ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Another possibility that has vet to be explored is that disecquilibrium chemistry may play a significant role in determining GJ 1214b's transmission spectrum., Another possibility that has yet to be explored is that disequilibrium chemistry may play a significant role in determining GJ 1214b's transmission spectrum.3 Previous modeling efforts have only considered hydrogen-vich compositions of GJ 1214b's aimosphere in thermochemical equilibriun with metallicilies between. 1 and 50 times solar (7?) as a starling point. but this may not be a valid assumption for the actual state of the planets atmosphere.," Previous modeling efforts have only considered hydrogen-rich compositions of GJ 1214b's atmosphere in thermochemical equilibrium with metallicities between 1 and 50 times solar \citep{mil10} as a starting point, but this may not be a valid assumption for the actual state of the planet's atmosphere."4" Non-equilibrium chemistry is known (o play a strong role in determining the atmospheric composition for many of the planets and (planet-sized moons) in our solar svstem and is also responsible lor the formation of clouds or hazes in the atimospheres of certain solar svslem bodies (e.g. H3SO, clouds on Venus and hydrocarbon hazes on Titan).", Non-equilibrium chemistry is known to play a strong role in determining the atmospheric composition for many of the planets and (planet-sized moons) in our solar system and is also responsible for the formation of clouds or hazes in the atmospheres of certain solar system bodies (e.g. $_2$ $_4$ clouds on Venus and hydrocarbon hazes on Titan).5 Processes that can perturb a planetary atmosphere away trom a state of thermochenmical equilibrium include photochemistry. dvnanmiücal mixing and winds. and are ultimatelv limited bv the finile zunount of time required for chemical reactions to proceed.," Processes that can perturb a planetary atmosphere away from a state of thermochemical equilibrium include photochemistry, dynamical mixing and winds, and are ultimately limited by the finite amount of time required for chemical reactions to proceed."6 Overall. if (he (nmescale for mixing or photochemical destruction of a species is shorter than the timescale for chemical reactions to return the gas ensemble to its equilibrium state. (hen non-equilibrium chemistry cannot be ignored.," Overall, if the timescale for mixing or photochemical destruction of a species is shorter than the timescale for chemical reactions to return the gas ensemble to its equilibrium state, then non-equilibrium chemistry cannot be ignored."7 In this paper we study the ellects Chat non-equilibrium chemistry can have on the overall composition of GJ 1214bs atmosphere. assuming (that it is composed of gas.," In this paper we study the effects that non-equilibrium chemistry can have on the overall composition of GJ 1214b's atmosphere, assuming that it is composed of hydrogen-rich gas."8 We apply a photochemical model. which accounts for UV photolvsis of molecules. vertical mixing in the atmosphere. and the finite timescales for chemical reactions to proceed.," We apply a photochemical model, which accounts for UV photolysis of molecules, vertical mixing in the atmosphere, and the finite timescales for chemical reactions to proceed."9 The result is a suite of non-equilibrium chemical compositions for GJ 1214b's atmosphere. based on a grid of assumptions for the planet's metallicity and eddy mixing rate. and UV irradiation by the host star.," The result is a suite of non-equilibrium chemical compositions for GJ 1214b's atmosphere, based on a grid of assumptions for the planet's metallicity and eddy mixing rate, and UV irradiation by the host star."10 For (ie non-equilibrium chemical compositions that we compute. we determine (he transmission spectra that would result.," For the non-equilibrium chemical compositions that we compute, we determine the transmission spectra that would result."11 We (hen compare the resulting transmission spectra against the currently available data for GJ 1214b., We then compare the resulting non-equilibrium transmission spectra against the currently available data for GJ 1214b.12 We also delve further into the question of clouds or hazes in GJ 1214b's atmosphere as a possible explanation for (he planet's flat transmission spectrum at near-IR wavelengths., We also delve further into the question of clouds or hazes in GJ 1214b's atmosphere as a possible explanation for the planet's flat transmission spectrum at near-IR wavelengths.13 The paper is laid. out as follows., The paper is laid out as follows.14 In Section 2. we describe our methodology ancl modeling efforts., In Section \ref{methods} we describe our methodology and modeling efforts.15 In Seclion 3 we present our modeling results for non-equilibrium chemical abundances and, In Section \ref{results} we present our modeling results for non-equilibrium chemical abundances and16By fitting the simultaneous 0.1-200 keV spectrum from BeppoSAX. the absorption corrected luminosity iu the 2-10 keV band is Lx(2.—10keV)=3«l0]eres! (Cuainazzi et al.. 20003).,"By fitting the simultaneous 0.1-200 keV spectrum from BeppoSAX, the absorption corrected luminosity in the 2-10 keV band is $\LX(2-10\KEV) = 3\xten{42}\ERG\S\1$ (Guainazzi et al., \cite{guainazzi}) )."17" I£ tho ACN in NGC 1915 has an iutriuxie spectral energy distribution simular to a quasar. then Ly(2Ἰ0κοLio,~0.03 (Elvis et al. 1991))"," If the AGN in NGC 4945 has an intrinsic spectral energy distribution similar to a quasar, then $\LX(2-10\KEV)/L_{\rm bol}\sim 0.03$ (Elvis et al. \cite{elvis}) )"18 therefore (Lyoiaax~10!ergst=2.6«LOL. which is thetotel far-IR Lbhuuiuositv of NGC 1915. measured by IRAS (Rice et al. 19858)).," therefore $(L_{\rm bol})_{\rm AGN}\sim \ten{44}\ERG\S\1 = 2.6\xten{10}\Lo$ which is the far-IR luminosity of NGC 4945, measured by IRAS (Rice et al., \cite{rice88}) )."19 Thus. a “uormal” ACN iu NGC 1915.could m principle power the total bolometric DIuuiuositv.," Thus, a ""normal"" AGN in NGC 4945 in principle power the total bolometric luminosity."20 For this scenario. we compare NGC 1915 with a nearby obscured object. the Cirecinus galaxy. now considered au example of a “standard” Sevfert 2 ealaxy (c.f," For this scenario, we compare NGC 4945 with a nearby obscured object, the Circinus galaxy, now considered an example of a “standard” Seyfert 2 galaxy (c.f."21 Oliva et al. 199L..," Oliva et al. \cite{oliva94},"22 Oliva ct al. 1998.. ," Oliva et al. \cite{oliva98}, ,"23Maiolino et al. 1998a.," Maiolino et al. \cite{maiolino98},"24. Matt et al. 1999..," Matt et al. \cite{matt99},"25 Storchi-Beremaun et al. 1999..," Storchi-Bergmann et al. \cite{storchi99},"26 Churan ct . 1999))., Curran et al. \cite{curran}) ).27 Iu. particular. Oliva. Marconi Moorwood (1999a)) and. previously. Aloorwood et al. (199660))," In particular, Oliva, Marconi Moorwood \cite{oliva99}) ) and, previously, Moorwood et al. \cite{moorwood96c}) )"28 showed that the total euergv output from the ACN required to explain the observed emission line spectrin is comparable to he total FIR huninosity. coucludiug that anv starburst coutribution to he bolometric bhpuuinuositv is xuall (~10%)).," showed that the total energy output from the AGN required to explain the observed emission line spectrum is comparable to the total FIR luminosity, concluding that any starburst contribution to the bolometric luminosity is small )."29" The choice of the Circiuus galaxy is motivated by the simular distance (D=lAIpc)}). FIR and hard N-rav luuiinosities as NGC 1915 Τ01ΟΤ, Sicbemmorgen et al."," The choice of the Circinus galaxy is motivated by the similar distance ), FIR and hard X-ray luminosities as NGC 4945 $\LFIR\sim1.2\xten{10}\Lo$ ; Siebenmorgen et al.,"30 1997 Lx(2.10keV)—Sdd1v&dO0Hergs 5: Matt et ab. 1999)).," \cite{sieben} – $\LX(2-10\KEV)\sim 3.4-17\xten{41}\ERG\S\1$ ; Matt et al., \cite{matt99}) )."31" Note that its Lx(2.lO0keV)/Lpjg ratio (~0.01. 0,05) is cousisteut with the average value for quasars (Elvis et al. 1991))."," Note that its $\LX (2-10\KEV)/\LFIR$ ratio $\sim 0.01-0.05$ ) is consistent with the average value for quasars (Elvis et al., \cite{elvis}) )."32 The overall spectral energyv distributious of NGC 1915 and Circinus are compared in Fig. 5.., The overall spectral energy distributions of NGC 4945 and Circinus are compared in Fig. \ref{fig:compare}. .33 The “stars” represent the TRAS photometric points (excep for the points with the largest wavelength which are the ninieasurements by Cohosh et al. 19923).," The ""stars"" represent the IRAS photometric points (except for the points with the largest wavelength which are the measurements by Ghosh et al. \cite{ghosh92}) )."34 Iu NGC L915 the points labeled with K. L aud N are the upper limits derived. from our observations. while iu Circinus they represent cussion from the unresolved unclear source corrected for stellar cussion (Moaioliuo et al. 1998a)).," In NGC 4945 the points labeled with ""K"", ""L"" and ""N"" are the upper limits derived from our observations, while in Circinus they represent emission from the unresolved nuclear source corrected for stellar emission (Maiolino et al. \cite{maiolino98}) )."35 The poiuts labeled “100 keV are from Done et al.," The points labeled ""100 keV"" are from Done et al."36 1996 (NGC L915) aud Matt. et al., \cite{done96} (NGC 4945) and Matt et al.37 1999 (Circiuux)., \cite{matt99} (Circinus).38" The bars between 13.6 aud 5L. eV are at a level given by vl,~QUID<hv>. where QUI) is the rate of W-ionizine photons aud <fv> is the mean photon euerev of the ionizing spectrum."," The bars between 13.6 and 54.4 eV are at a level given by $\nu L_\nu\sim Q(\mathrm{H}) <h\nu>$, where $Q(\mathrm{H})$ is the rate of H-ionizing photons and $<h\nu>$ is the mean photon energy of the ionizing spectrum."39 For NGC 915. QUIT) is derived from II recombination lines aud lus represeut the ecnerev which is racdiated by the voune starburst: we assumed «ij>= lGev.," For NGC 4945, $Q(\mathrm{H})$ is derived from H recombination lines and thus represent the energy which is radiated by the young starburst; we assumed $<h\nu>=16\EV$ ."40 For Circiuus. the point labeled with “Starburst” is sinularly derived from Drs cuiission associated with the starburst (Oliva ct al. 1990) ," For Circinus, the point labeled with ""Starburst"" is similarly derived from $\gamma$ emission associated with the starburst (Oliva et al. \cite{oliva94}) )"41while that labeled “AGN” is froin the estimate made by Oliva. Marconi Moorwood (1999a}).," while that labeled ""AGN"" is from the estimate made by Oliva, Marconi Moorwood \cite{oliva99}) )."42 Tn the lower panel. we represent the IR spectra of Circiuus by connecting the photometric poiuts just described.," In the lower panel, we represent the IR spectrum of Circinus by connecting the photometric points just described."43 We plot this same spectrum as a dotted lue in the upper panel. rescaling to match the 100 keV points.," We plot this same spectrum as a dotted line in the upper panel, rescaling to match the 100 keV points."44" NCC 1915 aud Circiuus have similar XN/FIR vb,(l00keV)/Lepe~2«1027 for Circinus and ~3<? for NGC 1915.", NGC 4945 and Circinus have similar X/FIR $\nu L_\nu(100 keV) / L_{FIR} \simeq 2\xten{-3}$ for Circinus and $\simeq 3\xten{-3}$ for NGC 4945.45 Note that. at each wavelength. both Circinus and NGC 1915 were observed with comparable resolution.," Note that, at each wavelength, both Circinus and NGC 4945 were observed with comparable resolution."46 Ifthe AGN in NGC 1915 dominates the luminosity and its iutvinsic spectrin is simular to that of Circinus. then the lack of ACN detections in the near-IR aud mid-IR require larger obscuration.," If the AGN in NGC 4945 dominates the luminosity and its intrinsic spectrum is similar to that of Circinus, then the lack of AGN detections in the near-IR and mid-IR require larger obscuration."47 Ii particular the nou-detection of a Ix baud point source or of dilution of the CO features can be used to estimate the extinction at¢an., In particular the non-detection of a K band point source or of dilution of the CO features can be used to estimate the extinction at.48. In Circinus from Maiolino et al., In Circinus from Maiolino et al.49 LO98a (Is band) aud. Matt et al. 1999..," \cite{maiolino98} (K band) and Matt et al. \cite{matt99},"50 we can derive ενον]ΟΛΕΣ}~0.5., we can derive $\nu L_\nu (K) / \nu L_\nu (100 keV)\simeq 0.5$.51" TE NGC 1915 has a simular near-IR over hard-N-vavs ratio then. given vl,Uy)ναΟΛ)<<ὃν10 BEEN xuxd pper lanit from CO and X-ray data from Done ct al. 1996))."," If NGC 4945 has a similar near-IR over hard-X-rays ratio then, given $\nu L_\nu (K) / \nu L_\nu (100 keV) < 8\xten{-4}$ (K band upper limit from CO and X-ray data from Done et al. \cite{done96}) ),"52 the extinctiou. toward the nucleus is AA> Tuas (Le. Ardy>TOmae) larecr than in the case of Circinus., the extinction toward the nucleus is $\Delta \mathrm{A}_\mathrm{K}>7$ mag (i.e. $\Delta\AV>70$ mag) larger than in the case of Circinus.53 Tot dust in NCC 1915 iust be hiddeu by at least ely>135anag. in agreement with the estimate bv Moorwood Class (19510). elyTO ancl. more recently. with an aualvsis of ISO CVF spectra inplviug AycLOOmae (CMadoliuo et al.," Hot dust in NGC 4945 must be hidden by at least $\AV>135\MAG$, in agreement with the estimate by Moorwood Glass \cite{moorwood84}) ), $\AV>70$ and, more recently, with an analysis of ISO CVF spectra implying $\AV\sim 100\MAG$ (Maiolino et al.,"54 2000. iu preparation).," 2000, in preparation)."55 We note that the required extinction is not unexpected and in agreement with the X-rav measurements., We note that the required extinction is not unexpected and in agreement with the X-ray measurements.56 The nieasured colhuun density in absorption iu tle N-ravs is Ny~few<10?tem? therefore the expected Ay. assundue a galactic gas-to-dust ratio is: The Ay measured from optical/IR data is estimated smaller than cerived frou N-vavs (Ay-R)~0d0.5A ON) Cranato. Danese Franceschini 19973). therefore the X-ray absorbing column density is in exccllent aereciuent with the required extinction.," The measured column density in absorption in the X-rays is $N_\mathrm{H}\sim {\rm few}\xten{24}\CM\2$ therefore the expected $A_V$, assuming a galactic gas-to-dust ratio is: The $A_V$ measured from optical/IR data is estimated smaller than derived from X-rays $A_V(\mathrm{IR})\sim 0.1-0.5\, A_V(\mathrm{X})$ ; Granato, Danese Franceschini \cite{granato}) ), therefore the X-ray absorbing column density is in excellent agreement with the required extinction."57 Verv hieh extinction. expected in the frame of the unified ACN model are observed iu mauv objects as discussed ancl sununarzed. for instance. in Maüoliuo et al.," Very high extinction, expected in the frame of the unified AGN model are observed in many objects as discussed and summarized, for instance, in Maiolino et al."58 L99S8b and in Risaliti et al. 1999..," \cite{maiolino98b}59 and in Risaliti et al. \cite{risaliti}."60 The higher extinction can also qualitatively explain the redder colors of the NGC 1915 FIR spectra., The higher extinction can also qualitatively explain the redder colors of the NGC 4945 FIR spectrum.61 The solid line in the upper panel is the spectriun of Circiuus after applying foreground extinction bv ely=15012ag., The solid line in the upper panel is the spectrum of Circinus after applying foreground extinction by $\AV=150\MAG$.62 We have applied the extinction law by Draine Lee (198 ) and the energy lost in the mid-IR las been reprocessed as dadust enmüssion (1.0. black body ciission at ccorrected for Abe CLUISSIVITY)., We have applied the extinction law by Draine Lee \cite{draine}) ) and the energy lost in the mid-IR has been reprocessed as dust emission (i.e. black body emission at corrected for $\WL^{-1.75}$ emissivity).63 Though a careful treatinent requires a full radiatiou trauster calculation. this simple plotdemonstrates that (1) the redder color of NGC1915 with respect to Circinus can be explaincel with extra absorption aud (1) that this is not energeticallv incompatible with the observed FIR luminosity. ie. the," Though a careful treatment requires a full radiation transfer calculation, this simple plotdemonstrates that (i) the redder color of NGC4945 with respect to Circinus can be explained with extra absorption and (ii) that this is not energetically incompatible with the observed FIR luminosity, i.e. the"64This piecewise construction of (he composite image is illustrated in Figures 1 - 2.. Binages,This piecewise construction of the composite image is illustrated in Figures \ref{fig:images-phi}~ - \ref{fig:image-composite}.65" from different ,2 are shown in Figure 1.. and their sum is plotted in Figure 2.."," Images from different $\varphi$ are shown in Figure \ref{fig:images-phi}, and their sum is plotted in Figure \ref{fig:image-composite}."66 We find that frame-clrageine of photons can cause emission from one quadrant of (he simulation domain to spread into all quadrants of the image plane., We find that frame-dragging of photons can cause emission from one quadrant of the simulation domain to spread into all quadrants of the image plane.67 The total flux of a quadrant varies with 4 since certain values orient. the cdisk's orbital velocity closer to the line of sight., The total flux of a quadrant varies with $\varphi$ since certain values orient the disk's orbital velocity closer to the line of sight.68 Figures 1 and 2 will be helpful references in our later discussion about how the artificial azimuthal svinmetry condition influences our variability. predictions in Section 3.4., Figures \ref{fig:images-phi} and \ref{fig:image-composite} will be helpful references in our later discussion about how the artificial azimuthal symmetry condition influences our variability predictions in Section \ref{sec:azim-symm-cond}.69 Tracking the light through the simulation data is complicated by the fact (hat spacetime's curvature means (hat a set of photons reaching an observer al one instant may originate from the accretion flow over a wide range of coordinate times., Tracking the light through the simulation data is complicated by the fact that spacetime's curvature means that a set of photons reaching an observer at one instant may originate from the accretion flow over a wide range of coordinate times.70 7. included the effect of time delays. but used an infinitesimally (hin emission region which intersected each geodesic only once.," \cite{AR03} included the effect of time delays, but used an infinitesimally thin emission region which intersected each geodesic only once."71 This meant that they did not have to propagate the light rays through the simulation data. as we must because our emission region is extended.," This meant that they did not have to propagate the light rays through the simulation data, as we must because our emission region is extended."72 There are many wavs to go about the bookkeeping inherent (o this problem. but different. aleorithms place vastly different. demands on computer memory.," There are many ways to go about the bookkeeping inherent to this problem, but different algorithms place vastly different demands on computer memory."73 Hav-(racing as (he simulation runs is expensive. memory intensive. and nol amenable to exploration since adjustments made to the rav-tracing scheme would require rerunning thesimulation?.," Ray-tracing as the simulation runs is expensive, memory intensive, and not amenable to exploration since adjustments made to the ray-tracing scheme would require rerunning the."74. For (his reason. we adopted a post-processing procedure. which means that our time resolution is set bv the rate al which we output simulation data.," For this reason, we adopted a post-processing procedure, which means that our time resolution is set by the rate at which we output simulation data."75 As a rav (raverses spacetime. we use quacd-linear (linear in space and time) interpolation to determine the necessary. quantities along the ravs path.," As a ray traverses spacetime, we use quad-linear (linear in space and time) interpolation to determine the necessary quantities along the ray's path."76 This interpolation is done with pairs of simulation data slices at a lime in order to reduce (he calculations memory footprint., This interpolation is done with pairs of simulation data slices at a time in order to reduce the calculation's memory footprint.77 Ravs are organized into stacks of snapshots. each representing a bate of rays distributed over the image plane (hat reach the observer svnchronously.," Rays are organized into stacks of snapshots, each representing a batch of rays distributed over the image plane that reach the observer synchronously."78 Each snapshot then depends on a finite span of simulation data. or rather. a given time slice of simulation data influences a sequence of snapshots.," Each snapshot then depends on a finite span of simulation data, or rather, a given time slice of simulation data influences a sequence of snapshots."79 In ?.. we spent much effort to ensure our rav (racing caleulation was converged with respect to the number of lisht ravs used per image: following (he analogy with a pinhole camera. we will refer to them as in ow camera.," In \cite{Noble09}, we spent much effort to ensure our ray tracing calculation was converged with respect to the number of light rays used per image; following the analogy with a pinhole camera, we will refer to them as in our camera."80 We found best performance using a nonuniform pixelation that approximates a projection of the simulations grid onto the image plane., We found best performance using a nonuniform pixelation that approximates a projection of the simulation's grid onto the image plane.81" Using the radial profile of flux at infinity dF/dr as our convergence criterion. we found that Nyis=255? nonuniform pixels and Ny,=12007 uniform pixels result in approximately the same level of accuracy (largest relative error over ris 5%) when compared to a caleulation with ;/N4;,pix=15007 uniform pixels."," Using the radial profile of flux at infinity $dF/dr$ as our convergence criterion, we found that $N_\mathrm{pix}=255^2$ nonuniform pixels and $N_\mathrm{pix}=1200^2$ uniform pixels result in approximately the same level of accuracy (largest relative error over $r$ is $5\%$ ) when compared to a calculation with $N_\mathrm{pix}=1500^2$ uniform pixels."82The dynamical rate applies when a gas mass which was previously selfsupporting against gravity ds. destabilized and falls freely on to the black hole.,The dynamical rate applies when a gas mass which was previously self–supporting against gravity is destabilized and falls freely on to the black hole.83 Equation(1)) describes the case where gas is initially in rough virial equilibrium in the bulge of a galaxy with velocity clispersion e and barvonic mass fraction fj., Equation\ref{dyn}) ) describes the case where gas is initially in rough virial equilibrium in the bulge of a galaxy with velocity dispersion $\sigma$ and baryonic mass fraction $f_g$.84 Parametrizing. we find where eu)=0/(200kms1). and we have taken 0.16.," Parametrizing, we find where $\sigma_{200} = \sigma/(200~{\rm km\, s^{-1}})$, and we have taken $f_g = 0.16$ ."85 We compare this with where Leag is the Edcineton Iuminosity. g the radiative cHicioney of accretion. ancl & the electron scattering opacity.," We compare this with where $\le$ is the Eddington luminosity, $\eta$ the radiative efficiency of accretion, and $\kappa$ the electron scattering opacity."86 We evaluate this for ay=0.1 and black hole masses M lying close to the observed AZ0 relation to find and thus an Eddington ratio where Aly=Mf10M.., We evaluate this for $\eta = 0.1$ and black hole masses $M$ lying close to the observed $M - \sigma$ relation to find and thus an Eddington ratio where $M_8 = M/10^8\msun$.87 Since 0.15AdsS10 for the black holes in ACN. and Alivy is an upper limit to Al. modest values m1 o£ the Exldington ratio are likely.," Since $0.1 \la M_8 \la 10$ for the black holes in AGN, and $\md$ is an upper limit to $\dot M$, modest values $\dot m \sim 1$ of the Eddington ratio are likely."88 For completeness E note that much higher Eddington ratios can occur if the gas mass which is destabilizecl was previously held together bv selfgravity. e.g. as in a star.," For completeness I note that much higher Eddington ratios can occur if the gas mass which is destabilized was previously held together by self–gravity, e.g. as in a star."89" In this case we find a maximum.dynamical. rate Alu9(usé2€~ALP. where AL, is the stellar mass and Poy.PP its orbital velocity and. period."," In this case we find a maximumdynamical rate $\md \sim v_{\rm orb}^3/2G \sim M_*/P$, where $M_*$ is the stellar mass and $v_{\rm orb}, P$ its orbital velocity and period."90 This gives rates Alien~OM./hr in stellarmass binary svstems., This gives rates $\md \sim 0.1\msun/{\rm hr}$ in stellar–mass binary systems.91 Rather lower values result. for tidal disruption of stars near SALBIL because the stellar debris is only aceretecl over a spread. in orbital times (e.g. Lodato et al.," Rather lower values result for tidal disruption of stars near SMBH because the stellar debris is only accreted over a spread in orbital times (e.g. Lodato et al.,"92 2009)., 2009).93 AMotivated by the results of the previous section. | examine 10 properties of winds from SMBDLIL accreting with modest Edelington ratios mi1.," Motivated by the results of the previous section, I examine the properties of winds from SMBH accreting with modest Eddington ratios $\dot m \sim 1$."94 EF assume that the winds are quasispherical. over solid angle 4x6. with b—1 (this is confirmed for POL211|143: Pounds Reeves. 2009).," I assume that the winds are quasi--spherical, over solid angle $4\pi b$, with $b \sim 1$ (this is confirmed for PG1211+143; Pounds Reeves, 2009)."95" Lt is well known that winds of this type have electron scattering optical depth To1. measured from infinity in to a distance of order the Schwarzschilel radius A,=2€Mc (e.g. King Pounds. 2003)."," It is well known that winds of this type have electron scattering optical depth $\tau \sim 1$ measured from infinity in to a distance of order the Schwarzschild radius $R_s = 2GM/c^2$ (e.g. King Pounds, 2003)."96 This means that on average every emitted. photon scatters about once before escaping to infinity. which in turn suggests that the total wind momentum must be of order the photon momentum. 1.6. as ds for example also found. for the winds of hot stars.," This means that on average every emitted photon scatters about once before escaping to infinity, which in turn suggests that the total wind momentum must be of order the photon momentum, i.e. as is for example also found for the winds of hot stars."97 Using (3)) gives the wind velocity This agrees with the fact that winds are always found to have a terminal velocity typical of the escape velocity from the radius at which they are launched. here several tens of Ες.," Using \ref{edd}) ) gives the wind velocity This agrees with the fact that winds are always found to have a terminal velocity typical of the escape velocity from the radius at which they are launched, here several tens of $R_s$."98 As expected. using this value of ο in the mass conservation equation where pC) is the mass density. selfconsistently shows that the optical depth 7 of the wind is 1 (cf Wing Pounds. 2003. eqn.," As expected, using this value of $v$ in the mass conservation equation where $\rho(R)$ is the mass density, self–consistently shows that the optical depth $\tau$ of the wind is $\sim 1$ (cf King Pounds, 2003, eqn."99 4)., 4).100 Since the wind moves with speed O.le. it can persist long after the AGN is observed. to have. become subI5ddington.," Since the wind moves with speed $\sim 0.1c$, it can persist long after the AGN is observed to have become sub--Eddington."101 The duration of the lag is 1072/0. where & is the radial extent of the wind (ic. the shock radius. as we shall see below).," The duration of the lag is $\sim 10R/c$, where $R$ is the radial extent of the wind (i.e. the shock radius, as we shall see below)."102 For R23 pe this lag is at least a century. and far longer lags are possible. as we shall sec.," For $R \ga 3$ pc this lag is at least a century, and far longer lags are possible, as we shall see."103 This may be the reason why AGN showing other signs of superI5ddington phenomena (e.g. narrowline Sevlert 2 galaxies) are nevertheless seen to have subοσοι luminosities (e.g. NGC 4051: Denney et al.," This may be the reason why AGN showing other signs of super--Eddington phenomena (e.g. narrow–line Seyfert 2 galaxies) are nevertheless seen to have sub–Eddington luminosities (e.g. NGC 4051: Denney et al.,"104 2009)., 2009).105 We can use (S..9)) to estimate the ionization parameter ofthe wind.," We can use \ref{v}, \ref{mass}) ) to estimate the ionization parameter of the wind."106" Here £;=(Ley is the ionizing luminosity. with /;«1l a dimensionless parameter specified by the quasar spectrum. and /N.—ppm,is the number density."," Here $L_i = l_i\le$ is the ionizing luminosity, with $l_i< 1$ a dimensionless parameter specified by the quasar spectrum, and $N = \rho/\mu m_p$is the number density."107 ‘This gives where fs25/107. and Yo.=gj0.1.," This gives where $l_2 = l_i/10^{-2}$, and $\eta_{0.1} = \eta/0.1$."108 Equation (11)) shows that the wind momentum and mass rates determine its ionization parameter: for à given quasar spectrum. the predominant ionization state is such that the threshold. photon energy. defining. £;. anc the corresponding ionization parameter £. together satisfy (11)).," Equation \ref{ion2}) ) shows that the wind momentum and mass rates determine its ionization parameter: for a given quasar spectrum, the predominant ionization state is such that the threshold photon energy defining $L_i$, and the corresponding ionization parameter $\xi$, together satisfy \ref{ion2}) )."109 This requires high excitation: a low threshold photon energy (sav in the infrared) would imply a laree value of fo. but the high. value of £ then given. by (11)). would: require the presence. of very highly tonizecl species. physically incompatible with such low excitation.," This requires high excitation: a low threshold photon energy (say in the infrared) would imply a large value of $l_2$, but the high value of $\xi$ then given by \ref{ion2}) ) would require the presence of very highly ionized species, physically incompatible with such low excitation."110 For suitably chosen continuum spectra. it is possible to envisage a range of solutions of (112). and it is even possible that a given spectrum may. allow more than one solution. the result being specified by initial conditions.," For suitably chosen continuum spectra, it is possible to envisage a range of solutions of \ref{ion2}) ), and it is even possible that a given spectrum may allow more than one solution, the result being specified by initial conditions."111 However for a typical quasar spectrum. an obvious self.consistent. solution of (11)) is/sc Loe1. £63) 1013.," However for a typical quasar spectrum, an obvious self–consistent solution of \ref{ion2}) ) is $l_2112\simeq 1$, $\dot m \simeq 1$, $\xi \simeq 3\times 10^4$ ."113 This describes the case where the quasar is currently. raciating at the Eddington limit., This describes the case where the quasar is currently radiating at the Eddington limit.114 However as remarked after eqn (9)). we can also have situations where the quasars luminosity has droppedafter an Eddington episode. but the wind is still owing. with rmx 1.," However as remarked after eqn \ref{mass}) ), we can also have situations where the quasar's luminosity has droppedafter an Eddington episode, but the wind is still flowing, with $\dot m115\simeq 1$ ."116 In this case the ionizing luminosity 10.νι in (11)) takes a lower value. giving a lower value of £.," In this case the ionizing luminosity $10^{-2}l_2\le$ in \ref{ion2}) ) takes a lower value, giving a lower value of $\xi$ ."117 For example a quasar of luminosity O34gitwould have £~ 107., For example a quasar of luminosity $0.3\le$would have $\xi \sim 10^4$ .118" ""his corresponds to a photon energy. threshold. appropriate for helium or hydrogenlike iron (Le. Pea~9 keV).", This corresponds to a photon energy threshold appropriate for helium– or hydrogenlike iron (i.e. $h\nu_{\rm threshold}\sim 9$ keV).119 We conclude that, We conclude that120As noted in the Introduction. the radio continuum observations give good evidence that tle parsec scale structure of 3C 81 includes an opposing pair of jets inclined at about £07 to ithe line-of-sight with significai (amounts of ionized gas iu the region |jetweenu the jets.,"As noted in the Introduction, the radio continuum observations give good evidence that the parsec scale structure of 3C 84 includes an opposing pair of jets inclined at about $40\cdeg$ to the line-of-sight with significant amounts of ionized gas in the region between the jets."121 The ionized eas is most likely associated with the accretion disk that would ye there in most AGN mocleS., The ionized gas is most likely associated with the accretion disk that would be there in most AGN models.122 The p'ojected distance [ro1i the norther1 feature to the core is about 2.9 pe so. with the above eeomelly. the region of the jel that emis the absorbed racliation is about 5 pe from where tle racliatjon passes through te disk on the way to the Earth.," The projected distance from the northern feature to the core is about 2.5 pc so, with the above geometry, the region of the jet that emits the absorbed radiation is about 5 pc from where the radiation passes through the disk on the way to the Earth."123 That 1« a small enough distance that. as aso uoted iu the IutrodticLL. gas al he disk would be sibjec to a sulliciently high radiation inteusity that radiation da)=.ig would ye expected to broadeu he H65a recombination line to thotsands ofLo preveitiug detectjon in our observat]ous.," That is a small enough distance that, as also noted in the Introduction, gas at the disk would be subject to a sufficiently high radiation intensity that radiation damping would be expected to broaden the $\alpha$ recombination line to thousands of, preventing detection in our observations."124 Our non-«dletection is consistent witl ils expectation., Our non-detection is consistent with this expectation.125 I a lite had been deteced. the lack of excessive raciation camping would coustrain the gas o lie jevond some imiuimur1 distaice from the radio eiuittiig regiums.," If a line had been detected, the lack of excessive radiation damping would constrain the gas to lie beyond some minimum distance from the radio emitting regions."126 The actual distance limit epeuds oi which portions of the overall radio source illuninate the absorbing gas., The actual distance limit depends on which portions of the overall radio source illuminate the absorbing gas.127 The bare LE.uma iIumination is [ron the ιο{μου feature. the featwe for which the [ree-free absorption is seen.," The bare minimum illumination is from the northern feature, the feature for which the free-free absorption is seen."128 If hat is the ouly racdiation iluminatiug tie absorbing gas. the separation between the οhern jet aud the absorbing region would have to be at least 11 pe for the radiation camping ine width o be »elow the a»proximatly 500 Uyper limit for vvhat cotld lave been cleected in our observations.," If that is the only radiation illuminating the absorbing gas, the separation between the northern jet and the absorbing region would have to be at least 11 pc for the radiation damping line width to be below the approximatly 500 upper limit for what could have been detected in our observations."129 That is over twice the distauce Jeween the nortler jet all the clisk in he geomet'N deived [rom the contiuuuim observations., That is over twice the distance between the northern jet and the disk in the geometry derived from the continuum observations.130 It is a bare iminimun distaice. because bot1 the soutlern fe:ure (uear side jet) aud the core region ost ikely also 1]uiminate tle absorpliol region.," It is a bare minimum distance, because both the southern feature (near side jet) and the core region most likely also illuminate the absorption region."131 With t additional illtinination. the minimum clintauc'e between the eiittiiD>oO all absorug reeiols WO need to be much higher. up to about 50 pc iL al reeiols illumirate the absorbiig gas.," With this additional illumination, the minimum distance between the emitting and absorbing regions would need to be much higher, up to about 50 pc if all regions illuminate the absorbing gas."132 ThIs dif a line had been o»xerved. aud the plivysies is rigl. theaINO‘bine reeion would have to be sufficienty far from he various radio sources that the idea tlat Π 1s associatec with tlie accretion cis. WOilc be wroi.," Thus if a line had been observed, and the physics is right, the absorbing region would have to be sufficiently far from the various radio sources that the idea that it is associated with the accretion disk would be wrong."133 TIal. in turi. would leave us strMODoOline o explain why oulv tle northern featire is [ree-Iree absorbed.," That, in turn, would leave us struggling to explain why only the northern feature is free-free absorbed."134 T1e ['ee-ree absorj»tiol of the nortieri feature gives he EM. Or ahy assumed temperature. of the jionized eas along the line-ol-sight (Walkeretal.2000).," The free-free absorption of the northern feature gives the EM, for any assumed temperature, of the ionized gas along the line-of-sight \citep{W00}."135. The E lis a function of the electrou density al dtle absorbiug regio1 thickess πο its value coustrailis those parameters., The EM is a function of the electron density and the absorbing region thickness so its value constrains those parameters.136 Tle upper pauel of Fieure | shows tlie COLIslFalüts for an assumed temperatue of 101 K. Constraints for a range of values of the E tare shuWH rep'esentiug the range observe over diffe‘elt positions alo the northeἩ feature., The upper panel of Figure \ref{recomb10000} shows the constraints for an assumed temperature of $10^4$ K. Constraints for a range of values of the EM are shown representing the range observed over different positions along the northern feature.137 Two other liinits are also shown., Two other limits are also shown.138 The horizoutal line is at 2.5 pc. the projecte core distace of the cenroid of the counerjet.," The horizontal line is at 2.5 pc, the projected core distance of the centroid of the counterjet."139 This is a rough uppe ‘limit for the thickness of t absorbing 'eelon i£ it is ssocialec| with the accretion disk., This is a rough upper limit for the thickness of the absorbing region if it is associated with the accretion disk.140 For the observed emissiou measures. tli thickness Iimit constralis the cetsity to values above about 104 .," For the observed emission measures, this thickness limit constrains the density to values above about $10^4$ $^{-3}$."141 À secon limit. given by t lack of significant. Thomson opti‘al depth. is also shown.," A second limit, given by the lack of significant Thomson optical depth, is also shown."142 Given the observed f'ee-[ree absorptio the Thompson optical «eptl WOid only be important at very large sizes aucl low cleusities.," Given the observed free-free absorption, the Thompson optical depth would only be important at very large sizes and low densities."143 Thi, This144weighted average is therefore much lower than the arithmetic average.,weighted average is therefore much lower than the arithmetic average.145 At this point one has to note that the estimation of the flux density of pulsars at high observational frequencies will always be affected by strong scintillations (except for some very low DM cases) and one has to take it into account when trying to measure the flux of these. for example for the purpose of acquiring pulsar spectra.," At this point one has to note that the estimation of the flux density of pulsars at high observational frequencies will always be affected by strong scintillations (except for some very low DM cases) and one has to take it into account when trying to measure the flux of these, for example for the purpose of acquiring pulsar spectra."146 To estimate the scintillation timescales. we used the structure function analysis of the flux density variations.," To estimate the scintillation timescales, we used the structure function analysis of the flux density variations."147 For uniformly sampled data the first order of the normalized structure function of the flux density is (Simonetti et al. 1985)), For uniformly sampled data the first order of the normalized structure function of the flux density is (Simonetti et al. \cite{simo}) )148 where / is the data index. j is the offset that corresponds to a time lag in the data for which the value of the structure function is calculated.," where $i$ is the data index, $j$ is the offset that corresponds to a time lag in the data for which the value of the structure function is calculated."149 (i) is the weighting factor (which is equal to | where the flux density exist for jth points and 0 otherwise). and ΔΕΟ=SwedD is the number of pairs of values found in the data that were found to have the offset equal to j (1.e. time lag equal to 7). The values of the structure function need to be corrected to remove white noise contribution.," $w(i)$ is the weighting factor (which is equal to 1 where the flux density exist for $j$ th points and 0 otherwise), and $N(j)=\sum w(i)w(i+j)$ is the number of pairs of values found in the data that were found to have the offset equal to $j$ (i.e. time lag equal to $\tau$ The values of the structure function need to be corrected to remove white noise contribution."150 This was made by subtracting the value of the structure function at the unit lag from all the structure function values., This was made by subtracting the value of the structure function at the unit lag from all the structure function values.151" If a quasi-periodic signal is present in the data the structure function will show a plateau at the value of D,4.", If a quasi-periodic signal is present in the data the structure function will show a plateau at the value of $D_{\rm sat}$.152" The timescale of the observedvariability 1s the ag corresponding to half the saturation value of the structure function after white noise correction: fjss=7(D,,4/2) (KS92).", The timescale of the observed variability is the lag corresponding to half the saturation value of the structure function after white noise correction: $t_{\rm ISS}=\tau(D_{\rm sat}/2)$ (KS92).153" The error of the timescale can be estimated by finding the time lags that correspond to the values of the structure function of (D,€0D.) /2.", The error of the timescale can be estimated by finding the time lags that correspond to the values of the structure function of $\left(D_{\rm sat}\pm\delta D_{\rm sat}\right)/2$ .154" The uncertainty of the saturation value of the structure function 0D is best estimated as OD/DaymQOfss/Tas)7. where Top, is the total duration of the observation. in our case the length of an individual observing session."," The uncertainty of the saturation value of the structure function $\delta D_{\rm sat}$ is best estimated as $\delta D_{sat}/D_{sat} \approx (2t_{\rm ISS}/T_{\rm obs})^{1/2}$, where $T_{\rm obs}$ is the total duration of the observation, in our case the length of an individual observing session."155 Since our project consisted of several observing sessions repeated over the course of three years. we decided to calculate the general average structure function as well.," Since our project consisted of several observing sessions repeated over the course of three years, we decided to calculate the general average structure function as well."156 This can be made either directly by applying structure function algorithm to the entire set of data. or by adding the values obtained for individual sessions. after de-normalizing them.," This can be made either directly by applying structure function algorithm to the entire set of data, or by adding the values obtained for individual sessions, after de-normalizing them."157 The values of the scintillation timescale. modulation index and their uncertainties for the general average structure function can then be calculated in the same manner as for the individual sessions.," The values of the scintillation timescale, modulation index and their uncertainties for the general average structure function can then be calculated in the same manner as for the individual sessions."158 Table 2. shows the results of the structure function analysis applied to our data., Table \ref{sf_table} shows the results of the structure function analysis applied to our data.159 This table has less individual session entries than Table | because it shows only those sessions for which the structure function saturated., This table has less individual session entries than Table 1 because it shows only those sessions for which the structure function saturated.160 The saturation of the SF was necessary to calculate the cited values of Ass and 1Η and their uncertainties (see the notes for Table 1)., The saturation of the SF was necessary to calculate the cited values of $t_{\rm ISS}$ and $m$ and their uncertainties (see the notes for Table 1).161 Figure 3. shows three of the structure functions obtained during the analysis., Figure \ref{fig2} shows three of the structure functions obtained during the analysis.162 The top plot shows the SF for the first and longest. 