ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 It is important. to note that in cach generation of a simplex. the increments should independently have equal chance of being added to or subtracted from the values of Nass so that no part of the parameter space is unfairly undersampled.," It is important to note that in each generation of a simplex, the increments should independently have equal chance of being added to or subtracted from the values of $\chi_{\rm guess}$ so that no part of the parameter space is unfairly undersampled."3 The algorithm makes tens of thousands of deformations of the simplex while T is linearly reduced to zero., The algorithm makes tens of thousands of deformations of the simplex while $T$ is linearly reduced to zero.4 This entire process is repeated some tens of times. after which we have a sample of local minima that are all obtained [roni Nass," This entire process is repeated some tens of times, after which we have a sample of local minima that are all obtained from $\chi_{\rm guess}$."5 We now update Nass to the location of the lowest of the minima just found. and initiate à new search., We now update $\chi_{\rm guess}$ to the location of the lowest of the minima just found and initiate a new search.6 The entire process is repeated until the value of the diagnostic function D'(x) hits a floor., The entire process is repeated until the value of the diagnostic function $D' (\chi)$ hits a floor.7 When this “oor lies higher than the numericalnoise Door. the attempt to find an orbit tha is consistent with the assumed. inputs has been a Failure ancl we infer that no such. orbit. exists.," When this floor lies higher than the numerical-noise floor, the attempt to find an orbit that is consistent with the assumed inputs has been a failure and we infer that no such orbit exists."8 When the floor coincides with the numerical-noise Hoor. we conclude tha the corresponding X specifies an orbit that is compatible with the inputs.," When the floor coincides with the numerical-noise floor, we conclude that the corresponding $\chi$ specifies an orbit that is compatible with the inputs."9 An approximate value for the numerica noise floor for a given problem may be obtained as follows: eiven input that perfectly delineates an orbit in the potentia in use. the value of D returned at the correct. distance is approximately the numerical-noise floor.," An approximate value for the numerical noise floor for a given problem may be obtained as follows: given input that perfectly delineates an orbit in the potential in use, the value of $D'$ returned at the correct distance is approximately the numerical-noise floor."10 Conclusive proof that a candidate track with a particular value of D is an orbit can be obtained by integrating the equations of motion from the position and velocity of any point on the track anc ensuring that the time integration essentially recovers the track., Conclusive proof that a candidate track with a particular value of $D'$ is an orbit can be obtained by integrating the equations of motion from the position and velocity of any point on the track and ensuring that the time integration essentially recovers the track.11 On account. of the stochastic nature of the algorithm. an attempt to find a solution at a particular distance occasionally sticks at ahigher value of 2’ than the uncerlving problem allows.," On account of the stochastic nature of the algorithm, an attempt to find a solution at a particular distance occasionally sticks at ahigher value of $D'$ than the underlying problem allows."12 This condition is identified. by scatter in the values of D reached on successive attempts and by inconsistency of these values with the values of LD achieved for nearby distanceswe see from al the function underlving the minima is smooth., This condition is identified by scatter in the values of $D'$ reached on successive attempts and by inconsistency of these values with the values of $D'$ achieved for nearby distances—we see from that the function underlying the minima is smooth.13 When 10 magnitude of this scatter is significant. one can only 'onfidently. declare an attempt to find an orbit a failure if vw DI achieved. is consistently higher than the noise [oor w more than the scatter: since the diagnostic measure LY uantifics the extent to which a candidate track satisfies the quations of motion. by definition. tracks with higher. D' jui the noise oor plus scatter cannot represent orbits.," When the magnitude of this scatter is significant, one can only confidently declare an attempt to find an orbit a failure if the $D'$ achieved is consistently higher than the noise floor by more than the scatter; since the diagnostic measure $D'$ quantifies the extent to which a candidate track satisfies the equations of motion, by definition, tracks with higher $D'$ than the noise floor plus scatter cannot represent orbits."14 When the observational constraints are weak. we expect several orbits το be compatible with them.," When the observational constraints are weak, we expect several orbits to be compatible with them."15 In particular. we will be able to find acceptable orbits for a range of initial distances sy.," In particular, we will be able to find acceptable orbits for a range of initial distances $s_0$."16 It is therefore important. for any given input. to run the algorithm starting from many dillerent. values of syn with os set to prevent the algorithm straving far from the specified son.," It is therefore important, for any given input, to run the algorithm starting from many different values of $s_{0\rm b}$ with $\delta s$ set to prevent the algorithm straying far from the specified $s_{0\rm b}$."17 In. this wav. the full range of allowable distances can be mapped out. and dynamical orbits found for cach distance in that range.," In this way, the full range of allowable distances can be mapped out, and dynamical orbits found for each distance in that range."18 In the case of significant scatter about the noise-ILoor. the range of distances at which valid orbits are found. is the range within which solutions viclel values of  smaller than the noise-Hoor plus scatter.," In the case of significant scatter about the noise-floor, the range of distances at which valid orbits are found is the range within which solutions yield values of $D'$ smaller than the noise-floor plus scatter."19 Similar degeneracies in the parameters controlling the astrometry and line-of-sight velocities are less of à concern because if. we have orbits that dilfer in these observables. we simply concentrate on the orbit that [ies closest to the baseline track.," Similar degeneracies in the parameters controlling the astrometry and line-of-sight velocities are less of a concern because if we have orbits that differ in these observables, we simply concentrate on the orbit that lies closest to the baseline track."20 To test this method. we used the N-body approximation o the Orphan Stream described in as our raw data.," To test this method, we used the N-body approximation to the Orphan Stream described in as our raw data."21 Sets of points of /.b] and. {ο were selected. by. eve to ie down the middle of the stream.," Sets of points of $[l, b]$ and $[l, v_\parallel]$ were selected by eye to lie down the middle of the stream."22 These sets were each itted with a low-order polynoniual to ensure smoothness. and these polynomials were sampled at 30points to produce he baseline input. data b(/) and. ο.," These sets were each fitted with a low-order polynomial to ensure smoothness, and these polynomials were sampled at 30points to produce the baseline input data $b(l)$ and $v_\parallel(l)$ ."23 To each. data set we attached. error estimates ob and de). which through the penalty functions pios and poa (eqs 2? and 77)) constrain he tracks that the Metropolis algorithm can try.," To each data set we attached error estimates $\delta b$ and $\delta v_\parallel$ , which through the penalty functions $p_{\rm pos}$ and $p_{\rm vel}$ (eqs \ref{eq:ppos} and \ref{eq:pvel}) ) constrain the tracks that the Metropolis algorithm can try."24 Details, Details25Πο loug-rauge correlations are discussed that develop in cold. eravitationally unstable svstems without energy dissipation.,"Here, long-range correlations are discussed that develop in cold, gravitationally unstable systems without energy dissipation."26" The correlations strength appearing in such dissipatiouless systems depends on the initial ratio between kinetic and potential energy. aΤΗ ie. ou the number of thermal Jeans masses given through AL/ALy=2a77,"," The correlations strength appearing in such dissipationless systems depends on the initial ratio between kinetic and potential energy, $a=T/|U|$, i.e., on the number of thermal Jeans masses given through $M/M_{\rm27 J}=2a^{-3/2}$."28 This is shown in Fig. 17., This is shown in Fig. \ref{ff_1}.29. For «=0.01 the iudex à of the velocitv-dispersiou-size relation remains zero at siuall, For $a=0.01$ the index $\delta$ of the velocity-dispersion-size relation remains zero at small30Here. we have supplied the time dependence of w from equation (55).,"Here, we have supplied the time dependence of $\omega$ from equation (55)."31 The constant Ep is and has the value οκLO1L... for our fiducial parameters.," The constant ${\dot E}_0$ is and has the value $9\times 10^{-4}\,\,\Lsun$ for our fiducial parameters."32 Evidently. the energy release does uot rival the radiative loss from the stars themselves until very late during the inspiral. when / is within a few percent of /..," Evidently, the energy release does not rival the radiative loss from the stars themselves until very late during the inspiral, when $t$ is within a few percent of $t_c$."33 At this point. the stars are separated by several AU.," At this point, the stars are separated by several AU."34 We may compare. at least in a qualitative mauner. our derived torque with that iudicated by the traditional theory of dynamical friction.," We may compare, at least in a qualitative manner, our derived torque with that indicated by the traditional theory of dynamical friction."35" According to equation (12) of Ostriker(1999).. the retarding force on a mass AM moving at speed V. through a cloud of density po is The [actor Z. essentially a Coulomb logarithin. is a nondimeusional μισο of the Mach number V/c, and the time since the mass first entered the cloud in question."," According to equation (12) of \citet{o99}, the retarding force on a mass $M$ moving at speed $V$ through a cloud of density $\rho_0$ is The factor $\cal I$, essentially a Coulomb logarithm, is a nondimensional function of the Mach number $V/c_s$ and the time since the mass first entered the cloud in question."36 Since Z will generally be of order unity. we may iguore it. along with other such factors. in the dimensional arguiuent that follows.," Since $\cal I$ will generally be of order unity, we may ignore it, along with other such factors, in the dimensional argument that follows."37 To apply this formula to the binary problem. we interpret V. as the compouents. relative velocity Vig. which is cei.," To apply this formula to the binary problem, we interpret $V$ as the components' relative velocity $V_{\rm rel}$, which is $\omega\,a_{\rm tot}$."38 Then the torque is of orderFpy.. so tliat Here. the moment of n.iuertia. has been approximated. asαπ.," Then the torque is of order, so that Here, the moment of inertia has been approximated as."39" ""Comparison⋅ to equation⋅ (39)/. shows that Upp is the true P multiplied by a factor(να).", Comparison to equation (39) shows that $\Gamma_{\rm DF}$ is the true $\Gamma$ multiplied by a factor.40 This factor can be much smaller than unity for the hard. binaries of interest., This factor can be much smaller than unity for the hard binaries of interest.41 On the other hand. the uoudiumeusioual Z formally diverges for a velocity of cy.," On the other hand, the nondimensional $\cal I$ formally diverges for a velocity of $c_s$."42 The traditional theory is thus unreliable in tliis context., The traditional theory is thus unreliable in this context.43 However. it is uot difficult to envision Circumstances in which the present theory requires modification.," However, it is not difficult to envision circumstances in which the present theory requires modification."44 From equation (35a). the Mach number associated with the radial velocity amplitude is," From equation (35a), the Mach number associated with the radial velocity amplitude is"45for the isothermal case. and for the polytropic case. where Ap=Opopn/PyGALanysΠρcy].,"for the isothermal case, and for the polytropic case, where $\Delta_D=-\phi_{D0}\rho_0/P_0=G M_* \mu m_p/[r_* k_B T_0 (2-\psi)]$."46" Notice that equations (12--13)) reduce to equations (7--8)) when A,=0.", Notice that equations \ref{eq:Capelo_iso}- \ref{eq:Capelo_poly}) ) reduce to equations \ref{eq:Makino_sol}- \ref{eq:Suto_sol}) ) when $M_*=0$.47 In this section. for a system with an NEW DAL halo and stars described by a Dehnen profile. we compare equilibrium gas density. profiles as a function of farce. the stellar mass fraction at the virial radius. c. the Dehnen parameter. and Z5. the central eas temperature.," In this section, for a system with an NFW DM halo and stars described by a Dehnen profile, we compare equilibrium gas density profiles as a function of $f_{star}$, the stellar mass fraction at the virial radius, $\psi$, the Dehnen parameter, and $T_0$, the central gas temperature."48 We also consider the case when stars are included in the total mass budget. but not in the total eravitational budget.," We also consider the case when stars are included in the total mass budget, but not in the total gravitational budget."49" We consider a svstem at redshift z. which consists of an isolated elliptical galaxy at the centre of an isolated. collapsed DM halo. wherein the density is given by where AMviaví(ro) is the DM mass enclosed. within the virial radius r.;;. and ον)=loll|65)Geir!Grip) is a function of the concentration parameter ei;=reafrs. Which depends on redshift and (total) virial mass οι, as where ¢ and à are constants that can be inferred from simulations (e.g. Bullock ct al."," We consider a system at redshift $z$, which consists of an isolated elliptical galaxy at the centre of an isolated, collapsed DM halo, wherein the density is given by where $M_{NFW}(r_{vir})$ is the DM mass enclosed within the virial radius $r_{vir}$, and $f(c_{vir}) = \ln(1+c_{vir})-c_{vir}/(1+c_{vir})$ is a function of the concentration parameter $c_{vir} = r_{vir}/r_s$, which depends on redshift and (total) virial mass $M_{vir}$ as where $c_0$ and $\alpha$ are constants that can be inferred from simulations (e.g. Bullock et al."50 2001: Llennawi ct al., 2001; Hennawi et al.51" 2007) and observations (e.g. Comerford Natarajan 2007: Mandelbaum. Scljak Llirata 2008). ancl Ades, is in units of M."," 2007) and observations (e.g. Comerford Natarajan 2007; Mandelbaum, Seljak Hirata 2008), and $M_{vir}$ is in units of $_{\odot}$."52" The virial radius is. by definition. the radius of a spherical region within which the mean (total) mass density is Av; times the mean criticaldensity where the virial overdensity Avi(2)81827|S2(Q,,02).1).39(0,(2).1)?2 (Bevan Norman1998)7.. the matter fraction OQ,(2)9Ou(1pz)POC|2)?OA]. and the mean critical density p(s)=345Ooh|zY*Ox]/(x6)."," The virial radius is, by definition, the radius of a spherical region within which the mean (total) mass density is $\Delta_{vir}$ times the mean critical: where the virial overdensity $\Delta_{vir}(z) \simeq 18 \pi^2 + 82(\Omega_m(z)-1) - 39(\Omega_m(z)-1)^2$ (Bryan Norman, the matter fraction $\Omega_m(z) = \Omega_0(1+z)^3/[\Omega_0(1+z)^3+\Omega_{\Lambda}]$, and the mean critical density $\rho_c(z) = 3 H_0^2 [\Omega_0(1+z)^3 + \Omega_{\Lambda}]/(8 \pi G)$."53" The NEW density profile function can be also re-written as in equation(5).. with 8.=fpeschff(eiu). and fos=AlxewrenMM,1.fulb,OQ,Oo. where fpy anc fj, are the DM and barvon fraction. respectively. within the virial raciius. 5, is the barvon fraction relative to the universal value. ancl we have assumed that the universal baryon fraction. Q,/Qu. is independent. of redshift."," The NFW density profile function can be also re-written as in equation, with $\delta_c = f_{DM} \Delta_{vir} c_{vir}^3/(3 f(c_{vir}))$, and $f_{DM} = M_{NFW}(r_{vir})/M_{vir} = 1-f_b = 1-b_b \Omega_b/\Omega_0$, where $f_{DM}$ and $f_b$ are the DM and baryon fraction, respectively, within the virial radius, $b_b$ is the baryon fraction relative to the universal value, and we have assumed that the universal baryon fraction, $\Omega_b/\Omega_0$, is independent of redshift."54 The elliptical galaxy stellar density. profile is given by equation (9)., The elliptical galaxy stellar density profile is given by equation .55". The total stellar mass Al, is calculated. by setting r=ray in equation and by Mp(ri;ó)=faisMos.", The total stellar mass $M_*$ is calculated by setting $r=r_{vir}$ in equation and by $M_D(r_{vir})=f_{star}M_{vir}$.56 Phe virial stellar mass fraction can be written. following c.g. Mamon Lookas (2005b). as where Y.g is the stellar mass-to-light ratio. Yg is the universal mass-to-light ratio. Ye is the galactic mass-to-light. ratio (all in M. /L.). and by is the (dimensionless) mass-to-light ratio bias. all in the D-band.," The virial stellar mass fraction can be written, following e.g. Mamon okas (2005b), as where $\Upsilon_{*,B}$ is the stellar mass-to-light ratio, $\overline{\Upsilon}_B$ is the universal mass-to-light ratio, $\Upsilon_B$ is the galactic mass-to-light ratio (all in $_{\odot}/$ $_{\odot}$ ), and $b_{\Upsilon}$ is the (dimensionless) mass-to-light ratio bias, all in the B-band."57" The scale radius r. is relatedto the elfective radius r, through a numerical fit (Dehnen 1993)."," The scale radius $r_*$ is relatedto the effective radius $r_e$ through a numerical fit (Dehnen 1993),"58to be the mean value of the densities of Earth and Neptune. yielding a radius of 0.22Rapier.,"to be the mean value of the densities of Earth and Neptune, yielding a radius of $0.22\,R_{Jupiter}$."59 CoRoT-7d has a minimum mass very similar to the mass of Neptune (16.5M5). so it Was assumed to have the same density. corresponding to a radius of 0.34 Κως.," d has a minimum mass very similar to the mass of Neptune $16.5 M_{Earth}$ ), so it was assumed to have the same density, corresponding to a radius of $0.34\,R_{Jupiter}$ ."60 Figures 13 and 14 show the duration of a transit of CoRoT-7e as a function of its inclination and the position of the ascending node., Figures \ref{fig:transitc} and \ref{fig:parttransitc} show the duration of a transit of c as a function of its inclination and the position of the ascending node.61 The reference plane is fixed to the plane of CoRoT-7b and the ascending node of 7b 1s assumed to be in the direction of the observer., The reference plane is fixed to the plane of b and the ascending node of b is assumed to be in the direction of the observer.62 Thus. the value of the inclination as shown in Fig.," Thus, the value of the inclination as shown in Fig."63 13. 1s not the apparent inclination as it would appear to an observer. but the in-system inclination with respect to the plane of CoRo," \ref{fig:transitc} is not the apparent inclination as it would appear to an observer, but the in-system inclination with respect to the plane of b. Fig."64T-7b. Fig. 14 i5 showing a enlarged detail of Fig., \ref{fig:parttransitc} is showing a enlarged detail of Fig.65 13. with labeled contours of equal transit duration., \ref{fig:transitc} with labeled contours of equal transit duration.66 The same calculation was done for CoRoT-7d. and qualitatively the same behaviour was found.," The same calculation was done for d, and qualitatively the same behaviour was found."67 Due to the similarity of the plots — the only difference being in the scale — we refrain from showing this figure., Due to the similarity of the plots – the only difference being in the scale – we refrain from showing this figure.68 The maximum transit duration is 153 minutes for CoRoT-7e. as can be seen in Figs.," The maximum transit duration is 153 minutes for c, as can be seen in Figs."69 13 and 14.. and 217 minutes for CoRoT-7d. In this investigation we estimated the TDV caused by inclined additional planets which reaches — although relatively small — values of some degrees and is therefore detectable with the CoRoT satellite.," \ref{fig:transitc} and \ref{fig:parttransitc}, and 217 minutes for d. In this investigation we estimated the TDV caused by inclined additional planets which reaches – although relatively small -- values of some degrees and is therefore detectable with the CoRoT satellite."70 This possibility stems from the fact that the CoRoT-7 system is à rapidly evolving extrasolar system with very close-in planets., This possibility stems from the fact that the CoRoT-7 system is a rapidly evolving extrasolar system with very close-in planets.71 We did our study using numerical integrations for the long term development of the system. as well as an analytical approach for short time intervals in the order of years.," We did our study using numerical integrations for the long term development of the system, as well as an analytical approach for short time intervals in the order of years."72 It turned out the system is quite stable even in the 3 planet model., It turned out the system is quite stable even in the 3 planet model.73 A quantitatively new result is the dependence on the difference in the ascending node on the short time development of 7b. The small phase shift in the dynamical development is not important for the qualitative behaviour for long time. but essential for the short time evolution of the orbit of CoRoT-7b. In our determination of the duration of the transit caused by the change of the inclination of CoRoT-7b we also discussed what kind of orbits of the outer planet(s) would lead to a transit of these planets.," A quantitatively new result is the dependence on the difference in the ascending node on the short time development of b. The small phase shift in the dynamical development is not important for the qualitative behaviour for long time, but essential for the short time evolution of the orbit of b. In our determination of the duration of the transit caused by the change of the inclination of b we also discussed what kind of orbits of the outer planet(s) would lead to a transit of these planets."74 Despite the constraints given by the incompleteness of the data derived from observations the main conclusion of our study is that after three years of observation of the EPS CoRoT- we would be able to determine -- via transit observations from space of the CoRoT satellite and additional ground based RV — whether the two (three planets) are on mutually inclined orbits or whether theyhave just small inclinations of the order of i«10°. (e.g.2?) ," Despite the constraints given by the incompleteness of the data derived from observations the main conclusion of our study is that after three years of observation of the EPS CoRoT-7 we would be able to determine – via transit observations from space of the CoRoT satellite and additional ground based RV – whether the two (three planets) are on mutually inclined orbits or whether theyhave just small inclinations of the order of $i<10^{\circ}$ \citep[e.g.][]{Bor03,Bor07} "75would retain more of its primordial brightness 2002).,would retain more of its primordial brightness .76. While age estimates for ILD 69330 range [rom «1 to 5 Gvr2007a).. older ages seem much more probable.," While age estimates for HD 69830 range from $<$ 1 to 5 Gyr, older ages seem much more probable."77" One new piece of information comes from a ""probable"" detection of a stellar rotation period for ILD 69330 of 3541 day."," One new piece of information comes from a “probable"" detection of a stellar rotation period for HD 69830 of $\pm$ 1 day."782010)... This period is consistent wilh expectations for a KOV star with the age of the Sun or greater2010)., This period is consistent with expectations for a K0V star with the age of the Sun or greater.79. Chromospheric and X-ray data similarly arene for ages >> 1 Gyr., Chromospheric and X-ray data similarly argue for ages $>>$ 1 Gyr.80" Measured values of Rij)=—4.98 and log(Ly /Lj,)—-6 both suggest ages of 4-5 Gyr 2008).", Measured values of $^\prime_{HK})=-4.98$ and $_X$ $_{Bol}$ )=-6 both suggest ages of 4-5 Gyr .81". At such an advanced age. agrees that a steady state model is hard to defend and that a transient origin for the IID 69830s excess is more likely,"," At such an advanced age, agrees that a steady state model is hard to defend and that a transient origin for the HD 69830's excess is more likely."82 Another source of an outburst could be the passage of a comet into the inner reaches of the planetary solar svstem2005)., Another source of an outburst could be the passage of a comet into the inner reaches of the planetary solar system.83. The brightening of the solar svstem's zodiacal cloud due to incursion of comets has been examined (quantitatively bv)., The brightening of the solar system's zodiacal cloud due to incursion of comets has been examined quantitatively by.84. A major argument against this mechanism is the spectral character of the dust emission which is fay more asteroidal (han cometary in nature and the lack of any gas steady state emission., A major argument against this mechanism is the spectral character of the dust emission which is far more asteroidal than cometary in nature and the lack of any gas steady state emission.85 A weaker argument against a cometary origin is the faet that this svstem has no detectable dust associated with a distant Kuiper Belt., A weaker argument against a cometary origin is the fact that this system has no detectable dust associated with a distant Kuiper Belt.86 As discussed in Beichman et al. (, As discussed in Beichman et al. (87"2006). the 70 {thax density limit corresponds to Ly/L,~5x10°(3o) for 50 IX dust.","2006), the 70 flux density limit corresponds to $L_d/L_*\sim 5 \times 10^{-6}\, (3\sigma)$ for 50 K dust."88 This level is only ~5 (mes greater (han the nominal range predicted for the Ixuiper Belt dust in our own solar svstem1996)., This level is only $\sim$ 5 times greater than the nominal range predicted for the Kuiper Belt dust in our own solar system.89. The [act that the reservoir for comets is not much larger or more dvnamically active than in our solar svstem argues that large scale cometary incursions must be rare., The fact that the reservoir for comets is not much larger or more dynamically active than in our solar system argues that large scale cometary incursions must be rare.90 One possible origin for temporal variability is Chat a traction of the disk material could be clifferentially heated as it orbits the star on an eccentric orbit., One possible origin for temporal variability is that a fraction of the disk material could be differentially heated as it orbits the star on an eccentric orbit.91 In analogy with the zodiacal dust bands in our own solar svstem. most of the debris material will be spreacl uniformly along (he orbit since the dynamical timescale for this spreading is just a few hundred. vears within an AU of the star2001).," In analogy with the zodiacal dust bands in our own solar system, most of the debris material will be spread uniformly along the orbit since the dynamical timescale for this spreading is just a few hundred years within an AU of the star."92. Material in an eccentric orbit would be hotter close to the star and cooler far away trom it., Material in an eccentric orbit would be hotter close to the star and cooler far away from it.93 This elfect is clearly seen in resolved maps of the Fomalhaut disk where the SE ansa is hotter ian the NW one., This effect is clearly seen in resolved maps of the Fomalhaut disk where the SE ansa is hotter than the NW one.94 But this steady-state spatial effect is not resolvable in any data presently available., But this steady-state spatial effect is not resolvable in any data presently available.95 Nor is temporal data available for svstems on such long period orbits., Nor is temporal data available for systems on such long period orbits.96 However. if rere were a clump of material. located. sav. al a resonant point with respect to the various," However, if there were a clump of material, located, say, at a resonant point with respect to the various"97 Oc( —0|en(r.AJ) (e—cl) (61) where defiued in(523). Itis straightforward to show that à was do wpdr Ndi. N= up Lone I (62) with απ cu=a. Tn (63))wecan choose eithersign for ,"Comparison with numerical results described in the next section suggest that the $m=0$ , $a \neq 980$ case functions can provide serviceable analytic approximations outside of the outer horizon for broad ranges of $m$ and $a$ .For example, with $m=1$ and $a=1/2$ , all of the quantities except $\rb$ in \ref{limf1}) ), \ref{limf2}) ) and \ref{limf3}) ) differ by no more than roughly 1 to 3 percent from the true (numerically integrated) values, outside of $r_+$ ."99e.depending onwhich sheet of thehorizon," $\rb$ converges only logarithmically to the Minkowski value in the limit $r \rightarrow \infty$, and of course diverges at the horizon)."100 isof interest. For example. 04audaw) areregular outhe “upward”, In Figure \ref{fig1} we illustrated the behaviour of the generators and the nature of the caustic that forms in the negative $r$ sheet of the Kerr manifold.101 (future) sheets ofbothouter anduer horizous. withthenice bonus , The $\lambda=constant$ curves were obtained by numerically integrating the evolution equations of the null generators of the hypersurface: with affine parameter $\tau$ .102"feature that44 is coustaut overcach future sheetsa/2imr, of(sav)thisthe outer horizon.pos"," In particular To detect the formation of a caustic (see \ref{caust}) ) we track the evolution of $\mu$, and to reconstruct surfaces of constant $\rb$ in the $r,\theta$ plane we calculate the change of $\rb$ along the generators."103sible We briefly mentionthat following standard methods one could coustruct aPenrose diagramo," If we treat $r$ as the independent variable, from \ref{rtdot}) ), \ref{solution}) ), \ref{dl_mu}) ) and \ref{d_mu}) ) we find and At the horizons $\rb$ and its derivative with respect to $r$ diverge."104f theerr spacetime using the WNiuskallike coordinates (60))., These divergences are coordinate singularities which can be avoided numerically by subtracting off the infinities that occur there.105valid upto formation ofthecaustic surface. Such a diagram , Thus define $\rt$ as where $\kappa_+$ $\kappa_-$ ] is the surface gravity at the $r_+$ $r_-$ )] horizon as defined in \ref{kappa}) ).106wouldnot lookauy different from the usual text, So we actually integrate $\rt$ along the generators and retrieve $\rb$ from the result using \ref{rt}) ).107book examples line-clement sin? The quasi-splierical coordinates+. audA= .. and the coefficientsin the quasi-splierical forms (3)av —0.," For asymptotic intitial conditions for$\mu$ and $\theta$, we use the relations listed in \ref{limf1}) ) and \ref{limf2}) ) for a sufficiently large initial $r$ Using \ref{I}) ) and \ref{du_dm}) ) one can show that $\mu(r,\lambda,m)-\mu(r,\lambda,m=0) \approx 108(a^2\lambda m/8\sin\theta \cos\theta) (1/r^2)$ and $\theta(r,\lambda,m)-109\theta(r,\lambda,m=0) \approx (a^4\lambda m \sin\theta \cos\theta / 1104)(1/r^5)$ for large $r$ along a given generator."111 ¢ 40: Thiswas studied in Sec., The initial condition for $\rb$ is arbitrary $\rb+constant$ is still a solution to \ref{pde}) )).112 andwe simply listthe results. 125 Aa| a? rose Va?y poa5 0. tan’. = oo tand.," Figure \ref{fig2} below is a close-up within the inner horizon of the case illustrated in Figure \ref{fig1}, showing the projections of surfaces of constant $\rb$ onto the $\sqrt{x^2+y^2},z$ plane."113" (61) y nu2|a)24sincosmn 7 ↽1 Sin↴⋅ costs Q- qas pe"" |a sun?"," This is the only region where $\rb = 114constant$ surfaces start showing significant deviations from the spheres of the massless scenario."115" P= vua vua? (sin. Os.) Lequa at0 02 cos( (66)"" 40. 0: just Sclowarzscluld"," Note that the caustic surface does not coincide with ahypersurface slice $\rb=constant$: followingthe generators inwarda caustic first developswhere the hypersurface meets the ring singularity, after which it quickly “unravels”."116" spacetimic.aud readily fds (1)im0 Thisis one dr . 1l r=] - ο2mjr sinο, Oar. pP=——. (GT)", We only present plots for $m=1$ and $a=1/2$ ; except for variations in scale there are no qualitative differences in the shapes of the curves and surfaces for arbitrary non-zero $a$ and positive $m$ .117The Legendre coefficient histories for the differential rotation are shown in Fig.,The Legendre coefficient histories for the differential rotation are shown in Fig.118 4 along with the smoothed sunspot number for reference to the phase of the sunspot cycle., 4 along with the smoothed sunspot number for reference to the phase of the sunspot cycle.119" The three symmetric components (Pj, Pl, and Pl) dominate so we only show the three associated coefficient histories."," The three symmetric components $P_1^1$ , $P_3^1$ , and $P_5^1$ ) dominate so we only show the three associated coefficient histories."120 These three coefficients show only a slight variation over the sunspot cycle with the amplitudes being smaller (less negative — weaker differential rotation) at sunspot cycle maximum (~ 2002)., These three coefficients show only a slight variation over the sunspot cycle with the amplitudes being smaller (less negative – weaker differential rotation) at sunspot cycle maximum $\sim 2002$ ).121" This “more rigid"" differential rotation at sunspot cycle maximum was previously noted by Kommetal. (1993A).", This “more rigid” differential rotation at sunspot cycle maximum was previously noted by \cite{Komm_etal93A}.122. The Legendre coefficient histories for the meridional flow are shown in Fig., The Legendre coefficient histories for the meridional flow are shown in Fig.123 5 along with the smoothed sunspot number., 5 along with the smoothed sunspot number.124" The two anti-symmetric components (Pl, and Pj) dominate so we only show the two associated coefficient histories."," The two anti-symmetric components $P_2^1$, and $P_4^1$ ) dominate so we only show the two associated coefficient histories."125 These two coefficients show substantial variations over the sunspot cycle with the amplitudes being smaller at sunspot cycle maximum., These two coefficients show substantial variations over the sunspot cycle with the amplitudes being smaller at sunspot cycle maximum.126 Kommetal.(1993B) found similar behavior for the time period 1978-1990., \cite{Komm_etal93B} found similar behavior for the time period 1978-1990.127 In addition to this systematic trend over the sunspot cycle (fast at minimum and slow at maximum) we find a secular variation in which the meridional flow speed was substantially (~20%) faster at the Cycle 23/24 minimum in 2008 than at the Cycle 22/23 minimum in 1996., In addition to this systematic trend over the sunspot cycle (fast at minimum and slow at maximum) we find a secular variation in which the meridional flow speed was substantially $\sim 20\%$ ) faster at the Cycle 23/24 minimum in 2008 than at the Cycle 22/23 minimum in 1996.128" As in Hathaway&Rightmire(2010) we note that the meridional flow speed was faster for the entire interval from 2004 on, than it was at the cycle minimum in 1996."," As in \cite{HathawayRightmire10} we note that the meridional flow speed was faster for the entire interval from 2004 on, than it was at the cycle minimum in 1996."129 This increase in meridional flow speed would explain the weak polar fields that were produced during that time period in the SFT models of Schrijver&Liu(2008) and Wangetal.(2009)., This increase in meridional flow speed would explain the weak polar fields that were produced during that time period in the SFT models of \cite{SchrijverLiu08} and \cite{Wang_etal09}.130. 'The variations in flow speed shown in the last section are produced by and accompanied by variations in flow structure., The variations in flow speed shown in the last section are produced by and accompanied by variations in flow structure.131 Our analysesproducelatitudinal profiles of the differential rotation and the meridional flow for each individual solar, Our analysesproducelatitudinal profiles of the differential rotation and the meridional flow for each individual solar132hadronization temperature. and hence (he source size for hadron emission must become larger.,"hadronization temperature, and hence the source size for hadron emission must become larger."133 In particular. it is expected to increase as a power οἱ the hadron multiplicity. since (his in turn. grows with the initial energy. density [24]..," In particular, it is expected to increase as a power of the hadron multiplicity, since this in turn grows with the initial energy density \cite{Stock}."134 S0 far. from AGS to RILIC. the source size lor hadron emission. as determined by Hanbury-Drown.Twiss (IID'T) methods (25) used in astvophysics. has not shown a significant increase [26]..," So far, from AGS to RHIC, the source size for hadron emission, as determined by Hanbury-Brown–Twiss (HBT) methods \cite{HBT} used in astrophysics, has not shown a significant increase \cite{Beca}."135" This ""IID'T-puzzle"" has been accounted for in terms of the relative role of meson and baryon production [21].. but al Ες energies. a clear increase of (he source volume is predicted."," This “HBT-puzzle” has been accounted for in terms of the relative role of meson and baryon production \cite{Adamova02}, but at LHC energies, a clear increase of the source volume is predicted."136 Such an increase seenis necessary dn a modelindependent wav. if the concept of hot primordial fireball production in nuclear collisions is to make any sense.," Such an increase seems necessary in a model-independent way, if the concept of hot primordial fireball production in nuclear collisions is to make any sense."137 We had noted that momentum spectra for real and virtual photons can in principle provide an internal thermometer of the QGP. with /dhyp) A recent analysis of ΠΟ εςAu data at Ys=200 GeV [28] has identified possible thermal photons. seen in a transverse momentum window between pion decay ancl prompt photon spectra.," We had noted that momentum spectra for real and virtual photons can in principle provide an internal thermometer of the QGP, with /dk_T) A recent analysis of RHIC $Au\!