ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 2. and 3))., \ref{f2} and \ref{f3}) ).3 The three incdepeudent measurements of the, The three independent measurements of the4The shocked envelope may look circular if most of the motion is in the radial direction as is the case for CCyg's space velocity.,The shocked envelope may look circular if most of the motion is in the radial direction as is the case for Cyg's space velocity.5" That there is no sign of the drift velocity between the dust and the gas envelopes, which one would expect to see if the detached shells were strictly of a thermal pulse origin, points more toward a wind—wind or a wind-ISM origin."," That there is no sign of the drift velocity between the dust and the gas envelopes, which one would expect to see if the detached shells were strictly of a thermal pulse origin, points more toward a wind–wind or a wind–ISM origin."6 Five synthetic detached shells were needed to model the PACS intensity profiles (Fig.2))., Five synthetic detached shells were needed to model the PACS intensity profiles \ref{profiles}) ).7 The angular separation between the shells suggest that the mass-loss varied every ~1500 yr., The angular separation between the shells suggest that the mass-loss varied every $\sim$ 1500 yr.8" Ant’’s intensity profile is very smooth with a detached shell located at 42"".", 's intensity profile is very smooth with a detached shell located at $\arcsec$.9" This suggests that the star experienced a brief increase in mass-loss some yyr ago, after which the mass-loss rate dropped and has not varied much since."," This suggests that the star experienced a brief increase in mass-loss some yr ago, after which the mass-loss rate dropped and has not varied much since."10" By imaging scattered light around AAnt, Gonzàllez Delgado et al. ("," By imaging scattered light around Ant, Gonzàllez Delgado et al. ("11"2001) proposed 4 shells at ~25”,,37”,,43"", and ((shell 1 to 4, respectively).","2001) proposed 4 shells at $\sim$, and (shell 1 to 4, respectively)."12 Shell 4 was confirmed by studying scattered polarised light (Gonzàllez Delgado et al., Shell 4 was confirmed by studying scattered polarised light (Gonzàllez Delgado et al.13 2003)., 2003).14" By assuming that the major fraction of polarised light comes from the dust and because of a difference in the polarisations of shells 3 and 4, they conclude that shell 4 consists mainly of dust, while shell 3 is gas dominated."," By assuming that the major fraction of polarised light comes from the dust and because of a difference in the polarisations of shells 3 and 4, they conclude that shell 4 consists mainly of dust, while shell 3 is gas dominated."15 Schóiier et al. (2005)), Schöiier et al. \cite{Schoe05}) )16 modelled single-dish CO data and inferred that a thin CO shell lies at the position of shell 3 (~43’’))., modelled single-dish CO data and inferred that a thin CO shell lies at the position of shell 3 $\sim$ ).17 Maercker et al. (2010)), Maercker et al. \cite{Maerc10}) )18 reobserved AAnt using scattered light and CO mapping and arrived at the same conclusion as Gonzallez Delgado et al. (, reobserved Ant using scattered light and CO mapping and arrived at the same conclusion as Gonzàllez Delgado et al. (19"2003) that shell 3 is at 43"" aand shell 4 at ~50”..",2003) that shell 3 is at $\sim$ and shell 4 at $\sim$.20 The peak intensity of the dust shell seen using PACS coincides with shell 3 as seen by Gonzallez Delgado et al. (, The peak intensity of the dust shell seen using PACS coincides with shell 3 as seen by Gonzàllez Delgado et al. (212003) and Maercker et al. (,2003) and Maercker et al. (22"2010), a result that they attribute to gas.","2010), a result that they attribute to gas."23 We neither see nor resolve another shell at the position of shell 4., We neither see nor resolve another shell at the position of shell 4.24" Since the CO data confirm the existence of a detached molecular shell at ~43”,, we conclude that the dust shell and the gas shell are co-spatial."," Since the CO data confirm the existence of a detached molecular shell at $\sim$, we conclude that the dust shell and the gas shell are co-spatial."25 This is similar to what is seen for CCyg and again raises questions about the absence of gas/dust drift., This is similar to what is seen for Cyg and again raises questions about the absence of gas/dust drift.26" Concerning shell 4, one can suggest that it is not resolved in the PACS data, but if that were the case, the peak intensity that we see at ~43” sshould have been clearly detected in polarised scattered light, but this is not the case."," Concerning shell 4, one can suggest that it is not resolved in the PACS data, but if that were the case, the peak intensity that we see at $\sim$ should have been clearly detected in polarised scattered light, but this is not the case."27 TheIRAS maps obtained 60 and 100 um by Izumiura et al. (1997)), TheIRAS maps obtained 60 and 100 $\mu$ m by Izumiura et al. \cite{Izumi97}) )28 indicate distant emission at about3'., indicate distant emission at about.29. Only part of this extended emission could be recovered by special treatment of the maps (see online Fig. 5))., Only part of this extended emission could be recovered by special treatment of the maps (see online Fig. \ref{UAntlow}) ).30 An improved data reduction may reveal all of the extended emission (see Sect. ??))., An improved data reduction may reveal all of the extended emission (see Sect. \ref{reduction}) ).31 Using one detached shell model does not lead to a reliable fit to the intensity profile., Using one detached shell model does not lead to a reliable fit to the intensity profile.32 Some of the emission seen within the outer shell is not accounted for., Some of the emission seen within the outer shell is not accounted for.33 Varying the density distribution does not improve the fit and using more than one detached shell introduces a variation in the intensity that is not seen in the profile (Fig.2))., Varying the density distribution does not improve the fit and using more than one detached shell introduces a variation in the intensity that is not seen in the profile \ref{profiles}) ).34 This discrepancy may be caused by the origin of the detached shell., This discrepancy may be caused by the origin of the detached shell.35" If it did originate from a wind-wind or wind-ISM interaction, the envelope would have slowed down with time."," If it did originate from a wind–wind or wind–ISM interaction, the envelope would have slowed down with time."36 This was not taken into account in our modelling., This was not taken into account in our modelling.37"in the Large Magellanic Cloud (a = 5h 35m 28.035. ὃ = 69° 16) 11.79"") (seereviewsbyPanagia2008andinInum-leretal. 2007)..","in the Large Magellanic Cloud $\alpha$ = 5h 35m 28.03s, $\delta$ = $-$ $^\circ$ $^\prime$ $^{\prime\prime}$ ) \citetext{see reviews by \citealp{panagia08} and in \citealp{immler20yrs07}}."38 Its progenitor was the blue supergiant Sk l (Panagia1987:Gilmozzietal.Barkat&Wheeler1988:Woosleyetal. 2002).," Its progenitor was the blue supergiant Sk 1 \citep{panagia87, gilmozzi87, barkat88, woosley02}."39. Ehe color of the progenitor. as well as the origin of the complex three-ring nebula in the remnant. are still unexplained.," The color of the progenitor, as well as the origin of the complex three-ring nebula in the remnant, are still unexplained."40" Detailed simulations of the evolutionary history of Sk 1. performed. hy Podsiadlowskietal. (2007).. support the theory that two massive stars merecd to form an oversized 20A. red supergiant οLO"" vears before the supernova. which eventually shrank as itsenvelope evaporated (e.g.Podsiadlowski&Joss1989:Podslaclowskietal. 1990)."," Detailed simulations of the evolutionary history of Sk 1, performed by \citet{podsiadlowski07}, support the theory that two massive stars merged to form an oversized $20 M_\odot$ red supergiant $2 \times 10^5$ years before the supernova, which eventually shrank as itsenvelope evaporated \citep[e.g.][]{podsiadlowski89, podsiadlowski90}."41. An alternative theory suggests that- Sk l was instead a single M. red supereiant which evolved into a blue supergiant via windedriven mass loss WoosleyLOSS:Saioetal.Sugermanct 2005).," An alternative theory suggests that Sk 1 was instead a single $M_\odot$ red supergiant which evolved into a blue supergiant via wind-driven mass loss \citep[e.g.][]{woosley88, saio88, sugerman05}."42. There is strong evidence for the existence of a neutron star in SNR 1987A. The progenitor mass range required to xoduce Type HE supernovae. M. which includes the above evolutionary scenarios. is the same range required to ooduce neutron star remnants (Woosleyetal.2002:HHegeretal. 2003).," There is strong evidence for the existence of a neutron star in SNR 1987A. The progenitor mass range required to produce Type II supernovae, $M_\odot$, which includes the above evolutionary scenarios, is the same range required to produce neutron star remnants \citep{woosley02, heger03}."43. The secure neutrino detections mentioned in Section 1| support thisconclusion., The secure neutrino detections mentioned in Section \ref{sec:ccintro} support thisconclusion.44 Although there have »en no confirmed pulsar. detections. numerous. searches 1ave placed. upper Limits on the flux and luminosity at raclio (<115pJvat1390MlIIz.Manchester2007).. optical/near-UV (c8S-LO eergss 2005). ancl soft X-ray («2.3LO ergs waveleneths.," Although there have been no confirmed pulsar detections, numerous searches have placed upper limits on the flux and luminosity at radio \citep[$< 115$ $\mu$Jy at 1390 MHz, ][]{manchester07}, optical/near-UV \citep[$< 8 \times 10^{33}$ ergs $^{-1}$, and soft X-ray \citep[$< 2.3 \times 10^{34}$ erg $^{-1}$ wavelengths."45" Micdleditehctal.(2000). reported finding an optical pulsar in SNR 1987 with a frequenev. of HEIz. modulated sinusoidally with a  I-ks period. consistent with precession for an ellipticity ofe~LO""."," \citet{middleditch00} reported finding an optical pulsar in SNR 1987A with a frequency of Hz, modulated sinusoidally with a $\sim$ 1-ks period, consistent with precession for an ellipticity of $\epsilon \sim 10^{-6}$."46 However. the pulsations were reported to have disappeared after 1996. (CMicddlecditceh2000) and were never confirmed independently.," However, the pulsations were reported to have disappeared after 1996 \citep{middleditch00} and were never confirmed independently."47 There are several possible reasons why a pulsar in SNA. LOSTA has not να been detected., There are several possible reasons why a pulsar in SNR 1987A has not yet been detected.48 LE its spin. period is greater than O.lss. it would not be bright enough. to be detectable in the optical hand (Pacini&Salvati1987:Alanchester 2007).," If its spin period is greater than s, it would not be bright enough to be detectable in the optical band \citep{pacini87, manchester07}."49. Lo the racio. emission is incoherent or the emission region is patchy. the pulses may. have been missed. even if the beam width is as wide as is typical for voung pulsars (Manchester2007).," If the radio emission is incoherent or the emission region is patchy, the pulses may have been missed, even if the beam width is as wide as is typical for young pulsars \citep{manchester07}."50. Shternin&Yakovlev(2008) argued that. although the neutron stars theoretical X-ray luminosity exceeds the observational upper limits by a [actor of 20.100. the current upper limits still allow for concealment behind an opaque shell formed. by. fallback (Woosley&Weaver1995).," \citet{shternin08} argued that, although the neutron star's theoretical X-ray luminosity exceeds the observational upper limits by a factor of 20–100, the current upper limits still allow for concealment behind an opaque shell formed by fallback \citep{woosley95}."51. Llowever. simulations by Fryeretal.(1999) suggest that. once fallback ceases. the aceretecl material cools. leaving no obscuring atmosphere.," However, simulations by \citet{fryer99} suggest that, once fallback ceases, the accreted material cools, leaving no obscuring atmosphere."52 Another possible reason why a pulsar has not vet been detected is that its magnetic field is too weak., Another possible reason why a pulsar has not yet been detected is that its magnetic field is too weak.53 The weak-field theory is supported by theoretical niocdels. in which the field. grows only after the neutron star is formed. and can take up to LO? vears to develop (e.g.Blandford&RomaniLoss:Reiscnegecr 2003).," The weak-field theory is supported by theoretical models, in which the field grows only after the neutron star is formed and can take up to $10^3$ years to develop \citep[e.g.][]{blandford88, reisenegger03}."54.. A growth model for SNR. LOSTA was proposed by Michel(1994).. in which the magnetic field of a millisecond pulsar intensifies [rom LOM OC at birth to ~1072 GG after several hundred. vears (exponential and linear erowth were considered. vielding growth times of ~ 0.30.7 ker). before the pulsar has time to spin down significantly.," A growth model for SNR 1987A was proposed by \citet{michel94}, in which the magnetic field of a millisecond pulsar intensifies from $10^{10}$ G at birth to $\sim 10^{12}$ G after several hundred years (exponential and linear growth were considered, yielding growth times of $\sim$ 0.3–0.7 kyr), before the pulsar has time to spin down significantly."55 In an alternative model. the neutron star is born with a strong magnetic field. which is amplified during the first [ew seconds of its life by dynamo action (e.g.Duncan&Thompson1992:," In an alternative model, the neutron star is born with a strong magnetic field, which is amplified during the first few seconds of its life by dynamo action \citep[e.g.][]{duncan92, bonanno05}."56 Assuming this mocel. measurements of the known spin periods of isolated radio pulsars imply a distribution of birth magnetic Lele strengths between 107 and 10776. CArzoumanianetal.2002:Paucher-Giguére&Ixaspi2006).," Assuming this model, measurements of the known spin periods of isolated radio pulsars imply a distribution of birth magnetic field strengths between $10^{12}$ G and $10^{13}$ G \citep{arzoumanian02, faucher06}."57. Several birth scenarios for the pulsar in SNR LOSTA were considered. by Ogelman&Alpar(2004) in this context. who concluded that the maximum magnetic dipole moment is «Ll107 GG emt? 2.5«107 GG em. and 2.5«107 GC em? for birth periods of mms. mms. ancl O.8ss respectively.," Several birth scenarios for the pulsar in SNR 1987A were considered by \citet{ogelman04} in this context, who concluded that the maximum magnetic dipole moment is $< 1.1 \times 10^{26}$ G $^3$, $2.5 \times 10^{28}$ G $^3$, and $2.5 \times 10^{30}$ G $^3$ for birth periods of ms, ms, and s respectively."58 However. the dynamo model. also accommocdates a magnetar in SNR 1987X. with magnetic dipole moment z2.4.10? GG en. regardless of the initial spin period (Ogelman&Alpar2004).," However, the dynamo model also accommodates a magnetar in SNR 1987A, with magnetic dipole moment $> 2.4 \times 10^{34}$ G $^3$, regardless of the initial spin period \citep{ogelman04}."59. Estimates of the birth spin of the pulsar in SNR 1987 are more uncertain., Estimates of the birth spin of the pulsar in SNR 1987A are more uncertain.60 Simulations of the bounce and post-bounce phases of core collapse were performed. by Ouetal.(2006). to determine the correlation between progenitor properties ancl birth spin., Simulations of the bounce and post-bounce phases of core collapse were performed by \citet{ott06} to determine the correlation between progenitor properties and birth spin.61 These authors found proto-neutron star spin periods of between 4.7140 ms. proportional to the progenitors spin period.," These authors found proto-neutron star spin periods of between 4.7–140 ms, proportional to the progenitor's spin period."62 A Monte Carlo population svnthesis study using known velocity clistributions GCXrzoumanianetal.2005} favoured. shorter millisccond periods. but. a similar population study by Faueher-Giguere&Ixaspi(2006). argued that the birth spin periods could. be as high as several hundred: milliseconds.," A Monte Carlo population synthesis study using known velocity distributions \citep{arzoumanian02} favoured shorter millisecond periods, but a similar population study by \citet{faucher06} argued that the birth spin periods could be as high as several hundred milliseconds."63 Faint. non-pulsed X-ray emission from SNIU LOSTA was firs observed. four months alter the supernova and. decreasec steacily in 1989 (Dotanictal.1987:Inoue1991).. leading to the suggestion. that a neutron star could be powering a plerion that is partially obscured by a fragmentec supernova envelope.," Faint, non-pulsed X-ray emission from SNR 1987A was first observed four months after the supernova and decreased steadily in 1989 \citep{dotani87, inoue91}, leading to the suggestion that a neutron star could be powering a plerion that is partially obscured by a fragmented supernova envelope."64 Bandieractal.(1955) modelled. the X-ray spectrum from a nebula containing a central pulsar. . ∖∖⋎∐↓↕⋜↧⊔↓⋜↧⋏∙≟↓⊔⊾⇂⊔∼↓⊓⊾↓∠⇂∪⇂↓∪≺∣≺∣⋜⋯∠⇂⋜⋯⋖⋅⇀∖↓≻⋜⋯⊳∖↓∪⊔↓⋅⋜⋯⊾∪ ⋠⋅ ⋅⊥⊐⊲⊲ ⋠ ⋅↱≻↓∪↴∖⊓⇍⊔↓⊳∖↓⊳↾↓," \citet{bandiera88} modelled the X-ray spectrum from a nebula containing a central pulsar, with a magnetic field of $10^{12}$ G and an expansion rate of $5 \times 10^8$ cm $^{-1}$."65∖↓↥∢⊾⋯∐↓↥∪↓⋅⊳∖⇂⋅∪⊔⊔∠⇂⋜↧∐↿↿∪↿⇂↥∢⋅∺↓∖⊽∐↓≤⋗↖∖⊤⇀∖ data for a pulsar spin period of mms., The authors founda fit to the SNR 1987A data for a pulsar spin period of ms.66 In this section. we briefly summarise the cross-correlation method. described in Dhurandhbaretal.(2008)... à. semi-coherent search algorithm: designed: specifically. to search for continuous-wave gravitational radiation.," In this section, we briefly summarise the cross-correlation method described in \citet{dhurandhar08}, a semi-coherent search algorithm designed specifically to search for continuous-wave gravitational radiation."67 It operates on Short Fourier Transforms (SEES) of data segments of length AT=30 min. whose duration is chosen to minimise the Doppler effects due to Earth's rotation.," It operates on Short Fourier Transforms (SFTs) of data segments of length $\Delta T = 30$ min, whose duration is chosen to minimise the Doppler effects due to Earth's rotation."68 In cach SET. the Ath frequency bin corresponds to the frequency y=hfAT [for 0xhkN22 and py—GSUND/INT For iN2xRUN 1. where IN is the total number of frequency. bins in the SET.," In each SFT, the$k$ th frequency bin corresponds to the frequency $\nu_k = k/\Delta T$ for $0 \leq k \leq N/2$ and $\nu_k = (k-N)/\Delta T$ for $N/2 \leq k \leq N-1$ , where $N$ is the total number of frequency bins in the SFT."69 The output (0) of a detector. is the sum of the instantaneous noise. n(/). and the gravitational wave signal. h(P).," The output $x(t)$ of a detector is the sum of the instantaneous noise, $n(t)$ , and the gravitational wave signal, $h(t)$ ."70 The noise is assumed to be zero mean. stationary. and Gaussian.," The noise is assumed to be zero mean, stationary, and Gaussian."71" Its power is characterised. by S, (7). the single- power spectral density. (Le. the frequency-dependent noise lloor) in the following wav: where 7 denotes complex conjugation."," Its power is characterised by $S_n(\nu)$ , the single-sided power spectral density (i.e. the frequency-dependent noise floor) in the following way: where $^*$ denotes complex conjugation."72 Therefore. in the low signal limit ([h€D]|« |n(0)|). the power in the &-th frequeney," Therefore, in the low signal limit $\lvert h(t) \rvert \ll \lvert n(t) \rvert$ ), the power in the $k$ -th frequency"73faite. Mpage. (Ixormendy.&Nennientt2004:CescuttiMatteucci2011).. Ixuijke,"$t_{\rm{Bulge}}$ ${\Delta}t_{\rm{Bulge}}$ \citep{2004ARA&A..42..603K,2011A&A...525A.126C,2011arXiv1109.2898I}."74n&Rich(2002) (2003) Clarksonetal.(2011). Bensbyetal.(2010.2011).. logg. Tar. ~3% (|/|SS5.2<|b]<5) «100 ομως<5 P«10? ," \citet{2002AJ....124.2054K} \citet{2003A&A...399..931Z} \citet{2011ApJ...735...37C} \citet{2010A&A...512A..41B,2011A&A...533A.134B}, $\log{g}$ $T_{\rm{eff}}$ $\sim$ $(|l| \lesssim 5, 2 \lesssim |b| \lesssim 5)$ $\sim$ $t_{\rm{Inferred}}\leq5$ $P < 10^{-5}$ "75with SIM will be used to remove the residual distortions of the grid reference svstem based on the red giants. with respect to the extra-galactic reference system based on (he quasars (Johnstonetal.|2003).,"with SIM will be used to remove the residual distortions of the grid reference system based on the red giants, with respect to the extra-galactic reference system based on the quasars \citep{john}."76. We note here. that in order to make the SIM reference. [rame ἐν inertial to accuracy better than Llµαςvrτν the residual spin present in the proper motion field and caused by the indefinite rotation of the grid solution. must be removed as well.," We note here, that in order to make the SIM reference frame truly inertial to accuracy better than $1~ \uasyr$, the residual spin present in the proper motion field and caused by the indefinite rotation of the grid solution, must be removed as well."77 Rigid rotations (spins) of the reference svstem around the coordinate axes X. Y. and Z are represented by the first three magnetic-tvpe vector harmonics of the observed proper motion field (Vitvazev&Shuksto2004).," Rigid rotations (spins) of the reference system around the coordinate axes $X$, $Y$ and $Z$ are represented by the first three magnetic-type vector harmonics of the observed proper motion field \citep{vit}."78. Hence. residual spins are orthogonal to the secular aberration effect ancl. for this reason. can be neatly separated [rom it in the vector harmonic space.," Hence, residual spins are orthogonal to the secular aberration effect and, for this reason, can be neatly separated from it in the vector harmonic space."79 This point can be effectively. demonstrated by comparing the pattern of the proper motion field induced by the secular aberration and shown in Figure 1.. against the patterns of the proper motion fields induced bv residual spins of the elobal solution about X.3.Z axes shown in Figures 2.. 3.. and 4. respectively.," This point can be effectively demonstrated by comparing the pattern of the proper motion field induced by the secular aberration and shown in Figure \ref{pmfield.fig}, against the patterns of the proper motion fields induced by residual spins of the global solution about $X,Y,Z$ axes shown in Figures \ref{pmfield-X}, \ref{pmfield-Y}, and \ref{pmfield-Z} respectively."80 The covariance matrix. Cov|a]. of the secular acceleration components is given in Table 2..," The covariance matrix, ${\rm Cov}[\hat a]$, of the secular acceleration components is given in Table \ref{tab1}."81 The diagonal elements of the matrix are (he unit-weight variances of (he corresponding X.Y.Z components of the proper motion field (?22)).," The diagonal elements of the matrix are the unit-weight variances of the corresponding $X,Y,Z$ components of the proper motion field \ref{ko}) )."82" For example. the standard deviation of a, in units of lis estimated as follows OEY and similarly lor other coefficients. where o; is the standare error of a single measurement (the interferometer path delav). expressed injs."," For example, the standard deviation of $a_1$ in units of is estimated as follows _0, and similarly for other coefficients, where $\sigma_0$ is the standard error of a single measurement (the interferometer path delay), expressed in."83 For quasars as bright as my=14 magnitude. single measurement errors of 15+20 could probably be achieved without spending too much integration time on these objects.," For quasars as bright as $m_V=14$ magnitude, single measurement errors of $15\div 20$ could probably be achieved without spending too much integration time on these objects."84 Hence. the largest component of the proper motion fieklin S5. which is proportional to the galactocentric component iy of the solar acceleration. will be determined with an error. σεν)c1.5 tas follows from equation (??)).," Hence, the largest component of the proper motion fieldin $\vec S_{11}^c$, which is proportional to the galactocentric component $A_X$ of the solar acceleration, will be determined with an error, $\sigma(A_X)\simeq 1.5$ as follows from equation \ref{ft}) )."85 This accuracy is sufficient. for a statistically robust detection of the acceleration al a signal-to-noise ratio of roughly 3., This accuracy is sufficient for a statistically robust detection of the acceleration at a signal-to-noise ratio of roughly 3.86 We have seen (hat. upon observing 110 optically bright quasars as grid objects. SIAL PlanetQuest will be able to detect the major galactocentric component of the acceleration ol the Sun.," We have seen that, upon observing 110 optically bright quasars as grid objects, SIM PlanetQuest will be able to detect the major galactocentric component of the acceleration of the Sun."87 At the same time. the anticipated accuracy of SIM is not high enough to detect the peculiar acceleration of the Sun with respect to the ΓΗ. nor to refine the fundamental constants [αι and A.," At the same time, the anticipated accuracy of SIM is not high enough to detect the peculiar acceleration of the Sun with respect to the LSR, nor to refine the fundamental constants $P_0$ and $R_0$ ."88 In order to do this a dedicated interferometric mission is required., In order to do this a dedicated interferometric mission is required.89and where vy.  are constants and Qo is the present-day (f= £0) angular frequency of the disc (rotation were taken from Sofue et al.,"and where $\nu_{\rm d}$ , $\nu'_{\rm d}$ are constants and $\Omega_0$ is the present-day $t=t_0$ ) angular frequency of the disc (rotation were taken from Sofue et al."90 1999)., 1999).91" To avoid unphysical “kinks” when switching between the two star formation regimes. a “smooth step function"". defined as. is used instead of an actual conditional expression."," To avoid unphysical ""kinks"" when switching between the two star formation regimes, a ""smooth step function"", defined as, is used instead of an actual conditional expression."92" This function will approach a regular Heaviside step function as k—oo, but here it is assumed that k=1."," This function will approach a regular Heaviside step function as $k\to \infty$, but here it is assumed that $k=1$."93 The eritical density x. may change along the disc. but for simplicity it is assumed that =.=7.0M. pe over the whole dise (Kennicutt1989).," The critical density $\Sigma_{\rm c}$ may change along the disc, but for simplicity it is assumed that $\Sigma_{\rm c} = 7.0 M_\odot$ $^{-2}$ over the whole disc \cite{Kennicutt89}."94". Two different star formation prescriptions are considered in this paper: (1) a Schmidt law as above with &=0.5 Fuchsetal.2009) above the critical gas density ὃς. and with lower efficiency according to a linear Schmidt-law X,=vqLeas. Where v4=0.251). and (2) a Schmidt law with evy=O and a strict threshold. Le. vi=0>X, below the critical density|)."," Two different star formation prescriptions are considered in this paper: (1) a Schmidt law as above with $\varepsilon = 0.5$ \cite[cf.][]{Fuchs09} above the critical gas density $\Sigma_{\rm c}$, and with lower efficiency according to a linear Schmidt-law $\dot{\Sigma}_\star = \nu'_{\rm d}\,\Sigma_{\rm gas}$, where $\nu'_{\rm d} = 0.25 \nu_{\rm d}$, and (2) a Schmidt law with $\varepsilon = 0$ and a strict threshold, i.e., $\nu'_{\rm d} = 0 \to \dot{\Sigma}_\star = 0$ below the critical density."95 The first case will be referred to as star formation law of type I. and the second case as type 2.," The first case will be referred to as star formation law of type 1, and the second case as type 2."96 It is assumed that stars are formed according to a stellar IMF that may. or may not. be time-dependent.," It is assumed that stars are formed according to a stellar IMF that may, or may not, be time-dependent."97 In its simplest form. the IMF is just a power-law with sharp cut-offs at the lower and upper ends.," In its simplest form, the IMF is just a power-law with sharp cut-offs at the lower and upper ends."98 It is well established. however. that the IMF turns over at low masses and is probably truncated at the high-mass end (see Fig.," It is well established, however, that the IMF turns over at low masses and is probably truncated at the high-mass end (see Fig."99 2. and references therein)., \ref{imf} and references therein).100" Hence. an IMF of the form is adopted. where mic. mu, are the masses defining the low-mass turn over and the high-mass truncation of theIMF. respectively."," Hence, an IMF of the form is adopted, where $m_{\rm c}$ , $m_{\rm u}$ are the masses defining the low-mass turn over and the high-mass truncation of theIMF, respectively."101" The two parameters 71.. 71, may be regarded as functions of time. thus allowing for an evolving IMF."," The two parameters $m_{\rm c}$, $m_{\rm u}$ may be regarded as functions of time, thus allowing for an evolving IMF."102 The constant do. which is obtained by the normalisation condition οis then also a function:. of- time.," The constant $\phi_0$, which is obtained by the normalisation condition is then also a function of time."103" More precisely.. where πμ.j is a dimensionless variable defined as and K, is the modified Bessel function of the second kind and order η."," More precisely, where $\mu$ is a dimensionless variable defined as and $K_n$ is the modified Bessel function of the second kind and order $n$."104 The mean stellar mass of this IMF is while the mostprobable mass is given by Both the mean and most probable masses are also functions of time in the general case., The mean stellar mass of this IMF is while the mostprobable mass is given by Both the mean and most probable masses are also functions of time in the general case.105 However. in the special case when Io)xmf). or p=const.. the situation is somewhat simpler.," However, in the special case when $m_{\rm c}(t) \propto m_{\rm u}(t)$, or $\mu = \mbox{const.}$, the situation is somewhat simpler."106 First of all. 6o becomes constant over time and the IMF to be renormalised at every time step.," First of all, $\phi_0$ becomes constant over time and the IMF to be renormalised at every time step."107 This simplifying assumption will be used throughout the following., This simplifying assumption will be used throughout the following.108 The time-evolution of the parameters m2. and 7j cannot be completely arbitrary., The time-evolution of the parameters $m_{\rm c}$ and $m_{\rm u}$ cannot be completely arbitrary.109 They are quite likely related to some characteristic mass-scale related to the physical origin of the IMF., They are quite likely related to some characteristic mass-scale related to the physical origin of the IMF.110 Larson (1995; 1996; 1998) pointed out that there should be a connection between the turn-over mass (or the characteristic stellar mass) and some fundamental mass-scale in the star formation process. such as the Jeans mass (Jeans1902).," Larson (1995; 1996; 1998) pointed out that there should be a connection between the turn-over mass (or the characteristic stellar mass) and some fundamental mass-scale in the star formation process, such as the Jeans mass \cite{Jeans02}."111. Recent observational evidence for an evolving IMF characteristic stellar masses which are consistent with such a picture (vanDokkum2008)., Recent observational evidence for an evolving IMF characteristic stellar masses which are consistent with such a picture \cite{vanDokkum08}.112. The thermal Jeans mass is given by the pressure and temperature of the collapsing cloud. ie. myeTP-'7.," The thermal Jeans mass is given by the pressure and temperature of the collapsing cloud, i.e., $m_{\rm J} \propto T^2 P^{-1/2}$."113 In a self-gravitating cloud. the pressure-gravity balance is such that the Jeans mass can also be expressed in terms of the gas surface density X as my«T7X! (see. e.g.. Larson 1985).," In a self-gravitating cloud, the pressure-gravity balance is such that the Jeans mass can also be expressed in terms of the gas surface density $\Sigma$ as $m_{\rm J} \propto T^2 \Sigma^{-1}$ (see, e.g., Larson 1985)."114 If the ISM is isothermal. the Jeans mass Is inversely proportional to thelocal surface density of the gas and if cooling ts inefficient. it may be close toconstant time.," If the ISM is isothermal, the Jeans mass is inversely proportional to thelocal surface density of the gas and if cooling is inefficient, it may be close toconstant ."115 In the following that the gas temperature T is a function of the gas density X alone. 1.e.. a polytropic," In the following that the gas temperature $T$ is a function of the gas density $\Sigma$ alone, i.e., a polytropic"116over 6 lu-loug periods).,over 6 hr-long periods).117 In this paper. the intraday variability aud the associated spectral changes in the s-ray baud of 3C12L3 are studied ancl comparisous are made with the findiugs obtained from earlier major flares.," In this paper, the intraday variability and the associated spectral changes in the $\gamma$ -ray band of 3C454.3 are studied and comparisons are made with the findings obtained from earlier major flares."118 In Section 2. observations and analysis of. Fermi-LAT. data from 2010 September 1 to December 13 are presented.," In Section 2, observations and analysis of -LAT data from 2010 September 1 to December 13 are presented."119 Results are presented in Section 3 aud discussion is given in Section L, Results are presented in Section 3 and discussion is given in Section 4.120" A flat ACDM cosmology with Hy=T1 lan + !. ,,=0.27 and Q\=0.73 is uxed iu this paper."," A flat $\Lambda$ CDM cosmology with $H_0=71\:$ km $^{-1}$ $^{-1}$, $\Omega_m=0.27$ and $\Omega_\Lambda$ =0.73 is used in this paper."121 The analysis performed for this paper is very σας to that reported in (2010).. to which we refer for details.," The analysis performed for this paper is very similar to that reported in \cite{2010ApJ...721.1383A}, to which we refer for details."122 The data presented in this paper are restricted to the 100 MeV-200 GeV range ail were collected from MJD55110 (2010 September 1) to MJD55513 (2010 December 13) iu survey 1uocde., The data presented in this paper are restricted to the $\:$ $\:$ GeV range and were collected from MJD55440 (2010 September 1) to MJD55543 (2010 December 13) in survey mode.123" Spectral analyses were performed by fitting the spectra with multiple different models over the whole energy range covered by the LAT at E> 100MeV. The spectral forms considered are a broken power law (BPL. NCE)=NoCEZEp,al)Mo wihi-litE«c« Elyal: aud 7=2if ΕEpale a log-parabola functionΕν] where Ey is fixed at GeV). a power law with exponential cutoff function (PLEC. ΕΕ). aud a PL moclel over equally spaced. logarithmic euergy bius with P kept coustant aud equal to the value fittecl over the whole rauge."," Spectral analyses were performed by fitting the spectra with multiple different models over the whole energy range covered by the LAT at $E>100\:$ MeV. The spectral forms considered are a broken power law (BPL, $N(E)=N_0124(E/E_\textit{break})^{-\Gamma_{i}}$, with $i=1$ if $E<E_\textit{break}$ and $i=2$ if $E>E_\textit{break}$ ), a log-parabola function, where $E_p$ is fixed at $\:$ GeV), a power law with exponential cutoff function (PLEC, ), and a PL model over equally spaced logarithmic energy bins with $\Gamma$ kept constant and equal to the value fitted over the whole range."125 Source variability was investigated by producing ligit curves with various time biuniugs (3hours. hours. day. week) auc over different energy ranges (E100 MeV. E21 GeV. GeV).," Source variability was investigated by producing light curves with various time binnings $\:$ hours, $\:$ hours, $\:$ day, $\:$ week) and over different energy ranges $>$ $\:$ MeV, $>$ $\:$ GeV, $\:$ GeV)."126 Although the actual spectral shape exhibits delinite curvature. light curves were produced. by mocleling the spectra in each time bin as a simple power law (PL) over the considered. energy range. suce the statistical uucertaiuties ou the power-law indices are sinaller than those obtained from BPL fits.," Although the actual spectral shape exhibits definite curvature, light curves were produced by modeling the spectra in each time bin as a simple power law (PL) over the considered energy range, since the statistical uncertainties on the power-law indices are smaller than those obtained from BPL fits."127" In order to minimize spurious correlations between integrated flix aud E. the fluxes Frsp,, were also computed above the “decorrelation energy” Ey where this correlation is minimal."," In order to minimize spurious correlations between integrated flux and $\Gamma$, the fluxes $F_{E>E_0}$ were also computed above the “decorrelation energy” $E_0$ where this correlation is minimal."128 For the 2009 December aud 2010 April flares. Ej was found to be MeV 2010).. ," For the 2009 December and 2010 April flares, $E_0$ was found to be $\:$ MeV \citep{2010ApJ...721.1383A}. ."129The same value las been used here for cousisteucy., The same value has been used here for consistency.130 The estimated systematic uncertainty on the [lux is at MeV. at MeV aud at GeV. The energy resolution is better than over the rangeof measured Ep," The estimated systematic uncertainty on the flux is at $\:$ MeV, at $\:$ MeV and at $\:$ GeV. The energy resolution is better than over the rangeof measured $_\textit{break}$ ."131"11D 46180 (CSC 0154-2360) is close visual pair in NGC 2244 composed. of components of V—9.1|9.3 at 6= 82°. and poc5.2"" (Masonetal.2001).","HD 46180 (GSC 0154-2360) is close visual pair in NGC 2244 composed of components of $V = 9.1 + 9.3$ at $\theta = 82\degr$ , and $\rho = 5.2''$ \citep{wds}."132. The stars were oriented almost along the spectrograph slit which enabled. us to simultaneously obtain spectra of either of the components on nights with the best seeing., The stars were oriented almost along the spectrograph slit which enabled us to simultaneously obtain spectra of either of the components on nights with the best seeing.133 Our spectroscopy shows that cach of the visual components is a binary star so that LID 46180 is a quadruple svstem., Our spectroscopy shows that each of the visual components is a binary star so that HD 46180 is a quadruple system.134 Unfortunately. we were able to obtain only 10 spectra of the brighter visual component and 4 of the fainter one (on other nights it was blended with the brighter component). which has prevented us to determine. the respective orbital periods.," Unfortunately, we were able to obtain only 10 spectra of the brighter visual component and 4 of the fainter one (on other nights it was blended with the brighter component), which has prevented us to determine the respective orbital periods."135 MOST satellite photometry refers to the whole quadruple svstem and shows that one of the binaries is an eclipsing one with the period of P?2=3.09 days and the photometric amplitude ofonly 0.02 mag., MOST satellite photometry refers to the whole quadruple system and shows that one of the binaries is an eclipsing one with the period of $P = 3.09$ days and the photometric amplitude of only 0.02 mag.136 The present data indicate that the brighter component of the visual pair is the variable one., The present data indicate that the brighter component of the visual pair is the variable one.137 Η 75638 (CSC 0814-0601) is a visual triple system WDS 08515|1208 consisting of components A (V= S28). BV 10.17) and € (VY=IL8).," HD 75638 (GSC 0814-0601) is a visual triple system WDS 08515+1208 consisting of components A $V = 8.28$ ), B ) and C $V = 11.8$ )."138 Our spectroscopy. refers to the mur XD. p = 1.4 aresec. which could not be separated on he DDO spectrograph slit.," Our spectroscopy refers to the pair AB, $\rho$ = 1.4 arcsec, which could not be separated on the DDO spectrograph slit."139 “Phe pair AB was suspected o be an SBS system in the survey of Nordstroenictal.(1997)., The pair AB was suspected to be an SB3 system in the survey of \citet{nord1997}.140.. Their analysis of 13 spectra showed two measurable components with eysing = SO km and essing = 10 uns 5. temperatures 71=7000A. and 75»=6750. and a uminosity ratio of 0.10.," Their analysis of 13 spectra showed two measurable components with $v_1 \sin i$ = 80 km $^{-1}$ and $v_2 \sin i$ = 10 km $^{-1}$, temperatures $T_1 = 7000 K$, and $T_2 = 6750 K$ , and a luminosity ratio of 0.10."141" A preliminary orbit for the fainter component was given: P? = 5.8167(9) days. Vu = 11.05(91) ums d. Αι = 289(12) km loe = 0.083(56). and aw =322(28)""."," A preliminary orbit for the fainter component was given: $P$ = 5.8167(9) days, $V_0$ = 11.05(91) km $^{-1}$, $K_1$ = 28.9(12) km $^{-1}$, $e$ = 0.083(56), and $\omega$ =."142. The spectroscopic orbit. most. likely corresponcls o the motion of the blend of a faint pair seen as component H>. The MOST. photometry showed: very. shallow (Am=)019) eclipses giving a preliminary mid-eclipse ephemeris. 