5-day session that was conducted between 2002 July 3-8.," The top plot shows the SF for the first and longest, 5-day session that was conducted between 2002 July 3-8."163 This structure function clearly shows two plateaus. which allowed us to obtain the values of two distinetive timescales present in the data.," This structure function clearly shows two plateaus, which allowed us to obtain the values of two distinctive timescales present in the data."164 As we mentioned above. at the observing frequency of 4.8 GHz PSR B0Q329+54 is believed to be close to the transition frequency. 1.9. switching from strong to weak scintillation regimes. diffractive and refractive timescales should be relatively close (yielding a low value of the strength of the scattering parameter 4).," As we mentioned above, at the observing frequency of 4.8 GHz PSR B0329+54 is believed to be close to the transition frequency, i.e. switching from strong to weak scintillation regimes, diffractive and refractive timescales should be relatively close (yielding a low value of the strength of the scattering parameter $u$ )."165 Hence we are convinced that those two plateaus correspond to two scintillation timescales. a shorter diffractive timescale (lower plateau). and a longer refractive timescale.," Hence we are convinced that those two plateaus correspond to two scintillation timescales, a shorter diffractive timescale (lower plateau), and a longer refractive timescale."166 This is even more convincing for the middle plot of Fig. 3," This is even more convincing for the middle plot of Fig. \ref{fig2},"167 which shows the general average structure. function., which shows the general average structure function.168 Two plateaus were also present for another session. 2002 September 18-19 (ca.," Two plateaus were also present for another session, 2002 September 18-19 (ca."169 30-hour session)., 30-hour session).170 The third and bottom subplot of Fig., The third and bottom subplot of Fig.171 43. shows a typical structure function. obtained during a single. typical 37-hour session. where one can see only the regular saturation of the structure function caused by the diffractive scintillations.," \ref{fig2} shows a typical structure function, obtained during a single, typical 37-hour session, where one can see only the regular saturation of the structure function caused by the diffractive scintillations."172 The horizontal Imes in all those plots show the SF saturation levels. vertical lines - the time lags that correspond tothe saturation (the values of the timescales are given in," The horizontal lines in all those plots show the SF saturation levels, vertical lines - the time lags that correspond tothe saturation (the values of the timescales are given in"173wave in the atmosphere (Mathias et al.,wave in the atmosphere (Mathias et al.174 2006). asx done by Sasselov ot al. (," 2006), as done by Sasselov et al. ("1751990).,1990).176 We present infrared CRIRES observations of ( Car obtained in 2008-2009 at four different pulsation phases (S/N of about 300 in the continuum)., We present infrared CRIRES observations of $\ell$ Car obtained in 2008-2009 at four different pulsation phases (S/N of about 300 in the continuum).177 We fiud lee unubleuded spectral lines. Bry and two metallic lines: Fell and Cal22090.0A.. In Fie.," We find three unblended spectral lines, $\gamma$ and two metallic lines: FeII and CaI. In Fig."178 3. we present the Cal spectral line flux as a unction of time.," 3, we present the CaI spectral line flux as a function of time."179 The first moment radial velocity aud depth (as a percentage of continuun) are indicated in Fig., The first moment radial velocity and depth (as a percentage of continuum) are indicated in Fig.180 together with TARPS observatious of a spectral line of similar depth.," 4, together with HARPS observations of a spectral line of similar depth."181 The dashed line iu Fie., The dashed line in Fig.182 { dower panel) is the optical TARPS radial velocity curve uultiplied by 1.30. showing that he infrared radial velocity curve has au amplitude that is about larecr han in the optical.," 4 (lower panel) is the optical HARPS radial velocity curve multiplied by 1.30, showing that the infrared radial velocity curve has an amplitude that is about larger than in the optical."183 The conclusion is that. even if these wo imnetallie lines in the optical aud iu the infrared have a simular depth (which means in principle that their line-ornmniues regions have a similar optical depths. am that hey form approximatively at the same position iu the atmosphere compared to the photosphere). the infrared auplitucde of the radial velocity curve is significantly lareer han the optical one.," The conclusion is that, even if these two metallic lines in the optical and in the infrared have a similar depth (which means in principle that their line-forming regions have a similar optical depths, and that they form approximatively at the same position in the atmosphere compared to the photosphere), the infrared amplitude of the radial velocity curve is significantly larger than the optical one."184 This suggests (as explained above) hat the plotospheric laver is probably forming higher iu he infrared than in the optical Gvhich secms to be in contradiction with Sasselov et al., This suggests (as explained above) that the photospheric layer is probably forming higher in the infrared than in the optical (which seems to be in contradiction with Sasselov et al.185 1990)., 1990).186 More data are required to confirm this result., More data are required to confirm this result.187 We address this question theoretically usine our hydrodvuamical models of 6 Cep and 6 Car., We address this question theoretically using our hydrodynamical models of $\delta$ Cep and $\ell$ Car.188 The model of € Car is described iu Paper 1. We cousider the solar iietallicitv., The model of $\ell$ Car is described in Paper I. We consider the solar metallicity.189 Concerning 9 Cep. the optical and infrared photospheric lavers (7.= 1) form at the same laver in the atinosphere. whereas for 6 Car the infrared plotosphere forms higher than the optical one.," Concerning $\delta$ Cep, the optical and infrared photospheric layers $\tau_{\mathrm{c}}=1$ ) form at the same layer in the atmosphere, whereas for $\ell$ Car the infrared photosphere forms higher than the optical one."190 This implies a increase oulv in the projection factor. which seeuis to be iu contradiction with Sasselov ot al. (," This implies a increase only in the projection factor, which seems to be in contradiction with Sasselov et al. ("1911990) and also CRIRES data.,1990) and also CRIRES data.192 This delicate question will be studied in more detail later. using a larger seuuple of infrared (resp.," This delicate question will be studied in more detail later, using a larger sample of infrared (resp."193 optical) spectroscopic (resp., optical) spectroscopic (resp.194 interferometric) data., interferometric) data.195" In either case. this effect (optical versus infrared) should affect the Milky Me and, LAIC ConclusionsCepheids in the same wav."," In either case, this effect (optical versus infrared) should affect the Milky Way and LMC Cepheids in the same way."196 We find that the S/N. metallicity. and optical-versus-infrared observations (but this last point has to be confirmed) cannot explain the diserepaucy between the theoretical aud empirical period-projection factor relation based on LAIC observations.," We find that the S/N, metallicity, and optical-versus-infrared observations (but this last point has to be confirmed) cannot explain the discrepancy between the theoretical and empirical period-projection factor relation based on LMC observations."197 Other possibilities can be considered. such as limi darkening for instance.," Other possibilities can be considered, such as limb darkening for instance."198 Indeed. following the relation by Storm ct al (," Indeed, following the relation by Storm et al. ("1992011a). the very short-period Cepheids should have a projection factor close to 1.15-1.5.,"2011a), the very short-period Cepheids should have a projection factor close to 1.45-1.5."200 This means a limb-cdarkening close to zero (uniforii disk)., This means a limb-darkening close to zero (uniform disk).201 By constrainiug this lub. darkening une interferometry (for instance VECA/CTIARA in optical. Mourard et al.," By constraining this limb darkening using interferometry (for instance VEGA/CHARA in optical, Mourard et al."202 2009). one can derive a geometric projection factor that should help in resolving the discrepancy.," 2009), one can derive a geometric projection factor that should help in resolving the discrepancy."203 However. our results secur to indicate that the relation is universal.," However, our results seem to indicate that the relation is universal."204 This is extremely precious when applying the BW incthod to extragalactic Cepheids., This is extremely precious when applying the BW method to extragalactic Cepheids.205demonstrated how iuverse compton scattering of CAIB photous from enerectic electrous iu he ICAL could be detectable as a (frequency clepeudent) cluperature change.,demonstrated how inverse compton scattering of CMB photons from energetic electrons in the ICM could be detectable as a (frequency dependent) temperature change.206 This effect conumuionlv referre o as theο or Sunvacy-Zeldovich effect has since become a standard tool for analyzing ICA xoperties (e.g.Muchove]etal.2007.andreferenceshereiu) Suuvaev&Zelclovich(1980). also noted that any notion of the ICM relative to the CMD rest frame wouk Hupart an additional (frequency iudepeudeut) doppler distortion to the temperature of the CMD dubbe he Suuvacy Zeldovich effect (KSZ) of order where rs the optical depth with respect to Thomson scattering.," This effect — commonly referred to as the or Sunyaev-Zeldovich effect --- has since become a standard tool for analyzing ICM properties \citep[e.g.][and references therein]{muchovej07}207 \citet{sunyaev80} also noted that any motion of the ICM relative to the CMB rest frame would impart an additional (frequency independent) doppler distortion to the temperature of the CMB — dubbed the Sunyaev Zeldovich effect (kSZ) — of order where $\tau$ is the optical depth with respect to Thomson scattering."208 The current generation of CAIB experiments should be able to use the kSZ effect to successfully measure the peculiar motions of galaxy clusters along the line-of-sight (seefore.g.Cunnamactal.2009).. which are expected iu ecneral to produce masini distortions AT~ 20;AN (Moluar&Birkinshaw2000).," The current generation of CMB experiments should be able to use the kSZ effect to successfully measure the peculiar motions of galaxy clusters along the line-of-sight \citep[see for e.g.][]{cunnama09}, which are expected in general to produce maximum distortions $\Delta T \sim 20 \mu$ K \citep{molnar00}."209. PR induced by the galaxy clusters transverse motion would be apparent as a dipole signature in the kSZ temperature distortion., PR induced by the galaxy cluster's transverse motion would be apparent as a dipole signature in the kSZ temperature distortion.210 The amplitude of this distortion would be simaller than the typical line-ofsight velocity sienature bv two factors: the first of order sin(yas (or for nearby galaxy. clusters) due to the projection effect: aud the secoud due to the fall-off in eas-deusity (and corresponding decrease iu 7) away frou the center of the galaxy cluster., The amplitude of this distortion would be smaller than the typical line-of-sight velocity signature by two factors: the first of order $\sin \theta_{\rm max}$ (or for nearby galaxy clusters) due to the projection effect; and the second due to the fall-off in gas-density (and corresponding decrease in $\tau$ ) away from the center of the galaxy cluster.211 Hence. we nught expect PR to induce a distortion of order 0.1-1 μῖν across nearby ealaxy clusters clearly a challeuge for neur-future experiments.," Hence, we might expect PR to induce a distortion of order 0.1-1 $\mu$ K across nearby galaxy clusters — clearly a challenge for near-future experiments."212 As before. the signal of PR in the kSZ effect will also be compcting with signatures of turbulent motions (expectedtobeoforderLOpTs.2003) and intrinsic rotation (expectedtobeoforder2y1v 2002).," As before, the signal of PR in the kSZ effect will also be competing with signatures of turbulent motions \citep[expected to be of order 10$\mu$K, see][]{sunyaev03} and intrinsic rotation \citep[expected to be of order 2$\mu$K due to tidally induced rotation alone][]{cooray02}."213 We have outlined three possible wavs to measure the PR of ealaxy clusters and estimate their transverse motions: from line-ofsight velocity measurements of ealaxy cluster galaxies. the motion of cluster eas and mapping the kSZ distortions in the CAIB.," We have outlined three possible ways to measure the PR of galaxy clusters and estimate their transverse motions: from line-of-sight velocity measurements of galaxy cluster galaxies, the motion of cluster gas and mapping the kSZ distortions in the CMB."214 All three of these measurements are unfeasible with the current data but could become feasible with uear future instruments or larger data sets;, All three of these measurements are unfeasible with the current data but could become feasible with near future instruments or larger data sets.215 The amplitude of PR is niost significaut for ealaxy clusters with larger angular extent., The amplitude of PR is most significant for galaxy clusters with larger angular extent.216 Hence. the most promising approach with current capabilities is to survey as large a sample as possible of spectra of galaxies in nearby galaxy. clusters.," Hence, the most promising approach with current capabilities is to survey as large a sample as possible of spectra of galaxies in nearby galaxy clusters."217 With all approaches. the signal of PR could be confused by random (or turbulent) motions aud mtrusic rotation of their svstem of targets.," With all approaches, the signal of PR could be confused by random (or turbulent) motions and intrinsic rotation of their system of targets."218 We are optimistic that it will be possible to disentangle these effects with sufficicutly large data sets since PR imposes a Tuque signature of solid-body rotation on top of these sources of confusion., We are optimistic that it will be possible to disentangle these effects with sufficiently large data sets since PR imposes a unique signature of solid-body rotation on top of these sources of confusion.219 Tncleed. Iaplinghat&Strigari(2008) found that. when they included a sinall iutriusic rotation in their models of dwarf splieroidal galaxies. the error bars on the transverse velocity estimates derived wo Cobserviug lue-ofsight velocities of stars in their uodels increased by oulv a factor of two.," Indeed, \citet{2008Kaplinghat} found that, when they included a small intrinsic rotation in their models of dwarf spheroidal galaxies, the error bars on the transverse velocity estimates derived by “observing” line-of-sight velocities of stars in their models increased by only a factor of two."220 While galaxy clusters are unlike dwarfs spheroidal galaxies in that hey are not expected to be as relaxed or spherically svinnetric. the Kaplinghat&Strigar(2008) study xovides a first step towards a comprehensive modeling effort.," While galaxy clusters are unlike dwarfs spheroidal galaxies in that they are not expected to be as relaxed or spherically symmetric, the \citet{2008Kaplinghat} study provides a first step towards a comprehensive modeling effort."221 Note that several other approaches to detecting rausverse iuotions of galaxy clusters lave also been xoposed., Note that several other approaches to detecting transverse motions of galaxy clusters have also been proposed.222 For example using polarization maps of the CAB (Sunvacy&Zeldovich1980).. eravitational leusiug of the CAID (Birkiushaw&Coll1983).. aud weak. aud strong lensing of background galaxies (Moluar&Birkin-shaw 2003).," For example using polarization maps of the CMB \citep{sunyaev80}, gravitational lensing of the CMB \citep{birkinshaw83}, and weak and strong lensing of background galaxies \citep{molnar03}."223. The strength of the signatures iu these methods are not depeudenut on the augular extent of the ealaxy cluster and heuce have the advantage over PR of being applicable to distant as well as nearby clusters., The strength of the signatures in these methods are not dependent on the angular extent of the galaxy cluster and hence have the advantage over PR of being applicable to distant as well as nearby clusters.224 With iultiple possible directious for detection. we conclude that measurements of the full space motions of galaxy clusters are on the horizon.," With multiple possible directions for detection, we conclude that measurements of the full space motions of galaxy clusters are on the horizon."225RV variable systems.,RV variable systems.226 In order to select the most promising targets for follow-up. we carried out numerical simulations and estimated the probability for a subdwarf binary with known RV shift to host a massive compact companion.," In order to select the most promising targets for follow-up, we carried out numerical simulations and estimated the probability for a subdwarf binary with known RV shift to host a massive compact companion."227 We created a mock sample of sdBs with a close binary fraction of 506c.," We created a mock sample of sdBs with a close binary fraction of $50\,\%$."228 We adopted the distribution of orbital periods of all known sdB binaries (see Table Al)) approximated by two Gaussians centered at 0.7d (width 0.3 d) and 5.0d (width 3.0d) days and assumed that 82% of the binaries belong to the short period population.," We adopted the distribution of orbital periods of all known sdB binaries (see Table \ref{tab:orbitslit}) ) approximated by two Gaussians centered at $0.7\,{\rm d}$ (width $0.3\,{\rm d}$ ) and $5.0\,{\rm d}$ (width $3.0\,{\rm d}$ ) days and assumed that $82\%$ of the binaries belong to the short period population."229 The short period Gaussian was truncated at 0.05d. which is considered the minimum period for an sdB binary. because the subdwarf primary starts filling its Roche lobe for shorter periods and typical companion masses.," The short period Gaussian was truncated at $0.05\,{\rm d}$, which is considered the minimum period for an sdB binary, because the subdwarf primary starts filling its Roche lobe for shorter periods and typical companion masses."230" Since stable Roche lobe overflow anc the accretion onto the companion would dramatically change the spectra of these stars. we can safely presume that our sample does not contain such objects,"," Since stable Roche lobe overflow and the accretion onto the companion would dramatically change the spectra of these stars, we can safely presume that our sample does not contain such objects."231 The orbital inclinatioi angles are assumed to be randomly distributed. but for geometrical reasons binaries at. high [clinations are more likely observed than binaries at low [clinations.," The orbital inclination angles are assumed to be randomly distributed, but for geometrical reasons binaries at high inclinations are more likely observed than binaries at low inclinations."232 To account for this. we used the method described in Gray (1992)) and adopted à realistic distribution of [clination angles.," To account for this, we used the method described in Gray \cite{gray92}) ) and adopted a realistic distribution of inclination angles."233 For the sdB mass the canonical value of 0.47M... was chosen.," For the sdB mass the canonical value of $0.47\,{\rm M_{\odot}}$ was chosen."234 The distribution of companion masses was based Cn the results by Geter et al. (2010b))., The distribution of companion masses was based on the results by Geier et al. \cite{geier10b}) ).235 The distribution of the low mass companions was approximated by a Gaussian centered at 0.4M.. (width 0.3 M).," The distribution of the low mass companions was approximated by a Gaussian centered at $0.4\,{\rm M_{\odot}}$ (width $0.3\,{\rm M_{\odot}}$ )."236 The fraction of massive compact companions is estimated to 26c of the close binary population based on binary population synthesis models (Geter et al. 2010b)).," The fraction of massive compact companions is estimated to $2\,\%$ of the close binary population based on binary population synthesis models (Geier et al. \cite{geier10b}) )."237 The mass distribution of these companions was approximated by a Gaussian centered at 2.0M. (width 1.0 Μ..).," The mass distribution of these companions was approximated by a Gaussian centered at $2.0\,{\rm M_{\odot}}$ (width $1.0\,{\rm M_{\odot}}$ )."238 For the system velocities a Gaussian distribution with a dispersion of 120kms∣ typical for halo stars was adopted (Brown et al. 2005)).," For the system velocities a Gaussian distribution with a dispersion of $120\,{\rm km\,s^{-1}}$ typical for halo stars was adopted (Brown et al. \cite{brown05}) )."239 Two RVs were taken from the model RV curves at random times and the RV difference was calculated for each of the 10° binaries in the simulatio sample., Two RVs were taken from the model RV curves at random times and the RV difference was calculated for each of the $10^{6}$ binaries in the simulation sample.240 This selection criterion corresponds to the HRV sample., This selection criterion corresponds to the HRV sample.241 For given RV difference and timespan between the measurements the fraction of systems with minimum. companio masses exceeding |M.. was counted.," For given RV difference and timespan between the measurements the fraction of systems with minimum companion masses exceeding $1\,{\rm M_{\odot}}$ was counted."242 In Fig., In Fig.243 7 the fraction of massive compact companions with unambiguous mass functions is plotted against the RV shift between two measurements at random times (solid curve)., \ref{muchfuss_sim} the fraction of massive compact companions with unambiguous mass functions is plotted against the RV shift between two measurements at random times (solid curve).244 It is quite obvious that binaries with high RV shifts are more likely to host massive companions., It is quite obvious that binaries with high RV shifts are more likely to host massive companions.245 The probability for a high mass companion (>1M4) at high inclination is raised by a factor of ten as soon as the RV shift exceeds 200kms7!.," The probability for a high mass companion $>1\,{\rm M_{\odot}}$ ) at high inclination is raised by a factor of ten as soon as the RV shift exceeds $200\,{\rm km\,s^{-1}}$."246 In order to cheek whether the selection of high velocities rather than high velocity shifts has an impact on the probability of finding sdB binaries with massive compact companions we used the same simulation., In order to check whether the selection of high velocities rather than high velocity shifts has an impact on the probability of finding sdB binaries with massive compact companions we used the same simulation.247 In Fig., In Fig.248 8. the fraction of these binaries is plotted against only one RV measurement taken at a random time., \ref{muchfuss_sim_const} the fraction of these binaries is plotted against only one RV measurement taken at a random time.249 It can be clearly seen that the detection probability rises significantly for stars with high RVs., It can be clearly seen that the detection probability rises significantly for stars with high RVs.250 Selecting the fastest stars in the halo therefore makes sense when searching for massive compact companions to sdB. Since the individual SDSS spectra were taken within short timespans. another simulation was performed corresponding to the RRV sample.," Selecting the fastest stars in the halo therefore makes sense when searching for massive compact companions to sdB. Since the individual SDSS spectra were taken within short timespans, another simulation was performed corresponding to the RRV sample."251 The first RV was taken at a random time. but the second one just 0.03d later.," The first RV was taken at a random time, but the second one just $0.03\,{\rm d}$ later."252 The dotted curve in Fig., The dotted curve in Fig.253 7 illustrates the outcome of this simulation., \ref{muchfuss_sim} illustrates the outcome of this simulation.254 As soon as the RV shift exceeds 30kms! within 0.03d the probability that the companion Is massive rises to = 10%.," As soon as the RV shift exceeds $30\,{\rm km\,s^{-1}}$ within $0.03\,{\rm d}$ the probability that the companion is massive rises to $\simeq10\%$ ."255 The reason why the probability does not increase significantly with increasing RV shift is that the most massive companions im our simulation have maximum RV shifts as high as 1000kms7!.," The reason why the probability does not increase significantly with increasing RV shift is that the most massive companions in our simulation have maximum RV shifts as high as $1000\,{\rm km\,s^{-1}}$."256 At the most likely periods of =0.5d the maximum RV shift within 0.03d is then of the order of 100kms!.," At the most likely periods of $\simeq0.5\,{\rm d}$ the maximum RV shift within $0.03\,{\rm d}$ is then of the order of $100\,{\rm km\,s^{-1}}$."257 Even higher RV shifts within short time are not physically plausible., Even higher RV shifts within short time are not physically plausible.258 Our simulation gives a quantitative estimate based on our current knowledge of the sdB binary populations., Our simulation gives a quantitative estimate based on our current knowledge of the sdB binary populations.259 It has to be pointed out that these numbers should be considered as rough estimates at most., It has to be pointed out that these numbers should be considered as rough estimates at most.260 The observed period and companion mass distributions are especially affected by selection effects., The observed period and companion mass distributions are especially affected by selection effects.261 The derived numbers are therefore only used to create a priority list and select the best targets for follow-up., The derived numbers are therefore only used to create a priority list and select the best targets for follow-up.262 Our sample of promising targets consists of 69 objects in total., Our sample of promising targets consists of $69$ objects in total.263 52 stars show significantRV shifts (>30 kms!) within 0.02— and are selected from the RRV sample. while 17 stars," $52$ stars show significantRV shifts $>30\,{\rm km\,s^{-1}}$ ) within $0.02-0.07\,{\rm d}$ and are selected from the RRV sample, while $17$ stars"264"voids and hence suppress |AT|/T, whereas the proper motion of a cluster or void would produce a dipole pattern without affecting the mean temperature.","voids and hence suppress $|\Delta T|/T$, whereas the proper motion of a cluster or void would produce a dipole pattern without affecting the mean temperature."265 We adopt the EdS universe as the background cosmology to isolate the intrinsic RS effect (we drop the word “intrinsic” hereafter)., We adopt the EdS universe as the background cosmology to isolate the intrinsic RS effect (we drop the word “intrinsic” hereafter).266" Because the growth rate of structures varies with the assumed cosmology, the RS effect is model dependent."," Because the growth rate of structures varies with the assumed cosmology, the RS effect is model dependent."267" For example, the combined RS and proper motion effects decrease by a factor of ~2 from the EdS universe to an open universe with matter fraction 0.3 (Tuluieetal.1996)."," For example, the combined RS and proper motion effects decrease by a factor of $\sim 2$ from the EdS universe to an open universe with matter fraction $0.3$ \citep{tuluie96}."268". One approach to investigate the RS effect is to analyze its power spectrum (e.g.,Seljak1996)."," One approach to investigate the RS effect is to analyze its power spectrum \citep[e.g.,][]{seljak96}."269. The linear ISW effect increases the CMB temperature fluctuation and hence the power of the modes by raising the temperature of overdense regions and lowering that of underdense regions., The linear ISW effect increases the CMB temperature fluctuation and hence the power of the modes by raising the temperature of overdense regions and lowering that of underdense regions.270" Because the RS effect produces a net temperature decrement for both clusters and voids (see for an explanation), it would not increase the temperature fluctuation as much even if it had the same amplitude as the linear ISW effect."," Because the RS effect produces a net temperature decrement for both clusters and voids (see for an explanation), it would not increase the temperature fluctuation as much even if it had the same amplitude as the linear ISW effect."271" Thus, power spectrum analyses may underestimate the importance of the RS effect."," Thus, power spectrum analyses may underestimate the importance of the RS effect."272" Ray-tracing through N-body simulations can provide a realistic estimate of the full ISW effect (e.g.,TuluieSmithetal.2009) To do so exactly, one needs to solve for the metric and its spatial-temporal derivatives, which appear in the geodesic equation."," Ray-tracing through $N$ -body simulations can provide a realistic estimate of the full ISW effect \citep[e.g.,][]{tuluie96, maturi07, cai09, cai10, smith09}273 To do so exactly, one needs to solve for the metric and its spatial-temporal derivatives, which appear in the geodesic equation."274" The ISW effect is roughly |AT|/T=|Az|/(1+z)e 10-79-1075 for super structures, so that a redshift error of the order 1077 or larger accumulated along the photon geodesic, or a comparable error from approximating the photon geodesic with a straight coordinate ray, can be a significant contamination to the results."," The ISW effect is roughly $|\Delta T|/T = |\Delta z|/(1+z) \sim 10^{-6}$ $10^{-5}$ for super structures, so that a redshift error of the order $10^{-7}$ or larger accumulated along the photon geodesic, or a comparable error from approximating the photon geodesic with a straight coordinate ray, can be a significant contamination to the results."275" Therefore, it is computationally challenging to trace photon geodesics in N-body simulations."," Therefore, it is computationally challenging to trace photon geodesics in $N$ -body simulations."276" In this paper, we study the effect of individual structures with toy models (see,e.g.,Thompson&Vishniac1987;Martinez-Gon"," In this paper, we study the effect of individual structures with toy models \citep[see, e.g.,][]{thompson87, martinez90}."277"zalez&Sanz The advantage of this approach is that (1) for 1990)..certain class of models, one can obtain analytic solutions of the underlying metric without worrying about spatial, temporal, or mass resolutions and (2) in models with symmetry, certain null geodesics can be computed in different ways, so that one can examine the precision of the calculations."," The advantage of this approach is that (1) for certain class of models, one can obtain analytic solutions of the underlying metric without worrying about spatial, temporal, or mass resolutions and (2) in models with symmetry, certain null geodesics can be computed in different ways, so that one can examine the precision of the calculations."278" Specifically, we model the clusters and voids with the spherically symmetric Lemaittre-Tolman—Bondi (LTB,Lemaitre1933;Tolman1934;Bondi1947,referencedherein) solution and solve generic photon geodesics through these structures (seealsoPanek1992;burg 2009)."," Specifically, we model the clusters and voids with the spherically symmetric Lema{\^i}ttre--Tolman--Bondi \citep[LTB,][referenced herein]{lemaitre33,279tolman34,bondi47} solution and solve generic photon geodesics through these structures \citep[see also][]{panek92,alnes06b,marra07,valkenburg09}."280". Separately, the RS effect has been studied for compensated voids and clusters (Inoue&Silk2006;Tomita&Inoue2008;Sakai2008) and for compensated shells (Afshordi,Slosar,&Wang2011) in the universe with thin-shell approximation, perturbative calculations, and numerical calculations."," Separately, the RS effect has been studied for compensated voids and clusters \citep{inoue06,tomita08,sakai08} and for compensated shells \citep*{afshordi11} in the universe with thin-shell approximation, perturbative calculations, and numerical calculations."281" The focus of this paper is on the effect caused solely by the evolution of the structures, so we do not include the cosmological constant A except for a simple case in 6."," The focus of this paper is on the effect caused solely by the evolution of the structures, so we do not include the cosmological constant $\Lambda$ except for a simple case in ."282". Our results are in qualitative agreement with those in the aforementioned works, and we extend the study to uncompensated structures as well."," Our results are in qualitative agreement with those in the aforementioned works, and we extend the study to uncompensated structures as well."283" As Rees&Sciama(1968) pointed out, redshift and time delay are the two major components of the RS effect."," As \citet{rees68} pointed out, redshift and time delay are the two major components of the RS effect."284 The redshift component includes both compensation for the time delay component and the evolution of the potential., The redshift component includes both compensation for the time delay component and the evolution of the potential.285" Since the effect of the potential evolution is usually subdominant, the two components of the RS effect often shift the CMB temperature with comparable magnitudes but in opposite directions."," Since the effect of the potential evolution is usually subdominant, the two components of the RS effect often shift the CMB temperature with comparable magnitudes but in opposite directions."286" Galaxy redshifts are directly measurable, so fractional changes to galaxy redshifts due to intervening structures are larger than that to the CMB temperature."," Galaxy redshifts are directly measurable, so fractional changes to galaxy redshifts due to intervening structures are larger than that to the CMB temperature."287 This foreground-induced change of galaxy redshifts is closely related to but different from the RS effect or the ISW effect in general because of the separation of the redshift effect and the time delay effect on galaxies., This foreground-induced change of galaxy redshifts is closely related to but different from the RS effect or the ISW effect in general because of the separation of the redshift effect and the time delay effect on galaxies.288" However, unlike the CMB, which has a standard temperature, galaxies are spread over redshift space."," However, unlike the CMB, which has a standard temperature, galaxies are spread over redshift space."289 Detecting such a redshift change is far more difficult than that of the RS effect., Detecting such a redshift change is far more difficult than that of the RS effect.290 Images of a strongly lensed source should have slightly different redshifts in general., Images of a strongly lensed source should have slightly different redshifts in general.291" Despite the extreme difficulty in measuring such redshift differences (Loeb1998),, we find in the ideal case that the redshift difference between two images of the source is considerably larger than that between two epochs of observations of the same image separated by the amount of the time delay between the two images."," Despite the extreme difficulty in measuring such redshift differences \citep{loeb98}, we find in the ideal case that the redshift difference between two images of the source is considerably larger than that between two epochs of observations of the same image separated by the amount of the time delay between the two images."292 The latter is known as the (Sandage1962;1998).," The latter is known as the \citep{sandage62,loeb98}."293. 