-\!Au$ data at $\sqrt s=200$ GeV \cite{phenix} has identified possible thermal photons, seen in a transverse momentum window between pion decay and prompt photon spectra."138 The corresponding temperature is with 7=221+19(stat.)&19(syst.) MeV above the hadronization value of about 175 MeV. If such thermal photons are indeed observable. (he LIC should lead to much hieher temperatures For electromagnetic raclialion.," The corresponding temperature is with $T=221 \pm 19({\rm stat.}) \pm 19({\rm syst.})$ MeV above the hadronization value of about 175 MeV. If such thermal photons are indeed observable, the LHC should lead to much higher temperatures for electromagnetic radiation."139 The last question addresses quarkonium production in nuclear collisions at the LIIC., The last question addresses quarkonium production in nuclear collisions at the LHC.140 The production rate in sla—Au collisions at RIHC is compatible with that [or central collisions at the SPS. once cold nuclear matter effects are taken into account.," The production rate in $Au-Au$ collisions at RHIC is compatible with that for central collisions at the SPS, once cold nuclear matter effects are taken into account."141 The remaining survival rate of about 50% is in accord. with suppression of the higherexcited states and \.)) and survival of the direct [29].., The remaining survival rate of about 50 is in accord with suppression of the higherexcited states and ) and survival of the direct \cite{KKS}.142 The much higher energy density of the LIIC should dissociate also the latter. leading to complete suppression (modulo B decay and corona production).," The much higher energy density of the LHC should dissociate also the latter, leading to complete suppression (modulo $B$ decay and corona production)."143 The expected survival pattern is illustrated in Fig. &.., The expected survival pattern is illustrated in Fig. \ref{seq}. .144velocities (interpreted as expansion) and on the angular extent of the filament system.,velocities (interpreted as expansion) and on the angular extent of the filament system.145" Age estimates range from ~1300 years for Danziger(1980) to ~2350 years for up to ~3500 years for Morse,Winkler&Kirshner (1995)."," Age estimates range from $\sim$ 1300 years for \cite{Danziger76, Lasker80} to $\sim$ 2350 years for \cite{Sutherland95a} up to $\sim$ 3500 years for \cite{Morse95}."146. The poor agreement between these different studies is a direct consequence of different assumptions about the shape of the O-rich ejecta., The poor agreement between these different studies is a direct consequence of different assumptions about the shape of the O-rich ejecta.147" Based on FOS UV/optical spectra of the O-rich knots, Blairetal.(2000) remarked upon the similarity of their composition with the predictions of the supernova nucleosynthesis models of Nomotoetal.(1997) for progenitor masses of the order of Mo."," Based on FOS UV/optical spectra of the O-rich knots, \cite{Blair00} remarked upon the similarity of their composition with the predictions of the core-collapse supernova nucleosynthesis models of \cite{Nomoto97} for progenitor masses of the order of 25-35 $_{\odot}$."148 N132D might therefore be the result of a Type Ib SN., N132D might therefore be the result of a Type Ib SN.149 Several other clumps located within the outer X-ray shell have been observed to contain hydrogen and other light elements., Several other clumps located within the outer X-ray shell have been observed to contain hydrogen and other light elements.150" Since these display an abundance similar to the LMC, it is certain that these represent clouds of pre-existing ISM now undergoing a radiative cloud shock phase."," Since these display an abundance similar to the LMC, it is certain that these represent clouds of pre-existing ISM now undergoing a radiative cloud shock phase."151" In particular, Blairetal.(2000) failed to find any nitrogen enhancement that would suggest a possible origin from mass loss in a stellar wind from a massive progenitor star."," In particular, \cite{Blair00} failed to find any nitrogen enhancement that would suggest a possible origin from mass loss in a stellar wind from a massive progenitor star."152" Those ISM clumps display radial velocities of the order of a few hundred km s-!, consistent with the expected cloud shock velocities."," Those ISM clumps display radial velocities of the order of a few hundred km $^{-1}$, consistent with the expected cloud shock velocities."153" In this paper, we present a new optical study of N132D. Our objective is to remove the uncertainties linked to the shape of the O-rich ejecta by creating a real 3D map of the ejecta Vogt&Dopita (2010a)."," In this paper, we present a new optical study of N132D. Our objective is to remove the uncertainties linked to the shape of the O-rich ejecta by creating a real 3D map of the ejecta \cite{Vogt10a}."154. We used the (WiFeS) on the 2.3m telescope operated by the Australian National University at the Siding Spring Observatory., We used the (WiFeS) on the 2.3m telescope operated by the Australian National University at the Siding Spring Observatory.155 'The instrument design has been described by Dopitaetal.(2007) and its on-telescope performance has been detailed in Dopitaetal.(2010)., The instrument design has been described by \citet{dopita2007} and its on-telescope performance has been detailed in \cite{dopita2010}.156". This instrument provides a (fully filled) field of view of 38x25 arc sec.,"," This instrument provides a (fully filled) field of view of $38\times25$ arc sec.,"157" a spatial resolution element of 1.0x0.5 arc sec, spectral resolutions of either 3000 or 7000, and a wavelength coverage of 3200-9600A."," a spatial resolution element of $1.0\times 0.5$ arc sec, spectral resolutions of either 3000 or 7000, and a wavelength coverage of 3200-9600."158 Our analysis is based on the dynamics of the [O III] eemitting filaments at a resolution of R=3000., Our analysis is based on the dynamics of the [O III] emitting filaments at a resolution of $R=3000$.159" The data is presented in Section ??,, and the reduction processes are described in Section ??.."," The data is presented in Section \ref{Sec:obs}, and the reduction processes are described in Section \ref{Sec:reduc}."160" Section presents the results, and our 3D map of the oxygen rich ejecta in N132D in is given in Section ??.."," Section \ref{Sec:results} presents the results, and our 3D map of the oxygen rich ejecta in N132D in is given in Section \ref{Sec:3d}."161" We discuss the interpretation of the observations in Section ??,, and our conclusions are presented in Section ??.."," We discuss the interpretation of the observations in Section \ref{Sec:RK}, and our conclusions are presented in Section \ref{Sec:concl}."162 We obtained spectroscopic maps of the supernova remnant N132D at a resolution R=3000 in the blue and R—7000 in the red., We obtained spectroscopic maps of the supernova remnant N132D at a resolution $R = 3000$ in the blue and $R = 7000$ in the red.163" Data were acquired over four consecutive nights on December 12th to 15th, 2009, using WiFeS (Wide Field Spectrograph, see Dopitaetal.(2007,2010))) on the ANU 2.3m telescope at the Siding Spring Observatory."," Data were acquired over four consecutive nights on December 12th to 15th, 2009, using WiFeS (Wide Field Spectrograph, see \cite{dopita2007,dopita2010}) ) on the ANU 2.3m telescope at the Siding Spring Observatory."164 The data consist of a mosaic of six fields covering the central and western regions of N132D. Each field spans 25x38 arc sec., The data consist of a mosaic of six fields covering the central and western regions of N132D. Each field spans $\times$ 38 arc sec.165 with 0.5 arc sec., with 0.5 arc sec.166 sampling in the spatial direction., sampling in the spatial direction.167 The data were subsequently interpolated to provide 0.5x arc sec., The data were subsequently interpolated to provide $0.5 \times 0.5$ arc sec.168 pixels., pixels.169 The total field of view covered spans ~81x73 arc sec., The total field of view covered spans $\sim$ $\times$ 73 arc sec.170" in RA and in Dec, respectively."," in RA and in Dec, respectively."171 An observational difficulty of observing the LMC over long periods of the night is that the instrument does not have an atmospheric dispersion compensator., An observational difficulty of observing the LMC over long periods of the night is that the instrument does not have an atmospheric dispersion compensator.172" As we have to observe at fixed position angle, the parallactic angle continuously rotates."," As we have to observe at fixed position angle, the parallactic angle continuously rotates."173" In addition, the pointing model for the telescope was imperfect at the time of the observation."," In addition, the pointing model for the telescope was imperfect at the time of the observation."174" Because of errors and drift in the pointing and the changes in atmospheric dispersion, the six fields did not properly overlap."," Because of errors and drift in the pointing and the changes in atmospheric dispersion, the six fields did not properly overlap."175" In particular, a noticeable gap is present to the bottom right of the mosaic."," In particular, a noticeable gap is present to the bottom right of the mosaic."176" Following the reduction of the data, described hereafter, we established the pointing of each field by referencing the star fields to the DSS images of the same area."," Following the reduction of the data, described hereafter, we established the pointing of each field by referencing the star fields to the DSS images of the same area."177 The accurate pointing position deduced for each field and their respective labeling is shown in Fig. 1.., The accurate pointing position deduced for each field and their respective labeling is shown in Fig. \ref{fig:fields}.178" 'The fields numbered 2,5 and 3 were acquired on the nights 1,2 and 3 respectively, with a poor mean seeing of ~3.5, ~3 and ~ 3.5 arc sec."," The fields numbered 2,5 and 3 were acquired on the nights 1,2 and 3 respectively, with a poor mean seeing of $\sim$ 3.5, $\sim$ 3 and $\sim$ 3.5 arc sec."179" The remaining fields 1,4 and 6 have been obtained in this order on the fourth night, with the seeing ranging from ~1.5 arc sec."," The remaining fields 1,4 and 6 have been obtained in this order on the fourth night, with the seeing ranging from $\sim$ 1.5 arc sec."180 at the beginning of the night to  2.5 arc sec., at the beginning of the night to $\sim$ 2.5 arc sec.181 at the end., at the end.182" Note that the relative spatial shift of field 6 is the worst, mostly resulting from the (large) effect of atmospheric dispersion."," Note that the relative spatial shift of field 6 is the worst, mostly resulting from the (large) effect of atmospheric dispersion."183" The spectral coverage ranges from A3200A to A5900À for the blue image, and A5290À to A7060 for the red image."," The spectral coverage ranges from $\lambda$ 3200 to $\lambda$ 5900 for the blue image, and $\lambda$ 5290 to $\lambda$ 7060 for the red image."184" Both the red and blue images are taken simultaneously, using the RT560 dichroic which has a cut at about 5700 Dopitaetal.(2010)."," Both the red and blue images are taken simultaneously, using the RT560 dichroic which has a cut at about 5700 \cite{dopita2010}."185. All images were acquired with 2x1 pixel binning ?T?esing the WiFeS “Nod-and-Shuffle” data acquisiton mode (seeDopitaetal.2010)..," All images were acquired with $2\times1$ pixel binning using the WiFeS “Nod-and-Shuffle"" data acquisiton mode \citep[see][]{dopita2010}."186 Each image consists of 6 cycles of 150 sec., Each image consists of 6 cycles of 150 sec.187 on the object and 6 interleaved cycles of 75 sec., on the object and 6 interleaved cycles of 75 sec.188" on the sky, giving a total on-object exposure of 1350 sec and a total image exposure time (including the overheads for guide-star acquisition and readout) of about 2740 sec."," on the sky, giving a total on-object exposure of 1350 sec and a total image exposure time (including the overheads for guide-star acquisition and readout) of about 2740 sec."189 Three such images of each of the six fields were taken to allow for adequate cosmic ray subtraction., Three such images of each of the six fields were taken to allow for adequate cosmic ray subtraction.190In Figures BI to B6 we present the residual images constructed as described in Section 3.6.,In Figures B1 to B6 we present the residual images constructed as described in Section 3.6.191 For each galaxy the left image is the NUV image as obtained from the GALEX archive. the centre panel is the residual after subtraction of the scaled H-band model. and the right panel the NUV image after subtraction of the scaled model.," For each galaxy the left image is the NUV image as obtained from the GALEX archive, the centre panel is the residual after subtraction of the scaled H-band model, and the right panel the NUV image after subtraction of the scaled model."192 Here we provide comments on the residual maps of individual - The NUV residual is negative. and id dominated by the metallicity gradient.," Here we provide comments on the residual maps of individual - The NUV residual is negative, and id dominated by the metallicity gradient."193 The FUV residual shows an extended and elongated UV excess distribution. and the effect of the metallicity gradient is also visible as a faint negative region around - The positive residual in the very centre of this galaxy is visible in all passbands. and is due to a poor fit of the Sérrsic function to the surface brightness profile.," The FUV residual shows an extended and elongated UV excess distribution, and the effect of the metallicity gradient is also visible as a faint negative region around - The positive residual in the very centre of this galaxy is visible in all passbands, and is due to a poor fit of the Sérrsic function to the surface brightness profile."194 The fit is also complicated by three other sources close to the core., The fit is also complicated by three other sources close to the core.195 There is a more extended excess in teh FUV residual map. and a region of negative residuals due to the metallicity - The NUV residual map is dominated by the negative region caused by the metallicity gradient. and a source to the west of the nucleus.," There is a more extended excess in teh FUV residual map, and a region of negative residuals due to the metallicity - The NUV residual map is dominated by the negative region caused by the metallicity gradient, and a source to the west of the nucleus."196 The FUV map shows a somewhat more compact FUV excess - This and subsequent galaxies have much shorter exposures and hence worse signal-to-noise in the residual maps than the first three., The FUV map shows a somewhat more compact FUV excess - This and subsequent galaxies have much shorter exposures and hence worse signal-to-noise in the residual maps than the first three.197 The NGC1407 residual maps show an excess at small radii. in this case the residual occurs in all wavebands and is due to excess light over the Sérrsic fit in the core.," The NGC1407 residual maps show an excess at small radii, in this case the residual occurs in all wavebands and is due to excess light over the Sérrsic fit in the core."198" The FUV excess in this galaxy is however apparant in the colour - This galaxy shows a moderate extended FUV excess. and in the NUV band a negative metallicity gradient - This also shows an extended FUV excess and a negative NUV - In addition to the FUV excess. this galaxy shows a point residual in the nucleus in longer bands. it is unclear whether this is a stellar ""extra light"" component or a weak nuclear - In this case there is a stronger FUV excess. and a weak positive residual in the nucleus at longer - This galaxy has an extended FUV excess region. and a negative NUV residual in the - This galaxy has an extended FUV excess region."," The FUV excess in this galaxy is however apparant in the colour - This galaxy shows a moderate extended FUV excess, and in the NUV band a negative metallicity gradient - This also shows an extended FUV excess and a negative NUV - In addition to the FUV excess, this galaxy shows a point residual in the nucleus in longer bands, it is unclear whether this is a stellar “extra light” component or a weak nuclear - In this case there is a stronger FUV excess, and a weak positive residual in the nucleus at longer - This galaxy has an extended FUV excess region, and a negative NUV residual in the - This galaxy has an extended FUV excess region."199 The positive residual in NUV is not seen at longer wavelengths. and we attribute this to a low level of star formation in the core. rather than failure of the Sérrsie - There is an extended FUV excess region. and in the NUV image a low surface brightness dwarf elliptical companion (NGC4A06B) to the - This galaxy has an extended FUV excess region. and a negative NUV residual in the - There is an extended FUV excess region. and a point residual caused by a poor Sérrsic fit in the - The fit to this galaxy is complicated by the close companion (NGC4647).," The positive residual in NUV is not seen at longer wavelengths, and we attribute this to a low level of star formation in the core, rather than failure of the Sérrsic - There is an extended FUV excess region, and in the NUV image a low surface brightness dwarf elliptical companion (NGC4406B) to the - This galaxy has an extended FUV excess region, and a negative NUV residual in the - There is an extended FUV excess region, and a point residual caused by a poor Sérrsic fit in the - The fit to this galaxy is complicated by the close companion (NGC4647)."200 However the extended NUV residual does not appear to be caused by a poor Sérrsie tit in the H-band. but by a low level of ongoing star formation. as suggested by Magris Bruzual - This galaxy has an extended FUV excess region. and a negative NUV residual in the - This galaxy has cD morphology. yet lies in the outer regions of the Coma cluster.," However the extended NUV residual does not appear to be caused by a poor Sérrsic fit in the H-band, but by a low level of ongoing star formation, as suggested by Magris Bruzual - This galaxy has an extended FUV excess region, and a negative NUV residual in the - This galaxy has cD morphology, yet lies in the outer regions of the Coma cluster."201 It has a clear extended FUV excess region. and a positive NUV residual which does not appear to be due to a poor Sérrsie fit in the core.," It has a clear extended FUV excess region, and a positive NUV residual which does not appear to be due to a poor Sérrsic fit in the core."202 We suggest that this galaxy. like NGC4649. has a low level of ongoing star formation in the core. -," We suggest that this galaxy, like NGC4649, has a low level of ongoing star formation in the core. -"203 This galaxy is in the centre of the Coma cluster and has cD morphology. yet it appears to have only a weak FUV excess.," This galaxy is in the centre of the Coma cluster and has cD morphology, yet it appears to have only a weak FUV excess."204 The there is little residual in - This is the brightest galaxy in the Coma cluster. albeit it has elliptical rather than cD morphology.," The there is little residual in - This is the brightest galaxy in the Coma cluster, albeit it has elliptical rather than cD morphology."205 The FUV excess is much stronger than in NGC4874., The FUV excess is much stronger than in NGC4874.206 The positive residual in NUV is not caused by a poor Sérrsic fit in the core. and again we suggest that there may be a low level of star formation in this - The FUV excess is weak. and there are no clear residuals in the NUV - There is a compact companion (NGC5846A) to the south.," The positive residual in NUV is not caused by a poor Sérrsic fit in the core, and again we suggest that there may be a low level of star formation in this - The FUV excess is weak, and there are no clear residuals in the NUV - There is a compact companion (NGC5846A) to the south."207 Residual maps are similar in FUV and NUV. suggesting that there is ongoing star - The FUV excess region is compact. and the NUV residual map shows no structure.," Residual maps are similar in FUV and NUV, suggesting that there is ongoing star - The FUV excess region is compact, and the NUV residual map shows no structure."208 There is a faint companion (SDSS J153839.55+592|34.3) to the - The FUV excess is weak and the positive residual seen in the NUV residual image occurs in all wavebands and is due to a poor fit of the Sérrsic function in the core. and will contribute to some extent to the FUV residual - There is an extended FUV excess residual. and in the NUV the Liner in the nucleus shows as a point - This shows a strong extended FUV excess residual. and negative residuals in - As with NGCIOS2 this shows and extended ΕΙΝ excess residual. and à nuclear NUV residual from the Liner. -," There is a faint companion (SDSS J153839.55+592134.3) to the - The FUV excess is weak and the positive residual seen in the NUV residual image occurs in all wavebands and is due to a poor fit of the Sérrsic function in the core, and will contribute to some extent to the FUV residual - There is an extended FUV excess residual, and in the NUV the Liner in the nucleus shows as a point - This shows a strong extended FUV excess residual, and negative residuals in - As with NGC1052 this shows and extended FUV excess residual, and a nuclear NUV residual from the Liner. -"209 This galaxy has a strong and extended UV excess. and negative residuals due to metallicity in NUV.," This galaxy has a strong and extended UV excess, and negative residuals due to metallicity in NUV."210 There is no indication of any nuclear - M87 shows the well known non-thermal nuclear source and jet in both FUV and NUV., There is no indication of any nuclear - M87 shows the well known non-thermal nuclear source and jet in both FUV and NUV.211 The extended FUV excess region is also clearly - In this case it is unclear whether the NUV residual is, The extended FUV excess region is also clearly - In this case it is unclear whether the NUV residual is212in column 14 of Table 1 (6 objects).,in column 14 of Table 1 (6 objects).213 For the AGNs in our sample which are not part of the Palomar survey. values of σ. derived from direct fitting analyses of the CaT lines are adopted from other published sources (see column 14 of ‘Table 1: 4 objects).," For the AGNs in our sample which are not part of the Palomar survey, values of $\sigma_*$ derived from direct fitting analyses of the CaT lines are adopted from other published sources (see column 14 of Table 1; 4 objects)."214 AME final adopted σι measurements are converted to Alba estimates using Equation Three of the AGNs within our sample (15Ο121-000 NGC 1448 and NGC 1792) currently lack archival clirect or indirect. SAIBLDE mass constraints.," All final adopted $\sigma_*$ measurements are converted to $\Mbh$ estimates using Equation Three of the AGNs within our sample (ESO121-G006, NGC 1448 and NGC 1792) currently lack archival direct or indirect SMBH mass constraints."215 Hence. for these three objects. we follow the formalism of Marconi Hunt. (2003: hereafter. MIIOS) and use 2ALASS A-band imaging andGALLIT. the two-dimensional imaging analysis software. of 7.. to constrain the bulge luminosities and therefore. Alou for these three ACGNs.," Hence, for these three objects, we follow the formalism of Marconi Hunt (2003; hereafter, MH03) and use 2MASS $K$ -band imaging and, the two-dimensional imaging analysis software of \citet{galfit}, to constrain the bulge luminosities and therefore, $\Mbh$ for these three AGNs."216 Near-H1t. 4.8 tun). emission. is a strong tracer. of stellar mass and is less susceptible to the effects of dust/gas extinction than optical emission., Near-IR $4.8\um$ ) emission is a strong tracer of stellar mass and is less susceptible to the effects of dust/gas extinction than optical emission.217 As a result of this. the A-band (2.2 jun) is shown to provide the strongest correlation ofall near-LH bands between the luminosity of the bulge and Alby CMLIIO3).," As a result of this, the }-band $2.2\um$ ) is shown to provide the strongest correlation of all near-IR bands between the luminosity of the bulge and $\Mbh$ (MH03)."218 For the bulec-dise decomposition image analysis. we have obtained archival A-band imaging for ESO 121-C006. NGC 1448 and NGC 1792.," For the bulge-disc decomposition image analysis, we have obtained archival -band imaging for ESO 121-G006, NGC 1448 and NGC 1792."219 Phese images were retrieved fron the Two Micron Al-Sky Survey (24LASS) extended. source catalogue ancl consist. of. pre-mosaicked. (1 areseconcl per pixel resolution) all-sky atlas images., These images were retrieved from the Two Micron All-Sky Survey (2MASS) extended source catalogue and consist of pre-mosaicked (1 arcsecond per pixel resolution) all-sky atlas images.220" The A-band images of the three galaxies were modeled with a central point spread function (PSE) and a constant sky background contribution. whilst the bulge and host-galaxy components were modeled using variations of the Sersie profile: where r, is the effective racius of the profile. X, is the surface brightness at the cllective radius. ? is the power-law (Sersic) index. ane & is coupled ton such that half of the total flux of the object is within the elfective radius."," The -band images of the three galaxies were modeled with a central point spread function (PSF) and a constant sky background contribution, whilst the bulge and host-galaxy components were modeled using variations of the Sersic profile: where $r_e$ is the effective radius of the profile, $\Sigma_e$ is the surface brightness at the effective radius, $n$ is the power-law (Sersic) index, and $\kappa$ is coupled to $n$ such that half of the total flux of the object is within the effective radius."221 We employ two special forms of the Sersie profile in our moceling. he exponential (n= 1) and the de Vaucouleurs (n= +) xofiles. which are classically used to model galactic disces andl bulges. respectively.," We employ two special forms of the Sersic profile in our modeling, the exponential $n=1$ ) and the de Vaucouleurs $n=4$ ) profiles, which are classically used to model galactic discs and bulges, respectively."222 ? have shown that the reliability. of the fitting parameters produced by are strongly. dependent on he initial estimates., \citet{haussler07} have shown that the reliability of the fitting parameters produced by are strongly dependent on the initial estimates.223 will in general. fail to [ind he overall global chi-squarecl (47) minimum to the fit if he initial estimates are poorly constrained.," will, in general, fail to find the overall global chi-squared $\chi^2$ ) minimum to the fit if the initial estimates are poorly constrained."224 Thus. to reduce his svstematic ellect. and aid the fitting routine. we use a simplified: l-dimensional fit to produce initial estimates of he fitting parameters.," Thus, to reduce this systematic effect, and aid the fitting routine, we use a simplified 1-dimensional fit to produce initial estimates of the fitting parameters."225 X lI-dimensional surface-brightness slice of the A-band image was taken across the major axis of each of the galaxies., A 1-dimensional surface-brightness slice of the -band image was taken across the major axis of each of the galaxies.226 A surface brightness profile extending rom the nucleus was produced by averaging the two semi-major axes from the slice. and removing the measured xickeround flux.," A surface brightness profile extending from the nucleus was produced by averaging the two semi-major axes from the slice, and removing the measured background flux."227 Few spiral galaxies are found to host bulges with true cle Vaucouleurs proliles. thus a global X7 reduction orocess was used to simultaneously Gt a generalised. Sersic wofile and a fixed (η=1) exponential dise to the I-d surface xiehtness profile.," Few spiral galaxies are found to host bulges with true de Vaucouleurs profiles, thus a global $\chi^2$ reduction process was used to simultaneously fit a generalised Sersic profile and a fixed $n=1$ ) exponential disc to the 1-d surface brightness profile."228 From these. we calculate Sersie and disc radii. as well as the Sersic index of the bulge.," From these, we calculate Sersic and disc radii, as well as the Sersic index of the bulge."229 Combining the l-d parameter estimates with the total A-band magnitude rom the 2ALASS Large Galaxy Atlas (7)... we generate an appropriate set of constraints and initial parameters to be input toGALLEIT.," Combining the 1-d parameter estimates with the total -band magnitude from the 2MASS Large Galaxy Atlas \citep{jarrett03}, we generate an appropriate set of constraints and initial parameters to be input to."230 Using the derived. parameter estimates. is used o Lit a generalised 2-d Sersic profile with an exponential disc o the A-band image.," Using the derived parameter estimates, is used to fit a generalised 2-d Sersic profile with an exponential disc to the -band image."231" To again aid the reduction analysis. particular attention is paid to simulating accurate ""SES for the 2ALASS images using known standard: stars (J. lt. Lucey private. “Results of this xilge/dise reduction for the three objects are. presented. in Fig."," To again aid the reduction analysis, particular attention is paid to simulating accurate PSFs for the 2MASS images using known standard stars (J. R. Lucey private Results of this bulge/disc reduction for the three objects are presented in Fig."232 1. and column 11 of Table 1., \ref{bd_decomp} and column 11 of Table 1.233 We have directly tested our robust method using he late-type galaxies (i.c... SO or later) presented. in the dataset of MEOS. ancl find. close agreement. (=0.1. dex).," We have directly tested our robust method using the late-type galaxies (i.e., S0 or later) presented in the dataset of MH03 and find close agreement $\approx 0.1$ dex)."234 We do note however. that we find a systematic ollsct of a [actor zc2 in bulge luminosity for the ACGNs in MEOS that are hosted in low-inclination angle late-tvpe galaxies. which is likely to be caused by over-estimating the contribution of the bulge to the total flux of the galaxy.," We do note however, that we find a systematic offset of a factor $\approx 2$ in bulge luminosity for the AGNs in MH03 that are hosted in low-inclination angle late-type galaxies, which is likely to be caused by over-estimating the contribution of the bulge to the total flux of the galaxy."235 Indeed. when directly comparing a sample of reverberation mapped X-ray detected AGNs to Mpg estimations using the ALIOS formalism. ? find similar results.," Indeed, when directly comparing a sample of reverberation mapped X-ray detected AGNs to $\Mbh$ estimations using the MH03 formalism, \citet{vasudevan09a} find similar results."236 However. the three galaxies fitted. in our sample are all moderately to highly-inclined and thus this svstematic clfect will be negligible.," However, the three galaxies fitted in our sample are all moderately to highly-inclined and thus this systematic effect will be negligible."237 In Fig., In Fig.238 1 we show the three produced. image cubes obtained following our bulge/disc fitting routines., \ref{bd_decomp} we show the three produced image cubes obtained following our bulge/disc fitting routines.239 Within each of the residual (observed model) images it is clear that the bulge is well fitted by a —-Sersic profile., Within each of the residual (observed – model) images it is clear that the bulge is well fitted by a Sersic profile.240 “Phe edge-on galaxy. ESO121-C006 is well fit bx an exponential disc combined with a Sersic profile. with no distinguishing residual features.," The edge-on galaxy ESO121-G006 is well fit by an exponential disc combined with a Sersic profile, with no distinguishing residual features."241 The residual of NGC 1448 highlights the existence of its spiral arms ancl shows the presence of a truncated dise combined with a possible bar structure which our simplified. modeling technique is incapable of fitting: however. the bulge fit does not appear to be compromised.," The residual of NGC 1448 highlights the existence of its spiral arms and shows the presence of a truncated disc combined with a possible bar structure which our simplified modeling technique is incapable of fitting; however, the bulge fit does not appear to be compromised."242 lndeed. our derived Mig estimations for ESO121-C(006 and NGC. 1H4S are consistent with the Mpg upper limits obtained [rom stellar mass-to-light ratio analyses (2)..," Indeed, our derived $\Mbh$ estimations for ESO121-G006 and NGC 1448 are consistent with the $\Mbh$ upper limits obtained from stellar mass-to-light ratio analyses \citep{ratnam00}."243 The residual image of the moderately inclined galaxy. NGC 1792. contains strong spiral arms as well as a point-like nuclear source.," The residual image of the moderately inclined galaxy, NGC 1792, contains strong spiral arms as well as a point-like nuclear source."244 We note that due to the inclination angle. of this source. the derived. Mpig may be systematically over-estimated bv a factor of z2 (see above).," We note that due to the inclination angle of this source, the derived $\Mbh$ may be systematically over-estimated by a factor of $\approx 2$ (see above)."245 Thus. our derived Eddington rate for NGC 1792. presentedin 855.1. should be considered a lower limit.," Thus, our derived Eddington rate for NGC 1792, presentedin 5.1, should be considered a lower limit."246 From the obtained A-band bulge magnitudes (column 11. Table 1) we calculate bulge luminosities (Li μα).," From the obtained -band bulge magnitudes (column 11, Table 1) we calculate bulge luminosities $L_{\rm K,bul}$ )."247 Using, Using248"Qr,=0.1 (andmoderateradialdrift,seeBai&Stone,2010c).","$\varOmega \tau_{\rm f}249\gtrsim 0.1$ \citep[and moderate radial drift, see][]{BaiStone2010c}."250". Clumping proceeds as initially very low amplitude particle overdensities accelerate the gas towards the Keplerian speed, hence reducing the local head-wind, which in turn slows the radial drift of the particles."," Clumping proceeds as initially very low amplitude particle overdensities accelerate the gas towards the Keplerian speed, hence reducing the local head-wind, which in turn slows the radial drift of the particles."251" Drifting particles pile up where the head-wind is slower, causing exponential growth of the particle density as the particles continue to increase their drag force influence on the gas."," Drifting particles pile up where the head-wind is slower, causing exponential growth of the particle density as the particles continue to increase their drag force influence on the gas."252 Johansenetal.