11JD 2454145.85|5.81.E. in good accord the spectroscopic pesult of Nordstroemetal.(1997). (see Pribullactal.(200511).," The spectroscopic orbit most likely corresponds to the motion of the blend of a faint pair seen as component B. The MOST photometry showed very shallow $\Delta m = 0.013$ ) eclipses giving a preliminary mid-eclipse ephemeris, HJD $2\,454\,145.85 + 5.81 \times E$, in good accord the spectroscopic result of \citet{nord1997} (see \citet{m67}) )."143 Our spectroscopic results are related to the AB components., Our spectroscopic results are related to the AB components.144 “The broadening functions (Fig. 1)), The broadening functions (Fig. \ref{bfplots}) )145 show the xiehter. rapidlv-rotating component (esin’z50 km 1j o be stationary in the racial velocity: this star is most Likely he A component of the visual pair.," show the brighter, rapidly-rotating component $v \sin i \approx 85$ km $^{-1}$ ) to be stationary in the radial velocity; this star is most likely the A component of the visual pair."146 The fainter component B occasionally splits into two., The fainter component B occasionally splits into two.147 ALL three components are always ended. suggesting that a high-resolution spectroscopy will o» necessary to reliably define orbits of both components.," All three components are always blended, suggesting that a high-resolution spectroscopy will be necessary to reliably define orbits of both components."148 The medium dispersion spectroscopic survey of the variable stars discovered. by the MOST. satellite was planned. to include some 150 targets observed. several times to Cully ascertain types of variability., The medium dispersion spectroscopic survey of the variable stars discovered by the MOST satellite was planned to include some 150 targets observed several times to fully ascertain types of variability.149 “Phis has not. been possible because of the DDO observatory closure., This has not been possible because of the DDO observatory closure.150 We publish here radial velocities and spectral tvpe estimates for 103 NOST targets. 96 being variables with 83 of them being new MOST etections.," We publish here radial velocities and spectral type estimates for 103 MOST targets, 96 being variables with 83 of them being new MOST detections."151 For 31 targets. we give the projected rotational velocities esin/.," For 31 targets, we give the projected rotational velocities $v \sin i$."152 The survey resulted in the discovery of seven new spectroscopic binaries., The survey resulted in the discovery of seven new spectroscopic binaries.153 For two of these binaries (LID. 73709. and GSC 0814-0323). which were found to show eclipses by the MOST satellite photometry. preliminary spectroscopic orbits were determined.," For two of these binaries (HD 73709, and GSC 0814-0323), which were found to show eclipses by the MOST satellite photometry, preliminary spectroscopic orbits were determined."154 LED 46180 was found to be composed of two binary stars forming. very probably. a physical quacruple system.," HD 46180 was found to be composed of two binary stars forming, very probably, a physical quadruple system."155 According to the MOST photometry. one of the binaries is eclipsing.," According to the MOST photometry, one of the binaries is eclipsing."156 “Phe newly discovered μα»ecetroscopic binaries will require further spectroscopy to refine their orbital periods ancl the remaining orbital paranictcrs., The newly discovered spectroscopic binaries will require further spectroscopy to refine their orbital periods and the remaining orbital parameters.157 This study has been funded by the Canadian Space Agency Space Enhancement Program (SSIZP) with TI holding a Post-Doctoral Fellowship position at the University of ‘Toronto., This study has been funded by the Canadian Space Agency Space Enhancement Program (SSEP) with TP holding a Post-Doctoral Fellowship position at the University of Toronto.158 The Natural Sciences and. Engineering. Research Council of Canada (NSERC) supports the research of SAIR., The Natural Sciences and Engineering Research Council of Canada (NSERC) supports the research of SMR.159 Support from the Polish Science Committee (xBN grants ρου 006 22and PO3D 003 24) to WO is acknowledged with gratitude., Support from the Polish Science Committee (KBN grants PO3D 006 22and P03D 003 24) to WO is acknowledged with gratitude.160 The authorswould like to thank the telescope operators, The authorswould like to thank the telescope operators161equivalent width versus the difference between IIST IIa aud B-baud maguitudoe. to really compare the Te line fiux above the continua with the equivalent width.,"equivalent width versus the difference between HST $\alpha$ and R-band magnitude, to really compare the $\alpha$ line flux above the continuum with the equivalent width."162 We also used archived VRI obtained with the FOcal Reducer/low clispersion Spectrograph No., We also used archived VRI obtained with the FOcal Reducer/low dispersion Spectrograph No.163" 1 (FORSL) at the ESO 5.211. telescope Autu. Unit Telescope 1 (UT1) of the VLT. with a scale of 0.2"" /pixel. duriic stb-are sec coucditions."," 1 (FORS1) at the ESO 8.2m telescope Antu, Unit Telescope 1 (UT1) of the VLT, with a scale of $0.2 ^{\prime \prime}$ /pixel, during sub-arc sec conditions."164 See Table 1 for the observations log., See Table 4 for the observations log.165 We re-vreduced the erouncd-based images., We re-reduced the ground-based images.166 Some conaiion Caleidates were also detected in the VET VRI nuages. magnitudes are elven in Table 3.," Some companion candidates were also detected in the VLT VRI images, magnitudes are given in Table 3."167 Comparison of the IIST R Τ inaguitudes (Vega syste) for all the Cha Tea 1 to 12 objects with the previously known erounud-based BR. I maguitides (Cousins bands) from C2000 shows that they agree well (£0.1 lage)., Comparison of the HST R I magnitudes (Vega system) for all the Cha $\alpha$ 1 to 12 objects with the previously known ground-based R I magnitudes (Cousins bands) from C2000 shows that they agree well $\pm 0.1$ mag).168" IB imaecs in JT, were obtained using the IR ager Sou of Isaac (Sofl) at t16 ESO 3.511, NTT on La Silla with 0.6 to 7” secius.", IR images in $_{\rm s}$ were obtained using the IR imager Son of Isaac (SofI) at the ESO 3.5m NTT on La Silla with $\sim 0.6$ to $^{\prime \prime}$ seeing.169 Tages ο three fields were taken in March 2001 with thefield to achieve the highest augulu resolulou possie (OLL7 /pixel) with 2 sec inclivicual exposure per frame., Images of three fields were taken in March 2001 with the to achieve the highest angular resolution possible $0.147 ^{\prime \prime}$ /pixel) with 2 sec individual exposure per frame.170" Two more nuages (II Is.) were already taken in Marchi 2000 with thefield (0.29"" /pixel). so that several Cha Πα primaries were m thο fledeof-view. with 3 sec individual exposure per frame."," Two more images (H $_{\rm s}$ ) were already taken in March 2000 with the $0.29 ^{\prime \prime}$ /pixel), so that several Cha $\alpha$ primaries were in the field-of-view, with 3 sec individual exposure per frame."171" Darks. flats. aud standards were taken im the sale nieht: S.did we performed standard data reduction with aud See Tae for the observations log and Table 3 for the HII, magutudes."," Darks, flats, and standards were taken in the same nights, and we performed standard data reduction with and See Table 4 for the observations log and Table 3 for the $_{\rm s}$ magnitudes."172" Our JU. data for the ormuaries (Table 3) :wree well with those eive rin C2000. who had obtained tjcir data with IRAC?2 at he ESO/AIPG 2.214. The new LIS, data listed in Tabe 3 for the ormuariespri also agree well with the DENIS uaenitudes listed in Neuhauuser Comeróun (1999) for Cha Πα 1 to 8."," Our $_{\rm s}$ data for the primaries (Table 3) agree well with those given in C2000, who had obtained their data with IRAC2 at the ESO/MPG 2.2m. The new $_{\rm s}$ data listed in Table 3 for the primaries also agree well with the DENIS magnitudes listed in Neuhäuuser Comerónn (1999) for Cha $\alpha$ 1 to 8."173 The ILbaud maenitude of Cha Πα 8 (Tale 3) was not known before. as this object was not observed in the IR » C200 anc as t1e I-band filter is not used for DENIS.," The H-band magnitude of Cha $\alpha$ 8 (Table 3) was not known before, as this object was not observed in the IR by C2000 and as the H-band filter is not used for DENIS."174 Tje J Kk. lnaeuitides for Cha Πα 8 eiven in Tade 3 (from tje Marc[um 2000 nuage) aeree with the DENIS imagnuitudes even- Neuliiuuser Comeroun {1999)., The J $_{\rm s}$ magnitudes for Cha $\alpha$ 8 given in Table 3 (from the March 2000 image) agree with the DENIS magnitudes given in Neuhäuuser Comerónn (1999).175" Mos of our erouud-based. VREFHTR., uaenitudes were deterjid by normal aperture photonuetrv. with the exception for the VRIJ-baid nuages for the very close colpaion candidate near Cha Πο 5. which is discussed in deti in Sect."," Most of our ground-based $_{\rm s}$ magnitudes were determined by normal aperture photometry, with the exception for the VRIJ-band images for the very close companion candidate near Cha $\alpha$ 5, which is discussed in detail in Sect."176 6., 6.177 Lower limits to the magΜποος for undetected objects are derived from mean backeround iuensifv (uad its, Lower limits to the magnitudes for undetected objects are derived from mean background intensity (and its178"same parent population, and P—0.00366 when only the barred galaxies are considered.","same parent population, and $P = 0.00366$ when only the barred galaxies are considered."179" Restricted to the DR7-only subsample, the signficance becomes even stronger: P=0.00318 for all SOs and P=0.00264 for barred S0s. ("," Restricted to the DR7-only subsample, the signficance becomes even stronger: $P = 0.00318$ for all S0s and $P = 0.00264$ for barred S0s. ("180"When the smaller number of galaxies are considered, the differences are significant.)","When the smaller number of galaxies are considered, the differences are significant.)"181 So the difference in outer-disk profiles between the Virgo Cluster and the local field is both large statistically significant., So the difference in outer-disk profiles between the Virgo Cluster and the local field is both large statistically significant.182" Could we be missing truncations at larger radii in the Virgo S0s, and thus mis-classifying them as Type I?"," Could we be missing truncations at larger radii in the Virgo S0s, and thus mis-classifying them as Type I?"183 This seems quite unlikely., This seems quite unlikely.184" Figure 3 shows that break radii for field SOs occur at R~ 2-12 kpc, with surface brightnesses at the break of pfiprkrR«24 mag arcsec-?; the mean is 22.7."," Figure \ref{fig:break-radii} shows that break radii for field S0s occur at $R \sim 2$ –12 kpc, with surface brightnesses at the break of $\mu_{\rm brk, R}185< 24$ mag $^{-2}$; the mean $\mu_{\rm brk, R}$ is 22.7."186" Also plotted are limits on any possible Hr,breaks for Type I profiles.", Also plotted are limits on any possible breaks for Type I profiles.187" The latter are all >26 mag arcsec”, much fainter than any observed breaks."," The latter are all $>18826$ mag $^{-2}$, much fainter than any observed breaks."189" We can summarize the difference between outer-disk profiles in the Virgo Cluster and the field thus: Type III profiles are equally common in Virgo and in the field; in (roughly)Virgo, the remaining profiles are Type L while in the fieldthey are half Type I and half Type IL ("," We can summarize the difference between outer-disk profiles in the Virgo Cluster and the field thus: Type III profiles are (roughly) equally common in Virgo and in the field; in Virgo, the remaining profiles are Type I, while in the fieldthey are half Type I and half Type II. ("190"We note that MMaltby et 22011 found no significant environmental differences for disk-profile frequencies in and around a multiple-cluster system at z~0.17; however, their classification scheme used a narrow surface-brightness range and is thus rather different from If we focus on the difference between Type I and II ours.""))profiles and assume that it is indeed directly due to environmental effects, we can posit two possibilities: either something in the cluster (or proto-cluster) environment transforms Type II profiles into Type I, or else something a Type I to Type II transition which is common in the field.","We note that \nocite{maltby11}M Maltby et 2011 found no significant environmental differences for disk-profile frequencies in and around a multiple-cluster system at $z \sim 0.17$; however, their classification scheme used a narrow surface-brightness range and is thus rather different from ) If we focus on the difference between Type I and II profiles and assume that it is indeed directly due to environmental effects, we can posit two possibilities: either something in the cluster (or proto-cluster) environment transforms Type II profiles into Type I, or else something a Type I to Type II transition which is common in the field."191 The most popular models for disk truncations combine two elements., The most popular models for disk truncations combine two elements.192" The first is a radial dropoff in efficient star formation, either because the gas density falls below some critical star-formation threshold (Kennicutt1989;Schaye2004;Elmegreen&Hunter2006) or because the gas density profile itself has a sharp break, possibly due to accretion-induced warping (Roskaretal.2008a;Sánchez-Blázquezetal.2009;Martínez-Serrano 2009)."," The first is a radial dropoff in efficient star formation, either because the gas density falls below some critical star-formation threshold \citep{kennicutt89,schaye04,elmegreen06} or because the gas density profile itself has a sharp break, possibly due to accretion-induced warping \citep{roskar08a,sanchez-blazquez09,martinezserrano09}."193". The second element is the outward scattering of stars from the inner disk, such as produced by transient spiral arms (Sellwood&Binney2002;Roskaretal.2008a,b;Sánchez- 2009).."," The second element is the outward scattering of stars from the inner disk, such as produced by transient spiral arms \citep{sellwood02,roskar08a,roskar08b,sanchez-blazquez09,martinezserrano09}. ."194 The main problem is that these models tend to approach, The main problem is that these models tend to approach195wherep is the mean censity of planet.,$\bar{\rho}$ is the mean density of planet.196 Note that Equation (24) is only appropriate for ionized planetary wind., Note that Equation (24) is only appropriate for ionized planetary wind.197 Bul. it is not an easy task (ο determine whether the wind is ionizecl.," But, it is not an easy task to determine whether the wind is ionized."198" To maintain an ionized wind. the photoionization rate should be larger than recombination rate. namely. 5544>5,4."," To maintain an ionized wind, the photoionization rate should be larger than recombination rate, namely, $\gamma_{pho}199> \gamma_{rec}$."200" Thus. we have AU R=151. the optical depth 7~0. and Tz:10000k. H the wind is ionized highly al R=1.5/8, the value ορ is about 10-100."," Thus, we have At $R=1.5R_{p}$, the optical depth $\tau \sim 0$, and $T\approx20110000$ k. If the wind is ionized highly at $R=1.5R_{p}$, the value $n_{p}/n_{h}$ is about 10-100."202 Inequality (25) can be changed to With the assumption of Fry= 10'erg/eni /s. the left of inequality (26) is about in the order of magnitude 10°.," Inequality (25) can be changed to With the assumption of $F_{UV}=10^{3}$ $cm^{2}$ /s, the left of inequality (26) is about in the order of magnitude $10^{9}$."203 Using the hydrostatic density profile. we can estimate the particle number density al 7?ο ," Using the hydrostatic density profile, we can estimate the particle number density at $R=1.5R_{p}$ ."204"For IID 209453b. n,c7x10? so that ny is of the order of 1011,"," For HD 209458b, $n_{p}\sim 7\times10^{9}$ so that $\frac{n_{p}}{n_{h}}n_{p}$ is of the order of $10^{11}$."205 Because the left term of inequality (26) is smaller than the right term. the wind of ID 209453b is not ionized.," Because the left term of inequality (26) is smaller than the right term, the wind of HD 209458b is not ionized."206" For ILD 189733. n,~105."," For HD 189733, $n_{p}\sim 10^{8}$."207 Thus the inequality (26) can be fulfilled roughly if Fy> 10'erg/s. Many planets in our solar svstem have magnetic fields of their own., Thus the inequality (26) can be fulfilled roughly if $F_{UV}\geqslant 10^{3}$ erg/s. Many planets in our solar system have magnetic fields of their own.208 For example. the inagnelic field at the surface of Jupiter is about. 4.3G. What role the magnetic field plavs on the upper atmosphere depends on their field strength.," For example, the magnetic field at the surface of Jupiter is about 4.3G. What role the magnetic field plays on the upper atmosphere depends on their field strength."209 For the planets without intrinsic magnetic fields. the magnetic fields could be induced at the interaction area between the stellar aud planetary. winds.," For the planets without intrinsic magnetic fields, the magnetic fields could be induced at the interaction area between the stellar and planetary winds."210 However. (he occurrence of strong magnetic fieldsoccurring al," However, the occurrence of strong magnetic fieldsoccurring at"211into (he new spectral classes L and T (Geballeetal.2002).. which are characterized by the very red colors due to dust extinction and by the strong bands of methane ancl water. respectively.,"into the new spectral classes L and T \citep{geb02}, which are characterized by the very red colors due to dust extinction and by the strong bands of methane and water, respectively."212 Extensive efforts have been made (o interpret these new objects in terms of atmospheric chemistry including formation of dust clouds. as reviewed recently by Burrows el al. (," Extensive efforts have been made to interpret these new objects in terms of atmospheric chemistry including formation of dust clouds, as reviewed recently by Burrows et al. ("2132001).,2001).214 Although L and T dwarls appear to be quite different. we proposed that they can be understood consistently with the unified cloudy models (UCMs) in which a thin dust cloud is formed. always near the dust condensation temperature and hence will be located relatively deep in the photosphere lor the cooler T dwarls while will appear in the optically (hin regime in (he warmer L dwarls (Tsuji2002).," Although L and T dwarfs appear to be quite different, we proposed that they can be understood consistently with the unified cloudy models (UCMs) in which a thin dust cloud is formed always near the dust condensation temperature and hence will be located relatively deep in the photosphere for the cooler T dwarfs while will appear in the optically thin regime in the warmer L dwarfs \citep{tsu02}."215. The presence of the dust cloud deep in the photospheres was also shown by an application of the planetary theory. 2002)., The presence of the dust cloud deep in the photospheres was also shown by an application of the planetary theory \citep{mar02}.216. It is interesting that the presence of the thin dust cloud deep in the photospheres of ultracool cdwarls has been concluded from the quite different approaches., It is interesting that the presence of the thin dust cloud deep in the photospheres of ultracool dwarfs has been concluded from the quite different approaches.217 The nature of the cloud. however. is bv no means clear vet.," The nature of the cloud, however, is by no means clear yet."218 One major interest is if the cloud is subject to the meteorological activities familiar with the planets in the solar svslem., One major interest is if the cloud is subject to the meteorological activities familiar with the planets in the solar system.219 Such a possibility has so [ar been suggested by observing photometric variabilities which may be due to the inhomogeneity of the dust clouds (e.g.Dailer-Jones&Mundt2001:Martin.ZapateroOsorio.&Lehto 2001).," Such a possibility has so far been suggested by observing photometric variabilities which may be due to the inhomogeneity of the dust clouds \citep[e.g.][]220{bai01,mart01}."221. Also. an interesting finding of the recent parallax measurements is that the J magnitude shows a large brightening in the early T dwarfs 2002).," Also, an interesting finding of the recent parallax measurements is that the $J$ magnitude shows a large brightening in the early T dwarfs \citep{dah02}."222. This result was interpreted as evidence for the disruption of the dust cloud in the L/T clwarl iransition (Durgasseretal.2002b)., This result was interpreted as evidence for the disruption of the dust cloud in the L/T dwarf transition \citep{bur02b}.223. Belore such a possibility is explored. however. it is important to remember a more classical application of the CM diagram: namely as a touchstone of stellar models.," Before such a possibility is explored, however, it is important to remember a more classical application of the CM diagram; namely as a touchstone of stellar models."224 For (his purpose. the observed CM diagram of ultracool dwarls including brown clwarls is now accurate enough to be confronted with the theoretical evolutionary models 2002).," For this purpose, the observed CM diagram of ultracool dwarfs including brown dwarfs is now accurate enough to be confronted with the theoretical evolutionary models \citep[e.g.][]{dah02}."225. On the other hand. theoretical evolutionary tracks of the substellar mass objects have been discussed by Lavashi&Nakano(1963). already in the 1960s. ancl recent developments with improved input physics have been discussed by Burrowsetal.(L997) and by (2000).," On the other hand, theoretical evolutionary tracks of the substellar mass objects have been discussed by \citet{hay63} already in the 1960's, and recent developments with improved input physics have been discussed by \citet{burr97} and by \citet{cha00}."226. Given that the observed CM diagram ancl theoretical evolutionary models are both reasonably well established. a missing link between them is a realistic model photosphere to be used for the conversion of the fundamental stellar parameters to the observables.," Given that the observed CM diagram and theoretical evolutionary models are both reasonably well established, a missing link between them is a realistic model photosphere to be used for the conversion of the fundamental stellar parameters to the observables."227 We show in this letter that the missing link might be found in the UCAIs (Tsuji 2002)., We show in this letter that the missing link might be found in the UCMs (Tsuji 2002).228 We applied the UCAIs (ο convert the νο aud Zr of the evolutionary models to more easily observable monochromatic absolute magnitudes. ancl color indices: we discuss Aj , We applied the UCMs to convert the $M_{\rm bol}$ and $T_{\rm eff}$ of the evolutionary models to more easily observable monochromatic absolute magnitudes and color indices; we discuss $M_J$ 229The recent null detection of hot Jupiters in the globular cluster 47 Tucanae is an imiportant puzzle.,The recent null detection of hot Jupiters in the globular cluster 47 Tucanae \citep{gil00} is an important puzzle.230 This search for planetary svstems was sensitive {ο the detection of eas-eiant planets in orbits of less than five davs (0.05 AU) about a parent star: (he so-called “hot Jupiters.," This search for planetary systems was sensitive to the detection of gas-giant planets in orbits of less than five days $\sim 0.05\,$ AU) about a main-sequence parent star: the so-called “hot Jupiters”."231 IL the frequency of hot Jupiters in the solar, If the frequency of hot Jupiters in the solar232The present analvsis has been performed by using the library of stellar models and isochrones computed lor (he a-enhanced mixture presented by Pietrinfernietal.(2006).,The present analysis has been performed by using the library of stellar models and isochrones computed for the $\alpha$ -enhanced mixture presented by \citet{Pie06}.233. These models cover the whole metallicity range of GGCs. and have been computed. by assumine a primordial Ile content equal to. Y20.245 (seeCassisietal.therein) and a Ile enrichment ratio AY/AZ=Ld.," These models cover the whole metallicity range of GGCs, and have been computed by assuming a primordial He content equal to Y=0.245 \citep[see][and references therein]{Cass03} and a He enrichment ratio $\Delta{Y}/\Delta{Z}=1.4$."234 From now on. these will be referred lo asreference isochrones.," From now on, these will be referred to as isochrones."235 For a detailed discussion of the adopted pliysical inputs we refer to Pietrinfernietal.(2004.2006).. while for a careful discussion of the adopted color-T;y; relation and bolometric scale we refer to Cassisietal.(2004) and Beclinetal.(2005).," For a detailed discussion of the adopted physical inputs we refer to \citet{Pie04, Pie06}, while for a careful discussion of the adopted $T_{eff}$ relation and bolometric scale we refer to \citet{Cass04} and \citet{bedin05}."236. For the aim of testing the impact of an enhanced Ile content. we have computed an accditional extended set of stellar models for low-mass stars for both the II- and He-burning stages. by adopting the same a-enhanced mixture but accounting lor three larger He contents: namely. Y=0.30. 0.35. and 0.40.," For the aim of testing the impact of an enhanced He content, we have computed an additional extended set of stellar models for low-mass stars for both the H- and He-burning stages, by adopting the same $\alpha$ -enhanced mixture but accounting for three larger He contents; namely, Y=0.30, 0.35, and 0.40."237 In this context. it is worth mentioning that for a fixed global metallicity (Z). a change in the adopted Ile content causes a variation in the corresponding iron content. |Fe/1l]. according to the well-known definition of [Fe/H] as a function of Z and Y. Usually. this change is very small because the Ie contents adopted in stellar model computations do nol differ greatly [rom the vvalue (0.245<Y 0.27).," In this context, it is worth mentioning that for a fixed global metallicity (Z), a change in the adopted He content causes a variation in the corresponding iron content, [Fe/H], according to the well-known definition of [Fe/H] as a function of Z and Y. Usually this change is very small because the He contents adopted in stellar model computations do not differ greatly from the value $0.245\le{Y}\le0.27$ )."238 However. when dealing with extvemely Ie rich populations. (his effect might not be completely neglieible.," However, when dealing with extremely He rich populations, this effect might not be completely negligible."239 Therefore. when computing models for a fixed [Ῥο/ and a given He abundance. we rescale the global metallicity Z in order to preserve the [Fe/H] value: the metallicity Z has to be reduced when the He content is increased.," Therefore, when computing models for a fixed [Fe/H] and a given He abundance, we rescale the global metallicity Z in order to preserve the [Fe/H] value: the metallicity Z has to be reduced when the He content is increased."240 ‘This choice allows us. when comparing isochrones for various Ie-content assumptions. to compare isochrones for the same iron content consistently.," This choice allows us, when comparing isochrones for various He-content assumptions, to compare isochrones for the same iron content consistently."241 We recognize that the adopted Ile enhancements with respect (to the canonical value (Y~ 0.25) could appear too large to be considered realistic for GOGCs., We recognize that the adopted He enhancements with respect to the canonical value $Y\sim0.25$ ) could appear too large to be considered realistic for GGCs.242 ILowever. we emphasize that. in the present analvsis. we want (ο investigate - on a purely theoretical basis - the dependence of the relative age determinations on unrecognized peculiar chemical patterns.," However, we emphasize that, in the present analysis, we want to investigate - on a purely theoretical basis - the dependence of the relative age determinations on unrecognized peculiar chemical patterns."243 For this reason. we also take into account these extreme Ile enhancements.," For this reason, we also take into account these extreme He enhancements."244" oCDM example has scalar [ield potential energy density (όλoóa""να20. at low reclshilt (Peebles Ratra 1938: Ratra Peebles 1983): again CDM plays a subdominant role.","$\phi$ CDM example has scalar field potential energy density $V(\phi) \propto \phi^{-\alpha},245\alpha>0$, at low redshift (Peebles Ratra 1988; Ratra Peebles 1988); again CDM plays a subdominant role."246 Also discussed is the NCDM parametrization for time-varving dark energy., Also discussed is the XCDM parametrization for time-varying dark energy.247 This parametrization approximates dark energy by a fluid with a negative time-independent equation of state parameter i=P/p. where P? is the fluid. pressure and p the energy density.," This parametrization approximates dark energy by a fluid with a negative time-independent equation of state parameter $w=P/\rho$, where $P$ is the fluid pressure and $\rho$ the energy density."248 This is an inaccurate approximation during the scalar field dominated epoch when ie is time dependent (see. e.g.. Ratra 1991).," This is an inaccurate approximation during the scalar field dominated epoch when $w$ is time dependent (see, e.g., Ratra 1991)."249 We consider spatially [lat spacetimes for the o0CDM model and the XCDM parametrization. but. allow spatial curvature to be a Iree parameter in the ACDAI case.," We consider spatially flat spacetimes for the $\phi$ CDM model and the XCDM parametrization, but allow spatial curvature to be a free parameter in the $\Lambda$ CDM case."250 In this paper we constrain parameters of these three models by using SNla and galaxy cluster data., In this paper we constrain parameters of these three models by using SNIa and galaxy cluster data.251 In 52 we show how we use (he supernova and galaxy cluster data to constrain cosmological parameters., In $\S\: 2$ we show how we use the supernova and galaxy cluster data to constrain cosmological parameters.252 Results are presented aud discussed in 53., Results are presented and discussed in $\S \:3$.253 We conclude in §4., We conclude in $\S \:4$.254 AQ4 list x-ray gas mass fractions for 26 rich clusters. determined from Chandra observations.," A04 list x-ray gas mass fractions for 26 rich clusters, determined from $Chandra$ observations."255 These clusters lie at redshifts between 0.03 and 0.89., These clusters lie at redshifts between 0.08 and 0.89.256" Following AOL and CR. we use this data to determine the probability distribution function (likelihood) LO(Q4,.p./)."," Following A04 and CR, we use this data to determine the probability distribution function (likelihood) $L^G (\Omega_M, p,257h)$."258 Here fi is the Hubble constant in units of LOO kins'Mpe| and p is the cosmological constant density parameter Q4 lor the ACDAL model. w for the NCDM parametrization. aud à lor the 0CDM model.," Here $h$ is the Hubble constant in units of 100 $\kmsmpc$, and $p$ is the cosmological constant density parameter $\Omega_{\Lambda}$ for the $\Lambda$ CDM model, $w$ for the XCDM parametrization, and $\alpha$ for the $\phi$ CDM model."259" To derive LU(O.p.h) we marginalize over the bias [actor b. as well as over Q7/7. where €, is the barvonic mass density parameter."," To derive $L^G (\Omega_M, p, h)$ we marginalize over the bias factor $b$, as well as over $\Omega_bh^2$ , where $\Omega_b$ is the baryonic mass density parameter."260 Later we will need to marginalize over /;., Later we will need to marginalize over $h$.261" We account [or uncertainties in b. Q,7. and fh by using Gaussian priors with b=0.3242:0.089. Ομ=0.02142:0.002. and —0.72£0.08. all one standard deviation See A04 and CR. for more detailed discussions of the procedure we use."," We account for uncertainties in $b$, $\Omega_bh^2$, and $h$ by using Gaussian priors with $b=0.824 \pm2620.089$, $\Omega_bh^2=0.0214 \pm 0.002$, and $h=0.72 \pm 0.08$, all one standard deviation See A04 and CR for more detailed discussions of the procedure we use."263 We also use the SNIa apparent magnitude versus redshift data from RO4. in particular. the &old data set of 156 SNIa with redshifts up to almost 1.8.," We also use the SNIa apparent magnitude versus redshift data from R04, in particular, the gold data set of 156 SNIa with redshifts up to almost 1.8."264 From (hisdata we determine, From thisdata we determine265ssystelus at 50.091 and z=0.221 by Rac» Turnshek (1998) aud Turnshek ((2000) places especially stringent upper lirits on the luminosities of the host galaxies.,systems at $z=0.091$ and $z=0.221$ by Rao Turnshek (1998) and Turnshek (2000) places especially stringent upper limits on the luminosities of the host galaxies.266" The igest arguimenut for the rotating disk hyj»otliesis is the analysis of imetal-line. kinematics m savelelis by Prochaska Wolfe (1997. 1998). who cousider a variety of simplified models for the velocity structure of the absorbers aid find tha only a population of cold. rotating disks with typice"" CLEClar velocities e.Z200kms1 Call ace'ount for the observed distribution of velocity spreacS aud ‘or the high frequency of “lopsiced? kineimatic profiles."," The strongest argument for the rotating disk hypothesis is the analysis of metal-line kinematics in systems by Prochaska Wolfe (1997, 1998), who consider a variety of simplified models for the velocity structure of the absorbers and find that only a population of cold, rotating disks with typical circular velocities $v_c \ga 200\;\vunits$ can account for the observed distribution of velocity spreads and for the high frequency of “lopsided” kinematic profiles."267 However. hierarchicalcl models of galaxy formation predict that such massive disks should be rare at 2~3.," However, hierarchical models of galaxy formation predict that such massive disks should be rare at $z \sim 3$."268 In an impDuant paper. Haehuelt. Stelnetz. ltauch. (1998) showed hat hydrodsnatiic simulatious of higl-redshift galaxies could accoul for the lopsided kinematic proliles and Large velocity spreads [oui by Prochaska Wolfe (1997. 1998) even with halo circular velocities subsaliially below 200kins+. because of large scale asviunmetries and departures f‘oun dyuanmical equilibritum (see also Ledouxetal.(1998))).," In an important paper, Haehnelt, Steinmetz, Rauch (1998) showed that hydrodynamic simulations of high-redshift galaxies could account for the lopsided kinematic profiles and large velocity spreads found by Prochaska Wolfe (1997, 1998) even with halo circular velocities substantially below $200\;\vunits$, because of large scale asymmetries and departures from dynamical equilibrium (see also \citet{LP98}) )."269 This result makes the ~100kims1 inedian halo circilar “'elocities found by Ikaulfiuaun. (1996) aud GIXHW for the SCDNI model potentialy conupaible wit1 the observed metal-line kinematics., This result makes the $\sim 100\;\vunits$ median halo circular velocities found by Kauffmann (1996) and GKHW for the SCDM model potentially compatible with the observed metal-line kinematics.270 Our present simulatious do not vet have en151 resolutionluti for us to repeat the Haehlnelt ((190908) analysis: we hope to do so with fuure sinulatiols to carry out a statistical comparison betwee results from a randomy chosen cosimological voluie aud the Prochaska Wolle (1997. 