'The rest of the paper is organized as follows., The rest of the paper is organized as follows.294 provides a brief introduction to the LTB solution and describes models of clusters and voids., provides a brief introduction to the LTB solution and describes models of clusters and voids.295 gives the details of solving the null geodesics numerically., gives the details of solving the null geodesics numerically.296" Results of the RS effect on CMB temperature profiles and tiny perturbations to galaxy redshifts caused by intervening structures are presented in Sections 4 and 5,, respectively."," Results of the RS effect on CMB temperature profiles and tiny perturbations to galaxy redshifts caused by intervening structures are presented in Sections \ref{sec:sup} and \ref{sec:gal}, respectively."297 Further discussion is made in6., Further discussion is made in.298". We model the structures as spherically symmetric, dust-filled objects embedded in the EdS universe."," We model the structures as spherically symmetric, dust-filled objects embedded in the EdS universe."299" The line element in such models is described by the LTB metric ds? = —de? ryap! where R(t,r) is the angular diameter distance of the coordinate r as viewed from the center, is the curvature function, a prime denotes a partial K(r)derivative with respect to r, and the speed of light has been set to unity."," The line element in such models is described by the LTB metric ds^2 = -dt^2 + ^2, where $R(t,r)$ is the angular diameter distance of the coordinate $r$ as viewed from the center, $K(r)$ is the curvature function, a prime denotes a partial derivative with respect to $r$, and the speed of light has been set to unity."300" The evolution of R(t,r) is determined by K(r) and the mass function M(r) ? (t7) —K(r)r?,(2) where G is Newton’s constant, and an overdot stands for a partial derivative with respect to t we suppress the variables t£ and r if there isno (hereafter,ambiguity in the context)."," The evolution of $R(t,r)$ is determined by $K(r)$ and the mass function $M(r)$ ^2(t,r) = - K(r)r^2, where $G$ is Newton's constant, and an overdot stands for a partial derivative with respect to $t$ (hereafter, we suppress the variables $t$ and $r$ if there isno ambiguity in the context)."301 The mass function is related to the acceleration = 7," The mass function is related to the acceleration = ,"302 The mass function is related to the acceleration = 77," The mass function is related to the acceleration = ,"303 The mass function is related to the acceleration = 773," The mass function is related to the acceleration = ,"304 The mass function is related to the acceleration = 773)," The mass function is related to the acceleration = ,"305held fixed.,held fixed.306 For the case of the LSST survey. with rus photo-z error 0.05(1|:). we fine that the “knec™ at a dark cucreyv deeradation of 1.21.3 occurs iu the rauge ΑγιοcMU 109.," For the case of the LSST survey with rms photo-z error $0.05(1+z)$, we find that the “knee” at a dark energy degradation of 1.2–1.3 occurs in the range $N_{\rm307 spect}\approx10^5$ $10^6$."308 For phloto-z models described by nondegencrate Gaussians. the size of the calibration sample varies by as nmmchn as LO times amone the 11 models studied.," For photo-z models described by nondegenerate Gaussians, the size of the calibration sample varies by as much as 40 times among the 14 models studied."309 Most of the variation is caused bv the different ability of the galaxy. photo-z distribution (tpn) to coustrai the nuderlving galaxy redshift distribution aud the photo-z probability distribution., Most of the variation is caused by the different ability of the galaxy photo-z distribution $n(z_{\rm ph})$ to constrain the underlying galaxy redshift distribution and the photo-z probability distribution.310 These photo-z models whose paralucters vary rapidly iu redshift are the ones that are least constrained., These photo-z models whose parameters vary rapidly in redshift are the ones that are least constrained.311 In reality. photo-z paramictcrs are expected to be smoothly varying i redshift.," In reality, photo-z parameters are expected to be smoothly varying in redshift."312 The νυν requirement would be oulv a factor of a few from that of the sinele-Caussian fiducial distribution., The $N_{\rm spect}$ requirement would be only a factor of a few from that of the single-Gaussian fiducial distribution.313 Finally. we show that the size of the calibration suuple can be effectively. reduced by optimization.," Finally, we show that the size of the calibration sample can be effectively reduced by optimization."314 Iu a snmnple example. au optimized calibration sample of 37.500 rvedshitts was able to reach the same dark energy degradation as a sample of 69.000 ealaxies uniforiulv distributed in redshift.," In a simple example, an optimized calibration sample of 37,500 redshifts was able to reach the same dark energy degradation as a sample of 69,000 galaxies uniformly distributed in redshift."315 We restrict this study to the effect of the core of the photo-z distributions., We restrict this study to the effect of the core of the photo-z distributions.316 Catastrophic photo-z errors could potentially be very damaging., Catastrophic photo-z errors could potentially be very damaging.317 The methodology provided iu this study is applicable to study the effect of catastrophic photo-z errors., The methodology provided in this study is applicable to study the effect of catastrophic photo-z errors.318 We leave this to future work., We leave this to future work.319 The methodology we use asstuues that the spectroscopic survey is aifair smuple of the photo-g error distribution aud is the formation available ou the photo-z error distribution., The methodology we use assumes that the spectroscopic survey is a sample of the photo-z error distribution and is the information available on the photo-z error distribution.320 Since we have used a Fisher matrix techuique. uo photo-z estimation method. reeardless of technique (neural net. template fitting. ete.)," Since we have used a Fisher matrix technique, no photo-z estimation method, regardless of technique (neural net, template fitting, etc.)"321 can surpass our forecasts under these couditions., can surpass our forecasts under these conditions.322 The calibrations success depends crucially on he spectroscopic redshifts beiug drawn without bias TOlu the redshift distribution of the photonmietric sample it represents., The calibration's success depends crucially on the spectroscopic redshifts being drawn without bias from the redshift distribution of the photometric sample it represents.323 The survey strategy must be carefully formmlated to make sure that this occurs., The survey strategy must be carefully formulated to make sure that this occurs.324 Differeutial incompleteness between. say. red and blue galaxies or redshift “deserts”. must be avoided.," Differential incompleteness between, say, red and blue galaxies or redshift “deserts”, must be avoided."325 This has not beeu ichieved by auv large redshift survey bevoud 2%0.5 to dato., This has not been achieved by any large redshift survey beyond $z\approx 0.5$ to date.326 Tt mav be possible o coustraàiu by other niens In the abseuce of a fair spectroscopicZ(:54]:) sample of the size we specify., It may be possible to constrain $P(z_{\rm ph}|z)$ by other means in the absence of a fair spectroscopic sample of the size we specify.327 One could invoke astroplivsical assumnptious. namely. that the spectra of faint galaxies are identical to those of brighter galaxies. iun an attenip to bootstrap a fair bright sample into a calibration for fainter galaxies.," One could invoke astrophysical assumptions, namely, that the spectra of faint galaxies are identical to those of brighter galaxies, in an attempt to bootstrap a fair bright sample into a calibration for fainter galaxies."328 Another suggestion (Schuecidereal. (2006):: J. Newman. private commuication) is tha the photometric sample be cross-correlated with au Incomplete spectroscopic sainuple to infer the redshift distribution of the former.," Another suggestion \cite{Schneider06}; J. Newman, private communication) is that the photometric sample be cross-correlated with an incomplete spectroscopic sample to infer the redshift distribution of the former."329 It remains to be seeu. however. whether| these techniques can attain the accuracy need to supplaut1 a direct für sample of >105 spectra.," It remains to be seen, however, whether these techniques can attain the accuracy needed to supplant a direct fair sample of $>10^5$ spectra."330 This would require somepriori bounds ou the evolution of ealaxy spectra aud the clustering correlation coefficients of different classes of galaxies;, This would require some bounds on the evolution of galaxy spectra and the clustering correlation coefficients of different classes of galaxies.331 We look forward to future progress in these techniques. keepine in munud that the demands for precision cosmology from WL tomograpliy are mich iore severe than the demauds that galaxy evolution studies typically place ou photometric redshift svstelus.Acknowledgments:," We look forward to future progress in these techniques, keeping in mind that the demands for precision cosmology from WL tomography are much more severe than the demands that galaxy evolution studies typically place on photometric redshift systems.:"332 We thank Warne Iu. Dragon IIuterer. aud Dhuvuesh Jain for useful discussions.," We thank Wayne Hu, Dragon Huterer, and Bhuvnesh Jain for useful discussions."333 Z.AL. and CD. are supported day Departineut of Energy erant DOE-DE-FO02-95ER10895., Z.M. and G.B. are supported by Department of Energy grant DOE-DE-FG02-95ER40893.334 COALB. acknowledges additional support from NASA eraut BEFS 01-0011-0015 and National Scieuce Foundation grant AST 06-07667., G.M.B. acknowledges additional support from NASA grant BEFS 04-0014-0018 and National Science Foundation grant AST 06-07667.335 If one draws NV eveuts from a sample with probability distribution function POr:@). where the componeuts of @ are the parameters specitving the distribution and e is the variable whose probability distribution is uuder cousicderation. what are the coustraimts ou the parameters 07," If one draws $N$ events from a sample with probability distribution function $P(x;{\bft})$, where the components of ${\bft}$ are the parameters specifying the distribution and $x$ is the variable whose probability distribution is under consideration, what are the constraints on the parameters ${\bft}$?"336 Let us first divide . iuto small bius and label the width of the bius as Aw;., Let us first divide $x$ into small bins and label the width of the bins as $\Delta x_i$.337 The nuuber of events that fall in the ;/th biu is Poisson distributed with mean N;=Αθ) Αι., The number of events that fall in the $i$ th bin is Poisson distributed with mean $\bar{N_i} = N P(x_i;{\bft}) \Delta x_i $ .338 The likelihood function can be expressed as natural logarithiuof £ is. £-— Ημ of £ with respect to the model piu:uueters @ ire OL N;\ matrix is. PL LON) Tn the special case where Por:@) is a Gaussian with mean fF and spread σ. we lave Plugeing these results iuto gives us," The likelihood function can be expressed as and thenatural logarithm of $L$ is, The derivatives of ${\mathcal L}$ with respect to the model parameters ${\bft}$ are The Fisher matrix is, In the special case where $P(x;{{\bft}})$ is a Gaussian with mean $\mu$ and spread $\sigma$, we have Plugging these results into \\ref{eqn:Nprior} gives us"339to improve the presentation of the results.,to improve the presentation of the results.340 This work was supported in part by grant NN 203 512638 from the Polish Ministry. of Science., This work was supported in part by grant NN 203 512638 from the Polish Ministry of Science.341 The ASM lighteurves were taken fron http://xte.mit.edu/., The ASM lightcurves were taken from http://xte.mit.edu/.342bars for detections are not symmetric in color and magnitude.,bars for detections are not symmetric in color and magnitude.343 These two effects are shown to be able to produce apparent color magnitude trends of the level seen in the lower signal io noise data from an underlving distribution with no trend at all (Nundu2008)., These two effects are shown to be able to produce apparent color magnitude trends of the level seen in the lower signal to noise data from an underlying distribution with no trend at all \citep{Kundu08}.344. The absence of a significant mass-metallicitv relation for globular clusters also suggests a funclamental dillerence between globular clusters and galaxies. as galaxies have a well-known mass metallicity relation.," The absence of a significant mass-metallicity relation for globular clusters also suggests a fundamental difference between globular clusters and galaxies, as galaxies have a well-known mass metallicity relation."345" Specificallv. using SDSS data. Tremontietal.(2004) founcl a mass metallicity relation of ZxM"" [or a very large sample of galaxies."," Specifically, using SDSS data, \citet{Tremonti} found a mass metallicity relation of $Z \propto M^{0.3}$ for a very large sample of galaxies."346 This was extended to nearby dwarl irregular galaxies by Leeetal.(2006).. who found a mass-metallicitv relation consistent with that for the more massive galaxies.," This was extended to nearby dwarf irregular galaxies by \citet{Lee06}, who found a mass-metallicity relation consistent with that for the more massive galaxies."347" This dwarf galaxy. sample extends down io M~10—10"". the range where the most massive globular clusters are found. and thus is suggestive of a fundamental difference between globular clusters and galaxies in their relations."," This dwarf galaxy sample extends down to $M\sim 10^6 - 10^7$, the range where the most massive globular clusters are found, and thus is suggestive of a fundamental difference between globular clusters and galaxies in their mass-metallicity relations."348 Such a cilference likely reflects differences in the formation histories of ealaxies and globular clusters., Such a difference likely reflects differences in the formation histories of galaxies and globular clusters.349 Lf globular clusters experience significant sell-enrichment. then ihe more massive clusters will appear more metal-rich. since (heir greater mass will enable ihem to retain more metals from earlier generations of stars.," If globular clusters experience significant self-enrichment, then the more massive clusters will appear more metal-rich, since their greater mass will enable them to retain more metals from earlier generations of stars."350 Anv self-enrichment of metals that affect (he broad-band colors will make (he more massive clusters redder. ancl produce color-Inuminosity and mass-metallicitv relations within a globular cluster svstem.," Any self-enrichment of metals that affect the broad-band colors will make the more massive clusters redder, and produce color-luminosity and mass-metallicity relations within a globular cluster system."351 Therefore. the weakness or absence of the observed color-huninosity and mass-metallicity relations for elobular clusters (hus sets a limit on the role of sell-enrichiment. and is à Κον target for future models of globular cluster formation.," Therefore, the weakness or absence of the observed color-luminosity and mass-metallicity relations for globular clusters thus sets a limit on the role of self-enrichment, and is a key target for future models of globular cluster formation."352 A natural explanation for the difference between the mass-metallicity relations of globular clusters ancl galaxies is Chat globular clusters form without extensive mass distributions or dark matter halos., A natural explanation for the difference between the mass-metallicity relations of globular clusters and galaxies is that globular clusters form without extensive mass distributions or dark matter halos.353 Without such. halos. globular clusters are unable to retain the material produced by (heir massive stars. preventing (he lormation of subsequent generations of metal-enriched stars.," Without such halos, globular clusters are unable to retain the material produced by their massive stars, preventing the formation of subsequent generations of metal-enriched stars."354 Such a picture is consistent with the compact. dense nature of globular clusters which implies short formation timescales. and with models in which globular cluster formation is a rapid. dvnanmie process in a high pressure starburst environment as suggested bv observations of elobular cluster formation in the local universe (AshmanLElmegreen&Efremov 1997).," Such a picture is consistent with the compact, dense nature of globular clusters which implies short formation timescales, and with models in which globular cluster formation is a rapid, dynamic process in a high pressure starburst environment as suggested by observations of globular cluster formation in the local universe \citep{AZ01,EE}."355. In contrast then. galaxies tend to form over time within larger dark-matter dominated structures that help retain metals to be incorporated in subsequent eeneralions to produce the observed galaxy. massanetallicity relation.," In contrast then, galaxies tend to form over time within larger dark-matter dominated structures that help retain metals to be incorporated in subsequent generations to produce the observed galaxy mass-metallicity relation."356 CZW and SEZ acknowledge support for this work trom UST erant number IIS1-105453 and NSF award AST-0406891., CZW and SEZ acknowledge support for this work from HST grant number HST-10543 and NSF award AST-0406891.357 We also acknowledge useful conversations with Ariunav Ixundu on possible sources of photometric error., We also acknowledge useful conversations with Arunav Kundu on possible sources of photometric error.358The class of pulsating stars known as Cepheids is a cornerstone in determining the distances to nearby galaxies.,The class of pulsating stars known as Cepheids is a cornerstone in determining the distances to nearby galaxies.359 This is because Cepheids exhibit a well-behaved period-Inminositv relation which ean be locally calibrated (Jacobyetal.1992)., This is because Cepheids exhibit a well-behaved period-luminosity relation which can be locally calibrated \citep{jacoby92}.360.. In addition. these stars are massive and thus intrinsically very. luminous. making it possible to observe Cepheids located in verv distant galaxies (Tanvir1999:Feast1999).," In addition, these stars are massive and thus intrinsically very luminous, making it possible to observe Cepheids located in very distant galaxies \citep{tan99,feast99}."361. Because of the usefulness ancl fundamental importance of Cepheids. it is important to calibrate their period-Iuminositv. relation.," Because of the usefulness and fundamental importance of Cepheids, it is important to calibrate their period-luminosity relation."362 This has been done using a variety of methods. including parallax (ESA1997;Feast&Catch- 1997).. Daade-Wesselink methods. (Wesselink1946:Dersierοἱal.1997). and surface brightness (Laney&Stobie1995:FouqueGieren1997:Ripepietal.," This has been done using a variety of methods, including parallax \citep{esa97,363fc97}, Baade-Wesselink methods \citep{wesselink46,bersier97} and surface brightness \citep{laney95,fg97,ripepi97}."3641997).. The luminosity relations used currently have uncertainties on the order of 0.09 mag (Feast1999).. which in turn make up a sienilicant portion of the systematic uncertaintv in estimates to the Large Magellanic Cloud.," The period-luminosity relations used currently have uncertainties on the order of 0.09 mag \citep{feast99}, which in turn make up a significant portion of the systematic uncertainty in estimates to the Large Magellanic Cloud."365 Usine long-baseline stellar interferometry it is possible (o resolve the diameter changes undergone by a nearby Cepheid during a pulsational excle., Using long-baseline stellar interferometry it is possible to resolve the diameter changes undergone by a nearby Cepheid during a pulsational cycle.366 When such diameter measurements are combined wilh radial velocity measurements of the stellar photosphere. it is possible to determine the size of and distance to the Cepheicl.," When such diameter measurements are combined with radial velocity measurements of the stellar photosphere, it is possible to determine the size of and distance to the Cepheid."367 Such a direct measurement is independent of photometric observations and (heir associated uncertainties., Such a direct measurement is independent of photometric observations and their associated uncertainties.368 The Palomar Testbed Interferometer (PTI) is located on Palomar Mountain near San Diego. CA (Colavitaetal.1999).," The Palomar Testbed Interferometer (PTI) is located on Palomar Mountain near San Diego, CA \citep{colavita99}."369. It combines starlight from two 40-cm apertures to measure (he amplitude (a.k.a., It combines starlight from two 40-cm apertures to measure the amplitude (a.k.a.370 visibilitv) of the resulting interference fringes., visibility) of the resulting interference fringes.371 There are two available baselines. one 110-m baseline oriented. roughly. North-South (hereafter ο). and one baseline oriented roughly North-Soutlwest (called N-W).," There are two available baselines, one 110-m baseline oriented roughly North-South (hereafter N-S), and one 85-m baseline oriented roughly North-Southwest (called N-W)."372 In a previous paper 2000) we presented observations using PTI of the Cepheid ¢ Gem., In a previous paper \citep{lane00} we presented observations using PTI of the Cepheid $\zeta$ Gem.373 Iere we report on additional interferometric observations of ¢ Gem. as well as a second Galactic Cepheid. 7 Aql.," Here we report on additional interferometric observations of $\zeta$ Gem, as well as a second Galactic Cepheid, $\eta$ Aql."374 These observations allow us to determine the distances to these Cepheids with the aim of reducing the uncertainty in currently used period-huninosity relations lor Cepheids., These observations allow us to determine the distances to these Cepheids with the aim of reducing the uncertainty in currently used period-luminosity relations for Cepheids.375 We observed the nearby galactic cepheids 7 Aql and ¢ Gem on 22 nights between 2001 March 13 and 2001 July 26., We observed the nearby galactic cepheids $\eta$ Aql and $\zeta$ Gem on 22 nights between 2001 March 13 and 2001 July 26.376 The observing procedure followed standard PTI practice Colavitaetal. 1999).," The observing procedure followed standard PTI practice \citep{boden98,colavita99}."377. For the observations of η Aql the N-W baseline was used. while observations of ¢ Gem used the N-S baseline.," For the observations of $\eta$ Aql the N-W baseline was used, while observations of $\zeta$ Gem used the N-S baseline."378 Each nightly observation consisted of approximately (en 130-seconcl integrations during which the fringe visibility was averaged., Each nightly observation consisted of approximately ten 130-second integrations during which the fringe visibility was averaged.379Our understanding of stellar structure and stability has been built upon classical analyical studies of equilibrium configurations of incompressible sell-gravitating svstems by Maclaurin. Jacobi. Dedekind. Darwin. Riemann. ancl especially Chandrasekhar(1969).,"Our understanding of stellar structure and stability has been built upon classical analytical studies of equilibrium configurations of incompressible self-gravitating systems by Maclaurin, Jacobi, Dedekind, Darwin, Riemann, and especially \cite{Ch69}."380.. With (he help of modern computers ancl numerical methods. such as the sell-consistent-fiekd (SCE) technique (Ostriker&Mark1968:Hachisu10δύα) and hydroclvuamiics techniques. these studies have been extended to compressible configurations by a variety of researchers (Tohline.Durisen.&lario.&Eriguehi 2002).," With the help of modern computers and numerical methods, such as the self-consistent-field (SCF) technique \citep{OM68, H86A}381 and hydrodynamics techniques, these studies have been extended to compressible configurations by a variety of researchers \citep{TDM85, H86A, H86B, WT88,CT00, SKE02}."382. ILowever. most three-dimensional (3D) hyclroclvnamical stuclies have been confined to a limited parameter space. ie.. starting from two-dimensional (2D) axisvimnmnetrie equilibrium models (compressible analogues of Maclaurin spheroids) because we have not been able to build 3D compressible equilibrium models with complicated flows.," However, most three-dimensional (3D) hydrodynamical studies have been confined to a limited parameter space, i.e., starting from two-dimensional (2D) axisymmetric equilibrium models (compressible analogues of Maclaurin spheroids) because we have not been able to build 3D compressible equilibrium models with complicated flows."383 To the authors knowledge. techniques have only been developed to build. compressible equilibrium models of nonaxisvnuuetric configurations for a lew svstems with simplified rotational profiles. e.g.. rigidly rotating svstems (Iachisu&Exiguchi1984:Hachisu 1," To the author's knowledge, techniques have only been developed to build compressible equilibrium models of nonaxisymmetric configurations for a few systems with simplified rotational profiles, e.g., rigidly rotating systems \citep{HE84,H86B}, ,"384 To the authors knowledge. techniques have only been developed to build. compressible equilibrium models of nonaxisvnuuetric configurations for a lew svstems with simplified rotational profiles. e.g.. rigidly rotating svstems (Iachisu&Exiguchi1984:Hachisu 19," To the author's knowledge, techniques have only been developed to build compressible equilibrium models of nonaxisymmetric configurations for a few systems with simplified rotational profiles, e.g., rigidly rotating systems \citep{HE84,H86B}, ,"385 To the authors knowledge. techniques have only been developed to build. compressible equilibrium models of nonaxisvnuuetric configurations for a lew svstems with simplified rotational profiles. e.g.. rigidly rotating svstems (Iachisu&Exiguchi1984:Hachisu 198," To the author's knowledge, techniques have only been developed to build compressible equilibrium models of nonaxisymmetric configurations for a few systems with simplified rotational profiles, e.g., rigidly rotating systems \citep{HE84,H86B}, ,"386 To the authors knowledge. techniques have only been developed to build. compressible equilibrium models of nonaxisvnuuetric configurations for a lew svstems with simplified rotational profiles. e.g.. rigidly rotating svstems (Iachisu&Exiguchi1984:Hachisu 1986," To the author's knowledge, techniques have only been developed to build compressible equilibrium models of nonaxisymmetric configurations for a few systems with simplified rotational profiles, e.g., rigidly rotating systems \citep{HE84,H86B}, ,"387 To the authors knowledge. techniques have only been developed to build. compressible equilibrium models of nonaxisvnuuetric configurations for a lew svstems with simplified rotational profiles. e.g.. rigidly rotating svstems (Iachisu&Exiguchi1984:Hachisu 1986b," To the author's knowledge, techniques have only been developed to build compressible equilibrium models of nonaxisymmetric configurations for a few systems with simplified rotational profiles, e.g., rigidly rotating systems \citep{HE84,H86B}, ,"388 To the authors knowledge. techniques have only been developed to build. compressible equilibrium models of nonaxisvnuuetric configurations for a lew svstems with simplified rotational profiles. e.g.. rigidly rotating svstems (Iachisu&Exiguchi1984:Hachisu 1986b)," To the author's knowledge, techniques have only been developed to build compressible equilibrium models of nonaxisymmetric configurations for a few systems with simplified rotational profiles, e.g., rigidly rotating systems \citep{HE84,H86B}, ,"389 To the authors knowledge. techniques have only been developed to build. compressible equilibrium models of nonaxisvnuuetric configurations for a lew svstems with simplified rotational profiles. e.g.. rigidly rotating svstems (Iachisu&Exiguchi1984:Hachisu 1986b).," To the author's knowledge, techniques have only been developed to build compressible equilibrium models of nonaxisymmetric configurations for a few systems with simplified rotational profiles, e.g., rigidly rotating systems \citep{HE84,H86B}, ,"390 To the authors knowledge. techniques have only been developed to build. compressible equilibrium models of nonaxisvnuuetric configurations for a lew svstems with simplified rotational profiles. e.g.. rigidly rotating svstems (Iachisu&Exiguchi1984:Hachisu 1986b)..," To the author's knowledge, techniques have only been developed to build compressible equilibrium models of nonaxisymmetric configurations for a few systems with simplified rotational profiles, e.g., rigidly rotating systems \citep{HE84,H86B}, ,"391PPARC Rolling Grant PPA/G/O/2001/00017 at the University of Oxford.,PPARC Rolling Grant PPA/G/O/2001/00017 at the University of Oxford.392 ," \nocite{1991MNRAS.249..481J}393 \nocite{1986ApJ...311..651K}394 \nocite{1990ApJ...357L...9G}395 \nocite{1990ApJ...348..371S}396 \nocite{1997MNRAS.288..404H}397 \nocite{metcalfe01}398 \nocite{1986seg..work..439S}399 \nocite{1986MNRAS.221..233P}400 \nocite{1995MNRAS.274..769M}401 \nocite{1991ApJ...369...79L}402 \nocite{1997A&A...317...43B}403 \nocite{1999A&A...341..641A}404 \nocite{1998MNRAS.294..147M}405 \nocite{1994MNRAS.268..393D}406 \nocite{1993MNRAS.260..241C}407 \nocite{1993AJ....105.2017S}408 \nocite{1991AJ....102..445P}409 \nocite{1995ApJ...449L.105S}410 \nocite{1995ApJ...449L..23D}411 \nocite{1995MNRAS.275L..19G}412 \nocite{1995ApJ...455...60L}413 \nocite{1998ApJ...506...33P}414 \nocite{2000A&A...364..349C}415 \nocite{1997ApJ...490...11W}416 \nocite{1996MNRAS.282L...1G}417 \nocite{1988ApJ...332L..29C}418 "419GC stars can also lead {ο measurable clillerences. particularly in line indices that tend to be stronger in (he spectra of eiant stus.,"GC stars can also lead to measurable differences, particularly in line indices that tend to be stronger in the spectra of giant stars."420 The problem with this explanation is (hat the stars that are subject to this kind of stochastic elleet contribute little light in the blue part of the spectrum., The problem with this explanation is that the stars that are subject to this kind of stochastic effect contribute little light in the blue part of the spectrum.421 Finally. NGC 6528 and 6553 may possess an unusually hieh population of blue stars. parüceularly blue stragglers.," Finally, NGC 6528 and 6553 may possess an unusually high population of blue stars, particularly blue stragglers."422 We find (his very. unlikely. since the residuals between (hese GC spectra and their M 31 counterparts show no strong evidence for contamination by A star light.," We find this very unlikely, since the residuals between these GC spectra and their M 31 counterparts show no strong evidence for contamination by A star light."423 This result also argues against the presence of anv important contamination bv [oreground A stars., This result also argues against the presence of any important contamination by foreground A stars.424 If nevertheless background subtraction errors. aud stochastic effects. and hot stars in the foreground or in the GC are not to blame. and indeed the GCs differ in their chemical composition. it is not entirely clear whether the differences between Galactic metal-rich clusters aud (heir M 31 counterparts can be ascribed to CN-enhancement of the latter.," If nevertheless background subtraction errors, and stochastic effects, and hot stars in the foreground or in the GC are not to blame, and indeed the GCs differ in their chemical composition, it is not entirely clear whether the differences between Galactic metal-rich clusters and their M 31 counterparts can be ascribed to CN-enhancement of the latter."425 The ratio spectrum suggests that there may be a slight metallicity dillerence between NGC! 6528 and its M 31 counterparts selected on the basis of {193 and (Fe) strengths. since residuals in other metal lines are also visible in Figure 15.. which may suggest the presence of differences between the (wo GC samples in abundance ratios other than |C/Fe] and |N/Fe].," The ratio spectrum suggests that there may be a slight metallicity difference between NGC 6528 and its M 31 counterparts selected on the basis of $H\beta$ and $\langle$ $\rangle$ strengths, since residuals in other metal lines are also visible in Figure \ref{ratio_6528}, which may suggest the presence of differences between the two GC samples in abundance ratios other than [C/Fe] and [N/Fe]."426 Belore concluding this section. we would like to comment on the differences between the strengths of Call HIx in M 31 and MWGC spectra.," Before concluding this section, we would like to comment on the differences between the strengths of CaII HK in M 31 and MWGC spectra."427 One can clearly see in comparisons of spectra in Figure 9 and in (he ratio spectra showed in Figures 14 and 15.. that Call IE and Ix lines are stronger in M 31 GC spectra than in those in the MW sample.," One can clearly see in comparisons of spectra in Figure \ref{spectra} and in the ratio spectra showed in Figures \ref{ratio}428 and \ref{ratio_6528}, that CaII H and K lines are stronger in M 31 GC spectra than in those in the MW sample."429 The differences are more signilicant on the hieh metallicity end., The differences are more significant on the high metallicity end.430 The hypothesis that CN differences between NGC 6528 and 6553 and their counterparts in M 31 are due to skv-subtraction errors could possibly also account for these Call II and Ix differences., The hypothesis that CN differences between NGC 6528 and 6553 and their counterparts in M 31 are due to sky-subtraction errors could possibly also account for these CaII H and K differences.431 Because they. are so strong. the signal in the core of the line is fairly weak. and so (hese lines are particularly sensitive to," Because they are so strong, the signal in the core of the line is fairly weak, and so these lines are particularly sensitive to"432e The distribution of the hal-lieht radii of putative elobular clusters in M31 is statistically indistinguishable from that of the distribution of the radii of Galactic globular clusters.,$\bullet$ The distribution of the half-light radii of putative globular clusters in M31 is statistically indistinguishable from that of the distribution of the radii of Galactic globular clusters.433 e [n both galaxies the most metal-rich clusters are concentrated at small galactocentric cistanuces., $\bullet$ In both galaxies the most metal-rich clusters are concentrated at small galactocentric distances.434 ILowever. the region containing metal-rich clusters is slightly larger in M31 than it is in the Galaxy.," However, the region containing metal-rich clusters is slightly larger in M31 than it is in the Galaxy."435 e At conlidence it is found that the most luminous elobulars in M31 are more concentrated towards the the center of this galaxy than are clusters of lesser luminosity., $\bullet$ At confidence it is found that the most luminous globulars in M31 are more concentrated towards the the center of this galaxy than are clusters of lesser luminosity.436 e The specific [requencey of globular clusters in M31 appears (ο be three or four times ereater than itis in the Galaxy., $\bullet$ The specific frequency of globular clusters in M31 appears to be three or four times greater than it is in the Galaxy.437 The excess of M31 clusters per unit mass seems {ο be even greater (han this., The excess of M31 clusters per unit mass seems to be even greater than this.438 e The hall-light radii of globular clusters in M31 and in the Galaxy seem to be very similar to those of the elobulars surrounding Iuminous earlv-tvpe galaxies in (he Virgo and Fornax clusters., $\bullet$ The half-light radii of globular clusters in M31 and in the Galaxy seem to be very similar to those of the globulars surrounding luminous early-type galaxies in the Virgo and Fornax clusters.439 This suggests that the radii with which clusters are formed in earlv-tvpe ealaxies are broadly independent of environment., This suggests that the radii with which clusters are formed in early-type galaxies are broadly independent of environment.440 It is of some interest to compare (he radii of Galactic globular clusters with those of the elobular clusters that are known to be associated with the dwarl spheroidal companions of Milky Way svstem., It is of some interest to compare the radii of Galactic globular clusters with those of the globular clusters that are known to be associated with the dwarf spheroidal companions of Milky Way system.441 Listed below in Table 5 are data on (he hall-light radii of (he five globular clusters associated with the Fornax dwarf. taken from van den Bergh Mackey (2004) and information on the hal[-lisht radii of seven elobular clusters which Law Majewski (2010) assign with. high or moderate. confidence to the Sagittarius dwarf.," Listed below in Table 5 are data on the half-light radii of the five globular clusters associated with the Fornax dwarf, taken from van den Bergh Mackey (2004) and information on the half-light radii of seven globular clusters which Law Majewski (2010) assign with, high or moderate, confidence to the Sagittarius dwarf."442 The most striking feature of the data in this table is that all 12 of these clusters have radii that, The most striking feature of the data in this table is that all 12 of these clusters have radii that443"from the Parkes Hall-Jansky Flat-spectrum Sample (PLIES) (Drinkwateretal.1997).. which consists of 32323 objects selected to be radio-loud GHz280.5 Jv). and have a Hat radio spectrum (osz;o20.5. Sv)xv"").","from the Parkes Half-Jansky Flat-spectrum Sample (PHFS) \cite{drinkwater97}, which consists of 323 objects selected to be radio-loud ${\rm S}_{2.7\ {\rm444GHz}}>0.5\ {\rm Jy}$ ), and have a flat radio spectrum $\alpha_{2.7/5.0}>-0.5$, $S(\nu)\propto \nu^\alpha$ )."445 These quasars have been shown (Websteretal.1995:Francisal.2000) to have a large spread in D.A colours. with the reddest objects having 1Ao7.," These quasars have been shown \cite{webster95,francis00} to have a large spread in $B-K$ colours, with the reddest objects having $B-K>7$."446 Masci. Webster Francis (1998) showed that this spread could not be accounted for by the emission [from the host-galaxy.," Masci, Webster Francis \shortcite{masci98} showed that this spread could not be accounted for by the emission from the host-galaxy."447 In this paper we test the idea that optical svnchrotron emission causes the red. optical-NIIt. colours of the PLIES quasars., In this paper we test the idea that optical synchrotron emission causes the red optical-NIR colours of the PHFS quasars.448 Models representing emission [rom both an optical svnchrotron component. and ai blue optical power law (representing the continuum. emission from an unreddened quasar) are fitted to broad-band optical-NIRo spectra., Models representing emission from both an optical synchrotron component and a blue optical power law (representing the continuum emission from an unreddened quasar) are fitted to broad-band optical-NIR spectra.449 Standard. goodness-of-fit techniques are used to determine models which are consistent with the observations., Standard goodness-of-fit techniques are used to determine models which are consistent with the observations.450 The dataset was compiled by Francis. Whiting Webster (2000) (EWW hereafter). ancl comprises broadband optical ancl NIIt photometry in the bands D. V. Rolo J. if ancl IN.," The dataset was compiled by Francis, Whiting Webster \shortcite{francis00} (FWW hereafter), and comprises broadband optical and NIR photometry in the bands $B$, $V$, $R$, $I$, $J$, $H$ and $K$."451 Vhis photometry is cquasi-simultaneous. meaning all observations fora given source were mace within several days (six at most) of one another.," This photometry is quasi-simultaneous, meaning all observations for a given source were made within several days (six at most) of one another."452 This minimises the ellects of source variability., This minimises the effects of source variability.453 Phe source selection used for this paper is explained in Section 2.., The source selection used for this paper is explained in Section \ref{sec-data}.454 Phe simultaneity. as well as the breadth and density of the spectral coverage of this dataset provides an excellent. basis to model the broadband emission from a large number of Dat-spectrum quasars.," The simultaneity, as well as the breadth and density of the spectral coverage of this dataset provides an excellent basis to model the broadband emission from a large number of flat-spectrum quasars."455 The dataset is described in Section 2.., The dataset is described in Section \ref{sec-data}.456 In Section 3 we test the hypothesis that the emission in the optical-NET region is well-fittecl bv. a single power Law., In Section \ref{sec-powerlaw} we test the hypothesis that the emission in the optical-NIR region is well-fitted by a single power law.457 In Section 4 we describe the more sophisticated model that was fitted to the data representing the accretion disk and synchrotron emission and the method that was used. to. perform the fitting., In Section \ref{sec-models} we describe the more sophisticated model that was fitted to the data – representing the accretion disk and synchrotron emission – and the method that was used to perform the fitting.458 The results. of this fitting are. described. in Sections 5 6.. while further tests of the ποσο fits are examined in Section 7.. using polarisation and emission line measurements.," The results of this fitting are described in Sections \ref{sec-results} \ref{sec-synchprops}, while further tests of the model fits are examined in Section \ref{sec-tests}, , using polarisation and emission line measurements."459 A possible rival model — that of black-bocdvy emission by hot clust is considered in Section S.., A possible rival model – that of black-body emission by hot dust – is considered in Section \ref{sec-dust}.460 Phe elfect of emission lines on the photometry ancl the resulting [fits is investigated in Section 9.., The effect of emission lines on the photometry and the resulting fits is investigated in Section \ref{sec-em-effect}.461 Finally. Section 10. contains discussion of the results and their implications.," Finally, Section \ref{sec-discuss}462 contains discussion of the results and their implications."463 The data which have been fitted. by these models. are described in detail in FW., The data which have been fitted by these models are described in detail in FWW.464 A total of 157 sources from the PHES were observed. with quasi-simullancous broadband photometry observations in the bands D. V. I. ἐν J. Lf and dy.," A total of 157 sources from the PHFS were observed, with quasi-simultaneous broadband photometry observations in the bands $B$, $V$, $R$, $I$, $J$, $H$ and $K$."465 μονο magnitudes were converted into broadband Duxes using the zero points given in the same paper., These magnitudes were converted into broadband fluxes using the zero points given in the same paper.466 Not. all