(2009) found that overdense regions contract when including particle self-gravity and that eventually a number of gravitationally bound clumps form., \cite{Johansen+etal2009} found that overdense regions contract when including particle self-gravity and that eventually a number of gravitationally bound clumps form.253 These models nevertheless did not include any particle collisions., These models nevertheless did not include any particle collisions.254 We perform 3-D simulations where the gas is modelled on a fixed grid and solid particles with superparticles., We perform 3-D simulations where the gas is modelled on a fixed grid and solid particles with superparticles.255 We solve the standard shearing box equations for gas and particles (same gravity)..," We solve the standard shearing box equations for gas and particles \citep[same as in][but with additional vertical256gravity]{JohansenYoudin2007}."257 The frame rotates at the Keplerian frequency Q at a fixed orbital distance r from the star., The frame rotates at the Keplerian frequency $\varOmega$ at a fixed orbital distance $r$ from the star.258" The coordinate axes are oriented such that x points radially outwards, y points along the rotation direction of the disc, while z points perpendicular to the disc along Q."," The coordinate axes are oriented such that $x$ points radially outwards, $y$ points along the rotation direction of the disc, while $z$ points perpendicular to the disc along $\vc{\varOmega}$."259" The gas is subjected to a radial pressure gradient which reduces its orbital speed by the positive amount Av=0.05c,."," The gas is subjected to a radial pressure gradient which reduces its orbital speed by the positive amount $\Delta v=0.05 c_{\rm260s}$."261" Particles do not feel this radial pressure gradient, and the resulting relative motion between particles and gas drives the streaming instability (Goodman&Pindor,2000;Youdin&Goodman, 2005)."," Particles do not feel this radial pressure gradient, and the resulting relative motion between particles and gas drives the streaming instability \citep{GoodmanPindor2000,YoudinGoodman2005}."262". We consider a cubic box with side lengths L,=Ly0.2H, where H=c,/Q is the gas scale height, to capture the fastest growing modes of the streaming instability of marginally coupled particles, Αςι/Η~nr/HAv/cs= 0.05."," We consider a cubic box with side lengths $L_x=L_y=L_z=0.2 H$, where $H=c_{\rm s}/\varOmega$ is the gas scale height, to capture the fastest growing modes of the streaming instability of marginally coupled particles, $\lambda_{\rm SI}/H\sim\eta r/H\sim\Delta263v/c_{\rm s}=0.05$ ."264" This is also the characteristic scale of Kelvin- instabilities, thriving in the vertical shear in the gas and particle velocity (Youdin&Shu,2002;Leeetal.,2010)., although Bai&Stone(2010b) demonstrated that the streaming instability is dominant over Kelvin-Helmholtz instabilities in setting the dynamics of particle layers with Qr;>0.1."," This is also the characteristic scale of Kelvin-Helmholtz instabilities, thriving in the vertical shear in the gas and particle velocity \citep{YoudinShu2002,Lee+etal2010}, although \cite{BaiStone2010b} demonstrated that the streaming instability is dominant over Kelvin-Helmholtz instabilities in setting the dynamics of particle layers with $\varOmega \tau_{\rm f}>0.1$."265" The friction time of the particles is fixed at Or;=0.3 in all simulations, corresponding to approximately 20-cm rocks around the location of the asteroid belt at 3 AU, and to 6- pebbles at 30 AU (Weidenschilling,1977)."," The friction time of the particles is fixed at $\varOmega \tau_{\rm f}=0.3$ in all simulations, corresponding to approximately 20-cm rocks around the location of the asteroid belt at 3 AU, and to 6-mm pebbles at 30 AU \citep{Weidenschilling1977}."266". The particle column density is set to of the total gas column density, the latter including the gas beyond the vertical boundaries of the box."," The particle column density is set to of the total gas column density, the latter including the gas beyond the vertical boundaries of the box."267 For our choice of Av strong particle clumping can only be obtained at such super-solar metallicity*.., For our choice of $\Delta v$ strong particle clumping can only be obtained at such super-solar .268 The average, The average269To the final list we have also added: the candidates available in the SDSS. but discovered in previous stuclics: three galaxies. found by examining the images of peculiar objects ancl galaxies with outer rings from the lists hy Nair&Abraham (2010).. who visually classified 14084 &alaxies in the SDSS/DR-A: three candidates that we found analyzing the notes to the MCCG catalogue (Vorontsov-Velvaminoyv&Ixrasnogorskaja 1962): SDSS J182533.22|272246.7 found bv Finkelmanctal.(2011). viewing the SUBARU deep lield: another galaxy [rom the ESO Press Release 14/98 SDSS J000911.57-003654.7 (Reshetnikoyctal.2011):: a distant. PRO SDSS J075234.33|202049.8 (Broschοἱal. 2010).. mentioned in the Introduction and. also 14 galaxies kindly provided us by Edo Finkelman (Finkelmansomeofhisgalaxiesarestudied in)..,"To the final list we have also added the candidates available in the SDSS, but discovered in previous studies: three galaxies, found by examining the images of peculiar objects and galaxies with outer rings from the lists by \citet{NairAbraham2010}, who visually classified $14\,034$ galaxies in the SDSS/DR4; three candidates that we found analyzing the notes to the MCG catalogue \citep{MCG}; ; SDSS J132533.22+272246.7 found by \citet{Finkelman2011} viewing the SUBARU deep field; another galaxy from the ESO Press Release 14/98 – SDSS J000911.57-003654.7 \citep{Resh2011}; a distant PRG SDSS J075234.33+292049.8 \citep{Brosch2010}, mentioned in the Introduction and also 14 galaxies kindly provided us by Ido Finkelman \citep[some of his galaxies are studied in]{FinkelmanNEW}."270" As a result. we compiled a list of 122 galaxies. which in itself significantly expands the list of ""genuine? candidates from the PRC. since the majority of. discovered: objects corresponds to the PRC-B and PRCO-C categories."," As a result, we compiled a list of 122 galaxies, which in itself significantly expands the list of “genuine” candidates from the PRC, since the majority of discovered objects corresponds to the PRC-B and PRC-C categories."271 However. this list obviously sulfers from a heavy incompleteness. since only a small fraction of the Galaxy Zoo volunteers reports on unusual galaxies in the forum.," However, this list obviously suffers from a heavy incompleteness, since only a small fraction of the Galaxy Zoo volunteers reports on unusual galaxies in the forum."272 Lintottctal.(2011). have recently. reported. the results of a simple morphological classification for almost. 900.000 ealaxies. made by Galaxy Zoo volunteers.," \citet{GalZoo2011} have recently reported the results of a simple morphological classification for almost 900,000 galaxies, made by Galaxy Zoo volunteers."273 They have published lists of 667.945 galaxies with known spectral redshifts (in the range 0.001.<2 0.025) and 225.268 galaxies without the spectra from the SDSS/DIV.," They have published lists of 667,945 galaxies with known spectral redshifts (in the range $0.001<z<0.025$ ) and 225,268 galaxies without the spectra from the SDSS/DR7."274 The catalogue contains the majority of extended objects. having in the r-band Petrosian magnitudes brighter than 17.777 as well as the galaxies from the SDSS spectral survey.," The catalogue contains the majority of extended objects, having in the $r$ -band Petrosian magnitudes brighter than $17.77^m$, as well as the galaxies from the SDSS spectral survey."275 The Classification of galaxies was carried out by the following simple tvpes: £L elliptical CULOW clockwise and anticlockwise spirals: DU spiral. seen edge-on: ALC interacting svstems: 2A (don't know) — unidentified.," The classification of galaxies was carried out by the following simple types: $EL$ – elliptical; $CW/ACW$ – clockwise and anticlockwise spirals; $EDGE$ – spiral, seen edge-on; $MG$ -- interacting systems; $DK$ (don't know) – unidentified."276 At a first glance it secms that this classification is too Coarse for our purposes. but the [act that for cach galaxy a large number (as a rule a few dozen) of independent evaluations were carried out greatly simplifies the situation.," At a first glance it seems that this classification is too coarse for our purposes, but the fact that for each galaxy a large number (as a rule – a few dozen) of independent evaluations were carried out greatly simplifies the situation."277 Lhe objects are hence characterised not simply by one of the above types. but rather by a fraction of votes cast for each type. which can be called. subject to restrictions. the probability of belonging to à particular type.," The objects are hence characterised not simply by one of the above types, but rather by a fraction of votes cast for each type, which can be called, subject to restrictions, the probability of belonging to a particular type."278 lig., Fig.279" 1 demonstrates these probabilities for all the Galaxy Zoo galaxies anc for the ""reference sample"" consisting of the known PRG candidates. classified in the Galaxy Zoo."," \ref{fig_zoo} demonstrates these probabilities for all the Galaxy Zoo galaxies and for the “reference sample” consisting of the known PRG candidates, classified in the Galaxy Zoo."280 Ehe reference sample contains 126 objects and includes galaxies. selected in Section 2.1 (for 103 of them the Galaxy Zoo has a classification) and all the galaxies rom the PRC catalogue. classified in the Galaxy.," The reference sample contains 126 objects and includes galaxies, selected in Section 2.1 (for 103 of them the Galaxy Zoo has a classification), and all the galaxies from the PRC catalogue, classified in the Galaxy."281Zoo.. For roth samples. these clistributions are significantly dillerent. except for the probability of belonging to spiral galaxies (COWPTACW).," For both samples, these distributions are significantly different, except for the probability of belonging to spiral galaxies (CW+ACW)."282 Peculiar shapes of PRC candidates do not allow the majority of respondents to rank them as elliptical ealaxies. hence for them LL<0.85.," Peculiar shapes of PRG candidates do not allow the majority of respondents to rank them as elliptical galaxies, hence for them $EL<0.85$."283 For the same reason. RC candidates reveal a much broader distribution. by he probability of merging. while most of the Galaxy Zoo galaxies are concentrated towards AZ.z0.," For the same reason, PRG candidates reveal a much broader distribution by the probability of merging, while most of the Galaxy Zoo galaxies are concentrated towards $MG\approx0$."284 Among the Gs there are. almost no spirals. oriented face-on. (i.c.. or which LDCz0). so the corresponding distribution is not only wider. but its peak is notably shifted: towards he higher DCE values because the edge-on configuration is much easier for the detection of polar structures.," Among the PRGs there are almost no spirals, oriented face-on (i.e., for which $EDGE\approx0$ ), so the corresponding distribution is not only wider, but its peak is notably shifted towards the higher $EDGE$ values because the edge-on configuration is much easier for the detection of polar structures."285 The distributions bv the DA. parameter do not vary as much. out we can still see that the peak of the PRG candidate distribution is shifted. from zero to Diyz0.07.," The distributions by the $DK$ parameter do not vary as much, but we can still see that the peak of the PRG candidate distribution is shifted from zero to $DK\approx0.07$ ."286 We can explain this by the [act that among the dozen of volunteers. classilving cach PRG. at least 12 respondents marked its unusual shape by belonging to the DA. type.," We can explain this by the fact that among the dozen of volunteers, classifying each PRG, at least 1–2 respondents marked its unusual shape by belonging to the $DK$ type."287 As a result. we can formulate the criteria. for. the selection of galaxies. similar (within the presented: tvpes) to the already. known candidate Ps. and hence greatly reduce the number of images for further examination.," As a result, we can formulate the criteria for the selection of galaxies, similar (within the presented types) to the already known candidate PRGs, and hence greatly reduce the number of images for further examination."288 We acdopted the following criteria for the selection of peculiar ealaxies: We introduced. no restrictions on the ἵνρο EL membership. since it follows [rom (1)) that EL«0.8.," We adopted the following criteria for the selection of peculiar galaxies: We introduced no restrictions on the type $EL$ membership, since it follows from \ref{e}) ) that $EL<0.8$."289 In the full Galaxy Zoo sample. 30.084. galaxies with known redshifts. and 11.874 objects without spectral data satisfy the (1)) eriteria.," In the full Galaxy Zoo sample, 30,084 galaxies with known redshifts, and 11,874 objects without spectral data satisfy the \ref{e}) ) criteria."290 From 126 PRG candidates. shown in Fig.," From 126 PRG candidates, shown in Fig."291 only 47 galaxies. ic. 37 per cent of the sample satisfy these criteria.," \ref{fig_zoo} only 47 galaxies, i.e. 37 per cent of the sample satisfy these criteria."292 Thus. if. we find ALL the potential PRCGs from the selected. 41.958. galaxies. their actual number in the whole Galaxy Zoo catalogue will be unclerestimated L/0.41z2.7 times.," Thus, if we find ALL the potential PRGs from the selected 41,958 galaxies, their actual number in the whole Galaxy Zoo catalogue will be underestimated $1/0.41\approx2.7$ times."293 But we have to agree to this. since the use of Less stringent criteria greatly increases the number of galaxies to examine.," But we have to agree to this, since the use of less stringent criteria greatly increases the number of galaxies to examine."294 In this way. if we reduce all the criteria in (1)) by a nere 015. they will be met by 68.412 objects in the total sample. while the number of objects in the PRC reference sample. falling under the eriteria will increase only up to 4N per cent.," In this way, if we reduce all the criteria in \ref{e}) ) by a mere 0.015, they will be met by 68,412 objects in the total sample, while the number of objects in the PRG reference sample, falling under the criteria will increase only up to 48 per cent."295 We viewed the images of all the galaxies. selected. in agreement with (1)).," We viewed the images of all the galaxies, selected in agreement with \ref{e}) )."296 The web interface SDSS Image Tool we used. allows to displav on one page 25 colour images. composed of the images in the g.r. filters at once.," The web interface SDSS Image Tool we used allows to display on one page 25 colour images, composed of the images in the $g,r,i$ filters at once."297 Looking through the images. we selected. candidate PGs mainly euiced by the selection criteria. listed in Section 2.1. as well as by a general similarity with the PRC catalogue objects.," Looking through the images, we selected candidate PRGs mainly guided by the selection criteria, listed in Section 2.1, as well as by a general similarity with the PRC catalogue objects."298 After examining nearly 42.000 images.we selected about 400. which were further investigated in moredetail for the final selection.," After examining nearly 42,000 images,we selected about 400, which were further investigated in moredetail for the final selection."299 The final list of PRG candidates contains 275 galaxies.," The final list of PRG candidates contains 275 galaxies,"300The right panel of Figure 6 shows horizontally integrated ciabatic heating rates throughout the atinosphere. whici are calculated. [rom the fluxes shown in the left panel: locally PP. where upward fux (iu the direction of lower pressure] is defined to be positive (see Section 2.1)).,"The right panel of Figure \ref{fig:d_heating} shows horizontally integrated diabatic heating rates throughout the atmosphere, which are calculated from the fluxes shown in the left panel; locally $dT/dt=(g/c_p)dF/dP$ , where upward flux (in the direction of lower pressure) is defined to be positive (see Section \ref{sec:rad}) )."301 When flux increases with increasing pressure. there is heatiug: this is the case for the d»wiiward (uegative) optical flix at the substellar point. which goes to zero as pressure Increases.," When flux increases with increasing pressure, there is heating; this is the case for the downward (negative) optical flux at the substellar point, which goes to zero as pressure increases."302 Likewise. iu the upper atmosphere the upward (positive) iufrared flux uear the antistellar. point decreases with decreasing pressure. which heats this regiou of the night side.," Likewise, in the upper atmosphere the upward (positive) infrared flux near the antistellar point decreases with decreasing pressure, which heats this region of the night side."303 For the globally av'eraged rates. the optical fux always leads to heating while the iufrared generally leads to cooling.," For the globally averaged rates, the optical flux always leads to heating while the infrared generally leads to cooling."304 The net globally averaged profile has cooling throughout most of tle atmosphere. aside from a region uear the optical photosphere where there is net heating.," The net globally averaged profile has cooling throughout most of the atmosphere, aside from a region near the optical photosphere where there is net heating."305 The global net heating rate is 3.9x1074 W. A planet in global radiative equilibrium should heive a net radiative heating rate o[ zero., The global net heating rate is $3.9\times 10^{21}$ W. A planet in global radiative equilibrium should have a net radiative heating rate of zero.306" However. for a steady state atinosphere. the dissipation ol wind kinetic euergy (numerical or physical) must. be balanced by a non-zero conversion frou. (ermodyuamic potential energy. which iu (πα must be generated by a uou-zero heating rate feο,Pearce1978)."," However, for a steady state atmosphere, the dissipation of wind kinetic energy (numerical or physical) must be balanced by a non-zero conversion from thermodynamic potential energy, which in turn must be generated by a non-zero heating rate \citep[e.g.][]{Pearce1978}."307. Physically. the cissipatiou of kinetic energy leads to frictional heating aud the ergeties are balanced.," Physically, the dissipation of kinetic energy leads to frictional heating and the energetics are balanced."308 However. in our fiical model the numerical dissipation of kinetic energy ποσα hyperdissipation or other numeri‘al loss) is not returued to the atmosphere as heating ad so the net radiative beating udust be non-zero to conipeusate.," However, in our fiducial model the numerical dissipation of kinetic energy (through hyperdissipation or other numerical loss) is not returned to the atmosphere as heating and so the net radiative heating must be non-zero to compensate."309 We can take the ratio of the uet heating rate aud the rate of eierey input iuto the moclel (the total of the incident stellar flux ad the cooling flux [rom the interior) to determine that in this model the rate of numerical loss of kijetic energy. is1256.. a significant value and similar to the numerical loss found in our previous version of this code (Rauscher&Menou2011).," We can take the ratio of the net heating rate and the rate of energy input into the model (the total of the incident stellar flux and the cooling flux from the interior) to determine that in this model the rate of numerical loss of kinetic energy is, a significant value and similar to the numerical loss found in our previous version of this code \citep{RM2011}."310. The temperature structure of the upper atinosplere. above the optical aud infrared photosphlieres. is cdominuated by the exterual stellar jeatiug.," The temperature structure of the upper atmosphere, above the optical and infrared photospheres, is dominated by the external stellar heating."311 At deeper pressures. however. tle atinosphlieric structure is set by the strength of the heat [Iix from the interior or. equivalently. the entropy of the interior adiabat.," At deeper pressures, however, the atmospheric structure is set by the strength of the heat flux from the interior or, equivalently, the entropy of the interior adiabat."312 Here we present two actclitional models to examine how the behavior of the deepest levels of our moclel depends on our choice OL and our use of the flux diffusion scheme (Section 2.2))., Here we present two additional models to examine how the behavior of the deepest levels of our model depends on our choice of and our use of the flux diffusion scheme (Section \ref{sec:fdiff}) ).313 The precise value [ora planet's interior heat [lux is difficult to diseutaugle [rom oter uncertaiuties iu system aud observed parameters., The precise value for a planet's interior heat flux is difficult to disentangle from other uncertainties in system and observed parameters.314" We chose Ty,=500 Ix for our fiducial model in order to match he analytic set-up of Figure 3) [roi1 Guillot(2010).. but values of down to 7100 Ix. may be 'easonable."," We chose $\Tint=500$ K for our fiducial model in order to match the analytic set-up of Figure 3 from \citet{Guillot2010}, but values of down to $\sim$ 100 K may be reasonable."315 As a test of the intlence of the choice of ou the atmospheric circulation. we rau a nodel with Zi=0 kx (and all other parameters identical to our fiducial run). with the resulting eniperature structure shown iu the left panel of Figure 7..," As a test of the influence of the choice of on the atmospheric circulation, we ran a model with $\Tint=0$ K (and all other parameters identical to our fiducial run), with the resulting temperature structure shown in the left panel of Figure \ref{fig:deep}."316 With no heating from the interior. a night side in radiative ecquilibrium would have zero eniperature.," With no heating from the interior, a night side in radiative equilibrium would have zero temperature."317 In our Ting=0 Ex model. all of the uight side heating is the result of advection [roi," In our $\Tint=0$ K model, all of the night side heating is the result of advection from"318Deuterium (D or ?ID is the only clement eutirelv produced by nuclear reactions in the first müuutes after Big Bang (Wagoner et al.,Deuterium (D or $^2$ H) is the only element entirely produced by nuclear reactions in the first minutes after Big Bang (Wagoner et al.319 1967)., 1967).320" The D viclds are the most scusitive to the unclear deusitv at the nucleosvuthesis epoch amoue the primorcial ight eleueuts “Ue. Πο aud ""Li. thus iakiug the D abunudauce the most seusitive nieasureiment of the barvon ¢ensitv in the universe (Wagoner 1973. Schramun Turjor 1998)."," The D yields are the most sensitive to the nuclear density at the nucleosynthesis epoch among the primordial light elements $^3$ He, $^4$ He and $^7$ Li, thus making the D abundance the most sensitive measurement of the baryon density in the universe (Wagoner 1973, Schramm Turner 1998)."321 Deuterium ds curently measured in the local interstellar 11ediuii (SAD). qs=(1.6201)&107 (Liuskv et al.," Deuterium is currently measured in the local interstellar medium (ISM), $_{\rm ISM} = (1.6\pm3220.1)\times 10^{-5}$ (Linsky et al."323 1993). but since whenever it ds cveled through stars it is completely burned away. extrapolation to the prinordial D/II value requires a modeling of the Galactic chemical evolution.," 1993), but since whenever it is cycled through stars it is completely burned away, extrapolation to the primordial D/H value requires a modeling of the Galactic chemical evolution."324 Direct D iuieasureiieuts of primordial material are thus of high interest., Direct D measurements of primordial material are thus of high interest.325 Adams (1976) sueeested that aluost primordial D could be measured in low iuetallicitv absorption line svstems in the spectra of distant quasars (QSOs)., Adams (1976) suggested that almost primordial D could be measured in low metallicity absorption line systems in the spectra of distant quasars (QSOs).326 This was recently achieved for a few systems. but with conflicting results differing by almost an order of magnitudo.," This was recently achieved for a few systems, but with conflicting results differing by almost an order of magnitude."327 A few svstenis provide D/TIT values (see c.g. Webb et al. (, A few systems provide D/H values (see e.g. Webb et al. (3281997) who measure z2«10.1). while two other svstenis give a abundance at (3.39+0.25)x10 (Biles Tytler 1998a.1998b).,"1997) who measure $\approx 3292\times 10^{-4}$ ), while two other systems give a abundance at $(3.39\pm 0.25)\times 10^{-5}$ (Burles Tytler 1998a,1998b)."330 An even lower D/II estimation was obtained by Molaro et al. (, An even lower D/H estimation was obtained by Molaro et al. (3311999). further ciscussed bv Levshakov et al. (,"1999), further discussed by Levshakov et al. ("3322000).,2000).333 Wivkian et al. (, Kirkman et al. (3342000) measured au upper But of 6.76«107.,2000) measured an upper limit of $6.76\times 10^{-5}$.335 The handful of D detectious fouud so far does not allow a fna conclusion., The handful of D detections found so far does not allow a firm conclusion.336 Differen avgunelrs favour a low prinordial D/II ratio: the possible coutamination of the absorption lines aud. ou the modeling side. the results by Tosi ct al. (," Different arguments favour a low primordial D/H ratio: the possible contamination of the absorption lines and, on the modeling side, the results by Tosi et al. ("3371998) which predict for a variety of clicmical evolution scenarios aud to be consistent with the Calactic data a 1iaximumna decrease of the primordial D abundance by a factor of 3.,1998) which predict for a variety of chemical evolution scenarios and to be consistent with the Galactic data a maximum decrease of the primordial D abundance by a factor of 3.338 The paucity of suitable absorption svstenis for accurate D/II measurements is due to the fact that ouly absorption line systems with simple velocity structures aud with intermediate column densities allow the detection of the lines;, The paucity of suitable absorption systems for accurate D/H measurements is due to the fact that only absorption line systems with simple velocity structures and with intermediate column densities allow the detection of the lines.339 At too low column deusities the lines are too weak for detection. whereas at high column deusities the lines are normally washed out by the saturation of the line.," At too low column densities the lines are too weak for detection, whereas at high column densities the lines are normally washed out by the saturation of the line."340 We show here for the first time that in the latter case the deuterium signature can be successfully detected through the higher members of the Lyiuau series. when the target is a damped Lya system og NULL) & 20.35) at high redshitt.," We show here for the first time that in the latter case the deuterium signature can be successfully detected through the higher members of the Lyman series, when the target is a damped $\a$ system $\log N$ ) $\geq 20.35$ ) at high redshift."341 This approach was first suggested by Ihersousky ot al. (, This approach was first suggested by Khersonsky et al. (3421995).,1995).343" The spectra of OSO 0317.3819 (V217.3. £44,= 3.23) were obtained during the Commissioning of the"," The spectra of QSO 0347–3819 (V=17.3, $z_{\rm em} = 3.23$ ) were obtained during the Commissioning of the"344wind plays an important role in the binary evolution. (,wind plays an important role in the binary evolution. (345see. e.g.. van Teeseling King 1998) A WD model would perhaps be the most natural explanation for the SSS in NGC 300. were it not for the high estimated bolometric luminosities.,"see, e.g., van Teeseling King 1998) A WD model would perhaps be the most natural explanation for the SSS in NGC 300, were it not for the high estimated bolometric luminosities."346 Note that it may be difficult to use beaming to circumvent the Eddington limit in these systems. since the inner region of the accretion disk can also become a luminous emitter of SSS radiation (Popham Stefano 1996).," Note that it may be difficult to use beaming to circumvent the Eddington limit in these systems, since the inner region of the accretion disk can also become a luminous emitter of SSS radiation (Popham Stefano 1996)."347 SSS emission is expected from accreting BHs., SSS emission is expected from accreting BHs.348" Modeling the aceretion disk as a thin disk which 15 optically thick. we can derive a relationship between the minimum mass of the aceretor, and the observed temperature and luminosity (Frank. King. Raine 2002)."," Modeling the accretion disk as a thin disk which is optically thick, we can derive a relationship between the minimum mass of the accretor, and the observed temperature and luminosity (Frank, King, Raine 2002)."349 Using kT=60 eV and Ly=10 (1079 eres7!)). we find that the accretor mass is greater than zz890M. (2800M..).," Using $kT=60$ eV and $L_X=10^{38}$ $10^{39}$ ), we find that the accretor mass is greater than $\approx 890 M_{\odot}$ $2800 M_{\odot}$ )."350 Although the fact that the observed luminosity is 10°—IO? times smaller than the Eddington luminosity may call the validity of the disk model into question. this calculation suggests that the accretor is an intermediate-mass BH.," Although the fact that the observed luminosity is $10^2-10^3$ times smaller than the Eddington luminosity may call the validity of the disk model into question, this calculation suggests that the accretor is an intermediate-mass BH."351 If the aceretor is a BH. we may use Lops=O0.ΠΟ (11/0... where m is the accretion rate and jj. the efficiency factor. is likely to be close to 0.1.," If the accretor is a BH, we may use $L_{obs}=0.1352\dot m c^2 (\eta/0.1)$ , where $\dot m$ is the accretion rate and $\eta$, the efficiency factor, is likely to be close to 0.1."353" This yields mz4.8«10Mi Zyr 8ο /yr) for Lipsο. (Lus,=10? ergs!))", This yields $\dot m\approx 1.8\times10^{-8} M_{\odot}$ /yr $1.8\times10^{-7} M_{\odot}$ /yr) for $L_{obs}=10^{38}$ $L_{obs}=10^{39}$ ).354 This would be consistent with an irradiation-driven wind from a low-mass donor., This would be consistent with an irradiation-driven wind from a low-mass donor.355 Measurement of the orbital period could provide supporting evidence., Measurement of the orbital period could provide supporting evidence.356" Indeed. if the donor fills its Roche lobe. then ο2(8.9hrsMaí/M..). where M, is the mass of the donor star."," Indeed, if the donor fills its Roche lobe, then $P_{orb}\approx(8.9~\mathrm{hrs})(M_d/M_{\odot})$, where $M_d$ is the mass of the donor star."357" If P,,5=5.4 hrs. then M,7:0.61M..."," If $P_{orb}=5.4$ hrs, then $M_d\approx0.61 M_{\odot}$."358 It is of course possible that the observed emission emanates from an accreting NS., It is of course possible that the observed emission emanates from an accreting NS.359 In this case the SSS emission would presumably emanate from a photosphere which ts much larger than the neutron star itself., In this case the SSS emission would presumably emanate from a photosphere which is much larger than the neutron star itself.360 The photospheric radius would be different in each observation: 3.7«10? em during theROSAT observation. 2.6«10? em during the high-state observation. and 6.8«10° em during the llow-state observation. corresponding to. the different temperatures and luminosities.," The photospheric radius would be different in each observation: $3.7 \times 10^9$ cm during the observation, $2.6 \times 10^9$ cm during the high-state observation, and $6.8 \times 10^8$ cm during the low-state observation, corresponding to the different temperatures and luminosities."361 At this point. neutron. star models seem conceptually unattractive because there is no obvious explanation for why the photosphere should achieve these relatively large sizes. and no way to relate them to the system’s fundamental physical parameters.," At this point, neutron star models seem conceptually unattractive because there is no obvious explanation for why the photosphere should achieve these relatively large sizes, and no way to relate them to the system's fundamental physical parameters."362 In addition. just as in the WD models. the luminosity appears to be super-Eddington during two of the observations. unless the neutron star has a mass as large as 3—4M... In this case. if the efficiency of turning accretion energy into X-rays is the same during all 3 observations. then the aceretion rate must have changed by an order of magnitude. approaching ος1077M.. yr! during the high state. (," In addition, just as in the WD models, the luminosity appears to be super-Eddington during two of the observations, unless the neutron star has a mass as large as $3-4\, M_\odot.$ In this case, if the efficiency of turning accretion energy into X-rays is the same during all $3$ observations, then the accretion rate must have changed by an order of magnitude, approaching $2\times 10^{-8} M_\odot$ $^{-1}$ during the high state. ("363see Stefano et al.,see Stefano et al.364 2002b for a similar model of the X-ray source in the globular cluster Bo 375.), 2002b for a similar model of the X-ray source in the globular cluster Bo 375.)365 If. on the other hand. the mass of the neutron star is close to 1.4M... then other ways around the Eddington limit must be found; e.g.. the energy could be beamed into a smaller solid angle during the 2 high- observations.," If, on the other hand, the mass of the neutron star is close to $1.4\, M_\odot,$ then other ways around the Eddington limit must be found; e.g., the energy could be beamed into a smaller solid angle during the $2$ high-state observations."366 In this case. the accretion rate could be significantly lower.," In this case, the accretion rate could be significantly lower."367 We have studied a recurrent luminous SSS in NGC300 withXMM-Newton., We have studied a recurrent luminous SSS in NGC300 with.368. The source was seen by un 1992 and fell below the detection limit in subsequent oobservations., The source was seen by in 1992 and fell below the detection limit in subsequent observations.369" It reappeared in recent oobservations with bolometric luminosities between 10°% and 10°?eres"").", It reappeared in recent observations with bolometric luminosities between $10^{38}$ and $10^{39}$.370".. During the ""low"" state. the source showed a 5.4-hr periodicity."," During the “low” state, the source showed a 5.4-hr periodicity."371 If we consider the periodicity 1s due to the orbital period. then the X-ray emission can be explained by WD. BH. and NS models.," If we consider the periodicity is due to the orbital period, then the X-ray emission can be explained by WD, BH, and NS models."372" However. WD and NS models appear to be unlikely due to the high X-raylummosity during the ""high"" state."," However, WD and NS models appear to be unlikely due to the high X-rayluminosity during the “high” state."373 Further repeated X-ray observations of the SSS in different states may permit diserimination among these models., Further repeated X-ray observations of the SSS in different states may permit discrimination among these models.374ionizing backerounds aud for solar relative abundance of Si/C. For the broadly distributed material (filled sviubols). evideut is the relative iuseusitivity to the spectral shape assunued for the metagalactic background in the span of most of the data.,"ionizing backgrounds and for solar relative abundance of Si/C. For the broadly distributed material (filled symbols), evident is the relative insensitivity to the spectral shape assumed for the metagalactic background in the span of most of the data."375 This allows componoeut values for Si/C distributed up to about three times solar. the level previously indicated at higher redshifts for svstem totals (Soneaila Cowie 1996: Rauch. Wachuelt Steinmetz 1997) although for clouds with log N(C ID/N(GC IV) 0.3 (0. at lower densities) values seen closer to solar.," This allows component values for Si/C distributed up to about three times solar, the level previously indicated at higher redshifts for system totals (Songaila Cowie 1996; Rauch, Haehnelt Steinmetz 1997) although for clouds with log N(C II)/N(C IV) $\lesssim -0.3$ (i.e., at lower densities) values seem closer to solar."376 The sue conclusion comes for clouds close to the QSO (open sviubols). here using the more appropriate pure power luv spectrun.," The same conclusion comes for clouds close to the QSO (open symbols), here using the more appropriate pure power law spectrum."377 On the other hand. if the ionizine spectrum is dominated bv local effects roni massive stars. hieher values of N(S81 IV)/N(C IV) will result (Cüroux Shull 1997: Savaglioa," On the other hand, if the ionizing spectrum is dominated by local effects from massive stars, higher values of N(Si IV)/N(C IV) will result (Giroux Shull 1997; Savaglio."378l 1997) and S1/C max be closer to the solar value hroughout. as illustrated here with use of a 500001& star model spectrum.," 1997) and Si/C may be closer to the solar value throughout, as illustrated here with use of a 50000K star model spectrum."379 Au alternative display using the same model ionizing spectra to construct the ratios N(Si ID/N(C ID vs NGC ID/ZN(GC TV). also shown in Figure 23. gives ess overall dependency oi spectral shape so is a better mdicator of relative abundance. again in the span of most of the data.," An alternative display using the same model ionizing spectra to construct the ratios ${\rm N(Si\ II)}$ /N(C II) vs N(C II)/N(C IV), also shown in Figure 3, gives less overall dependency on spectral shape so is a better indicator of relative abundance, again in the span of most of the data."380 A similar distribution or Si/C again results., A similar distribution for Si/C again results.381 Taken together. the two representations indicate that ocal stellar sources do not donünate the radiation euvironmnment for these absorbers. although the not complete cousistency between them suggests sonic. rot unexpected. departure frou strict photoionization equilibrium (¢.¢.. Rauch. Ilaehuelt Steimmetz).," Taken together, the two representations indicate that local stellar sources do not dominate the radiation environment for these absorbers, although the not complete consistency between them suggests some, not unexpected, departure from strict photoionization equilibrium (e.g., Rauch, Haehnelt Steinmetz)."382 This is developed iu a more complete investigation including several other ious m a later paper (in preparation)., This is developed in a more complete investigation including several other ions in a later paper (in preparation).383medium (ICAL). iUs evolution. anc the member galaxy population is currently unclear 2001:Tornatoreetal.2003:VoitDorgani 2004).,"medium (ICM), it's evolution, and the member galaxy population is currently unclear \citep{toz01,tor03,voi03,bor04}."384 At a distance of about 20.5 Alpe (e.g. Ferrareseetαἱ.