it should be. we evolved the model using the respective GADGET? code.," To check whether this was indeed near equilibrium, as it should be, we evolved the model using the respective GADGET2 code."188 The evolution of the gaseous disk over 0.4 Gyr Is giver in Fig. 2.," The evolution of the gaseous disk over 0.4 Gyr is given in Fig. \ref{fig_gas.iso},"189 and shows that the gaseous disk conserves its structural and dynamical properties very well., and shows that the gaseous disk conserves its structural and dynamical properties very well.190 We also checkec the absence of evolution for the stellar disk and the halo., We also checked the absence of evolution for the stellar disk and the halo.191 For reasons of conciseness we do not present the corresponding figures here., For reasons of conciseness we do not present the corresponding figures here.192 We conclude that the constructed model is indeec close to equilibrium., We conclude that the constructed model is indeed close to equilibrium.193 Here we will deseribe how to overcome the assumption of axisymmetry and thus to construct equilibrium models with triaxial haloes., Here we will describe how to overcome the assumption of axisymmetry and thus to construct equilibrium models with triaxial haloes.194 Because of the powerful. yet simple basic idea of our iterative method we can remove this assumption relatively easily.," Because of the powerful, yet simple basic idea of our iterative method we can remove this assumption relatively easily."195 As in the axisymmetric case. we will construct each component of the galaxy in the potential of all other components and then will assemble all components together to obtain the final live equilibrium model.," As in the axisymmetric case, we will construct each component of the galaxy in the potential of all other components and then will assemble all components together to obtain the final live equilibrium model."196 We will start from the problem of the construction of equilibrium stellar disk in presence of the external non-axisymmetric potential (created by all other components of the galaxy)., We will start from the problem of the construction of equilibrium stellar disk in presence of the external non-axisymmetric potential (created by all other components of the galaxy).197 The first problem whose solution is not obvious is deciding which shape the stellar disk should have to be in equilibrium within a triaxial external potential., The first problem whose solution is not obvious is deciding which shape the stellar disk should have to be in equilibrium within a triaxial external potential.198 There are two possibilities., There are two possibilities.199 One possibility is to somehow define the shape of the disk and then try to construct an equilibrium model with this shape. 1.8. model with given mass distribution.," One possibility is to somehow define the shape of the disk and then try to construct an equilibrium model with this shape, i.e. model with given mass distribution."200 For example. Machado&Athanassoula(2010) obtained an approximate shape of the disk via the epicyclic approximation.," For example, \citet{M10} obtained an approximate shape of the disk via the epicyclic approximation."201 This. nevertheless. is only an approximation and there has been no other. more accurate way proposed so far.," This, nevertheless, is only an approximation and there has been no other, more accurate way proposed so far."202 For this reason. we will let the iterative method itself find the appropriate shape of the disk.," For this reason, we will let the iterative method itself find the appropriate shape of the disk."203 We do it in the following way., We do it in the following way.204 We do not ask the iterative method to construct a model with a fully defined space distribution of particles., We do not ask the iterative method to construct a model with a fully defined space distribution of particles.205 Instead. we fix only the vertical and. radial distributions of particles. but not the azimuthal distribution.," Instead, we fix only the vertical and radial distributions of particles, but not the azimuthal distribution."206 This means that the R and z coordinates of the particles are defined by a given distribution. but the ᾧ coordinate together with velocities is not fixed.," This means that the $R$ and $z$ coordinates of the particles are defined by a given distribution, but the $\varphi$ coordinate together with velocities is not fixed."207 The idea described in the last sentence Is very similar to the idea of the algorithm we used for constructing the gaseous disk. where we fixed only the surface density (1.9. the radial and azimuthal distribution of particles) but we did not fix the vertical distribution of the particles (see section 2.1)).," The idea described in the last sentence is very similar to the idea of the algorithm we used for constructing the gaseous disk, where we fixed only the surface density (i.e. the radial and azimuthal distribution of particles) but we did not fix the vertical distribution of the particles (see section \ref{s_gmethod}) )."208 Consequently the algorithm is also very similar to the ones presented in section 2..., Consequently the algorithm is also very similar to the ones presented in section \ref{s_gmethod}.209 To apply the general scheme of the iterative method (see Fig. 1) , To apply the general scheme of the iterative method (see Fig. \ref{fig_scheme}) )210we need to specify an initial model and the parameters which we want to fix during the iterative procedure., we need to specify an initial model and the parameters which we want to fix during the iterative procedure.211 Our initial model is an axisymmetric disk with a given radial and vertical distribution., Our initial model is an axisymmetric disk with a given radial and vertical distribution.212 The azimuthal velocity of each particle is set equal to the circular velocity., The azimuthal velocity of each particle is set equal to the circular velocity.213 With this inital model. we start the iterations. which. as always. consist of a sequence of short time evolutions followed by steps during which we fix the desired parameters or properties (see Fig. 1)).," With this initial model, we start the iterations, which, as always, consist of a sequence of short time evolutions followed by steps during which we fix the desired parameters or properties (see Fig. \ref{fig_scheme}) )."214 In this case we fix the Our algorithm for fixing the vertical and. the radial distribution of particles is very similar to the algorithm which we used for fixing the surface density in section 2.1..., In this case we fix the Our algorithm for fixing the vertical and the radial distribution of particles is very similar to the algorithm which we used for fixing the surface density in section \ref{s_gmethod}.215 We construct a stellar disk with the desired vertical and. radial distribution of particles. but with velocities and azimuthal coordinates chosen according to the velocities and. the azimuthal coordinates of the disk resulting from the evolution step.," We construct a stellar disk with the desired vertical and radial distribution of particles, but with velocities and azimuthal coordinates chosen according to the velocities and the azimuthal coordinates of the disk resulting from the evolution step."216" We transfer the azimuthal coordinate of the particle during the ""transfer"" procedure together with the velocities (see section 2.1)) to the “nearest” particle. which in this case is found in the two-dimensional R—z space."," We transfer the azimuthal coordinate of the particle during the “transfer” procedure together with the velocities (see section \ref{s_gmethod}) ) to the “nearest” particle, which in this case is found in the two-dimensional $R-z$ space."217 There is one potential problem with the symmetry., There is one potential problem with the symmetry.218 Indeed. if we fix only the distribution of particles in the vertical and radial directions. then the constructed model can be non-symmetrical in the disk plane.," Indeed, if we fix only the distribution of particles in the vertical and radial directions, then the constructed model can be non-symmetrical in the disk plane."219 Partially. this is what we aimed for because our target was to avoid axisymmetry.," Partially, this is what we aimed for because our target was to avoid axisymmetry."220 However. even in a triaxial potential we would like the equilibrium model to have a certain level of symmetry and a smooth density distribution.," However, even in a triaxial potential we would like the equilibrium model to have a certain level of symmetry and a smooth density distribution."221 We can enforce our model to have reflection symmetry about the XZ and YZ planes by fixing these symmetries duringthe iterative procedure (see Fig. 1))., We can enforce our model to have reflection symmetry about the $XZ$ and $YZ$ planes by fixing these symmetries duringthe iterative procedure (see Fig. \ref{fig_scheme}) ).222" But we should take into account that our disk rotates about the z-axis,", But we should take into account that our disk rotates about the $z$ -axis.223" Reflection symmetry about the XZ plane is fixed by changing the sign of y and v, for all particles with à probability of 1/2.", Reflection symmetry about the $XZ$ plane is fixed by changing the sign of $y$ and $v_x$ for all particles with a probability of $1/2$.224" Reflection symmetry about the YZ plane is fixed by changing the sign of x and v, with a probability of 1/2.", Reflection symmetry about the $YZ$ plane is fixed by changing the sign of $x$ and $v_y$ with a probability of $1/2$ .225 Let us note. however. that our experiments show for the stellar disks that fixing this symmetry is not so crucial.," Let us note, however, that our experiments show for the stellar disks that fixing this symmetry is not so crucial."226 In nost, In most227where the dise density has increased most in the encounter.,where the disc density has increased most in the encounter.228 Here. the density. gradient is increased and the effectiveness of viscous transport later on in (he time evolution should be considerably enhanced.," Here, the density gradient is increased and the effectiveness of viscous transport later on in the time evolution should be considerably enhanced."229 In summary. encounters appear to have a (vo-Fold effect on angular momentum: Thev lead to a considerable angular momentum transport theniselves even more so when a bound system is produced. and thev probably increase (he efficiency. of viscous angular momentum transport near the disc center.," In summary, encounters appear to have a two-fold effect on angular momentum: They lead to a considerable angular momentum transport themselves even more so when a bound system is produced, and they probably increase the efficiency of viscous angular momentum transport near the disc center."230"of the Milky Wavy (power-law slopes of 0.2 and of around LSto 2.0 for the low ancl high-mass regimes respectively. a turn-olf mass of 1.5QM... and lower and upper mass limits of 1tVAL, and. 14PALL. respectively). the application of his Formulae shows that the initial mass of the GCS is decreased by 40. per cent. while the fraction of surviving clusters is 16 per cent.","of the Milky Way (power-law slopes of –0.2 and of around –1.8 to –2.0 for the low and high-mass regimes respectively, a turn-off mass of $1.5 \times 10^5 {\rm M}_{\odot}$, and lower and upper mass limits of $10^4 {\rm M}_{\odot}$ and $10^6 {\rm M}_{\odot}$, respectively), the application of his formulae shows that the initial mass of the GCS is decreased by 40 per cent, while the fraction of surviving clusters is 16 per cent."231" In case of a lower limit for the cluster initial mass range. sav Q'M, the contrast between the decreases in mass and number is even more striking. Le, the survivors still represent 44 per cent of the initial total mass but 2 per cent of the initial number only."," In case of a lower limit for the cluster initial mass range, say $10^3 {\rm M}_{\odot}$, the contrast between the decreases in mass and number is even more striking, i.e., the survivors still represent 44 per cent of the initial total mass but 2 per cent of the initial number only."232" AleLaughlin (1999) ""s formulae thus illustrate that. compared to number related quantities. mass related quantities are less markedly alfoected by a GCGyvr long evolution."," McLaughlin (1999) 's formulae thus illustrate that, compared to number related quantities, mass related quantities are less markedly affected by a Gyr long evolution."233 As a result. the racial mass density profile of the halo GCS may be considered. as a reasonably reliable estimator of their initial distribution around the Galactic centre.," As a result, the radial mass density profile of the halo GCS may be considered as a reasonably reliable estimator of their initial distribution around the Galactic centre."234 We will make this point more quantitative in Section 4 and show that such an hypothesis is ineleecl robust., We will make this point more quantitative in Section \ref{sec:evol_rho_D} and show that such an hypothesis is indeed robust.235 In this paper. we are interested. in understanding the origin of the initial spatial distribution of the halo GCS mass within the Milky Was. which we approximate by the presently observed: mass density profile at. this stage of the. discussion.," In this paper, we are interested in understanding the origin of the initial spatial distribution of the halo GCS mass within the Milky Way, which we approximate by the presently observed mass density profile at this stage of the discussion."236 We do not consider the more metal-rich. presumably: second. generation. bulge/cdise CC's{(οη] 3 0.8).," We do not consider the more metal-rich, presumably second generation, bulge/disc GCs ([Fe/H] $\geq -0.8$ )."237 Also. the halo (Fe/H) < 0.8)) subsystem itself could be divided into two groups. traditionally— referred to as ihe OLLI and the YIL(see. e.g.. Zinn 1993. Van den Bereh 199 Mackey Gilmoreals2004).," Also, the halo ([Fe/H] $< -0.8$ ) subsystem itself could be divided into two groups, traditionally referred to as the OH and the YH (see, e.g., Zinn 1993, Van den Bergh 1993, Mackey Gilmore 2004)."238 Evidence supporting the existence ol such two distinct subsystems have been accumulating over the past vears., Evidence supporting the existence of such two distinct halo subsystems have been accumulating over the past years.239 OIL and. YII GCs show dilferences in jorizontal. branch morphology. age. kinematics. spatial clistribution(see Parmentier et al.," OH and YH GCs show differences in horizontal branch morphology, age, kinematics, spatial distribution (see Parmentier et al."240 2000. their Section 2. for a review). as well as differences in the distribution of their core radius (Alackey Gilmore 2004)-," 2000, their Section 2, for a review), as well as differences in the distribution of their core radius (Mackey Gilmore 2004)."241 Phe properties of the OL group are Consistent with the majority of its members having been formed 7in situ” during the large-scale collapse of he protogalactic as envisioned by IEgeen. Lvnden-30| Sandage(19.," The properties of the OH group are consistent with the majority of its members having been formed ""in situ"" during the large-scale collapse of the protogalactic cloud, as envisioned by Eggen, Lynden-Bell Sandage (1962)."242 nOn the other hand. the YL GC's are not native to ibe nw( probably having been formed in external dwarl galaxies and afterwards accreted into the οιcr halo while their host. galaxies were being swallowed by the Milky Way. as suggested by Searle Zinn((LOTS).," On the other hand, the YH GCs are not native to the Galaxy, probably having been formed in external dwarf galaxies and afterwards accreted into the outer halo while their host galaxies were being swallowed by the Milky Way, as suggested by Searle Zinn (1978)."243 The current accretion of theSagittarius dwarf galaxy. and of its small GCS is the smoking gun of this process., The current accretion of the Sagittarius dwarf galaxy and of its small GCS is the smoking gun of this process.244 As we are interested in the mass density profile of the GCS which formed within the original potential well of the Galaxy. we restrict our attention to the OLL GCs.," As we are interested in the mass density profile of the GCS which formed within the original potential well of the Galaxy, we restrict our attention to the OH GCs."245 This OLL/YLI division has already been proven most. fruitful as the ΟΙ CC's shows a metallicity &racient and obeys a mass-moetallicity relation. features predicted by simple self-enrichment modeLg (Parmentier et al.," This OH/YH division has already been proven most fruitful as the OH GCS shows a metallicity gradient and obeys a mass-metallicity relation, features predicted by simple self-enrichment models (Parmentier et al."246 2000 anc Parmentier Gilmore 200 respectively). while the whole halo GCS COLL|YID) does not.," 2000 and Parmentier Gilmore 2001, respectively), while the whole halo GCS (OH+YH) does not."247 Lists of Oll and. ΥΗ GC's are. provided. in Lee οἱ al. (, Lists of OH and YH GCs are provided in Lee et al. (2481904) and Da Costa Armandroll (1995).,1994) and Da Costa Armandroff (1995).249 With respect to these. we have mace two slight changes however.," With respect to these, we have made two slight changes however."250 In our present OLI sample. we ignore NGC 2419.," In our present OH sample, we ignore NGC 2419."251 Althoug= coeval with the inner halo (Llarris οἱ al.," Although coeval with the inner halo (Harris et al.,"252 1997: Salaris weiss 2002). this GC is located at a galactocentric distance of order kkpe and is thus unlikely to belong to the main body of the Galaxy.," 1997; Salaris weiss 2002), this GC is located at a galactocentric distance of order kpc and is thus unlikely to belong to the main body of the Galaxy."253 Moreover. van den Bereh Alackey (2004) show that NCC 2419 and w Cen on the one hand. and the other halo GC's on the other hand. are at. cülferent locii in a halt-light radius vs absolute visual magnitude cliagram.," Moreover, van den Bergh Mackey (2004) show that NGC 2419 and $\omega$ Cen on the one hand, and the other halo GCs on the other hand, are at different locii in a half-light radius vs absolute visual magnitude diagram."254 They thus suggest that. as c Con (which we also exclude from our sample). NGC 2419 might be the iclally stripped. core of a former dwarf spwroidal galaxy.," They thus suggest that, as $\omega$ Cen (which we also exclude from our sample), NGC 2419 might be the tidally stripped core of a former dwarf spheroidal galaxy."255 An cllicient tidal stripping would however require. NCC 2419 tO Cross the inner Galactic regions., An efficient tidal stripping would however require NGC 2419 to cross the inner Galactic regions.256 Unfortunately. its orbit is still ill-determined.," Unfortunately, its orbit is still ill-determined."257 Also. unike aw Cen. there is no evidence for a metallicity spreack among the cluster elants.," Also, unlike $\omega$ Cen, there is no evidence for a metallicity spread among the cluster giants."258 IE NGC 2419 is actually the remnant of a former chvarl galaxy. the parent gaaxy might. like the Ursa Minor chvarl ealaxy (van den Bere1 2000) have produced a single generation of metal-poor stars.," If NGC 2419 is actually the remnant of a former dwarf galaxy, the parent galaxy might, like the Ursa Minor dwarf galaxy (van den Bergh 2000), have produced a single generation of metal-poor stars."259 Bearing these caveals in müncd. we thus note that the main peculiarity of Νας' 2419 with respect to the bulk of t1 OLL is its large galactocentric distance.," Bearing these caveats in mind, we thus note that the main peculiarity of NGC 2419 with respect to the bulk of the OH is its large galactocentric distance."260 Negecting NGC 2419. the OIL is thoroughly. contained within Ds4tOkkpe.," Neglecting NGC 2419, the OH is thoroughly contained within $\lesssim$ kpc."261 Additionally. we have moved the cluster NGC 6864 from the YII group to the OLL group.," Additionally, we have moved the cluster NGC 6864 from the YH group to the OH group."262 According to the former (1999) edition o ‘the GC MeMaster Catalog (Llarris. 1096). the metallicity and. the horizontal branch ratio (IIDBBR) of NGC 6864 are. 1.32 and 0.42. respectively.," According to the former (1999) edition of the GC McMaster Catalog (Harris 1996), the metallicity and the horizontal branch ratio (HBR) of NGC 6864 are –1.32 and –0.42, respectively."263 The updated (2003) values being Fe/LJ=1.16 and UBR=0.07. the location of this cluster in the Fe/1I] vs LIBR. diagram shows that it is more likely a member of the OLL group rather than a YI GC.," The updated (2003) values being [Fe/H]=–1.16 and HBR=–0.07, the location of this cluster in the [Fe/H] vs HBR diagram shows that it is more likely a member of the OH group rather than a YH GC."264 Finally. about 25 halo GC's of the Llarris Catalogue still miss HD. index measurements.," Finally, about 25 halo GCs of the Harris Catalogue still miss HB index measurements."265 Using recently published: colour-magnitucde diagrams. (e.g... Piotto ct aL.," Using recently published colour-magnitude diagrams, (e.g., Piotto et al.,"266 2002). Alackey Gilmore (2004) have sorteck most of these vet undefined GCs.," 2002), Mackey Gilmore (2004) have sorted most of these yet undefined GCs."267 ALL the GCs to which Alackey Gilmore (2004) have assigned an OLL membership have been added to our OLL sample., All the GCs to which Mackey Gilmore (2004) have assigned an OH membership have been added to our OH sample.268 This one is presented in Table 1, This one is presented in Table \ref{tab:OH}.269" 3elore proceeding further. we derive estimates for the parameters ~ ane D, appropriate [or the sole OLI. as"," Before proceeding further, we derive estimates for the parameters $\gamma$ and $D_c$ appropriate for the sole OH, as"270Analvsis of the differential field distribution function /(5) (the magnetic field function) introduced by Fabrikaetal.(L997) is of exeat importance in understanding (the origin of stellar magnetic fields.,Analysis of the differential field distribution function $f({\cal B})$ (the magnetic field function) introduced by \cite{1997PAZh...23...47F} is of great importance in understanding the origin of stellar magnetic fields.271 The finction (5) is defined as N/(B)AB. where V(B.B+AB) is the number of stars in the interval of mean magnetic fields (5.8+AB). N is the total number of stars with measured B.," The function $f({\cal B})$ is defined as N, where $N({\cal B},{\cal B}+\Delta {\cal B})$ is the number of stars in the interval of mean magnetic fields $({\cal B},{\cal B}+\Delta {\cal B})$, $N$ is the total number of stars with measured ${\cal B}$."272 In this paper. we restrict ourselves only to D stars. because the iunber of O stars wilh measured magnetic fields is insufficient for statistical studies.," In this paper, we restrict ourselves only to B stars, because the number of O stars with measured magnetic fields is insufficient for statistical studies."273 After the application of criterion (10). there were 130 objects in the list of stars with statistically significant fields.," After the application of criterion (10), there were 130 objects in the list of stars with statistically significant fields."274 The distribution function /(B8) constructed from (he data of the catalog by Byehkov et al. (, The distribution function $f({\cal B})$ constructed from the data of the catalog by Bychkov et al. (2752009) is shown in Fig.,2009) is shown in Fig.276 4., 4.277 We chose the bins of mean magnetic fields in such a wav that at least eight stars fell within each bin., We chose the bins of mean magnetic fields in such a way that at least eight stars fell within each bin.278 Only in the regions 5«0.06 kG and B> 5kG did the number of stars turn out to be smaller than eight. because the number ol stars with very small and very. large magnetic field strengths was small.," Only in the regions ${\cal B}<0.06\,$ kG and ${\cal B}>5\,$ kG did the number of stars turn out to be smaller than eight, because the number of stars with very small and very large magnetic field strengths was small."279 The derived funcüon f(5) for B>400 G can be fitted by a power law: WB)= Avoi," The derived function $f({\cal B})$ for ${\cal B}\ge 400\,$ G can be fitted by a power law: )= A_0."280"um lt tuned out that in a wide range of 6 (0,(0.40. — 12 kG). the NEM function /(5) could be described by a single expression (12) with parametersAy=0.33+0.04 and 40.07. as shown in Fie."," It turned out that in a wide range of ${\cal B}$ (0.40 – 12 kG), the distribution function $f({\cal B})$ could be described by a single expression (12) with parameters $A_0=0.33\pm 0.04$ and $\gamma=1.82\pm 0.07$ , as shown in Fig."281 4., 4.282" Moninetal.(2000) constructed the magnetic field fanction from a sample of 57 bright (Vκ 4"".0) magnetic main-sequence D3.— F9 stars.", \cite{2000PreprintSAO..150} constructed the magnetic field function from a sample of 57 bright $V<4^m.0$ ) magnetic main-sequence B3 – F9 stars.283 These authors fitted the magnetic field [function bv a power law., These authors fitted the magnetic field function by a power law.284" For 6,> Εκ, where 5, is (he stellar surface field. which is approximately triple the value of B Moninetal.(2000).. the authors obtained +=2.2. which is close to the value found here."," For ${\cal B}_s>4\,$ kG, where ${\cal B}_s$ is the stellar surface field, which is approximately triple the value of ${\cal B}$ \cite{2000PreprintSAO..150}, the authors obtained $\gamma=2.2$, which is close to the value found here."285" In the range of magnetic fields 1 6 kG. these authors obtained z1 and concluded that there was a break in the magnetic field function in the range DJ,= 3—5kG. Our data are consistent with the conclusion about the existence of such a break (see Fig."," In the range of magnetic fields 1 – 6 kG, these authors obtained $\gamma \approx 1$ and concluded that there was a break in the magnetic field function in the range $B_s= 3 - 5\,$ kG. Our data are consistent with the conclusion about the existence of such a break (see Fig."286 4)., 4).287 IIlowever. since the number of stars with measured magnetic fields in the above range is relatively small. thevalue of the parameter 5 in (his range cannot be established reliably.," However, since the number of stars with measured magnetic fields in the above range is relatively small, thevalue of the parameter $\gamma$ in this range cannot be established reliably."288presented in 822 and 833. with detailed results on individual objects given in St. and a brief discussion in 855.,"presented in 2 and 3, with detailed results on individual objects given in 4, and a brief discussion in 5."289 The majority of the 43 targets. listed in Table 1. come from the white dwarl catalog of MeCook&Sion(1999).. and were selected because their Two Micron All Sky Survey (2\LASS) JHNN. photometry suggested near-infrared excess emission.," The majority of the 43 targets listed in Table \ref{tbl1} come from the white dwarf catalog of \citet{mcc99}, and were selected because their Two Micron All Sky Survey (2MASS) $JHK_s$ photometry suggested near-infrared excess emission."290" ""These are primarily white dwarf plus low mass stellar or. substellar companion candidates. a significant fraction of which are taken from Farihietal.(2005).. and. Wachteretal.(2003)."," These are primarily white dwarf plus low mass stellar or substellar companion candidates, a significant fraction of which are taken from \citet{far05}, and \citet{wac03}."291.. A small number of these stars are known or suspected magnetic white dwarfs. but were not intentionally selectec as such. and. hence these targets overlap with the sample analyzecl by Wellhouseοἱal. (2005).," A small number of these stars are known or suspected magnetic white dwarfs, but were not intentionally selected as such, and hence these targets overlap with the sample analyzed by \citet{wel05}."292.. Another subset of targets. were chosen [roni various literature sources as binary suspects based on optical spectroscopy and. photometry: many. of these are. double degenerate suspects (e.g. Bergeronetal. 19902). X., Another subset of targets were chosen from various literature sources as binary suspects based on optical spectroscopy and photometry; many of these are double degenerate suspects (e.g. \citealt{ber90}) ).293 final subset of targets are metal-rich white cbwarfs with low or questionable quality 2ALASS photometry. most of which are part of various Spiser programs aimed at searching [for circumstellar dust. (Parihietal.2009.2008b:Juract 2007).," A final subset of targets are metal-rich white dwarfs with low or questionable quality 2MASS photometry, most of which are part of various programs aimed at searching for circumstellar dust \citep{far09,far08b,jur07}."294. Data were obtained at the NASA Infrared. Telescope Facility (ARTE) using the mecium-resolution spectrograph and imager SpeX (Ravneretal.2003) on 2006 October 7. Mand 2007 April 79., Data were obtained at the NASA Infrared Telescope Facility (IRTF) using the medium-resolution spectrograph and imager SpeX \citep{rayn03} on 2006 October $7-9$ and 2007 April $7-9$.295 Conditions were photometric or near-photometric for all of the imaging observations. while thin cirrus was present cluring some of the spectroscopy.," Conditions were photometric or near-photometric for all of the imaging observations, while thin cirrus was present during some of the spectroscopy."296 The instrument was used. primarily for imaging. but also in its intended spectrographic configuration.," The instrument was used primarily for imaging, but also in its intended spectrographic configuration."297 Science target images were taken at JLI. using individual exposure times hat were tvpically 30 seconds., Science target images were taken at $JHK$ using individual exposure times that were typically 30 seconds.298 A seven point dither pattern was repeated once or twice. resulting in total integration ines between 3.5 and. 7.0 minutes.," A seven point dither pattern was repeated once or twice, resulting in total integration times between 3.5 and 7.0 minutes."299 Photometric standard stars were observed. in a similar manner a few to several ines during cach night to measure the zero point in cach σπα, Photometric standard stars were observed in a similar manner a few to several times during each night to measure the zero point in each passband.300 Spectroscopy of select targets was performed with SpeX using the low-resolution prism mode that covers the entire VS2.5 pum region in a single exposure setting., Spectroscopy of select targets was performed with SpeX using the low-resolution prism mode that covers the entire $0.8-2.5$ $\mu$ m region in a single exposure setting.301 The 07S slit was used to maximize gathered light at. the expense of resolution. resulting in #z100 at 77 band.," The $0\farcs8$ slit was used to maximize gathered light at the expense of resolution, resulting in $R\approx100$ at $H$ band."302 Individual exposures of 120 seconds were used at (wo positions along 1e slit. repeated ten times for a total integration time of 20 minutes.," Individual exposures of 120 seconds were used at two positions along the slit, repeated ten times for a total integration time of 20 minutes."303 An AOV telluric standard. star was observed immediately following each science observation. as were spectral flat fields and arc lamp images.," An A0V telluric standard star was observed immediately following each science observation, as were spectral flat fields and arc lamp images."304 Near-infrared images for 41 targets were reduced in the standard fashion. with long exposure sky frames normalized to serve as Hat fields.," Near-infrared images for 41 targets were reduced in the standard fashion, with long exposure sky frames normalized to serve as flat fields."305 Images of each target at each bandpass were skvy-subtracted by removing the median of the raw image stack. Uat-fielded. then registered. and. recombined bv averaging.," Images of each target at each bandpass were sky-subtracted by removing the median of the raw image stack, flat-fielded, then registered and recombined by averaging."306 Photometry of science targets ancl standard stars was performed with aperture radii between r=10 and 20 pixels. corresponding to 17530. and. generally measured at the widest possible radius while avoiding contamination from nearby. objects or companions.," Photometry of science targets and standard stars was performed with aperture radii between $r=10$ and 20 pixels, corresponding to $1\farcs5-3\farcs0$, and generally measured at the widest possible radius while avoiding contamination from nearby objects or companions."307 Where possible. 