sources in. FWW were. used., Not all sources in FWW were used.467 δν we only considered. those sources with complete contemporaneous whotometry in all bands. or those with only one observation nussing (either not observed or an upper limit).," Firstly, we only considered those sources with complete contemporaneous photometry in all bands, or those with only one observation missing (either not observed or an upper limit)."468 This was o ensure that the number of degrees of freedom in the model fitting was greater than zero., This was to ensure that the number of degrees of freedom in the model fitting was greater than zero.469 Phose sources with more iun one band müssing were not included in the analysis., Those sources with more than one band missing were not included in the analysis.470 Sources without à measured. redshift were also excluded. since the redshift is needed to obtain the correct. shape of 16 observed svnchrotron spectrum.," Sources without a measured redshift were also excluded, since the redshift is needed to obtain the correct shape of the observed synchrotron spectrum."471 One of the sources that jul an unknown redshift (2=0) in Drinkwater et shorteitecdrinkwaterO7.. | 046. has a published redshift value of 2=0.18 (Ealomo1901).. which is used here.," One of the sources that had an unknown redshift $z=0$ ) in Drinkwater et \\shortcite{drinkwater97}, $+$ 046, has a published redshift value of $z=0.18$ \cite{falomo91}, which is used here."472 Also excluded were low redshift galaxies. which had a prominent bbreak between the D and Y bands.," Also excluded were low redshift galaxies, which had a prominent break between the $B$ and $V$ bands."473 These sources show strong evidence for Dux from the underlying galaxy in their spectra (Mascietal.1998)... and thus need an additional galactic component to be mocdelled accurately.," These sources show strong evidence for flux from the underlying galaxy in their spectra \cite{masci98}, and thus need an additional galactic component to be modelled accurately."474 Sources with 2om4 were also excluded. as these had strong Lya breaks present between D. and V.," Sources with $z>3$ were also excluded, as these had strong $\alpha$ breaks present between $B$ and $V$."475 This reduced. the number of sources [from 157 to 117., This reduced the number of sources from 157 to 117.476 Twenty-one of the νους sources (13Aoc5) in the subsample were amongst. those excluded. as they have only upper limits on D. V and. possibly 22. or no redshift.," Twenty-one of the reddest sources $B-K > 5$ ) in the subsample were amongst those excluded, as they have only upper limits on $B$, $V$ and possibly $R$, or no redshift."477 The sources with upper limits are both red. and optically faint., The sources with upper limits are both red and optically faint.478 Since the Dux of these sources. typically decreases rapidly in the blue from V. to. D). there are three possible explanations for them.," Since the flux of these sources typically decreases rapidly in the blue from $V$ to $B$ ), there are three possible explanations for them."479 They. are either dust-reddened: (causing the blue. decrease. in flux). high redshift (and hence absorbed). or they are dominate by svnchrotron that turns over rapidly.," They are either dust-reddened (causing the blue decrease in flux), high redshift (and hence absorbed), or they are dominated by synchrotron that turns over rapidly."480 Future analysis of the spectral energy. distributions (SEDs) of these sources will only strengthen our final conclusions., Future analysis of the spectral energy distributions (SEDs) of these sources will only strengthen our final conclusions.481" ""hose sources excluded purely because of their lack of measured redshift generally have high 5dy colours (BA 5). sinee the most likely reason they have no redshif is that they are faint in the optical (and in particular in the blue)."," Those sources excluded purely because of their lack of measured redshift generally have high $B-K$ colours $B-K>5$ ), since the most likely reason they have no redshift is that they are faint in the optical (and in particular in the blue)."482 Further discussion of the sources excluded: [rom the sample is given in Section 10.., Further discussion of the sources excluded from the sample is given in Section \ref{sec-discuss}.483 The photometry given in FW quoted error bars. where the estimated. error comprised. two parts: a random error component and an assumed. error in the photometric zero points. which were added together in quadrature.," The photometry given in FWW quoted error bars, where the estimated error comprised two parts: a random error component and an assumed error in the photometric zero points, which were added together in quadrature."484 Phe photometric zero point errors were estimated. from the scatter in zero points between different standard star measurements in an individual night: Francis et aacopted a value of to account. for this CLEOL., The photometric zero point errors were estimated from the scatter in zero points between different standard star measurements in an individual night: Francis et adopted a value of to account for this error.485 llowever. this zero point error ignores a number of [actors that we believemay be important for the analysis in this paper.," However, this zero point error ignores a number of factors that we believemay be important for the analysis in this paper."486 These factors are as follows:, These factors are as follows:487Iu Fig.,In Fig.488 2 we show the distribution of photou iudices. obtained from the spectral fits. versus the Sevfert type (we have plotted NLS1s at an x-axis value of 0.9).," \ref{fig_gamma_type_s1} we show the distribution of photon indices, obtained from the spectral fits, versus the Seyfert type (we have plotted NLS1s at an x-axis value of 0.9)."489 Ouly Sevtert galaxies with errors in the photon iudex smaller than 0.5 have been iucluded., Only Seyfert galaxies with errors in the photon index smaller than 0.5 have been included.490 As expected. NLSIs show the largest values of the photon index. compared to Sevfert l salaxies.," As expected, NLS1s show the largest values of the photon index, compared to Seyfert 1 galaxies."491 Sevfert 2 ealaxies show simular steep X-rav continua compared to NESIs., Seyfert 2 galaxies show similar steep X-ray continua compared to NLS1s.492 The Sevfert 1 galaxies show simular values of the plioton iudices as eiven by Walter Fiuk (1993)., The Seyfert 1 galaxies show similar values of the photon indices as given by Walter Fink (1993).493 Iu order to derive the interaction streneth Q we concentrate on the tidal force per unit mass produced by a conrpanion on a primary galaxy. which is proportional o AL.R.," In order to derive the interaction strength $Q$ we concentrate on the tidal force per unit mass produced by a companion on a primary galaxy, which is proportional to $M_{\rm c} \cdot494R^{-3}$."495m Me as the iaass of the companion and & is its distance from he center of the primary galaxy., $M_{\rm c}$ is the mass of the companion and $R$ is its distance from the center of the primary galaxy.496" Iu nost cases. Af, aud the absolute value of Rare ποσο."," In most cases, $M_{\rm c}$ and the absolute value of $R$ are unknown."497 Tustead. these paraiucters are related to the dimeusions of he pai.," Instead, these parameters are related to the dimensions of the pair."498 Rubin et al. (, Rubin et al. (4991982) describe the depeucence of he mass AY of a galaxy on the size of its major axis d as Alxd and we use 5=1.5 (Daluui. 198D).,"1982) describe the dependence of the mass $M$ of a galaxy on the size of its major axis $d$ as $M \propto d^{\gamma}$ and we use $\gamma = 1.5$ (Dahari, 1984)."500" Tf we use the appareut diameter of the primary galaxy DA, as a scaling actor. we obtain: Usiug these relatious we ect as dimnensionless eravitatioual interaction strength Q: This parameter djs obviously large for close and relatively large Fie."," If we use the apparent diameter of the primary galaxy $D_{\rm p}$ as a scaling factor, we obtain: Using these relations we get as dimensionless gravitational interaction strength $Q$: This parameter is obviously large for close and relatively large Fig."501" 3 shows the interaction streneth (Q vs. the far-infrared luuinosity Lag, for Sevtert 1 salaxies.", \ref{fig_Lir_Q_s1} shows the interaction strength $Q$ vs. the far-infrared luminosity $L_{\rm fir}$ for Seyfert 1 galaxies.502 For Sevtert 1. ealaxics. the far-infrared huninosity iucreases with interaction streneth.," For Seyfert 1 galaxies, the far-infrared luminosity increases with interaction strength."503 The low-huninosity Sevtert 1 ealaxies NGC 5273. NGC 1278. NGC 3227. (NGC. 1258 is not detected in the IRAS Faint Source Catalogue) also show the treud of iucreasiug XN-rav and fu-imfrared hnuninositv with interaction streneth ο). We speculaλα large interaction strength of Q=15.14Ll for the ealaxy Mknu 1010 causes the relatively high ταν (Seo fis. D) ," The low-luminosity Seyfert 1 galaxies NGC 5273, NGC 4278, NGC 3227, (NGC 4258 is not detected in the IRAS Faint Source Catalogue) also show the trend of increasing X-ray and far-infrared luminosity with interaction strength Q. We speculate a large interaction strength of $Q=15.1\pm4.4$ for the galaxy Mkn 1040 causes the relatively high X-ray (see fig. \ref{fig_Lx_Q_s1}) )"504aud far-infrared huuinositv aud that the galaxy belongs to the low-huninosity population discussed above., and far-infrared luminosity and that the galaxy belongs to the low-luminosity population discussed above.505 To test the correlation we have calculated the. linear-correlation coefficient rand he probability Pr.N) for a linear correlation.," To test the correlation we have calculated the linear-correlation coefficient $r$ and the probability $P(r,N)$ for a linear correlation."506 For the ligh-huninosity objects we obtain r=0.3271 and P(r.22)zzsh&(~1.50). whereas we got for the low-huninosity Sevterts 7=05115 and Pird)22SS(~1.59).," For the high-luminosity objects we obtain $r=0.3271$ and $P(r,22)\approx85\% \;(\sim1.5\sigma)$, whereas we got for the low-luminosity Seyferts $r=0.8478$ and $P(r,4)\approx85\%\;(\sim1.5\sigma)$."507 Fie., Fig.508 1 shows the interaction streugth Q vs. the soft N-ray huuinositv Ly for Sevtert 1 galaxies., \ref{fig_Lx_Q_s1} shows the interaction strength $Q$ vs. the soft X-ray luminosity $L_{\rm X}$ for Seyfert 1 galaxies.509 For Sevtert l galaxies with Lx>10/2 there is a tendency for a huninosity increase with increasing interaction streneth., For Seyfert 1 galaxies with $L_{\rm X} > 10^{42}$ there is a tendency for a luminosity increase with increasing interaction strength.510 The labelled sources refer to the low-huninosity Sevtert l galaxies in our sample., The labelled sources refer to the low-luminosity Seyfert 1 galaxies in our sample.511 As discussed for the relation between the far-infrared huuinositv aud the interaction streneth Q. both the low-luninosity Sevfert Us and the lugh-huninosity Sevfert Ls increase m X-ray uuniunositv when the interaction streneth C) is increased.," As discussed for the relation between the far-infrared luminosity and the interaction strength Q, both the low-luminosity Seyfert 1's and the high-luminosity Seyfert 1's increase in X-ray luminosity when the interaction strength Q is increased."512 The high spread of the distribution is quite likely produced by an overlap of effects. from starburst and ACN., The high spread of the distribution is quite likely produced by an overlap of effects from starburst and AGN.513 Iu the case of iutrared huuinositv (fis. 3)), In the case of infrared luminosity (fig. \ref{fig_Lir_Q_s1}) )514 oulv the starburst plav a role., only the starburst play a role.515 The linear-correlation test resulted iu £7=|2880 ancl P(r.27)=SX(~1.5o) for the ligh-luuinosity Sevterts," The linear-correlation test resulted in $r=0.2880$ and $P(r,27)\approx85\%\;(\sim1.5\sigma)$ for the high-luminosity Seyferts"516oeferentiallv the intermediate over-density region.,preferentially the intermediate over-density region.517 A two-sided. Ixolmogorov-Smirnov. test. for the two cumulative distributions shown gives 2=0.31. corresponding to a oobabilitv of 0.03 that the the two samples are drawn rom the same distribution.," A two-sided Kolmogorov-Smirnov test for the two cumulative distributions shown gives $D=0.31$, corresponding to a probability of 0.03 that the the two samples are drawn from the same distribution."518 We checked. that adopting a slightly [arger or smaller. volume (scales of 2-5 )) does not change our results significantly., We checked that adopting a slightly larger or smaller volume (scales of 2-5 ) does not change our results significantly.519 We do not. find a strong tendenev for fossil svstems to be preferentiallv located in low density environments., We do not find a strong tendency for fossil systems to be preferentially located in low density environments.520 We suggest. therefore that observations might be biased το find. fossil groups preferentially in low density regions. which could be due to eroup selection elTects.," We suggest therefore that observations might be biased to find fossil groups preferentially in low density regions, which could be due to group selection effects."521 The halo formation redshift is defined as the epoch at which the svstem assembled of its final mass (e.g.?).., The halo formation redshift is defined as the epoch at which the system assembled of its final mass \cite[e.g.][]{Lacey1993a}.522 Figure 2 shows a correlation between the magnitude-gap parameter and the formation redshift of the host halo for all the fossil systems (triangles) ancl the normal groups (grey circles)., Figure 2 shows a correlation between the magnitude-gap parameter and the formation redshift of the host halo for all the fossil systems (triangles) and the normal groups (grey circles).523 As already pointed out in 2? this correlation shows that fossil groups tend to form earlier than normal groups. albeit with large scatter.," As already pointed out in \citet[][]{dOnghia2005a,524 dOnghia2007a} this correlation shows that fossil groups tend to form earlier than normal groups, albeit with large scatter."525 ln order to assess this correlation we draw the mean and upper and lower quartiles (the solid and dotted lines in Figure 2)., In order to assess this correlation we draw the mean and upper and lower quartiles (the solid and dotted lines in Figure 2).526 Phe visual impression is quantified bv statistical measures as the Pearson's linear correlation coefficient r=0.39. implving a weak linear correlation between the magnitude-gap and the formation time.," The visual impression is quantified by statistical measures as the Pearson's linear correlation coefficient $r = 0.39$, implying a weak linear correlation between the magnitude-gap and the formation time."527 The carly formation redshift is also rellected in a higher concentration paramelor ().., The early formation redshift is also reflected in a higher concentration parameter \cite[][]{Navarro1997a}.528" We define the concentration of our haloes by the ratio of the virial radius of the host halo to the radius of a sphere enclosing one fifth of its virial mass: ορ2,=reif.", We define the concentration of our haloes by the ratio of the virial radius of the host halo to the radius of a sphere enclosing one fifth of its virial mass: $c_{1/5} = r_{\rm vir}/r_{1/5}$.529 ‘This definition of the halo concentration allows for a robust concentration determination when the haloes are merger remnants and un-relaxecl (?).., This definition of the halo concentration allows for a robust concentration determination when the haloes are merger remnants and un-relaxed \cite[][]{AvilaReese2005a}.530 The correlation shown in Figure 3 between formation redshift and. concentration is well fitted by a linear relation μμ=—0.79|0.279eyes (marked with the dashed. bold line)., The correlation shown in Figure 3 between formation redshift and concentration is well fitted by a linear relation $z_{\rm form} = -0.79 + 0.27 \times c_{1/5}$ (marked with the dashed bold line).531 The fossil groups clearly. populate the early. formed. more concentrated. part of the plot. ancl have a mean," The fossil groups clearly populate the early formed, more concentrated part of the plot, and have a mean"532"gives a single micasure of bar strength. Q,.","gives a single measure of bar strength, $Q_g$."533 The main assumptions are that the imass-to-luminosity ratio is constant in the bar region. aud that the vertical light istributiou can be approximated by an exponcutial.," The main assumptions are that the mass-to-luminosity ratio is constant in the bar region, and that the vertical light distribution can be approximated by an exponential."534" The scale height. /.. was estimated from an empirical --‘elation between f/f. aud the de Vaucouleurs type iudex T (de (ης 1998). where P, is the radial scale leugth of the disk."," The scale height, $h_z$, was estimated from an empirical relation between $h_r$ $h_z$ and the de Vaucouleurs type index T (de Grijs 1998), where $h_r$ is the radial scale length of the disk."535 The nuages were taken from the literature and are generally not τον deep., The images were taken from the literature and are generally not very deep.536" Therefore. oeisteadl of estimating 7, frou the new cecompositious. we used mainly the 1, values from Dageoett et al. ("," Therefore, instead of estimating $h_r$ from the new decompositions, we used mainly the $h_r$ values from Baggett et al. ("537"1998): if it was not available. we used other sources in the literature where deep optical images had been used to erive h,..","1998); if it was not available, we used other sources in the literature where deep optical images had been used to derive $h_r$."538" For two galaxies P, was taken to be the mean value for our sample of 31 galaxies.", For two galaxies $h_r$ was taken to be the mean value for our sample of 31 galaxies.539 The same Fourier method gives us also the 11—2 amplitudes of bar iuteusitv contrast in the bar region., The same Fourier method gives us also the m=2 amplitudes of bar intensity contrast in the bar region.540" For soe of the. galaxies. Table 1 gives Q, aud Alo but not the effective bulee radius."," For some of the galaxies, Table 1 gives $Q_g$ and $A_2$ but not the effective bulge radius."541" This is because application of the 2D decomposition method requires deeper tages than the methods used to calculate Q, and ly.", This is because application of the 2D decomposition method requires deeper images than the methods used to calculate $Q_g$ and $A_2$.542" Figure 1 shows bar streugth Q, plotted against the j0rnialized velocity dispersion 6/0, for 26 galaxies.", Figure 1 shows bar strength $Q_g$ plotted against the normalized velocity dispersion $\sigma_{e}/v_g$ for 26 galaxies.543" Although there ave 31 galaxies in the sample. we couk use only 26 because the effective radius RR, coule rot be calculated for a few cases."," Although there are 31 galaxies in the sample, we could use only 26 because the effective radius $R_e$ could not be calculated for a few cases."544 The errors have con calculated using the standard error propagation equation aud include the uncertainties iu the observe quautities., The errors have been calculated using the standard error propagation equation and include the uncertainties in the observed quantities.545 The majority of galaxies ποσα to follow a rend ofdecreasing bar streugth with increasing ceutra velocity dispersion., The majority of galaxies seem to follow a trend of decreasing bar strength with increasing central velocity dispersion.546 We quantified the correlation in two wavs., We quantified the correlation in two ways.547 The linear correlation coefficieut for this sample of 26 ealaxics is r=0.50 aud the probabiltv that they are from a random sample P. is P.<1(s, The linear correlation coefficient for this sample of 26 galaxies is $r=-0.50$ and the probabilty that they are from a random sample $P_r$ is $P_r~<~1$.548 This method does not mclude he errors on both axes., This method does not include the errors on both axes.549 A more accurate estimate would be a weighted correlation coefficient. but this is difficult to obtain im practice (Feieclson Babu 1992).," A more accurate estimate would be a weighted correlation coefficient, but this is difficult to obtain in practice (Feigelson Babu 1992)."550 Instead we used a simple Monte Carlo simulation that randomly samples the errors on both axes and determines a mean weighted correlation cocficicut «6r>., Instead we used a simple Monte Carlo simulation that randomly samples the errors on both axes and determines a mean weighted correlation coefficient $<r>$.551 We used 50.000 linear fits and obtained a value of <r>=16.," We used 50,000 linear fits and obtained a value of $<r>=-0.46$."552 The second method that we used to quantity the correlation was the EKeudall-Tau cocficicut which assigus relative ranks to the different values., The second method that we used to quantify the correlation was the Kendall-Tau coefficient which assigns relative ranks to the different values.553 This is perhaps a more robust way of examine the correlation expecially when the saunple size is relatively small as iu our case., This is perhaps a more robust way of examining the correlation especially when the sample size is relatively small as in our case.554 The Ikeudall-Tau cocficient for the 26 ealaxies in Figure 1 is κοτς0.35 aud the probability that they are from a random sample is [Όντο122, The Kendall-Tau coefficient for the 26 galaxies in Figure 1 is $<r_{KT}>=-0.35$ and the probability that they are from a random sample is $P_{KT}\sim1.3$.555" Figure 2 shows the plot of A» against the normalized velocity dispersion o, for 25 galaxies.", Figure 2 shows the plot of $A_{2}$ against the normalized velocity dispersion $\sigma_{e}$ for 25 galaxies.556 Here again we calculated the linear correlation coefficieut which is 7= P.-0.5:, Here again we calculated the linear correlation coefficient which is $r=-0.54$ and $P_r~<~0.5$.557 When the errors are sampled using a Moute Carlo simulation we obtain a value of p>0.51., When the errors are sampled using a Monte Carlo simulation we obtain a value of $<r>=-0.51$.558 The I&eudall-Tau cocticicut for the 25 ealaxies is <oryp>=0.33) and Per<, The Kendall-Tau coefficient for the 25 galaxies is $<r_{KT}>=-0.33$ and $P_{KT}~<~2$.559 Thus both Figures 1 aud 2 suggest that there is a correlation between the bar strenethoO im oOealaxies aud their ceutral velocity dispersions., Thus both Figures 1 and 2 suggest that there is a correlation between the bar strength in galaxies and their central velocity dispersions.560 The main result of this paper are shown in Figures 1 2., The main result of this paper are shown in Figures 1 2.561 There are 26 galaxies in the plots of which about wf are intermediate type spirals and the remaining a mixture of carly aud late type spirals., There are 26 galaxies in the plots of which about half are intermediate type spirals and the remaining a mixture of early and late type spirals.562 Since the nuuber of galaxies in each IIubble type is not very arge. we cannot investigate trends within the differcut IIubble types.," Since the number of galaxies in each Hubble type is not very large, we cannot investigate trends within the different Hubble types."563 But from Figures 1 2. it appears dat carly type spirals have relatively lower central aispersious: this may be because they have larger bulges where rotational velocity is comparatively higher aud 1ο central velocity dispersion lower compared » the ater IIubble types.," But from Figures 1 2, it appears that early type spirals have relatively lower central dispersions; this may be because they have larger bulges where rotational velocity is comparatively higher and the central velocity dispersion lower compared to the later Hubble types."564" Since the correlation is significant but not very strong we exanunmed the two ealaxies that define the üeher au lower lanits of Q, and sly.", Since the correlation is significant but not very strong we examined the two galaxies that define the higher and lower limits of $Q_g$ and $A_2$.565 We looked at 1c closely to sec if they are odd im some way. aud uot characteristic of the rest of the sample. 4," We looked at them closely to see if they are odd in some way, and not characteristic of the rest of the sample. ("5664) NGC 3162 (oef cyml.3) This is an intermediate type spiral ealaxy with a weak bar and prominent bulec.,i) NGC 3162 $\sigma_{e}/v_g$ =1.13): This is an intermediate type spiral galaxy with a weak bar and prominent bulge.567 There may also be a rug in the center., There may also be a ring in the center.568 Though the spiral arlus are somewhat asvuuuctric. the nucleus i fairlv uudisturbed. G," Though the spiral arms are somewhat asymmetric, the nucleus is fairly undisturbed. ("569i) NGC. 1311. (of 040.18) This ds a bright. carly type galaxv with a strong bar and lareeOo iXlee with a LINER type imceleus.,"ii) NGC 4314 $\sigma_{e}/v_g$ =0.18): This is a bright, early type galaxy with a strong bar and large bulge with a LINER type nucleus."570 There may be significant rotation in the nuclear region which may ↕∪↖↖⇁↸∖↥⋅↕∐∖∪↿∙⊀≚↕↴∖↴∪∙, There may be significant rotation in the nuclear region which may lower the $\sigma_{e}$.571↑↕∐∖⋯⋜↧↴∖∷∖↴⊔⋜↧∙↖↽↴⋝↸∖↕⊔∪↥⋅↸∖↖↖↽↕≺∐∖∙↖⇁ ≺∐↴∖↴↑↥⋅∏⋝∏↑↸∖≺↧∪↖⇁↸∖↥⋅↑↕∐∖↴⋝⋯⊳↕↸∖⋜⊔≼↧↕∐∖⋯∖∐∪↑⋜↧↴∖↴↸⊳↸∖∐⊓⋅⋜↧↕⋅↖⇁ concentrated as im NGC 3162.," Also, the mass may be more widely distributed over the bucle and hence not as centrally concentrated as in NGC 3162."572 There appears to be a ring of star formation in the nucleus as well (Conzalez Deleado et al., There appears to be a ring of star formation in the nucleus as well (Gonzalez Delgado et al.573 1997)., 1997).574 Both salaxies are thus fairly normal aud not unusually differeut from the rest of the siuuple galaxies., Both galaxies are thus fairly normal and not unusually different from the rest of the sample galaxies.575 Figures 1 2 sugeest that ealaxies with dynamically hotter nuclei have weaker bars., Figures 1 2 suggest that galaxies with dynamically hotter nuclei have weaker bars.576 It is now well established that a galaxv« central black hole mass ancl πιοo velocity dispersion are correlated (Ferrarese Merzitt 2000: Cebhardt et al., It is now well established that a galaxy's central black hole mass and bulge velocity dispersion are correlated (Ferrarese Merritt 2000; Gebhardt et al.577 2000)., 2000).578 Later results show that, Later results show that579(9) the source for the distance: (10) the method used to derive the distance.,(9) the source for the distance; (10) the method used to derive the distance.580 The references corresponding to the source codes are listed at the end of the table., The references corresponding to the source codes are listed at the end of the table.581 An asterisk denotes data which are not. known., An asterisk denotes data which are not known.582 Galaxies known (o be part of the Local Group are not included. to avoid a possible dvnamical bias at the small end of the distance scale.," Galaxies known to be part of the Local Group are not included, to avoid a possible dynamical bias at the small end of the distance scale."583 Of course. distances derived [rom a velocily model were of no use for this purpose.," Of course, distances derived from a velocity model were of no use for this purpose."584" Those available were based on Cepheids (""ceph in the table). brightness of the tip of the Red Giant Branch (TRGB: in one case. ihe tip of the Asvanptotie Giant Branch. TAGB). surface brightness luctuations (SBF). a geometric method involving water masers (geo). or the brightness of the brightest stars (stars)."," Those available were based on Cepheids (“ceph” in the table), brightness of the tip of the Red Giant Branch (TRGB; in one case, the tip of the Asymptotic Giant Branch, TAGB), surface brightness fluctuations (SBF), a geometric method involving water masers (geo), or the brightness of the brightest stars (stars)."585 The former methods have «quoted accuracies of d 0.2 magnitudes or less in distance modulus., The former methods have quoted accuracies of $\pm$ 0.2 magnitudes or less in distance modulus.586 The last method was found by Iarachentsev&Tikhonov(1994) to have an accuracy of 0.3 (0 0.45 magnitudes. depending on exactly how it was applied.," The last method was found by \citet{KT94} to have an accuracy of 0.3 to 0.45 magnitudes, depending on exactly how it was applied."587 However. in several cases (see. for example. Croneοἱal.(2000).. and compare Narachentsey(1996) with Aparicio&Tikhonov(2000) for the case of DDO 109 = UGC 9240) it has been found to be in error by a [actor of two or more.," However, in several cases (see, for example, \citet{CSH00},, and compare \citet{KMa96}588 with \citet{AT00} for the case of DDO 109 = UGC 9240) it has been found to be in error by a factor of two or more."589 li what follows caleulations will be performed separately on both on the full data set of 98 galaxies (so as to lake advantage of the larger number of objects) and on the set of 35 galaxies with more reliable distances., In what follows calculations will be performed separately on both on the full data set of 98 galaxies (so as to take advantage of the larger number of objects) and on the set of 35 galaxies with more reliable distances.590 Although the data come from many sources and some diíIiculties could be anticipated from that fact. in practice there were no problems along those lines.," Although the data come from many sources and some difficulties could be anticipated from that fact, in practice there were no problems along those lines."591 Each of the TRGB distances used (he same calibration (Lee.Freedinan&Maclore1993).. as did the Cepheid distances within the stated errors: and all used as a zero-point the Large Magellanic Cloud αἱ a distance modulus of 18.50.," Each of the TRGB distances used the same calibration \citep{LFM93}, as did the Cepheid distances within the stated errors; and all used as a zero-point the Large Magellanic Cloud at a distance modulus of 18.50."592 The SBF method itself was calibrated using TRGB and Cepheid data. most of which found its way into this data set.," The SBF method itself was calibrated using TRGB and Cepheid data, most of which found its way into this data set."593" The internal consistency of the better-quality distances is thereforereliable"".", The internal consistency of the better-quality distances is therefore.594 As noted. the brightest-star distances are treated. with less confidence here. and the better-quality. data will be examined separately when possible.," As noted, the brightest-star distances are treated with less confidence here, and the better-quality data will be examined separately when possible."595 In the case of NGC 4258 the Cepheicl and geometric distances do not agree within their stated errors (7.98 and 7.2 Ape. respectively).," In the case of NGC 4258 the Cepheid and geometric distances do not agree within their stated errors (7.98 and 7.2 Mpc, respectively)."596 The distance shown is the average., The distance shown is the average.597 It is worth poinüng out that the data amount (ο a minority of the galaxies estimated to lie in this volume., It is worth pointing out that the data amount to a minority of the galaxies estimated to lie in this volume.598 Including the brightest-star galaxies possibly as much as a quarter of the population is represented: restricting ourselves to the better data. less than a tenth.In," Including the brightest-star galaxies possibly as much as a quarter of the population is represented; restricting ourselves to the better data, less than a .In"599 , 600that we calculate all quantities at the time when the third axisvirialises.,that we calculate all quantities at the time when the third axis.601". Thus, we also have to compare these quantities those from the spherical-collapse model that are also calculated at the time of virialisation and not of collapse, i.e. when R=Ru/2 and not R=0 for EdS. This leads to slightly lower reference values ofὃς and A, since ζοοι«zy."," Thus, we also have to compare these quantities those from the spherical-collapse model that are also calculated at the time of virialisation and not of collapse, i.e. when $R=R_\mathrm{ta}/2$ and not $R=0$ for EdS. This leads to slightly lower reference values of$\delta_\cc$ and $\Delta_\vv$ since $z_\mathrm{col}<z_\vv$."602 Here the subscript ‘col’ denotes collapse., Here the subscript `col' denotes collapse.603" Using the parametric solutions of ? for the linear and the non-linear overdensity, respectively, and 0=37t/2 at virialisation, we find that ὃς= and A,=147 for the EdS universe at R=R, independent of zy."," Using the parametric solutions of \citet{Ohta2004} for the linear and the non-linear overdensity, respectively, and $\theta=3\pi/2$ at virialisation, we find that $\delta_\cc=1.583$ and $\Delta_\vv=147$ for the EdS universe at $R=R_\vv$ independent of $z_\vv$."604" Recently, ? arrived at the same values when accounting for the time of virialisation instead of collapse."," Recently, \citet{Lee2009} arrived at the same values when accounting for the time of virialisation instead of collapse."605 The top panels of Fig., The top panels of Fig.606" [4] show δε and A, for three different cosmologies for e=p 0, i.e. spherical systems."," \ref{fig:deltasFixed} show $\delta_\cc$ and $\Delta_\vv$ for three different cosmologies for $e=p=0$ , i.e. spherical systems."607 The OCDM cosmology is the same as our reference ACDM model except that O4=0., The OCDM cosmology is the same as our reference $\Lambda$ CDM model except that $\Omega_\Lambda=0$.608 For the EdS model we set Qn=1 and0., For the EdS model we set $\Omega_\mm=1$ and.609" Indeed, for the EdS universe the constant values derived analytically are also reproduced by solving Eq."," Indeed, for the EdS universe the constant values derived analytically are also reproduced by solving Eq."610 numerically., numerically.611 Thisdemonstrates again that Eqs. (5]. [[3))," Thisdemonstrates again that Eqs. \ref{eq:basicEvolutionA}, \ref{eq:virCondition}) )"612 are fully consistent with the well-known spherical-collapse model., are fully consistent with the well-known spherical-collapse model.613" Note that the qualitative behaviour of A,(z,) is the same as Ay(Zco1) (comparee.g.with ?)..", Note that the qualitative behaviour of $\Delta_\vv(z_\vv)$ is the same as $\Delta_\vv(z_\mathrm{col})$ \citep[compare e.g. with][]{Bartelmann2006}. .614" However, there is a difference for the critical linear overdensity whose shape as a function of z, differs substantially from the shape as a function of Zo."," However, there is a difference for the critical linear overdensity whose shape as a function of $z_\vv$ differs substantially from the shape as a function of $z_\mathrm{col}$."615" This should illustrate that the time chosen in the model when virialisation actually occurs (Zy OF ζεοι) can already have substantial impact on the qualitative behaviour of relevant quantities as a function of redshift, hence it is not necessarily a consequence of ellipsoidal collapse alone."," This should illustrate that the time chosen in the model when virialisation actually occurs $z_\vv$ or $z_\mathrm{col}$ ) can already have substantial impact on the qualitative behaviour of relevant quantities as a function of redshift, hence it is not necessarily a consequence of ellipsoidal collapse alone."616 The bottom panels of Fig., The bottom panels of Fig.617" A] show ὃς and A, for a triaxial halo with e=0.2 and p=—0.1.", \ref{fig:deltasFixed} show $\delta_\cc$ and $\Delta_\vv$ for a triaxial halo with $e=0.2$ and $p=-0.1$.618" Also in this case both parameters are independent of z, for the EdS universe, although 6, changes from 1.583 to 2.058, while A, stays almost the same, 148 instead of 147."," Also in this case both parameters are independent of $z_\vv$ for the EdS universe, although $\delta_\cc$ changes from $1.583$ to $2.058$ , while $\Delta_\vv$ stays almost the same, $148$ instead of$147$ ."619" Interestingly, the mostdrastic changes in the shapes of both parameters occur for the OCDM model, for which the total density is only approximately a third"," Interestingly, the mostdrastic changes in the shapes of both parameters occur for the OCDM model, for which the total density is only approximately a third"620P-L intercepts.,P-L intercepts.621 These sugeestedOO that the svuthetic P-L relatious may not be iude]deut of metallicity., These suggested that the synthetic P-L relations may not be independent of metallicity.622 Pulsators from various model sets. as described iu Section 2. ean also be use to construct the svuthetic p-c relatious iu the IRAC bands.," Pulsators from various model sets, as described in Section 2, can also be used to construct the synthetic P-C relations in the IRAC bands."623 For brevity. colors from 2.6/1 and £550 biiIs are denoted as [3.6].|L5]. and so on.," For brevity, colors from $3.6\mu{\mathrm m}$ and $4.5\mu{\mathrm m}$ bands are denoted as $[3.6]-[4.5]$, and so on."624 Two examples o| the svuthetic P-C relations are presented in Figure 9.., Two examples of the synthetic P-C relations are presented in Figure \ref{pc_example}.625 Results of the svuthetic P-C relations are suniniarized iu Table L., Results of the synthetic P-C relations are summarized in Table \ref{tab_pc}.626 Asin the case of the svuthetic P-L relations. pusators with 0.Lxlog(P)2.0 were used to fit the P-C relations.," As in the case of the synthetic P-L relations, pulsators with $0.4 \leq \log(P) \leq 2.0$ were used to fit the P-C relations."627 The P-C slopes aud intercepts do not deviate b vonnore than 0.006 if all the pulsators were included., The P-C slopes and intercepts do not deviate by more than $0.006$ if all the pulsators were included.628" Tje svuthetic P-C slopesaud intercepts were plotted as a funcjon of 12|log(O/IT) iu Figures 10 and 11. respectively,"," The synthetic P-C slopesand intercepts were plotted as a function of $12+\log(O/H)$ in Figures \ref{pcslope} and \ref{pczp}, respectively."629 From these figures. it is clear that P-C relations exist or certain combinations of IRAC baud filters aud metalicity. and not all of the svuthetic P-C relations are indepeudent of metallicity.," From these figures, it is clear that P-C relations exist for certain combinations of IRAC band filters and metallicity, and not all of the synthetic P-C relations are independent of metallicity."630 The P-C relations that are ineependent or sensitive to metallicity are the [3.6].—[s.0| and |L.5]10.5 P-C relations. especially for those wihi 12|logtO/IT)— 8.9. M," The P-C relations that are independent or insensitive to metallicity are the $[3.6]-[8.0]$ and $[4.5]-[5.8]$ P-C relations, especially for those with $12+\log(O/H)<8.9$ ."631arengooetal.(2010) found a significant [3.6] P-C relation for the Galactic Cepheids. with the expression[5.0]. of [3.6][L0]=0002901000 0.058CEO.O0LI).," \citet{mar10} found a significant $[3.6]-[8.0]$ P-C relation for the Galactic Cepheids, with the expression of $[3.6]-[8.0]=0.039(\pm0.008)\log(P) - 0.058(\pm0.014)$ ."632 This empirical uon-zero P-C5} logslopeCP?) is là conracdiction with the svuthetic P-C slopesgiven, This empirical non-zero P-C slope is in contradiction with the synthetic P-C slopesgiven633must be <10 km + so that random motions do not wash out the sharp cut-olf within one revolution time (Jensen Thuan 1982: see also WS. May James 1984). or the sharp cut-oll must be à transient feature (e... Sasaki LOST).,"must be $\le 10$ km $^{-1}$ so that random motions do not wash out the sharp cut-off within one revolution time (Jensen Thuan 1982; see also KS1, May James 1984), or the sharp cut-off must be a transient feature (e.g., Sasaki 1987)."634 This low upper limit for teg2 is close to the minimum value of . ∿−≽↓∡⊔↓⊳∖⊔⋖⋅⋖⋅∠⇂⋖⋅∠⊓∪≱∖⋜∐↓≱∖∙∖⇁↓∪∪⊔↓↓⋅∢⋅≱∖⊔≤⋗↻≟∃≼∼↓⋅↓∩⋅↓⋅↓∪⊔∪⇂n poc : ⋅ . local stability for clise galaxies. ancl thus for star formation.," This low upper limit for $\langle v^2_R635\rangle^{1/2}$ is close to the minimum value of $\sim 2$ km $^{-1}$ needed to satisfy Toomre's (1964) criterion of local stability for disc galaxies, and thus for star formation."636 Alternatively. in the case of a disce formation scenario in which the disc grows from the inside outward (o.g.. Larson 1976. Gunn 1982. Seiden 1983. Seiden et al.," Alternatively, in the case of a disc formation scenario in which the disc grows from the inside outward (e.g., Larson 1976, Gunn 1982, Seiden 1983, Seiden et al."637 1984) a sharp edge can be maintained i£ this outward growth is sulliciently rapid. so that the random motion of the stars does not smear out the edge.," 1984) a sharp edge can be maintained if this outward growth is sufficiently rapid, so that the random motion of the stars does not smear out the edge."638 Note. however. that the disc truncations in our sample galaxies are not as sharp as those found by KSI4. among others. which will relax these requirements.," Note, however, that the disc truncations in our sample galaxies are not as sharp as those found by KS1–4, among others, which will relax these requirements."639 The situation becomes more complicated if the ealactic disc is lopsided or if the truncations occur at dilferent raclii., The situation becomes more complicated if the galactic disc is lopsided or if the truncations occur at different radii.640" Following the epievelie description of Baldwin. Lsnden-Dell Saneisi (1980). van der Ixruit (LOSS) estimates a smearing time of L7«101"" vr for the Galactic disc. and he concludes that a variation in the truncation radii of order. may just survive a Hubble time."," Following the epicyclic description of Baldwin, Lynden-Bell Sancisi (1980), van der Kruit (1988) estimates a smearing time of $1.7 \times 10^{10}$ yr for the Galactic disc, and he concludes that a variation in the truncation radii of order may just survive a Hubble time."641 With the possible exception of ESO 416-G25. our sample galaxies appear to comfortably meet this requirement.," With the possible exception of ESO 416-G25, our sample galaxies appear to comfortably meet this requirement."642 Casertano (1983) has shown that a truncated: stellar disc leaves a signature on the rotation curve in the form of a region of slowly varying velocity followed by a steep decline just outside the truncation radius (see also Hunter. Ball Gottesman 1984).," Casertano (1983) has shown that a truncated stellar disc leaves a signature on the rotation curve in the form of a region of slowly varying velocity followed by a steep decline just outside the truncation radius (see also Hunter, Ball Gottesman 1984)."643 The amount of this decrease is a measure of the disc mass., The amount of this decrease is a measure of the disc mass.644 The effect of a truncation is aflaffenéig of the rotation curve inside the truncation itself. from. some racius Ry to fg. and a steep decrease of the velocity outside.," The effect of a truncation is a of the rotation curve inside the truncation itself, from some radius $R_0$ to $R_{\rm max}$, and a steep decrease of the velocity outside."645 The well-known warped cclee-on galaxy NGC 4013. for which Bottema (1995) suspected. a sudden decrease in the mass density. corresponding to the truncation radius. has indeed been shown to exhibit a sudden drop in the rotational velocity of about 20 Emi s.