ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Then. gg 0.003.," Then, $y_{\rm K} \sim$ 0.003."3" Rodeers CGlassgod (1991) ""standard! model predicts gg20.01 at the radial distance equivaleut to 50 aresec at d= 110 pe.", Rodgers Glassgold (1991) `standard' model predicts $y_{\rm K} \simeq 0.01$ at the radial distance equivalent to 50 arcsec at $d$ = 140 pc.4 This is fair agreement with observation eiven the various (uncertai1) ingredients that cuter into both estimates., This is fair agreement with observation given the various (uncertain) ingredients that enter into both estimates.5 Tho mass iu he shell amoruts to about 2 AL... at a distance of 1ü ος and assunidueg gy=0.01.," The mass in the shell amounts to about $^{-2}$ $_{\odot}$, at a distance of 140 pc and assuming $y_{\rm K} = 0.01$."6 As noted above the S2 shell is not a COlisSCquencec of à varviug Nhotospherie illuniuation: the light travel ue across the shell is ouly about a cda. aud the shell is onlv about 50 πο davs from the star.," As noted above the S2 shell is not a consequence of a varying photospheric illumination; the light travel time across the shell is only about a day, and the shell is only about 50 light days from the star."7 In addition. he shell seen iu absorption iu the 19τος. (Goldberg et al," In addition, the shell seen in absorption in the 1970s (Goldberg et al."8 1975: Bernat et al., 1975; Bernat et al.9 1979) is plausidv identified with the cnussion shell seeu in 1991., 1979) is plausibly identified with the emission shell seen in 1994.10 The simpest explanation or the shell may be that it is niass ejecte at a substautiaIv higher than average rate at a rearlicr tine., The simplest explanation for the shell may be that it is mass ejected at a substantially higher than average rate at an earlier time.11 Itf the expansion velocity has bee1 constant. eas travelling at 15 lau Lonand now at 50 aresec from the star was ejected ]900 voars ago (d = LLO pe is assuned).," If the expansion velocity has been constant, gas travelling at 18 km $^{-1}$ and now at 50 arcsec from the star was ejected 1900 years ago $d$ = 140 pc is assumed)."12 A shell thickness of l second of arc implies ejection lasted about 10 vr dat this is a guess because the velocity of ejection presuiiably varied too., A shell thickness of 1 second of arc implies ejection lasted about 40 yr but this is a guess because the velocity of ejection presumably varied too.13 The she Las it ap]x‘ars in Fie., The shell as it appears in Fig.14 1 is nof 1uiformlv bright., \ref{fig4} is not uniformly bright.15 It is alikely that the observed contrast around the shell is due to the presence of bright spot on theisk a the time of the observations., It is unlikely that the observed contrast around the shell is due to the presence of bright spot on the disk at the time of the observations.16 A possible explanation is that mass ejection occurred prefereitial above a spot L900 voars ago., A possible explanation is that mass ejection occurred preferentially above a spot 1900 years ago.17 Stellar rotation (the rotation iod of Beelgetse ds at least a few vears). ¢ould have led ο lnaterial cine ejected into the shell at a variable rate over the life1nie «X the spot.," Stellar rotation (the rotation period of Betelgeuse is at least a few years), could have led to material being ejected into the shell at a variable rate over the lifetime of the spot."18 There appear to he a least wo other shells o: auocdlerate completeness which suggestsOO hat sienificaut 1creases du luass loss may occur οταν several huucred years., There appear to be at least two other shells of moderate completeness which suggests that significant increases in mass loss may occur every several hundred years.19 Multiple shells were also deected around p Cep by Mauron. (1997). with a characteristic nue scale between two successive inoreases i lass loss of about one thousaud vears.," Multiple shells were also detected around $\mu$ Cep by Mauron (1997), with a characteristic time scale between two successive increases in mass loss of about one thousand years."20 Detached shells are also observed around ACB stars. where they are attributed to a Uelimm shell flash that induces both a niass loss Increase and a two-wilnd iteraction due to the 1icreased outflow velocity (Steffen aud Schónuberuer 2000).," Detached shells are also observed around AGB stars, where they are attributed to a Helium shell flash that induces both a mass loss increase and a two-wind interaction due to the increased outflow velocity (Steffen and Schönnberner 2000)."21 Clearly. an alternative nechauisumi uust be operating i swyorelaut stars like Dotelgeusc.," Clearly, an alternative mechanism must be operating in supergiant stars like Betelgeuse."22 Future observations of the emission frou he shell should be made to semrci for changes im the S2 shell., Future observations of the emission from the shell should be made to search for changes in the S2 shell.23 Measuring the S24 expawion will be a challege: the proper motion expected is a mere 0.03 aresec per year., Measuring the S2's expansion will be a challenge: the proper motion expected is a mere 0.03 arcsec per year.24 As triking feature of our velocitv-positiou maps. especially those acquired in the best secing is the appearance of chumps or kuos of enüssion: Fig. 3.6," A striking feature of our velocity-position maps, especially those acquired in the best seeing is the appearance of clumps or knots of emission; Fig. \ref{fig3},"25 and 7 show chumps extendiig du size down to the velocity aud spatial resolution of the αμα)., \ref{fig5a} and \ref{fig5b} show clumps extending in size down to the velocity and spatial resolution of the map.26 There are locations where chuups appear connected sugeestiis they are condeusations in a sheet or shel., There are locations where clumps appear connected suggesting they are condensations in a sheet or shell.27 Iu general. the collection οchumps in luaiv velocity-position nma]os accounts for more than half of the emitted flux.," In general, the collection of clumps in many velocity-position maps accounts for more than half of the emitted flux."28 The iuxession of elliptical structures is larecly gained from gas at large augular disances from the sar., The impression of elliptical structures is largely gained from gas at large angular distances from the star.29 Many of our exposures. expecially hose taken with πα. inipact parameers. were too short to reveal fain distant structures.," Many of our exposures, especially those taken with small impact parameters, were too short to reveal faint distant structures."30 TlCs8C are the first observations of πιsuch clumps iu DBetelgeuse’s wind., These are the first observations of such clumps in Betelgeuse's wind.31" Mauro (1997) from loue-slit Spec‘tra showing cussion from µ Copwel reports houoscnueities with an appareut size of 1” to D whe1 the augular resolution was about 0.6"",", Mauron (1997) from long-slit spectra showing emission from $\mu$ Cephei reports `inhomogeneities' with an apparent size of $^{\prime\prime}$ to $^{\prime\prime}$ when the angular resolution was about $^{\prime\prime}$.32 In velocity space. g Cop's clumps were unresolved at the moderate resolution of lus ! of these observations.," In velocity space, $\mu$ Cep's clumps were unresolved at the moderate resolution of 40 km $^{-1}$ of these observations."33 Since ji Cep is about 5 times more distant than Detelgeuse. its suallest chumps woul appear to ο” to 10 larger than those we have detected.," Since $\mu$ Cep is about 5 times more distant than Betelgeuse, its smallest clumps would appear to be 5 to 10 larger than those we have detected."34 There Is a lint tha the prevalence of clumps ls ligher close to the star than at the largest distances probed by otrv spectra., There is a hint that the prevalence of clumps is higher close to the star than at the largest distances probed by our spectra.35" This eucourages the speculation that the chumps"" orig)lo quay be traceable through the inhomogencous iuncr shell (Liu et al.", This encourages the speculation that the clumps' origin may be traceable through the inhomogeneous inner shell (Lim et al.36 1998) and chromosphere to the stellaz surface., 1998) and chromosphere to the stellar surface.37 The ereater visibility of shells at large disances nav be due to the dissolution aud merger of clumps at à couumon distance., The greater visibility of shells at large distances may be due to the dissolution and merger of clumps at a common distance.38 Although chumps are seen by fluorescent oeniüssion. heir sape and size are attributable to au cuhanced concentration of potassium atoms in the wiud aud not to intensifv valatious over he surface of the illuminating rotosphere: a bright piotospherie spot will euhauce fuorescence over approxinately 32z of solid angle not a uere few arcsec.," Although clumps are seen by fluorescent emission, their shape and size are attributable to an enhanced concentration of potassium atoms in the wind and not to intensity variations over the surface of the illuminating photosphere; a bright photospheric spot will enhance fluorescence over approximately $\pi$ of solid angle not a mere few arcsec."39 The chmps are probably not regions of reduced. xmization of potassiun atoms because the characteristic timescale for photoionization is shorter that he expansion timescale (t16 time required to reach a given ieular distance at a constaut expansion velocity): it is a, The clumps are probably not regions of reduced ionization of potassium atoms because the characteristic timescale for photoionization is shorter that the expansion timescale (the time required to reach a given angular distance at a constant expansion velocity): it is a40"We have applied Equation (10)) to different. recently published staucdard solar models listed inTable Ὁ.. and derive Yi""=0.278+0.006 (Equation 11))","We have applied Equation \ref{eq:final}) ) to different, recently published standard solar models listed inTable \ref{tab:results}, and derive $\yims=0.278 \pm 0.006$ (Equation \ref{eq:res1}) )."41 The uncertainty is dominated by uncertainties in the diffusion rate of elements and those in the helioseismic determination of the solar surface helium abundance., The uncertainty is dominated by uncertainties in the diffusion rate of elements and those in the helioseismic determination of the solar surface helium abundance.42 The dispersion in the results for the different solar moclels is one order of magnitude smaller., The dispersion in the results for the different solar models is one order of magnitude smaller.43 The results are also robust in terms of the standard solar models used to derive Equation 10.., The results are also robust in terms of the standard solar models used to derive Equation \ref{eq:final}.44 To test further the robustness of our results. we have compiled results [rom literature for standard and non-standard solar models (though only those non-standard solar models (hat improve agreement with helioseismic inferences of solar structure).," To test further the robustness of our results, we have compiled results from literature for standard and non-standard solar models (though only those non-standard solar models that improve agreement with helioseismic inferences of solar structure)."45" In all cases. even for (he non-standard ones. applying Equation 10. (o results [rom solar models vield Y! results consistent to within lo of our central value of Yi""=0.278+0.006."," In all cases, even for the non-standard ones, applying Equation \ref{eq:final} to results from solar models yield $\yims$ results consistent to within $1\sigma$ of our central value of $\yims=0.278 \pm 0.006$."46 Finally. we have also computed solar models including turbulent diffusion as a phenomenological approach to eliminate the bump in (the sound-speed difference between models and the Sun that is seen below the convective envelope.," Finally, we have also computed solar models including turbulent diffusion as a phenomenological approach to eliminate the bump in the sound-speed difference between models and the Sun that is seen below the convective envelope."47 For these models. a small value of the [ree parameter Dy. Dy=300cnPs!. leads to Y?!=0.2725. consistent within lo with our predicGon given in Equation 11..," For these models, a small value of the free parameter $D_0$, $D_0=300\, \mathrm{cm^2s^{-1}}$, leads to $\yims=0.2725$, consistent within $1\sigma$ with our prediction given in Equation \ref{eq:res1}."48 Larger values of Dy predict svstematically lower values for YM put Ίος to slightly degraded agreement with helioseismology. as evinced by frequency separation ratios (probably a result of the lower central helium abundance predicted by (hese models).," Larger values of $D_0$ predict systematically lower values for $\yims$ but lead to slightly degraded agreement with helioseismology, as evinced by frequency separation ratios (probably a result of the lower central helium abundance predicted by these models)."49 Thus. we find no evidence. at least Irom helioseismology data. that support the need of larger. Do values.," Thus, we find no evidence, at least from helioseismology data, that support the need of larger $D_0$ values."50 It has to be kept in mind that (his formulation of turbulent. diffusion represents only a phenomenological approach to eliminating the bump in the sound-speed difference profile., It has to be kept in mind that this formulation of turbulent diffusion represents only a phenomenological approach to eliminating the bump in the sound-speed difference profile.51" More realistic models that. account lor rotationallv-induced mixing. like that one derived by Pinsonneaultοἱal.(1999). lead again to YPi=0,2725."," More realistic models that account for rotationally-induced mixing, like that one derived by \citet{pinsonneault:1999}, lead again to $\yims=0.2725$."52" We conclude (hat (he initial solar helium abundance. as inferred [rom (he present-day solar surface helium. abundance determined bv helioseismologyv. is 37""=0.278d0.006."," We conclude that the initial solar helium abundance, as inferred from the present-day solar surface helium abundance determined by helioseismology, is $\yims=0.27853\pm 0.006$."54 Although solar models are used to reach this conclusion. we find this result is almost independent of which solar models are used in ils derivation.," Although solar models are used to reach this conclusion, we find this result is almost independent of which solar models are used in its derivation."55" If Y?"" is determined [rom non-standard solar models that account [or the effects of extra mixing. we obtain 0.006."," If $\yims$ is determined from non-standard solar models that account for the effects of extra mixing, we obtain $\yims = 0.273\pm 0.006$ ."56 In all cases. ie.. for both standard ancl non-standard models. we infer )ii values that are higher than the initial helium abundance obtained in solar models that use the solar abundances by Asphinelοἱal.(2005) or the most recent determination by al. (2009).," In all cases, i.e., for both standard and non-standard models, we infer $\yims$ values that are higher than the initial helium abundance obtained in solar models that use the solar abundances by \citet{ags05} or the most recent determination by \citet{agss09}."57. This result points towards a deficit in solar models using (hese abundances: whether (he problem lies in the abundance determinations or in (he constitutive plivsics of (he models is bevond the scope of this work., This result points towards a deficit in solar models using these abundances; whether the problem lies in the abundance determinations or in the constitutive physics of the models is beyond the scope of this work.58 Depending on the solar metalicitv adopted. we derive a helium-to-metal enrichment of AYV/AZ~1.7— 2.2. in line with standard predietions of Galactic chemical evolution and," Depending on the solar metalicity adopted, we derive a helium-to-metal enrichment of $\Delta Y/\Delta Z \sim 1.7-2.2$ , in line with standard predictions of Galactic chemical evolution and"59]xurtevοἱal.(2001) in the 11613 ealaxy (My=9.62 mag and 2=640.7 day).,"\citet{k3} in the 1613 galaxy $_K = -9.62$ mag and $60P = 640.7$ day)."61" However the amplitude of the 11613 Mira is only ""2.5.3 mag in # band.", However the amplitude of the 1613 Mira is only $2.5 - 3$ mag in $R$ band.62 In the PL plane for May luminosities LMC the star HDS2006] 40671 is located in the same place as the 11613. Mira. (Ixurtev.al. 2001)., In the PL plane for $_K$ luminosities for LMC the star [HBS2006] 40671 is located in the same place as the 1613 Mira \citep{k3}.63. Both stars are located in the zone of the first- pulsating Mira. variables., Both stars are located in the zone of the first-overtone pulsating Mira variables.64 Woodetal.(1983). found that long-period variables are eroupec into two classes: core-helium-burning supergiants which are brightest. and AGB stars which are at least fainter at a given period.," \citet{w1} found that long-period variables are grouped into two classes: core-helium-burning supergiants which are brightest, and AGB stars which are at least fainter at a given period."65 The supergiant LPVs form a distinct. PL relation and. they have lower amplitudes., The supergiant LPVs form a distinct PL relation and they have lower amplitudes.66 The PL relation for six core-helium-burning supergiants in 333 was presented by Ixinmanctal.(1987) in their Fig., The PL relation for six core-helium-burning supergiants in 33 was presented by \citet{k4} in their Fig.67 S., 8.68 The A magnitude for supergiants with the 665 clay period. is expected to be 13.9., The $K$ magnitude for supergiants with the 665 day period is expected to be 13.9.69 Phe 241ASS A magnitude of Η252006] 40671 is 1.5 mag fainter. what suggests that this object is an AGB star.," The 2MASS $K$ magnitude of [HBS2006] 40671 is 1.5 mag fainter, what suggests that this object is an AGB star."70 AGB stars in 1929 and AL331 are discussed in papers by Javacdietal.(2010). ancl Richetal.(1993)., AGB stars in 33 and 31 are discussed in papers by \citet{j0} and \citet{r2}.71 Whitelock(2010) discussed. à. type of. long-period variables which are undergoing a hot bottom burning (11219) in the base of their convective envelopes., \citet{w0} discussed a type of long-period variables which are undergoing a hot bottom burning (HBB) in the base of their convective envelopes.72 They lic above the PL relation of Αι Mira-ty variables., They lie above the PL relation of AGB Mira-type variables.73 In LMC they are large amplitude variable stars peadditionally showing a lithium and s-process enrichment., In LMC they are large amplitude variable stars additionally showing a lithium and s-process enrichment.74 As an example. she refers to 641-cay Mira in LC 1613 studied by Ixurtevetal.(2001). that locates above the PL relation. 1," As an example, she refers to 641-day Mira in IC 1613 studied by \citet{k3} that locates above the PL relation. ["751BS2006] 40671 also locates 0.35 mag above the PL relation for AGB stars with periods over 400 cays derived by Hughes&Wood(1990) along with three LIBB stars studied by Whitelocketal.(2003). in LMC.,HBS2006] 40671 also locates 0.35 mag above the PL relation for AGB stars with periods over 400 days derived by \citet{h2} along with three HBB stars studied by \citet{w3} in LMC.76 We did not find lithium or other s-process elements in our low-resolution spectrum. but the Luminosity excess is evident as that in the IC 1613 Mira. variable.," We did not find lithium or other s-process elements in our low-resolution spectrum, but the luminosity excess is evident as that in the IC 1613 Mira variable."77 We conclude that the star LD82006] 40671in 333is O Mira-tvpe variable with extreme properties., We conclude that the star [HBS2006] 40671 in 33 is O Mira-type variable with extreme properties.78 Is pulsation amplitude is not less than 7 magnitudes in # band. the period of  665 cays is one of the longest known for Mira- variables.," Its pulsation amplitude is not less than 7 magnitudes in $R$ band, the period of $\sim$ 665 days is one of the longest known for Mira-type variables."79 The mean absolute magnitude of the star in A band is My~5., The mean absolute magnitude of the star in $K$ band is $_K \sim -9.5$.80 In maximum light its bolometric magnituce is estimated as Mo;&—7.4., In maximum light its bolometric magnitude is estimated as $_{bol} \approx -7.4$.81 Ht shows a spectrum of type M2e.M36., It shows a spectrum of type M2e–M3e.82 There is a strong negative excess of 210 km/s in the star. velocity relative to the racial velocity. of the star's location projected to the galactic disk., There is a strong negative excess of $-$ 210 km/s in the star velocity relative to the radial velocity of the star's location projected to the galactic disk.83 This is a peculiar motion of the star., This is a peculiar motion of the star.84 According to Feast(2007) the velocity dispersion of Galactic O-Mirasis in the range 30 to SO kms. They belong to the galactic populations ranging from the thin disk to the extended. disk., According to \citet{Feast} the velocity dispersion of Galactic O-Miras is in the range 30 to 80 km/s. They belong to the galactic populations ranging from the thin disk to the extended disk.85 In. spite of the enhanced velocity dispersion of the Galactic Mira-stzus the peculiar velocity of ~ ) km/s in the 1IBS200(j] 40671 is rather big., In spite of the enhanced velocity dispersion of the Galactic Mira-stars the peculiar velocity of $\sim -$ 200 km/s in the [HBS2006] 40671 is rather big.86 The radial velocity of the narrow Lla eemission line is [355cx10 km/s relative to that of the star itself., The radial velocity of the narrow $\alpha$ emission line is $+35 \pm 10$ km/s relative to that of the star itself.87 Such a shift in the IIo. eemission is twpical for Mira stars., Such a shift in the $\alpha$ emission is typical for Mira stars.88 Lt can be explained by stellar pulsations and shocks in an expanding atmosphere., It can be explained by stellar pulsations and shocks in an expanding atmosphere.89 ALL the properties make the new Mira. star important for further studies. 1, All the properties make the new Mira star important for further studies. [901DS20t)6] 40671 is the first spectroscopically confirmed. Mira star in 333.,HBS2006] 40671 is the first spectroscopically confirmed Mira star in 33.91 We are grateful to WK. Nishivama anc E. Ixabashima for providing us with their unpublished photometrical data., We are grateful to K. Nishiyama and F. Kabashima for providing us with their unpublished photometrical data.92 We thank Joanna Alikolajewska for useful cliscussion., We thank Joanna Mikolajewska for useful discussion.93 Authors thank the Russian Foundation lor Basie Research for support bv erants No., Authors thank the Russian Foundation for Basic Research for support by grants No.94 O7-02-00630. 09-02-00163 ancl LO-02-00463. Federal Programme “Seientilic ancl educational cadre of innovating Russia 200920137. No.," 07-02-00630, 09-02-00163 and 10-02-00463, Federal Programme “Scientific and educational cadre of innovating Russia 2009–2013”, No."95 1244 and the grant “Leading Scientific Schools. of Russia” No., 1244 and the grant “Leading Scientific Schools of Russia” No.96 5473.2010.2., 5473.2010.2.97 We gratefully acknowledge the support of the LDAP which was produced at Landessternwarte Leidelberg-Ixoenigstuhl under grant No., We gratefully acknowledge the support of the HDAP which was produced at Landessternwarte Heidelberg-Koenigstuhl under grant No.98 00.071.2005. of the. Wlaus-'Tschira-Foundation., 00.071.2005 of the Klaus-Tschira-Foundation.99 This paper makes use of data obtained from the Isaac Newton Group Archive which is maintained as part of the CASU. Astronomical Data Centre at the Institute of Astronomy. Cambridge.," This paper makes use of data obtained from the Isaac Newton Group Archive which is maintained as part of the CASU Astronomical Data Centre at the Institute of Astronomy, Cambridge."100 I0 is also. based. on data collected. at Subaru Telescope and obtained from the SALOWA. which is operated by the Astronomy Data Center. National Astronomical Observatory of Japan.," It is also based on data collected at Subaru Telescope and obtained from the SMOKA, which is operated by the Astronomy Data Center, National Astronomical Observatory of Japan."101 This research has made use of the SIAIBAD clatabase. operated at CDS. Strasbourg. France. and of NASA's Astrophysics Data System Bibliographic Services.," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and of NASA's Astrophysics Data System Bibliographic Services."102As explained in the Introduction. the inverse elfect. (in our case the proximity clleet) is most likely as result. of an enhancement of the UV ionizing field in the neighbourhood of a QSO which consequently. increases the ionization [raction of the cclouds.,"As explained in the Introduction, the inverse effect (in our case the proximity effect) is most likely as result of an enhancement of the UV ionizing field in the neighbourhood of a QSO which consequently increases the ionization fraction of the clouds."103 Although other models with simiar philosophy may also explain the inverse effect. (for cxample eravitational itwall of the cclouds onto the QSO). we have modefeck the proximity cllect in terms of photoionization of low-clensity highly ionized clouds of gas much similar to the wav that BDO modelled the inverse ellect but including the ionization [rom the foreground QSO.," Although other models with similar philosophy may also explain the inverse effect (for example gravitational infall of the clouds onto the QSO), we have modelled the proximity effect in terms of photoionization of low-density highly ionized clouds of gas – much similar to the way that BDO modelled the inverse effect but including the ionization from the foreground QSO."104 The basic idea is that for a highvy ionizecl plasma. where collisional ionization can be ignored. the neutral gas density is inversely. proportional to the total UV ionizing intensity.," The basic idea is that for a highly ionized plasma, where collisional ionization can be ignored, the neutral gas density is inversely proportional to the total UV ionizing intensity."105 If Jy is the general. UV. background. intensity (in οσοι“ssΤΗtsrack +) at the local Lyman init ancl⋅ foo is mthe UY .flux (in ergs1 em27Lz[requeney.1 ) produced by a QSO located at a distance do from the ccloud. the LL column. density will be. reduced. bv. the presence of the QSO according to where The tus of the QSO on the ecloud is just Lo(πάς) where Lo is the QSO Luninosity at the local Lyman limit frequency. anc do is the distance from the QSO to the ecloud.," If $J_0$ is the general UV background intensity (in $\erg$ ) at the local Lyman limit frequency, and $F_Q$ is the UV flux (in ${\rm erg}\, {\rm s}^{-1}\, {\rm cm}^{-2}\, {\rm Hz}^{-1}$ ) produced by a QSO located at a distance $d_Q$ from the cloud, the HI column density will be reduced by the presence of the QSO according to where The flux of the QSO on the cloud is just $L_Q/(4\pi d_Q^2)$ where $L_Q$ is the QSO luminosity at the local Lyman limit frequency and $d_Q$ is the distance from the QSO to the cloud."106 We have estimated Lo in the same way as Tytler (1987). by using the measured. V. magnitude ancl a suitable dy correction.," We have estimated $L_Q$ in the same way as Tytler (1987), by using the measured V magnitude and a suitable $K$ correction."107 We have used the A. correction presented. by E Q fo," We have used the $K$ correction presented by Evans Hart (1977), assuming that it holds up to a redshift of 2.7."108reground QSO is isotropic (i.c.. no beaming) and that the measured magnitude has not been seriously contaminated by gravitational lensing or micro-Iensing amplification along the line of sight.," We have also assumed that the emission from the foreground QSO is isotropic (i.e., no beaming) and that the measured magnitude has not been seriously contaminated by gravitational lensing or micro-lensing amplification along the line of sight."109 Another implicit assumption in this ⇂⋅↓⋅⋜⋯↓∢⊾∖∖⊽∪↓⋅↓∡⊲↓⊳∖↿↓⋯⇂↿↓↥⋖⋅⇂⋅∪↓⋅∢⋅⋏∙≟↓⋅∪⊔⊔∠⇂≺≥∺≺≽↓⊔⊔↓⊲↓⊔∪⊳∖⊀∐∙∖⇁⊀↓⊳∖⊔∪↿ variable., Another implicit assumption in this framework is that the foreground QSO luminosity is not variable.110 We will discuss this point further in Section 6., We will discuss this point further in Section 6.111 Within this simple framework. the net elect of he presence of a nearby. QSO would be to he column densities of ssvstemis.," Within this simple framework, the net effect of the presence of a nearby QSO would be to the column densities of systems."112 Since we are working with column-densitv-limited samples. some of the elouds that would be detectable in the absence of the proximity effect will now eet a column density below our thresholds and they will therefore disappear.," Since we are working with column-density-limited samples, some of the clouds that would be detectable in the absence of the proximity effect will now get a column density below our thresholds and they will therefore disappear."113 Now the number of absorption lines (for à fixed ο) above the completeness threshold will decrease by a factor (1|wo)!, Now the number of absorption lines (for a fixed $\omega_Q$ ) above the completeness threshold will decrease by a factor $(1+\omega_Q)^{1-\beta}$.114 Therefore the redshift distribution given by equajon (1) has to be revised by the presence of both the background. and the foreground QSO. ic. for cach QSO clistribution.," Therefore the redshift distribution given by equation (1) has to be revised by the presence of both the background and the foreground QSO, i.e., for each QSO distribution."115 Notice that if we adopt the values of=8.5.5 =LOST and the estimates of the QSO luminosities as. discussed above. the only free parameter in this equation is the UV background. Ju.," Notice that if we adopt the values $A=8.5$, $\gamma=1.987$ and the estimates of the QSO luminosities as discussed above, the only free parameter in this equation is the UV background $J_0$."116 Lo what follows we shall assume that Jj does not depend on redshift. given the relatively restricted redshift range spanned by our observations.," In what follows we shall assume that $J_0$ does not depend on redshift, given the relatively restricted redshift range spanned by our observations."117 In fact. models for the origin of the UV. background. in terms of the integrated QSO emission produce a UV background. which does not vary very much in the range under consideration.," In fact, models for the origin of the UV background in terms of the integrated QSO emission produce a UV background which does not vary very much in the range under consideration."118 This is à result of the cancellation of the expansion of the universe by the peak in the redshift distribution of the QSO population (see. e.g.. Atwood. Baldwin Carswell 1955: Aochtold et al.," This is a result of the cancellation of the expansion of the universe by the peak in the redshift distribution of the QSO population (see, e.g., Atwood, Baldwin Carswell 1985; Bechtold et al."119 LOST)., 1987).120 Since we are interested. in the proximity ellect caused by the foreground QSOs. we will ignore the inverse effect portion of the different spectra. Le. the region where piotoionization by the background QSO will allect the distribution of lines.," Since we are interested in the proximity effect caused by the foreground QSOs, we will ignore the inverse effect portion of the different spectra, i.e., the region where photoionization by the background QSO will affect the distribution of lines."121 This is only relevant to the spectrum © QSO1222|228 in which we have ignored a range of WOkms around the redshift of the QSO.," This is only relevant to the spectrum of QSO1222+228 in which we have ignored a range of $5000\, \kms$ around the redshift of the QSO."122 We checked ith our best-littine values for Jy that this region was large enough to exclude the inverse effect region of this QSO., We checked with our best-fitting values for $J_0$ that this region was large enough to exclude the inverse effect region of this QSO.123 This also allows us to ignore: the (1|oy)1C factor in eq (7))., This also allows us to ignore the $(1+\omega_b)^{1-\beta}$ factor in eq (7).124be decreased by a Iarger factor than that of clusters.,be decreased by a larger factor than that of clusters.125 Non-eravitational energy injection also explains the shape of the observed Lx -T relation and the entropy [oor of eroups. as cliscussecl in the introduction.," Non-gravitational energy injection also explains the shape of the observed $_X$ -T relation and the entropy floor of groups, as discussed in the introduction."126 The origin and epoch of the energy injection is unknown., The origin and epoch of the energy injection is unknown.127 Kinetic energv. from GN jets or outllows. or supernova-driven galaxy winds. have been suggested. (eg.," Kinetic energy from AGN jets or outflows, or supernova-driven galaxy winds, have been suggested (eg."128 Valageas Sill 1909). either before. (eg.," Valageas Silk 1999), either before (eg."129 Ponman 1999). during. or after cluster collapse (eg.," Ponman 1999), during, or after cluster collapse (eg."130 Lowenstein 2000)., Lowenstein 2000).131 Phe observed lack of evolution of the X-ray luminosity function to z=0.5 at the low luminosities of galaxy groups suggests that the thermal properties ofthe X-ray gas has not stenificanthy altered over the corresponding look-back time of &6 Civr., The observed lack of evolution of the X-ray luminosity function to z=0.5 at the low luminosities of galaxy groups suggests that the thermal properties of the X-ray gas has not significantly altered over the corresponding look-back time of $\approx$ 6 Gyr.132 Thus the epoch of energy. injection must. have been largely at z20.5., Thus the epoch of energy injection must have been largely at $>$ 0.5.133 Several authors (Menei Cavaliere 2000. Wu 2000. Bower 2000) have made theoretical. progress. by extending semi-analvtic models. of galaxy. formation and evolution to include the hot. X-raw emitting gas phase »edieted to be at the virial temperatures of halos of galaxy mass and larger.," Several authors (Menci Cavaliere 2000, Wu 2000, Bower 2000) have made theoretical progress by extending semi-analytic models of galaxy formation and evolution to include the hot, X-ray emitting gas phase predicted to be at the virial temperatures of halos of galaxy mass and larger."134 In the models. the cooling of this eas via X- emission allows a galaxy to form.," In the models, the cooling of this gas via X-ray emission allows a galaxy to form."135 The cooling gas may » reheate by stellar and supernova-driven winds. whose streneth depends on the star formation rate in the galaxy.," The cooling gas may be reheated by stellar and supernova-driven winds, whose strength depends on the star formation rate in the galaxy."136 The mass of infalline gas whieh will form stars is limite » the fraction of the gas which is heated. ancl possibly ejected. by this feedback mechanism.," The mass of infalling gas which will form stars is limited by the fraction of the gas which is heated, and possibly ejected, by this feedback mechanism."137 The net result is tha energy is injected. into the IGM and less gas is converte into stars., The net result is that energy is injected into the IGM and less gas is converted into stars.138" Feedback is required in the models. especially in high redshift. low mass but dense halos. to prevent a ""cooling catastrophe, (White Rees 1978) and an overproduction of chvarl galaxies."," Feedback is required in the models, especially in high redshift, low mass but dense halos, to prevent a `cooling catastrophe' (White Rees 1978) and an overproduction of dwarf galaxies."139 Η the Menei Cavaliere (2000) model: parameters controlling the star formation timescale anc the feedback are set to produce strong feedback in low mass halos and match the local galaxy. luminosity function (their mocdoel A). then the star formation rate peaks at zzz1.5. and declines at z«l and zz2. as in the original \ladau-Lilly plot. (Macau 1996).," If the Menci Cavaliere (2000) model parameters controlling the star formation timescale and the feedback are set to produce strong feedback in low mass halos and match the local galaxy luminosity function (their model A), then the star formation rate peaks at $\approx$ 1.5, and declines at $<$ 1 and $>$ 2, as in the original Madau-Lilly plot (Madau 1996)."140 Phe οποίον input into the IGM from the strong feedback. results in a prediction of a small amount of evolution of the group XLE at z=0.5. which is within the observed. limits.," The energy input into the IGM from the strong feedback results in a prediction of a small amount of evolution of the group XLF at z=0.5, which is within the observed limits."141" Similarly. Bower (2000) predict. very ittle evolution of the NLP of groups if the energy input rate ollows the star formation rate of the semi-analytical mocel ( ""Cole (2000)."," Similarly, Bower (2000) predict very little evolution of the XLF of groups if the energy input rate follows the star formation rate of the semi-analytical model of Cole (2000)."142 1 the Alenci Cavaliere (2000) model. feedback. in ow mass halos is severely reduced. (an extreme case). the star formation rate at 239 becomes constant with recshillt. in agreement with cxtinction-corrected star. formation ustories.," If the Menci Cavaliere (2000) model feedback in low mass halos is severely reduced (an extreme case), the star formation rate at $>$ 2 becomes constant with redshift, in agreement with extinction-corrected star formation histories."143 dn this case the hot gas is retained in shallow »otentials. increasing Ly. and strong positive evolution of he XLE at group luminosities is predicted (a factor 30 at z—landLx-10077 13).," In this case the hot gas is retained in shallow potentials, increasing $_X$, and strong positive evolution of the XLF at group luminosities is predicted (a factor $\approx$ 30 at z=1 and $_X$ $^{42.5}$ )."144 At z=0.5. the epoch observed here. the evolution predicted is significantly less than at z=1 (a [actor of 4.5: Menci. private communication) but is still only mareinally consistent with the observed XLE (and may also be inconsistent with the residual X-ray background at 0.25 keV: Pen 1999).," At z=0.5, the epoch observed here, the evolution predicted is significantly less than at z=1 (a factor of $\approx$ 4.5; Menci, private communication) but is still only marginally consistent with the observed XLF (and may also be inconsistent with the residual X-ray background at 0.25 keV; Pen 1999)."145 Our observations thus support the need for feedback in semi-analytic models., Our observations thus support the need for feedback in semi-analytic models.146 Not all the excess energy may come from supernovae ancl star formation-relatecd activity., Not all the excess energy may come from supernovae and star formation-related activity.147 Several authors (eg., Several authors (eg.148 Valageas Silk 1990. Wu 2000. Ixravtsov Yepes 2000. Bower 2000) have emphasized that the energy required (~0.5- keV per particle. depending on the epoch) can only be supplied by supernovae if most of the kinetic energy of each explosion goes into heating the LGAL," Valageas Silk 1999, Wu 2000, Kravtsov Yepes 2000, Bower 2000) have emphasized that the energy required $\sim$ 0.5-3 keV per particle, depending on the epoch) can only be supplied by supernovae if most of the kinetic energy of each explosion goes into heating the IGM."149 AGN. on the other hand. can casily meet the energetic requirements.," AGN, on the other hand, can easily meet the energetic requirements."150 The X-ray properties of groups at high redshifts can be used to constrain the epoch of energy injection. irrespective of the origin of the energy.," The X-ray properties of groups at high redshifts can be used to constrain the epoch of energy injection, irrespective of the origin of the energy."151 More energy. input is required (to produce the excess entropy. of Ponman 1999) if it is injected at high redshifts when collapsed systems were denser., More energy input is required (to produce the excess entropy of Ponman 1999) if it is injected at high redshifts when collapsed systems were denser.152 More energy input inflates the N-ray. gas. decreases the central density. ancl produces lower X-ray Iuminosities.," More energy input inflates the X-ray gas, decreases the central density, and produces lower X-ray luminosities."153 If all the non-gravitational heating occurs at very high redshifts (222). Bower (2000) predict. that at. zzz2 eroups have significantlv lower luminosities (for a eiven temperature) compared to 250. and that the space density of low Luminosity (Ly 21077 1)) svstenis is lower than ab z=0.," If all the non-gravitational heating occurs at very high redshifts $>$ 2), Bower (2000) predict that at $\approx$ 2 groups have significantly lower luminosities (for a given temperature) compared to z=0, and that the space density of low luminosity $_X$ $^{43}$ ) systems is lower than at z=0."154 However. only a very small degree. of evolution of the XNLE is. predicted. between z=0 anc z=0.5 (Bower. private communication). consistent with the observations.," However, only a very small degree of evolution of the XLF is predicted between z=0 and z=0.5 (Bower, private communication), consistent with the observations."155 Other. preheating. models. in which the energy. injection occurred at very carly epochs. before the groups collapsed. similarly. predict little or no evolution of the XLI at z~0.5 and Ly 2107 (eg.," Other, preheating, models, in which the energy injection occurred at very early epochs, before the groups collapsed, similarly predict little or no evolution of the XLF at $\sim$ 0.5 and $_X$ $^{43}$ (eg."156 Ixaiser 1991. Bower 1997).," Kaiser 1991, Bower 1997)."157 Ifthe rate of energy injectionJ is constant with redshift. the space density of Lx —105 svstenis Is. predicted. to be a factor 23 higher at z=0.5 than at z=0 (Bower. private communication). just consistent with the observed. NLE.," If the rate of energy injection is constant with redshift, the space density of $_X$ $^{43}$ systems is predicted to be a factor $\approx$ 3 higher at z=0.5 than at z=0 (Bower, private communication), just consistent with the observed XLF."158 Whilst. the results described. here were based on deep ROSAL surveys. they represent the population which serendipitous Chandra. and particularly NMM-Newton. surveys usingfypicad exposures are sampling.," Whilst the results described here were based on deep $ROSAT$ surveys, they represent the population which serendipitous Chandra, and particularly XMM-Newton, surveys using exposures are sampling."159 Thus the sroperties of large numbers of very low-luminosity groups at moderate redshifts. ancl poor clusters at. high. recdshilts (Z1). will soon become accessible.," Thus the properties of large numbers of very low-luminosity groups at moderate redshifts, and poor clusters at high redshifts $\ga$ 1), will soon become accessible."160 Measurements of the evolution of large-scale. structure will be possible with contiguous surveys., Measurements of the evolution of large-scale structure will be possible with contiguous surveys.161 We have already started: to sample he large-scale structure in this single fick., We have already started to sample the large-scale structure in this single field.162 A laree improvement in the statistical aceuraey of the NLP will »' achieved. reaching lower luminosities than sampled here.," A large improvement in the statistical accuracy of the XLF will be achieved, reaching lower luminosities than sampled here,"163Phe recent discovery.. of extrasolar giant. planets orbiting- around nearby solartype stars (Marey Butler 1998. 