24LASS sources within the SpeX field of view were used. to. corroborate the photometric calibration.," Where possible, 2MASS sources within the SpeX field of view were used to corroborate the photometric calibration."308 Median extinction values for Alauna lea were used. ο correct all photometry to airmass 1.00. and the zero point of each filter for each night was established by averaging the measurements for three to four standard. stars.," Median extinction values for Mauna Kea were used to correct all photometry to airmass 1.00, and the zero point of each filter for each night was established by averaging the measurements for three to four standard stars."309 Phe. zero volts for all nights during both observing runs were found o agree within a few percent., The zero points for all nights during both observing runs were found to agree within a few percent.310 Spectroscopic data for 11 targets were reduced. with Spextool (Cushingctal.2004)... including sky-subtraction. lat-iekding. spectral extraction ancl averaging.," Spectroscopic data for 11 targets were reduced with Spextool \citep{cus04}, including sky-subtraction, flat-fielding, spectral extraction and averaging."311 Spextool also was used to perform wavelength calibration. tclluric eature removal. sensitivity correction. and [ux calibration.," Spextool also was used to perform wavelength calibration, telluric feature removal, sensitivity correction, and flux calibration."312 However. due to slit losses and other sources of error. the inal flux. calibrations of the science target spectra. were established using photometry.," However, due to slit losses and other sources of error, the final flux calibrations of the science target spectra were established using photometry."313 The resulting near-infrared photometry and spectroscopy for all 43 targets are listed in Table 2 and plotted together with the ultraviolet ancl optical spectral energy. distributions in Figures Al A52.. ordered. by. right ascension.," The resulting near-infrared photometry and spectroscopy for all 43 targets are listed in Table \ref{tbl2} and plotted together with the ultraviolet and optical spectral energy distributions in Figures \ref{fig1} – \ref{fig52}, ordered by right ascension."314 Optical photometric cata plotted. in the figures were taken from various literature sources. including but not limited to the Sloan Digital Sky Survey CXdelman-MeCarthyetal.2008).. DENIS (DENISConsortium2005).. the white chwarl catalog of MeCook&Sion(1999) ancl references therein.," Optical photometric data plotted in the figures were taken from various literature sources, including but not limited to the Sloan Digital Sky Survey \citep{ade08}, DENIS \citep{den05}, the white dwarf catalog of \citet{mcc99} and references therein."315 Phere are a few cases with photographic photometry (SpaceTele- where superior data were unavailable.," There are a few cases with photographic photometry \citep{sts06,cmc06,316zac05,mon03} where superior data were unavailable."317 The SDSS Iluxes were assumed to have errors lor the following reasons: 1) the quoted photometric errors in SDSS DIU are often less than 0.01 mag. which is unlikely to be realistic: 2) where two flux measurements of a single source are available. they sometimes ciller by or greater in a given banepass: 3) many of the flux measurements carry micdcdle-gracde photometric quality ασ»: ancl 4) several objects cataloged as point sources are in [fact members of close double or multiple systems. implving further photometric error.," The SDSS fluxes were assumed to have errors for the following reasons: 1) the quoted photometric errors in SDSS DR7 are often less than 0.01 mag, which is unlikely to be realistic; 2) where two flux measurements of a single source are available, they sometimes differ by or greater in a given bandpass; 3) many of the flux measurements carry middle-grade photometric quality flags; and 4) several objects cataloged as point sources are in fact members of close double or multiple systems, implying further photometric error."318 Acelitionally. availableGALEX. far- ancl near-ultraviolet luxes are included in the plots: a weighted average was taken where multiple measurements are given.," Additionally, available far- and near-ultraviolet fluxes are included in the plots; a weighted average was taken where multiple measurements are given."319 These fluxes. are uncorrected for extinction. anc minimum. errors have oen assigned.," These fluxes are uncorrected for extinction, and minimum errors have been assigned."320 Where available. 24LASS JI. photometry (Skrutskieetal.2006). is plotted alongside the ΕΤ data or direct comparison.," Where available, 2MASS $JHK_s$ photometry \citep{skr06} is plotted alongside the IRTF data for direct comparison."321 The optical ancl ultraviolet. photometry for all stars were fitted with model spectra of the appropriate cllective emperatures. which sometimes cleviatecl from. previously xiblished literature values.," The optical and ultraviolet photometry for all stars were fitted with model spectra of the appropriate effective temperatures, which sometimes deviated from previously published literature values."322 Hydrogen atmosphere stars were itted with log g=S0 white dwarf spectral models. of ]xoester.(2009)... while blackbody spectra were usec for wliume-rich stars.," Hydrogen atmosphere stars were fitted with log $g=8.0$ white dwarf spectral models of \citet{koe09}, while blackbody spectra were used for helium-rich stars."323 La most cases. the model Z;4 could be adjusted to match the near-infrared. photometry. consistent with emission from the stellar photosphere.," In most cases, the model $T_{\rm eff}$ could be adjusted to match the near-infrared photometry, consistent with emission from the stellar photosphere."324 In cases where a potential near-infrared excess was indicated. in a single or multiple bandpasses. those data were not. emploved. to adjust the mocdel fits.," In cases where a potential near-infrared excess was indicated in a single or multiple bandpasses, those data were not employed to adjust the model fits."325 The white cwarl mass (via log g) was not varied in the mocel fits. as the focus of the study was to establish the presence or absence ofa near-infrared excess.," The white dwarf mass (via log $g$ ) was not varied in the model fits, as the focus of the study was to establish the presence or absence ofa near-infrared excess,"326outer parameters « and c turn out to be related to the inner parameter .. (and rj; when applicable) in terms of the cluster age. as explained below.,"outer parameters $a$ and $c$ turn out to be related to the inner parameter $k_c$ (and $r_f$ when applicable) in terms of the cluster age, as explained below."327 Thus the CC clusters with their low value of @ appear to be generally structures. currently 1n their stage of slow and smooth acceretion. with the main action taking place in the outskirts under the form of calm entropy deposition by gravitational accretion shocks.," Thus the CC clusters with their low value of $a$ appear to be generally structures, currently in their stage of slow and smooth accretion, with the main action taking place in the outskirts under the form of calm entropy deposition by gravitational accretion shocks."328 Toward the center. the CC hallmark is constituted by a temperature peak (cf.," Toward the center, the CC hallmark is constituted by a temperature peak (cf."329 Fig., Fig.330" 3 in CLFFO9) the peak in c at ry,7107!R (ef."," 3 in CLFF09) the peak in $\sigma^2$ at $r_m\approx 10^{-1}\, R$ (cf."331 the profiles of A2199 and A2597 in Figs., the profiles of A2199 and A2597 in Figs.332 1-3)., 1-3).333" The condition for the peak to occur after the SM is a low value of the central entropy K,<3«107. which comes to 30—50 keV enm."," The condition for the peak to occur after the SM is a low value of the central entropy $\bar{k}_c \la 3\times 10^{-2}$, which comes to $30-50$ keV $^2$."334 This behavior is highlighted in terms of TG)xKkG)n()7: as the ICP density (7) rises monotonically inward. Z(7) will peak and then decline toward the center as &(r) decreases sharply toward a low central value κ...," This behavior is highlighted in terms of $T(r) \propto335k(r)\, n(r)^{2/3}$; as the ICP density $n(r)$ rises monotonically inward, $T(r)$ will peak and then decline toward the center as $k(r)$ decreases sharply toward a low central value $k_c$."336 Such an inward decline of 7(7 to a low but finite central value 7.xk? links to a high density 7. to constitute thecore.. a feature of the non-radiative K;!SM equilibrium (also present in simulations discussed by Borgant et al.," Such an inward decline of $T(r)$ to a low but finite central value $T_c \propto k_c^{0.35}$ links to a high density $n_c337\propto k_c^{-1}$ to constitute the, a feature of the non-radiative SM equilibrium (also present in simulations discussed by Borgani et al."338 2008)., 2008).339" As expanded upon by CLFFO9. the SM does not include enhanced cooling. even less any related inflow: it rather focuses the conditions for enhanced radiation and fast cooling to set in on the timescale 1,20.305./15keVem?)7 Gyr."," As expanded upon by CLFF09, the SM does not include enhanced cooling, even less any related inflow; it rather focuses the conditions for enhanced radiation and fast cooling to set in on the timescale $t_c\approx 0.3\,(k_c/15~\mathrm{keV}~\mathrm{cm}^2)^{1.2}$ Gyr."340 This would lead to a cooling catastrophe (e.g.. White Rees 1978: Blanchard et al.," This would lead to a cooling catastrophe (e.g., White Rees 1978; Blanchard et al."341 1992). that may be stabilized by ICP condensing around and into a central massive galaxy to trigger accretion on the nuclear black hole.," 1992), that may be stabilized by ICP condensing around and into a central massive galaxy to trigger accretion on the nuclear black hole."342 These conditions kindle up AGN activities that drive rising bubbles or even outgoing blastwaves. feed back entropy. and distribute it widely into the ICP (see Binney Tabor 1995; Ciotti Ostriker 2001: Cavaliere et al.," These conditions kindle up AGN activities that drive rising bubbles or even outgoing blastwaves, feed back entropy, and distribute it widely into the ICP (see Binney Tabor 1995; Ciotti Ostriker 2001; Cavaliere et al."343 2002: Churazov et al., 2002; Churazov et al.344 2005: Lapi et al., 2005; Lapi et al.345 2005: Voit Donahue 2005; Tucker et al., 2005; Voit Donahue 2005; Tucker et al.346 2007)., 2007).347 We have analyzed in detail the two CC clusters A2199 and A2597 with their inward decrease of the temperature., We have analyzed in detail the two CC clusters A2199 and A2597 with their inward decrease of the temperature.348" We have found central entropy levels &,15 keV ceni typical of CCs. with little or no need for an extended< entropy floor."," We have found central entropy levels $k_c\la 15$ keV $^{2}$ typical of CCs, with little or no need for an extended entropy floor."349 We have derived outer powerlaw slopes «&| (see Table 1). lower than the standard value 1.1 corresponding to the standard concentration οz4.," We have derived outer powerlaw slopes $a\la 1$ (see Table 1), lower than the standard value $1.1$ corresponding to the standard concentration $c\approx 4$."350" This trend culminates with A1689, à cluster with a CC-like inner profile but featuring interesting peculiarities."," This trend culminates with A1689, a cluster with a CC-like inner profile but featuring interesting peculiarities."351 On an empirical stand. our SM. analysis confirms the results by Lemze et al. (," On an empirical stand, our SM analysis confirms the results by Lemze et al. ("3522008) concerning the high halo concentration ο~10 (concurring with the gravitational lensing analysis by Broadhurst et al.,2008) concerning the high halo concentration $c\approx 10$ (concurring with the gravitational lensing analysis by Broadhurst et al.353 2008: Lapi Cavaliere 2009b) and involving the slope «~0.8 for the outer entropy profile., 2008; Lapi Cavaliere 2009b) and involving the slope $a\approx 0.8$ for the outer entropy profile.354 But we go beyond. and show in terms Eqs. (," But we go beyond, and show in terms Eqs. ("3553) and (4) why these values deviate from the standard ones οzz4 and ez1.1. as spelled out above.,"3) and (4) why these values deviate from the standard ones $c\approx 4$ and $a\approx 1.1$, as spelled out above."356 In the same vein. CLFFOO9 find that a density slope g=3(a+bhp)/Sc2.4 is to apply in the outskirts.," In the same vein, CLFF09 find that a density slope $g = 3\,(a+b_R)/5\approx 2.4$ is to apply in the outskirts."357" The high concentration of A1689 implies this to be an old structure with the bulk region dating back to a transition epoch as early as z,z1.5.", The high concentration of A1689 implies this to be an old structure with the bulk region dating back to a transition epoch as early as $z_t\approx 1.5$.358" In fact. the feature common to CC clusters like A2199, A2597. and A1689 is constituted by low values of «X1 and high values c>4 (see Table 1). that follow from their being generally structures with shallow outer potential wells."," In fact, the feature common to CC clusters like A2199, A2597, and A1689 is constituted by low values of $a\la 1$ and high values $c>4$ (see Table 1), that follow from their being generally structures with shallow outer potential wells."359 At the other extreme. the NCC clusters appear to be dynamically structures from our determination of DM concentration and slope in the outer entropy profile.," At the other extreme, the NCC clusters appear to be dynamically structures from our determination of DM concentration and slope in the outer entropy profile."360 For example. in Al656 (Coma Cluster) our SM fit requires a value az1.3. and relatedly (see Eqs.," For example, in A1656 (Coma Cluster) our SM fit requires a value $a \approx 1.3$, and relatedly (see Eqs."361" 3 and 4) a concentration ¢=4 and young age z;,0.5.", 3 and 4) a concentration $c\approx 4$ and young age $z_t \la 0.5$.362 Toward the center. the NCC clusters are marked by a rising or flat temperature profile and by à generally flat brightness distribution.," Toward the center, the NCC clusters are marked by a rising or flat temperature profile and by a generally flat brightness distribution."363 This occurs for central levels of ΚΟ some 50 keV cnr. and also points toward a thermodynamically young age for the ICP.," This occurs for central levels of $k_c$ some $50$ keV $^{2}$, and also points toward a thermodynamically young age for the ICP."364 In fact. frequent and intense merger/AGN activity is expected in these clusters observed in the aftermath of their fast initial collapse. with considerable residual occurrence of mergers and AGN outbursts that lead to large central injections of energy and entropy.," In fact, frequent and intense merger/AGN activity is expected in these clusters observed in the aftermath of their fast initial collapse, with considerable residual occurrence of mergers and AGN outbursts that lead to large central injections of energy and entropy."365 Such features are exhibited. in a sequence of increasing complexity. by A1656. A2256 and A644.," Such features are exhibited, in a sequence of increasing complexity, by A1656, A2256 and A644."366 Here. the SM elicits not only a high level. but also a for the entropy deposited in the form of a floor extended out to r;.," Here, the SM elicits not only a high level, but also a for the entropy deposited in the form of a floor extended out to $r_f$."367 This we interpret in terms of the stallation radius attained by a powerful. outbound blast either triggered by a major head-on merger (cf.," This we interpret in terms of the stallation radius attained by a powerful, outbound blast either triggered by a major head-on merger (cf."368 simulations by Schindler et al., simulations by Schindler et al.369 2002. Vazza et al.," 2002, Vazza et al."370 2009) or driven by a violent AGN outburst (see Formar et al., 2009) or driven by a violent AGN outburst (see Forman et al.371 2005: Cavaliere Lapi 2006: McNamara Nulset 2007: Puchwein et al., 2005; Cavaliere Lapi 2006; McNamara Nulsen 2007; Puchwein et al.372 2008). before being degraded into adiabatic sound waves of the kind caught in action by Fabiar et al. (," 2008), before being degraded into adiabatic sound waves of the kind caught in action by Fabian et al. ("3732006) in the Perseus cluster.,2006) in the Perseus cluster.374" To reach r;z250 kpe it takes a rather extreme merger delivering about 107 erg anc triggering a Sedov blastwave that expands as RyxΕΙον with decreasing Mach number: alternatively. it takes an AG outburst of about 10° erg continuously driving a blastwave to expand at constant Mach number with R,xE!*r. see Lapi et al. ("," To reach $r_f\approx 250$ kpc it takes a rather extreme merger delivering about $10^{64}$ erg and triggering a Sedov blastwave that expands as $R_s\propto375E^{1/3}\,t^{2/3}$ with decreasing Mach number; alternatively, it takes an AGN outburst of about $10^{62}$ erg continuously driving a blastwave to expand at constant Mach number with $R_s\propto E^{1/3}\,t$ , see Lapi et al. ("3762005) and Cavaliere et al. (,2005) and Cavaliere et al. (3772006) for details.,2006) for details.378 As discussed in 4.4 and 4.5. in the NCC clusters Al656 and A2256 analyzed here such values of r; are accompanied by evidence of ongoing mergers. hallmarks of a recent cluster formation.," As discussed in 4.4 and 4.5, in the NCC clusters A1656 and A2256 analyzed here such values of $r_f$ are accompanied by evidence of ongoing mergers, hallmarks of a recent cluster formation."379 This interpretation. relates +; to the of the merger responsible for the energy/entropy input: the good performance of the SM implies such a time to be intermediate between the blast transit time r;/.Mvym107* Gyr (see Cavaliere Lapi 2006) and the time 0.3(5./15keVem)z1 Gyr needed by radiative cooling to erode an entropy floor of about 50 keV em.," This interpretation relates $r_f$ to the of the merger responsible for the energy/entropy input; the good performance of the SM implies such a time to be intermediate between the blast transit time $r_f/ \mathcal{M}\, v_s \approx38010^{-1}$ Gyr (see Cavaliere Lapi 2006), and the time $0.3\,(k_c/15~\mathrm{keV}~\mathrm{cm}^2)^{1.2}\approx 1$ Gyr needed by radiative cooling to erode an entropy floor of about $50$ keV $^2$."381 Such à timing also guarantees that an accurate description of the ICP thermodynamic state for both CC and NCC clusters is provided by the SM based on the hydrostatic equilibrium expressed by Eq. (, Such a timing also guarantees that an accurate description of the ICP thermodynamic state for both CC and NCC clusters is provided by the SM based on the hydrostatic equilibrium expressed by Eq. (3821).,1).383 To complete the issue. note that not only the equilibrium of the ICP is somewhat faster to attain than the DM's (see Ricker Sarazin 2001: Lapi et al.," To complete the issue, note that not only the equilibrium of the ICP is somewhat faster to attain than the DM's (see Ricker Sarazin 2001; Lapi et al."384 2005). but also that cireularized data (integrated over annuli. see Snowden et al.," 2005), but also that circularized data (integrated over annuli, see Snowden et al."385" 2008) tend to effectively smooth out local. limited deviations from spherical hydrostatics and to better agree with equilibrium,"," 2008) tend to effectively smooth out local, limited deviations from spherical hydrostatics and to better agree with equilibrium."386 How does the SM face the challenge of posed by substructures as observed in A2256 and A644?, How does the SM face the challenge of posed by substructures as observed in A2256 and A644?387 Interestingly. we still obtain good fits if we extrapolate the SM out to. or perhaps beyond its literal limits. toward conditions where T(r) varies on the scale rj. or differs around two locations (cf.," Interestingly, we still obtain good fits if we extrapolate the SM out to, or perhaps beyond its literal limits, toward conditions where $T(r)$ varies on the scale $r_f$, or differs around two locations (cf."388 Figs., Figs.389 8-11): these conditions highlight the capabilities of the SM as a mere fitting tool., 8-11); these conditions highlight the capabilities of the SM as a mere fitting tool.390" By the same token. the SM provides sharp snapshots of physical conditions even when these are spatially complex (as for A644). and strongly suggests that they may be traced back to two merger outcomes: a ""hot spot imprinted in A2256 to partially erase a previous cool state and to yield a nascent NCC: or a ‘cold drop’ imported into the hot medium of A644 that will offset cooling."," By the same token, the SM provides sharp snapshots of physical conditions even when these are spatially complex (as for A644), and strongly suggests that they may be traced back to two merger outcomes: a `hot spot' imprinted in A2256 to partially erase a previous cool state and to yield a nascent NCC; or a `cold drop' imported into the hot medium of A644 that will offset cooling."391 Focusing on thecold component. such cases may be termed as RCCs for Remnant," Focusing on thecold component, such cases may be termed as RCCs for Remnant"392 , 393Iu the non-relativistic lait it reduces to (21)) with relativistic corrections in the lowest order as Iu the classical (dispersiouless) limit (25)) becomes equation of the hydrodvuamic tvpe Iu the non-relativistic limit it reduces to the dispersiouless Burgers equation with the lowest relativistic correction The general iaplicit solution of (28)) is and it develops shock at a finite time.,In the non-relativistic limit it reduces to \ref{NBS}) ) with relativistic corrections in the lowest order as In the classical (dispersionless) limit \ref{SRBS}) ) becomes equation of the hydrodynamic type In the non-relativistic limit it reduces to the dispersionless Burgers equation with the lowest relativistic correction The general implicit solution of \ref{DLSRBS}) ) is and it develops shock at a finite time.394" By the boost trausforinatiou of Section 1. from a eiven solution V4 of the Schroddinger equation (1)) we cau generate another solution as Using identity for complex velocities V,=/—IuW,. (a=1.2). we obtain the Baccklind transformation For the nou-velativistic quantum mechanics (8)) it gives conmiplex Dácckluud transformation"," By the boost transformation of Section 1, from a given solution $\Psi_1$ of the Schröddinger equation \ref{Schrodinger}) ) we can generate another solution as Using identity for complex velocities $V_a = -i \frac{\hbar}{m} \ln \Psi_a$, $(a=1,2)$, we obtain the Bäccklund transformation For the non-relativistic quantum mechanics \ref{NH}) ) it gives complex Bäccklund transformation"395limb region.,limb region.396 Local Correlation Tracking (LCT) technique(November&Simon1988) was applied to the well aligned foreshortening- G-band image sequences to acquire horizontal proper motions and their evolution in this active region., Local Correlation Tracking (LCT) technique\citep{November+Simon1988ApJ...333..427N} was applied to the well aligned foreshortening-corrected G-band image sequences to acquire horizontal proper motions and their evolution in this active region.397 A Gaussian window with a FWHM of 1200 km shape(Vermaapodization&Denker2011) was used as the sampling window in the LCT algorithm., A Gaussian shape apodization window with a FWHM of 1200 km \citep{Verma+Denker} was used as the sampling window in the LCT algorithm.398" To reduce the noise and uncertainty of the individual LCT proper motion map obtained from two successive G-band images, a running temporal average of 10 consecutive LCT proper motion maps traversing 20 minutes was carried out and provides a robust velocity pattern at the center time of each 20-minute interval (see Fig. 3))."," To reduce the noise and uncertainty of the individual LCT proper motion map obtained from two successive G-band images, a running temporal average of 10 consecutive LCT proper motion maps traversing 20 minutes was carried out and provides a robust velocity pattern at the center time of each 20-minute interval (see Fig. \ref{FIG:VELO}) )."399 A running temporal average of 20 consecutive LCT proper motion maps was used to evaluate the evolution of the mean horizontal flow speed in the ROI (see Fig. 5((, A running temporal average of 20 consecutive LCT proper motion maps was used to evaluate the evolution of the mean horizontal flow speed in the ROI (see Fig. \ref{FIG:PLOT}( (400b)).,b)).401 Fig., Fig.402 2 shows the evolution of NOAA AR 10930 associated with the X6.5 flare in G-band and HH images., \ref{FIG:IMGS} shows the evolution of NOAA AR 10930 associated with the X6.5 flare in G-band and H images.403" The flare peaked in white-light and HXR at 18:43:38 UT, showing strong ribbons that separated from the ROI."," The flare peaked in white-light and HXR at 18:43:38 UT, showing strong ribbons that separated from the ROI."404 The sunspot structure remained almost unchanged for at least 4 hours before the flare (see 1, The sunspot structure remained almost unchanged for at least 4 hours before the flare (see Fig.405" (5), 2"," \ref{FIG:DEPROJ} $(b)$, Fig."406 (a) and (b))., \ref{FIG:IMGS} $(a)$ and $(b)$ ).407" The outer penumbrae, as Fig.pointed by the Fig.blue arrows, are found dramatically decayed since 19:13 UT (the first available post-flare image) about 20 minutes after the flare ribbon sweeps across these regions."," The outer penumbrae, as pointed by the blue arrows, are found dramatically decayed since 19:13 UT (the first available post-flare image) about 20 minutes after the flare ribbon sweeps across these regions."408 Meanwhile the central penumbra becomes darker., Meanwhile the central penumbra becomes darker.409" According to the G-band penumbral structure and the HH images, it is reasonable to state that there are magnetic connections between P1-P3 and N1-N3 before the flare."," According to the G-band penumbral structure and the H images, it is reasonable to state that there are magnetic connections between P1-P3 and N1-N3 before the flare."410" After the flare, as pointed out by the pink arrows in Fig."," After the flare, as pointed out by the pink arrows in Fig."411" 2 (A), some field lines on either side of the neutral line get connected, ie. new connections between P1-P3 and N4 are formed meanwhile the connections between P1-P3 and N1-N3 would correspondingly be weakened due to this reconnection."," \ref{FIG:IMGS} $(h)$, some field lines on either side of the neutral line get connected, i.e., new connections between P1-P3 and N4 are formed meanwhile the connections between P1-P3 and N1-N3 would correspondingly be weakened due to this reconnection."412" The reconnecting magnetic field lines rooted at P1-P3 change from fanning out (connect with N1-N3) that contributes to the outer penumbrae, to inward connection (connect with N4), which naturally results in weaker/stronger horizontal field in the outer/central region relative to the pre-flare configuration and consequently the decay/enhancement of the outer/central penumbrae."," The reconnecting magnetic field lines rooted at P1-P3 change from fanning out (connect with N1-N3) that contributes to the outer penumbrae, to inward connection (connect with N4), which naturally results in weaker/stronger horizontal field in the outer/central region relative to the pre-flare configuration and consequently the decay/enhancement of the outer/central penumbrae."413" Viewing the HH movie, we also see the contraction of these newly formed overlying loops throughout the available ~1-hr post-flare phase."," Viewing the H movie, we also see the contraction of these newly formed overlying loops throughout the available $\sim$ 1-hr post-flare phase."414 Fig., Fig.415 3 depicts the horizontal proper motions in NOAA AR 10930 before and after the flare., \ref{FIG:VELO} depicts the horizontal proper motions in NOAA AR 10930 before and after the flare.416 The surface flows in the ROI are carried by penumbrae and mainly follow the neutral line direction that is tangential to the umbrae., The surface flows in the ROI are carried by penumbrae and mainly follow the neutral line direction that is tangential to the umbrae.417 We therefore call them sheared Evershed flows., We therefore call them sheared Evershed flows.418" Comparing panels (d) (e) with (a) (b), it is quite obvious that the sheared Evershed flows in the ROI dramatically enhanced after the flare."," Comparing panels $(d)$ $(e)$ with $(a)$ $(b)$, it is quite obvious that the sheared Evershed flows in the ROI dramatically enhanced after the flare."419 They are more organized along the neutral line with larger speed and extend to larger areas., They are more organized along the neutral line with larger speed and extend to larger areas.420" To explicitly illustrate the flare- changes in sunspot structure and surface flows, we further construct the difference maps between post- and as shown in Fig. 4.."," To explicitly illustrate the flare-associated changes in sunspot structure and surface flows, we further construct the difference maps between post- and pre-flare phases as shown in Fig. \ref{FIG:DIF}."421" Similar to previous studies pre-flare(e.g.,phasesLiuetal.2005),, the intensity difference map (Fig."," Similar to previous studies \citep[e.g.,][]{LiuC+etal2005ApJ...622..722L}, the intensity difference map (Fig."422" 4 (a)) appears bright in the periphery and dark in the central region, manifesting the decay or disappearance of outer penumbrae and darkening of the central structure."," \ref{FIG:DIF} $(a)$ ) appears bright in the periphery and dark in the central region, manifesting the decay or disappearance of outer penumbrae and darkening of the central structure."423 The bright/dark features in the flow speed difference map (Fig., The bright/dark features in the flow speed difference map (Fig.424 4 (b)) represent surface flow speed increase/decrease., \ref{FIG:DIF} $(b)$ ) represent surface flow speed increase/decrease.425 The flow speed clearly increased in most areas of the ROI., The flow speed clearly increased in most areas of the ROI.426" In the decayed penumbral regions, some areas show a strong decrease in speed, some others only show a faint decrease in part of areas."," In the decayed penumbral regions, some areas show a strong decrease in speed, some others only show a faint decrease in part of areas."427 The speed decrease mainly occurs at the penumbral edge., The speed decrease mainly occurs at the penumbral edge.428 The flow azimuth difference (Fig., The flow azimuth difference map (Fig.429 4 (c)) reveals a large change of surface flow direction mapmainly in the ROI., \ref{FIG:DIF} $(c)$ ) reveals a large change of surface flow direction mainly in the ROI.430 Flow azimuth changes are also found in some areas of the decayed penumbrae., Flow azimuth changes are also found in some areas of the decayed penumbrae.431 5, Fig.432 illustrates the temporal evolution of the G-band intensityFig. averaged in the ROI and decayed outer penumbrae (a) and the temporal evolution of the horizontal flow speed averaged in the ROI and in a reference region (0)., \ref{FIG:PLOT} illustrates the temporal evolution of the G-band intensity averaged in the ROI and decayed outer penumbrae $(a)$ and the temporal evolution of the horizontal flow speed averaged in the ROI and in a reference region $(b)$ .433 Comparing, Comparing434this woulcl reduce the strength of the line profiles for small inipact. parameters.,this would reduce the strength of the line profiles for small impact parameters.435 As noted above. the chemical behaviour of ICO ina core undergoing depletion is complicated.," As noted above, the chemical behaviour of ${\rm HCO^+}$ in a core undergoing depletion is complicated."436 3ellocheetal.(2003) have carried out a detailed study of the Class 0 protostar ΑΔ 04101|1522 and conclude that the inner region of HAM. 0419111522 is undergoing fast cillerential rotation while the outer regions are onlv slowly rotating., \citet{belloche.et.al02} have carried out a detailed study of the Class 0 protostar IRAM 04191+1522 and conclude that the inner region of IRAM 04191+1522 is undergoing fast differential rotation while the outer regions are only slowly rotating.437 Since they also argue that this source has only recently become a protostar it is constructive to compare it with LIGSOB which may be on the verge of collapse., Since they also argue that this source has only recently become a protostar it is constructive to compare it with L1689B which may be on the verge of collapse.438 Firstly. uncer the assumption that both objects have been adequately modelled. the angular velocity is comparable: wr=9.4kms at 3000 AU in the best fit model for LIGSOB while for WRAL 04191|1522. ar=9+3kms| at 2800 AU.," Firstly, under the assumption that both objects have been adequately modelled, the angular velocity is comparable: $\omega r=9.4~{\rm km~s^{-1}}$ at 3000 AU in the best fit model for L1689B while for IRAM 04191+1522, $\omega r=9\pm4393~{\rm km~s^{-1}}$ at 2800 AU."440 LRAM 04191|1522 may. be decoupling from the outer envelope at a radius. of 2000-4000 AU (Bellochectal.2008) which compares with the rotation racius of 3000 AU estimated here for L1689D. Solid body rotation is firmly ruled out for the inner region of IAM. 04191]1522 with dillerential rotation providing a much better fit to the observations (specifically. the angular velocity. gradient is found to change from. approximately," IRAM 04191+1522 may be decoupling from the outer envelope at a radius of 2000-4000 AU \citep{belloche.et.al02}441 which compares with the rotation radius of 3000 AU estimated here for L1689B. Solid body rotation is firmly ruled out for the inner region of IRAM 04191+1522 with differential rotation providing a much better fit to the observations (specifically, the angular velocity gradient is found to change from approximately"442for haloes of cüllerent mass.,for haloes of different mass.443 Notice that some haloes form at low recshift vet still contain few subhaloes., Notice that some haloes form at low redshift yet still contain few subhaloes.444 Examination of some specilic cases suggests that these are products of recent mergers between isolated. similar mass haloes which rac previouslyA eliminated: much of their substructure.," Examination of some specific cases suggests that these are products of recent mergers between isolated, similar mass haloes which had previously eliminated much of their substructure."445 In order to avoid such cases. the right-hand. panel of Fig.," In order to avoid such cases, the right-hand panel of Fig."446 S xots subhalo abundance against a formation time defined as the redshift when the most massive progenitor has 25 ver cent of the final mass., 8 plots subhalo abundance against a formation time defined as the redshift when the most massive progenitor has 25 per cent of the final mass.447 Phe number of recently. formed objects with little substructure is reduced and the relation oetween substructure and formation time appears cleaner., The number of recently formed objects with little substructure is reduced and the relation between substructure and formation time appears cleaner.448 A final point to note from Lig., A final point to note from Fig.449 S is the scatter in the number of subhaloes within objects of given concentration or ormation time., 8 is the scatter in the number of subhaloes within objects of given concentration or formation time.450 The values span a range of up to a factor of our. and the scatter is at most weakly related to halo mass.," The values span a range of up to a factor of four, and the scatter is at most weakly related to halo mass."451 Clearly the variety of possible formation paths for haloes of given global properties is large enough to produce widely diflerent subhalo populations even among rather similar objects., Clearly the variety of possible formation paths for haloes of given global properties is large enough to produce widely different subhalo populations even among rather similar objects.452 Our analysis so [ar has concentrated on the subhalo distribution within our simulated. haloes at redshift z=0., Our analysis so far has concentrated on the subhalo distribution within our simulated haloes at redshift $z=0$.453 Although this is the time when our simulations have the best cllective resolution and so can give information over the widest range of scales. it is nevertheless interesting to look at other redshifts in order to investigate the evolution of subhalo properties.," Although this is the time when our simulations have the best effective resolution and so can give information over the widest range of scales, it is nevertheless interesting to look at other redshifts in order to investigate the evolution of subhalo properties."454 Given the near universality we found above. it seems natural to concentrate on the variation with redshift of the abundance of subhaloes per unit parent halo mass. and to compare this with the abundance of haloes per unit mass in the Universe as a whole.," Given the near universality we found above, it seems natural to concentrate on the variation with redshift of the abundance of subhaloes per unit parent halo mass, and to compare this with the abundance of haloes per unit mass in the Universe as a whole."455 Εις comparison is made in Fig., This comparison is made in Fig.456 9 using the abundance of subhaloes in the most massive progenitor of our “Alilky Way halo in GA3n. and of the main cluster in each of our eight. cluster simulations.," 9 using the abundance of subhaloes in the most massive progenitor of our `Milky Way' halo in GA3n, and of the main cluster in each of our eight cluster simulations."457 For these plots we multiply the dillerential abundance distributions by the square of the (sub)halo mass in order to remove the dominant variation., For these plots we multiply the differential abundance distributions by the square of the (sub)halo mass in order to remove the dominant variation.458 We can then plot results corresponding to a range of fourteen orders of magnitude in abundance and seven orders of magnitude in (sub)halo mass., We can then plot results corresponding to a range of fourteen orders of magnitude in abundance and seven orders of magnitude in (sub)halo mass.459 The simulation results are shown twice in these plots. for reasons discussed below.," The simulation results are shown twice in these plots, for reasons discussed below."460 The halo abundance predicted for the Universe as a whole by the Sheth Tormen (1999) mass function is shown by a dashed line in cach panel., The halo abundance predicted for the Universe as a whole by the Sheth Tormen (1999) mass function is shown by a dashed line in each panel.461 Fig., Fig.462 9 shows that subhalo abundance distributions vary rather little with recshilt (see also Ixravtsov et al., 9 shows that subhalo abundance distributions vary rather little with redshift (see also Kravtsov et al.463 20042)., 2004a).464 At all recishifts we find the result already noted above for 2=0., At all redshifts we find the result already noted above for $z=0$.465 Normalised to total available mass. the subhalo abundance within haloes is verv similar to the halo abundance in the Universe as a whole.," Normalised to total available mass, the subhalo abundance within haloes is very similar to the halo abundance in the Universe as a whole."466 Phe olfset between the two (the points without error bars and the dashed lines in Fig., The offset between the two (the points without error bars and the dashed lines in Fig.467 9) is almost independent of mass and epoch and is roughly a factor of four in abundance at fixed mass. corresponding to a factor of two in mass at fixed abundance.," 9) is almost independent of mass and epoch and is roughly a factor of four in abundance at fixed mass, corresponding to a factor of two in mass at fixed abundance."468 This olfset can be ascribed to the dillerent. ways in which we define the, This offset can be ascribed to the different ways in which we define the469calculations by Ormeletal.