| just at the optical edge (Bottema. Shostak van der Wruit LOST. Bottema 1995. 1996).," The well-known warped edge-on galaxy NGC 4013, for which Bottema (1995) suspected a sudden decrease in the mass density corresponding to the truncation radius, has indeed been shown to exhibit a sudden drop in the rotational velocity of about 20 km $^{-1}$ just at the optical edge (Bottema, Shostak van der Kruit 1987, Bottema 1995, 1996)."646 This drop can be understood. if one realises hat near the edge of the galactic disc the mass distribution will be irregular: there is no smooth. circular end to the disc. but it likely ends in spiral arms.," This drop can be understood if one realises that near the edge of the galactic disc the mass distribution will be irregular: there is no smooth, circular end to the disc, but it likely ends in spiral arms."647 DBottema (1996) argues hat therefore gas moving in the potential of such patches of stellar matter will not be in precise circular motion and rence the radial velocity along the line of sight is somewhat ower than the true rotation., Bottema (1996) argues that therefore gas moving in the potential of such patches of stellar matter will not be in precise circular motion and hence the radial velocity along the line of sight is somewhat lower than the true rotation.648" Finally. Baheall (1983) showed. that. for Sb or Se ealaxies like NGC 891 or the Galaxy. the feature in he rotation curve due to the truncated stellar cise is observable only if uus“<doe (smaller for galaxies with more prominent bulges). if the truncation length is small compared to fy. and if the halo mass inside f, is smaller than the disc mass (Casertano 1983)."," Finally, Bahcall (1983) showed that, for Sb or Sc galaxies like NGC 891 or the Galaxy, the feature in the rotation curve due to the truncated stellar disc is observable only if $R_{\rm max} \le 4 h_R$ (smaller for galaxies with more prominent bulges), if the truncation length is small compared to $h_R$, and if the halo mass inside $R_{\rm max}$ is smaller than the disc mass (Casertano 1983)."649 Unfortunately. he currently available velocity information for the four galaxies in our pilot sample does not allow us to confirm the presence of sharp runcations in the disc mass based on the shape of the rotation curves: only for ESO 446-C18 and ESO 446-C44 rotation curves have been published. for the Ha. emission (Mathewson ct al.," Unfortunately, the currently available velocity information for the four galaxies in our pilot sample does not allow us to confirm the presence of sharp truncations in the disc mass based on the shape of the rotation curves: only for ESO 446-G18 and ESO 446-G44 rotation curves have been published, for the $\alpha$ emission (Mathewson et al."650 1992) and the component (Persic Salucci 1995. based on the raw Mathewson ct al.," 1992) and the component (Persic Salucci 1995, based on the raw Mathewson et al."651 1992 data). but these rotation curves do not or just barely reach hose raclii where we expect to be able to see a truncation signature.," 1992 data), but these rotation curves do not or just barely reach those radii where we expect to be able to see a truncation signature."652 In this paper we have presented the first results of a systematic analysis of galactic disc structure in general anc of racially truncated: exponential disces in particular for a pilot sample of four “normal” disc-dominated edge-on spira galaxies., In this paper we have presented the first results of a systematic analysis of galactic disc structure in general and of radially truncated exponential discs in particular for a pilot sample of four “normal” disc-dominated edge-on spiral galaxies.653 We have carefully considered. the importance of (residual) dust. deviations from 90° inclinations. and spira arms. and concluded: that these effects do not allect our results significantly.," We have carefully considered the importance of (residual) dust, deviations from $^\circ$ inclinations, and spiral arms, and concluded that these effects do not affect our results significantly."654 We have also shown that the truncate discs in our sample galaxies are not caused artificially by inaccurate sky subtraction. but are real deviations from the radial exponential light. profiles.," We have also shown that the truncated discs in our sample galaxies are not caused artificially by inaccurate sky subtraction, but are real deviations from the radial exponential light profiles."655 An independent. approach to obtain the statistics of runcated galactic discs. using a sample of galaxies selectec in a uniform way. is needed in order to better unclerstaric heir overall propertics and. physical implications.," An independent approach to obtain the statistics of truncated galactic discs, using a sample of galaxies selected in a uniform way, is needed in order to better understand their overall properties and physical implications."656 If the runcations seen in the stellar light are also present in the mass distribution. they would have important dvnamica consequences1 at the discs outer edges.," If the truncations seen in the stellar light are also present in the mass distribution, they would have important dynamical consequences at the disc's outer edges."657g We have shown hat the truncated. luminosity. distributions of our pilo sample galaxies. if also. present in the mass distributions. comfortably meet the requirements for longevity.," We have shown that the truncated luminosity distributions of our pilot sample galaxies, if also present in the mass distributions, comfortably meet the requirements for longevity."658- The truncation radii. expressed in units of fy. for the disces of ESO 201-C22. ESO 416-C25. and ESO 446-GI8 are comparable to those found by INSI.d and Bottema (1995). while ESO 446-C44 is truncated. at much. smaller. (ασ.," The truncation radii, expressed in units of $h_R$, for the discs of ESO 201-G22, ESO 416-G25, and ESO 446-G18 are comparable to those found by KS1–4 and Bottema (1995), while ESO 446-G44 is truncated at much smaller radii."659 In fact. the truncations of the disces of ESO 416-625 and ESO 446-C44 are within the range found by Pohlen et. al. (," In fact, the truncations of the discs of ESO 416-G25 and ESO 446-G44 are within the range found by Pohlen et al. ("66020004) for their seumple of 31 nearby edge-on spiral galaxies.,2000a) for their sample of 31 nearby edge-on spiral galaxies.661 In general. the clises of our sample galaxies are truncated at similar radii on either side of their centres. within the observational uncertainties. with the exception of ESO 201-(122.," In general, the discs of our sample galaxies are truncated at similar radii on either side of their centres, within the observational uncertainties, with the exception of ESO 201-G22."662 With the possible exception of the disc of ESO 416-Ci25. -- appears that our sample galaxies are fairlv symmetric. in terms of both the sharpness of their disc truncations and 1ο truncation length. although the truncations occur over a larger region ancl not as abruptly as found in previous studies.," With the possible exception of the disc of ESO 416-G25, it appears that our sample galaxies are fairly symmetric, in terms of both the sharpness of their disc truncations and the truncation length, although the truncations occur over a larger region and not as abruptly as found in previous studies."663 The northern edge of the disc of ESO 416-CG25 is very sharply truncated compared to its southern edge., The northern edge of the disc of ESO 416-G25 is very sharply truncated compared to its southern edge.664 We believe that this may be explained by the fact that we likely observe the outer stellar envelope of a spiral arm. whereas," We believe that this may be explained by the fact that we likely observe the outer stellar envelope of a spiral arm, whereas"665inner disk accretion rate AZ for a standarcl dust opacity law. — Lsx10 (CL)?10 > (PAL n where a is the viscosity parameter aud the fiducial active layer surface deusity is the estimated penetration depth of cosmic rays.,"inner disk accretion rate $\mdot$ for a standard dust opacity law, = 1.8 ( )^2 ( )^3, where $\alpha$ is the viscosity parameter and the fiducial active layer surface density is the estimated penetration depth of cosmic rays."666 Remarkably. this ficlucial value of the mass accretion rate is of the sale order as the accretion rates seen in typical T Tauri stars of uear-solar mass (Gullbring 19985: Hartmann 1998: also Valenti 1993.," Remarkably, this fiducial value of the mass accretion rate is of the same order as the accretion rates seen in typical T Tauri stars of near-solar mass (Gullbring 1998; Hartmann 1998; also Valenti 1993)."667 However. eqalion 3 exhibits uo dependence upon stellar mass. which does not agree withthe oservatLous.," However, equation \ref{eq:mdotgam} exhibits no dependence upon stellar mass, which does not agree withthe observations."668 E-ation 3. assumes that irradiatiou heating X the disk by t ‘al star is uot important., Equation \ref{eq:mdotgam} assumes that irradiation heating of the disk by the central star is not important.669 This may not be the case for the more massive. IuOUS slars. ΠΟΥ ΤΟΝΙ dwarfs. which bave extremely low mass accretion rates anc therefor srestumably low s heating.," This may not be the case for the more massive, luminous stars, nor for the brown dwarfs, which have extremely low mass accretion rates and therefore presumably low viscous heating."670 The situation is uninect for solar-imass T Tauri stars. whose teiiperature structu e innermost disk ay or may not be domiuated by viscous heating. depeig upon the properties of the cust eralis there (e.g.. Figure 5a in D'Alessio et al.," The situation is mixed for solar-mass T Tauri stars, whose temperature structure in the innermost disk may or may not be dominated by viscous heating, depending upon the properties of the dust grains there (e.g., Figure 5a in D'Alessio et al."671 2001)., 2001).672 We the'elore consider the linitiig case in which he clisk heating is set mainly by the absorption of radiati1 from the central star., We therefore consider the limiting case in which the disk heating is set mainly by the absorption of radiation from the central star.673 Iu Caminie's model. M decreases with decreasing racliis.," In Gammie's model, $\mdot$ decreases with decreasing radius."674 The mass accretion rate in tje tuner disk (and therefore the rate onto the central sta‘J is set by the accretion rate of the layered model at the critical radius Z2. where the temperature Vises toa evel (taken to be 1000 Ix) sullicient Lor thermal ionization to activate the MRL, The mass accretion rate in the inner disk (and therefore the rate onto the central star) is set by the accretion rate of the layered model at the critical radius $R_c$ where the temperature rises to a level (taken to be 1000 K) sufficient for thermal ionization to activate the MRI.675 Iu the 1yodel with pure viscous heating. Re = 0.13 45;(ay=) ET3 y.(M.," In the model with pure viscous heating, R_c = 0.13 ( ( (."676 Iu the case where irradiation cdomiuates. the temperature of tlie irradiated disk at cylindrical radius Ro will be," In the case where irradiation dominates, the temperature of the irradiated disk at cylindrical radius R will be T^4 ,"677filamentation NN,filamentation + .678 The second two λα...terms on the right hand side of equation Zi]]) T Predrepresent thel eladvectioni. obt z»| withih the LLLow., The second two terms on the right hand side of equation \ref{MHDj}) ) represent the advection of $A_\|$ with the flow.679" οOn sma‘"" scales.‘[ wherei thel velocitv: Dogracüientsi ‘are steep.1 (Desei ternis dominate over the first term."," On small scales, where the velocity gradients are steep, these terms dominate over the first term."680 However. since the continued expansion. of. small scale loops is. eventually inhibited... by neighbouring. cavities... (Bell2004:Reville:etal.2008).. on sulliciently.v large length scales the first⋅ term will: dominate.," However, since the continued expansion of small scale loops is eventually inhibited by neighbouring cavities, \citep{bell04,revilleetal08}, on sufficiently large length scales the first term will dominate."681: The ordering5 of these terms will be verified in section 4.., The ordering of these terms will be verified in section \ref{compare_sect}.682" Neglecting the last‘ two terms in equation (27)). we find the following ΕΕ...growth rate for⋅ the filamentation⋅ ⇂↸≜∖≜∆⊓↔instabilityLp where C, ENis the cosmic-. enerev density.per) ui=Pminfme the Lorentz factor of the lowest energy cosmic. ravs drivingDu the instability."" (ic.. those satisfving puiuc3»cn li). and g is a numerical factor that depends on the shape of the cosmic-ray spectrum."," Neglecting the last two terms in equation \ref{MHDj}) ), we find the following growth rate for the filamentation instability where $U_{\rm cr}$ is the cosmic-ray energy density, $\gamma_{\rm min}=p_{\rm min}/mc$ the Lorentz factor of the lowest energy cosmic rays driving the instability (i.e. those satisfying $p_{\rm min}c\gg eu_{\rm sh}A_\|$ ), and $\eta$ is a numerical factor that depends on the shape of the cosmic-ray spectrum."683 For a spectrum fxp Lin the momentum interval (DaxDpm Puin). this parameter is =Lf/In(puaxpiii).," For a spectrum $f\propto p^{-4}$ in the momentum interval $(p_{\rm max}>p>p_{\rm min})$ , this parameter is $\eta=1/\sqrt{\ln(p_{\rm max}/p_{\rm min})}$."684 Phe growth rate is scale independent. ancl depends only on the root mean square of the perpendicular magnetic field. enclosed on that scale. as expected from the qualitative description above.," The growth rate is scale independent, and depends only on the root mean square of the perpendicular magnetic field enclosed on that scale, as expected from the qualitative description above."685 Since the non-resonant mode cdiseussed in has a growth rate that decreases monotonically with increasing wavelength. the filamentation must dominate the amplification. of magnetic field. on some scale.," Since the non-resonant mode discussed in has a growth rate that decreases monotonically with increasing wavelength, the filamentation must dominate the amplification of magnetic field on some scale."686" However. for the growth rate of the filamentation instability to be sulliciently⋅⋆ rapid; to influence; the scattering; of""s high-energy cosmic ravs. the mean squared magnetic field on small scales must be amplified to values well in excess of the ambient Ποια."," However, for the growth rate of the filamentation instability to be sufficiently rapid to influence the scattering of high-energy cosmic rays, the mean squared magnetic field on small scales must be amplified to values well in excess of the ambient field."687 Thus. the filamentation instability can be considered as à bootstrap to the non resonant instability..2. described. in. 201(2004). ane Bell(2005).," Thus, the filamentation instability can be considered as a bootstrap to the non resonant instability described in \citet{bell04} and \citet{bell05}."688. The necessary conditions for the filamentation to play an important role are discussed in detail in section 4.., The necessary conditions for the filamentation to play an important role are discussed in detail in section \ref{compare_sect}.689 The transfer of magnetic energv from small scales to longer wavelengths in the context of diffusive shock accelerationsai has previouslyvu. been suggested to occur --via an inverse. cascade (e.g.PelletierRetal.−2006:⋅Diamond.&Malkov.- 2007).," The transfer of magnetic energy from small scales to longer wavelengths in the context of diffusive shock acceleration has previously been suggested to occur via an inverse cascade \citep[e.g.][]{pelletieretal06,diamondmalkov07}."690. Whether⇁ this⋠ cascade can bridge⋠ the larec separation⋠ of⋅ scales remains.: uncertain., Whether this cascade can bridge the large separation of scales remains uncertain.691 ∙⊀⊳∖Phe mechanism⊀ cescribed» here. . ∢⋅∙ ↓≻⊓⊾⊳∖⋖⋅⊔↿⊳∖⋜⊔⊔∐⋖⊾⊓⊾⊔⇂⋜↧≻↓≻↓∪⋯⇍↓↕∖∖⋎↓↕⋖⋅⊓⊾⇂↓↕⋖⋅≼∼∪⊔↓≻↓↓⊔⋏∙≟∪⇂↿↓↕⋖⋅⊳∖≼⇍⋜↧↓⋖⊾⊳∖∙ ∙ ⊀ ⋅ is. mediated. by. the filamentation., The mechanism described here presents a different approach where the coupling of the scales is mediated by the filamentation.692. sThe coupling. of⋅ small anc laparge scale magnetic ⊲⋅fields has also been found⋅ in MENsimulations. of⋅ sheared [lows with. small scale turbulence (Yousef⊳⋅οἱal.. : −≻∪∪↖∖⊐↓⊔↿↓⊔⋅≼⇍∪⊔∩⋅⇀∖↿∪⇂⊔↓⋖⋅⋜⋯−↓⊓⋅↓∠⇂∠⇂∙∖⇁⊔, The coupling of small and large scale magnetic fields has also been found in simulations of sheared flows with small scale turbulence \citep{yousefetal08} in the context of mean-field dynamo theory.693⋜⋯↓∪↿↓↕∢⋅∪↓⋅∙∖⇁⊳∐∐⊳∖⋅ ⋅ pp approach. has also recentIy. been applied. to case of ⋅∙precursors∙∙ with an external cosmic-ray current. (Bykovetal.2011:Schure&Dell 2011).," This approach has also recently been applied to case of precursors with an external cosmic-ray current \citep{bykovetal11,schurebell11}."694. Numerical simulations are performed to verily the analysis of the previous section., Numerical simulations are performed to verify the analysis of the previous section.695 To investigate these processes. it is necessary to have a kinetic description of the cosmic-ravs.," To investigate these processes, it is necessary to have a kinetic description of the cosmic-rays."696 A code has been developed: similar to that described bv Zachary&Cohen(1986) and Lucek&Bell(2000).. where the background: plasma is treated as an ALD tui and the cosmic rays are treated using a particle-in-cell (PLC) approach.," A code has been developed similar to that described by \citet{zacharycohen86} and \citet{lucekbell00}, where the background plasma is treated as an MHD fluid and the cosmic rays are treated using a particle-in-cell (PIC) approach."697 This method is appropriate for modelling plasmas, This method is appropriate for modelling plasmas698lis shortcomine can be remedied with reasonable observational effort.,this shortcoming can be remedied with reasonable observational effort.699" The variation in Y,. which for stellar clusters is equivalent to Y.. vs. age has a natural explanation iu terms of stellar population evolution."," The variation in $\Upsilon_{e}$, which for stellar clusters is equivalent to $\Upsilon_*$, vs. age has a natural explanation in terms of stellar population evolution."700" In Figure 10. we conpare estimates of Y, based on the FAL Y,pa. to those based on the model values of Y. Lejnog. tabulated by MeLaushlin&vanderAMarel(2005). uius their preferred Bruzual-Charlot models with a Chabrier initial mass function (IME)."," In Figure \ref{fig:comp} we compare estimates of $\Upsilon_e$ based on the FM, $\Upsilon_{e,FM}$, to those based on the model values of $\Upsilon_*$, $\Upsilon_{*,mod}$, tabulated by \cite{clusters} using their preferred Bruzual-Charlot models with a Chabrier initial mass function (IMF)."701" The sense of the behavior of Y, with time is cousisteut for both ωρα aud Y. sugecsting that we are indeed ποιο the effects of stellar evolution on Y,.."," The sense of the behavior of $\Upsilon_e$ with time is consistent for both $\Upsilon_{e,FM}$ and $\Upsilon_{*,mod}$ suggesting that we are indeed seeing the effects of stellar evolution on $\Upsilon_e$."702" However. the quautitative agreement is poor. With Y,.pa; overestimating Y.,,,4 at voung ages and underestimating it at old ages."," However, the quantitative agreement is poor, with $\Upsilon_{e,FM}$ overestimating $\Upsilon_{*,mod}$ at young ages and underestimating it at old ages."703" The existence ofa siguificaut difference between Y. and Y,pay. particularly at old ages. is independent of the particular model or mitial mass function. amoug those currently iu general use."," The existence of a significant difference between $\Upsilon_{*,mod}$ and $\Upsilon_{e,FM}$, particularly at old ages, is independent of the particular model or initial mass function, among those currently in general use."704" We compare Y,ra; to the full ranee of Y.,,,/! presented bv MeLaughlin&vanderMazel(2005) in Figure l1.."," We compare $\Upsilon_{e,FM}$ to the full range of $\Upsilon_{*,mod}$ presented by \cite{clusters} in Figure \ref{fig:stpops}."705 We find simular results after colparing to 2007 Druzual-Charlot models. which are rot included im McLEbaushllin&vauderMarel(2005).," We find similar results after comparing to 2007 Bruzual-Charlot models, which are not included in \cite{clusters}."706".. The uaenitude of the differences hetween Y, and Y,Fay is sinuilar to that of the differences among the stellar yopulation models themselves."," The magnitude of the differences between $\Upsilon_{*,mod}$ and $\Upsilon_{e,FM}$ is similar to that of the differences among the stellar population models themselves."707 It is therefore possible hat there are problems with the stellar population nodels at this level., It is therefore possible that there are problems with the stellar population models at this level.708 Conrov.Cuun.&White(2008) explore the uncertainty in stellar population models. the omlk of which comes from modeling intermediate aud OW-lnass stars near the end of their lives where they ecole far more huuimous but for short periods of time.," \cite{conroy} explore the uncertainty in stellar population models, the bulk of which comes from modeling intermediate and low-mass stars near the end of their lives where they become far more luminous but for short periods of time."709 Touletal.(2008). show that includiug the thermalls-xlsatins ACD phase can increase the emission fou an iutermediate age galaxv by 1 magnitude in the A-ud., \cite{tonini} show that including the thermally-pulsating AGB phase can increase the emission from an intermediate age galaxy by 1 magnitude in the $K$ -band.710 The level of the discrepancy sugeested by our FAL analysis is consisteut with these potential problems in Yoou," The level of the discrepancy suggested by our FM analysis is consistent with these potential problems in $\Upsilon_{*,mod}$."711" Even at the vouug (low Y,.) end of things. there are clear differences among the models. with those using the Salpeter IMIF producing results more in line with those from the FAL"," Even at the young (low $\Upsilon_e$ ) end of things, there are clear differences among the models, with those using the Salpeter IMF producing results more in line with those from the FM."712 Further discussion of the details of stellar population models is bevoud the scope of this, Further discussion of the details of stellar population models is beyond the scope of this713is reached if. for example. NGC 7332 is excluded from the analvsis.,"is reached if, for example, NGC 7332 is excluded from the analysis."714 Although there does appear to be a significant. correlation between measured black hole mass and galaxy age estimate. it is not necessarily astrophysical in origin.," Although there does appear to be a significant correlation between measured black hole mass and galaxy age estimate, it is not necessarily astrophysical in origin."715 We must. first consider the possibility that it arises from some systematic error in the analysis., We must first consider the possibility that it arises from some systematic error in the analysis.716 However. the kinematic data [rom which the black hole masses were inferred. are completely independent from the line index cata that provide the age estimates.," However, the kinematic data from which the black hole masses were inferred are completely independent from the line index data that provide the age estimates."717 Since the line index data were not selected with this project in mind. and the black hole mass estimates plaved no role in the choice of sample. the selection. process cannot have induced the correlation that is seen in Fig.," Since the line index data were not selected with this project in mind, and the black hole mass estimates played no role in the choice of sample, the selection process cannot have induced the correlation that is seen in Fig."718 1., 1.719 Further. the independent nature of the data sets used. to measure the two ordinates means that there can be nothing in this analysis that might preferentially over-estimate the black hole masses in old galaxies. or underestimate the masses in voung svstenis.," Further, the independent nature of the data sets used to measure the two ordinates means that there can be nothing in this analysis that might preferentially over-estimate the black hole masses in old galaxies, or underestimate the masses in young systems."720 Lt should. also be borne in mind that the absolute calibrations of the black hole masses and galaxy ages are significantly. uncertain., It should also be borne in mind that the absolute calibrations of the black hole masses and galaxy ages are significantly uncertain.721 In the case of the absorption line indices. for example. the age estimates are derived: from spectral svnthesis modelling. whieh remains a somewhat uncertain process. so the absolute values of the ages of two ealaxies may be quite ill-determined.," In the case of the absorption line indices, for example, the age estimates are derived from spectral synthesis modelling, which remains a somewhat uncertain process, so the absolute values of the ages of two galaxies may be quite ill-determined."722 However. the fact that one is older than the other can be determined: relatively reliably bv. this. modelling process. so the approximate ordering of galaxy ages can be determined quite robustly.," However, the fact that one is older than the other can be determined relatively reliably by this modelling process, so the approximate ordering of galaxy ages can be determined quite robustly."723 Since the Spearman rank test described above depends only on this ordering. the statistical significance of the correlation is not dependent on the details of the adopted calibration.," Since the Spearman rank test described above depends only on this ordering, the statistical significance of the correlation is not dependent on the details of the adopted calibration."724 ]t would. thus appear that there is an undoerlving astrophysical correlation between the fraction of a galaxys mass in its central black hole and the age of its most recently formed stellar component., It would thus appear that there is an underlying astrophysical correlation between the fraction of a galaxy's mass in its central black hole and the age of its most recently formed stellar component.725" Hence. in addition to the established: correlation between black hole mass. Mog and galaxy mass. Main. there seems to be a ""second. parameter"" correlation with the age of the voungest stellar component."," Hence, in addition to the established correlation between black hole mass, $M_{\rm BH}$ and galaxy mass, $M_{\rm sph}$, there seems to be a “second parameter” correlation with the age of the youngest stellar component."726 At any given value of Adj. dillerent age galaxies will have different values of A/py. so this secondary correlation must eo some wav toward explaining the scatter in the primary relation.," At any given value of $M_{\rm sph}$, different age galaxies will have different values of $M_{\rm BH}$, so this secondary correlation must go some way toward explaining the scatter in the primary relation."727 We have sought to quantify the contribution of this second parameter to the scatter in the relation between Aa and AMyg by calculating This process corrects the mass ratio for the effects of age by subtracting the simplest. possible linear fit to the correlation in Fig., We have sought to quantify the contribution of this second parameter to the scatter in the relation between $M_{\rm sph}$ and $M_{\rm BH}$ by calculating This process corrects the mass ratio for the effects of age by subtracting the simplest possible linear fit to the correlation in Fig.728 1l., 1.729 As one would expect. this correction reduces the scatter in the relation: for the data in this sample. the dispersion in logCMpgMun) is 0.42 dex while hat in log(AMpg/M.on) is only 0.31. dex.," As one would expect, this correction reduces the scatter in the relation: for the data in this sample, the dispersion in $\log(M_{\rm BH}/M_{\rm sph})$ is 0.42 dex while that in $\log(M_{\rm730BH}/M_{\rm sph})^*$ is only 0.31 dex."731 Clearly. even he corrected mass ratio still contains considerable scatter.," Clearly, even the corrected mass ratio still contains considerable scatter."732 llowever. given the large uncertainties in the individual lack hole mass and galaxv age determinations. it would o* very surprising if the dispersion. were reduced. below a actor of two (70.3 dex)," However, given the large uncertainties in the individual black hole mass and galaxy age determinations, it would be very surprising if the dispersion were reduced below a factor of two $\sim 0.3$ dex)."733 The simplest. explanation. for the existence of the second. parameter correlation is that a single. physical »ocess couples the growth of the central black hole to the rigeering of star formation in a galaxy., The simplest explanation for the existence of the second parameter correlation is that a single physical process couples the growth of the central black hole to the triggering of star formation in a galaxy.734 As outlined in the Introduction. the hierachical picture of galaxy and. black vole evolution described by Ixaulfmann Llachnelt (2000) sugeests that galaxy mergers. lic behind. both processes.," As outlined in the Introduction, the hierachical picture of galaxy and black hole evolution described by Kauffmann Haehnelt (2000) suggests that galaxy mergers lie behind both processes."735 Where the last major merger occurred. long ago. it will rave taken place in à gas-rich environment that will provide ample fuel to augment the mass of the black hole.," Where the last major merger occurred long ago, it will have taken place in a gas-rich environment that will provide ample fuel to augment the mass of the black hole."736 Since the ast major episode of star formation will also be triggered in he merger. such galaxies will contain old stellar populations ancl massive black holes.," Since the last major episode of star formation will also be triggered in the merger, such galaxies will contain old stellar populations and massive black holes."737 Conversely. galaxies formed in more recent mergers will contain under-massive black holes and vounger stellar populations.," Conversely, galaxies formed in more recent mergers will contain under-massive black holes and younger stellar populations."738 Although the correlation between black hole mass and galaxy age is predicted by the hierarchical merging mocels. it should be borne in mind that such a correlation is a fairly generic prediction of any model in which the black hole mass grows over time.," Although the correlation between black hole mass and galaxy age is predicted by the hierarchical merging models, it should be borne in mind that such a correlation is a fairly generic prediction of any model in which the black hole mass grows over time."739 Even if galaxies form monolithically. hose that form first and hence contain the oldest. stellar »)pulations will have had time to grow the largest: black voles.," Even if galaxies form monolithically, those that form first – and hence contain the oldest stellar populations – will have had time to grow the largest black holes."740 Phe models that co not fit easily with this correlation are those in which the black holes ancl stellar components orm at entirely different times it would be hard to explain he observed correlation if. for example. the central. black roles were entirely. primordial.," The models that do not fit easily with this correlation are those in which the black holes and stellar components form at entirely different times – it would be hard to explain the observed correlation if, for example, the central black holes were entirely primordial."741 The study of black hole demographics is maturing, The study of black hole demographics is maturing742our radio luminosity-mass relationship.,our radio luminosity-mass relationship.743 We begin by calculating the best fits for the radio luminosity-mass relationships for both of our simulations., We begin by calculating the best fits for the radio luminosity-mass relationships for both of our simulations.744" Next, we take fits from ? for the mass function at redshift 0 and 1."," Next, we take fits from \citet{Warren:2006aa} for the mass function at redshift 0 and 1."745 We then convert the mass in the mass function to the expected radio luminosity from our fits in Table 1.., We then convert the mass in the mass function to the expected radio luminosity from our fits in Table \ref{tab:fitpars}.746 The results of this fitting are shown in the left panel of Figure 12.., The results of this fitting are shown in the left panel of Figure \ref{fig:lum_func}.747" Because of the scatter in the radio-mass luminosity function, we are able to place rough lower and upper limits on the luminosity function."," Because of the scatter in the radio-mass luminosity function, we are able to place rough lower and upper limits on the luminosity function."748 This scatter will be constrained by future simulations that cover a larger mass scale of galaxy clusters., This scatter will be constrained by future simulations that cover a larger mass scale of galaxy clusters.749" As we have done for our other results in Appendix A, we varied the magnetic field model to examine its effects on the luminosity function."," As we have done for our other results in Appendix A, we varied the magnetic field model to examine its effects on the luminosity function."750" The first parameter we changed is the normalization of the magnetic field, Bo."," The first parameter we changed is the normalization of the magnetic field, $\mathrm{B_0}$."751" In Figure 12,, we show Bo={0.01,0.03,0.1,0.3,1.0}uG."," In Figure \ref{fig:lum_func}, we show $\mathrm{B_0=\{0.01,0.03,0.1,0.3,1.0\}\mu G}$."752" Since the emitted power is roughly proportional to B5/? (see Section 3.1), as we increase Bo the luminosity function shifts quite dramatically to larger luminosities."," Since the emitted power is roughly proportional to $B^{5/2}$ (see Section 3.1), as we increase $\mathrm{B_0}$ the luminosity function shifts quite dramatically to larger luminosities."753" At low values of Bo the increase is close to the expected increase of B?/?. while at higher values B approaches Boome, reducing the effect of the increased local field strength."," At low values of $B_0$ the increase is close to the expected increase of $B^{5/2}$, while at higher values $B$ approaches $B_{CMB}$, reducing the effect of the increased local field strength."754 The second variation was in the scaling of the magnetic field with respect to theelectron density., The second variation was in the scaling of the magnetic field with respect to theelectron density.755" The line labeled “B-Flat” corresponds to B=Bo, whereas “B-Scale” denotes B«xBone."," The line labeled “B-Flat” corresponds to $B=B_0$, whereas “B-Scale” denotes $B \propto B_0 n_e$."756 In both cases we set Bo=0.1uG., In both cases we set $B_0=0.1\mu G$.757" With a uniform magnetic field, we see that the number of high-luminosity objects decreases dramatically, while the number of low luminosity objects increases slightly."," With a uniform magnetic field, we see that the number of high-luminosity objects decreases dramatically, while the number of low luminosity objects increases slightly."758" This is understandable given that the highest luminosity objects come from the most massive clusters, which have the highest densities."," This is understandable given that the highest luminosity objects come from the most massive clusters, which have the highest densities."759" In this case, the density doesn't correspond to higher magnetic fields, and the radio luminosity is diminished with respect to the adiabatic scaling."," In this case, the density doesn't correspond to higher magnetic fields, and the radio luminosity is diminished with respect to the adiabatic scaling."760" Similarly, in the “B-Scale” case, the magnetic field strength is even higher in the dense parts of the largest clusters, leading to a shallower slope in the luminosity function."," Similarly, in the “B-Scale” case, the magnetic field strength is even higher in the dense parts of the largest clusters, leading to a shallower slope in the luminosity function."761"By comparison, ? also found a slope of —2/3 using the same model as the By=0.14G line in 12,, adding verification to both results.","By comparison, \citet{Hoeft:2008aa} also found a slope of $-2/3$ using the same model as the $B_0=0.1\mu G$ line in \ref{fig:lum_func}, adding verification to both results."762" 'To determine the number of clusters for a given survey area and redshift depth, we integrate the cosmological volume out to z=0.5 for a given survey area dQ), with where Dy is the angular diameter distance."," To determine the number of clusters for a given survey area and redshift depth, we integrate the cosmological volume out to $z=0.5$ for a given survey area $d\Omega$, with where $D_A$ is the angular diameter distance."763 The result of this is that an all-sky survey out to z=0.5 covers 26.1 (Gpc/h)?.," The result of this is that an all-sky survey out to $z=0.5$ covers $26.1764~(\mathrm{Gpc}/h)^3$ ."765" In combination with our estimates from the relic200 simulation in Figure 12, we expect to"," In combination with our estimates from the $relic200$ simulation in Figure \ref{fig:lum_func}, , we expect to"766The existence of such a new class might help understand some otherwise puzzling observations of the. pre-main-sequence and post-main-sequence intermediate mass stars.,The existence of such a new class might help understand some otherwise puzzling observations of the pre-main-sequence and post-main-sequence intermediate mass stars.767 The Herbig Ae/Be stars show a strong activity (e.g.Bohm&Catala.1995) which has led investigators to suspect a widespread presence of magnetic fields in these stars (Catalaetal..1989)., The Herbig Ae/Be stars show a strong activity \citep[e.g.][]{Boh95} which has led investigators to suspect a widespread presence of magnetic fields in these stars \citep{Cat89}.768", Nevertheless. these magnetic fields have not been found. since only a small fraction of Herbig Ae/Be stars appears to host one (Wadeetal..2009)."," Nevertheless, these magnetic fields have not been found, since only a small fraction of Herbig Ae/Be stars appears to host one \citep{Wade09}."769. Note that a similar discrepancy between widespread activity and a small fraction of detected fields exists in OB stars (Henrichsetal..2005;Schnerr2008).," Note that a similar discrepancy between widespread activity and a small fraction of detected fields exists in OB stars \citep{Hen05,Schnerr08}."770.. A new class of magnetic A-type stars would shed new light on this issue., A new class of magnetic A-type stars would shed new light on this issue.771 Indeed. the progenitors of these magnetic A-type stars could be the Herbig Ae/Be stars where magnetic fields have not been detected yet. this non-detections being compatible with the fact that magnetic fields of the same intensity are much more difficult to detect in the faint Herbig Ae/Be stars than in à bright A-type star like Vega.," Indeed, the progenitors of these magnetic A-type stars could be the Herbig Ae/Be stars where magnetic fields have not been detected yet, this non-detections being compatible with the fact that magnetic fields of the same intensity are much more difficult to detect in the faint Herbig Ae/Be stars than in a bright A-type star like Vega."772 On the post-main-sequence side. the study of the white dwarf magnetic fields suggests that Ap/Bp stars are not sufficient to be the progenitors of magnetic white dwarfs (Wickramasinghe&Ferrario.2005).," On the post-main-sequence side, the study of the white dwarf magnetic fields suggests that Ap/Bp stars are not sufficient to be the progenitors of magnetic white dwarfs \citep{Wick05}."773.. A new class of magnetic A-type stars might also help to resolve this issue., A new class of magnetic A-type stars might also help to resolve this issue.774 The consequences for Vega itself should also be considered., The consequences for Vega itself should also be considered.775 Its magnetic field could indeed trigger active phenomena in its atmosphere., Its magnetic field could indeed trigger active phenomena in its atmosphere.776 Signs of spectroscopic variability have been reported. but have not been confirmed since (Charlton&Meyer. 