2000: Alavor Queloz 1995) has stimulated: renewed. interest. in ∙⋅the theory of∙ planet. formation.,"The recent discovery of extrasolar giant planets orbiting around nearby solar–type stars (Marcy Butler 1998, 2000; Mayor Queloz 1995) has stimulated renewed interest in the theory of planet formation."164"∙. The objects. observed so far have masses. νι that are characteristic of giant planets. de. 0.4NL;M,sdiM. Aly denoting a Jupiter mass."," The objects observed so far have masses, $M_p$, that are characteristic of giant planets, i.e. $0.4 \; {\rm M}_J \; \ls \; M_p165\ \ls \; 11 \; {\rm M}_J$, $_J$ denoting a Jupiter mass."166 The orbital semi-major axes are in the range )OtauSaS25au. and orbital eccentricities in the range 1.08=0.67 (Marcy Butler 2000).," The orbital semi-major axes are in the range $0.04 \; {\rm au} \; \ls \; a \; \ls167\; 2.5 \; {\rm au}$, and orbital eccentricities in the range $ 0.0 \;168\ls \; e \; \ls \; 0.67$ (Marcy Butler 2000)."169 lt is a challenge to formation theories to explain the observed masses and orbital clement distributions., It is a challenge to formation theories to explain the observed masses and orbital element distributions.170 Phere are wo main theories of giant planet formation (see Papaloizou. Terquem Nelson 1999 and references therein).," There are two main theories of giant planet formation (see Papaloizou, Terquem Nelson 1999 and references therein)."171 One is the core instability scenario., One is the core instability scenario.172 In this. a solid core of several earth masses is built up in the protostellar disc. at which point it is able to begino to accrete ὃνgas and evolve to become a giant. planet.," In this, a solid core of several earth masses is built up in the protostellar disc, at which point it is able to begin to accrete gas and evolve to become a giant planet."173 Once massive enough it is able to open a eap in: the disc: and undergo. orbitaln migration⊲⋅⊀ through. disc: protoplanet. interactions.⋅⋠ (e.g. Lin. NENPapaloizou. 1993)., Once massive enough it is able to open a gap in the disc and undergo orbital migration through disc protoplanet interactions (e.g. Lin Papaloizou 1993).174-- It has been suggested that the high.. orbitalaso eccentricitiescos for⋅⋅ extrasolar planets might be explained. by disc-protoplanet interactions (Xrtvmowicz 1992)., It has been suggested that the high orbital eccentricities for extrasolar planets might be explained by disc-protoplanet interactions (Artymowicz 1992).175 Recent simulations of protoplancts in. the observed mass range (Ixlev 1999. Drvden et al.," Recent simulations of protoplanets in the observed mass range (Kley 1999, Bryden et al."176 1999. Lubow. Seibert Artvmowicz 19t99) interacting with a disc with parameters thought. Τε» be typical of protoplanctary discs. but constrained. to »' in circular orbit. indicate eap formation and upper mass limit consistent with the observations.," 1999, Lubow, Seibert Artymowicz 1999) interacting with a disc with parameters thought to be typical of protoplanetary discs, but constrained to be in circular orbit, indicate gap formation and upper mass limit consistent with the observations."177 However. simuations by Nelson et al. (," However, simulations by Nelson et al. ("1782000) that relaxec the assumption of fixed cireular orbits found inward. migration and that the disc-protoplanet interaction,2000) that relaxed the assumption of fixed circular orbits found inward migration and that the disc-protoplanet interaction1798.9 Ajupiter.,8.9 $M_{\rm Jupiter}$.180 They used a stellar mass of 1.05 AZ. from AllendePrieto&Lambert(1999).. who compared the absolute visual magnitude and (2—V) color [rom Iipparcos data with theoretical isochrones from Bertellietal.(1994)..," They used a stellar mass of 1.05 $M_\odot$ from \citet{1999AandA...352..555A}, who compared the absolute visual magnitude and $B-V$ ) color from Hipparcos data with theoretical isochrones from \citet{1994AandAS..106..275B}."181 ILowever. Frink et al.," However, Frink et al."182 acknowledge that evolutionary tracks for a range of masses are close together on the II-R. diagram. so any slight change in the evolutionary model can have a laree impact on the derived mass.," acknowledge that evolutionary tracks for a range of masses are close together on the H-R diagram, so any slight change in the evolutionary model can have a large impact on the derived mass."183 Zecimeisterοἱal.(2008.hereafterZ08) observed + Dra in search of stellar oscillations using three separate instruments over almost 8 vears in order to refine (he orbital parameters of the planet and determine (he mass of the central star., \citet[][hereafter Z08]{2008AandA...491..531Z} observed $\iota$ Dra in search of stellar oscillations using three separate instruments over almost 8 years in order to refine the orbital parameters of the planet and determine the mass of the central star.184" They found low amplitude. oscillations with a frequency of 3.8 d.|! in two of the datasets and deriveda stellar mass of 2.2 M. using the equations and where Mos is the oscillation velocity zunplitude.. fyia, is (he Irequency of the strongest mode. and Z;y is the effective temperature."," They found low amplitude, solar-like oscillations with a frequency of 3.8 $^{-1}$ in two of the datasets and deriveda stellar mass of 2.2 $M_\odot$ using the equations and where $\nu_{\rm osc}$ is the oscillation velocity amplitude, $f_{\rm max}$ is the frequency of the strongest mode, and $T_{\rm eff}$ is the effective temperature."185 They. used a luminosity of 64.242.1 L. from the Hipparcos catalog and Tuy = 4490 Ix from MeWilliun(1990).., They used a luminosity of $\pm$ 2.1 $L_\odot$ from the Hipparcos catalog and $T_{\rm eff}$ = 4490 K from \citet{1990ApJS...74.1075M}.186 Z08 then compared (heir 2.2 M. value to those derived using Tig. surface gravities (log g). and metallicities ([Fe/1l]) from the literattwe and the PARAAI stellar model by Girardietal.(2000). ancl daSilvaοἱ(2006) /egi-bin/param.1.0...," Z08 then compared their 2.2 $M_\odot$ value to those derived using $T_{\rm eff}$, surface gravities (log $g$ ), and metallicities ([Fe/H]) from the literature and the PARAM stellar model by \citet{2000AandAS..141..371G} and \citet{2006AandA...458..609D} ."187 The masses ranged from 1.05+0.36 AL. based on values from AllendePrieto&Lambert(1999). to 1.71220.38 AL. based on values [rom Santosetal.(2004).., The masses ranged from $\pm$ 0.36 $M_\odot$ based on values from \citet{1999AandA...352..555A} to $\pm$ 0.38 $M_\odot$ based on values from \citet{2004AandA...415.1153S}.188 Decause ZÜSs mass was significantly higher {han those derived using the model. they chose à mass of 1.4 AL. to caleulate (he minimum nass of the companion. which they list as 10.3 ALjupites.," Because Z08's mass was significantly higher than those derived using the model, they chose a mass of 1.4 $M_\odot$ to calculate the minimum mass of the companion, which they list as 10.3 $M_{\rm Jupiter}$."189 A more accurate way to estimate the stars mass would be to investigate the frequency splitting (N/5) using the equation combined with an interferometrically measured radius. but unfortunately Z0Ss dataset was not suitable lor measuring A i.," A more accurate way to estimate the star's mass would be to investigate the frequency splitting $\Delta f_{\rm 0}$ ) using the equation combined with an interferometrically measured radius, but unfortunately Z08's dataset was not suitable for measuring $\Delta f_{\rm 0}$ ."190 The advantage interferometry brings is the ability. to directly. measure the angular diauneter of (he star., The advantage interferometry brings is the ability to directly measure the angular diameter of the star.191 Then the physical radius can be determined using the distance from, Then the physical radius can be determined using the distance from192"serendipitouslv. spanning the luminosity range Lx(0.οedt.10""3.10H units..","serendipitously, spanning the luminosity range $\rm L_X( 0.1 - 2.4 \, keV) \approx 4\times 10^{37}-193 3\times10^{41}$ ."194" We estimate the logCf,/f.) ratio from the Q.1- keV Bux and the D-band magnitude.", We estimate the $\log(f_x/f_o)$ ratio from the 0.1-2.4 keV flux and the $B$ -band magnitude.195 We find that no galaxy Dies above the [ουf.)=2 cut. despite he fact that highly luminous galaxies are included in the sample.," We find that no galaxy lies above the $\log(f_x/f_o)=-2$ cut, despite the fact that highly luminous galaxies are included in the sample."196" Nevertheless. we note that the most N-ray luminous (=210"" 1)) star-forming system known. NCGC3256 (Moran. Lehnert Ilelfand. 1999). which is not included in the Llo ct al. ("," Nevertheless, we note that the most X-ray luminous $\approx 2\times10^{42}$ ) star-forming system known, NGC3256 (Moran, Lehnert Helfand 1999), which is not included in the Ho et al. ("1971997) sample. has a relatively high X-ravtooptical Dux ratio. logCf./f.)&αντ.,"1997) sample, has a relatively high X-ray--to--optical flux ratio, $\log (f_x/f_o) \approx198 -1.7$."199 This suggests hat some very X-ray luminous galaxies would evade our olf.ffi)<2 criterion., This suggests that some very X-ray luminous galaxies would evade our $\log (f_x/f_o) < -2$ criterion.200 This elfect may be exacerbated at higher redshift., This effect may be exacerbated at higher redshift.201" Indeed. in a scenario where the log(f,/f.) increases with redshift (Llornschemeier et al. ("," Indeed, in a scenario where the $\log(f_x/f_o)$ increases with redshift (Hornschemeier et al. ("2022003). the traction of missed galaxies will be higher.,"2003), the fraction of missed galaxies will be higher."203 We further attempt to estimate the contamination of our sample by Low Luminosity ACN., We further attempt to estimate the contamination of our sample by Low Luminosity AGN.204 We use the late-type galaxy sample of Shapley ct al. (, We use the late-type galaxy sample of Shapley et al. (2052001) comprising a total of LOL svstems with loe(fi/fi)«2.,"2001) comprising a total of 101 systems with $\log(f_x/f_o)206 <-2$."207 X number of these are classified AGNs. primarily using information from the optical spectra obtained by. Lo et al. (," A number of these are classified AGNs, primarily using information from the optical spectra obtained by Ho et al. ("2081997).,1997).209 Note that we include only the Sevfert ancl Linerl.9 objects in the AGN class., Note that we include only the Seyfert and Liner1.9 objects in the AGN class.210 We find 15 such objects which satisfy the above criteria and this roughly translates to ~15 per cent contamination in the Shapley et al., We find 15 such objects which satisfy the above criteria and this roughly translates to $\sim$ 15 per cent contamination in the Shapley et al.211 sample., sample.212 Vhis may only. represent a lower limit as not all galaxies in Shapley ct al., This may only represent a lower limit as not all galaxies in Shapley et al.213 are common with Llo et al. (, are common with Ho et al. (2141997) Le. many systems do not have good quality spectra.,1997) i.e. many systems do not have good quality spectra.215 We note nevertheless. that even in the case where a small fraction. of residual. Low Luminosity ACN is included: in our sample (because of the quality of the optical spectra). this does not necessarily mean that. the X-ray emission comes only from the ACN in these objects. e.g. Terashima Wilson (2003).," We note nevertheless, that even in the case where a small fraction of residual Low Luminosity AGN is included in our sample (because of the quality of the optical spectra), this does not necessarily mean that the X-ray emission comes only from the AGN in these objects, e.g. Terashima Wilson (2003)."216 The X-ray luminosity function of the combined sample, The X-ray luminosity function of the combined sample217"Its adjustable parameters are the dark matter and baryon densities Ὡς and C), the Hubble parameter h, and the perturbation amplitude Ag and spectral index ns.","Its adjustable parameters are the dark matter and baryon densities $\Omega_{\rm c}$ and $\Omega_{\rm b}$, the Hubble parameter $h$, and the perturbation amplitude $A_{\rm s}$ and spectral index $n_{\rm218s}$."219 These are fixed to WMAP3 best-fit (Spergel et al., These are fixed to WMAP3 best-fit (Spergel et al.220" 2007) for Q?, Och”, the projected sound horizon 0, A,exp(—27) and ns."," 2007) for $\Omega_{\rm b} h^2$ , $\Omega_{\rm c} h^2$ , the projected sound horizon $\theta$, $A_s \exp(-2\tau)$ and $n_s$."221 We then study the reionization signal from the TE and EE spectra out to 6 of 100., We then study the reionization signal from the TE and EE spectra out to $\ell$ of 100.222" It is possible to use such an analysis procedure because the non-reionization parameters are very well determined by the TT spectrum, and because the large-scale signal in CMB polarization is independent of the other parameters."," It is possible to use such an analysis procedure because the non-reionization parameters are very well determined by the TT spectrum, and because the large-scale signal in CMB polarization is independent of the other parameters."223 A similar procedure has been followed in works including Kaplinghat et al. (, A similar procedure has been followed in works including Kaplinghat et al. (224"2003), Holder et al. (","2003), Holder et al. ("225"2003), and Mortonson Hu (2008a,b).","2003), and Mortonson Hu (2008a,b)."226 The uncertainty on 7 derived holding these parameters fixed is expected to be an underestimate by about (Mortonson Hu 20082)., The uncertainty on $\tau$ derived holding these parameters fixed is expected to be an underestimate by about (Mortonson Hu 2008a).227 We assume standard recombination., We assume standard recombination.228" If the recombination model eventually needs to be modified to account for two-photon decays (Dubrovich Grachev 2005; Wong Scott 2007; Chluba Sunyaev 2008; Hirata 2008), this should not affect the model comparisons we present here because it would be common to all the models."," If the recombination model eventually needs to be modified to account for two-photon decays (Dubrovich Grachev 2005; Wong Scott 2007; Chluba Sunyaev 2008; Hirata 2008), this should not affect the model comparisons we present here because it would be common to all the models."229" In addition, the spectrum changes on intermediate to small scales while we are using only the large scales here."," In addition, the spectrum changes on intermediate to small scales while we are using only the large scales here."230" We mainly consider a two-parameter reionization model defined by the ionization fraction history where ze refers to the ionization fraction, 7; and rj;—1 refer to consecutive time steps, η to the conformal time at the i-th time step, 2, is the redshift at which the ionization fraction is 0.5, ης, is the conformal time corresponding to that redshift, and d;, gives the (inverse) width of the transition."," We mainly consider a two-parameter reionization model defined by the ionization fraction history where $x_e$ refers to the ionization fraction, $\eta_i$ and $\eta_{i-1}$ refer to consecutive time steps, $\eta$ to the conformal time at the $i$ -th time step, $z_{\rm r}$ is the redshift at which the ionization fraction is 0.5, $\eta_{z_{\rm r}}$ is the conformal time corresponding to that redshift, and $d_{\eta}$ gives the (inverse) width of the transition."231" Such a transition is implemented in CAMB (Lewis, Challinor Lasenby 2000), and the commonly-used instantaneous reionization scenario corresponds to d;, having a large enough value, such as 50, that z, is effectively the redshift of instantaneous We additionally force the ionization fraction to unity for 6,, to avoid conflict with quasar absorption spectrum data, and to zero for z730 as no ionizing sources are expected so early."," Such a transition is implemented in CAMB (Lewis, Challinor Lasenby 2000), and the commonly-used instantaneous reionization scenario corresponds to $d_{\eta}$ having a large enough value, such as 50, that $z_{\rm r}$ is effectively the redshift of instantaneous We additionally force the ionization fraction to unity for , to avoid conflict with quasar absorption spectrum data, and to zero for $z>30$ as no ionizing sources are expected so early."232 The optical depth 7 is computed numerically for any such reionization history., The optical depth $\tau$ is computed numerically for any such reionization history.233" Given the reionization history, we compute the CMB power spectra using a version of CAMB with minor modifications."," Given the reionization history, we compute the CMB power spectra using a version of CAMB with minor modifications."234" Our assumed cosmological model has only scalar initial perturbations, and so we do not compute the BB polarization spectra."," Our assumed cosmological model has only scalar initial perturbations, and so we do not compute the BB polarization spectra."235" Figures 1 and 2 show some predicted power spectra for these models, showing in particular that 7 is indeed mainly responsible for variations in the predictions and hence the most readily measured parameter."," Figures \ref{f:models3} and \ref{f:models4} show some predicted power spectra for these models, showing in particular that $\tau$ is indeed mainly responsible for variations in the predictions and hence the most readily measured parameter."236"Furthermore, atfixed 7 it is clear from figure 2 that all the discriminating power isin the polarization spectra rather than temperature.","Furthermore, atfixed $\tau$ it is clear from figure \ref{f:models4} that all the discriminating power isin the polarization spectra rather than temperature."237equations through the pressure boundary condition at the stream edge. which is set equal to the ambient. pressure in the envelope.,"equations through the pressure boundary condition at the stream edge, which is set equal to the ambient pressure in the envelope."238 The density within the stream is related to the pressure by the acliabatic constant of the secondary material s=Pip=const., The density within the stream is related to the pressure by the adiabatic constant of the secondary material $s = P/\rho^\gamma = \const$.239 Together with a specified mass-Llow rate. this set of equations provides a complete set that completely describes the dynamics of the stream in this phase.," Together with a specified mass-flow rate, this set of equations provides a complete set that completely describes the dynamics of the stream in this phase."240 The initial conditions for the hyelrodyvnamical simulations are taken directly from the parameters obtained. from the ballistic calculations for a range of binary parameters., The initial conditions for the hydrodynamical simulations are taken directly from the parameters obtained from the ballistic calculations for a range of binary parameters.241 Specifically. we consider parameters representing the in and subsequent merger of a secondary of 1 and iinside a cevolyed supergiant which has completed. helium. burning in the core and has à core mass of ~TAL...," Specifically, we consider parameters representing the spiral-in and subsequent merger of a secondary of 1 and inside a evolved supergiant which has completed helium burning in the core and has a core mass of $\sim2427\Msun$."243 To model the seconcdaries. we first followed their evolution to the same age as the primary and then evolved them further. subjecting theme to very fast mass loss to model their adiabatic response to mass loss.," To model the secondaries, we first followed their evolution to the same age as the primary and then evolved them further, subjecting them to very fast mass loss to model their adiabatic response to mass loss."244 These calculations give the radii of the stars and their surface entropics as a function of current stcllar lass., These calculations give the radii of the stars and their surface entropies as a function of current stellar mass.245 For the hwdrodvnamical simulations of the streamcore interactions we use a code based on the PROSMIZTLLIEUS hvedrodynamical code (Ervxell. Mülller Arnett 1989).," For the hydrodynamical simulations of the stream–core interactions we use a code based on the PROMETHEUS hydrodynamical code (Fryxell, Mülller Arnett 1989)."246 This is an Eulerian code. which uses a second-order Godunov-type scheme to solve the hydrodynamical equations. the piecewise parabolic method (PPM) of Colella Woodward (1994).," This is an Eulerian code, which uses a second-order Godunov-type scheme to solve the hydrodynamical equations, the piecewise parabolic method (PPM) of Colella Woodward (1994)."247" ""This code has been widely used by different groups (see e.g. Ixercek. Hillebrandt ""Truran 1998: WIT). and we refer to these papers for a detailed description of the code and numerical tests."," This code has been widely used by different groups (see e.g. Kercek, Hillebrandt Truran 1998; KHT), and we refer to these papers for a detailed description of the code and numerical tests."248 To make it applicable to our problem. we had to make a number of modifications to the original code. in. particular to the treatment of the gravity. field. the boundary. conditions. to the equation of state and. the hyerodsnamical equations themselves (to take into account the elfects of a frame co-rotating with the binary).," To make it applicable to our problem, we had to make a number of modifications to the original code, in particular to the treatment of the gravity field, the boundary conditions, to the equation of state and the hydrodynamical equations themselves (to take into account the effects of a frame co-rotating with the binary)."249 Since the mass transfer occurs in an opaque environment. radiative losses are not important and have been neglected.," Since the mass transfer occurs in an opaque environment, radiative losses are not important and have been neglected."250 In the presence of a large pressure gradient at the coreenvelope interface and a correspondinglv: strong gravitational field. Godunoy-type schemes produce intrinsic accelerations. which during a few dynamical time-scales fy create significant. outward. motion (INIT).," In the presence of a large pressure gradient at the core–envelope interface and a correspondingly strong gravitational field, Godunov-type schemes produce intrinsic accelerations, which during a few dynamical time-scales $t_{\rm d } $ create significant outward motion (KHT)."251 For a first-order Codunov method it is possible to find an analytical formula to mocdifv the interface states., For a first-order Godunov method it is possible to find an analytical formula to modify the interface states.252 Then source ternis (the gravitational Geld in our case) will be balanced bv Hux differences (LeVeque 1998)., Then source terms (the gravitational field in our case) will be balanced by flux differences (LeVeque 1998).253 Fhis is not possible for higher-order Ciodunov-tvpe schemes. where cach problem requires a separate treatment (IKTEE).," This is not possible for higher-order Godunov-type schemes, where each problem requires a separate treatment (KHT)."254 To reduce the artificial acceleration in our case. we assume that the gravitational lield can be considered as constant in time and that there is no sell-egravity.," To reduce the artificial acceleration in our case, we assume that the gravitational field can be considered as constant in time and that there is no self-gravity."255 Then. in cach time step. we mocdifv. the interface values before applying the Ricmann solver. by reducing them from both (lelt and right) interfaces by a pressure [lux caused by gravity.," Then, in each time step, we modify the interface values before applying the Riemann solver, by reducing them from both (left and right) interfaces by a pressure flux caused by gravity."256 Furthermore. we enforce the condition of hvdrostatie equilibrium at the boundary (for ghost cells*)) in the direction of the gravity field.," Furthermore, we enforce the condition of hydrostatic equilibrium at the boundary (for ghost ) in the direction of the gravity field."257 These πιοσαος ensure that any initial model remains stable for arbitrarily long time., These modifications ensure that any initial model remains stable for arbitrarily long time.258 We performed 2-dimensional calculations in polar evlindrical coordinates. where we usually usec 300...300. ericl points.," We performed 2-dimensional calculations in polar cylindrical coordinates, where we usually used $300 \times 300$ grid points."259 In the case of very narrow streams. we increased the resolution to 600.GOO erid points.," In the case of very narrow streams, we increased the resolution to $600260\times 600$ grid points."261 We also carried: out test calculations with erids of higher resolution to satisfy ourselves that further increasing the number of grid. points does not significantly alleet the results., We also carried out test calculations with grids of higher resolution to satisfy ourselves that further increasing the number of grid points does not significantly affect the results.262 As a general rule. we ensure that the inllowing stream contains at least 20 erid points in the azimuthal direction.," As a general rule, we ensure that the inflowing stream contains at least 20 grid points in the azimuthal direction."263 We also carried out a few 3-dimensional calculations (in spherical coordinates) for the case of a svmmoetrical (non-inclined) stream in a non-rotating frame., We also carried out a few 3-dimensional calculations (in spherical coordinates) for the case of a symmetrical (non-inclined) stream in a non-rotating frame.264 The results of these calculations showed that there were no significant dillerences between the 2- and. 3-dimensional calculations with the same initial. parameters., The results of these calculations showed that there were no significant differences between the 2- and 3-dimensional calculations with the same initial parameters.265 In particular. the penetration depths of the stream were very similar in both cases.," In particular, the penetration depths of the stream were very similar in both cases."266 To model the region. of interest. for the streamcore interaction inside the common envelope. we adopt. power-law distributions for the temperature and the pressure. Le d(r)=T(ro)(ro/r)'* and PO)=ο)νο. We fitted these power laws to the structure in actual CE calculations (as ceseribec in detail in LP).," To model the region of interest for the stream–core interaction inside the common envelope, we adopt power-law distributions for the temperature and the pressure, i.e $ T(r)=T(r_0) \left (267{{r_0}/{r}}\right )^{\alpha_{T}} $ and $P(r)=P(r_0) \left268({{r_0}/{r}}\right )^{\alpha_{P}}.$ We fitted these power laws to the structure in actual CE calculations (as described in detail in IP)."269 Typical values or ap and ap are in the range (1.3:5.2)+(0.8:3.2). but can be as high as (1.7:7) (corresponding to a structure with an adiabatic index 544457 1.44) and reasonably describe he regions of the stellar models at the the evolutionary stage of interest (LP).," Typical values for $\alpha_{T}$ and $\alpha_{P}$ are in the range $(1.3;5.2)\div (0.8;3.2)$, but can be as high as $(1.7;7)$ (corresponding to a structure with an adiabatic index $\gamma_{\rm amb } \approx1.44$ ) and reasonably describe the regions of the stellar models at the the evolutionary stage of interest (IP)."270 For our caleulations here. we adopted xwameters (αρα.=(1.3:5.2) ancl (0.8:3.2) for models representing a 20|1 and a 2015 CI simulation. respectively.," For our calculations here, we adopted parameters $ (\alpha_{ T } ; \alpha_{ P } ) = (1.3 ; 5.2)$ and $(0.8;2713.2)$ for models representing a 20+1 and a 20+5 CE simulation, respectively."272 Throughout the domain of our calculations. we assume that he ambient matter has a constant composition. similar to he composition in the core region of the primary. mainly wlitun.," Throughout the domain of our calculations, we assume that the ambient matter has a constant composition, similar to the composition in the core region of the primary, mainly helium."273 In the full stellar models. hydrogen is exhausted low a radius of4.LOM em. and the hydrogen mass fraction increases to 0.1 at the outer edge of the domain (at 17.5107 em J.," In the full stellar models, hydrogen is exhausted below a radius of $4\times 10^{10}\,$ cm, and the hydrogen mass fraction increases to $\sim 0.1$ at the outer edge of the domain (at $7.5\times 10^{10}\,$ cm )."274 We have tested that these differences do not allect the results appreciably., We have tested that these differences do not affect the results appreciably.275 In this parametrized. mocel. we assume that the ambient matter is initially in (quasi-Jhvelrostatic equilibrium: as the model is parametrized. by the pressure ancl temperature gradient. the gravitational Ποιά. is then defined. implicitly by the initial pressure eracient of the [rame and the initial density. cistribution.," In this parametrized model, we assume that the ambient matter is initially in (quasi-)hydrostatic equilibrium; as the model is parametrized by the pressure and temperature gradient, the gravitational field is then defined implicitly by the initial pressure gradient of the frame and the initial density distribution."276 In calculations where nuclear burning is included. we use a nuclear reactions network with 27 isotopes. which includes," In calculations where nuclear burning is included, we use a nuclear reactions network with 27 isotopes, which includes"277luminosity function.,luminosity function.278 Figure 9 shows the evolution of the luminosity density in the / filter. while Figure 160 displays the corresponding plot for the rest-frame // band.," Figure \ref{fig:lumden_J} shows the evolution of the luminosity density in the $J$ filter, while Figure \ref{fig:lumden_H} displays the corresponding plot for the rest-frame $H$ band."279 Values of the luminosity density at each redshift and for each filter are presented in Table 5.., Values of the luminosity density at each redshift and for each filter are presented in Table \ref{tab:lumden}.280 In order to be less sensitive to the derived faint end slope of the LE. we also computed the luminosity density assuming two different limiting absolute magnitudes.," In order to be less sensitive to the derived faint end slope of the LF, we also computed the luminosity density assuming two different limiting absolute magnitudes."281" First. the luminosity density p was derived using the absolute magnitude limits of our survey in each redshift bin. i.e. Adri,—20.21.21.5.22. and Adan,=20.21.22.22.5. for the redshift intervals centered at 2=1.75.2.25.2.175.5.25. respectively."," First, the luminosity density $\bar{\rho}$ was derived using the absolute magnitude limits of our survey in each redshift bin, i.e., $M_{J,lim}=-20, -21,-21.5,-22$, and $M_{H,lim}=-20,-21,-22,-22.5$, for the redshift intervals centered at $z=1.75, 2.25, 2.75, 3.25$, respectively."282" Second. the luminosity density p was derived assuming a limiting absolute magnitude equal to the brightest limit over the entire targeted redshift range. ie. Adi,=—20.0."," Second, the luminosity density $\rho^*$ was derived assuming a limiting absolute magnitude equal to the brightest limit over the entire targeted redshift range, i.e. $M_{lim}=-20.0$."283 The values of p are also plotted in Figures 9 and 160 as grey symbols., The values of $\rho^*$ are also plotted in Figures \ref{fig:lumden_J} and \ref{fig:lumden_H} as grey symbols.284 The overall plot of the ./-band luminosity density shows a constant value ΤουςZOS.— L.0., The overall plot of the $J$ -band luminosity density shows a constant value for $z \lesssim 0.8-1.0$ .285" At zzQS.1.0. the luminosity density starts to decrease down to 2z3.5. where p, is of the -=0 value."," At $z\approx 0.8-1.0$, the luminosity density starts to decrease down to $z\approx 3.5$, where $\rho_J$ is of the $z=0$ value."286 This can be better visualized by comparing this plot with the top and middle panels of Figure 7.., This can be better visualized by comparing this plot with the top and middle panels of Figure \ref{fig:sch_evol_J}.287 Here we see in fact that for 2.ss1 the decrease in number of galaxies is balanced by a brightening of the characteristic magnitude., Here we see in fact that for $z\lesssim1$ the decrease in number of galaxies is balanced by a brightening of the characteristic magnitude.288 At 2<1. both quantities decrease. with the resulting decrease of the luminosity density.," At $z \gtrsim 1$, both quantities decrease, with the resulting decrease of the luminosity density."289 Using the expression ofEq., Using the expression ofEq.290 10. and Eq., \ref{eq:fit_phi} and Eq.291 11. in Eq. [2..," \ref{eq:sch_ms} in Eq. \ref{eq:rho},"292 it is possible to obtain a functional representation of the luminosity density., it is possible to obtain a functional representation of the luminosity density.293 The dashed line in Figure 9 represents the luminosity density for the rest-frame ./ band obtained with this method and adopting the best-tit values of the parameters previously recovered., The dashed line in Figure \ref{fig:lumden_J} represents the luminosity density for the rest-frame $J$ band obtained with this method and adopting the best-fit values of the parameters previously recovered.294 The agreement with the points is good over the entire redshift range., The agreement with the points is good over the entire redshift range.295 We would like to stress that no best fit has been done using —qe data of the luminosity density., We would like to stress that no best fit has been done using the data of the luminosity density.296 Similarly to the case of the LF. the luminosity density in the // filter has been poorly studied. sothat it is more difficult to derive its evolution.," Similarly to the case of the LF, the luminosity density in the $H$ filter has been poorly studied, sothat it is more difficult to derive its evolution."297 Our data however indicate a decline with redshift of the LD. similar in shape to the one found in the ./ band. with a faster evolution from 2=3.5 to 2=1.5. followed by a much slower evolution. decreasing by a factor of ~7 from 2=Oto +=3.5.," Our data however indicate a decline with redshift of the LD, similar in shape to the one found in the $J$ band, with a faster evolution from $z=3.5$ to $z=1.5$, followed by a much slower evolution, decreasing by a factor of $\sim 7$ from $z=0$ to $z=3.5$."298Ia An exercise similar to what done for the -/-band luminosity density. introducing our parameterizations. is shown as a dashed line in Figure 10..The agreement is quite good over the whole redshift range. although more measurements are necessary at intermediate redshifts (2«1.5).," An exercise similar to what done for the $J$ -band luminosity density, introducing our parameterizations, is shown as a dashed line in Figure \ref{fig:lumden_H}.The agreement is quite good over the whole redshift range, although more measurements are necessary at intermediate redshifts $z<1.5$ )."299 In Fig., In Fig.300 ||. we present the evolution of the Schechter parameters oO (top panel) and AL* (bottom. panel) for the rest-frame JV band. collected from the literature (coloured points - see legend for details) and overplotted to the corresponding parameterization of the rest-frame ./ band (taken from Fig. 7:," \ref{fig:LF_K_comp} we present the evolution of the Schechter parameters $\phi^*$ (top panel) and $M^*$ (bottom panel) for the rest-frame $K$ band, collected from the literature (coloured points - see legend for details) and overplotted to the corresponding parameterization of the rest-frame $J$ band (taken from Fig. \ref{fig:sch_evol_J};"301 black line)., black line).302 The previously measured. rest-frame /y-band LFs are taken from Mobasher.Sharples.&Ellis(1993):Glazebrooketal.(1995):etal.(2006):CaputiCirasuolo(2007.2010). - see also Table 5 in Saraccoetal.(2006) which we used as reference for the literature works.," The previously measured rest-frame $K$ -band LFs are taken from \citet{mobasher93,glazebrook1995,cowie96,gardner97,szokoly98,loveday2000,kochanek2001,cole2001,bolzonella2002,feulner2003,huang2003,pozzetti2003,kashikawa2003,saracco2006,caputi2006,cirasuolo2007,cirasuolo2010} - see also Table 5 in \citet{saracco2006} which we used as reference for the literature works."303 Using the rest-frame A-band data. we performed the same analysis as done for the rest-frame ./ and // bands. modeling the evolution of the Schechter parameters with redshift using Eq.," Using the rest-frame $K$ -band data, we performed the same analysis as done for the rest-frame $J$ and $H$ bands, modeling the evolution of the Schechter parameters with redshift using Eq."304 10 and L1I.., \ref{eq:fit_phi} and \ref{eq:sch_ms}.305 The best-fit values of the parameters obtained in modeling of the A'-band points are: Qj—3:8+0.1107 t 5 w=O1LLEO02 y=2.20.1 for the parameters of Eq. lO:," The best-fit values of the parameters obtained in modeling of the $K$ -band points are: $\theta_K=3.8 \pm 0.1 \times 10^{-3} $ $^{-1}$ $^{-3}$, $\gamma_K=-0.11 \pm 0.02$, $\beta_K=-2.2 \pm 0.1$ for the parameters of Eq. \ref{eq:fit_phi};"306gry=2.640402 =1103-46. gy=0.058E0.007 for Eg. lH," $\mu_K=-29.6\pm 0.4$ , $z^*_K=113\pm 46$, $\eta_K=0.058\pm 0.007$ for Eq. \ref{eq:sch_ms};"307zandog=1.12:0.16., and $\bar{\alpha}_K=-1.12 \pm 0.16$.308 The resulting curves are plotted in Fig., The resulting curves are plotted in Fig.309 |} as red dot-dashed curves. together with those already discussed for the rest-frame ./ band (black dashed curves).," \ref{fig:LF_K_comp} as red dot-dashed curves, together with those already discussed for the rest-frame $J$ band (black dashed curves)."310 The rest-frame {ν -band characteristic density. ój;. decreases by a factor of ~15 from z~0 to z~ 3.3. about twice as much than the redshift evolution of the rest-frame ./-band characteristic density. ©}.," The rest-frame $K$ -band characteristic density, $\phi_{\rm K}^*$, decreases by a factor of $\sim 15$ from $z\sim 0$ to $z\sim 3.3$ , about twice as much than the redshift evolution of the rest-frame $J$ -band characteristic density, $\phi_{\rm J}^*$."311 Specifically. the data in the rest-frame ./ band indicate an evolution with redshift broadly consistent to the rest-frame dy band out to 2~2.3. and a milder evolution at zz 2.," Specifically, the data in the rest-frame $J$ band indicate an evolution with redshift broadly consistent to the rest-frame $K$ band out to $z\sim2.3$, and a milder evolution at $z\gtrsim 2$ ."312 Quantitatively. while 03 decreases by a factor of ~2 from >~1.5 to z~ 3.3. Og decreases by a factor of ~5 over the same redshift interval. although these differences are significant only at the 2 o level.," Quantitatively, while $\phi_{\rm J}^*$ decreases by a factor of $\sim 2$ from $z\sim1.5$ to $z\sim3.3$ , $\phi_{\rm K}^*$ decreases by a factor of $\sim 5$ over the same redshift interval, although these differences are significant only at the 2 $\sigma$ level."313 Differences between the rest-frame ./ band and the rest-frame ἐν band are also found when comparing the evolution with redshift of the characteristic magnitudes AJ and AZ; (bottom panel of Fig. HD., Differences between the rest-frame $J$ band and the rest-frame $K$ band are also found when comparing the evolution with redshift of the characteristic magnitudes $M_{\rm K}^*$ and $M_{\rm J}^*$ (bottom panel of Fig. \ref{fig:LF_K_comp}) ).314 ΑςX1. similar evolutions with redshift of Adj. and Adj are found. with the characteristic magnitudes brightening by ~0.5 mag from 2~ Oto:~I.," At $z \lesssim 1$, similar evolutions with redshift of $M_{\rm K}^*$ and $M_{\rm J}^*$ are found, with the characteristic magnitudes brightening by $\sim 0.8$ mag from $z\sim0$ to $z\sim1$."315 However. for:21. AL; is monotonically decreasing. brightening by 0.5 mag in the range >0C1.5.3.3). whereas A7 shows a small dimming (if any) over the same redshift interval. after reaching its brightest value somewhere inthe redshift interval 1.5.