(2009) (see. in particular. their Table 3).,"calculations by \cite{2009A&A...502..845O} (see, in particular, their Table 3)."470 Inclusion of this effect is beyond the scope of this paper., Inclusion of this effect is beyond the scope of this paper.471 Although the density of the post-shock models can be as high as 2x10+ οι”. these do not simulate fully-formed dense cores given their low extinction. but rather the cloud material such às that from which derse cores form.," Although the density of the post-shock models can be as high as $2\times 10^{4}$ $^{-3}$, these do not simulate fully-formed dense cores given their low extinction, but rather the cloud material such as that from which dense cores form."472 Can relevant comparison be made with existiig observational data. or are our results best used as initial conditions for models of normal dense cold cores?," Can relevant comparison be made with existing observational data, or are our results best used as initial conditions for models of normal dense cold cores?"473 The dark cloud in Taurus is perhaps the best region to explore this questior for measurements of ices. while a large sample of CO(g) observations exists for diffse and translucent clouds. as well as sone lines of sight in Taurus.," The dark cloud in Taurus is perhaps the best region to explore this question for measurements of ices, while a large sample of CO(g) observations exists for diffuse and translucent clouds, as well as some lines of sight in Taurus."474 One must also remember that our results represent cold material in the act of forming larger structures via a specific post-shock process. whereas there is no guarantee that the observed sources are transitional in this sense.," One must also remember that our results represent cold material in the act of forming larger structures via a specific post-shock process, whereas there is no guarantee that the observed sources are transitional in this sense."475 Indeed. at low visual extinction and/or H» column densities. our objects tend to be denser. smaller. and colder than well-studied diffuse clouds.," Indeed, at low visual extinction and/or $_{2}$ column densities, our objects tend to be denser, smaller, and colder than well-studied diffuse clouds."476 Estimates of N[CO(g)] along darker lines of sight in the Taurus dark cloud were presented by Whittetetal.(1989) based on observations of Frerkingetal.(1982) and Crutcher(1955)., Estimates of $N$ [CO(g)] along darker lines of sight in the Taurus dark cloud were presented by \citet{Whittet89} based on observations of \citet{Frerking82} and \citet{Crutcher85}.477 Observations of NICO(g)] in more translucent and diffuse clouds have been reported by Liszt(2008):Burghetal.(2007): (1994).. and references therein.," Observations of $N$ [CO(g)] in more translucent and diffuse clouds have been reported by \citet{Liszt08, Burgh07, Sheffer07, Sonnentrucker07, Gredel94}, and references therein."478 The value of Ay was reported for some of these sources by Rachfordetal.(2009). while for the majority only N[H*(g)] was reported.," The value of $A_V$ was reported for some of these sources by \citet{Rachford09}, while for the majority only $N$ $_2$ (g)] was reported."479 The N[CO(g)] vs. Ay data appear in Figure 2((a) as circles for the darker lines of sight. seen in the Taurus cloud. and asterisks for the translucent lines of sight except for one upper limit. shown as an inverted triangle.," The $N[\rm{CO(g)}]$ vs. $A_V$ data appear in Figure \ref{fig-2NH}( (a) as circles for the darker lines of sight, seen in the Taurus cloud, and asterisks for the translucent lines of sight except for one upper limit, shown as an inverted triangle."480 It is apparent from this figure that many of the data points fall within the model curves in the lower Ay range. and that all four shock models with," It is apparent from this figure that many of the data points fall within the model curves in the lower $A_V$ range, and that all four shock models with"481 , 482calculate accurate globular cluster orbits and to identify periods of encounters with the solar system.,calculate accurate globular cluster orbits and to identify periods of encounters with the solar system.483 Encounters between globular clusters with an exceptionally elevated number of close binaries (Pooley&Hut.2006) can be identified as potential point in time for a nearby GRB explosion., Encounters between globular clusters with an exceptionally elevated number of close binaries \citep{pooley2006} can be identified as potential point in time for a nearby GRB explosion.484 These points in time can be compared to events of mass extinction and for the case that there is no correlation with such events. the geological record can be searched for any terrestrial signatures connected to a nearby GRB explosion.," These points in time can be compared to events of mass extinction and for the case that there is no correlation with such events, the geological record can be searched for any terrestrial signatures connected to a nearby GRB explosion."485this time.,this time.486 Our work is finally summarized in 84., Our work is finally summarized in 4.487 The evolution of a superbubble powered by a continuous energy has been calculated by Weaver οἱ al. (, The evolution of a superbubble powered by a continuous energy has been calculated by Weaver et al. (488LOTT: see also MacLow MeCray. 1988: Shull Saken 1995).,1977; see also MacLow McCray 1988; Shull Saken 1995).489 Weaver οἱ al., Weaver et al.490 derived a similarity solution in terms of the equivalent mechanical ]uminositv of supernovae. Lax. ambient density pij and time /.," derived a similarity solution in terms of the equivalent mechanical luminosity of supernovae, $L_{\rm SN}$, ambient density $\rho_0$ and time $t$."491 This vields the time-evolution of the superbubble radius = Grp and velocity (15.7kuis Dp," This yields the time-evolution of the superbubble radius R = (267 ), and velocity (15.7 )."492! Here nj is the atomic number density (inem. 1). /;=//(10vr) and La;=Lyx/(10Peress1) is (the equivalent of one SN of οποιον Fey=10?! eres occurring every," Here $n_0$ is the atomic number density (in $^{-3}$ ), $t_7=t/(10^7{\rm yr})$ and $L_{38}=493L_{\rm SN}/(10^{38}{\rm ergs~s^{-1}})$ is the equivalent of one SN of energy $E_{\rm SN}=10^{51}$ ergs occurring every"494and the terminal velocity ος=MHuQ6; ,and the terminal velocity $\vinfty=\sum_{i=1}^{n} \tilde v_i$.495To ensure the orthogonality in the interval |0.1| we use shifted Legendre polynomials here.," To ensure the orthogonality in the interval $[0,1]$ we use shifted Legendre polynomials here."496 The first four are The relations between coefficients ; and c; follow from Eqs., The first four are The relations between coefficients $\tilde v_i$ and $v_i$ follow from Eqs.497 2 and 3 Only three of these (¢;) coefficients are independent.," \ref{vulkan}498 and \ref{belana}499 Only three of these $\tilde v_i$ ) coefficients are independent."500 To demonstrate the convenience of the formulas Eq., To demonstrate the convenience of the formulas Eq.501 2 we fit the radial velocity structure obtained from hydrodynamical NLTE wind models with CMF line force ofJemfl., \ref{vulkan} we fit the radial velocity structure obtained from hydrodynamical NLTE wind models with CMF line force of.502 The best-fit parameters of the beta velocity law and polynomial fit Eq., The best-fit parameters of the beta velocity law and polynomial fit Eq.503 2b with η=3 for individual stars are given in Table |.., \ref{spok} with $n=3$ for individual stars are given in Table \ref{sedma}.504 To test the global accuracy of individual orders of the velocity approximatio Eq. 2..," To test the global accuracy of individual orders of the velocity approximation Eq. \ref{vulkan},"505" we plot the relative difference between the velocity from the numerical models ¢™ and its approximations e?!"" (Eq.", we plot the relative difference between the velocity from the numerical models $\vmod$ and its approximations $\vapp$ (Eq.506 for )=1.2.3 and Eq. 1))," \ref{spok} for $n=1,2,3$ and Eq. \ref{paris}) )"507 averaged over individual stars 1 Table I.. (|(oορ]οςj .as a function of radius in Fig. 2..," averaged over individual stars in Table \ref{sedma}, $\langle|(\vmod-\vapp)/\vapp|\rangle$ , as a function of radius in Fig. \ref{harry}."508 Already the first term 1n. Eq. 2a..," Already the first term in Eq. \ref{tuvok},"509ie. the approximatio eir)=c(l R.fr) n fact Eq.,"i.e. the approximation $v(r)=v_1510\zav{1-{R_*}/{r}}$ (in fact Eq."511 1. for /= 1). provide:PA reasonable approximation to the wind velocity law suitable for simplified analysis (see Fig. 2)).," \ref{paris} for $\beta=1$ ), provides reasonable approximation to the wind velocity law suitable for simplified analysis (see Fig. \ref{harry}) )."512 Including the second term 1 Eq., Including the second term in Eq.513 2a we obtain better approximation than the usual beta velocity law both for the velocity and its derivative using the same number of free parameters (./ and οςο for the beta velocity law. ej and ου for Eq. 2a).," \ref{tuvok} we obtain better approximation than the usual beta velocity law both for the velocity and its derivative using the same number of free parameters $\beta$ and $\vinfbet$ for the beta velocity law, $v_1$ and $v_2$ for Eq. \ref{tuvok}) )."514 The agreement in the outer parts of the wind (r/FR.= 1.1) ean be improved further by adding the third term in Eq., The agreement in the outer parts of the wind $r/R_*\gtrsim1.1$ ) can be improved further by adding the third term in Eq.515 2a. (see Fig. 2))., \ref{tuvok} (see Fig. \ref{harry}) ).516 It has not escaped our attention. that even relatively high order polynomials do not provide reasonable fits in the region close to the star. for r/R.=<1.1.," It has not escaped our attention that even relatively high order polynomials do not provide reasonable fits in the region close to the star, for $r/R_*\lesssim1.1$."517" We do not aim to fit the velocity in this region. because here the wind density approaches the hydrostatic density stratification,"," We do not aim to fit the velocity in this region, because here the wind density approaches the hydrostatic density stratification."518 Consequently. it would be better to derive the velocity from the continuity equation using density from the hydrostatic equilibrium equation instead of a polynomial.," Consequently, it would be better to derive the velocity from the continuity equation using density from the hydrostatic equilibrium equation instead of a polynomial."519 Many studies fit the observed line profiles of particular stars using sophisticated radiative transfer calculations by the velocity law of type Eq., Many studies fit the observed line profiles of particular stars using sophisticated radiative transfer calculations by the velocity law of type Eq.520 1. and trying to find the most suitable. value of the parameter ./ in combination with the value of the terminal velocity cx., \ref{paris} and trying to find the most suitable value of the parameter $\beta$ in combination with the value of the terminal velocity .521.. Although our formulae Eq., Although our formulae Eq.522 2 were derived to fit the results of numerical hydrodynamical calculations. 1t might be interesting to use them to also fit the beta velocity profiles.," \ref{vulkan} were derived to fit the results of numerical hydrodynamical calculations, it might be interesting to use them to also fit the beta velocity profiles."523 The test showed that the polynomial approximation Eq., The test showed that the polynomial approximation Eq.524 2. with n=2 provides very good fits to beta laws (Eq. 1)), \ref{vulkan} with $n=2$ provides very good fits to beta laws (Eq. \ref{paris}) )525 both with small)<1 and large +=1 and to the combined law of(1999)., both with small $\beta<1$ and large $\beta>1$ and to the combined law of.526. Only for large)z2.3 is it better to increase the polynomial degree (7= 3) to assure the positivity of the fit close to the star., Only for large $\beta\gtrsim2.3$ is it better to increase the polynomial degree $n=3$ ) to assure the positivity of the fit close to the star.527 The modified beta law eir)=eyflpes) with additional parameter b.<1 is frequently used to improve the fit close to the star., The modified beta law $v(r)=\vinfbet\zav{1-b\frac{R_*}{r}}^\beta$ with additional parameter $b<1$ is frequently used to improve the fit close to the star.528 It can be satisfactorily reproduced byeither introducing a fixed low value of cy in Eq., It can be satisfactorily reproduced byeither introducing a fixed low value of $v_0$ in Eq.529 2a. or by a substitution ο=1/—PR.fr in Eq. 2b.., \ref{tuvok} or by a substitution $x=1-bR_*/r$ in Eq. \ref{spok}. .530 Moreover. our experiments with fitting the trial P Cygni line profiles have," Moreover, our experiments with fitting the trial P Cygni line profiles have"531been shown that PAH anions bands fall on the red side of the 11.2 um peak and could contribute to the red wing (?)..,been shown that PAH anions bands fall on the red side of the 11.2 $\mu$ m peak and could contribute to the red wing \citep{baus}.532" By separating the observed spectra into component signals, we found that the main carrier of the 11.2 wmemission feature is PAH?."," By separating the observed spectra into component signals, we found that the main carrier of the 11.2 $\mu$ memission feature is $^0$."533" However, the observed spatial variations in the profile result in a PAH? source signal that is mainly symmetric with only a weak anharmonic red wing."," However, the observed spatial variations in the profile result in a $^0$ source signal that is mainly symmetric with only a weak anharmonic red wing."534" The BSS analysis shows that the red wing is mainly due to a changing contribution of the VSG to the observed spectra; e.g. as the VSG signal becomes more prominent towards the outer edge of the PDR, its contribution to the observed spectra also increases (c.f."," The BSS analysis shows that the red wing is mainly due to a changing contribution of the VSG to the observed spectra; e.g. as the VSG signal becomes more prominent towards the outer edge of the PDR, its contribution to the observed spectra also increases (c.f."535 Figure 6))., Figure \ref{fig:spec_comp}) ).536" We note that in NGC 7023, position which are near to the exciting star are characterized by a more symmetric 11.2 um profile while positions further away have a more pronounced red wing (cf.,"," We note that in NGC 7023, position which are near to the exciting star are characterized by a more symmetric 11.2 $\mu$ m profile while positions further away have a more pronounced red wing (cf.,"537 Figure 9))., Figure \ref{fig:analysis}) ).538" The feature at 11.2 uim has been observed to shift peak position between 11.2 to 11.3 um. Studying Figure 6,, there are clear emission contributions from each component species throughout the 11.0 to 11.3 um range."," The feature at 11.2 $\mu$ m has been observed to shift peak position between 11.2 to 11.3 $\mu$ m. Studying Figure \ref{fig:spec_comp}, there are clear emission contributions from each component species throughout the 11.0 to 11.3 $\mu$ m range."539 We propose that the variation of abundances of VSGs and PAHs in the observed spectra causes the shifting peak position of the 11.2 um band., We propose that the variation of abundances of VSGs and PAHs in the observed spectra causes the shifting peak position of the 11.2 $\mu$ m band.540" If there is a stronger contribution of PAHs in a certain region, the peak is observed to be blue-shifted."," If there is a stronger contribution of PAHs in a certain region, the peak is observed to be blue-shifted."541" If the VSGs become more abundant, the peak is redshifted."," If the VSGs become more abundant, the peak is redshifted."542" This is in disagreement with ?,, where they notice a redshifted peak with a more symmetric profile."," This is in disagreement with \citet{peeters}, , where they notice a redshifted peak with a more symmetric profile."543"a loose group (Barnes 1989), a rapid build-up of the stellar mass and the following quick end of the star-formation activity in most of the brightest member galaxies need to be invoked.","a loose group (Barnes 1989), a rapid build-up of the stellar mass and the following quick end of the star-formation activity in most of the brightest member galaxies need to be invoked."544" Interestingly, this is what compact groups in the local Universe seem to have experienced (Tzanavaris et al."," Interestingly, this is what compact groups in the local Universe seem to have experienced (Tzanavaris et al."545 2010; Walker et al., 2010; Walker et al.546 2010 and references therein)., 2010 and references therein).547" If two channels lead to the formation of a fossil group and there is a sort of density environment bias on identification and inference on the progenitor from observations, the stellar populations of the BCG of a fossil group do not necessarily have to be remarkably different from those of field, massive early-type galaxies of similar optical and X-ray luminosities at z~0 (cf."," If two channels lead to the formation of a fossil group and there is a sort of density environment bias on identification and inference on the progenitor from observations, the stellar populations of the BCG of a fossil group do not necessarily have to be remarkably different from those of field, massive early-type galaxies of similar optical and X-ray luminosities at $z \sim 0$ (cf."548 La Barbera et al., La Barbera et al.549 2009)., 2009).550" Furthermore, the size of environmental effects on typical red-sequence galaxies is still a controversial issue, and might be quite small at large stellar masses (cf."," Furthermore, the size of environmental effects on typical red-sequence galaxies is still a controversial issue, and might be quite small at large stellar masses (cf."551" e.g., Thomas et al."," e.g., Thomas et al."552" 2005, 2010; Pannella et al."," 2005, 2010; Pannella et al."553 2009; Cooper et al., 2009; Cooper et al.554 2010)., 2010).555" Hence, there might be less tension between our conclusions and the result of La Barbera et al."," Hence, there might be less tension between our conclusions and the result of La Barbera et al."556"(2009)'*.. Future multi-wavelength studies of statistical samples of fossil groups with different masses and redshifts (e.g., Santos et al."," Future multi-wavelength studies of statistical samples of fossil groups with different masses and redshifts (e.g., Santos et al."557" 2007), located in different density regions of the LSS, will provide a test of our interpretation and hypotheses."," 2007), located in different density regions of the LSS, will provide a test of our interpretation and hypotheses."558" Here we discuss if the contribution from low-surface brightness, diffuse stellar emission not associated with galaxies (the so-called intracluster light - ICL) could explain the rather low value of L;/Lx found in Sect."," Here we discuss if the contribution from low-surface brightness, diffuse stellar emission not associated with galaxies (the so-called intracluster light - ICL) could explain the rather low value of $L_i/L_{{\mathrm X}}$ found in Sect."559" 2 for the more massive fossil group, 0095951--0140.8."," 2 for the more massive fossil group, $+$ 0140.8."560" The impact on the total stellar mass budget of the ICL has already been pointed out in the literature, and with different scales, from observations (cf."," The impact on the total stellar mass budget of the ICL has already been pointed out in the literature, and with different scales, from observations (cf."561" e.g., Zibetti et al."," e.g., Zibetti et al."562 2005 and Gonzalez et al., 2005 and Gonzalez et al.563 2007)., 2007).564" In simulations, most of the ICL seems to be associated with the build-up of the BCG (e.g., Murante et al."," In simulations, most of the ICL seems to be associated with the build-up of the BCG (e.g., Murante et al."565 2007 and references therein)., 2007 and references therein).566" The expected amount of ICL is uncertain as well as the observed one - to of all stars in groups at z—0 (e.g., Kapferer et al."," The expected amount of ICL is uncertain as well as the observed one - to of all stars in groups at $z = 0$ (e.g., Kapferer et al."567" 2010 and references therein) - and seems to be independent of the mass-scale of the galaxy system (e.g., Dolag, Murante Borgani 2010 and references therein)."," 2010 and references therein) - and seems to be independent of the mass-scale of the galaxy system (e.g., Dolag, Murante Borgani 2010 and references therein)."568" Groups of galaxies that formed early (as fossil groups, potentially) might be particularly effective at producing ICL, as interactions in the group environment begin to liberate tidal material."," Groups of galaxies that formed early (as fossil groups, potentially) might be particularly effective at producing ICL, as interactions in the group environment begin to liberate tidal material."569" Galaxy systems as massive as the two fossil groups under study have smaller velocity dispersions than do massive clusters, meaning that interactions on the group scales can be slow and damaging as opposite to the impulsive high speed encounters, e.g. by harrassment, on the cluster scale."," Galaxy systems as massive as the two fossil groups under study have smaller velocity dispersions than do massive clusters, meaning that interactions on the group scales can be slow and damaging as opposite to the impulsive high speed encounters, e.g. by harrassment, on the cluster scale."570" These slow tidal interactions can strip material from rotating disc galaxies into loosely bound tidal structures, forming long tails of stars and gas (D'Onghia et al."," These slow tidal interactions can strip material from rotating disc galaxies into loosely bound tidal structures, forming long tails of stars and gas (D'Onghia et al."571 2009)., 2009).572 It is then interesting to estimate this additional amount of unbound stars that can escape detection in the present data., It is then interesting to estimate this additional amount of unbound stars that can escape detection in the present data.573" In particular, we use the approximations developed in D’Onghia et al. ("," In particular, we use the approximations developed in D'Onghia et al. ("5742010) to compute the fraction of ICL that a disc galaxy with a dynamical mass equal to 5x101Me (of which 2x1019 is in the disc) produces passing on a parabolic orbit within Mothe potential of a typical group.,2010) to compute the fraction of ICL that a disc galaxy with a dynamical mass equal to $5 \times 10^{11}~\mathrm{M}_{\sun}$ (of which $2 \times 10^{10}~\mathrm{M}_{\sun}$ is in the disc) produces passing on a parabolic orbit within the potential of a typical group.575 Such a galaxy has a stellar mass of the order of 1015Mo., Such a galaxy has a stellar mass of the order of $10^{10}~\mathrm{M}_{\sun}$.576 Figure 5 shows that the smaller the pericentric distance the larger the fraction of light stripped into the intergalactic medium., Figure 5 shows that the smaller the pericentric distance the larger the fraction of light stripped into the intergalactic medium.577 The fraction of ICL computed for the model galaxy is given by the ratio of the number of unbound stars to the total amount of stars bound to all the galaxies of the group., The fraction of ICL computed for the model galaxy is given by the ratio of the number of unbound stars to the total amount of stars bound to all the galaxies of the group.578" This galaxy, passing at 30-40 kpc from the group center, can contribute up to of the total light in the group galaxies."," This galaxy, passing at 30-40 kpc from the group center, can contribute up to of the total light in the group galaxies."579" Hence, slow tidal interactions likely provide a marginal contribution to the total stellar budget of a low-mass fossil group as 0095951+0212.6, but a non-neglible one for a fossil group as massive as CXGG0095951+0140.8."," Hence, slow tidal interactions likely provide a marginal contribution to the total stellar budget of a low-mass fossil group as $+$ 0212.6, but a non-neglible one for a fossil group as massive as $+$ 0140.8."580" Given these rough estimates, we will estimate the ICL contribution to the total stellar luminosity of the two fossil groups under study in the future, thanks to the deep B- and R-band photometry recently obtained by us with the Wide Field Imager (Baade et al."," Given these rough estimates, we will estimate the ICL contribution to the total stellar luminosity of the two fossil groups under study in the future, thanks to the deep B- and R-band photometry recently obtained by us with the Wide Field Imager (Baade et al."581" 1999), mounted at the Cassegrain focus of the MPG/ESO 2.2m telescope in La Silla, Chile."," 1999), mounted at the Cassegrain focus of the MPG/ESO $2.2~\mathrm{m}$ telescope in La Silla, Chile."582" For the first time, the galaxy stellar mass function (GSMF) was computed, down to a stellar mass M***'*~10? and in a robust statistical way, for two fossil groups Mg,discovered at z£z 0.4: 00959514-0212.6 and 0095951+0140.8."," For the first time, the galaxy stellar mass function (GSMF) was computed, down to a stellar mass $M^{\mathrm{stars}} \sim 10^{9}~\mathrm{M}_{\sun}$ and in a robust statistical way, for two fossil groups discovered at $z \approx 0.4$ :$+$ 0212.6 and $+$ 0140.8."583" These groups have also well- total masses (M200) equal to 1.9(+0.41)x1035 and 9.5(40.42)x10?Mo, respectively."," These groups have also well-determined total masses $M_{200}$ ) equal to $1.9~(\pm 0.41) \times 10^{13}$ and $9.5~(\pm 0.42) \times 10^{13}~\mathrm{M}_{\sun}$, respectively."584 This was possible, This was possible585were nearly indistinguishable from each other with no difference being larger Chan a minor fraction of the formal uncertainty associated with anv data point.,were nearly indistinguishable from each other with no difference being larger than a minor fraction of the formal uncertainty associated with any data point.586 In order (to assess whether any individual observation was introducing noise structure in the region of C i] absorption. we coadded the data for each target in all combinations of 2 and 3 exposures.," In order to assess whether any individual observation was introducing noise structure in the region of C ] absorption, we coadded the data for each target in all combinations of 2 and 3 exposures."587 No anomalous noise [rom a single observation was detected above the level of uncertainties in the data., No anomalous noise from a single observation was detected above the level of uncertainties in the data.588 Each of the independent data reduction procedures found that for the lower-quality observations (S/N S 100) structure that could not be associated with spectral features persisted in the data., Each of the independent data reduction procedures found that for the lower-quality observations (S/N $\lesssim 100$ ) structure that could not be associated with spectral features persisted in the data.589 This noise structure is almost exclusively in a downward direction and mimics small absorption features (of up to about 1.5 mA)) in the spectra., This noise structure is almost exclusively in a downward direction and mimics small absorption features (of up to about 1.5 ) in the spectra.590 The highest-quality data (those or ΠΟ 27778 and WD 27061) appear to have much less of (his structure with the noise ooking nearly statistical., The highest-quality data (those for HD 27778 and HD 37061) appear to have much less of this structure with the noise looking nearly statistical.591 The analvses of the cata were performed independently at each of the three anthor-, The analyses of the data were performed independently at each of the three author-institutions.592 Analyses included continuum fitting the spectra. measuring the ecqtivalent widths of absorption features aud determining the error associated wil (he equivalent width neasurements.," Analyses included continuum fitting the spectra, measuring the equivalent widths of absorption features and determining the error associated with the equivalent width measurements."593 The formal error budgets included both statistical and continuum placement uncertainties: uncertainties in the oscillator strengths were not included., The formal error budgets included both statistical and continuum placement uncertainties; uncertainties in the oscillator strengths were not included.594 The stellar spectra were all quite well behaved in the region of the C 11] absorption. so the continua across the features were easily fit with a low-order polvnomial.," The stellar spectra were all quite well behaved in the region of the C ] absorption, so the continua across the features were easily fit with a low-order polynomial."595 Since (the noise structure mentioned above could contaminate the small absorption features being measured. (he oxveen profiles (from Cycle 8 STIS observations) were used to define the limits over which (he C proliles were integrated to find equivalent widths.," Since the noise structure mentioned above could contaminate the small absorption features being measured, the oxygen profiles (from Cycle 8 STIS observations) were used to define the limits over which the C profiles were integrated to find equivalent widths."596 Figure 1 shows the normalized C (solid line) and O (dotted Ime) absorption features for each sightline superimposed on different vertical scales., Figure 1 shows the normalized C (solid line) and O (dotted line) absorption features for each sightline superimposed on different vertical scales.597 The effects of the structured noise can be seen in at least one of the C ii| lines: the HD 37021 spectrum's C 11] profile seems to show absorption at velocities longward of the O absorption., The effects of the structured noise can be seen in at least one of the C ] lines; the HD 37021 spectrum's C ] profile seems to show absorption at velocities longward of the O absorption.598 The uncertainty introduced by the noise structure is always in the direction of increasing (he apparent column density of the feature., The uncertainty introduced by the noise structure is always in the direction of increasing the apparent column density of the feature.599 Figure 1 shows that the noise structure is sparse and does not dominate the spectra., Figure 1 shows that the noise structure is sparse and does not dominate the spectra.600 The interstellar gas-phase carbon along (he target sishtlines was expected to be primarily in the form of ground-state C11. No higher ion states of carbon were expected (to reside in the neutral gas since C 11s ionization energy is well above hvdrogens. but some carbon could exist as neutral C and/or in molecules.," The interstellar gas-phase carbon along the target sightlines was expected to be primarily in the form of ground-state C. No higher ion states of carbon were expected to reside in the neutral gas since C 's ionization energy is well above hydrogen's, but some carbon could exist as neutral C and/or in molecules."601 Each of the sightlines was previously observed with STIS at wavelengths that sampled C and the dominant carbon-containing molecule. CO.," Each of the sightlines was previously observed with STIS at wavelengths that sampled C and the dominant carbon-containing molecule, CO."602 These observations showed (hat. as expected. CO and C are generally minor reservoirs of C.," These observations showed that, as expected, CO and C are generally minor reservoirs of C."603-lem,-1cm604 1999).. Fossatiefa£.