1985).," Signs of spectroscopic variability have been reported, but have not been confirmed since \citep{Char85}."777. On the other hand. despite its status as a photometric standard. a photometric variability of 1—2% with occasional excursions to 4% has been reported (Gray. 2007).," On the other hand, despite its status as a photometric standard, a photometric variability of $1-2 \%$ with occasional excursions to $4\%$ has been reported \citep[][]{Gr07}."778 This might be produced by photospheric temperature inhomogeneities induced by its magnetic field., This might be produced by photospheric temperature inhomogeneities induced by its magnetic field.779 However. because of the near pole-on configuration of Vega. the variability would rather be due to intrinsic. changes of the magnetic field than to rotational modulation.," However, because of the near pole-on configuration of Vega, the variability would rather be due to intrinsic changes of the magnetic field than to rotational modulation."780 The origin of Vega’s magnetic field could be attributed to one of the three mechanisms generally invoked for early-type stars. namely (1) the fossil field hypothesis. (1) the envelope dynamo. (11) the convective core dynamo.," The origin of Vega's magnetic field could be attributed to one of the three mechanisms generally invoked for early-type stars, namely (i) the fossil field hypothesis, (ii) the envelope dynamo, (iii) the convective core dynamo."781 Let us first consider the fossil field hypothesis. whereby the ISM magnetic field is confined and amplified during stellar formation.," Let us first consider the fossil field hypothesis, whereby the ISM magnetic field is confined and amplified during stellar formation."782 It is regarded as the most consistent explanation of the magnetic fields observed in Ap/Bp stars (Moss.2001).. but. as proposed by Auriéreetal.(2007).. it could also account for another population of stars hosting weak longitudinal magnetic fields.," It is regarded as the most consistent explanation of the magnetic fields observed in Ap/Bp stars \citep{Mo01}, but, as proposed by \citet{Au07}, it could also account for another population of stars hosting weak longitudinal magnetic fields."783 Their argument is based on the fact that large-scale. organized magnetic field configurations are subjected to a pinch-type instability driven by differential rotation (Tayler.1973;Spruit.1999) when the magnetic field drops below a eritical value.," Their argument is based on the fact that large-scale, organized magnetic field configurations are subjected to a pinch-type instability driven by differential rotation \citep{Tay73,Sp99} when the magnetic field drops below a critical value."784 Consequently. for a distribution of large scale organized fields of different strengths issued from the star formation process. the instability would produce a magnetic dichotomy between a population of strong and stable large scale fields like in Ap/Bp stars and another population. where the destabilized configuration is now structured at small length scales. thus resulting in a weak longitudinal field.," Consequently, for a distribution of large scale organized fields of different strengths issued from the star formation process, the instability would produce a magnetic dichotomy between a population of strong and stable large scale fields like in Ap/Bp stars and another population where the destabilized configuration is now structured at small length scales, thus resulting in a weak longitudinal field."785 A simple estimate of the critical field has been found to be consistent with the reported lower limit of Ap/Bp stars., A simple estimate of the critical field has been found to be consistent with the reported lower limit of Ap/Bp stars.786 Here. both the detection of a very small longitudinal field in Vega and the gap between this field and the lowest magnetic fields of Ap/Bp stars reinforce this scenario.," Here, both the detection of a very small longitudinal field in Vega and the gap between this field and the lowest magnetic fields of Ap/Bp stars reinforce this scenario."787 Nevertheless. this scenario is not complete as it does not say what happens to the destabilized field configuration. which could either decay or be regenerated by à dynamo.," Nevertheless, this scenario is not complete as it does not say what happens to the destabilized field configuration, which could either decay or be regenerated by a dynamo."788 The magnetic field of Vega could indeed be generated by an envelope dynamo where the energy source is the rotation of the star., The magnetic field of Vega could indeed be generated by an envelope dynamo where the energy source is the rotation of the star.789 Following Spruit(2002).. the dynamo loop initiated by the differential rotation could be closed by the pinch-type instability mentioned. above.," Following \citet{Sp02}, the dynamo loop initiated by the differential rotation could be closed by the pinch-type instability mentioned above."790 This interesting possibility has been investigated by numerical simulations in. à. simplified cylindrical configuration (Braithwaite.2006) and in a solar context (Zahnetal..2007).. leading to opposite outcomes.," This interesting possibility has been investigated by numerical simulations in a simplified cylindrical configuration \citep{Brai06} and in a solar context \citep{Za07}, leading to opposite outcomes."791 Simulations in more realistic conditions for A-type stars are clearly needed to test this envelope dynamo., Simulations in more realistic conditions for A-type stars are clearly needed to test this envelope dynamo.792 An important issue concerns the origin of the envelope differential rotation. which is a basic ingredient of this dynamo but which is not forced by a strong stellar wind in A-type stars. contrary to what Is expected to occur in OB and Herbig Ae/Be stars (Ligniéresetal..1996).," An important issue concerns the origin of the envelope differential rotation, which is a basic ingredient of this dynamo but which is not forced by a strong stellar wind in A-type stars, contrary to what is expected to occur in OB and Herbig Ae/Be stars \citep{Lign96}."793. The third possibility i$ a dynamo in the convection core., The third possibility is a dynamo in the convection core.794 While magnetic fields are likely to be generated there. an efficient mechanism to transport it throughout the radiative envelope to the star surface has not yet clearly been identified (MacDonald&Mullan.2004).," While magnetic fields are likely to be generated there, an efficient mechanism to transport it throughout the radiative envelope to the star surface has not yet clearly been identified \citep{Mac04}."795. We note that in the three cases considered. the magnetic field is expected to be structured at small scales and also probably variable in time.," We note that in the three cases considered, the magnetic field is expected to be structured at small scales and also probably variable in time."796 This calls for a spectropolarimetric monitoring of Vega that will investigate the surface distribution and the temporal variation of its magnetic field., This calls for a spectropolarimetric monitoring of Vega that will investigate the surface distribution and the temporal variation of its magnetic field.797 A circularly polarized signal has been detected by accumulating à large number of high-quality echelle spectra of Vega with the NARVAL spectropolarimeter., A circularly polarized signal has been detected by accumulating a large number of high-quality echelle spectra of Vega with the NARVAL spectropolarimeter.798 The data analysis strongly supports a stellar origin of the polarization and thus the presence of a magnetic field on Vega., The data analysis strongly supports a stellar origin of the polarization and thus the presence of a magnetic field on Vega.799 Due to the unprecedented low level of the detected polarization. new independent measurements will still be important to confirm this result.," Due to the unprecedented low level of the detected polarization, new independent measurements will still be important to confirm this result."800 A magnetic field on Vega suggests that other A-type stars which are not Ap/Bp stars host weak magnetic fields and that their study can shed a new light on early-type star magnetism., A magnetic field on Vega suggests that other A-type stars which are not Ap/Bp stars host weak magnetic fields and that their study can shed a new light on early-type star magnetism.801 While a spectropolarimetrie survey of bright A-type stars will be necessary to find these stars. a detailed investigation of Vega's magnetic field should also. provide clues to the origin of this magnetism.," While a spectropolarimetric survey of bright A-type stars will be necessary to find these stars, a detailed investigation of Vega's magnetic field should also provide clues to the origin of this magnetism."802interstellar medium show that these dense regions with CO might not always be the most shielded ones (?)..,interstellar medium show that these dense regions with CO might not always be the most shielded ones \citep{Glover:2009hb}.803" In this case, the velocity dispersion in the CO emitting regions would not be representative of the velocity dispersion of the molecular gas located also in lower density regions."," In this case, the velocity dispersion in the CO emitting regions would not be representative of the velocity dispersion of the molecular gas located also in lower density regions."804 The CO line width would then underestimate the velocity dispersion of the molecular gas due to its preferential location in the densest and less turbulent regions., The CO line width would then underestimate the velocity dispersion of the molecular gas due to its preferential location in the densest and less turbulent regions.805" Such a difference has been observed between the CO and HI line width in high latitude clouds in the Solar Neighbourhood on a few parsec scale (?),, but it is unclear if such a difference would exist on larger scales where many shocks at different locations of the cloud must be occuring."," Such a difference has been observed between the CO and HI line width in high latitude clouds in the Solar Neighbourhood on a few parsec scale \citep{Barriault:2010fk}, but it is unclear if such a difference would exist on larger scales where many shocks at different locations of the cloud must be occuring."806" Due to the low metallicity of the SMC, a Galactic analog to understand the CO emitting clouds in the SMC may be denser molecular environments."," Due to the low metallicity of the SMC, a Galactic analog to understand the CO emitting clouds in the SMC may be denser molecular environments."807" Indeed, if the H5» abundance varies as the product of the mean gas number density and the metallicity (?),, the motions observed in CO and the mass observed in the dust continuum can be compared to the velocity of molecular cores and the relation to their enveloppes in our Galaxy."," Indeed, if the $_2$ abundance varies as the product of the mean gas number density and the metallicity \citep{Glover:2010uq}, the motions observed in CO and the mass observed in the dust continuum can be compared to the velocity of molecular cores and the relation to their enveloppes in our Galaxy."808" In ""extinction super cores"", ? observed that the inner N3H* or C!80 starless cores show a velocity dispersion that is systematically lower than the one expected for a gravitational support of the region in extinction."," In ""extinction super cores"", \citet{kirk:2007kx} observed that the inner $_2$ $^+$ or $^{18}$ O starless cores show a velocity dispersion that is systematically lower than the one expected for a gravitational support of the region in extinction."809" The motions between the densest molecular entities are hence not sufficient to support the enveloppes against gravity, similarly to what we observe in the giant molecular clouds in the south-west of the SMC."," The motions between the densest molecular entities are hence not sufficient to support the enveloppes against gravity, similarly to what we observe in the giant molecular clouds in the south-west of the SMC."810" Our analysis of the two mass estimates was done in a way to avoid as much as possible the known caveats (CO-devoid envelope, enhanced dust emissivity): fluxes are extracted from regions restricted to where CO is observed, we attempt to remove the extended emission surrounding the CO peaks and the dust emissivity is taken for molecular environments."," Our analysis of the two mass estimates was done in a way to avoid as much as possible the known caveats (CO-devoid envelope, enhanced dust emissivity): fluxes are extracted from regions restricted to where CO is observed, we attempt to remove the extended emission surrounding the CO peaks and the dust emissivity is taken for molecular environments."811 The impact of such effects on the masses deduced is checked in Appendix AppendixA:.., The impact of such effects on the masses deduced is checked in Appendix \ref{append}.812 Here we discuss the possible remaining biasses that could hamper the analysis and result in the mass discrepancy., Here we discuss the possible remaining biasses that could hamper the analysis and result in the mass discrepancy.813 We also discuss alternative interpretations for the mass discrepancy we observe., We also discuss alternative interpretations for the mass discrepancy we observe.814" In the scenario where CO is confined inside a large Ho envelope, then the dust emission will trace the total cloud (CO-emitting cloud+envelope)."," In the scenario where CO is confined inside a large $_2$ envelope, then the dust emission will trace the total cloud (CO-emitting cloud+envelope)."815" In order to minimize the effect of the CO-devoid envelope on the dust emission, we performed a local estimate of the extended emission around the detected region and removed it from the measured (sub-)millimeter fluxes."," In order to minimize the effect of the CO-devoid envelope on the dust emission, we performed a local estimate of the extended emission around the CO-detected region and removed it from the measured (sub-)millimeter fluxes."816" However, the effectiveness of this removal depends on the size of the envelope and on the density profile of the cloud."," However, the effectiveness of this removal depends on the size of the envelope and on the density profile of the cloud."817" For the same configuration, the virial mass is obtained from the CO velocities and the radius of the CO cloud."," For the same configuration, the virial mass is obtained from the CO velocities and the radius of the CO cloud."818 This radius may be overestimated from the observations if the CO clumps are not resolved and the virial masses will be overestimated., This radius may be overestimated from the observations if the CO clumps are not resolved and the virial masses will be overestimated.819" The dimension differences between the dust emitting region, the CO emitting region and the area deduced from the observations (i.e. the aperture) may then still bias the ratio M,j/M,,;, in either direction (enhancing or decreasing the mass ratio)."," The dimension differences between the dust emitting region, the CO emitting region and the area deduced from the observations (i.e. the aperture) may then still bias the ratio $_{vir}$ $_{mm}$ in either direction (enhancing or decreasing the mass ratio)."820" The exact magnitude of such biases is a complicated function of the real structure of the cloud (e.g. density), the definition of the CO cloud and aperture, and the extent of any CO-free dusty envelope surrounding the cloud."," The exact magnitude of such biases is a complicated function of the real structure of the cloud (e.g. density), the definition of the CO cloud and aperture, and the extent of any CO-free dusty envelope surrounding the cloud."821 We tested the magnitude of a geometric bias for a range of density profiles with a simple model., We tested the magnitude of a geometric bias for a range of density profiles with a simple model.822" In this model, the CO cloud and the envelope are spherical."," In this model, the CO cloud and the envelope are spherical."823" A circular aperture defines the radius that enters the virial mass calculation, while also defining the impact of the background subtraction to the mass deduced from the dust emission."," A circular aperture defines the radius that enters the virial mass calculation, while also defining the impact of the background subtraction to the mass deduced from the dust emission."824" We find that for a simple model in which dust emerges from a cloud twice the size of the CO cloud and the aperture covers the portion of the cloud not showing CO emission, the bias almost never exceeds ~30%.."," We find that for a simple model in which dust emerges from a cloud twice the size of the CO cloud and the aperture covers the portion of the cloud not showing CO emission, the bias almost never exceeds $\sim$."825" However, if the CO cloud is actually substantially smaller than the values quoted in Table 1 (e.g. CO clumps are not resolved at the SEST resolution), if the dust envelope is very large compared to the CO cloud, or if the aperture extends too far from the surface of"," However, if the CO cloud is actually substantially smaller than the values quoted in Table \ref{tab1} (e.g. CO clumps are not resolved at the SEST resolution), if the dust envelope is very large compared to the CO cloud, or if the aperture extends too far from the surface of"826partition function is converged to better than 0.03 when testing our choice of basis set size.,partition function is converged to better than 0.03 when testing our choice of basis set size.827" There are, of course, other factors that give rise to errors in our computed partition functions."," There are, of course, other factors that give rise to errors in our computed partition functions."828" One of these is the potential energy function, which is only reasonably accurately fitted to low-lying ro-vibrational levels."," One of these is the potential energy function, which is only reasonably accurately fitted to low-lying ro-vibrational levels."829 We will address the nature of the partition function of ammonia in greater details elsewhere., We will address the nature of the partition function of ammonia in greater details elsewhere.830 Figs., Figs.831" 4 and 5 illustrate the T-dependence of the absorption spectra of ammonia, and give an overview of the complete range as well of the four selected regions computed at T= 300 K, 600 K, 900 K, 12200 K, and 15500 K. As expected, the spectrum profiles at higher T become less extreme as the populations from the lower vibrational states are reduced in favour of the vibrationally excited states."," \ref{f:absorp:total:diff-T} and \ref{f:absorp:ABCD} illustrate the $T$ -dependence of the absorption spectra of ammonia, and give an overview of the complete range as well of the four selected regions computed at $T =$ 300 K, 600 K, 900 K, 200 K, and 500 K. As expected, the spectrum profiles at higher $T$ become less extreme as the populations from the lower vibrational states are reduced in favour of the vibrationally excited states."832" Only those few bands that are the most pronounced features at T=300 K are still recognizable at T=1500 K. Our ‘cold’ NH3 paper (Yurchenkoetal.2009) contained detailed comparisons with the HITRAN database which demonstrated the accuracy of our procedure and also, that even at 300 K, HITRAN is missing significant ddata."," Only those few bands that are the most pronounced features at $T=300$ K are still recognizable at $T=1\,500$ K. Our `cold' $_3$ paper \citep{NH3-T300K-paper} contained detailed comparisons with the HITRAN database \citep{HITRAN} which demonstrated the accuracy of our procedure and also, that even at 300 K, HITRAN is missing significant data."833" In BYTe we have improved our ability to reproduce the HITRAN data, see Fig. 6;;"," In BYTe we have improved our ability to reproduce the HITRAN data, see Fig. \ref{f:absorb:T300K};"834 however we do not show the entire comparison here., however we do not show the entire comparison here.835" As we were completing our calculations, a high temperature emission spectra of ammonia (T'=900 K) for the ground and v2 states of ammonia was reported by Yuetal.(2010).."," As we were completing our calculations, a high temperature emission spectra of ammonia $T=900$ K) for the ground and $\nu_2$ states of ammonia was reported by \citet{Yu-NH3-T900K}."836 We use this spectrum to provide an independent validation of the BYTe line list., We use this spectrum to provide an independent validation of the BYTe line list.837 To this end we used BYTe to generate a 900 K synthetic emission spectrum of iin the same spectral region., To this end we used BYTe to generate a 900 K synthetic emission spectrum of in the same spectral region.838 This is shown in Fig., This is shown in Fig.839 7 (lower part).," \ref{f:emiss:T900K}840 (lower part)."841 The ‘experimental’ spectrum on this figure was generated using the Einstein coefficients from the synthetic line list reported by Yuetal.(2010).., The `experimental' spectrum on this figure was generated using the Einstein coefficients from the synthetic line list reported by \citet{Yu-NH3-T900K}.842 The spectra agree not only qualitatively but also quantitatively in terms of the absolute intensity values., The spectra agree not only qualitatively but also quantitatively in terms of the absolute intensity values.843 The additional lines in the upper part of Fig., The additional lines in the upper part of Fig.844" 7 are present because our synthetic spectrum includes all possible transitions falling into the region including hot bands, while Yu al’s data is only for the ground and νο states ofNHa."," \ref{f:emiss:T900K} are present because our synthetic spectrum includes all possible transitions falling into the region including hot bands, while Yu 's data is only for the ground and $\nu_2$ states of."845. We have calculated to a high level of accuracy the frequencies and Einstein A coefficients of all the transitions that are present in the emission and absorption spectrum ofNH3., We have calculated to a high level of accuracy the frequencies and Einstein $A$ coefficients of all the transitions that are present in the emission and absorption spectrum of.846". The only limitations are: upper states with energies above 180000 aare excluded; there is an effective short-end wavelength cut-off of 1 4m, due to the incompleteness of our data at frequencies above 100000 ((the excluded region is unimportant for NH3)), and extremely weak lines have been excluded, which is of little physical significance."," The only limitations are: upper states with energies above 000 are excluded; there is an effective short-end wavelength cut-off of 1 $\mu$ m, due to the incompleteness of our data at frequencies above 000 (the excluded region is unimportant for ), and extremely weak lines have been excluded, which is of little physical significance."847" Although the BYTe line list is explicitly aimed at modelling hot ammonia, it improves on our previous cold line list (Yurchenkoetal.2009) in terms of the quality of the potential energy surface used, in the size of the basis sets employed and in the range of frequencies studied."," Although the BYTe line list is explicitly aimed at modelling hot ammonia, it improves on our previous cold line list \citep{NH3-T300K-paper}848 in terms of the quality of the potential energy surface used, in the size of the basis sets employed and in the range of frequencies studied."849 We therefore recommend the use of BYTe for all temperatures up to 15500 K. The line list is freely available and can download in its entirety or in parts from: Te., We therefore recommend the use of BYTe for all temperatures up to 500 K. The line list is freely available and can download in its entirety or in parts from: .850been enough to slow down. over 2000 vears. a B—5x1012 G magnetar to current period. provided that the initial spin period should be 2=300 ms.,"been enough to slow down, over 2000 years, a $B=5\times 10^{15}$ G magnetar to current period, provided that the initial spin period should be $P_{\rm i}\ga 300$ ms."851 Magnetic field in magnetars is generally thought to be generated by turbulent dvnamo. whose strength depends on the stars rotation rate (Duncan&Thompson1992.seehowever.VinkKuiper2006)..," Magnetic field in magnetars is generally thought to be generated by turbulent dynamo, whose strength depends on the star's rotation rate \citep[][see however, Vink \& Kuiper8522006]{dun92}."853 Such a period seems (o be (too long for magnetars. although its possibility cannot be ruled out.," Such a period seems to be too long for magnetars, although its possibility cannot be ruled out."854 Additionally. the known magnetars include the anomalous X-ray pulsars (AXPs) and soft gammnmna-ray repeaters (SGT). which are rotating al ~5—10 s 2006).," Additionally, the known magnetars include the anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs), which are rotating at $\sim 5-10$ s \citep{woo06}."855. IL 1E1612 is a magnetar. one needs to explain why its period is much longer (han those of AXPs and SGRs.," If 1E1613 is a magnetar, one needs to explain why its period is much longer than those of AXPs and SGRs."856" The mode of interaction between a NS ancl a surrounding disk is determined by the location of the inner radius Ry, of the disk with respect to the characteristic radii. the corolation radius R.=(GAD?/4z2)! . and the light evlinder radius Ry=cDP/2z. where AM is (he mass of the NS (e.g.Hlarionov&Sunvaev1975;Lipunov1992)."," The mode of interaction between a NS and a surrounding disk is determined by the location of the inner radius $R_{\rm in}$ of the disk with respect to the characteristic radii, the corotation radius $R_{\rm c}=(GMP^2/4\pi^2)^{1/3}$ , and the light cylinder radius $R_{\rm L}=cP/2\pi$, where $M$ is the mass of the NS \citep[e.g.][]{ill75,lip92}."857. The position of the inner radius of the disk can be estimated by comparing (he electromagnetic energy. density eenerated by the NS with the kinetic energy densitv of the disk., The position of the inner radius of the disk can be estimated by comparing the electromagnetic energy density generated by the NS with the kinetic energy density of the disk.858 The Ns is expected (ο be in (he propeller and ejector (radio pulsar) stage if the inner radius of the disk is bevond the corotation and lisht evlinder radius. respectively.," The NS is expected to be in the propeller and ejector (radio pulsar) stage if the inner radius of the disk is beyond the corotation and light cylinder radius, respectively."859 Since the kinetic energy density in (he disk has the dependence xr>? on the radial distance r [rom the center of the NS. steeper than the electromagnetic energv density (or radiation pressure) outside the light evlinder (x77). stable equilibrium of the disk outsile the light evlinder is not allowed. unless it is bevond the eravitational capture radius (Lipunov1992).," Since the kinetic energy density in the disk has the dependence $\propto860r^{-5/2}$ on the radial distance $r$ from the center of the NS, steeper than the electromagnetic energy density (or radiation pressure) outside the light cylinder $\propto r^{-2}$ ), stable equilibrium of the disk outside the light cylinder is not allowed, unless it is beyond the gravitational capture radius \citep{lip92}."861. In their calculations DeLucaetal.(2006). have adopted the traditional estimates of the radiation pressure from a NS by emplovinge a rotatinge magnetiee dipole in vacuum to egenerate {he electromagnetic fields., In their calculations \citet{luc06} have adopted the traditional estimates of the radiation pressure from a NS by employing a rotating magnetic dipole in vacuum to generate the electromagnetic fields.862 Recently Eksi&Alpar(2005) derived the electromagnetic energy density from the elobal electromagnetic field solution of Deutsch.(1955) for obliquely rotating magnetic dipoles., Recently \citet{eks05} derived the electromagnetic energy density from the global electromagnetic field solution of \citet{deu55} for obliquely rotating magnetic dipoles.863 They showed that the electromagnetic energy density of a rotating dipole makes a rather broad transition for disk existence across the lieht cvlinder for small inclination angles., They showed that the electromagnetic energy density of a rotating dipole makes a rather broad transition for disk existence across the light cylinder for small inclination angles.864on. To exanune to what extent the fallback disks affect the spin evolution of magnetars. we carried out. Monte Carlo simulations of the evolution of 105 NSs based on the spin-down model presented in Lipunov(1992.seealsoLi2002)..," To examine to what extent the fallback disks affect the spin evolution of magnetars, we carried out Monte Carlo simulations of the evolution of $10^6$ NSs based on the spin-down model presented in \citet[][see also Li 2002]{lip92}."865 As the mass of a fallback clisk is not replenished. mass flow rate in the disk declines aud (he inner radius of the disk moves out.," As the mass of a fallback disk is not replenished, mass flow rate in the disk declines and the inner radius of the disk moves out."866 The NS in this case generally. passes three evolutionary stages. (, The NS in this case generally passes three evolutionary stages. (867"1) First is the ""ejector"" phase. in which the radiative pressure from the NS is sufficient to keep (he surrounding plasma away from thelight exlinder: (he NS evolves as a radio pulsar.","1) First is the “ejector"" phase, in which the radiative pressure from the NS is sufficient to keep the surrounding plasma away from thelight cylinder; the NS evolves as a radio pulsar."868 Ποιο we assume that, Here we assume that869The sole remaining factor affecting Cepheid distances remains the treatineut of interstellar aud intergalactic reddening.,The sole remaining factor affecting Cepheid distances remains the treatment of interstellar and intergalactic reddening.870 The zero-point established by Galactic calibrators Wing in calibrating clusters and eroups or havingLEST parallaxes appears to be very solid. aud eliminates the need to rely on Magellanic Cloud Cepheids (Benedictetal.2007:Fouquéetal.2007) or surface brightuess relations (Fouquéetal.2007) to establish the extragalactic distance scale.," The zero-point established by Galactic calibrators lying in calibrating clusters and groups or having parallaxes appears to be very solid, and eliminates the need to rely on Magellanic Cloud Cepheids \citep{bn07,fo07} or surface brightness relations \citep{fo07} to establish the extragalactic distance scale."871" The near-solar metallicities of most Galactic calibrators also make them more similar o the Cepheids sampled in other spiral galaxies. al unuportaut factor when adjusting distances for netallicity effects; certainly in the aud bauds rere,"," The near-solar metallicities of most Galactic calibrators also make them more similar to the Cepheids sampled in other spiral galaxies, an important factor when adjusting distances for metallicity effects, certainly in the and bands used here."872 The iamner of treating reddening affects the Wesenheit formulation. however. aud nav also influence the echuique of PL-fittiug in different wavelength ας(ag. aud ἢ hat are used iu most extragalactic studies.," The manner of treating reddening affects the Wesenheit formulation, however, and may also influence the technique of PL-fitting in different wavelength bands, and ) that are used in most extragalactic studies."873 Amy Mferencees between he extinction properties of ust iu ucarby regious of the Galaxy aud those iu other galaxies may ve have an important influence ou the extragalactic distance scale., Any differences between the extinction properties of dust in nearby regions of the Galaxy and those in other galaxies may yet have an important influence on the extragalactic distance scale.874one night during 1999.,one night during 1999.875 The general appearance is tvpical of all nights. as well as seen in. previously published. light curves (?22)).," The general appearance is typical of all nights, as well as seen in previously published light curves \citealt{1997A&A...324L..57A, 1997A&A...318..134A}) )."876 As those papers demonstrated. a 39-minute wave is always present. with a small even-odel asymmetry suggesting that the fundamental period is actually the double. 7S minutes. (confirmed. by spectroscopy).," As those papers demonstrated, a 39-minute wave is always present, with a small even-odd asymmetry suggesting that the fundamental period is actually the double, 78 minutes (confirmed by spectroscopy)."877 The middle frame shows the L999 couble-humped orbital light curve. similar to that of 1457 (see Figure 3. above).," The middle frame shows the 1999 double-humped orbital light curve, similar to that of J1457 (see Figure \ref{fig:fold18} above)."878 Study of the seasonal timings vielded a 1995.— 2009 ephemoeris: Orbital maximum LID 2.450.032.182(3) 0.05432392(2) L. The average nightly power spectrum. the incoherent sum of the Li nights of best quality. is shown in the bottoni frame of Figure 6...," Study of the seasonal timings yielded a 1995 – 2009 ephemeris: Orbital maximum = HJD 2,450,032.182(3) + 0.05432392(2) E. The average nightly power spectrum, the incoherent sum of the 11 nights of best quality, is shown in the bottom frame of Figure \ref{fig:1}."879 Power excesses near 72 (20 min) and 143 t (10 min) are evident., Power excesses near 72 $^{-1}$ (20 min) and 143 $^{-1}$ (10 min) are evident.880 In order to study these higher-frequeney. signals in more detail. adjacent nights were added together. and the coherent. power speetrüm was constructed.," In order to study these higher-frequency signals in more detail, adjacent nights were added together, and the coherent power spectrum was constructed."881 However. even though the 72 and the 143 signals were always present. they were always broad. complex. and slightly variable in freequeney (similar to J1457).," However, even though the 72 $^{-1}$ and the 143 $^{-1}$ signals were always present, they were always broad, complex, and slightly variable in frequency (similar to J1457)."882 This is usually a sign that the actual signals violate the assumptions of Fourier analysis: constaney in. period. amplitude and. phase.," This is usually a sign that the actual signals violate the assumptions of Fourier analysis: constancy in period, amplitude and phase."883 During 2001. observatories at three longitudes in Chile. New Zealand and South Africa. contributed with good nightly coverage of BW Sel.," During 2001, observatories at three longitudes in Chile, New Zealand and South Africa, contributed with good nightly coverage of BW Scl."884 A very low Lickering background is seen in the light curves of BW Sel. enabling detection of periodic signals as weak as 0.002 magnitudes.," A very low flickering background is seen in the light curves of BW Scl, enabling detection of periodic signals as weak as $\sim 0.002$ magnitudes."885 The upper frames of Figure 7 shows the nightly mean power spectrum. with significant signals marked to an aecuraey of 0.5 |.," The upper frames of Figure \ref{fig:2} shows the nightly mean power spectrum, with significant signals marked to an accuracy of 0.5 $^{-1}$ ."886 Both the orbital period ancl the signal at 72 + (20 min) were present. along with two other signals at low frequeney: a powerful signal at 16.6 + (86.7 min). and a weak signal at 50.5 edd+ (28.5 min).," Both the orbital period and the signal at 72 $^{-1}$ (20 min) were present, along with two other signals at low frequency: a powerful signal at 16.6 $^{-1}$ (86.7 min), and a weak signal at 50.5 $^{-1}$ (28.5 min)."887 At higher frequeney. signals are detected at 153 edd (9.4 min). 307 (4.7 min). and. 724 edd.+ (2 min). though the latter is likely to be caused. by instrumental effects.," At higher frequency, signals are detected at 153 $^{-1}$ (9.4 min), 307 $^{-1}$ (4.7 min), and 724 $^{-1}$ (2 min), though the latter is likely to be caused by instrumental effects."888 Many telescopes have worm. gears which turn with a period of exactly 120. sidereal seconds. ancl this period was reported in research on many types of stars during 1960 1990. Lc. during the photolectrie-photometer cra.," Many telescopes have worm gears which turn with a period of exactly 120 sidereal seconds, and this period was reported in research on many types of stars during 1960 – 1990, i.e. during the photolectric-photometer era."889 CCDs are much less prone to this error., CCDs are much less prone to this error.890 However. since 724 + 2 + corresponds to. 120. sidereal seconds (to within the measurement error). we interpret the signal to be caused by his instrumental effect.," However, since 724 $\pm$ 2 $^{-1}$ corresponds to 120 sidereal seconds (to within the measurement error), we interpret the signal to be caused by this instrumental effect."891 We interpret the signal at. 153 cdd. as a pulsation requeney. with a significant first harmonic.," We interpret the signal at 153 $^{-1}$ as a pulsation frequency, with a significant first harmonic."892 Examination of individual nights showed: this signal to be somewhat ransient. at least in amplitude.," Examination of individual nights showed this signal to be somewhat transient, at least in amplitude."893 This behaviour was seen on 7 of the 15 good-quality nights., This behaviour was seen on 7 of the 15 good-quality nights.894 Since the orbital frequeney is known precisely. and. sinceits photometric signature. is »»verful ancl constant. we subtracted its Grst harmonic," Since the orbital frequency is known precisely, and sinceits photometric signature is powerful and constant, we subtracted its first harmonic"895without a maceic field. one with a maenetic field parallel to the ealactic midplane. and one with a maeuetic field perpendicular to the midplane.,"without a magnetic field, one with a magnetic field parallel to the galactic midplane, and one with a magnetic field perpendicular to the midplane."896 We use the ΕΤΑΠ maenetolhydrodvuaimics code to simulate SNRs in an ambicut backerouud reoeseutative of the ISM in the viciuiv of the solar circle. ic. with a stratified density aud eravitational potential witli respect to Leight above the ealactic iidplaue.," We use the FLASH magnetohydrodynamics code to simulate SNRs in an ambient background representative of the ISM in the vicinity of the solar circle, i.e. with a stratified density and gravitational potential with respect to height above the galactic midplane."897 In cach case we set off à SN explosion at 100 pe above the plane aud felow the evolution of the bubble for Sto 12 Myis., In each case we set off a SN explosion at 400 pc above the plane and follow the evolution of the bubble for 8 to 12 Myrs.898 For the simulation without a maeuetic field. we evolve the SNR uuilit dissipates.," For the simulation without a magnetic field, we evolve the SNR until it dissipates."899 Section 2 disasses the computational method and physical parameters., Section 2 discusses the computational method and physical parameters.900 Section 3 cdlescribes the results of the sinaiulations for oir three ¢cases. no aenetic field (subsection 31). à bg parallel to the galactic nii-plane (subsection 3.2.1). anda £ pC maguetic field perpendicular to the galactic mid-plane (subsection 3.2.2).," Section 3 describes the results of the simulations for our three cases, no magnetic field (subsection 3.1), a 4 $\mu$ G parallel to the galactic mid-plane (subsection 3.2.1), and a 4 $\mu$ G magnetic field perpendicular to the galactic mid-plane (subsection 3.2.2)."901 Section Ll cliscusses our conchisions about buovaucy of the lot gas. the vertical motion of cool gu aud SNR morphology.," Section 4 discusses our conclusions about buoyancy of the hot gas, the vertical motion of cool gas, and SNR morphology."902 Ii section. [sve also discuss why galactic shear would not have ΙΟ of an effect ou such |nbbles., In section 4 we also discuss why galactic shear would not have much of an effect on such bubbles.903) Version 2.5 of the FLASTT magueto-bydrodvuamics code was used for this project., Version 2.5 of the FLASH magneto-hydrodynamics code was used for this project.904 FLASID simulates flows in multiple dimensions on an Eulerian erid., FLASH simulates magneto-hydrodynamic flows in multiple dimensions on an Eulerian grid.905 For nonauagnuetie flows it uses the Piecewise Parabolic Method (PPM. ColellaandWoodward(198 1))}. aud for magnetic flows 1 uses (1x default} a Roc-type solver 1999).," For non-magnetic flows it uses the Piecewise Parabolic Method (PPM, \citet{c&w}) ), and for magnetic flows it uses (by default) a Roe-type solver \citep{powell}."906 The code uses dynamic Adaptive Mesh Refinement (AMR) techniqtes and is parallelized., The code uses dynamic Adaptive Mesh Refinement (AMR) techniques and is parallelized.907 The FLASII code is described further in Fivselletal.