1998) data.," Our present simulations do not yet have enough resolution for us to repeat the Haehnelt (1998) analysis; we hope to do so with future simulations to carry out a statistical comparison between results from a randomly chosen cosmological volume and the Prochaska Wolfe (1997, 1998) data."271 However. we can aδαν exteld the CISHW atalysis to other cosmological models. predictiig the fractio1 of aabsorpion arising ii halos ofdiffereut. circtlar velocities.," However, we can already extend the GKHW analysis to other cosmological models, predicting the fraction of absorption arising in halos of different circular velocities."272 We also revisit au important issue expored by IKWHM for the SCDAL model. the predicted distribuion of »ojected separaions betwee1 aaud ssyslens and hiel-redshift galaxies.," We also revisit an important issue explored by KWHM for the SCDM model, the predicted distribution of projected separations between and systems and high-redshift galaxies."273 Given tre number of recent attempts to directly image hhost galaxies. our predictions will be useful in testing the compatibility of the size and. probable luminosity of ow sinulated hhosts with the imagine cata.," Given the number of recent attempts to directly image host galaxies, our predictions will be useful in testing the compatibility of the size and probable luminosity of our simulated hosts with the imaging data."274 Section 2 ¢escribes the simulations aud our analysis methods., Section 2 describes the simulations and our analysis methods.275 Section 3 presents our analysis of the aaud ssystetus resolved by the simulations., Section 3 presents our analysis of the and systems resolved by the simulations.276 Section | describes aud applies our procedures for computiug the contribution Grom unresolved Lalos., Section 4 describes and applies our procedures for computing the contribution from unresolved halos.277 We discuss the implicatious of our results aud present our conclusions in 2., We discuss the implications of our results and present our conclusions in 5.278There is no pronounced blue star population in 664.,There is no pronounced blue star population in 64.279" Dozen of bluish stars, situated outside RGB in the colour-magnitude diagram, are spread over the ACS image and most of them have brighter close companion."," Dozen of bluish stars, situated outside RGB in the colour-magnitude diagram, are spread over the ACS image and most of them have brighter close companion."280 The precise knowledge of the distance is crucial to determine the star formation history from CMD analysis., The precise knowledge of the distance is crucial to determine the star formation history from CMD analysis.281 The photometric tip of the red giant branch (TRGB) distances to the galaxies were previously obtained by ? using HST/WFPC? images., The photometric tip of the red giant branch (TRGB) distances to the galaxies were previously obtained by \citet{k00} using HST/WFPC2 images.282 The true distance moduli given in that work are 27.78+0.15 for 661 and 27.84€0.15 for 664., The true distance moduli given in that work are $27.78\pm0.15$ for 61 and $27.84\pm0.15$ for 64.283" The corresponding distances are 3.6 Mpc and 3.7 Mpc, respectively."," The corresponding distances are 3.6 Mpc and 3.7 Mpc, respectively."284 ? has obtained distance moduli of 27.61+0.17 (D=3.3 Mpc) for 661 and 27.74€0.18 (3.5 Mpc) for 664 using surface brightness fluctuation (SBF) method based on B- and R-band images obtained with the Nordic Optical Telescope., \citet{recola05} has obtained distance moduli of $27.61\pm0.17$ $D = 3.3$ Mpc) for 61 and $27.74\pm0.18$ (3.5 Mpc) for 64 using surface brightness fluctuation (SBF) method based on $B$ - and $R$ -band images obtained with the Nordic Optical Telescope.285 Both measurements give consistent distances for our galaxies although the SBF measurements seem to give a little shorter scale., Both measurements give consistent distances for our galaxies although the SBF measurements seem to give a little shorter scale.286" However, the difference is inside the error bars."," However, the difference is inside the error bars."287" 'The present photometry is deeper and it has a higher quality, due to the advantage of the ACS detectors in comparison to the WFPC2."," The present photometry is deeper and it has a higher quality, due to the advantage of the ACS detectors in comparison to the WFPC2."288 There are also a number of recent improvements implemented to the TRGB method itself., There are also a number of recent improvements implemented to the TRGB method itself.289" We have determined the photometric TRGB distances with ourtrgbtool program, which uses a maximum-likelihood algorithm to determine the magnitude of tip of the red giant branch from the stellar luminosity function (?).."," We have determined the photometric TRGB distances with our program, which uses a maximum-likelihood algorithm to determine the magnitude of tip of the red giant branch from the stellar luminosity function \citep{makarov06}."290 The measured TRGB magnitudes are F814Wrresp=23.84+0.02 for KDG661 and F'814Wrres=23.87+0.02 for 664 in the ACS instrumental system., The measured TRGB magnitudes are $F814W_{TRGB} = 23.84\pm0.02$ for 61 and $F814W_{TRGB} = 23.87\pm0.02$ for 64 in the ACS instrumental system.291" As pointed in ?,, reaching measurements of this quality, the precision on the Galactic extinction becomes a major source of uncertainty."," As pointed in \citet{rizzietal07}, reaching measurements of this quality, the precision on the Galactic extinction becomes a major source of uncertainty."292" The precision of the extinction on the Schlegel’s maps is 16 perccents, resulting in an uncertainty of mmag in the J band."," The precision of the extinction on the Schlegel's maps is 16 cents, resulting in an uncertainty of mag in the $I$ band."293 The last source of error is the calibration of the TRGB distance indicator., The last source of error is the calibration of the TRGB distance indicator.294" Using the calibration for the TRGB distance indicator by ?,, and adding all the sources or errors, we derived the true distance moduli for 661: L(0)=27.77x:0.04 (D=3.58+0.07 Mpc) and 664: u(0)=27.84+0.00 (D=3.70+0.07 MMpc)."," Using the calibration for the TRGB distance indicator by \citet{rizzietal07}, , and adding all the sources or errors, we derived the true distance moduli for 61: $\mu(0) = 27.77\pm0.04$ $D = 3.58\pm0.07$ Mpc) and 64: $\mu(0) = 27.84\pm0.04$ $D = 3.70\pm0.07$ Mpc)."295 These new distances are in a good agreement with the previous estimations and they have a better precision., These new distances are in a good agreement with the previous estimations and they have a better precision.296 TRGB distances for several galaxies in M881 group were recently measured also by ? within their ANGST project., TRGB distances for several galaxies in 81 group were recently measured also by \citet{dalcanton09} within their ANGST project.297 The distance moduli of KDG661 (27.72) and 664 (27.85) are in good agreement with our values., The distance moduli of 61 (27.72) and 64 (27.85) are in good agreement with our values.298" The original Cepheid distance to 881, 3.63+0.34 Mpc (?),, was revised to 3.55+0.13 Mpc (?) (u=27.75+ 0.08)."," The original Cepheid distance to 81, $3.63 \pm 0.34$ Mpc \citep{freedman94}, was revised to $3.55 \pm 0.13$ Mpc \citep{freedman01} $\mu = 27.75 \pm 0.08$ )."299 This value is in close agreement with the TRGB distance from ?.., This value is in close agreement with the TRGB distance from \citet{dalcanton09}.300 Recently an independent geometric estimation using the size of the expanding shell around SN1993J gave the distance 3.96+0.29 Mpc (?).., Recently an independent geometric estimation using the size of the expanding shell around SN1993J gave the distance $3.96 \pm 0.29$ Mpc \citep{bartel07}.301" It is also consistent within the uncertainties, but larger than the two other determinations by 10 perccents."," It is also consistent within the uncertainties, but larger than the two other determinations by 10 cents."302" Discarding this last value, we adopt a distance 3.584-0.04 Mpc."," Discarding this last value, we adopt a distance $3.58 \pm 0.04$ Mpc."303" Beside the value from ?,, the distance to 33077 was determined by the surface brightness fluctuation (7) (0)=28.03+0.13 (4.04€0.15 Mpc) and TRGB methods (?) (0)=27.91 (3.82 Mpc)."," Beside the value from \citet{dalcanton09}, the distance to 3077 was determined by the surface brightness fluctuation \citep{tonry01}304 $\mu(0) = 28.03 \pm 0.13 $ $4.04 \pm 0.15$ Mpc) and TRGB methods \citep{karachentsev03}305 $\mu(0) = 27.91$ $3.82$ Mpc)."306" The two TRGB distances agree, and the SBF measurements is larger."," The two TRGB distances agree, and the SBF measurements is larger."307" We adopt the ANGST value (0)=27.92+0.02 (3.83+0.04 Mpc) These accurate distances for the two dwarf galaxies allow us to estimate their location within the group of galaxies, and more particularly with respect to M881 and 33077."," We adopt the ANGST value $\mu(0) = 27.92 \pm 0.02 $ $3.83 \pm 0.04$ Mpc) These accurate distances for the two dwarf galaxies allow us to estimate their location within the group of galaxies, and more particularly with respect to 81 and 3077."308" Taking into account the distances and angular separation of the objects on the sky, we estimate the spatial separation to M881 to be about kkpc for 661 and about kkpc for 664."," Taking into account the distances and angular separation of the objects on the sky, we estimate the spatial separation to 81 to be about kpc for 61 and about kpc for 64."309 661 is situated very close to the central body of the group., 61 is situated very close to the central body of the group.310 The only galaxies which are likely closer to 881 are Holmberg IX and BK3N tidal dwarfs., The only galaxies which are likely closer to 81 are Holmberg IX and BK3N tidal dwarfs.311 664 is probably situated on the back side of M881 and possibly slightly in front of 33077., 64 is probably situated on the back side of 81 and possibly slightly in front of 3077.312 The spatial separationwith 33077 is about kkpc., The spatial separationwith 3077 is about kpc.313 Both 661 and 64 are located at the same distance to 881 as the dSph satellites of the Milky Way kkpc to kkpc)., Both 61 and 64 are located at the same distance to 81 as the dSph satellites of the Milky Way kpc to kpc).314velocity dispersion. and hence. in the FP relation. are better reflected in the Sérrsic parameter. and hence. in the PHP relation.,"velocity dispersion, and hence, in the FP relation, are better reflected in the Sérrsic parameter, and hence, in the PHP relation."315 In addition. the larger errors in velocity dispersion measurements for ⊲⊲∡fainter dEs may be responsible ∡⋅⊲for their. larger scatter about the conventional FP compared to the PHP.," In addition, the larger errors in velocity dispersion measurements for fainter dEs may be responsible for their larger scatter about the conventional FP compared to the PHP."316 In Figure 6.. we present the correlations between the Sérrsic index of the sample galaxies and Asjj. (foe. pro. 0 and concentration parameter.," In Figure \ref{fig:logn5}, we present the correlations between the Sérrsic index of the sample galaxies and $M_{814}$ , $\langle \mu \rangle_e$, $\mu_0$, $\sigma$ and concentration parameter."317" We find a linear trend between the Sérrsic index and the central surface brightness as logyu(n)=(2.00+0.35)(0.090.02), with the correlation. coefficient of -W. This is entirely consistent with the relation between these quantities found by Graham Guzmánn (2003).", We find a linear trend between the Sérrsic index and the central surface brightness as $log_{10}(n)=(2.00\pm0.35)-(0.09\pm0.02)\mu_0$ with the correlation coefficient of -W. This is entirely consistent with the relation between these quantities found by Graham Guzmánn (2003).318 Replacing η by σ we find a similar relation (i.e. /ogjo(o)=(3.97£0.56)(0.12+ 0.02)/40) with weaker correlation coefficient of -0.80., Replacing $n$ by $\sigma$ we find a similar relation (i.e. $log_{10}(\sigma)=(3.97\pm0.56)-(0.12\pm0.02)\mu_0$ ) with weaker correlation coefficient of -0.80.319 We ignore the outliers in the fitting process. which are the galaxies with poor Sérrsie fit. represented by open asterisks.," We ignore the outliers in the fitting process, which are the galaxies with poor Sérrsic fit, represented by open asterisks."320 Figure 6 indicates another correlation between the central. velocity dispersion of our sample galaxies. c. and their Sérrsic indices. n. with the correlation coefficient of 0.79.," Figure \ref{fig:logn5} indicates another correlation between the central velocity dispersion of our sample galaxies, $\sigma$, and their Sérrsic indices, $n$, with the correlation coefficient of 0.79."321" This correlation enables us to construct a relation @ and η as logiu(o)=(0.50-EO.14Yogi,u(0n)(0.77£0.20) where misin kms", This correlation enables us to construct a relation $\sigma$ and $n$ as $log_{10}(\sigma)=(0.59\pm0.14)log_{10}(n)-(0.77\pm0.20)$ where $\sigma$ is in km $^{-1}$.322 The correlation between the light concentration. in galaxies and their Sérrsic index is also presented in the bottom panel of Figure 6.., The correlation between the light concentration in galaxies and their Sérrsic index is also presented in the bottom panel of Figure \ref{fig:logn5}.323 Ignoring the outliers which are illustrated with open asterisks. this relation is written as logi(n)=(0.36+0.06(0.980.18) with the correlation coefficient of 0.95. where C is he concentration parameter and is defined as Co=5{ου(Γκυroo).," Ignoring the outliers which are illustrated with open asterisks, this relation is written as $log_{10}(n)=(0.36\pm0.06)C-(0.98\pm0.18)$ with the correlation coefficient of 0.95, where C is the concentration parameter and is defined as $C=5~log_{10}({r_{80}/r_{20})}$."324 The process of determining the Sérrsic index is model dependent while the concentration parameter is model independent and well determined using a simple photometric analysis., The process of determining the Sérrsic index is model dependent while the concentration parameter is model independent and well determined using a simple photometric analysis.325" The €*'n relation shows that ""C and ""»"" could be interchangely used."," The $C-n$ relation shows that $C$ "" and $n$ "" could be interchangely used."326" The linear relation between the effective surface brightness. Ho. and half-Hght radius. 4). of elliptical galaxies. also known as Kormendy relation (KR. Kormendy 1977). is represented as Figure 7 shows the best fit of KR for our dEs in different luminosity ranges. ήν<20. 20«Maus1δαπά IS<Alsi,16."," The linear relation between the effective surface brightness, $\langle \mu \rangle_e$, and half-light radius, $R_e$, of elliptical galaxies, also known as Kormendy relation (KR, Kormendy 1977), is represented as Figure \ref{fig:kormendy} shows the best fit of KR for our dEs in different luminosity ranges, $M_{814}<-20$, $-20<M_{814}<-18$ and $-18<M_{814}<-16$."327" For our brightest galaxies CM,«— 20). we find the KR slope as 4.274-0.18 which is significantly comparable to 2.43+0.15 fora sample of giant galaxies in Coma cluster with central velocity dispersion oc200 km s| (Ziegler et al."," For our brightest galaxies $M_{814}<-20$ ), we find the KR slope as $\pm$ 0.18 which is significantly comparable to $\pm$ 0.15 for a sample of giant galaxies in Coma cluster with central velocity dispersion $\sigma>200$ km $^{-1}$ (Ziegler et al."328" 1999),", 1999).329 We attribute this discrepancy to the fact that our sample covers different range of size and magnitude compared with the galaxies studied by Ziegler et al. (, We attribute this discrepancy to the fact that our sample covers different range of size and magnitude compared with the galaxies studied by Ziegler et al. (3301999).,1999).331 The typical velocity dispersion of our dEs is lessthan lOOkms + and the average size of our dEs is 7.1.5 Kpc., The typical velocity dispersion of our dEs is less than 100 km $^{-1}$ and the average size of our dEs is $\sim$ 1.5 Kpc.332 Moreover. the effective radii of our galaxies with Muas20 are less than ~4.5 Kpe. while all other studies of KR cover galaxies with larger sizes €10 Κρο) in this magnitude range (e.g. La Berbera et al. (," Moreover, the effective radii of our galaxies with $M_{814}<-20$ are less than $\sim$ 4.5 Kpc, while all other studies of KR cover galaxies with larger sizes $>\sim 10 $ Kpc) in this magnitude range (e.g. La Berbera et al. ("3332010): Ziegler et al.,2010); Ziegler et al.334 1999: D'Onofrio et al., 1999; D'Onofrio et al.335 2006)., 2006).336" The imposed systematic restrictions on our sample of dEs. such as luminosity and size cuts. changes the geometric shape of the distribution of galaxies on the ους 23-605, plane. and therefore results in different KR slope (Nigoche-Netro et al."," The imposed systematic restrictions on our sample of dEs, such as luminosity and size cuts, changes the geometric shape of the distribution of galaxies on the $R_e$ $\langle \mu \rangle_e$ plane, and therefore results in different KR slope (Nigoche-Netro et al."337 2008)., 2008).338 Fitting the KR to our dEs in the magnitude range 20<Maj;ςIS and 18«Mau<16. we found the KR slope— as 5.2350.37 and 5.17+0.28. respectively.," Fitting the KR to our dEs in the magnitude range $-20<M_{814}<-18$ and $-18<M_{814}<-16$, we found the KR slope as $\pm$ 0.37 and $\pm$ 0.28, respectively."339 In agreement with our results. Khosroshahi et al. (," In agreement with our results, Khosroshahi et al. ("3402004) have also found the slope of KR as —5.2 for dwarf ellipticals of 16 nearby galaxy groups with 14«Alp<Is.,2004) have also found the slope of KR as $\sim$ 5.2 for dwarf ellipticals of 16 nearby galaxy groups with $-14<M_R<-18$.341" The KR is originated from the definition of the effective radius. //.. which relates the luminosity and effective surface brightness as L=254,2°."," The KR is originated from the definition of the effective radius, $R_e$, which relates the luminosity and effective surface brightness as $L=2\pi I_eR_e^2$."342" Theoretically. p equals 5. and any difference from 5 is the results of the change in geometric shape of the distribution of galaxies on the log, (0), plane."," Theoretically, $p$ equals 5, and any difference from 5 is the results of the change in geometric shape of the distribution of galaxies on the $R_e$ $\langle \mu \rangle_e$ plane."343 Any change in magnitude range of the galaxies and the shape of the magnitude distribution results in different slope of KR (Nigoche-Netro et al., Any change in magnitude range of the galaxies and the shape of the magnitude distribution results in different slope of KR (Nigoche-Netro et al.344 2008)., 2008).345 In agreement with Khosroshahi et al., In agreement with Khosroshahi et al.346 2004 and D'Onofrio et al. (, 2004 and D'Onofrio et al. (3472006). Figure 7. shows that forfainter galaxies the logt 5/0. linear trend is steeper than that of the brighter galaxies CM< 20).,"2006), Figure \ref{fig:kormendy} shows that forfainter galaxies the $R_e$ $\langle \mu \rangle_e$ linear trend is steeper than that of the brighter galaxies $M_{814}<-20$ )."348" We also noticed that the slopes of KR for our galaxies in the magnitude range 20cMaa<15 and. IS<Alsi,16 are consistent within the error bars.", We also noticed that the slopes of KR for our galaxies in the magnitude range $-20<M_{814}<-18$ and $-18<M_{814}<-16$ are consistent within the error bars.349" Due to the limited /?,. range. we did not fit the KR for galaxies with —16« Maj."," Due to the limited $R_e$ range, we did not fit the KR for galaxies with $-16<M_{814}$ ."350However. it is also possible that tidally stripped halos loose their stars more rapidly thau they loose their dark matter.,"However, it is also possible that tidally stripped halos loose their stars more rapidly than they loose their dark matter."351 Thus. they may quickly transform from luminous to dark halos.," Thus, they may quickly transform from luminous to dark halos."352 Such a behavior has been found by ?.., Such a behavior has been found by \cite{PenarrubiaNM08}.353 Accorcing to this scenario. tically stripped dark halos may uot account for the observed ultra-laint population.," According to this scenario, tidally stripped dark halos may not account for the observed ultra-faint population."354 To sumainarize. if the number of dark halos that have or had in the past e<20 kis is smaller than the number of luminous Milky Way satellites we may couclude that some cwarls are fossils.," To summarize, if the number of dark halos that have or had in the past $v_c \simgt 20$ km/s is smaller than the number of luminous Milky Way satellites we may conclude that some dwarfs are fossils."355 Vice versa. i£ the number is larger. we cannot make auy conclusive statement about tlie origin of Milky Way satellites.," Vice versa, if the number is larger, we cannot make any conclusive statement about the origin of Milky Way satellites."356 High resolution N-bodsy simulatious of the Milky Way system give the nunber of clark halos in the Milky Way as a function of their circular velocity ος at z—0., High resolution N-body simulations of the Milky Way system give the number of dark halos in the Milky Way as a function of their circular velocity $v_{c}$ at $z=0$.357" The ""Via Lactea simulation by ?. finds: with ρου&27.7 and a3."," The “Via Lactea” simulation by \cite{Diemandetal07a} finds: with $N_{dm, 20} \approx 27.7$ and $\alpha \approx 3$."358 However. a recent work by ? (the Aquarius simulaticJd. finds a factor 2.5 more satellites at any given eLe... Naysg%09 aud as3.15.," However, a recent work by \cite{Springeletal08} (the Aquarius simulations) finds a factor 2.5 more satellites at any given $v_{c}$, $N_{dm, 20}359\approx 69$ and $\alpha \approx 3.15$."360 Although the Acuarius simulations have higher resolution than the Via Lactea simulation. the large clisagreement between the two works is due to a systematic difference. possibly related to the creation of tle initial conditious. and it is not due to the improved resolution.," Although the Aquarius simulations have higher resolution than the Via Lactea simulation, the large disagreement between the two works is due to a systematic difference, possibly related to the creation of the initial conditions, and it is not due to the improved resolution."361 Although the Aquarius simulation is likely correct. we will provide predictions for both simulatious (we have become aware of the Aquarium simulation results. that are not published yet. after this work had been mostly completed.)," Although the Aquarius simulation is likely correct, we will provide predictions for both simulations (we have become aware of the Aquarium simulation results, that are not published yet, after this work had been mostly completed.)"362 To determine the importance of tidal mass loss for satellites around the Milky Way we use results from ?.., To determine the importance of tidal mass loss for satellites around the Milky Way we use results from \cite{KravtsovGnedinKlypin04}.363 Figure 5 in?) gives the fraction of halos. f(60). that presently have circular velocity te. but some time inthe past had a circular velocity X077=20 kin/s. where as (77=max(e.(/))," Figure 5 in \cite{KravtsovGnedinKlypin04} gives the fraction of halos, $f(v_{c})$, that presently have circular velocity $v_c$, but some time in the past had a circular velocity $\le v_{c}^{max}=20$ km/s, where as $v_{c}^{max} \equiv \max(v_{c}(t))$."364 We approximate the ?. results for f(0.) with thepower law (ο)2(0/20 kin D with dzz3.7.," We approximate the \cite{KravtsovGnedinKlypin04} results for $f(v_c)$ with thepower law $f(v_c) \approx (v_c/20$ km $^{-1})^{\beta}$, with $\beta \approx3653.7$."366" We then calculate the number of dark halos Ny),ου...>36 kms 1) analytically: = Uminf20km/s.andvi, 2 «o0.>10kin5 !l equals the mean observed velocity dispersion of the stars. «o,>. of ullva-laint dwarf satellites."," We then calculate the number of dark halos $N_{dm}(v_{c}^{max} > 20$ km $^{-1})$ analytically: where $x_{min}=v_{min}/20~{\rm km/s}$, and $v_{min} \simgt <\sigma_*>367\approx 10$ km $^{-1}$ roughly equals the mean observed velocity dispersion of the stars, $<\sigma_*>$, of ultra-faint dwarf satellites."368" The rationale [or iutegratiug to 7,5, is that observed satellites are dark matter dominated aud cannot be hosted iu dark halos that have v «σι. unless o, is not a tracer lor the dark matter conteut of the halo(e.g... due to tidal heating)."," The rationale for integrating to $v_{min}$ is that observed satellites are dark matter dominated and cannot be hosted in dark halos that have $v_{c} < \sigma_*$ , unless $\sigma_*$ is not a tracer for the dark matter content of the halo, due to tidal heating)."369 Using the above equation. we find 73£16 and 182+40 halos with Nag(77[>20 kins1) within Z4. for the Via Lactea and Aquarius simulations respectively.," Using the above equation, we find $73 \pm 16$ and $182 \pm 40$ halos with $N_{dm}(v_{c}^{max} > 20$ km $^{-1})$ within $R_{vir}$, for the Via Lactea and Aquarius simulations respectively."370 Both these numbers are stnaller thai the 300)—1000 luminous Milky Way satellites estimated by ?.., Both these numbers are smaller than the $300-1000$ luminous Milky Way satellites estimated by \cite{Tollerudetal08}. .371 Taken at [ace value. these numbers indicate that a fractionof Milky Way satellites are true pre-reionization [ossils.," Taken at face value, these numbers indicate that a fractionof Milky Way satellites are true pre-reionization fossils."372"'To establish an automatic detection for nova candidates, we apply the following criteria for candidates selection based on the measured R-band PSF flux (as mentioned in Sect.","To establish an automatic detection for nova candidates, we apply the following criteria for candidates selection based on the measured $R$ -band PSF flux (as mentioned in Sect."373With initial velocities now parallel to Ay (aud again isotropic). this becomes — aL?oop hudkaiae Ay cosοWa,"With initial velocities now parallel to ${\bk}_0$ (and again isotropic), this becomes = _0 L^2 k_0 dk_0 ^2(k_0) ^2(W-W_0)."374" For gQ/x1. the augular integral is approximated by εί (CL ) 2491 + coste kg? — //1). where the second approximation"". comes [romJ emploving. the method of+ stationary.. In the short-wavelenetl limit. then. CE-(401 1)) = 2404 CE = 0))."," For $q \Omega t \gg 1$, the angular integral is approximated by | (1 + ) 2 q t + (c_s k_0 q t^2 - /4), where the second approximation comes from employing the method of stationary In the short-wavelength limit, then, (q t 1) = 2 q t (t = 0)."375.E Thus the kinetic energy of an initially isotropic distribution of compressive sliwaves grows. presumably at the expeuse of the background shear flow.," Thus the kinetic energy of an initially isotropic distribution of compressive shwaves grows, presumably at the expense of the background shear flow."376 The fate of a single Compressive shiwave is to steepen into a weak shock train aud then decay., The fate of a single compressive shwave is to steepen into a weak shock train and then decay.377 The fate of the field of weak shocks generated by an eusemble of compressive sliwaves is less clear. but the mere presence of weak shocks does not indicate a transition to turbulence.," The fate of the field of weak shocks generated by an ensemble of compressive shwaves is less clear, but the mere presence of weak shocks does not indicate a transition to turbulence."378 We now generalize our analysis to include the possibility that the backerouud density. and pressure varies with wr: tliis stratification is required for the manifestation ofa couvective instability., We now generalize our analysis to include the possibility that the background density and pressure varies with $x$; this stratification is required for the manifestation of a convective instability.379 In order to use the sliwave formalisur we must assume that the background varies on a scale L~H« Reso that the local model expausion (e.g.. the neglect of curvature terms in tle equations of motion) is still valid.," In order to use the shwave formalism we must assume that the background varies on a scale $L \sim H \ll R$ so that the local model expansion (e.g., the neglect of curvature terms in the equations of motion) is still valid."3802006)).,).381" We choose the bright limit of 37,=23 to avoid the rarer and most luminous galaxies in 28LAQ. which are likely to be more biased. and to mitigate the effects of lummosity-dependent clustering (as described above)."," We choose the bright limit of $M_r=-23$ to avoid the rarer and most luminous galaxies in 2SLAQ, which are likely to be more biased, and to mitigate the effects of luminosity-dependent clustering (as described above)."382" With these choices. we study major mergers. with lumimosityratio cob: where the secondary is at least 4 times less luminous than the primary galaxy"". for M,«—21.5."," With these choices, we study major mergers, with luminosityratio $\geq 1:4$, where the secondary is at least 4 times less luminous than the primary , for $M_r < -21.5$."383 We can translate our luminosity range into a stellar mass range using the conversion between + band absolute magnitude and stellar mass by Baldryetal. (2006).. for typical LRG colors (+> 3) and with assumptions as to stellar populations as in Baldryetal.(2006).," We can translate our luminosity range into a stellar mass range using the conversion between $r$ band absolute magnitude and stellar mass by \cite{baldry06}, , for typical LRG colors $u-r >3$ ) and with assumptions as to stellar populations as in \cite{baldry06}."384". With these choices our 23«M,<21.5 luminosity range corresponds to a stellar mass range of 16-5«10419 ..."," With these choices our $-23 < M_r < -21.5$ luminosity range corresponds to a stellar mass range of $16$ $5 \times 38510^{10}$ $_{\odot}$."386 The pair fraction that we actually measure needs to be corrected to the value that would be observed in an ideal volume-limited survey., The pair fraction that we actually measure needs to be corrected to the value that would be observed in an ideal volume-limited survey.387 In a flux-limited sample. primary galaxies at lower redshifts will have a greater likelihooc of having a secondary companion within the survey thai galaxies at higher redshift.," In a flux-limited sample, primary galaxies at lower redshifts will have a greater likelihood of having a secondary companion within the survey than galaxies at higher redshift."388 We correct for this bias by assigning a greater weight to the rarer companions founc at the high redshift end of the survey., We correct for this bias by assigning a greater weight to the rarer companions found at the high redshift end of the survey.389 This is carried out by computing for each galaxy a weight that renormalizes the sample to the density corresponding to a volume limitec sample within {νε<M«M»., This is carried out by computing for each galaxy a weight that renormalizes the sample to the density corresponding to a volume limited sample within $M_{bright} < M < M_2$.390 The weight is calculated by integrating the luminosity function over the appropriate ranges in absolute magnitude., The weight is calculated by integrating the luminosity function over the appropriate ranges in absolute magnitude.391 At each redshift. we then search for pairs of galaxies withi Απρ and a redshift-dependent absolute magnitude limit MiisC). which is defined as: where /=19.8 mag.," At each redshift, we then search for pairs of galaxies within $M_{bright}$ and a redshift-dependent absolute magnitude limit $M_{lim} (z)$, which is defined as: where $i=19.8$ mag."392 is the apparent magnitude limit of the survey. dr(:) Is the luminosity distance and &(:) and c6) are the & and evolutionary corrections.," is the apparent magnitude limit of the survey, $d_L(z)$ is the luminosity distance and $k(z)$ and $e(z)$ are the $k$ and evolutionary corrections."393 Recall that here AMyaing IS set to coincide with 15., Recall that here $M_{faint}$ is set to coincide with $M_2$.394" The &|© corrections are taken to be the maximal corrections for à galaxy formed at high redshift and undergoing pure passive evolution. as other choiceswould allow galaxies to fall in and out of the sample according to their star formation histories (POO, PO2)."," The $k+e$ corrections are taken to be the maximal corrections for a galaxy formed at high redshift and undergoing pure passive evolution, as other choiceswould allow galaxies to fall in and out of the sample according to their star formation histories (P00, P02)."395 Note that here imax means ‘the brightest of’ rather than the (arithmetically) larger quantity., Note that here ${\rm max}$ means `the brightest of' rather than the (arithmetically) larger quantity.396 Fig., Fig.397 ] shows this selection limit as applied to 2SLAQ data., 1 shows this selection limit as applied to 2SLAQ data.398 Each secondary galaxy is weighted by the inverse of a selection function 5(:) defined as the ratio of densities in volume-limited vs. flux-limited samples: where L(M)=10ME and (AL) is the LRG luminosity function fromM. Wakeetal.(2006)., Each secondary galaxy is weighted by the inverse of a selection function $S(z)$ defined as the ratio of densities in volume-limited vs. flux-limited samples: where $L(M)=10^{0.4(M-M_{\odot})} L_{\odot}$ and $\Phi(M)$ is the LRG luminosity function from \cite{wake06}.399". The integrals run from 3/,,,,"" to either the faint absolute limit A» (in the denominator) or to the redshift dependent absolute magnitude limit 1/j;,,(:) (in the numerator) set by the apparent magnitude limit of the survey.", The integrals run from $M_{bright}$ to either the faint absolute limit $M_2$ (in the denominator) or to the redshift dependent absolute magnitude limit $M_{lim} (z)$ (in the numerator) set by the apparent magnitude limit of the survey.400 Galaxies in the primary sample at low redshift will also have the largest number of observed companions. while primaries at higher redshifts will have fewer observed companions.," Galaxies in the primary sample at low redshift will also have the largest number of observed companions, while primaries at higher redshifts will have fewer observed companions."401 This effect is corrected in a similar fashion as for galaxies in the secondary sample. by applying the inverse of the secondaries” weight to primaries. re Sa(+) and 57(:).," This effect is corrected in a similar fashion as for galaxies in the secondary sample, by applying the inverse of the secondaries' weight to primaries, i.e $S_N(z)$ and $S_L(z)$."402 We need to account for pairs missed because one of the galaxies falls outside of the survey footprint., We need to account for pairs missed because one of the galaxies falls outside of the survey footprint.403 À potential companion may lie beyond the survey limits on the sky or be hidden in the ‘shadow’ of a bright star. where galaxies cannot be detected or the spectra are contaminated!!.," A potential companion may lie beyond the survey limits on the sky or be hidden in the `shadow' of a bright star, where galaxies cannot be detected or the spectra are ."404.. For each primary galaxy we compute the fraction |7; of the RI area that may lie outside of the effective survey area., For each primary galaxy we compute the fraction $1-f_b$ of the $\pi r_p^2$ area that may lie outside of the effective survey area.405" The weight to be applied to the secondary galaxies is then wy,=1/fy."," The weight to be applied to the secondary galaxies is then $w_{b_2}=4061/f_b$."407" Primary galaxies may similarly be lost in the survey boundaries and the appropriate weight to be applied to the primary sample is «5,=fiwn,d.", Primary galaxies may similarly be lost in the survey boundaries and the appropriate weight to be applied to the primary sample is $w_{b_1}=f_b=w^{-1}_{b_2}$.408 For objects with small separations. SDSS photometric pipeline tends to merge pairs into a single thegalaxy.," For objects with small separations, the SDSS photometric pipeline tends to merge pairs into a single galaxy."409" For the LRG sample studied by Masjedietal.(2006) the pipeline becomes unreliable for +,< 3"".", For the LRG sample studied by \cite{masjedi06} the pipeline becomes unreliable for $r_p < 3''$ .410" The20 7lKpe search radius we use corresponds to angular separations of 1.91"" to LOT” at 0.15τς 0.65."," The$20$ $h^{-1}$kpc search radius we use corresponds to angular separations of $4.91''$ to $4.07''$ at $0.45 < z <4110.65$ ."412" We inspected all our 7889 images to verify whether the SDSSpipeline correctly identifies photometric companions. using the SDSS ""Image List/Navigate"" tools."," We inspected all our 7889 images to verify whether the SDSSpipeline correctly identifies photometric companions, using the SDSS 'Image List/Navigate' tools."413erouped with a minima of 25 counts per bin.,grouped with a minimum of 25 counts per bin.414 The AXP was observed by the )) observatory (?) on 2002 October 5 and 2002 October 7 (Table 1)) with the European Photon Inaging Camera (EPIC) pn (?)| camera operating in huge window mode and the EPIC) MOS cameras (?) in [full window mode., The AXP was observed by the ) observatory \citep{jla+01} on 2002 October 5 and 2002 October 7 (Table \ref{obstab}) ) with the European Photon Imaging Camera (EPIC) pn \citep{sbd+01} camera operating in large window mode and the EPIC MOS cameras \citep{taa+01} in full window mode.415 For our analysis. we used the Science Analvsis Svstem (SAS) version and calibrations (updated 2008 Oct 3).," For our analysis, we used the Science Analysis System ) version and calibrations (updated 2008 Oct 3)."416 Given the pn and MOS cameras angular resolution. can be resolved from Ixes 73.," Given the pn and MOS cameras' angular resolution, can be resolved from Kes 73."417 For the two observations. we used only the data from the EPIC pn camera to take advantage of its larger photon collecting area ancl to avoid issues between (he pn camera and the mos cameras.," For the two observations, we used only the data from the EPIC pn camera to take advantage of its larger photon collecting area and to avoid cross-calibration issues between the pn camera and the mos cameras."418" We extracted (he pulsar's spectrum [rom a cireular region of radius 32"".5 (a radius laree enough to capture more than of the photon events from the point source) centered| on the pulsar.", We extracted the pulsar's spectrum from a circular region of radius $''$ .5 (a radius large enough to capture more than of the photon events from the point source) centered on the pulsar.419" Background spectra were extracted [rom an annular region of radius between 35"" and 115"" centered on the pulsar.", Background spectra were extracted from an annular region of radius between $''$ and $''$ centered on the pulsar.420 The pulsar spectrum was grouped with a minimum of 25 counts per bin and then combined with the background spectrum and RAIF ancl ARF files generated by the software., The pulsar spectrum was grouped with a minimum of 25 counts per bin and then combined with the background spectrum and RMF and ARF files generated by the software.421 AXP I341—045and Kes τὸ were also observed by the Suzakiobservatory (7) on 2006 April 19 (Table 1))., AXP and Kes 73 were also observed by the observatory \citep{suzaku} on 2006 April 19 (Table \ref{obstab}) ).422 The data analysis was reported by ?.., The data analysis was reported by \citet{mks+08}.423 Onboard Suzaku... there are (wo X-ray detectors: (he X-ray Lnagine Spectrometer (XLS. ?.. consisting of four CCDs sensitive in soft-N-rav. band) and the Hard. X-ray Detector (IND. ?.. sensitive to LO600 keV X-rays).," Onboard , there are two X-ray detectors: the X-ray Imaging Spectrometer (XIS, \citealt{suzakuxis}, consisting of four CCDs sensitive in soft-X-ray band) and the Hard X-ray Detector (HXD, \citealt{suzakuhxd}, sensitive to 10–600 keV X-rays)."424 Here we present a spectral analvsis of the AXIS data only., Here we present a spectral analysis of the XIS data only.425 Given the angular resolution of the AIS. the SNR was unresolvable in the NIS image.," Given the angular resolution of the XIS, the SNR was unresolvable in the XIS image."426 Therefore the spectra we extracted [rom the AIS detectors contain photons from both the AXP and the SNR., Therefore the spectra we extracted from the XIS detectors contain photons from both the AXP and the SNR.427 We used cleaned events screened by the standard pipeline processing version2., We used cleaned events screened by the standard pipeline processing version.428"0.6.13°.. The source spectra were extracted from a cireular region of 260"" radius.", The source spectra were extracted from a circular region of $''$ radius.429" Backeround spectra were extracted from an annulus region of radius between 260"" ancl 520"".", Background spectra were extracted from an annulus region of radius between $''$ and $''$.430 The extracted spectra were grouped wilh a minimum of 25 counts per bin. and then combined with the RAIF and," The extracted spectra were grouped with a minimum of 25 counts per bin, and then combined with the RMF and"431uPhe open cluster NGCu 2401 (=OCL 588 = C0727-138) is. an almost unstudied:: compact. grouping. of ⋅⋅⊀faint stars. but for ..identification⊲⋅≜ and. eve estimates. of .its angular size. and richness.,"The open cluster NGC 2401 (=OCL 588 = C0727-138) is an almost unstudied compact grouping of faint stars, but for identification and eye estimates of its angular size and richness."432". According. to the ((1987). classification.""EN this: object. is. a sTrumpler class 11 9. p with: about 2 .in diameter.. which ≜⊲is the same diameter. listed. in. Dias. et al. ("," According to the (1987) classification, this object is a Trumpler class II 3 p with about $2^{\prime}$ in diameter, which is the same diameter listed in Dias et al. ("4332002).,2002).434 X recent. photometric. study on this. area carried.. out by Sujatham et al. (, A recent photometric study on this area carried out by Sujatha et al. (4352004) vielded:. an intriguing⊀⊲⊲ result where a relatively. far. cluster (located at a distance. of about 3.1 kpc) shows only a color excess {μι=0.,2004) yielded an intriguing result where a relatively far cluster (located at a distance of about 3.1 kpc) shows only a color excess $E_{B-V} = 0$.436 This fact alone deserves our total attention., This fact alone deserves our total attention.437" Moreover. since NGC 201 is placed in the Puppis region (/=220.67"": b= |lLs5) in the poorly studied: Third. Quadrant: of the Galaxy. the determination of its basic parameters will contribute. together with other cluster studies in the region. o describe more pprecisely the spiral! structure and the star ⋅ormation. historv. in thisκα part of. the Galaxy."," Moreover, since NGC 2401 is placed in the Puppis region $l =438229.67^{\circ}$; $b = +1.85^{\circ}$ ) in the poorly studied Third Quadrant of the Galaxy, the determination of its basic parameters will contribute, together with other cluster studies in the region, to describe more precisely the spiral structure and the star formation history in this part of the Galaxy."439. NMThis region. contains. several distant.. clusters through which. information⋠⋅. on the kinematics. and evolutionary. status of⋅ the stellar »»pulation. in the outermost parts of⋅ the galactie qidisk can x: obtained., This region contains several distant clusters through which information on the kinematics and evolutionary status of the stellar population in the outermost parts of the galactic disk can be obtained.440. In fact.. since. the detection. of the 0.Canis Major. over-density. (see p.e.," In fact, since the detection of the Canis Major over-density (see p.e."441 Martin. et al., Martin et al.442 2004. Momany et al.," 2004, Momany et al."443 2004 or more details). there is a growing interest to get a better deseription.. of⋅ the stellar population. in. this. region. of⋅ the Galaxy.," 2004 for more details), there is a growing interest to get a better description of the stellar population in this region of the Galaxy."444 Preliminary results of NGC 2401 can be found in a COD EBVRE photometric database by Moitinho (2001. 2002) containing brief information for 30 open clusters in the galactic longitude range 2177<f2607.," Preliminary results of NGC 2401 can be found in a CCD $UBVRI$ photometric database by Moitinho (2001, 2002) containing brief information for 30 open clusters in the galactic longitude range $217^{\circ}< l < 260^{\circ}$."445 Also recently. Cüorgi ct al. (," Also recently, Giorgi et al. ("4462002. 