(1998): Muckeefa£(1997).. (Salamon&Stecker.1996:1993).. (Zhouetal.1997;Mattosefalf.1997).," \citep{har99}. \citet{fos98}; \citet{muc97}. \citep{sal96,ste93,fan98}. \citep{zho97,mat97},"605 > Aluckeefa£.(1997) Bnupey(1996) Zhang. (Bloom&Marscher1996:Ghisellini.Maraschi.Treves1985) ," $>$ \citet{muc97} \citet{imp96} \citet{muc97} \citet{zha01} \citep{blo96,ghi85} "606do use an ad-hoc prescription to. reduce. the barvonie mass in small halos. or overprecdict small halos 2007).. although agreement is improving as semianalvtic models improve in sophistication 2010b).,"do use an ad-hoc prescription to reduce the baryonic mass in small halos, or overpredict small halos , although agreement is improving as semianalytic models improve in sophistication ."607. However. hvdrodynamic simulations seem to require no such prescription: they most often. report a faint-end mass spectrum slope in the vicinity of -0.9 -1.2 ).," However, hydrodynamic simulations seem to require no such prescription: they most often report a faint-end mass spectrum slope in the vicinity of -0.9 – -1.2 ."608 While there are some exceptions report à=1.45 for their best- model: find - 1.96). 1 would appear this is à result which is cillieult to get. wrong.," While there are some exceptions report $\alpha=-1.45$ for their best-fit model; find $\alpha=-1.96$ ), it would appear this is a result which is difficult to get wrong."609 were the first to. propose a mechanism of gas being heated (by. local supernovae) and driven out of low-mass halos., were the first to propose a mechanism of gas being heated (by local supernovae) and driven out of low-mass halos.610 introduced the idea of the ionizing background. radiation. being the relevant mechanism. and used a smooth particle hyelrodvnamic (SPLHD) simulation to show that a photoionizing background does stronely inhibit 16 cooling and infall of eas into halos of virial mass below 4.10°AL..," introduced the idea of the ionizing background radiation being the relevant mechanism, and used a smooth particle hydrodynamic (SPH) simulation to show that a photoionizing background does strongly inhibit the cooling and infall of gas into halos of virial mass below $4\times 10^9 M_{\odot}$."611 did the same with a 1D Lagrangian code., did the same with a 1D Lagrangian code.612 showed that the UV background reduced the cooled gas acereted to disk galaxies by half with late-acereting gas preferentially. lected.," showed that the UV background reduced the cooled gas accreted to disk galaxies by half, with late-accreting gas preferentially affected."613" used simulations of reionization to determine that the mass scale at which gas is stripped by photoionization from the background radiation corresponds to the ""filtering"" length scale. the scale at which barvonic matter is smoothed compared to the underlying dark matter in linear perturbation theory: however using CLADGIZE-2found a somewhat smaller critical mass of LOMAL. (similar values were obtained by and 2007)) and. significantly. reported that their SPILL result was well approximated by a simple prescription comparing the eas temperature to the virial temperature of the halo."," used simulations of reionization to determine that the mass scale at which gas is stripped by photoionization from the background radiation corresponds to the “filtering” length scale, the scale at which baryonic matter is smoothed compared to the underlying dark matter in linear perturbation theory; however using GADGET-2found a somewhat smaller critical mass of $10^{10} M_{\odot}$ (similar values were obtained by and ) and, significantly, reported that their SPH result was well approximated by a simple prescription comparing the gas temperature to the virial temperature of the halo."614 and macle semianalvtie calculations of galaxy evolution and. likewise Found that galaxies fainter than £L; have their star formation suppressed or squelched by a photoionizing background., and made semianalytic calculations of galaxy evolution and likewise found that galaxies fainter than $L_*$ have their star formation suppressed or “squelched” by a photoionizing background.615 Aleanwhile. the role of supernova feedback in driving gas from small halos ancl thereby suppressing star formation has continued to be studied2008).," Meanwhile, the role of supernova feedback in driving gas from small halos and thereby suppressing star formation has continued to be studied."616. have even performed. a simulation showing that the UV output of local stars can alleet the SER., have even performed a simulation showing that the UV output of local stars can affect the SFR.617 However. while these processes are certainlv present ancl important. our focus here is on the ionizing background. which we will show to be both necessary and sullicient to reproduce the observed Schechter à.," However, while these processes are certainly present and important, our focus here is on the ionizing background, which we will show to be both necessary and sufficient to reproduce the observed Schechter $\alpha$."618" Lt should. be noted that. despite the terminology of ""critical, or ""cutoff"" masses. a sharp cutoll in galaxy masses is not consistent with the observations: there are. low-mass (chwarl) galaxies. merely fewer than expected."," It should be noted that despite the terminology of “critical” or “cutoff” masses, a sharp cutoff in galaxy masses is not consistent with the observations: there are low-mass (dwarf) galaxies, merely fewer than expected."619 Several mechanisms have been proposed to explain this., Several mechanisms have been proposed to explain this.620" proposed that some intermediate-nmiass halos bUCoirev25.35 km/s. or AL~LOLS AL.) have star formation ab early times. then lose their remaining gas at the time of reionization ancl become ""red. ancl dead dwarfs at. the oesent."," proposed that some intermediate-mass halos $v_{\text{circ}}\sim 25-35$ km/s, or $M \sim 10^{10} M_{\odot}$ ) have star formation at early times, then lose their remaining gas at the time of reionization and become “red and dead” dwarfs at the present."621 suggested. that present chvarl satellites such as those around the Milky Way were originally larger but were reduced to their present. sizehy idal stripping., suggested that present dwarf satellites such as those around the Milky Way were originally larger but were reduced to their present sizeby tidal stripping.622 Such mechanisms max be needed to explain the very low luminosity Cz.1075.) Milky Way satellites discovered in recent vears).," Such mechanisms may be needed to explain the very low luminosity $\ga 10^3623L_{\odot}$ ) Milky Way satellites discovered in recent years."624. Two recent studies are of particular interest., Two recent studies are of particular interest.625 studied the evolution ofclwarl galaxies in isolation ancl found that both feedback. and a UV background. are necessary £o reproduce the observed. properties of the Local Group dwarf spheroidals., studied the evolution of dwarf galaxies in isolation and found that both feedback and a UV background are necessary to reproduce the observed properties of the Local Group dwarf spheroidals.626 4n particular. they saw that the UV. background cllicicntly suppresses star. formation alter the epoch of reionization [or svstemis below 10AZ..," In particular, they saw that the UV background efficiently suppresses star formation after the epoch of reionization for systems below $10^9 M_{\odot}$."627 Similarly. simulate a Milky Way-like @alaxy and its satellites and find a threshold circular speed of 12 km/s ( δι107AZ.) for halos which can form stars.," Similarly, simulate a Milky Way-like galaxy and its satellites and find a threshold circular speed of 12 km/s ( $\sim 8\times 10^8628M_{\odot}$ ) for halos which can form stars."629 We also note that even though it has been known at least since that including the X-rav background has a substantial elfect on the tempterature of the ICM (and henee. as we will see. on star formation). [ew simulations have incorporated this component.," We also note that even though it has been known at least since that including the X-ray background has a substantial effect on the tempterature of the IGM (and hence, as we will see, on star formation), few simulations have incorporated this component."630 studied its cllect on dwarl galaxies and found a critical barvon retention mass. but only looked at z>SN.," studied its effect on dwarf galaxies and found a critical baryon retention mass, but only looked at $z>8$."631 We remedy this deficit by including an X-ray background in some of our simulations to study its elect on small galaxies [rom moderate redshift to the present., We remedy this deficit by including an X-ray background in some of our simulations to study its effect on small galaxies from moderate redshift to the present.632 In a previous paperD.. we explored the ellect of the ionizing background on the stellar and gas properties of large elliptical galaxies.," In a previous paper, we explored the effect of the ionizing background on the stellar and gas properties of large elliptical galaxies."633 llere. we use a similar set of UV. and X-ray backgrounds to examine their elfect on the low end of the galaxy mass spectrum. namely the satellites of those ellipticals.," Here, we use a similar set of UV and X-ray backgrounds to examine their effect on the low end of the galaxy mass spectrum, namely the satellites of those ellipticals."634 Section 2 presents a simple physical argument for why any efficient eas-heating mechanism will vield. a [lattening of the low- slope., Section 2 presents a simple physical argument for why any efficient gas-heating mechanism will yield a flattening of the low-mass slope.635 Section 3 presents the details of the simulations we performed. to test this argument: section ??.— gives the results of the same., Section 3 presents the details of the simulations we performed to test this argument; section \ref{sect:results} gives the results of the same.636 Section ?? is discussion and conclusions., Section \ref{sect:disc} is discussion and conclusions.637 Our argument. which dates back to and (1992).. compares the escape velocity of gas in a virialized halo to the sound speed of that eas.," Our argument, which dates back to and , compares the escape velocity of gas in a virialized halo to the sound speed of that gas."638 The escape velocity for a halo of mass AZ and radius r is given hy We relate AZ and r by fixing the density at the standard Dviralized value. where p is the mean density of the universe at à given epoch (we calculate the result for 2= 0. and assume η= 0.3. as in our simulations).Then the escape velocity becomes The sound speed. meanwhile. is given for a gas of temperature 1) and mean particle mass m hy," The escape velocity for a halo of mass $M$ and radius $r$ is given by We relate $M$ and $r$ by fixing the density at the standard “virialized” value, where $\bar{\rho}$ is the mean density of the universe at a given epoch (we calculate the result for $z=0$ , and assume $\Omega_M=0.3$ , as in our simulations).Then the escape velocity becomes The sound speed, meanwhile, is given for a gas of temperature $T$ and mean particle mass $m$ by"639be nulls.,be nulls.640 Simultaneous multi-frequencey. observations (e.g.Barteletal.1982). show that both nulline and mode changing are broad-bancl phenomena.," Simultaneous multi-frequency observations \citep[e.g.,][]{bmsh82} show that both nulling and mode changing are broad-band phenomena."641 Finally. there is the fascinating observation by Wrameretal.(2006) of the change in slow-down rate of PSR. 121921|24 when the pulsar is in a null state.," Finally, there is the fascinating observation by \citet{klo+06} of the change in slow-down rate of PSR B1931+24 when the pulsar is in a null state."642 All of these observations suggest. that both nulling ane mode changing result from large-scale anc persisten changes in the magnetospheric current. distribution., All of these observations suggest that both nulling and mode changing result from large-scale and persistent changes in the magnetospheric current distribution.643 Moce changes must be a manifestation of a redistribution. of current [flow in the magnetosphere. resulting in changes in he radio beam emission pattern and hence in the observec »ulse. profile.," Mode changes must be a manifestation of a redistribution of current flow in the magnetosphere, resulting in changes in the radio beam emission pattern and hence in the observed pulse profile."644 Nulls may result. from a cessation of (or a cast à large reduction in) the current as suggested by the observations of PSR D1931|24 (Ixrameretal.2006).. bu mav also result from a current redistribution which leads toa om pattern with little or no power in our direction.," Nulls may result from a cessation of (or at least a large reduction in) the current as suggested by the observations of PSR B1931+24 \citep{klo+06}, but may also result from a current redistribution which leads to a beam pattern with little or no power in our direction."645 This atter interpretation is favoured. by the increasing number of detections of weak emission. generally with a cdilferent suse profile. in apparent null intervals.," This latter interpretation is favoured by the increasing number of detections of weak emission, generally with a different pulse profile, in apparent null intervals."646 Both nulls aud mode changes are typically sudden: transitions. occurring within one pulse period. although exceptions apparently exist (Deichctal.1986:Lewandowskiet2004)..," Both nulls and mode changes are typically sudden transitions, occurring within one pulse period, although exceptions apparently exist \citep{dchr86,lwf+04}."647 The concept of “tipping points” is well known in the study of non-linear complex svstenis. for example. in climate science.," The concept of “tipping points” is well known in the study of non-linear complex systems, for example, in climate science."648" ""his is a situation where a small perturbation can lead to a sudden change to a dillerent quasi-table state.", This is a situation where a small perturbation can lead to a sudden change to a different quasi-stable state.649 The transitions are fundamentally related: to positive feedback and can be Evidently the pulsar pulse emission process in at least some pulsars is subject to such instabilities., The transitions are fundamentally related to positive feedback and can be Evidently the pulsar pulse emission process in at least some pulsars is subject to such instabilities.650 For example. if à small perturbation in current How results in a change in the accelerating potential or magnetic field configuration which enhances the change. an instability could. develop.," For example, if a small perturbation in current flow results in a change in the accelerating potential or magnetic field configuration which enhances the change, an instability could develop."651 The observations implv changes in current [low which are quite drastic. completely. changing the observed. pulse profile and its polarisation and modulation characteristics. and in some cases making the pulsar unobservable.," The observations imply changes in current flow which are quite drastic, completely changing the observed pulse profile and its polarisation and modulation characteristics, and in some cases making the pulsar unobservable."652 What causes these instablities. why they tend to be bistable and what determines their timescale are currently unanswered questions.," What causes these instablities, why they tend to be bistable and what determines their timescale are currently unanswered questions."653 Lt is clear that they are most. common in old pulsars but there is a wide range in the observed. properties of pulsars which are subject to mode changing and nulling., It is clear that they are most common in old pulsars but there is a wide range in the observed properties of pulsars which are subject to mode changing and nulling.654 The Parkes radio telescope is part of the Australia Telescope which is funded by the Commonwealth Government. for operation as a National Facility managed by CSLRO., The Parkes radio telescope is part of the Australia Telescope which is funded by the Commonwealth Government for operation as a National Facility managed by CSIRO.655"at 1.3mmm have large W)(Ha), indicative of high accretion, but most of the non-detections have much lower values.","at mm have large $W_\lambda({\rm H}\alpha)$, indicative of high accretion, but most of the non-detections have much lower values."656 About two-thirds of the non-detections with measurements have equivalent widths less than the W)(Ha)minimum of the detected disks., About two-thirds of the non-detections with $W_\lambda({\rm H}\alpha)$ measurements have equivalent widths less than the minimum of the detected disks.657" Based on the spectral type dependent W,(Ha) cutoff defined by White&Basri most of the sources that are not detected in our (2003),,SMA survey are weak-lined T-Tauri stars (WTTS)."," Based on the spectral type dependent $W_\lambda({\rm H}\alpha)$ cutoff defined by \cite{2003ApJ...582.1109W}, most of the sources that are not detected in our SMA survey are weak-lined T-Tauri stars (WTTS)."658" However, we only detect 9 out of the 25 identified CTTS."," However, we only detect 9 out of the 25 identified CTTS."659" The sensitivity limitations of our survey prevent us from drawing any strong conclusions, but the general correspondence between the millimeter detections and high W)(Ha) suggests that the gas and dust depletion timescales are not greatly dissimilar."," The sensitivity limitations of our survey prevent us from drawing any strong conclusions, but the general correspondence between the millimeter detections and high $W_\lambda({\rm H}\alpha)$ suggests that the gas and dust depletion timescales are not greatly dissimilar."660" The situation is encapsulated in the IRAC color-color plot in Figure 6 where different symbols represent CTTS, WTTS and SMA detections."," The situation is encapsulated in the IRAC color-color plot in Figure \ref{fig:colcol} where different symbols represent CTTS, WTTS and SMA detections."661" The vertical and horizontal dotted lines show the boundaries used by Ciezaetal.(2007) to distinguish between YSOs with colors consistent with a stellar photosphere (lower left corner), transition disks with excess infrared emission only apparent at wavelengths greater than 4.5jum, and “full” disks with excesses at 4.5 and 8jum. All the CTTSs in our sample display excess emission at 8jum, and the nine disks detected by the SMA exhibit excess emission at both 4.5um and 8jum. However, most disks with an infrared excess were not detected in our millimeter survey and there is no correlation between disk mass and the amount of infrared excess."," The vertical and horizontal dotted lines show the boundaries used by \cite{2007ApJ...667..308C}662 to distinguish between YSOs with colors consistent with a stellar photosphere (lower left corner), transition disks with excess infrared emission only apparent at wavelengths greater than $4.5\,\mu$ m, and “full” disks with excesses at $4.5$ and $8\,\mu$ m. All the CTTSs in our sample display excess emission at $8\,\mu$ m, and the nine disks detected by the SMA exhibit excess emission at both $4.5\,\mu$ m and $8\,\mu$ m. However, most disks with an infrared excess were not detected in our millimeter survey and there is no correlation between disk mass and the amount of infrared excess."663" We stacked the SMA emission from all of the stars with infrared excesses that were not individually detected with the SMA, but did not find a significant detection."," We stacked the SMA emission from all of the stars with infrared excesses that were not individually detected with the SMA, but did not find a significant detection."664 'There are 45 X-ray sources within our survey &Zinnecker2002).., There are 45 X-ray sources within our survey \citep{2002AJ....123.1613P}.665 40 of these are coincident with(Preibisch known cluster members from Luhmanetal.(2003) and are active YSOs., 40 of these are coincident with known cluster members from \cite{2003ApJ...593.1093L} and are active YSOs.666 5 were detected with the SMA (including IRAS 03410+3152) but we do not see any clear trend between the millimeter properties of the X-ray detected and undetected sources., 5 were detected with the SMA (including IRAS 03410+3152) but we do not see any clear trend between the millimeter properties of the X-ray detected and undetected sources.667 The other 5 sources have no optical or infrared counterpart to a level that rules out highly extincted substellar objects., The other 5 sources have no optical or infrared counterpart to a level that rules out highly extincted substellar objects.668" These are indicated by blue crosses in Figures 2a[Online-only],2b and, as Preibisch&Zinnecker(2002) concluded, are most likely extragalactic contaminants."," These are indicated by blue crosses in Figures \ref{fig:mosaic1}, \ref{fig:mosaic2} and, as \cite{2002AJ....123.1613P} concluded, are most likely extragalactic contaminants."669" Interestingly, we detect one of these, source 195 in field V (the lowest noise map in our survey), with a flux 1.230.4 mmJy."," Interestingly, we detect one of these, source 195 in field V (the lowest noise map in our survey), with a flux $1.2\pm 0.4$ mJy."670 Most YSOs in IC348 are between 2 and 3MMyr old but there is likely to be a significant dispersion., Most YSOs in IC348 are between 2 and Myr old but there is likely to be a significant dispersion.671 A simple explanation of our results would be that the detected disks are younger than the non-detections., A simple explanation of our results would be that the detected disks are younger than the non-detections.672" In principle, protostellar ages and masses can be inferred by comparing their luminosity and effective temperature against model isochrones of pre-main-sequence tracks but, in practice, the associated errors are large."," In principle, protostellar ages and masses can be inferred by comparing their luminosity and effective temperature against model isochrones of pre-main-sequence tracks but, in practice, the associated errors are large."673" Using the model isochrones of D’Antona&Mazzitelli(1997),, we do not find any significant difference in the estimated ages of the millimeter detected and non-detected YSOs."," Using the model isochrones of \cite{1997MmSAI..68..807D}, we do not find any significant difference in the estimated ages of the millimeter detected and non-detected YSOs."674 This is not too surprising given previous failed searches for differences between CTTS and WTTS in individual clusters (Gomezetal. which show that age is not the sole determinant of 1992)disk evolution.," This is not too surprising given previous failed searches for differences between CTTS and WTTS in individual clusters \citep{1992AJ....104..762G}675 which show that age is not the sole determinant of disk evolution."676 Protoplanetary disk masses are also known to scale with stellar mass (Williams&Cieza2011).., Protoplanetary disk masses are also known to scale with stellar mass \citep{2011arXiv1103.0556W}.677 The inferred stellar masses of the detected disks are all sub-solar but range widely from 0.02 to 0.77Mo.," The inferred stellar masses of the detected disks are all sub-solar but range widely from 0.02 to $0.77\,M_\odot$."678" In this small sample, there is no evidence for a dependency on stellar mass but the detection of a disk around source 468, a M8.25 brown dwarf, is noteworthy."," In this small sample, there is no evidence for a dependency on stellar mass but the detection of a disk around source 468, a M8.25 brown dwarf, is noteworthy."679" Based on the lack of detections of relatively massive disks, Carpenter(2002) concluded that disks in IC348 have significantly lower masses than those in Taurus."," Based on the lack of detections of relatively massive disks, \cite{2002AJ....124.1593C} concluded that disks in IC348 have significantly lower masses than those in Taurus."680 The high sensitivity of this SMA survey has allowed us to make the first mass measurements of IC348 disks and the results provide an important benchmark for tracking disk evolution at timescales comparable to their statistical half-life., The high sensitivity of this SMA survey has allowed us to make the first mass measurements of IC348 disks and the results provide an important benchmark for tracking disk evolution at timescales comparable to their statistical half-life.681" Due to the large number of non- and because the sensitivity of the observations varied from field to field, we plot the cumulative disk"," Due to the large number of non-detections and because the sensitivity of the observations varied from field to field, we plot the cumulative disk"682principally from{οσα variatious of the mass reservolr while the impact from wider environments becomes sjenificaut onlv at later times. as indeed suggested by SU9.,"principally from variations of the mass reservoir while the impact from wider environments becomes significant only at later times, as indeed suggested by S09."683 An aremucut raised by $09 is that long-term (o fry) accretion can eventually modify the DIF and wipe out the initial (CAIF) conditions., An argument raised by S09 is that long-term $t\gg t_{ff}$ ) accretion can eventually modify the IMF and wipe out the initial (CMF) conditions.684 Iowever. as ποσα du Fie.2.. even if accretion is pursued over several dynamical times. the CAIF-IAIF correlation is still of the order of about half à core mass. and thus is bv no meaus completely wiped out.," However, as seen in \ref{dist2}, even if accretion is pursued over several dynamical times, the CMF-IMF correlation is still of the order of about half a core mass, and thus is by no means completely wiped out."685 Moreover. such long lasting significant accretion seenis unlikely (see e.g. Offer et al. (," Moreover, such long lasting significant accretion seems unlikely (see e.g. Offner et al. ("6862009). Fig.,"2009), Fig."687 8)., 8).688" Indeed. there is observational evidence that accretion decreases siguificantly after the class-Q0 phase (about l to 2 fay, ): furtlicrinore. recent observations sugecst that the ceutral protostar builts up essentially all its mass dunug a few episodes of violent accretion before this latter decreases substantially. with about half the mass of a 0.5 AL. deuse prestellar core being accreted duriug less than of the Class I lifetime. Le a fraction of a frec-fall time (Evans ct al."," Indeed, there is observational evidence that accretion decreases significantly after the class-0 phase (about 1 to 2 $t_{dyn}$ ); furthermore, recent observations suggest that the central protostar builts up essentially all its mass during a few episodes of violent accretion before this latter decreases substantially, with about half the mass of a 0.5 $\msol$ dense prestellar core being accreted during less than of the Class I lifetime, i.e a fraction of a free-fall time (Evans et al."689" 2009),", 2009).690 A scenario supported bv numerical simnulatious (Vorobvov Basu 2006)., A scenario supported by numerical simulations (Vorobyov Basu 2006).691 Therefore. it ποσα» unlikely that significant accretion lasts long enough for the strong correlation between the (initial) CAIF aud the (final) IME to be completely washed out.," Therefore, it seems unlikely that significant accretion lasts long enough for the strong correlation between the (initial) CMF and the (final) IMF to be completely washed out."692 This issue needs to be explored with dedicated nuuerical simulations iucludiug laree- and simall-scale radiative aud magnetic feedback processes., This issue needs to be explored with dedicated numerical simulations including large- and small-scale radiative and magnetic feedback processes.693 In the same vein. the collision timescale between prestellar cores im dense star foriumg clips appears to be significantly longer than the core lifetimes. sugecstine that the cores should evolve individually to form a small nuuber of stars rather than compcting for eas accretion. leading to a natural mapping of the CME outo the IMF (André et al.," In the same vein, the collision timescale between prestellar cores in dense star forming clumps appears to be significantly longer than the core lifetimes, suggesting that the cores should evolve individually to form a small number of stars rather than competing for gas accretion, leading to a natural mapping of the CMF onto the IMF (André et al."694 2007. 2009: Evans et al.," 2007, 2009; Evans et al."695 2008)., 2008).696 According to the present analysis. the final stellar IMFE cau be determined reasonably accurately. ou astatistical basis. Lo. not for individual objects. from the initial core mass distribution in the cloud. i.c. the CAIF. with some unavoidable scatter. leading naturally to two similar mass distributions (seo Fie.," According to the present analysis, the final stellar IMF can be determined reasonably accurately, on a basis, i.e. not for individual objects, from the initial core mass distribution in the cloud, i.e. the CMF, with some unavoidable scatter, leading naturally to two similar mass distributions (see Fig."697 3)., 3).698 Exploring a larger dynamical mass range with siuulations. or conducting such a statistical analysis from.observed CMEP/IME. à. task possibly iu. reach with the IIERSCTIEL iission. would certainly help assessing this result.," Exploring a larger dynamical mass range with simulations, or conducting such a statistical analysis from CMF/IMF, a task possibly in reach with the HERSCHEL mission, would certainly help assessing this result."699 Such a correlation between the CAF and the IAIF argues in favor of the IAIF being essentiallv deteruuned by the ecneral properties of the arent cloud Guean temperature aud density. large-scale velocity dispersion. with scaling properties following the Larson relatious). as recently theorized by IHeunebelle and Chabrier (2008.2009). aud being only weakly affected w the various enviromental factors beyond the parent core mass reservoir.," Such a correlation between the CMF and the IMF argues in favor of the IMF being essentially determined by the general properties of the parent cloud (mean temperature and density, large-scale velocity dispersion, with scaling properties following the Larson relations), as recently theorized by Hennebelle and Chabrier (2008,2009), and being only weakly affected by the various environmental factors beyond the parent core mass reservoir."700 Accordingly. the final IMF of a star ormiue region can be determined reasonably accurately. xovided some average uniforii cficiency factor. frou he initial CALF obtained fro nuu- or sub-nuni survevs.," Accordingly, the final IMF of a star forming region can be determined reasonably accurately, provided some average uniform efficiency factor, from the initial CMF obtained from mm- or sub-mm surveys."701 Tuterestingly cnough. the present caleulatious also show hat the aforemeutioned statistical variations amone the core propertics vield a final IME extending further down in the low-mass domain than the parent CALIF. providing a natural explanation for the fact that this latter appears to underestimate the wuuber of “pre brown dwarf cores compared with the observatiouallv-derived. brown: dwarf IME.," Interestingly enough, the present calculations also show that the aforementioned statistical variations among the core properties yield a final IMF extending further down in the low-mass domain than the parent CMF, providing a natural explanation for the fact that this latter appears to underestimate the number of ""pre brown dwarf"" cores compared with the observationally-derived brown dwarf IMF."702 These couclusious will have to be confronted to the wealth of data expected from the HIERSCTIEL iission. as naling down this issue bears major consequences to nuderstand the fundamental origin of star formation.," These conclusions will have to be confronted to the wealth of data expected from the HERSCHEL mission, as nailing down this issue bears major consequences to understand the fundamental origin of star formation."703 The authors are grateful to Rowan Smith. Ian Bouuecll and Paul Clark for stimulating discussions and for sharing their data.," The authors are grateful to Rowan Smith, Ian Bonnell and Paul Clark for stimulating discussions and for sharing their data."704 We are also thankful to Philippe Audré for fruitful conversations and insightful cohunents and to the auouvmious referee for helping us mrproviue the manuscript., We are also thankful to Philippe André for fruitful conversations and insightful comments and to the anonymous referee for helping us improving the manuscript.705 We acknowledge finding from the European Research Council under the Europeau Community 7th Framework Proerauune (FP7/2007-2013 Caant Aereciment uo., We acknowledge funding from the European Research Council under the European Community 7th Framework Programme (FP7/2007-2013 Grant Agreement no.706 217060., 247060.707.,.708 Radio images of the source. 