(2000)., The FLASH code is described further in \citet{FLASH}.908. ΕΤΑΡΗ version 2.5 does not include full radiative transfer that is coupatible with the àID modules. but does include a radiative cooling algorithim.," FLASH version 2.5 does not include full radiative transfer that is compatible with the MHD modules, but does include a radiative cooling algorithm."909 We replaced the default radiative cooling aeorithin with a more algoritlun derived from the Ctaetzctal.(1988) tables., We replaced the default radiative cooling algorithm with a more temperature-sensitive algorithm derived from the \citet{Gaetz} tables.910 Iu order to hold the undisturbed medium within the simulation erid at a constant temperature. we universally preveutec racdiaive cool1ο in cells whose temperatures were less than 15054 of the cells initial temperature.," In order to hold the undisturbed medium within the simulation grid at a constant temperature, we universally prevented radiative cooling in cells whose temperatures were less than $150\%$ of the cell's initial temperature."911 Tus coustraiwt also prevented disurbed gas from radiativolv cooling to a teniperature far below its initial temperature., This constraint also prevented disturbed gas from radiatively cooling to a temperature far below its initial temperature.912 Our coustraiit did no prevent adiabatic cooling., Our constraint did not prevent adiabatic cooling.913 The simulation erid was oriented with the irection perpendieular o the ealactic midplane and the . and 5g directions parallel to the midplane., The simulation grid was oriented with the $\hat{z}$ direction perpendicular to the galactic midplane and the $\hat{x}$ and $\hat{y}$ directions parallel to the midplane.914 In our simulatious witha naenetic field. Mode D has the magnetic field along the y-direction such that the three directions are unigte: the eraviational poteutial is 1ithe z-direction. the magnetic field is in the y-direction. aud the .c-direcion has ucitler a eravitatiοιal acceeration. nor a magnetic field parallel to it.," In our simulations with a magnetic field, Model B has the magnetic field along the $\hat{y}$ -direction such that the three directions are unique; the gravitational potential is in the $\hat{z}$ -direction, the magnetic field is in the $\hat{y}$ -direction, and the $\hat{x}$ -direction has neither a gravitational acceleration, nor a magnetic field parallel to it."915 Model € has the magnetic field along the directin such tha tl1C Orces 1ithe we and y direction are not qualitatively different: the eravitational acceleration and maeneic field are oth along tlic5 D-din ection., Model C has the magnetic field along the $\hat{z}$ -direction such that the forces in the $\hat{x}$ and $\hat{y}$ direction are not qualitatively different; the gravitational acceleration and magnetic field are both along the $\hat{z}$ -direction.916 For the simulations prescuted in this paper. we placed the supernova explosion a (rey.τν}=(0.0.100 pc). thus at the itersection of x=0 (v-z plano) Hid v=0 (x-z plane) aud midway up he + axis within the suuulatio1 eri.," For the simulations presented in this paper, we placed the supernova explosion at $(x,y,z) = (0,0,400$ pc), thus at the intersection of x=0 (y-z plane) and y=0 (x-z plane) and midway up the $\hat{z}$ axis within the simulation grid."917 The SNRs iare sviunietric across x-—U (v-z pane) aud vy=0 (x-z plane)., The SNRs are symmetric across x=0 (y-z plane) and y=0 (x-z plane).918 Therefore. it is possible to determine the properties of an eifie remnant from a simulation O: oulv one fourth of the remmaut. (," Therefore, it is possible to determine the properties of an entire remnant from a simulation of only one fourth of the remnant. ("919See Section 2.1.),See Section 2.1.)920 For the purpose of «escribing th(* boundary conditions required for a partial remmaut simulation. we ¢efine tljo Inner c boundary as he boundary wit ithe smallest coustaut . value. and outer «as the boundary with the largest constant e value.," For the purpose of describing the boundary conditions required for a partial remnant simulation, we define the inner $x$ boundary as the boundary with the smallest constant $x$ value, and outer $x$ as the boundary with the largest constant $x$ value."921 The inner ug. outeY og. 3uner τν and outer : boundarics are defined aiilogouslv.," The inner $y$, outer $y$, inner $z$, and outer $z$ boundaries are defined analogously."922 By sctting the explosion iu this location iux setting the |voundary coucditious aloug the iuner wand y planes to simulate reflection. we were able to simulate qialter reninants a1 hence reduce the needed CPU time aud nieruorv by," By setting the explosion in this location and setting the boundary conditions along the inner $x$ and $y$ planes to simulate reflection, we were able to simulate quarter remnants and hence reduce the needed CPU time and memory by."923 «As a check ou the accuracy of this tecllique. we also siated full remmauts to several hundred thorsaud vears. which we found to have mdistinguisliab5 temperature. density. and pressure structures as those of the «uarter remuiuts.," As a check on the accuracy of this technique, we also simulated full remnants to several hundred thousand years, which we found to have indistinguishable temperature, density, and pressure structures as those of the quarter remnants."924 Ax for the «ther boundary conditions. we used fixed boundary C4vlitions in the + direction aud outflow boundary conditious iu the « and y directions at he far .c and y sides.," As for the other boundary conditions, we used fixed boundary conditions in the $\hat{z}$ direction and outflow boundary conditions in the $\hat{x}$ and $\hat{y}$ directions at the far $x$ and $y$ sides."925 By fixed bouucarv couditious we mean that we fix the values at the nda such that they are coustaut in time aud suffhicieit fex the :uubieut medium to be in bydrostatic equilibrium., By fixed boundary conditions we mean that we fix the values at the boundary such that they are constant in time and sufficient for the ambient medium to be in hydrostatic equilibrium.926 Outflow |)ouudary conditioIs 1n he z directious would alow the remnant of the shock to leave the exid., Outflow boundary conditions in the $\hat{z}$ directions would allow the remnant of the shock to leave the grid.927" Ilowever. it is difficult to maintain IISE at the boundaries of tjo snmilatioi exid under normal circumstances (d.e. without a shock) when the boundary coxcditi)is are set to ""outfkw ."," However, it is difficult to maintain HSE at the boundaries of the simulation grid under normal circumstances (i.e. without a shock) when the boundary conditions are set to “outflow”."928Ii that case. züuubient material leaks off the exid. andl this ςisturbs IISE.," In that case, ambient material leaks off the grid, and this disturbs HSE."929 For this reason we haye used fixed bouncary conditiois at the upper aud lower + boundaries., For this reason we have used fixed boundary conditions at the upper and lower $\hat{z}$ boundaries.930" It tie whole exids were at the finest level 6ft refinement. the «ze o [the AMR exis wouldο «256 «512 cells for the simulation with uo maguetic fiecL aux 200BSL δι cels for the Emilation with the 1maeuetic field parallel to he midplane and 1604160 δ0ῦςells for the simulation wit1 the mae""neic field perpenten to the unidpane."," If the whole grids were at the finest level of refinement, the size of the AMR grids would be $\times$ $\times$ 512 cells for the simulation with no magnetic field and $\times$ $\times$ 384 cells for the simulation with the magnetic field parallel to the midplane and $\times$ $\times$ 800 cells for the simulation with the magnetic field perpendicular to the midplane."931 Where the density or pressure eradienut:s were arge (greater thaw ¢ifercuce in deusity. or iu pressure between adjacent cells).tle AMR subdiviced ¢els down.," Where the density or pressure gradients were large (greater than $\%$ difference in density, or $\%$ in pressure between adjacent cells),the AMR subdivided cells down."932 It will subdivide cells to volumes of ~1.25? pe?. iu, It will subdivide cells to volumes of $\stackrel{<}{\sim} 1.25^3$ $^{3}$.933toFor the simmlation with uo magnetic field. we divide the y and τ clirectious into EMi i)ocks aud dividet the.v ‘Mock.direction 2 blocks(a total of 18 blocks): we then allow5 levels o: rofiuenent for each bος. and & cells per sub," For the simulation with no magnetic field, we divide the $\hat{y}$ and $\hat{z}$ directions into 3 blocks and divide the $\hat{x}$ direction into 2 blocks (a total of 18 blocks); we then allow 5 levels of refinement for each block, and 8 cells per sub-block."934 For the simulation with a naenetic field parallel to the ddaue. we divide the z direction iuto 2 blocks: wihin each of these blocks we allow 6 evels ¢Xf refinement. aud 8 cells per sub-block.," For the simulation with a magnetic field parallel to the midplane, we divide the $\hat{z}$ direction into 2 blocks; within each of these blocks we allow 6 levels of refinement, and 8 cells per sub-block."935 En the sinulaion with a magnetic field perpendicular to the midplane. we divide the + direction iuto 5 blocks. audalow 5 Disheslevels of refinement in cachrheX‘kk: within each refined sub-block we ive 10 cells.," For the simulation with a magnetic field perpendicular to the midplane, we divide the $\hat{z}$ direction into 5 blocks, and allow 5 levels of refinement in each block; within each refined sub-block we have 10 cells."936 This vields a resohtion (at the level o refinement) of appre]whuately 1.25 pe in cach direction., This yields a resolution (at the highest level of refinement) of approximately 1.25 $pc$ in each direction.937 cleAvillez&Breitsclavcrdt(200 ESrowed hat such resolution Is wecessary auk sufficient for mocels of supernova reated eas in the interstellar miceiun., \cite{avillez_breit} showed that such resolution is necessary and sufficient for models of supernova heated gas in the interstellar medium.938 We cxupire our FLASII2.5 simulation with no imewnetie field with an carlicr sinulatiou we did with ZEUS-MP Nornuui2000:Stonectal.1992a.b.c) with 10 Magetic field and an explosion icieht of LOO pe.," We compare our FLASH2.5 simulation with no magnetic field with an earlier simulation we did with ZEUS-MP \citep{zeusmp,zeus2d_1,zeus2d_2,zeus2d_3} with no magnetic field and an explosion height of 400 pc."939 Our ZEUS-MP sinalation aad a deusitv eradieut that was a function of our eravitational potential and an isothermalbackeround at S10! K. Despite these differeuces; we still see a uimshroom shaped cloud at 8," Our ZEUS-MP simulation had a density gradient that was a function of our gravitational potential and an isothermal background at $\times 10^4$ K. Despite these differences, we still see a mushroom shaped cloud at 8"940where the gravitational mass within a sphere of radius + is determined by The metric fonction ó(r) is determined through the following dillerential equation: with the boundary condition at r=HR To proceed to the solution of these equations. it is necessary (ο provide the EOS οἱ stellar matter in the lorm P(e).,"where the gravitational mass within a sphere of radius $r$ is determined by The metric function $\phi(r)$ is determined through the following differential equation: with the boundary condition at $r=R$ To proceed to the solution of these equations, it is necessary to provide the EOS of stellar matter in the form $P(\epsilon)$."941 Starting from some central energy density e.=e(0) al the center of the star (Gr= 0). and with the initial condition (0)=0. the above equations can be integrated outward until the pressure vanishes. signilving that the stellar edge is reached.," Starting from some central energy density $\epsilon_c=\epsilon(0)$ at the center of the star $(r=0)$ , and with the initial condition $m(0)=0$, the above equations can be integrated outward until the pressure vanishes, signifying that the stellar edge is reached."942 Some care should be taken al 7=0 since. as seen above. the TOV equation is singular there.," Some care should be taken at $r=0$ since, as seen above, the TOV equation is singular there."943 The point r=R where the pressure vanishes defines the radius of the star and M—am(H)-—4xIno607Pedr’ its gravitational mass., The point $r=R$ where the pressure vanishes defines the radius of the star and $M=m(R)=4\pi\int_0^R\epsilon(r')r'^2dr'$ its gravitational mass.944 For a given EOS. there is a unique relationship between the stellar mass and the central density ε..," For a given EOS, there is a unique relationship between the stellar mass and the central density $\epsilon_c$."945 Thus. for à particular EOS. (here is a unique sequence of stis parameterized by the central density. (or equivalently (he central pressure ?(0)).," Thus, for a particular EOS, there is a unique sequence of stars parameterized by the central density (or equivalently the central pressure $P(0)$ )."946 Equations of stellar structure of (rapidly) rotating neutron stus are considerably more complex (han those of spherically svanmnetrie stars (Weber1999).., Equations of stellar structure of (rapidly) rotating neutron stars are considerably more complex than those of spherically symmetric stars \citep{Weber:1999a}.947 These complications arise due to the rotational delormations in rotating stars (i.e.. flattening at the poles and buleine al (he equator). which lead to a dependence of the stars metric on the polar coordinate 0.," These complications arise due to the rotational deformations in rotating stars (i.e., flattening at the poles and bulging at the equator), which lead to a dependence of the star's metric on the polar coordinate $\theta$."948 In addition. rotation stabilizes (he star against gravitational collapse and therefore rotating neuron stars are more massive (han static ones.," In addition, rotation stabilizes the star against gravitational collapse and therefore rotating neuron stars are more massive than static ones."949 A larger mass. however. causes greater curvature of space-time.," A larger mass, however, causes greater curvature of space-time."950 This renders the metric functions Irequency-dependent., This renders the metric functions frequency-dependent.951" Finally. the general relativistic effect of dragging the local inertial Games implies the occurrence of an additional non-diagonal term. feog. in the metric tensor fu?g""."," Finally, the general relativistic effect of dragging the local inertial frames implies the occurrence of an additional non-diagonal term, $g^{t\phi}$, in the metric tensor $g^{\mu\nu}$."952 This term imposes a condition onthe stellar structure equations. since the degree al which the local," This term imposes a self-consistency condition onthe stellar structure equations, since the degree at which the local"953"Although diffuse radio halos were discovered in clusters of galaxies more than 50 years ago (7), complete statistical information about them has only been forthcoming within the past decade, owing to their rarity, steep spectra, and low surface brightnesses.","Although diffuse radio halos were discovered in clusters of galaxies more than 50 years ago \citep{LARGE1959}, complete statistical information about them has only been forthcoming within the past decade, owing to their rarity, steep spectra, and low surface brightnesses."954" Radio surveys using the Very Large Array (VLA;???),, the Westerbork Synthesis Radio Telescope (WSRT;?),, and the Giant Metrewave Radio Telescope (GMRT;?) have detected ~30 radio halos at redshifts up to Z~0.5, along with a variety of smaller-scale radio features in clusters (?).."," Radio surveys using the Very Large Array \citep[VLA;][]{GIOVANNINI1999,Cohen2007,Giovannini2009a}, the Westerbork Synthesis Radio Telescope \citep[WSRT;][]{Kempner2001}, and the Giant Metrewave Radio Telescope \citep[GMRT;][]{Venturi2009} have detected $\sim 30$ radio halos at redshifts up to $z \sim 0.5$, along with a variety of smaller-scale radio features in clusters \citep{Kempner2004}."955" Only about 1/3 of massive (>1015 Mo) clusters are known to host radio halos, and the halos themselves are not associated with any particular member galaxy, but rather dispersed throughout the intracluster medium (ICM;?).."," Only about $1/3$ of massive $>10^{15} \msol$ ) clusters are known to host radio halos, and the halos themselves are not associated with any particular member galaxy, but rather dispersed throughout the intracluster medium \citep[ICM;][]{Feretti2004}."956" For clusters that do host halos, strong correlationsare seen between radio power and X-ray luminosity halo mass and gas velocity dispersion (?).. Also, (?"," For clusters that do host halos, strong correlationsare seen between radio power and X-ray luminosity \citep{Liang2000,Bacchi2003,Cassano2006,Brunetti2007}, halo mass \citep{Cassano2006}, and gas velocity dispersion \citep{Cassano2008}."957"??7?),,observations (?),,indicate a strong connection between the presence of a halo and morphological evidence for recent mergers (??7),, although some exceptions do exist "," Also, observations indicate a strong connection between the presence of a halo and morphological evidence for recent mergers \citep{Buote2001, Brunetti2009, Cassano2010c}, although some exceptions do exist \citep{Russell2011}."958"Indeed, recent simulations of merging clusters suggest (?)..that the fraction of turbulent clusters is roughly equal to the fraction of clusters hosting radio halos (?).."," Indeed, recent simulations of merging clusters suggest that the fraction of turbulent clusters is roughly equal to the fraction of clusters hosting radio halos \citep{Vazza2010a}."959" The proximate cause of diffuse radio halos is synchrotron emission by high-energy electrons in galaxy cluster magnetic fields, but the means of generating and accelerating these electrons remains an open question, since these electrons have relatively short (~0.1 Gyr) lifetimes."," The proximate cause of diffuse radio halos is synchrotron emission by high-energy electrons in galaxy cluster magnetic fields, but the means of generating and accelerating these electrons remains an open question, since these electrons have relatively short $\sim 0.1$ Gyr) lifetimes."960 ? proposed that cosmic-ray (CR) electrons are produced as secondary particles by collisions of >1 GeV CR protons with ambient thermal ICM protons., \citet{Dennison1980} proposed that cosmic-ray (CR) electrons are produced as secondary particles by collisions of $>1$ GeV CR protons with ambient thermal ICM protons.961" The CR protons can be accelerated by shocks and diffuse throughout the cluster; because of their larger mass, they have much longer synchrotron lifetimes than the electrons."," The CR protons can be accelerated by shocks and diffuse throughout the cluster; because of their larger mass, they have much longer synchrotron lifetimes than the electrons."962" This naturally explains the diffuse, cluster-wide properties of radio halos ?"," This naturally explains the diffuse, cluster-wide properties of radio halos \citep{Pfrommer2008,Blasi1999a}."963" and ? discuss a way in which the correlation (7?)..between radio and X-ray surface brightness can be explained by hadronic secondary-type models, although this approach requires an extremely strong magnetic field (~5µία at radii 1 Mpc for z=0.2— 0.4), which conflicts with some estimates of cluster magnetic fields (?).."," \citet{Kushnir2009} and \citet{Keshet2010b} discuss a way in which the correlation between radio and X-ray surface brightness can be explained by hadronic secondary-type models, although this approach requires an extremely strong magnetic field $\sim 5~\mg$ at radii $\sim 1$ Mpc for $z=0.2-0.4$ ), which conflicts with some estimates of cluster magnetic fields \citep{Bonafede2011}."964" Gamma-ray observations place limits on the abundance of high-energy protons, since in addition to producing charged pions that decay into the secondary electrons, the proton- collisions produce neutral pions, which decay into gamma-ray photons "," Gamma-ray observations place limits on the abundance of high-energy protons, since in addition to producing charged pions that decay into the secondary electrons, the proton-proton collisions produce neutral pions, which decay into gamma-ray photons \citep{Blasi1999,Wolfe2008}. ."965These observations indicate that hadronic CRs may (??)..contribute at most 5-1096 of the total pressure support in clusters (?).., These observations indicate that hadronic CRs may contribute at most $5$ $10$ of the total pressure support in clusters \citep{Ackermann2010}. .966 While gamma-ray, While gamma-ray967ranges considered.,ranges considered.968 Lt should. also be kept in mind. that the models represent. total luminositw of a galaxy. while the observations in practice are performed. with a eiven aperture (although ‘total Εαν) in photometry is attempted. as cliscussecl above)," It should also be kept in mind, that the models represent total luminosity of a galaxy, while the observations in practice are performed with a given aperture (although `total flux' in photometry is attempted, as discussed above)."969 1n general. the emission. [rom galaxies in near-Hi bands is due to the stellar contribution. the τμ carries information on the PALL contribution. and any strong 15[un emission would indicate warm dust.," In general, the emission from galaxies in near-IR bands is due to the stellar contribution, the $6.7\umu$ m carries information on the PAH contribution, and any strong $15 \umu$ m emission would indicate warm dust."970 There are thus several colour indices which may be useful in studying the relative strengths of these components and. processes., There are thus several colour indices which may be useful in studying the relative strengths of these components and processes.971 For example. the 6.7/15pun [ux ratio is expected to trace activity in the ISAL of galaxies.," For example, the $6.7/15 \umu$ m flux ratio is expected to trace activity in the ISM of galaxies."972 Figs., Figs.973 4 and 5 show the 6.7/15] ratio against. 2.2/15] and 6.7/15]., \ref{6715-vs-k15-ii} and \ref{6715-vs-k67} show the $[6.7/15]$ ratio against $[2.2/15]$ and $[6.7/15]$.974 Phe first compares the relative strength of the stellar ancl warm ISM component., The first compares the relative strength of the stellar and warm ISM component.975 Objects to the right are dominated by stellar emission. and those to the loft by warn dust. while the vertical axis tells about the heating activity and the relations of PAIHs and warm dust.," Objects to the right are dominated by stellar emission, and those to the left by warm dust, while the vertical axis tells about the heating activity and the relations of PAHs and warm dust."976 The second figure depicts the stellar PPALL contribution., The second figure depicts the stellar PAH contribution.977 To further study the 67/15] ratio. the ISOCAM bands are plotted. against each other in Fig. 6..," To further study the $[6.7/15]$ ratio, the ISOCAM bands are plotted against each other in Fig. \ref{15k-vs-7k},"978 normalizing with the NIIS lux. which in addition to stellar light is expected to be a good measure of stellar mass in a galaxy Ixaullmann Charlot 1998).," normalizing with the NIR flux, which in addition to stellar light is expected to be a good measure of stellar mass in a galaxy Kauffmann Charlot 1998)."979 The implications of this will be discussed more in Section 4.., The implications of this will be discussed more in Section \ref{discussion}.980 Aodels presented. in Section 3.1. are overplotted. in all the colour-colour figures for a range z=01., Models presented in Section \ref{models} are overplotted in all the colour-colour figures for a range $z = 0-1$.981 Note hat the UID. features move rapidly beyond. the 0 τμχ iler with redshift. which results in decreasing 6.7/15] in models including strong PALL emission. (especially Se and starbursts).," Note that the UIB features move rapidly beyond the $6.7 \umu$ m filter with redshift, which results in decreasing $[6.7/15]$ in models including strong PAH emission (especially Sc and starbursts)."982 The colour of Sa tvpe galaxies. on the other iand. starts to change only at z0.75.," The colour of Sa type galaxies, on the other hand, starts to change only at $z\sim0.75$."983 Lllipticals at. zero-redshift occupy the same region as red stars. as expected.," Ellipticals at zero-redshift occupy the same region as red stars, as expected."984 Most. of the ELAIS galaxies with data in both mid-LH ranicls appear to group at a region where the mocels predic ow-redshift. z=0.10.4. Iate-tvpe Se spirals.," Most of the ELAIS galaxies with data in both mid-IR bands appear to group at a region where the models predict low-redshift, $z=0.1 - 0.4$, late-type Sc spirals."985 According o the models. the near- to micd-LR SEDs of all spirals woule ook fairly similar at 2~1.," According to the models, the near- to mid-IR SEDs of all spirals would look fairly similar at $z\sim1$."986 However. it is unlikely that such objects are detected to the ELADIS survey limits.," However, it is unlikely that such objects are detected to the ELAIS survey limits."987 AGN on he other hand are expected to lie at the extreme upper righ in Fig., AGN on the other hand are expected to lie at the extreme upper right in Fig.988 6 due to their steeply rising continuum Lauren 2000)., \ref{15k-vs-7k} due to their steeply rising continuum Laurent 2000).989 The two mic-LR filters deteet surprisingly dilleren populations., The two mid-IR filters detect surprisingly different populations.990 As can be seen from Table 1. of the 97 identifie ealaxies which are from an areacovered with both maiicl-Lh bands. only 29 are common to both LW2 and LAWS.," As can be seen from Table 1, of the 97 identified galaxies which are from an areacovered with both mid-IR bands, only 29 are common to both LW2 and LW3."991 Phere are 55 galaxies detected only at L5pun. ancl 13 galaxies detector only at 6.7pun. For those ISOC'AM sources with a detection in only one micl-LRo band the JA colour might. provide additional clues.," There are 55 galaxies detected only at $15 \umu$ m, and 13 galaxies detected only at $6.7 \umu$ m. For those ISOCAM sources with a detection in only one mid-IR band the $J-K$ colour might provide additional clues."992 For example. starbursting galaxies shoulc have very red Jdy colours.," For example, starbursting galaxies should have very red $J-K$ colours."993 Fig., Fig.994 7 plots the 2.2/15] agains Joi., \ref{j-k_plot} plots the $[2.2/15]$ against $J-K$.995 While there are a number of sources with ared JA. they do not constitute a large population.," While there are a number of sources with a red $J-K$, they do not constitute a large population."996 More strikingly. compared to Figs.," More strikingly, compared to Figs."997 4. and 6.. there are many more sources at alow 2.215] ratio.," \ref{6715-vs-k15-ii} and \ref{15k-vs-7k}, there are many more sources at a low $[2.2/15]$ ratio."998 While the most extreme sources are too faint to acquire any definite morphological information from our data. we can constrain the nature of the sources missed in the 6.7 tun band by examining detections limits.," While the most extreme sources are too faint to acquire any definite morphological information from our data, we can constrain the nature of the sources missed in the 6.7 $\umu$ m band by examining detections limits."999 Since the 15 qum Duxes of the missed. 51. galaxies range from 1 to 3 mJ. typical 6.7/15] ratios should be around 0.45 to be consistent with the SO per cent LAV2 completeness limit detection limit.," Since the 15 $\umu$ m fluxes of the missed 51 galaxies range from 1 to 3 mJy, typical $[6.7/15]$ ratios should be around 0.45 to be consistent with the 80 per cent LW2 completeness limit detection limit."1000 This implies Se galaxies or starbursts around 2&0.15 or Sb's ab zo0.5., This implies Sc galaxies or starbursts around $z\approx 0.15$ or Sb's at $z\sim 0.5$.1001 Accordingly. most 2.2/15] ratios of the missed sources (empty squares in Fig. 7))," Accordingly, most $[2.2/15]$ ratios of the missed sources (empty squares in Fig. \ref{j-k_plot}) )"1002 do lie by the Sc and starburst mocel curves., do lie by the Sc and starburst model curves.1003 We also derived a rough estimate for rc expected 6.7 pun Dux from a mean correlation of 15/2.2] with 6.7/2.2]. using the ELALS sources in Fig.," We also derived a rough estimate for the expected 6.7 $\umu$ m flux from a mean correlation of $[15/2.2]$ with $[6.7/2.2]$, using the ELAIS sources in Fig."1004 6 and also | comparison sample discussed below in Section 3.3.., \ref{15k-vs-7k} and also a comparison sample discussed below in Section \ref{compsamp}.1005 The erivecd fi. (6.71) are shown in Fig. S.., The derived $f_{\nu}$ $\umu$ m) are shown in Fig. \ref{derseds}.1006" Galaxies with the lowest, 2.2/15] ratios fall below the LW2 detection limit while still being detected. in LAWS.", Galaxies with the lowest $[2.2/15]$ ratios fall below the LW2 detection limit while still being detected in LW3.1007 Lt is thus clear that 1e faintest late type spirals ancl starbursts make up the majority of LW2-missed. sources., It is thus clear that the faintest late type spirals and starbursts make up the majority of LW2-missed sources.1008 However. statistically we ga1ould. find only approximately 5 sources withL2 fluxes between 1 and 2 mJy in the figure.," However, statistically we should find only approximately 5 sources withLW2 fluxes between 1 and 2 mJy in the figure."1009 There are around 20. many of them with α 2.2/15] ratio typical of earlier type μαxrals (Sb's).," There are around 20, many of them with a $[2.2/15]$ ratio typical of earlier type spirals (Sb's)."1010 These might harbour some form of activity resulting in a lower than expected 6.7/15] ratio., These might harbour some form of activity resulting in a lower than expected $[6.7/15]$ ratio.1011 The objects seen in 6.7 pum but not in L5pun are plotted in Fig. 9.., The objects seen in $6.7\umu$ m but not in $15 \umu$ m are plotted in Fig. \ref{j-k_plot2}.1012 As seen there and in bie. S..," As seen there and in Fig. \ref{derseds},"1013 almost half of the LN3-missed objects appear to be ISM-deficient carly types., almost half of the LW3-missed objects appear to be ISM-deficient early types.1014 However. since the LAWS catalogue should be more than 90 per cent complete above 2 mv. the derived: fi (155m) at least for some of the galaxies might be too high.," However, since the LW3 catalogue should be more than 90 per cent complete above 2 mJy, the derived $f_{\nu}$ $15\umu$ m) at least for some of the galaxies might be too high."1015 Surprisingly. two confirmed. QSOs are among LW3-missed. objects. (see Section 4.3)).," Surprisingly, two confirmed QSOs are among LW3-missed objects (see Section \ref{qsos}) )."1016 However. numbers are small. and the 6.7 jun Iluxes are low. close to the detection limit. so it is cdiflicult to conclude anything definite.," However, numbers are small, and the 6.7 $\umu$ m fluxes are low, close to the detection limit, so it is difficult to conclude anything definite."1017 In order to compare our resulting ILES near- to mic-LR colours το a local sample of galaxies observed. with750. and to discuss how well the galaxy tvpes can be separated with near- and mid-Llt colours. we made use of the sets of Roussel et al. (," In order to compare our resulting ELAIS near- to mid-IR colours to a local sample of galaxies observed with, and to discuss how well the galaxy types can be separated with near- and mid-IR colours, we made use of the data-sets of Roussel et al. ("101820012). Dale et al. (,"2001a), Dale et al. ("10192000). and Bosclli et al. (,"2000), and Boselli et al. ("10201998).,1998).1021 Naturally. there exists a [large body. of work performed. withALS galaxies establishing near- ancl micIt databases Spinoglio 1995). however. to avoid complications of band conversions we restrict ourselves only to recent £5O-data.," Naturally, there exists a large body of work performed with galaxies establishing near- and mid-IR databases Spinoglio 1995) – however, to avoid complications of band conversions we restrict ourselves only to recent -data."1022 Ehe Itoussel et sset consists of nearby spirals. ancl it includes a subset of the DBoselli sample. which are Vireo cluster. galaxies.," The Roussel et set consists of nearby spirals, and it includes a subset of the Boselli sample, which are Virgo cluster galaxies."1023 The Dale ct ssample are galaxies from the 750 U.S. kev Project “Normal Galaxies’., The Dale et sample are galaxies from the U.S. Key Project `Normal Galaxies'.1024 The main dillicultv in the comparison are the various photometric techniques used both in the near-H11. and 750 data (see Spinoglio 1995)., The main difficulty in the comparison are the various photometric techniques used both in the near-IR and data (see Spinoglio 1995).1025 A large number of the nearby galaxies have near-LR. data available from NED., A large number of the nearby galaxies have near-IR data available from NED.1026 llowever. to have consistent. photometry we decided. to," However, to have consistent photometry we decided to"1027we obtain an medication for /2507.,we obtain an indication for $i\simeq50^{\circ}$.1028 The two peaks in the amplitide spectzuui DET. described i the previous section. could also be due to the period spacing between inodes with successive overtones.," The two peaks in the amplitude spectrum DFT, described in the previous section, could also be due to the period spacing between modes with successive overtones."1029 Iu Figure 7 (left panels) we show the DFT of the period spectrum (amplitude spectrum in the period ¢olain)., In Figure 7 (left panels) we show the DFT of the period spectrum (amplitude spectrum in the period domain).1030 For the upper panel we used a subset of the period spectrum with periods between 1000 aid ss. while or the lower panel we used a narrower part with periods spanning sx. Excluding the peak at about ss. which is related to the one dav alias as discussed iu he previous section. the most significant period spacings are ss and bss (at least iu the lower evapl: in the upper eraph the Lss peak appears more uncertain).," For the upper panel we used a subset of the period spectrum with periods between 1000 and s, while for the lower panel we used a narrower part with periods spanning s. Excluding the peak at about s, which is related to the one day alias as discussed in the previous section, the most significant period spacings are s and s (at least in the lower graph; in the upper graph the s peak appears more uncertain)."1031 Their ratio is close (aceuracv better fwu )) to the asvimptotic value of 3. sugecstingOO that 18.5 and Lss might correspoud to the l=1 aud 172 period spacings.," Their ratio is close (accuracy better than ) to the asymptotic value of $\sqrt{3}$, suggesting that 18.8 and s might correspond to the l=1 and l=2 period spacings."1032 In this lhiypothlesis. the differences between the wo left panels of Figure 7 sugeest hat the 122 modes might be present oulv (or mainly) iu he high-uuplitude region between 2000 and ss. An attempt to confirm he hypothesis tha the modes of 22521 are equally spaced im period (aud not iu yequency) has been done applying the IKohlnogorov-Sumurunov (Is-S) test (I[Niwaler 1988) aud the Inverse Variance techuique (O'Donoghue 1991) to the first 12 periods listed im Table 2 (excluding the linear colubinations).," In this hypothesis, the differences between the two left panels of Figure 7 suggest that the l=2 modes might be present only (or mainly) in the high-amplitude region between 2000 and s. An attempt to confirm the hypothesis that the modes of 2324 are equally spaced in period (and not in frequency) has been done applying the Kolmogorov-Smirnov (K-S) test (Kawaler 1988) and the Inverse Variance technique (O'Donoghue 1994) to the first 12 periods listed in Table 2 (excluding the linear combinations)."1033 The results. reported iu Figure 7 (right panels). do not confrii that the modes are equally spaced iu period.," The results, reported in Figure 7 (right panels), do not confirm that the modes are equally spaced in period."1034 Moreover. the lack of amy siguificaut period spacing further indicates that the period list is nof complete," Moreover, the lack of any significant period spacing further indicates that the period list is not complete."1035 Nothing nav be said about the trapped modes phenomenon apart the following., Nothing may be said about the trapped modes phenomenon apart the following.1036 The ratio between the, The ratio between the1037distributed more smoothly than MS stars (Fig.,distributed more smoothly than MS stars (Fig.1038 6bb). however their surface deusity is larger in the ligh-surlace-brightness part of the main body.," \ref{Fig6}b b), however their surface density is larger in the high-surface-brightness part of the main body."1039 As for the AGB aud RGB stars. they show a smooth distribution over the whole WEPC? field of view (Fig.," As for the AGB and RGB stars, they show a smooth distribution over the whole WFPC2 field of view (Fig."1040 Gee — 6dd)., \ref{Fig6}c c – \ref{Fig6}d d).1041 There is a clear correlation of he spatial extent of a stellar population with its age: the older the stellar population. tle smoother auc more extended is its spatial distribution.," There is a clear correlation of the spatial extent of a stellar population with its age: the older the stellar population, the smoother and more extended is its spatial distribution."1042 Such population gradieuts have been known for a loug lune. starting with the pioneering studies of the Milky Way by Walter Baade in the 1950s.," Such population gradients have been known for a long time, starting with the pioneering studies of the Milky Way by Walter Baade in the 1950's."1043 They lave also been observed in other dwarl galaxies resolved byHST (e.g..Lyudsetal.1998:Schulte-Ladbecketal.1998:Crone2000:Izotov&Thuan 2002).," They have also been observed in other dwarf galaxies resolved by \citep[e.g.,][]{Ly98,Sc98,Cr00,Iz02}."1044. They are likely a consequeuce of the diffusion aud relaxation processes of stellar eusenmibles., They are likely a consequence of the diffusion and relaxation processes of stellar ensembles.1045 We discuss next selected regious of NGC 2366 in more cetail., We discuss next selected regions of NGC 2366 in more detail.1046 Nlost of the regious I (= NGC 2363 = Mrk 71) aud HE have been imaged with the PC. although some parts of region II are also in the WEI frame (Fig. 1)).," Most of the regions I $\equiv$ NGC 2363 $\equiv$ Mrk 71) and II have been imaged with the PC, although some parts of region II are also in the WF4 frame (Fig. \ref{Fig1}) )."1047 Fig., Fig.1048 7 shows zoomed V. aud 7 views of the two regions., \ref{Fig7} shows zoomed $V$ and $I$ views of the two regions.1049 Widespread ionized gas emission resulting mainly from strong [O riu] A5007 line enission. can be seeu iu the V. image (Fig.," Widespread ionized gas emission resulting mainly from strong [O ] $\lambda$ 5007 line emission, can be seen in the $V$ image (Fig."1050 Yaa)., \ref{Fig7}a a).1051 However. exteuclecl iouized gas eimission is also present in the J image (Fig.," However, extended ionized gas emission is also present in the $I$ image (Fig."1052 ΤΟ). iu tliis case beiug mainly. gaseous continuuur eiuission.," \ref{Fig7}b b), in this case being mainly gaseous continuum emission."1053 Regiou I contains two young compact clusters which we label A aud B following je notation of (2000)., Region I contains two young compact clusters which we label A and B following the notation of \citet{Dr00}.1054. They are marked by circles in Fig., They are marked by circles in Fig.1055 Tob. The LBV star discovered by is labeled as V1., \ref{Fig7}b b. The LBV star discovered by \citet{Dr97} is labeled as V1.1056 Unfortunately. the LBV star is saturated in both our V. aud / images and cluster A is saturated in the V. image. preventing us from performing photometryRm) of these two objects in those bauds.," Unfortunately, the LBV star is saturated in both our $V$ and $I$ images and cluster A is saturated in the $V$ image, preventing us from performing photometry of these two objects in those bands."1057 Fig Taa shows that the ionization of the gas in region[n] I is mostly caused by cluster A. The ionization of the eeas in reeione II is not as important. sugeestiugMODOm that extremely vouug massive stars are absent there.," Fig \ref{Fig7}a a shows that the ionization of the gas in region I is mostly caused by cluster A. The ionization of the gas in region II is not as important, suggesting that extremely young massive stars are absent there."1058 Fig., Fig.1059 ΤΟ shows also the presence of uunerous bright RSC stars in region II., \ref{Fig7}b b shows also the presence of numerous bright RSG stars in region II.1060 A more detailed view of region Lin { and V.—Jf is shown iu Fig. 8.., A more detailed view of region I in $I$ and $V-I$ is shown in Fig. \ref{Fig8}.1061 Although both clusters A aud B are very compact (Fig., Although both clusters A and B are very compact (Fig.1062 Saa). they are margiually resolved.," \ref{Fig8}a a), they are marginally resolved."1063 The FWHM. of circular-shaped cluster A on the J image (which is not saturated) is 3.5 pixels or 2.8 pc. similar to the super-star cluster (SSC) Ro 136a in the Large Magellanic Cloud. aud to σος iu other galaxies.," The FWHM of circular-shaped cluster A on the $I$ image (which is not saturated) is 3.8 pixels or 2.8 pc, similar to the super-star cluster (SSC) R 136a in the Large Magellanic Cloud and to SSCs in other galaxies."1064 The FWHM oL elongated-shaped cluster B is larger. being  L7 pixels or ~ 3.5 pe.," The FWHM of elongated-shaped cluster B is larger, being $\sim$ 4.7 pixels or $\sim$ 3.5 pc."1065 Both clusters are blue as evideuced from the V—£ image (Fig., Both clusters are blue as evidenced from the $V-I$ image (Fig.1066 Sbb) with cluster A being slightly redder because of eulianced dust extinction (Drissenetal.2000) aud saturation of the ceutral pixels of its V. image., \ref{Fig8}b b) with cluster A being slightly redder because of enhanced dust extinction \citep{Dr00} and saturation of the central pixels of its $V$ image.1067 The relatively high internal extinction in cluster A (αν ~ 0.3 mag) is confirmed by spectroscopic observations (Masegosaetal.1991:Ciouzález-DelgadoIzotov&Hollman1999:Noeskeetal. 