«2 2.5.," However, for $z \gtrsim 1$, $M^*_K$ is monotonically decreasing, brightening by 0.5 mag in the range $z\in[1.5, 3.3]$, whereas $M^*_J$ shows a small dimming (if any) over the same redshift interval, after reaching its brightest value somewhere inthe redshift interval $1.5<z<2.5$ ."316 We note that. also in the case of 1. these differences are only marginally significant (within 2 7).," We note that, also in the case of $M^*$ , these differences are only marginally significant (within 2 $\sigma$ )."317 Figure 12. shows the comparison of the evolutions with redshift of the rest-frame A'- and -/-band LDs., Figure \ref{fig:LD_K_comp} shows the comparison of the evolutions with redshift of the rest-frame $K$ - and $J$ -band LDs.318 As the differences in theevolutions with redshift of O° and M between the Jand AC bandsgo in opposite directions. in the computation of the LDs these differences partly cancel out.," As the differences in theevolutions with redshift of $\phi^*$ and $M^*$ between the $J$and $K$ bandsgo in opposite directions, in the computation of the LDs these differences partly cancel out."319 As shown in Figure 12.. the evolution of the rest-frame A -band LD with redshift is qualitatively similar to," As shown in Figure \ref{fig:LD_K_comp}, , the evolution of the rest-frame $K$ -band LD with redshift is qualitatively similar to"320of turbulence in. Class O LI protostellar envelopes. by measuring the peak separation in a sample of protostars.,of turbulence in Class 0 I protostellar envelopes by measuring the peak separation in a sample of protostars.321 Furthermore. we interpret the variation in separations observed in terms of our recent radiative transfer moclel results.," Furthermore, we interpret the variation in separations observed in terms of our recent radiative transfer model results."322 In this model the velocity separation of the peaks is seen to be dominated by the relative level of turbulence in the infalling protostellar envelope., In this model the velocity separation of the peaks is seen to be dominated by the relative level of turbulence in the infalling protostellar envelope.323 The presence of non-thermal motions in molecular. cloud regions where stars are formed has been recognised for some time (e.g. Caselli Myers 1995)., The presence of non-thermal motions in molecular cloud regions where stars are formed has been recognised for some time (e.g. Caselli Myers 1995).324 These non-thermal motions are usually attributed to the presence of turbulence (c.g. Padoan Nordlund 2002)., These non-thermal motions are usually attributed to the presence of turbulence (e.g. Padoan Nordlund 2002).325 Measuring the exact. levels of turbulence in. molecular. clouds can be. complicated., Measuring the exact levels of turbulence in molecular clouds can be complicated.326 Llowever. the fact that turbulence plavs a significant role in the star formation process is now widely recognised (e.g. Elmeereen 2002 and references therein).," However, the fact that turbulence plays a significant role in the star formation process is now widely recognised (e.g. Elmegreen 2002 and references therein)."327 We have recently carried out detailed spectral modelling of protostellar infall candidates (Ward-Phompson Buckley 2001)., We have recently carried out detailed spectral modelling of protostellar infall candidates (Ward-Thompson Buckley 2001).328 This process uses a radiative transfer. A-iteration moclel based on the method ofStenholm (1977)., This process uses a radiative transfer $\Lambda$ -iteration model based on the method of Stenholm (1977).329 The method was refined by subsequent workers (Matthews 1986: Lleaton et al., The method was refined by subsequent workers (Matthews 1986; Heaton et al.330 1993: Buekley 1997)., 1993; Buckley 1997).331 Le solves the spectral line raciative transfer problem for the rotational transitions of linear molecules in a spherically symmetric model eloud., It solves the spectral line radiative transfer problem for the rotational transitions of linear molecules in a spherically symmetric model cloud.332 The racial profiles of infall velocity. temperature. density. tracer molecule abundance and micro-turbulent velocity dispersion may be specified (Ward-Thompson Buckley 2001).," The radial profiles of infall velocity, temperature, density, tracer molecule abundance and micro-turbulent velocity dispersion may be specified (Ward-Thompson Buckley 2001)."333 The method is begun by choosing an initial radiation Held in a more or less arbitrary manner., The method is begun by choosing an initial radiation field in a more or less arbitrary manner.334" From this. a false"" set of molecular energy. level populations are calculated."," From this, a `false' set of molecular energy level populations are calculated."335 Raclative transitions between these populations will generally produce a radiation field which departs from the initial field., Radiative transitions between these populations will generally produce a radiation field which departs from the initial field.336 Lf this radiation field is used to caleulate a new set of populations. and the procedure is repeated a sulliciently large. number of times. the radiation field and populations should eventually converge on a mutually consistent solution (for further details see Ward-Thompson Buckley 2001).," If this radiation field is used to calculate a new set of populations, and the procedure is repeated a sufficiently large number of times, the radiation field and populations should eventually converge on a mutually consistent solution (for further details see Ward-Thompson Buckley 2001)."337 The output spectra are convolved with a chosen beam size to match any given set. of observations., The output spectra are convolved with a chosen beam size to match any given set of observations.338 We have applied the method to | and €S spectral line observations of protostellar envelopes and. modelled: their infall parameters., We have applied the method to $^+$ and CS spectral line observations of protostellar envelopes and modelled their infall parameters.339 Figure 1 shows the predicted line profiles that would be observed. at the James Clerk Maxwell Telescope (JCMT) in the 23) and :4) molecular. line transitions to mateh some of the cata we show below., Figure 1 shows the predicted line profiles that would be observed at the James Clerk Maxwell Telescope (JCMT) in the $^+$ $\rightarrow$ 3) and $\rightarrow$ 4) molecular line transitions to match some of the data we show below.340 The beam convolution to match the Caltech Submillimeter Observatory (CSO) data also shown below does. not significantly alter the results., The beam convolution to match the Caltech Submillimeter Observatory (CSO) data also shown below does not significantly alter the results.341 The moclel assumes an inside-out collapse in which an expansion wave has reached a radius that we call the infall radius. outside of which the velocity is ZOLO.," The model assumes an inside-out collapse in which an expansion wave has reached a radius that we call the infall radius, outside of which the velocity is zero."342 We assume that a mass M. /2 has already aceretecl onto the central protostar. and a further AL. /2 of envelope eas is infalline towards it.," We assume that a mass $_{\odot}$ /2 has already accreted onto the central protostar, and a further $_{\odot}$ /2 of envelope gas is infalling towards it."343 We choose an cllective sound speed of erp=0.35kms," We choose an effective sound speed of $a_{\rm eff}=0.35\,{\rm km\, s}^{-1}$."344 We use model relations. for the radial velocity and. density. profiles consistent with the inside-out collapse scenario of pxr inside the infall radius and pxr7 outside the infall radius., We use model relations for the radial velocity and density profiles consistent with the inside-out collapse scenario of $\rho\propto r^{-3/2}$ inside the infall radius and $\rho\propto r^{-2}$ outside the infall radius.345 We truncate the density profile at an outer radius of 10000AU. which encloses a total mass of MM...," We truncate the density profile at an outer radius of AU, which encloses a total mass of $_{\odot}$."346 Ehe temperature profile in the optically thin part of the envelope is chosen to have a canonical. profile⋅ ulTxrUsb. c, The temperature profile in the optically thin part of the envelope is chosen to have a canonical profile $T\propto r^{-0.4}$.347qThe parameter normalisations. used in the radiative transfer modelling are given by Warel-Thompson Buckley (2001) and the molecular constants are taken from the catalogue of Povnter Pickett (1985)., The parameter normalisations used in the radiative transfer modelling are given by Ward-Thompson Buckley (2001) and the molecular constants are taken from the catalogue of Poynter Pickett (1985).348 Figure 1 shows how the line profiles depend on the magnitude of the turbulent velocity. dispersion. ej. when itis assumed to be uniform throughout the envelope.," Figure 1 shows how the line profiles depend on the magnitude of the turbulent velocity dispersion, $\sigma_{\rm tb}$, when it is assumed to be uniform throughout the envelope."349 As the turbulent velocity dispersion increases. the most apparent elfect on the line profile is to increase the velocity separation between the two peaks.," As the turbulent velocity dispersion increases, the most apparent effect on the line profile is to increase the velocity separation between the two peaks."350 Figure 1 shows the results for 9). and CS(J=5 4).," Figure 1 shows the results for $^+$ $\rightarrow$ 3), and $\rightarrow$ 4)."351 X similar result. is also seen in the +2) transition., A similar result is also seen in the $^+$ $\rightarrow$ 2) transition.352 The magnitude of the change in the line-shape observed in Figure | is totally dillerent to that caused by increasing the optical depth., The magnitude of the change in the line-shape observed in Figure 1 is totally different to that caused by increasing the optical depth.353 Myers et al. (, Myers et al. (3541996) explored the manner in which increasing the optical depth changed the line-shape,1996) explored the manner in which increasing the optical depth changed the line-shape355more abundant. smaller mass Blls may power quasars.,"more abundant, smaller mass BHs may power quasars."356 For the case with {αναμα=10' L. almost a quarter of sources are predicted. to be above z~6 at the lowest Hux level plotted.," For the case with $L_{\rm peak,min} =35710^9$ $_{\sun}$ almost a quarter of sources are predicted to be above $z \sim 6$ at the lowest flux level plotted."358 The fraction of sources expected above 2=4.6.8 for each of the models at the three Dux limits shown in Figure 5 is tabulated in Table 1.," The fraction of sources expected above $z = 4,6,8$ for each of the models at the three flux limits shown in Figure 5 is tabulated in Table 1."359 The Cosmic X-ray Dackground (CXRDB) ando dis unresolved. Component provides an important. consistency check for models of the number of faint sources., The Cosmic X-ray Background (CXRB) and its unresolved component provides an important consistency check for models of the number of faint sources.360 We may calculate the contribution of quasars in a redshift’ band. (2.2|dz) to the X-ray background. in an observed band VY by integrating over the QLE. where D; is the luminosity distance ancl the limits of integration are determined [rom the limiting sensitivity fuia.," We may calculate the contribution of quasars in a redshift band $(z,z+dz)$ to the X-ray background in an observed band $X$ by integrating over the QLF, where $D_L$ is the luminosity distance and the limits of integration are determined from the limiting sensitivity $f_{\rm361min}$."362 In Figures 7 and S we compare the total CARB Uux predicted. for the slow fading model. and the rapid. fading models with low and high Lysine to the measurement of the total CARB from ?..," In Figures 7 and 8 we compare the total CXRB flux predicted for the slow fading model, and the rapid fading models with low and high $L_{\rm peak,min}$ , to the measurement of the total CXRB from \citet{moretti2003}."363 This contribution is plotted as a function of the minimum. detectable Dux for sources with redshilts above z=0.01.2.4..6.8 and 10.," This contribution is plotted as a function of the minimum detectable flux for sources with redshifts above $z =3640.01,2,4,,6,8$ and $10$."365 We note that the resolved fraction is sensitive to uncertainties in the absolute value of the CARB., We note that the resolved fraction is sensitive to uncertainties in the absolute value of the CXRB.366 We restrict our anaIvsis of the resolved raction to energies below LO keV. where variations in the normalisation between experiments diller by ~10 per cent (sce.ge.7)..," We restrict our analysis of the resolved fraction to energies below 10 keV, where variations in the normalisation between experiments differ by $\sim 10$ per cent \citep[see, e.g.][]{moretti2003}."367 In the 210 keV band. we find. that all models are consistent with the total measured. €ARB.," In the $2-10$ keV band, we find that all models are consistent with the total measured CXRB."368" Our moclels xediet that ~7078 per cent of the total2 10 keV CARB is due to AGN with [luxes above the best current sensitivity evel in this band (~14.10.1"" ces)."," Our models predict that $\sim 70369-78$ per cent of the total $2-10$ keV CXRB is due to AGN with fluxes above the best current sensitivity level in this band $\sim 1.4\times37010^{-16}$ cgs)."371" ""his result is consistent with the ~SO per cent. resolved. fraction. measured. by. ? and ?..", This result is consistent with the $\sim 80$ per cent resolved fraction measured by \citet{worsley2005} and \citet{hickox2006}.372 Our models remain consistent Wwith the total CXIRD at lower Dux limits., Our models remain consistent with the total CXRB at lower flux limits.373 At a sensitivity of 3.10% CES - a sensitivity within reach of next generation instruments (sec Section 5.3) - the resolved fraction increases to NT per cent depending on the model., At a sensitivity of $3 \times 10^{-18}$ cgs - a sensitivity within reach of next generation instruments (see Section 5.3) - the resolved fraction increases to $\sim 87$ per cent depending on the model.374 Our models tjus still leave room. for the very hard. spectrum sources need to make up the CXILD at cnergics >S keV (7) and/or the population of star-forming ealaxies expected to contribute significantly at low Ilux levels (c.g.7).., Our models thus still leave room for the very hard spectrum sources need to make up the CXRB at energies $> 8$ keV \citep{worsley2005} and/or the population of star-forming galaxies expected to contribute significantly at low flux levels \citep[e.g.][]{bauer2004}. .375 We note that our caleulated resolved fractions also deperid on the analvtic fits we have used below >=2., We note that our calculated resolved fractions also depend on the analytic fits we have used below $z = 2$.376 Using the nxxe recent LDDE model from ? we obtain lower resolved fractions (62τὸ per cent due to sources above the current cletection level). consistent with the more stringent optical selection criteria for this sample.," Using the more recent LDDE model from \citet{silverman2007} we obtain lower resolved fractions $\sim 62 -75$ per cent due to sources above the current detection level), consistent with the more stringent optical selection criteria for this sample."377 1n the soft X-ray band (0.52 keV). the fraction of the total CXID flux eltle to sources above the current sensitivity level (~2.5«101° ces) in our models is again consistent with the SO90 per cent found. by ? and 2..," In the soft X-ray band $0.5 - 2$ keV), the fraction of the total CXRB flux due to sources above the current sensitivity level $\sim 2.5378\times 10^{-17}$ cgs) in our models is again consistent with the $80 -37990$ per cent found by \citet{worsley2005} and \citet{hickox2006}."380 However. at fainter flux levels the slow facing model overpredicts the total CXIUD. again rellecting the excess of faint sources at 2o2 compared to the observed. OLE.," However, at fainter flux levels the slow fading model overpredicts the total CXRB, again reflecting the excess of faint sources at $z \sim 2$ compared to the observed QLF."381 This contribution again depends on the faint end behaviour of the fits to the data that we have adopted. below z~2., This contribution again depends on the faint end behaviour of the fits to the data that we have adopted below $z \sim 2$.382 As mentioned. for the soft. N-rav yancl we have chosen to use the LDDI2 model [rom ? which is constructed to reproduce 90 of the total κο N-rav backeround when integrated out to z5.," As mentioned, for the soft X-ray band we have chosen to use the LDDE2 model from \citet{miyaji2001} which is constructed to reproduce $\sim 90$ of the total soft X-ray background when integrated out to $z \sim 5$ ."383 Alternate faint enc extrapolations may somewhat ease this excess., Alternate faint end extrapolations may somewhat ease this excess.384 Using the ? LDDE fit to the LE of tvpe-1 AGN below >=2 we Lind that he slow facing model saturates. but does not overpreclict. he soft X-ray background.," Using the \citet{hasinger2005}385 LDDE fit to the LF of type-1 AGN below $z=2$ we find that the slow fading model saturates, but does not overpredict, the soft X-ray background."386 However the LDDE fit to the soft X-ray tvpe-1 QLE only accounts for ~35 per cent of he soft band. CARB. rellecting the fact that the sample of tvpe-] ACN used in?) account for only around 30 per cent of sources at faint and bright Dux levels.," However the \citet{hasinger2005} LDDE fit to the soft X-ray type-1 QLF only accounts for $\sim 35$ per cent of the soft band CXRB, reflecting the fact that the sample of type-1 AGN used in \citet{hasinger2005} account for only around 30 per cent of sources at faint and bright flux levels."387 The resolvec fractions are naturally lower for the slow ancl rapid. facing models with Lyentsanin=lot? L. (chosen to reproduce the soft X-ray OLE at z~ 2). and with this choice the slow Lacling model remains consistent with the total CXBD.," The resolved fractions are naturally lower for the slow and rapid fading models with $L_{\rm peak,min} = 10^{12}$ $_{\sun}$ (chosen to reproduce the soft X-ray QLF at $z \sim 2$ ), and with this choice the slow fading model remains consistent with the total CXRB."388 Recently. (7) and ?/ have pushed the limit for the unresolved. background. further by taking into account the stacked emission. [rom galaxies. detected withST andIBAC.," Recently, \citep{worsley2005} and \citet{hickox2006} have pushed the limit for the unresolved background further by taking into account the stacked emission from galaxies detected with and."389 Indeed we find that if we integrate the Lux due to sourcesbelow the οιwrent detection level and compare this to the measurement of the unresolved component as derived by 7..the soft and hare X-ray components are both too large for the slow fading model.," Indeed we find that if we integrate the flux due to sources the current detection level and compare this to the measurement of the unresolved component as derived by \citet{hickox2006},the soft and hard X-ray components are both too large for the slow fading model."390 Aloctels like this for which sources with relatively flat spectra recover the entire unresolved CXRB in the soft and hard bands are likely to be in conllict with the overall nxasured shape of the CXNRB above 8 keV (e.g. TTT). ," Models like this for which sources with relatively flat spectra recover the entire unresolved CXRB in the soft and hard bands are likely to be in conflict with the overall measured shape of the CXRB above $8$ keV \citep[e.g.][]{worsley2005,comastri1995, gilli2007}. ."391Thisconsistency check argues further against theslow facing nxxlel as we have applied it. but wenote," Thisconsistency check argues further against theslow fading model as we have applied it, but wenote"392of the svstem response would manifest itself in the arrival time residuals of this remarkable pulsar.,of the system response would manifest itself in the arrival time residuals of this remarkable pulsar.393 The Parkes Observatory is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed. by CSLRO., The Parkes Observatory is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO.394 This research was supported by the Commonwealth. Scholarship and Fellowship Plan., This research was supported by the Commonwealth Scholarship and Fellowship Plan.395 E am grateful to Matthew: Britton and Simon Johnston. with whom I have shared many stimulating discussions on radio polarimetry.," I am grateful to Matthew Britton and Simon Johnston, with whom I have shared many stimulating discussions on radio polarimetry."396 Phanks also to Matthew Bailes and Stephen Ord. for assistance with observing and helpful comments on the text., Thanks also to Matthew Bailes and Stephen Ord for assistance with observing and helpful comments on the text.397 The imstirineutal frequency response matrix used in calibrating the data presented in this paper was paraeterized by The boost component may be solved most casily using the quatermion form of equation (12)). where |Z$.L| are the measured off-pulse Stokes parameters. producing The two rotations. aandRe(AWV).. may be determined by considering the equivalent three-dimeusional Enclidian rotations. aaud(A). of the input polarization vector.," The instrumental frequency response matrix used in calibrating the data presented in this paper was parameterized by The boost component may be solved most easily using the quaternion form of equation \ref{eqn:boost_soln}) ), where $[\bar{L}_0^\prime,\bar{\mbf{L}}^\prime]$ are the measured off-pulse Stokes parameters, producing The two rotations, and, may be determined by considering the equivalent three-dimensional Euclidian rotations, and, of the input polarization vector."398 Civen that the noise diodes iustalled in the receivers at the Parkes radio-telescope have a position augle nearly equal to.157.. the input Stokes parameters are |l.Που. where H=(0.1.0) (c£.," Given that the noise diodes installed in the receivers at the Parkes radio-telescope have a position angle nearly equal to, the input Stokes parameters are $[1,\bar{\mbf{H}}]C_0$, where $\bar{\mbf{H}}=(0,1,0)$ (cf."399 eq. 13]., eq. \ref{eqn:high_cal}] ]).400" Therefore. $5 audAW nay be found by solving where HisH. the normalized- polarization. vector after"" the observed Stokes] parameters have becu corrected forJ the boost."," Therefore, $\Phi_I$ and$\Delta\Psi$ may be found by solving where $\bar{\mbf{H}}^{\prime\prime}$ is the normalized polarization vector after the observed Stokes parameters have been corrected for the boost."401" It is given by where P, are the observed Stokes paramcters.", It is given by where $\bar{\bf{P}}_H^{\prime}$ are the observed Stokes parameters.402 Frou equation (A L)). Notice that |./|. Ty. and Cy cancel out in cach of equations CÀ3)) aud (AG)). obviating the need to solve for these paramctors at this stage.," From equation \ref{eqn:rotate_euclid}) ), Notice that $|J|^2$ , $T_0$, and $C_0$ cancel out in each of equations \ref{eqn:boost_solve}) ) and \ref{eqn:rotate_solve}) ), obviating the need to solve for these parameters at this stage."403 The vector compoucuts of the boost quaternion. (By.Bo.B4)=sinhJar. as well as $; aud AW. are plotted as a function of frequency in Figure 1..," The vector components of the boost quaternion, $(B_1,B_2,B_3)=\sinh\beta\,\mbf{\hat m}$, as well as $\Phi_I$ and $\Delta\Psi$, are plotted as a function of frequency in Figure \ref{fig:pcal}."404 Tt is assunued that the reader has some fanuliavity with the more common. one-dimensional form of cvclical convolution as it is performed in the frequency domain using the Fast Fourier Transform (FFT)(Presse£af1992. §13.1)..," It is assumed that the reader has some familiarity with the more common, one-dimensional form of cyclical convolution as it is performed in the frequency domain using the Fast Fourier Transform (FFT)\citep[ \S 13.1]{ptvf92}. ."405 In. the two-dimensional vector case. there are simply two wuique processes sampled at the same time interval. sav p(f;) aud qtf;).," In the two-dimensional vector case, there are simply two unique processes sampled at the same time interval, say $p(t_i)$ and $q(t_i)$."406 A one-dimensional. N-point. forward FFT is performed separately on cach of p aud 4. forming two spectra. Pv) aud Op). 0xEzIN.," A one-dimensional, $N$ -point, forward FFT is performed separately on each of $p$ and $q$, forming two spectra, $P(\nu_k)$ and $Q(\nu_k)$, $0\le k<N$."407 Corresponding elements from cach of the spectra are treated as the components of a column 2-vector. Ευ)=(Pony).Ορ). and iultiplil by the inverse of the frequeuey espouse matrix. forming ΕνανιΕν) (c£.," Corresponding elements from each of the spectra are treated as the components of a column 2-vector, $\mbf{E}(\nu_k)=(P(\nu_k),Q(\nu_k))$, and multiplied by the inverse of the frequency response matrix, forming $\mbf{E}^\prime(\nu_k)={\bf{J}}^{-1}(\nu_k)\mbf{E}(\nu_k)$ (cf."408 eq. [1]., eq. \ref{eqn:convolution_nu}] ]).409 The components of the result. P14.) aud Q(rj). ave once again treated as unique spectra. and separately transformed back iuto the time domain using the one-dimensional backward FET.," The components of the result, $P^\prime(\nu_k)$ and $Q^\prime(\nu_k)$ , are once again treated as unique spectra, and separately transformed back into the time domain using the one-dimensional backward FFT."410 Iu the case of the pulsar data preseuted iu this paper. p(f;) aud q(f;) are the signals from the two linear feeds in the receiver. and ο(1) consists of the instruneutal frequency respouse matrix. as determined in Appendix A.. multiplied by the dispersion kerucl. 1ο) (Taukins&Rickett 1975)..," In the case of the pulsar data presented in this paper, $p(t_i)$ and $q(t_i)$ are the signals from the two linear feeds in the receiver, and ${\bf{J}}(\nu_k)$ consists of the instrumental frequency response matrix, as determined in Appendix \ref{app:solve}, , multiplied by the dispersion kernel, $H(\nu_k)$ \citep{hr75}. ."411 Whensvuthesizine au Af-chamnel coherent filterbauls. £7(7;) is divided in frequency intoAY distinct dispersion kernels. cach tuned to the ceutre frequency.of the resulting filterbank chauucel.," Whensynthesizing an $M$ -channel coherent filterbank, $H(\nu_k)$ is divided in frequency into$M$ distinct dispersion kernels, each tuned to the centre frequencyof the resulting filterbank channel."412"luid clises X and X take the power-law form of xr"" with a common o exponent vet dilferent proportional coellicients. while the disc rotation curves e, and ey take the power-aw form of xr.. with a common : exponent vet dilferent »oportional coellicients.","fluid discs $\Sigma_0^s$ and $\Sigma_0^g$ take the power-law form of $\propto r^{-\alpha}$ with a common $\alpha$ exponent yet different proportional coefficients, while the disc rotation curves $v_s$ and $v_g$ take the power-law form of $\propto r^{-\beta}$ with a common $\beta$ exponent yet different proportional coefficients."413 The special case of 7=0 gives two lat rotation curves with οςzxey being allowed in general (Lou Shen 2003)., The special case of $\beta=0$ gives two flat rotation curves with $v_s\neq v_g$ being allowed in general (Lou Shen 2003).414 For the background equilibrium. we also ve πο=uj0. =ro. and jy=roy.," For the background equilibrium, we also have $u_0^s=u_0^g=0$, $j_0^s=rv_s$ and $j_0^g=rv_g$."415 By imposing hese conditions in equations (4) (particularly racial momentum eqn. (, By imposing these conditions in equations $-$ (4) [particularly radial momentum eqn. (41621. we obtain To compute the gravitational potential Oy arising [rom the equilibrium total surface mass density where ej and e$ are two constant coellicients. we simply take equation (115) in. Appendix A of Syer “Premaine (1996) and readily obtain where we introduce an auxiliary parameter function (Ixalnajs 1971).,"2)], we obtain To compute the gravitational potential $\phi_0$ arising from the equilibrium total surface mass density where $\sigma_0^s$ and $\sigma_0^g$ are two constant coefficients, we simply take equation $(A5)$ in Appendix A of Syer Tremaine (1996) and readily obtain where we introduce an auxiliary parameter function (Kalnajs 1971)."417 The requirement of radial force balance (7)) for all raclii (i.e. the scale-free condition) implies which gives the relationship among a. 37 and n. namely (Sver ‘Tremaine 1996).," The requirement of radial force balance \ref{relation0}) ) for all radii (i.e., the scale-free condition) implies which gives the relationship among $\alpha$, $\beta$ and $n$, namely (Syer Tremaine 1996)."418 It follows from »0 in barotropic equation of state (5)) for warm disces that 3 1/4., It follows from $n>0$ in barotropic equation of state \ref{poly}) ) for warm discs that $\beta >-1/4$ .419 For cold disces (Le. A O0). this inequality is UDDecessauv.," For cold discs (i.e., $K\rightarrow 0$ ), this inequality is unnecessary."420 As discussed. in Sver Tremaine (1996). mass distributions with 3z1/2 (a 2) would be unphysical because they contain infinite point masses.," As discussed in Syer Tremaine (1996), mass distributions with $\beta>1/2$ $\alpha>2$ ) would be unphysical because they contain infinite point masses."421 Furthermore. Poisson integral (4)) for óy converges lor 1<a2 and thus O<S1/2 for a system of axisvmmetry: the range of a (and thus of .3) is broader lor nonaxisvnunetric systems.," Furthermore, Poisson integral \ref{fish}) ) for $\phi_0$ converges for $1<\alpha<2$ and thus $0<\beta<1/2$ for a system of axisymmetry; the range of $\alpha$ (and thus of $\beta$ ) is broader for nonaxisymmetric systems."422 However. the total force arising from axisvmametric equilibrium surface mass densities. remains finite in an extended range of 2C(1/2.1/2) (0«&a< 2).," However, the total force arising from axisymmetric equilibrium surface mass densities remains finite in an extended range of $\beta\in(-1/2,1/2)$ $0<\alpha<2$ )."423 In summary. we therefore have —1/4«31/2 the left bound is implied bv ncO for warm. disces and the right bound. is required such that the central point mass will not cliverge (Sver ‘Tremaine 1996)].," In summary, we therefore have $-1/4<\beta<1/2$ [the left bound is implied by $n>0$ for warm discs and the right bound is required such that the central point mass will not diverge (Syer Tremaine 1996)]."424 For cold discs (Le. A= 0). the 2 range can be extended to 1/2«2< 1/2.," For cold discs (i.e., $K=0$ ), the $\beta$ range can be extended to $-1/2<\beta<1/2$ ."425 When 3=0 for Lat rotation curves. we have surface mass densities proportional to r+ corresponding to a composite svstent of two SIDs (Lou Shen 2003: Shen Lou 2003: Lou Zou 2004: Lou Wu 2004).," When $\beta=0$ for flat rotation curves, we have surface mass densities proportional to $r^{-1}$ corresponding to a composite system of two SIDs (Lou Shen 2003; Shen Lou 2003; Lou Zou 2004; Lou Wu 2004)."426" According to equilibrium condition (7)). we have where e2Yr. and a?2,r72ο23) with V and A being two constant coellicients."," According to equilibrium condition \ref{relation0}) ), we have where $v={\cal V}r^{-\beta}$ and $a^2=A^2r^{-2\beta}/(1+2\beta)$ with ${\cal V}$ and $A$ being two constant coefficients."427 By introducing V—AD to define a dimensionless parameter D. we obtain where 8—NU/N5 is the ratio of the surface mass density of the gaseous dise to that of the stellar disc.," By introducing ${\cal V}\equiv AD$ to define a dimensionless parameter $D$, we obtain where $\delta\equiv\Sigma_0^g/\Sigma_0^s$ is the ratio of the surface mass density of the gaseous disc to that of the stellar disc."428" We note that the value o£ 2.77, falls within (0.c) for c(.1/4.1/2) and is equal to 1 when 2=0 for the case of SIDs."," We note that the value of $2\beta{\cal P}_0$ falls within $(0,\infty)$ for $\beta\in(-1/4,1/2)$ and is equal to 1 when $\beta=0$ for the case of SIDs."429" An equivalent. version of requirement (13)) is where D, and D, are two dimensionless rotation parameters and y=.UAL=aq; is the square of the ratio of the velocity dispersion in the stellar dise to the sound speed in the gaseous disc.", An equivalent version of requirement \ref{ADeqn0}) ) is where $D_s$ and $D_g$ are two dimensionless rotation parameters and $\eta\equiv A_s^2/A_g^2=a_s^2/a_g^2$ is the square of the ratio of the velocity dispersion in the stellar disc to the sound speed in the gaseous disc.430 Note that sf is actually related to. the sound. speed @xr but scaled. by a factor (1|2:37 7] and the parameter £2 is essentially the ellective Mach. number for disc rotation., Note that $A$ is actually related to the sound speed $a\propto r^{-\beta}$ [but scaled by a factor $(1+2\beta)^{1/2}$ ] and the parameter $D$ is essentially the effective Mach number for disc rotation.431 We are going to express other equilibrium physical variables in terms of 24 ancl D., We are going to express other equilibrium physical variables in terms of $A$ and $D$.432 Besicles. we have also introduced two dimensionless »wanmeters to compare properties of the two clises.," Besides, we have also introduced two dimensionless parameters to compare properties of the two discs."433 The firs one is the surface mass density ratio 0=Ni/NG., The first one is the surface mass density ratio $\delta\equiv\Sigma_0^g/\Sigma_0^s$.434 The seconc xuwanmeter is the square of the ratio of the ellective sour speeds in two dises y=«EB , The second parameter is the square of the ratio of the effective sound speeds in two discs $\eta\equiv A_s^2/A_g^2$.435For disc galaxies. ratio ὃ can » either greater or less than 1 depending on whether the system is stellar matter dominant or gas material dominan (in the carly universe).," For disc galaxies, ratio $\delta$ can be either greater or less than $1$ depending on whether the system is stellar matter dominant or gas material dominant (in the early universe)."436 Without loss of geoneralitv. we may ake ypz loas the situation is svmumetric for n«1 anc vpically the stellar velocity dispersion. (mimicked. by a sound speed) in the stellar disc is greater than the sounc speed in the gaseous disc.," Without loss of generality, we may take $\eta>1$ as the situation is symmetric for $\eta<1$ and typically the stellar velocity dispersion (mimicked by a sound speed) in the stellar disc is greater than the sound speed in the gaseous disc."437 Phe special case of 5=1 shouk eive some [familiar results of a single disc except for an additional mode due to gravitational coupling. as we have alreacly learned. from the simpler case of two coupled SIDs (Lou Fan 1998: Lou Shen 2003).," The special case of $\eta=1$ should give some familiar results of a single disc except for an additional mode due to gravitational coupling, as we have already learned from the simpler case of two coupled SIDs (Lou Fan 1998; Lou Shen 2003)."438 The specific 2. component angular momenta (jj and Ji) and the sound speeds (ας and ἄν) of the two discs in an equilibrium state simply read Similarly. the dise angular rotation speed. Q—ήν and the epievclic frequeney &(20rylo20di]2 are expressed in ternis of two cimensionless parameters οἱ and Das and therefore wehave ολοαν=(1Nespn26£C20Q0) that simplifies the Linear perturbation equations displaved in the next subsection.," The specific $z-$ component angular momenta $j_0^s$ and $j_0^{g}$ ) and the sound speeds $a_s$ and $a_g$ ) of the two discs in an equilibrium state simply read Similarly, the disc angular rotation speed $\Omega\equiv j_0/r^2$ and the epicyclic frequency $\kappa\equiv [(2\Omega/r)d(r^2\Omega)/dr]^{1/2}$ are expressed in terms of two dimensionless parameters $A$ and $D$ as and therefore wehave $dj_0/dr=(1-\beta)v=r\kappa^2/(2\Omega)$ that simplifies the linear perturbation equations displayed in the next subsection."439 For the convenience of comparison ancl cross referencing. we note that our chosen notations for parameters have counterparts in those adopted by previous authors (Lemos. Walnajs Lvnden-Dell 1991: Sver," For the convenience of comparison and cross referencing, we note that our chosen notations for parameters have counterparts in those adopted by previous authors (Lemos, Kalnajs Lynden-Bell 1991; Syer"440than one magnitude larger than the average main sequence for the respective B—V value. and found that most stars previously identified as MM candidates are evolved stars and therefore not comparable to the Sun's Maunder minimum state.,"than one magnitude larger than the average main sequence for the respective $B-V$ value, and found that most stars previously identified as MM candidates are evolved stars and therefore not comparable to the Sun's Maunder minimum state."441 This led ? to the question if the minimum (Rip) level for main sequence stars to qualify as an MM candidate should be higher than —5.1. and also to consider flat-activity time profiles and UV- and X-ray data to identify MM candidates.," This led \cite{judgesaar2007} to the question if the minimum $\langle R^{'}_{HK}\rangle$ level for main sequence stars to qualify as an MM candidate should be higher than $-5.1$, and also to consider flat-activity time profiles and UV- and X-ray data to identify MM candidates."442 A recent study by ? suggests that minimum levels of Rug depend on stellar metallicity. with metal-poor stars from the examined sample having a higher minimal Rug:," A recent study by \cite{hallhenry2009} suggests that minimum levels of $R^{'}_{HK}$ depend on stellar metallicity, with metal-poor stars from the examined sample having a higher minimal $R^{'}_{HK}$."443 In this picture. 5] Peg as a metal-rich star still has low chromospherie activity as measured by Ring but this alone does not necessarily qualify it to be a Maunder minimum candidate.," In this picture, 51 Peg as a metal-rich star still has low chromospheric activity as measured by $R^{'}_{HK}$, but this alone does not necessarily qualify it to be a Maunder minimum candidate."444 However. as recent results show (??).. the absolute magnetic excess flux A7jy seems to be a more reliable indicator for stellar activity than Rig," However, as recent results show \citep{halllockwoodskiff2007,hallhenry2009}, the absolute magnetic excess flux $\Delta \mathcal{F}_{HK}$ seems to be a more reliable indicator for stellar activity than $R^{'}_{HK}$."445 In terms of this quantity. 5] Peg's activity level is even lower compared to the quiescent Sun than indicated by δι or the S index. supporting our interpretation of 5] Peg as being extremely inactive.," In terms of this quantity, 51 Peg's activity level is even lower compared to the quiescent Sun than indicated by $R^{'}_{HK}$ or the S index, supporting our interpretation of 51 Peg as being extremely inactive."446 The strongest line of evidence for 51 Peg being a Maunder minimum candidate is its flat activity. profile as seen over decades in the Mount Wilson program (?) and in observations at Lowell Observatory (?).. as well as the extremely low X-ray surface fluxes. which have not changed significantly since the 1992ROSAT observations.," The strongest line of evidence for 51 Peg being a Maunder minimum candidate is its flat activity profile as seen over decades in the Mount Wilson program \citep{baliunasdonahuesoon1995} and in observations at Lowell Observatory \citep{halllockwoodskiff2007}, as well as the extremely low X-ray surface fluxes, which have not changed significantly since the 1992 observations."447" That 51 Peg is a slow rotator with P,=30-40 d (??) fits the picture. making 51 Peg the first MM candidate star with a close-in giant planet."," That 51 Peg is a slow rotator with $P_{\star}\approx30-40$ d \citep{baliunassokoloff1996, mayorqueloz1995} fits the picture, making 51 Peg the first MM candidate star with a close-in giant planet."448 A statistical analysis of the X-ray luminosities of planet-bearing host stars has recently been conducted (?).., A statistical analysis of the X-ray luminosities of planet-bearing host stars has recently been conducted \citep{kashyapdrakesaar2008}.449 Its authors claim that stars with close-in giant planet. such as 5] Peg. are on average X-ray brighter by a factor of two compared to stars with far away planets.," Its authors claim that stars with close-in giant planet, such as 51 Peg, are on average X-ray brighter by a factor of two compared to stars with far away planets."450 Apparently. 