131.17 observed at WSRT. baudwidth 20 MIIz.," Radio images of the source 4C34.47 observed at WSRT, bandwidth 20 MHz."709 Upper row. left panel: ceutral frequency 315 MIIZ. without REI witigation svsteni: right panel: ceutral frequency 315 MITZ. with RFI mitigation svstem.," Upper row, left panel: central frequency 345 MHz, without RFI mitigation system; right panel: central frequency 345 MHz, with RFI mitigation system."710 Notice the difference of the intensity levels in the figures., Notice the difference of the intensity levels in the figures.711 Low row (“toxicity test). left panel: central frequency 1420 MITz without RET iitigation svete.," Low row (“toxicity"" test), left panel: central frequency 1420 MHz without RFI mitigation system."712 right paucl: central frequency 1120 MIIz with RFT mitigation svstem., right panel: central frequency 1420 MHz with RFI mitigation system.713 After subtracting one mage from the other tle uoise is less than 0.7 indy/beaim which signifies a good simularity iu the images., After subtracting one image from the other the noise is less than 0.7 mJy/beam which signifies a good similarity in the images.714resolution of the SDSS spectra). land,"resolution of the SDSS spectra), and."715 Three values of the doublet ratio are incorporated into the search: 2:1 (corresponding to unsaturated Lines on the linear part. of the curve of growth). d:l (for saturated. lines on the Hat part of the curve of growth) and an intermediate case. 4:3.," Three values of the doublet ratio are incorporated into the search: 2:1 (corresponding to unsaturated lines on the linear part of the curve of growth), 1:1 (for saturated lines on the flat part of the curve of growth) and an intermediate case, 4:3."716 A further template with doublet ratio 1:1 and flat-bottomed absorber profiles. lin extent. is also used to optimise the detection of very high. EW doublets.," A further template with doublet ratio 1:1 and flat-bottomed absorber profiles, in extent, is also used to optimise the detection of very high EW doublets."717 At cach pixel the template giving the minimum X2 value is determined. and candidate absorbers selected by applying a threshold value of ZG., At each pixel the template giving the minimum $\chi2$ value is determined and candidate absorbers selected by applying a threshold value of $\ge$ $\sigma$.718 A total of 193315. ssvstems are indentilied but we confine our analysis to the sub-sample of 7719 systems with EW of the [line (Mum AL. The lefi-banel e ⋠⋠⋠ ↓≻⋜⋯⋖⋅, A total of 315 systems are indentified but we confine our analysis to the sub-sample of 719 systems with EW of the line $W_0^{\lambda2796}$ $\ge$.719↓∪↓⊲↓⋏∙≟⊳↓⊳∖↓↥∪∖∖⊽≱∖↿⇂↥⋖⋅∠↓⊳, The left-hand panel of Fig.720∖⇂↓⋅↓∣⋡⋯↓∪⊔∪⇂⊓⊓∖−⊔∖∖⊽⊔↓↕⋃∢⋅ ⇂⊽⊓∖⇉⊤⋅⋯∶↓⇀∖−−⊲↓⊔↓⊲∐↕↓↕∠⇂↕≼⇍⋜↧↿⋖⊾∠⇂⊳↾∐↥⋖⊾↓⋅⊲↓⋏∙≟↓∐−↓↕⋜⋯∠⇂↓≻⋜⋯⋖⋅↓∪⇂⋅↓⊲⇝↓⋏∙≟⊳↓ ≱∖⇂↥∪, \ref{cap:newz} shows the distribution of $W_0^{\lambda2796}$ with the $W_0^{\lambda2796}$ -limit indicated.721∖∖⊽≱∖⇂↥⋖⊾↓⋅∢⋅∠⇂⊳∖↓↕∐⋅⇂∠⇂⋠↓≱∖↿, The right-hand panel of Fig.722↓⋰↓∣⋡⋯⊀↓∪⊔⇂⋅∪↓⋅↿↓∐⋅⊳↓ ⇀∖⇀∖⊳∖⊳∖⋜⋯↓↓≻↓∢⊾⊳↓↴↓⋅∪∖⋰⊔⇂⊀↓⊔⋏∙≟↿↕⋜⊔⋜⋯∙∖⇁∠⇂⊔⊳∖⇂, \ref{cap:newz} shows the redshift distribution for the $\ge$ sample.723⋜↧⊳∖⊳∖⋯⋰↓⋜⋯⋅∠⇂∖∖⋰↓↓↕ ↿↓↥⋖⋅↳∖↓⋏∙≟∐⋯∩≱∖∪↓⋅∣⋊⋅↓⋅↓≻∪↓≻⊔↓⋜⊔⊲↓∪⊔↓⋅⋖⊾⊳∖⊔⊓⊳∖↕↓↕⋜↧↓↥⋖⋅⇀∖⇂↕↓↕≼∼↿↕⋖⋟↓↕ curve whose shape is not strongly dependent on Mg2106 the investigation presented here is not sensitive to. the completeness of the absorber catalogue.," Providing that any dust associated with the absorber population results in an extinction curve whose shape is not strongly dependent on $W_0^{\lambda2796}$, the investigation presented here is not sensitive to the completeness of the absorber catalogue."724 However. the statistical properties of the absorber catalogue are. in excellent agreement with previous work (72)..," However, the statistical properties of the absorber catalogue are in excellent agreement with previous work \citep{2005ApJ...628..637N}."725" Phe catalogue is highly complete down to Wy2708 aand. [from a combination of visual inspection. and investigation of the properties of other absorption specics in ""backed? ssvstems. contamination by false cetections is found to be «5 per cent."," The catalogue is highly complete down to $W_0^{\lambda2796}$ and, from a combination of visual inspection and investigation of the properties of other absorption species in `stacked' systems, contamination by false detections is found to be $<$ 5 per cent."726 There are 73318 quasars with a single intervening aabsorber. 10019 quasars with two absorbers anc 116 quasars with more than two absorbers.," There are 318 quasars with a single intervening absorber, 019 quasars with two absorbers and 116 quasars with more than two absorbers."727 Due to the increased uncertainty in the determination. of the dust. content of incividual absorption svstenms in quasars containing multiple absorbers (i.e. 2-2 systems). we chose to retain only (quasars with single or double intervening aabsorbers.," Due to the increased uncertainty in the determination of the dust content of individual absorption systems in quasars containing multiple absorbers (i.e. $> 2$ systems), we chose to retain only quasars with single or double intervening absorbers."728 Lo the case of a double absorber we consider only the stronger system., In the case of a double absorber we consider only the stronger system.729 The vast majority of double absorbers involve one or more low EW systems. however. we remove from the sample the S/1019 spectra that possess two absorbers with an ολλ2.5. tto leave a total of N3329 svstems.," The vast majority of double absorbers involve one or more low EW systems, however, we remove from the sample the $8/1019$ spectra that possess two absorbers with an $>2.5$ to leave a total of 329 systems."730 The results and conclusions derived in the paper are not sensitive to whether we use only single systems or single plus double svstcHis., The results and conclusions derived in the paper are not sensitive to whether we use only single systems or single plus double systems.731 labeolclustThe presence of dust in an aabsorber allects the observed. spectrum of the background. quasar., The presence of dust in an absorber affects the observed spectrum of the background quasar.732 The degree of reddening of a spectral energy. distribution. (SED) is described by an associated. extinction curve. and the cust content is parameterised by a corresponding (D.V)! (c.c. ?)).," The degree of reddening of a spectral energy distribution (SED) is described by an associated extinction curve, and the dust content is parameterised by a corresponding $E(B-V)$ (e.g. \citet{1994ApJ...429..172K}) )."733 The large and homogenous SDSS DRG spectroscopic catalogue provides an opportunity to obtain estimates of the dust. content. for many thousands of absorbers., The large and homogenous SDSS DR6 spectroscopic catalogue provides an opportunity to obtain estimates of the dust content for many thousands of absorbers.734 Llowever. one must be sure that intrinsic quasar-lo-quasar SED variations do not. produce significant systematic biases in. or acd significant scatter to. the 12 determinations of the absorbers.," However, one must be sure that intrinsic quasar-to-quasar SED variations do not produce significant systematic biases in, or add significant scatter to, the $E(B-V)$ determinations of the absorbers."735 The population of aabsorbers is reported to have a mean dust content of onlv (D.V)20.02.0.03mag (?7).. which implies onlv small alterations to the shape of the SEDs of background quasars.," The population of absorbers is reported to have a mean dust content of only $E(B-V)\simeq0.02\,-\,0.03\,\mathrm{mag}$ \citep{2006MNRAS.367..211W,2006MNRAS.367..945Y}, which implies only small alterations to the shape of the SEDs of background quasars."736 Pherefore. care must be taken to construct a quasar ‘control’ spectrum. which represents accurately the spectrum of an unabsorbecl quasar.," Therefore, care must be taken to construct a quasar `control' spectrum, which represents accurately the spectrum of an unabsorbed quasar."737 Such a spectrum then enables us to isolate the effect of dust in an absorber on the background quasar spectrum., Such a spectrum then enables us to isolate the effect of dust in an absorber on the background quasar spectrum.738 We have adopted. an approach similar to ? ane 7.. which involves using the two-dimensional. recshilt. versus magnitude. m;. plane to identify a sample of quasars from which to construct a control spectrum.," We have adopted an approach similar to \citet{2005MNRAS.361L..30W} and \citet{2006MNRAS.367..945Y}, which involves using the two-dimensional redshift, $z$, versus magnitude, $m_i$, plane to identify a sample of quasars from which to construct a control spectrum."739" Lhe use of ""neighbour! quasars with similar redshifts in the contro sample ensures that the wavelength coverage of contro quasars is nearly identical to that of the target) quasar. while also ensuring that the control sample quasars do no"," The use of `neighbour' quasars with similar redshifts in the control sample ensures that the wavelength coverage of control quasars is nearly identical to that of the target quasar, while also ensuring that the control sample quasars do not"740Adopting au analytic form for this rate. the drag force follows.,"Adopting an analytic form for this rate, the drag force follows."741 This force first rises with V. and then falls. remaining finite at all Mach numbers.," This force first rises with $V$ and then falls, remaining finite at all Mach numbers."742 Moreover. there is a coutribution from the direct accretion of [Iuid momentum onto the body.," Moreover, there is a contribution from the direct accretion of fluid momentum onto the body."743 This coutribution is abseut in the stellar dyuaimical problem. but is here comparable to the gravitational tug from the wake.," This contribution is absent in the stellar dynamical problem, but is here comparable to the gravitational tug from the wake."744 Iu Section 2 below. we introduce a perturbative series expausion to analyze the far-Held density aud velocity.," In Section \ref{sec:method} below, we introduce a perturbative series expansion to analyze the far-field density and velocity."745 In Section 3.. we use this expausion to derive a hierarchy of dyuamical equatious. of which we ueed ouly solve the first two sets.," In Section \ref{sec:outer}, we use this expansion to derive a hierarchy of dynamical equations, of which we need only solve the first two sets."746 Section L shows how tlie mass accretion rate Is counectec to solutions of our seconcd-order equatious., Section \ref{sec:mass} shows how the mass accretion rate is connected to solutions of our second-order equations.747 Lu Section 5.. we similarly relate the friction force to these solutions. aud derive the central connection between this force aud the accretion rate.," In Section \ref{sec:friction}, we similarly relate the friction force to these solutions, and derive the central connection between this force and the accretion rate."748 Using a moclified version of the Boucli interpolation formula for the latter. we fiud explicitly the deceleration of an isolated. mass in Section 6..," Using a modified version of the Bondi interpolation formula for the latter, we find explicitly the deceleration of an isolated mass in Section \ref{sec:velocity}."749 Finally. Section 7 compares our result with existing numerical simulations and suggestsMOD future avenues of inquiry.," Finally, Section \ref{sec:summary} compares our result with existing numerical simulations and suggests future avenues of inquiry."750 Let the gravitating mass AZ travel in a straight line with speed V. through the extended gas cloud., Let the gravitating mass $M$ travel in a straight line with speed $V$ through the extended gas cloud.751 Following previous analytic studies of dsyuaimieal [rietion. we assume the gas to be isothermal. with an associated sound speed cy.," Following previous analytic studies of dynamical friction, we assume the gas to be isothermal, with an associated sound speed $c_s$."752 Very [ar (rom the mass. the density is spatially uniform aud has the value py.," Very far from the mass, the density is spatially uniform and has the value $\rho_0$."753 We choose a reference frame whose origin is auchored ou the perturbing mass., We choose a reference frame whose origin is anchored on the perturbing mass.754 In this frame. it is the gas that has speed V. [ar [rom the mass.," In this frame, it is the gas that has speed $V$ far from the mass."755 We let the gas velocity be directed along the c-axis. aud employ spherical coordinates r aud 0 (see Fig. 1)).," We let the gas velocity be directed along the $z$ -axis, and employ spherical coordinates $r$ and $\theta$ (see Fig. \ref{fig:coord}) )."756 We now seek a steady-state. axisymauetric solution for the flow. which is takeu to be inviscid.," We now seek a steady-state, axisymmetric solution for the flow, which is taken to be inviscid."757 We neglect the sell-gravity ol the eas. alid assume that each fluid elemeut feels only. a pressure gradient and the gravitational pull of the potut mass.," We neglect the self-gravity of the gas, and assume that each fluid element feels only a pressure gradient and the gravitational pull of the point mass."758 Strictly speakiug. there is no steady flow. as this mass clecelerates and Vo continually changes ίοιο..Fathi2010).," Strictly speaking, there is no steady flow, as this mass decelerates and $V$ continually changes \citep[e.g.,][]{f10}."759. What. then. is the meaning of the force we are calculating?," What, then, is the meaning of the force we are calculating?"760 Lnagine the object being draggedMD by a massless string through the gas at the fixed speed V., Imagine the object being dragged by a massless string through the gas at the fixed speed $V$.761 After a long time. a steady-state flow 1s indeed. established throughout the surrounding gas. aud the tensiou iu the string[n] approaches a constant value.," After a long time, a steady-state flow is indeed established throughout the surrounding gas, and the tension in the string approaches a constant value."762 This limiting tension is the dyuaiical friction force beiug calculated here., This limiting tension is the dynamical friction force being calculated here.763 Return now to the actual case. in which there is no string and the mass clecelerates.," Return now to the actual case, in which there is no string and the mass decelerates."764 As stated previously. there is no global. steady-state flow.," As stated previously, there is no global, steady-state flow."765 The flow is quasi-steady. liowever. within soie distauce over which the altered. motion of the mass is communicated by sound waves.," The flow is quasi-steady, however, within some distance over which the altered motion of the mass is communicated by sound waves."766 We shall quautifv this distauce later. after we have established the flow assuming steady-state coucitious.," We shall quantify this distance later, after we have established the flow assuming steady-state conditions."767 One important property of the flow is that it is irrotational., One important property of the flow is that it is irrotational.768 Eulers equation in steady state, Euler's equation in steady state769and (17)) can be derived.,and \ref{eq:1.18}) ) can be derived.770" The main difference is that ος is replaced by 7,44, in the exponent of 7,. which is due to the fact that the main contribution to the inverse Compton flux now comes Irom electrons with =j."," The main difference is that $\gamma_{\rm c}$ is replaced by $\gamma_{\rm min}$ in the exponent of $\tau_{\rm o}$, which is due to the fact that the main contribution to the inverse Compton flux now comes from electrons with $\gamma =\gamma_{\rm min}$."771 These results also remain valid for the regime +.<4nin., These results also remain valid for the regime $\gamma_{\rm c} <\gamma_{\rm min}$.772" In order to relate the properties of the svuchrotron component to those of the inverse Compton component. the value of 544, needs to be determined sell-consistentlv."," In order to relate the properties of the synchrotron component to those of the inverse Compton component, the value of $\gamma_{\rm abs}$ needs to be determined self-consistently."773" Since the main parameter in the multiple inverse Compton scenario is το, in (his section attention is restricted (to the case when only the column density of electrons varies."," Since the main parameter in the multiple inverse Compton scenario is $\tau_{\rm o}$, in this section attention is restricted to the case when only the column density of electrons varies."774" When 5,>45. standard svinchrotron theory gives Coolinge affects the absorption properties for .<{ape 44. since the column clensitv of electrons with Lorentz [actor 544, varies as (5./245,) ."," When $\gamma_{\rm c} > \gamma_{\rm abs}$, standard synchrotron theory gives Cooling affects the absorption properties for $\gamma_{\rm c} < \gamma_{\rm abs}$ , since the column density of electrons with Lorentz factor $ \gamma_{\rm abs}$ varies as $\left(\gamma_{\rm c} / \gamma_{\rm abs}\right)^{\alpha}$ ."775" Hence. the expression for 544, in this case is obtained bv letting 7,—(οσοσαν) in equation (19)). which leads to The expression lor 5. to use in equation (20)) is that given either in equation (15)) forthe external photon case or equation (17)) for the S5C-case."," Hence, the expression for $\gamma_{\rm abs}$ in this case is obtained by letting $\tau_{\rm o} \rightarrow \tau_{\rm o} \left(\gamma_{\rm c} / \gamma_{\rm abs}\right)^{\alpha}$ in equation \ref{eq:2.1}) ), which leads to The expression for $\gamma_{\rm c}$ to use in equation \ref{eq:2.2}) ) is that given either in equation \ref{eq:1.16}) ) forthe external photon case or equation \ref{eq:1.18}) ) for the SSC-case."776 For external seed photons. this vields where equation (6)) has been used.," For external seed photons, this yields where equation \ref{eq:1.8}) ) has been used."777" As mentioned above. for a.<(p—1)/2 the expression for 544, 1s quite similar to the one for a>(p— 1)/2. except that , is replaced by 5,44."," As mentioned above, for $\alpha < (p-1)/2$ the expression for $\gamma_{\rm abs}$ is quite similar to the one for $\alpha > (p-1)/2$ , except that $\gamma_{\rm c}$ is replaced by $\gamma_{\rm min}$."778" In the SSC-case. the variation of 2, with 7, is considerably slower (han for external photons (οἱ."," In the SSC-case, the variation of $\gamma_{\rm c}$ with $\tau_{\rm o}$ is considerably slower than for external photons (cf."779 eqns. [15]], eqns. \ref{eq:1.16}] ]780 and |17]]) and. hence. the exponent in equation (21)) is correspondingly smaller.," and \ref{eq:1.18}] ]) and, hence, the exponent in equation \ref{eq:2.3}) ) is correspondingly smaller."781 llowever. the actual value of (he exponent is likely to be rather similar in the two cases. since the value of yis expected to be much larger in the 55C-case as compared to (he external photon case (e.g.. yeLOM for B.e Las compared to jy~10? for optical seed photons).," However, the actual value of the exponent is likely to be rather similar in the two cases, since the value of $y$is expected to be much larger in the SSC-case as compared to the external photon case (e.g., $y\sim 10^{14}$ for $B \sim 1$ as compared to $y\sim 10^{5}$ for optical seed photons)."782" With aeme€54,fab7107. it is likely that Iny>2n, independent of the originoO of the seedphotons."," With $\gamma_{\rm c} \lesssim \gamma_{\rm abs} \sim 10^2$, it is likely that $\ln y > 2\ln \gamma_{\rm c}$ independent of the origin of the seedphotons."783" The dependenceof 5,4; on 7, would then reverse as compared to the case >.27 545 instead of having a value of 54, Increasing with το. ilnow decreases."," The dependenceof $\gamma_{\rm abs}$ on $\tau_{\rm o}$ would then reverse as compared to the case $\gamma_{\rm c} > \gamma_{\rm abs}$ ; instead of having a value of $\gamma_{\rm abs}$ increasing with $\tau_{\rm o}$ , itnow decreases."784diffusion of protons (?)..,diffusion of protons \citep{Jedamzik01}.785" The effective diffusion coefficient of protons is then where στ is the Thomson cross-section and p,, the photon energy density."," The effective diffusion coefficient of protons is then where $\sigma_T$ is the Thomson cross-section and $\rho_\gamma$, the photon energy density."786" In the most general case, the computation of the annihilation rate is a difficult task (?).."," In the most general case, the computation of the annihilation rate is a difficult task \citep{Aly_rate1978}."787" However, with our simplified approach based on diffusion, the estimation of the annihilation rate is rather straightforward."," However, with our simplified approach based on diffusion, the estimation of the annihilation rate is rather straightforward."788 The annihilation rate is the number of annihilations per unit of time and surface., The annihilation rate is the number of annihilations per unit of time and surface.789" The quantity of matter (and antimatter) annihilated over a Hubble time is njLig, so that the annihilation rate is simply this quantity divided by the Hubble timefracnpLaigtg."," The quantity of matter (and antimatter) annihilated over a Hubble time is $n_bL_{\rm{diff}}$, so that the annihilation rate is simply this quantity divided by the Hubble time."790 This simple expression is found to be in good agreement with the one derived in ?.., This simple expression is found to be in good agreement with the one derived in \citet{Cohen1998}.791" For simplicity, and following previous studies of antimatter BBN (??), we made the hypothesis that hydrodynamic turbulence, which could be produced by energy release near the domain boundary, can be neglected."," For simplicity, and following previous studies of antimatter BBN \citep{Kurki00b, Rehm01}, we made the hypothesis that hydrodynamic turbulence, which could be produced by energy release near the domain boundary, can be neglected."792 The secondary production of light elements by He photodisintegration can occur in many scenarios and has been extensively discussed in the literature., The secondary production of light elements by $^4$ He photodisintegration can occur in many scenarios and has been extensively discussed in the literature.793" In the framework of standard cosmology, this mechanism is known to produce D and ?He nuclei (??).."," In the framework of standard cosmology, this mechanism is known to produce D and $^3$ He nuclei \citep{Ellis1992, Protheroe1995}."794" Proton-antiproton annihilations result in the production of neutral pions, which themselves decay to high-energy photons."," Proton-antiproton annihilations result in the production of neutral pions, which themselves decay to high-energy photons."795" Depending on the temperature of the background and their energy, these photons can create e*e~ pairs on CMB-photons."," Depending on the temperature of the background and their energy, these photons can create $e^+e^-$ pairs on CMB-photons."796 These newly created pairs can also interact with CMB photons and therefore lead to the creation of electromagnetic cascades (??).," These newly created pairs can also interact with CMB photons and therefore lead to the creation of electromagnetic cascades \citep{Ellis1992, Protheroe1995}."797" These cascades stop when the energy of a photon becomes lower than the pair creation threshold Epair=m2/Ey, where Εγ is the energy of a thermal photon."," These cascades stop when the energy of a photon becomes lower than the pair creation threshold $E_{\rm{pair}}=m_e^2/E_\gamma$, where $E_\gamma$ is the energy of a thermal photon."798" Owing to the high number of thermal photons, the threshold energy for pair creation is Ema,~m2/22T (?).."," Owing to the high number of thermal photons, the threshold energy for pair creation is $E_{max}\sim m^2_e/22T$ \citep{Ellis1992}. ."799" Photons with energy lower than Ej, but higher than E.~m2/80T also undergo elastic scattering on background photons (?)..", Photons with energy lower than $E_{\rm{max}}$ but higher than $E_c\sim m_e^2/80T$ also undergo elastic scattering on background photons \citep{Svensson1990}. .800" The resulting spectrum of cascaded photons can be parametrized by (??)right..,"," The resulting spectrum of cascaded photons can be parametrized by \citep{Ellis1992, Kurki00b}801.,"802" where A=3EQE/[7—(E./Emax)°] is a normalization constant, and £j is the total energy injected."," where $A= 3 E_0E_c^{-2}/ [7-(E_c/E_{\rm{max}})^3]$ is a normalization constant, and $E_0$ is the total energy injected."803" Photodisintegration reactions (He(y, p? H, *He(y,n)*He, and He(y,np)D) require photons with energies higher than the respective threshold energies QsHe(y,npyp=26.07MeV, OsHe—y,p3H=19.81MeV, and O'He(y,n?He=20.58MeV (?).."," Photodisintegration reactions $^4$ $\gamma,\rm{p})^3$ H, $^4$ $\gamma,$ $^3$ He, and $^4$ $\gamma,$ np)D) require photons with energies higher than the respective threshold energies $Q_{^4\rm{He}(\gamma, np)\rm{D}}=26.07 \;\rm{MeV}$, $Q_{^4\rm{He}(\gamma, p)^3\rm{H}}= 19.81\;\rm{MeV}$, and $Q_{^4\rm{He}(\gamma, n)^3\rm{He}}=20.58\;\rm{MeV}$ \citep{Cyburt03}."804" The existence of these threshold energies implies that photodisintegration is a late process, as it becomes efficient only when Eg4, becomes higher than one of the previous threshold values."," The existence of these threshold energies implies that photodisintegration is a late process, as it becomes efficient only when $E_{\rm{max}}$ becomes higher than one of the previous threshold values."805" This happens at a temperature Tp,~0.5keV.", This happens at a temperature $T_{\rm{ph}}\sim 0.5\;\rm{keV}$.806 High-energy photons responsible for He photodisintegration mainly interact with ambient electrons by means of Compton scattering or with ambient nuclei by means of the Bethe-Heitler process (?).., High-energy photons responsible for $^4$ He photodisintegration mainly interact with ambient electrons by means of Compton scattering or with ambient nuclei by means of the Bethe-Heitler process \citep{Jedamzik2006}.807" Taking this into account, the number of D nuclei produced per pp annihilation is given byheat where f(Ey)= nyopgu(Ey,l)+Πασβη(Εγ.2) K(Ey)neoxn(Ey), cpu is the Bethe-Heitler process cross-section, Oxy is the Compton scattering section in the Klein-Nishina regime (?),, and K(Ey)31-4/3[InQE,/m,)+1/2]! is the mean fractional energy loss ompton scattering (?).."," Taking this into account, the number of D nuclei produced per $p\bar{p}$ annihilation is given by, where $f(E_\gamma)=n_p\sigma_{BH}(\eg,1)+n_{\alpha}\sigma_{BH}(\eg,2)+k(\eg)n_e\sigma_{KN}(\eg)$ , $\sigma_{BH}$ is the Bethe-Heitler process cross-section, $\sigma_{KN}$ is the Compton scattering cross-section in the Klein-Nishina regime \citep{RL79}, and $k(E_\gamma)\approx 1-{4/3}{[\ln(2E_\gamma/m_e)+1/2]^{-1}}$ is the mean fractional energy loss by Compton scattering \citep{Protheroe1995}."808 A similar formula exists for ?He., A similar formula exists for $^3$ He.809 DbFigure 7 presents the results of this calculation., Figure \ref{photo_p} presents the results of this calculation.810" When photodisintegration is most effective (around T~ eV),the mean free path of high energy photons relative to these processes is longer than the diffusion length, implying that D and ?He nuclei produced byphotodisintegration will be able to survive and add to the overall light element"," When photodisintegration is most effective (around $T\sim 100\;\rm{eV}$ ),the mean free path of high energy photons relative to these processes is longer than the diffusion length, implying that D and $^3$ He nuclei produced byphotodisintegration will be able to survive and add to the overall light element"811"the observed EC (star)break energy . considered process proceeds within the Thomson regime for - The EC(star) radiation is determined by the jet parameters |vL,].upe. Vase. D and 9. as well as by properties of the host galaxy. (Lau. ete).","and the observed EC(star) break energy The considered process proceeds within the Thomson regime for The EC(star) radiation is determined by the jet parameters $[\nu L_{\nu}]_{syn,812 \, br}$ , $\nu_{syn, \, br}$ , $B$ and $\delta$, as well as by properties of the host galaxy $L_{star}$, etc)."813" For non-relativistic jets. typical Vowi0dl. νο< land Bo,e1l. the break energy. of the considered emission is Cesaride0vOL TeV. and the observed energy. flux is [/S,]quu),<LOI""Dy/sergenr."," For non-relativistic jets, typical $\nu_{syn, \,814 14} \sim 1$, $[\nu L_{\nu}]_{syn, \, 42} < 1$ and $B_{-4} \sim 1$, the break energy of the considered emission is $\varepsilon_{ec(star), \, br} \sim 0.1$ TeV, and the observed energy flux is $[\nu S_{\nu}]_{ec(star), \, br} <815 10^{-10} \, D_{10}^{-2} \, {\rm erg / s \, cm^2}$."816 llowever. this relatively strong radiation can be significantly decreased in the case of relativistic jet velocities and large jet inclinations to the line of sight due to both the INN and the Doppler effects (equations 30 ancl 28. respectively).," However, this relatively strong radiation can be significantly decreased in the case of relativistic jet velocities and large jet inclinations to the line of sight due to both the KN and the Doppler effects (equations 30 and 28, respectively)."817 The eventuall Doppler-hide results from the beamine pattern of the EC(star) emission. which contrary to the discussed before SSC and EC(bl) processes — is maximised for small jet. viewing angles (for a given [vyLy)synn one has [SpJenusseXxJE?~ὅτι equation 23).," The eventuall Doppler-hide results from the beaming pattern of the EC(star) emission, which – contrary to the discussed before SSC and EC(bl) processes – is maximised for small jet viewing angles (for a given $[\nu L_{\nu}]_{syn, \,818 br}$ one has $[\nu S_{\nu}]_{ec(star), \, br} \propto f_{+} \, \Gamma^2 \sim819 \delta^2$; equation 28)."820 Comptonisation of the galactic infrared enussion. as well as of the CAB racliation. is not expected (to suffer such a decrease connected with the INN regime.," Comptonisation of the galactic infrared emission, as well as of the CMB radiation, is not expected to suffer such a decrease connected with the KN regime."821 For example. the Thomson regime condition lor the EC(dust) process can be rewritten as τι«60;0T7.," For example, the Thomson regime condition for the EC(dust) process can be rewritten as $\nu_{syn, \, 14} < 60 \, B_{-4} \, \delta822 \, \Gamma^{-2}$."823" For the standard nonrelativistic jet parameters. one can therefore put an upper limit [pS,]uuu)<10.7Dyerg/sen? at τμ7.10 GeV. At even lower photon energies the EC(CAIB) emission dominates. proceeding well in the Thomson regime. with the maximum placed near ερ]~0.1 GeV. The observed flux of this radiation is relatively low. ομως10PDyeere/sem?."," For the standard nonrelativistic jet parameters, one can therefore put an upper limit $[\nu S_{\nu}]_{ec(dust), \, br} < 10^{-12} \,824 D_{10}^{-2} \, {\rm erg / s \, cm^2}$ at $\varepsilon_{ec(dust), \, br} \geq825 10$ GeV. At even lower photon energies the EC(CMB) emission dominates, proceeding well in the Thomson regime, with the maximum placed near $\varepsilon_{ec(CMB), \, br} \sim 0.1$ GeV. The observed flux of this radiation is relatively low, $[\nu S_{\nu}]_{ec(CMB), \, br} < 10^{-13} \,826 D_{10}^{-2} \, {\rm erg / s \, cm^2}$."827" Detection of (his emission from the FR I jets located further than a few Alpes (ue. further than Centaurus A) by future 5-ravy telescopes is therefore possible only if the jet Doppler factor is signilicaatlv larger than unity. and/or if κb,,."," Detection of this emission from the FR I jets located further than a few Mpcs (i.e. further than Centaurus A) by future $\gamma$ -ray telescopes is therefore possible only if the jet Doppler factor is significantly larger than unity, and/or if $B \ll B_{eq}$."828 On the other hand. large values of ὁ ave unlikely to occur in the FR I jets. allhough. as mentioned in section 2.1. (he optical ancl X-ray jets can constitute the exceptions from this picture.," On the other hand, large values of $\delta$ are unlikely to occur in the FR I jets, although, as mentioned in section 2.1, the optical and X-ray jets can constitute the exceptions from this picture."829 The resulüng inverse-Compton [fluxes and break energiesevaluated in(he previous section depend on several [ree parameters., The resulting inverse-Compton fluxes and break energiesevaluated inthe previous section depend on several free parameters.830 Because of relatively wide range of values covered, Because of relatively wide range of values covered831significant number of timesteps.,significant number of timesteps.832 Under such circumstances. the lower opacity along the short axis means that photons preferentially dilfuse in that direction. making the energy density on an 2:1 ellipsoidal surface peak at the points of intersection with the short axis.," Under such circumstances, the lower opacity along the short axis means that photons preferentially diffuse in that direction, making the energy density on an 2:1 ellipsoidal surface peak at the points of intersection with the short axis."833 At earlier times. this ellect is enhanced by the time-dependent nature of the calculations: fewer packets manage to reach outer ellipsoidal shells than would. be predicted. in a quasicstatic description. because they have hac insullicient time to cilfuse far enough.," At earlier times, this effect is enhanced by the time-dependent nature of the calculations; fewer packets manage to reach outer ellipsoidal shells than would be predicted in a quasi-static description because they have had insufficient time to diffuse far enough."834 The difference in diffusion time means that this alfects the energy clensity along the long axis more significantly than along the short axis and thus acts to enhance the effect expected from the quasi-static case., The difference in diffusion time means that this affects the energy density along the long axis more significantly than along the short axis and thus acts to enhance the effect expected from the quasi-static case.835 As time passes. the shapes of the contours of radiation energy density evolve slightly and the outward decline becomes somewhat less steep (this can be seen by comparing the /—12 days and {~40 days results in Figure 5).," As time passes, the shapes of the contours of radiation energy density evolve slightly and the outward decline becomes somewhat less steep (this can be seen by comparing the $t \sim 12$ days and $t \sim 40$ days results in Figure 5)."836 However. throughout the time range considered here. a departure from 2:1 ellipticity remains.," However, throughout the time range considered here, a departure from 2:1 ellipticity remains."837 Since both the effects described above are the result of angular variations in the optical depth to 2:1 ellipsoidal surfaces. both persist while the ejecta remains optically thick.," Since both the effects described above are the result of angular variations in the optical depth to 2:1 ellipsoidal surfaces, both persist while the ejecta remains optically thick."838 They slowly decrease in strength. during the decay phase as expansion causes the optical depths to drop: at very late times the entire ejecta will become optically thin to radiation such that the light curve will become independent of viewing angle., They slowly decrease in strength during the decay phase as expansion causes the optical depths to drop; at very late times the entire ejecta will become optically thin to radiation such that the light curve will become independent of viewing angle.839 For the mocel adopted here. however. this nebular phase will not. begin. until several hundred days later than the times considered. here.," For the model adopted here, however, this nebular phase will not begin until several hundred days later than the times considered here."840 The viewing-angle dependeney of the light curves computed. from these simple. models. may have some interesting ramifications for understanding the observed properties of SNla light curves., The viewing-angle dependency of the light curves computed from these simple models may have some interesting ramifications for understanding the observed properties of SNIa light curves.841 As pointed out by Wang et al. (, As pointed out by Wang et al. (8422003) in the context of SN2001eL. directional dependence of the luminosity as predicted: for. elliptical models. of supernovae would lead. to dispersion in the observed. peak magnitudes (based on the earlier work by Lolllich 1991 and their implied asphericity of =10 per cent for SN2001eL. they