2000).," The relatively high internal extinction in cluster A $A_V$ $\sim$ 0.3 mag) is confirmed by spectroscopic observations \citep{Ma91,Go94,Iz97,Hu99,No00}."1068. In fact. Fig.," In fact, Fig."1069 Sbb shows that extinction is not coulined to cluster A. It is also present in the exteucded red region (white in Figure 8bb) to the south of cluster A. The red color of this region is due partly to two bright RSC stars aid a few other fainter stars. but also to dust.," \ref{Fig8}b b shows that extinction is not confined to cluster A. It is also present in the extended red region (white in Figure \ref{Fig8}b b) to the south of cluster A. The red color of this region is due partly to two bright RSG stars and a few other fainter stars, but also to dust."1070"old and young populations decreases wilh increasing halo mass up to Afzz10.U,. al which the voung population starts to surpass the old population in (he bias factor.","old and young populations decreases with increasing halo mass up to $M\approx 10 M_{\ast}$, at which the young population starts to surpass the old population in the bias factor."1071" For M>20.M,. the bias factor lor the voung population is about 1054 higher than that of the old population. with weak dependence on halo mass."," For $M>20M_{\ast}$, the bias factor for the young population is about $10\%$ higher than that of the old population, with weak dependence on halo mass."1072 Although the difference in the bias factor between the old and voung populations is small at the high mass end. it is detected al a high statistical confidence (~106).," Although the difference in the bias factor between the old and young populations is small at the high mass end, it is detected at a high statistical confidence $\sim107310\sigma$ )."1074 The concentration of each halo is obtained following the fitting method of Jing(2000)., The concentration of each halo is obtained following the fitting method of \citet{jing00}.1075". The density distribution within each halo is fitted with a NEW profile to obtain the scale radius ry. and the concentration is defined as ¢—Γης. where r,. is the virial radius within which the mean densitv is 361 times (he mean density of the universe."," The density distribution within each halo is fitted with a NFW profile to obtain the scale radius $r_s$, and the concentration is defined as $c=r_v/r_s$, where $r_v$ is the virial radius within which the mean density is 361 times the mean density of the universe."1076 Here only halos with 320 particles or more are used. because the concentration mav not be measured accurately or halos containing; smaller number of particles (e.g.Wechsleretal.2006).," Here only halos with 320 particles or more are used, because the concentration may not be measured accurately for halos containing smaller number of particles \citep[e.g.][]{Wechsler06}."1077". The lower (wo panels of Figure 3. show the bias factoras a function of wavenumber or massive halos with M=35.M, and Af=134V,.", The lower two panels of Figure \ref{fig:fig1} show the bias factoras a function of wavenumber for massive halos with $M=35 M_{\ast}$ and $M=134 M_{\ast}$.1078 Results for the least concentrated. are plotted in the lower left panel. while those for the most concentrated are in the ower right panel.," Results for the least concentrated are plotted in the lower left panel, while those for the most concentrated are in the lower right panel."1079 Ποιο again. (he bias [actor is almost scale-independent.," Here again, the bias factor is almost scale-independent."1080 The amplitude of the bias factor for massive halos clearly depends on concentration. wilh halos with higher concentration less strongly biased.," The amplitude of the bias factor for massive halos clearly depends on concentration, with halos with higher concentration less strongly biased."1081 To see how the concentration-dependence changes with halo mass. we plot in (he lower panel of Figure 4. the bias [actor for the most concentraed and the least concentrated of the halos in each of the mass bins.," To see how the concentration-dependence changes with halo mass, we plot in the lower panel of Figure \ref{fig:fig2} the bias factor for the most concentraed and the least concentrated of the halos in each of the mass bins."1082 Note that there is eood agreement between simulations with different box sizes. suggesting that 320 particles nav be sullicient to sample the concentration Lor (he purpose of (he present paper.," Note that there is good agreement between simulations with different box sizes, suggesting that 320 particles may be sufficient to sample the concentration for the purpose of the present paper."1083"Our results show clearly that the more concentrated halos have a larger bias for Af<AL...but the trend is reversed [ον Af>M,. in qualitative agreement wilh the results in Wechslerοἱal.(2006).","Our results show clearly that the more concentrated halos have a larger bias for $M<M_{\ast}$,but the trend is reversed for $M>M_{\ast}$, in qualitative agreement with the results in \citet{Wechsler06}."1084" Comparing the results here with the dependence on the formation epoch (the upper panel). we see (hal the concentration dependence is weaker (han (he age dependence [or AMP<M,. but stronger for Af29. M,."," Comparing the results here with the dependence on the formation epoch (the upper panel), we see that the concentration dependence is weaker than the age dependence for $M<M_{\ast}$, but stronger for $M \gg M_{\ast}$ ."1085" The difference in the bias factor between the most concentrated and the least concentrated is about [or M=LOAL, - LOOAL,. larger than the between the voungest and oldest 20%."," The difference in the bias factor between the most concentrated and the least concentrated is about for $M=10M_{\ast}$ - $100 M_{\ast}$, larger than the between the youngest and oldest ."1086". This may be why concentration dependence was but age dependence was not found [or halos with AM2Ad‘, in previous investigations (Gaoetal.2005:Zhu2006:WechslerWetzelοἱ2006)."," This may be why concentration dependence was but age dependence was not found for halos with $M>M_{\ast}$ in previous investigations \citep{gao05,zhu06,Wechsler06,white06}."1087". Our results also show that the concentration dependence reverses almost exactly at Af= AL,. while the reversal of agedependence occurs al a much larger mass. Afzz 10,."," Our results also show that the concentration dependence reverses almost exactly at $M=M_{\ast}$ , while the reversal of agedependence occurs at a much larger mass, $M \approx 10 M_{\ast}$ ."1088 Finally.," Finally,"1089observable NieAds.A).,"observable $N (>M_{\rm ap},\theta)$."1090 We have plotted. this observable in Figure 5 às a function. of the aperture mass., We have plotted this observable in Figure \ref{numbermap} as a function of the aperture mass.1091" The dependence of (37)) on Ady, ancl 8 can be understood. as ollows: Since the aperture mass. May is a monotonically increasing function of the halo mass (for a fixed. reclshilt and filter scale: see Figure. 1)) we expect ING»Alas8) o decrease with increasing AZ. Hf."," The dependence of \ref{number}) ) on $M_{\rm ap}$ and $\theta$ can be understood as follows: Since the aperture mass $M_{\rm ap}$ is a monotonically increasing function of the halo mass (for a fixed redshift and filter scale; see Figure \ref{map}) ) we expect $N (>M_{\rm ap},\theta)$ to decrease with increasing $M_{\rm ap}$."1092" we enlarge the filter radius the values of Mj become smaller and. because of he monotony of AA, in the halo mass. for fixed. AM, he corresponding threshold mass My, increases."," If we enlarge the filter radius the values of $M_{\rm ap}$ become smaller and, because of the monotony of $M_{\rm ap}$ in the halo mass, for fixed $M_{\rm ap}$ the corresponding threshold mass $M_{\rm t}$ increases."1093 Therefore he number of haloes decreases with increasing filter size., Therefore the number of haloes decreases with increasing filter size.1094" Because of this behaviour of NC»Ad...) we can select a ilter radius ancl a value for Ady, which allows us to count a sullicient number of haloes used for finding a significant dilference between the various cosmologies."," Because of this behaviour of $N (>M_{\rm ap},\theta)$ we can select a filter radius and a value for $M_{\rm ap}$ which allows us to count a sufficient number of haloes used for finding a significant difference between the various cosmologies."1095 In. practice we have to determine a signal-to-noise ratio threshold. above which we can consider a significant detection., In practice we have to determine a signal-to-noise ratio threshold above which we can consider a significant detection.1096 We will use here mainly a threshold value of S.—5., We will use here mainly a threshold value of $S_{\rm c}=5$.1097 In Figure 4. we have plotted the number of haloes per square degree with aperture masses vielding a signal-to-noise ratio above the threshold. value S.=5 for cdilferent. filter scales., In Figure \ref{snoise} we have plotted the number of haloes per square degree with aperture masses yielding a signal-to-noise ratio above the threshold value $S_{\rm c}=5$ for different filter scales.1098 Xecording to Figure 4 we count in all cosmologies the maximum number of haloes for ϐ=2aremin., According to Figure \ref{snoise} we count in all cosmologies the maximum number of haloes for $\theta=2 \ \mbox{arcmin}$.1099 We will use this ‘optimal’ filter scale for our calculations., We will use this `optimal' filter scale for our calculations.1100" According to (30)) the corresponding aperture mass is Ma,=0.04 for the ""optimal filter radius and the signal-to-noise ratio threshold.", According to \ref{sig1}) ) the corresponding aperture mass is $M_{\rm ap}=0.04$ for the `optimal' filter radius and the signal-to-noise ratio threshold.1101in GX 339-4 (see Figure 9).,in GX $-$ 4 (see Figure 9).1102 Moreover. a broad. relativistic Fe Ka emission line i5 revealed. which ts again suggestive of a disk which extends to 6GM/c7 or less (see Figure 10).," Moreover, a broad, relativistic Fe $\alpha$ emission line is revealed, which is again suggestive of a disk which extends to $6~GM/c^{2}$ or less (see Figure 10)."1103 Before including a disk component. the best fit statistic that can be achieved with this power-law index is y/r15.000/764.," Before including a disk component, the best fit statistic that can be achieved with this power-law index is $\chi^{2}/\nu > 15,000/764$ ."1104 Allowing the column density to float within of the standard value. which is a common deviation between instruments. an improved fit was again found.," Allowing the column density to float within of the standard value, which is a common deviation between instruments, an improved fit was again found."1105" Next including ""diskbb"" and ""laor"" line components each separately improved the fit at more than the 86 level confidence.", Next including “diskbb” and “laor” line components each separately improved the fit at more than the $\sigma$ level confidence.1106" This simple model yielded the following parameters: kT=0.22(1) keV for Rj,=5.8(6)R, (assuming d=2.5 kpe. /230°. and M210.. Miller et 22002b. Herrero et 11995). Ejj,,=6.9007) keV for Ri,=6(2)Ry. Wine=250630) eV. T=1.85(5). and v/v=1317/7539."," This simple model yielded the following parameters: $kT = 0.22(1)$ keV for $R_{in} = 5.8(6)~R_{g}$ (assuming $d=2.5$ kpc, $i=30^{\circ}$ , and $M=10~M_{\odot}$, Miller et 2002b, Herrero et 1995), $E_{line} = 6.90(7)$ keV for $R_{line} = 6(2)~R_{g}$, $W_{line}1107= 250(30)$ eV, $\Gamma = 1.85(5)$, and $\chi^{2}/\nu = 1317/759$."1108 Again. radii inferred from disk continuum fits must be regarded cautiously. though in this case the radius is still broadly consistent with the [SCO after inner torque and hardening corrections are made (see Zimmerman et 22004: Merlont. Fabian. Ross 2000).," Again, radii inferred from disk continuum fits must be regarded cautiously, though in this case the radius is still broadly consistent with the ISCO after inner torque and hardening corrections are made (see Zimmerman et 2004; Merloni, Fabian, Ross 2000)."1109 The fit is not formally acceptable due to instrumental response errors around 2 keV: however. the statistical need for disk and disk line components does not arise due to response Issues.," The fit is not formally acceptable due to instrumental response errors around 2 keV; however, the statistical need for disk and disk line components does not arise due to response issues."1110 To explore the low/hard state at a lower fraction of the Eddington limit. Ly/Lj;;—0.001. we began a new investigation of the Chandra/LETGS spectrum of XTE J11184480 in the low-hard state (see McClintock et 22001. Miller et 220026).," To explore the low/hard state at a lower fraction of the Eddington limit, $L_{X}/L_{Edd} \simeq 0.001$, we began a new investigation of the /LETGS spectrum of XTE $+$ 480 in the low–hard state (see McClintock et 2001, Miller et 2002c)."1111 There is potential evidence for a cool X-ray disk remaining at the ISCO in this spectrum also., There is potential evidence for a cool X-ray disk remaining at the ISCO in this spectrum also.1112 However. to make a robust determination. remaining uncertainties in the instrumental response and spectrum itself must be investigated m full. and we will report on this analysis in a later paper.," However, to make a robust determination, remaining uncertainties in the instrumental response and spectrum itself must be investigated in full, and we will report on this analysis in a later paper."1113 We have conducted an analysis of andRXTE spectra of GX 339—4 in a low-hard state., We have conducted an analysis of and spectra of GX $-$ 4 in a low–hard state.1114 Our results suggest that a standard cool accretion disk may extend to the innermost stable circular orbit in the low-hard state., Our results suggest that a standard cool accretion disk may extend to the innermost stable circular orbit in the low–hard state.1115 In a brief analysis of archival spectrum. we find that similar results are readily obtained for Cygnus X-1.," In a brief analysis of archival spectrum, we find that similar results are readily obtained for Cygnus X-1."1116 Moreover. a spectrum recently obtained from the black hole candidate SWIFT J1753.5—0127 (Miller. Homan. Miniutti 2006) during the decline of its outburst appears to support this disk geometry.," Moreover, a spectrum recently obtained from the black hole candidate SWIFT $-$ 0127 (Miller, Homan, Miniutti 2006) during the decline of its outburst appears to support this disk geometry."1117 Although we observed GX 339-4 in a rising phase. SWIFT J1753.5—0127 was observed during outburst decline. and Cygnus X-] is à persistent. source. suggesting that disks may commonly remain at or close to the ISCO in bright phases of the low—hard state.," Although we observed GX $-$ 4 in a rising phase, SWIFT $-$ 0127 was observed during outburst decline, and Cygnus X-1 is a persistent source, suggesting that disks may commonly remain at or close to the ISCO in bright phases of the low–hard state."1118 These results have a number of consequences., These results have a number of consequences.1119 Transitions between low-hard and high-soft states in black hole binaries may not necessarily signal a change in inner disk radius., Transitions between low–hard and high–soft states in black hole binaries may not necessarily signal a change in inner disk radius.1120 Moreover. in apparent contrast to the absence of Jets in disk-dominated high-soft states (see. e.g.. Fender. Belloni. Gallo 2004). it may be possible to maintain a compact. steady jet while the disk remains at the innermost stable circular orbit.," Moreover, in apparent contrast to the absence of jets in disk-dominated high–soft states (see, e.g., Fender, Belloni, Gallo 2004), it may be possible to maintain a compact, steady jet while the disk remains at the innermost stable circular orbit."1121 Homan et ((2001) noted that state transitions may be partly related to changes in the corona: our results strengthens this suggestion., Homan et (2001) noted that state transitions may be partly related to changes in the corona; our results strengthens this suggestion.1122 The idea that a transition into the low-hard state marks the onset of an ADAF with a truncated inner disk (e.g.. Esin. MeClintock. Narayan 1997) has become a near-paradigm m studies of acereting black holes.," The idea that a transition into the low–hard state marks the onset of an ADAF with a truncated inner disk (e.g., Esin, McClintock, Narayan 1997) has become a near-paradigm in studies of accreting black holes."1123 Our results suggest that an optically-thick aceretion disk with properties closely related to disks observed at higher inferred accretion rates can operate in the low-hard state., Our results suggest that an optically-thick accretion disk with properties closely related to disks observed at higher inferred accretion rates can operate in the low–hard state.1124 However. simple theoretical considerations suggest that it is very unlikely that a standard thin disk is part of the inner accretion flow in quiescence.," However, simple theoretical considerations suggest that it is very unlikely that a standard thin disk is part of the inner accretion flow in quiescence."1125 Observational evidence also appears to rule-out the possibility of a standard accretion disk at the ISCO in quiescence (see. e.g.. MeClintock. Horne. Remillard 1995).," Observational evidence also appears to rule-out the possibility of a standard accretion disk at the ISCO in quiescence (see, e.g., McClintock, Horne, Remillard 1995)."1126 By extension. then. our findings suggest that the accretion flow geometry in quiescence may not be a simple extrapolation of the geometry of the flow in the low—hard state.," By extension, then, our findings suggest that the accretion flow geometry in quiescence may not be a simple extrapolation of the geometry of the flow in the low–hard state."1127 Fits to the spectra with reflection models reveal a covering fraction significantly less than unity (see Table 2). consistent with prior disk reflection fits in. the. low-hard. state (e.g. Gierlinski et 11997).," Fits to the spectra with reflection models reveal a covering fraction significantly less than unity (see Table 2), consistent with prior disk reflection fits in the low–hard state (e.g. Gierlinski et 1997)."1128 While a recessed disk would serve to give less disk reflection. this possibility is inconsistent with our results.," While a recessed disk would serve to give less disk reflection, this possibility is inconsistent with our results."1129 A hard component which is mildly beamed away from the disk provides a plausible way to reconcile these findings., A hard component which is mildly beamed away from the disk provides a plausible way to reconcile these findings.1130 Beloborodov (1999) described a model wherein the corona is fed by magnetic flares from the disk. and the height of such flares determines the nature of the corona.," Beloborodov (1999) described a model wherein the corona is fed by magnetic flares from the disk, and the height of such flares determines the nature of the corona."1131 In the hard state. the flares reach mildly relativistic velocities (v/c——0.3). sufficient to mildly beam the hard X-ray emission away from the disk.," In the low--hard state, the flares reach mildly relativistic velocities $v/c \simeq 0.3$ ), sufficient to mildly beam the hard X-ray emission away from the disk."1132 A broadly similar scenario has been described by Merloni Fabian (2002): in that work. the ability of a magnetically—dominated corona to launch jets is considered.," A broadly similar scenario has been described by Merloni Fabian (2002); in that work, the ability of a magnetically–dominated corona to launch jets is considered."1133 These models may give insight into how disks might be connected to jets through a corona. and/or give a sense of how a corona might act as the base of a jet.," These models may give insight into how disks might be connected to jets through a corona, and/or give a sense of how a corona might act as the base of a jet."1134 Separately. the possible role of a jet in producing hard X-ray emission in the low-hard state has been discussed in detail.," Separately, the possible role of a jet in producing hard X-ray emission in the low–hard state has been discussed in detail."1135 Markoff. Falcke. Fender (2001) suggested that all of the hard X-ray emisstor in XTE 311184480. may be due to the steady. compact jet implied by radio observations.," Markoff, Falcke, Fender (2001) suggested that all of the hard X-ray emission in XTE $+$ 480 may be due to the steady, compact jet implied by radio observations."1136 Subsequent studies have focusec more on the role of synchrotron self-Comptonization: in. this sense. they partially bridge the gap between synchrotron-dominated jet models and traditional thermal Comptonizatior models of the corona.," Subsequent studies have focused more on the role of synchrotron self-Comptonization; in this sense, they partially bridge the gap between synchrotron--dominated jet models and traditional thermal Comptonization models of the corona."1137 Markoff Nowak (2004) have showed that the level of disk reflection predicted by jet-dominated emission models is consistent with observations., Markoff Nowak (2004) have showed that the level of disk reflection predicted by jet-dominated emission models is consistent with observations.1138 While our deep observation of GX 339—4 may provide the most convincing evidence that a standard thin disk is important in the low—hard state. it is not the first such evidence.," While our deep observation of GX $-$ 4 may provide the most convincing evidence that a standard thin disk is important in the low–hard state, it is not the first such evidence."1139 Prior reports of cool disks in the low-hard state have sometimes been overlooked and/or regarded skeptically., Prior reports of cool disks in the low–hard state have sometimes been overlooked and/or regarded skeptically.1140. A cool. soft excess in the low-hard state spectrum of Cygnus X-1 was previously reported by Ebisawa et ((1996). in the same spectrum we considered above.," A cool soft excess in the low–hard state spectrum of Cygnus X-1 was previously reported by Ebisawa et (1996), in the same spectrum we considered above."1141 The presence of a cool thermal component in the low-hard state of Cygnus X-] can be traced back much farther: Barr van der Woerd (1990) and Balucinska Hasinger (1991) both reported that à soft excess was required to describe the low—-hard state spectrum of Cygnus ΧΙ., The presence of a cool thermal component in the low–hard state of Cygnus X-1 can be traced back much farther: Barr van der Woerd (1990) and Balucinska Hasinger (1991) both reported that a soft excess was required to describe the low–hard state spectrum of Cygnus X-1.1142 The interpretation of this component as a disk was complicated by the possibility that the black hole may partially accrete from the wind of its massive companion., The interpretation of this component as a disk was complicated by the possibility that the black hole may partially accrete from the wind of its massive companion.1143 However. such a wind is clearly not present in GX 339—4. and the evidence for a disk in the low-hard state of GX 339-4 supports the disk interpetation of the soft component in Cygnus X-I.," However, such a wind is clearly not present in GX $-$ 4, and the evidence for a disk in the low–hard state of GX $-$ 4 supports the disk interpetation of the soft component in Cygnus X-1."1144 If à disk interpretation of this component was doubted because the black hole maypartially aecrete via the wind from its massive companion. the clear evidence for a disk in the low- binary GX 339-4 should make its interpretation clear.," If a disk interpretation of this component was doubted because the black hole maypartially accrete via the wind from its massive companion, the clear evidence for a disk in the low-mass binary GX $-$ 4 should make its interpretation clear."1145the right-hand side of (1)).,the right-hand side of \ref{eq:split}) ).1146 However. when these galaxies are subject to the tidal gravitational force of the same matter structure (e.g. they formed under the influence of the same massive dark matter halo). their shapes can intrinsically align and become correlated. giving rise to a nonvanishing III term.," However, when these galaxies are subject to the tidal gravitational force of the same matter structure (e.g. they formed under the influence of the same massive dark matter halo), their shapes can intrinsically align and become correlated, giving rise to a nonvanishing III term."1147 Furthermore. GGI and GI terms can be generated when a matter structure tidally influences close-by galaxies and at the same time contributes to the shear signal of background objects. leading to correlations among them.," Furthermore, GGI and GII terms can be generated when a matter structure tidally influences close-by galaxies and at the same time contributes to the shear signal of background objects, leading to correlations among them."1148 In two-point statistics. the corresponding intrinsic (IL) and intrinsic-shear (GI) terms have been subject to detailed studies both theoretically(e.g. Catelanetal.(2001):Croft&Metzler (2010)))," In two-point statistics, the corresponding intrinsic (II) and intrinsic-shear (GI) terms have been subject to detailed studies both theoretically(e.g. \citet{catelan01, croft00, heavens00, hui02, mackey02, jing02, hirata04, heymans06, bridle07, schneider09}) )"1149 and observationally (Brownetal.2002:HeymansOkumura&Jing 2009)..," and observationally \citep{brown02, heymans04, mandel06, mandel09, hirata07, fu08, brainerd09, okumura09a, okumura09b}."1150 Although the results of these studies show large variations. most of them are consistent with a 6c contamination by both II and GI correlations for future surveys with photometric redshift information.," Although the results of these studies show large variations, most of them are consistent with a $\,\%$ contamination by both II and GI correlations for future surveys with photometric redshift information."1151 Especially. neglecting these correlations can bias thedark energy equation of state parameter wo by as much as 50% (Bridle&King2007) for a “shallow” survey described in Amara&Réfrégier(2007).," Especially, neglecting these correlations can bias thedark energy equation of state parameter $w_0$ by as much as $50\,\%$ \citep{bridle07b} for a “shallow” survey described in \citet{amara07}."1152. For three-point shear statistics. there have been few measurements up to now (Bernardeauetal.2002b:Pen2003:Jarvis 2004).," For three-point shear statistics, there have been few measurements up to now \citep{ber02,pen03,jarvis04}."1153. However the potential systematics level in these studies is found to be high., However the potential systematics level in these studies is found to be high.1154 A recent numerical study by Sembolont showed that intrinsic alignments affect three- weak lensing statistics more strongly than at the two- level for a given survey depth., A recent numerical study by \citet{sembo08} showed that intrinsic alignments affect three-point weak lensing statistics more strongly than at the two-point level for a given survey depth.1155 In particular. neglecting GGI and GIL systematics would lead to an underestimation of the GGG signal by 5—10% for a moderately deep survey like the CFHTLS Wide.," In particular, neglecting GGI and GII systematics would lead to an underestimation of the GGG signal by $5-10\,\%$ for a moderately deep survey like the CFHTLS Wide."1156 Therefore. to match the statistical power expected for cosmic shear in the future surveys. it is essential to control these systematics.," Therefore, to match the statistical power expected for cosmic shear in the future surveys, it is essential to control these systematics."1157 The intrinsic alignment. GIID in the ((three-) point case. Is relatively straightforward to eliminate. since it requires that the galaxies in consideration are physically close to each other. te. have very similar redshifts and angular positions (King&Schneider2002.2003:HeymansHeavens2003;Takada&White 2004).," The intrinsic alignment, (III) in the (three-) point case, is relatively straightforward to eliminate, since it requires that the galaxies in consideration are physically close to each other, i.e. have very similar redshifts and angular positions \citep{king02,king03,HH03,TW04}."1158. The control of intrinsic-shear systematics. GI for the two-point case and GGI in the three-point case (GII also requires that two of the three galaxies are physically close and thus can be eliminated in the same way as IL and HI. turns out to be a much greater challenge.," The control of intrinsic-shear systematics, GI for the two-point case and GGI in the three-point case (GII also requires that two of the three galaxies are physically close and thus can be eliminated in the same way as II and III), turns out to be a much greater challenge."1159 However. as already pointed out by HSO4. the characteristic dependence on galaxy redshifts is a valuable piece of information that helps to control the intrinsic-shear alignments.," However, as already pointed out by HS04, the characteristic dependence on galaxy redshifts is a valuable piece of information that helps to control the intrinsic-shear alignments."1160 Several methods for this have already been constructed in the context of two-point statistics., Several methods for this have already been constructed in the context of two-point statistics.1161 They can be roughly classified into three categories: modeling (King2005:Bri-dle&King 2007). nulling (Joachimi.&Schneider2008.. JS08 hereafter; Joachimi&Schneider 2009)) and self-calibration (Zhang2008:Joachimi&Bridle2009)..," They can be roughly classified into three categories: modeling \citep{king05,bridle07b}, nulling \citealp{JS08b}, JS08 hereafter; \citealp{joachimi09a}) ) and self-calibration \citep{zhang08, joachimi09c}."1162 Modeling separates cosmic shear from the intrinsic-shear alignment effect by constructing template functions for the latter., Modeling separates cosmic shear from the intrinsic-shear alignment effect by constructing template functions for the latter.1163 It suffers. from. uncertainties of the model due to the lack of knowledge of the angular scale and redshift dependence of the intrinsic-shear signal., It suffers from uncertainties of the model due to the lack of knowledge of the angular scale and redshift dependence of the intrinsic-shear signal.1164" The nulling technique employs the characteristic redshift dependence of the intrinsic-shear signal to “null it out"".", The nulling technique employs the characteristic redshift dependence of the intrinsic-shear signal to “null it out”.1165 It is a purely geometrical method and is model-independent. but suffers from a significant information loss.," It is a purely geometrical method and is model-independent, but suffers from a significant information loss."1166 Self-calibration intends to solve the problem of information loss by using additional information from the galaxy distribution to “calibrate” the signal., Self-calibration intends to solve the problem of information loss by using additional information from the galaxy distribution to “calibrate” the signal.1167 The original form of self-calibration. proposed by Zhang(2008). is independent but strong assumptions have been made.," The original form of self-calibration, proposed by \citet{zhang08}, is model-independent but strong assumptions have been made."1168 Joachimi&Bridle(2009) then develop it into a modeling method. by treating intrinsic alignments and galaxy biasing as free functions of scale and redshift.," \citet{joachimi09c} then develop it into a modeling method, by treating intrinsic alignments and galaxy biasing as free functions of scale and redshift."1169 All these methods have the potential of being generalized to three-point statistics., All these methods have the potential of being generalized to three-point statistics.1170 In this paper we focus on the nulling technique. and establish it as a method to reduce the three-point intrinsic-shear alignments GGI and GH.," In this paper we focus on the nulling technique, and establish it as a method to reduce the three-point intrinsic-shear alignments GGI and GII."1171 Since GII can be removed by discarding close pairs of galaxies as in the case of II controlling (e.g.Heymans&Heavens2003).. we focus on the control of GGI systematics.," Since GII can be removed by discarding close pairs of galaxies as in the case of II controlling \citep[e.g.][]{HH03}, we focus on the control of GGI systematics."1172 As known from the case of two-point statistics. the nulling technique introduces significant information loss while (in principle) completely removing the intrinsic-shear alignment from the signal.," As known from the case of two-point statistics, the nulling technique introduces significant information loss while (in principle) completely removing the intrinsic-shear alignment from the signal."1173 In this work we compare the nulling technique to an unconditioned linear compression of the data. distinguish different sources of such information loss. and discuss the possible ways of reducing it.," In this work we compare the nulling technique to an unconditioned linear compression of the data, distinguish different sources of such information loss, and discuss the possible ways of reducing it."1174 We also study the combined constraints on cosmological parameters with both two- and three-point cosmic shear statistics., We also study the combined constraints on cosmological parameters with both two- and three-point cosmic shear statistics.1175 In Sect.2 we demonstrate why and how the nulling technique can be applied to three-point lensing statistics.," In $\,$ 2 we demonstrate why and how the nulling technique can be applied to three-point lensing statistics."1176 We then apply the nulling technique to the modeled lensing bispectrum which we contaminate by intrinsic-shear alignment., We then apply the nulling technique to the modeled lensing bispectrum which we contaminate by intrinsic-shear alignment.1177 The modeling details are described in 3.," The modeling details are described in $\,$ 3."1178 The method of nulling weights construction and the corresponding results are shown in Seet.4. while the results concerning the constraints on cosmological parameters are presented in 5.," The method of nulling weights construction and the corresponding results are shown in $\,$ 4, while the results concerning the constraints on cosmological parameters are presented in $\,$ 5."1179 We conclude in 6.," We conclude in $\,$ 6."1180 We will work in the context of a spatially flat CDM cosmology with a variable dark energy whose equation of state Ww Is parameterized as w=woη—a). with a the cosmic scale factor.," We will work in the context of a spatially flat CDM cosmology with a variable dark energy whose equation of state $w$ is parameterized as $w = w_0 + w_a (1-a)$, with $a$ the cosmic scale factor."1181" The adopted fiducial values for cosmological parameters are €,=0.3. Oy=0.045. Qu.=0.7. wo=—0.95. wy=00. h=0.7. i,=1.0. and os=0.8."," The adopted fiducial values for cosmological parameters are $\Omega_{\rm m}=0.3$, $\Omega_{\rm b}=0.045$, $\Omega_{\rm de}=0.7$, $w_0=-0.95$, $w_a=0.0$, $h=0.7$, $n_s=1.0$, and $\sigma_8=0.8$."1182" Here. O44. Oy and Quy. are the density parameters of the matter (including cold dark matter and baryons). baryons and the dark energy at present time. 7, 1s the spectral 1dex of the primordial power spectrum of scalar perturbations. { is the dimensionless Hubble parameter defined by Hy=100/7 km/s/Mpce. and os is the rms mass fluctuation in spheres of radius 8/77! Mpe."," Here, $\Omega_{\rm m}$ , $\Omega_{\rm b}$ and $\Omega_{\rm de}$ are the density parameters of the matter (including cold dark matter and baryons), baryons and the dark energy at present time, $n_s$ is the spectral index of the primordial power spectrum of scalar perturbations, $h$ is the dimensionless Hubble parameter defined by $H_0=100\, h\, {\textrm{km/s/Mpc}}$ , and $\sigma_8$ is the rms mass fluctuation in spheres of radius $8h^{-1}$ Mpc."1183slow the cooling (komaetal.2006:Burrows2007).. then a planet would have more reavy elements than found here.,"slow the cooling \citep{Ikoma06,Burrows07}, then a planet would have more heavy elements than found here."1184 The required heavy. element mass to fit the radius is determined as (he average ol the avered and mixed cases., The required heavy element mass to fit the radius is determined as the average of the layered and mixed cases.1185 Each of the the observed svstem parameters (A5. age. a. Mj) has an associated error on its published value.," Each of the the observed system parameters $R_p$ , age, $a$, $M_p$ ) has an associated error on its published value."1186" The propagated error ou the heavy element mass (Gg) is given bv: where ση. TAge σα ond Ty, ave Lhe observationally determined errors in planet radius. svslen age. semi-najor axis. and planet mass respectively."," The propagated error on the heavy element mass $\sigma_H$ ) is given by: where $\sigma_{R_p}$, $\sigma_{\textrm{Age}}$, $\sigma_a$, and $\sigma_{M_p}$ are the observationally determined errors in planet radius, system age, semi-major axis, and planet mass respectively."1187" The derivatives aval,an (calculated al the observed. planet. parameters assuming core heavy. elements) describe (he sensitivity of the predicted heavy. element mass will respect to changes in a given parameter. X."," The derivatives $\frac{\partial M_c}{\partial X}$ (calculated at the observed planet parameters assuming core heavy elements) describe the sensitivity of the predicted heavy element mass with respect to changes in a given parameter, $X$."1188 The final term of the expression is the uncertainty due to the unknown structure of the planet., The final term of the expression is the uncertainty due to the unknown structure of the planet.1189 Af. and Moy are the predicted heavy. element masses if the heavy. elements are within the core. or the envelope. respectivelv.," $M_c$ and $M_{\textrm{env}}$ are the predicted heavy element masses if the heavy elements are within the core, or the envelope, respectively."1190 We use the metallicity of the star [Fe/II] as given in each paper in Table 1., We use the metallicity of the star [Fe/H] as given in each paper in Table 1.1191" For each svslem. we compute the heavy element mass fraction Za,=0.0142x ο“. assuming that the total heavy element composition of other svstems scales with their iron abundance. normalized to the solar metalicity as in Asplundetal.(2009)."," For each system, we compute the heavy element mass fraction $Z_{\textrm{star}} \equiv 0.0142 \times 10^{[Fe/H]}$ - assuming that the total heavy element composition of other systems scales with their iron abundance, normalized to the solar metalicity as in \citet{Asplund09}."1192 In Figure 2 we plot the stellar metallicity. ΕΟΤ). against the planet heavy element mass for each of these svstems.," In Figure 2 we plot the stellar metallicity, [Fe/H], against the planet heavy element mass for each of these systems."1193 Using a least squares fit. we find that logMz=(0.32c0.08)0.39)ΡΟΗ for stars with [Fe/IHI]>—0.05.," Using a least squares fit, we find that $\log M_Z = (0.82 \pm 0.08) + (3.40 \pm 0.39) [\textrm{Fe/H}]$ for stars with $\textrm{ [Fe/H]} > -0.05$."1194 The reduced Chi-squarec value of 1.95 implies (hat not all of the scatter can be explained by observational error., The reduced Chi-squared value of 1.95 implies that not all of the scatter can be explained by observational error.1195 We expect a lairly flat relation (the dotted line in Figure 2) at subsolar stellar metallicity if 10-15 oof heavy elements are needed (o trigger planet lormation., We expect a fairly flat relation (the dotted line in Figure 2) at subsolar stellar metallicity if 10-15 of heavy elements are needed to trigger planet formation.1196 In Table 1 we list the planets and observed parameters used., In Table 1 we list the planets and observed parameters used.1197 For each planet. we list the average predicted heavy elements between the core model] and mixed model with the 50-50 rock-ice composition.," For each planet, we list the average predicted heavy elements between the core model and mixed model with the 50-50 rock-ice composition."1198 We have examined the sensitivity of our findings to alternate choices [or the heavyelement EOS. and the differences are small.," We have examined the sensitivity of our findings to alternate choices for the heavyelement EOS, and the differences are small."1199 On the low densitv EOS end. we have used," On the low density EOS end, we have used"1200neighbouring galaxies. but with the cluster potential itself.,"neighbouring galaxies, but with the cluster potential itself."

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