2005). Carraro Alunari (2004). Baume et al. (,"2002, 2005), Carraro Munari (2004), Baume et al. ("4472004). Carraro et al. (,"2004), Carraro et al. ("4482005a) ancl Aloitinho οἱ al. (,2005a) and Moitinho et al. (4492005) published studies of a series of largely overlooked open clusters in the same ealactic region.,2005) published studies of a series of largely overlooked open clusters in the same galactic region.450 In this paper we present a detailed study of the membership. reddening. distance. anc age of NGC 2401.," In this paper we present a detailed study of the membership, reddening, distance and age of NGC 2401."451Iepler is ao reconnaissance ΕΕο. to obtain nuc-series optical photometry of —150.000o stayso iu πάα to determine characteristics of Earth-size aud arecr extrasolar planets: frequencies. sizes. orbital listributious. and correlations with the properties of he host stars (Boruckictal.2010).," is a reconnaissance mission to obtain time-series optical photometry of $\sim$ 150,000 stars in order to determine characteristics of Earth-size and larger extrasolar planets: frequencies, sizes, orbital distributions, and correlations with the properties of the host stars \citep{Borucki10}."452. To achieve these eoals.Kepler requires exceptional long-term pliotomotric stability and precision (Nochetal.2010).," To achieve these goals, requires exceptional long-term photometric stability and precision \citep{Koch10}."453. In addition to he discovery aspect of the mission. this unprecedoenutec photometric capability provides exquisite observations of a host of astroplivsical objects. including the previously shown extrasolar planets in theWepler field of view.," In addition to the discovery aspect of the mission, this unprecedented photometric capability provides exquisite observations of a host of astrophysical objects, including the previously known extrasolar planets in the field of view."454 Iu lisLetter. we exiuuine the carlyAepler observatious of he planet ITAT-P-7).," In this, we examine the early observations of the planet HAT-P-7b."455 Discovered via the project. the transiting Xauet ILAT-P-7b revolves in a tight circular orbi (a=0.0388 AU. P=2.20173 d) around a bright (V—10.5 nae) F6 star (Paletal.2008).," Discovered via the project, the transiting planet HAT-P-7b revolves in a tight circular orbit (a=0.038 AU, P=2.20473 d) around a bright (V=10.5 mag) F6 star \citep{Pal08}."456 The proximity to its 6350 I& host star (Palctal.2008) means the anet is liehly mradiated. resulting im very high eniperatures (~2110 I&). making it an extreme pillype planet (Fortneyctal.2008).," The proximity to its 6350 K host star \citep{Pal08} means the planet is highly irradiated, resulting in very high temperatures $\sim$ 2140 K), making it an extreme pM-type planet \citep{Fortney08}."457. Using observations of the Rossiter-A\IcLaughlin effect. Naritactal.(2009) and Winnetal.(2009) find that the planet’s orbital axis is extremely tilted compared to the stars spin axis. iid probably even retrograde. implying au interesting formation aud orbital evolution history.," Using observations of the Rossiter-McLaughlin effect, \citet{Narita09} and \citet{Winn09} find that the planet's orbital axis is extremely tilted compared to the star's spin axis, and probably even retrograde, implying an interesting formation and orbital evolution history."458 Additionally. the radial velocitics exhibit an acceleration. sugecsting the presence of another body in the system. perhaps responsible for the tilted orbit (Winnctal.2009).," Additionally, the radial velocities exhibit an acceleration, suggesting the presence of another body in the system, perhaps responsible for the tilted orbit \citep{Winn09}."459. Observations of ILAT-P-7 divine the 10 davs of cohbunissiomine of theAepler plotometer revealed the preseuce of an occultation (also known as a “secoudary eclipse) as the planet passes behind the star (Boruckietal. 2009)., Observations of HAT-P-7 during the 10 days of commissioning of the photometer revealed the presence of an occultation (also known as a “secondary eclipse”) as the planet passes behind the star \citep{Borucki09}.460". These data also show the phase ""reflected? light from the planet. a result of both scattered and thermal cinission."," These data also show the phase “reflected” light from the planet, a result of both scattered and thermal emission."461 Additional observations of ILAT-P-7 have been obtained. aud we preseut these im 822.," Additional observations of HAT-P-7 have been obtained, and we present these in 2."462 Iu 8323 we describe our modeling method. with particular cluplasis on the ellipsoidal variatious from the star.," In 3 we describe our modeling method, with particular emphasis on the ellipsoidal variations from the star."463 Iu §ll we present aud discuss our findings., In 4 we present and discuss our findings.464 ILAT-P-7 was monitored continuously for 33.5 d duriug the 2000 May 13Jun 15 “Quarter 17 (O1) epoch in short-cadence mode., HAT-P-7 was monitored continuously for 33.5 d during the 2009 May 13–Jun 15 “Quarter 1” (Q1) epoch in short-cadence mode.465 The 12.Kepler CCDs were reac out every 6 s and co-added ou-board to achieve approximately 1 nin sampling cadence., The 42 CCDs were read out every 6 s and co-added on-board to achieve approximately 1 min sampling cadence.466 The photometer has no shutter. so an overscan region is used to remove the effects of sincaring during readout.," The photometer has no shutter, so an overscan region is used to remove the effects of smearing during readout."467" Iu. 6 3 exposures ILAT-P-7 saturates the CCD: however. because theKepler photometer is such a stable platform. this does not hamper the relative precision aud superb photometryis possible,"," In 6 s exposures HAT-P-7 saturates the CCD; however, because the photometer is such a stable platform, this does not hamper the relative precision and superb photometryis possible."468 For details on the design aud performance of the Kepler photometer. see I&ochctal.(2010). ancl Jeukiusetal. (2010)..," For details on the design and performance of the photometer, see \citet{Koch10} and \citet{Jenkins10}. ."469The primary star grows rapidly in mass by accreting from the surrounding over-density.,The primary star grows rapidly in mass by accreting from the surrounding over-density.470 The inflow is anisotropic. being strongest in the plane of the flattened over-density. lumpy. and variable.," The inflow is anisotropic, being strongest in the plane of the flattened over-density, lumpy, and variable."471 Usually it also has net angular momentum relative to the primary star. and in this case à eircum-primary disc forms.," Usually it also has net angular momentum relative to the primary star, and in this case a circum-primary disc forms."472 Due to the lumpy. variable accretion. these dises become unstable to spiral modes and fragment to produce secondary objects.," Due to the lumpy, variable accretion, these discs become unstable to spiral modes and fragment to produce secondary objects."473 The genesis of secondary objects 1s usually concentrated in a burst between 0.07 and 0.08Myr after the start of the simulation (or 0.01 to 0.03Myr after the primary star forms).," The genesis of secondary objects is usually concentrated in a burst between 0.07 and $0.08\,{\rm Myr}$ after the start of the simulation (or 0.01 to $0.03\,{\rm Myr}$ after the primary star forms)."474 The evolution of Run A022 is shown in Figs., The evolution of Run A022 is shown in Figs.475 5 and 6.. as an illustration of these processes at work.," \ref{fig:spiral} and \ref{fig:further}, as an illustration of these processes at work."476 In all frames the primary star is at the centre of co-ordinates., In all frames the primary star is at the centre of co-ordinates.477 Fig., Fig.478 5. shows the lumpy accretion flow onto the primary star. concentrated preferentially through two streams on either side of the primary star.," \ref{fig:spiral} shows the lumpy accretion flow onto the primary star, concentrated preferentially through two streams on either side of the primary star."479 The lumpy inflow causes the disc to become unstable. forming spiral arms.," The lumpy inflow causes the disc to become unstable, forming spiral arms."480 Eventually one of these arms sweeps up sufficient. material to detach and condense into à secondary object. as shown in Fig. 6::," Eventually one of these arms sweeps up sufficient material to detach and condense into a secondary object, as shown in Fig. \ref{fig:further};"481 the knot that forms the secondary object is at (v.v).~(€-225au.-100au) in the first panel of Fig. 6..," the knot that forms the secondary object is at $(x,y) 482\sim (+225{\rm au},-100{\rm au})$ in the first panel of Fig. \ref{fig:further},"483 and orbits the primary anti-clockwise. ending up as a newly-formed sink at (x.v)~(—8Oau.+200au) in the final panel of Fig. 6..," and orbits the primary anti-clockwise, ending up as a newly-formed sink at $(x,y) \sim (-80{\rm au},+200{\rm au})$ in the final panel of Fig. \ref{fig:further}."484 We emphasise that this knot has already condensed out of the spiral arm that spawned it. by the time that it becomes a sink.," We emphasise that this knot has already condensed out of the spiral arm that spawned it, by the time that it becomes a sink."485 A third sink is formed shortly after the illustrated sequence ends. from a knot that can be seen in the last three panels moving anti-clockwise from (—50au.+LOQau) to (x.Y)(—S0au.-50au).," A third sink is formed shortly after the illustrated sequence ends, from a knot that can be seen in the last three panels moving anti-clockwise from $(x,y) \sim (-50{\rm au},+100{\rm au})$ to $(x,y) \sim (-50{\rm au},-50{\rm au})$."486 Not all the knots that form in this way evolve into sinks., Not all the knots that form in this way evolve into sinks.487 Some are destroyed by tidal interaction and/or merger with an existing sink., Some are destroyed by tidal interaction and/or merger with an existing sink.488 An example of this can be seen in Fig., An example of this can be seen in Fig.489 6 where a dense knot at (v.y)~(Oau.-80au) in the first panel spirals into. merges with. the primary star.," \ref{fig:further} where a dense knot at $(x,y) \sim (0{\rm au},+80{\rm au})$ in the first panel spirals into, merges with, the primary star."490 The most significant factor in forming multiple objects appears to be the ability of the turbulent flows to create an extended overdense region in the vicinity of the primary star., The most significant factor in forming multiple objects appears to be the ability of the turbulent flows to create an extended overdense region in the vicinity of the primary star.491 The more material that is delivered into this region. the more objects that form.," The more material that is delivered into this region, the more objects that form."492 When an extended overdense region does not form around the primary star. the result is that no further objects form. e.g. runs A020. A021. A028 and A030.," When an extended overdense region does not form around the primary star, the result is that no further objects form, e.g. runs A020, A021, A028 and A030."493 Whilst this may appear similar to fragmentation of a disc formed from the collapse of a purely rotating cloud. there are significant. differences in the scenario. outlined. above.," Whilst this may appear similar to fragmentation of a disc formed from the collapse of a purely rotating cloud, there are significant differences in the scenario outlined above."494 Turbulence generates the angular momentum required to create à disc. but this angular momentum is. provided by the turbulence in the vicinity of the first object. and not from any bulk properties of the core.," Turbulence generates the angular momentum required to create a disc, but this angular momentum is provided by the turbulence in the vicinity of the first object, and not from any bulk properties of the core."495 It is then the clumpy. inhomogeneous inflow from the turbulent surroundings onto this disc that causes the dise to become unstable.," It is then the clumpy, inhomogeneous inflow from the turbulent surroundings onto this disc that causes the disc to become unstable."496 There ts, There is497to lh+ Mpe top bat window).,to $1h^{-1}$ Mpc top hat window).498 The window function for specific heating models can be obtained from hydrodsuamie simulation by comparing the gas power spectrum to t1ο dark matter power spectrum (Ma and Pen. 2000).," The window function for specific heating models can be obtained from hydrodynamic simulation by comparing the gas power spectrum to the dark matter power spectrum (Ma and Pen, 2000)."499 We also need to relate the gas temperature with the density., We also need to relate the gas temperature with the density.500 First. we consider the gravitational heating.," First, we consider the gravitational heating."501 We adopt the cosmic euergy theoreu (Peebles1980) for he gas temperatu‘e model. which specifies the ratio betweel gravitatlonul binding energy and otal kiuetic energy dv.," We adopt the cosmic energy theorem \citep{Peebles80} for the gas temperature model, which specifies the ratio between gravitational binding energy and total kinetic energy $K$."502 The pressure depends on the thermized fraction o“dy., The pressure depends on the thermalized fraction of $K$.503 The translational &uetic energy is tleralized [rom the energy released whe1 particles shell cross., The translational kinetic energy is thermalized from the energy released when particles shell cross.504 A model of the hermalizecl energy is thus given by the dillerence in energv between two j»articles separated. by a non-liuear scale in LagranglaL space. which is the cistace at which they can be expected to rave shell crossed.," A model of the thermalized energy is thus given by the difference in energy between two particles separated by a non-linear scale in Lagrangian space, which is the distance at which they can be expected to have shell crossed."505 The exact procedure amounts to solvitig the non-liuear evolion equations directly., The exact procedure amounts to solving the non-linear evolution equations directly.506 But we ca1 treat the effect statistically in a linear ashion., But we can treat the effect statistically in a linear fashion.507 Iu the i1itial jiuear evolution. he gravitational prtential remains constant.," In the initial linear evolution, the gravitational potential remains constant."508 Alter virialization. the gravitational eergy at a fixed ocatiou remalus almost constant.," After virialization, the gravitational energy at a fixed location remains almost constant."509 In an Euleriau description. we can describe hee erey of particles at a final virialized location as the energy released as a particle travels from its initial position to he final virialized location.," In an Eulerian description, we can describe the energy of particles at a final virialized location as the energy released as a particle travels from its initial position to the final virialized location."510 While the initial position is uot exactly known. we take a spherical average over the non-linear scale to average over all possible initial locations.," While the initial position is not exactly known, we take a spherical average over the non-linear scale to average over all possible initial locations."511 We thus have V is the gravitational potential. X7W=—lrGpard.," We thus have $\Psi$ is the gravitational potential, $\bigtriangledown^2 \Psi=-4\pi G \bar{\rho} a^2512\delta$."513" Wor)=ΕΝ)μετ.r|jd?r (hereafter call the “electron window function”) is the potential averaged over the non-linear scale r,.", $\bar{\Psi}(x)=\int \Psi(r)W_e(|x-r|)d^3r$ (hereafter call the “electron window function”) is the potential averaged over the non-linear scale $r_e$.514 We choose a Gaussian window [uncetion I(r) with the the non-linear scale ο. which for 2=ϐ is rec0i Mpc.," We choose a Gaussian window function $W_e(r)$ with the the non-linear scale $r_e$, which for $z=0$ is $r_e \sim 5 h^{-1}$ Mpc."515" Hereafter we will adopt this value of r,.", Hereafter we will adopt this value of $r_e$.516 X=().76 is the mass ractiou of the hydrogen 1ii baryonic nater., $X=0.76$ is the mass fraction of the hydrogen in baryonic matter.517" Then. (AL,px(E)1—WOO]he=OC)."," Then, $(kT_g)_k \propto \delta(k)518\left[1-W_e(k)\right]/k^2 \equiv \delta(k) f_e(k)$."519 Here. exp(—4-6;(2)/2) is the Fourier trausforlh ¢of the electron window fuictiou.," Here, $W_e(k,z)=\exp(-k^2520r_e^2(z)/2)$ is the Fourier transform of the electron window function."521 Equatior (5)) has some uuphysical statistical properties., Equation \ref{eqn:temp}) ) has some unphysical statistical properties.522 The spaial average of the temperature. Or exaliple. Is exactly zero. and or our iuodel using Craussiat rauco fields. it wi| be negative 1 half tte volume.," The spatial average of the temperature, for example, is exactly zero, and for our model using Gaussian random fields, it will be negative in half the volume."523 BuI for purposes of mo«eling he SZ ellect. emperature Is only «)yservable whet uultipied by deusity. aud regious of positive temperature wil have high density. wile tle negative temperature regio only contribute negiginly to the SZ ellect.," But for purposes of modeling the SZ effect, temperature is only observable when multiplied by density, and regions of positive temperature will have high density, while the negative temperature regions only contribute negligibly to the SZ effect."524 This model is uot neant to be at exact ¢escription. b hopefully. captures he statisical prope‘ties. while beiug simple aid thus exactly solvable.," This model is not meant to be an exact description, but hopefully captures the statistical properties, while being simple and thus exactly solvable."525" In order to esinate the accuracy of these assuumptio1S. we first COupute the gas densityP weighted tempe""altre ancl {1e eal y parameter."," In order to estimate the accuracy of these assumptions, we first compute the gas density weighted temperature and the mean $y$ parameter."526" We define our)z(2a)ID,we)exp(—ilh. the power spectruni Plfr)={δε}2 and the variaice NT(E)mnP)/2miy?."," We define $\delta(x)\equiv (2 \pi)^{-3} \int\delta_k \exp(-i k\cdot x)d^3 k$, the power spectrum $P(k)\equiv\langle|\delta_k|^2\rangle$ and the variance $\Delta^2(k)\equiv k^3 P(k)/2 \pi^2$."527 We adopt the initial power spectrum (Peebes1953:Davisetal.1985) /neake)xhtIAbUTI+OE?+P) (here. kis in unit of Ομ /M.IC cuid we choose the Harrisoi-Zeldovicli-Peebles scale invariaut spectrum v=—1 correspondiug to a 0). ‘luster-normalizec deusity fluctuation at Sj tMpe by ex=0.5: [3=0.53 for ACDNI and 3=0.15 lor OCD I1] (Pen1998) and the PeacockandDodds( ," We adopt the initial power spectrum \citep{Peebles83, Davis85} $P_{linear}(k)\propto 528k^{1+\alpha}/(1+1.7 k+9 k^{1.5}+k^2)$ (here, $k$ is in unit of $\Omega_0 h^2$ /Mpc and we choose the Harrison-Zel'dovich-Peebles scale invariant spectrum $n=-1$ corresponding to $\alpha=0$ ), cluster-normalized density fluctuation at $8 h^{-1}$ Mpc by $\sigma_8=0.53 \Omega^{-\beta}$ $\beta=0.53$ for $\Lambda$ CDM and $\beta=0.45$ for OCDM ] \citep{Pen98} and the \citet{Peacock96} "529summarize studies of angular momentum and assembly bias at low redshift to provide the framework for our findings at high redshift.,summarize studies of angular momentum and assembly bias at low redshift to provide the framework for our findings at high redshift.530 We describe our simulations in Section 3.. and present the results of convergence tests in Section 4...," We describe our simulations in Section \ref{sec:sims}, and present the results of convergence tests in Section \ref{sec:CT}."531 Our results from the correlation of the spin parameter to the halo environment are presented. in Section 5..in and that of the elfect of angular momentum on halo structure in Section 6..," Our results from the correlation of the spin parameter to the halo environment are presented in Section \ref{sec:environ}, and that of the effect of angular momentum on halo structure in Section \ref{sec:structure}."532 We conclude with a discussion of the implications of our results for high redshift galaxy. formation., We conclude with a discussion of the implications of our results for high redshift galaxy formation.533 In this section. we sunimarize earlier findings pertaining to measurements of halo spin and clustering {ο provide the context for our findings.," In this section, we summarize earlier findings pertaining to measurements of halo spin and clustering to provide the context for our findings."534 Many. numerical simulations have shown that for massive haloes at low redshift. the distribution of the climensionless spin parameter follows a log-normal distribution. with typical values of Ay=0.035 and σ&0.5 (c.g.1995:Warrenetal.1992)," Many numerical simulations have shown that for massive haloes at low redshift, the distribution of the dimensionless spin parameter follows a log-normal distribution, with typical values of $\lambda_0 \approx 0.035$ and $\sigma \approx 0.5$ \citep[e.g.,][]{donghia07, Bett07, bailin05, cole96, steinmetz95, warren92}."535 Previous studies have also shown that dark. matter haloes are generally triaxial with a preference for prolateness (c.g.Bottetal.2007:Bailin&reinmetz2005:Faltenbacheretal. 1988).," Previous studies have also shown that dark matter haloes are generally triaxial with a preference for prolateness \citep[e.g.][]{Bett07, bailin05, Faltenbacher02, cole96, warren92, Frenk88}."536. Bettοἱal.(2007 [lind that nearly spherical haloes have smaller spins. while there is only à weak trend of halo triaxiality with spin.," \citet{Bett07} find that nearly spherical haloes have smaller spins, while there is only a weak trend of halo triaxiality with spin."537 In studying halo concentration versus spin. it ds seen that when unrelaxccl haloes are eliminated: from the sample there is only a very weak surviving (if any) correlation between these two parameters (Maccióetal.2007:NetoctBullock200112)," In studying halo concentration versus spin, it is seen that when unrelaxed haloes are eliminated from the sample there is only a very weak surviving (if any) correlation between these two parameters \citep{Maccio07, Neto07, Bullock01B} ."538 Bettetal.(2007)Gao&White aux Laltenbacher&White(2010). all find that haloes with larger spins are more clustered. than low spin haloes at a eiven mass.," \citet{Bett07, Gao07} and \citet{Faltenbacher09} all find that haloes with larger spins are more clustered than low spin haloes at a given mass."539 However. Avila-Reesectal.(2005). and Recetal.(2005). fined in their simulations that haloes in cluster environments have smaller spins and are more spherical than heir counterparts in the field. and Lahnetal.(2007). fii hat haloes in filaments have larger spins than haloes of he same mass in clusters or in voids.," However, \citet{Avila05} and \citet{Reed05} find in their simulations that haloes in cluster environments have smaller spins and are more spherical than their counterparts in the field, and \citet{Hahn07} find that haloes in filaments have larger spins than haloes of the same mass in clusters or in voids."540 Maccióetal.(2007) ind that there is no environmental dependence on the spin xvwameter for haloes at à given mass., \citet{Maccio07} find that there is no environmental dependence on the spin parameter for haloes at a given mass.541 Phus. there appears to »e some question as to the extent to which the environment alfects the angular momentum properties of clark matter aloes.," Thus, there appears to be some question as to the extent to which the environment affects the angular momentum properties of dark matter haloes."542 In this work. we explore this relationship at high redshift’ using both the clustering strength. anc the local density to characterize the environment.," In this work, we explore this relationship at high redshift using both the clustering strength and the local density to characterize the environment."543 We run a series of N-body simulations to follow the growth of dark. matter haloes from 2=100 down to z=6., We run a series of N-body simulations to follow the growth of dark matter haloes from $z\approx 100$ down to $z=6$.544" We choose the particle mass such that a 10""M./h dark matter halo has 100 particles.", We choose the particle mass such that a $10^6 \Msunh$ dark matter halo has 100 particles.545 Por 512% particles. this requirement sets the comoving box size at 2.46Mpc/h and the particle mass at Mp;=1.0.103M.fh.," For $512^3$ particles, this requirement sets the comoving box size at $2.46 \Mpch$ and the particle mass at $M_{\rm{DM}} = 1.0 \times 10^4 \Msunh$."546 The initial conditions are eenerated using a parallelized version of Ciralic (Prunetetal.2008).. which calculates the Gaussian random. oe ae the dark matter particles.," The initial conditions are generated using a parallelized version of Grafic \citep{mpgrafic}, which calculates the Gaussian random field for the dark matter particles."547" We use Gadget-2 (Springel""n2 to follow dark matter particles down to a redshift 2=6. with output snapshots at z=15.12.H1.10.9.8D6."," We use Gadget-2 \citep{Gadget05} to follow dark matter particles down to a redshift of $z=6$, with output snapshots at $z=15,12,11,10,9,8,7,6$."548" We use the WMLADPA (QVOVh.n.m) = MsDm 0.762. 0416. 0.732. 0.958.ae""n the WALADPS (ΓοννιΟιfh.n.os) = (00.ORA. ndi OAL. A719. 0.963. parameters For our simulaions."," We use the WMAP3 \citep[\{$\Omega_{\rm{M}}, \Omega_\Lambda, \Omega_{\rm{b}}, h, n, \sigma_8$\} = 0.238, 0.762, 0.0416, 0.732, 0.958, and the WMAP5 \citep[\{$\Omega_{\rm{M}}, \Omega_\Lambda, \Omega_{\rm{b}}, h, n, \sigma_8$\} = 0.258, 0.742, 0.044, 0.719, 0.963, cosmological parameters for our simulations."549 Phe WALAPS cosmology was used for our first runs studving numerical convergence of our measurements of the angular momentum. and the \WALAPS cosmology was used for the results presented in Sections 5 and 6..," The WMAP3 cosmology was used for our first runs studying numerical convergence of our measurements of the angular momentum, and the WMAP5 cosmology was used for the results presented in Sections \ref{sec:environ} and \ref{sec:structure}."550 Table 1 shows the runs and the relevant. parameters used in this paper., Table 1 shows the runs and the relevant parameters used in this paper.551 CGacdget-2 uses a softening length. e. to soften the eravitational force to. prevent. spurious. 2-body interactions.," Gadget-2 uses a softening length, $\epsilon$, to soften the gravitational force to prevent spurious 2-body interactions."552" To identify, collapsed. dark matter haloes. we use the xiblicly available LOI! code provided by Eisenstein&Llut(1998)."," To identify collapsed dark matter haloes, we use the publicly available HOP code provided by \citet{HOP}."553. This method. groups particles with their densest neighbor., This method groups particles with their densest neighbor.554 After grouping. density thresholds. are used. to ensure that haloes are not being over counted due to à halo xàng a subhalo within a larger overdensitv.," After grouping, density thresholds are used to ensure that haloes are not being over counted due to a halo being a subhalo within a larger overdensity."555" We choose the density thresholds in order to match the high redshift mass ""unction described in Reedetal.(2007).", We choose the density thresholds in order to match the high redshift mass function described in \citet{reed07}.556. Once the haloes are identified. cach particle in the ido is tested to see if it is actually bound. to the halo.," Once the haloes are identified, each particle in the halo is tested to see if it is actually bound to the halo."557 We use SINID (Stadel2001) to do the unbinding.," We use SKID \citep{skid}558 to do the unbinding."559 SIXID inds the potential anc kinetic energies for all. particles in à given halo and removes the most unbound particle rom the halo., SKID finds the potential and kinetic energies for all particles in a given halo and removes the most unbound particle from the halo.560 Successive iterations are performed. until all xwlicles are either bound or there are no more particles in he halo., Successive iterations are performed until all particles are either bound or there are no more particles in the halo.561 Without unbinding. angular momentum properties could casily be dominated by a fes transient. particles not representative of the collapsed. halo.," Without unbinding, angular momentum properties could easily be dominated by a few transient particles not representative of the collapsed halo."562 We then define. the jio mass as the total mass of all the particles assigned to he halo., We then define the halo mass as the total mass of all the particles assigned to the halo.563 Having calculated masses for our haloes. we can measure the mass function of our sample. and find that the mass function of haloes does not match that of Reedοἱal.(2007) at the low mass end unless particles are unbound.," Having calculated masses for our haloes, we can measure the mass function of our sample, and find that the mass function of haloes does not match that of \citet{reed07} at the low mass end unless particles are unbound."564 We have in our halo catalogue zz24.200 haloes in the mass μα ↓⋅⋜⋯⋏∙≟⋖⋅↓∪⊔≓≓↳∖⋅⋜∐∶∶↻⊳⋜⋯∠⇂≈⋅ 16.100 at z=10.," We have in our halo catalogue $\approx 24,200$ haloes in the mass range $10^{6\pm0.2}\Msun$ at $z=6$, and $\approx 16,100$ at $z=10$."565 In the mass range 10777τσ»M. we have z2.600 haloes at z=6 and αν1250 at z—10.," In the mass range $10^{7\pm0.2}\Msun$ we have $\approx 2,600$ haloes at $z=6$ and $\approx 1250$ at $z=10$."566 To ensure that our halo sample is representative. we verily the halo mass function of our runs against theoretical predictions. as well as against other simulations.," To ensure that our halo sample is representative, we verify the halo mass function of our runs against theoretical predictions, as well as against other simulations."567" We use the Press-Schechter (Press&Schechter1974). and Sheth-''ocmen (Sheth&""Tormen1999) mass functions. and the fitting function provided by Ieedetal.(2007). derived from their simulations."," We use the Press-Schechter \citep{PS74} and Sheth-Tormen \citep{st99} mass functions, and the fitting function provided by \citet{reed07} derived from their simulations."568 We show in Figure 1. the results from the AledRes (whieh uses the WALAP 3 cosmology) run and the WAIS run., We show in Figure \ref{mfunc} the results from the MedRes (which uses the WMAP 3 cosmology) run and the WM5 run.569 In both cosmologies. we find the mass function is poorly fit bv the Press-Schechter mass function.," In both cosmologies, we find the mass function is poorly fit by the Press-Schechter mass function."570 As the density thresholds were chosen to match the Reecοἱal. mass function. it is unsurprising that it provides a better Gt than the Press-Schechter function.," As the density thresholds were chosen to match the \citet{reed07} mass function, it is unsurprising that it provides a better fit than the Press-Schechter function."571 However. we note that the Shethi-Tormen function provides a good fit: one that is slightly better than the Reedetal.(2007). function.," However, we note that the Sheth-Tormen function provides a good fit: one that is slightly better than the \citet{reed07} function."572 1n order to calculate. A for our halos. we must. first," In order to calculate $\lambda$ for our halos, we must first"573‘The sensitivity which N’-bocly integrations exhibit to smal changes in initial conditions and to numerical errors has been an active area of research since Miller's. landmark study.,The sensitivity which $N$ -body integrations exhibit to small changes in initial conditions and to numerical errors has been an active area of research since Miller's landmark study.574 Miller(1964) demonstrated the exponentiai divergence of near-by orbits for svstems with Nox32 and found. that the separation of nearby orbits increases rapidly when close binary interactions occur., \cite{Miller} demonstrated the exponential divergence of near-by orbits for systems with $N\leq 32$ and found that the separation of nearby orbits increases rapidly when close binary interactions occur.575 He suggeste hat the divergence of near-by orbits is too rapid to be solely accounted. by binary interactions and suggests tha here must be a collective effect to account for the results., He suggested that the divergence of near-by orbits is too rapid to be solely accounted by binary interactions and suggests that there must be a collective effect to account for the results.576 llowever. Stanclish(1968) showed that the divergence rate was reduced if the potential was replaced with a softenec xotential ancl concluded that the divergence is mainly due o close binary interactions.," However, \cite{Standish} showed that the divergence rate was reduced if the potential was replaced with a softened potential and concluded that the divergence is mainly due to close binary interactions."577 Vhe dramatic. elfects of numerical errors on N-body integrations was also demonstrated in an important. paper wv Lecar(1968).., The dramatic effects of numerical errors on $N$ -body integrations was also demonstrated in an important paper by \cite{Lecar}.578 After coordinating a study with 11 different integrations of the same 25-body. problem for 2.5 crossing times. Lecar found that quantities such as half mass radius and the moment of inertia can change by as much as 100 percent.," After coordinating a study with 11 different integrations of the same 25-body problem for 2.5 crossing times, Lecar found that quantities such as half mass radius and the moment of inertia can change by as much as 100 percent."579" In a study with No=3. DejongheandLut(2001) demonstrated that the amplification of initial errors can increase by as much. as 107""."," In a study with $N=3$, \cite{Hut} demonstrated that the amplification of initial errors can increase by as much as $10^{20}$."580 In addition. they showed that the growth of errors during close encounters can be amplilied by as much as 107. however some of the growth can be recovered after the encounter is over.," In addition, they showed that the growth of errors during close encounters can be amplified by as much as $10^4$, however some of the growth can be recovered after the encounter is over."581 The sensitivity to small changes in initial conditions anc numerical errors is à property associated: with chaotic SVSems., The sensitivity to small changes in initial conditions and numerical errors is a property associated with chaotic systems.582 A measure of the sensitivity. of numerical errors can be determined by the Lyapunov exponent A., A measure of the sensitivity of numerical errors can be determined by the Lyapunov exponent $\lambda$.583" Early work suggested that the Lvapunov exponent is inversely proportional to t10 crossing time /,,. (IxandrupandSmith1991:LlegeicGoodmanet.al. 1993)."," Early work suggested that the Lyapunov exponent is inversely proportional to the crossing time $t_{cr}$ \citep{Kandrup,HeggieNbody,Goodman}. ."584". llowever. Goodmanctal.{1993) sugeest a dependence on IN of the form \+=£f,ος Nor perhaps Àt=Lflog(log(N)). implving that as oN increases the rate of separation decreases and the Lyapunoy exponent increases."," However, \cite{Goodman} suggest a dependence on $N$ of the form $ \lambda^{-1} = t_{cr}/\log{N}$ or perhaps $\lambda^{-1} = t_{cr}/\log(\log(N))$, implying that as $N$ increases the rate of separation decreases and the Lyapunov exponent increases."585 The logtN’) dependence was ater numerically verified bv. LemsendorfandMerritt(1, The $\log(N)$ dependence was later numerically verified by \cite{Merritt}.58699 Despite the clilliculty calculating solutions to IN-bodvy integrations. com»uters still remain a useful tool to study self eravitating svstems.," Despite the difficulty calculating solutions to $N$ -body integrations, computers still remain a useful tool to study self gravitating systems."587 Lf numerical errors in numerical solutions to the A ‘body problem cause such drastic changes in the actual pxsitions ancl velocities of particles how can we trust the dyvnanmics that these solutions represent?, If numerical errors in numerical solutions to the $N$ -body problem cause such drastic changes in the actual positions and velocities of particles how can we trust the dynamics that these solutions represent?588 Shadowing is a way of proving that a true solution to a dynamical svstem follows close to a numerical solution., Shadowing is a way of proving that a true solution to a dynamical system follows close to a numerical solution.589 Lf true orbits can he! found. close to numerical orbits then the dynamics represented by the numerical solutions represents true dynamics., If true orbits can be found close to numerical orbits then the dynamics represented by the numerical solutions represents true dynamics.590 ‘This study wal discuss the existence of shadow. orbits for the gravitational 3-body. problem., This study will discuss the existence of shadow orbits for the gravitational 3-body problem.591 First. definitions ancl concepts related to shadowing of dvnamücal svstems will be introduced.," First, definitions and concepts related to shadowing of dynamical systems will be introduced."592 Next. a refinement. procedure which makes corrections to numerical orbits to reduce the errors incurred at cach time step will be presented.," Next, a refinement procedure which makes corrections to numerical orbits to reduce the errors incurred at each time step will be presented."593 The Sitnikoy problem. will then be presented and used as a simple model to discuss escape and capture of orbits., The Sitnikov problem will then be presented and used as a simple model to discuss escape and capture of orbits.594 An approximate Poincaré map is then presented to model orbits of the Sitnikoy problem and will be used in conjunction with the refinement. procedure to discuss the validity of numericalsolutions by wav of shadowing., An approximate Poincaré map is then presented to model orbits of the Sitnikov problem and will be used in conjunction with the refinement procedure to discuss the validity of numericalsolutions by way of shadowing.595 The failure of the refinement. procedure to find, The failure of the refinement procedure to find596The images. cleaned from Calactic foregroun contanunation. reveal the morphology and exteut of may of the galaxies for the first time.,"The images, cleaned from Galactic foreground contamination, reveal the morphology and extent of many of the galaxies for the first time."597 For 56 galaxies. we derive radial huuinosity profiles. cllipticities. aud position angles. together with global parameters such as tota magnitude. mean effective surface briehtuess. halt-lieli radius. Sérrsic parameters. and stellar mass.," For 56 galaxies, we derive radial luminosity profiles, ellipticities, and position angles, together with global parameters such as total magnitude, mean effective surface brightness, half-light radius, Sérrsic parameters, and stellar mass."598 No eenuume voune galaxies have been found in this survey., No genuine young galaxies have been found in this survey.599 Sole saüuple galaxies were previously ideutifie ou B-baud photographic plates but remain uudetected im the near-IR., Some sample galaxies were previously identified on $B$ -band photographic plates but remain undetected in the near-IR.600 In each case there is a plausible alternative explanation for the non-detection: We also detected a double nucleus in WISS2000-09 and propose to reclassify this svsteni as a peculiar galaxy., In each case there is a plausible alternative explanation for the non-detection: We also detected a double nucleus in KKS2000-09 and propose to reclassify this system as a peculiar galaxy.601" IWINS2000-25 was shown to have distinct spiral avis in the Z/-baud and thus should be classified as ""Sb"," KKS2000-25 was shown to have distinct spiral arms in the $H$ -band and thus should be classified as “Sb""."602 Morphology aud aneular size strongly sugecst that this isa backerouud galaxy bevoud MMpc., Morphology and angular size strongly suggest that this is a background galaxy beyond Mpc.603 We found compelling evidence that the short iufeeration time of 2ALASS resulted. in serious uuderestimation of a ealaxws lDunünositv., We found compelling evidence that the short integration time of 2MASS resulted in serious underestimation of a galaxy's luminosity.604 The magnitudes of ealaxies. with Z7-baud surface brightuesses fainter than 7. obtained in om study are up fo 2.5nunag brighter than those obtained by 2N[ASS.," The magnitudes of galaxies, with $H$ -band surface brightnesses fainter than ${}^{-2}$, obtained in our study are up to mag brighter than those obtained by 2MASS."605 As the mean effective surface brightuess correlates with the huninositv of a ealaxy. we expect serious selection biases for a 2MASS-based ff-Daud galaxy lununesitv. function fainter than My=20anmae.," As the mean effective surface brightness correlates with the luminosity of a galaxy, we expect serious selection biases for a 2MASS-based $H$ -band galaxy luminosity function fainter than $_{H}=-20$ mag."606 There is a tight correlation (correlation coefficient = 0.97) between the B- aud ZI-baud magnitudes of a galaxy and this correlation has been demonstrated over a rauge of 15 maeguitudes., There is a tight correlation (correlation coefficient = 0.97) between the $B$ - and $H$ -band magnitudes of a galaxy and this correlation has been demonstrated over a range of 15 magnitudes.607 The linear transformation between the D- aud IT-bauds has a small scatter (0.3 mae} for bright ealaxies., The linear transformation between the $B$ - and $H$ -bands has a small scatter (0.3 mag) for bright galaxies.608 Iu the dwarf regine. there is à niarginal merease in scatter and possibly a slight treud for galaxies to be redder (by approximately 1 maguitude) than iudicated by the transformation found for bright galaxies.," In the dwarf