(2000))) the Fornax. cluster is second. onlv to the Virgo cluster in the readiness with which high physical resolution multi-waveleneth data may be obtained., At a distance of about 20.5 Mpc (e.g. \citet{fer00}) ) the Fornax cluster is second only to the Virgo cluster in the readiness with which high physical resolution multi-wavelength data may be obtained.385" With a best resolution of zz1"". offers an unprecedented access (ο X-ray. structures as small as LOO pe in Fornax."," With a best resolution of $\approx 1''$, offers an unprecedented access to X-ray structures as small as 100 pc in Fornax."386 In this work we describe (he first results [rom the Fornax Survey. (CES) which consists of ten mosaicecl pointings of 50 ksee exposure with ACIS-I. covering the innermost ~1 of the cluster.," In this work we describe the first results from the Fornax Survey (CFS) which consists of ten mosaiced pointings of 50 ksec exposure with ACIS-I, covering the innermost $\sim 1^{\circ}$ of the cluster."387 The aim of the CFS is to provide an X-ray dataset of sullicentlv hieh quality to allow: a detailed study of the properties of the ICM. its relationship to the galaxies in Fornax. (he N-rayv properties of those galaxies themselves. and (he properties of point sources such as X-ray. binaries. anc accreting black holes.," The aim of the CFS is to provide an X-ray dataset of sufficently high quality to allow; a detailed study of the properties of the ICM, its relationship to the galaxies in Fornax, the X-ray properties of those galaxies themselves, and the properties of point sources such as X-ray binaries, and accreting black holes."388 Recent investigations of Fornax have revealed several characteristics of this cluster which point towards a highly complex environment., Recent investigations of Fornax have revealed several characteristics of this cluster which point towards a highly complex environment.389 These include: a possible intra-cluster stellar population amounting to at least of the total cluster stellar mass (Theuns&WarrenCiardulloetal.2002:INarick.Drinkwater.&Gregg2003:Neill.Shara.Oegerle 2004).," These include; a possible intra-cluster stellar population amounting to at least of the total cluster stellar mass \citep{the97,cia02,kar03,nei04}."390. secondly. a population of ultra-compact intracluster stellar svstems (Drinkwater often referred (o as ultra-compact-objects or dwarls (UCOs or UCDs) which are not readily Classifiable as either galaxies or globular clusters.," Secondly, a population of ultra-compact intracluster stellar systems \citep{dri03} often referred to as ultra-compact-objects or dwarfs (UCOs or UCDs) which are not readily classifiable as either galaxies or globular clusters."391 Thirdly. approximately 1 Alpe to the of (he cluster center is an inlalline poor group. suggesting signilicant dvnanmical activity in Fornax (Drinkwater.Gregg.&Colless2001).," Thirdly, approximately 1 Mpc to the south-west of the cluster center is an infalling poor group, suggesting significant dynamical activity in Fornax \citep{dri01}."392. In (his paper we present the initial results from the CFS., In this paper we present the initial results from the CFS.393 In 82 we describe the basic data processing. in 822.1 we present multi-band images of the CES. ancl in 822.2 we present an estimated gas temperature map of Fornax together with confidence regions aud an example ol narrow-band imaging designed to indicate relative metal abunclances in the ICM.," In 2 we describe the basic data processing, in 2.1 we present multi-band images of the CFS, and in 2.2 we present an estimated gas temperature map of Fornax together with confidence regions and an example of narrow-band imaging designed to indicate relative metal abundances in the ICM."394 In 833.1 we discuss the infalling galaxy NGC 1404. and in 83.2 the tentative motion of NGC! 1387 and the possible truncation of its hot IGM by the surrounding Fornax ICM.," In 3.1 we discuss the infalling galaxy NGC 1404, and in 3.2 the tentative motion of NGC 1387 and the possible truncation of its hot IGM by the surrounding Fornax ICM."395 In 84 we present first results from elforts to compile an X-ray. source catalog of over TOO detections in the CF5. together with ταν color-color classifications.," In 4 we present first results from efforts to compile an X-ray source catalog of over 700 detections in the CFS, together with X-ray color-color classifications."396 In 84.1 we discuss the X-ray counterparts to known bright Fornax galaxy members. and in 84.2 we present N-rav. measurements of counterparts to two possible intra-cluster globular clusters in the outermost regions of the central galaxv NGC 1399.," In 4.1 we discuss the X-ray counterparts to known bright Fornax galaxy members, and in 4.2 we present X-ray measurements of counterparts to two possible intra-cluster globular clusters in the outermost regions of the central galaxy NGC 1399."397 In 85 we present an analvsis of what is likely a distant. hot. background cluster of galaxies seen to the immediate East of NGC 1399.," In 5 we present an analysis of what is likely a distant, hot, background cluster of galaxies seen to the immediate East of NGC 1399."398 Finally. in 86 we summarize the results presented here and discuss some of the implications for the overall Fornax environment.," Finally, in 6 we summarize the results presented here and discuss some of the implications for the overall Fornax environment."399where dldz(L|29 and E is the observed eamni-ray energy al 2=0.,where $dl/dz'=l_H(z')/(1+z')$ and $E$ is the observed gamma-ray energy at $z=0$.400 As mentioned above. the lower limit of z-integration that can be taken in our model is Lada=+: for additional absorption from the range >Ξ04. we can only consult. other models at the moment (e.g. ]xneiske ct al.," As mentioned above, the lower limit of $z$ -integration that can be taken in our model is $z_{\min}=4$; for additional absorption from the range $z=0-4$, we can only consult other models at the moment (e.g. Kneiske et al."401 2004. hereafter Ix04: Stecker ct al.," 2004, hereafter K04; Stecker et al."402 2006: ltazzaque et al., 2006; Razzaque et al.403 2009: Gilmore et al., 2009; Gilmore et al.404 2009)., 2009).405 Overlaved here for comparison is WO4’s 7high stellar UV model”. which gives their best description of OSO proximity effect measurements ab l24.," Overlayed here for comparison is K04's “high stellar UV model”, which gives their best description of QSO proximity effect measurements at $z \sim 2-4$."406 As we could. infer. from Fig.2.. our mocdel predicts appreciable opacity at observed. energies £ες12 GeV [or sources ab z5. with notable differences out to z~SN.," As we could infer from \ref{fig:tauloc}, our model predicts appreciable opacity at observed energies $E \lesssim 12$ GeV for sources at $z \gtrsim 5$, with notable differences out to $z \sim 8$."407 Llowever. the relative effects. of further absorption from 2oeS may be practically indiscernible.," However, the relative effects of further absorption from $z \gtrsim 8$ may be practically indiscernible."408 Nevertheless. the spectral attenuation feature itself should. be observable in hish-- eanuma-ray sources by current or future ganima-ray facilities. ancl possibly distinguishable in the range 2~58 for sullicienthy bright objects (84)).," Nevertheless, the spectral attenuation feature itself should be observable in $z$ gamma-ray sources by current or future gamma-ray facilities, and possibly distinguishable in the range $z \sim 5-8$ for sufficiently bright objects \ref{sec:detect}) )."409 Owing to the drop in ? opacity at LyecLS GeV (Fig.2)). the dillerences in absorption in this 2 range are caused in-situ by the evolution of UV UREs just below the Lyman edge energy. including the crucial Lye and Lyman-Werner bands.," Owing to the drop in $\gamma\gamma$ opacity at $E_{\rm rest} < 18$ GeV \ref{fig:tauloc}) ), the differences in absorption in this $z$ range are caused in-situ by the evolution of UV IRFs just below the Lyman edge energy, including the crucial $\alpha$ and Lyman-Werner bands."410 We also recall that in this model. Pop ILLE stars continued. to be significant contributors to the UV. IRE down to z~7. where they are comparable with Pop LL stars for ionizing photons.," We also recall that in this model, Pop III stars continued to be significant contributors to the UV IRF down to $z \sim 7$, where they are comparable with Pop II stars for ionizing photons."411 Measurements of these effects would thus provide an important check of current models of cosmic reionization in its latter stages. as well as a unique and invaluable probe of evolving UV HiEs in the sub-Lyman edge regime during the era of carly star formation (84)).," Measurements of these effects would thus provide an important check of current models of cosmic reionization in its latter stages, as well as a unique and invaluable probe of evolving UV IRFs in the sub-Lyman edge regime during the era of early star formation \ref{sec:detect}) )."412 In Figs., In Figs.413 4 and 5.. respectively. we plot the spectra attenuation factor exp.τί) and the observed energy f(r=1) where the optical depth is unity.," \ref{fig:expdet_com} and \ref{fig:Etau1_com}, respectively, we plot the spectral attenuation factor $\exp [-\tau(E)]$ and the observed energy $E(\tau=1)$ where the optical depth is unity."414 Here the fiducia results are compared with. those of an alternative. niocdel that does not include Pop ILE stars. in which reionization is driven only by Pop LL stars and occurs relatively late a 2o6 (similar to the late reionization mocdel of Callerani et al.," Here the fiducial results are compared with those of an alternative model that does not include Pop III stars, in which reionization is driven only by Pop II stars and occurs relatively late at $z \sim 6$ (similar to the late reionization model of Gallerani et al."415 2008)., 2008).416 The fact that Pop Lb stars are less elficien sources of ionizing photons compared to Pop LL stars mandates a larger SER. more intense IRE for ο«ος and hence larger 55 opacity.," The fact that Pop II stars are less efficient sources of ionizing photons compared to Pop III stars mandates a larger SFR, more intense IRF for $\epsilon < \epsilon_{\rm LE}$ and hence larger $\gamma\gamma$ opacity."417 However. since the SER. a 2αςϐ is observationally constrained. notable differences appear only at zS. which should be challenging to distinguish in practice.," However, since the SFR at $z \lesssim 6$ is observationally constrained, notable differences appear only at $z \gtrsim 8$, which should be challenging to distinguish in practice."418 Εις gamma-ray absorption may not be a sensitive probe of the reionization history itself., Thus gamma-ray absorption may not be a sensitive probe of the reionization history itself.419 We have also investigated: various other models. e.g. those with more realistic prescriptions for radiative feedback that Gt the current high-: observations nearly equally well. and. found that they generally do not leac to laree cillerences.," We have also investigated various other models, e.g. those with more realistic prescriptions for radiative feedback that fit the current $z$ observations nearly equally well, and found that they generally do not lead to large differences."420 Conversely. being constrained by existing data. our predictions may be considered. reasonably robust. a least within the framework of our model.," Conversely, being constrained by existing data, our predictions may be considered reasonably robust, at least within the framework of our model."421 Nevertheless. we caution that relaxing some of the present assumptions. e.g. regarding the stellar LALP or the QSO contribution. may ve allow a wider range of possibilities.," Nevertheless, we caution that relaxing some of the present assumptions, e.g. regarding the stellar IMF or the QSO contribution, may yet allow a wider range of possibilities."422 Note that although some other recent models (e.g. Itazzaeque ct al., Note that although some other recent models (e.g. Razzaque et al.423 2009. Cilmore e al.," 2009, Gilmore et al."424 2009) predict somewhat less absorption at 275.6. they are not directly comparable with ours as their focus is on the z<6 universe (e.g. Gilmore et al.," 2009) predict somewhat less absorption at $z \sim 5-6$, they are not directly comparable with ours as their focus is on the $z<6$ universe (e.g. Gilmore et al."425 2009 do not attemp to fit the Lya ellective optical depths at 25.5 as we do), 2009 do not attempt to fit the $\alpha$ effective optical depths at $z \gtrsim 5.5$ as we do).426 The fact that 55. absorption is sensitive το photons with energies below the Lyman limit rather than the ionizing radiation (82)) actually points to a unique, The fact that $\gamma\gamma$ absorption is sensitive to photons with energies below the Lyman limit rather than the ionizing radiation \ref{sec:model}) ) actually points to a unique427Be stars are rapidly rotating stars surrounded by an ionized circumstellar disk. whose emission is best known for the distinct doubly peaked Ha lines.,"Be stars are rapidly rotating stars surrounded by an ionized circumstellar disk, whose emission is best known for the distinct doubly peaked $\alpha$ lines."428 About of all B stars belong to the Be category (2.chap.9).. making them a significant component of the hot. massive star population.," About of all B stars belong to the Be category \citep[chap. 9]{jaschek_book}, making them a significant component of the hot, massive star population."429 However. the origin of the circumstellar disks around Be stars is still an unsolved mystery (see e.g. the review by 2).," However, the origin of the circumstellar disks around Be stars is still an unsolved mystery (see e.g. the review by \citealt{porter_review}) )."430 Binarity has sometimes been proposed to be responsible for the Be phenomenon., Binarity has sometimes been proposed to be responsible for the Be phenomenon.431 For example. ?. investigate the effects of a detached. secondary component's gravitational field on the mass ejection into the equatorial plane from the primary.," For example, \citet{harmanec_2002} investigate the effects of a detached, secondary component's gravitational field on the mass ejection into the equatorial plane from the primary."432 ?. discuss the rotational history of © Per. and find the (compact) companion has πιά a significant tidal effect on the central Be star.," \citet{gies_1998} discuss the rotational history of $\phi$ Per, and find the (compact) companion has had a significant tidal effect on the central Be star."433 In addition. it should be noted that companions are also known to affect the disks wroperties such as its density law or even size (e.g. ? on & Dra).," In addition, it should be noted that companions are also known to affect the disk's properties such as its density law or even size (e.g. \citealt{jones_2008} on $\kappa$ Dra)."434 Most models based on binarity have in common that close binaries with separations of order AU. are responsible for the ormation of a disk (for an overview. see 2)).," Most models based on binarity have in common that close binaries with separations of order AU, are responsible for the formation of a disk (for an overview, see \citealt{Neg_2007}) )."435 When one considers he more general case of binaries. it is plausible that disks are affected during the star formation stages by the presence of a companion star. even in the case of a wide binary.," When one considers the more general case of binaries, it is plausible that disks are affected during the star formation stages by the presence of a companion star, even in the case of a wide binary."436 However. to be able to address binarity as a crucial ingredient for the existence of Be stars. we need to know whether Be stars are found in binary," However, to be able to address binarity as a crucial ingredient for the existence of Be stars, we need to know whether Be stars are found in binary"437"Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England.","Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."438 The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions., The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions.439" The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington."," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington."440 The anonymous referee is thanked for helpful comments., The anonymous referee is thanked for helpful comments.441measured.,measured.442 The parameters found in fit are: a.=0.080+0.078 and b=0.242+ 0.054., The parameters found in fit are: $a = 0.080\pm 0.078$ and $b = 0.242\pm 0.054$ .443" with X?=1.01 at 5 degrees of freedom, giving a rejection probability of 0.038."," with $\chi^2 = 1.01$ at 5 degrees of freedom, giving a rejection probability of 0.038."444" We expect the fraction of number of bursts with redshift Ν.(p) to the overall number of bursts JV,(p), for any given p, to obey the relation: Figure B2.."," We expect the fraction of number of bursts with redshift $N_{z}(p)$ to the overall number of bursts $N_{\gamma}(p)$, for any given $p$ to obey the relation: Figure \ref{fig:zdetprob_ap}."445" depicts the fraction of bursts with a measured redshift and the linear fit, for the absorption and photometry redshifts."," depicts the fraction of bursts with a measured redshift and the linear fit, for the absorption and photometry redshifts."446 Although the fit is acceptable the significant of the effect is just one standard deviation (c) - so with the current observations the option of no dependence of redshift detection probability with peak flux (a—0) is still marginally consistent., Although the fit is acceptable the significant of the effect is just one standard deviation $(\sigma)$ - so with the current observations the option of no dependence of redshift detection probability with peak flux $(a = 0)$ is still marginally consistent.447" Whereas the detection fraction can be fitted well with a linear model for the redshifts obtained using absorption lines, the case is different when considering redshifts obtained using emission lines."," Whereas the detection fraction can be fitted well with a linear model for the redshifts obtained using absorption lines, the case is different when considering redshifts obtained using emission lines."448 Figure B3.., Figure \ref{fig:zdetprob_eh}.449 shows the measured redshift fraction and the linear fit for the emission lines redshifts., shows the measured redshift fraction and the linear fit for the emission lines redshifts.450" The emission lines redshifts are obtained preferably for high flux bursts, but very few are obtained for low and medium fluxes: 24% for logigp>1 and only 6.5% for logiop<1."," The emission lines redshifts are obtained preferably for high flux bursts, but very few are obtained for low and medium fluxes: $24\%$ for $log_{10}p > 1$ and only $6.5\%$ for $log_{10}p \leq 1$."451 This feature of the emission lines redshifts is associated with a strong bias toward lower redshifts as shown on Figure 1.., This feature of the emission lines redshifts is associated with a strong bias toward lower redshifts as shown on Figure \ref{fig:zmethodsdist}.452 These results supports our approach of selecting only the absorption lines and photometry redshifts as it make a sample which is less biased and easier to model., These results supports our approach of selecting only the absorption lines and photometry redshifts as it make a sample which is less biased and easier to model.453" The productof the above probabilities for burst detection and redshift measurement,gives the"," The productof the above probabilities for burst detection and redshift measurement,gives the"454 forH whichη the miuinal.η value ofH the y-suum> aud the chance probabilitymu ofH drawiugH tle measurect distribution given a coustaut [Iux. the gooduess-of-lit. would be This iudicates some scatter in the distribution of flux values bevond what must be expected ou statistical grounds.,"(> ) = for which the minimal value of the $\chi^2$ -sum and the chance probability of drawing the measured distribution given a constant flux, the goodness-of-fit, would be This indicates some scatter in the distribution of flux values beyond what must be expected on statistical grounds."455 We can estimate the amplitude of that scatter by Gaussian acing of a systematic uncertainty 6=yf to the [lux measurement error.," We can estimate the amplitude of that scatter by Gaussian adding of a systematic uncertainty $\delta = y\,\overline{F}$ to the flux measurement error."456 The amplitude of scatter is then approximately given by the value of y. for which the minimal value of the \7-stun equals the number ol degrees of [reeclou (22 in this test).," The amplitude of scatter is then approximately given by the value of $y$, for which the minimal value of the $\chi^2$ -sum equals the number of degrees of freedom (22 in this test)."457 The resulting estimate for the aiuplitude of variations is = Q.197 which is just twice the expected level of absolute calibration error., The resulting estimate for the amplitude of variations is = 0.197 which is just twice the expected level of absolute calibration error.458 This euergvOe band is part of the energyCM band. the results for which we liave just discussed.," This energy band is part of the energy band, the results for which we have just discussed."459 It is thus not statistically tudepencent., It is thus not statistically independent.460 The scaling parameter of ciffuse emission. Cj has best-fit values that are characterizecl by =0.11s," The scaling parameter of diffuse emission, $\gm$, has best-fit values that are characterized by =0.118"461equally redistributed among gas. stars aud dark matter.,"equally redistributed among gas, stars and dark matter."462" A Pluuuuer poteutial is used to soften gravity at small scales, with constant softenius leugths of e280 pc for all particles."," A Plummer potential is used to soften gravity at small scales, with constant softening lengths of $\epsilon=280$ pc for all particles."463 The gas is modelled as isothermal. with a temperature Tyas=10!K.," The gas is modelled as isothermal, with a temperature $T_{gas}= 10^4 \;\mathrm{K}$."464 The assunmtiou of an isothermal ISM is justified by the short cooling times in the gaseous disk at the resolution of our models. such that fiuctuatious in the gas temperature. those due to SN explosions for example. would be quickv radiated away (seethediscussioniu.e.g...Milios&Ieruquist1996).," The assumption of an isothermal ISM is justified by the short cooling times in the gaseous disk at the resolution of our models, such that fluctuations in the gas temperature, those due to SN explosions for example, would be quicky radiated away \citep[see the discussion in, e.g., ][]{mihos96}."465. We refer the reader to Seiieliu&Combes(2002) for a detail description of aud the tests performed to validate the code., We refer the reader to \citet{benoit02} for a detail description of and the tests performed to validate the code.466 Other tests have been xeseuted iu DiMatteoetal. (2008)., Other tests have been presented in \citet{dimatteo08}.467. The equations of motion are iutegrated usimg a leapfrog aleorithim with a fixed time step of At=5x105 vr.," The equations of motion are integrated using a leapfrog algorithm with a fixed time step of $\Delta468t = 5 \times 10^5\;\mathrm{yr}$ ."469 The nuuerical recipes used to implement star formation and ietal curichmenut have been fully described elsewhere (DiMatteoetal.2007:Chilingarian2010).. thus here we ον sunnarise those features that are most directly relevant to our analvsis.," The numerical recipes used to implement star formation and metal enrichment have been fully described elsewhere \citep{dimatteo07,470chili10}, thus here we only summarise those features that are most directly relevant to our analysis."471 Star formation efficieucy las been paranuetrised as: where ων ds the gas nass of a particle. and Pgas the local gas density.," Star formation efficiency has been parametrised as: where $M_{gas}$ is the gas mass of a particle, and $\rho_{gas}$ the local gas density."472 The coustaut C—0.3.pc?3/2AL.1/2Cyr+ has been chosen such tha the isolated disk galaxies form stars at an average rate of ~1]Mao1, The constant $C=0.3 \mathrm{ \; pc^{3/2} \; M_{\sun}^{-1/2}\; Gyr^{-1}}$ has been chosen such that the isolated disk galaxies form stars at an average rate of $\sim 1 \;\mathrm{M_{\sun}\; yr^{-1}}$.473 Once the star formation recipe is defined. we apply it to gas particles. using the hvbrid method described in Milos&Teruquist(199Ib).," Once the star formation recipe is defined, we apply it to gas particles, using the hybrid method described in \citet{mihos94b}."474. The effect of star formation on the surouncdiug iuterstellar iuediuni has been müuplemeute as follows., The effect of star formation on the surrounding interstellar medium has been implemented as follows.475 For each stir-foriuimug hwbrid particle. we evaluate the fraction of stars formed with masses NN. adopting a Miller&Sealo(1979) initial mass function (IME). and We assunie that stars above this mass threshold iustantaneouslv become supernovae.," For each star-forming hybrid particle, we evaluate the fraction of stars formed with masses $> 8 \;\mathrm{M_{\sun}}$, adopting a \citet{miller79} initial mass function (IMF), and we assume that stars above this mass threshold instantaneously become supernovae."476 Each of the SN leave ροήπιο a rominaut of L1ME: and releases their τολμάιο uas to the simroundius ISM., Each of the SN leave behind a remnant of $1.4 \;\mathrm{M_{\sun}}$ and releases their remaining mass to the surrounding ISM.477 The mass released also enriches the surrounding gas with metals., The mass released also enriches the surrounding gas with metals.478 This is done assundue a vield y=MagfA0.02. where μμ... he total mass of all reprocessed uctals and M. the total Παπ din stars.," This is done assuming a yield $y=M_{ret}/M_{*}\;=\;0.02$, where $M_{ret}$ is the total mass of all reprocessed metals and $M_{*}$ the total mass in stars."479 For cach gas particle. the return of mass and uetals is applied to the ΤΗ neighbour eas particle. using aweielit «e; based on the s3uoothiug kernel.," For each gas particle, the return of mass and metals is applied to the $i-th$ neighbour gas particle, using a weight $w_i$ based on the smoothing kernel."480" The metallicity is initially distributed im a eradieut of the form: with R the particle distance from the galaxy ceutre and ty32. (ναιetal.2003:\laerini2007: 2005), evolves with time. as star formation proceeds."," The metallicity is initially distributed in a gradient of the form: with $R$ the particle distance from the galaxy centre and $z_{0}=3 \,481z_{\sun}$ \citep{kennicutt03,magrini07,lemasle08}, evolves with time, as star formation proceeds."482 Supernovae explosions also inject energev iuto the surrounding ISML, Supernovae explosions also inject energy into the surrounding ISM.483" This is taken iuto account assumnius hat a fraction. €,;,. of the euergv. Loy. released by a SNe goes iuto kinetic enerev giving a radial kick to the velocities of ucighbouringi88Oo gas particles."," This is taken into account assuming that a fraction, $\epsilon_{kin}$, of the energy, $E_{SN}$, released by a SNe goes into kinetic energy giving a radial kick to the velocities of neighbouring gas particles."484 The value of ej; iis been chosen such that the total amount of kinetic energv received bv a gas particle due to the contribution roni all the surroundiugo neighbours. is less than 1 ki 1 hus preventingC» a rapid C»erowth of the vertical thickness of the gaseous disk.," The value of $\epsilon_{kin}$ has been chosen such that the total amount of kinetic energy received by a gas particle due to the contribution from all the surrounding neighbours, is less than 1 km $^{-1}$ , thus preventing a rapid growth of the vertical thickness of the gaseous disk."485 A more detailed description of the Huplementation of feedback recipes used iu our code is eiven in Semelin&Combes(2002):Chilingarian(2010).," A more detailed description of the implementation of feedback recipes used in our code is given in \citet{benoit02, chili10}."486 It is known that close passages of galaxies can destabilise ealaxy disks. producing asvnuunetries. such απ bars. which are efBeieut mechanisius for driving gas into the circunmnuclear region of a ealaxy. producing a burst of star formation (Ionoetal.2001:Combes2008).," It is known that close passages of galaxies can destabilise galaxy disks, producing asymmetries, such as bars, which are efficient mechanisms for driving gas into the circumnuclear region of a galaxy, producing a burst of star formation \citep{iono04, combes08}."487. If. prior o the interaction. the eas is distributed iu the disk with a weative mietallicity eradient. with the outer regious being relatively more metal poor than the iuner ones as observed in local galaxies (Shields1990:Dinersteiu1996).. then a »ortion of this low-netallicitv eas will fall iuto the nuclear regions. diluting the pre-existing eas with eas of lower netallicity.," If, prior to the interaction, the gas is distributed in the disk with a negative metallicity gradient, with the outer regions being relatively more metal poor than the inner ones as observed in local galaxies \citep{shields90, diner96}, then a portion of this low-metallicity gas will fall into the nuclear regions, diluting the pre-existing gas with gas of lower metallicity."488 This dilution will ast until the star formation. which is enhanced by the gas inflow. releases reprocessed aet:s to enrich the gas.," This dilution will last until the star formation, which is enhanced by the gas inflow, releases reprocessed metals to enrich the gas."489 This cvele (dilution aud euricluneut) is shown in Fies., This cycle (dilution and enrichment) is shown in Figs.490 and 2 for some of our galaxy merser simulations.," \ref{fig:timeevol}491 and \ref{fig:timeevol_fly} for some of our galaxy merger simulations."492" For he analysis of the effect of merecrs on the metallicity of ealaxies. we have defined the metallicity dilution (often referred. to as simaply dilution) as i/i,l. where τ is he ietallicitv of à galaxy in the pair diving the merecr or fivbv and i;4,15 the corresponding value for the same ealaxy evolved isolated."," For the analysis of the effect of mergers on the metallicity of galaxies, we have defined the metallicity dilution (often referred to as simply dilution) as $z/z_{iso}< 1$, where $z$ is the metallicity of a galaxy in the pair during the merger or flyby and $z_{iso}$ is the corresponding value for the same galaxy evolved isolated."493 Both + and +). are measured iu apertures of 1-2 kpc aud thus represent the evolution of the metallicity for the nuclear or cireiuninmclear regions of ealaxies (which also corresponds reasonably well with the aperture sizes used to estimate the metallicities of ealaxies: see discussion iu the 51)., Both $z$ and $z_{iso}$ are measured in apertures of 1-2 kpc and thus represent the evolution of the metallicity for the nuclear or circumnuclear regions of galaxies (which also corresponds reasonably well with the aperture sizes used to estimate the metallicities of galaxies; see discussion in the 1).494 We find that as soon as the two galaxies have undergone their first periccutre passage. an intense inflow of eas. lasting for 300-100 Avr. takes place.," We find that as soon as the two galaxies have undergone their first pericentre passage, an intense inflow of gas, lasting for 300-400 Myr, takes place."495 A detailed discussion of the mechanism gencrating the eas inflows we observe iu our sinulations is elven iu DiMatteoeti. (2007)., A detailed discussion of the mechanism generating the gas inflows we observe in our simulations is given in \citet{dimatteo07}.496. They show that cach close passage of the two interacting galaxies is accompanied by the amplification of stellar asviunetries — stellar bars., They show that each close passage of the two interacting galaxies is accompanied by the amplification of stellar asymmetries – stellar bars.497 These stellar bars are responsible of removing augular 1uionieutum from gas. transferriug it to the stellar coniponent. aud im regulatiug the subsequent inflow of eas in the mnerkpc.," These stellar bars are responsible of removing angular momentum from gas, transferring it to the stellar component, and in regulating the subsequent inflow of gas in the innerkpc."498 We note, We note499such studies. the initiation phase of the CAIE. as well as peak of their acceleration could be observed.,"such studies, the initiation phase of the CME, as well as peak of their acceleration could be observed."500 The CORI] and COR2 coronagraphs together image the solar corona Irom 1.4 to 15.0... however these are only the plane-ol-skv FOVs of the coronagraphs.," The COR1 and COR2 coronagraphs together image the solar corona from $1.4$ to $15.0\Rsun$, however these are only the plane-of-sky FOVs of the coronagraphs."501 The minimum value of (rue height of reconstructed features the corona is approximately 2.01..., The minimum value of true height of reconstructed features the corona is approximately $2.0\Rsun$.502 Thus. in most of the cases we do not capture the rise phase acceleration of the LE of CALE.," Thus, in most of the cases we do not capture the rise phase acceleration of the LE of CME."503 In all but one case studied here. the acceleration peak has already. passed [rom the time we start observing the CME.," In all but one case studied here, the acceleration peak has already passed from the time we start observing the CME."504 At this point. it is necessary to point out that the heights determined in this study ave true heliocentric distances. hence they are seen to be significantly different than the heights obtained from previous studies which relied upon observations from a single spacecralt.," At this point, it is necessary to point out that the heights determined in this study are true heliocentric distances, hence they are seen to be significantly different than the heights obtained from previous studies which relied upon observations from a single spacecraft."505 The CAMIE on 2007 December 31 was associated with a flare having X-ray. class Cs. however it still showed a verv high value of acceleration of over 1500ms7.," The CME on 2007 December 31 was associated with a flare having X-ray class C8, however it still showed a very high value of acceleration of over $1500\mpss$."506 Earlier studies have shown that the acceleration phase of CMESs coincides with the increase in soft X-ray [ας due to the associated flare (Neupertetal.2001:Shanmugaraju2003).," Earlier studies have shown that the acceleration phase of CMEs coincides with the increase in soft X-ray flux due to the associated flare \citep{Neupert.etal2001,Shanmugaraju.etal2003}."507. οἱal.(2007) have also shown that both the velocity and acceleration of the CME show a significant correlation with the X-ray class of the associated flare., \citet{Maricic.etal2007} have also shown that both the velocity and acceleration of the CME show a significant correlation with the X-ray class of the associated flare.508 As per the least scares fit obtained [rom their study. acceleration of the CAIE associated with a C3 flare should be around 300ms7.," As per the least squares fit obtained from their study, acceleration of the CME associated with a C8 flare should be around $300\mpss$."509 The value calculated by us however. is 5 times more. suggesting that the flare energv alone might not be the only one to drive the CAIEs.," The value calculated by us however, is 5 times more, suggesting that the flare energy alone might not be the only one to drive the CMEs."510 In such a scenario. the supposition that impulsive ancl gradual CMES are respectively associated. with flares and EPs (MacQueen&Fisher1983:Moonοἱal.2002). should also be subjected to further serutinv.," In such a scenario, the supposition that impulsive and gradual CMEs are respectively associated with flares and EPs \citep{MacQueen.Fisher1983,Moon.etal2002} should also be subjected to further scrutiny."511 Also. deviations to the findings reported by Mariciéetal.(2007).. where acceleration of CAIEs is correlated with the X-ray class of the associated flare. should not be ignored.," Also, deviations to the findings reported by \citet{Maricic.etal2007}, where acceleration of CMEs is correlated with the X-ray class of the associated flare, should not be ignored."512 Ralleryοἱal.