speculate that this dispersion. would. be around 0.1 mag).,"2003) in the context of SN2001el, directional dependence of the luminosity as predicted for elliptical models of supernovae would lead to dispersion in the observed peak magnitudes (based on the earlier work by Höfflich 1991 and their implied asphericity of $\approx 10$ per cent for SN2001el, they speculate that this dispersion would be around 0.1 mag)."843 The results. obtained. here support this argument ancl indicate that if the degree of asphericity were larger in some cases (ee. SN 1999by: Lowell et al., The results obtained here support this argument and indicate that if the degree of asphericity were larger in some cases (e.g. SN 1999by; Howell et al.844 2001) the spread in the rcs magnitude could be greater. zz0.4 mag.," 2001) the spread in the peak magnitude could be greater, $\approx 0.4$ mag."845 Furthermore. the full light. curves. computed: here allow this dispersion. relative to the known relationship o*ween light curve shape ancl peak luminosity {ο be examined.," Furthermore, the full light curves computed here allow this dispersion relative to the known relationship between light curve shape and peak luminosity to be examined."846" ""This trend. the so-called 7Phillips. relation"" ollowing Phillips (1993). expresses the negative correlation xtween peak brightness and the AZ,;-parameter measured rom observed light curves of SNla."," This trend, the so-called “Phillips relation” following Phillips (1993), expresses the negative correlation between peak brightness and the $\Delta M_{15}$ -parameter measured from observed light curves of SNIa."847 For both the models considered. here. the variation of AAJ); with viewing angle is in the opposite sense to the standard. relationship.," For both the models considered here, the variation of $\Delta M_{15}$ with viewing angle is in the opposite sense to the standard relationship."848 This is illustrated. in Figure 6 where the six light curves shown in Figures 3 and 4 are represented as points in the NM; Myo plane., This is illustrated in Figure 6 where the six light curves shown in Figures 3 and 4 are represented as points in the $\Delta M_{15}$ $M_{\mbox{\scriptsize peak}}$ plane.849 The gradient of the standard Phillips relation (describing the mean observed. relationship between AALL- and. Mosa) in the B-bancd is plotted for comparison in the Figure., The gradient of the standard Phillips relation (describing the mean observed relationship between $\Delta M_{15}$ and $M_{\mbox{\scriptsize peak}}$ ) in the B-band is plotted for comparison in the Figure.850 This effect would Iead to a detectable scatter about the Phillips relation and thus may have a major role to play in understanding the diversity. of supernova observations: the results plotted in Figure 6 would suggest that if SNla explosions were moderately elliptical (such that the mocel with axis ration of 5:4 were approximately applicable). viewing angle effects could explain a scatter of several tenths of a magnitude about the mean relationship.," This effect would lead to a detectable scatter about the Phillips relation and thus may have a major role to play in understanding the diversity of supernova observations: the results plotted in Figure 6 would suggest that if SNIa explosions were moderately elliptical (such that the model with axis ration of 5:4 were approximately applicable), viewing angle effects could explain a scatter of several tenths of a magnitude about the mean relationship."851 Significant caution must be applied in interpreting this result since the erev-treatment adopted: here. does not. allow bauxd-limited light curves to be studied. for direct. comparison with observations — quantitative differences may occur if 10 frequency-depencence of the opacity were taken into recount., Significant caution must be applied in interpreting this result since the grey-treatment adopted here does not allow band-limited light curves to be studied for direct comparison with observations – quantitative differences may occur if the frequency-dependence of the opacity were taken into account.852 Furthermore. the models used here have predicted i1 angular variation of the radiation energv density and ius. by implication. the temperature of the ejecta.," Furthermore, the models used here have predicted an angular variation of the radiation energy density and thus, by implication, the temperature of the ejecta."853 Such C variation further contradiets the used ofa uniform opacity uxi highlights the need for the consideration. of more etailed: micro-phiysies., Such a variation further contradicts the used of a uniform opacity and highlights the need for the consideration of more detailed micro-physics.854" Also. the particularly simple mocel chosen (uniform density with centrally concentrated. ""Ni ancl time-independent mean opacity) produces significantly smaller absolute values of M5; than are typically observed thus further work using more realistic models of aspherical supernovae are needed."," Also, the particularly simple model chosen (uniform density with centrally concentrated $^{56}$ Ni and time-independent mean opacity) produces significantly smaller absolute values of $\Delta M_{15}$ than are typically observed – thus further work using more realistic models of aspherical supernovae are needed."855 Alodern SNla explosion models. predict. complex. threc-dimensional sub-structure (e.g. Reinecke et al.," Modern SNIa explosion models predict complex, three-dimensional sub-structure (e.g. Reinecke et al."856 2002: Ganiezo et al., 2002; Gamezo et al.857 2003: Bóppke 2005: Roppke et al., 2003; Röppke 2005; Röppke et al.858 2006) within the explosion., 2006) within the explosion.859 In contrast. most. models used to compute light curves for comparison with observation have a smooth. one-dimensional density-/composition-profile.," In contrast, most models used to compute light curves for comparison with observation have a smooth, one-dimensional density-/composition-profile."860 In this section. the elfect of the predicted inhomogenelty on model light curves will be investigated.," In this section, the effect of the predicted inhomogeneity on model light curves will be investigated."861 In. principle. there are two classes of cllect which are of interest. here:," In principle, there are two classes of effect which are of interest here:"862To examine the Fe line powers we fitted a spectral model made up of an absorbed powerlaw plus Gaussians. fitted to the first order spectra between [4 and18.5À extracted from 99 per cent of the PSF.,"To examine the Fe line powers we fitted a spectral model made up of an absorbed powerlaw plus Gaussians, fitted to the first order spectra between 14 and extracted from 99 per cent of the PSF."863 We used a Gaussian for each of the distinct Fe lines (Table 3). two Gaussians at 16.07 and for Fe and Οvill. and Fe Gaussians at and17.," We used a Gaussian for each of the distinct Fe lines (Table \ref{tab:mdotlines}) ), two Gaussians at 16.07 and for Fe and O, and Fe Gaussians at and."86462À. The strong lines at 15.01. 16.00. 16.07. and 17.06 were allowed to have variable widths.," The strong lines at 15.01, 16.00, 16.07, and 17.06 were allowed to have variable widths."865 The other lines were fixed at zero width., The other lines were fixed at zero width.866 Galactic absorption was fixed at 8.56x10em2. Table 3. shows the best fitting widths and de-absorbed line luminosities., Galactic absorption was fixed at $8.56 \times 10^{20}\psqcm$ Table \ref{tab:mdotlines} shows the best fitting widths and de-absorbed line luminosities.867 Fig., Fig.868 13. shows the data with best fitting model., \ref{fig:xvii_spec} shows the data with best fitting model.869 The line powers would be increased if there were any internal absorption within the cluster (as suggested by ? and ο)., The line powers would be increased if there were any internal absorption within the cluster (as suggested by \citealt{Crawford05} and \citealt{SandersReson06}) ).870 We convert hese powers into mass deposition rate by comparing them against the expected flux from a cooling flow model., We convert these powers into mass deposition rate by comparing them against the expected flux from a cooling flow model.871 This was done by firstly simulating a high signal-to-noise spectrum using a LOM.ye| model. cooling between 4.5 and 0.0808. keV. with Solar abundance. absorbed with Galactic absorption.," This was done by firstly simulating a high signal-to-noise spectrum using a $10\Msunpyr$ model, cooling between 4.5 and 0.0808 keV, with Solar abundance, absorbed with Galactic absorption."872 We then measured the fluxes in the simulated lines by fitting the same absorbed powerlaw plus Gaussian model as we did to the data., We then measured the fluxes in the simulated lines by fitting the same absorbed powerlaw plus Gaussian model as we did to the data.873 The ratio of the line flux in the data compared to the simultated model was used to obtain a mass deposition rate., The ratio of the line flux in the data compared to the simultated model was used to obtain a mass deposition rate.874 Note that the assumed relative abundance can make a substantial difference to these values., Note that the assumed relative abundance can make a substantial difference to these values.875 The mass deposition rates obtained for three of the lines agree at 1.6M.yr|. but the blended line is substantially stronger than the others.," The mass deposition rates obtained for three of the lines agree at $\sim 1.6 \Msunpyr$, but the blended line is substantially stronger than the others."876 The model predicts that the line should be more powerful than the17.06À blended line over a wide range of temperatures., The model predicts that the line should be more powerful than the blended line over a wide range of temperatures.877 However in our data the lines are 56 per cent brighter than the15.01 line., However in our data the lines are 56 per cent brighter than the line.878 A possible cause for this is resonant scattering. as the transition is resonant with a large oscillator strength.," A possible cause for this is resonant scattering, as the transition is resonant with a large oscillator strength."879 If this were the case the scattered radiation would have to be absorbed. as scattering only increases the spectral width of the line. redistributing the fiux.," If this were the case the scattered radiation would have to be absorbed, as scattering only increases the spectral width of the line, redistributing the flux."880 However. a likely reason for the discrepancy in brightness may be due to uncertainties in spectral models.," However, a likely reason for the discrepancy in brightness may be due to uncertainties in spectral models."881 We plot in Fig., We plot in Fig.882 |4 the predicted ratio of the 15.0 to bended lines versus the temperature for some different plasma codes. includingAPEC.. (moditied results using a many-body perturbation theory method to calculate new values for the emissivities of Fe and Ni L-shell lines: 3). (the latest results from the package: ?)) and (22). ," \ref{fig:xvii_ratio} the predicted ratio of the 15.0 to blended lines versus the temperature for some different plasma codes, including, (modified results using a many-body perturbation theory method to calculate new values for the emissivities of Fe and Ni L-shell lines; \citealt{Gu07}) ), (the latest results from the package; \citealt{Kaastra00}) ) and \citep{Dere97,Landi06}. ."883It appears cannot reproduce the observed line ratio (as found by 1)., It appears cannot reproduce the observed line ratio (as found by \citealt{Xu02}) ).884 The other plasma codes are able to and agree fairly well., The other plasma codes are able to and agree fairly well.885 The line ratio appears to indicate that the Fe line emission comes from an average temperature of 0.25nokeV., The line ratio appears to indicate that the Fe line emission comes from an average temperature of $0.25^{+0.20}_{-0.09} \keV$.886 Note that although appears to fit the data worse here. its quality of fit to the total spectra is at least Ax~300 better than the model overall.," Note that although appears to fit the data worse here, its quality of fit to the total spectra is at least $\Delta \chi^2 \sim 300$ better than the model overall."887 The Fe17.06À line width of translates into a HEW of 36 arcsec (including the effect of the mirrors)., The Fe line width of translates into a HEW of 36 arcsec (including the effect of the mirrors).888 This is larger than the width of the emission line in the cross-dispersion direction (Fig. 5::, This is larger than the width of the emission line in the cross-dispersion direction (Fig. \ref{fig:lineprof_fe};889 compatible with the PSF)., compatible with the PSF).890 The longer observation analysed here has the cross-dispersion direction placed along the plume., The longer observation analysed here has the cross-dispersion direction placed along the plume.891 The difference in source extent between the line widths and eross-dispersion profiles may be due to the very coolest gas being extended in the direction perpendicular to the dispersion direction (Fig. 11:: 29)., The difference in source extent between the line widths and cross-dispersion profiles may be due to the very coolest gas being extended in the direction perpendicular to the cross-dispersion direction (Fig. \ref{fig:sizemaps}; \citealt{Crawford05}) ).892 If a cooling flow model plus powerlaw continuum is fit to this region of the spectra containing the Fe lines. the best fitting mass deposition rate is 1.90.0.13M.yr.! .This is for a cooling flow at Solar abundance coolingfrom 4.5 to 0.0808 KeV.," If a cooling flow model plus powerlaw continuum is fit to this region of the spectra containing the Fe lines, the best fitting mass deposition rate is $1.90 \pm 0.13 \Msunpyr$ .This is for a cooling flow at Solar abundance coolingfrom 4.5 to 0.0808 keV."893lime-averaged Lorentz actor iu tlie jes. While leaving oher quantities essentially uuchauged: iu eeneral terius. the magjetic field geneated by the MRI is the inain d‘iver of the accretion flow and hence he jets. wluch are Led by uagnuetized [uid injected. at. theiY base from the accretion flow.,"time-averaged Lorentz factor in the jets, while leaving other quantities essentially unchanged; in general terms, the magnetic field generated by the MRI is the main driver of the accretion flow and hence the jets, which are fed by magnetized fluid injected at their base from the accretion flow."894" The time- averaged distribtion «cX Lorentz factor shows :| spin-depeuclent collimatiorof the ultra-relatis""jstic jet iuaerial: iu the hiο siunulatios. the jets seeu to become cyliudrically collimated or r/M& οίο (130 kLL scaed to collapsar cijenslons)."," The time- averaged distribution of Lorentz factor shows a spin-dependent collimation of the ultra-relativistic jet material; in the high-spin simulations, the jets seem to become cylindrically collimated for $r/M \gtrsim$ 300 (130 km scaled to collapsar dimensions)."895 Based Ol OUL slitalious. the action of the inner eeine in the cai0nical collapsar inodel of W93 cat [9]=ly power GRBs at tlie low eud of the distribution of long-duration bursts.," Based on our simulations, the action of the inner engine in the canonical collapsar model of W93 can only power GRBs at the low end of the distribution of long-duration bursts."896 However. the collapsa: model also euvisages [eecling he accretion cdisk over time froi1 the outer layer o ‘a star.," However, the collapsar model also envisages feeding the accretion disk over time from the outer layer of a Wolf-Rayet star."897 Qur results show that sucl a process would be cisrupted following the establishuuentlis of the sroug coronal winds (which cai easily clisplac‘ea considerable amount of infalline dust)., Our results show that such a process would be disrupted following the establishment of the strong coronal winds (which can easily displace a considerable amount of infalling dust).898 Asstt& that some remnant material does manage [9] 1ake its way o the main accretio disk. hen the lifetime and total energy of the inner engine coild be plausibly exteuded.," Assuming that some remnant material does manage to make its way to the main accretion disk, then the lifetime and total energy of the inner engine could be plausibly extended."899 Howeve‘this incline ¢oes not necessarily argue against tle collapsar moclel iu explaing extreme cluratio[un πο.» as discussed by Toma et al. (," However, this finding does not necessarily argue against the collapsar model in explaining extreme duration bursts; as discussed by Toma et al. ("9002005). the GRBs at the uppe end of thec istribution for loug-di'allon dusts can be explained as statistical outliers related to οbservational ellects.,"2005), the GRBs at the upper end of the distribution for long-duration bursts can be explained as statistical outliers related to observational effects."901 ]t is importan to emghasize that these simulations obe ouly tie clynaimics of the coapsar nodel in a fixed hb:ickerouud spacetime., It is important to emphasize that these simulations probe only the dynamics of the collapsar model in a fixed background spacetime.902 More sophisticated treatimens should ideally. incorj)0rate a dyainical black tole spacetime (especially if more massive accretion disks are to be iodeed) as well as self} consistent calclations of radiative trausport., More sophisticated treatments should ideally incorporate a dynamical black hole spacetime (especially if more massive accretion disks are to be modeled) as well as self- consistent calculations of radiative transport.903 Such a code is not vet available: however. it is |oped that sot1ο rogfess cau be made at extracting observables (rom the fluxes reported here by ¢upline the CIRMHD code to a ray tracer and a suitable emission model. which will provide a Ino'e complete piοτιre o ‘the time-clepencent siguals received by cdistaut observers.," Such a code is not yet available; however, it is hoped that some progress can be made at extracting observables from the fluxes reported here by coupling the GRMHD code to a ray tracer and a suitable emission model, which will provide a more complete picture of the time-dependent signals received by distant observers."904 This work is currently uuderway. aid should be reported iu the near future.," This work is currently underway, and should be reported in the near future."905" The GRAMHD coce. clescribed in detail in DHO3. is used to study the dynamical properties of a maguetized fluid iu the background spacetime of a Ixerr black hole by numerically solving the equation [9] continuity. V,(pU)=0. the energy-momentum Conservation law. Vj,T/"" 0. aud the Maxwell's equations. V,RM=Lied” and VTFP""Q0. which. in the MHD approximation. reduce to the ineuction equation OyFy3+0,Fay04F5,=0."," The GRMHD code, described in detail in DH03, is used to study the dynamical properties of a magnetized fluid in the background spacetime of a Kerr black hole by numerically solving the equation of continuity, $\nabla_\mu \left(\rho\,U^\mu\right)=0$, the energy-momentum conservation law, $\nabla_\mu\,T^{\mu \nu} = 0$ , and the Maxwell's equations, $\nabla_\mu F^{\mu \nu} = 4\,\pi\,J^\nu$ and $\nabla_\mu {}^*F^{\mu \nu} = 0$, which, in the MHD approximation, reduce to the induction equation $\partial_\delta\,F_{\alpha \beta} + 906\partial_\alpha\,F_{\beta \delta} + 907\partial_\beta\,F_{\delta \alpha} = 0$."908 The GRMHD code evolves a set of primitive aud secolidary code va‘tables directly: tlese variables were close1 to correspoud directly. or through simple reatious. to plivsical variabes (e.g. magueic field. gas cdensity. velocity).," The GRMHD code evolves a set of primitive and secondary code variables directly; these variables were chosen to correspond directly, or through simple relations, to physical variables (e.g. magnetic field, gas density, velocity)."909 This avoids costly calculaticMIS 1ο extirac physical. variabes from teusor quantities., This avoids costly calculations to extract physical variables from tensor quantities.910" In the above expressions. p is the censiv. UP the Lyelocity. 77 heeuergy-nolientunm tenso and £34 the electromagnetic field ""reneth ensor."," In the above expressions, $\rho$ is the density, $U^\mu$ the 4-velocity, $T^{\mu \nu}$ the energy-momentum tensor, and $F_{\alpha \beta}$ the electromagnetic field strength tensor."911" The eiergy moruenun ensor 1s gi venby T""=(onsiP)UP""U""4(P|ae7gh!—bfv Wwvere //—1L+e4+P/p is the specilic enthalpy. witl e the specific internal energy aud P=pe(V—1) the ideal gas pressure (E is the aciabaic expone1): [lo]=0""b, is the magnetic fieldintensity: and bfΕςla) is the magtetic field [-vector."," The energy momentum tensor is given by $T^{\mu \nu} = \left[ \left(\rho\,h+{\|b\|}^2\right)\,U^\mu\,U^\nu + 912\left(P+{{\|b\|}^2 \over 2}\right)\,g^{\mu \nu} - b^\mu\,b^\nu\right]$ where $h=1 + \epsilon + P/\rho$ is the specific enthalpy, with $\epsilon$ the specific internal energy and $P=\rho\,\epsilon\,(\Gamma-1)$ the ideal gas pressure $\Gamma$ is the adiabatic exponent); ${\|b\|}^2=b^\mu\,b_\mu$ is the magnetic fieldintensity; and $b^\mu = {}^*F^{\mu \nu}\,U_\nu/(4\,\pi)$ is the magnetic field 4-vector."913 The iuduction equation is rewritten iu terms, The induction equation is rewritten in terms914the Large Magellanic Cloud.,the Large Magellanic Cloud.915relationship iu the Local Ciroup may be irrelevant for the cluster deusity-morphology relatiouship.,relationship in the Local Group may be irrelevant for the cluster density–morphology relationship.916 A more comprehensive study of kinematics in dE galaxies in both environments is warranted., A more comprehensive study of kinematics in dE galaxies in both environments is warranted.917 Based ou the data in liaud. however. it is clear that enviroumental pathways for dl to dE conversiou must be considered: if further observations support the (οι indicated in Figure 5.. relevant theories for the formation aud evolution of dwarf galaxies must. include euviroumenutal factors as well as internal processes.," Based on the data in hand, however, it is clear that environmental pathways for dI to dE conversion must be considered; if further observations support the trend indicated in Figure \ref{fig:cluster}, relevant theories for the formation and evolution of dwarf galaxies must include environmental factors as well as internal processes."918 We present long-slit optical spectroscopy along the major axis of 16 dwarf elliptical galaxies in the Virgo Cluster., We present long-slit optical spectroscopy along the major axis of 16 dwarf elliptical galaxies in the Virgo Cluster.919 The major results of these observations are as follows: (1) Approximately half of the Virgo dE sample has a siguilicaut rotation Component. with rotation curve slopes > 20 5l (," The major results of these observations are as follows: (1) Approximately half of the Virgo dE sample has a significant rotation component, with rotation curve slopes $>$ 20 $^{-1}$. ("9202) Five of the 11 galaxies with measured velocity dispersions have anisotropy paraiieters (v/om)* > 1l.,"2) Five of the 14 galaxies with measured velocity dispersions have anisotropy parameters $\sigma_m$ )* $>$ 1.,"921 indicating significant rotational flattening., indicating significant rotational flattening.922" Ouly one of the remaining 9 dEs has (v/o,,)* « 0.3.", Only one of the remaining 9 dEs has $\sigma_m$ )* $<$ 0.3.923 The remainder have modest auisotropy parameters. indicating that rotational lattening may be signilicaut lor the majority ofdwarf elliptical galaxies in this sample. (," The remainder have modest anisotropy parameters, indicating that rotational flattening may be significant for the majority of dwarf elliptical galaxies in this sample. ("9243) Based ou the observed maximum rotation velocities. the rotating dwarf galaxies appear to ollow the Tulls-Fisher relatiou for gas-rich dwarl aud spiral galaxies.,"3) Based on the observed maximum rotation velocities, the rotating dwarf galaxies appear to follow the Tully-Fisher relation for gas-rich dwarf and spiral galaxies."925 These kinematic results re-open the possibility that dwarf elliptical galaxies may be the eud srocducts of dwarl irregular galaxies that have lost their ISM via ram pressure stripping or other lon-Catastrophic processes., These kinematic results re-open the possibility that dwarf elliptical galaxies may be the end products of dwarf irregular galaxies that have lost their ISM via ram pressure stripping or other non-catastrophic processes.926 The morphological similarities between gas-ricli dwarf irregular galaxies aud gas-poor dwarf elliptical galaxies appear to extend beyond the stellar distributions aud metal eurichuient: many gas-rich and eas-poor dwarf galaxies have common dyuaiical properties. as would be expected for passive evolution moclels.," The morphological similarities between gas-rich dwarf irregular galaxies and gas-poor dwarf elliptical galaxies appear to extend beyond the stellar distributions and metal enrichment; many gas-rich and gas-poor dwarf galaxies have common dynamical properties, as would be expected for passive evolution models."927 We dedicate this paper in memory of BBev Oke. whose spectrograplis have enabled a plethora oL scieuce lor mauy decades aud whose dedication aud kinduess encouraged several generations of scieutists to use tliose spectrographis well.," We dedicate this paper in memory of Bev Oke, whose spectrographs have enabled a plethora of science for many decades and whose dedication and kindness encouraged several generations of scientists to use those spectrographs well."928 LvZ thanks Elizabeth Barton for many thought-provokiug conversations about galaxy formation and evolutiou., LvZ thanks Elizabeth Barton for many thought-provoking conversations about galaxy formation and evolution.929 This research las mace use ofthe NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. Califoruia lustitute of Technology. under contract with the National Aeronautics and Space Administration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."930 LvZ acknowledges partial support [rom the Herzberg LIustitute of Astrophysics aud the National Research Council of Canada: LvZ also acknowledges partial support from Iudiaua University., LvZ acknowledges partial support from the Herzberg Institute of Astrophysics and the National Research Council of Canada; LvZ also acknowledges partial support from Indiana University.931 EDS is erateftl for partial support Grom a NASA LTSARP eraut No., EDS is grateful for partial support from a NASA LTSARP grant No.932 NAG5-9221 aud the University of Alinnesota., NAG5-9221 and the University of Minnesota.933 MPH has been supported by NSF erants AST-9900695 and AST-0307396., MPH has been supported by NSF grants AST-9900695 and AST-0307396.934"with <50 C atoms are quickly destroyed under typical interstellar conditions (Allainetal.1996a,b;LePageetal.2003) while large PAHs persist longer under the same ISM conditions.","with $\lesssim50$ C atoms are quickly destroyed under typical interstellar conditions \citep{allain96a,allain96b,lepage03} while large PAHs persist longer under the same ISM conditions."935" Similar trends hold true for processing by shocks, cosmic rays and hot gas (Micelottaetal.2010b,a, 2011)."," Similar trends hold true for processing by shocks, cosmic rays and hot gas \citep{micelotta10a,micelotta10b,micelotta11}."936". Therefore, since small PAHs are destroyed more easily than larger PAHs in the ISM, explaining a deficit of large PAHs cannot be the effect of ISM processing unless the destruction process turns large PAHs into small PAHs as side-effect."," Therefore, since small PAHs are destroyed more easily than larger PAHs in the ISM, explaining a deficit of large PAHs cannot be the effect of ISM processing unless the destruction process turns large PAHs into small PAHs as a side-effect."937 Recent studies by Micelottaetal.(2010b)a suggest that this is not the case., Recent studies by \citet{micelotta10a} suggest that this is not the case.938 The dominant destruction mechanism for large PAHs is through interaction with supernova shocks and they find that “daughter” PAHs formed by the fragmentation of the larger grains are very quickly destroyed in the shocked gas., The dominant destruction mechanism for large PAHs is through interaction with supernova shocks and they find that “daughter” PAHs formed by the fragmentation of the larger grains are very quickly destroyed in the shocked gas.939" Thus, since small PAHs are destroyed more easily in all ISM processes and they are likely not replenished by the fragmentation of larger PAHs, explaining a deficit of large PAHs cannot be the effect of ISM processing."," Thus, since small PAHs are destroyed more easily in all ISM processes and they are likely not replenished by the fragmentation of larger PAHs, explaining a deficit of large PAHs cannot be the effect of ISM processing."940" We do, however, have ample evidence that processing in the ISM can affect the PAH size distribution in the sense of selectivelyremoving small PAHs."," We do, however, have ample evidence that processing in the ISM can affect the PAH size distribution in the sense of selectively small PAHs."941" In the vicinity of AGN, multiple studies have shown a decrease in the 6—9 ffeatures relative to the 11.3 aand longer wavelength features (Smithetal.2007b;etal."," In the vicinity of AGN, multiple studies have shown a decrease in the $-$ 9 features relative to the 11.3 and longer wavelength features \citep{smith07a,odowd09,diamond-stanic10,wu10}."942" Smithetal. also found that the 11.3/17.0 2010)..ratio decreases in the (2007b)presence of an AGN, suggesting a stronger contribution from the 17.0 ffeature—a tracer of larger PAHs."," \citet{smith07a} also found that the 11.3/17.0 ratio decreases in the presence of an AGN, suggesting a stronger contribution from the 17.0 feature—a tracer of larger PAHs."943" These trends suggest that the ISM conditions in the vicinity of the AGN have selectively removed the more fragile, smaller PAHs."," These trends suggest that the ISM conditions in the vicinity of the AGN have selectively removed the more fragile, smaller PAHs."944" An interesting counterpoint to our study of the SMC is that by Huntetal.(2010),, who presented a study of the PAH band ratios in a sample of blue compact dwarf galaxies (BCDs)."," An interesting counterpoint to our study of the SMC is that by \citet{hunt10}, who presented a study of the PAH band ratios in a sample of blue compact dwarf galaxies (BCDs)."945 These BCDs have particularly intense radiation fields as well as low metallicities and very low dust-to-gas ratios (hence decreased dust shielding)., These BCDs have particularly intense radiation fields as well as low metallicities and very low dust-to-gas ratios (hence decreased dust shielding).946" Huntetal.(2010) found that the band ratios in these galaxies suggested a size distribution shifted towards larger PAHs relative to the galaxies in the SINGS sample (with no AGN), particularly in the strength of the 8.6 ffeature and the low ratios of short-to-long wavelength bands."," \citet{hunt10}947 found that the band ratios in these galaxies suggested a size distribution shifted towards larger PAHs relative to the galaxies in the SINGS sample (with no AGN), particularly in the strength of the 8.6 feature and the low ratios of short-to-long wavelength bands."948" Because of the low metallicity of these galaxies, we might expect them to show a size distribution shifted towards smaller PAHs, as we have seen in the SMC."," Because of the low metallicity of these galaxies, we might expect them to show a size distribution shifted towards smaller PAHs, as we have seen in the SMC."949" It may be the case in these extreme objects that the radiation field is intense enough to remove small PAHs to such a degree that once again larger PAHs dominate the size distribution, regardless of the scarcity of large PAHs."," It may be the case in these extreme objects that the radiation field is intense enough to remove small PAHs to such a degree that once again larger PAHs dominate the size distribution, regardless of the scarcity of large PAHs."950" If this were the case, we would expect the abundance of PAHs relative to dust the PAH fraction) to be very low in the BCDs."," If this were the case, we would expect the abundance of PAHs relative to dust (i.e. the PAH fraction) to be very low in the BCDs."951" Indeed, (i.e.Huntetal.(2010) found that the ratio of PAH emission to the total infrared emission (SPAH/TIR), which should trace the PAH fraction, is depressed by more than an order of magnitude on average in these galaxies compared to the SINGS sample."," Indeed, \citet{hunt10} found that the ratio of PAH emission to the total infrared emission $\Sigma{\rm PAH}$ /TIR), which should trace the PAH fraction, is depressed by more than an order of magnitude on average in these galaxies compared to the SINGS sample."952" If processing in the ISM cannot produce the size distribution shifted towards smaller PAHs that we observe, the only other option is that PAHs are formed with smaller sizes in the SMC."," If processing in the ISM cannot produce the size distribution shifted towards smaller PAHs that we observe, the only other option is that PAHs are formed with smaller sizes in the SMC."953" Forming PAHs with smaller average sizes in low-metallicity galaxies could be the result of a change with metallicity in the dominant formation mechanisms (ie. AGB stars, coagulation or"," Forming PAHs with smaller average sizes in low-metallicity galaxies could be the result of a change with metallicity in the dominant formation mechanisms (i.e. AGB stars, coagulation or"954above ~5 keV. similar to the total fractional variability spectra of this and other NLSI1s (Vaughan&Fabian.2003).,"above $\sim 5$ keV, similar to the total fractional variability spectra of this and other NLS1s \citep{Vaughan766}."955. At high frequencies; however. the shape of the ezsaz is lilferent. as shown by the dashed line in Figs.," At high frequencies, however, the shape of the $\sigma^2_{\rm NXS}$ is different, as shown by the dashed line in Figs."956 1 and 2.., \ref{NXS_999_1003} and \ref{NXS_265}.957 The Η1 normalised excess variance shows a stronger dip at low energies while the high energy. dip is reduced or disappears completely. within the observational uncertainties.," The HF normalised excess variance shows a stronger dip at low energies while the high energy dip is reduced or disappears completely, within the observational uncertainties."958 Note that. for each case. the LE and HE sspectra have been normalised by the same time-averaged enerey spectrum (i.e. total count rate per cnerey bin). so 1e clilference in shape of the LE and HE spectra reveal a time-scale dependence of the variable spectral component only.," Note that, for each case, the LF and HF spectra have been normalised by the same time-averaged energy spectrum (i.e. total count rate per energy bin), so the difference in shape of the LF and HF spectra reveal a time-scale dependence of the variable spectral component only."959 In the two-component interpretation of the main spectral variability. the energy. spectra contains two fixed-shape components which vary in amplitude.," In the two-component interpretation of the main spectral variability, the energy spectra contains two fixed-shape components which vary in amplitude."960 Lf the two components vary independently. the variance spectrum can be decomposed as where σον{ή} terms represent the rms spectra in a given frequeney range Af. and ας). terms are the time-averaged energy spectra of components | and 2.," If the two components vary independently, the variance spectrum can be decomposed as where $\sigma_{\rm rms,\Delta f}(E)$ terms represent the rms spectra in a given frequency range $\Delta f$, and $\bar x (E)$ terms are the time-averaged energy spectra of components 1 and 2."961 To produce rw curved shape of the variance spectra (in. Figs. 1..," To produce the curved shape of the variance spectra (in Figs. \ref{NXS_999_1003},"962 2 uxl BY). a constant. or less variable. component (1) must ominate the energy spectrum at low and high. energies. yerefore reducing essνι(10) at those energies. while the more variable component (2) usually assumed to be a power aw. might have a constant gusLCI)frie) throughout 1o energy range.," \ref{NXS_265} and \ref{NXS_999}) ), a constant, or less variable, component (1) must dominate the energy spectrum at low and high energies, therefore reducing $\sigma^2_{\rm NXS,\Delta f}(E)$ at those energies, while the more variable component (2) usually assumed to be a power law, might have a constant $\sigma _{\rm rms,\Delta f}(E)/\bar x _{1}(E)$ throughout the energy range."963" The observed hardening of the σεή.) μαvectra towards higher frequencies implies that one orνι both of the spectral components. 