regime, there is a marginal increase in scatter and possibly a slight trend for galaxies to be redder (by approximately 1 magnitude) than indicated by the transformation found for bright galaxies."609 The ealaxy hDuuinositv mean effective surface brightness relation has been analysed to derive a scuui- stellar mass-to-light ratio of Y=0.78£0.08 in the ZI-baud., The galaxy luminosity – mean effective surface brightness relation has been analysed to derive a semi-empirical stellar mass-to-light ratio of $\Upsilon_{\ast}^H=0.78\pm0.08$ in the $H$ -band.610 All rase and reduced Z£-baud images of the 57 program ealaxies iu this near-IR survey will be made publicly available and can be obtained via email request., All raw and reduced $H$ -band images of the 57 program galaxies in this near-IR survey will be made publicly available and can be obtained via email request.611 We thauk the referee for the useful couunucuts., We thank the referee for the useful comments.612 The authors acknowledge fluaucial support frou the Australian Research Council Discovery. Project Craut DPOL51126., The authors acknowledge financial support from the Australian Research Council Discovery Project Grant DP0451426.613 This paper is based on data obtained witli the Anelo-Australian Telescope., This paper is based on data obtained with the Anglo-Australian Telescope.614 The study made use of data products from the Two Micron. All Sky Survey (2\TASS). which is a joint project of the University of Massachusetts aud the Iufrared Processing and Analysis Center/California Iustitute of Technology. fuuded by the National Aeronautics and Space Acdainiuistration aud the National Science Foundation.," The study made use of data products from the Two Micron All Sky Survey (2MASS), which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation."615 Support for IRIS2 data reduction within ORAC-DR is provided by the Joiut Astronomy Centre., Support for IRIS2 data reduction within ORAC-DR is provided by the Joint Astronomy Centre.616 This research has made use of the GOLD Aline Database., This research has made use of the GOLD Mine Database.617 This research has made use of the NÀSA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Tustitute of Technology. uncer contract with the National Acronantics aud Space Acimiuistratiou.," 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."618 This research has made use of NASA's Astroplivsics Data Syste., This research has made use of NASA's Astrophysics Data System.619nnatural-weighted integrated intensity map is shown in Figure 25..,natural-weighted integrated intensity map is shown in Figure \ref{fig:holecomp}.620 Comparison of the overlays shows the physical implications of the results discussed in the previous sections., Comparison of the overlays shows the physical implications of the results discussed in the previous sections.621" Inspection of the hhole overlay appears to show an excess of small holes, especially in the inner disk."," Inspection of the hole overlay appears to show an excess of small holes, especially in the inner disk."622 Figure 26 shows a histogram of the derived diameters of holes in both the ((dashed) and ((solid) catalogs., Figure \ref{fig:ic2574-holecomphisto-diam} shows a histogram of the derived diameters of holes in both the (dashed) and (solid) catalogs.623 The difference is indicative of the extra contrast provided byMSCLEAN., The difference is indicative of the extra contrast provided by.624". Without the smoother background of the rresidual pedestal, structures are better defined and with a higher contrast."," Without the smoother background of the residual pedestal, structures are better defined and with a higher contrast."625" Whether this extra population of small holes is related to, sstar-formation events, or whether we are observing small scale turbulence, or as yet unrecognized systematic effects is beyond the scope of this paper."," Whether this extra population of small holes is related to, star-formation events, or whether we are observing small scale turbulence, or as yet unrecognized systematic effects is beyond the scope of this paper."626"the theoretical values for stellar atmospheres given by Auer Mihalas (1973) we derive a spectral type of B2 (T, = 20000 + 2500 K. log g = 4.0).","the theoretical values for stellar atmospheres given by Auer Mihalas (1973) we derive a spectral type of B2 $_{eff}$ = 20000 $\pm$ 2500 K, log g = 4.0)."627 This is consistent with the presence of NI emission lines which are confined to hotter Be type stars ϱue to their high-ionization energy (14.5 eV) and the large line excitation (~ 10 eV) (Andrillat et al., This is consistent with the presence of NI emission lines which are confined to hotter Be type stars due to their high-ionization energy (14.5 eV) and the large line excitation $\sim$ 10 eV) (Andrillat et al.628 1988)., 1988).629 The relative strength of Fell with respect to neutral Fel also requires the presence of a more tonized line-emitting region than associated with classical T-Tauri stars (Hamann Persson 1992). where Fel lines often rival the strength of Fell.," The relative strength of FeII with respect to neutral FeI also requires the presence of a more ionized line-emitting region than associated with classical T-Tauri stars (Hamann Persson 1992), where FeI lines often rival the strength of FeII."630 In order to derive the rotational velocity of IRSI from the He I lines we have used the rotational broadening function given by Gray (1976)., In order to derive the rotational velocity of IRS1 from the He I lines we have used the rotational broadening function given by Gray (1976).631 We obtain v sin(1) = 158 + 25 km/s. in agreement with a pre-main-sequence star of intermediate mass (Finkenzeller 1985).," We obtain v sin(i) = 158 $\pm$ 25 km/s, in agreement with a pre-main-sequence star of intermediate mass (Finkenzeller 1985)."632 A small nebulosity (size 1S \ 8 aresec?. PA = 40°) around IRSI which is visible on POSS-B and -R plates was covered by our long slit spectra and identified as a reflection nebula.," A small nebulosity (size 15 $\times$ 8 $^{2}$, PA = $^{\circ}$ ) around IRS1 which is visible on POSS-B and -R plates was covered by our long slit spectra and identified as a reflection nebula."633 Its presence and the association with the dark cloud C1 make the emission line object IRSI by definition a Herbig Be star (Herbig 1960)., Its presence and the association with the dark cloud C1 make the emission line object IRS1 by definition a Herbig Be star (Herbig 1960).634 According to the most comprehensive catalogue of Herbig Ae/Be stars compiled by Thé et al. (, According to the most comprehensive catalogue of Herbig Ae/Be stars compiled by Thé et al. (6351994). only 20 objects known to date have a spectral type B2 or earlier.,"1994), only 20 objects known to date have a spectral type B2 or earlier."636 IRSI (=MSXSC_GG075.5314-01.8159) was detected by ΜΟΝ at 8.3. 12.1 and 14.7 jm and ts included in the MSX point source catalogue (Egan et al.," IRS1 G075.5314-01.8159) was detected by MSX at 8.3, 12.1 and 14.7 $\mu$ m and is included in the MSX point source catalogue (Egan et al."637 1999)., 1999).638 The source is unresolved by the small MSX telescope (beam ~ 12 arcsec)., The source is unresolved by the small MSX telescope (beam $\sim$ 12 arcsec).639 In order to explore the nature of the thermal excess emissio1 of warm dust around IRSI we have obtained diffraction-ltnited sub-aresecond images with the thermal infrared camera MAX at UKIRT., In order to explore the nature of the thermal excess emission of warm dust around IRS1 we have obtained diffraction-limited sub-arcsecond images with the thermal infrared camera MAX at UKIRT.640 The observations cover the M. N and Q bands as well as narrow-bands centered on the 9.7 jm silicate feature and two strong PAH bands accessible from ground at 8.7 and 11.6 pm. The high-resolution data confirm the presence of a compact mid-infrared source coinciding with IRSI.," The observations cover the M, N and Q bands as well as narrow-bands centered on the 9.7 $\mu$ m silicate feature and two strong PAH bands accessible from ground at 8.7 and 11.6 $\mu$ m. The high-resolution data confirm the presence of a compact mid-infrared source coinciding with IRS1."641 An unresolved point source (size < 0.5 aresec FWHM) accounts for the bulk ( 80 %)) of emission., An unresolved point source (size $\la$ 0.5 arcsec FWHM) accounts for the bulk ( $\sim$ 80 ) of emission.642 The image obtained in the 11.6 μπι PAH band shown in Fig., The image obtained in the 11.6 $\mu$ m PAH band shown in Fig.643 10. shows the presence of a faint extended emission region towards the north of the stellar source., \ref{mir_imaging} shows the presence of a faint extended emission region towards the north of the stellar source.644 Optical broadband photometry of the source in the Johnson BVRI bands have been performed in order to cover the spectral energy distribution of the stellar photosphere of IRS1., Optical broadband photometry of the source in the Johnson BVRI bands have been performed in order to cover the spectral energy distribution of the stellar photosphere of IRS1.645 Tab., Tab.646 6. presents our optical and mid-infrared photometry of IRSI., \ref{photometry_herbig} presents our optical and mid-infrared photometry of IRS1.647compositions. so some interaction wilh the ambient magnetic field is expected.,"compositions, so some interaction with the ambient magnetic field is expected."648 The most stable energy state is achieved when the erain longest axis rotates perpendicularly to the lield lines., The most stable energy state is achieved when the grain longest axis rotates perpendicularly to the field lines.649 Consequently. dust emission polarization vectors as observed in subamnillimeter polarimetry have to be rotated by 90° in order to be parallel to the plane-ol-skv (POS) component of the magnetic field.," Consequently, dust emission polarization vectors as observed in submillimeter polarimetry have to be rotated by $\degr$ in order to be parallel to the plane-of-sky (POS) component of the magnetic field."650 The LOS field component adds no information to the 2D polarization map because the spinning dust grains produce zero polarization flux., The LOS field component adds no information to the 2D polarization map because the spinning dust grains produce zero polarization flux.651 If a strong LOS component is expected. a decrease in net polarization flux is observed. and alternative techniques must be used to measure it (e... Zeeman elfect observations: Troland&Crutcheretal. (1993))).," If a strong LOS component is expected, a decrease in net polarization flux is observed, and alternative techniques must be used to measure it (e.g., Zeeman effect observations: \citet{Troland82,Crutcher93}) )."652 Therefore. the polarization map of Figure 4.. when rotated by 907. traces the projection of the 3D magnetic field morphology on the plane-ol-skv (see Figure 9)).," Therefore, the polarization map of Figure \ref{fir5pol}, , when rotated by $\degr$, traces the projection of the 3D magnetic field morphology on the plane-of-sky (see Figure \ref{field}) )."653 For FIR 5A. the field geometry is described bv curved Ines centered on the protostellar core.," For FIR 5A, the field geometry is described by curved lines centered on the protostellar core."654 Toward the elongated emission associated with FIR 5B. the field lines are parallel to (he core's major axis. implving a 90° change in the direction wilh respect to the FIR 5A mean direction.," Toward the elongated emission associated with FIR 5B, the field lines are parallel to the core's major axis, implying a $\degr$ change in the direction with respect to the FIR 5A mean direction."655 Dv relaxing the signal-to-noise level down to σ. one can see that (his change in (he magnetic field direction is not abrupt. and an hourglass morphology can be roughly derived for (he main component (Figure 9.. upper right box).," By relaxing the signal-to-noise level down to $\sigma$, one can see that this change in the magnetic field direction is not abrupt, and an hourglass morphology can be roughly derived for the main component (Figure \ref{field}, upper right box)."656 Several theoretical works have performed 3D simulations of collapsing magnetized clouds., Several theoretical works have performed 3D simulations of collapsing magnetized clouds.657 They all agree that the POS projection of the magnetic field morphology in those class of objects is à hourglass shape (Ostrikeretal.2001:Goncalvesοἱ2008).," They all agree that the POS projection of the magnetic field morphology in those class of objects is a hourglass shape \citep{Ostriker01,Goncalves08}."658. Our results. and many others (e.g. Girartetal.(2006):Rao (2009))) provide observational support to these models.," Our results, and many others (e.g. \citet{Girart06,Rao09}) ) provide observational support to these models."659 50 lar. (he CF relation developed by Chandrasekhar&Fermi(1953) is still the most straightforward method to estimate (he plane-olskyv component of the magnetic field.," So far, the CF relation developed by \citet{CF53} is still the most straightforward method to estimate the plane-of-sky component of the magnetic field."660 Assuming energv equipartition between kinetic and perturbed magnetic energies as (where ὀτοςis the observational rms velocity along the line-of-sight and. p is the, Assuming energy equipartition between kinetic and perturbed magnetic energies as (where $\delta V_{LOS}$is the observational rms velocity along the line-of-sight and $\rho$ is the661"range shows the range predicted by different fitting methods from Table 1,, lines the cumulative best-fit.","range shows the range predicted by different fitting methods from Table \ref{tbl:slopes}, lines the cumulative best-fit."662" The form of L.(z) is taken from Hopkinsetal.(2005e,f),, but is based directly on fits to the observedQLFs of Uedaetal.(2003),, Richardsetal. (2005),, and Hasingeretal.(2005)."," The form of $\lstar(z)$ is taken from \citet{H05e,H05f}, but is based directly on fits to the observedQLFs of \citet{Ueda03}, \citet{Richards05}, and \citet{HMS05}."663". We compare this to observations in the hard X-ray (Ueda et 22003, blue squares), soft X-ray (Hasinger et 22005, red circles), optical (cyan; Wolf et 22003, diamonds; Hunt et 22004, star; Richards et 22005, x; Pei 1995, +), and radio (green; Sadler et 22002, κ; Cirasuolo et 22005, triangle)."," We compare this to observations in the hard X-ray (Ueda et 2003, blue squares), soft X-ray (Hasinger et 2005, red circles), optical (cyan; Wolf et 2003, diamonds; Hunt et 2004, star; Richards et 2005, $\times$; Pei 1995, $+$ ), and radio (green; Sadler et 2002, $\ast$; Cirasuolo et 2005, triangle)."664" We convert these to bolometric luminosities and re-fit or rescale Υ with the bolometric corrections of Marconietal.(2004),, which are also discussed in detail in Hopkinsetal.(2005d,e) and are similar to those in citetRichardsO5.."," We convert these to bolometric luminosities and re-fit or rescale $\slope$ with the bolometric corrections of \citet{Marconi04}, which are also discussed in detail in \citet{H05d,H05e} and are similar to those in \\citet{Richards05}."665" Although the uncertainties in the observed faint-end slope  are large, we reproduce its value at all redshifts."," Although the uncertainties in the observed faint-end slope $\slope$ are large, we reproduce its value at all redshifts."666" Figure 4 demonstrates how our prediction for the evolution of y with redshift translates to a “luminosity-dependent evolution"" (LDDE).", Figure \ref{fig:ldde} demonstrates how our prediction for the evolution of $\slope$ with redshift translates to a “luminosity-dependent density evolution” (LDDE).667" In each panel, the integrated densitynumber density Φ (per comoving volume) of quasars in each of several luminosity intervals is plotted as a function of redshift for z«5."," In each panel, the integrated number density $\Phi$ (per comoving volume) of quasars in each of several luminosity intervals is plotted as a function of redshift for $z<5$."668" The upper left shows Φ for intervals in bolometric L: = 9-10 (black solid line), 10--11 (blue luminositydotted), 11--12 log(L/Lo)(light blue short dashed), 12--13 (green dot-dash), 12--14 (orange triple-dot-dash), and 14--15 (red long dash)."," The upper left shows $\Phi$ for intervals in bolometric luminosity $L$: $\log(L/L_{\sun})$ = $9-10$ (black solid line), $10-11$ (blue dotted), $11-12$ (light blue short dashed), $12-13$ (green dot-dash), $12-14$ (orange triple-dot-dash), and $14-15$ (red long dash)."669" The effects traditionally fitted to LDDE forms are clear; the density of higher-L systems rises more rapidly to a peak at higher redshift, then falls off more slowly."," The effects traditionally fitted to LDDE forms are clear; the density of $L$ systems rises more rapidly to a peak at higher redshift, then falls off more slowly."670" The difference in evolution between two L intervals becomes less dramatic with increasing L, as observed."," The difference in evolution between two $L$ intervals becomes less dramatic with increasing $L$, as observed."671" Using the bolometric conversions of Marconietal.(2004) described above, we also consider the observed density evolution in other bands."," Using the bolometric conversions of \citet{Marconi04} described above, we also consider the observed density evolution in other bands."672" The upper right shows density evolution in the B-band in intervals of B-band magnitude, —20>Mg-22.5 (black solid), -22.5>Mg—25 (blue dotted), -25>Mz—27.5 (green dashed), —27.5>Mg—30 (red dot-dash)."," The upper right shows density evolution in the B-band in intervals of B-band magnitude, $-20>M_{B}>-22.5$ (black solid), $-22.5>M_{B}>-25$ (blue dotted), $-25>M_{B}>-27.5$ (green dashed), $-27.5>M_{B}>-30$ (red dot-dash)."673" This modeling immediately demonstrates why observations in the optical have not found the dramatic LDDE seen in X-ray samples, as the effects do not become pronounced until very low luminosities not usually probed in B-band samples (as low as Mp= —18), and the bolometric corrections actually “blur out” the effect as well."," This modeling immediately demonstrates why observations in the optical have not found the dramatic LDDE seen in X-ray samples, as the effects do not become pronounced until very low luminosities not usually probed in B-band samples (as low as $M_{B}\gtrsim-18$ ), and the bolometric corrections actually slightly “blur out” the effect as well."674" The lower left shows our predictionslightly for the hard X-ray, in three intervals of L(2-10 keV) = Lyx."," The lower left shows our prediction for the hard X-ray, in three intervals of $L$ (2-10 keV) = $L_{HX}$."675" In order to directly compare with the observations of Uedaetal.(2003), we adopt cgs units and consider the intervals log(Lyx/ergs.) = 41.5—43 (black solid), 43—44.5 (blue dotted), 44.5—46 (green dashed)."," In order to directly compare with the observations of \citet{Ueda03}, we adopt cgs units and consider the intervals $\log(L_{HX}/{\rm erg\,s^{-1}})$ = $41.5-43$ (black solid), $43-44.5$ (blue dotted), $44.5-46$ (green dashed)."676" For each, we show the observed best-fit LDDE model with approximate 1o errors, in each observed redshift interval (filled circles of appropriate color)."," For each, we show the observed best-fit LDDE model with approximate $1\sigma$ errors, in each observed redshift interval (filled circles of appropriate color)."677" Likewise, the lower right shows our prediction for the soft X-ray in intervals of L(0.5-2 keV) = Lsy."," Likewise, the lower right shows our prediction for the soft X-ray in intervals of $L$ (0.5-2 keV) = $L_{SX}$."678" We compare directly to Hasingeretal.(2005) in the intervals log(Lsx/ergs!) = 42—43 (black solid), 43—44 (blue dotted), 44 (green dashed), 45—46 (yellow dot-dash), >46 (red triple-dot-dash)."," We compare directly to \citet{HMS05} in the intervals $\log(L_{SX}/{\rm erg\,s^{-1}})$ = $42-43$ (black solid), $43-44$ (blue dotted), $44-45$ (green dashed), $45-46$ (yellow dot-dash), $> 46$ (red triple-dot-dash)."679"—45 Again we show the observed best-fit LDDE model in each observed interval (filled circles of matching color), but we have multipliedz the QLF normalization of Hasingeretal.(2005) by factor of 10 to account for the mean obscured fraction (Hopkinsaetal. 2005e).."," Again we show the observed best-fit LDDE model in each observed $z$ interval (filled circles of matching color), but we have multiplied the QLF normalization of \citet{HMS05} by a factor of 10 to account for the mean obscured fraction \citep{H05e}. ."680 For all the, For all the681"The second line of evidence is related to the double-RC of the Galactic bulge, seen on sightlines within ~2 degrees of the bulge minor axis and at least 5 degrees removed from the plane.","The second line of evidence is related to the double-RC of the Galactic bulge, seen on sightlines within $\sim$ 2 degrees of the bulge minor axis and at least $\sim$ 5 degrees removed from the plane."682" The two RCs are approximately equally populated, have equal or very nearly equal (V—I) and (J—K) color, and are separated in brightness by ~0.5 mag (Natafetal.Zoccali 2010).."," The two RCs are approximately equally populated, have equal or very nearly equal $(V-I)$ and $(J-K)$ color, and are separated in brightness by $\sim$ 0.5 mag \citep{2010ApJ...721L..28N,2010ApJ...724.1491M}."683" For double-clump fields, combining data from different sightlines with different reddening is non-trivial, however we can use the residuals to a fit on small scales as a preliminary diagnostic."," For double-clump fields, combining data from different sightlines with different reddening is non-trivial, however we can use the residuals to a single-clump fit on small scales as a preliminary diagnostic."684 The signal is clear: two clumps and two bumps., The signal is clear: two clumps and two bumps.685" If the two clump-bump pairs are found to have the same separation in brightness, and the same population fraction, it would rule out explanations of the double clump based on age and chemistry and confirm an X-shaped Milky Way bulge as the explanation."," If the two clump-bump pairs are found to have the same separation in brightness, and the same population fraction, it would rule out explanations of the double clump based on age and chemistry and confirm an X-shaped Milky Way bulge as the explanation."686 Both those statements appear approximately correct based on the distribution of residuals., Both those statements appear approximately correct based on the distribution of residuals.687" If detailed analysis confirm that the two populations have the same metallicity as one another,"," If detailed analysis confirm that the two populations have the same metallicity as one another,"688are plivsical. aud the sub-critical solutions are uuplivsical bevoud the turnaround point.,"are physical, and the sub-critical solutions are unphysical beyond the turnaround point."689 Turning now to the iugoiug plasima flow. the topology of the black hole accretion solution space also las a simular structure: that is. (1) a trans-Alfvénn MIID iugoiug flow with E—£p. which means a trans-fast MIID ineoing flow discussed in this paper (critical). Gi) trans-Alfvénun MIID ingoing flows with E<Eg (sub-critical) aud. (1i) trans-Alfvénn ATID iusoius flows with E>Eg (super-critical).," Turning now to the ingoing plasma flow, the topology of the black hole accretion solution space also has a similar structure; that is, (i) a trans-Alfvénn MHD ingoing flow with $E = E_{\rm F}$, which means a trans-fast MHD ingoing flow discussed in this paper (critical), (ii) trans-Alfvénn MHD ingoing flows with $E < E_{\rm F}$ (sub-critical) and (iii) trans-Alfvénn MHD ingoing flows with $E > E_{\rm F}$ (super-critical)."690 Under the ideal MITD. approximation. the physical solution is ouly the critical solution (1): the super-critical solutions (1) are unplivsical for the reason meutioned above.," Under the ideal MHD approximation, the physical solution is only the critical solution (i); the super-critical solutions (iii) are unphysical for the reason mentioned above."691 In addition to these. for accretion onto a black hole. we must consider (iv) sub-Alfvénu (or sul-slow ATID) ineoine flows. although they do uot pass through the Alfvéóun pointA.," In addition to these, for accretion onto a black hole, we must consider (iv) sub-Alfvénn (or sub-slow MHD) ingoing flows, although they do not pass through the Alfvénn point."692 The breakdown of ideal MITD approximation between the horizou aud the iuner helt surface is imdicated by Puusly(2001).. and then nou-ideal MIID solutions classified iuto (3). (31) aud (iv) would be realized as accretion solutions onto a black hole (see 5).," The breakdown of ideal MHD approximation between the horizon and the inner light surface is indicated by \citet{Punsly01}, and then non-ideal MHD solutions classified into (ii), (iii) and (iv) would be realized as accretion solutions onto a black hole (see 5)."693 The main purpose of this paper is to examine the thermal effects ou an ideal MITD plasiua streaming iu a black hole magnetosphere (see Fig. 1)), The main purpose of this paper is to examine the thermal effects on an ideal MHD plasma streaming in a black hole magnetosphere (see Fig. \ref{fig:acc}) )694 bv studyiug the critical couclitious at those maegnuetosonic poiuts., by studying the critical conditions at those magnetosonic points.695 Now. the slow magnetosonic point appears on the MIID flow solutions.," Now, the slow magnetosonic point appears on the MHD flow solutions."696 The details of critical conditions at he fast and slow magnuetosonic poiuts are discussed m 23., The details of critical conditions at the fast and slow magnetosonic points are discussed in 3.697 We derive the critical conditions at the fast and slow maenetosouic points. which are denoted im terms of the location of the fast aud slow maguetosouic xnts. the sound velocity at the fast and slow maguectosonic points aud the locatious of the Alfvénn aud ight surfaces.," We derive the critical conditions at the fast and slow magnetosonic points, which are denoted in terms of the location of the fast and slow magnetosonic points, the sound velocity at the fast and slow magnetosonic points and the locations of the Alfvénn and light surfaces."698 Iu [. we clarify the thermal effects on the ANID flows. and discuss its dependence on the rotation of the black hole maeuctosphere aud the divergence of the cross-section of a magnetic flux-tube along he field line.," In 4, we clarify the thermal effects on the MHD flows, and discuss its dependence on the rotation of the black hole magnetosphere and the divergence of the cross-section of a magnetic flux-tube along the field line."699" Then. we can fud two kinds of traus-fast MIID fow solutions for both iuflows and outflows: ""hvdro-like MIID flow and “maegueto-like” MIID flow."," Then, we can find two kinds of trans-fast MHD flow solutions for both inflows and outflows: “hydro-like” MHD flow and “magneto-like” MHD flow."700 The main differcuce between the two solutions is the vchavior of the magnetization parameter. which is the ratio of the fuid and electromagnetic parts of the otal cnerey of the flow.," The main difference between the two solutions is the behavior of the magnetization parameter, which is the ratio of the fluid and electromagnetic parts of the total energy of the flow."701 The lydro-like MIID flow solution is a somewhat lydrodvuamical solution aud. iu he weak magnetic feld luit. this trans-fast maguetosonic flow solution becomes a trans-souic flow solution discussed by Abramowicez(1981) aud Lu(1986) in the hydrodyaiuuical case;," The hydro-like MHD flow solution is a somewhat hydrodynamical solution and, in the weak magnetic field limit, this trans-fast magnetosonic flow solution becomes a trans-sonic flow solution discussed by \citet{Abramowicz81} and \citet{Lu86} in the hydrodynamical case."702 We also uuifv lydrodvuaniuc dows with hot MIID flows i a common formaliui, We also unify hydrodynamic flows with hot MHD flows in a common formalism.703 The lyvdro-like MIID fow solution disappears for a uaeneticallv-dominated magnetosphere., The hydro-like MHD flow solution disappears for a magnetically-dominated magnetosphere.704 On the coutrary. the magucto-like MIID flow solution results in the uaeneticallv-dominated flow. although that cliisappears for hotter plasiua cases;," On the contrary, the magneto-like MHD flow solution results in the magnetically-dominated flow, although that disappears for hotter plasma cases."705 Iu 5. we sunniuize our results.," In 5, we summarize our results."706 We present basic equations of a stationary and axisviunetrie ideal MITD Sow., We present basic equations of a stationary and axisymmetric ideal MHD flow.707 The Sow streams along a magnetic field line iu the black hole iiaguetosphlere. aud accretes outo the black hole or blows away to a far distant region.," The flow streams along a magnetic field line in the black hole magnetosphere, and accretes onto the black hole or blows away to a far distant region."708 To determine the configuration of magnetic field lines aud the velocity of MIID flows streaming along cach maenetic field linc. we must solve seltf-cousisteutlv what is called the Bernoulli equation along maeuctic field Hues and the magnetic force-balauce equation.," To determine the configuration of magnetic field lines and the velocity of MHD flows streaming along each magnetic field line, we must solve self-consistently what is called the Bernoulli equation along magnetic field lines and the magnetic force-balance equation."709" These equations are derived from the equation of motion for relativistic MUD plana the conservation law for particle number (ia),,=0. the ideal ANID couditiou a""F,;,=0 aud Maxsvell's equations."," These equations are derived from the equation of motion for relativistic MHD plasma the conservation law for particle number $(nu^\mu)_{;\mu}=0$, the ideal MHD condition $u^\mu F_{\mu\nu}=0$ and Maxwell's equations."710 Here. p. P aud à» aye the total energy density. the pressure of the plasima and the proper particle munhber density.," Here, $\rho$, $P$ and $n$ are the total energy density, the pressure of the plasma and the proper particle number density."711 The electromagnetic field tensor Fi satisfies Maxwell equations aud 0 is the four-velocitv, The electromagnetic field tensor $F^{\mu\nu}$ satisfies Maxwell equations and $u^\mu$ is the four-velocity712"SSPIRE resolution, we obtained the Ha and ffluxes with the same input parameters as the ones used in the SPIRE iimage.","SPIRE resolution, we obtained the $\alpha$ and fluxes with the same input parameters as the ones used in the SPIRE image."713" In the upper panel of Fig. 2,,"," In the upper panel of Fig. \ref{fig:spire250Ha24},"714 we show the Ho and ]luminosities as a function of the SPIRE lluminosity for the final 159 sources., we show the $\alpha$ and luminosities as a function of the SPIRE luminosity for the final 159 sources.715" Remarkable correlations appear between the Ho and ]luminosities and the ]luminosity of these sources, confirming that the cool dust compact emission, as traced by the bright SPIRE eemission, is closely linked to SF."," Remarkable correlations appear between the $\alpha$ and luminosities and the luminosity of these sources, confirming that the cool dust compact emission, as traced by the bright SPIRE emission, is closely linked to SF."716" The eemission presents a very high Pearson correlation coefficient (ro4=0.94, using the logarithmic values of the luminosities, as displayed in Fig. 2)),"," The emission presents a very high Pearson correlation coefficient $r_{24} = 0.94$, using the logarithmic values of the luminosities, as displayed in Fig. \ref{fig:spire250Ha24}) ),"717" while, although rather strongly correlated (rga= 0.83) with the eemission, the Ho presents more scatter."," while, although rather strongly correlated $r_{\rm H\alpha} = 0.83$ ) with the emission, the $\alpha$ presents more scatter."718" That the eemission correlates better with the eemission is not surprising because both are linked to dust, either cool for oor warm for themicron, while the Ha emission directly reflects the ionising photons of hot OB stars."," That the emission correlates better with the emission is not surprising because both are linked to dust, either cool for or warm for the, while the $\alpha$ emission directly reflects the ionising photons of hot OB stars."719 Part of the scatter of the Ha observed luminosity can also be due to emission extincted by dust., Part of the scatter of the $\alpha$ observed luminosity can also be due to emission extincted by dust.720" A certain scatter between micron) and SFR is therefore expected because of variations in dust temperature, metallicity, maybe a varying initial mass function, and although minimised in our analysis, possibly heating due to the interstellar radiation field."," A certain scatter between ) and SFR is therefore expected because of variations in dust temperature, metallicity, maybe a varying initial mass function, and although minimised in our analysis, possibly heating due to the interstellar radiation field."721" As the Ha and ccompact emissions are standard star formation rate (SFR) tracers, we can use the calibrations given by ?? for rregions to obtain the SFR of these sources."," As the $\alpha$ and compact emissions are standard star formation rate (SFR) tracers, we can use the calibrations given by \citet{2007ApJ...666..870C,2010ApJ...714.1256C} for regions to obtain the SFR of these sources."722" To calibrate the SFR from the eemission, we use Eq."," To calibrate the SFR from the emission, we use Eq."723" 13 in ? while for the combined Ha+24 SSFR calibration, we use their Eq."," 13 in \citet{2010ApJ...714.1256C} while for the combined $\alpha$ SFR calibration, we use their Eq."724 16., 16.725" We can therefore obtain the calibration to recover the SFR from the eemission alone, by matching the existing Ha+24 aand SSFR for rregions."," We can therefore obtain the calibration to recover the SFR from the emission alone, by matching the existing $\alpha$ and SFR for regions."726" To recover the Ha+24 SSFR, our best fit leads to where L(250jum) is in erg 5."," To recover the $\alpha$ SFR, our best fit leads to where $L(250\,\mu{\rm m})$ is in erg $^{-1}$."727" To recover the SFR(24), we need the following calibration: also with L(250jum) in erg s!."," To recover the SFR(24), we need the following calibration: also with $L(250\,\mu{\rm m})$ in erg $^{-1}$."728 The uncertainties are 0.04 and 0.03 for the exponents in Eqs., The uncertainties are 0.04 and 0.03 for the exponents in Eqs.729" 1 and 2,, respectively, while the calibration constants have uncertainties of 4.0 and2.796, respectively."," \ref{eq:sfrMix} and \ref{eq:sfr24}, respectively, while the calibration constants have uncertainties of 4.0 and, respectively."730" The two equations show rather similar exponents, compatible to unity within lo, and reflect the almost linear behaviour of the compact eemission with respect to SFR."," The two equations show rather similar exponents, compatible to unity within $1 \sigma$, and reflect the almost linear behaviour of the compact emission with respect to SFR."731" These recipes would then be valid to obtain SFR in rregions using the compact eemission for 1075<L(250um) 104995eergss-!, approximately."," These recipes would then be valid to obtain SFR in regions using the compact emission for $10^{38} \leq L(250\,\mu{\rm m}) \leq 10^{40.5}$ $^{-1}$, approximately."732 The high resolutionof theHerschel data for 333 allows us to perform a deeper comparison of the emission distributions within the star-forming regions., The high resolutionof the data for 33 allows us to perform a deeper comparison of the emission distributions within the star-forming regions.733" Following the work in ? and ?,, we focus on SPIRE emission in the interior of the most luminous rregions."," Following the work in \citet{2009ApJ...699.1125R} and \citet{2010MNRAS.402.1635R}, we focus on SPIRE emission in the interior of the most luminous regions."734Herschel wavelengths are particularly well-suited for this study because they trace the cool dust components that play a primordial role in rregions., wavelengths are particularly well-suited for this study because they trace the cool dust components that play a primordial role in regions.735" From inspection of the two most luminous rregions in 333, 6604 and 5595, we see that in general the SPIRE-bands are displaced from the Ha and FUV emission in the interior of the regions and have a more diffuse component extended towards the outer parts."," From inspection of the two most luminous regions in 33, 604 and 595, we see that in general the SPIRE-bands are displaced from the $\alpha$ and FUV emission in the interior of the regions and have a more diffuse component extended towards the outer parts."736 Similar displacement between the infrared and FUV emissions has already been noticed by ? for about half of the studied rregions in M55la., Similar displacement between the infrared and FUV emissions has already been noticed by \citet{2005ApJ...633..871C} for about half of the studied regions in 51a.737" As Ha corresponds to the last 10 MMyr of SF and FUV to the last ~100 MMyr, we can propose two possible explanations for the displacement: 1) as Ha forms on the dust grains, then everything (dust and gas) collapses to form stars, and it takes between 10 and MMyr for all the reservoir of dust in a given region to be consumed this way; 2) the UV field emitted mainly by OB stars and other non-ionising stars can be so strong that it pushes away the dust from the star-forming region in less than ~100 MMyr."," As $\alpha$ corresponds to the last $\sim10$ Myr of SF and FUV to the last $\sim100$ Myr, we can propose two possible explanations for the displacement: 1) as $_2$ forms on the dust grains, then everything (dust and gas) collapses to form stars, and it takes between 10 and Myr for all the reservoir of dust in a given region to be consumed this way; 2) the UV field emitted mainly by OB stars and other non-ionising stars can be so strong that it pushes away the dust from the star-forming region in less than $\sim100$ Myr."738 Support for the second explanation is the emission distribution for the most prominent shells in the north part of 333 presented in Fig. 3.., Support for the second explanation is the emission distribution for the most prominent shells in the north part of 33 presented in Fig. \ref{fig:shell}. .739 We compare in this, We compare in this740dolar regions.oO creatinge a bipolar (D)PN.,"polar regions, creating a bipolar (P)PN."741 The development of axisvnunetry. and in particular the origin of the equatorial torus needed to create it in the GISW moclel. has been attributed to various mechanisms.," The development of axisymmetry, and in particular the origin of the equatorial torus needed to create it in the GISW model, has been attributed to various mechanisms."742 Here. the presence of a companion star. fast rotating AGD stars. magnetic fields. and the compression of gas into the equatorial region bv two jets have been considered in various wavs.," Here, the presence of a companion star, fast rotating AGB stars, magnetic fields, and the compression of gas into the equatorial region by two jets have been considered in various ways."743 We will brielly discuss these mechanisms below., We will briefly discuss these mechanisms below.744 A companion star may have several elfects., A companion star may have several effects.745 First. it may cause the AGB star to spin- (e.g.HarpazanclSoker1994:andILarpaz2000)..," First, it may cause the AGB star to spin-up \citep[e.g.][]{1994MNRAS.270..734H,2000MNRAS.317..861S}."746 This spin-up max lead to small deviations [rom spherical symmetry of the AGB star itself. which are subsequently amplified in the dust condensation region due to the non-linear behavior and the strong temperature and density dependence of the dust formation process (DorfiandHófer1996)..," This spin-up may lead to small deviations from spherical symmetry of the AGB star itself, which are subsequently amplified in the dust condensation region due to the non-linear behavior and the strong temperature and density dependence of the dust formation process \citep{1996A&A...313..605D}."747 This then leads to preferential mass loss along the equator., This then leads to preferential mass loss along the equator.748 Second. io spin-up an AGB star. the companion must be close (see relsectvaliditvofassumptions for a quantification of the necessary proximity).," Second, to spin-up an AGB star, the companion must be close (see \\ref{sect:validityofassumptions} for a quantification of the necessary proximity)."749 Η the companion is close however. and the AGB stars mass loss rate is high enough. the companion mar accrele mass and create jets in (he process.," If the companion is close however, and the AGB star's mass loss rate is high enough, the companion may accrete mass and create jets in the process."750 This also leads to axisvimnmnetry (Soker therein)..," This also leads to axisymmetry \citep[][and references751therein]{2005AJ....129..947S}."752 Finally. the gravitational influence of a companion star may help shape ihe AGB stars envelope into an axisvmmetrie geometry 19990)..," Finally, the gravitational influence of a companion star may help shape the AGB star's envelope into an axisymmetric geometry \citep{1998ApJ...497..303M,1999ApJ...523..357M}."753 Several AGB stars and PNe show magnetic fields in their circiunstellar environments. and (hese fields are often suggested to be the main agent responsible for creating axisvimnmietrvy.," Several AGB stars and PNe show magnetic fields in their circumstellar environments, and these fields are often suggested to be the main agent responsible for creating axisymmetry."754 llowever. Soker(2006) argues (hat a single star can not supply the enerev ancl angular momentum to create the large coherent magnetic fields required for shaping (he cireumstellar wind. allhough magnetic fields may have a secondary role.," However, \cite{2006PASP..118..260S} argues that a single star can not supply the energy and angular momentum to create the large coherent magnetic fields required for shaping the circumstellar wind, although magnetic fields may have a secondary role."755 Equatorially enhanced densities are commonly attributed to the equatoriallv-enhanced mass loss ofan AGB star., Equatorially enhanced densities are commonly attributed to the equatorially-enhanced mass loss of an AGB star.756 However. they may also originate from the compression of gas into (he equatorial region by bipolar jets.," However, they may also originate from the compression of gas into the equatorial region by bipolar jets."757 SokerandRappaport(2000) argue that the interaction ol a slow AGB wind with a collimated fast wind (CFW) blown by a main-sequence or white cwarf companion leads (o equatorial density enhancements., \cite{2000ApJ...538..241S} argue that the interaction of a slow AGB wind with a collimated fast wind (CFW) blown by a main-sequence or white dwarf companion leads to equatorial density enhancements.758 Here. the CFW originates from the accretion of the AGB wind into a disk around the companion.," Here, the CFW originates from the accretion of the AGB wind into a disk around the companion."759 The CFW forms two jets (lobes) along the svnumetry axis which compress the slow AGB wind near the equatorial plane. leading to the formation of a dense slowly expanding ring.," The CFW forms two jets (lobes) along the symmetry axis which compress the slow AGB wind near the equatorial plane, leading to the formation of a dense slowly expanding ring."760 Later. after the CEW and slow AGB wind cease. the primary star leaves the AGB and blows a second. more spherical. [ast wind.," Later, after the CFW and slow AGB wind cease, the primary star leaves the AGB and blows a second, more spherical, fast wind."761 This wind is then collimated by the dense equatorial material aud leads to a bipolar PN as described by the GISW model., This wind is then collimated by the dense equatorial material and leads to a bipolar PN as described by the GISW model.762"A fraction as high as of Sev[ert 2 galaxies in the nearby Universe are obscured in the Xrav band by column densities of the order οἱ. or larger than the inverse of the Thomson cross-section (Vy,>σι.c1.5x107! 