(2010) have used soft and hard. X-ray observations in addition to STEREO observations (Linetal.2010) to analvse the 2007 December 31 CME. and have found that it follows the tether-eutting reconnection model.," \citet{Raftery.etal2010} have used soft and hard X-ray observations in addition to STEREO observations \citep{Lin.etal2010} to analyse the 2007 December 31 CME, and have found that it follows the tether-cutting reconnection model."513most are fairly definite. some are cerlainiv arguable aud we do not pretend that our listing is infallible in all cases.,"most are fairly definite, some are certainly arguable and we do not pretend that our listing is infallible in all cases."514SubstitutingC» into the definition of the plase-lae:Oo = yp At this point. two additional assumptions are introduced: The first is an inuplicit condition for the validity of a PIC sumiulation. when the photon formation time is comparable or shorter than the time step.,"Substituting into the definition of the phase-lag: ) = ) ^4) = ) ^3) At this point, two additional assumptions are introduced: The first is an implicit condition for the validity of a PIC simulation, when the photon formation time is comparable or shorter than the time step."515 The second is fulfilled wuder normal conditions ([E|<|B)., The second is fulfilled under normal conditions $\left|E\right|\lesssim\left|B\right|$ ).516 Then. writingTEN aud JA At the frequencies of interest (i~ x). the dominant contribution to the iuteerals. which arises for gy— 1. occurs for socl.," Then, writing ^3 one finds ] ] and ) At the frequencies of interest $\omega\sim\omega_{\rm c}$ ), the dominant contribution to the integrals, which arises for $g\sim1$ , occurs for $x\sim1$."517 Tn this case. the the contribution of the first two non-vanishing terms in the Tavlor expansions of both g aud gare comparable. Thus. in expanding the iutegrands in (51)) it is necessary to include both these terms. whereas the lowest order non-vauishiug contributionsto dA aud 3-09 are sufficicut.," In this case, the the contribution of the first two non-vanishing terms in the Taylor expansions of both $g$ and $\dot{g}$ are comparable, Thus, in expanding the integrands in \ref{instpower}) ) it is necessary to include both these terms, whereas the lowest order non-vanishing contributionsto $\delta\Delta$ and $\bm{\beta}\cdot\delta{\bm{\beta}}$ are sufficient."518" The instantaneous power (51)) isthen ""EET A50) WritineC» τω ως."," The instantaneous power \ref{instpower}) ) isthen ( ] Writing $\eta=\omega/\omega_{\rm c}$ ,"519between 16 and 50 mm and with a total mass of 512 kg.,between 16 and 50 mm and with a total mass of 512 kg.520 Besicles serving as a veto for the SPI eermanium spectrometer. the ACS is able to detect gamma-ray bursts from a large fraction of the sky (von Iienlin et al.," Besides serving as a veto for the SPI germanium spectrometer, the ACS is able to detect gamma-ray bursts from a large fraction of the sky (von Kienlin et al."521 2003)., 2003).522 The data used here consist of the overall ACS count rate (i.e. the read out from (he sum of the 91 ervstals) saaipled in (nme intervals of 50 ms., The data used here consist of the overall ACS count rate (i.e. the read out from the sum of the 91 crystals) sampled in time intervals of 50 ms.523 No energy or directional information is available., No energy or directional information is available.524 The ACS is sensitive to photons above a low-energv threshold corresponding to approximately 80 keV. However. due to the different properties of the various BGO blocks. (heir associated photomulüpliers. aud the chosen redundancy. concept (the signals Irom (wo dillerent crystals are fed (o the same front-end electronics). this threshold is not sharp and its exact value not well determined.," The ACS is sensitive to photons above a low-energy threshold corresponding to approximately 80 keV. However, due to the different properties of the various BGO blocks, their associated photomultipliers, and the chosen redundancy concept (the signals from two different crystals are fed to the same front-end electronics), this threshold is not sharp and its exact value not well determined."525 Dead time and saturation elfects in the ervstals anc electronics are negligible (15 )) [or total count rates smaller than a few 10? cis !;, Dead time and saturation effects in the crystals and electronics are negligible $<$ ) for total count rates smaller than a few $^5$ cts $^{-1}$.526 When this condition is verified we can easily convert the observed count rates to an incident energv [Iux. assuming a spectral shape and knowing the AC'S effective area.," When this condition is verified we can easily convert the observed count rates to an incident energy flux, assuming a spectral shape and knowing the ACS effective area."527 The latter is a function of the incidence angle. with a maximum for directions nearly orthogonal to the satellite pointing axis and unobstructed by other instruments.," The latter is a function of the incidence angle, with a maximum for directions nearly orthogonal to the satellite pointing axis and unobstructed by other instruments."528" At the time of the flare wwas al a zenith angle θ-- 1003 [rom the SPI pointing axis ancl al an azimuth angle o=0° (9=0"" corresponds to the satellite Sun-pointing side. i.e. the direction fom SPI toward the IBIS instrrunent)."," At the time of the flare was at a zenith angle $\theta$ $^{\circ}$ from the SPI pointing axis and at an azimuth angle $\phi$ $^{\circ}$ $\phi$ $^{\circ}$ corresponds to the satellite Sun-pointing side, i.e. the direction from SPI toward the IBIS instrument)."529 The ACS effective area as a function of energv for (his direction. has been computed by means of Monte Carlo simulations based on detailed mass modelling (Weidenspointner οἱ al., The ACS effective area as a function of energy for this direction has been computed by means of Monte Carlo simulations based on detailed mass modelling (Weidenspointner et al.530 2003. and references (herein) of SPI and of the surrounding material (satellite structure and other instruments).," 2003, and references therein) of SPI and of the surrounding material (satellite structure and other instruments)."531 The effective area increasesmonotonicallv with energv: it is 340 em? at 100 keV. 1150 em? at 200 keV. and larger than 3000 em? above 1 MeV. Thus the ACS provides the data with the best statisties in the soft +-ray range available for (this giant flare.," The effective area increasesmonotonically with energy; it is $\sim$ 340 $^2$ at 100 keV, $\sim$ 1150 $^2$ at 200 keV, and larger than 3000 $^2$ above 1 MeV. Thus the ACS provides the data with the best statistics in the soft $\gamma$ -ray range available for this giant flare."532" For an optically thin thermal bremsstrahlung spectrum with kT,,=30 keV we obtain a conversion [actor of 1. ACS count | —43x10! erg 7s ! (30-2000 keV).", For an optically thin thermal bremsstrahlung spectrum with $_{br}$ =30 keV we obtain a conversion factor of 1 ACS count $^{-1}$ $\sim$ $\times10^{-10}$ erg $^{-2}$ $^{-1}$ (80-2000 keV).533 The total light curve of the flare. obtained by binning αἱ 2.5 s the original ACS data. is shown in Fig. l..," The total light curve of the flare, obtained by binning at 2.5 s the original ACS data, is shown in Fig. \ref{total},"534 while Fig., while Fig.535 2. displavs at full resolution (50 ms) the initial part of the pulsating tail., \ref{initialfit} displays at full resolution (50 ms) the initial part of the pulsating tail.536 We have defined (=0 at 21:30:26.55 UT of 2004 December 27. approximately coinciding with the risetime of the flare.," We have defined t=0 at 21:30:26.55 UT of 2004 December 27, approximately coinciding with the risetime of the flare."537 The giant flare starts with a short and extremely intense spike., The giant flare starts with a short and extremely intense .538. The measured count rate at the peak. ~2xLO® counts +. is strongly," The measured count rate at the peak, $\sim2\times10^6$ counts $^{-1}$ , is strongly"539Note that there are some other CSFR models. similar to or different. [rom the five models adopt here. not included since our aim is not to make a complete survey on this issue bul to phenomenologically investigate its influences on the SGWD [from an ensemble of astrophysical sources.,"Note that there are some other CSFR models, similar to or different from the five models adopt here, not included since our aim is not to make a complete survey on this issue but to phenomenologically investigate its influences on the SGWB from an ensemble of astrophysical sources."540 We refer readers to Calura Matteucci (2003). Daigne et al. (," We refer readers to Calura Matteucci (2003), Daigne et al. ("5412004). Dromm Loeb (2006). Nagamine et al. (,"2004), Bromm Loeb (2006), Nagamine et al. ("5422006) ancl Fardal et al. (,2006) and Fardal et al. (5432007) for details of other studies on the determination of CSFR.,2007) for details of other studies on the determination of CSFR.544 In the following sections we will investigate how dilferent CSFRs affect the rate of NS formation and spectral properties of AGWD., In the following sections we will investigate how different CSFRs affect the rate of NS formation and spectral properties of AGWB.545 since the evolving rate of CCSNe closely tracks the star formation rate. using CSER models presented in Section 2 we can estimate the number of NSs formed per unit (ime within the comoving volume out to redshift z (Ferrari et al.," Since the evolving rate of CCSNe closely tracks the star formation rate, using CSFR models presented in Section 2 we can estimate the number of NSs formed per unit time within the comoving volume out to redshift z (Ferrari et al."546" 1999): where f,.(2) is the CSER density. dV/dz is the comoving volume element. and (1) is the IME."," 1999a): where $\dot{\rho}_{\ast}(z)$ is the CSFR density, $dV/dz$ is the comoving volume element, and $\Phi(m)$ is the IMF."547 Here we assume that each CCSN results in either a NS or a BIL and take a NS progenitor mass range of SAL.—25AL.., Here we assume that each CCSN results in either a NS or a BH and take a NS progenitor mass range of $8 M_{\odot} - 25 M_{\odot}$.548 In order (o make comparison with Ferrari οἱ al. (, In order to make comparison with Ferrari et al. (549"1999b) we also consider a lower upper limit lor NS progenitor masses mj,=20M. as indicated from core collapse simulations by Frver (1999).",1999b) we also consider a lower upper limit for NS progenitor masses $m_{\rm{max}}=20 M_{\odot}$ as indicated from core collapse simulations by Fryer (1999).550 However according to Belezvuski Taam (2008) the mass of NS progenitor might be greater than 40... lor stars in a binary svslem., However according to Belczynski Taam (2008) the mass of NS progenitor might be greater than $40 M_{\odot}$ for stars in a binary system.551 So we will also include a higher limit of mg;=40M. [or our ealeulations of NS formation rate (lu Siel 2006 the progenitor mass to form a NS ranges from LOAL. (o 40.4. ).," So we will also include a higher limit of $m_{\rm{max}}=40552M_{\odot}$ for our calculations of NS formation rate (In Sigl 2006 the progenitor mass to form a NS ranges from $10 M_{\odot}$ to $40553M_{\odot}$ )."554 Note that in some studies (e.g.. Coward et al.," Note that in some studies (e.g., Coward et al."555 2001: de Araujo et al., 2001; de Araujo et al.556 2004: Regimbau Alandie 2008) with respect to AGWD there is an additional (1+2) term in Eq.(4)) dividing the CSEHR (to account for the time dilatation of CSFR due to cosmic expansion., 2004; Regimbau Mandic 2008) with respect to AGWB there is an additional $(1+z)$ term in \ref{dR_NS}) ) dividing the CSFR to account for the time dilatation of CSFR due to cosmic expansion.557 Ilere we do not include such a term according to de Araujo Miranda (2005) who argue thatthe inclusion of (his additional term is inadequate., Here we do not include such a term according to de Araujo Miranda (2005) who argue thatthe inclusion of this additional term is inadequate.558 To integrate through Eq.(4)) one still needs to know the forms of dV/dz and (m)., To integrate through \ref{dR_NS}) ) one still needs to know the forms of $dV/dz$ and $\Phi(m)$.559" Following Regimbau Mandic (2008). the comoving volume element is related to z through where //, the Hubble constant. £(Q.2)=(/Q,cO,(L+z)* and r(z) the comoving distance related to the luminosity distance by dp=r.(1-4 2)."," Following Regimbau Mandic (2008), the comoving volume element is related to z through where $H_{0}$ the Hubble constant, $E(\Omega560,z)=\sqrt{\Omega_{\Lambda}+\Omega_{m}(1+z)^{3}}$ and $r(z)$ the comoving distance related to the luminosity distance by $d_{L}=r_{z}(1+z)$ ."561"Incremental Release Point Source Catalog (7,=15.17£0.06 and WV,=11.69d: 0.10).","Incremental Release Point Source Catalog $J_s = 15.47 \pm 0.06$ and $K_s = 14.69 \pm5620.10$ )."563 The HST observations were carried out under the ToO programme 8189 (Principal Investigator. Fruchter et al. 1999)).," The HST observations were carried out under the ToO programme 8189 (Principal Investigator, Fruchter et al. \cite{Fruch99}) )."564 The observations were performed at an epoch 299 days after the GRB (see Table 1)) where the OA contribution is negligible., The observations were performed at an epoch 299 days after the GRB (see Table \ref{table1}) ) where the OA contribution is negligible.565" The observations were performed with STIS. which yields a vain of | cf/ADU. a physical pixel seale of 0705 and a FOV of 52”ος52"" (STSel 2000))."," The observations were performed with STIS, which yields a gain of 1 $e^{-}/ADU$, a physical pixel scale of $0\farcs05$ and a FOV of $52^{\prime \prime} \times 52^{\prime \prime}$ (STScI \cite{Stsc00}) )."566 The data were obtained with the 50CCD or CEL filter., The data were obtained with the 50CCD or $CL$ filter.567 The STIS reduction pipeline calstisofIRAF was used to calibrate the raw data., The STIS reduction pipeline of IRAF was used to calibrate the raw data.568 The raw images were reduced following normal procedures (bias and dark subtraction. and division by a normalised flat field).," The raw images were reduced following normal procedures (bias and dark subtraction, and division by a normalised flat field)."569 The individual images were combined using the task of IRAF (Fruchter Hook 2002))., The individual images were combined using the task of IRAF (Fruchter Hook \cite{Fruch02}) ).570 In the drizzling of the data the parameters and were used., In the drizzling of the data the parameters and were used.571 These values yield an output grid of 2k « 2k pixels with a pixel scale of 07025 l/pix., These values yield an output grid of 2k $\times$ 2k pixels with a pixel scale of $0\farcs0254$ /pix.572 We performed aperture photometry of the host with a radius of 50 drizzled pixels., We performed aperture photometry of the host with a radius of 50 drizzled pixels.573 The count rate (C. measured in :1DU/s) was converted into the CL-band AB magnitude following: mA=26.38692.5logC' (STScI 2000).," The count rate $C$ , measured in $ADU$ /s) was converted into the $CL$ -band AB magnitude following: $m^{\rm AB}_{CL}=26.386 - 2.5 \log C $ (STScI \cite{Stsc00}) )."574 In order to fit the observed Vega system magnitudes (717) using a given template (either empirical or synthetic). the values of 0 were converted into flux densities (f) using the corresponding offsets to the AB magnitude system (Oke 1990)).," In order to fit the observed Vega system magnitudes $m$ ) using a given template (either empirical or synthetic), the values of $m$ were converted into flux densities $f_{\nu}$ ) using the corresponding offsets to the AB magnitude system (Oke \cite{Oke90}) )."575" The AB offset is defined as ABoff=ipn. Where map=2.45«logf.I8.60 Cf, measured in erg ! ? !) is the magnitude in the AB system."," The AB offset is defined as $= m_{\rm AB} - m$, where $m_{\rm AB} = -2.5 \times576\log f_{\nu} - 48.60$ $f_{\nu}$ measured in erg $^{-1}$ $^{-2}$ $^{-1}$ ) is the magnitude in the AB system."577 The AB offsets of our nine bands were derived convolving the Vega spectrum taken from the GISSEL98 (Bruzual Charlot 1993)) library (a Lyrae ry=0 in all bands by definition) with the UBVRIZIAC L-band filters and the corresponding CCD efficiency curves., The AB offsets of our nine bands were derived convolving the Vega spectrum taken from the GISSEL98 (Bruzual Charlot \cite{Bruz93}) ) library $\alpha$ Lyrae $m=0$ in all bands by definition) with the $UBVRIZJ_sK_sCL$ -band filters and the corresponding CCD efficiency curves.578 Table 2 displays the AB offsets and effective wavelengths of the nine bands used to construct the SED., Table \ref{table2} displays the AB offsets and effective wavelengths of the nine bands used to construct the SED.579 Prior to performing the SED fit. the derived BVRIZ SINCL- flux densities were dereddenedof the Galactie extinction," Prior to performing the SED fit, the derived $UBVRIZJ_sK_sCL$ -band flux densities were dereddenedof the Galactic extinction"580with au effective radius equal to the half light radius.,with an effective radius equal to the half light radius.581 Note that variatious iu the observational aud plivsical parameters within these rauges do not ecucrally alter the error from the quadrupole moment alone., Note that variations in the observational and physical parameters within these ranges do not generally alter the error from the quadrupole moment alone.582 This is because im this regine. the quadrupole error is dominated by the iutriusic variation in cllipticitics. rather than measurement errors.," This is because in this regime, the quadrupole error is dominated by the intrinsic variation in ellipticities, rather than measurement errors."583 Hf such is the case. then we are necessarily Buaited by shot noise in the uuuber of sources rather than Poissou noise.," If such is the case, then we are necessarily limited by shot noise in the number of sources rather than Poisson noise."584 If the iutriusic scatter iu the octopole momeut is sufficicutly larec. this may be the case for the octopole estimator as well.," If the intrinsic scatter in the octopole moment is sufficiently large, this may be the case for the octopole estimator as well."585 However. we reiterate that this statistic is not well-stucied.," However, we reiterate that this statistic is not well-studied."586 For brighter sources or longer exposures. the quality of estimates for the octopoles improves quickly. as do the estimates if the distance to the lens decreases. even if this is not accompanied by a corresponding increase i local shear.," For brighter sources or longer exposures, the quality of estimates for the octopoles improves quickly, as do the estimates if the distance to the lens decreases, even if this is not accompanied by a corresponding increase in local shear."587 Iu this paper. we have introduced a new aud potentially powerful way of analyzing weak lensing shear ficlds using the octopole iiomieuts of the observed light distribution as a secoud-order estimator of the shear.," In this paper, we have introduced a new and potentially powerful way of analyzing weak lensing shear fields – using the octopole moments of the observed light distribution as a second-order estimator of the shear."588 In addition to the shear. we also obtain an estimate of its radial derivative.," In addition to the shear, we also obtain an estimate of its radial derivative."589 The radial derivative of the shear field provides au inportanut constraint on the mass profiles of the dark matter halos that host galaxies., The radial derivative of the shear field provides an important constraint on the mass profiles of the dark matter halos that host galaxies.590 There are few other iiethods that can probe that variation., There are few other methods that can probe that variation.591" Wile we have demoustrated that within the range of reasonable plivsical and observational parameters the correspondiug measurement uncertainties for the octopole may be comparable to those found. using traditional ellipticity estimates of the shear. iimch remains to be done. both theoretically aud observationally,"," While we have demonstrated that within the range of reasonable physical and observational parameters the corresponding measurement uncertainties for the octopole may be comparable to those found using traditional ellipticity estimates of the shear, much remains to be done, both theoretically and observationally."592 The Gaussian mask used in estimating the octopole and quadrupole moments is almost certainly not optimal for this technique., The Gaussian mask used in estimating the octopole and quadrupole moments is almost certainly not optimal for this technique.593 In order to apply this to observations. shape estimators must be used which can compute these higher-order moments with πιαπα signal to noise.," In order to apply this to observations, shape estimators must be used which can compute these higher-order moments with maximum signal to noise."594 One avenue of inquiry is to apply a second-order analysis to the Shapelet (Refreeier. 2001: Retreeier Bacon. 2001) techuique iu order to eot a comparable signal.," One avenue of inquiry is to apply a second-order analysis to the Shapelet (Refregier, 2001; Refregier Bacon, 2001) technique in order to get a comparable signal."595 Iu additiou. we have created a somewhat simplistic model of the lens as a circular svstem.," In addition, we have created a somewhat simplistic model of the lens as a circular system."596 Schneider Darteliiaun, Schneider Bartelmann597with either broad emission lines in their optical spectra and/or a prominent nuclear point source in their optical images (SDSS or HST/ACS survey of the AEGIS/GOODS).,with either broad emission lines in their optical spectra and/or a prominent nuclear point source in their optical images (SDSS or HST/ACS survey of the AEGIS/GOODS).598 The optical continua of those sources are contaminated by AGN light., The optical continua of those sources are contaminated by AGN light.599 This introduces biases in the determination of the host galaxy absolute optical magnitude and stellar mass., This introduces biases in the determination of the host galaxy absolute optical magnitude and stellar mass.600" Also, the colours of those sources do not provide information on the dominant stellar population of their hosts."," Also, the colours of those sources do not provide information on the dominant stellar population of their hosts."601" We note however, that AGN dominated sourcesare included in the determination of both the total XLF (i.e. not split by colour) and the total X-ray luminosity density."," We note however, that AGN dominated sources included in the determination of both the total XLF (i.e. not split by colour) and the total X-ray luminosity density."602" Figure 3 and Table 2 present the 2-10kkeV XLFs of the XMM/SDSS, NHS and AEGIS+GOODS surveys at median redshifts of 0.1, 0.3 and 0.8 respectively."," Figure \ref{fig_xlf} and Table \ref{tab_XLF} present the keV XLFs of the XMM/SDSS, NHS and AEGIS+GOODS surveys at median redshifts of 0.1, 0.3 and 0.8 respectively."603" At all three redshifts, the estimated XLFs are in good agreement with the Luminosity And Density Evolution (LADE) model of Aird et al. ("," At all three redshifts, the estimated XLFs are in good agreement with the Luminosity And Density Evolution (LADE) model of Aird et al. ("604"2010), which is also plotted in the figure.","2010), which is also plotted in the figure."605" Although our X-ray samples are apparent magnitude limited, this selection effect is correctly accounted for in the 1/Vmax calculation."," Although our X-ray samples are apparent magnitude limited, this selection effect is correctly accounted for in the 1/Vmax calculation."606" For the NHS in particular, the exclusion of optically unresolved X-ray sources, for which optical spectra have not been obtained as part of our ESO follow-up programs (section ??)), does not appear to introduce incompleteness in XLF estimation."," For the NHS in particular, the exclusion of optically unresolved X-ray sources, for which optical spectra have not been obtained as part of our ESO follow-up programs (section \ref{sec_xagn}) ), does not appear to introduce incompleteness in XLF estimation."607 This is consistent with our finding that optically unresolved sources are dominated by AGN outside the redshift range 0.1-0.5 probed by the NHS., This is consistent with our finding that optically unresolved sources are dominated by AGN outside the redshift range 0.1-0.5 probed by the NHS.608 Next we split the three samples by rest-frame 94((u—g) colour to explore changes with redshift of the space density of X-ray AGN in red/blue hosts and get insights into the dominant accretion mode onto SMBHs at different epochs., Next we split the three samples by rest-frame $^{0.1}(u-g)$ colour to explore changes with redshift of the space density of X-ray AGN in red/blue hosts and get insights into the dominant accretion mode onto SMBHs at different epochs.609 AGN dominated sources are excluded from the analysis., AGN dominated sources are excluded from the analysis.610" The total numbers of red cloud [ρω—g)> 1.4], blue cloud [!(u—g)« 1.4] and dominated sources in each sample are listed in Table 1.."," The total numbers of red cloud $^{0.1}(u-g)>1.4$ ], blue cloud $^{0.1}(u-g)<1.4$ ] and AGN-dominated sources in each sample are listed in Table \ref{tab_sample}."611 The XLFs of red cloud AGN are shown in Figure 3 and are listed in Table 2.., The XLFs of red cloud AGN are shown in Figure \ref{fig_xlf} and are listed in Table \ref{tab_XLF}.612 The ratio of the integrated XLF of AGN in red hosts over the total integrated XLF is plotted in Figure 4.., The ratio of the integrated XLF of AGN in red hosts over the total integrated XLF is plotted in Figure \ref{fig_xlf_fraction}.613 It demonstrates that within the errors there is no strong evidence for evolution of the red host AGN fraction since z*0.8., It demonstrates that within the errors there is no strong evidence for evolution of the red host AGN fraction since $z\approx0.8$.614 Similar results are obtained for the AGN in blue hosts., Similar results are obtained for the AGN in blue hosts.615 More relevant in the study of the dominant AGN accretion mode as a function of redshift is the fraction of the accretion power of the Universe that is associated with red/blue hosts at different epochs., More relevant in the study of the dominant AGN accretion mode as a function of redshift is the fraction of the accretion power of the Universe that is associated with red/blue hosts at different epochs.616 Figure 5 plots the hard band X-ray luminosity density as a function of luminosity for the three samples used in this paper., Figure \ref{fig_ld} plots the hard band X-ray luminosity density as a function of luminosity for the three samples used in this paper.617 At each redshift bin we sum up separately the luminosity density of AGN in red/blue hosts and X-ray sources with colours dominated by the central engine and divide with the total luminosity density., At each redshift bin we sum up separately the luminosity density of AGN in red/blue hosts and X-ray sources with colours dominated by the central engine and divide with the total luminosity density.618 The results are plotted as a function of lookback time and redshift in Figure 6.., The results are plotted as a function of lookback time and redshift in Figure \ref{fig_ld_fraction}.619 Within the uncertainties there is little change with redshift of the relative fraction of the accretion power in red/blue AGN hosts from z=0.8 to z=0.1., Within the uncertainties there is little change with redshift of the relative fraction of the accretion power in red/blue AGN hosts from $z=0.8$ to $z=0.1$.620 This statement is quantified by fitting a straight line to the luminosity density fraction versus redshift datapoints of Figure 6.., This statement is quantified by fitting a straight line to the luminosity density fraction versus redshift datapoints of Figure \ref{fig_ld_fraction}.621 For the slope of the line we find best fit values and 68 per cent confidence level errors (Ax?= 1) of --0.01*0-15 (blue AGN hosts) and —0.05*0:13 (red AGN hosts)., For the slope of the line we find best fit values and 68 per cent confidence level errors $\Delta\chi^2=1$ ) of $+0.01^{+0.14}_{-0.15}$ (blue AGN hosts) and $-0.05^{+0.13}_{-0.15}$ (red AGN hosts).622 Based on the uncertainty in the slope of the linear fit we then estimate that at the 68 per cent confidence level the luminosity density associated with blue AGN hosts cannot increase or decrease more than a factor of about 1.4 between z=0.8 and z=0.1., Based on the uncertainty in the slope of the linear fit we then estimate that at the 68 per cent confidence level the luminosity density associated with blue AGN hosts cannot increase or decrease more than a factor of about 1.4 between $z=0.8$ and $z=0.1$.623" For AGN in red hosts we find that their luminosity density cannot increase or decrease more than factors of 1.6 and 1.2 respectively,"," For AGN in red hosts we find that their luminosity density cannot increase or decrease more than factors of 1.6 and 1.2 respectively,"624"their evolution will they be brighter than Mj;=Ἐlinag or logNp,=50.981. respectively.","their evolution will they be brighter than $M_H = -14\,$ mag or $\log N_{\rm Ly} = 50.9\,{\rm s}^{-1}$, respectively."625 For a more extended period of star formation we have used outputs of Ricke et al. (, For a more extended period of star formation we have used outputs of Rieke et al. (6261993) models with a Gaussian star formation rate of ολλ ΕΠΙ,1993) models with a Gaussian star formation rate of Myr FWHM.627" The results are presented iu Figure 6 for two clusters with masses 5&10ML, and 5<10*M. for a truncated SalpeterIME?."," The results are presented in Figure 6 for two clusters with masses $5\times10^4\,{\rm M}_\odot$ and $5\times10^5\,{\rm M}_\odot$ for a truncated Salpeter."628", Figure 6 is coded in the same wav as Fieure 5.", Figure 6 is coded in the same way as Figure 5.629 It is ‘lear that the different star formation rates will produce different fractions of regions. coicidences and star cluster detectious.," It is clear that the different star formation rates will produce different fractions of regions, coincidences and star cluster detections."630" For instance. in tle case of a 5«100M, ‘hister formed im a Gaussian burst. we will detect regions alone between 3 aud ADINIv. before the £f-haucd uuinositv of the cluster becomes detectable."," For instance, in the case of a $5\times10^5\,{\rm M}_\odot$ cluster formed in a Gaussian burst, we will detect regions alone between 3 and Myr, before the $H$ -band luminosity of the cluster becomes detectable."631 In the case of re SS ΕΙ because the star formation period is nore extended than iu the instantancous burst. it is still xossible to have coiecidences for a short period of time. )otween 9 aud MAIvr.," In the case of the $5\times10^4\,{\rm M}_\odot$ cluster, because the star formation period is more extended than in the instantaneous burst, it is still possible to have coincidences for a short period of time, between 9 and Myr."632 We now need to assume a nass distribution for the star clusters., We now need to assume a mass distribution for the star clusters.633 Ehuegreen Efremiov. (1997) proposed that all vpes of clusters (vouug star clusters. elobular clusters. open clusters and associations) forma with nearly constant efficiency in eas clouds.," Elmegreen Efremov (1997) proposed that all types of clusters (young star clusters, globular clusters, open clusters and associations) form with nearly constant efficiency in gas clouds."634 This universal nechauisui applies hen to all regions regardless of epoch or geometry., This universal mechanism applies then to all regions regardless of epoch or geometry.635 Thus he mass distribution of the star clusters iu NGC 3256 and Arp 299 can be represeuted as a power Luv: where e is the slope of the distribution., Thus the mass distribution of the star clusters in NGC 3256 and Arp 299 can be represented as a power law: where $a$ is the slope of the distribution.636 From star cluster and region LFs. it is found that the slope has values of a=1L.72 (see Ehneerecn Efremov 1997 aud references therein).," From star cluster and region LFs, it is found that the slope has values of $a = 1.7-2$ (see Elmegreen Efremov 1997 and references therein)."637 In particular. Zeptet al. (," In particular, Zepf et al. ("6381999) have found a slope of «=1.8 for the optical LF of the voung star clusters iu NGC 3256.,1999) have found a slope of $a=1.8$ for the optical LF of the young star clusters in NGC 3256.639 The next step is to assume an age distributiou for the star clusters., The next step is to assume an age distribution for the star clusters.640 From optical spectroscopy of tle regious of Arp 299. we measured a range of equivalent widths of IIo (a simular situation is found in NGC 3256. see Lippari et al.," From optical spectroscopy of the regions of Arp 299, we measured a range of equivalent widths of $\alpha$ (a similar situation is found in NGC 3256, see pari et al."641 2000) which iuplies that the star regions are not coeval., 2000) which implies that the star regions are not coeval.642 We will assume that clusters are formed at a coustant rate. so there is a rauge of ages.," We will assume that clusters are formed at a constant rate, so there is a range of ages."643 Using Equation (2) for the mass distribution of the star clusters. aud the evolutionary svuthesis models presented above. we cau obtain au estimate the fractious of voung. intermediate and old clusters.," Using Equation (2) for the mass distribution of the star clusters, and the evolutionary synthesis models presented above, we can obtain an estimate the fractions of young, intermediate and old clusters."644 For the two ealaxics in consideration we will ouly need to take iuto account star clusters with masses between ~5<104M. aud 109ML...," For the two galaxies in consideration we will only need to take into account star clusters with masses between $\simeq 5\times 10^4\,{\rm M}_\odot$ and $10^6\,{\rm M}_\odot$."645 Less massive clusters will not be observed with the prescut detection threshold. whereas the upper huit of the 11-baud ποπτν distribution (Mj;2 17.2amae) indicaisl that there are uo star clusters more massive than 109AL...," Less massive clusters will not be observed with the present detection threshold, whereas the upper limit of the $H$ -band luminosity distribution $M_H\simeq -17.2\,$ mag) indicates that there are no star clusters more massive than $10^6\,{\rm M}_\odot$."646 The latter seeimis to be true for all the interacting/niereiug LIRGs iu our sample., The latter seems to be true for all the interacting/merging LIRGs in our sample.647 The first result is that the relative nuunibers of voune regions/clusters. iutermediate aud old clusters depeud oulv slightly ou the slope of the mass distribution (for the range a=1.7 2).," The first result is that the relative numbers of young regions/clusters, intermediate and old clusters depend only slightly on the slope of the mass distribution (for the range $a = 1.7-2$ )."648 The main factors determining these fractions are the age distribution of the star clusters (that is the age of the oldest clusters). aud. the adopted form for the IMIF aud star formation rate.," The main factors determining these fractions are the age distribution of the star clusters (that is the age of the oldest clusters), and the adopted form for the IMF and star formation rate."649 See Sections 5.1 aud 5.5 for a discussion on the effects of extinction and cluster destruction., See Sections 5.4 and 5.5 for a discussion on the effects of extinction and cluster destruction.650 Iu Table 5 we sunuuarize the results for a cluster mass distribution with a slope of &=1.7., In Table 5 we summarize the results for a cluster mass distribution with a slope of $a =1.7$.651 The first part of the table are the results for au instantaneous burst. whereas the secoud part are those for a more extended period of star formation.," The first part of the table are the results for an instantaneous burst, whereas the second part are those for a more extended period of star formation."652 The model predictions can be compared with the fractious for the complete distributions of NGC 3256 aud Arp 299 eiven in the second part of Table 1., The model predictions can be compared with the fractions for the complete distributions of NGC 3256 and Arp 299 given in the second part of Table 4.653 Tuspection of Figures 5 aud 6. and taking mto account that less massive clusters are more nunierous thaw more massive clusters. shows that the amore extended star formation activity of Ricke et al. (," Inspection of Figures 5 and 6, and taking into account that less massive clusters are more numerous than more massive clusters, shows that the more extended star formation activity of Rieke et al. ("6541993) models will always produce more coincidences than observed. regardless of the ani aee of the star clusters.,"1993) models will always produce more coincidences than observed, regardless of the maximum age of the star clusters."655 This probably iudicates that the instantaneous star formation is a better choice to account for the observed properties of star clusters., This probably indicates that the instantaneous star formation is a better choice to account for the observed properties of star clusters.656" This seenis to be the case for local star clusters where the age spread is at most just a few million vears (οι, Lulunan et al."," This seems to be the case for local star clusters where the age spread is at most just a few million years (e.g., Luhman et al."657 1998: Palla Stabler 2000)., 1998; Palla Stahler 2000).658 This is not true in eeucral for the nuclei of interacting galaxies. aud reeious of high star formation activity (sec AATIOO and AATIOL) where we have found that more exteuded periods of star formation are required to explain the observed properties.," This is not true in general for the nuclei of interacting galaxies, and regions of high star formation activity (see AAH00 and AAH01) where we have found that more extended periods of star formation are required to explain the observed properties."659 Figures 5 and 6 also illustrate the dependence of the cluster huuimositv with the model assumptions. which in turn translates into different ass estimates frou the observed absolute ff-baucd magnitudes.," Figures 5 and 6 also illustrate the dependence of the cluster luminosity with the model assumptions, which in turn translates into different mass estimates from the observed absolute $H$ -band magnitudes."660 Usine the iustautancous star formation aud a Salpeter TIF betwee- Land 100ΔΕ we cau coustrain the masses of the identified star clusters in NGC 3256 and Arp 299 between ~5«&105ML. and z109AL...," Using the instantaneous star formation and a Salpeter IMF between 1 and $100\,{\rm M}_{\odot}$ we can constrain the masses of the identified star clusters in NGC 3256 and Arp 299 between $\simeq 5 \times 10^4\,{\rm M}_\odot$ and $\simeq 10^6\,{\rm M}_\odot$."661 The high eud of our photometric celasses is du good agreement with the dynamical masses jeasured by Moeugel et al. (, The high end of our photometric masses is in good agreement with the dynamical masses measured by Mengel et al. (6622002) for compact voune star clusters in the Auteunae system.,2002) for compact young star clusters in the Antennae system.663 Another interesting result fom our simulations is that i6 observed relative fractions of voung regious) and old (near-intrared star clusters) populations provide sole iuformiation on the age spread of the last epoch of star formation., Another interesting result from our simulations is that the observed relative fractions of young regions) and old (near-infrared star clusters) populations provide some information on the age spread of the last epoch of star formation.664 From the statistical poiut of view our xnnulatious show that most of the stellar population im Arp 299 and NGC 3256 shows au age spread of between NMSyr and NM. as otherwise we should have ineasured a higher fraction of old clusters (e.g.. for an age distribution of up to Avr this faction is ~80% )).," From the statistical point of view our simulations show that most of the stellar population in Arp 299 and NGC 3256 shows an age spread of between Myr and Myr, as otherwise we should have measured a higher fraction of old clusters (e.g., for an age distribution of up to Myr this faction is $\simeq 80$ )."665 Zepfet al. (, Zepf et al. (6661999) also deduced vouug ages for the NGC 3256 star clusters detected in the optical based ou the lack of a strong color-TJuninosity relation.,1999) also deduced young ages for the NGC 3256 star clusters detected in the optical based on the lack of a strong color-luminosity relation.667 The vouth of the detected clusters does not exclude the presence of older clusters possibly created in this or previous episodes of star formation., The youth of the detected clusters does not exclude the presence of older clusters possibly created in this or previous episodes of star formation.668 These clusters however cannot be identified with the prescut detection threshold., These clusters however cannot be identified with the present detection threshold.669 Tn this section we diseuss some limitations of the coluparison between the observed fractions of reeions. old clusters aud the model predictions.," In this section we discuss some limitations of the comparison between the observed fractions of regions, old clusters and the model predictions."670Glitches. observed Irom more than 30 isolated puls:us (Lyne.Waneetal. 