51 Peg's overall activity is not enhanced by the presence of its Hot Jupiter.," Apparently, 51 Peg's overall activity is not enhanced by the presence of its Hot Jupiter."451 However. at a distance of order of 50 Κιν only a weak interaction between an inactive star and its planet might be expected.," However, at a distance of order of 50 $R_{Jup}$ only a weak interaction between an inactive star and its planet might be expected."452 We have detected X-ray emission from 51 Peg in a 55 ks observation with and 5 ks observations with ACIS-S and HRC-I each., We have detected X-ray emission from 51 Peg in a 55 ks observation with and 5 ks observations with ACIS-S and HRC-I each.453 The detection of 51 Peg with a low count rate in the pointing and the clear source signal in the much shorter observations can be explained by the different effective response of the detectors at low energies and 51 Peg having an extremely cool corona., The detection of 51 Peg with a low count rate in the pointing and the clear source signal in the much shorter observations can be explained by the different effective response of the detectors at low energies and 51 Peg having an extremely cool corona.454 Our main results are summarized as follows:, Our main results are summarized as follows:455shown in Figure 3. over half of the cluster lenses. in both the low- and medium-redshift MACS subsamples. produce multiple ares.,"shown in Figure 3, over half of the cluster lenses, in both the low- and medium-redshift MACS subsamples, produce multiple arcs."456 A similar result was found in the XBACs sample of HOS. in which 17 ares Qwith Zwz 8). in 7 out of the 10 clusters at zzz0.2. were detected.," A similar result was found in the XBACs sample of H05, in which 17 arcs (with $l/w \geq 8$ ), in 7 out of the 10 clusters at $z\approx 0.2$, were detected."457 In terms of the distribution of the angular separation of ares from the cluster centres. in the low-redshift MACS subsample. as shown in Fig.," In terms of the distribution of the angular separation of arcs from the cluster centres, in the low-redshift MACS subsample, as shown in Fig."458" 4. the lensed ares are uniformly distributed a separation angles of 10""—50""."," 4, the lensed arcs are uniformly distributed at separation angles of $10''-50''$."459 In the medium-redshift MACS sample. the ares are distributed slightly closer to the cluster centres. but both distributions are consistent. given the smal numbers per bin.," In the medium-redshift MACS sample, the arcs are distributed slightly closer to the cluster centres, but both distributions are consistent, given the small numbers per bin."460" There are no ares in this sample beyond 35"".", There are no arcs in this sample beyond $35''$.461 Since there is an uncertainty concerning the centre position. of the cluster 7715. as discussed below. we do no include its ares in the above analysis.," Since there is an uncertainty concerning the centre position of the cluster $+$ 7715, as discussed below, we do not include its arcs in the above analysis."462 In addition. each of the apparently merging are. pairs MACSJOS20.7. 1328 BI/B2 and 5320 BI/B2. are treated as one arc.," In addition, each of the apparently merging arc pairs $-$ 1328 B1/B2 and $+$ 5320 B1/B2, are treated as one arc."463 We also exclude the ares in 3745 from this analysis. since this cluster is highly disturbed (Ma. Ebeling. Barrett: 2009) and therefore its centre cannot be easily determined.," We also exclude the arcs in $+$ 3745 from this analysis, since this cluster is highly disturbed (Ma, Ebeling, Barrett; 2009) and therefore its centre cannot be easily determined."464 Only two ares are detected in the low-redshift RCS cluster subsample., Only two arcs are detected in the low-redshift RCS cluster subsample.465" While both ares have //w10. they are still relatively short 5”) compared to some of the arcs found in the MACS sample. (<which can be as long as 20""."," While both arcs have $l/w \geq 10$, they are still relatively short $<5''$ ) compared to some of the arcs found in the MACS sample, which can be as long as $20''$."466 In the medium-redshift optical subsample. 5 ares are found in 4 out of the 18 clusters.," In the medium-redshift optical subsample, $5$ arcs are found in $4$ out of the $18$ clusters."467 two of these ares (in one cluster. see Table 6) have been previously reported.," two of these arcs (in one cluster, see Table 6) have been previously reported."468 No ares are detected among the [6 clusters of the high-redshift (0.7xz 1) optical subsample.," No arcs are detected among the $16$ clusters of the high-redshift $0.7 \leq z469\leq 1$ ) optical subsample."470 As seen in Fig., As seen in Fig.471" 4 and Table 6. compared to the X-ray sample. the ares in the RCS sample occur at signiticantly smaller separations. generally «20"". and sometimes only 3.5"","," 4 and Table 6, compared to the X-ray sample, the arcs in the RCS sample occur at significantly smaller separations, generally $<20''$, and sometimes only $3-5''$."472" The only exception is 0201.4. whose arc appears 48"" from the cluster centre."," The only exception is $-$ 0201.4, whose arc appears $48''$ from the cluster centre."473 However. as seen in Figs.," However, as seen in Figs."474 | and 2. this are may actually be a small-separation image produced by the local mass concentration traced by the galaxies near the are.," 1 and 2, this arc may actually be a small-separation image produced by the local mass concentration traced by the galaxies near the arc."475 Since ares occur near critical curves. the small separations suggest signiticantly smaller Einstein radii. and hence masses. for the RCS clusters.," Since arcs occur near critical curves, the small separations suggest significantly smaller Einstein radii, and hence masses, for the RCS clusters."476! Table 7 summarizes the are statistics of our various cluster subsamples., Table $7$ summarizes the arc statistics of our various cluster subsamples.477 As noted above. only two ares are detectedin the RCS low-redshift subsample. compared to the 26 ares detected in the low-redshift MACS subsample.," As noted above, only two arcs are detectedin the RCS low-redshift subsample, compared to the $26$ arcs detected in the low-redshift MACS subsample."478 The are production efficiencies are. therefore. 0.11 MEN and [.13EH ares per cluster for the RCS and MACS subsamples. respectively. where we cite a 68% confidence interval assuming Poisson statistics.," The arc production efficiencies are, therefore, $0.11^{+0.15}_{-0.07}$ , and $1.13^{+0.27}_{-0.22}$ arcs per cluster for the RCS and MACS subsamples, respectively, where we cite a $68 \%$ confidence interval assuming Poisson statistics."479 In the medium-redshift bin. the MACS clusters are also more efficient lenses than the RCS clusters. with efficiencies of 1.334ü. and 0.284M ares per cluster. respectively.," In the medium-redshift bin, the MACS clusters are also more efficient lenses than the RCS clusters, with efficiencies of $1.33^{+0.42}_{-0.33}$, and $0.28^{+0.19}_{-0.12}$ arcs per cluster, respectively."480 With zero detected arcs. the high-redshift RCS sample has an are production efficiency of <0.24 ares per cluster (95% confidence). which is consistent with the RCS efficiencies at lower 5.," With zero detected arcs, the high-redshift RCS sample has an arc production efficiency of $< 0.24$ arcs per cluster $95 \%$ confidence), which is consistent with the RCS efficiencies at lower $z$ ."481 As the are occurrence frequency is consistent amongdifferent, As the arc occurrence frequency is consistent amongdifferent482the front is less than 2&1019 cii duriusc» the whole heatingc» phase.,the front is less than $2 \times 10^{10}$ cm during the whole heating phase.483 Fig.3 shows distributious of temperature. density. pressure and vertical component of velocity aloug the ceutral Z axis at various times of the decay phase. in the reference simulation.," \ref{fig:hydro2} shows distributions of temperature, density, pressure and vertical component of velocity along the central Z axis at various times of the decay phase, in the reference simulation."484 As the heating is switched off (t = 150 s). the eniperature suddenly decreases in the heating region: it jalves (from 12 to 6 AUN) in about 5 s at the ceuter of he heating release.," As the heating is switched off (t = 150 s), the temperature suddenly decreases in the heating region: it halves (from 12 to 6 MK) in about 5 s at the center of the heating release."485 The cause is the cooling by thermal conduction. particularly efficient because the density. of he hot plasma remains relatively low (<LO? ?).," The cause is the cooling by thermal conduction, particularly efficient because the density of the hot plasma remains relatively low $< 10^9$ $^{-3}$ )."486" The cooling frout propagates racially from tlic heating region. while the internal temperature gets lower aud lower,"," The cooling front propagates radially from the heating region, while the internal temperature gets lower and lower."487 The iot front produced by the heating impulse has instead weakened and practically disappeared when reaching the eher and relatively hotter (but verv thin) corona., The hot front produced by the heating impulse has instead weakened and practically disappeared when reaching the higher and relatively hotter (but very thin) corona.488 After one minute since the heating switch off (t z210 s). the cluperature along he Z axis overshoots below the initial cluperature of zx] AUS.," After one minute since the heating switch off (t $\approx 210$ s), the temperature along the $Z$ axis overshoots below the initial temperature of $\approx 1$ MK."489 At t = 300 s only a shell at s1010 cà from the systein origi. aud ~1019 cu thick. is still (slightly) hotter than the initial atinospliere. while he originally heated region is practically all cooler thau 1 MK.," At t = 300 s only a shell at $\sim49010^{10}$ cm from the system origin, and $\sim 10^{10}$ cm thick, is still (slightly) hotter than the initial atmosphere, while the originally heated region is practically all cooler than 1 MK."491 While such a fast cooling is occurring in the heated region. the evaporation frout continues to propagate upwards aud outwards.," While such a fast cooling is occurring in the heated region, the evaporation front continues to propagate upwards and outwards."492 The shell expands but maintaius more or less the same shape. becomine ecouetrically thicker aud thicker.," The shell expands but maintains more or less the same shape, becoming geometrically thicker and thicker."493 The head frout is at speed around 100. kiis. he back front is steadily slightly below 500 laus. The difference in speed causes the acciunaulation.," The head front is at speed around 400 km/s, the back front is steadily slightly below 800 km/s. The difference in speed causes the accumulation."494 The depression formed behind the head frout deepeus and expands coutinuously behind the evaporation front after the heating is switched off., The depression formed behind the head front deepens and expands continuously behind the evaporation front after the heating is switched off.495 At first it is coufiued to a rather small region behind the head frout. but it extends for ~1019 cm below the head frout at t = 2300 s. At this nue. the thickness of the head frout. with a density ~5 ines higher than the backerouud atinosphiere. is around 5«10? cu: the frout has reached a height Z~21010 cin above the stellar surface aud las a diameter(distance from the R=0 axis) of ~1.5«LO! cm.," At first it is confined to a rather small region behind the head front, but it extends for $\sim 10^{10}$ cm below the head front at t = 300 s. At this time, the thickness of the head front, with a density $\sim 5$ times higher than the background atmosphere, is around $5 \times 10^{9}$ cm; the front has reached a height $Z \sim 2 \times 10^{10}$ cm above the stellar surface and has a diameter(distance from the $R=0$ axis) of $\sim 1.5 \times 10^{10}$ cm."496 The deusity in the head frout reduces from ~3«105 5m {ο ~105 P as if moves away. while the region belind ess and less dense. the core of it decreasing below 7.," The density in the head front reduces from $\sim 3 \times 10^{8}$ $^{-3}$ to $\sim 10^{8}$ $^{-3}$ as it moves away, while the region behind gets less and less dense, the core of it decreasing below $10^7$ $^{-3}$."497 The pressure in that core. but even below it. iu a laver 1019 cm thick. is around 0.01 dyne cu7. 1/10 xinaller than the initial onc.," The pressure in that core, but even below it, in a layer $10^{10}$ cm thick, is around 0.01 dyne $^{-2}$, 1/10 smaller than the initial one."498 After t = 300 s the cooling of the ceutral regions aud the expansion of the evaporation shell progress with no new feature to τος., After t = 300 s the cooling of the central regions and the expansion of the evaporation shell progress with no new feature to remark.499 At t = δ00 s lo teniperature chhancement is visible auvwhere. while he evaporation frout is still well evident with the top above 3os1010 cni from the surface. a height where he density of the background corona is below 10* aud the tail all above 1tLU cn.," At t = 800 s no temperature enhancement is visible anywhere, while the evaporation front is still well evident with the top above $3 \times50010^{10}$ cm from the surface, a height where the density of the background corona is below $10^7$ $^{-3}$ , and the tail all above $10^{10}$ cm."501 The diameter of the shell is ~5«1079 ein," The diameter of the shell is $\sim 5 \times 10^{10}$ cm,"502 The diameter of the shell is ~5«1079 ein.," The diameter of the shell is $\sim 5 \times 10^{10}$ cm,"503lt is well known (see e.g. Matt 2002 for a review. and references therein) that most ACN are ‘obscured? in. Xravs.,"It is well known (see e.g. Matt 2002 for a review, and references therein) that most AGN are `obscured' in X--rays."504 Their observed. spectrum depends on the (hydrogen equivalent) column. density. Ny. of the absorber.," Their observed spectrum depends on the (hydrogen equivalent) column density, $N_{\rm H}$, of the absorber."505" I£ the column density exceeds the value. o,11.5 ?! 7. for which the Compton scattering optical depth. becomes equal to 1. the sources are called. ""Comptonthick’."," If the column density exceeds the value, $\sigma_T^{-1}$ $\times$ $^{-24}$ $^{-2}$, for which the Compton scattering optical depth becomes equal to 1, the sources are called `Compton–thick'."506" I the column clensity is smaller than oy"" but still in excess of the Galactic one. the source is called “Comptonthin’."," If the column density is smaller than $\sigma_T^{-1}$ but still in excess of the Galactic one, the source is called `Compton–thin'."507 Assuming the simple geometry depicted in Fig., Assuming the simple geometry depicted in Fig.508 1. (in which he absorbing matter ds assumed to form a &eometricallv hick torus. accoreing to the popular Unification models. see Antonucci 1993). he expected spectrum is shown in Fig. 2..," \ref{torus} (in which the absorbing matter is assumed to form a geometrically thick torus, according to the popular Unification models, see Antonucci 1993), the expected spectrum is shown in Fig. \ref{cthall}."509 In the Comptonhin case. the nuclear spectrum. (assumed or simplicity to be à power law with photon spectral index 2) can be «irectly observed above a lew keV. and a luorescent iron line. (with. EW~LlO eV for Ng 2107 em2 and 7100 eV for Ng 21075 em >see Fig. 3)).," In the Compton–thin case, the nuclear spectrum (assumed for simplicity to be a power law with photon spectral index 2) can be directly observed above a few keV, and a fluorescent iron line (with $\sim$ 10 eV for $_H$ $^{22}$ $^{-2}$ and $\sim$ 100 eV for $_H$ $^{23}$ $^{-2}$, see Fig. \ref{reflew}) ),"510 is produced., is produced.511 In the moderately Comptonthick case (Ng —4 1075 7) he spectrum below 10 keV. is dominated by the rellection continuum (plus a prominent iron line with EW~l keV: CGhisellini et al., In the moderately Compton–thick case $_H$ $4\times$ $^{24}$ $^{-2}$ ) the spectrum below 10 keV is dominated by the reflection continuum (plus a prominent iron line with $\sim$ 1 keV: Ghisellini et al.512 1994: Ixrolik et al., 1994; Krolik et al.513 1994: Matt ct al., 1994; Matt et al.514 1996) xoduced by the visible part of the inner wall of the torus itself. (see Fig. 1)).," 1996) produced by the visible part of the inner wall of the torus itself (see Fig. \ref{torus}) ),"515 while the nuclear radiation can he directly visible in transmission at higher energies., while the nuclear radiation can be directly visible in transmission at higher energies.516 This is. or instance. the case of two out of the three closest ACN. he Cireinus Galaxy (Matt. et al.," This is, for instance, the case of two out of the three closest AGN, the Circinus Galaxy (Matt et al."517.. 1999) and NGC 4945 (Iwasawa et al., 1999) and NGC 4945 (Iwasawa et al.518 1993: CGuainazzi et al., 1993; Guainazzi et al.519 2000)., 2000).520 For column densities exceeding NZz —107' 7. no nuclear radiation is ransmütted. and only the rellection. component is. visible (sce for instance NGC LOGS. Matt et al.," For column densities exceeding $_H$ $^{25}$ $^{-2}$, no nuclear radiation is transmitted, and only the reflection component is visible (see for instance NGC 1068, Matt et al."521 1997)., 1997).522 Le is worth noting that rellection from highly ionized matter can also »* present (ef., It is worth noting that reflection from highly ionized matter can also be present (cf.523 Matt ct al., Matt et al.524" 2000). ancl that the ionization state of the ""cold rellector may include also mildly ionized components (Bianchi et al."," 2000), and that the ionization state of the “cold"" reflector may include also mildly ionized components (Bianchi et al."525 2001)., 2001).526 However. for simplicity we will discuss cold rellectors only.," However, for simplicity we will discuss cold reflectors only."527 Also the spectrum rellected by the torus depends on its column density., Also the spectrum reflected by the torus depends on its column density.528 “Phe iron line EW (caleulated with respect to both the reflection continuum and the total one). is shown in Fig.," The iron line EW (calculated with respect to both the reflection continuum and the total one), is shown in Fig."529 3. for a torus seen faceon as a function of the Ny in the equatorial plane., \ref{reflew} for a torus seen face–on as a function of the $N_{\rm H}$ in the equatorial plane.530 In Fig., In Fig.531 4. the reflection spectrum is shown., \ref{refl} the reflection spectrum is shown.532 For Comptonthick material. the spectrum is wellknown (e.g. George Fabian 1991: Matt et al.," For Compton–thick material, the spectrum is well--known (e.g. George Fabian 1991; Matt et al."533 1991) while for Comptonthin matter it is very dilferent in shape and. overall. less prominent. (," 1991) while for Compton–thin matter it is very different in shape and, overall, less prominent. ("534Both figures are based on Monte Carlo simulations: see Ghisellini et al.,Both figures are based on Monte Carlo simulations; see Ghisellini et al.535 1994. for details on the simulation codo.), 1994 for details on the simulation code.)536 A rellectiondominated spectrum. is. usually assumed as evidence of Comptonthick absorption. expecially when using instruments working up to 10 keV. and therefore unable to detect the primary emission through mocerately thick absorbers.," A reflection–dominated spectrum is usually assumed as evidence of Compton–thick absorption, expecially when using instruments working up to $\sim$ 10 keV, and therefore unable to detect the primary emission through moderately thick absorbers."537 However. such a spectrum may occur not," However, such a spectrum may occur not"538simulations to a satellite halo.,simulations to a satellite halo.539" Therefore. the observed 10?A, galaxies could be in the same precarious position as our 10!A. galaxies."," Therefore, the observed $10^{9} M_{\odot}$ galaxies could be in the same precarious position as our $10^{10} M_{\odot}$ galaxies."540" If such a wide range of luminosities in the Milky Wav satellites can be produced by similar initial mass galaxies undergoing different histories. ibis possible that the sensitivity of our. 10!A, reflects the sensitivity of real galaxies of similar mass."," If such a wide range of luminosities in the Milky Way satellites can be produced by similar initial mass galaxies undergoing different histories, it is possible that the sensitivity of our $10^{10} M_{\odot}$ reflects the sensitivity of real galaxies of similar mass."541 Our studies demonstrates that slightly different amounts of feedback and ease of mass loss can completely change the structure and SEIL of this mass of galaxy., Our studies demonstrates that slightly different amounts of feedback and ease of mass loss can completely change the structure and SFH of this mass of galaxy.542 While in this study. those differences were the result of changes to resolution. these could also be caused by differing merger and gas accretion histories.," While in this study, those differences were the result of changes to resolution, these could also be caused by differing merger and gas accretion histories."543 One question when examining (hese results is how universal the requirements for convergence are., One question when examining these results is how universal the requirements for convergence are.544 In particular. will the same resolution be necessary in galaxies created [from clilferent initial conditions. galaxies using different star formation parameters. ancl galaxies that are evolved with different feedback recipes?," In particular, will the same resolution be necessary in galaxies created from different initial conditions, galaxies using different star formation parameters, and galaxies that are evolved with different feedback recipes?"545 Similar mass resolution was recquired for convergence ol the total amount of SF in cosmological runs ofMilkv Wav mass galaxies (??).. with slightly different [eedback energies ancl SF effidencies. implving that the resolution necessary [or convergence is mostly independent of the initial conditions and of small changes in (hose two SF parameters.," Similar mass resolution was required for convergence of the total amount of SF in cosmological runs of Milky Way mass galaxies \citep{Brooks07, Governato07}, with slightly different feedback energies and SF efficiencies, implying that the resolution necessary for convergence is mostly independent of the initial conditions and of small changes in those two SF parameters."546 Feedback regulated SF tends (o reach an equilibrium wilh increased SF efficiency resulting in stronger feedback which then hinders the formation of more stars., Feedback regulated SF tends to reach an equilibrium with increased SF efficiency resulting in stronger feedback which then hinders the formation of more stars.547 Based on the relative insensilivily (o these parameters. we can assume that similar mass resolution would be necessary even with different values for these parameters.," Based on the relative insensitivity to these parameters, we can assume that similar mass resolution would be necessary even with different values for these parameters."548 The minimum density for SE. jj; Is the single parameter one would expect to be sivongly linked to resolution.," The minimum density for SF, $\eta_{min}$, is the single parameter one would expect to be strongly linked to resolution."549 As lower mass and spatial resolution results in less high densitv gas. increasing Ymin Vequires resolving the structure of the ISM to a greater degree (?)..," As lower mass and spatial resolution results in less high density gas, increasing $\eta_{min}$ requires resolving the structure of the ISM to a greater degree \citep{Governato10}."550 Simulations with high values of tii). therefore. should need greater resolution for convergence.," Simulations with high values of $\eta_{min}$, therefore, should need greater resolution for convergence."551" A more complete discussion of the relationship between effidencey. 75,5, and resolution may be found in ?.."," A more complete discussion of the relationship between efficiency, $\eta_{min}$ and resolution may be found in \citet{Saitoh08}."552 A more difficult issue is the robustness of our results across different feedback recipes., A more difficult issue is the robustness of our results across different feedback recipes.553 Although most low-resolution SPI simulations tend to have depressed amounts of SF caused bv the presence of a smooth. thick gas disk. (he actual mass resolution necessary [or convergence appears to be highly dependent on the feedback recipe.," Although most low-resolution SPH simulations tend to have depressed amounts of SF caused by the presence of a smooth, thick gas disk, the actual mass resolution necessary for convergence appears to be highly dependent on the feedback recipe."554 For example. in the ? recipe used in GADGET individual gas particles represent a multi-phase ISAT and some of the energy from feedback is transferred (o selected nearby gas. particles in the form of kicks to (heir velocities.," For example, in the \citet{SpringelANDHernquist03a} recipe used in GADGET individual gas particles represent a multi-phase ISM and some of the energy from feedback is transferred to selected nearby gas particles in the form of kicks to their velocities."555 As seen in Figure 12 of ?.. (his approach has the advantage of being relatively insensitive lo mass resolution.," As seen in Figure 12 of \citet{SpringelANDHernquist03a}, this approach has the advantage of being relatively insensitive to mass resolution."556 By imposing an equation of state upon the gas particles. sell-regulation of SF is assumed: by allowing sub-grid multi-phases of the ISAT within gas particles. dillerent phases of the ISM need not be resolved.," By imposing an equation of state upon the gas particles, self-regulation of SF is assumed; by allowing sub-grid multi-phases of the ISM within gas particles, different phases of the ISM need not be resolved."557 The cost of these advantages. however. is ease in describing non-equilibrium feedback configurations.," The cost of these advantages, however, is ease in describing non-equilibrium feedback configurations."558 For SF to be shut olf or for superbubbles to be formed. a model for galactic winds must be assumed.," For SF to be shut off or for superbubbles to be formed, a model for galactic winds must be assumed."559 One approach when modeling galactic winds is to temporarily decouple the winds hvdrodsnamically from, One approach when modeling galactic winds is to temporarily decouple the winds hydrodynamically from560set m=3.,set $m=3$.561 The width of the filter. Le. np—|lis determined with the approach of ROL: np is set to be equal to the number of data points corresponding to a timescale 77 time spanned by the brightest 1004 of the total counts above the background (for details see ROT).," The width of the filter, i.e. $n_{\rm P}\equiv n_{\rm L} + n_{\rm R}+ 1$, is determined with the approach of R01: $n_{\rm P}$ is set to be equal to the number of data points corresponding to a timescale $T_f$ --the time spanned by the brightest $100f\%$ of the total counts above the background (for details see R01)."562 Ht turns out that f—0.5 most suits our purpose (rather than the f.=0.45 used by ROL and C05: see Section 5).," It turns out that $f=0.5$ most suits our purpose (rather than the $f=5630.45$ used by R01 and G05; see Section 5)."564 So. throughout the paper we use np determined by Zi>.," So, throughout the paper we use $n_{\rm P}$ determined by $T_{0.5}$."565 We then define np=int(np1)2]. and l.," We then define $n_{\rm L}={\rm int} [(n_{\rm P}-1)/2]$, and $n_{\rm R} = 566n_{\rm P}-n_{\rm L}-1$ ."567 l£ np ds odd. we have ng= np. Lo. the filter is svmametric about the point to smooth.," If $n_{\rm P}$ is odd, we have $n_{\rm R}=n_{\rm L}$ , i.e. the filter is symmetric about the point to smooth."568" IH np is even. we have pp=n,| the filter is asvmmoetric."," If $n_{\rm P}$ is even, we have $n_{\rm R}=n_{\rm L}+1$ , the filter is asymmetric."569 In this case. we smooth the lighteurve twice: first we use the ni and np defined above. then we switch py and ap.," In this case, we smooth the lightcurve twice: first we use the $n_{\rm L}$ and $n_{\rm R}$ defined above, then we switch $n_{\rm L}$ and $n_{\rm R}$."570 The results are then averaged., The results are then averaged.571 Suppose we have obtained a reference. lightcurve by applving the Savitzky-Colay filter to the raw lighteurve., Suppose we have obtained a reference lightcurve by applying the Savitzky-Golay filter to the raw lightcurve.572 Let us denote the count of the raw data in the ;-th time bin bv € 5. the count given by the reference lishteurve by Y;.," Let us denote the count of the raw data in the $i$ -th time bin by $C_i$ , the count given by the reference lightcurve by $Y_i$."573 The total squared. deviation of raw lighteurve from the reference lightcurve is then authebovieCSY. where Nu is the total number of bins to summed.," The total squared deviation of the raw lightcurve from the reference lightcurve is then $\sum_{i=1}^{N_{\rm bin}} \left(C_i -Y_i\right)^2$, where $N_{\rm 574bin}$ is the total number of bins to be summed."575 We obtain the intrinsic squareddeviation by subtracting the Poisson noise Npsseon where Wooopps(aym1) is à statistical weight accounting for the fact that among the mp cata points only npom larestatistically independent., We obtain the intrinsic squareddeviation by subtracting the Poisson noise $N_{\rm Poisson}$ where $W \equiv n_{\rm P}/\left(n_{\rm P}-m-1\right)$ is a statistical weight accounting for the fact that among the $n_{\rm P}$ data points only $n_{\rm P}-m-1$ are statistically independent.576 Phe inclusion of V. allows us to apply the variability definition to any lighteurve with npcom|1.," The inclusion of $W$ allows us to apply the variability definition to any lightcurve with $n_{\rm P}577>m+1$."578 The summation in equation. (1)) is from time fy (corresponding to /= 1) to time /» (corresponding to {εξ Nu). enclosing a major part of the lighteurve.," The summation in equation \ref{dc2}) ) is from time $t_1$ (corresponding to $i=1$ ) to time $t_2$ (corresponding to $i=N_{\rm bin}$ ), enclosing a major part of the lightcurve."579 Following FROO and OI we define ἐν to be the start of Poy. fo to be the end of Zou. where Zou is the time during which the cumulative counts of the CRB increase [rom to above background (Ixouveliotouetal.," Following FR00 and R01, we define $t_1$ to be the start of $T_{90}$, $t_2$ to be the end of $T_{90}$, where $T_{90}$ is the time during which the cumulative counts of the GRB increase from to above background \citep{kou93}."5801993) The Poisson noise is calculated by where Ci) is the background. the factor £ is the ratio of the background. Uuetuation to the Poisson noise of the background (given by the reduced x7 of the background fit).," The Poisson noise is calculated by where $C_{{\rm bg},i}$ is the background, the factor $\xi$ is the ratio of the background fluctuation to the Poisson noise of the background (given by the reduced $\chi^2$ of the background fit)."581 For GRBs detected by wwe found that £ is often significantly. larger than unity. indicating that the background: Ductuation is quite non-Poissonian.," For GRBs detected by we found that $\xi$ is often significantly larger than unity, indicating that the background fluctuation is quite non-Poissonian."582 Thevariability of the lehteurve is defined by the normalized. squared. deviation., The of the lightcurve is defined by the normalized squared deviation.583 We find that the following definition. leads to the tightest correlation between. the variability and the peak luminosity. where ACT/(Niin1) is the average of the squared deviation. ημων is the net peak count (ic.. the background is subtracted).," We find that the following definition leads to the tightest correlation between the variability and the peak luminosity where $\Delta C^2/\left(N_{\rm bin}-1\right)$ is the average of the squared deviation, $C_{\rm max}$ is the net peak count (i.e., the background is subtracted)."584 Our variability is defined in the observer's frame. so that the information of GRB redshift is not needed.," Our variability is defined in the observer's frame, so that the information of GRB redshift is not needed."585 This not only makes the computation of variability simple. but also eliminates an uncertainty arising [rom the assumption about the dependence of lighteurve variability on photon οποιον.," This not only makes the computation of variability simple, but also eliminates an uncertainty arising from the assumption about the dependence of lightcurve variability on photon energy."586 The ellect of GRB redshift was considered by ROL and FROO who defined their variabilities in the GRB frame. but the dependence of variability on redshift turned out to be verv weak.," The effect of GRB redshift was considered by R01 and FR00 who defined their variabilities in the GRB frame, but the dependence of variability on redshift turned out to be very weak."587 As we applied our smoothing procedure to the GRBs in the sample described in the next section. we found that the tightest correlation between the variability and the peak luminosity is obtained if we iteratively apply the Savitzky-Colay filter Nie times. where Ni is the integer closest to foofly (Lo. Nite: is roughly the number of moving windows contained in Loy).," As we applied our smoothing procedure to the GRBs in the sample described in the next section, we found that the tightest correlation between the variability and the peak luminosity is obtained if we iteratively apply the Savitzky-Golay filter $N_{\rm iter}$ times, where $N_{\rm iter}$ is the integer closest to $T_{90}/T_f$ (i.e., $N_{\rm iter}$ is roughly the number of moving windows contained in $T_{90}$ )."588 lo summary. our definition of variability cillers fron that. of FROO and ROL in the following aspects: (1) Our variability. is defined in the observers frame. while the variabilities of FROO and. ROL are defined. in the CIltD's frame. (," In summary, our definition of variability differs from that of FR00 and R01 in the following aspects: (1) Our variability is defined in the observer's frame, while the variabilities of FR00 and R01 are defined in the GRB's frame. ("5892) We normalize the average of the squared deviation by the squared. peak count (the same as FROO). while Rol normalize the total squared deviation by the sum of squared counts. (,"2) We normalize the average of the squared deviation by the squared peak count (the same as FR00), while R01 normalize the total squared deviation by the sum of squared counts. ("5903) FROO and ROL use a linear box-car filter. while we use a nonlinear Savitzky-Golay filter.,"3) FR00 and R01 use a linear box-car filter, while we use a nonlinear Savitzky-Golay filter."591 Our GIU sample contains 19 CRBs from the sample in (100 and 6 more GRBs detected bv aandσ," Our GRB sample contains 19 GRBs from the sample in G05, and 6 more GRBs detected by and."592ι So. the total number of GRBs in our sample is 25.," So, the total number of GRBs in our sample is 25."593" They. are listed in Table 1.. with measured redshift. calculated isotropic-cquivalent peak luminosity. calculated variability. and the number of iterations in applying theSavitzky-Golay filter,"," They are listed in Table \ref{grb}, with measured redshift, calculated isotropic-equivalent peak luminosity, calculated variability, and the number of iterations in applying the Savitzky-Golay filter."594 We have chosen to use the GRBs with data available publicly. which include GRBs detected DATSE/CGRO.HETE-2.. and ‘To obtain a reliable calculation of variability. we have/ only selected €{Bs with more than of total counts above he 3-0 of background.," We have chosen to use the GRBs with data available publicly, which include GRBs detected by, and To obtain a reliable calculation of variability, we have only selected GRBs with more than of total counts above the $\sigma$ of background."595 As a result. those CltDs with too ow signal-to-noise ratios are not M Our opes," As a result, those GRBs with too low signal-to-noise ratios are not included in our sample."596" The 19 GRBs from iare: 0012197050 n""71214. ""980425""m 980103. 990123. 990506.»""i990510.5 y. 151. 0124. 020813. 030325. 0329.5 041006. 050401. 050505. 150525. and 050603."," The 19 GRBs from G05 are: 970508, 971214, 980425, 980703, 990123, 990506, 990510, 991216, 000131, 010921, 020124, 020813, 030328, 030329, 041006, 050401, 050505, 050525, and 050603."597 Their peak Iuminosities are taken from he same paper., Their peak luminosities are taken from the same paper.598 The rest 13 GRBs in (105 are not included in our sample for various reasons: either their data are not xibliely available(noticeably the7 GRBs detected by but not by BAVSE or HETE-2)). or their cata are incomplete or havetoo lowsignal-to-noise ratios.," The rest 13 GRBs in G05 are not included in our sample for various reasons: either their data are not publicly available (noticeably the 7 GRBs detected by but not by BATSE or ), or their data are incomplete or havetoo lowsignal-to-noise ratios."599 Although 50315 ancl 050319in G05 were detected by Suwiff.. heir data were not available to us since as this paper was written the archive of oonlv contained data taken after 1 M05.," Although 050315 and 050319in G05 were detected by , their data were not available to us since as this paper was written the archive of only contained data taken after 1 April 2005."600 The 6 newly added GRBs are030115a. 030528. 050408," The 6 newly added GRBs are 030115a, 030528, 050408"601data Forbesetal. 2001: Larsenet.al. 2003). and IR. imaging (Ixissloer-Patig.Brodic.&Alinniti 2002: Puziaetal. 2002) have indicated. the presence of voung GC's in apparently otherwise unclisturbed elliptical galaxies. suggesting complex formation histories for at least a subset of ellipticals.,"data \citeANP{Forbes01} 2001; \citeANP{Larsen03} 2003) and IR imaging \citeANP{KisslerPatig02}602 2002; \citeANP{Puzia02} 2002) have indicated the presence of young GCs in apparently otherwise undisturbed elliptical galaxies, suggesting complex formation histories for at least a subset of ellipticals."603 The situation for disk galaxies is even less well known., The situation for disk galaxies is even less well known.604" Larsen (2002) presented: a spectroscopic study of a small sample of high S/N Sombrero galaxy (ALLOL) GC's, and found that the clusters in this relatively luminous (Mg = 21.8) Sa spiral appear old. ancl coeval. similar to the Alilky Way cluster system."," Larsen (2002) presented a spectroscopic study of a small sample of high S/N Sombrero galaxy (M104) GCs, and found that the clusters in this relatively luminous $_B$ = –21.8) Sa spiral appear old and coeval, similar to the Milky Way cluster system."605 ποσο authors found. alpha-to-iron ratios for the clusters of o /EFe] ~ |04. typical of luminous galaxy spheroids Frageretal. 1998).," These authors found alpha-to-iron ratios for the clusters of $\alpha$ /Fe] $\sim$ +0.4, typical of luminous galaxy spheroids \citeANP{Trager98} 1998)."606 ltecentlv. Ixuntschneretal. (2002) have obtained high-quality spectra for 17. GC's in the nearby (~ 10. Alpe) lenticular galaxy NGC 3115.," Recently, \citeANP{Kuntschner02} (2002) have obtained high-quality spectra for 17 GCs in the nearby $\sim$ 10 Mpc) lenticular galaxy NGC 3115."607 Similar to the Sombrero GC's. the GCs in NGC 3115. generally. appear old. although interestingly. Wuntschneretal. (2002) were able to demonstrate a spread. in a Fe] ratios amongst both the metal-rich and. metal-poor GCs. indicative. of multiple phases of GC formation.," Similar to the Sombrero GCs, the GCs in NGC 3115 generally appear old, although interestingly, \citeANP{Kuntschner02} (2002) were able to demonstrate a spread in $\alpha$ /Fe] ratios amongst both the metal-rich and metal-poor GCs, indicative of multiple phases of GC formation."608 These latter results are particularly intriguing. since we know that the Milky Way GCs are old (1.0. 2 S Civr. Salaris 2002) and generally exhibit non-solar a Le] ratios (Carney&Larris 2001).," These latter results are particularly intriguing, since we know that the Milky Way GCs are old (i.e. $>$ 8 Gyr, \citeANP{Salaris02} 2002) and generally exhibit non-solar $\alpha$ /Fe] ratios \citeANP{Harris01} 2001)."609 Clearly. few firm conclusions can be drawn from such a small ancl restricted sample. and more information is required. with regards to late-tvpe galaxies.," Clearly few firm conclusions can be drawn from such a small and restricted sample, and more information is required with regards to late-type galaxies."610 NGC 524 is an SA(rs)O galaxy. dominating the small NGC 524 group some 28.2 Ape distant. (deVaucouleursetal.," NGC 524 is an SA(rs)0 galaxy, dominating the small NGC 524 group some 28.2 Mpc distant \cite{RC3}."611 1991). Its GC system was first studied in any detail by Harris&Llanes (1985). who identified a rich. and spatially extended system.," Its GC system was first studied in any detail by \citeANP{Harris85} (1985), who identified a rich, and spatially extended system."612 In fact it possesses one of the richest GC systems known for an SO galaxy. with 4430 +4 950 CC's (Ilarris1991).," In fact it possesses one of the richest GC systems known for an S0 galaxy, with 4430 $\pm$ 950 GCs \cite{Harris91}."613. More recently. the GC svstem of NGC 524 as been studied with ΛΕΡΟΣ by Larsenet.al. (2001).," More recently, the GC system of NGC 524 has been studied with /WFPC2 by \citeANP{Larsen01} (2001)."614 From two pointings they identified a total of 617 GCs to a magnitude limit of. V— 26., From two pointings they identified a total of 617 GCs to a magnitude limit of $\V \sim$ 26.615 Emploving the IXMM est (Ashman.Bird.