7). hence dubbed Compton thick (CT).","A fraction as high as of Seyfert 2 galaxies in the nearby Universe are obscured in the X–ray band by column densities of the order of, or larger than the inverse of the Thomson cross-section $N_H\ge \sigma_T^{-1} \simeq 1.5 \times 10^{24}$ $^{-2}$ ), hence dubbed Compton thick (CT)."763 If the optical depth (7= Nyop) for Compton scattering does not exceed values of the order of feu. Xray photons with energies hieher than 10.15 keV are able to penetrate the obscuring material ancl reach the observer.," If the optical depth $\tau = N_H \sigma_T$ ) for Compton scattering does not exceed values of the order of "", X–ray photons with energies higher than 10–15 keV are able to penetrate the obscuring material and reach the observer."764 For higher values of 7. the entire Xray spectrum is depressed by Compton down scattering and the X.ray photons are effectively trapped by the obscuring material irrespective of their energv.," For higher values of $\tau$, the entire X–ray spectrum is depressed by Compton down scattering and the X–ray photons are effectively trapped by the obscuring material irrespective of their energy."765 The former class of sources (mildly CFT) can be efficiently detected by Xrav instruments sensitive above 10 keV. while for the latter (heavily CT) their nature may be inferred through indirect arguments. such as the presence of a strong iron Ka line over a [lat reflected. continuum.," The former class of sources (mildly CT) can be efficiently detected by X–ray instruments sensitive above 10 keV, while for the latter (heavily CT) their nature may be inferred through indirect arguments, such as the presence of a strong iron $\alpha$ line over a flat reflected continuum."766 The search [or and the characterization of the physical properties of CT AGN is relevant to understand the evolution of accreting Supermassive Black Holes (SAIBIIs)., The search for and the characterization of the physical properties of CT AGN is relevant to understand the evolution of accreting Supermassive Black Holes (SMBHs).767 In. particular. mildly CT AGN are the most promising candidates to explain the so far largely. unresolved spectrum of the X.rav background around its 30 keV peak (Worslev et al.," In particular, mildly CT AGN are the most promising candidates to explain the so far largely unresolved spectrum of the X–ray background around its 30 keV peak (Worsley et al."768 2005: Treister Urry 2005: Gilli et al., 2005; Treister Urry 2005; Gilli et al.769 2007)., 2007).770 According to the Gilli et al. (, According to the Gilli et al. (7712007) XRD svnthesis model. their integral contribution to the hard X.ray. background is of the order of30%.,"2007) XRB synthesis model, their integral contribution to the hard X–ray background is of the order of."772. This [Iraction has been estimated under simplified hypotheses., This fraction has been estimated under simplified hypotheses.773" In particular. (he same DIuminosity function aud cosmological evolution of unobseured and Compton thin AGN is assumed: moreover. (he number density of ""heavilv CT AGN is the same of “mildly” CT."," In particular, the same luminosity function and cosmological evolution of unobscured and Compton thin AGN is assumed; moreover, the number density of “heavily"" CT AGN is the same of “mildly"" CT."774 While these assumptions are nol inconsistent wilh the present observational framework (Risaliti et al., While these assumptions are not inconsistent with the present observational framework (Risaliti et al.775 1999: Guainazzi οἱ al., 1999; Guainazzi et al.776 2005). it should be noted that absorption column densities in excess of 1071 were measured or inferred. for about a few tens of nearby AGN (Comastri 2004: Della Ceca οἱ al.," 2005), it should be noted that absorption column densities in excess of $^{24}$ were measured or inferred for about a few tens of nearby AGN (Comastri 2004; Della Ceca et al."777 2008). and only a ΠαπΠα] of them are known bevond the local Universe (Norman," 2008), and only a handful of them are known beyond the local Universe (Norman"778Clearly asymmetric sources (e.g. G123.0 and W3(OID): see Figure 1. Table 1).,"clearly asymmetric sources (e.g. G123.0 and W3(OH); see Figure 1, Table 1)."779 Furthermore. line asvinmetries do not always agree between different transitions of the same molecule (e.g. Gregersen et al.," Furthermore, line asymmetries do not always agree between different transitions of the same molecule (e.g. Gregersen et al."780 1997)., 1997).781 Additional observations in other molecules ancl at higher resolution are evidentlv necessary before a single source can be considered a strong candidate for collapse., Additional observations in other molecules and at higher resolution are evidently necessary before a single source can be considered a strong candidate for collapse.782 In the next section. we compare our ]line asymmetry results to previous studies of line asvinmetries in (hese sources using other molecular tracers.," In the next section, we compare our line asymmetry results to previous studies of line asymmetries in these sources using other molecular tracers."783 Twenty-four of our 27 sources have also been observed in HCN 3-2 ον Wu et al. (, Twenty-four of our 27 sources have also been observed in HCN 3-2 by Wu et al. (7842010).,2010).785 Comparing our eclassifieation with their HCN classifications. we find that eight of (he nine sources we identily as blue asvinmetrie in ((requinng that the line be consicered blue bv at least (wo diagnostics) are also blue asvmmnietric in LCN even though (density required to excite a Typ=1 Ix line [or gas at {η=20 Ix. see Evans 1999. Reiter οἱ al.," Comparing our classification with their HCN classifications, we find that eight of the nine sources we identify as blue asymmetric in (requiring that the line be considered blue by at least two diagnostics) are also blue asymmetric in HCN even though (density required to excite a $T_R =1$ K line for gas at $T_{kin}=20$ K, see Evans 1999, Reiter et al."786 2011) of the two molecules are different by nearly an order of magnitude (πω2.3x10! ο for, 2011) of the two molecules are different by nearly an order of magnitude $= 2.3 \times 10^4$ $^{-3}$ for787band.,band.788 These parameters are converted to α΄ and p in eq.CX1))., These parameters are converted to $\kappa$ and $p$ in \ref{NT_spec}) ).789 The other fitting parameter Veollote Isa function of Ey; in eq.CA1)) and magnetic field (2) as is shown below 1999):: This equation gives constraint on (he maximum electron energy Z4 aud magnetic field D., The other fitting parameter $\nu_{\rm rolloff}$ isa function of $E_{\rm max}$ in \ref{NT_spec}) ) and magnetic field $B$ ) as is shown below \citep{reynolds1999}; This equation gives constraint on the maximum electron energy $E_{\rm max}$ and magnetic field $B$.790 since available radio data ol SN 1006 have spatial resolution far larger (han (he scale of the X-ray filaments. we have no accurate radio flux nor index from (he position of the X-ray filaments.," Since available radio data of SN 1006 have spatial resolution far larger than the scale of the X-ray filaments, we have no accurate radio flux nor index from the position of the X-ray filaments."791 We therefore fixed the radio index (o the poor resolution radio result of p=2.14 bv Allen.Petre.&Gotthell(2001) and the radio flux is treated as a [ree parameter lor the present filling., We therefore fixed the radio index to the poor resolution radio result of $p=2.14$ by \citet{allen} and the radio flux is treated as a free parameter for the present fitting.792 Allowing the radio index to vary [rom p=2.0 to p=2.2. we see no significant difference in (he best-fit parameters within (he statistical errors.," Allowing the radio index to vary from $p=2.0$ to $p=2.2$, we see no significant difference in the best-fit parameters within the statistical errors."793 The spatial structure of the relativistic electrons produced by the diffusive shock acceleration across the shock is determined by (he competing process ol diffusion ancl advection., The spatial structure of the relativistic electrons produced by the diffusive shock acceleration across the shock is determined by the competing process of diffusion and advection.794" The advection time scale (7,4) Is given by where ie dis (he scale width of the spatial distribution of the relativistic electrons ancl wu is the flow speecl.", The advection time scale $\tau_{\rm ad}$ ) is given by where $w$ is the scale width of the spatial distribution of the relativistic electrons and $u$ is the flow speed.795 The diffusion time scale (vq) is given from the random-walk theory. as: where A is the diffusion coefficient., The diffusion time scale $\tau_{\rm dif}$ ) is given from the random-walk theory as; where $K$ is the diffusion coefficient.796 In order (that. the high energy. electrons are accelerated at shock front. electrons. in upstream should be diffusedback to the shock front against the advection to the downstream side (shock flow).," In order that the high energy electrons are accelerated at shock front, electrons in upstream should be diffusedback to the shock front against the advection to the downstream side (shock flow)."797" Therelore. z,4 should be nearly equal to τι. hence “= A "," Therefore, $\tau_{\rm ad}$ should be nearly equal to $\tau_{\rm dif}$ , hence $\frac{w_{\rm u}}{u_{\rm u}} \simeq \frac{w_{\rm u}^2}{K_{\rm u}}$ ."798We thus obtain:, We thus obtain;799pixels.,pixels.800Deconvolulion.. lu spatially constant seeing case is Chat equation (1)) has a convolutionalstructure A;(Cr.y)=κ).," In spatially constant seeing case is that equation \ref{eq:Fredholm}) ) has a convolutionalstructure $k_i(x,y) \equiv k_i(x - y)$."801 The advantage of Fourier based methods is that the operator A; decomposes nicely in the Fourier domain., The advantage of Fourier based methods is that the operator $K_i$ decomposes nicely in the Fourier domain.802 An inherent disadvantage io the Fourier approach is that oOgreat care must be used to avoid oulcomes such as Fig., An inherent disadvantage to the Fourier approach is that great care must be used to avoid outcomes such as Fig.803"e 1..The approach outlined in Kaiser(2004) is to Fourier transform each image and estimate the a""ih Fourier coefficient of g by a weighted average of the uw""ih Fourier coelficient of each image.", \ref{fig:FourierInvOperator}.The approach outlined in \citet{kais2004} is to Fourier transform each image and estimate the $u^{th}$ Fourier coefficient of $g$ by a weighted average of the $u^{th}$ Fourier coefficient of each image.804 The weighting is accomplished so that the images with better seeing are weiehted more heavily in the average., The weighting is accomplished so that the images with better seeing are weighted more heavily in the average.805 This method has some associated optimality properties., This method has some associated optimality properties.806B: Llowever. in: practice.B: these properties.» turn out to not be. useful.," However, in practice, these properties turn out to not be useful."807t See1 below. fort a more thorough description., See below for a more thorough description.808 Note that. as presented. this method makes three nontrivial assumptions.," Note that, as presented, this method makes three nontrivial assumptions."809 First. il assumes that each F;Cr.y)=Αα—y). that is. spatially constant seeing.," First, it assumes that each $k_i(x,y) \equiv k_i(x-y)$, that is, spatially constant seeing."810 As we describe in section ??.. while this assumption could have sienilicant consequences when seeing varies spatially. in practice. it does not appear to cause much problem.," As we describe in Section \ref{sec:results}, while this assumption could have significant consequences when seeing varies spatially, in practice, it does not appear to cause much problem."811 The second assumption is (hat the 6;;'s are large enough that the Gaussian approximation to the Poisson is accurate across (he image., The second assumption is that the $\theta_{ij}$ 's are large enough that the Gaussian approximation to the Poisson is accurate across the image.812" The third assumption is that the variance of the Gaussian is a value oF that depends only on the image ὁ,", The third assumption is that the variance of the Gaussian is a value $\sigma^2_i$ that depends only on the image $i$.813 These last (wo assumptions make the analvsis easier. and while (hev are often reasonable. thev need not hold in practice.," These last two assumptions make the analysis easier, and while they are often reasonable, they need not hold in practice."814" To define the Fourier Deconvolution estimator. first expand g into the Fourier basis. which we write as (6, ). In general. we use the notation [ for the Fourier transform of the function f. "," To define the Fourier Deconvolution estimator, first expand $g$ into the Fourier basis, which we write as $(\phi_u)$ , In general, we use the notation $\tilde{f}$ for the Fourier transform of the function $f$ "815"Under these assumptions. then. the mass of the halo of an L5, galaxy is given by and the deflection of a light rav emanating from a source galaxy is given by llere D, is the angular diameter distance between the observer and the source. Dj; is the angular diameter distance between the lens and the source. and X. is the ratio of the impact parameter of the lieht rav aud the characteristic radius. s. of the lens (i.e... X=Rs: see BBS).","Under these assumptions, then, the mass of the halo of an $L_B^\ast$ galaxy is given by and the deflection of a light ray emanating from a source galaxy is given by Here $D_s$ is the angular diameter distance between the observer and the source, $D_{ls}$ is the angular diameter distance between the lens and the source, and $X$ is the ratio of the impact parameter of the light ray and the characteristic radius, $s$ , of the lens (i.e., $X \equiv R/s$; see BBS)."816 lt is worth noting that galaxv-galaxy lensing has. of course. been detected in the (e.g.. dellAntonio Tyson 1996: LIudson et 11998): however due to the verv small number of galaxies in the ILDE-N. the galaxy-galaxy lensing signal can only be detected with relatively low significance.," It is worth noting that galaxy-galaxy lensing has, of course, been detected in the HDF-N (e.g., dell'Antonio Tyson 1996; Hudson et 1998); however due to the very small number of galaxies in the HDF-N, the galaxy-galaxy lensing signal can only be detected with relatively low significance."817 In particular. (here are simply too few actual source galaxies {ο carry out a detailed investigation of the ellects of multiple deflections using only the observed sources.," In particular, there are simply too few actual source galaxies to carry out a detailed investigation of the effects of multiple deflections using only the observed sources."818 It is for this reason that Monte Carlo simulations are adopted here., It is for this reason that Monte Carlo simulations are adopted here.819 The completeness limits of the redshift survey are. unfortunately. different for the itself and the surrounding area of the sky. (he survey being deeper in (he region of the," The completeness limits of the redshift survey are, unfortunately, different for the HDF-N itself and the surrounding area of the sky, the survey being deeper in the region of the HDF-N."820 This gives rise to a somewhat different redshift distribution for galaxies with measured redshifts in the center of the field versus galaxies with measured redshifts in the outer region of the field., This gives rise to a somewhat different redshift distribution for galaxies with measured redshifts in the center of the field versus galaxies with measured redshifts in the outer region of the field.821 In order to make an accurate prediction for the theoretical shear field. it is important that the redshift completeness limit for the lenses in the Monte Carlo simulations be uniform across the field.," In order to make an accurate prediction for the theoretical shear field, it is important that the redshift completeness limit for the lenses in the Monte Carlo simulations be uniform across the field."822 Therefore. a conservative completeness limit of /?=23 is imposed here. and the lenses in the Monte Carlo simulations consist of the 427 galaxies with R<23 in Cohen et ((2000) and Cohen (2001) for which spectroscopic redshifts and rest-frame blue luminosities are known.," Therefore, a conservative completeness limit of $R = 23$ is imposed here, and the lenses in the Monte Carlo simulations consist of the 427 galaxies with $R \le 23$ in Cohen et (2000) and Cohen (2001) for which spectroscopic redshifts and rest-frame blue luminosities are known."823 The median redshift of the lens galaxies is therefore το=0.55., The median redshift of the lens galaxies is therefore $z_{\rm med} = 0.55$.824 Two approaches are taken (o model the redshifts of the source galaxy population: (i) source galaxies are simply placed in a simele plane of redshilt z; and (41) source galaxies are distributed in redshift space according to the observed redshift distribution of faint galaxies., Two approaches are taken to model the redshifts of the source galaxy population: (i) source galaxies are simply placed in a single plane of redshift $z_s$ and (ii) source galaxies are distributed in redshift space according to the observed redshift distribution of faint galaxies.825 The first approach allows an investigation of the frequency of multiple weak deflections as a [unction of discrete source redshift., The first approach allows an investigation of the frequency of multiple weak deflections as a function of discrete source redshift.826 The second approach demonstrates the overall effect that would be expected to occur in a deep galaxy-galaxy. lensing data set., The second approach demonstrates the overall effect that would be expected to occur in a deep galaxy-galaxy lensing data set.827 Each Monte Carlo simulation includes 10 million source galaxies that are assigned random positions (RA and DEC)within a circle of radius 2.5 arcminutes. centered on the," Each Monte Carlo simulation includes 10 million source galaxies that are assigned random positions (RA and DEC)within a circle of radius 2.5 arcminutes, centered on the"828"exhibit flat circular velocity curves, as indicated by the dashed lines in Fig. 16..","exhibit flat circular velocity curves, as indicated by the dashed lines in Fig. \ref{rot_curves}."829" However, due to the non-negligible contribution of the stellar component, the total circular velocity curves are not completely flat in the outer regions."," However, due to the non-negligible contribution of the stellar component, the total circular velocity curves are not completely flat in the outer regions."830 The differences between the peak circular velocity and the velocity at r—30 kpc are of the order of 10 to 2096 and are larger than in most observed galaxies., The differences between the peak circular velocity and the velocity at $r= 30$ kpc are of the order of $10$ to $20\%$ and are larger than in most observed galaxies.831" This is a common problem in cosmological galaxy formation simulations, but in our case it is not very severe."," This is a common problem in cosmological galaxy formation simulations, but in our case it is not very severe."832" In the case of the gas components (dotted-dashed lines), we find very low circular velocities, indicative of the small amount of left over cold gas in the central regions (Fig. 3,,"," In the case of the gas components (dotted-dashed lines), we find very low circular velocities, indicative of the small amount of left over cold gas in the central regions (Fig. \ref{baryonic_mass_evol},"833 see also Table 1))., see also Table \ref{simulations_table}) ).834" The circular velocities are a proxy for the mass, rather than real velocities."," The circular velocities are a proxy for the mass, rather than real velocities."835 From Figs., From Figs.836" 3 and 16,, it is clear that the gas contributes very little to the total circular velocity; however, the gas is, in most cases, on nearly circular orbits in the disc plane."," \ref{baryonic_mass_evol} and \ref{rot_curves}, it is clear that the gas contributes very little to the total circular velocity; however, the gas is, in most cases, on nearly circular orbits in the disc plane."837" This can be seen from the open circles in Fig. 16,,"," This can be seen from the open circles in Fig. \ref{rot_curves},"838" which represent the mean gas velocity as a function of radius for the different simulations (we have done this calculation after doing an extra projection, in order to get the rotation plane of the gas which is not always the same as that of the stellar discs)."," which represent the mean gas velocity as a function of radius for the different simulations (we have done this calculation after doing an extra projection, in order to get the rotation plane of the gas which is not always the same as that of the stellar discs)."839" The mean gas velocities are relatively high, but their structure is complex, due to the non trivial interplay between cooling and heating by SN feedback."," The mean gas velocities are relatively high, but their structure is complex, due to the non trivial interplay between cooling and heating by SN feedback."840" This complexity can also be observed in Fig. 17,,"," This complexity can also be observed in Fig. \ref{vtita_maps_gas},"841" where we show the mean tangential velocities for the gas, in a 2D view (with the galaxies face-on)."," where we show the mean tangential velocities for the gas, in a 2D view (with the galaxies face-on)."842" The velocity distributions usually present strong asymmetries and, in some cases such as Aq-E-5, the mean tangential velocities are negative, indicating that the gas disc is counter-rotating with respect to the stellar disc."," The velocity distributions usually present strong asymmetries and, in some cases such as Aq-E-5, the mean tangential velocities are negative, indicating that the gas disc is counter-rotating with respect to the stellar disc."843 This results from significant late accretion of gas with misaligned angular momentum (see S09)., This results from significant late accretion of gas with misaligned angular momentum (see S09).844" As for the stars, we detect little rotation in the gas component of Aq-F-5, the galaxy with a recent major merger."," As for the stars, we detect little rotation in the gas component of Aq-F-5, the galaxy with a recent major merger."845" The circular velocity curves are similar for varying resolution, although the inner parts show differences that reflect those found for the total stellar masses in each simulation (Table 2))."," The circular velocity curves are similar for varying resolution, although the inner parts show differences that reflect those found for the total stellar masses in each simulation (Table \ref{resolution_global}) )."846" In particular, Aq-C-6 has a 1296 lower peak velocity and a 896 lower velocity at 30 kpc compared to Aq-C-5; and in Aq-E-6b (Aq-E-6) the peak velocities and velocities at 30 kpc are 4% (26%) and 0.1% (9%) lower than those found for Aq-E-5."," In particular, Aq-C-6 has a $12\%$ lower peak velocity and a $8\%$ lower velocity at $30$ kpc compared to Aq-C-5; and in Aq-E-6b (Aq-E-6) the peak velocities and velocities at $30$ kpc are $4\%$ $26\%$ ) and $0.1\%$ $9\%$ ) lower than those found for Aq-E-5."847 We have continued our study of the properties of discs and spheroids in eight simulations of galaxy formation in a ACDM cosmology., We have continued our study of the properties of discs and spheroids in eight simulations of galaxy formation in a $\Lambda$ CDM cosmology.848 The simulations correspond to haloes with present day virial masses in the range 7—16x1011 Mo and spin parameters between 0.01 and 0.05., The simulations correspond to haloes with present day virial masses in the range $7-16\times 10^{11}$ $_\odot$ and spin parameters between $0.01$ and $0.05$.849 We use a kinematic decomposition to separate discs from spheroids., We use a kinematic decomposition to separate discs from spheroids.850" Four of the eight galaxies have significant discs, three have small discs, and one is a pure spheroid."," Four of the eight galaxies have significant discs, three have small discs, and one is a pure spheroid."851 None could represent a late-type spiral., None could represent a late-type spiral.852" We compared the formation histories,situ fractions, structure and dynamical properties within and between galaxies, subdividing also by age and by radius."," We compared the formation histories, fractions, structure and dynamical properties within and between galaxies, subdividing also by age and by radius."853 Our main results are summarized below., Our main results are summarized below.854 We found significant differences between the formation histories and time-scales of discs and spheroids., We found significant differences between the formation histories and time-scales of discs and spheroids.855" Spheroids are formed early and on short time-scales, while discs are younger and have broad age distributions, often with a number of different bursts."," Spheroids are formed early and on short time-scales, while discs are younger and have broad age distributions, often with a number of different bursts."856" Typical (mass-weighted) ages for spheroids and discs are Z;10 Gyr and [4—9] Gyr, respectively."," Typical (mass-weighted) ages for spheroids and discs are $\gtrsim 10$ Gyr and $4-9$ ] Gyr, respectively."857 Because spheroids are, Because spheroids are858the photoionization code Version S4.12a (Ferland 903) using the AGN continuum described in Mathews Ferland (1987). although effectively identical results are obtained for power laws with a range of spectral index.,"the photoionization code Version 84.12a (Ferland 1993) using the AGN continuum described in Mathews Ferland (1987), although effectively identical results are obtained for power laws with a range of spectral index."859 Over he range of ellective ionization parameter typical of the ‘LR. the luminosity is only. very. weakly dependent on the strength of the ionizing continuum.," Over the range of effective ionization parameter typical of the NLR, the luminosity is only very weakly dependent on the strength of the ionizing continuum."860 Whereas a hundredfold increase in C increases the luminosity of ry a factor of ~200. the luminosity becomes only ~4 times larger.," Whereas a hundredfold increase in $U$ increases the luminosity of by a factor of $\sim 200$, the luminosity becomes only $\sim 4$ times larger."861 Although a single plane-parallel slab is obviously an overly simplistic mocel for he NLR. there is very little density dependence in the way he line luminosities vary with ionization parameter.," Although a single plane-parallel slab is obviously an overly simplistic model for the NLR, there is very little density dependence in the way the line luminosities vary with ionization parameter."862 The lessening of the cllect at higher redshift is easy to understand. since in the fus-limitech 3CRo sample this corresponds to higher luminosity and therefore a larger mean opening angle.," The lessening of the effect at higher redshift is easy to understand, since in the flux-limited 3CR sample this corresponds to higher luminosity and therefore a larger mean opening angle."863 At such large angles. variations in luminosity of an order of magnitude or less have little elfect on the angle. anc hence the bias towards more [uminous objects being seen as quasars is smaller.," At such large angles, variations in luminosity of an order of magnitude or less have little effect on the angle, and hence the bias towards more luminous objects being seen as quasars is smaller."864 This is apparent in Fieure 4.., This is apparent in Figure \ref{fig:rellum}.865 Although racio galaxies outnumber quasars al low z. at z21 the ratio is nearly reversed.," Although radio galaxies outnumber quasars 2:1 at low $z$, at $z > 1$ the ratio is nearly reversed."866 In actelition. there may be many objects like ος 22 (Economou et 11995: Rawlings et 11995) or 3€ 41 (Simpson. Rawlings Lacy 1998: Economou et 14998) that possess broad Lla which is cillicult to observe from the ground at 2x=1.1 duetoit being redshiltec into regions of poor atmospheric transmission or the Lf window. whose strong OLL airglow lines haniper the detection of broad. features.," In addition, there may be many objects like 3C 22 (Economou et 1995; Rawlings et 1995) or 3C 41 (Simpson, Rawlings Lacy 1998; Economou et 1998) that possess broad $\alpha$ which is difficult to observe from the ground at $z \simgt 1.1$ due to it being redshifted into regions of poor atmospheric transmission or the $H$ window, whose strong OH airglow lines hamper the detection of broad features."867" The observed radio galaxy fraction of ~40% at zcI should therefore be considered an upper limit. and it provides a lower limit to 8,z10."," The observed radio galaxy fraction of $\sim86840$ at $z > 1$ should therefore be considered an upper limit, and it provides a lower limit to $\theta_0 \simgt 70\degree$."869 This corresponds to (Loso?/iLbno)«1.7. and the ratio would drop below 1.5 if only one third of those objects currently classified: as radio galaxies are really quasars.," This corresponds to $\langle L_{\rm QSO} \rangle / \langle L_{\rm RG} \rangle < 1.7$, and the ratio would drop below 1.5 if only one third of those objects currently classified as radio galaxies are really quasars."870 It should also be noted that measuremoent errors tend to be rather larger in near-infrared than in optical spectroscopy. and so the study ofJackson Rawlings (1997) is less sensitive to cdilferences in the two classes than are low redshift stuclies.," It should also be noted that measurement errors tend to be rather larger in near-infrared than in optical spectroscopy, and so the study of Jackson Rawlings (1997) is less sensitive to differences in the two classes than are low redshift studies."871 Jackson Rawlings (1997) do not olfer any explanation as to why they fail to observe a similar οσοι to that. of Jackson Browne (1990). vet it is naturally explained in our model as a luminosity. rather than a redshift. dependence.," Jackson Rawlings (1997) do not offer any explanation as to why they fail to observe a similar effect to that of Jackson Browne (1990), yet it is naturally explained in our model as a luminosity, rather than a redshift, dependence."872 Although our. model might appear to predict that high redshift samples whose luminosities are similar to those of ow redshift 83CRR. objects aa sample from the τς catalogue) should also display a separation in luminosity with broad/narrow line class. such a prediction also depends on the assumption that the average torus icbght does not vary with redshift since this also controls he mean opening angle.," Although our model might appear to predict that high redshift samples whose luminosities are similar to those of low redshift 3CRR objects a sample from the 7C catalogue) should also display a separation in luminosity with broad/narrow line class, such a prediction also depends on the assumption that the average torus height does not vary with redshift since this also controls the mean opening angle."873 We can predict that the dilference tween the luminosities of radio galaxies and quasars should be a 'unction of quasar fraction (Figures 3. and 4)). and should effectively vanish for samples with a Large (ZSO) quasar fraction.," We can predict that the difference between the luminosities of radio galaxies and quasars should be a function of quasar fraction (Figures \ref{fig:frg} and \ref{fig:rellum}) ), and should effectively vanish for samples with a large $\simgt 80$ ) quasar fraction."874 Since our model requires that cllectively all the eemission is seen directly. it appears to be in contradiction with the recent. detection of polarized iin racio galaxies by ci Serego Alighieri et ((1997).," Since our model requires that effectively all the emission is seen directly, it appears to be in contradiction with the recent detection of polarized in radio galaxies by di Serego Alighieri et (1997)."875 These authors calculate that of the total comission is obscured in radio galaxies. but their calculations assume that the observed featureless continuum is entirely scattered.," These authors calculate that of the total emission is obscured in radio galaxies, but their calculations assume that the observed featureless continuum is entirely scattered."876 Lt is known that Sevlert galaxies possess an extended: featureless continuum (FC?: Tran. 1995) ane it is reasonable to imagine that radio galaxies do also. thus lowering the estimate of the obscured fraction.," It is known that Seyfert galaxies possess an extended featureless continuum (FC2; Tran 1995) and it is reasonable to imagine that radio galaxies do also, thus lowering the estimate of the obscured fraction."877 In. addition. e. mission. may. be polarized. even if none is obscured. if 10 scattering region is distributed anisotropicallv.," In addition, the emission may be polarized, even if none is obscured, if the scattering region is distributed anisotropically."878 Although di Serego Alighieri et clclisfavour this idea. it is not in conllict with observations. and. would. be expected. if the scattering material is associated with the outllow.," Although di Serego Alighieri et disfavour this idea, it is not in conflict with observations, and would be expected if the scattering material is associated with the outflow."879 The fact iit polarized comission is detected. in. 3€ 227 despite our. relatively clear view of the nucleus seems to indicate that significant obscuration is not required. for the line emission. {ο be polarized., The fact that polarized emission is detected in 3C 227 despite our relatively clear view of the nucleus seems to indicate that significant obscuration is not required for the line emission to be polarized.880 We also note that the size of the LLL]-emitting region that must be obscured is much larger than estimates for the height of the torus derived from the dust evaporation radius and cone opening angle., We also note that the size of the -emitting region that must be obscured is much larger than estimates for the height of the torus derived from the dust evaporation radius and cone opening angle.881 While the polarization data are intriguing. we therefore feel that our model is not in conllict with then.," While the polarization data are intriguing, we therefore feel that our model is not in conflict with them."882 We have used a simple receding torus model. whose free parameters are constrained by observation. to show that low redshift 3CRR. quasars should be. on average. about twice as luminous in their ionizing continua as radio galaxies of the same racio laminosity.," We have used a simple receding torus model, whose free parameters are constrained by observation, to show that low redshift 3CRR quasars should be, on average, about twice as luminous in their ionizing continua as radio galaxies of the same radio luminosity."883 This difference should also be seen in yir.LI]... but not theirLH]... emission line luminosities. in agreement with observation.," This difference should also be seen in their, but not their, emission line luminosities, in agreement with observation."884 For samples with a higher uasar fraction. such as the high redshift οςRR objects. the iference in ionizing luminosities between quasars and racio ealaxies should be smaller. and there should therefore be less of a difference in thei Lhuminosities. agzün in line with observation.," For samples with a higher quasar fraction, such as the high redshift 3CRR objects, the difference in ionizing luminosities between quasars and radio galaxies should be smaller, and there should therefore be less of a difference in their luminosities, again in line with observation."885 This model leads το the conclusion. that the A5007 emission line. and not the A3727 doublet. is an unbiased. indicator of the intrinsic opticalultraviolet luminosity of both quasars and radio galaxies.," This model leads to the conclusion that the $\lambda$ 5007 emission line, and not the $\lambda$ 3727 doublet, is an unbiased indicator of the intrinsic optical–ultraviolet luminosity of both quasars and radio galaxies."886 Vhe author would like to thank Peter Lisenharclt for a useful discussion and Steve Rawlines for a critical reading, The author would like to thank Peter Eisenhardt for a useful discussion and Steve Rawlings for a critical reading887 Lya 7 ~ (Fanal.1999:Spinradct1998).. 2~ (Taian," $\alpha$ $z$ $\sim$ \citep{fan1,hugal,spinrad}."888&Loch1997:Fukugita&Kawasaki1991).. (DonalneShull1987:Valageas&Silk1999).. (Giroux.Chiu&Ostriker2000:Cinediu2000).. CCüroux&Shapiro1996:Teemarketal.1991).. (Caroux&Shapiro'Tuulin," $z \sim$ \citep{hl97,fuka}, \citep{donshull87,valsilk}, \citep{gs96,madrees99,ciardi,chiuost,gn00}, \citep{gs96,tsb94}. \citep{gs96,tumshull}."889"sou&Shull2000).. :~3 (Jalkobsenetal.1991:Hogan1997:ReinersIrisetal.2001). Do6. i~3. high-:. (Faunal.9001Όλι, Magorrianetal.(1998):Isormen"," $z \sim8903$ \citep{jakobsen,hog97,reim97,kriss}, $z \sim8916$ $z \sim 3$ $z$ \citep{fan2, fan3}. \citet{magor,korm})"892dy&Gebhardt(2001))). 