2000).. are a sudden jump in pulsar rotation 1‘ale.,"Glitches, observed from more than 30 isolated pulsars \citep{lyn00, wan00}, are a sudden jump in pulsar rotation rate."671 Slow recovery of a rotation rate following these events implies (he presence of loosely-coupled fIuids or neutron superfluids in (he interior of a neutron star., Slow recovery of a rotation rate following these events implies the presence of loosely-coupled fluids or neutron superfluids in the interior of a neutron star.672 The transfer of angular momentum from (he rotating neutron, The transfer of angular momentum from the rotating neutron673aud envelope mass. we calculated zeὉ age horizontal branch evolutionary models aud determined the stars’ temperature. radius. total LOnent of inertia. auc moment of inertia of the couvection zone on the horizontal brauch.,"and envelope mass, we calculated zero age horizontal branch evolutionary models and determined the stars' temperature, radius, total moment of inertia, and moment of inertia of the convection zone on the horizontal branch."674 The sLUCural properties of each horizoutal brauch moclel are given in table I., The structural properties of each horizontal branch model are given in table 1.675 The total amount of angular monellum that survives iu the convective euvelope and radiative core depeuds uot ouly upon the aiLOULwoof mass and angular momentum loss. but also upon the efficiency of internal angular moineitum transport from the contracting radiative core iuto the expancdiug couvective envelope. aud the augular moientuu distribution within the convective euvelope.," The total amount of angular momentum that survives in the convective envelope and radiative core depends not only upon the amount of mass and angular momentum loss, but also upon the efficiency of internal angular momentum transport from the contracting radiative core into the expanding convective envelope, and the angular momentum distribution within the convective envelope."676 We outline below the limiting cases we have chosen to investigate the cliffereut possibilities., We outline below the limiting cases we have chosen to investigate the different possibilities.677 The radiative core on the egiant branch is a potentia reservoir of angular momentum which could be redistributed to the surace layers after the heliuu flash., The radiative core on the giant branch is a potential reservoir of angular momentum which could be redistributed to the surface layers after the helium flash.678 There is a sigtilicant. Craction of the initial uass (0.313 AL.) wluch is never incorporate Lin the outer convective euvelope., There is a significant fraction of the initial mass (0.313 $M_{\sun}$ ) which is never incorporated in the outer convective envelope.679 This lnner core COLtains of the 1rolmeut of inertia. aud tlerefore augular niomenttin. of the nalu secence turolf precursor assting solid body rotation.," This inner core contains of the moment of inertia, and therefore angular momentum, of the main sequence turnoff precursor assuming solid body rotation."680 Another 0.156 AZ. [roin the convective euvelope falls into the radiative interior between the poiit of maximum depth i lass alc the helium flash: the angular momentun content of this component depens ou the auglar momentta distribution in convective regions., Another 0.156 $M_{\sun}$ from the convective envelope falls into the radiative interior between the point of maximum depth in mass and the helium flash; the angular momentum content of this component depends on the angular momentum distribution in convective regions.681 We coisider two limiting cases lor the augular momentuui conten of the radiative core οἱ the eiant branch:, We consider two limiting cases for the angular momentum content of the radiative core on the giant branch:682other also becomes faint.,other also becomes faint.683" If we reduce the contribution of the long baselines, both become brighter and show a small peak (~ 596)) brightness difference."," If we reduce the contribution of the long baselines, both become brighter and show a small peak $\sim5$ ) brightness difference."684" Due to the limited sensitivity and u - v coverage during the 1.2-hour observations, neither components can be unambiguously identified as a true jet component."," Due to the limited sensitivity and $u$ – $v$ coverage during the 1.2-hour observations, neither components can be unambiguously identified as a true jet component."685" However, there is evidence for the extended emission for the source as the total restored flux density is much lower than that (~16 mJy at 5.5 GHz) measured by the ATCA (Brocksopp et al."," However, there is evidence for the extended emission for the source as the total restored flux density is much lower than that $\sim16$ mJy at 5.5 GHz) measured by the ATCA (Brocksopp et al."686 in prep.)., in prep.).687" In the followup VLBA observations, the higher resolution and sensitivity are achieved by more telescopes and longer observing time."," In the follow-up VLBA observations, the higher resolution and sensitivity are achieved by more telescopes and longer observing time."688" To image the extended source, we used natural weighting again."," To image the extended source, we used natural weighting again."689" Because of the resolved structure and the decaying peak flux density, the source is only seen clearly in the dirty map with the synthesised beam (16.2x3.9 mas at position angle —15°6) at the first VLBA epoch."," Because of the resolved structure and the decaying peak flux density, the source is only seen clearly in the dirty map with the synthesised beam $16.2\times3.9$ mas at position angle $-15\fdg6$ ) at the first VLBA epoch."690" However, the large-scale beam pattern around the faint source could also be easily identified at the later two epochs."," However, the large-scale beam pattern around the faint source could also be easily identified at the later two epochs."691" If we taper the long baselines, use the short baselines only, or increase the image pixel size, the source becomes significantly brighter in the dirty map at the later two epochs."," If we taper the long baselines, use the short baselines only, or increase the image pixel size, the source becomes significantly brighter in the dirty map at the later two epochs."692 None of the suspected ejecta candidates in the EVN image are further seen after 7 days in the later VLBA images., None of the suspected ejecta candidates in the EVN image are further seen after 7 days in the later VLBA images.693" Because the diffuse emission can not be well restored by clean components, Gaussian models were used in making all the VLBI images of Fig. 1.."," Because the diffuse emission can not be well restored by clean components, Gaussian models were used in making all the VLBI images of Fig. \ref{fig1}."694" Due to the limited SNR (6 — 12), circular rather than elliptical Gaussian model fitting was adopted to reduce the number of free parameters."," Due to the limited SNR (6 -- 12), circular rather than elliptical Gaussian model fitting was adopted to reduce the number of free parameters."695 Table 2 lists the best-fit parameters of the circular Gaussian model., Table \ref{tab2} lists the best-fit parameters of the circular Gaussian model.696" To show the motion of component A, we take the position of component A measured at the first epoch as the reference origin."," To show the motion of component A, we take the position of component A measured at the first epoch as the reference origin."697" The random position error was estimated by binajbmin where bmaj and bmin are the size of the major and minor -—5sxg--—,axes of the used restoring beam, SNR is the signal to noise ratio (Speak) listed in Column (7) of Table 2.."," The random position error was estimated by $\frac{\sqrt{b_\mathrm{maj}b_\mathrm{min}}}{2\mathrm{SNR}}$, where $b_\mathrm{maj}$ and $b_\mathrm{min}$ are the size of the major and minor axes of the used restoring beam, $\mathrm{SNR}$ is the signal to noise ratio $\frac{S_\mathrm{peak}}{\sigma_\mathrm{rms}}$ ) listed in Column (7) of Table \ref{tab2}."698 Note that the rather large systematic position error from the reference source will not affect our proper motion measurements., Note that the rather large systematic position error from the reference source will not affect our proper motion measurements.699 The fitted size has the same random error as the position for each component., The fitted size has the same random error as the position for each component.700" Since the measured sizes (>8 mas) are much larger than that (4.2 mas) of the reference source, they should be very close to the true size of the ejecta."," Since the measured sizes $\geq8$ mas) are much larger than that (4.2 mas) of the reference source, they should be very close to the true size of the ejecta."701" At the second epoch, we notice that component A shows an elongated structure in the East-West direction and the eastern side is brighter than the western side."," At the second epoch, we notice that component A shows an elongated structure in the East-West direction and the eastern side is brighter than the western side."702" This brightness distribution caused a slightly different position angle of the component, compared to what is measured at later epochs."," This brightness distribution caused a slightly different position angle of the component, compared to what is measured at later epochs."703 The VLBI flux density errors are usually ~5%., The VLBI flux density errors are usually $\sim5\%$.704 The angular separation of component A versus time is shown in the right panel of Fig. 1.., The angular separation of component A versus time is shown in the right panel of Fig. \ref{fig1}.705 We take the position and the time of component A measured at the first epoch as the reference origin., We take the position and the time of component A measured at the first epoch as the reference origin.706" We fit these data points to the following proper motion model:where r is the angular separation; t is the observing time; ro and po are the angular separation and the proper motion at t= 0, ji is the apparent deceleration rate."," We fit these data points to the following proper motion model:where $r$ is the angular separation; $t$ is the observing time; $r_0$ and $\mu_0$ are the angular separation and the proper motion at $t=0$ , $\dot\mu$ is the apparent deceleration rate."707The,The708spectrum shows enuüsson features superposed ou the pseudo-coutinnun.,spectrum shows emission features superposed on the pseudo-continuum.709 The 18-22 feature exteuds to Ac26 jan. However. as Fig.," The $\mu$ m feature extends to $\lambda \approx 26$ $\mu$ m. However, as Fig."710 7 clearly shows for both plots. there are crystalline features present within this waveleusth region. in particular. the 17.520 yan complex.," \ref{oh104} clearly shows for both plots, there are crystalline features present within this wavelength region, in particular, the 17.5--20 $\mu$ m complex."711 For reference. the continmau-subtracted spectrum of AFGL 1106 (Molster et al. 1999a))," For reference, the continuum-subtracted spectrum of AFGL 4106 (Molster et al. \cite{molster}) )"712 is also plotted., is also plotted.713 The 20.6 ju emissiou feature is probably related to crystalline silicates. although it is not vet identified (Molster et al. 1999a::," The 20.6 $\mu$ m emission feature is probably related to crystalline silicates, although it is not yet identified (Molster et al. \cite{molster};"714 Voors 1999))., Voors \cite{voors}) ).715 These OII/IR. star spectra are he first to show crystalline silicates 1n clission sinultaneouslv with amorphous silicates in absorption iu the same wavelength region., These OH/IR star spectra are the first to show crystalline silicates in emission simultaneously with amorphous silicates in absorption in the same wavelength region.716 The presence of crystalline cuiission features in the spectrun of OITIIOLO. at wavelengths where the amorphous dust compoucut is still iu absorption. implics that the crystalline silicate cust iuust have a different spatial distribution than the amorphous silicate dust.," The presence of crystalline emission features in the spectrum of OH104.9, at wavelengths where the amorphous dust component is still in absorption, implies that the crystalline silicate dust must have a different spatial distribution than the amorphous silicate dust."717 We consider two possible ecometrics: spherical and axi-sviunetrical., We consider two possible geometries: spherical and axi-symmetrical.718 For the case of a spherically svaiunietzrie distribution. the crystalline «ist can have a ciffereut radial distribution and be located further out in the cuvelope than the anorplhous dus.," For the case of a spherically symmetric distribution, the crystalline dust can have a different radial distribution and be located further out in the envelope than the amorphous dust."719 The SWS aud LAVS beat sizes are much larger than the augular size of the dus shells of these OIL/IR stars. so he amorphous silicate absorption cau originate from the entire dust shell. while the crvstalline silicate emission can arise frou the cool outer lavers of the dust shell. where the material is optically thin.," The SWS and LWS beam sizes are much larger than the angular size of the dust shells of these OH/IR stars, so the amorphous silicate absorption can originate from the entire dust shell, while the crystalline silicate emission can arise from the cool outer layers of the dust shell, where the material is optically thin."720 If the crystalline silicates are located further out. we can conclude that the crystalline and amorphous dust has not formed at the same time. but that the amorphous dust," If the crystalline silicates are located further out, we can conclude that the crystalline and amorphous dust has not formed at the same time, but that the amorphous dust"721Case Western Burrell Schimidt telescope at INitt Peak National Observatory.,Case Western Burrell Schmidt telescope at Kitt Peak National Observatory.722 The + [NI] image was obtained with a narrow-band.744A.. filler centered alG568A.," The + [NII] image was obtained with a narrow-band, filter centered at."723. A narrow-band.72A.. line-free filter centered αἱG48LA.. was used to obtain the continuum image.," A narrow-band, line-free filter centered at, was used to obtain the continuum image."724 Results and analysis of (he M 31 data are presented in Devereux.Jacoby&Ciardullo(1995)., Results and analysis of the M 81 data are presented in \citet{Devereux1995}.725. Images for five galaxies (NGC 3705. NGC 4192. NGC 4419. NGC 4450. and NGC 4984) were kindly provided by Rebecca Koopman.," Images for five galaxies (NGC 3705, NGC 4192, NGC 4419, NGC 4450, and NGC 4984) were kindly provided by Rebecca Koopman."726 All of these galaxies. except NGC 4934. were imaged with the 0.9 m telescope at IXRPNO.," All of these galaxies, except NGC 4984, were imaged with the 0.9 m telescope at KPNO."727 The image of NGC 4984 was obtained with ihe 0.9 m telescope located at CTIO., The image of NGC 4984 was obtained with the 0.9 m telescope located at CTIO.728 All of IXoopmiaur's images were obtained with a filter and a broadband I. filler was used for the continuum images., All of Koopman's images were obtained with a narrow-band filter and a broadband R filter was used for the continuum images.729 Details of (hese observations are presented in Noopman(1997)., Details of these observations are presented in \citet{Koopman1997}.730. There are several galaxies in our survey that have published fluxes., There are several galaxies in our survey that have published fluxes.731 Figure 1 compares fluxes for 15 galaxies measured bv us in the same aperture as those in the literature., Figure 1 compares fluxes for 15 galaxies measured by us in the same aperture as those in the literature.732 Figure 1. includes fluxes for seven galaxies published previously in IID99., Figure 1 includes fluxes for seven galaxies published previously in HD99.733 Overall. there is good agreement. between (he measurements.," Overall, there is good agreement between the measurements."734 There are. however. (wo exceptions.," There are, however, two exceptions."735 Our flux for NGC 4736 is 196. below the value obtained by Youngefal(1996). and our measurement for NGC 3718 is 1804 above the value quoted by Young (1996)., Our flux for NGC 4736 is $\%$ below the value obtained by \citet{Young1996} and our measurement for NGC 3718 is $\%$ above the value quoted by Young (1996).736 lxennicutt&Ixent.(1983) also measured the [hix of NGC 4736 and their value is within 29%. of our measured flux., \citet{KK1983} also measured the flux of NGC 4736 and their value is within $\%$ of our measured flux.737 We do not know the reason for the difference of our flux. value from that of Younga£., We do not know the reason for the difference of our flux value from that of Young.738.. Ilowever. we should note that there are 4 other galaxies (hat are in common with Young “ss sample. aud their fluxes are within 2%(NGC 3504). 5 (NGC 660). 222CNGC 2146). and 67 (NGC 3623) of our values.," However, we should note that there are 4 other galaxies that are in common with Young s sample, and their fluxes are within $\%$ (NGC 3504), $\%$ (NGC 660), $\%$ (NGC 2146), and $\%$ (NGC 3623) of our values."739 Overall. the mean ratio of our [lux measurements to the other studies is 1.19 + 0.6.," Overall, the mean ratio of our flux measurements to the other studies is 1.19 $\pm$ 0.6."740 ILowever. the ratio drops down to 1.10 + 0.4 if we exelude NGC 3718 and NGC 4736.," However, the ratio drops down to 1.10 $\pm$ 0.4 if we exclude NGC 3718 and NGC 4736."741 The fluxes and equivalent widths presented in this paper include contributions from the two satellite [NI] lines at and6584., The fluxes and equivalent widths presented in this paper include contributions from the two satellite [NII] lines at and.742.. Complete inclusion of these lines in our line filters allows the possibility to later correct for [NU] contamination. when more information is available.," Complete inclusion of these lines in our line filters allows the possibility to later correct for [NII] contamination, when more information is available."743 Previous work has indicated that the ratio varies from one galaxy to the next and within individual galaxies (Nennicutt&IXent.1933:Nennientt 1992)..," Previous work has indicated that the ratio varies from one galaxy to the next and within individual galaxies \citep{KK1983, Kennicutt1992}. ."744respect to the disk.,respect to the disk.745 Coutours of radial velocity are defined by: The line xoadenius will be determined by the leugth of he contours at a given velocity., Contours of radial velocity are defined by: The line broadening will be determined by the length of the contours at a given velocity.746 Frou. equation 11 we see that the resulting profile is svinmmetric and will have a peak correspoucding to the longest contour which will just touch the outer οσο of the disk at :—ρε aud cos?=0., From equation \ref{eqn:contour} we see that the resulting profile is symmetric and will have a peak corresponding to the longest contour which will just touch the outer edge of the disk at $R=R_{out}$ and $\cos \theta = 0$.747 We can define a characteristic broadenius (see Ciuillotea et al., We can define a characteristic broadening (see Guilloteau et al.748 2006) bv the longest isovelocity contour described by Eq., 2006) by the longest isovelocity contour described by Eq.749 L1 as: According to Leeetal.(2009).. if the eas motions rear the source are Ieplerian. they then imply hat the ceutral object (or objects) have a total uass of about 0.05+40.015 AL...," 14 as: According to \citet{lee2009}, if the gas motions near the source are Keplerian, they then imply that the central object (or objects) have a total mass of about $0.05 \pm 0.015$ $_\odot$."750 Tf we assume i~BNDU. n central uass of M0.05 AL... au outer radius consistent with half the svuthesized un of our map (Rou= 27). aud that there is NIIS(1.1) e1iission from the disk. we then estimate iat an unresolved Weplerian disk could coutribute samuch as Atyepter~0.56⋅kins1 to the non-ieriual broadening iu the anuuouia line eaissiou rear the source position.," If we assume $i \sim 85\arcdeg$, a central mass of $ = 0.05$ $_{\odot}$, an outer radius consistent with half the synthesized beam of our map $R_{out} = 2\arcsec$ ), and that there is $_3$ (1,1) emission from the disk, we then estimate that an unresolved Keplerian disk could contribute as much as $\Delta v_{Kepler} \sim 0.56 \mbox{ km s}^{-1}$ to the non-thermal broadening in the ammonia line emission near the source position."751 This is siguificautly larger iui the maximum ine width observe near the source (0.I8 kins 1)., This is significantly larger than the maximum line width observe near the source (0.48 km $^{-1}$ ).752 It appears that our μα observations do not probe the imucr rotating structure close to TT 211-nuau. either because the disk does not extend fur bevoud what is observed bv Lee et al. (," It appears that our ammonia observations do not probe the inner rotating structure close to HH 211-mm, either because the disk does not extend far beyond what is observed by Lee et al. ("7531999) (1.0... it is πιο] smaller than our bea) or the auuuonia line cussion is not a eood tracer of the disk. or both.,"1999) (i.e., it is much smaller than our beam) or the ammonia line emission is not a good tracer of the disk, or both."754 Although the increase in line width close to the source is partially due to an increase in the hermal width. substantial nou-thermal motions are needed to explain the observed line broadening.," Although the increase in line width close to the source is partially due to an increase in the thermal width, substantial non-thermal motions are needed to explain the observed line broadening."755 The thermal line width in this region is about L2 Κα 1ὃν and as we diseuss below. the outflow appears to be responsible for a non-thenual xoadenimg of the line ( Across) of about L3 kan + along its axis.," The thermal line width in this region is about 0.2 km $^{-1}$, and as we discuss below, the outflow appears to be responsible for a non-thermal broadening of the line ( $\Delta v_{outflow}$ ) of about 0.3 km $^{-1}$ along its axis."756 Adding these two in quadrature results in a total width of 0.36 kin 1 sienificautly smaller than the observed line width near the source.," Adding these two in quadrature results in a total width of 0.36 km $^{-1}$, significantly smaller than the observed line width near the source."757 A possible source of additional non-thermal motions may come from iufall motions close to the protostar., A possible source of additional non-thermal motions may come from infall motions close to the protostar.758 In 3.7 we sugeest that the region within about 005 x nav be collapsing. and unresolved iufal notions lay result in au increase line width.," In \ref{sec:velocity} we suggest that the region within about 0.005 pc may be collapsing, and unresolved infall motions may result in an increase line width."759 Another possibility is that ACourflow Increases near the source., Another possibility is that $\Delta v_{outflow}$ increases near the source.760 Evidence for this is secu iu the increase in the range of outflow velocities observed close to the source (Lee et al., Evidence for this is seen in the increase in the range of outflow velocities observed close to the source (Lee et al.761 2007: 2009)., 2007; 2009).762" Theher angular resolution observations that cau probe the high density eas within 5"" of the source are needed to further investigate the dyuauices of the inner envelope.", Higher angular resolution observations that can probe the high density gas within $5\arcsec$ of the source are needed to further investigate the dynamics of the inner envelope.763 As discussed in Section ??.. and seen in Figure 5.. the velocity eracieut of the envelope is mostly along the major axis of the euvelope.," As discussed in Section \ref{sec:rotation}, and seen in Figure \ref{fig:velmap}, the velocity gradient of the envelope is mostly along the major axis of the envelope."764 However. rere is a deviation from this gradient in the reeion close to the protostar aud outflow axis. as 1e velocity contours here follow a distinct pattern compared to the contours in the envelope outskirts (see Figure 5)).," However, there is a deviation from this gradient in the region close to the protostar and outflow axis, as the velocity contours here follow a distinct pattern compared to the contours in the envelope outskirts (see Figure \ref{fig:velmap}) )."765 To further study this. we examine je velocitv eradieut along the minor axis of the (welope. which we preseut in Figure 9..," To further study this, we examine the velocity gradient along the minor axis of the envelope, which we present in Figure \ref{fig:velgrad_minor}."766" Each »t in the figure represents the central (LSR) velocity frou tle προσ iu a 2"" pixel. aud the error bars indicate the lo in the velocity estimate (using the procedure described in 3.13)."," Each point in the figure represents the central (LSR) velocity from the spectrum in a $2\arcsec$ pixel, and the error bars indicate the $1\sigma$ in the velocity estimate (using the procedure described in \ref{sec:spectralmodeling}) )."767 Ouly vincls within a strip that is S wide (two beam widths) aud ceutered ou the jet axis are included., Only pixels within a strip that is $8 \arcsec$ wide (two beam widths) and centered on the jet axis are included.768 The plot shows that. alone the outflow axis. most κοιν nortlsvest of the source are redshitted with respect fo he central (source position) velocity. while imost pixels southeast of the source are dueshifted.," The plot shows that, along the outflow axis, most pixels northwest of the source are redshifted with respect to the central (source position) velocity, while most pixels southeast of the source are blueshifted."769 A fit to the velocity eracdicnt alone he envelope minor axis vields a eradieut of approximately 3.5 lau | 1+. increasing (from Xue to red velocities) from southeast to northwest of the source.," A fit to the velocity gradient along the envelope minor axis yields a gradient of approximately $3.5$ km $^{-1}$ $^{-1}$, increasing (from blue to red velocities) from southeast to northwest of the source."770 We attribute the velocity distribution along the nunor axis of the anunonia cuvelope to the effect of the IIII 211 outflow ou the deuse eas sumrounudius the protostar., We attribute the velocity distribution along the minor axis of the ammonia envelope to the effect of the HH 211 outflow on the dense gas surrounding the protostar.771 As mentioned above we are most likely viewing the anunonia envelope edge-on. so the eas southeast and northwest of the source (along the munor axis) correspoud to regions above and below the mid-plane of the envelope.," As mentioned above we are most likely viewing the ammonia envelope edge-on, so the gas southeast and northwest of the source (along the minor axis) correspond to regions above and below the mid-plane of the envelope."772 The outflow originates very close to the protostar (within ~100 AU. Lee et al.," The outflow originates very close to the protostar (within $\sim 100$ AU, Lee et al."773 2009). aud iust," 2009), and must"774 (e.g..2??)..," \citep[e.g.,][]{2007MugrauerSeifahrtNeuhauser,2006Raghavan_etal,7752006Chauvin_etal}."776" 0.08—1.1M... ?. 5 > msinG)1.7 My, (??).. (22).."," $\sim0.08 - 1.1\,M_{\odot}$ \citet{2007EggenbergerUdry} $\gamma$ $\gamma$ $m\sin(i)\sim1.7$ $M_{Jup}$ \citep{1988Campbell_etal,2003Hatzes_etal}. \citep{ 2003Hatzes_etal,2007Torres_gcep}."777 + ? + ? ?.. ? + ο > accretion. disk and to explore which disk parameters allow planet formation to occur given that the disk is truncated by the stellar companion.," $\gamma$ \citet{2006Haghighipour_gcep} $\gamma$ \citet{2004Thebault_gcep} \citet{hayashi}, \citet{2008PaardekooperThebaultMellema} $\gamma$ \citet{2008KleyNelson} $\gamma$ accretion disk and to explore which disk parameters allow planet formation to occur given that the disk is truncated by the stellar companion."778 This analysis is similar to that done in? (henceforth Paper 1) for the extremely close triple system HD 188753., This analysis is similar to that done in \citet{HJChd188753} (henceforth Paper 1) for the extremely close triple system HD 188753.779 Paper | concluded that HD 188753 was unlikely to support a disk sufficiently massiveto support planet formation., Paper 1 concluded that HD 188753 was unlikely to support a disk sufficiently massiveto support planet formation.780 Indeed. the initial claim of a Jupiter-mass planet in HD 188753 (?). has since been refuted (?)..," Indeed, the initial claim of a Jupiter-mass planet in HD 188753 \citep{HD188753} has since been refuted \citep{2007Eggenberger_etal}."781 This does not rule out the possibility that the planet could form around a single star or in a wide binary and then undergo dynamical evolution. such as through close encounters with another star (??).. but this is outside the scope of this paper.," This does not rule out the possibility that the planet could form around a single star or in a wide binary and then undergo dynamical evolution, such as through close encounters with another star \citep{2005PortegiesZwart_McMillan,2005Pfahl}, but this is outside the scope of this paper."782 We adopt orbital parameters for the ~ Cep system from ?.. as follows: primary mass 1.40M... secondary mass 0.409M... eccentricity 0.41. and semi-major axis 20.18 AU.," We adopt orbital parameters for the $\gamma$ Cep system from \citet{2007Neuhauser_gcep}, as follows: primary mass $1.40\,M_{\sun}$, secondary mass $0.409\,M_{\sun}$, eccentricity $0.41$, and semi-major axis $20.18$ AU."783 We ignore the orbit of the planet. since we are interested in pre-planetary conditions of the diskaround the 1.4 M.. primary.," We ignore the orbit of the planet, since we are interested in pre-planetary conditions of the diskaround the 1.4 $M_{\sun}$ primary."784 We assume that the stars have not undergone significant mass loss or orbital evolution since their formation. so we can model the properties for ~ CCepA based on a pre-main sequence stellar model fora 1.4 M.. star.," We assume that the stars have not undergone significant mass loss or orbital evolution since their formation, so we can model the properties for $\gamma$ CepA based on a pre-main sequence stellar model for a 1.4 $M_{\sun}$ star."785 Since the typical age of a T Tauri star is | Myr. we assume this age for our model.," Since the typical age of a T Tauri star is 1 Myr, we assume this age for our model."786 The calculation for the disk models is described in detail in Paper | and ??..," The calculation for the disk models is described in detail in Paper 1 and \citet{paper1,paper2}."787" We assume an «-disk model. where the viscosity v is given by v=oci where c, is the sound speed. /i is the thermal scale height of the disk. and a is a dimensionless parameter (??).."," We assume an $\alpha$ -disk model, where the viscosity $\nu$ is given by $\nu=\alpha c_s h$ where $c_s$ is the sound speed, $h$ is the thermal scale height of the disk, and $\alpha$ is a dimensionless parameter \citep{shaksun,pringle}."788 The disk temperature ts set by stellar irradiation at the surface and viscous heating at the midplane., The disk temperature is set by stellar irradiation at the surface and viscous heating at the midplane.789 The radial and vertical density and temperature structure of the disk are calculated iteratively for self-consistency., The radial and vertical density and temperature structure of the disk are calculated iteratively for self-consistency.790 We adopt effective temperature 7.=4500 K. and radius ΑΔ.=3.0R... corresponding toa M.=14M...1Myrold star with metallicity Z20.02 (?)