&Zepf1994). these authors determined he GC colour distribution to be bimodal with peaks at UV [2098 and V1 — 1.19 in the ratio ~ 2:1., Employing the KMM test \cite{Ashman94} these authors determined the GC colour distribution to be bimodal with peaks at $V-I$ = 0.98 and $V-I$ = 1.19 in the ratio $\sim$ 2:1.616 Using he colour-metallicity relation of Ixissler-Patigetal. (1998). hese peaks correspond to sub-populations with Fe/ll] — l.3and 0.6.," Using the colour-metallicity relation of \citeANP{KisslerPatig98} (1998), these peaks correspond to sub-populations with [Fe/H] $\sim$ –1.3 and –0.6."617 In this paper. we present an analysis of the broad-band imaging and spectroscopy for CC candidates: associated with this galaxy. the first such study to spectroscopically investigate the GC system of NGC 524.," In this paper, we present an analysis of the broad-band imaging and spectroscopy for GC candidates associated with this galaxy, the first such study to spectroscopically investigate the GC system of NGC 524."618 This paper is ordered in the following wav: in & 2 we discuss the data acquisition ancl reduction. procedures., This paper is ordered in the following way: in $\S$ \ref{Observations} we discuss the data acquisition and reduction procedures.619 Next. in 8 3.. we derive. metallicities [rom our integrated spectra. and. compare linc-streneth indices of the clusters to stellar population models.," Next, in $\S$ \ref{Indices}, we derive metallicities from our integrated spectra, and compare line-strength indices of the clusters to stellar population models."620 In § 4. we then investigate the kinematical properties of the cluster. system and sub-populations. and derive. dynamical mass estimates for NGC 524.," In $\S$ \ref{Radial} we then investigate the kinematical properties of the cluster system and sub-populations, and derive dynamical mass estimates for NGC 524."621 Finally. we present a summary ancl our conclusions in 5 5..," Finally, we present a summary and our conclusions in $\S$ \ref{Conclusions}."622 Broadband imaging of NGC 524 in the V. 2 and { filters was obtained at the Week-b telescope in. 1996. September Sth using the Low Resolution Imaging Spectrometer (LIUS: Okeetal. 1995).," Broad–band imaging of NGC 524 in the $\V$, $\R$ and $\I$ filters was obtained at the Keck-I telescope in 1996, September 8th using the Low Resolution Imaging Spectrometer (LRIS; \citeANP{Oke95} 1995)."623 Ehe LRIS instrument. equipped with a TEI. 2048 CCD. is mounted on the C'assegrain focus ooviding a 0.215arescepixel.| imaging scale and a 67' 1ο]ofview.," The LRIS instrument, equipped with a TEK $2048 \times 2048$ CCD, is mounted on the Cassegrain focus providing a $0.215\,\mathrm{arcsec\,pixel^{-1}}$ imaging scale and a $6^{\prime}\times7^{\prime}$ field–of–view."624 The total exposure times were 630 secs in. |. 330 secs in # and 300 secs in {.," The total exposure times were 630 secs in $\V$, 330 secs in $\R$ and 300 secs in $\I$."625 Secing conditions were good. with a median of  0.6 aresec.," Seeing conditions were good, with a median of $\sim$ 0.6 arcsec."626 TFhese cata were reduced ollowing standard procedures. using URAL software.," These data were reduced following standard procedures, using IRAF software."627 The reduced images were found to be flat to better than ~2%., The reduced images were found to be flat to better than $\sim2\%$.628" ""hotometric calibration was performed using standard stars rom Lanclolt’ (1992).", Photometric calibration was performed using standard stars from \citeANP{Landolt92} (1992).629 Selection of CC candidates. from our. LRIS multi-iler imaging was undertaken using the following selection criteria: 20.5 <V« 24.0.5 «V. [«20andO0«V.—A« 1.0.," Selection of GC candidates from our LRIS multi-filter imaging was undertaken using the following selection criteria: 20.5 $< \V <$ 24, 0.5 $< V-I <$ 2.0 and 0 $< V-R <$ 1.0."630 The magnitude limits ensured that we selected the more uminous CC's (necessary [or spectroscopy) whilst excluding xight foreground. stars., The magnitude limits ensured that we selected the more luminous GCs (necessary for spectroscopy) whilst excluding bright foreground stars.631 The colour cuts covered. the full range expected for GCs including photometric errors. whilst excluding extremely blue objects which were unlikely to be real GC's.," The colour cuts covered the full range expected for GCs including photometric errors, whilst excluding extremely blue objects which were unlikely to be real GCs."632 After these selection criteria. we were left with a total of 245 GC candidates.," After these selection criteria, we were left with a total of 245 GC candidates."633 1n Figure 1 we show the colour distribution of our 245 GC candidates in NCC 524 (open histogram) and those for which we have obtained LIS spectra (filled histogram)., In Figure \ref{fig:colours} we show the colour distribution of our 245 GC candidates in NGC 524 (open histogram) and those for which we have obtained LRIS spectra (filled histogram).634 The distribution shows a broad peak at V7~ 1.0. with possible enhancements at Vf~ 0.9 and 1.1. similar to those seen in the LIST data of Larsenetal. (2001).," The distribution shows a broad peak at $V-I \sim$ 1.0, with possible enhancements at $V-I \sim$ 0.9 and 1.1, similar to those seen in the HST data of \citeANP{Larsen01}635 (2001)."636 In an ellort to, In an effort to637The rotation matrices are defined by The gravitational potential then reads: where € is the gravitational constant. Ad the mass of the Sun. Gr.jJ.2) the unit vector pointing at the Sun in the frame Cfi.fo.fa). while d is the distance Sun-Mercury. (expanded in eccentricity and mean anomaly).,"The rotation matrices are defined by The gravitational potential then reads: where $\mathcal{G}$ is the gravitational constant, $M$ the mass of the Sun, $(x,y,z)$ the unit vector pointing at the Sun in the frame $(\vec{f_1},\vec{f_2},\vec{f_3})$, while $d$ is the distance Sun-Mercury (expanded in eccentricity and mean anomaly)."638 Let us note that unlike Lenrard(2008)... we consider that the perturbation is applied to the whole planet and not only to its mantle.," Let us note that unlike \citet{h08}, we consider that the perturbation is applied to the whole planet and not only to its mantle."639 We address the dynamical consequences later in the From the variables wr. y and 2. it is easy to introduce the set of variables defined in (28)).," We address the dynamical consequences later in the From the variables $x$, $y$ and $z$, it is easy to introduce the set of variables defined in \ref{eq:chvar}) )."640 We also modifv the moment Ao associated with £. (that appears in the expressions of c and. y) in such way that all our variables are now canonical with multiplier L/n€' and our gravitational potential becomes (after division by n) Finally. we use the formulae (30)) and (34)) to get the Hamiltonian of the svstem: The four degrees of freedom of this Hamiltonian are the spin (p. P). the obliquity Gr. 2). the wobble of the whole body (£1. i) and the wobble of the core (£o. e).," We also modify the moment $\Lambda_o$ associated with $l_o$ (that appears in the expressions of $x$ and $y$ ) in such way that all our variables are now canonical with multiplier $1/nC$ and our gravitational potential becomes (after division by $nC$ ) Finally, we use the formulae \ref{equ:HG4}) ) and \ref{equ:pull2}) ) to get the Hamiltonian of the system: The four degrees of freedom of this Hamiltonian are the spin $p$, $P$ ), the obliquity $r$, $R$ ), the wobble of the whole body $\xi_1$, $\eta_1$ ) and the wobble of the core $\xi_2$, $\eta_2$ )."641 In this study. we name “wobble” every motion dealing with a shift between the angular momentum of the body or its core. and its geometrical pole axis.," In this study, we name ""wobble"" every motion dealing with a shift between the angular momentum of the body or its core, and its geometrical pole axis."642 I is dilferent from the polar motion that concerns the rotation axis instead of the angular momentum., It is different from the polar motion that concerns the rotation axis instead of the angular momentum.643 Contrary to the Chandler wobble for the Earth. we include in the term “wobble” every. periodic contribution constituting this motion.," Contrary to the Chandler wobble for the Earth, we include in the term ""wobble"" every periodic contribution constituting this motion."644 To study this problem. we use both analvtical ancl numerical methods that allow us to compare their efficiencies and. check the reliability of the results.," To study this problem, we use both analytical and numerical methods that allow us to compare their efficiencies and check the reliability of the results."645 In à previous paper by the authors (Duleyetal.2009)... our mocel was a 2-degree of freedom. Hamiltonian neelecting the wobble J. but including the planetary perturbations.," In a previous paper by the authors \citep{dnrl09}, our model was a 2-degree of freedom Hamiltonian neglecting the wobble $J$, but including the planetary perturbations."646 Here we have a 4-degree of freedom Llamiltonian. but the way we perform our analytical study is similar to our. previous paper.," Here we have a 4-degree of freedom Hamiltonian, but the way we perform our analytical study is similar to our previous paper."647 However there are some kev dillerences that we will highlight in this section., However there are some key differences that we will highlight in this section.648 All the computations were mace using our algebraic manipulator called MSNam (LHenrard.1986), All the computations were made using our algebraic manipulator called MSNam \citep{h86}.649 As mentioned earlier. it is a known fact that Mercury is in a 3:2 spin-orbit resonance.," As mentioned earlier, it is a known fact that Mercury is in a 3:2 spin-orbit resonance."650 In other words. the rotation speed of Mercury p (where p=71g|h. the spin angle of Mercury) is 1.5 times larger than its mean motion n. Lc. p—2n.," In other words, the rotation speed of Mercury $\dot p$ (where $p=l+g+h$, the spin angle of Mercury) is 1.5 times larger than its mean motion $n$, i.e. $\dot p=\frac{3}{2}n$."651" The angle describing this resonance is 0;=f,Sp x. with =, the longitude of the perihelion."," The angle describing this resonance is $\sigma_1=l_o-\frac{3}{2}p-\varpi_o$ , with $\varpi_o$ the longitude of the perihelion."652" Phe angle σι actually represents the libration in The second resonant angle characterizes the 1:1 commoensurabilitv between the orbital ancl rotational nodes. rhoins the 3rd of C'assini's laws (Colombo(1966). or Lemaitreetal.(2006) for C'assini's laws applied to Mercury): o»=r|O,. ""m""with (2, being the longitude of the ascending node."," The angle $\sigma_1$ actually represents the libration in The second resonant angle characterizes the 1:1 commensurability between the orbital and rotational nodes, following the 3rd of Cassini's laws \citet{c66} or \citet{ldr06} for Cassini's laws applied to Mercury): $\sigma_2=r+\Omega_o$, with $\Omega_o$ being the longitude of the ascending node."653 This angle is actually linked to the latitudinal motion of Mercury its conjugated moment 2 which depends on the ecliptic obliquity A). Introducing the resonant angles in the Hamiltonian (35)) and using cartesian-like coordinates (expanded to order 5)for, This angle is actually linked to the latitudinal motion of Mercury (through its conjugated moment $R$ which depends on the ecliptic obliquity $K$ Introducing the resonant angles in the Hamiltonian \ref{equ:hamiltout}) ) and using cartesian-like coordinates (expanded to order 5)for654scale variations can be suppressed to some extent the addition of synthetic smoothing to the desired PSF byI'(r).,scale variations can be suppressed to some extent by the addition of synthetic smoothing to the desired PSF $\Gamma({\bf r})$.655" Considering the effect upon the MTF I’(u), this can be seen simply as a suppression of the high-frequency modes that are most challenging to recover in the presence of plate scale variations."," Considering the effect upon the MTF $\tilde{\Gamma}({\bf u})$, this can be seen simply as a suppression of the high-frequency modes that are most challenging to recover in the presence of plate scale variations."656" The choice of optimal smoothing filter will, in general, depend closely upon the nature of the plate scale variations encountered between and on the dither strategy employed."," The choice of optimal smoothing filter will, in general, depend closely upon the nature of the plate scale variations encountered between input exposures, and on the dither strategy employed."657" The successfulinput linear exposures,reconstruction of has been shown to be sensitive to this effect: further inputstudy imagesaimed at finding optimal mitigating strategies, using more realistic simulations, will be needed."," The successful linear reconstruction of input images has been shown to be sensitive to this effect: further study aimed at finding optimal mitigating strategies, using more realistic simulations, will be needed."658 This concludes our first set of trials for the optimal linear image combination formalism., This concludes our first set of trials for the optimal linear image combination formalism.659 These early results suggest that the technique has merit as a design tool and can be used to explore competing dither strategies for , These early results suggest that the technique has merit as a design tool and can be used to explore competing dither strategies for generating oversampled output.660It has been used to identify generatingencouraging oversampledrobustness of output.linear reconstruction to, It has been used to identify encouraging robustness of linear reconstruction to661Gamma-ray bursts. (5) are. brief pulses. of. 5-rav radiation observed on average once à cay at random directions in the sky.,Gamma-ray bursts (GRBs) are brief pulses of$\gamma$ -ray radiation observed on average once a day at random directions in the sky.662 Vhey are the brightest sources in this region of the electromagnetic spectrum. and they have been systematically studied in the past two decades (e.g.Mészáros2006.andreferences therein)..," They are the brightest sources in this region of the electromagnetic spectrum, and they have been systematically studied in the past two decades \citep[e.g.][and references663therein]{Mes06}."664 Phe origin of GRBs is cosmological. as determined from the measurement: of their redshifts (e.g.Metzgeretal.1997:Bloom.Djorgov-ski&Ixulkarni2001:Bloometal. 2003).. and in many cases. their host galaxies have been identified (seeLeFloehreferences. therein)...," The origin of GRBs is cosmological, as determined from the measurement of their redshifts \citep*[e.g.][]{Met97,Blo01,Blo03}, and in many cases, their host galaxies have been identified \citep*[see][and references therein]{LeF03,Sav09}."665 Their distances imply the release. of large amounts of energy. (107! eres) in a short tinic-scale. which suggests that the origin of these phenomena could be associated to the accretion of matter onto a compact object (Woosley1993:Fryeretal.1999:Macbadyen&Woosley1999:Panaitescu&Kumar2001:Frailetal. 2001).," Their distances imply the release of large amounts of energy $\sim10^{51}\,{\rm ergs}$ ) in a short time-scale, which suggests that the origin of these phenomena could be associated to the accretion of matter onto a compact object \citep{Woo93,Fry99,McF99,Pan01,Fra01}."666. Two populations of GRBs are apparent [from the distribution of their curation (IXouveliotouetal. 1993)., Two populations of GRBs are apparent from the distribution of their duration \citep{Kou93}. .667. Those lasting less than 2s are known as short GRBs. while," Those lasting less than $2\,{\rmn s}$ are known as short GRBs, while"66852 km.,52 km.669 This short-spacing limit fillers out all spatial structure larger (han about 0.42., This short-spacing limit filters out all spatial structure larger than about $0\rlap{.}^{''}42$.670 Table 1 summarizes (he parameters of these observations., Table 1 summarizes the parameters of these observations.671" The observations emploved noclding-stvle phase relerencing. using the calibrator (S,4eq,=0.4 Jv). with a evele time of 4 min. 3 min on the target source and 1 min on the calibrator."," The observations employed nodding-style phase referencing, using the calibrator J1335--0511 $S_{\rm 1.4~GHz}=0.4$ Jy), with a cycle time of 4 min, 3 min on the target source and 1 min on the calibrator."672 A munber of test eveles were also included to monitor the coherence of the phase relerencing., A number of test cycles were also included to monitor the coherence of the phase referencing.673" These tests involved switching between (wo calibrators. the pliase calibrator J13350511 and the phase-check calibrator J1332.0509 (ντο,=0.3 Jv). using a similar evele time (ο that used for the target source."," These tests involved switching between two calibrators, the phase calibrator J1335–0511 and the phase-check calibrator J1332–0509 $S_{\rm 1.4~GHz}=0.3$ Jy), using a similar cycle time to that used for the target source."674 The accuracy of (the phase calibrator position is important in pliase-relerencing observations (Walker1999).. as this determines (he accuracy of the absolute position of the target source and any associated. Components.," The accuracy of the phase calibrator position is important in phase-referencing observations \citep {WAL99}, as this determines the accuracy of the absolute position of the target source and any associated components."675 Phase referencing. as used here. is known (o preserve absolute astrometric positions to better than 0:01 (Fomalont1999).," Phase referencing, as used here, is known to preserve absolute astrometric positions to better than $\pm 0\rlap{.}^{''}01$ \citep{FOM99}."676. Data reduction and analvsis were performed using the Astronomical Image Processing System (AIPS) ancl Astronomical Information Processing Svstem (AIPS++) of the NRAO., Data reduction and analysis were performed using the Astronomical Image Processing System (AIPS) and Astronomical Information Processing System $++$ ) of the NRAO.677 After applvingpriori [lagging. amplitude calibration was performed using measurements of the antenna gain and svstem temperature for each station.," After applying flagging, amplitude calibration was performed using measurements of the antenna gain and system temperature for each station."678" lonospheric corrections were applied using the AIPS task ΤΕΟΙ,", Ionospheric corrections were applied using the AIPS task “TECOR”.679 The phase calibrator J1335.0511 was self-calibrated in both phase and amplitude and imaged in an iterative cycle., The phase calibrator J1335–0511 was self-calibrated in both phase and amplitude and imaged in an iterative cycle.680 Images of the phase-check calibrator. J1332.0509. were deconvolved using two different approaches: (a) bv applving the phase and the amplitude sell-calibration solutions of the phase relerence source J13350511 (Figure La). and (b) bv self calibrating J1332.0509 i(sell. in both phase and amplitude (Figure 15).," Images of the phase-check calibrator, J1332–0509, were deconvolved using two different approaches: (a) by applying the phase and the amplitude self-calibration solutions of the phase reference source J1335–0511 (Figure ), and (b) by self calibrating J1332–0509 itself, in both phase and amplitude (Figure )."681 The peak surface brightness ratio of the final images [rom the (wo approaches gives a measure of the effect of residual phase errors after phase referencing (i.e. ‘the coherence’ due to phase relerencing)., The peak surface brightness ratio of the final images from the two approaches gives a measure of the effect of residual phase errors after phase referencing (i.e. `the coherence' due to phase referencing).682 At all times. the coherence was found to be better than9814.," At all times, the coherence was found to be better than."683.. The sell-calibration solutions of the phase calibrator. J18350511. were applied on the targete source. BRI 13350417. which was then deconvolved and imagedc» at various spatial resolutions by tapering the visibility data.," The self-calibration solutions of the phase calibrator, J1335–0511, were applied on the target source, BRI 1335–0417, which was then deconvolved and imaged at various spatial resolutions by tapering the visibility data."684 Tinaging the target source at the full resolution of the VLBI array. which is 32x7 mas (211x46 pc. PÀ-— 7). achieved an rms noise level of 8.5 j(Jy +. but did not reveal any continuum component in the field of BRI 13350417.," Imaging the target source at the full resolution of the VLBI array, which is $32 \times 7$ mas $211 \times 46$ pc, $-7^{\circ}$ ), achieved an rms noise level of $8.5~\mu$ Jy $^{-1}$, but did not reveal any continuum component in the field of BRI 1335–0417."685 This indicates the absence of any, This indicates the absence of any686in a channel separation of 12.2 ΚΙ (2.6 1)) for a total observed bandwidth of 1.56 MlIIz.,in a channel separation of 12.2 kHz (2.6 ) for a total observed bandwidth of 1.56 MHz.687 For spectral line data (hat are taken using on-line Hanning smoothing. the velocity resolution is equal to the channel separation. and so is also 2.6/.," For spectral line data that are taken using on-line Hanning smoothing, the velocity resolution is equal to the channel separation, and so is also 2.6."688. Observations of the nearby continuum source O713+438 (J2000) were made for phase calibration of both data sets: observations of the sources 0121291 (J2000) and 13314-305 (J2000) were made for calibration of the flux and bandpass of the C ancl D-conlfiguration data. respectively.," Observations of the nearby continuum source 0713+438 (J2000) were made for phase calibration of both data sets; observations of the sources 0137+331 (J2000) and 1331+305 (J2000) were made for calibration of the flux and bandpass of the C and D-configuration data, respectively."689 Calibration of both data sets was perlormed using the standard routines in AIPS., Calibration of both data sets was performed using the standard routines in AIPS.690 Observational information is provided in Table 1.., Observational information is provided in Table \ref{tab:HI}.691 The D-configuration source data were affected. by solar contamination on the short baselines., The D-configuration source data were affected by solar contamination on the short baselines.692 The corrupted data were flagged. removing approximately of the total number ol visibilities.," The corrupted data were flagged, removing approximately of the total number of visibilities."693 There were three strong continuum sources in the field: there was no sign ol continuum emission from DDO 43., There were three strong continuum sources in the field; there was no sign of continuum emission from DDO 43.694 The continuum was satisfactorily subtracted in thewe plane by using lne-free channels {ο make a linear fit to the continuum emission., The continuum was satisfactorily subtracted in the plane by using line-free channels to make a linear fit to the continuum emission.695 The resulting continuum-free data was then imaged using the AIPS taskIMAGR., The resulting continuum-free data was then imaged using the AIPS task.696 To ensure the best sensitivity to low levels of emission. natural weighting was used.," To ensure the best sensitivity to low levels of emission, natural weighting was used."697" The data were CLEANed during imagine to reduce (he sidelobes produced by non-gaussian features in (he ""dirt beam.", The data were ed during imaging to reduce the sidelobes produced by non-gaussian features in the “dirty” beam.698 No clean boxes were speciliecl so the delault of a box ten pixels smaller (han (the lage size was used.," No clean boxes were specified, so the default of a box ten pixels smaller than the image size was used."699 No zero-spacing [lux was assumed., No zero-spacing flux was assumed.700 The specified flux. cutoff of 0.83 mJv/D (~lo in a single channel) was reached in less than 3000 iterations in each channel. which is less than the 10.000 iteration cutoff set in the task.," The specified flux cutoff of 0.83 mJy/B $\sim 1\sigma$ in a single channel) was reached in less than 3000 iterations in each channel, which is less than the 10,000 iteration cutoff set in the task."701" The resulting data cube (one channel for each observed. [requencev) has a beam size ol 54.8""x53.7"" aand a single channel oof 0.81 mJv/B. Line emission appears from approximately 300420Ll.", The resulting data cube (one channel for each observed frequency) has a beam size of $54.8\arcsec\times 53.7\arcsec$ and a single channel of 0.81 mJy/B. Line emission appears from approximately 300–420.702 The data cube was integrated in velocity with the task (0 produce moment maps of the integrated flux density. the [Iux-weighted velocity Ποια. ancl the velocity dispersions.," The data cube was integrated in velocity with the task to produce moment maps of the integrated flux density, the flux-weighted velocity field, and the velocity dispersions."703 The integration task first smooths the data spatially and {hen in velocity space to create a lower-noise mask., The integration task first smooths the data spatially and then in velocity space to create a lower-noise mask.704 A cutoff of approximately 1.5 times the sinele-channel wwas applied to the mask. and pixels in (he original. unsmoothed cube corresponding to the mask pixels higher (han the cutoff flux were integrate.," A cutoff of approximately 1.5 times the single-channel was applied to the mask, and pixels in the original, unsmoothed cube corresponding to the mask pixels higher than the cutoff flux were integrated."705 The C-configuration data were very well behaved resulting in minimal data. editiug., The C-configuration data were very well behaved resulting in minimal data editing.706 No solar contamination was present. but like (he D configuration. there were still (he three strong continuum sources.," No solar contamination was present, but like the D configuration, there were still the three strong continuum sources."707 This continuum enission was subtracted as for the D-configuration data., This continuum emission was subtracted as for the D-configuration data.708 The imaging was done using uniform weighing = 1) however. to produce high resolution images with only a slight degredation in sensitivity.," The imaging was done using uniform weighting = 1) however, to produce high resolution images with only a slight degredation in sensitivity."709" This resulted in a beam size of 14.0""x11.0"" aand a single-channel oof 1.05 mJv/B. As for the D-configuration data. the data were CLEANed during imaging."," This resulted in a beam size of $14.0\arcsec\times 11.0\arcsec$ and a single-channel of 1.05 mJy/B. As for the D-configuration data, the data were ed during imaging."710 In this case. a test showed that the component [lux leveled off after the first 500 iterations. and so an iteration cutoff of 2500," In this case, a test showed that the component flux leveled off after the first 500 iterations, and so an iteration cutoff of 2500"711(upper panel). the jet contributes 40% and ~30% of the emission in Avs and ff. respectively.,"(upper panel), the jet contributes $\sim 40$ and $\sim 30$ of the emission in $Ks$ and $H$, respectively."712 H£ the jet is the source of he polarisation and the star and any other contributions are not polarised. this implies the jet itselfis 15dE54. polarised in Avs and 1643:54 polarised in 4/4.," If the jet is the source of the polarisation and the star and any other contributions are not polarised, this implies the jet itselfis $15\pm 5$ polarised in $Ks$ and $16\pm 5$ polarised in $H$."713 We would not expect this evel of LP from the optically thick jet. so the jet spectrum must turn over to become optically thin (a= 0.6) at some requeney above ~51077 Hz (contrarytothemodelsofAligliarietal. 2007).," We would not expect this level of LP from the optically thick jet, so the jet spectrum must turn over to become optically thin $\alpha \approx -0.6$ ) at some frequency above $\sim 5\times 10^{13}$ Hz \citep[contrary to the models of][]{miglet07}."714". H£ we take the faintest possible NLR. jet scenario.. one where the turnover is. at 510""nm Iz and the optically thin spectrum is steep (à= 0.8)) jet. would contribute of the light at Avs and at Lf."," If we take the faintest possible NIR jet scenario, one where the turnover is at $5\times 10^{13}$ Hz and the optically thin spectrum is steep $\alpha = -0.8$ ), the jet would contribute of the light at $Ks$ and at $H$."715 theVhis would result in a jet LP of 42413% in vs and 52417% in 44., This would result in a jet LP of $42\pm 13$ in $Ks$ and $52\pm 17$ in $H$.716 The likely level of jet contribution is between the two above estimates. so a jet LP of in Ns and in Lf can explain the data.," The likely level of jet contribution is between the two above estimates, so a jet LP of in $Ks$ and in $H$ can explain the data."717 These results indicate a fairly ordered magnetic field. with f£.=0.412:0.19 from the A s-band result (The ££-band is less constraining).," These results indicate a fairly ordered magnetic field, with $f = 0.41\pm 0.19$ from the $Ks$ -band result (The $H$ -band is less constraining)."718 In addition. the Hux from GRO J165540 is marginally variable in dvs (T2 standard deviation: column XN of Table 3) on short timescales (~20 see time resolution).," In addition, the flux from GRO J1655–40 is marginally variable in $Ks$ $\pm$ standard deviation; column X of Table 3) on short timescales $\sim 20$ sec time resolution)."719 Lf the star is not variable then this suggests the jet component is varving by48%., If the star is not variable then this suggests the jet component is varying by.720. ‘This is consistent with observations of other sources: large-amplitude variability has been seen associated with ΝΗΙ optically thin svnchrotron. emission from the jets in NPE J1IIS|480 (Hlvnesetal.2006)., This is consistent with observations of other sources; large-amplitude variability has been seen associated with NIR optically thin synchrotron emission from the jets in XTE J1118+480 \citep{hyneet06}.721.. We note however that strong variability can also be observed from other components. such as irradiation of the accretion disc.J04224-32:," We note however that strong variability can also be observed from other components, such as irradiation of the accretion disc.:"722: The apparent magnitudes and Jdy colour of this source are found to be consistent with the quiescent values measured by Gelino&Larrison(2003)., The apparent magnitudes and $J-K$ colour of this source are found to be consistent with the quiescent values measured by \cite{geliha03}.723. The S/N is low: we are able to place a 36. upper limit on the -band polarisation: LP<11., The S/N is low; we are able to place a $\sigma$ upper limit on the $J$ -band polarisation; $<$ .7246%.. Ht has been shown that the star likely dominates the NUR light. (Gelino&Larrison2003) although recent observations detect a strong [lickering component which may come [rom the cise 2007).., It has been shown that the star likely dominates the NIR light \citep{geliha03} although recent observations detect a strong flickering component which may come from the disc \citep*{reynet07}. .725"absorption baud due to the stretching mode of a triply bonded CN-bearing species. the so-called ""XNCN baud.","absorption band due to the stretching mode of a triply bonded CN-bearing species, the so-called `XCN' band."726 Tudeed. low resolution spectral studies report the presence of this band toward cceutered at 1.62 citeplacvsLl.chiaQs. pend99..," Indeed, low resolution spectral studies report the presence of this band toward centered at 4.62 \\citep{lacy84, chia98, pend99}."727 We therefore chose to extrapolate the straight line coutimmun defined at high wavelength toward lower waveleusths., We therefore chose to extrapolate the straight line continuum defined at high wavelength toward lower wavelengths.728 This results iu an “XCN? absorption featire with an optical depth of 7-0.13 at 1.62juu., This results in an `XCN' absorption feature with an optical depth of $\tau$ =0.13 at 4.62.729 This is ks than the vaue of 0.31. quotexl iu Pendletouetal.0999).. which w«| believe is maiY (Ar=0.1) due to contamination bv bended. uresolvxl eas phase CO lines in heir low resolion spectrum. hiit also partly due to the lack of short wavelength οσοΕΙ in our spectrum.," This is less than the value of 0.31 quoted in \citet{pend99}, which we believe is mainly $\Delta \tau$ =0.1) due to contamination by blended, unresolved gas phase CO lines in their low resolution spectrum, but also partly due to the lack of short wavelength continuum in our spectrum."730 Althoueh little flux is left in the bottom of the solid αραιά. this band is not saturated as is shown by the xeseuce of the P(1) line of gaseous in the bottom of the ice baud (CFig.1)).," Although little flux is left in the bottom of the solid band, this band is not saturated as is shown by the presence of the P(1) line of gaseous in the bottom of the ice band \ref{f:obs}) )."731 The peak optical depth of the solid ους is 7(0C0)23.6-0.2. an important umuuber for our isotope ratio doetermünatioun (83.2).," The peak optical depth of the solid band is $\tau$ $\pm$ 0.2, an important number for our isotope ratio determination 3.2)."732 The uncertaiutv of L2 ds determined from three difference noddiug pairs. and shows the data is reliable even in extremely deep absorption bands.," The uncertainty of 0.2 is determined from three difference nodding pairs, and shows the data is reliable even in extremely deep absorption bands."733 However. τίςο) is significantly hueer han the value of 2.6 previously reported (Lacyctal.1981:Tieleusetal. L991).," However, $\tau$ (CO) is significantly larger than the value of 2.6 previously reported \citep{lacy84, tiel91}."734. This is partly explained bx instrumental broadening of the narrow apolar CO band x the previous low resolution spectrometers., This is partly explained by instrumental broadening of the narrow apolar CO band by the previous low resolution spectrometers.735 We calculate hat the depth of the CO band would be reduced by A r(CO)J-O0.6 aud 0.3 at the resolution of the data in Lacyetal.(1981) and Tieleusetal.(1991) respectively., We calculate that the depth of the CO band would be reduced by $\Delta \tau$ (CO)=0.6 and 0.3 at the resolution of the data in \citet{lacy84} and \citet{tiel91} respectively.736 An additional uucertaintv iav result from the contimmn determination in the preseuce of many unresolved strong eas phase CO absorption lines., An additional uncertainty may result from the continuum determination in the presence of many unresolved strong gas phase CO absorption lines.737 The newly detected absorption baud of solid lis an indepeudent tracer of the composition of iev erain mautles., The newly detected absorption band of solid is an independent tracer of the composition of icy grain mantles.738 Its identification is discussed in 83.1.1., Its identification is discussed in 3.1.1.739 Extra information is obtained by: comparing the bbaud with the apolar component of the bband (83.1.2)., Extra information is obtained by comparing the band with the apolar component of the band 3.1.2).740 In 83.2 we derive the Hsotope ratio im interstellar ices. for which a new approach to decompose the polar and apolar lico conmiponents is introduced.," In 3.2 we derive the isotope ratio in interstellar ices, for which a new approach to decompose the polar and apolar ice components is introduced."741 TheὉ astroplivsical iuplications of these results are discussed in 81., The astrophysical implications of these results are discussed in 4.742 Iu order to characterize the absorption feature detected at 2092 inthe spectrmm ofIRS9.. Gaussian fits were carried out.," In order to characterize the absorption feature detected at 2092 inthe spectrum of, Gaussian fits were carried out."743" We find a peak frequency of v=2092.30£0.21Ll. a peak optical depth of r=0.08940.010, and a width of FWA = 1.5040.15 (2σ errors)."," We find a peak frequency of $\nu$ $\pm$ 0.21, a peak optical depth of $\tau$ $\pm$ 0.010, and a width of FWHM = $\pm$ 0.45 $\sigma$ errors)."744 At the NIRSPEC resolving power of R=25.000 (Av=0.08 13) the feature is well resolved. and fortunately well separated frou the forest of sumrouuding interstellar and telluric gas phase absorption and ciuission features.," At the NIRSPEC resolving power of $R=25,000$ $\Delta \nu=0.084$ ) the feature is well resolved, and fortunately well separated from the forest of surrounding interstellar and telluric gas phase absorption and emission features."745 Features providing the ercatest interfercuce are the unresolved P(1) absorption line of interstellar gaseous aat 2092.39 aand a telburie feature at slightly lareer frequency., Features providing the greatest interference are the unresolved P(1) absorption line of interstellar gaseous at 2092.39 and a telluric feature at slightly larger frequency.746 The deepest part of the telluvic feature was removed from the data., The deepest part of the telluric feature was removed from the data.747" Despite these liuitatious. the Πίος, Gaussian parauueters are sinilar in the observations made on the three different nights (82)."," Despite these limitations, the fitted Gaussian parameters are similar in the observations made on the three different nights 2)."748 The laboratory experiments ou solid CO from the works of Ehreufreundetal.