2Z6 (Tatman&Loeb1998)., $z \ga 6$ \citep{hl98}.893 ;Z3 high-: (Callietal.1999).., $z \ga 3$ $z$ \citep{gilli}.894" (Mushotzkvetal.2000:Cüacconietal.2001) Shaveretal.(1999) =2,5, high-: 52 TT (Shull&vauSteeubere (ισα&Ostriker1997:ValageasSilk 2 "," \citep{mush, giac} \citet{shaver} $z > 2.5$ $z$ $\geq$ \citep{svs85} \citep{go97,valsilk,sgb94,gs96}, $z$ "895but the cosmological parameters used are same às this work: Oy2 0.3. O420.7. and Ha=70kms!Mpe',"but the cosmological parameters used are same as this work: $\Omega_{\rm M}=0.3$ , $\Omega_{\Lambda}=0.7$ , and $H_0=70~ {\rm km~s^{-1}~Mpc^{-1}}$."896" The central black hole masses My, can be estimated from the velocities νι of the clouds in the BLRs.eewherethemotionso fthecloudsareassumedtobevéiritageitud pata"," The central black hole masses $M_{\rm bh}$ can be estimated from the velocities $v_{\rm BLR}$ of the clouds in the BLRs, where the motions of the clouds are assumed to be virilized and isotropic."897 tides fgg loudsinkk Roughly are derived from the width of the broad emission lines., The velocities of the clouds in BLRs $v_{\rm BLR}$ are derived from the width of the broad emission lines.898 For most quasars. the BLR sizes have not been measured by the reverberation mapping method. and the empirical relation (1)) is instead used to estimate the BLR sizes.," For most quasars, the BLR sizes have not been measured by the reverberation mapping method, and the empirical relation \ref{rblr}) ) is instead used to estimate the BLR sizes."899 The central black hole masses of quasars have been estimated from their broad-line widths and optical continuum luminosity (e.g. Laor. 2000: MeLure Dunlop 2001: Cao Jiang 2002).," The central black hole masses of quasars have been estimated from their broad-line widths and optical continuum luminosity (e.g., Laor, 2000; McLure Dunlop 2001; Cao Jiang 2002)."900 For normal bright quasars. the bolometric luminosity can be estimated from their optical luminosity Ly at 5100 by (Καεριetal.2000)o," For normal bright quasars, the bolometric luminosity can be estimated from their optical luminosity $L_{\lambda,\rm opt}$ at 5100 $\AA$ by \citep{k00} ."901pt: Assuming a constant aceretion efficiency for all quasars. we have the conventional defined dimensionless accretion rate," Assuming a constant accretion efficiency for all quasars, we have the conventional defined dimensionless accretion rate."902 The dust clouds at the inner edge of the torus irradiated by the AGN central engine produce thermal emission mostly in the NIR waveband (e.g.. Kobayashi et al..," The dust clouds at the inner edge of the torus irradiated by the AGN central engine produce thermal emission mostly in the NIR waveband (e.g., Kobayashi et al.,"903" 1993). so the NIR lummosity of the dust torus is estimated byHf eewhereLi is the bolometric luminosity of the AGN. AO,from1 the solid angle subtended by the dust torus as seen the central source at the inner radius Rj, of the torus. and the factor fi, describes the covering factor of the clouds at the inner radius of the torus and the uncertainties."," 1993), so the NIR luminosity of the dust torus is estimated by, where $L_{\rm bol}$ is the bolometric luminosity of the AGN, $\Delta\Omega_{\rm torus}$ is the solid angle subtended by the dust torus as seen from the central source at the inner radius $R_{\rm in}$ of the torus, and the factor $f_{\rm in}$ describes the covering factor of the clouds at the inner radius of the torus and the uncertainties."904 The uncertainties arising from the NIR emission contributed by the central continuum emission of the AGN and starbursts in the AGN host galaxy may not be large. because this emission can be neglected compared with the NIR emission from the tori in most PG quasars (Haasetal.2003).," The uncertainties arising from the NIR emission contributed by the central continuum emission of the AGN and starbursts in the AGN host galaxy may not be large, because this emission can be neglected compared with the NIR emission from the tori in most PG quasars \citep{h03}."905. Thus. we can infer the dust torus geometry from the NIR and bolometric luminosities of AGNs. .eeifthecovering Faetoroftheduste distribution," Thus, we can infer the dust torus geometry from the NIR and bolometric luminosities of AGNs, if the covering factor of the dust clouds at the inner edge of the torus is known."906" skhehemeny,É M DERmissiono fq mp. eewherethecovering factorfz Visadopted. becausetheputativetor EERE geile galaxies on(Antonucci 1993)."," If we assume all the IR emission of quasars is from the dust torus irradiated by the AGNs, we can estimate the solid angle subtended by the whole dust torus by, where the covering factor $f=1$ is adopted, because the putative torus is required to be able to obscure the nuclear emission while it is seen edge-on \citep{a93}."907".. fthetorusissubtendedataconstantsolidangle ip {11 likestructure).thecovering factorf,, at the inner radius Ri, can be estimated by f eeThesolidangleestiniated 640in romEq.Ty)"," If the torus is subtended at a constant solid angle with radius (i.e., cone-like structure), the covering factor $f_{\rm in}$ at the inner radius $R_{\rm in}$ can be estimated by The solid angle estimated from Eq. \ref{domega2}) )"908"isanupperlimitizpigongesetkaqall cladesanalysis,tit d HALLE ""hat galee AST portante ", is an upper limit for some sources of which the IR emission from the host galaxies is important compared with that from the dust tori.909"The solid angle subtended by the torus AGO, isI where H is the thickness of the torus."," The solid angle subtended by the torus $\Delta\Omega_{\rm torus}$ is, where $H$ is the thickness of the torus."910" For the case of H/R<1. Equation (9)) can be approximated as"""," For the case of $H/R\la 1$, Equation \ref{domegah}) ) can be approximated as."911" seo clog {and estimate the torus thickness at its inner edge bype. where the inner radius Rj, of the torus is given by (Lo4/LOWal? pe (Netzer&Laor1996:Hill.Goodrich.Depoy1996)."," Combining the relations \ref{domega1}) ) and \ref{domegah}) ), we can roughly estimate the torus thickness at its inner edge by, where the inner radius $R_{\rm in}$ of the torus is given by $R_{\rm in}\simeq 0.06(L_{\rm bol}/10^{38}{\rm912W})^{1/2}$ pc \citep{nl93,hgd96}."913. Haasetal.(2003) provided a sample of 64 PG quasars with infrared spectral energy distributions (3—150j/m) observed by the ISO., \citet{h03} provided a sample of 64 PG quasars with infrared spectral energy distributions $3-150{\rm {\mu}m}$ ) observed by the ISO.914 The PG quasars have high infrared detection rate of more than 80 per cent., The PG quasars have high infrared detection rate of more than 80 per cent.915 As discussed in Sect., As discussed in Sect.916 2. the central black hole masses in quasars can be estimated from their broad-line widths of H./ and optical continuum luminosities ALA(5100).," 2, the central black hole masses in quasars can be estimated from their broad-line widths of $\beta$ and optical continuum luminosities $\lambda917L_{\lambda}(5100 {\AA})$."918 The full widths at half maximum (FWHM) of broad-line H./ for 51 sources in this sample are available in Boroson&Green(1992)., The full widths at half maximum (FWHM) of broad-line $\beta$ for 51 sources in this sample are available in \citet{bg92}.919. For the remainder. they are at relatively high mb (zz2kmD.," For the remainder, they are at relatively high redshifts $z\ga 1$ )."920s We search the literature and find FWHM(H./)25100HM.) for 90-4030 (Brotherton 1996):: and j-960] km s. 4613 km s! for 16344706 and 17184481. respectively (Shieldsal.2003).," We search the literature and find $\beta$ )=5100 km $^{-1}$ for $+$ 030 \citep{b96}; ; and $\beta$ )=9601 km $^{-1}$, 4613 km $^{-1}$ for $+$ 706 and $+$ 481, respectively \citep{s03}."921. hole It leads to a sample of 54 quasars with estimated black masses. which includes 41 radio-quiet quasars and 13 radio-loud quasars (4 flat-spectrum and 9 steep-spectrum radio quasars).," It leads to a sample of 54 quasars with estimated black hole masses, which includes 41 radio-quiet quasars and 13 radio-loud quasars (4 flat-spectrum and 9 steep-spectrum radio quasars)."922 There are ten sources with 0) 2000 km s! in this sample (hereafter we refer to those quasars with FWHM(H./)z» 2000 km s! as broad-line(BL) quasars)., There are ten sources with $\beta$ $<2000$ km $^{-1}$ in this sample (hereafter we refer to those quasars with $\beta$ $\ge2000$ km $^{-1}$ as broad-line(BL) quasars).923 We estimate the central black hole masses of these PG quasars using their broad-line widths of H./ and optical continuum luminosities as deseribed in Sect., We estimate the central black hole masses of these PG quasars using their broad-line widths of $\beta$ and optical continuum luminosities as described in Sect.924 2., 2.925 The NIR luminosities. νι of the PG quasars in the waveband of 3-10jm given by Haasetal.(2003) are used in this work to explore the properties of the tori at their inner radit. because the emission from the inner region of the dust torus irradiated by the AGN ts dominant in the NIR waveband.," The NIR luminosities $L_{\rm926NIR}$ of the PG quasars in the waveband of $3-10~{\mu{\rm m}}$ given by \citet{h03} are used in this work to explore the properties of the tori at their inner radii, because the emission from the inner region of the dust torus irradiated by the AGN is dominant in the NIR waveband."927 This is supported by the thermal dust reverberation measurements on NGC4151 (Minezakietal.2004)., This is supported by the thermal dust reverberation measurements on NGC4151 \citep{m04}.928. In Fig. 1..," In Fig. \ref{fig1},"929 we plot the relation between the ratios ζωα and Lyin/Lo.," we plot the relation between the ratios $L_{\rm930bol}/L_{\rm Edd}$ and $L_{\rm NIR}/L_{\rm bol}$."931 No correlation is found between these two ratios., No correlation is found between these two ratios.932 tial aeWTAR for their dust Joudasdena sisse:surrounding. the AGNs., \citet{h03} suggested a scheme of quasar evolution for their dust distribution surrounding the AGNs.933 The sources are divided into different classes according to their evolutionary sequence., The sources are divided into different classes according to their evolutionary sequence.934 The classes O and ] represent cool and warm usivreguicedtultra-Iuminous infrared ngedeeue, The classes 0 and 1 represent cool and warm ultra-luminous infrared galaxies respectively.935ndisstonpquaisseqpedge—respectively. Class Patti PEOGONEBands with the torus emission.," Class 2 sources are young quasars, and the starbursts are still important in IR wavebands compared with the torus emission."936" There are two class 2 quasars inthiscomparedsample. and we leave out these two infrared luminous quasars 0157-001 and 1351+ our statistic, because the contribution, saidi in these two quasars may not be neglected. though these two sources would only affect little on the statistic results."," There are two class 2 quasars inthissample, and we leave out these two infrared luminous quasars $0157+001$ and $1351+640$ in all our statistic analysis, because the contribution in the infrared waveband by the dustheated by the stars in these two quasars may not be neglected, though these two sources would only affect little on the statistic results."937 The relation between the black hole mass My and the ratio Lui/Loj is plotted in Fig. 2.., The relation between the black hole mass $M_{\rm bh}$ and the ratio $L_{\rm NIR}/L_{\rm bol}$ is plotted in Fig. \ref{fig2}. .938 The generalized Kendall's 7 , The generalized Kendall's $\tau$ 939The link between galaxy stellar mass and star formation rate (SER). and its cosmic evolution is crucial to shed light on the processes of galaxy formation.,"The link between galaxy stellar mass and star formation rate (SFR), and its cosmic evolution is crucial to shed light on the processes of galaxy formation."940 The specific SFR (SSFR = SFR/mass) plays an important role as it measures the star formation efficiency of a galaxy and the fraction of a galaxy mass can be converted into stars per unit time (see e.g. de Cunha et al., The specific SFR (SSFR = SFR/mass) plays an important role as it measures the star formation efficiency of a galaxy and the fraction of a galaxy mass can be converted into stars per unit time (see e.g. de Cunha et al.941 2010)., 2010).942 Several studies at 0< <3 report similar findings: (1) the SSER increases with redshift at all masses: (2) the SSFR of massive galaxies is lower at all z (e.g. Feulner et al., Several studies at $0<z<3$ report similar findings: (1) the SSFR increases with redshift at all masses; (2) the SSFR of massive galaxies is lower at all $z$ (e.g. Feulner et al.943 2005. Erb et al.," 2005, Erb et al."944 2006. Perez-Gonzalez et al.," 2006, Perez-Gonzalez et al."945 2008. Dametr et al.," 2008, Damen et al."946 2009. Dunne et al.," 2009, Dunne et al."947 2009)., 2009).948 However. the scatter and the exact slopes of these relations are still not clear.," However, the scatter and the exact slopes of these relations are still not clear."949 In particular. the dependence of SSFR on mass is one of the most debatec open questions.," In particular, the dependence of SSFR on mass is one of the most debated open questions."950 On the one hand. radio-stacking analysis of galaxies at z=1.5—2.0 selected in the K-band found a weak (or even absent) SSFR-mass correlation. with an indicatior of steepening at higher redshift (Pannella et al.," On the one hand, radio-stacking analysis of galaxies at $z=1.5-2.0$ selected in the $K$ -band found a weak (or even absent) SSFR-mass correlation, with an indication of steepening at higher redshift (Pannella et al."951 2009. Dunne et al.," 2009, Dunne et al."952 2009)., 2009).953 On the other hand. other results based on UV to mid-IR SER tracers indicate a clear decrease of the SSFR with increasing mass (e.g. Feulner et al.," On the other hand, other results based on UV to mid-IR SFR tracers indicate a clear decrease of the SSFR with increasing mass (e.g. Feulner et al."954 2005. Erb et al.," 2005, Erb et al."955 2006. Noeske et al.," 2006, Noeske et al."956 2007b. Cowie Barger 2008).," 2007b, Cowie Barger 2008)."957 Some of these discrepancies could be due on one hand to the effects of dust extinction corrections for the SER estimates based on UV-optical indicators. and or the other hand to the assumptions and large extrapolations on the infrared SED shape and luminosity adopted for the SFR estimates based on μηι data.," Some of these discrepancies could be due on one hand to the effects of dust extinction corrections for the SFR estimates based on UV--optical indicators, and on the other hand to the assumptions and large extrapolations on the infrared SED shape and luminosity adopted for the SFR estimates based on $\mu$ m data."958 The advent of the (Pilbratt et al. (, The advent of the (Pilbratt et al. (9592010) finally allows us to robustly derive the total infrared (IR) luminosity 1) of galaxies. by directly sampling the peak of the thermal emission of dusty galaxies up to 7~3.,"2010) finally allows us to robustly derive the total infrared (IR) luminosity $L_{IR}$ ) of galaxies, by directly sampling the peak of the thermal emission of dusty galaxies up to $z\sim3$."960 In order to place new and stringent constraints on the SSER evolution. in this work we exploit the PACS Evolutionary Probe (PEP) guaranteed time data collected in the GOODS-North field with the PACS (Poglitsch et al.," In order to place new and stringent constraints on the SSFR evolution, in this work we exploit the PACS Evolutionary Probe (PEP) guaranteed time data collected in the GOODS-North field with the PACS (Poglitsch et al."961 2010) instrument., 2010) instrument.962 The PEP observations are described in Berta et al. (, The PEP observations are described in Berta et al. (9632010. this Issue Appendix A).,"2010, this Issue Appendix A)."964 Ancillary data. both photometric and spectroscopic. including UV (GALEX). optical (HST). near-IR (FLAMINGOS. IRAC/Spitzer) and mid-IR (MIPS/Spitzer) data. have been collected to build up a reliable multiwavelength catalog and photometric redshifts.," Ancillary data, both photometric and spectroscopic, including UV (GALEX), optical (HST), near-IR (FLAMINGOS, ) and mid-IR ) data, have been collected to build up a reliable multiwavelength catalog and photometric redshifts."965" We adopt 20.7. 0.73 and Q,,=0.27."," We adopt $h = 0.7$, $\Omega_{\Lambda}=0.73$ and $\Omega_m= 0.27$."966 Our aim ts to investigate the evolutionary link between stellar mass and star formation avoiding strong biases and selection effects., Our aim is to investigate the evolutionary link between stellar mass and star formation avoiding strong biases and selection effects.967" Thus. the main galaxy sample was selected at 4.5m with IRAC (magis,«23.0. AB) in order to ensure sensitivity to stellar mass up to z~2—3."," Thus, the main galaxy sample was selected at $\mu$ m with IRAC $_{4.5 \mu m}<23.0$, AB) in order to ensure sensitivity to stellar mass up to $z\sim 2-3$."968 At this limiting magnitude. the IRAC sample is ~80% flux complete (Mancini et al.," At this limiting magnitude, the IRAC sample is $\sim$ flux complete (Mancini et al."969 2009). it is ot strongly affected by confusion (see Rodighiero et al.," 2009), it is not strongly affected by confusion (see Rodighiero et al."970 2010) and it includes 4459 sources., 2010) and it includes 4459 sources.971 On the IRAC positions we fitted PSFs to the MIPS and PACS images (however. for detections in the PACS maps we used only IRAC positions with a 24um detection).," On the IRAC positions we fitted PSFs to the MIPS and PACS images (however, for detections in the PACS maps we used only IRAC positions with a 24um detection)."972 Out of the 4459 IRAC sources. 1887 (351) sources have MIPS (PACS) fluxes with signal-to-noise ratio (SNR) greater than 3.," Out of the 4459 IRAC sources, 1887 (351) sources have MIPS (PACS) fluxes with signal-to-noise ratio (SNR) greater than 3."973 The typical 24m. 100m and 160gm fluxes in this catalog reach the 3-c limit. that is ~20uJy (Magnelli et al.," The typical $\mu$ m, $\mu$ m and $\mu$ m fluxes in this catalog reach the $\sigma$ limit, that is $\sim$ $\mu$ Jy (Magnelli et al."974 2009). ~3mJy and ~5.7mJy. respectively.," 2009), $\sim$ 3mJy and $\sim$ 5.7mJy, respectively."975 With this selection we miss only 2 PACS-detected objects with low signal-to-noise ratio (SNR~ 3)., With this selection we miss only 2 PACS-detected objects with low signal-to-noise ratio $\sim3$ ).976 About40%.. ~52% and ~70% of the IRAC. MIPS and PACS subsamples have an optical spectroscopic redshift (mainly from Barger et al.," About, $\sim52\%$ and $\sim70\%$ of the IRAC, MIPS and PACS subsamples have an optical spectroscopic redshift (mainly from Barger et al."977 2008). respectively.," 2008), respectively."978 Following the approach of Rodighiero et al. (, Following the approach of Rodighiero et al. (9792007). stellar masses were estimated by setting the redshift (photometric or spectroscopic) of each IRAC-selected object and using the Hvperz code (Bolzonella et al.,"2007), stellar masses were estimated by setting the redshift (photometric or spectroscopic) of each IRAC-selected object and using the $Hyperz$ code (Bolzonella et al."980 2000) applied to the photometric SEDs in the optical-to-5.8y7m range., 2000) applied to the photometric SEDs in the $\mu$ m range.981 For an easier comparison with literature data. we used the stellar-population synthesis models of Bruzual Charlot (2003. hereafter BCO3) with a Salpeter IMF. exponentially declining 7 models for the SFR. and solar metallicity.," For an easier comparison with literature data, we used the stellar-population synthesis models of Bruzual Charlot (2003, hereafter BC03) with a Salpeter IMF, exponentially declining $\tau$ models for the SFR, and solar metallicity."982 We estimated the stellar mass completeness as a function of redshift as described in Mancini et al. (, We estimated the stellar mass completeness as a function of redshift as described in Mancini et al. (9832009) (see online Figure A1)).,2009) (see online Figure \ref{chiara}) ).984"also explore the clumping factor with no lower density threshold (total range A,<100).",also explore the clumping factor with no lower density threshold (total range $\Delta_b < 100$ ).985" Our results. presented in Section 3.1. show a small increase in Cn(z) [rom the wider range in densities bv including low-clensity cells with A,<1."," Our results, presented in Section 3.1, show a small increase in $C_H(z)$ from the wider range in densities by including low-density cells with $\Delta_b < 1$."986 However. these low-densitv. voids do not contribute substantially to the recombination rate.," However, these low-density voids do not contribute substantially to the recombination rate."987 In summary. our prescriptions for calculating the chunpine factor vield a more physical representation of the enhanced recombination rate that is an important component (to many reionization models.," In summary, our prescriptions for calculating the clumping factor yield a more physical representation of the enhanced recombination rate that is an important component to many reionization models."988 By not assuming a fully ionized medium and by specifically following Dy. we are able to exclude denser neutral gas that does not contribute appreciably to the recombination rate.," By not assuming a fully ionized medium and by specifically following $n_{\rm HII}$, we are able to exclude denser neutral gas that does not contribute appreciably to the recombination rate."989 We make simple assumptions on (he reionization process and reionization history (Section 3.2). turning on the ionizing radiation field at redshifis 2=7 or and following the thermal history arising [from photoelectric heating. radiative cooling. and pressure smoothing (Pawliketal. 2009).," We make simple assumptions on the reionization process and reionization history (Section 3.2), turning on the ionizing radiation field at redshifts $z = 7$ or $z = 9$ and following the thermal history arising from photoelectric heating, radiative cooling, and pressure smoothing (Pawlik 2009)."990 The metalline aud molecular cooling. metal transport. and feedback included in our simulations also allow us to accurately represent the thermodynamics of the gas. which has been shown to have a significant effect on the evolution of the clumping factor.," The metal-line and molecular cooling, metal transport, and feedback included in our simulations also allow us to accurately represent the thermodynamics of the gas, which has been shown to have a significant effect on the evolution of the clumping factor."991 Future models will include discrete sources and radiative transler. accounüng for temperature increases arising lrom photo-healing with spectral hardening (Abel & Haehnelt 1999).," Future models will include discrete sources and radiative transfer, accounting for temperature increases arising from photo-heating with spectral hardening (Abel & Haehnelt 1999)."992 Because our current simulations employ a spatially constant ionizing radiation fiekl. we anticipate carrving out these more realistic situations.," Because our current simulations employ a spatially constant ionizing radiation field, we anticipate carrying out these more realistic situations."993" Early studies of IGAL clumping adopted high values. Cy,240 al 2«5 (Gnedin & Ostriker 1997)."," Early studies of IGM clumping adopted high values, $ C_H > 40$ at $z < 5$ (Gnedin & Ostriker 1997)."994 As discussed earlier. we believe these values are too high lor the ionized IGAI filaments. which have expanded as a result of the heat deposited bv LyC photons.," As discussed earlier, we believe these values are too high for the ionized IGM filaments, which have expanded as a result of the heat deposited by LyC photons."995 The differences between observations and inferred critical SER densities can largely be attributed to this high clumping factor (Sawicki & Thompson 2006: Bouwensetal. 2007)., The differences between observations and inferred critical SFR densities can largely be attributed to this high clumping factor (Sawicki & Thompson 2006; Bouwens 2007).996 More recent studies have trended towards less clamping., More recent studies have trended towards less clumping.997 Raiceevic & Theuns (2011) argue that using a elobal clamping factor overestimates the recombination rate. aud (hat local values should be used instead.," Raičeević & Theuns (2011) argue that using a global clumping factor overestimates the recombination rate, and that local values should be used instead."998 In (his study. we caleulate the clumping factor for a series of high-resolution cosmological simulations for ionized hydrogen ancl helium (that explore how the photoheating," In this study, we calculate the clumping factor for a series of high-resolution cosmological simulations for ionized hydrogen and helium that explore how the photoheating"999We adopted the terminology. pseudo-caustic because 1) a pseuclo-caustie curve can form cusps in conjunction wilh open cause curves and 2) we can continue to use the (erm “caustic domains” to describe the domains of (he source plane wilh definite number of images that are defined not only by caustics but also by pseudo-caustics.,"We adopted the terminology pseudo-caustic because 1) a pseudo-caustic curve can form cusps in conjunction with open caustic curves and 2) we can continue to use the term “caustic domains"" to describe the domains of the source plane with definite number of images that are defined not only by caustics but also by pseudo-caustics."1000 In section 2 we discuss the pseudo-caustics of various lens equations., In section \ref{secTwo} we discuss the pseudo-caustics of various lens equations.1001 The outside equation of a generic elliptically symmetric lens is shown (o have a pseuco-caustic (hat arises from a branch cut., The outside equation of a generic elliptically symmetric lens is shown to have a pseudo-caustic that arises from a branch cut.1002 The inside equation of an elliptically svimuetric finite density lens does not have a pseudo-caustic., The inside equation of an elliptically symmetric finite density lens does not have a pseudo-caustic.1003 Thus a bounded ellipücally sviunetric lens violates the invariance of the total parity of the images: the arguments of smooth density fanctions for Durke's theorem are invalidated., Thus a bounded elliptically symmetric lens violates the invariance of the total parity of the images; the arguments of smooth density functions for Burke's theorem are invalidated.1004 In section 2. we give a summary and raise a possibility (o approximate a bounded mass density by a smooth function with infinite extension to preserve (he invariance of the total parity of the images., In section \ref{secThree} we give a summary and raise a possibility to approximate a bounded mass density by a smooth function with infinite extension to preserve the invariance of the total parity of the images.1005 We leave the details to a separate work., We leave the details to a separate work.1006 It is a natural wonder if other tvpes of singularities than point singularities and branch cuts mav be to be found in gravitational lensing., It is a natural wonder if other types of singularities than point singularities and branch cuts may be to be found in gravitational lensing.1007 In the Appendix. we reproduce the deflection angle formula of BourassaandIxantowski(1975) using the Schwarz function of the ellipse (Fassnachtetal.2007:IKhavinsonaudLundberg2009) and derive various lens equations used in section 2: we also spell out the inside and outside lens equations of an arbitrary set of cireularly svnuuetric lenses ancl elliplically svaumetric lenses as a reasonable model for ealaxy and cluster lenses: they. are represented as points. sticks. and disks.," In the Appendix, we reproduce the deflection angle formula of \citet{bourassa} using the Schwarz function of the ellipse \citep{FKK07,KL09} and derive various lens equations used in section \ref{secTwo}; we also spell out the inside and outside lens equations of an arbitrary set of circularly symmetric lenses and elliptically symmetric lenses as a reasonable model for galaxy and cluster lenses; they are represented as points, sticks, and disks."1008 We start wilh examining the singular isothermal lens in which (he pseudo-caustic arises from a point mass density singularitv where (he Durke's vector field is ill defined ancl move on to discussing (he pseuco-causlics of various elliplically svimietric lenses (ESL)., We start with examining the singular isothermal lens in which the pseudo-caustic arises from a point mass density singularity where the Burke's vector field is ill defined and move on to discussing the pseudo-caustics of various elliptically symmetric lenses (ESL).1009 We will see that the outside lens equation of any bounded ESL (mass density. vanishes outside a certain linite radius) has a pseudo-caustic (hat arises from the double-valuedness of the c-cut. that is [rom a branch eut., We will see that the outside lens equation of any bounded ESL (mass density vanishes outside a certain finite radius) has a pseudo-caustic that arises from the double-valuedness of the c-cut that is from a branch cut.1010 The inside equation of a bounded ESL does not have a pseudo-caustic., The inside equation of a bounded ESL does not have a pseudo-caustic.1011 Thus a bounded ESL violates the invariance of the total parity., Thus a bounded ESL violates the invariance of the total parity.1012" The ""curious behavior, of a pseucdo-caustic was noted first in an analvsis of (he isothermal sphere of an infinite extension. whose projected mass densitv is inversely. proportional to the radius (referred (ο as SIS: singular isothermal sphere). and was attributed to the density"," The “curious behavior"" of a pseudo-caustic was noted first in an analysis of the isothermal sphere of an infinite extension, whose projected mass density is inversely proportional to the radius (referred to as SIS: singular isothermal sphere), and was attributed to the density"1013for average metal abundances of 1.15. 1.52. and 1.66 rrespectively.,"for average metal abundances of $-1.15$ , $-1.52$ , and $-1.66$ respectively."1014 Lhe result or BUB stars is quite heavily influcncec by the colour correction for the non-horizontalitv of the LIB. which max oe as large as 0.6 mag and it is quite uncertain.," The result for BHB stars is quite heavily influenced by the colour correction for the non-horizontality of the HB, which may be as large as 0.6 mag and it is quite uncertain."1015 Llowever. he average magnitude changes by only 0.02 mag (up to Al(RA)=0.71 £0.19) when only stars with (IVo) aare considered.," However, the average magnitude changes by only 0.02 mag (up to $M_V(RR)=0.71\pm 0.19$ ) when only stars with $(B-V)_0>0$ are considered."1016 We conclude that our result is only> marginally depenent on the colour correction for the jorizontalitv of the LIB., We conclude that our result is only marginally dependent on the colour correction for the non-horizontality of the HB.1017 The uncertainties present in this estimate for the average magnitude of the LB preclude an accurate estimate of the dependence of LB magnitude on metallicits-, The uncertainties present in this estimate for the average magnitude of the HB preclude an accurate estimate of the dependence of HB magnitude on metallicity.1018 In fact if we divide our sampleinto three eroups according to metal abundance Fe/M]e—1.5. 15« FejI]« l.and Fe/l]- 1). we lind the average magnitudes Listed in Table 2: a weighted mean square fit through these three »onts then glves: The large error bar for the slope of this relation makes it compatible with all Literature estimates.," In fact, if we divide our sampleinto three groups according to metal abundance $<-1.5$, $-1.5<$ $<-1$, and $>-1$ ), we find the average magnitudes listed in Table 2; a weighted mean square fit through these three points then gives: The large error bar for the slope of this relation makes it compatible with all literature estimates."1019 On the whole. estimates of the absolute magnitude: of he HB for metal-poor stars provide contradictory results.," On the whole, estimates of the absolute magnitude of the HB for metal-poor stars provide contradictory results."1020 Other determinations from. cirect observation o field LB stars. lead to values very close. to. that cderivec| in this xiper., Other determinations from direct observation of field HB stars lead to values very close to that derived in this paper.1021 Lavden et al. (, Layden et al. (10221996) obtained. Ady(AR)=10.71+1.12 lor 1.6. and AL(PR)=10.79£0.30 [for 0.76 ffrom (ground-based) statistical parallaxes of Ut Lyrae stars.,"1996) obtained $M_V(RR)=+0.71\pm 0.12$ for $-1.6$, and $M_V(RR)=+0.79\pm 0.30$ for $-0.76$ from (ground-based) statistical parallaxes of RR Lyrae stars."1023 Similar faint magnitudes are obtained [rom application of the Baacke-Wesselink method to RR: Lyraes: ‘or instance Clementini ct al. (, Similar faint magnitudes are obtained from application of the Baade-Wesselink method to RR Lyraes; for instance Clementini et al. (10241995) obtained: Very similar relations were previoushy obtained by Carey. Storm Jones (1992) ane Fernley (1993): note however that brighter absolute magnitudes anc a steeper slope has been recently obtained by MeNamara (1907) from a reanalysis of Daade-Wesselink results using a higher temperature scale: The value. for the slope of the Αν(ΠΠ) rrelation is lively debated (for à discussion. see e.g. Carney et al.,"1995) obtained: Very similar relations were previously obtained by Carney, Storm Jones (1992) and Fernley (1993); note however that brighter absolute magnitudes and a steeper slope has been recently obtained by McNamara (1997) from a reanalysis of Baade-Wesselink results using a higher temperature scale: The value for the slope of the $-M_V(RR)$ relation is lively debated (for a discussion, see e.g. Carney et al."1025 1992)., 1992).1026 As mentioned above. this slope cannot. be determined from cata of the present. paper alone.," As mentioned above, this slope cannot be determined from data of the present paper alone."1027 However. if we arbitrarily adopt the slope given by Clementini et al. (," However, if we arbitrarily adopt the slope given by Clementini et al. ("10281995). we found: 1t we now consider the constant term. the agreement with the value. from Clementini οἱ al. (,"1995), we found: If we now consider the constant term, the agreement with the value from Clementini et al. ("10291995) is fully satisfactory (a marginal agreement is found. also with the relation of MleNamara).,1995) is fully satisfactory (a marginal agreement is found also with the relation of McNamara).1030 On the other side. i£ LILDLTO72 is eliminated. the relation would be: still in agreement with the value obtained using the Baacle-Wesselink technique.," On the other side, if HD17072 is eliminated, the relation would be: still in agreement with the value obtained using the Baade-Wesselink technique."1031 On the other hand. much brighter magnitudes: are obtained by those estimates based on the LB of globular clusters.," On the other hand, much brighter magnitudes are obtained by those estimates based on the HB of globular clusters."1032 As an example. Cratton et al. (," As an example, Gratton et al. ("10331997b) determined the magnitude of the HB from a calibration of globular cluster distances based on subchwarls: where we consider eq. (,1997b) determined the magnitude of the HB from a calibration of globular cluster distances based on subdwarfs: where we consider eq. (103411) of Gratton et al.,"11) of Gratton et al.,"1035 that is more appropriate for a comparison with field LIB stars because it takes into account the evolution of stars olf t1ο zero age horizontal branch (ZALIB)., that is more appropriate for a comparison with field HB stars because it takes into account the evolution of stars off the zero age horizontal branch (ZAHB).1036 Very. recently. Graton et al. (," Very recently, Gratton et al. ("10371997c) revised this relation to the following: using a more extended: sample which includes: nearly 60 metal-poor subdwarfs with accurate parallaxes.,1997c) revised this relation to the following: using a more extended sample which includes nearly 60 metal-poor subdwarfs with accurate parallaxes.1038 The average magnitude of the LLB obtained in the present paper is 0.19. mag fainter than the relation provided. by the calibration of globular cluster distances based on subdwarls., The average magnitude of the HB obtained in the present paper is 0.19 mag fainter than the relation provided by the calibration of globular cluster distances based on subdwarfs.1039 The disagreement is even worse if the distance scale found by lteid (1997) is considered: and it decreases only marginally. if 1vw distance scale considered. by Pont et al. (, The disagreement is even worse if the distance scale found by Reid (1997) is considered; and it decreases only marginally if the distance scale considered by Pont et al. (10401997) is acojted.,1997) is adopted.1041 Note however that the average magnitude: we obtain eliminating HD17072 is in marginal agreement with hat found using the calibration of globular cluster distances xised on subclwarls., Note however that the average magnitude we obtain eliminating HD17072 is in marginal agreement with that found using the calibration of globular cluster distances based on subdwarfs.1042 Another argument in favour of along distance scale (longer than found here) is provided hy consideration of the Ut Lyrac in various clusters in the Large Magellanic Clouc (LAIC) (with an average Fe/ll]l2— 1.9). whose distance is assumed. to be identical to that of the LAIC obtainec rom other calibrators.," Another argument in favour of a distance scale (longer than found here) is provided by consideration of the RR Lyrae in various clusters in the Large Magellanic Cloud (LMC) (with an average $=-1.9$ ), whose distance is assumed to be identical to that of the LMC obtained from other calibrators."1043 The first determination by Walker (1992) was Ady=0.44. for an LAIC true cistance modulus of (ALm)o=18.50 bbased on pre-Llipparcos calibration of he period-Iuminosity. relation for the Cepheicds.," The first determination by Walker (1992) was $M_V=0.44$, for an LMC true distance modulus of $(M-m)_0=18.50$ based on pre-Hipparcos calibration of the period-luminosity relation for the Cepheids."1044 “Phe value was been recently revised to AL=(241X0.10 bby Feas Catchpole (1007) using a calibration of the C'ephek »riod-Iuninosity. relation based on Hipparcos data., The value has been recently revised to $M_V=0.24\pm 0.10$ by Feast Catchpole (1997) using a calibration of the Cepheid period-luminosity relation based on Hipparcos data.1045" Less extreme. but still bright magnitudes are obtained using the LAIC distance modulus from LHipparcos calibration for Miras (My,=04040.2: van Lecuwen οἱ al."," Less extreme, but still bright magnitudes are obtained using the LMC distance modulus from Hipparcos calibration for Miras $M_V=0.40\pm 0.2$: van Leeuwen et al."1046" 1991). and [rom he expanding ringaroundSNIOSTa (AM,=0.36+ 0.03: '""anagia ct al."," 1997), and from the expanding ringaroundSN1987a $M_V=0.36\pm 0.03$ : Panagia et al."1047 LOOT: note however that a fainter value of Ady>»0.50 hhas been obtained bv Gould Uza 1997)., 1997; note however that a fainter value of $M_V>0.50$ has been obtained by Gould Uza 1997).1048 Even, Even1049We first ciscuss our results for the models where the composition included metals.,We first discuss our results for the models where the composition included metals.1050 We treat helium and metals in LTE., We treat helium and metals in LTE.1051 Uvclrogen is always treated in NLTE., Hydrogen is always treated in NLTE.1052 Recall that {hese svstems are termed Models C and D lor the 4-level and 921-level hydrogen atom models. respectively.," Recall that these systems are termed Models C and D for the 4-level and 921-level hydrogen atom models, respectively."1053 Figure 1. shows the hydrogen ionization fraction for Models C and D. There is a significant change in the hydrogen ionization level. fj. between Models C and D. The quantity /7 decreases in (he multi-level atom case in the lower optical depth regine.," Figure \ref{ionfrac_CD} shows the hydrogen ionization fraction for Models C and D. There is a significant change in the hydrogen ionization level, $f_{H}$, between Models C and D. The quantity $f_{H}$ decreases in the multi-level atom case in the lower optical depth regime."1054 For το20.1 the ionization levels among Models C and D are not very dillerent., For $\tau_{std}>0.1$ the ionization levels among Models C and D