..," We adopt effective temperature $T_* = 4500$ K, and radius $R_* = 3.0\:\mathrm{R}_{\sun}$, correspondingto a $M_* = 1.4\,\msun$,1Myrold star with metallicity $Z=0.02$ \citep{siess_etal}. ."791 The two remaining free parameters for our disk models are the mass accretion rate onto the star M. andtheViscosity parameter o.," The two remaining free parameters for our disk models are the mass accretion rate onto the star $\dot{M}$ , andtheviscosity parameter $\alpha$ ."792 The exact values for these parameters are, The exact values for these parameters are793of the population producing the NRB is harder. aud the discrepancies between the model predictions aud the hard counts are somewhat reduced (though not completely eliminated).,"of the population producing the XRB is harder, and the discrepancies between the model predictions and the hard counts are somewhat reduced (though not completely eliminated)."794 The iain difference between models Al and A2 is the fractional contribution of tvpe 1 AGNs to the XRD: this contribution is dominated by objects close to the NLF break at redshifts close το i44. aud is not well constrained bv the data.," The main difference between models A1 and A2 is the fractional contribution of type 1 AGNs to the XRB; this contribution is dominated by objects close to the XLF break at redshifts close to $z_{cut}$, and is not well constrained by the data."795 In the former model of the 1keV ARB is due to type 1s. so the local value of the type ratio Rs is suffücieut to account for the entire ARB: the average spectrum. though. is too soft. and the softuess shows up in a iareinal discrepancy with the NRB spectrum) at >10 keV (Fig.," In the former model of the 1–keV XRB is due to type 1s, so the local value of the type ratio $R_{\rm S}$ is sufficient to account for the entire XRB; the average spectrum, though, is too soft, and the softness shows up in a marginal discrepancy with the XRB spectrum at $>40$ keV (Fig."796 2). aud unacceptable discrepancies with the jud counts (Figs.," 2), and unacceptable discrepancies with the hard counts (Figs."797 | and 5)., 4 and 5).798 In the latter model he type 1s account for oulv ofthe 1keV XRD. auc making up the eutire NRB requires an Ry πο larecr than the local value: Ow the average spectrun is harder. the shape discrepancy disappears and the count discrepaucics are reduced (Fig.," In the latter model the type 1s account for only of the 1–keV XRB, and making up the entire XRB requires an $R_{\rm S}$ much larger than the local value; now the average spectrum is harder, the shape discrepancy disappears and the count discrepancies are reduced (Fig."799 6)., 6).800 By extrapolating from these two models we cau make qualitative predictious on still different paramctrizatious, By extrapolating from these two models we can make qualitative predictions on still different parametrizations801One of the great mysteries of the universe today ds jo HeUe of dark οποιον which drives the late time cosmic acceleration.,One of the great mysteries of the universe today is the nature of dark energy which drives the late time cosmic acceleration.802 ‘This has been confirmed by number of observational results inclucing Tvpe-Ia Supernovae (Riessetal.2003:tiesset20 04).. cosmic microwave background radiation (€MBI) Ilxlxomatsu et al. (," This has been confirmed by number of observational results including Type-Ia Supernovae \citep{Riess1998,Perlmutter1999,Tonry2003,Knop2003,Riess2004}, cosmic microwave background radiation (CMBR) Komatsu et al. ("8032011)) as well as he latest survevs of the large scale strucure Eisenstein al. (,2011)) as well as the latest surveys of the large scale structure Eisenstein et al. (8042005)).,2005)).805 There has been wide range of contrasting proposals to explain this late time cosmic acceleration., There has been wide range of contrasting proposals to explain this late time cosmic acceleration.806 Most »opular of these is to include a clark candilate with a laree negallve pressure (also known as clark enerev) in the energy xidieet. of the universe BBean οἱ al. (, Most popular of these is to include a dark candidate with a large negative pressure (also known as dark energy) in the energy budget of the universe Bean et al. (8072005). CC'opeland et al. (,"2005), Copeland et al. ("8082006). LLi et al. ,"2006), Li et al. ("809PPacmanalyhan(2003). Peebles Ratra (2003). SSahni Starobinsky (20€)0)).,"2011), Padmanabhan(2003), Peebles Ratra (2003), Sahni Starobinsky (2000))."810 The simplest candidate for this dark energv ds a cosmological constant uA., The simplest candidate for this dark energy is a cosmological constant $\Lambda$.811 llowever. the well-known line uning and coincidence problems render A a rather unattractive »roposa [rom a theoretical. point of. view.," However, the well-known fine tuning and coincidence problems render $\Lambda$ a rather unattractive proposal from a theoretical point of view."812 Going bevond AL scalar field. models with generic features are perhaps he simplest alternatives to a cosmological constant.," Going beyond $\Lambda$, scalar field models with generic features are perhaps the simplest alternatives to a cosmological constant."813 A larec class of scalar [field models including quintessence RRatra Peebles ος‘alelwell et al., A large class of scalar field models including quintessence Ratra Peebles Caldwell et al.814 LLidcdle Scherrer. SS‘nhardt et al. n(, Liddle Scherrer Steinhardt et al. (8151999)). tachvon AAbramo Finelli BBagla et ,"1999)), tachyon Abramo Finelli Bagla et al."816AXguirregabiria M CCopeland et al. -(, Aguirregabiria Lazkoz Copeland et al. (81720053)ndariz DM οςαἰάννο (2¢)02)) and k-essence Ag et al.,2005)) phantom Caldwell (2002)) and k-essence Armendariz et al.818" SScherrer (2004). SSen (2006). VVikman (20053) "" been thoroughly: investigated: in recent Vers o explain the late time acceleration. of the universe."," Scherrer (2004), Sen (2006), Vikman (2005)) have been thoroughly investigated in recent years to explain the late time acceleration of the universe."819 The advantage of these scalar field mocels is that not onlv Cah hey alleviate the fine tuning and coincidence problem. they can also mimick a cosmological constant at present. epoch.," The advantage of these scalar field models is that not only can they alleviate the fine tuning and coincidence problem, they can also mimick a cosmological constant at present epoch."820 These models have equation of state as a function of recshifts., These models have equation of state as a function of redshifts.821 Phis feature is important to clistineuish these scalar field mocels from cosmological constant as large amount observational data from hieher redshifts are coming in or expected to come in near future., This feature is important to distinguish these scalar field models from cosmological constant as large amount observational data from higher redshifts are coming in or expected to come in near future.822 The simplest scalar field is the one with linear potential having a canonical kinteic energy., The simplest scalar field is the one with linear potential having a canonical kinteic energy.823 In this case. the scalar field is frozen initially due to large Llubble damping and behaves like a cosmological constant with «—1.," In this case, the scalar field is frozen initially due to large Hubble damping and behaves like a cosmological constant with $w \sim -1$."824 As the universe cxpands ancl Hubble damping decreases. the field starts rolling and the equation of state starts deviating away [rom we=1.," As the universe expands and Hubble damping decreases, the field starts rolling and the equation of state starts deviating away from $w=-1$."825 But because the potential has no minima. the model gives a collapsing universe in future which results in a finite history for our universe Whratochvil et al. (," But because the potential has no minima, the model gives a collapsing universe in future which results in a finite history for our universe Kratochvil et al. ("8262004)).,2004)).827 Alore complicated scalar field models can be. divided in to two broad. classes: the fast roll ancl slow roll models. also termed. as. freezing{tracking and thawing CCaldwell Lincer (2005)).," More complicated scalar field models can be divided in to two broad classes: the fast roll and slow roll models, also termed as freezing/tracking and thawing Caldwell Linder (2005))."828 The fast roll. models. have steep. potentials allowing the scalar field to. mimick the background. matter/radiation. and to remain subdominant for most of the history of the universe.," The fast roll models have steep potentials allowing the scalar field to mimick the background matter/radiation, and to remain subdominant for most of the history of the universe."829 Only at [ate times.," Only at late times,"830velocily along the accretion line is given by equation (6) in Lyttleton (1972).,velocity along the accretion line is given by equation (6) in Lyttleton (1972).831" The velocity of the flow e(r). in units of eo. for the case of a stagnation point αἱ a distance of c;—Race from the accreting body. is presented in Figure 3:0 is (he coordinate along the accretion line measured [rom the accreting body. given in the figure in units of H2, (this is the solution of equation [6] of Lvttleton. with his a=2)."," The velocity of the flow $v(x)$, in units of $v_0$, for the case of a stagnation point at a distance of $x_s=R_{\rm acc}$ from the accreting body, is presented in Figure 3; $x$ is the coordinate along the accretion line measured from the accreting body, given in the figure in units of $R_{\rm acc}$ (this is the solution of equation [6] of Lyttleton, with his $\alpha=2$ )."832 It is compared with the Neplerian velocity along a circular orbit around the accreting body vy., It is compared with the Keplerian velocity along a circular orbit around the accreting body $v_K$.833 The mass per unit length is given then by στapatyRace(ts—-0)//rir}. and it is plottedin figure 3 (dashed line) in units of 2apyle...," The mass per unit length is given then by $\sigma=\pi \rho_0 v_0 R_{\rm acc} (x_s-x)/\vert v(x) \vert$, and it is plottedin figure 3 (dashed line) in units of $2 \pi \rho_0 R_{\rm acc}^2$."834" When accreting onto a binary svstem. (his solution does not hold any more at distances pSom, where a, is the distance of the more massive star in the accreting binary svstem from the center of mass of the binary system."," When accreting onto a binary system, this solution does not hold any more at distances $x \lesssim a_1$, where $a_1$ is the distance of the more massive star in the accreting binary system from the center of mass of the binary system."835 Each of the two stars. masses Mag and Ms. accretes mass mainiv [rom the dense flow along the accretion line. ie.. from the accretion column.," Each of the two stars, masses $M_{b1}$ and $M_{b2}$, accretes mass mainly from the dense flow along the accretion line, i.e., from the accretion column."836 The accretion Mow onto each star does not reach a steady state. since each star. periodically changes ils distance [rom the accretion column as il orbits (he center of mass (besile the case of exactly perpendicular orbital planes: see subsection 3.2).," The accretion flow onto each star does not reach a steady state, since each star periodically changes its distance from the accretion column as it orbits the center of mass (beside the case of exactly perpendicular orbital planes; see subsection 3.2)."837 I consider now the accretion on star Aj., I consider now the accretion on star $M_{b1}$.838" At closest approach of the star to the accretion column. its orbital velocity is perpendicular to the velocily of gas in the accretion column. and its relative velocity to the gas is where As=My+Adj. eg, is the orbital velocity of the star around the center of nass. Py ds (he Ixeplerian orbital velocity around (he binary svstem. v(e4) is the velocity ol gas in (he accretion column relative {ο the center of mass of the binary svstem. and (4=yoMgfCM+Mis) is the distance of the star [rom (he center of mass of (he binary svstem."," At closest approach of the star to the accretion column, its orbital velocity is perpendicular to the velocity of gas in the accretion column, and its relative velocity to the gas is where $M_{12} \equiv M_{b1}+M_{b2}$, $v_{K1}$ is the orbital velocity of the star around the center of mass, $v_K$ is the Keplerian orbital velocity around the binary system, $v(a_1)$ is the velocity of gas in the accretion column relative to the center of mass of the binary system, and $a_1=a_{12}M_{b2}/(M_{b1}+M_{b2})$ is the distance of the star from the center of mass of the binary system."839 In the second equality I used (he result presented in Figure 3. concerning the inwarcl flow in the accretion column. assuming that ayo«Race.," In the second equality I used the result presented in Figure 3, concerning the inward flow in the accretion column, assuming that $a_{12} \ll R_{\rm acc}$."840 Assuming an accretion flow from the accretion column to the star similar to a DBondi-IIovle-Lvttleton flow. the accretion radius of the star is Race772GMj/ 04.," Assuming an accretion flow from the accretion column to the star similar to a Bondi-Hoyle-Lyttleton flow, the accretion radius of the star is $R_{\rm acc1} \simeq 2 GM_{b1}/v_{r1}^2$ ."841 The ratio of the accretion radius of the star to its distance, The ratio of the accretion radius of the star to its distance842The inter-particle collision frequency. controls the time-scale to reach the cdilfusive equilibrium. which is given. by Paper I. where Ls=L/(10°em) and 7s=T/GQOIS).,"The inter-particle collision frequency controls the time-scale to reach the diffusive equilibrium, which is given by Paper I, where $L_5\equiv L/(10^5 \mathrm{cm})$ and $T_8\equiv T/(10^8 \mathrm{K})$."843" H£ the beta decays ave much faster. the chemical equilibrium state 9/5,=Opt. is reached in a time-scale controlled. by the beta decay rate. Thus. we have two relevant limits: The transition between these limits is achieved. when fragesas."," If the beta decays are much faster, the chemical equilibrium state $\delta \mu_n=\delta \mu_c$ is reached in a time-scale controlled by the beta decay rate, Thus, we have two relevant limits: The transition between these limits is achieved when $t_{drag}\sim t_{weak}$."844 From Eqs. (11)), From Eqs. \ref{tnccgen}) )845 and (12)) we infer that the condition for this transition is Tk~5.6L.I. which gives Lag~bocaldL23NE.," and \ref{dmu1gen}) ) we infer that the condition for this transition is $T_8 \sim 5.6~L_5^{-1/4}$, which gives $t_{drag}\sim t_{weak}\sim 14~ L_5^{3/2}~ \mathrm{yr}$."846 Since the density perturbations are assumed to be small. these will not involve large motions of the particles. and therefore not cause a substantial change in the magnetic Hux distribution.," Since the density perturbations are assumed to be small, these will not involve large motions of the particles, and therefore not cause a substantial change in the magnetic flux distribution."847 Note. however. that these two equilibria are incompatible with each other as long as a spatially non-uniform magnetic field is present. therefore a Pull equilibrium. will only be reached in a much longer time-scale. on which the magnetic Ποια is made uniform (in our model) or expelled from. the system. (likely more realistic in a true astrophysical setting).," Note, however, that these two equilibria are incompatible with each other as long as a spatially non-uniform magnetic field is present, therefore a full equilibrium will only be reached in a much longer time-scale, on which the magnetic field is made uniform (in our model) or expelled from the system (likely more realistic in a true astrophysical setting)."848 For the determination of this much longer time-scale. on which the magnetic field does evolve substantially. we again consider the two opposite regimes discussed. above.," For the determination of this much longer time-scale, on which the magnetic field does evolve substantially, we again consider the two opposite regimes discussed above."849 In. themil. the system reached the diffusive equilibrium. but not. the chemical equilibrium. during the previous stage.," In the, the system reached the diffusive equilibrium but not the chemical equilibrium, during the previous stage."850 During this much longer stage. the weak interactions slowly convert. charged particles into neutrons in a tendency to reduce the eharged-particle pressure gradient that counterbalances the magnetic pressure gradient.," During this much longer stage, the weak interactions slowly convert charged particles into neutrons in a tendency to reduce the charged-particle pressure gradient that counterbalances the magnetic pressure gradient."851 This causes a slight deviation from the diffusive equilibrium. producing a joint transport of. the charged particles and the magnetic flux at a small ambipolar diffusion velocity ey. always keeping the system very. close to dilfusive equilibrium.," This causes a slight deviation from the diffusive equilibrium, producing a joint transport of the charged particles and the magnetic flux at a small ambipolar diffusion velocity $v_A$, always keeping the system very close to diffusive equilibrium."852" This interplay continues until both the pressure ancl magnetic field gradients dissapear. which occurs in a long time-scale that. depends on the magnetic lield strength and the weak interaction rate: with 4μμfron),(BOc1. which is roughly the ratio of the charged particle pressure to the magnetic pressure ancl we delined Dj;=D(1027€)."," This interplay continues until both the pressure and magnetic field gradients dissapear, which occurs in a long time-scale that depends on the magnetic field strength and the weak interaction rate: with $\beta \equiv 8\pi n_{0c} n_{0n} \left(\partial853\mu_{0n}/\partial n_{0B}\right)_{n_{0c}}/B^2\gg 1$, which is roughly the ratio of the charged particle pressure to the magnetic pressure and we defined $B_{15}\equiv B/(10^{15} \mathrm{G})$."854 In themil. the relative motion of the charged. particles and neutrons is strongly suppressed by the inter-particle collisions. which delay the diffusive ecquilibrium state. while in comparison the chemical equilibrium is reached quickly.," In the, the relative motion of the charged particles and neutrons is strongly suppressed by the inter-particle collisions, which delay the diffusive equilibrium state, while in comparison the chemical equilibrium is reached quickly."855 Phe deviation from. diffusive equilibrium promotes. as before. a joint motion of the charged particles and the magnetic Dux. with a very small ambipolar diffusion velocity ey.," The deviation from diffusive equilibrium promotes, as before, a joint motion of the charged particles and the magnetic flux, with a very small ambipolar diffusion velocity $v_A$."856" Fhis movement vields the cilfusive equilibrium in a very lon time-scale controlled. by the collision rate between particles and by the magnetic-field amplitude. Note that at the transition between the strong. and ∖∖⊽⋖⊾⋜∐≼⇍∪⊔↓≻↓↓⊔⋏∙≟↓↓⊔⊔↿⊳∖∪↴∖∿⋅↱≻⋅≼≻∠↴∃⊳↿↓↕⋖⋅⋜⋯↓∣⋡↓↓≻∪↓∥↓⋅ : -. ⊳⇁⋅⊥⊥ ⋠ diffusionEN timescales. are of the same order (65542,bag)7TUUS~5.5.LotBye5Leoa3ye. METhis value corresponds to-- the shortest. possible ambipolar diffusion time. since the relevant timescales increase both towards higher and lower temperatures."," This movement yields the diffusive equilibrium in a very lon time-scale controlled by the collision rate between particles and by the magnetic-field amplitude, Note that at the transition between the strong and weak coupling limits $T_8 \sim 5.6~L_5^{-1/4}$ ), the ambipolar diffusion timescales are of the same order: $t_{ambip}^{(drag)}\sim t_{ambip}^{(weak)} \sim 5.5 \times 10^{4}~ B_{15}^{-2}~ L_{5}^{3/2}~\mathrm{yr}.$ This value corresponds to the shortest possible ambipolar diffusion time, since the relevant timescales increase both towards higher and lower temperatures."857 Although the Hall effect is not. present. in our one-dimensional caleulations. it is important to asses its potential importance relative to. ambipolar. dülfusion.," Although the Hall effect is not present in our one-dimensional calculations, it is important to asses its potential importance relative to ambipolar diffusion."858 Consider its timescale.: compared to. the minimum ambipolar cülfusion timescale estimated above.," Consider its timescale,: compared to the minimum ambipolar diffusion timescale estimated above."859 We find that. if Ds«0.2L-p the Hall απ is likely to play à dominant role.," We find that, if $B_{15} < 0.2~ L_5^{-1/2}$, the Hall drift is likely to play a dominant role."860 It might. not be important in magnetars. where By.71. except possibly in reconnection lavers. where Lz<1.," It might not be important in magnetars, where $B_{15} > 1$, except possibly in reconnection layers, where $L_5\ll 1$."861 In the present paper. we are interested. in the details of the evolution of the magnetic field in the strong and weak coupling limits.," In the present paper, we are interested in the details of the evolution of the magnetic field in the strong and weak coupling limits."862 Pherefore. in the next sections we will obtain the cillerential equations modelling the evolution of the magnetic field in the time-scales given by Eqs. (13))," Therefore, in the next sections we will obtain the differential equations modelling the evolution of the magnetic field in the time-scales given by Eqs. \ref{tbp2}) )"863 and (14)., and \ref{tambi22p2}) ).864 In this section. we derive a single integro-cüllerential equation that models the magnetic field. evolution in themal (Lug bocuk). in which neutral and charged. particles drift casily with respect to cach other. and the main bottleneck is the (slow) rate at which they can be converted into each other. in order to decrease he charged-particle pressure gradients that balance the Lorentz force. impeding the magnetic [ux to spread.," In this section, we derive a single integro-differential equation that models the magnetic field evolution in the $t_{drag} \ll t_{weak}$ ), in which neutral and charged particles drift easily with respect to each other, and the main bottleneck is the (slow) rate at which they can be converted into each other, in order to decrease the charged-particle pressure gradients that balance the Lorentz force, impeding the magnetic flux to spread."865 This imit is not likely to be relevant in the interstellar mecum. (Shu1983).. although it roughly corresponds to one of the imits considered by Mouschovias&Paleologou(1981).," This limit is not likely to be relevant in the interstellar medium \citep{Shu-83}, although it roughly corresponds to one of the limits considered by \citet{MouschoviasPaleologou81}."866. In neutron stars. it. becomes important at later stages. once heir temperature is low enough.," In neutron stars, it becomes important at later stages, once their temperature is low enough."867 llereafter. we take the background. properties to. be j0niogeneous. Le. the variables with a subscript 0 do not," Hereafter, we take the background properties to be homogeneous, i.e. the variables with a subscript $0$ do not"868 The Orion Molecular Cloud 1 (OMC-1) is a complex region of the interstellar medium (ISM) stretching over more than 2.4 pe (20'. roughly north-south) on the sky (Kutneretal..1976).," The Orion Molecular Cloud 1 (OMC-1) is a complex region of the interstellar medium (ISM) stretching over more than 2.4 pc $20\arcmin$, roughly north-south) on the sky \citep{Kutner1976}."869. Its densest part. toward which the Great Orion Nebula (M42). a classical compact “blister” rregion. and its associated Orion Nebular Cluster (ONC) appear in projection. is one of the best-studied regions in astronomy.," Its densest part, toward which the Great Orion Nebula (M42), a classical compact ”blister” region, and its associated Orion Nebular Cluster (ONC) appear in projection, is one of the best-studied regions in astronomy."870 It is a test bed for studies of (proto)stars and clusters and the formation of low-. intermediate-. and high-mass stars (forare-viewofthisregion.seeO'Dell.2001:O'Delletal.. 2008).," It is a test bed for studies of (proto)stars and clusters and the formation of low-, intermediate-, and high-mass stars \citep[for a review of this region, see][]{O'Dell2001,O'Dell2008}."871. Much of this region's prominence is due to its distance of just 43]47 pe (Mentenetal..2007).. which makes the ONC and OMC-1 the closest regions of recent (few million years old) and ongoing high-mass star formation.," Much of this region's prominence is due to its distance of just $414\pm7$ pc \citep{Menten2007}, which makes the ONC and OMC-1 the closest regions of recent (few million years old) and ongoing high-mass star formation."872" In the following. we shall use the term ""OMC-1I core"" or even just OMC-1for the roughly 8» 8/- or | pc-sized dense molecular cloud region. which is located closely (0.1—0.2 pe) behind M42 and most of the stars in the ONC (seeZuckerman.1973;Genzel&Stutzki.andits phenomena).."," In the following, we shall use the term “OMC-1 core” or even just OMC-1for the roughly $8\arcmin\times8\arcmin$ - or 1 $^{2}$ -sized dense molecular cloud region, which is located closely (0.1–0.2 pc) behind M42 and most of the stars in the ONC \citep[see][the latter give a comprehensive overview of this region and its phenomena]{Zuckerman1973,Genzel1989}."873 The OMC-I core region may be divided into three main zones. all of which show bright (sub)millimeter wavelength emission from warm dust and molecular gas: the Becklin-Neugebauer/Kleinmann-Low (BN/KL) region. Orion South (OMC-1S or Orion-S) and the Orion Bar.," The OMC-1 core region may be divided into three main zones, all of which show bright (sub)millimeter wavelength emission from warm dust and molecular gas: the Becklin-Neugebauer/Kleinmann-Low (BN/KL) region, Orion South (OMC-1S or Orion-S) and the Orion Bar."874" The Orion BN/KL and Orton South regions are considered to be ""twin"" high-mass star forming regions because they have similar masses (x 100 M.) and bolometric luminosities (107—10°Li.Mezgeretal..1990:Drapatz1983). anc show comparable levels of star-forming activity (O'Delletal.. 2008)."," The Orion BN/KL and Orion South regions are considered to be “twin” high-mass star forming regions because they have similar masses $\lesssim$ 100 ) and bolometric luminosities \citep[$10^4-10^5$ \Lsol,][]{Mezger1990,Drapatz1983} and show comparable levels of star-forming activity \citep{O'Dell2008}."875". The BN/KL region harbors the eponymous “hot core"" (Massonetal..1984).. which was (and commonly still is) taker to be the prototype of the hot dense regions observed arounc many newly formed stars (see.e.g..Kurtzetal..2000)."," The BN/KL region harbors the eponymous “hot core” \citep{Masson1984}, which was (and commonly still is) taken to be the prototype of the hot dense regions observed around many newly formed stars \citep[see, e.g.,][]{Kurtz2000}."876.. Ai interesting alternative explanation for this region's energetics (other than being powered by an embedded central heating source) is a protostellar merger event that released a few times 10% ere of energy about 500 years ago (Bally&Zinnecker.2005:Zapataetal..2011:Bally201 1).," An interesting alternative explanation for this region's energetics (other than being powered by an embedded central heating source) is a protostellar merger event that released a few times $10^{47}$ erg of energy about 500 years ago \citep{Bally2005,Zapata2011,Bally2011}."877". The Orion Bar ts a well-described photon-dominated region (PDR) located at the side of the OMC-1 core. facing M42. which is heated and partially tonized by far-ultraviolet (FUV) photons from the young massive stars (most of them from 6! C. a spectral type O5-O7 star) that form the ""Irapezium"" at the center of the ONC (see.e.g..Hollenbach&Tielens.1997:Walmsleyetal.. 2000)."," The Orion Bar is a well-described photon-dominated region (PDR) located at the side of the OMC-1 core, facing M42, which is heated and partially ionized by far-ultraviolet (FUV) photons from the young massive stars (most of them from $\theta^1$ C, a spectral type O5–O7 star) that form the “Trapezium” at the center of the ONC \citep[see, e.g.,][]{Hollenbach1997,Walmsley2000}."878. In addition. the Orion Bar appears to be located at the edge of the bblister tangential to the line of sight.," In addition, the Orion Bar appears to be located at the edge of the blister tangential to the line of sight."879 On giant molecular cloud (GMC) seales. low-rotational level (J) eemission (commonly from the J=1—0 line) of the ambient. low density gas is usually used to trace the mass of the molecular ISM under a range of assumptions (Bloemenetal.. 1985).," On giant molecular cloud (GMC) scales, low-rotational level $J$ ) emission (commonly from the $J=1-0$ line) of the ambient, low density gas is usually used to trace the mass of the molecular ISM under a range of assumptions \citep{Bloemen1984,Dame1985}."880. However. in massive star forming regions with much higher densities and temperatures. observations of the submillimeter and far-infrared (FIR) wavelength mid- or high-J transitions of aand its PC and O isotopologues are required. for determinations of the gas temperature and density. usually in conjunction with Large Velocity Gradient (LVG) radiative transfer and PDR modelings.," However, in massive star forming regions with much higher densities and temperatures, observations of the submillimeter and far-infrared (FIR) wavelength mid- or $J$ transitions of and its $^{13}$ C and $^{18}$ O isotopologues are required for determinations of the gas temperature and density, usually in conjunction with Large Velocity Gradient (LVG) radiative transfer and PDR modelings."881 Much of the eemission from the OMC-] core has been proposed to arise from the neutral and partially tonized back side of the bblister. l.e.. the PDR (Genzel&Stutzki.1989).," Much of the emission from the OMC-1 core has been proposed to arise from the neutral and partially ionized back side of the blister, i.e., the PDR \citep{Genzel1989}."882. The pioneering observations of the J=7-6.6-Sand'*CO J=7-6transitionshySchinid—Burgketal. (1989)undGrafetal. (1990)r7eve 10 cm) and elevated temperatures (P.> 50 K) in all parts of the OMC-1 core region.," The pioneering observations of the $J=7-6$ , $6-5$ and $J=7-6$ transitions by \citet{Schmid-Burgk1989} and \citet{Graf1990} revealed high density gas $n\geq$ $10^{4}$ $^{-3}$ ) and elevated temperatures $T\geq$ 50 K) in all parts of the OMC-1 core region."883 Observations of the even more highly excited, Observations of the even more highly excited884the assumption of negligible particle escape is nol always. justified.,the assumption of negligible particle escape is not always justified.885 In. order {ο estimate the possible suppression of the low-Irequeney. cascade emission due to particle escape. we calculate the critical electron energy for which the Compton cooling lime scale τις(ο) equals the escape time scale. Tas=Reg/(ecos05).," In order to estimate the possible suppression of the low-frequency cascade emission due to particle escape, we calculate the critical electron energy for which the Compton cooling time scale $\tau_{\rm IC} (\gamma)$ equals the escape time scale, $\tau_{\rm esc}886= R_{\rm ext} / (c \, \cos\theta_B)$."887" Using a characteristic thermal photon energy of ey,=2:8KT/nc). the resulting Compton scattered photon energy. e, below which we expect to see the effects of particle escape aud. hence. inellicient radiative cooling. is corresponding (o an actual enerev (in GeV) οἱ where T=10*T4 IX. t4=10Ou5 erg  and R=LOM44 em."," Using a characteristic thermal photon energy of $\epsilon_{\rm Th} = 2.8 \, k T / (m_e c^2)$, the resulting Compton scattered photon energy, $\epsilon_{\rm esc}$ below which we expect to see the effects of particle escape and, hence, inefficient radiative cooling, is corresponding to an actual energy (in GeV) of where $T = 10^3 \, T_3$ K, $u_{\rm ext} = 10^{-5} \, u_{-5}$ erg $^{-3}$, and $R = 10^{18} \, R_{18}$ cm."888 Therefore. for our standard parameters. we expect the low-frequency (E< a few GeV) to be significantly allected by particle escape.," Therefore, for our standard parameters, we expect the low-frequency $E \lesssim$ a few GeV) to be significantly affected by particle escape."889 This explains why (he low-energy photon spectra shown in Figure 2 are harder than pF?., This explains why the low-energy photon spectra shown in Figure \ref{standardfig} are harder than $\nu^{1/2}$.890 The cascade emission is progressively suppressed at high energies with increasing viewing angle due (o incomplete isotropization of the hiehes(-enerev secondary parücles., The cascade emission is progressively suppressed at high energies with increasing viewing angle due to incomplete isotropization of the highest-energy secondary particles.891" This effect. becomes important bevond the energy. Eje, of Compton-scattered photons bv secondary electrons/positrons for which the Compton-scattering length. Aye equals the distance travelled along the gvrational motion over an angle 9. Aye(4)=ra(5). which is given by where B=107 mG (Roustazadeh&Boticher2010)."," This effect becomes important beyond the energy $E_{\rm IC, br}$ of Compton-scattered photons by secondary electrons/positrons for which the Compton-scattering length $\lambda_{IC}$ equals the distance travelled along the gyrational motion over an angle $\theta$, $\lambda_{IC}(\gamma) = \theta r_{\rm gyr}(\gamma)$, which is given by where $B = 10^{-3}$ mG \citep{rb10}."892. Fieure 3. shows (he cascade spectra for different values of the external radiation field energv density We., Figure \ref{ufig} shows the cascade spectra for different values of the external radiation field energy density $u_{\rm ext}$.893" For large energv densities veg2LO! erg 7. 7,>>1 for photons above the pair production threshokl +> so (hat essentially all VUE photons will be absorbed and the photon flux from the cascade becomes independent of wey."," For large energy densities $u_{\rm ext} \gtrsim 10^{-4}$ erg $^{-3}$, $\tau_{\gamma\gamma}894\gg 1$ for photons above the pair production threshold $\gamma\gamma$ so that essentially all VHE photons will be absorbed and the photon flux from the cascade becomes independent of $u_{\rm ext}$ ."895 The figure confirms our discussion concerning escape and hence inellicient racliative cooling of low-enerev particles above (see Eq. 4))., The figure confirms our discussion concerning escape and hence inefficient radiative cooling of low-energy particles above (see Eq. \ref{Eesc}) ).896 For large values of deg. the Compton loss time scale For all relativistic electrons producing 5-ravs in the considered range. is much shorter than the escape time scale.," For large values of $u_{\rm ext}$, the Compton loss time scale for all relativistic electrons producing $\gamma$ -rays in the considered range, is much shorter than the escape time scale."897" Hence. the expected uF,xpU? shape results."," Hence, the expected $\nu F_{\nu} \propto \nu^{1/2}$ shape results."898 In the ων Case. escape allects even ultrarelativistic electrons. resulting in asubstantial hardening of the low-energv photon spectrum.," In the $u_{\rm ext}$ case, escape affects even ultrarelativistic electrons, resulting in asubstantial hardening of the low-energy photon spectrum."899Two different approaches are widely used to test. theories of galaxy formation.,Two different approaches are widely used to test theories of galaxy formation.900 Both make use of developing computational resources to integrate a set of coupled differential equations forward in time. where cach equation applies physical constraints. or empirical laws. to some of the system's properties.," Both make use of developing computational resources to integrate a set of coupled differential equations forward in time, where each equation applies physical constraints, or empirical laws, to some of the system's properties."901 The semi-analvtic method (White&Erenk1901). can be characterised by the intent to encapsulate as much of the physical behaviour as possible in the equations themselves. chosen to deseribe properties. (virialisation. conservation of angular momentum. etc.)," The semi-analytic method \cite{White91} can be characterised by the intent to encapsulate as much of the physical behaviour as possible in the equations themselves, chosen to describe properties (virialisation, conservation of angular momentum, etc.)"902 and thus leaving the minimum to numerical calculation., and thus leaving the minimum to numerical calculation.903 Inherently different to this is the approach taken. by simulations. where the ethos is to apply equations which are known to govern theparticular properties. (c.g. the gravitational force between two particles) and demonstrate. by skilfully programmed. numerical caleulation. that these reproduce macroscopic properties.," Inherently different to this is the approach taken by simulations, where the ethos is to apply equations which are known to govern the properties (e.g. the gravitational force between two particles) and demonstrate, by skilfully programmed numerical calculation, that these reproduce macroscopic properties."904 In practice. adjustment will always need to be made to account for the fact that cach simulated. particle represents many many real particles.," In practice, adjustment will always need to be made to account for the fact that each simulated particle represents many, many real particles."905 In traditional simulations which considered. only gravity. this adjustment. is. purely mathematical.," In traditional simulations which considered only gravity, this adjustment is purely mathematical."906 When gravity is the dominant. interaction. results are therefore very robust and simulations are mostly accepted as being a faithful realisation of the Universe at large scales. where this is the case.," When gravity is the dominant interaction, results are therefore very robust and simulations are mostly accepted as being a faithful realisation of the Universe at large scales, where this is the case."907 A notable measure of this acceptance is that semi-analvtie models have taken to using samples of halos taken directly fron simulations (Ixauffimannetal.1999:LLellyetal.20023:Llatton 2003).. rather than samples created statistically using methods based on the analytic argumen4. of Press&Schechter(1914).," A notable measure of this acceptance is that semi-analytic models have taken to using samples of halos taken directly from simulations \cite{Kauffmann99,Helly03,Hatton03}, rather than samples created statistically using methods based on the analytic arguments of \scite{Press74}."908. In general. though. there must come a scale below whicl the governing equations are no longer describing. particle interactions but emergent phenomena.," In general, though, there must come a scale below which the governing equations are no longer describing particle interactions but emergent phenomena."909 At these. smaller scales. the two largely contrasting approaches begin to look more similar.," At these smaller scales, the two largely contrasting approaches begin to look more similar."910 As an inumeciate example. simulations which encompass an entire galaxy have not attempted. to resolve incliviclual stars and must therefore apply an equation which approximates the conversion rate of large. bodies. of gas into stars. based on locally averaged density.," As an immediate example, simulations which encompass an entire galaxy have not attempted to resolve individual stars and must therefore apply an equation which approximates the conversion rate of large bodies of gas into stars, based on locally averaged density."911 An equivalent