954,(CE) get Blatter at higher pequencies."," The observed hardening of the $\sigma^2_{\rm NXS,\Delta f}(E)$ spectra towards higher frequencies implies that one or both of the spectral components, $\sigma ^2_{\rm rms,\Delta f}(E)$ get flatter at higher frequencies."964" This can mean that either the variable power aw gets harder at higher frequencies. or that the hard part of ""constant"" component appears constant on long time-scales rut contributes significantly to the variance on shorter time-scales."," This can mean that either the variable power law gets harder at higher frequencies, or that the hard part of `constant' component appears constant on long time-scales but contributes significantly to the variance on shorter time-scales."965 To establish the energv-spectral shape of the variable components. we will fit the un-normalised sspectra in the following section.," To establish the energy-spectral shape of the variable components, we will fit the un-normalised spectra in the following section."966 The sspectva of all individual orbits are qualitatively similar except for the lowest [lux observation. during orbit 090. shown in Fig. 3..," The spectra of all individual orbits are qualitatively similar except for the lowest flux observation, during orbit 999, shown in Fig. \ref{NXS_999}."967 In this case. the MIP sspectrum is notably dillerent. to the LE spectrum.," In this case, the MF spectrum is notably different to the LF spectrum."968 We will examine the variable components of this observation in detail in Sec. 6.., We will examine the variable components of this observation in detail in Sec. \ref{constant}.969 As the data [rom orbit 999 appear to behave dilferentIy to all other observations. we will do the spectral fitting analysis to the combined. 9991003 ane 1000.1003 data sets separately.," As the data from orbit 999 appear to behave differently to all other observations, we will do the spectral fitting analysis to the combined 999–1003 and 1000–1003 data sets separately."970value of the slope s above onlv slishtly. from -2.5 to -2.3. but still more than half of the clouds (55%)) show negative values of s.,"value of the slope $s$ above only slightly, from -2.5 to -2.3, but still more than half of the clouds ) show negative values of $s$."971 spectra from low latitude surveys of the inner galaxy can only be understood in terms of radiative transfer in a partially absorbing medium., spectra from low latitude surveys of the inner galaxy can only be understood in terms of radiative transfer in a partially absorbing medium.972 The gas is Far from optically thin. and ib ds far from isothermal. so neither of these simplifications can be used to understand the brgh(ness temperatures we see in enüssion.," The gas is far from optically thin, and it is far from isothermal, so neither of these simplifications can be used to understand the brightness temperatures we see in emission."973 In (his paper we study enission-absorption spectrum pairs to trv to understand the relationship between the optical clepth and the brightness temperature through various clouds along several lines of sight., In this paper we study emission-absorption spectrum pairs to try to understand the relationship between the optical depth and the brightness temperature through various clouds along several lines of sight.974 This paper concentrates on a few spectra in a relatively small area of (he Galactic plane im (he fourth quadrant., This paper concentrates on a few spectra in a relatively small area of the Galactic plane in the fourth quadrant.975 We hope that the techniques described here will be useful to analvze spectra toward many more continuum sources throughout the SGPS. and perhaps in other similar surveys as well.," We hope that the techniques described here will be useful to analyze spectra toward many more continuum sources throughout the SGPS, and perhaps in other similar surveys as well."976 Since the sample is small. the results described here must be considered as only representative: more precise. quantitative measurements of the properties of the cool neutral medium will come from larger samples of spectra.," Since the sample is small, the results described here must be considered as only representative; more precise, quantitative measurements of the properties of the cool neutral medium will come from larger samples of spectra."977" The three quantities (hat determine the characteristics of the emission spectra that we see in low latitude surveys are (he warm phase density. »,. the temperature of the cool clouds. τω and the average densitv of the cool medium. which sets the value of <n>."," The three quantities that determine the characteristics of the emission spectra that we see in low latitude surveys are the warm phase density, $n_w$, the temperature of the cool clouds, $T_{cool}$, and the average density of the cool medium, which sets the value of $<\kappa>$."978 This paper discusses the last (wo. the first has been determined [rom earlier surveys. wilh lower resolution (see reviews by Burton. 1988. Dickey and Lockman. 1990).," This paper discusses the last two, the first has been determined from earlier surveys with lower resolution (see reviews by Burton, 1988, Dickey and Lockman, 1990)."979 With these three quantities in hand. we can understand (he peak brightness of the emission. the Iraction ol atomic gas in the warm and cool phases. and the significance and abundanee of ΗΡΑ features.," With these three quantities in hand, we can understand the peak brightness of the emission, the fraction of atomic gas in the warm and cool phases, and the significance and abundance of HISA features."980 The major findingshere are:, The major findingshere are:981 (Piran1999), \citep{Piran99}.982 +ray↖∶⋅ (Tayloral.2001).2. ∙↴ (ShomiD€&Pian1990:tELith&SariS2001)..2 ∙∙− ↸∖⋜∐⋅↕↖↽≼∶↕⊰↕≧⋜↕↕≯↑↸∖↥⋅∩⊾↕∪↖↖↽∐∩⊾∐↑↸⊳↿∐⋅↖⇁↸∖∖↴↕⊔⋜↧∏↘↽∖↴∐↸∖≺∐∖↸⊳↸∖↕↸∖↥⋅⋜↧↑↕∪∐ (Sari&1999:009:Molinari?ὶetal.2007).2 ⋅∙⋅ (Peeretal.2007).," $\gamma-$ \citep{Taylor04}. \citep{SP90,LS01}. \citep{SP99,Molinari07}. \citep{Peer07}."9832. factor of CRB outflows (Zou&Piran2010)., factor of GRB outflows \citep{Zou10}.984". AbuuvS$usft GRBs were followed bv cucreetic X-ray flares,", Many GRBs were followed by energetic X-ray flares.985 sally the» flilees al ouls about 110 of that of1 prompt Io, Usually their fluences are only about $1-10\%$ of that of prompt emission.986wever in quite a few events. the enerev of X-rayenasson. flare is comparable to that of prompt cluission.," However in quite a few events, the energy of X-ray flare is comparable to that of prompt emission."987" The temporal behavior aud the harducss ratio evoution of ταν flares MIC Siuilar n those of prompt Ciden pu (¢etal.E the adea twat tLON MMLLG the same physica onouDp o tx prompt cluission. Ίνοι, they are also due to the activity of central(sal cetreeug (oo.(cFE:Fan&κWeiWap20052005:Alhaneetetalal.90062006)."," The temporal behavior and the hardness ratio evolution of X-ray flares are similar to those of prompt emission pulses \citep{Chincarini10}, supporting the idea that they have the same physical origin of the prompt emission, i.e., they are also due to the activity of central engine \cite[e.g.][]{Fan05,Zhang06}."988. Iu such a kiud nmodel. the central engineZhang lammiches Low outflow at late oftimes.," In such a kind of model, the central engine launches new outflow at late times."989" As in the prompt eiuission pliasc. lk factor of the flax ontflow is a eneial paraucter,"," As in the prompt emission phase, the bulk Lorentz factor of the flare outflow is a crucial parameter."990"the LonUnfortunately,uz most models constraining the bulk Lorentz factor of the CRB outfloware invalid for the X-ray.- flares."," Unfortunately, most models constraining the bulk Lorentz factor of the GRB outfloware invalid for the X-ray flares."991 For example. the methods developed in: Saniens\AjPiranDue100€ aud; -PianPie(2010)on Hnavo suce there (1999).is a precedingZou aud more GRD irelevautoutflow expanding iuto the mediuu.," For example, the methods developed in \citet{SP99} and \citet{Zou10} are irrelevant since there is a preceding and more energetic GRB outflow expanding into the medium."992" So energeticfar there an three kindsof speculations on tre bulk Loreutz factor of the flare outflows: (a) The typical bulk Lorentz factor of+ flares is. just. teus and isB considerablyB sinaller than ∏⋯↾∪↕↾↕⊔∖∪∏↾∏∪∖↸⊽↻∪∖↸⊽↸∖↕⋅↕⊔∶↰≔↻↕∪⊔↻↾↸∖⊔↕↴∖↴↴∖↴↕∪∐≺⋮⋮⋯↖∖⊽ : ⋅⋅ WeiQU 2005): (b) The typical3n bulkT Lorentz ⋅∖factor⋅ oft flaresfaoc but not nmch higher that of the ontiow Dgiving higherrie to prompt emission Han(Dirrowsetal.2005:Zhanghaneοἳeto;al—2"" 2006)."," So far there are three kinds of speculations on the bulk Lorentz factor of the flare outflows: (a) The typical bulk Lorentz factor of flares is just tens and is considerably smaller than that of the outflow powering prompt emission \citep{Fan05}; (b) The typical bulk Lorentz factor of flares is higher but not much higher than that of the outflow giving rise to prompt emission \citep{Burrows05,Zhang06}."993 PleaseHorse note. thatth: m. ]both caseMUN (a) and case (b). the flare photons are powered by the enerev dissipation within the newly launched outflow. (," Please note that in both case (a) and case (b), the flare photons are powered by the energy dissipation within the newly launched outflow. ("994"c) Tn the N-vav- flare moclel of. wp-scattered forward. shock Cluission. late outflow with a bulk Loreutz factor ~10"" is required (Panaitescu 2008).","c) In the X-ray flare model of up-scattered forward shock emission, late outflow with a bulk Lorentz factor $\sim 10^5$ is required \citep{Panaitescu08}."995.. The divergency between V. De , The divergency between these arguments are very large.996Wt M deven ΜΙΣΟΣ αυ.”MBCTDOC.id. AS bose.GOSCIIDOCGM IM SCCTIOU TO estimateWo the lull Lorentz factorof the outflows.," In this work, we develop two different methods, as described in section \ref{sec:model}, to estimate the bulk Lorentz factorof the outflows."997ci.The case studies. are presentedin⋅ section ⋅⋅⋅ 77...,The case studies are presentedin section \ref{sec:Case}. .998 We- stmunarize: our result with some discussion iu section ??.., We summarize our result with some discussion in section \ref{sec:DS}. .999"such as A5007 (35.1 eV), have been used as proxies for hard X-ray emission in AGNs, and hence, their intrinsic luminosity (Laan; e.g., ????)).","such as $\lambda 5007$ (35.1 eV), have been used as proxies for hard X-ray emission in AGNs, and hence, their intrinsic luminosity $L_{\rm1000 AGN}$ ; e.g., \citealt{mulchaey94,alonso97,heckman05,panessa06}) )."1001" However, such emission may also be readily excited by strong star formation as well as being subject to significant dust extinction within the host galaxy."," However, such emission may also be readily excited by strong star formation as well as being subject to significant dust extinction within the host galaxy."1002" By contrast, mid-IR high-excitation narrow-line emission (e.g., [Nev]; [Orv]) is an excellent extinction-free indicator of Laan (see Section 3.3)) and, when combined with sensitive X-ray data, can provide good first order constraints on whether an AGN is Compton thick."," By contrast, mid-IR high-excitation narrow-line emission (e.g., ]; ]) is an excellent extinction-free indicator of $L_{\rm AGN}$ (see Section \ref{subsec:spitz_emiss_line_fluxes}) ) and, when combined with sensitive X-ray data, can provide good first order constraints on whether an AGN is Compton thick."1003 In Fig., In Fig.1004 5aa we present the observed 2-10 keV X-ray upper-limit luminosities from the data versus the mid-IR luminosity for our candidate Compton-thick AGNs and compare them to the intrinsic properties found for local ‘bona-fide’ Compton-thick AGNs., \ref{fig:6um_xray}a a we present the observed 2–10 keV X-ray upper-limit luminosities from the data versus the mid-IR luminosity for our candidate Compton-thick AGNs and compare them to the intrinsic properties found for local `bona-fide' Compton-thick AGNs.1005" We find that the candidate Compton-thick AGNs are spread over a wide range of luminosities, Ljorv]7 (0.13-20)10*!ergs”! ; for the sources in our sample which we find to be dominated by SF at mid-IR wavelengths (column 7 of Table 2)), fluxes have conservatively been adjusted for contamination from [Fell] emission (see section 3.3))."," We find that the candidate Compton-thick AGNs are spread over a wide range of luminosities, $L_{\rm [OIV]} \approx1006(0.13$ $20) \times 10^{41} \ergps$ ; for the sources in our sample which we find to be dominated by SF at mid-IR wavelengths (column 7 of Table \ref{tab:ir_phot_spec}) ), fluxes have conservatively been adjusted for contamination from ] emission (see section \ref{subsec:spitz_emiss_line_fluxes}) )."1007" We find that based on the observed X-ray upper-limits, none of the objects in our sample are consistent with the local intrinsic relation of AGNs from ?,, suggesting that the X-ray emission is heavily obscured."," We find that based on the observed X-ray upper-limits, none of the objects in our sample are consistent with the local intrinsic relation of AGNs from \citet{goulding10}, , suggesting that the X-ray emission is heavily obscured."1008" However, as we illustrate in Fig."," However, as we illustrate in Fig."1009" 5aa, the observed Lx/Liorv; for our sample (mean ratio m 3.6) is consistent with the observed Lx/Ljorv; ratio for a sample of well-studied local ‘bona-fide’ Compton-thick AGNs (i.e., Circinus, Mrk 3, NGC 1068 and NGC 6240).Furthermore,the Lx/Ljory) luminosity ratio of these four"," \ref{fig:6um_xray}a a, the observed $L_X / L_{\rm [OIV]}$ for our sample (mean ratio $\approx10103.6$ ) is consistent with the observed $L_X / L_{\rm [OIV]}$ ratio for a sample of well-studied local `bona-fide' Compton-thick AGNs (i.e., Circinus, Mrk 3, NGC 1068 and NGC 6240).Furthermore,the $L_X /1011L_{\rm [OIV]}$ luminosity ratio of these four"1012below). the mass range of their progenitor is thus similar to the one of canonical ΝΟ.,"below), the mass range of their progenitor is thus similar to the one of canonical SNeII."1013 If hvpernovae occured in the early stage of the Galactic evolution and. induced. star. formation. their. abundance pattern may still be observable in the atmospheres of some low-mass halo stars.," If hypernovae occured in the early stage of the Galactic evolution and induced star formation, their abundance pattern may still be observable in the atmospheres of some low-mass halo stars."1014 As for the case of star formation triggered by single SNelL. we can derive an estimate of the metallicity of these halo stars using Eq.," As for the case of star formation triggered by single SNeII, we can derive an estimate of the metallicity of these halo stars using Eq."1015 38. and hypernoya vields., \ref{single_SN} and hypernova yields.1016 Nakamura et al. (, Nakamura et al. (10172001) have investigated in detail the nucleosvnthesis of core-collapse hvpernovae and. compared it with the vields of canonical (Le... {αν~1075 eeres) core-collapse SNeLL with similar progenitor mass.,"2001) have investigated in detail the nucleosynthesis of core-collapse hypernovae and compared it with the yields of canonical (i.e., $E_0 \sim 10^{51}$ ergs) core-collapse SNeII with similar progenitor mass."1018 Their Tables 2-5 show that ΟΛΟΙ and hypernovae with similar progenitor mass release much the same amount of metals., Their Tables 2-5 show that SNeII and hypernovae with similar progenitor mass release much the same amount of metals.1019 The resulting metallicity of stars formed in hvpernova remnants are given in Table 1. following the same of line of reasoning as in the oevious section.," The resulting metallicity of stars formed in hypernova remnants are given in Table 1, following the same of line of reasoning as in the previous section."1020 HIxpernoyae. being much more energetic han ΝΟ. and the mass of interstellar gas swept by the last wave being roughly proportional to the explosion energv (leq. 38)).," Hypernovae being much more energetic than SNeII, and the mass of interstellar gas swept by the blast wave being roughly proportional to the explosion energy (Eq. \ref{single_SN}) ),"1021 they will collect a. larger amount. of interstellar gas., they will collect a larger amount of interstellar gas.1022 Pherefore. should core-collapse hvpernovae ος able to trigger the formation of new stars. these stars will » more metal-poor than the ones formed in the remnants of canonical SNell.," Therefore, should core-collapse hypernovae be able to trigger the formation of new stars, these stars will be more metal-poor than the ones formed in the remnants of canonical SNeII."1023" ""πας. they may be well-suited to explain he formation of stars with a metallicity as low as Ve/LI] ~4 (see Table 1)."," Thus, they may be well-suited to explain the formation of stars with a metallicity as low as [Fe/H] $\simeq -4$ (see Table 1)."1024 The most significant feature οἱ hvpernova nucleosvnthesis is their iron production.— this one being larecr than in ΟΛΟΙ by a factor 2 to 10 (Nakamura. et al.," The most significant feature of hypernova nucleosynthesis is their iron production, this one being larger than in SNeII by a factor 2 to 10 (Nakamura et al."1025 2001)., 2001).1026 This leads to small abundance ratios of a elements over iron., This leads to small abundance ratios of $\alpha$ elements over iron.1027 Nakamura et al. (, Nakamura et al. (10282001) thus suggested that the eas oul of which the very metal-poor binary CS 22873-1390 CFefll] = 34) formed hac been contaminated. by. the ejecta of an hypernova as this halo star shows almost. solar Me/Fe] and Ca/Fe] ratios.,2001) thus suggested that the gas out of which the very metal-poor binary CS 22873-139 ([Fe/H] = $-$ 3.4) formed had been contaminated by the ejecta of an hypernova as this halo star shows almost solar [Mg/Fe] and [Ca/Fe] ratios.1029 On the other hand. while stars with 25XFefl]S0 show Zn/Ee] = 0 (e.g.. Primas et al.," On the other hand, while stars with $-2.5 \lesssim {\rm [Fe/H]} \lesssim 0$ show [Zn/Fe] $\simeq$ 0 (e.g., Primas et al."1030 2000). this abundance ratio is steadily increasing towards Zn/Ec] ~ 0.5 as the metallicity decreases. for stars more metal-poor than ο) —2.5 (e.g... Cavrel et al.," 2000), this abundance ratio is steadily increasing towards [Zn/Fe] $\sim$ 0.5 as the metallicity decreases, for stars more metal-poor than [Fe/H] $\sim -2.5$ (e.g., Cayrel et al."1031 2003)., 2003).1032 Umeda Nomoto (2002) notice that such a large Zn/Fe] ratio arises naturally in their own hypernova model and thus conclude that core-collapse hvpernovae are likely to have contributed to the early Galactic chemical evolution., Umeda Nomoto (2002) notice that such a large [Zn/Fe] ratio arises naturally in their own hypernova model and thus conclude that core-collapse hypernovae are likely to have contributed to the early Galactic chemical evolution.1033 μονο very massive (2 MM.) objects exploding with ££1η cores. they are also called hypernovae.," These very massive $\simeq$ $_{\odot}$ ) objects exploding with $E \gtrsim 10^{52}$ ergs, they are also called hypernovae."1034 Their name (1e. “pair instability) refers to the clectron-positvon pair instability process encountered during. the central oxveen-burning stages (see Umeda Nomoto 2002. their appendix. for a detailed description).," Their name (i.e., “pair instability”) refers to the electron-positron pair instability process encountered during the central oxygen-burning stages (see Umeda Nomoto 2002, their appendix for a detailed description)."1035 The main feature of these very massive stars is their ability to “pass carbon and oxygen from the helium-burning core through the hvdrogen-burning shell. in such a wav that it is CNO processed. to nitrogen before entering the hyvelrogen envelope (Carr. Bond Arnett 984).," The main feature of these very massive stars is their ability to “pass carbon and oxygen from the helium-burning core through the hydrogen-burning shell, in such a way that it is CNO processed to nitrogen before entering the hydrogen envelope” (Carr, Bond Arnett 1984)."1036 These stars thus produce large supersolar values of N/Ie. an effect not predicted: by models. of Galactic chemical enrichment based. on stars less massive than MM.," These stars thus produce large supersolar values of N/Fe, an effect not predicted by models of Galactic chemical enrichment based on stars less massive than $_{\odot}$."1037 Following their discovery of C'S 22949-0317. a very metal-poor star (Fe/L] = 3.8) showing extreme nitrogen enhancement ΝΟ = 2.3). Norris et al. (," Following their discovery of CS 22949-037, a very metal-poor star ([Fe/H] = $-$ 3.8) showing extreme nitrogen enhancement ([N/Fe] = 2.3), Norris et al. ("10382002) suggested that this star may have been formed. out of gas polluted and compressed by such a very massive hypernova.,2002) suggested that this star may have been formed out of gas polluted and compressed by such a very massive hypernova.1039 On the other hand. in marked contrast with core-collapse hypernova vields. Umeda Nomoto (2002) quote that pair-instability hyvpernovae. are. unlikely το produce Zn/Fe] ratios as large as in very metal-poor stars where Zn/Fe] ranges from solar up to 20.5 (Cayrel et al.," On the other hand, in marked contrast with core-collapse hypernova yields, Umeda Nomoto (2002) quote that pair-instability hypernovae are unlikely to produce [Zn/Fe] ratios as large as in very metal-poor stars where [Zn/Fe] ranges from solar up to $\simeq$ 0.5 (Cayrel et al."1040 2003)., 2003).1041 Actually. the abundance ratio derived from their hypernova vields is of order 1.5. that is. 1 to 2 dex smaller than in very metal-poor stars.," Actually, the abundance ratio derived from their hypernova yields is of order $-$ 1.5, that is, 1 to 2 dex smaller than in very metal-poor stars."1042 Aclelitionally. Ποσο Woosley (2002) note the absence of the r-process in hese massive objects. which conflicts. with observations showing appreciable amounts of r-process elements in. very metal-poor stars (e.g... Burris et al.," Additionally, Heger Woosley (2002) note the absence of the r-process in these massive objects, which conflicts with observations showing appreciable amounts of r-process elements in very metal-poor stars (e.g., Burris et al."1043 2000)., 2000).1044 Based on these wo arguments. Lc. the low abundance ratio Zn/Ic] as well as the absence of r-process elements in pair instability ivpernova ejecta. Umeda Nomoto (2002) and Leger Woosley (2002) conclude that the abundances of very metal-poor stars cannot be ascribed. το pair. instability ivpernovae only and must include the contribution of an aclelitional nucleosvnthetic component. namely those lower mass stars that make “regular” supernovac.," Based on these two arguments, i.e., the low abundance ratio [Zn/Fe] as well as the absence of r-process elements in pair instability hypernova ejecta, Umeda Nomoto (2002) and Heger Woosley (2002) conclude that the abundances of very metal-poor stars cannot be ascribed to pair instability hypernovae only and must include the contribution of an additional nucleosynthetic component, namely those lower mass stars that make “regular” supernovae."1045 We also note hat pair-instabilitv hvpernovae release fairly large amounts of metals in the interstellar medium. of order LOO M. (Umeda Nomoto 2002. their Lables 19-15).," We also note that pair-instability hypernovae release fairly large amounts of metals in the interstellar medium, of order 100 $_{\odot}$ (Umeda Nomoto 2002, their Tables 15-18)."1046" Ln fact. hese stars disrupt completely when exploding. leaving no compact remnant after the explosion (νου, no issue of 7mass-cut” or ""[fall-back. see Heger Woosley 2002)."," In fact, these stars disrupt completely when exploding, leaving no compact remnant after the explosion (i.e., no issue of ``mass-cut'' or “fall-back”, see Heger Woosley 2002)."1047" The mixing of so large an amount of metals with a mass of primordial eas of 05«10""M. (E=10 ceres) or c5«109M. (E,=100«10 ceres) will lead. to metallicities of order", The mixing of so large an amount of metals with a mass of primordial gas of $\simeq 5 \times 10^5 {\rm M}_{\odot}$ $_{0} = 10 \times 10^{51}$ ergs) or $\simeq 5 \times 10^6 {\rm M}_{\odot}$ $_{0} = 100 \times 10^{51}$ ergs) will lead to metallicities of order1048resolution in dense galactie disks is uot so pronüneut in DCDs.,resolution in dense galactic disks is not so prominent in BCDs.1049 Furthermore. the small nuniber of statistics nav also contribute to the observed lieher dispersion iu ου! ratios in metal-poor dwarf galaxies.," Furthermore, the small number of statistics may also contribute to the observed higher dispersion in $_{24}$ ratios in metal-poor dwarf galaxies."1050 We investigate row inetallicity.§ affects the qo; ratios bw dividing he dwarf galaxies in our sample iuto two groups: a ower inetallicity eroup with loe(O/T<s.0 aud a veher metallicity eroup with loe(O/TD)>s.0., We investigate how metallicity affects the $_{24}$ ratios by dividing the dwarf galaxies in our sample into two groups: a lower metallicity group with $\le$ 8.0 and a higher metallicity group with $>$ 8.0.1051 This uctallicity threshold was selected following Roscubereetal.(2007) who uoticed a chauge in the properties of he star-foriiiug dwarf galaxies they studied around this uctallicity value., This metallicity threshold was selected following \citet{Rosenberg07} who noticed a change in the properties of the star-forming dwarf galaxies they studied around this metallicity value.1052" We find a mean qo, —1.12:0.179 for the first eroup and qo,= 1.30.1 for the second one.", We find a mean $_{24}= $ $\pm$ for the first group and $_{24}=$ $\pm$ 0.1 for the second one.1053" If we calculate the qo, for the low metallicity eroup without including SDS0335-052E. we fiud a πιο lower qo)= LOO."," If we calculate the $_{24}$ for the low metallicity group without including SBS0335-052E, we find a much lower $_{24}=$ $\pm$ 0.1."1054" We also notice that it appears qo, generally decreases with reduced metallicity for sources with 5.0. with SBS035-052E as a clear outlier. and| the slope flattens out at 8.0 (see Fie."," We also notice that it appears $_{24}$ generally decreases with reduced metallicity for sources with $<$ 8.0, with SBS035-052E as a clear outlier, and the slope flattens out at $>$ 8.0 (see Fig."1055 3)., 3).1056 This scatter iu qo; at higher metallicitics could be attributed to the more dispersion in the mid-IR ciission in these sources aud is consistent with a nuuber of other studies that have found iucreased dispersion in the q ratios for verv high bhuunmositv galaxies (which usually have higher metallicities) (Condonetal.1991:Yunal.2001:Bell 2003).," This scatter in $_{24}$ at higher metallicities could be attributed to the more dispersion in the mid-IR emission in these sources and is consistent with a number of other studies that have found increased dispersion in the q ratios for very high luminosity galaxies (which usually have higher metallicities) \citep{Condon91, Yun01,Bell03}."1057. IIunuueclctal.(1988) have found evidence that. for a given ealaxy. there is a small decrease iu F(100;1n)/S(20cc11) when the dust temperature increases.," \citet{Hummel88} have found evidence that, for a given galaxy, there is a small decrease in $\mu$ cm) when the dust temperature increases."1058 The latter can be traced by the ratio of jn) Εμ]. Ro, The latter can be traced by the ratio of $\mu$ $\mu$ m).1059usseletal.(2003). reached a, \citet{Roussel03} reached a1060(AAO).,(AAO).1061 RAVEs input catalogue for the most has oulv a magnitude selection criterion of 9«£13. thus creating a sample with no kincmatic biases.," RAVE's input catalogue for the most has only a magnitude selection criterion of $9<I<13$, thus creating a sample with no kinematic biases."1062 The observations are iu the Ca-triplet spectral region at 810 nu to 875 nu with au effective resolution of 17500., The observations are in the Ca-triplet spectral region at 840 nm to 875 nm with an effective resolution of $R=7500$ .1063 Starting in April 2003. at the cud of 2009 RAVE had collected more than LOO.000 spectra.," Starting in April 2003, at the end of 2009 RAVE had collected more than 400,000 spectra."1064" RAVE’s radial velocities are accurate ΕΣ+ when compared to external measurements, while the repeat observations exhibit an accuracy of 2kuslo(Zwdtter etal.2008)."," RAVE's radial velocities are accurate to $1.3\,\kms$ when compared to external measurements, while the repeat observations exhibit an accuracy of $2\,\kms$ \citep{Zwitter2008}."1065 These highly accurate radial velocities make RAVE ideal to search for kinematic substructures in an exteuded region around the sun., These highly accurate radial velocities make RAVE ideal to search for kinematic substructures in an extended region around the sun.1066 Indeed. with RAVE we now move away from studyiug the (c.g. Nordstrometal.(2001): d0.2 kpc) to examining the (a< Lippe).," Indeed, with RAVE we now move away from studying the (e.g. \citet{Nordstrom2004}: $d < 0.2\,\textrm{kpc}$ ) to examining the $d < 4\,\kpc$ )."1067 Using RAVE’s highly accurate radial velocities we have discovered a stream that lies mostly within the constellation of Aquarius at a distance of 0.5zdX LOkpe. in the directiou (7.5b)~(557.607) aud at Vow=200lhus1," Using RAVE's highly accurate radial velocities, we have discovered a stream that lies mostly within the constellation of Aquarius at a distance of $0.5\lesssim d\lesssim 10\,\kpc$ , in the direction $(l,\ b)\sim(55^\circ,\ -60^\circ)$ and at $\RV=-200\,\kms$."1068 The velocity places the stream as part of the Galaxy's halo., The velocity places the stream as part of the Galaxy's halo.1069 As it lies in the direction of the constellation of Aquarius we lave named it the Aquarius stream., As it lies in the direction of the constellation of Aquarius we have named it the Aquarius stream.1070 The detection of this stream is described in Section 2.., The detection of this stream is described in Section \ref{sec:Stream}.1071" In Section 3. we compare the RAVE data to mock data from the Besangoou Calaxy mode aud the newh-cdeveloped galaxy modelling code Galaxia, which offers a umber of significant advantages."," In Section \ref{sec:Bes} we compare the RAVE data to mock data from the Besançoon Galaxy mode and the newly-developed galaxy modelling code Galaxia, which offers a number of significant advantages."1072 Using these models we determine the significance of the detection and coustrain its localization., Using these models we determine the significance of the detection and constrain its localization.1073 In Section 1. we use RAVE’s stellar parameters combined with 2\TASS GIILN) photometry to iufer basic properties of the stream population aud derive distauce estimates., In Section \ref{sec:Pop} we use RAVE's stellar parameters combined with 2MASS $JHK$ ) photometry to infer basic properties of the stream population and derive distance estimates.1074 We also use Reduced Proper Motions to obtain another estimate of the distances., We also use Reduced Proper Motions to obtain another estimate of the distances.1075 The stream appears to be highly localized. on the sky which is interesting cousideriug the apparent proximity of the stream., The stream appears to be highly localized on the sky which is interesting considering the apparent proximity of the stream.1076 In Section 5. we explore possible connections of the Aquarius stream to other known spatial aud kincmatic streams. finding that it is not huked to any previously reported structure.," In Section \ref{sec:Pos} we explore possible connections of the Aquarius stream to other known spatial and kinematic streams, finding that it is not linked to any previously reported structure."1077 Iu Section 6 we investigate possible connections to other Guareinal) over-deusitics in the RAVE dataset. aud conclude that the stream is uulikelv to be associated with any of them.," In Section \ref{sec:Nat} we investigate possible connections to other (marginal) over-densities in the RAVE dataset, and conclude that the stream is unlikely to be associated with any of them."1078 A simple model of the recent disruption of a satellite iu the Galaxy's potential is able to account for the observed localization., A simple model of the recent disruption of a satellite in the Galaxy's potential is able to account for the observed localization.1079 The Aquarius stream thus is a new and nearby euignia in the \Glky Was halo., The Aquarius stream thus is a new and nearby enigma in the Milky Way's halo.1080 RAVE aecasures the velocities of stars that are selected purely ou the basis of thei photometry. so it ds free of kinematic liases.," RAVE measures the velocities of stars that are selected purely on the basis of their photometry, so it is free of kinematic biases."1081 Over most of the skv the probability of a stars selection depends cutirely on its apparent magnitude: only iu directions towards the Galactic Centre is selection based ou colour as well as magnitude (DRI: Steimuetzetal.