are not very different.1055 The quantitative difference is also tabulated in Table 2 which shows the physical parameters for Models CC and D when the 25 process was or was not included., The quantitative difference is also tabulated in Table $\ref{equilibrium_table}$ which shows the physical parameters for Models C and D when the $\gamma$ process was or was not included.1056 The reduction in /j due to additional angular momentum sub-states was about a [actor of 3 at an optical depth of about 744~LO (when the 25 process was included in both the models).," The reduction in $f_{H}$ due to additional angular momentum sub-states was about a factor of 3 at an optical depth of about $\tau_{std}1057\sim 10^{-4}$ (when the $\gamma$ process was included in both the models)."1058 The difference in /j decreases as the optical depth increases., The difference in $f_{H}$ decreases as the optical depth increases.1059 In metal-rich svstems. (Models C and D). the exclusion of the 25 process did not seem (o have any signilicant effect for almost all optical depths of interest.," In metal-rich systems, (Models C and D), the exclusion of the $\gamma$ process did not seem to have any significant effect for almost all optical depths of interest."1060" Figure 2. displavs the net photo-onization rate [rom any bound state of the hydrogen atom. 2. for the levels 2p4;5 and 2ps;5 for Model C. The profile of 2, lor Model C is not monotonic. but there is an overall trend (o increase wil optical depth. Tag."," Figure \ref{photo_C}1061 displays the net photo-ionization rate from any bound state of the hydrogen atom, $P_{n}$, for the levels $p_{1/2}$ and $p_{3/2}$ for Model C. The profile of $P_{n}$ for Model C is not monotonic, but there is an overall trend to increase with optical depth, $\tau_{std}$."1062" lhis increase in P, is expected due to the fact that photo-ionization dominates over recombination at higher optical depths due to higher temperatures.", This increase in $P_{n}$ is expected due to the fact that photo-ionization dominates over recombination at higher optical depths due to higher temperatures.1063 Figure 3 shows the net photo-ionization rate as a function of wave number of each energy level for Model D. Dillerent panels show different τει regimes., Figure \ref{photo_D} shows the net photo-ionization rate as a function of wave number of each energy level for Model D. Different panels show different $\tau_{std}$ regimes.1064" The 2, values increase will increasing T4, for a given energv level.", The $P_{n}$ values increase with increasing $\tau_{std}$ for a given energy level.1065 Also the net photo-ionizalion rate does nol change significantly with the change in the energy level of the bound state., Also the net photo-ionization rate does not change significantly with the change in the energy level of the bound state.1066" There is a drop in the 2, prolile at energy levels very close to the conünuum.", There is a drop in the $P_{n}$ profile at energy levels very close to the continuum.1067 This mary be, This may be1068The adiabatic growth model has been used by vanderMarel(1999). to explain various observational properties of black holes. such as the central density. cusp aud its correlation wilh the luminosity of (he galactic bulge.,"The adiabatic growth model has been used by \citet{mar99} to explain various observational properties of black holes, such as the central density cusp and its correlation with the luminosity of the galactic bulge."1069 His analvsis included properties both intrinsic to the acliabalic growth as well as scaling relations based on fundamental-plane-like observations., His analysis included properties both intrinsic to the adiabatic growth as well as scaling relations based on fundamental-plane-like observations.1070" We repeal his analvsis here (to explore the Wy,—& relation.", We repeat his analysis here to explore the $M_{bh} - \sigma$ relation.1071 First we calculate any intrinsic relation between the DII mass and the velocity dispersion of the bulge that may arise naturally [rom the adiabatie growth of the central DII., First we calculate any intrinsic relation between the BH mass and the velocity dispersion of the bulge that may arise naturally from the adiabatic growth of the central BH.1072 Neep in nund. however. (hat (he calculations (hat follow cannot be compared directly wilh observations. since (hey are noise-Iree and have an infinite resolution.," Keep in mind, however, that the calculations that follow cannot be compared directly with observations, since they are noise-free and have an infinite resolution."1073 Regardless. they should give a sense ol whether or not the BIL growth can give a relation like (19)).," Regardless, they should give a sense of whether or not the BH growth can give a relation like \ref{eq:mbh-sigma}) )."1074 The line-oF-sight velocity dispersion is lound by projecting the radial and. transverse velocity moments on the plane of the sky., The line-of-sight velocity dispersion is found by projecting the radial and transverse velocity moments on the plane of the sky.1075" The velocity moments are calculated from the sky gives ATUM 2 [q* where Z2, is the projected radius. and X is the projected density. given by It is a simple matter to predict the dispersion near the centre of the svstem."," The velocity moments are calculated from projecting them on the sky gives where $R_p$ is the projected radius, and $\Sigma$ is the projected density, given by It is a simple matter to predict the dispersion near the centre of the system."1076 As stated above. the velocity moments simply reflect (he Keplerian potential near the DII: thus they take the form and| this form is identical regardless of the inGial svstem.," As stated above, the velocity moments simply reflect the Keplerian potential near the BH; thus they take the form and this form is identical regardless of the intial system."1077 Writing the dispersion as g—«V?2]U?. this relation is simply Of course. this relation is applicable onlv in (he innermost regions.," Writing the dispersion as $\sigma = [<V^2>]^{1/2}$, this relation is simply Of course, this relation is applicable only in the innermost regions."1078 Observations are usually done much farther from the centre twpically near the effective. or hall-light. radius," Observations are usually done much farther from the centre – typically near the effective, or half-light, radius"10792000).,.1080". This auounts to deduce the map coefficients 01,5, iin the spherical harmonic basis throieh a rotation of a Fourier decomposition of the observed data.", This amounts to deduce the map coefficients $a_{lm}$ in the spherical harmonic basis through a rotation of a Fourier decomposition of the observed data.1081" The map will then be a simple visualisaion device. while the 0;,, would Iο ready to use directly or à component separation (as in (BouchetaidGispert1996:TeemarkandEfstathiou1996:BouchetandCaspert 1998))) aud the CAIB power PA)octruni estimate."," The map will then be a simple visualisation device, while the $a_{lm}$ would be ready to use directly for a component separation (as in \cite{BoGi96,TeEf96,BoGi98}) ) and the CMB power spectrum estimate."1082 Whie potentially very interesting. this approach will not be ecnerally applicable (at least ficicutly). and we now turn to a practical (ecucral) solution of eqation (5)) w iterative means.," While potentially very interesting, this approach will not be generally applicable (at least efficiently), and we now turn to a practical (general) solution of equation \ref{eq:noprior}) ) by iterative means."1083" We solve the mapanakiug problem by adapting to our particular case the eenueral ""nulti-exid method” (Pressetal. 1992).", We solve the map-making problem by adapting to our particular case the general “multi-grid method” \cite{PrTe92}.1084. Multi-erid methods are commonly used to speed up the convergence of a traditional relaxation method (iu our case the Jacobi method. as in (Pruuetetal. 2000))) defined at resolution Gra. (ee below).," Multi-grid methods are commonly used to speed up the convergence of a traditional relaxation method (in our case the Jacobi method, as in \cite{PrNe00}) ) defined at resolution $\ell_{max}$ (see below)."1085" A set of recursively defined coarser grids (6« 6,,,,) are used as temporary conrputational space. in order to ierease the convergence rate of the relaxation process."," A set of recursively defined coarser grids $\ell < \ell_{max}$ ) are used as temporary computational space, in order to increase the convergence rate of the relaxation process."1086 To be fully profitable. this algoritlin implies for cach resolution both à rebiunius iu space (resolution change) aud in time (resampling).," To be fully profitable, this algorithm implies for each resolution both a rebinning in space (resolution change) and in time (resampling)."1087 Iu this paper. we use the IIEALDPix pixclisation of the sphere (Corskietal.1998).," In this paper, we use the HEALPix pixelisation of the sphere \cite{GoHi98}."1088 Iu this scheme. the sphere is covered by 12 basic quadrilaterals. further divided recursively iuto pixels of equal area.," In this scheme, the sphere is covered by 12 basic quadrilaterals, further divided recursively into pixels of equal area."1089 The map resolution is labeled by Iu: the uuuber of pixels aloug the side of one basic quadrilateral., The map resolution is labeled by $N_{side}$: the number of pixels along the side of one basic quadrilateral.1090 Hence. INS;= leans that the sphere is covered by 12 huge pixels only.," Hence, $N_{side}=1$ means that the sphere is covered by 12 large pixels only."1091 The πα of pixels is eiven by IN;=1272stile?, The number of pixels is given by $N_{pix}=12 N_{side}^2$.1092 Nus=256 corresponds to a pixel size of 13.7 arcium.," $N_{side}1093= 256$ corresponds to a pixel size of $13.7$ arcmin."1094" For practical reasons. we necd to define the k of à TEALPix map as The ""uestedpixel uunberiug scheme of TEALPix (Córslietal.L998) allows au easy inpleieutation of the coarsening (Ckk 1) ancl refining (À> 1) operators that we use imteusivelv in our multierid ποποιο,"," For practical reasons, we need to define the $k$ of a HEALPix map as The “nested”pixel numbering scheme of HEALPix \cite{GoHi98} allows an easy implementation of the coarsening $k \rightarrow1095k-1$ ) and refining $k \rightarrow k+1$ ) operators that we use intensively in our multigrid scheme."1096 Let us now ect into the details of our implementation aud cliscuss successively the exact svstem we solve. the way we solve it and the actual steps of the multi-erid algoritlin.," Let us now get into the details of our implementation and discuss successively the exact system we solve, the way we solve it and the actual steps of the multi-grid algorithm."1097" We aimi at solving for the optimal παρ, ata eiven spatial resolution Á using ΑΝJe = AUNaM. where Ay is the ""observation? operator (from spatial to temporal domain) aud AT is the “projection” operator (frou temporal to spatial domain)."," We aim at solving for the optimal map $\hat{x}_{k}$ at a given spatial resolution $k$ using ^T = ^T, where $A_{k}$ is the “observation” operator (from spatial to temporal domain) and $A_{k}^T$ is the “projection” operator (from temporal to spatial domain)."1098" Iu a noise-free experiment. the optimal map would be straightforwardly eiven by the co-added map Gutroducing the ""co-additiou"" operator P) d= GTDA dd The time line is given by 4=Avay|os where sa ds the sky map at “infinite” resolution (4=|x in our notations)."," In a noise-free experiment, the optimal map would be straightforwardly given by the co-added map (introducing the “co-addition” operator $P_{k}$ ) = d ^T d The time line is given by $ d = A_{\infty} x_{\infty} + n$ where $x_{\infty}$ is the sky map at “infinite” resolution $k=+\infty$ in our notations)."1099 In order to check the accuracy of this trivial noise-free map imnakiug. it is natural to compute the residual with »=0 d= Aw which will be non-zero iu practice. as soon as one works with finite spatial resolution.," In order to check the accuracy of this trivial noise-free map making, it is natural to compute the residual with $n=0$ = - d = - which will be non-zero in practice, as soon as one works with finite spatial resolution."1100 We call this residual the n, We call this residual the .1101"oise, Since we assume here that he iustrumieutal beam is svuuuctric. the sky map is considered as the true sky convolved by. si; a Cassia oun Of augular diuueter Δρ."," Since we assume here that the instrumental beam is symmetric, the sky map is considered as the true sky convolved by, say, a Gaussian beam of angular diameter $\Delta1102\theta_B$."1103 This introduces a low-ass spatial filter in the problem., This introduces a low-pass spatial filter in the problem.1104 Tn other words. as the resolution iucrease. the pixclisation noise should decrease owards zero.," In other words, as the resolution increase, the pixelisation noise should decrease towards zero."1105 We have estimated. that the order of naguitude of the pixelisatiou noise cau be approximated »* The norms used in the above formmla cau be either the αππα over the time line (a very strong constraint) or the variance over the time line (a weaker coustraint)., We have estimated that the order of magnitude of the pixelisation noise can be approximated by The norms used in the above formula can be either the maximum over the time line (a very strong constraint) or the variance over the time line (a weaker constraint).1106 Since the pixelisation noise is strouglv correlated with the skv signal. point sources or Galaxy crossings are potential candidates for large aud localised bursts of pixolisatiou κλίκ.," Since the pixelisation noise is strongly correlated with the sky signal, point sources or Galaxy crossings are potential candidates for large and localised bursts of pixelisation noise."1107 The correct working resolution ων is set by requiring that the pixclisation noise retains low compared to the actual instrmucutal noise. or equivalently Most of the CAIB experiments are noise dominated along the time line. constraining the effective lap resolution to be of the order of the iustrumueutal beam or even larger.," The correct working resolution $k_{max}$ is set by requiring that the pixelisation noise remains low compared to the actual instrumental noise, or equivalently Most of the CMB experiments are noise dominated along the time line, constraining the effective map resolution to be of the order of the instrumental beam or even larger."1108 Note however that the pixclisation noise is strouelv non Gaussian (point sources or Galaxy cerossiugxs) and can bealways considered as a potential source of residual stripes m the final maps., Note however that the pixelisation noise is strongly non Gaussian (point sources or Galaxy crossings) and can bealways considered as a potential source of residual stripes in the final maps.1109 Tustead of solving for .c sve perform thechange of variable dd, Instead of solving for $\hat{x}$ we perform thechange of variable = - d1110the Lasota-Wazewska model.,the Lasota-Wazewska model.1111 By analogy. with equation11 we guessthat js is a global attractor when The parameters Mj.Mo71 when Using equation 5 we find that the second. of these conditions is equivalent to à constraint on the timescale to reach equilibrium Thus when two conditions are satislied we predict periodic solutions: We consider how the amplitude of oscillations depends on the parameters.," By analogy with equation\ref{eqn:m2alpha1} we guessthat $y_*$ is a global attractor when The parameters $M_1,M_2>1$ when Using equation \ref{eqn:teq} we find that the second of these conditions is equivalent to a constraint on the timescale to reach equilibrium Thus when two conditions are satisfied we predict periodic solutions: We consider how the amplitude of oscillations depends on the parameters."1112 We describe the amplitude of oscillations as the ratio of the maximum .r clivided bv the minimum in an oscillation period. after the svstem has converged to a evele.," We describe the amplitude of oscillations as the ratio of the maximum $x$ divided by the minimum in an oscillation period, after the system has converged to a cycle."1113 Oscillation amplitudes are shown in Figure 2. as a function of r and strength. 5. for index a=1 and a=1.5.," Oscillation amplitudes are shown in Figure \ref{fig:bar} as a function of $\bar \tau$ and strength $S$, for index $\alpha=1$ and $\alpha=1.5$."1114" The ""urther away from the line dividing asvmptoticallv decaving solutions from those with periodic solutions. the larger the oscillations about the equilibrium value."," The further away from the line dividing asymptotically decaying solutions from those with periodic solutions, the larger the oscillations about the equilibrium value."1115 The amplitude of he oscillations does not depend on the initial conditions but rather on the parameters defining the dilferential equation., The amplitude of the oscillations does not depend on the initial conditions but rather on the parameters defining the differential equation.1116 Since .r cannot cross zero when large oscillations are present. he periodic solutions are less symmetric or less like sinusoicds rut exhibit spikes followed by longer periods of Low periods of aceretion when the amplitudes are high (see figure. 1)).," Since $x$ cannot cross zero when large oscillations are present, the periodic solutions are less symmetric or less like sinusoids but exhibit spikes followed by longer periods of low periods of accretion when the amplitudes are high (see figure \ref{fig:oned_all}) )."1117 This follows as the accretion rate depends on the exponential ofr so when wr is high. it can take a long time for the svsten to recover [rom a previous episode of star formation.," This follows as the accretion rate depends on the exponential of $x$ so when $x$ is high, it can take a long time for the system to recover from a previous episode of star formation."1118 Our DDE model for delaved feedback is appropriate if the mean gas density averaged over long periods of time is nearly constant., Our DDE model for delayed feedback is appropriate if the mean gas density averaged over long periods of time is nearly constant.1119 This follows because the form. we have for the accretion or cloud formation rate does not change. though it does depend on the past disk density.," This follows because the form we have for the accretion or cloud formation rate does not change, though it does depend on the past disk density."1120 The DDIE model is best applied to systems that reevele eas and only slowly remove eas [rom the svstem., The DDE model is best applied to systems that recycle gas and only slowly remove gas from the system.1121 Star formation laws illustrate that star formation is inellicient., Star formation laws illustrate that star formation is inefficient.1122 For example. Ixenniceutt(1998) found that star formation rates in nearby galaxies could be described with X—«MO. where Q is the angular rotation rate and the ellicienev is low. €0.017 (Ixennicutt.1998).," For example, \citet{kennicutt98} found that star formation rates in nearby galaxies could be described with $\dot \Sigma \sim \epsilon \Sigma \Omega$, where $\Omega$ is the angular rotation rate and the efficiency is low, $\epsilon \sim 0.017$ \citep{kennicutt98}."1123. This suggests that we should. not adopt as our defining variable the total density in molecular and atomic eas but rather that in molecular clouds or sell-eravitating clouds as adopted in explanations for the Schmidt-Ixennicutt star formation law and observational studies of molecular gas in ealaxiesWS)., This suggests that we should not adopt as our defining variable the total density in molecular and atomic gas but rather that in molecular clouds or self-gravitating clouds as adopted in explanations for the Schmidt-Kennicutt star formation law and observational studies of molecular gas in galaxies.1124 In this case the DDE tracks cloud. formation ancl ‘loud clisruption following star formation., In this case the DDE tracks cloud formation and cloud disruption following star formation.1125 Molecular clouds are estimated to last feo~ ves and are disrupted. following star formation (Blitzct 2007)., Molecular clouds are estimated to last $t_C \sim 2-3 \times 10^7$ yrs and are disrupted following star formation \citep{blitz07}.1126. Theoretical work suggests that clouds disperse after a few times their free. fall or dynamical timescale (Ixrumholz&Melxee2005). so [ifetimes of star forming clouds. could be shorter in denser environments (Wacla& 2007).. such as cireumnuclear disks.," Theoretical work suggests that clouds disperse after a few times their free fall or dynamical timescale \citep{krumholz05} so lifetimes of star forming clouds could be shorter in denser environments \citep{wada07}, , such as circumnuclear disks."1127 “Phe depletion term in equation 7 has B=|eL and index a= l. so the consumption timescale in our mocdoel is the mean cloud lifetime. beano fen," The depletion term in equation \ref{eqn:delay} has $B = t_C^{-1}$ and index $\alpha=1$ , so the consumption timescale in our model is the mean cloud lifetime, $t_{con} \sim t_C$ ."1128in principle that the ejected dust cloud occupies aud cools a gas miss larger than that ejected from the star. ng.,"in principle that the ejected dust cloud occupies and cools a gas mass larger than that ejected from the star, $m_{ej}$."1129" IE the cooled mass exceeds i,j; by a factor w. then the correspondius cooling evolutiou is found simply bv replacing 6 in Equation I with df."," If the cooled mass exceeds $m_{ej}$ by a factor $\omega$, then the corresponding cooling evolution is found simply by replacing $\delta$ in Equation 4 with $\delta/\omega$."1130 Iu Figure lewe show cooling curves for w=2 at the same two galactic radii for erains of iuitial radius ej=0.1 micron., In Figure 1cwe show cooling curves for $\omega = 2$ at the same two galactic radii for grains of initial radius $a_0 = 0.1$ micron.1131 Both cooling times exceed the dvianical time at the galactic radii cousidered. so the cooling gas may have a more complex dvuamical evolution that may inhibit the cooling.," Both cooling times exceed the dynamical time at the galactic radii considered, so the cooling gas may have a more complex dynamical evolution that may inhibit the cooling."1132" Stellar mass loss has been regarded as an miportaut internal source of hot eas within group or cluster-ceutered E ealaxies,", Stellar mass loss has been regarded as an important internal source of hot gas within group or cluster-centered E galaxies.1133" A ~13 Chr old stellar population of total mass AM typically expels AL~L5(AL,flo AL. +.", A $\sim 13$ Gyr old stellar population of total mass $M_{*t}$ typically expels ${\dot M}_* \sim 1.5 (M_{*t}/10^{12}~M_{\odot})$ $M_{\odot}$ $^{-1}$.1134 Tn chuster-ceutered galaxies. such as MBST in Vireo and NGC Ιστ lin the Coma cluster. the eas temperature rapidly decreases in the ceutral ~15 kpc from the virial temperature of the cluster (3 - 8 keV) to the stellar virial temperature ~1 keV at sx3 kpc (Moleudi 2002: Vikhlin et al.," In cluster-centered galaxies, such as M87 in Virgo and NGC 4874 in the Coma cluster, the gas temperature rapidly decreases in the central $\sim 15$ kpc from the virial temperature of the cluster (3 - 8 keV) to the stellar virial temperature $\sim 1$ keV at $r \lta 3$ kpc (Molendi 2002; Vikhliin et al."1135 2001)., 2001).1136 Detailed easdvnamical 1ocdols of traditional cooling inflows in these chuster-centered ealaxies indicate that this steep temperature eracdieut can oulv be understood if eas is being cooled by thermalization of stellar ejecta (Drigheuti Mathews 2002a)., Detailed gasdynamical models of traditional cooling inflows in these cluster-centered galaxies indicate that this steep temperature gradient can only be understood if gas is being cooled by thermalization of stellar ejecta (Brighenti Mathews 2002a).1137 The Increase in the hot eas oxveen abundance toward the center of MIST (Gastaldello Moleudi 2002) is expected if mass lost from the SNU-euriched stars has thermally muxed iuto the hot ISM. and if the stars are more O- than the Virgo cluster gas., The increase in the hot gas oxygen abundance toward the center of M87 (Gastaldello Molendi 2002) is expected if mass lost from the SNII-enriched stars has thermally mixed into the hot ISM and if the stars are more O-rich than the Virgo cluster gas.1138 Nevertheless. we propose here that the dust component cau cool the stellar ejecta soon after it thermally merges with the ambicut hot gas. particularly at rX1l kpe.," Nevertheless, we propose here that the dust component can cool the stellar ejecta soon after it thermally merges with the ambient hot gas, particularly at $r \lta 1$ kpc."1139 We now review how dust-cuhanced cooling applies to the issues discussed iu the Iutroduction. (, We now review how dust-enhanced cooling applies to the issues discussed in the Introduction. (11401)galacies? vau Dokkuni Fraux (1995) and others describe small ceutral dust disks. lanes or clouds typically a few LOO pe iu size.,"1) van Dokkum Franx (1995) and others describe small central dust disks, lanes or clouds typically a few 100 pc in size."1141 The small masses of dust <10!107 AL. in these cores cun easilv be produced in ~LOS10? vrs as dust-rich gas cools near the ealactic ceuter with incomplete sputtering., The small masses of dust $\lta 10^4 - 10^5$ $M_{\odot}$ in these cores can easily be produced in $\sim 10^8 - 10^9$ yrs as dust-rich gas cools near the galactic center with incomplete sputtering.1142 Tt is difficult to accurately estimate the rate that dust accumulates near the center without kuowledee of the dust size distribution. the exact thermal history T(f) of he stellar ejecta. or the star formation rate iu the cold. dusty clouds.," It is difficult to accurately estimate the rate that dust accumulates near the center without knowledge of the dust size distribution, the exact thermal history $T(t)$ of the stellar ejecta, or the star formation rate in the cold, dusty clouds."1143 Since Type Ia supernova reninanuts occupy a very παπα fraction of the iuterstellar volue at any iue (Mathews 1990). heating by Type Ia supernovae is ulikelv to interfere with the cooling we describe here.," Since Type Ia supernova remnants occupy a very small fraction of the interstellar volume at any time (Mathews 1990), heating by Type Ia supernovae is unlikely to interfere with the cooling we describe here."1144 Ueating by active galactic nuclei has often beeu suggested o explain why the hot eas in E galaxies fails to cool to ow temperatures (e.g. Rosuner Tucker 1989: Binney Tabor 1995: Brigheuti Mathews 20025).," Heating by active galactic nuclei has often been suggested to explain why the hot gas in E galaxies fails to cool to low temperatures (e.g., Rosner Tucker 1989; Binney Tabor 1995; Brighenti Mathews 2002b)."1145 If such jeating occurs. it must be gentle enough not to destroy the observed central dust clouds or this dust must be rapidly reecuerated. (," If such heating occurs, it must be gentle enough not to destroy the observed central dust clouds or this dust must be rapidly regenerated. ("11462)yalacics7 The velocities of this diffuse ciission are unrelated to stellar velocities (Caou et al.,2) The velocities of this diffuse emission are unrelated to stellar velocities (Caon et al.1147 2000)., 2000).1148 Tn some E galaxies the optical Hue cussion spatially correlates with X-rav features (e.g. Trinchicri (οπου. 2002) or traces the perunucters but uot the centers of N-rav cavities (McNamara. O'Connell Sarazin 1996: Dlautou ct al.," In some E galaxies the optical line emission spatially correlates with X-ray features (e.g. Trinchieri Goudfrooij 2002) or traces the perimeters but not the centers of X-ray cavities (McNamara, O'Connell Sarazin 1996; Blanton et al."1149 2001)., 2001).1150 While these observations sugeest that some gas cools to 104 IS from the Lot phase. there is uo evidence for this inVALAL N-raw spectra.," While these observations suggest that some gas cools to $\sim 10^4$ K from the hot phase, there is no evidence for this in X-ray spectra."1151" However. even if dusty eas ejected frou, metalaxich stars is heated to ~ας. it can quickly cool back to ~LO! EK where the cooling may be temporarily arrested by absorption of galactic UV starlieht (Binette et al."," However, even if dusty gas ejected from metal-rich stars is heated to $\sim T_{vir}$, it can quickly cool back to $\sim 10^4$ K where the cooling may be temporarily arrested by absorption of galactic UV starlight (Binette et al."1152 1991)., 1994).1153 Exactly what happens next is unclear. but the dust can help cool the eas to much lower temperatures if the clouds become optically thick to UV radiation.," Exactly what happens next is unclear, but the dust can help cool the gas to much lower temperatures if the clouds become optically thick to UV radiation."1154 It has often becu sueeested that dusty gas at T~LO! K derives from iuergers with easrich dwarf ealaxics (e.g. Caon ct al., It has often been suggested that dusty gas at $T \sim 10^4$ K derives from mergers with gas-rich dwarf galaxies (e.g. Caon et al.1155 2000: Tirinchieri Coudfrooij 2002): this can be verified if the 10! Ik eas is counterrotating., 2000; Trinchieri Goudfrooij 2002); this can be verified if the $10^4$ K gas is counter-rotating.1156 Nevertheless. cold. dusty eas can arise naturally from stars in E ealaxy cores. (," Nevertheless, cold, dusty gas can arise naturally from stars in E galaxy cores. ("11573)low? Nuct al. (,3) Xu et al. (11582001) found from ROS NMM observations of elliptical galaxy NGC 1636 that X-ray lines expected from gas cooling near T~2«109 I ave unusually weak. indicating a total cooling rate of ΕΤ... iu rz2.5 kpe (for d=17 Ape).,"2001) found from RGS XMM observations of elliptical galaxy NGC 4636 that X-ray lines expected from gas cooling near $T \sim 2 \times 10^6$ K are unusually weak, indicating a total cooling rate of ${\dot M} \lta 0.30$ $M_{\odot}$ $^{-1}$ in $r \lta 2.5$ kpc (for $d = 17$ Mpc)."1159 FUSE observations of OVI lines in NGC 1636 (emitted at T~3«10? I) indicate MxOATE002 A. 3 within L2 kpc (Breeian ct al., FUSE observations of OVI lines in NGC 4636 (emitted at $T \sim 3 \times 10^5$ K) indicate ${\dot M} \approx 0.17 \pm 0.02$ $M_{\odot}$ $^{-1}$ within 1.2 kpc (Bregman et al.1160 2001)., 2001).1161 Both cooling rates are less than the ~1.2 Mx | predicted in traditional cooling flow models (e.g. Bertin Toniazzo 1995)., Both cooling rates are less than the $\sim 1 - 2$ $M_{\odot}$ $^{-1}$ predicted in traditional cooling flow models (e.g. Bertin Toniazzo 1995).1162 Rapid dust-assisted cooling may be relevant to this discrepancy in two wavs: (1) by reducing the total rate that eas euters the hot phase. and (2) by reducing the ταν chussion from cooling thermal eas at subvirial temperatures.," Rapid dust-assisted cooling may be relevant to this discrepancy in two ways: (1) by reducing the total rate that gas enters the hot phase, and (2) by reducing the X-ray emission from cooling thermal gas at subvirial temperatures."1163 Tn models of traditional cooling flows. gas ejected from stars is usually asstmed to cuter the hot interstellar gas.," In models of traditional cooling flows, gas ejected from stars is usually assumed to enter the hot interstellar gas."1164 The stellar mass loss rate iu a giant E galaxv. ~LAL. ft. is au important source of gas since it is comparable to the expected cooling rate of the lot eas.," The stellar mass loss rate in a giant E galaxy, $\sim 1 M_{\odot}$ $^{-1}$, is an important source of gas since it is comparable to the expected cooling rate of the hot gas."1165" In gas dynamical models the cooling rate AT near the ceuter of the flow varies inversely with the specific rate of stellar mass loss. a,=AL/M.."," In gas dynamical models the cooling rate ${\dot M}$ near the center of the flow varies inversely with the specific rate of stellar mass loss, $\alpha_* = {\dot M}_*/M_*$."1166 This is true even when there is an extended reservoir of circtuuealactic hot eas due to cosmic accretion onto the surrounding ealaxyv eroup., This is true even when there is an extended reservoir of circumgalactic hot gas due to cosmic accretion onto the surrounding galaxy group.1167 Therefore. the apparent cooling rate AL observed with NAINI should be reduced approximately i proportion o the fraction of stellar eas that fails to euter the hot gas jecause of clust-assisted cooling.," Therefore, the apparent cooling rate ${\dot M}$ observed with XMM should be reduced approximately in proportion to the fraction of stellar gas that fails to enter the hot gas because of dust-assisted cooling."1168 However. if more than 90 percent of the stellar ejecta fails to cuter the hot phase. our σαςνασα. models indicate that the deusity of hot interstellar eas is lowered sufficiently to initiate a strous galactic wind driven by Type Ia cuerey.," However, if more than $\sim 90$ percent of the stellar ejecta fails to enter the hot phase, our gasdynamical models indicate that the density of hot interstellar gas is lowered sufficiently to initiate a strong galactic wind driven by Type Ia energy."1169 The rausition to wind flows is rather sudden., The transition to wind flows is rather sudden.1170" Since the verv ow L, characteristic of strong winds are not observed. lis sets a limit on the eficiency of cust-assisted coolingdescribed here."," Since the very low $L_x$ characteristic of strong winds are not observed, this sets a limit on the efficiency of dust-assisted coolingdescribed here."1171 If dustv eas frou stars is indeed heated to ~ μι. NALD observations require that it not cuit thermal X- at intermediate temperatures citler as it is heated or as it cools afterward.," If dusty gas from stars is indeed heated to $\sim T_{vir}$ , XMM observations require that it not emit thermal X-rays at intermediate temperatures either as it is heated or as it cools afterward."1172 We argue above that the heating phase is likely to be rapid. Xty.~LO yes.," We argue above that the heating phase is likely to be rapid, $\lta t_{H\alpha} \sim 10^5$ yrs."1173 When heated to  {ων the stellar eas may undergo rapid," When heated to $\sim T_{vir}$ , the stellar gas may undergo rapid"1174In this section we describe the lithium depletion caleulations and the input physics that define our reference LDD-Iumninositv-age relation.,In this section we describe the lithium depletion calculations and the input physics that define our reference LDB-luminosity-age relation.1175 This reference relation serves as the standard to quantity the uncertainty in LDD ages., This reference relation serves as the standard to quantify the uncertainty in LDB ages.1176 We use (he Yale Rotation Evolution Coce (YREC) (sills.Pinsonneault.&Terndrup2000) for all stellar model calculations., We use the Yale Rotation Evolution Code (YREC) \citep{sil00} for all stellar model calculations.1177 For the relerence caleulation. we select standard. non-rotating. solar-calibrated stellar models with masses (hat range from 0.065 to 0.30 NL...," For the reference calculation, we select standard, non-rotating, solar-calibrated stellar models with masses that range from 0.065 to 0.30 $_{\odot}$."1178 The upper mass limit ensures full convection during lithium depletion and minimizes the impact of initial conditions., The upper mass limit ensures full convection during lithium depletion and minimizes the impact of initial conditions.1179 Through accretion aud mass loss. a star interacts with iis surroundings during (the earliest phases of its life.," Through accretion and mass loss, a star interacts with its surroundings during the earliest phases of its life."1180 ILowever. anv structural changes to the star that may occur due to (this complex interaction wilh its surroundings is erased after several IXelvin-Ilelmholtz time scales.," However, any structural changes to the star that may occur due to this complex interaction with its surroundings is erased after several Kelvin-Helmholtz time scales."1181 The IXelvin-Ilelmholtz time scale for our M—0.3 M. starting model is one-tenth of the time lor litbium depletion. makine these complications negligible.," The Kelvin-Helmholtz time scale for our M=0.3 $_{\odot}$ starting model is one-tenth of the time for lithium depletion, making these complications negligible."1182 Stars wilh Mx0.06 M. never reach temperatures high enough to destroy lithium completely (D'Antona&Mazzitelli1994).. and our reference calculations confirm this fact.," Stars with $\leq$ 0.06 $_{\odot}$ never reach temperatures high enough to destroy lithium completely \citep{dan94}, and our reference calculations confirm this fact."1183 The above mass limits constrain the validity of the LDD age technique to stellar populations with ages between 20 and 200 Myr., The above mass limits constrain the validity of the LDB age technique to stellar populations with ages between 20 and 200 Myr.1184" For clusters witli ages less than 20 Myr. the uncertain initial conditions. deuterium burning. ancl adopted zero-age (which all occur on timescales of a few 10"" vears) become an increasing fraction of the LDD age."," For clusters with ages less than 20 Myr, the uncertain initial conditions, deuterium burning, and adopted zero-age (which all occur on timescales of a few $^{6}$ years) become an increasing fraction of the LDB age."1185 For clusters wilh ages older (han 200 Myr. lithium is depleted over a larger width of luminosity. and lacks a clearly defined LDL.," For clusters with ages older than 200 Myr, lithium is depleted over a larger width of luminosity, and lacks a clearly defined LDB."1186" Adopting a solar metallicity. 45500198. and (he heavy element mix of (1993).. we determine the ratio of mixing length parameter to pressure scale height aud heliun abundance by calibrating to the solar data. resulting in a=/,/I],1.75 and Y=0.27. respectively,"," Adopting a solar metallicity, Z=0.0188, and the heavy element mix of \citet{gre93}, we determine the ratio of mixing length parameter to pressure scale height and helium abundance by calibrating to the solar data, resulting in $\alpha\equiv l_{m}/H_{p}=1.75$ and Y=0.27, respectively."1187 We use the OPAL equation of state from (1996) where it is available and (he equation of state of Saumon. otherwise.," We use the OPAL equation of state from \citet{rog96}1188 where it is available and the equation of state of \citet{sau95}1189 otherwise."1190 We investigate the effect of the latest OPAL 2001 equation of state on the LDB ages in Section ??.., We investigate the effect of the latest OPAL 2001 equation of state \citep{rog02} on the LDB ages in Section \ref{eos}.1191 The low temperature atmospheres of Tauschildt.Allard.&Baron(1999) provide the pressure al T=Tell. which we apply as the outer boundary condition.," The low temperature atmospheres of \citet{hau99} provide the pressure at T=Teff, which we apply as the outer boundary condition."1192 Physical conditions in low mass stars [all outside opacity tables emploved to mocel solaa-(wpe stus., Physical conditions in low mass stars fall outside opacity tables employed to model solar-type stars.1193 Figure 1. shows several stellar density profiles as a Function of temperature for the low mass stellar regime applicable to this studs., Figure \ref{runrho} shows several stellar density profiles as a function of temperature for the low mass stellar regime applicable to this study.1194" The two solid lines trace the run of density for the 0.3 M. reference models at the initial and lithium depletion epochs: lower and higher densitv. respectively,"," The two solid lines trace the run of density for the 0.3 $_{\odot}$ reference models at the initial and lithium depletion epochs; lower and higher density, respectively."1195 The (wo dashed lines show the density evolution for the 0.065 M. reference model., The two dashed lines show the density evolution for the 0.065 $_{\odot}$ reference model.1196 The dotted lines represent the various opacity table boundaries., The dotted lines represent the various opacity table boundaries.1197 The diagonal dotted line in Figure 1. shows the upper density boundary αἱ R= p/T?=1 , The diagonal dotted line in Figure \ref{runrho} shows the upper density boundary at $\equiv\rho/$ $^{3}_{6}=1$ 1198operated by the Jet Propulsion Laboratory. California Lustitute of Technology under a contract with NASA.,"operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA."1199Observationallv. the fold and cusp relations are violated in several lens systems (e.g..Hogg&Blancdford2003.2005)..,"Observationally, the fold and cusp relations are violated in several lens systems \citep[e.g.,][]{Hogg_1422, Falco_0414, Keeton-shear-ellip,1200Keeton-cusp, Keeton-fold}."

Showing the first 1,200 of 10409 lines. Download the file for the rest.