(1997) were used with the goal of identifving the 2092 ffeature with absorption by solid aand to further coustrain the composition of interstellar ices., The laboratory experiments on solid CO from the works of \citet{ehre97} were used with the goal of identifying the 2092 feature with absorption by solid and to further constrain the composition of interstellar ices.749 These laboratory spectra have the high spectral resolution (1.0 ')}) and signal-to-noise required to study the baud profile of the weal. aud narrow ffeature., These laboratory spectra have the high spectral resolution (1.0 ) and signal-to-noise required to study the band profile of the weak and narrow feature.750 Other relevant laboratory studies. such as the No:CO experiments of Elsila. Allamaucdola. Saudford (1997) and the pure CO study of Baratta&|Paluubo(1998) unfortunately lack sufficient spectral resolution to resolve aud characterize the feature.," Other relevant laboratory studies, such as the $_2$ :CO experiments of Elsila, Allamandola, Sandford (1997) and the pure CO study of \citet{bara98} unfortunately lack sufficient spectral resolution to resolve and characterize the feature."751 The laboratory profiles of the sstrotching mode were analyzed in a way simile to that done for citepboogO02.., The laboratory profiles of the stretching mode were analyzed in a way similar to that done for \\citep{boog02}.752 After a careful baseliue subtraction. the peak position aud width were determined as a function of ice composition and temperature.," After a careful baseline subtraction, the peak position and width were determined as a function of ice composition and temperature."753 Generally. the same trends fouud for the Dband are recognized in (Fie. 2)).," Generally, the same trends found for the band are recognized in (Fig. \ref{f:lab}) )."754 The baud of iii a pure amorphous CO ice peaks at 2092.3 aaud is very narrow (FWIIM=L.5 '))., The band of in a pure amorphous CO ice peaks at 2092.3 and is very narrow (FWHM=1.5 ).755 An extreme broadening aud shift to larger waveleneths are observed when CO is mixed with ILO ice. because of the Luge dipole moment of the IIO molecules.," An extreme broadening and shift to larger wavelengths are observed when CO is mixed with $_2$ O ice, because of the large dipole moment of the $_2$ O molecules."756 Similarly larec effects are expected for other astroplysically relevaut molecules with large dipole moments (CIT;OIT. NID). but uo laboratory experiucuts are available for these mixtures prescut.," Similarly large effects are expected for other astrophysically relevant molecules with large dipole moments $_3$ OH, $_3$ ), but no laboratory experiments are available for these mixtures at present."757 Mixtures of CO with the apolar species CO». ad to a lesser degree with Ov. can also give drastically broadened Dhauds.," Mixtures of CO with the apolar species $_2$, and to a lesser degree with $_2$, can also give drastically broadened bands."758 A fragile amorphous structure is formed between the CO ποιους and CO. and Ov. providing an absorption feature that is broadest at mixing ratios of 1:1 (Ehreufreuudetal.1997).," A fragile amorphous structure is formed between the CO molecules and $_2$ and $_2$, providing an absorption feature that is broadest at mixing ratios of 1:1 \citep{ehre97}."759. Upon warming this structure is destroved and the baud narrows. although iu particular or COs. mixtures the width is still larger than that of a mire CO ice.," Upon warming this structure is destroyed and the band narrows, although in particular for $_2$ mixtures the width is still larger than that of a pure CO ice."760 In coutrast. only a very. μα broadening is observed in mixtures of CO with No. even at L:1 mixing ratios (FWITM=Ls8 13," In contrast, only a very small broadening is observed in mixtures of CO with $_2$, even at 1:1 mixing ratios (FWHM=1.8 )."761) Finally. the peak position does uot shift in mixtures of CO with Os. but the baud (as well as the ορ) shifts by 0.5L to shorter waveleneths when mixed with COs and by 0.5 wwhen mixed with No.," Finally, the peak position does not shift in mixtures of CO with $_2$, but the band (as well as the band) shifts by 0.5–1 to shorter wavelengths when mixed with $_2$ and by 0.5 when mixed with $_2$ ."762 Using these results. we conclude that the peak aud width of the 2092 aabsorptiou feature observed toward aare best explained by the stretching mode of jin a pure CO ice (Fig.," Using these results, we conclude that the peak and width of the 2092 absorption feature observed toward are best explained by the stretching mode of in a pure CO ice (Fig."763 90) aud d), \ref{f:labfit1}b b and d).764 At low laboratory, At low laboratory765or |--endssion iu our spectra. so there is no evideuce that our age estimates are affected by nebular emission.,"or -emission in our spectra, so there is no evidence that our age estimates are affected by nebular emission."766 Iu Figure 2« we show the [MegF052] ‘age-nctallicity diagnostic diagram (|MgEe52] = ψλΙοῦ< ," In Figure \ref{fig:age_sig}{ we show the [MgFe52] age-metallicity diagnostic diagram ([MgFe52] = $\sqrt{{\rm Mg}\,767 b \times {\rm Fe5270}}$."768Iu order to probe the stellar populations of the decoupled core with respect to the main ealaxy we have averaged ie line-streneth in certain kev regions (sce also Figure 1.. snlarecd core region).," In order to probe the stellar populations of the decoupled core with respect to the main galaxy we have averaged the line-strength in certain key regions (see also Figure \ref{fig:color}, enlarged core region)."769 The very ceutral region (60) of ie galaxy is veprescuted by an open circle., The very central region $r<$ 6) of the galaxy is represented by an open circle.770 Furthermore. we have ideutified the decoupled core using the velocity naps and plot the average value for the line-streneths in this region as an open diuuonud.," Furthermore, we have identified the decoupled core using the velocity maps and plot the average value for the line-strengths in this region as an open diamond."771 Comparing this with ie average line-streneths of the main galaxy at the radius along the minor axis (open square) we find that rese two kinematically distinct regions have identical stellar populatious., Comparing this with the average line-strengths of the main galaxy at the radius along the minor axis (open square) we find that these two kinematically distinct regions have identical stellar populations.772 At larger radii (à> 5700) we averaged all lenslets im elliptical auuuli (filled circles)., At larger radii $r > $ 0) we averaged all lenslets in elliptical annuli (filled circles).773 The metal ine-streneth decreases with mereasiug radius aud there is a πα increase in ‘absorptioni streneth., The metal line-strength decreases with increasing radius and there is a small increase in absorption strength.774" Iu order to make age ancl metallicity estimates, we use the Vazdekis(1999) models. which utilizo the clupirical stellar library of Jones(1997) to predict linc-streugths for a sinele-burst stellar population as a function of age and metallicity."," In order to make age and metallicity estimates, we use the \citet{vaz1999} models, which utilize the empirical stellar library of \citet{jon1997} to predict line-strengths for a single-burst stellar population as a function of age and metallicity."775 The models were smoothed to the Lick/IDS resolution aud include iuproved stellar population paraiueters (Vazdekis 2001. in preparation).," The models were smoothed to the Lick/IDS resolution and include improved stellar population parameters (Vazdekis 2001, in preparation)."776 The model predietions are shown in Figure 26c., The model predictions are shown in Figure \ref{fig:age_sig}{.777 The central metallicity is estimated to be 1.15 Z... decreasing towards larger radii (220.3 dex per dex m radius) at a roughly conustaut age of Ll Corr (Figure 24).," The central metallicity is estimated to be 1.15 $Z_{\odot}$, decreasing towards larger radii $\approx$ 0.3 dex per dex in radius) at a roughly constant age of 14 Gyr (Figure \ref{fig:age_sig}{ )."778 We note that the absolute age calibration of the models remaius subject to svstinatic errors. but all our conclusions are based on relative age differences which are mmch mere robust.," We note that the absolute age calibration of the models remains subject to systmatic errors, but all our conclusions are based on relative age differences which are much more robust."779 The small increase iu absorption at the very center (rz 176) sneeests a huninositv-welehted aee of z]2 Grr., The small increase in $\beta$ absorption at the very center $r\lta 1\farcs6$ ) suggests a luminosity-weighted age of $\approx$ 12 Gyr.780 We can account for this bv superimposing a Fe523t9iuueer population on that of the main body: of the lnass in a stellar population with the same metallicity aud an age of 5 Cas is sufficient., We can account for this by superimposing a younger population on that of the main body: of the mass in a stellar population with the same metallicity and an age of 5 Gyrs is sufficient.781 Figure 2b shows the σ relation within 11365., Figure \ref{fig:age_sig}{ shows the $\sigma$ relation within 4365.782 The central data poiuts agree well with the relation for the cores of early-type ealaxies (Collessetal. 1999).. sugeestingCoco that the core properties of [1365 are similar to those of other ellipticals.," The central data points agree well with the relation for the cores of early-type galaxies \citep{col1999}, , suggesting that the core properties of 4365 are similar to those of other ellipticals."783" For +Zi6"".. the local 0 relation shows a steeper slope than the global relation. but overall the eradicut in this diagram is typical of simular ealaxics studied by Davies.Sadler.&Peletier(1993). and &Danziger(199 1)."," For $r \lta 6$, the local $\sigma$ relation shows a steeper slope than the global relation, but overall the gradient in this diagram is typical of similar galaxies studied by \citet*{dsp1993} and \citet*{cd1994}."784. Iu Figure 2c we plot Fe5270., In Figure \ref{fig:age_sig}{ we plot Fe5270.785 Stellar population models (Vazdekis1999). at solar abundance ratios aud for ages 12.6 aud 17.5 Cor are overplotted., Stellar population models \citep{vaz1999} at solar abundance ratios and for ages 12.6 and 17.8 Gyr are overplotted.786 Iu these coordinates the effects of age and inetallicitv are alinost completely degenerate heuce he model predictions overlap., In these coordinates the effects of age and metallicity are almost completely degenerate hence the model predictions overlap.787 Consistent with other eiat ellipticals (seee.2..Iuutschuer1998:IKuutschueret 2001).. the data points for £1365 lie off the solar ratio uodels towards larger values of and lower Εσυ line-treugth.," Consistent with other giant ellipticals \citep[see \eg][]{kun1998,kun2001}, the data points for 4365 lie off the solar ratio models towards larger values of and lower Fe5270 line-strength."788 Using the corrections oeiven bv Trageretal.(2000) πο also plot stellar lation models at [Mg/Fe] = 0.22 dex. which are a good representation of the whole of 11365.," Using the corrections given by \citet{tra2000} we also plot stellar population models at [Mg/Fe] = 0.22 dex, which are a good representation of the whole of 4365."789" There is ιο difference between the decoupled core region aud thenain body of the galaxy,", There is no difference between the decoupled core region and themain body of the galaxy.790 SB find that the maguesiun- ratio is further enhanced im the very ceuter., SB find that the magnesium-to-iron ratio is further enhanced in the very center.791 Our, Our792Periodic variability of emission from Cyg X-I flux at. various frequencies at the period of ~150 d has been reported by. e.g. Brocksoppetal. (1999a).. Pooley.Fender&Brocksopp (1999). Ozdemir&Demircan(2001). Benllochetal.(2001. 2004). Karitskayaetal.(2001). and. Lachowiezetal.(2006.here-after LOG)..,"Periodic variability of emission from Cyg X-1 flux at various frequencies at the period of $\sim$ 150 d has been reported by, e.g., \citet*{brock}, , \citet*{poo99}, , \citet{od01}, \citet{benlloch01, benlloch04}, \citet{k01} and \citet[][ hereafter L06]{l06}."793 This period is much longer than the 5.6-d orbital period (Brocksoppetal.1999b).. and this type of periodicity tor quasi-periodicity) in binaries is called superorbital.," This period is much longer than the 5.6-d orbital period \citep{brock2}, and this type of periodicity (or quasi-periodicity) in binaries is called superorbital."794 The generally accepted interpretation of the underlying cause of superorbital periodicity in X-ray binaries is precession of the accretion disc and/or jet L.tor0S.capO06:: L06: but with the exception of 4U 1820-303. e.g. Zdziarski.Wen&Gierlinski 2007).," The generally accepted interpretation of the underlying cause of superorbital periodicity in X-ray binaries is precession of the accretion disc and/or jet \\citealt{k73,k80,l98,wp99,ogdu01,tor05,cap06}; L06; but with the exception of 4U 1820–303, e.g., \citealt*{zwg07}) )."795 However. the question arises in which way the precession causes the modulation of the observed flux.," However, the question arises in which way the precession causes the modulation of the observed flux."796 There appears to be a number of possibilities., There appears to be a number of possibilities.797 Considering the X-ray modulation first. the outer edge of the optically thick dise may partially cover the X-ray source.," Considering the X-ray modulation first, the outer edge of the optically thick disc may partially cover the X-ray source."798 This. however. would require extreme fine-tuning.," This, however, would require extreme fine-tuning."799" Namely. the X-ray source has the size ~1074/2, (where Re—C Mc. as indicated by the X-ray power spectrum and agreement with heoretical prediction on the range of radii where most of the accretion power is released. while the dise size is generally much arger. up to the order of the size of the Roche lobe (~101, in Cyg X-1)."," Namely, the X-ray source has the size $\sim 10^2 R_{\rm g}$ (where $R_{\rm g}\equiv GM/c^2$ ), as indicated by the X-ray power spectrum and agreement with theoretical prediction on the range of radii where most of the accretion power is released, while the disc size is generally much larger, up to the order of the size of the Roche lobe $\sim 10^6 R_{\rm g}$ in Cyg X-1)."800 Another possibility is that the outer part of the dise ully obscures the X-ray source. but we see the X-rays scattered in a large corona above the dise (this appears to take place. e.g.. in Her Χ-Ι. Leahy 20025).," Another possibility is that the outer part of the disc fully obscures the X-ray source, but we see the X-rays scattered in a large corona above the disc (this appears to take place, e.g., in Her X-1, \citealt{l02}) )."801 This. however. would dramatically affect he X-ray power spectrum. removing oscillations at all frequencies above | Hz. which effect is clearly not seen. and thus this scenario can be ruled out.," This, however, would dramatically affect the X-ray power spectrum, removing oscillations at all frequencies above 1 Hz, which effect is clearly not seen, and thus this scenario can be ruled out."802 The bound-free absorption in a spatially extended medium of moderate optical depth associated with the outer regions of the dise appears to be ruled out as there are a rather weak or no energy dependencies of the modulation. see LO6 and Section 3 below. (," The bound-free absorption in a spatially extended medium of moderate optical depth associated with the outer regions of the disc appears to be ruled out as there are a rather weak or no energy dependencies of the modulation, see L06 and Section \ref{s:period} below. ("803"Bound-free absorption in the wind from the companion is responsible for theorbital modulation of the X-rays in Cyg Wenetal. 19995),","Bound-free absorption in the wind from the companion is responsible for the modulation of the X-rays in Cyg X-1, \citealt{wen99}) )."804 On the other hand. a viable scenario is the wind/corona around the outer dise being almost fullyionized. withscattering away from the line of sight being responsible for the superorbital modulation.," On the other hand, a viable scenario is the wind/corona around the outer disc being almost fullyionized, withscattering away from the line of sight being responsible for the X-ray superorbital modulation."805It is just as well to mention that the structure indices of the sources may change as a function of time and that not all sources were observed close to the dates when these indices were determined (see Tables 2. and 3)),It is just as well to mention that the structure indices of the sources may change as a function of time and that not all sources were observed close to the dates when these indices were determined (see Tables \ref{table2} and \ref{table3}) ).806 Table 3 reports. as obtained from the BVID. data from the 3 most recent years of experiments (when available).," Table \ref{table3}807 reports, as obtained from the BVID, data from the 3 most recent years of experiments (when available)."808 It is possible to notice that the time variation of these indices. as far as the sources here studied are concerned. typically do not exceed one.," It is possible to notice that the time variation of these indices, as far as the sources here studied are concerned, typically do not exceed one."809 This is often true also when we consider. when available to the same experiments. dates older tha those from the 3 most recent years in the BVID.," This is often true also when we consider, when available to the same experiments, dates older than those from the 3 most recent years in the BVID."810 One clear exception 1s the source 0440—003., One clear exception is the source $-$ 003.811 A. Collioud (2011. personnal comm.)," A. Collioud (2011, personnal comm.)"812 determined the continuous X-band structure index (?) to this source and found the value of 1.83 to the experiment of 1995., determined the continuous X-band structure index \citep{2011A&A...526A.102B} to this source and found the value of 1.83 to the experiment of 1995.813 This indicates. therefore. a variation from about 2 to 4 which ts less pronounced than that of 1 to 4.," This indicates, therefore, a variation from about 2 to 4 which is less pronounced than that of 1 to 4."814 In general. it is then reasonable to assume that the results pointed out by Fig.," In general, it is then reasonable to assume that the results pointed out by Fig."815 6 remain the same although observation dates are not always close to those of the respective VLBI experiments., \ref{figure6} remain the same although observation dates are not always close to those of the respective VLBI experiments.816 Source 0743-673 has its position given by both SOAR and ESO/MPG telescopes. where a difference of 43 mas and 30 mas is seen. respectively. between the right ascension and declination as determined from both instruments.," Source $-$ 673 has its position given by both SOAR and ESO/MPG telescopes, where a difference of 43 mas and 30 mas is seen, respectively, between the right ascension and declination as determined from both instruments."817 It should also be noticed that the number of reference stars used to obtain the final position of this source from the ESO/MPG ts 380. whereas only 8 were used to obtain the final position from the SOAR.," It should also be noticed that the number of reference stars used to obtain the final position of this source from the ESO/MPG is 380, whereas only 8 were used to obtain the final position from the SOAR."818 It is just as well to remember that the area on the sky covered by the WFI is about 30 times that of the SOL, It is just as well to remember that the area on the sky covered by the WFI is about 30 times that of the SOI.819 In this context. a possible important contribution for the above difference comes from the materialization of the celestial frame as given by two," In this context, a possible important contribution for the above difference comes from the materialization of the celestial frame as given by two"820and an age of 2.11+0.26 Car.,and an age of $2.14 \pm 0.26$ Gyr.821 We note that the age estimate reflects the specific assumptions in the Yonscei-Yale evolution calculations: as indicated Iv Fig., We note that the age estimate reflects the specific assumptions in the Yonsei-Yale evolution calculations; as indicated by Fig.822 2dd the true uncertainty in the age determunation is likely somewhat larger., \ref{fig:chisq}d d the true uncertainty in the age determination is likely somewhat larger.823 For HLAT-P-11 the oscillation amplitudes were much s1inaller than in ILAT-P-7. as expected from the general scaling of amplitudes with stellar mass and Duuinositv (o.@..Ixjoldsen&Bedding1995).," For HAT-P-11 the oscillation amplitudes were much smaller than in HAT-P-7, as expected from the general scaling of amplitudes with stellar mass and luminosity \citep[e.g.,][]{Kjelds1995}."824. Thus with the preseut short run of data it has only been possible to determine the large separation Amy—180.1wz from the maxininun in the correlation analysis., Thus with the present short run of data it has only been possible to determine the large separation $\Delta \nu_0 = 180.1 \muHz$ from the maximum in the correlation analysis.825 We have matched this to a exid of models. includiue diffusion aud settling of elim. with masses between 0.7 and (OAL. and [Fe/II] between 0.21 and 0.11.," We have matched this to a grid of models, including diffusion and settling of helium, with masses between 0.7 and $0.9 \, \Msun$ and [Fe/H] between 0.21 and 0.41."826 These models provide a good fit to the observed Zig and L/L.: note that in the present case the luminosity is based on a reasonably well-determined parallax., These models provide a good fit to the observed $T_{\rm eff}$ and $L/\Lsun$; note that in the present case the luminosity is based on a reasonably well-determined parallax.827 We have determined au estimate of (p.j bv averaging the results of those models which match the observed Ary aud Le within 2 standard deviations (4100 IIS) from the value of Tig. provided by Dakosctal. (2010): the result is (p)=2.5127+0.00095 ," We have determined an estimate of $\rhomean$ by averaging the results of those models which match the observed $\Delta \nu_0$ and lie within 2 standard deviations $\pm 100$ K) from the value of $T_{\rm eff}$ provided by \citet{Bakos2010}; the result is $\rhomean = 2.5127 \pm 0.0009 \, {\rm g \, cm^{-3}}$."828Although the formal error is extremely siuall. owing&cm to a tight relation between the large separation aud the nien density for stars in this region iu the WR ciagrai. the true error ds 1idoubtedlv substanally lareer.," Although the formal error is extremely small, owing to a tight relation between the large separation and the mean density for stars in this region in the HR diagram, the true error is undoubtedly substantially larger."829 m particular. we ucelected the eror in the determination of Avy aud these data have not allowed a correction for the systematic errors iu the modeling of the near-surface lavers of the star.," In particular, we neglected the error in the determination of $\Delta \nu_0$ and these data have not allowed a correction for the systematic errors in the modeling of the near-surface layers of the star."830 Here also we were unable to determine individual requencies frou the present set of data., Here also we were unable to determine individual frequencies from the present set of data.831 The expected almplitucdes are sinaller than for ILAT-P-7. aud the noise evel higher due to the fainter magnitude of TYES-2.," The expected amplitudes are smaller than for HAT-P-7, and the noise level higher due to the fainter magnitude of TrES-2."832 The correlation analysis vielded two possible values of Amy: 97.5plz and 130.7pz., The correlation analysis yielded two possible values of $\Delta \nu_0$ : $97.7 \muHz$ and $130.7 \muHz$.833 For this star (pi) has con determined from the analysis of the transit licht curve., For this star $\rhomean$ has been determined from the analysis of the transit light curve.834 Sozzettictal.(2007). obtained £p.)= 7. while Southworth(2009) found. {p.)=1.12£013¢cn 7.," \citet{Sozzet2007} obtained $\rhomean = 1.375 \pm 0.065 \, {\rm g \, cm^{-3}}$ , while \citet{Southw2009} found $\rhomean = 1.42 \pm 0.13 \,{\rm g \, cm^{-3}}$ ."835 From the scaling with (9.2? the sxunaler of the two possible values of Amy is clearly inconsistent with these values of ip while Avy=130.7gllz vields models that are consistent with the observedZig aud log(g) of Sozzettietal.(2007) as well as with these values of the mean deuity.," From the scaling with $\rhomean^{1/2}$ the smaller of the two possible values of $\Delta \nu_0$ is clearly inconsistent with these values of $\rhomean$, while $\Delta \nu_0 = 130.7 \muHz$ yields models that are consistent with the observed$T_{\rm eff}$ and $\log(g)$ of \citet{Sozzet2007}836 as well as with these values of the mean density."837 Hore we considered a grid of models with νοµ diffusion and settling. masses between 0.55 and LIAL. and [Fe/T]| between 0.25 and 0.05.," Here we considered a grid of models with helium diffusion and settling, masses between 0.85 and $1.1 \, \Msun$ and [Fe/H] between $-0.25$ and $-0.05$."838 Determining again the mean value of (p.? for those models that matched Amy aud had τω within two standard deviations of the value of Sozzettietal.(2007) we obtained (po)=1.3233+0.0027ecm7.," Determining again the mean value of $\rhomean$ for those models that matched $\Delta \nu_0$ and had $T_{\rm eff}$ within two standard deviations of the value of \citet{Sozzet2007} we obtained $\rhomean = 1.3233 \pm 0.0027 \, {\rm g \, cm^{-3}}$ ."839 As in the case of TAT-P-11 the true error is likely substantially higher., As in the case of HAT-P-11 the true error is likely substantially higher.840 The present preliminary analysis provides a striking demoustration of the potential— ofNepler asteroscismologv aud its supporting role iu the analysis of planct hosts., The present preliminary analysis provides a striking demonstration of the potential of asteroseismology and its supporting role in the analysis of planet hosts.841 These stars will undoubtedly be observed throughout the mission aud hence the quality of the data will increase substautiallv., These stars will undoubtedly be observed throughout the mission and hence the quality of the data will increase substantially.842 For ILAT-P-7 the detected frequencies are already close to what will be required for a detailed analysis of the stellar interior. bevoud the determination of the basic parameters of the star.," For HAT-P-7 the detected frequencies are already close to what will be required for a detailed analysis of the stellar interior, beyond the determination of the basic parameters of the star."843 Thus here we can look forward to a test of the assmuptionus of the stellar modeling: the resulting iurproveieuts will further coustrain the overall properties of the star. in particular its age.," Thus here we can look forward to a test of the assumptions of the stellar modeling; the resulting improvements will further constrain the overall properties of the star, in particular its age."844 Also. given he observed esiu/ we expect a rotational splitting 'nparable to that observed in the Sun. aud hence likely detectable with a few mouths of observations.," Also, given the observed $v \sin i$ we expect a rotational splitting comparable to that observed in the Sun, and hence likely detectable with a few months of observations."845 For the other two stars there is strong evidence for the presence of solar-like oscillations: thus continued observations will very likely result in the determination of iudividual frequencies aud hence further constraints on the properties of the stars., For the other two stars there is strong evidence for the presence of solar-like oscillations; thus continued observations will very likely result in the determination of individual frequencies and hence further constraints on the properties of the stars.846 Funding for this Discovery iissiou is provided bv NASA’s Scicuce Mission Directorate., Funding for this Discovery mission is provided by NASA's Science Mission Directorate.847 We are very erateful to the entire. Aepler teu. whose efforts have led to this exceptional mission.," We are very grateful to the entire team, whose efforts have led to this exceptional mission."848 The present work wassupported by the Danish Natural Science Research Council., The present work wassupported by the Danish Natural Science Research Council.849A fundamental question in cosmology is the relation between the galaxy distribution. and the underlving density. Ποια of the gravitationally dominant. dark matter.,A fundamental question in cosmology is the relation between the galaxy distribution and the underlying density field of the gravitationally dominant dark matter.850 According to the standard paracigm of striicture formation. galaxies are harbored. in stable virializecl objects (halos) made of clark matter particles.," According to the standard paradigm of structure formation, galaxies are harbored in stable virialized objects (halos) made of dark matter particles."851 An assumption that has been often mace is that the clustering properies of halos depend. on their mass alone., An assumption that has been often made is that the clustering properties of halos depend on their mass alone.852 Although the asstμηρό seenis over-simplistic-. given the complexity of the hierarchical process of halo formation. it is sustained by t10 excursion set theory (Dond 1991: Lacey Cole 1993: Mo White 1996) and by results of N-simulations of intermediate resolution (Lemson WKaullmann 1999: Percival 2003).," Although the assumption seems over-simplistic given the complexity of the hierarchical process of halo formation, it is sustained by the excursion set theory (Bond 1991; Lacey Cole 1993; Mo White 1996) and by results of N-simulations of intermediate resolution (Lemson Kauffmann 1999; Percival 2003)."853 Only recently Gao. Springel White (2005) usec a simulation of exceptionally large dynamical range (the Millennium Simulation. Springel et al.," Only recently Gao, Springel White (2005) used a simulation of exceptionally large dynamical range (the Millennium Simulation, Springel et al."854 2005) to show that the clustering of halos depend also on the their age. which is deined as the time since a halo acquired. half of its current mass.," 2005) to show that the clustering of halos depend also on the their age, which is defined as the time since a halo acquired half of its current mass."855" They have found. that the ""oldest 1054 of the halos wih mass 107.PAL. are more than 5 times more correlate hen the “youngest” 104 halos ol the same mass."," They have found, that the “oldest” $10\%$ of the halos with mass $10^{11}h^{-1}M_{\odot}$ are more than 5 times more correlated then the “youngest” $10\%$ halos of the same mass."856 This assemaly bias has been confirmed by Hlarker (2006) using marked correlation functions on the same simulation. anc by Wechsler (2006) and Jing Mo (2006) using independent. simulations.," This assembly bias has been confirmed by Harker (2006) using marked correlation functions on the same simulation, and by Wechsler (2006) and Jing Mo (2006) using independent simulations."857 Wetzel (2007) also ound dependence of clustering on halo history. but only when using a dillerent definition for the assembly recshilt.," Wetzel (2007) also found dependence of clustering on halo history, but only when using a different definition for the assembly redshift."858 We stil lack a completely satisfactory explanation for the origin of assembly. bias., We still lack a completely satisfactory explanation for the origin of assembly bias.859 For gaussian initial conditions. simple arguments. based. on the spherical collapse mocel applied to narrow and. broad. initial density peaks which would. collapse to halos of the same mass at the present time do predict an assembly bias. but with vounger halos being more clustered. than older ones.," For gaussian initial conditions, simple arguments based on the spherical collapse model applied to narrow and broad initial density peaks which would collapse to halos of the same mass at the present time do predict an assembly bias, but with younger halos being more clustered than older ones."860 This trend. of the bias is opposite to what is seen in simulations., This trend of the bias is opposite to what is seen in simulations.861 'Tidal stripping has been also invoked. as a possible mechanism (e.g. Diemand. Ixuhlen. Aladau 2007).," Tidal stripping has been also invoked as a possible mechanism (e.g. Diemand, Kuhlen Madau 2007)."862 Because of mass stripping bv the tidal gravitational field of the large mass concentration. nearby halos would have been of higher mass in a dillerent. environment.," Because of mass stripping by the tidal gravitational field of the large mass concentration, nearby halos would have been of higher mass in a different environment."863 Therefore. these halos would have earlier. formation times and would be more biased than halos of the same mass in the field.," Therefore, these halos would have earlier formation times and would be more biased than halos of the same mass in the field."864 Avila-Reese (2005) suggested tidal stripping as a mechanism responsible for generation of assembly bias in the high density regions whereas in low-density regions the cosmological initial conditions play a more important role., Avila-Reese (2005) suggested tidal stripping as a mechanism responsible for generation of assembly bias in the high density regions whereas in low-density regions the cosmological initial conditions play a more important role.865 Maulbetsch, Maulbetsch866We are grateful to R. Castillo for the help provided at La Silla and to M. de Santos-Lleó for fruitful discussions.,We are grateful to R. Castillo for the help provided at La Silla and to M. de Santos-Lleó for fruitful discussions.867 This work has been partially supported by Spanish CICYT grant ESP95-0389-C02-02 and by the University of Bologna (Funds for selected research topics)., This work has been partially supported by Spanish CICYT grant ESP95-0389-C02-02 and by the University of Bologna (Funds for selected research topics).868 Jochen Heidt and Thomas Seitz acknowledge support by the Deutsche Forschungsgemeinschaft through SFB 328., Jochen Heidt and Thomas Seitz acknowledge support by the Deutsche Forschungsgemeinschaft through SFB 328.869"a critical density universe. heuce O,, since fx(0.6“tu","a critical density universe, hence $\Om$ since $f\simeq \Om^{0.6}$."870"o On the other hand. while clustering alone the transverse directions of statistical standard rulers such as BAO eives the augular distance. realspace clustering along the longitudinal direction gives the ITubble rate. so that colmplementary information can be derived frou, both ivections. and one can use the longitudiual/trausverse ratio to perform the Alcock-Paczyvuski test (?).."," On the other hand, while clustering along the transverse directions of statistical standard rulers such as BAO gives the angular distance, real-space clustering along the longitudinal direction gives the Hubble rate, so that complementary information can be derived from both directions, and one can use the longitudinal/transverse ratio to perform the Alcock-Paczynski test \citep{Alcock1979}."871 Thus. it is interesting to extend the analysis presented i the previous sections to the redshift-space power xctima.," Thus, it is interesting to extend the analysis presented in the previous sections to the redshift-space power spectrum."872 Rather than expanding on multipoles. we focus u the clustering along the radial direction. as compared ith the transverse directions.," Rather than expanding on multipoles, we focus on the clustering along the radial direction, as compared with the transverse directions."873 Of course. another effect at comes into plav in galaxy survevs is the bias. which iav show some scale dependence.," Of course, another effect that comes into play in galaxy surveys is the bias, which may show some scale dependence."874 However. we do not udyv this effect here. as this is a rather differeut process.," However, we do not study this effect here, as this is a rather different process."875 Wo first recall the nonlinear redshift-space power spectruni associated with the Zeldovich cyvuamics., We first recall the nonlinear redshift-space power spectrum associated with the Zeldovich dynamics.876The redshift-space coordinate s of a galaxy is Xl e. where x ds its conmioviug position. v=«x its peculiar velocity. aud e. the uit vector of theline of sight.,"The redshift-space coordinate $\vs$ of a galaxy is + _z, where $\vx$ is its comoving position, $\vv=a\dot{\vx}$ its peculiar velocity, and $\ve_z$ the unit vector of theline of sight."877 Within the Zeldovich dvuauices (1)) the peculiar velocity is V(90) TM leading to siiq..f) = | Wei fleur. Lie. where D ds the Lnear growth factor aud f(:) dluD/dlue.," Within the Zeldovich dynamics \ref{Zeldef}) ) the peculiar velocity is = a _L = _L, leading to ,t) = + _L + f _L) _z where $D$ is the linear growth factor and $f(z)= \dd\ln D/\dd\ln a$ ."878 Tn the following we use a “plane-parallel” approximation and we denote the longitudinal and transverse directions to the line of sight bv the subscripts | and L., In the following we use a “plane-parallel” approximation and we denote the longitudinal and transverse directions to the line of sight by the subscripts $\parallel$ and $\perp$.879" Thus we have LE|FN,. (v, "," Thus we have = + (1+f), =."880"The conservation of matter reads againas p(s)ds pdq. where we denote the redshift-space quantities by a superscript "". and as in Eqs.(3))-(7)) the redshift-space power spectrum readsas 191] soi]."," The conservation of matter reads againas $\rho^{s}(\vs)\dd\vs=\rhob\dd\vq$ , where we denote the redshift-space quantities by a superscript “s”, and as in \ref{rhox}) \ref{Pkxq}) ) the redshift-space power spectrum readsas ) = ."881 Following ?.. it is convenieut to introduce the vector K. which is the wavevector k stretched by (1|f) along the line of sight. K= (Lif) yey.," Following \citet{Taylor1996}, it is convenient to introduce the vector $\vK$ , which is the wavevector $\vk$ stretched by $(1+f)$ along the line of sight, = (1+f) _z +."882" Then Eq.(81)) writes as (sce Eq.(13))) P*(k)) =PiU], = where jig,—(8q)/(vq)."," Then \ref{Pkq-s}) ) writes as (see \ref{PkIn}) )) ) = = , where $\mu_{Kq}=(\vK\cdot\vq)/(Kq)$."883 Using spherical coordinates about the vector K. expaudiug parts of the exponentials and using Eq.(11)) we obtain P*(k))= ( zu with iB kc244 i204FEDN," Using spherical coordinates about the vector $\vK$, expanding parts of the exponentials and using \ref{int-mu}) ) we obtain ) = )^m, with _k=, = , K^2= k^2 _k^2(2f+f^2)]."884 Expression (89)) holds for amy wavemuuber k and (μον how the redshift-space power spectrmu depends on both A and pj., Expression \ref{Psjn}) ) holds for any wavenumber $\vk$ and shows how the redshift-space power spectrum depends on both $k$ and $\mu_k$.885 As recalled above and as is obvious ποια Eq.(83)). the redshift-space power spectrum for wavevectors perpendicular to the line of sight is equal to the real-spacepower spectrui. hy) p= DG). and we can check that we recover Eq.(18)) from Eq.(89)}) for µε= 0. Forlougitudinal wavevectors. we suuply have K=(1| f)k. so that Exq.(88)) simplifiesas = otal] where p=(Kk:q/(hq)=qifq. as in Eq.{13)).," As recalled above and as is obvious from \ref{sd-perp}) ), the redshift-space power spectrum for wavevectors perpendicular to the line of sight is equal to the real-spacepower spectrum, ) = ), and we can check that we recover \ref{Pkjn}) ) from \ref{Psjn}) ) for $\mu_k=0$ Forlongitudinal wavevectors, we simply have $\vK=(1+f)\vk$ , so that\ref{Psk-Iq}) ) simplifiesas = , where $\mu=(\vk\cdot\vq)/(k q)=q_{\parallel}/q$, as in\ref{PkIn}) )."886 Thus we see at ounce that. along the line of sight.the effect of," Thus we see at once that, along the line of sight,the effect of"887the possibility. of the disc warp having a substantial amplitude in the centre of the disc.,the possibility of the disc warp having a substantial amplitude in the centre of the disc.888 Nelson Papaloizou (2000) did not find such warps in their non-linear SIL computations and attribute this failure to a presumption that “non-linear ellects. lead to the damping of short wavelength warps]. and thus cause the alignment of inner disc regions in which the tilt amplitude would otherwise change rapidly on small length-scales.," Nelson Papaloizou (2000) did not find such warps in their non-linear SPH computations and attribute this failure to a presumption that “non-linear effects lead to the damping of short wavelength [warps], and thus cause the alignment of inner disc regions in which the tilt amplitude would otherwise change rapidly on small length-scales”."889 Although this may be the case. we note that for the case we consider. with Hilt~OL. the radial leneth-scales of the warps are e&enerallv at. least of order the local radius. A. (Fig.," Although this may be the case, we note that for the case we consider, with $H/R \sim 0.1$, the radial length-scales of the warps are generally at least of order the local radius, $R$, (Fig."890 2) and are not small compared to the local disc scale Lf., 2) and are not small compared to the local disc scale $H$.891 We note further that once the radial Iength-scale of the warp variation becomes short. the clispersive nature of the warp waves is likely to become significant and may delay the onset of non-linearity of the waves.," We note further that once the radial length-scale of the warp variation becomes short, the dispersive nature of the warp waves is likely to become significant and may delay the onset of non-linearity of the waves."892 In addition. in their original paper. Ivanov Llarionoy (1997) point out that although the formal computations predict a cise warp at inner raclii. such predictions might be nullified if the warp itself gives rise to turbulence within the disc. and. so a hieh local elfective viscosity.," In addition, in their original paper, Ivanov Illarionov (1997) point out that although the formal computations predict a disc warp at inner radii, such predictions might be nullified if the warp itself gives rise to turbulence within the disc, and so a high local effective viscosity."893 They. suggest that the oscillatory vertical shear within the cise caused by the warp (Papaloizou Pringle 1983) might become shear unstable., They suggest that the oscillatory vertical shear within the disc caused by the warp (Papaloizou Pringle 1983) might become shear unstable.894 Ciammie. Goocman Osgilvie (2000) have investigated this possibility. and. show that instability occurs through a parametric effect. ancl is likely to set in when A|z308€.," Gammie, Goodman Ogilvie (2000) have investigated this possibility, and show that instability occurs through a parametric effect and is likely to set in when $|A|\ga 30895\alpha\Omega$."896 We have not discussed the interesting δαquestion of the net torque between the disc and the black hole. or the time-scale for mutual alignment. under conditions such that the warp propagates in a wavelike manner.," We have not discussed the interesting question of the net torque between the disc and the black hole, or the time-scale for mutual alignment, under conditions such that the warp propagates in a wavelike manner."897 The torque may be considered to be exerted. in launching the steady train of inwardly propagating bending waves. which carries a certain llux of angular momentum.," The torque may be considered to be exerted in launching the steady train of inwardly propagating bending waves, which carries a certain flux of angular momentum."898 Unlike the case of resonantly launched waves in problems of clises subject to periodic tical forcing (Ciolclreich “Premaine 1979). the torque cannot be simply expressed in terms of the properties of the disc in the neighbourhood of a certain radius.," Unlike the case of resonantly launched waves in problems of discs subject to periodic tidal forcing (Goldreich Tremaine 1979), the torque cannot be simply expressed in terms of the properties of the disc in the neighbourhood of a certain radius."899 Furthermore. if the viscosity is small enough that the waves reach the inner radius and reflect. from. it. the torque that would. cause a mutual alignment is partially or completely: cancelled.," Furthermore, if the viscosity is small enough that the waves reach the inner radius and reflect from it, the torque that would cause a mutual alignment is partially or completely cancelled."900 For example. in the case ν=i loading to the solution (26)) in the absence of viscosity. the integrated. horizontal torque is given in termi of an integral over the disc of the relevant components of the local torque FUR).," For example, in the case $\nu={\textstyle{{1}\over{2}}}$ leading to the solution \ref{cos_solution}) ) in the absence of viscosity, the integrated horizontal torque is given in term of an integral over the disc of the relevant components of the local torque $\bT(R,t)$."901 Writing To—gHD.the total horizontal torque is Rather than causing a mutual alignment. this torquc causes a slow mutual precession of the disc and. black role.," Writing $T =902T_x + iT_y$, the total horizontal torque is Rather than causing a mutual alignment, this torque causes a slow mutual precession of the disc and black hole."903 Phe direction and magnitude of the precession depend sensitively on the parameters of the disc., The direction and magnitude of the precession depend sensitively on the parameters of the disc.904 Finally. we note that if the outer clise and the black role are misaligned by more than 907 so that the disc can of considered. retrograde. the steady wavelike solution is replaced. by an evanescent solution.," Finally, we note that if the outer disc and the black hole are misaligned by more than $90\degr$ so that the disc can be considered retrograde, the steady wavelike solution is replaced by an evanescent solution."905 This occurs. because he nodal and apsidal precession are in Opposite senses (see equations LO. 14 and 15)).," This occurs because the nodal and apsidal precession are in opposite senses (see equations \ref{k2h2}, \ref{kerr2}906 and \ref{kerr3}) )."907 In that case the steady shape of he disc may be expected to be qualitatively similar to that envisaged by Dardeen Petterson (1975). with the inner disc aligned with the equator of the black hole but rotating in the opposite sense.," In that case the steady shape of the disc may be expected to be qualitatively similar to that envisaged by Bardeen Petterson (1975), with the inner disc aligned with the equator of the black hole but rotating in the opposite sense."908 We illustrate this in Fig., We illustrate this in Fig.909 6., 6.910 Vhe result that. in low-viscosity cliscs around a νο black hole. the inner parts of the disc are not necessarily aligned with the black hole. as found by Ivanov Llarionoy (1997). is a general one.," The result that, in low-viscosity discs around a Kerr black hole, the inner parts of the disc are not necessarily aligned with the black hole, as found by Ivanov Illarionov (1997), is a general one."911 Indeed. depending on the dise properties. it is possible for the inner disc to be tilted at a greater angle to the hole than the outer parts of the. disc.," Indeed, depending on the disc properties, it is possible for the inner disc to be tilted at a greater angle to the hole than the outer parts of the disc."912 In addition. because the inner disc shape depends sensitively on the radial dependence of dise properties (such as surface density ancl dise thickness). a change (for cxample) in the accretion rate can give rise to à change in the inner disc warp. even without changing the tilt of the outer disc.," In addition, because the inner disc shape depends sensitively on the radial dependence of disc properties (such as surface density and disc thickness), a change (for example) in the accretion rate can give rise to a change in the inner disc warp, even without changing the tilt of the outer disc."913 These results contrast with the usual finding (e.g. Nelson Papaloizou 2000) and/or assumption (e.g. Natarajan unele5 1998) that the inner regions5 of the disc align5 with he equator of the hole., These results contrast with the usual finding (e.g. Nelson Papaloizou 2000) and/or assumption (e.g. Natarajan Pringle 1998) that the inner regions of the disc align with the equator of the hole.914 In the discussion above. we have noted above that confirmation of these results awaits a oper calculation using full general relativity. as well as an assessment of possible non-linear. dispersive anc parametric ellects.," In the discussion above, we have noted above that confirmation of these results awaits a proper calculation using full general relativity, as well as an assessment of possible non-linear, dispersive and parametric effects."915 Nevertheless. it is evident that the results presented rere could have important implications for the directions in which jets might emanate from accreting spinning black doles.," Nevertheless, it is evident that the results presented here could have important implications for the directions in which jets might emanate from accreting spinning black holes."916 Indeed. if the region responsible for direction of jet collimation is at several γα from the hole. which is likely o be the case for relativistic jets. then the Newtonian approximations applied above may be adequate to confirm he effect. even if the very inner regions of the disc are indeed aligned by the fully relativistic effects close to the hole.," Indeed, if the region responsible for direction of jet collimation is at several radii from the hole, which is likely to be the case for relativistic jets, then the Newtonian approximations applied above may be adequate to confirm the effect, even if the very inner regions of the disc are indeed aligned by the fully relativistic effects close to the hole."917 A, A918on convective Three-cimensional numerical studies on stellar differential rotation also exist (Brownal.2008:Miesch&Toomre 2009)..,"on convective Three-dimensional numerical studies on stellar differential rotation also exist \citep{2008ApJ...689.1354B,2009AnRFM..41..317M}."919 In these studies. thev resolve stellar thermal driven convection and can calculate a sell-consistent. turbulent angular momentum transport and anisotropy. of turbulent thermal conductivity.," In these studies, they resolve stellar thermal driven convection and can calculate a self-consistent turbulent angular momentum transport and anisotropy of turbulent thermal conductivity."920 The subaciabatic laver below the convection zone. however. 