(2006).. DR2: Zwitteretal. (2008))).," Over most of the sky the probability of a star's selection depends entirely on its apparent magnitude; only in directions towards the Galactic Centre is selection based on colour as well as magnitude (DR1: \citet{Steinmetz2006}, DR2: \citet{Zwitter2008}) )."1082 Furthermore. ΠΑΝΤΟs radial velocities are accurate to <2kiums so fine substructures are best detected using radial velocities alone: combining them with proper motions and distances mean a significant loss of accuracy.," Furthermore, RAVE's radial velocities are accurate to $\le2\,\kms$ so fine substructures are best detected using radial velocities alone: combining them with proper motions and distances mean a significant loss of accuracy."1083 The Aquarius stream was discovered in RAVE data as a structure secu in heliocentric radial velocity vs Galactic latitudelongitude space., The Aquarius stream was discovered in RAVE data as a structure seen in heliocentric radial velocity vs Galactic latitude/longitude space.1084 When the stream was first noted. it was found to be most clearly defined by faint stars with low eravitics. which suggests that the structure is at some distance from the Sun.," When the stream was first noted, it was found to be most clearly defined by faint stars with low gravities, which suggests that the structure is at some distance from the Sun."1085 Removing forceround eiauts culauces its visibility., Removing foreground giants enhances its visibility.1086 We use the internal release of RAVE from Jaunary 2010 that contains 332.717 RVs of 252.790 individual stars.," We use the internal release of RAVE from January 2010 that contains 332,747 RVs of 252,790 individual stars."1087 We use only those observations for which the signal-to-noise ratio SNR»13 aud the Tourv aud Davis cross-correlation cocficient RosὉ to remove potentially erroneous observations., We use only those observations for which the signal-to-noise ratio $SNR>13$ and the Tonry and Davis cross-correlation coefficient $R>5$ to remove potentially erroneous observations.1088" Note that. since not all observations have the more accurate signal-to-noise estimation, S2.N. we use the SNR value which cau nuderestimate the signal-to-noise (see DR2)."," Note that, since not all observations have the more accurate signal-to-noise estimation, $S2N$, we use the $SNR$ value which can underestimate the signal-to-noise (see DR2)."1089 For multiple observations of single stars the VW. were averaged. as were the stellar parameters for those observations that vielded an estimate of these parameters.," For multiple observations of single stars the $\vrad$ were averaged, as were the stellar parameters for those observations that yielded an estimate of these parameters."1090 The Aquarius stream was found iu the Calactic latitude slice τοῦ<bo507., The Aquarius stream was found in the Galactic latitude slice $-70^\circ<b<-50^\circ$.1091 As described above. it is also more marked for fainter stars.," As described above, it is also more marked for fainter stars."1092 We therefore introduce an upper brightuess Bit to cuhance the visibility. of the stream., We therefore introduce an upper brightness limit to enhance the visibility of the stream.1093 As noted in the first and second data release papers. a subset of the RAVE input catalog have Fo inaguitudes frou the SuperCOSALOS Sky Survey (Ibuublv2001).. which show an offset to DENIS f magnitudes.," As noted in the first and second data release papers, a subset of the RAVE input catalog have $I$ magnitudes from the SuperCOSMOS Sky Survey \citep{Hambly2001}, which show an offset to DENIS $I$ magnitudes."1094 Not all RAVE stars have DENIS 7 magnitudes either., Not all RAVE stars have DENIS $I$ magnitudes either.1095 We therefore turned to 2\LASS bands for our magnitude limit. even though this tends to bias against cool stars im our saiple. aud we potentially miss sole candidates.," We therefore turned to 2MASS bands for our magnitude limit, even though this tends to bias against cool stars in our sample, and we potentially miss some candidates."1096 We found that a limit of J>10.3 produced the best differentiation of the stream from the backeround population. removing the brighter. nearby ejauts.," We found that a limit of $J>10.3$ produced the best differentiation of the stream from the background population, removing the brighter, nearby giants."1097" Figure laa shows the structure secu iu heliocentric radial velocity. Vj. against Calactic longitude. /. for the stars with the selection criteria τοῦbeHOP, J>10.3."," Figure \ref{f1}a a shows the structure seen in heliocentric radial velocity, $\RV$, against Galactic longitude, $l$, for the stars with the selection criteria $-70^\circ<b<-50^\circ$, $J>10.3$."1098" A clear structure begius at Vo.—1501s1 at /=307 aud extends down to Vj,,=2OOkms lat |—157."," A clear structure begins at $\RV\sim-150\,\kms$ at $l=30^\circ$ and extends down to $\RV=-200\,\kms$ at $l=75^\circ$."1099" This overdeusityv is particularly clear in Figure lbb. where we plot the histoerin for Vj, in the region TO«b«x HOP. Jm10.3. 307cP "," This overdensity is particularly clear in Figure \ref{f1}b b, where we plot the histogram for $\vrad$ in the region $-70^\circ<b<-50^\circ$ , $J>10.3$, $30^\circ<l<75^\circ$ ."1100Πο can be seen as an excess of stars at negative velocities that is distinct from the general population., The stream can be seen as an excess of stars at negative velocities that is distinct from the general population.1101 We establish limits of 250<Vo. L50laus 307«—PoTHA J>10.3 to choose 15 candidates of the Aquarius stream. which are outlined by the red box in Fieure 1 and listed in Table 1..," We establish limits of $-250<\RV<-150\,\kms$, $30^\circ<l<75^\circ$, $J>10.3$ to choose 15 candidates of the Aquarius stream, which are outlined by the red box in Figure \ref{f1} and listed in Table \ref{tab1}."1102 αν stream candidates lack stellar parameter estimates. since they were observed carly on by RAVE (DRI does not include such estimates: see the data release papers for details).," Many stream candidates lack stellar parameter estimates, since they were observed early on by RAVE (DR1 does not include such estimates; see the data release papers for details)."1103" The average SNR is 20 for the stream candidates and 1 star (C2231120-082619) has a repeat observation. which is listed to show the cousisteucv of the Vi, results."," The average SNR is 20 for the stream candidates and 1 star (C2234420-082649) has a repeat observation, which is listed to show the consistency of the $\vrad$ results."1104 As a double-check. the template fits to each of the spectra were eve-balled as were the zero-point fits (sine skv radial velocities) forthefields the stars were observed in.," As a double-check, the template fits to each of the spectra were eye-balled as were the zero-point fits (using sky radial velocities) forthefields the stars were observed in."1105 No abnormalities were detected., No abnormalities were detected.1106(this is a condition of pressure balance between the wind and the ram pressure of ISM in the frame of the CD).,(this is a condition of pressure balance between the wind and the ram pressure of ISM in the frame of the CD).1107 For constant luminosity Eq. (3.3)), For constant luminosity Eq. \ref{L}) )1108 gives Eq. (3.1)), gives Eq. \ref{GammaISM}) )1109 for the Lorentz factor of the CD., for the Lorentz factor of the CD.1110" This is exactly the same estimate as for the intermediate scale in €«1 supersonic flows, since LoEisoc/A; also this is the same scaling as in the case of relativistic fluid reverse shock (?).."," This is exactly the same estimate as for the intermediate scale in $\xi< 1$ supersonic flows, since $L_\Omega\sim E_{\rm iso} c/\Delta$; also this is the same scaling as in the case of relativistic fluid reverse shock \citep{Sari97}."1111" We stress that in the limit of strong FS, Eq. (2.1)), flow,"," We stress that in the limit of strong FS, Eq. \ref{rhoex1}) ),"1112" only the total power is important, Eq. (3.3))."," only the total power is important, Eq. \ref{L}) )."1113" The early stage lasts for r«ra, Eq. (3.2))."," The early stage lasts for $r<r_\Delta$, Eq. \ref{RDelta}) )."1114 At larger radii the flow enters the self-similar Sedov-Blandford-McKee stage., At larger radii the flow enters the self-similar Sedov-Blandford-McKee stage.1115" At this stage, only a fraction of the shell is interacting with the external medium, while the newly shocked ejecta material keeps adding energy and momentum to the shocked shell and the ISM, which evolve, effectively, as a flow with energy supply."," At this stage, only a fraction of the shell is interacting with the external medium, while the newly shocked ejecta material keeps adding energy and momentum to the shocked shell and the ISM, which evolve, effectively, as a flow with energy supply."1116" Finally, for r7rw the shock enters Blandford-McKee stage, with Lorentz factor given by Eq. (3.1))."," Finally, for $r> r_\Delta$ the shock enters Blandford-McKee stage, with Lorentz factor given by Eq. \ref{McKee}) )."1117 In this paper we discuss the dynamics of strongly magnetized outflows in GRBs., In this paper we discuss the dynamics of strongly magnetized outflows in GRBs.1118 We find that, We find that1119"In this final section, we show how a computer assisted proof of absolute continuity of the measure js can be developed in a specific case.","In this final section, we show how a computer assisted proof of absolute continuity of the measure $\mu$ can be developed in a specific case."1120 Use eq. (22)), Use eq. \ref{ftr3}) )1121" to express log/O(y), and use the convenient notation $;(y):—log|n?(y)|."," to express $\log1122\widehat{\mu^{(2)}}(y)$, and use the convenient notation $\Phi_j(y) :=1123\log |\widehat{\mu^{(j)}}(y)|$."1124 Gather terms (some algebra required) to obtain Nt) = (+1)NÓ ?t)--N ↕≼⊂⋝≏⋟⊣−≺↕≽ 22:34)4, Gather terms (some algebra required) to obtain t) = (l+1) ^2 t) + N t) + _2(t).1125" $,(5,Observe that all 22,,functions 9; are less than, or equal to, zero so that by keeping only the |=Ν—1 term in the summation at r.h.s."," Observe that all functions $\Phi_j$ are less than, or equal to, zero so that by keeping only the $l=N-1$ term in the summation at r.h.s."1126 of eq. (8)), of eq. \ref{ftr31}) )1127 and, and1128keV and al ~7.9 keV are of lower statistical significance wilh respect to those at ~5.6 keV. e»G4 keV and ~7.0 keV. Following these indications. we tried to reproduce (he observed spectrum with a power law and five narrow Gaussian lines.,"keV and at $\sim 7.9$ keV are of lower statistical significance with respect to those at $\sim 5.6\,\:$ keV, $\sim 6.4\,\:$ keV and $\sim 7.0\,\:$ keV. Following these indications, we tried to reproduce the observed spectrum with a power law and five narrow Gaussian lines."1129 The best fit spectral parameters are reported in Table 1 while (he ratio between the data and this possible best fit model is V.j0wn in Fig.5 (, The best fit spectral parameters are reported in Table \ref{tab:gauss} while the ratio between the data and this possible best fit model is shown in Fig.\ref{fig:ratiocfr} (1130panel a).,panel a).1131 The line al 6.39η keV ~700 eV) is positionallv consistent with the emission line. while the line al 7.02[33 keV ~600 eV) is positionally consistent both with the emission line (rest [rame energy. 7—7.058 keV) or with the enission line (rest [rame energy. £=6.96 keV).," The line at $6.39^{+0.07}_{-0.06}\,\:$ keV $\,\:\sim 700\,\:$ eV) is positionally consistent with the emission line, while the line at $7.02^{+0.29}_{-0.12}\,\:$ keV $\,\:\sim 600\,\:$ eV) is positionally consistent both with the emission line (rest frame energy $E=7.058\,\:$ keV) or with the emission line (rest frame energy $E=6.96\,\:$ keV)."1132 However the association with the line is unlikely since the measured fIux from this line should be at a fixed ratio (~0.11) with the emission flux. clearly in disagreement with the measured EWs.," However the association with the line is unlikely since the measured flux from this line should be at a fixed ratio $\sim 0.11$ ) with the emission flux, clearly in disagreement with the measured EWs."1133 The association wilh seems to be more plausible given that this line could be very. prominent (and sometimes with an EW comparable with the narrow line) in Type 1 AGN (see e.g. (he case of the Sevlert 1 galaxy NGC 7314 discussed in Yaqoobetal.2003))., The association with seems to be more plausible given that this line could be very prominent (and sometimes with an EW comparable with the narrow line) in Type 1 AGN (see e.g. the case of the Seyfert 1 galaxy NGC 7314 discussed in \citealt{yaqoob03}) ).1134 The line al T.85.(5. keV is positionally consistent with theIXa.. while for the remaining two lines (E=4.4902 keV and 5.55(is keV) there are no clear associations with well known and expected elements.," The line at $7.85^{+0.73}_{-0.76}\,\:$ keV is positionally consistent with the, while for the remaining two lines $E=4.49^{+0.13}_{-0.17}\:\,$ keV and $5.55^{+0.06}_{-0.05}\:\,$ keV) there are no clear associations with well known and expected elements."1135 The strongest expected lines in (he spallation model are the Cr Ixa al 5.4 keV and the Mni Ka at 5.9 keV (Skibo1997)., The strongest expected lines in the spallation model are the Cr $\alpha$ at 5.4 keV and the Mn $\alpha$ at 5.9 keV \citep{skibo97}.1136. Both these lines are ruled. out by ihe mismateh with the measured. energy. lines centroid., Both these lines are ruled out by the mismatch with the measured energy lines centroid.1137 So. unless an energy. shill occurs (but we do not observe anv enerev shift for the line). the spallation model is an unlikely explanation of the data.," So, unless an energy shift occurs (but we do not observe any energy shift for the line), the spallation model is an unlikely explanation of the data."1138 We have also evaluated the upper limits for Fe XAXV (D) al E~6.64 keV and lor Fe XNV (r) al Ee6.70 keV since the strenght of these lines. when combined with the strenght of other ionized Fe lines. can constrain emission models (cfr.," We have also evaluated the upper limits for Fe XXV (f) at $E \sim 6.64\:\,$ keV and for Fe XXV (r) at $E \sim 6.70\:\,$ keV since the strenght of these lines, when combined with the strenght of other ionized Fe lines, can constrain emission models (cfr."1139 Yaqooh&Pacmanabhan2004 and reference therein)., \citealt{yaqoob04} and reference therein).1140 These (wo lines are not required by the current data set and the upper limit on their EW is ~400 eV. The complex structure detected in the spectrum of could suggest a prolile of a Fe line produced by an accretion disk.," These two lines are not required by the current data set and the upper limit on their EW is $\sim 400\:\,$ eV. The complex structure detected in the spectrum of could suggest a profile of a Fe line produced by an accretion disk."1141 We explored (is interesting possibility using the DISILINE model (Fabian.Rees.Stella.&White1939).. which assumes a non- Schwarzschild black holet.. The relativistic effectshave been introduced also in the description of the rellected continuum. replacing the simple power law model with the," We explored this interesting possibility using the DISKLINE model \citep{disk}, which assumes a non-rotating Schwarzschild black The relativistic effectshave been introduced also in the description of the reflected continuum, replacing the simple power law model with the"1142"tto study where mmight be optically thick, but the main MALT90 survey will include HN?C instead of because of its hyperfine structure, is less likely to be ((HCN,,optically thick for similar line intensities).","to study where might be optically thick, but the main MALT90 survey will include $^{13}$ C instead of, because of its hyperfine structure, is less likely to be optically thick for similar line intensities)."1143 The first goal of the MALT90 pilot survey was to select an input catalog for the full MALT90 survey., The first goal of the MALT90 pilot survey was to select an input catalog for the full MALT90 survey.1144" Of the 6 catalogs tested, only HOPS, ATLASGAL and IRAS had sufficiently high (> 90%) detection rates to be used as input catalogs for the main MALT90 survey."," Of the 6 catalogs tested, only HOPS, ATLASGAL and IRAS had sufficiently high $>90\%$ ) detection rates to be used as input catalogs for the main MALT90 survey."1145 There are significant scientific and logistical benefits to using a single catalog when selecting sources., There are significant scientific and logistical benefits to using a single catalog when selecting sources.1146" The main advantages are the ability to use a simple and uniform criteria for choosing sources, the ability to compare our observed line properties against properties of the input catalog, and the ability to describe the significance of non-detections."," The main advantages are the ability to use a simple and uniform criteria for choosing sources, the ability to compare our observed line properties against properties of the input catalog, and the ability to describe the significance of non-detections."1147 The ATLASGAL catalog provides the optimal source list for MALT90., The ATLASGAL catalog provides the optimal source list for MALT90.1148 There are three major, There are three major1149Supernova survevs because the gy test has a remarkable efficicucy.,supernova surveys because the $q_0$ test has a remarkable efficiency.1150 There is no doubt that the search for a non-zero cosmological constant corresponds to a high priority observiug programm without waiting for the NAP. and Plauck Survevor surveys., There is no doubt that the search for a non-zero cosmological constant corresponds to a high priority observing program without waiting for the MAP and Planck Surveyor surveys.1151 At present aud from the observational point of view it is still too early to make a case for a non-zero cosmological constant., At present and from the observational point of view it is still too early to make a case for a non-zero cosmological constant.1152 More reliable observational facts have to be acciunulated., More reliable observational facts have to be accumulated.1153 We thauk F. Bernardeau. P. Schueider. S. Seitz and L. van Waerbeke for fruitful discussions aud cuthusiastic collaboratious.," We thank F. Bernardeau, P. Schneider, S. Seitz and L. van Waerbeke for fruitful discussions and enthusiastic collaborations."1154 We thank J. Lequeux for his comments on the mamuscript., We thank J. Lequeux for his comments on the manuscript.1155"A web application also provides (Table Access Protocol) services, which, being a successor of IVOA ConeSearch protocol, enables the user to query the dataset with arbitrary filters either from graphical clients or using endpoint URL and custom software client optionally developed by users (see the Appendix).","A web application also provides (Table Access Protocol) services, which, being a successor of IVOA ConeSearch protocol, enables the user to query the dataset with arbitrary filters either from graphical clients or using endpoint URL and custom software client optionally developed by users (see the Appendix)."1156 All the present description of the database is summarized in the README.html file which will be updated to account for future evolutions., All the present description of the database is summarized in the README.html file which will be updated to account for future evolutions.1157 The database is part of the Extrasolar Planets Encyclopaedia available athttp://exoplanet., The database is part of the Extrasolar Planets Encyclopaedia available at.1158eu. It has been designed since 1995 to encourage and facilitate the development of all exoplanet activities and communication between researchers., It has been designed since 1995 to encourage and facilitate the development of all exoplanet activities and communication between researchers.1159" It gives the latest news, access to online tutorials and general papers, a list of current and projected ground and space searches for planets, an extended bibliography, a list of past and future meetings, links to theory work and to other sites (Fig 11)."," It gives the latest news, access to online tutorials and general papers, a list of current and projected ground and space searches for planets, an extended bibliography, a list of past and future meetings, links to theory work and to other sites (Fig 11)."1160" The bibliography gives more than 8000 references (from Epicurus to today): articles in professional journals and preprints, books, conference proceedings, PhD theses."," The bibliography gives more than 8000 references (from Epicurus to today): articles in professional journals and preprints, books, conference proceedings, PhD theses."1161" It is updated daily and can be queried directly by author names, paper titles or The database will be upgraded continuously in several aspects: addition of new planets, addition of new data for each planet, addition of new links and services. -"," It is updated daily and can be queried directly by author names, paper titles or The database will be upgraded continuously in several aspects: addition of new planets, addition of new data for each planet, addition of new links and services. -"1162" We will add several new planet characteristics such as the position angle, number of planets in multiple systems, spectra, albedos, planet calculated and measured temperature, rings, moons, etc."," We will add several new planet characteristics such as the position angle, number of planets in multiple systems, spectra, albedos, planet calculated and measured temperature, rings, moons, etc."1163" By anticipation of the discovery of exomoon-like companions (and possibly binary planets (Cabrera Schneider 2007)), which can happen any time now by transits, we propose the following solution for their naming: NNN bl, b2 etc, if they have a similar semi-major axis and if the separation between the companions b1, b2 etc is permanently less than the Hill radius (in order to make a distinction with other types of 1:1 resonances like exchange orbits (Funk et al."," By anticipation of the discovery of exomoon-like companions (and possibly binary planets (Cabrera Schneider 2007)), which can happen any time now by transits, we propose the following solution for their naming: NNN b1, b2 etc, if they have a similar semi-major axis and if the separation between the companions b1, b2 etc is permanently less than the Hill radius (in order to make a distinction with other types of 1:1 resonances like exchange orbits (Funk et al."1164" 2010), eccentric resonances (Nauenberg 2002) and Trojan planets (Dvorak et al."," 2010), eccentric resonances (Nauenberg 2002) and Trojan planets (Dvorak et al."1165 2004)). -, 2004)). -1166" Links to NStED and Exoplanet Data Explorer individual pages for planets, links to data tables at CDS. -"," Links to NStED and Exoplanet Data Explorer individual pages for planets, links to data tables at CDS. -"1167" We are preparing the management of multiple star names, multiple filters, etc."," We are preparing the management of multiple star names, multiple filters, etc."1168" For the VO aspects of the database, we are preparing a new version of web applications distributing the catalogue."," For the VO aspects of the database, we are preparing a new version of web applications distributing the catalogue."1169" We plan to implement an advanced cross-platform client toolkit for easy intercommunication with arbitrary VO applications by means ofSAMP, Simple Application Messaging Protocol."," We plan to implement an advanced cross-platform client toolkit for easy intercommunication with arbitrary VO applications by means of, Simple Application Messaging Protocol."1170" The goal is to make a web browser act like a data browser which helps users to locate datasets they need and send it flawlessly to dedicated VO tools launched before in a background, where in turn all scientific analysis takes place."," The goal is to make a web browser act like a data browser which helps users to locate datasets they need and send it flawlessly to dedicated VO tools launched before in a background, where in turn all scientific analysis takes place."1171 This significantly enriches the user interaction with the data adding an opportunity to do sophisticated scientific analysis online., This significantly enriches the user interaction with the data adding an opportunity to do sophisticated scientific analysis online.1172T Cha system interesting whether or not the companion mass lies above or below the BD cutoff.,T Cha system interesting whether or not the companion mass lies above or below the BD cutoff.1173" Because disk gaps can be the result of dust clearing owing to planet formation, we also investigated if the companion candidate could be a recently formed planet within the disk."," Because disk gaps can be the result of dust clearing owing to planet formation, we also investigated if the companion candidate could be a recently formed planet within the disk."1174 The T Cha system shows properties that are consistent with this scenario., The T Cha system shows properties that are consistent with this scenario.1175" First, the object is detected well within the disk gap."," First, the object is detected well within the disk gap."1176" The total disk mass derived by ? is 1.74+0.25x107-? MMo, while the average accretion rate is 4x107? Mo/yr."," The total disk mass derived by \citet[][]{Olofsson2011} is $\pm$ $\times$ $^{-2}$ $_{\odot}$, while the average accretion rate is $\times10^{-9}$ $M_{\odot}/yr$."1177" These properties seem consistent with a planet-forming disk according to ?,, keeping in mind that both measurements can be affected by large uncertainties."," These properties seem consistent with a planet-forming disk according to \citet{AlexArmi2007}, keeping in mind that both measurements can be affected by large uncertainties."1178" If this is the case, the evolutionary models used here are not well suited to derive the mass of planetary objects, because we are probably observing the planet at the initial formation phase, when the brightness depends only on the accretion history and accretion rate."," If this is the case, the evolutionary models used here are not well suited to derive the mass of planetary objects, because we are probably observing the planet at the initial formation phase, when the brightness depends only on the accretion history and accretion rate."1179" Indeed, one of the biggest advantages of observing transitional disks is that recently formed planets are probably still accreting material and therefore should be in their brightest evolutionary phase."," Indeed, one of the biggest advantages of observing transitional disks is that recently formed planets are probably still accreting material and therefore should be in their brightest evolutionary phase."1180" Additional observations are needed to shed light on the nature of this exciting object, the first potential substellar object detected within the gap of a transitional disk."," Additional observations are needed to shed light on the nature of this exciting object, the first potential substellar object detected within the gap of a transitional disk."1181" In particular, observations that detect this object at other wavelengths or determine the disk position angle and inclination would be most useful."," In particular, observations that detect this object at other wavelengths or determine the disk position angle and inclination would be most useful."1182" We have observed T Cha with NACO/SAM in two filters, L/ and K,."," We have observed T Cha with NACO/SAM in two filters, $L'$ and $K_s$."1183 Our main results can be summarized as follows:, Our main results can be summarized as follows:1184"which is a version of the normal pousex in which the volume elements. Ἐν. are weighted by the estimated overdensities. 4,,.","which is a version of the normal $\Vm$ in which the volume elements, $V_p$, are weighted by the estimated overdensities, $\Delta_p$."1185" Using this notation. we can rewrite the two constraint equations as which rearrange to give the coupled equations To the extent to which the maximum likelihood model is a good description of the data Nin,=ior and so these equations simplify to quite intuitive estimators The first of these equations simply says that the estimate of the overdensity is the measured density divided by that predicted by the LF. while the second equation is equivalent to with the sum being over galaxies within that luminosity bin. ie. the normal 1/1""77 estimator. but with V""77 replaced by \velo"," Using this notation we can rewrite the two constraint equations as which rearrange to give the coupled equations To the extent to which the maximum likelihood model is a good description of the data $\hat N_{\rm tot}=N_{\rm tot}$ and so these equations simplify to quite intuitive estimators The first of these equations simply says that the estimate of the overdensity is the measured density divided by that predicted by the LF, while the second equation is equivalent to with the sum being over galaxies within that luminosity bin, i.e. the normal $1/\Vm$ estimator, but with $\Vm$ replaced by $\Vme$."1186"tes We note that this maximum likelihood estimate of the LF is equivalent to the standard 1/17 estimator if one makes the prior assumption that A,=1. ie. that there are no fluctuations in the radial galaxy density."," We note that this maximum likelihood estimate of the LF is equivalent to the standard $1/\Vm$ estimator if one makes the prior assumption that $\Delta_q\equiv 1$, i.e. that there are no fluctuations in the radial galaxy density."1187 9? derived the same estimator of the LF using a different approach in which it was assumed that the number of galaxies in a given luminosity and redshift bin were drawn from a Poisson distribution., \cite{Cholon86} derived the same estimator of the LF using a different approach in which it was assumed that the number of galaxies in a given luminosity and redshift bin were drawn from a Poisson distribution.1188 Our derivation shows that the estimator does not depend on the details of the assumed statistical distribution., Our derivation shows that the estimator does not depend on the details of the assumed statistical distribution.1189 The same density estimator was derived by maximum likelihood in section 8 of ?.., The same density estimator was derived by maximum likelihood in section 8 of \citet{Saunders90}.1190 They also stated that an improved estimate of the LF could be made by making the same to VN though they did not derive this result via maximum likelihood.," They also stated that an improved estimate of the LF could be made by making the same to $\Vm$, though they did not derive this result via maximum likelihood."1191 Another related analysis is that of 2.., Another related analysis is that of \cite{Heyl97}.1192 They followed similar steps but choose not to make the separability assumption of equation ¢1)} so us to be able to directly probe evolution of the shape of the LF using wide redshift bins., They followed similar steps but choose not to make the separability assumption of equation \ref{eq:separable}) ) so as to be able to directly probe evolution of the shape of the LF using wide redshift bins.1193 Before detailing our simple algorithm for generating a random catalogue that is consistent with the LF given by equation C15). we will generalize this result to take account of redshift evolution.," Before detailing our simple algorithm for generating a random catalogue that is consistent with the LF given by equation \ref{eq:LF1}) ), we will generalize this result to take account of redshift evolution."1194 The resulting algorithm. described in Section ??.. can then be applied to surveys that span a wide range of redshifts.," The resulting algorithm, described in Section \ref{sec:rancat}, can then be applied to surveys that span a wide range of redshifts."1195 First let us consider the case where one has external knowledge of the evolution of the galaxy population., First let us consider the case where one has external knowledge of the evolution of the galaxy population.1196 For instance. one might have evolutionary corrections for each galaxy or an average for the population based on fitting stellar population synthesis models (e.g.2?) to the observed galaxy colours.," For instance, one might have evolutionary corrections for each galaxy or an average for the population based on fitting stellar population synthesis models \citep[e.g.][]{BC03,Blanton07} to the observed galaxy colours."1197 One could also have a pre-imposed model for density evolution. e.g. that the amplitude of the galaxy luminosity function. . varies with redshift as b(2)=P(z)d*(0).," One could also have a pre-imposed model for density evolution, e.g. that the amplitude of the galaxy luminosity function, $\Phi^*$, varies with redshift as $\Phi^*(z)= \Q(z) \Phi^*(0)$."1198 In this case the only changes that are needed to the above estimators are: Thus. we redetine V for galaxy à used in equation (159) to be which simply represents and integral over the survey volume weighted by the combined factor εδλος) with limits set by the redshift range over which galaxy à. would satisfy the survey selection criteria.," In this case the only changes that are needed to the above estimators are: Thus, we redefine $\Vme$ for galaxy $\alpha$ used in equation \ref{eq:LF1}) ) to be which simply represents and integral over the survey volume weighted by the combined factor $\Delta(z)\Q(z)$ with limits set by the redshift range over which galaxy $\alpha$ would satisfy the survey selection criteria."1199 If one does not have foreknowledge of the evolution one can instead parameterise the evolution and use the survey data to constrain its parameters by an extension of the maximum likelihood technique., If one does not have foreknowledge of the evolution one can instead parameterise the evolution and use the survey data to constrain its parameters by an extension of the maximum likelihood technique.1200 For instance for the (2) model of 4 evolution introduced above. equation (6)) becomes Here the parametric form of (2) might simply be (2)=ez with « being the evolution parameter we wish to determine.," For instance for the $\Q(z)$ model of $\Phi^*$ evolution introduced above, equation \ref{eq:lnL}) ) becomes Here the parametric form of $\Q(z)$ might simply be $\Q(z)=1+az$ with $a$ being the evolution parameter we wish to determine."

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