1s not included.," The subadiabatic layer below the convection zone, however, is not included."921 The effects of anisotropy. of turbulent thermal conductivity and the subadiabatic laver are discussed in this paper., The effects of anisotropy of turbulent thermal conductivity and the subadiabatic layer are discussed in this paper.922 Usine numerical set(ines similar to those of Rempels (2005b). we solve (he axisvuunetric hyvdrocvuamic equations in spherical geometry. (7.0). where r is the radius. and 0 is the colatitude.," Using numerical settings similar to those of Rempel's (2005b), we solve the axisymmetric hydrodynamic equations in spherical geometry $(r,\theta)$, where $r$ is the radius, and $\theta$ is the colatitude."923 The basic assumptions are as follows., The basic assumptions are as follows.924"= logApm - logex X). where log€.(X) is the solar abundance of the element ""X"".","= $\log{A_{pm}}$ - $\log\epsilon_\odot(X)$ , where $\log\epsilon_\odot(X)$ is the solar abundance of the element “X”."925 The uncertainty is calculated by For [X1/X2] the Vrbemuncertainties are determined by Uncertainties on elements are shown in parenthesis in Tab., The uncertainty is calculated by For [X1/X2] the uncertainties are determined by Uncertainties on elements are shown in parenthesis in Tab.926 2 and by the error bars in figures., \ref{medxfe} and by the error bars in figures.927 Abundances for the sample stars are shown in Figs., Abundances for the sample stars are shown in Figs.928 | to 4., 1 to 4.929 In order to compare our stars with stars of different classifications. we have also added strong and mild Ba-stars to the plots. and normal field stars from Boyarchuk et al. (," In order to compare our stars with stars of different classifications, we have also added strong and mild Ba-stars to the plots, and normal field stars from Boyarchuk et al. ("9302002). Liangetal. (2003).. Yushchenkoetal. (2004).. Allen Barbuy (2006) and Allen Porto de Mello (in preparation).,"2002), \citet{lia03}, \citet{yush04}, Allen Barbuy (2006) and Allen Porto de Mello (in preparation)."931 Carbon and N abundances are plotted in Fig., Carbon and N abundances are plotted in Fig.932 1 as a function of [Fe/H] and log g. As can be seen in this figure. C is slightly enhancedin both HD 11397," 1 as a function of [Fe/H] and log g. As can be seen in this figure, C is slightly enhancedin both HD 11397"933A correspondiug code has been designed in 777 and C languages for procedures of the CMDB sky imap analysis.,A corresponding code has been designed in 77 and C languages for procedures of the CMB sky map analysis.934" The aij, calculation is the main goal.", The $a_{\ell m}$ calculation is the main goal.935 εως are used in colmponent separation methods and tests for non-Caussianity (Chiang ef alt? 2003: Naselekv et alttt? 2003b. 2001).," $a_{\ell m}$ -s are used in component separation methods and tests for non-Gaussianity (Chiang et $^{10}$ 2003; Naselsky et $^{11,12}$ 2003b, 2004)."936" It is oriented on the fast and accurate calculation of the 6;,, for the given resolution specifies by the beam size.", It is oriented on the fast and accurate calculation of the $a_{\ell m}$ for the given resolution specified by the beam size.937" Using accurately calculated 0;,,-3. one can reproduce any pixclization scheme by the eiven pixe centers: GLESP. HIEALPix. Igloo or Icosaliedron."," Using accurately calculated $a_{\ell m}$ -s, one can reproduce any pixelization scheme by the given pixel centers: GLESP, HEALPix, Igloo or Icosahedron."938Acknowledginents.. This paper was supporte in put by Dammark Cauudforskuigsfoud through its support for the establishiment of the Theorica Astroplivsics Ceuter., This paper was supported in part by Danmark Grundforskningsfond through its support for the establishment of the Theorical Astrophysics Center.939 Authors are thankful to Vladislav Stolvarov for testing parallel capabilities aud GGL visualization tool for current pre-release version of GLESDP., Authors are thankful to Vladislav Stolyarov for testing parallel capabilities and GL visualization tool for current pre-release version of GLESP.940 OVV thauks the RFBR for partial support of the work through its eraut 0207.90038., OVV thanks the RFBR for partial support of the work through its grant 02–07–90038.941 Some of the results iu this paper have been derived using the TEALPix package (Cdvrski. Iivon. aud Waudelt® 1999).," Some of the results in this paper have been derived using the HEALPix package (Górrski, Hivon, and $^{6}$ 1999)."942 theory so that irregularly shaped particles can be simulated.,) theory so that irregularly shaped particles can be simulated.943"2005)) In addition, the three grain sizes used are 0.1, 1.5 and 6.0 zm, representing well the spectroscopic behaviour of very small, intermediate-sized and large grains."," In addition, the three grain sizes used are 0.1, 1.5 and 6.0 $\mu$ m, representing well the spectroscopic behaviour of very small, intermediate-sized and large grains."944" For the crystalline species, however, the code is limited to only 2 grain sizes (0.1 and 1.5 um)."," For the crystalline species, however, the code is limited to only 2 grain sizes (0.1 and 1.5 $\mu$ m)."945" This restriction is imposed because large crystalline grains are highly degenerate with large amorphous grains can be seen in Figure 1 of Olofssonetal. 2010)), and (asbecause the production of large 6.0 jum pure crystals is not expected via thermal annealing (Gail"," This restriction is imposed because large crystalline grains are highly degenerate with large amorphous grains (as can be seen in Figure 1 of \citealt{OF10}) ), and because the production of large 6.0 $\mu$ m pure crystals is not expected via thermal annealing \citep{GA04}."946 The B2C method 2004)..itself consists of three steps., The B2C method itself consists of three steps.947" First, the continuum is estimated and subtracted from the observed spectrum."," First, the continuum is estimated and subtracted from the observed spectrum."948 The adopted continuum is built by using a power-law plus a black-body at temperature Teont-, The adopted continuum is built by using a power-law plus a black-body at temperature $T_{\rm cont}$.949 The power-law represents the mid-IR tail of emission from the star and inner disk rim., The power-law represents the mid-IR tail of emission from the star and inner disk rim.950" The black-body is designed to contribute at longer wavelengths, and is therefore constrained to be less than 150 K. Each dust component is then fitted separately to the continuum-subtracted spectrum."," The black-body is designed to contribute at longer wavelengths, and is therefore constrained to be less than 150 K. Each dust component is then fitted separately to the continuum-subtracted spectrum."951" The second step is to fit the warm component to reproduce the 10 um silicate feature between ~7.5 and 13.5 um. This is done by summing up the 13 mass absorption coefficients (Nspecies = 5, Neizes = 3 or 2, for amorphous and crystalline species, respectively), multiplied by a black-body B,(Ty) at a given warm temperature Ty."," The second step is to fit the warm component to reproduce the 10 $\mu$ m silicate feature between $\sim$ 7.5 and 13.5 $\mu$ m. This is done by summing up the 13 mass absorption coefficients $N_{\rm952 species}$ = 5, $N_{\rm sizes}$ = 3 or 2, for amorphous and crystalline species, respectively), multiplied by a black-body $B_{\nu} (T_{\rm w})$ at a given warm temperature $T_{\rm w}$."953" The third step is to fit the residuals, mostly at longer wavelengths, over the entire spectral range — 35 um)."," The third step is to fit the residuals, mostly at longer wavelengths, over the entire spectral range (5 – 35 $\mu$ m)."954" This is done in a similar manner, for a (5given cold temperature Ίο."," This is done in a similar manner, for a given cold temperature $T_{\rm c}$."955" The final fit is a sum of the three fits described, as can be seen in Figure 1.."," The final fit is a sum of the three fits described, as can be seen in Figure \ref{f_fit}."956" The entire fitting process is based on a Bayesian analysis, combined with a Monte Carlo Markov chain, in order to randomly explore the space of free parameters."," The entire fitting process is based on a Bayesian analysis, combined with a Monte Carlo Markov chain, in order to randomly explore the space of free parameters."957" The resulting mean mass-average grain size is the sum of all sizes fitted, each size being weighted by their corresponding masses, as: where a;=O.lym (small grains), ag=1.5m (intermediate-sized grains) and a3=6jum (large grains)."," The resulting mean mass-average grain size is the sum of all sizes fitted, each size being weighted by their corresponding masses, as: where $a_1 = 0.1\,\mu$ m (small grains), $a_2 = 1.5\,\mu$ m (intermediate-sized grains) and $a_3 = 6\,\mu$ m (large grains)."958 Further details and tests of the B2C procedure can be found in Olofssonetal.(2010)., Further details and tests of the B2C procedure can be found in \citet{OF10}.959". That paper also demonstrates that the procedure is robust for statistical samples, and that the relative comparisons between samples, which are the focus of this paper, should not suffer from the assumptions that enter in the procedure."," That paper also demonstrates that the procedure is robust for statistical samples, and that the relative comparisons between samples, which are the focus of this paper, should not suffer from the assumptions that enter in the procedure."960" 'The robustness of the procedure is evaluated by fitting synthetic spectra, and is discussed in detail in their Appendix A. The influence of the continuum estimate is also discussed, especially for the cold component for both grain sizes and crystallinity fractions, and it is shown that prescriptions that do not use large 6 jum grains (which are, to some degree, degenerate with the continuum) give fits that are not so good."," The robustness of the procedure is evaluated by fitting synthetic spectra, and is discussed in detail in their Appendix A. The influence of the continuum estimate is also discussed, especially for the cold component for both grain sizes and crystallinity fractions, and it is shown that prescriptions that do not use large 6 $\mu$ m grains (which are, to some degree, degenerate with the continuum) give fits that are not so good."961" For the amorphous grains, the B2C procedure uses the Mie scattering theory to compute mass absorption coefficients."," For the amorphous grains, the B2C procedure uses the Mie scattering theory to compute mass absorption coefficients."962" However, Minetal.(2007) found that they could best reproduce the extinction profile toward the galactic center using the DHS scattering theory, with a maximum filling factor of 0.7."," However, \citet{MI07}963 found that they could best reproduce the extinction profile toward the galactic center using the DHS scattering theory, with a maximum filling factor of 0.7."964 The most striking difference between Mie and DHS mass absorption coefficients is seen for the O-Si-O bending mode around 20 um. Here we investigate the influence of the use of DHS instead of Mie for amorphous grain with an olivine or pyroxene stoichiometry., The most striking difference between Mie and DHS mass absorption coefficients is seen for the O–Si–O bending mode around 20 $\mu$ m. Here we investigate the influence of the use of DHS instead of Mie for amorphous grain with an olivine or pyroxene stoichiometry.965 We conducted tests on a sub-sample of 30 objects (15 in Serpens and 15 in Taurus)., We conducted tests on a sub-sample of 30 objects (15 in Serpens and 15 in Taurus).966 The conclusion of such tests is that it has a small influence on the quantities we discuss in this study., The conclusion of such tests is that it has a small influence on the quantities we discuss in this study.967" For the warm component of the 30 objects, we find a change in the mean crystallinity fraction of (the mean crystallinity for this sub-sample using DHS is versus using Mie), which is in the range of uncertainties claimed in this study."," For the warm component of the 30 objects, we find a change in the mean crystallinity fraction of (the mean crystallinity for this sub-sample using DHS is versus using Mie), which is in the range of uncertainties claimed in this study."968 We also computed the mean slope of grain size distributions to gauge the effectof using DHS on grain sizes., We also computed the mean slope of grain size distributions to gauge the effectof using DHS on grain sizes.969" On average, the grain size distribution indices are steeper by ~0.2 (with a mean slope of -3.01 for this sub-sample using DHS versus -2.80 using Mie)."," On average, the grain size distribution indices are steeper by $\sim$ 0.2 (with a mean slope of -3.01 for this sub-sample using DHS versus -2.80 using Mie)."970" Therefore, our main conclusions are preserved for the warm component."," Therefore, our main conclusions are preserved for the warm component."971" Concerning the cold component, the inferred crystallinity fraction using DHS is versus with Mie, a mean increase of7."," Concerning the cold component, the inferred crystallinity fraction using DHS is versus with Mie, a mean increase of."972"4%.. For the mean slope of grain size distributions, a negligible decrease is found (-3.07 using DHS versus -3.01 for Mie)."," For the mean slope of grain size distributions, a negligible decrease is found (-3.07 using DHS versus -3.01 for Mie)."973" Again, the differences found are within our significant errors for the cold component and do not change any of our conclusions."," Again, the differences found are within our significant errors for the cold component and do not change any of our conclusions."974 It is important to note that the S/N generally degrades at longer wavelengths when compared to shorter wavelengths., It is important to note that the S/N generally degrades at longer wavelengths when compared to shorter wavelengths.975 The lower S/N reflect on the cold component fits and will most likely result in larger uncertainties., The lower S/N reflect on the cold component fits and will most likely result in larger uncertainties.976 We evaluate that the fits to the cold component are reliable and add important information on the dust mineralogy (albeit with larger uncertainties) and thus those results are included in the following discussion., We evaluate that the fits to the cold component are reliable and add important information on the dust mineralogy (albeit with larger uncertainties) and thus those results are included in the following discussion.977 The IRS spectra of the 139 YSOs with IR excess discussed in 2 were fitted with the B2C spectral decomposition procedure., The IRS spectra of the 139 YSOs with IR excess discussed in \ref{sdata} were fitted with the B2C spectral decomposition procedure.978 The relative abundances derived for all objects are shown in Appendix A.., The relative abundances derived for all objects are shown in Appendix \ref{sabun}. .979 The, The980Figure 4 shows the distribution of the primary sample in M; versus redshift.,Figure \ref{fig:z-absmag} shows the distribution of the primary sample in $M_r$ versus redshift.981" Note not all the redshifts come from the GAMA AAOmega campaign with the breakdown as follows: 2671 GAMA, 2007 SDSS, 444 2dF Galaxy Redshift Survey, 64 Millennium Galaxy Catalogue, 10 6dF Galaxy Survey, 6 Updated Zwicky Catalogue, 6 Liverpool Telescope, and 2 others via the NASA/IPAC Extragalactic Database."," Note not all the redshifts come from the GAMA AAOmega campaign with the breakdown as follows: 2671 GAMA, 2007 SDSS, 444 2dF Galaxy Redshift Survey, 64 Millennium Galaxy Catalogue, 10 6dF Galaxy Survey, 6 Updated Zwicky Catalogue, 6 Liverpool Telescope, and 2 others via the NASA/IPAC Extragalactic Database."982" The Petrosian photometry, used for selection of the sample, is highly reliable having undergone various visual checks."," The Petrosian photometry, used for selection of the sample, is highly reliable having undergone various visual checks."983 The exception is for overdeblended sources., The exception is for overdeblended sources.984 For these the deblended parts have been identified and associated with a target galaxy., For these the deblended parts have been identified and associated with a target galaxy.985 The r-band Petrosian photometry of these overdeblended sources is recomputed by summing the flux from identified parts., The $r$ -band Petrosian photometry of these overdeblended sources is recomputed by summing the flux from identified parts.986" About 100 galaxies have their Petrosian magnitude brightened by >0.1 mmag from this, with 14 brightened by more than a magnitude (the target part has not been assigned the majority of flux in a few cases)."," About 100 galaxies have their Petrosian magnitude brightened by $>0.1$ mag from this, with 14 brightened by more than a magnitude (the target part has not been assigned the majority of flux in a few cases)."987 It is important to do this prior to calculating Vinax because a nearby galaxy that is deblended into parts would not be deblended nearly so significantly if placed at higher redshift., It is important to do this prior to calculating $\vmax$ because a nearby galaxy that is deblended into parts would not be deblended nearly so significantly if placed at higher redshift.988" A standard method to compute binned GLFs is through weighting each galaxy by 1/Vmax (Schmidt1968),, which is the comoving volume over which the galaxy could be observed within the survey limits (Zmax is the corresponding maximum redshift)."," A standard method to compute binned GLFs is through weighting each galaxy by $1/\vmax$ \citep{Schmidt68}, which is the comoving volume over which the galaxy could be observed within the survey limits $z_{\rm max}$ is the corresponding maximum redshift)."989" In the presence of large-scale structure, large variations in the number density versus redshift, this method can distort the shape ofthe GLF (Efsta"," In the presence of large-scale structure, large variations in the number density versus redshift, this method can distort the shape of the GLF \citep{EEP88}."990thiouetal.1988).. Figure 5 shows the large-scale structure in and around the GAMA regions., Figure \ref{fig:cone-plot} shows the large-scale structure in and around the GAMA regions.991 There are a few substantial overdensities and underdensities as a function of redshift within each region., There are a few substantial overdensities and underdensities as a function of redshift within each region.992ie. binaries plus genuine. single. MS stars (hereafter the )).,"i.e., binaries plus genuine, single, MS stars (hereafter the )."993" The ""MS population"" is defined as the set of stars having a color difference from the MS ridge line (MSRL) smaller (han three (mes the tvpical photometric error at that magnitude level (see Figure5 3)).", The “MS population” is defined as the set of stars having a color difference from the MS ridge line (MSRL) smaller than three times the typical photometric error at that magnitude level (see Figure \ref{regions}) ).994 The operational definition of the “binary population” is 5given in Sects., The operational definition of the “binary population” is given in Sects.995 ?? and 1.3.., \ref{fmin} and \ref{fglob}.996 The high photometric quality and the spatial coverage of the data-sets previously described. allowed us (o study. the binary fraction at different. distances from the cluster centre., The high photometric quality and the spatial coverage of the data-sets previously described allowed us to study the binary fraction at different distances from the cluster centre.997 In particular. here we have defined three concentric annuli bounded by the core radius and the hall-mass radius.," In particular, here we have defined three concentric annuli bounded by the core radius and the half-mass radius."998 The adopted centre of gravity aud structural parameters have been recently determined [rom resolved star counts (Dalessandro et al., The adopted centre of gravity and structural parameters have been recently determined from resolved star counts (Dalessandro et al.999" 2011): the coordinates of the centre are Ajo)=16257""8,925. dono)=—4558.01"": the core. hall-mass and. tidal radii are ος=487. ry=LAT. and r;=19.3"". respectively."," 2011): the coordinates of the centre are $\alpha_{\rm J2000} = 16^{\rm h}\, 57^{\rm m}\, 8.92^{\rm s}$, $\delta_{J2000} = -4\arcdeg\,5\arcmin\, 58.07\arcsec$; the core, half-mass and tidal radii are $r_c=48\arcsec$, $r_h= 147\arcsec$, and $r_t=19.3\arcmin$, respectively."1000" This center is located al ~3.5"" North-West from the one quoted bv Goldsbury et al 2010. a dillerence that has no impact on the following analvsis and the obtained results."," This center is located at $\sim3.5\arcsec$ North-West from the one quoted by Goldsbury et al 2010, a difference that has no impact on the following analysis and the obtained results."1001 Hlence. the first two radial bins (r<r; aud rocorc orgy) are sampled by the ACS data-set. while the third one (r>rj) is covered by the WEDPC? data (see Fig. 1)).," Hence, the first two radial bins $r<r_c$ and $r_c<r<r_h$ ) are sampled by the ACS data-set, while the third one $r>r_h$ ) is covered by the WFPC2 data (see Fig. \ref{map}) )."1002 Since the two data-sets have different saturation ancl completeness levels (see Sect. 2)).," Since the two data-sets have different saturation and completeness levels (see Sect. \ref{data}) ),"1003 we perfomed the analvsis in two different magnitude ranges: the adopted euts along the MSRL are 18.8<J«21.5 for the ACS sample. and 20.3<123 [or the WFPC? one (see Figs.," we perfomed the analysis in two different magnitude ranges: the adopted cuts along the MSRL are $18.8<I<21.5$ for the ACS sample, and $20.3<I<23$ for the WFPC2 one (see Figs."1004 2. and 3))., \ref{cmd} and \ref{regions}) ).1005 These intervals define what we call the magnitude range ol the two data-sets., These intervals define what we call the magnitude range” of the two data-sets.1006 Then. with the aim of having an interval of magnitudes in common between the (wo samples where to directly compare the computed binary fractious. we considered three magnitude sub-ranges defined as follows: a range’ corresponding io IS«I20.3. an range’ ad 20.3&I< 21.5. and a rangee al 21.5<I«23 (all the quoted maenitudee values are measured alonee the MSRL).," Then, with the aim of having an interval of magnitudes in common between the two samples where to directly compare the computed binary fractions, we considered three magnitude sub-ranges defined as follows: a range” corresponding to $18.8<I<20.3$, an range” at $20.3<I<21.5$ , and a range” at $21.5<I<23$ (all the quoted magnitude values are measured along the MSRL)."1007 As is apparent from Fies., As is apparent from Figs.1008 2. and 3.. the range is probed only by the ACS data-set. (he range is found only in the WEPC2 sample. while the range is in Common between thetwo.," \ref{cmd} and \ref{regions}, the range is probed only by the ACS data-set, the range is found only in the WFPC2 sample, while the range is in common between thetwo."1009 (Djorgovski&Davis1987).. Mg» c (Terlevichetal.1981).. Mg» Mg» (Trageretal.2000;Kuntschner2000) Mg» Mg»-o (Trageretal.2000).. Carteretal.1986;Terlevich1990:OI- (Cenarroetal.2001a.b.2002).. Vazdekisetal.2003.. Cenarro," \citep{dd87}, $_2$ $\sigma$ \citep{terlevich81}, $_2$ $_2$ \citep{trager00,kuntschner00} $_2$ $_2$$\sigma$ \citep{trager00}. \citealt{carter86,terlevich90,olszewski91,bica98}) \citep{cen1,cen2,cen3}. \citealt{vazdekis03}, \citet[ hereafter CEN02]{centhesis},"1010 c. c Sagliaetal.(2002.hereafterSAGO?) c. σ c Balcells&Peletier(1994)... Faleón-Barrosoetal.(2002).," $\sigma$ $\sigma$ \citet[ hereafter SAG02]{saglia02} $\sigma$ $\sigma$ $\sigma$ \citet{bp94}, \citet{fpb02}."1011. citepeen! citepaliascenthesis.. Armandroff&Zinn1988;Diazetal.1989;Rutledge Cenarroetal.2001a (4p. r4:/2. aresec? ," \\citep{cen1} \\citepalias{centhesis}, \citealt{armandroff88,diaz89,rutledge97}) \citealt{cen1} $_{\rm eff}$ $_{\rm eff}$ $^2$ "1012Due to the non-Ixeplerian. potential in this test. gas and stellar orbits precess.,"Due to the non-Keplerian potential in this test, gas and stellar orbits precess."1013 Phe precession rate is dilferent at dillerent. radii. and therefore gas orbits become mixed and somewhat circularized over time.," The precession rate is different at different radii, and therefore gas orbits become mixed and somewhat circularized over time."1014 This is most. clearly seen in the last snapshot (lower right) in Fig. 13..," This is most clearly seen in the last snapshot (lower right) in Fig. \ref{fig:ellipt},"1015 where an inner. only mildly. eccentric gaseous ring is present.," where an inner, only mildly eccentric gaseous ring is present."1016 The simulation Ece was run for twice longer than our usual 10 time units., The simulation Ecc was run for twice longer than our usual $10^3$ time units.1017 Nevertheless. at the end of the simulation only 30%2 of eas was turned into stars.," Nevertheless, at the end of the simulation only $\sim 30$ of gas was turned into stars."1018 We hence estimate the disc half-life time fap to be around 3000d time units., We hence estimate the disc half-life time $t_{\rm half}$ to be around 3000 time units.1019 This is 35r times longer than that of the corresponding simulation El with circular orbits., This is $\sim 35$ times longer than that of the corresponding simulation E1 with circular orbits.1020 While some of the dillerence is simply due to a longer orbital time at the location of the gas in test Eec. a fair fraction of the dillerence is due to a comparatively slower star formation.," While some of the difference is simply due to a longer orbital time at the location of the gas in test Ecc, a fair fraction of the difference is due to a comparatively slower star formation."1021 This is not altogether surprising. as gas is heated due to shocks in the eccentric. precessing dise of simulation Ecc.," This is not altogether surprising, as gas is heated due to shocks in the eccentric, precessing disc of simulation Ecc."1022 Figure 14 presents an edge-on view of the column density of the disc and stellar positions at the end of the run Eee., Figure \ref{fig:ecc_side} presents an edge-on view of the column density of the disc and stellar positions at the end of the run Ecc.1023 His quite noticeable that the stellar disc is much thicker than the gaseous disc., It is quite noticeable that the stellar disc is much thicker than the gaseous disc.1024 While it is dillicult to pinpoint the exact reason for this high. geometrical thickness. it is most likely due to interactions between stars (e.g...Navak-shin&Cuaclra.2005:Alexanderetal.. 2006).. which can be substantial given that this simulation has been run for over 10 vears.," While it is difficult to pinpoint the exact reason for this high geometrical thickness, it is most likely due to interactions between stars \citep[e.g.,][]{NC05,AlexanderBA06}, which can be substantial given that this simulation has been run for over $10^5$ years."1025 Disruptions of gasstar clumps at. their orbits’ pericentres or during collisions with cach other in the disc could. also be important., Disruptions of gas–star clumps at their orbits' pericentres or during collisions with each other in the disc could also be important.1026 Several authors speculated that sell-gravitating AGN discs can form very massive objects., Several authors speculated that self-gravitating AGN discs can form very massive objects.1027 Coocman&Tan argued that massive stars formed in such clises will, \cite{GoodmanTan04} argued that massive stars formed in such discs will1028evolved moclel and observed CMESs.,evolved model and observed CMFs.1029 Pherefore.zf we assume hat Daumgardt Alakino’s (2003) IN-body. simulations ediet. approximately the appropriate cluster disruption ime-scale for MS2 D.," Therefore, we assume that Baumgardt Makino's (2003) $N$ -body simulations predict approximately the appropriate cluster disruption time-scale for M82 B, Fig."1030 Eο. 2 shows that the observed cluster mass distribution be retrieved from an initial power-aw CME., \ref{powerlaw.fig} shows that the observed cluster mass distribution be retrieved from an initial power-law CMF.1031 We will now approach this issue starting from an initia og-normal CAL., We will now approach this issue starting from an initial log-normal CMF.1032 We have assumed that. the initial log-normal CME matches that of the almost universal. mass distribution of old GC systems in the local Universe. (ane hus that of the theoretical. (quasi-Jequilibrium CALF of Vesperini 1998)., We have assumed that the initial log-normal CMF matches that of the almost universal mass distribution of old GC systems in the local Universe (and thus that of the theoretical (quasi-)equilibrium CMF of Vesperini 1998).1033" ΠΕ the Daumgardt Makino (2003) results apply (Le. £1,~0.5OS Cyr at an ambient density typica of MS? B (Le. fuuscOS2.5 M. pe ) most of the clusters in the log-normal initial CME of Fie."," If the Baumgardt Makino (2003) results apply (i.e., $t_{\rm dis}^4 \sim 0.5{\rm -}0.8$ Gyr at an ambient density typical of M82 B (i.e., $\rho_{\rm amb} \simeq 0.8{\rm -}2.5$ $_\odot$ $^{-3}$ ), most of the clusters in the log-normal initial CMF of Fig."1034 3. will no vet have been significantly: allected by disruption., \ref{lognormal.fig} will not yet have been significantly affected by disruption.1035 Thus. when we evolve this initial CALF to an age of 1 Gyr. the CALF approximately retains its initial shape. as shown in Fie. 3.," Thus, when we evolve this initial CMF to an age of 1 Gyr, the CMF approximately retains its initial shape, as shown in Fig. \ref{lognormal.fig}."1036 This result. holds. irrespective. of the underlving cluster age and distance distributions and. irrespective of je average ambient density. assumed. (Le. the evolved ο.όν derived in cases 12.4] are identical well within the oervational uncertainties).," This result holds irrespective of the underlying cluster age and distance distributions and irrespective of the average ambient density assumed (i.e., the evolved CMFs derived in cases [1,2,4] are identical well within the observational uncertainties)."1037 The main dillerence. between 10 initial ancl evolved CMES is therefore. caused by. the fects of stellar evolution: the shift. of the peak of the distribution bv AlogiAly/AL.)0.15 is the result of up ο 25 per cent of stellar evolutionary mass loss.," The main difference between the initial and evolved CMFs is therefore caused by the effects of stellar evolution: the shift of the peak of the distribution by $\Delta \log(M_{\rm cl}/{\rm1038M}_\odot) \sim -0.15$ is the result of up to 25 per cent of stellar evolutionary mass loss."1039 With the short. disruption time-seale of cle Crijs ct al. (, With the short disruption time-scale of de Grijs et al. (10402003a). the inal distribution is somewhat more depleted in high-nmiass clusters (case 3] in Fig. 3)).,"2003a), the final distribution is somewhat more depleted in high-mass clusters (case [3] in Fig. \ref{lognormal.fig}) )."1041 We also show the evolved. 1 CGvr-old. CME assuming a slightly. longer disruption time-scale Fl50 Myr (ease M 3]., We also show the evolved 1 Gyr-old CMF assuming a slightly longer disruption time-scale $t_{\rm dis}^4 \sim 50$ Myr (case $'$ ]).1042 A an ambient. density: of 2.5 M. pe7. this is 10. shorter than that. derived from Daumgardt Alakino s (2003) N-body simulations.," At an ambient density of 2.5 $_\odot$ $^{-3}$, this is $10\times$ shorter than that derived from Baumgardt Makino 's (2003) $N$ -body simulations."1043 The predicted CALF still matches the observed distribution satisfactorilv., The predicted CMF still matches the observed distribution satisfactorily.1044 Fherefore. we note that when starting from an initial log-normal CME. the evolved. mass distributions match the observed distribution in MS2 B (Fig.," Therefore, we note that when starting from an initial log-normal CMF, the evolved mass distributions match the observed distribution in M82 B (Fig."1045 Hbb) fairly closely. and that this result. holdsf," \ref{turnover.fig}b b) fairly closely, and that this result holds."1046"ane-scales, ‘To assess the robustness of the results presented in Figs.", To assess the robustness of the results presented in Figs.1047 2 and 3.. we have also evolved the log-normal and power-law initial CMESs using Eq. (," \ref{powerlaw.fig} and \ref{lognormal.fig}, we have also evolved the log-normal and power-law initial CMFs using Eq. ("104812) of Baumgardt Alakino (2003).,12) of Baumgardt Makino (2003).1049 A detailed. comparison shows that the results derived: based on Iq. (2)), A detailed comparison shows that the results derived based on Eq. \ref{cl_mass_evol_L.eq}) )1050 above appear robust: the shape of the Gaussian CALF is unallected by the 1 Cwr-lone evolution in either case. and the turnover of the evolved power-law CALF is discrepant with the observed. peak by more than one order of magnitucle.," above appear robust: the shape of the Gaussian CMF is unaffected by the 1 Gyr-long evolution in either case, and the turnover of the evolved power-law CMF is discrepant with the observed peak by more than one order of magnitude."1051 We note. however. that Baumeardt Alakino’s (2003) N-bocky simulations were performed assuming a smooth uncerlving tidal field: they do not include the cllects of external perturbations such as those caused. by encounters with giant molecular clouds.," We note, however, that Baumgardt Makino's (2003) $N$ -body simulations were performed assuming a smooth underlying tidal field; they do not include the effects of external perturbations such as those caused by encounters with giant molecular clouds."1052 As a result. their eluster disruption time-scale is therefore an upper limit.," As a result, their cluster disruption time-scale is therefore an upper limit."1053 In. view of the uncertainties inherent to the precise disruption time-scale governing M82 D we cannot use this analysis by itself to distinguish conclusively between the loe-normal vs. power-law initial C'ME., In view of the uncertainties inherent to the precise disruption time-scale governing M82 B we cannot use this analysis by itself to distinguish conclusively between the log-normal vs. power-law initial CMF.1054 Phe key question is then whether the combination of (1) an initial power-law CALE. (ii) the present number (and mass) of 1 €ivr-old. clusters. ancl (ii) the very short disruption time-sceale of ~30 Myr for à 107 AL. cluster can be accommodated in a physically realistic scenario.," The key question is then whether the combination of (i) an initial power-law CMF, (ii) the present number (and mass) of 1 Gyr-old clusters, and (iii) the very short disruption time-scale of $\sim 30$ Myr for a $10^4$ $_\odot$ cluster can be accommodated in a physically realistic scenario."1055" Starting from a power-law initial CALF with masses between LO? and 310"" AL... the ratio of the final (ie.. at an age of 1 Gyr) to initial number of clusters is £y~5.10tif [νι~30 Myr."," Starting from a power-law initial CMF with masses between $10^3$ and $3 \times 10^6$ $_\odot$, the ratio of the final (i.e., at an age of 1 Gyr) to initial number of clusters is $F_N \simeq 5 \times 10^{-4}$ if $t_{\rm dis}^4 \sim 30$ Myr."1056 In this ease. the 1 Gyr-old clusters considered here are the survivors of an initial population of ~8107 clusters.," In this case, the 1 Gyr-old clusters considered here are the survivors of an initial population of $\simeq10578 \times 10^{4}$ clusters."1058" However. this is a lower limit since these42 clusters constitute a subsample of the AIS2 D. cluster. population. ναι. those located at the ""surface"" of the region.and [or which reliable age estimates could be obtained."," However, this is a lower limit since these42 clusters constitute a subsample of the M82 B cluster population, i.e., those located at the “surface” of the region for which reliable age estimates could be obtained."1059" For an initial cluster mass range with a lower limit o£ 10* M... the initial number of clusters is significantly lower. οι, some 8.000. but still very. large for the spatially confined MS2 D region."," For an initial cluster mass range with a lower limit of $10^4$ $_\odot$, the initial number of clusters is significantly lower, i.e., some 8,000, but still very large for the spatially confined M82 B region."1060 The ratio P3; of the final to the initial mass in clusters is Z1 vcr cent., The ratio $F_{\rm M}$ of the final to the initial mass in clusters is $\lesssim 1$ per cent.1061 The present mass of the observed. cluster svsten is ~105 AL. (and likely much more considering hat we have only sampled the outer surface of the region)., The present mass of the observed cluster system is $\sim 10^7$ $_\odot$ (and likely much more considering that we have only sampled the outer surface of the region).1062 ‘This implies. therefore. that the initial mass in (bound. lone-ived) clusters alone must have been on the order of 10 AL.. conlined to a threc-dimensional volume of <5105 pet (de Cirijs et al.," This implies, therefore, that the initial mass in (bound, long-lived) clusters alone must have been on the order of $10^9$ $_\odot$, confined to a three-dimensional volume of $\lesssim 5 \times 10^7$ $^3$ (de Grijs et al."1063 2003a.b).," 2003a,b)."1064 Phe initial mean density must therefore have been =20 M. if he initial CME were a power-law distribution.," The initial mean density must therefore have been $\gtrsim 20$ $_\odot$ $^{-3}$, if the initial CMF were a power-law distribution."1065 This is at cast an order of magnitude higher than the currentsiellay density in MS2 BD. as well as in the actively cluster-orming centre of M51 (Lamers et al.," This is at least an order of magnitude higher than the current density in M82 B, as well as in the actively cluster-forming centre of M51 (Lamers et al."1066 2005a)., 2005a).1067 Since the mass in clusters generally only. comprises a lew per cent of the otal mass in disce galaxies. up to about 30 per cent in dense starburst regions like AIS2D7.. it follows that the initial otal stellar density. required. may be as high as 60 AL. *.," Since the mass in clusters generally only comprises a few per cent of the total mass in disc galaxies, up to about 30 per cent in dense starburst regions like M82, it follows that the initial total stellar density required may be as high as $\sim 60$ $_\odot$ $^{-3}$."1068 Such densities are physically unrealistic in disc regions of “normal” galaxies. even in dense starburst regions.," Such densities are physically unrealistic in disc regions of “normal” galaxies, even in dense starburst regions."1069 We note in passing that these calculations refer to the (initially) round clusters only: if unbouncl clusters were included. the expected initial mean density would be even higer.," We note in passing that these calculations refer to the (initially) bound clusters only; if unbound clusters were included, the expected initial mean density would be even higer."1070 Therefore. we conclude that our observations of the esent MS2 B CME are inconsistent with a scenario in which the 1 Civr-old. cluster population originated from. an initial power-law mass distribution.," Therefore, we conclude that our observations of the present M82 B CMF are inconsistent with a scenario in which the 1 Gyr-old cluster population originated from an initial power-law mass distribution."1071 Note that this applies th to the very short disruption time-scale of 30 Myr. as well as to the longer time-scale based on the Baumgardt Makino (2003) results. for which we concluded above that he resulting present-day. CALIF would. peak at. much. lower masses than observed.," Note that this applies both to the very short disruption time-scale of $\sim 30$ Myr, as well as to the longer time-scale based on the Baumgardt Makino (2003) results, for which we concluded above that the resulting present-day CMF would peak at much lower masses than observed."1072" For a log-normal initial CME combined with the Daumgardt Makino (2003) clisruption time-scale (£i,1στ15OS Gyr). most of the clusters survive the | Cwr-lone evolution. Le. fy2 0.9."," For a log-normal initial CMF combined with the Baumgardt Makino (2003) disruption time-scale $t_{\rm dis}^4 \simeq 0.5{\rm -}0.8$ Gyr), most of the clusters survive the 1 Gyr-long evolution, i.e. $F_N \simeq 0.9$ ."1073 The initial and final numbers of clusters are thus very similar., The initial and final numbers of clusters are thus very similar.1074 In. order to. explore whether the good match between the evolved: Gaussian model CALF and the observed distribution actually depends on the small initial number of clusters. implied. by. this, In order to explore whether the good match between the evolved Gaussian model CMF and the observed distribution actually depends on the small initial number of clusters implied by this1075Figure Lisa spectral enerey distribution (SED) of NGC 1115 using the photometry derived frou the NICMOS and AIIRBLIN observations. combined with photometry frou other sources (Carico et al.,"Figure 4 is a spectral energy distribution (SED) of NGC 4418 using the photometry derived from the NICMOS and MIRLIN observations, combined with photometry from other sources (Carico et al."1076 1990: TIRAS FSC) 1990: Dale et al., 1990; IRAS FSC 1990; Dale et al.1077 2000): the beam sizes are listed iu the Figure legend., 2000); the beam sizes are listed in the Figure legend.1078 For comparison. the ISO-PITT-S data from Spoon ct al. (," For comparison, the ISO-PHT-S data from Spoon et al. ("10792001) are also plotted.,2001) are also plotted.1080 Three kev features of this SED are a near-infrared thermal courponeut which is likely due to the late-type supergiaut population.(72) the shape of the MIRLIN SED at inid-nfrared wavelengths which clearly shows the presence of the silicate absorption feature iu NGC 1118 observed by Roche et al. (," Three key features of this SED are a near-infrared thermal component which is likely due to the late-type supergiant population, the shape of the MIRLIN SED at mid-infrared wavelengths which clearly shows the presence of the silicate absorption feature in NGC 4418 observed by Roche et al. ("10811986) aud Spoon et al. (,1986) and Spoon et al. (10822001) aud. the size of the 12 aud 25:10 flux densities measured by IRAS which are recovered by the unresolved LIN cussion at those wavelengths.,2001) and the size of the 12 and $\mu$ m flux densities measured by IRAS which are recovered by the unresolved MIRLIN emission at those wavelengths.1083 From the latter two AMIRfeatures. it can be concluded that the cucrey source(s) heating the silicate grains are confined to an area no iore than 50 pe (~ 0.67) across.," From the latter two features, it can be concluded that the energy source(s) heating the silicate grains are confined to an area no more than 80 pc $\sim 0.6\arcsec$ ) across."1084" Further. the lighest resolution radio map of NGC 1118 obtained to date shows the radio cussion to be less than 0.17"" in exteut (Eales et al."," Further, the highest resolution radio map of NGC 4418 obtained to date shows the radio emission to be less than $0.47\arcsec$ in extent (Eales et al."1085 1990). providing further proof of the importance of the inner NO pe to the total energy output of the galaxy.," 1990), providing further proof of the importance of the inner 80 pc to the total energy output of the galaxy."1086 Even given the overwhchuineg evidence at iiddufrared and radio wavelengths that the euergv sources i NGC llis are confined iu a nuclear region no more that S0 20 across. a direct measuremeut at the wavelength where nost of the energy of NCC [118 is emanatiug from the ar-nfrared — ds ideally desired.," Even given the overwhelming evidence at mid-infrared and radio wavelengths that the energy sources in NGC 4418 are confined in a nuclear region no more that 80 pc across, a direct measurement at the wavelength where most of the energy of NGC 4418 is emanating from – the far-infrared – is ideally desired."1087 Wigh-resolution imaging of he ealaxy at these wavelengths is not preseuthy possible. rowever. additional support for a compact far-infrared cnussion region can be provided via two approximations.," High-resolution imaging of the galaxy at these wavelengths is not presently possible, however, additional support for a compact far-infrared emission region can be provided via two approximations."1088 For the first approximation. the assumption is made hat the unclear dust that is re-cradiatiug ποτ from the uibedded nuclear source(s) in NCC [118 is distributed in an optically thick sphere of diameter D and outer dackbodyw temperature. Tous.," For the first approximation, the assumption is made that the nuclear dust that is re-radiating light from the imbedded nuclear source(s) in NGC 4418 is distributed in an optically thick sphere of diameter $D$ and outer blackbody temperature, $T_{\rm dust}$."1089 The dust temperature is calculated from the GO and LOO pan ux deusities. foun ancl frogjan Via the equation (e.g. sce Solomon et al.," The dust temperature is calculated from the 60 and 100 $\micron$ flux densities, $f_{60\mu{\rm m}}$ and $f_{100\mu{\rm m}}$, via the equation (e.g., see Solomon et al."1090 1997)., 1997).1091 For fouja10.68 Jy aud Fivvjan~32.80 Jy Tau~85 IS. The blackbody diameter is thus calculated via the equation where 0 is the Stefan-Boltzimaun constant. which vields a diameter of I (00 pc).," For $f_{60\mu{\rm m}} \sim 40.68$ Jy and $f_{100\mu{\rm m}} \sim 32.80$ Jy, $T_{\rm dust} \sim 85$ K. The blackbody diameter is thus calculated via the equation where $\sigma$ is the Stefan-Boltzmann constant, which yields a diameter of $\arcsec$ (70 pc)."1092" This is equivalent to the upper size limit of the 254,21. and radio cussion of NCC ΤΗΝ. as well as the FWIIM of its 2.271 cinission."," This is equivalent to the upper size limit of the $\mu$ m and radio emission of NGC 4418, as well as the FWHM of its $\mu$ m emission."1093" Note that a source with a brightuess temperature of 8S5Íl& aud a flux deusitv of 9.32 Jy at 25 pou has a diameter of 0.11"" (53 pc). which is also consistent with the measured wpper But of the 25 san emission."," Note that a source with a brightness temperature of 85K and a flux density of 9.32 Jy at 25 $\mu$ m has a diameter of $\arcsec$ (53 pc), which is also consistent with the measured upper limit of the 25 $\mu$ m emission."1094 If the «dust cmitting the far-infrared ciissiou is associated with the star-forming molecular gas in NGC liis. the distribution of this gas iu the nucleus of NGC [118 can be used as an independent secoucl approximation to the extent of the far-infrared emission.," If the dust emitting the far-infrared emission is associated with the star-forming molecular gas in NGC 4418, the distribution of this gas in the nucleus of NGC 4418 can be used as an independent second approximation to the extent of the far-infrared emission."1095 No interferometric CO(L>0) data preseuth exist of NGC 1115. however siuele-dish measurements have been made which provide a CO huuinosity. Γιο. and a velocity dispersion.," No interferometric $1\to0$ ) data presently exist of NGC 4418, however single-dish measurements have been made which provide a CO luminosity, $L'_{\rm CO}$, and a velocity dispersion."1096 Using these data. the asstuption is made that the brightness temperature of the (ο»0) euission is equal to the dust temperature and that the eas has a unity filline factor.," Using these data, the assumption is made that the brightness temperature of the $1\to0$ ) emission is equal to the dust temperature and that the gas has a unity filling factor."1097 Thus. the CO diameter. Dow. is derived via where Acgwipa is the full width at half the πιακι intensity velocity width (= 120 kins +: Sanders. Scoville. Soifer 1991).," Thus, the CO diameter, $D_{\rm CO}$, is derived via where $\Delta v_{\rm FWHM}$ is the full width at half the maximum intensity velocity width (= 120 km $^{-1}$: Sanders, Scoville, Soifer 1991)."1098" The CO diameter is calculated to be 1.5"" (200 pe}.", The CO diameter is calculated to be $\arcsec$ (200 pc).1099 It the size of 70 pc is adopted for the mid-to-far infrared enission region. then the surface brightuess of NGC £118 is calculated to be LEyp/rD?~2.«101 L. kpe?.," If the size of 70 pc is adopted for the mid-to-far infrared emission region, then the surface brightness of NGC 4418 is calculated to be $41100L_{\rm IR} / \pi D^2 \sim 2.1\times10^{13}$ $_\odot$ $^2$."1101 Figure 5 is a plot of iufrared. surface brightuess versus infrared luminosity for a sample of galaxies imaged at midaáufrared wavelengths by Soifer et al. (, Figure 5 is a plot of infrared surface brightness versus infrared luminosity for a sample of galaxies imaged at mid-infrared wavelengths by Soifer et al. (11022000: 2001). as well as the Orion star-forming complex aud M82 (sec also Soifer et al.,"2000; 2001), as well as the Orion star-forming complex and M82 (see also Soifer et al."1103 2001)., 2001).1104" The surface brightuess of NGC Lis is extreme. beiug comparable to that of the wari. —-2Itraluninous infrared ealaxies (c.g.. IRAS 05189-252|. RAS 08572|3915. and Mrk 231) and cool ultraluniuous oeifraved galaxies <0.2: which may he powered, primarily (fonoby starburst.fou ACN. or both) such as Arp 220. UGC 5101. aud Myrk 273. a factor of 100 larecr iu that of M82. and a factor of ten larger than that of the star forming complex iu Iu comparison to starburst galaxies with infrared huninosities moderately ieher than NOC Lis (1.0. NGC 1614. NGC 2625. IC 882. NGC 6090. Atk 331: Soifer et al."," The surface brightness of NGC 4418 is extreme, being comparable to that of the warm ultraluminous infrared galaxies (e.g., IRAS 05189-2524, IRAS 08572+3915, and Mrk 231) and cool ultraluminous infrared galaxies $f_{25\mu m} / f_{60\mu m} <11050.2$; which may be powered primarily by starburst, AGN, or both) such as Arp 220, UGC 5101, and Mrk 273, a factor of 100 larger than that of M82, and a factor of ten larger than that of the star forming complex in In comparison to starburst galaxies with infrared luminosities moderately higher than NGC 4418 (i.e., NGC 1614, NGC 2623, IC 883, NGC 6090, Mrk 331: Soifer et al."1106 2001). NGC 1118 has au infrared surface brightness a factor of 2.100 ligher.," 2001), NGC 4418 has an infrared surface brightness a factor of 2–100 higher."1107 From he lanited nuuber of objects plotted iu Figure 5. there is 10 clear indication that infrared surface brightness alone can be used as a diagnostic between ACN aud starburst οποιον SOUYCOS.," From the limited number of objects plotted in Figure 5, there is no clear indication that infrared surface brightness alone can be used as a diagnostic between AGN and starburst energy sources."1108 As previously mentioned. dark lanes are observed to be associated with the ceutral high surface brightuess neu-infrared peaks of NGC E118.," As previously mentioned, dark lanes are observed to be associated with the central high surface brightness near-infrared peak of NGC 4418."1109" Figure Id shows au mgaijaa - HH6,04 Anage of NGC L[I18: in this image. the dark Innes appear as cones extending away frou the uucleus."," Figure 1d shows an $m_{1.1\mu{\rm m}}$ - $m_{1.6\mu{\rm m}}$ image of NGC 4418; in this image, the dark lanes appear as cones extending away from the nucleus."1110 There are two likely explanations for the nature of the dark lanes in the nucleus of NCC LI15., There are two likely explanations for the nature of the dark lanes in the nucleus of NGC 4418.1111 The first possibility is that the features are dust lanes., The first possibility is that the features are dust lanes.1112 Such radial dust lanes are observed in the nucleus of spiral ealaxy M51. albeit on a sinaller scale (50 pe: Coilluair 1997 and references therein).," Such radial dust lanes are observed in the nucleus of spiral galaxy M51, albeit on a smaller scale (50 pc: Grillmair 1997 and references therein)."1113 The presence of such dust lanes. if they Bo in the forceround of the nuclear mfrared disk. may explain the," The presence of such dust lanes, if they lie in the foreground of the nuclear infrared disk, may explain the"1114which then leads to a unique relationship between 93 aud Sot. which is shown to be correct in Appendix D3..,"which then leads to a unique relationship between $S_3$ and $S_2^\text{M}$, which is shown to be correct in Appendix \ref{S3_analytic}. ."1115 The coustaut sj can be chosen arbitrarily just as with 54 (which depeuds ou 0)., The constant $S_1^\text{M}$ can be chosen arbitrarily just as with $S_1$ (which depends on $w_1$ ).1116 If oue considers theInuit as>ay and simultaneously requires that the star rotate uniformly. then provides the unique value for ay. which is equivalent to making a choice for SM different from the one made in Có67a. but no more and no less physically nieaniusful.," If one considers the $a_2\to a_1$ and simultaneously requires that the star rotate uniformly, then provides the unique value for $w_1$, which is equivalent to making a choice for $S_1^\text{M}$ different from the one made in C67a, but no more and no less physically meaningful."1117 The most siguificant result of the analvsis of the axisviunietric lait is that shows us that the rigidly rotating limit (074= 0) and the original choice of velocity field in CETS (ay=wy= 0) are incompatible., The most significant result of the analysis of the axisymmetric limit is that shows us that the rigidly rotating limit $r_1=0$ ) and the original choice of velocity field in CE78 $w_1=w_2=0$ ) are incompatible.1118 While it is possible with that velocity field to find the post-Newtonian Maclamin solution the bifurcation point. this solution is not continuously connected to any other solution.," While it is possible with that velocity field to find the post-Newtonian Maclaurin solution the bifurcation point, this solution is not continuously connected to any other solution."1119" When considering the question of the existence or noi-existence of non-axiallv svuuuetre but stationary solutions. if seecnüs nuportaunt to retain the possibility of studviug a neighbourhood of the axially svuunetric and uniformly rotating limit. especially since such solutions are known toexist""."," When considering the question of the existence or non-existence of non-axially symmetric but stationary solutions, it seems important to retain the possibility of studying a neighbourhood of the axially symmetric and uniformly rotating limit, especially since such solutions are known to."1120 This possibility was excluded by the approach taken in CETS8., This possibility was excluded by the approach taken in CE78.1121 Iun a follow-up paper. we intend to tackle the problem with a more general approach that lends itself better to proceeding to higher post-Newtoman orders. is nof as restrictive in the solutions it permits and allows one to show that the siaποπ discussed in CETS is an artefact ofthe specific method chosen aud not au inherent property of the post-Newtoman Dedekind solutions (cf.?2)..," In a follow-up paper, we intend to tackle the problem with a more general approach that lends itself better to proceeding to higher post-Newtonian orders, is not as restrictive in the solutions it permits and allows one to show that the singularity discussed in CE78 is an artefact of the specific method chosen and not an inherent property of the post-Newtonian Dedekind solutions \citep[cf.][]{GP10}."1122 We eratefully acknowledge helpful discussious with AAnsore. BBic¢ukk. FRFricdian aud MMoéeinel.," We gratefully acknowledge helpful discussions with Ansorg, Bi\v{c}\\'akk, Friedman and Meinel."1123" The first author was fuanciallv supported by the erauts QGAUR 116-10/258025 and GACR 205/09/TI033 and thesecond by the Deutsche Forschunueseenceiuschaft as part of the project ""Ciravitational Wave Astronomy” (SFB/TR7Dl).", The first author was financially supported by the grants GAUK 116-10/258025 and GACR 205/09/H033 and thesecond by the Deutsche Forschungsgemeinschaft as part of the project “Gravitational Wave Astronomy” (SFB/TR7–B1).1124as a function of age and metallicity for all star particles and stochastically determine at each timestep if a SNe occurs.,as a function of age and metallicity for all star particles and stochastically determine at each timestep if a SNe occurs.1125" If so, the appropriate mechanical luminosity is injected as thermal energy in the gas within a smoothing length (nearest 32 gas neighbors) of the star particle. ("," If so, the appropriate mechanical luminosity is injected as thermal energy in the gas within a smoothing length (nearest 32 gas neighbors) of the star particle. ("1126"3) Gas mass is returned to the ISM from stellar evolution, at a rate tabulated from SNe and stellar mass loss (integrated fraction ~ 0.3).","3) Gas mass is returned to the ISM from stellar evolution, at a rate tabulated from SNe and stellar mass loss (integrated fraction $\approx0.3$ )."1127 The SNe heating is described above., The SNe heating is described above.1128" Similarly, stellar winds are assumed to shock locally and inject the appropriate tabulated mechanical luminosity L(t,Z) as a function of age and metallicity into the gas within a smoothing length. ("," Similarly, stellar winds are assumed to shock locally and inject the appropriate tabulated mechanical luminosity $L(t,\,Z)$ as a function of age and metallicity into the gas within a smoothing length. ("1129"4)Regions: We also tabulate the rate of production of ionizing photons for each star particle; moving radially outwards from the star, we then ionize each neutral gas particle (using its density and state to determine the necessary photon number) until the photon budget is exhausted.","4): We also tabulate the rate of production of ionizing photons for each star particle; moving radially outwards from the star, we then ionize each neutral gas particle (using its density and state to determine the necessary photon number) until the photon budget is exhausted."1130 Ionized gas is maintained at a minimum ~ 10*K until it falls outside an HII region. (," Ionized gas is maintained at a minimum $\sim10^{4}\,$ K until it falls outside an HII region. ("11315) Photons which escape the local GMC (not absorbed in mechanism (1) above) can be absorbed at larger radii.,5) Photons which escape the local GMC (not absorbed in mechanism (1) above) can be absorbed at larger radii.1132" Knowing the intrinsic SED of each star particle, we attenuate integrating the local gas density and gradients to convergence."," Knowing the intrinsic SED of each star particle, we attenuate integrating the local gas density and gradients to convergence."1133" The resulting ""escaped"" SED gives a flux that propagates to large distances, and can be treated in the same manner as the gravity tree to give the local net incident flux on a gas particle."," The resulting “escaped” SED gives a flux that propagates to large distances, and can be treated in the same manner as the gravity tree to give the local net incident flux on a gas particle."1134" The local absorption is then calculated integrating over a frequency-dependent opacity that scales with metallicity, and the radiation pressure force is imparted (and luminosity removed)."," The local absorption is then calculated integrating over a frequency-dependent opacity that scales with metallicity, and the radiation pressure force is imparted (and luminosity removed)."1135" In implementing (1)-(5),all energy, mass, and momentum-injection rates are taken from stellar population models(?),, assuming a IMF, without any free parameters."," In implementing (1)-(5),all energy, mass, and momentum-injection rates are taken from stellar population models, assuming a IMF, without any free parameters."1136" More details, numerical tests, and resolution studies (up to 10? particles with 3.5 pc softening lengths) for these models are discussed inΠ."," More details, numerical tests, and resolution studies (up to $10^{9}$ particles with $3.5\,$ pc softening lengths) for these models are discussed in."1137. We note that some recent studies of low-resolution cosmological simulations comparingGADGET and the moving mesh code have highlighted some differences between smoothed particle hydrodynamics and grid methods for some cosmological inflow problems (???).., We note that some recent studies of low-resolution cosmological simulations comparing and the moving mesh code have highlighted some differences between smoothed particle hydrodynamics and grid methods for some cosmological inflow problems .1138" However, we have"," However, we have"1139For the dark matter. errors on the bandpowers are straüghtlorward.,"For the dark matter, errors on the bandpowers are straightforward."1140 They are simply the diagonal terms of the inverse covariance matrix divided bv the number of simulations., They are simply the diagonal terms of the inverse covariance matrix divided by the number of simulations.1141 We use (he model covariance matrix in Eqn., We use the model covariance matrix in Eqn.1142 13. to compute the inverse: Ol course. the beat coupling leads to off-diagonal terms in both the covariance matrix and ils inverse: (hese terms must be included when estimating errors on moclel We also estimate an error on our estimate of the covariance matrix.," \ref{cijmodel} to compute the inverse: Of course, the beat coupling leads to off-diagonal terms in both the covariance matrix and its inverse; these terms must be included when estimating errors on model We also estimate an error on our estimate of the covariance matrix."1143 We ignore correlations between the ü C5;'s in our error estimates. thoughg thev are certainly The situation for the mock catalogs is more tricky.," We ignore correlations between the $C_{ij}$ 's in our error estimates, though they are certainly The situation for the mock catalogs is more tricky."1144" For each of the s=1...Nein, N-body simulations we produce mi=1.....N,,,/5; mock catalogs using our fixed HOD parameters {ο reduce the shot noise contribution."," For each of the $s = 1,..,N_{sim}$ $N$ -body simulations we produce $m = 1,..,N_{mocks}$ mock catalogs using our fixed HOD parameters to reduce the shot noise contribution."1145" We define lere P.,(h;) denotes the band power for mock catalog im populating simulation s. D.) denotes the band power in a single sinmlation s averaged over the mock catalogs populating s. and P(4;) denotes a band power averaged over (he entire set of NuXNas catalogs."," We define Here $P_{sm}(k_i)$ denotes the band power for mock catalog $m$ populating simulation $s$, $\bar{P_s}(k_i)$ denotes the band power in a single simulation $s$ averaged over the $m$ mock catalogs populating $s$ , and $\bar{P}(k_i)$ denotes a band power averaged over the entire set of $N_{mocks} \times N_{sim}$ catalogs."1146 Co)yor 1s Lhe covariance matrix lor this set of mock catalogs.," $C_{ij,tot}$ is the covariance matrix for this set of mock catalogs."1147" C;op is the variance introduced by sampling the same matter density field with dillerent mock catalog realizations and C5;,;4 is the reduced covariance of the power spectra Irom each simulation after averaging over N44; calalogs in each simulation."," $C_{ij,HOD}$ is the variance introduced by sampling the same matter density field with different mock catalog realizations and $C_{ij,red}$ is the reduced covariance of the power spectra from each simulation after averaging over $N_{mocks}$ catalogs in each simulation."1148 The expectederror on bandpower P(;) is then, The expectederror on bandpower $P(k_i)$ is then1149various reasons. the observed PSF chiuges in size aud anisotropy across the field aud also over time.,"various reasons, the observed PSF changes in size and anisotropy across the field and also over time."1150 Moreover. we nee the PSF extrapolated to the positions of ealaxies. whereas the PSF model is constructed from the Hel S/N stars that are iimch less densely distributed.," Moreover, we need the PSF extrapolated to the positions of galaxies, whereas the PSF model is constructed from the high S/N stars that are much less densely distributed."1151 Therefore. iu addition to very low surface briehtuess ints. a kev factor in precision leusiug lies in one’s ability o carefully model and remove the complicated effects of ΡΡΕΣ.," Therefore, in addition to very low surface brightness limits, a key factor in precision lensing lies in one's ability to carefully model and remove the complicated effects of PSFs."1152 Although the secius at the LSST site is amoung the vest in existing erouud-based facilities. the accurate description of the PSF is highly challeugig because of he optical and focal plaue design.," Although the seeing at the LSST site is among the best in existing ground-based facilities, the accurate description of the PSF is highly challenging because of the optical and focal plane design."1153 As described below. he telescope optics and camera are continuously aligned via wavefrout seusiug.," As described below, the telescope optics and camera are continuously aligned via wavefront sensing."1154 Optimized for the unprecedented aree field of view. the effective. faatio of LSST is sinall fí~1.2. which makes the optical aberration lighly sensitive to alieument aud focal plaue deviation.," Optimized for the unprecedented large field of view, the effective $f$ -ratio of LSST is small $f/\sim1.2$, which makes the optical aberration highly sensitive to alignment and focal plane deviation."1155 Because LSST’s focal plane will be tiled with 189 Ik « 1X CCDs. anv height fluctuation both across and within the CCDs will translate iuto a verv complicated PSF pattern. which is characterized by abrupt changes across the CCD eaps and smooth. but possibly ligh-frequency variatious within the CCDs.," Because LSST's focal plane will be tiled with 189 4k $\times$ 4k CCDs, any height fluctuation both across and within the CCDs will translate into a very complicated PSF pattern, which is characterized by abrupt changes across the CCD gaps and smooth, but possibly high-frequency variations within the CCDs."1156 Αν sub-optimal modcling of these PSEs will leave systematic residuals ou the scales of the CCD sizes aud the “potato chip”cffect?., Any sub-optimal modeling of these PSFs will leave systematic residuals on the scales of the CCD sizes and the “potato chip”.1157. These systematic residuals. münuückiug lensing signals. will. of course. hamper the correct interpretation of the leusimg analysis.," These systematic residuals, mimicking lensing signals, will, of course, hamper the correct interpretation of the lensing analysis."1158 Unfortunately. with the existing algoritlius the ability to precisely. describe the PSF alone does uot. guarautee the success in the extraction of gravitational shear to the accuracy that future LSST-like sveak-leusiug survers require.," Unfortunately, with the existing algorithms the ability to precisely describe the PSF alone does not guarantee the success in the extraction of gravitational shear to the accuracy that future LSST-like weak-lensing surveys require."1159 This obstacle is well noted iu the recent large collaborative shear measurement campaigu GREATOS Challenge (Bridle et al., This obstacle is well noted in the recent large collaborative shear measurement campaign GREAT08 Challenge (Bridle et al.1160 2010)., 2010).1161 The campaign let the participauts perform blind shear measurenmeuts on simulated nuages. where the PSF was known. but the input shear was unknown.," The campaign let the participants perform blind shear measurements on simulated images, where the PSF was known, but the input shear was unknown."1162 Although many algoritlins were shown to provide the accuracy for lieh S/N images suitable for the existing survey data. no method came close to the target accuracy (Q~1000 when the noise level of the iuages matched the realistic value (see Bridle et al.," Although many algorithms were shown to provide the accuracy for high S/N images suitable for the existing survey data, no method came close to the target accuracy $Q\sim1000$ when the noise level of the images matched the realistic value (see Bridle et al."1163 2010 for the definition of Q)., 2010 for the definition of $Q$ ).1164 Nevertheless. it is Huportaut to note that the main challenge is purely mathematicalstatistical and thus iuprovable as more Inathematical sophistication is mucorporated in the aleorithius.," Nevertheless, it is important to note that the main challenge is purely mathematical/statistical and thus improvable as more mathematical sophistication is incorporated in the algorithms."1165 For example. Derusteiu (2010) claims that when the bias arising when the true galaxy profiles do uot match the models beiug fit is properly addressed. the resulting algorithiu can achieve (Q~3000 for high S/N ealaxies of the CREATOS sample.," For example, Bernstein (2010) claims that when the bias arising when the true galaxy profiles do not match the models being fit is properly addressed, the resulting algorithm can achieve $Q\sim3000$ for high S/N galaxies of the GREAT08 sample."1166 We launched the LSST shear calibration. project iu order to diagnose the key factors in the telescope aud calucra cheinecring specifications affecting the weals-leusiug science aud to develop new algorithis for optimal shear extraction in the presence of different combinations of systematics., We launched the LSST shear calibration project in order to diagnose the key factors in the telescope and camera engineering specifications affecting the weak-lensing science and to develop new algorithms for optimal shear extraction in the presence of different combinations of systematics.1167 The current paper is the first iu the series of this topic with au emphasis ou the realization. characterization. aud reconstruction of LSST PSE«.," The current paper is the first in the series of this topic with an emphasis on the realization, characterization, and reconstruction of LSST PSFs."1168 The paper is organized as follows., The paper is organized as follows.1169 Tn refsectionjsstpties.. weprocideabric frecicwonthetelescopooptics.," In \\ref{section_lsst_optics}, we provide a brief review on the telescope optics."1170C Li , Our implementation of the atmospheric turbulence is described in \\ref{section_atmosphere}.1171Section wediscussthe focal plancdesignof LSSTa nd F," In Section \\ref{section_focal_plane}, we discuss the focal plane design of LSST and the resulting behavior of the PSF."1172scctionycaprescitsouralgorithintoicasurcandrccoinstructtheT, \\ref{section_pca} presents our algorithm to measure and reconstruct the PSFs.1173 scetioninalation.. wedeseribeoursimulation.," In \\ref{section_simulation}, , we describe our simulation."1174Finally.thedetai scetionnalgsisbeforctheconclusionin onelusion.," Finally, the detailed comparison between the observed and modeled PSFs is presented in \\ref{section_analysis} before the conclusion in \\ref{section_conclusion}."1175", Figure d shows the optical design of the LSST. which is a 1iocdified Paul-Daker threce-uiror svstem."," Figure \ref{fig_lsst_optics} shows the optical design of the LSST, which is a modified Paul-Baker three-mirror system."1176" The active optics telescope consists of an 8.1 m f/1.18 concave primary. a3. ban £/1.0 conver secondary. and 5.2 m £/0.83 concave tertiary στους,"," The active optics telescope consists of an 8.4 m f/1.18 concave primary, a 3.4 m f/1.0 convex secondary, and 5.2 m f/0.83 concave tertiary mirrors."1177" The final focal ratio f/1.23 (focal leueth of 10.3 11). gives a plate scale 0.0197""ἡμιι over the GL cim diameter focal plane (3.57.&3.57).", The final focal ratio f/1.23 (focal length of 10.3 m) gives a plate scale $0.0197\arcsec/\micron$ over the 64 cm diameter focal plane $3.5\degr \times 3.5\degr$ ).1178 The obscuration vields a total effective light collecting area of 35 nC which corresponds to an effective 6.7 ii diameter clear circular aperture.," The obscuration yields a total effective light collecting area of 35 $\mbox{m}^2$, which corresponds to an effective 6.7 m diameter clear circular aperture."1179 Current wide field telescopes were not desigued for the stringent PSF demands of LSST weak lensing coals., Current wide field telescopes were not designed for the stringent PSF demands of LSST weak lensing goals.1180 This optical design provides a wide field of view while a lnaintaimine uniforiui image qualitv across the field (Seppala 2002)., This optical design provides a wide field of view while a maintaining uniform image quality across the field (Seppala 2002).1181 The remarkably small variation of the PSF size over the field is illustrated in Figure 2.. where the ditfraction-lamited PSF images are generated with ZEMAN at the uominal flat focal plane.," The remarkably small variation of the PSF size over the field is illustrated in Figure \ref{fig_lsst_ee}, where the diffraction-limited PSF images are generated with ZEMAX at the nominal flat focal plane."1182 The peak-to-valley eucircled enerev radius is within ~7% of the niei value from the center to ~1.17 for simulated / filter point sources;, The peak-to-valley encircled energy radius is within $\sim7$ of the mean value from the center to $\sim1.4\degr$ for simulated $i$ filter point sources.1183 The maxima deviation (17 )) is seen atf the οσο of the field (1.757)., The maximum deviation $\sim17$ ) is seen at the edge of the field $1.75\degr$ ).1184 The nuage brightness is stable across the field. providing a nearlv uniforii illuniuation within a radius of 1.27 aud about decrease at the edge (Seppala 2002: LSST Science Collaboratious 2010).," The image brightness is stable across the field, providing a nearly uniform illumination within a radius of $\degr$ and about decrease at the edge (Seppala 2002; 	LSST Science Collaborations 2010)."1185 Finally. the LSST field. distortion is remarkably πα]: less than over the full field.," Finally, the LSST field distortion is remarkably small: less than over the full field."1186 LSST will have coutinuous correction of its optics. using curvature wavefrout seusiug.," LSST will have continuous correction of its optics, using curvature wavefront sensing."1187 Four special purpose rafts. mounted at the corners of the scieuce array. coutaiu wavefrout sensors and guide sensors (right panel of Figure 1)).," Four special purpose rafts, mounted at the corners of the science array, contain wavefront sensors and guide sensors (right panel of Figure \ref{fig_lsst_optics}) )."1188" Wavefrout iieasuremients are accomplished using curvature ποιο, m which the spatial iuteusityv distribution of de-focused stars ix measured at equal distances on either side of focus."," Wavefront measurements are accomplished using curvature sensing, in which the spatial intensity distribution of de-focused stars is measured at equal distances on either side of focus."1189 Each curvature seusor is composed of two CCD detectors. with one positioned slightly above the focal plane. the other positioned slightly below the focal plane.," Each curvature sensor is composed of two CCD detectors, with one positioned slightly above the focal plane, the other positioned slightly below the focal plane."1190 The CCD technology for the curvature sensors is identical to that used for the science detectors in the focal plane. except that the curvature sensor detectors are halfsize so they can be mounted as an in-out defocus pair.," The CCD technology for the curvature sensors is identical to that used for the science detectors in the focal plane, except that the curvature sensor detectors are half-size so they can be mounted as an in-out defocus pair."1191 Detailed analyses (Alanuel et al., Detailed analyses (Manuel et al.1192 2010) have verified that this configuration can reconstruct the wavefrout within the = 0.2;an accuracy., 2010) have verified that this configuration can reconstruct the wavefront within the $\lesssim0.2\mu$ m accuracy.1193 These four corner rafts also hold two guide sensors cach., These four corner rafts also hold two guide sensors each.1194 The guide seusors monitor the locations of xieht stars at a frequency of ~10 Iz to provide feedback or a loop that controls aud maintains precision tracking of the telescope during ii exposure., The guide sensors monitor the locations of bright stars at a frequency of $\sim10$ Hz to provide feedback for a loop that controls and maintains precision tracking of the telescope during an exposure.1195 The fast focal ratio and the rapid pointing changes nake any hardware-based atinospheric dispersion correction teclinicallv dificult., The fast focal ratio and the rapid pointing changes make any hardware-based atmospheric dispersion correction technically difficult.1196 Consequently. the effect of he atinosplieric dispersion sets the maxi angle away roni the zenith.," Consequently, the effect of the atmospheric dispersion sets the maximum angle away from the zenith."1197 We estimatethe atmospheric ditfereutial, We estimatethe atmospheric differential1198order to investigate the dependence of the relative star-dust ecometry on the attenuation.,order to investigate the dependence of the relative star-dust geometry on the attenuation.1199 The last parameter in our galaxy model is the total V band optical depth zy., The last parameter in our galaxy model is the total $V$ band optical depth $\tau_V$.1200 Again. a realistic value for the optical depth in disc galaxies has been a subject of debate or a long time already.," Again, a realistic value for the optical depth in disc galaxies has been a subject of debate for a long time already."

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