ancl sometimes identical equation appears in. semi-analvtic models re(StarFormation))., An equivalent and sometimes identical equation appears in semi-analytic models \\ref{StarFormation}) ).912 Both approaches have had sonic success in.for the observed. properties of galaxies., Both approaches have had some success in the observed properties of galaxies.913Predictive power. on the other hand. relies on surety in the underlying equations. or a clear. understanding. of how differing underlving assumptions map on to final observable quantities.," power, on the other hand, relies on surety in the underlying equations, or a clear understanding of how differing underlying assumptions map on to final observable quantities."914 To bolster this crucial understanding. it is extremely helpful to study. in. detail. the predicted: evolution. of a single. large galaxy and its satellites. as followed by these two different techniques.," To bolster this crucial understanding, it is extremely helpful to study, in detail, the predicted evolution of a single, large galaxy and its satellites, as followed by these two different techniques."915 I£ the analytic model begins from the precise halo merger history found in the simulation. ancl applies the same assumptions about the physics at simaller scales. will it prediet the same observable properties and. if not. where and why do the two caleulations diverge?," If the analytic model begins from the precise halo merger history found in the simulation, and applies the same assumptions about the physics at smaller scales, will it predict the same observable properties and, if not, where and why do the two calculations diverge?"916 Existing quantitative Comparisons between simulations and, Existing quantitative comparisons between simulations and917corresponding temperatures. (hat are higher (han (the nearly [lat continuum. would imply.,"corresponding temperatures, that are higher than the nearly flat continuum would imply."918 This result is consistent with line formation in a large z high temperature region., This result is consistent with line formation in a large $z$ high temperature region.919 Anomalous line strengths of C. N. Si. and Ile have a possible interpretation in terms of composition ellects. but excitation effects cannot be disentangled. (," Anomalous line strengths of C, N, Si, and He have a possible interpretation in terms of composition effects, but excitation effects cannot be disentangled. ("9205) The slight blue shift of the absorption lines (~—200kms.1). as compared with the svslem racial velocity of —35kms indicates that the absorption lines are formed in a low velocily wind. which is coextensive with (he large z high temperature region.,"5) The slight blue shift of the absorption lines ${\sim}-200\,\mathrm{km\,s^{-1}}$ ), as compared with the system radial velocity of $-35\,\mathrm{km\,s^{-1}}$, indicates that the absorption lines are formed in a low velocity wind, which is coextensive with the large $z$ high temperature region."921 There is no apparent difference in velocity between the emission line intermediate state spectrum ancl the high state absorption line spectrum: the wind and high temperature structures appear to be present in both the intermediate and high states. (, There is no apparent difference in velocity between the emission line intermediate state spectrum and the high state absorption line spectrum; the wind and high temperature structures appear to be present in both the intermediate and high states. (922"6) The difference between the physical conditions under which the absorption and enussion lines form in a wind and (he physical conditions assumed by our hwydrostatic equilibrium anulus models. used (o calculate the svuthetic spectra. may explain our difficulty in [itting the high state and intermediate state continua accurately,","6) The difference between the physical conditions under which the absorption and emission lines form in a wind and the physical conditions assumed by our hydrostatic equilibrium annulus models, used to calculate the synthetic spectra, may explain our difficulty in fitting the high state and intermediate state continua accurately."923 The same problem max explain the failure of our synthetic spectra to represent the high excitation absorption lines in the high state LIST spectra., The same problem may explain the failure of our synthetic spectra to represent the high excitation absorption lines in the high state HST spectra.924 We thank the anonvmous referee for detailed comments which improved the presentation ol this paper., We thank the anonymous referee for detailed comments which improved the presentation of this paper.925 APL and PS are grateful for partial support Irom NASA Grant GO-9357 [rom ihe Space Telescope Science Institute ancl for FUSE grant NAG 5-12203., APL and PS are grateful for partial support from NASA Grant GO-9357 from the Space Telescope Science Institute and for FUSE grant NAG 5-12203.926 PS. KSL and EMS also acknowledge support for this work provided bv NASA through grants GO-9357 and from the Space Telescope Science Institute. which is operated by AURA. Inc.. under NASA contract NAS 5-26555.," PS, KSL and EMS also acknowledge support for this work provided by NASA through grants GO-9357 and GO-9724 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555."927 ΕΤ was supported by à PPARC Advanced Fellowship., BTG was supported by a PPARC Advanced Fellowship.928Powerful radio sources. such as radio galaxies ancl quasars. race the most massive galaxies (Jarvis et al.,"Powerful radio sources, such as radio galaxies and quasars, trace the most massive galaxies (Jarvis et al."929 2001a: De Breuck οἱ al., 2001a; De Breuck et al.930 2002: Willott et al., 2002; Willott et al.931 2003: Zirm. Dickinson Dev 2003) and are associated with the most massive black roles (Dunlop et al.," 2003; Zirm, Dickinson Dey 2003) and are associated with the most massive black holes (Dunlop et al."932 2003: AleLure et al., 2003; McLure et al.933 2004: AleLure Jarvis 2004) in the Universe. at all cosmic epochs.," 2004; McLure Jarvis 2004) in the Universe, at all cosmic epochs."934 Raclio galaxies have been detected: up to redshifts of just. above ive (van Breugel ct al., Radio galaxies have been detected up to redshifts of just above five (van Breugel et al.935 1999). and quasars up to and ονομα redshifts of six (Fan οἱ al.," 1999), and quasars up to and beyond redshifts of six (Fan et al."936 2003). leaving little time during which quasars and their host. galaxies could. form.," 2003), leaving little time during which quasars and their host galaxies could form."937 This provides a challenge for hierarchical galaxy. formation models. though some recent semi-analvtie models are able to produce significant numbers of massive galaxies at high redshilts (c.g. Bower ct 22006: Night et 22006).," This provides a challenge for hierarchical galaxy formation models, though some recent semi-analytic models are able to produce significant numbers of massive galaxies at high redshifts (e.g. Bower et 2006; Night et 2006)."938 Constraining the space-density of high-redshift radio sources is therefore important. as it has implications on the theories of galaxy ane structure formation.," Constraining the space-density of high-redshift radio sources is therefore important, as it has implications on the theories of galaxy and structure formation."939 Using radio sources is also advantageous in this respect because they are selected on the basis of their radio emission and are thus free of the problems associated with optical selection methods. such as dust obscuration (cf.," Using radio sources is also advantageous in this respect because they are selected on the basis of their radio emission and are thus free of the problems associated with optical selection methods, such as dust obscuration (cf."940 optically selected. quasars)., optically selected quasars).941 lt is clear that the co-moving space densities of the rarest. most powerful racio sources were much higher around 2o2 than they are at present (Longair 1966). but. the form of the evolution bevond that redshift is still a matter of debate.," It is clear that the co-moving space densities of the rarest, most powerful radio sources were much higher around $z \sim 2$ than they are at present (Longair 1966), but the form of the evolution beyond that redshift is still a matter of debate."942 The question of a ‘redshift cut-oll” (Dunlop Peacock 1990) in the radio source population has come uncer careful serutiny in recent vears (Jarvis Rawlings 2000: Jarvis et al., The question of a `redshift cut-off' (Dunlop Peacock 1990) in the radio source population has come under careful scrutiny in recent years (Jarvis Rawlings 2000; Jarvis et al.943 200le)., 2001c).944 The current situation is one in which there is no compelling evidence of a high-redshift’ decline. in. low-frequency selected: (ie. predominantly steepespectrum) radio sources. whereas there is evidence for a slight decline in raclio-loucl quasars from high-frequeney selected: (νο. predominantly. Hat-spectrum) samples (Dunlop Peacock 1990. Shaver et al.," The current situation is one in which there is no compelling evidence of a high-redshift decline in low-frequency selected (i.e. predominantly steep-spectrum) radio sources, whereas there is evidence for a slight decline in radio-loud quasars from high-frequency selected (i.e. predominantly flat-spectrum) samples (Dunlop Peacock 1990, Shaver et al."945 1996: Jarvis Rawlines 2000: Wall ct al., 1996; Jarvis Rawlings 2000; Wall et al.946 2005)., 2005).947 In this study we focus on the low-frequency selected population (predominantly radio galaxies)., In this study we focus on the low-frequency selected population (predominantly radio galaxies).948" To this οἱσοι, we use à new sample of radio sources drawn from the 151 MllIz 6C survey. which. has been filtered with radio criteria designed to optimize the chances of finding radio galaxies ab zoDd."," To this effect, we use a new sample of radio sources drawn from the 151 MHz 6C survey, which has been filtered with radio criteria designed to optimize the chances of finding radio galaxies at $z > 4$."949 This sample. namely 6€C**. has been selected. to be brighter than 0.5 Jv at 151. MlIz.," This sample, namely 6C**, has been selected to be brighter than 0.5 Jy at 151 MHz."950 Additional selection, Additional selection9512005).. edge-on spirals (Sethetal.200G6).. and. dwarf elliptical galaxies (Cotéetal.2006).,", edge-on spirals \citep{SethEtal06}, and dwarf elliptical galaxies \citep{CoteEtal06}."952". The cluster. masses range [rom 10"" to LOM. (althoughevenmoremassiveclus-tershavebeenfoundrecentlyby.Ixormendyetal. 2009). whereas their sizes are only a few to a [ew tens parsec."," The cluster masses range from $10^6$ to $10^8\msun$ \citep[although even more massive clusters have953 been found recently by][]{KormendyEtal09}, whereas their sizes are only a few to a few tens parsec."954 Intriguinely. for ciwarf ellipticals the masses of NC's correlate with the host properties.," Intriguingly, for dwarf ellipticals the masses of NCs correlate with the host properties."955 Namely.. Ferrareseetal. found that the NC mass is related. to the bulge velocity dispersion in exactlv same wav as the SMDII velocity dispersion relation. but with normalisation ollset by about an order of magnitude.," Namely, \citet{FerrareseEtal06} found that the NC mass is related to the bulge velocity dispersion in exactly same way as the SMBH – velocity dispersion relation, but with normalisation offset by about an order of magnitude."956 The cluster masses are also almost linearly proportional to the total bulge mass (Ferrareseetal.2006:Wehner&Lla," The cluster masses are also almost linearly proportional to the total bulge mass \citep{FerrareseEtal06, Wehner06}."957rris 2006).. AleLaughlinetal.(2006) proposed that the observed Alpe0 relation for dwarl elliptical galaxies follows naturally from an extension of the above argument (hing(2003. 2005))) to the outllows from voung star clusters containing massive stars.," \cite{McLaughlinEtal06} proposed that the observed $M_{\rm NC} -\sigma$ relation for dwarf elliptical galaxies follows naturally from an extension of the above argument \cite{King03,King05}) ) to the outflows from young star clusters containing massive stars."958 These individual stars are also Eddingtonlimited. ancl produce outllows with momentum outllow rate Learfe where Lea dis caleulatecd from the stars mass.," These individual stars are also Eddington–limited, and produce outflows with momentum outflow rate $\sim959L_{\rm Edd}/c$ where $L_{\rm Edd}$ is calculated from the star's mass."960 Young star clusters with normal LIMES produce momentum outllow rate where Àzz0.05 and Lg is now formally the Ecelington value corresponding to the total cluster mass., Young star clusters with normal IMFs produce momentum outflow rate where $\lambda \approx 0.05$ and $L_{\rm Edd}$ is now formally the Eddington value corresponding to the total cluster mass.961 To produce the same amount of momentum feedback. a voung star cluster must therefore be 1/À times more massive than a SALDLIL ασιαας at the Edclineton limit. and hence: Strikingly. L1/A is quite elose to the ollset in. mass between the Adpy σ and Myc o relations.," To produce the same amount of momentum feedback, a young star cluster must therefore be $1/\lambda$ times more massive than a SMBH radiating at the Eddington limit, and hence: Strikingly, $1/\lambda$ is quite close to the offset in mass between the $M_{\rm BH}$ $\sigma$ and $M_{\rm NC}$ $\sigma$ relations."962 Furthermore. while equation Lis very plausible (seeKing&Pouncls 2003).. the momentum outllow rates from stars are known in detail observationallv.," Furthermore, while equation \ref{pismbh} is very plausible \citep[see][]{KP03}, the momentum outflow rates from stars are known in detail observationally."963 The Largest. uncertainty in the equation 4 is therefore the stellar IME. which is observationally fairly constant. (ee.Kroupa2002).," The largest uncertainty in the equation \ref{pinc} is therefore the stellar IMF, which is observationally fairly constant \citep[e.g.,][]{Kroupa02}."964.. The AleLaughlinetal.(2006) explanation of Aine @ relation thus appears similarly robust to the King(2008.2005) mocel for SMBLL feedback.," The \cite{McLaughlinEtal06}965 explanation of $M_{\rm NC}$ $\sigma$ relation thus appears similarly robust to the \cite{King03,King05} model for SMBH feedback."966 lHlowever. MeLaughlinctal.(2006) cid not olfer an explanation of why bulges with smaller & contain nuclear clusters. while more massive galaxies contain SAIBIIs and not NC's.," However, \cite{McLaughlinEtal06} did not offer an explanation of why bulges with smaller $\sigma$ contain nuclear clusters, while more massive galaxies contain SMBHs and not NCs."967 Lere we propose an explanation. noting that timescales are important in this problem as well as energeties.," Here we propose an explanation, noting that timescales are important in this problem as well as energetics."968 Our simple theory for the observed. bimocdality. of NC and SMDIIS is based. on the premise that the dominant object must be able to grow quickly. ancl vet stay active for long enough to provide the needed feedback., Our simple theory for the observed bimodality of NC and SMBHs is based on the premise that the dominant object must be able to grow quickly and yet stay active for long enough to provide the needed feedback.969 As we show below. in small bulges this argument favours nuclear star clusters whereas in larger ones the situation is reversed.," As we show below, in small bulges this argument favours nuclear star clusters whereas in larger ones the situation is reversed."970 3olow we explain our idea. address observational constraints and conditions needed. for it to work. and suggest. possible astrophysical implications.," Below we explain our idea, address observational constraints and conditions needed for it to work, and suggest possible astrophysical implications."971 We note that nuclear star. clusters could. in. principle form elsewhere in the galaxies and then migrate inwarels due to dynamical friction with the background stars., We note that nuclear star clusters could in principle form elsewhere in the galaxies and then migrate inwards due to dynamical friction with the background stars.972 However. Milosavljeviéó(2004) argues against this possibility due to the short time scales available for this process. ancl argues instead that these clusters may form in situ.," However, \cite{Milosavljevic04a} argues against this possibility due to the short time scales available for this process, and argues instead that these clusters may form in situ."973 We agree with this point. and further note that observations of voung massive stars in the central parsec of the Milky Was oller direct support to the in-situ formation model (Navakshin&2005).," We agree with this point, and further note that observations of young massive stars in the central parsec of the Milky Way offer direct support to the in-situ formation model \citep{NC05,PaumardEtal06,NS05}."974. The exact geometrical arrangement of the forming stars (a thick disc or a quasi-spherical cluster) is irrelevant on the scales of the parent galaxy., The exact geometrical arrangement of the forming stars (a thick disc or a quasi-spherical cluster) is irrelevant on the scales of the parent galaxy.975 Black holes and nuclear clusters cach evolve. on characteristic timescales., Black holes and nuclear clusters each evolve on characteristic timescales.976 SAIBIT growth is limited by the Eddington accretion rate. Apad=μι(κο). where €~0.1 is the radiative ellicieney of accretion.," SMBH growth is limited by the Eddington accretion rate, $\dot M_{\rm Edd} = L_{\rm Edd}/(\epsilon c^2)$, where $\epsilon \sim9770.1$ is the radiative efficiency of accretion."978 SAIBLE masses can grow no faster than exp(//fsiay). where is the Salpeter time. with cy.=c/0.1.," SMBH masses can grow no faster than $\exp(t/t_{\rm Salp})$, where is the Salpeter time, with $\epsilon_{0.1} = \epsilon/0.1$."979" Star formation can occur on the free.fall or dynamical timescale fg, of the svstem. which is less than a million vears for many ohservec voung star clusters (e.g.Hillenbrand.1997)."," Star formation can occur on the free–fall or dynamical timescale $t_{\rm980 dyn}$ of the system, which is less than a million years for many observed young star clusters \citep[e.g.,][]{Hillenbrand97}."981. Once a SAIBLI is created. its feedback can be activate at any time. provided that the accretion rate is high enough.," Once a SMBH is created, its feedback can be activated at any time, provided that the accretion rate is high enough."982 ὃν contrast. star cluster feedback has a “hall life” of arounc lis222.510 vr. since this is the mainsequence Lifetime of the massive stars contributing most to the feedback (c.g.Leithereretal. 1992).," By contrast, star cluster feedback has a “half life” of around $t_{\rm MS} \simlt 2\times 10^7$ yr, since this is the main–sequence lifetime of the massive stars contributing most to the feedback \citep[e.g.][]{Leitherer1992}."983.. This timescale is only a factor of two shorter than the Salpeter time., This timescale is only a factor of two shorter than the Salpeter time.984 After this time fui). the ability of the nuclear clusters to expel gas from the ealaxy is severely reduced.," After this time $t=t_{\rm ms}$ ), the ability of the nuclear clusters to expel gas from the galaxy is severely reduced."985 They would have to be rebuile their population of massive voung stars to restart., They would have to be rebuild their population of massive young stars to restart.986 It is no obvious that this is physically possible inside an existing dense stellar cluster., It is not obvious that this is physically possible inside an existing dense stellar cluster.987 Consider a bulge where the dynamical time (equation 7 below) is much shorter than the Salpeter time., Consider a bulge where the dynamical time (equation \ref{tvir} below) is much shorter than the Salpeter time.988 In a gas [feeding event (e.g. a merger). the bulge regains dynamical equilibrium before any significant SMDBIL growth and feedback sets in. and there is nothing to prevent gas from collecting in the bulge centre.," In a gas feeding event (e.g. a merger), the bulge regains dynamical equilibrium before any significant SMBH growth and feedback sets in, and there is nothing to prevent gas from collecting in the bulge centre."989 The accumulated gas is then consumed by star formation in nuclear regions. forming nuclear clusters which quickly reach their Aye: σ limiting mass.," The accumulated gas is then consumed by star formation in nuclear regions, forming nuclear clusters which quickly reach their $M_{\rm NC}$ $\sigma$ limiting mass."990 This cuts olf growth of everything the bulge. the NC and the SMBLHL as well.," This cuts off growth of everything – the bulge, the NC and the SMBH as well."991 Phe SMBDBLL in these bulges are thus bound to be underweight compared to the Alpy (0 relation., The SMBH in these bulges are thus bound to be underweight compared to the $M_{\rm BH}$ $\sigma$ relation.992 In the opposite extreme. when the bulge dynamical time is longer than the Salpeter time. the SMDBLIL can grow quickly enough to reach its limiting AMpg 6 mass.," In the opposite extreme, when the bulge dynamical time is longer than the Salpeter time, the SMBH can grow quickly enough to reach its limiting $M_{\rm BH}$ $\sigma$ mass."993 While nuclear star clusters might be created there as well. their feedback quickly (ie. in about 20 million vears) becomes negligible.," While nuclear star clusters might be created there as well, their feedback quickly (i.e. in about 20 million years) becomes negligible."994 The situation is thus the reverse of the last paragraph. anc it is the nuclear star clusters that are underweight in these bulges.," The situation is thus the reverse of the last paragraph, and it is the nuclear star clusters that are underweight in these bulges."995" Below we estimate A444, as a function of bulge mass or velocity. dispersion.", Below we estimate $t_{\rm dyn}$ as a function of bulge mass or velocity dispersion.996" We find that. fsa,lacs dn smaller bulges (στ150 1 7) and μμfen dn: larger ones.", We find that $t_{\rm Salp} \ga t_{\rm dyn}$ in smaller bulges $\sigma \la 150$ $^{-1}$ ) and $t_{\rm Salp} \la t_{\rm dyn}$ in larger ones.997Figure Lob shows the helt curve of an —11 hours quiesceut period obtained by ou February 26. 2002.,"Figure \ref{fig1}b b shows the light curve of an $\sim$ 11 hours quiescent period obtained by on February 26, 2002."998" Figure 2aa displavs the light curve of the very first flare reported frou, AA* dated October 26. 2000. observed with aud published by Baganoff ct al. (2001))."," Figure \ref{fig2}a a displays the light curve of the very first flare reported from A* dated October 26, 2000, observed with and published by Baganoff et al. \cite{B2001}) )."999 We choose a slightlv different cuerey band aud a different biuniue., We choose a slightly different energy band and a different binning.1000" AA* was observed for. 16.5 hours on λίαν 5ο, 2002 without a breht dare occurring. and he light curve is shown in Figure 2bb. Because of the umimerous peaks the source is apparently nof iu a rue quiescent state but exhibits quite a uuuboer of smaller Hux increases or stuall fares."," A* was observed for 46.5 hours on May 5/6, 2002 without a bright flare occurring, and the light curve is shown in Figure \ref{fig2}b b. Because of the numerous peaks the source is apparently not in a true quiescent state but exhibits quite a number of smaller flux increases or small flares."1001 The esseutial observationaldetails are sunuuarized in Table 1.., The essential observationaldetails are summarized in Table \ref{obslog}.1002 The data have been proprictary PI data. which by now are ibliclv available.," The data have been proprietary PI data, which by now are publicly available."1003 The data have heen extracted yon the public archive (level 2 processed eveut ist. provided bv the Center).," The data have been extracted from the public archive (level 2 processed event list, provided by the )."1004 We restrict our analyses to just these four cata sets because they cover he two brieltest fares aud the other two observations rave the lougest exposure of the so-called quiesceut state., We restrict our analyses to just these four data sets because they cover the two brightest flares and the other two observations have the longest exposure of the so-called quiescent state.1005 For the timing analysis we added PN. MOS1 and MOS2 data in one set using counts. which were for extracted froma circleof radius with energies between 2.6 - 10 keV. For the data the extraction radius was around the archived source position. and the enerev band is 2.0 S keV. Because of the relatively broad point spread function of the extraction radius of contaius Cluission frou nore objects than just AA*.," For the timing analysis we added PN, MOS1 and MOS2 data in one set using counts, which were for extracted from a circle of radius with energies between 2.6 - 10 keV. For the data the extraction radius was around the archived source position, and the energy band is 2.0 – 8 keV. Because of the relatively broad point spread function of the extraction radius of contains emission from more objects than just A*."1006 The iuage reveals another four or five additioual sources as well as diffuse cussion., The image reveals another four or five additional sources as well as diffuse emission.1007 Baganotf et al. (2003)), Baganoff et al. \cite{BMM2003}) )1008 estimate a net count rate of LEO.LO κ 7 1 for A* in its quiescent state., estimate a net count rate of $\pm$ 0.40 $\times$ $\sp{-3}$ $\sp{-1}$ for A* in its quiescent state.1009" The power law spectrun has a photon iudex of D, = |yo1:3> and an absorbing⋅↜ coluniu density. Nyy n.* 44221077 2 7."," The power law spectrum has a photon index of $\Gamma\sb{\rm q}$ = $\sp{+1.3}\sb{-0.9}$ and an absorbing column density $\sb{\rm{H,q}}$ $\sp{+4.4}\sb{-3.0} \times$ $\sp{22}$ $\sp{-2}$ ."1010 Using the best fit values we estimate a AA* quiescent state count rate of 0.029 + 0.003 1 for 22|PN. so tha the couversion factor is 5 + 0.5 between the two iustruient combinations.," Using the best fit values we estimate a A* quiescent state count rate of 0.029 $\pm$ 0.003 $^{-1}$ for 2+PN, so that the conversion factor is 5 $\pm$ 0.5 between the two instrument combinations."1011 The mean EPIC count rate of AA? in its quiesceut state amounts to L1G | (c.f, The mean EPIC count rate of A* in its quiescent state amounts to 0.16 $\sp {-1}$ (c.f.1012 Fie., Fig.1013 1bb). which means that the background sources are likely to contribute on average 0.013 | or oof the total during the AA* quicsceut state. xovided that neither the backeround sources nor AA* wave changed significantly compared to the October 26. 2000 observation.," \ref{fig1}b b), which means that the background sources are likely to contribute on average 0.013 $\sp {-1}$ or of the total during the A* quiescent state, provided that neither the background sources nor A* have changed significantly compared to the October 26, 2000 observation."1014 When we subtract the count rate of the ckeround from the flare observation (fig., When we subtract the count rate of the background from the flare observation (fig.1015 laa) the pea- count rate during the time preceding the actual flare has a level of 0.1252-0.03. +. which meaus that tle x»eeursor section is ~L times brighter than AA* im its quiescent state.," \ref{fig1}a a) the peak count rate during the time preceding the actual flare has a level of $\pm$ 0.03 $^{-1}$, which means that the precursor section is $\sim$ 4 times brighter than A* in its quiescent state."1016 It is interesting that flares observed iu he infrared by Cenzel et al. (2003)), It is interesting that flares observed in the infrared by Genzel et al. \cite{Ge2003}) )1017 show about the sam ratio of the fare peak intensity aud the quiesceut level., show about the same ratio of the flare peak intensity and the quiescent level.1018 This suggests that the N-vayv precursor aud the imfrared dares originated in the same process aud that. eiven the mee N-rav flares. mach xiehter mfrared flares still await heir detections.," This suggests that the X-ray precursor and the infrared flares originated in the same process and that, given the huge X-ray flares, much brighter infrared flares still await their detections."1019 Conversion of iustrmment count rates to flux density requires knowledge of the source spectrum and coli- deusitv of the photoelectrical absorption., Conversion of instrument count rates to flux density requires knowledge of the source spectrum and column density of the photoelectrical absorption.1020 This is available for the quiescent state neasured by (Baganoft et al. 2003) ).," This is available for the quiescent state measured by (Baganoff et al. \cite{BMM2003}) ),"1021 the October 26. 2000 flare measured by (Daganotff ct al. 2001))," the October 26, 2000 flare measured by (Baganoff et al. \cite{B2001}) )"1022 and the October 3. 2002 flare measured hy (Porquet ct al. 20033).," and the October 3, 2002 flare measured by (Porquet et al. \cite{P2003}) )."1023 Since both the spectrum and the absorptio- column deusitv differ among the three observations we provide conversion factors for the EPIC count rate and the ACIS-I count rate for each of the three states., Since both the spectrum and the absorption column density differ among the three observations we provide conversion factors for the EPIC count rate and the ACIS-I count rate for each of the three states.1024 These are: 9.5 μον (EPIC lo qT.6 py. CACIS-I E (quiesceut): nSJy (EPIC l να pw CACIS-I. flare): 12.3 pdy (EPIC |. 718. py (ACIS-I + flare).," These are: 9.5 $\mu$ Jy (EPIC $\sp{-1}$, 47.6 $\mu$ Jy (ACIS-I $\sp{-1}$ (quiescent); $\sp{+1.1}\sb{-0.3}~\mu$ Jy (EPIC $\sp{-1}$, $\sp{+6.1}\sb{-2.0}~\mu$ Jy (ACIS-I $\sp{-1}$ flare); 12.3 $\mu$ Jy (EPIC $\sp{-1}$, 71.8 $\mu$ Jy (ACIS-I $\sp{-1}$ flare)."1025 The relatively large uncertaiuty of the conversion factor for the flare are due to the nucertain spectrum and column deusitv., The relatively large uncertainty of the conversion factor for the flare are due to the uncertain spectrum and column density.1026 The cnerey fiux densities are eiven for E = 1 keV. From the light curves shown in Figures 1. and 2.. power density spectra (PDS) have been created by a Fourier ilalvsis of six data sets.," The energy flux densities are given for E = 1 keV. From the light curves shown in Figures \ref{fig1} and \ref{fig2}, power density spectra (PDS) have been created by a Fourier analysis of six data sets."1027 Two sets cover the time section of just the flare. one cach forNewton," Two sets cover the time section of just the flare, one each for (Fig."1028 (Fie. 3aa) and (Fig., \ref{fig3}a a) and (Fig.1029 laa): another two sets cover the time sections before aud after the flare (Figs., \ref{fig4}a a); another two sets cover the time sections before and after the flare (Figs.1030 3bb aud tbh)., \ref{fig3}b b and \ref{fig4}b b).1031 For these PDS the ata of the flare proper have been removed aud replaced by data with a mean flix ichtical to that of the time preceding the flareassuming a Poissoulan statistical distribution., For these PDS the data of the flare proper have been removed and replaced by data with a mean flux identical to that of the time preceding the flareassuming a Poissonian statistical distribution.1032 The final two sets correspond. to the two observations of the quiesceut level (Fies., The final two sets correspond to the two observations of the quiescent level (Figs.1033 5 and 6))., \ref{fig5} and \ref{fig6}) ).1034" We define the power spectral density psd, at a frequeucv f£, and wave uunber n as Όσα, (a2 b2)/(2 4Af?) «Tia, and b, are the Fourier coefficients. Afis the sampling or binning time and T is the total observing time (Table 1))."," We define the power spectral density $\sb{n}$ at a frequency $\sb{n}$ and wave number n as $\sb{n}$ = $\sb{n}\sp 2$ $\sb{n}\sp 2$ $\times\Delta t\sp 2)\times T$; $\sb{n}$ and $\sb{n}$ are the Fourier coefficients, $\Delta t$is the sampling or binning time and $T$ is the total observing time (Table \ref{obslog}) )."1035 The Fourier cocficients are 1n units of ACIS-I | for the observations aud EPIC | for the observations., The Fourier coefficients are in units of ACIS-I $^{-1}$ for the observations and EPIC $^{-1}$ for the observations.1036 Because of the different efficiencies the pscdys are expected to ecnerally differ bv a factor, Because of the different efficiencies the $\sb{\rm n}$ 's are expected to generally differ by a factor1037line widths corrected. for inclination exeecel LOO 4ns.+).,line widths corrected for inclination exceed 100 $km~s^{-1}$ ).1038 The LL line profiles in the literature were individually inspected., The HI line profiles in the literature were individually inspected.1039 H£ more than one measurement was available we choosed the one with higher S/N ratio (references to these measurements are listect in Table NGC 4496. one of the 5. galaxies with C'epheids nieasurements. is not included in the present analysis because another galaxy is superimposed on its disk. making the extraction. of its. photometric parameters. uncertain.," If more than one measurement was available we choosed the one with higher S/N ratio (references to these measurements are listed in Table NGC 4496, one of the 5 galaxies with Cepheids measurements, is not included in the present analysis because another galaxy is superimposed on its disk, making the extraction of its photometric parameters uncertain."1040 Conversely two other galaxies with Cepheids (NCC 4321 and 4571) are included in the present work in spite of their low inclination (27 degrees)., Conversely two other galaxies with Cepheids (NGC 4321 and 4571) are included in the present work in spite of their low inclination (27 degrees).1041 ln various runs from 1904 to 1997 we took NIB. LI (1.65 jim) or Wo (2.1 pm) band images of 206 of the 233 galaxies selected. from the VC and €CGCCG. using the PIRGO 1.5 m and the Calar Alto m telescopes.," In various runs from 1994 to 1997 we took NIR H (1.65 $\mu$ m) or K' (2.1 $\mu$ m) band images of 206 of the 233 galaxies selected from the VCC and CGCG, using the TIRGO 1.5 m and the Calar Alto 2.2 m telescopes."1042 Eight galaxies were not observed because they have velocity larger than 3000Ams thus they do not belong to the cluster. and four because their angular size (al arcmin) exceeds that of the available NICAIOSS detectors.," Eight galaxies were not observed because they have velocity larger than $3000 ~km~s^{-1}$, thus they do not belong to the cluster, and four because their angular size $a>4$ arcmin) exceeds that of the available NICMOS3 detectors."1043 Phe remaining 15 objects were not observed due to time limitations., The remaining 15 objects were not observed due to time limitations.1044 Images of 6 galaxies are not usable. because the frames were ruined by stray light from the moon.," Images of 6 galaxies are not usable, because the frames were ruined by stray light from the moon."1045 Of the 200 images available. 166 were taken in Ll band. and 34 in Wo band.," Of the 200 images available, 166 were taken in H band, and 34 in K' band."1046 The Wo data are converted into HE band using <ffAY>=0.25x0.13 mag., The K' data are converted into H band using $<H-K'>=0.25 \pm 0.13$ mag.1047 This color. based on 425 measurements not all included in this work. depends little on morphological tvpoe (0.24 for E180: 0.27 for S|Ler).," This color, based on 425 measurements not all included in this work, depends little on morphological type (0.24 for E+S0; 0.27 for S+Irr)."1048 NIK images are available for 111 [ate-tvpe galaxies: S3 at 11 band and 28 at WO band., NIR images are available for 111 late-type galaxies: 83 at H band and 28 at K' band.1049 The Wo band observations (and 19 of the LE band ones) were taken in 1994-1996 with the Calar Alto 2.2 m telescope. and are published. in. Boselli et al. (," The K' band observations (and 19 of the H band ones) were taken in 1994-1996 with the Calar Alto 2.2 m telescope, and are published in Boselli et al. ("10501997).,1997).1051 LE band. observations of 15 Ilate-tvpe galaxies were taken in 1995 with the Γιο 1.5 m telescope. and are published in Gavazzi et al.," H band observations of 15 late-type galaxies were taken in 1995 with the TIRGO 1.5 m telescope, and are published in Gavazzi et al."1052 Images in the LE band for the remaining 49 galaxies were obtained during three photometric nights of February. 1997 with the Calar Alto 2.2 m telescope. in seeing conditions of typically 1-2 aresec.," Images in the H band for the remaining 49 galaxies were obtained during three photometric nights of February 1997 with the Calar Alto 2.2 m telescope, in seeing conditions of typically $\,$ $\,$ 2 arcsec."1053 The Cassegrain locus of the telescope was equipped with the MAGIC 256.256 pixel NICMOS3 infrared array (Llerbst et al., The Cassegrain focus of the telescope was equipped with the MAGIC $256 \times 256$ pixel NICMOS3 infrared array (Herbst et al.1054 1993) with an optical setup of the detector chosen to give the largest possible field of view. i.c. OS6.8 arcmin. with a pixel size of 1.61 aresec.," 1993) with an optical setup of the detector chosen to give the largest possible field of view, i.e. $6.8 \times 6.8$ $^2$, with a pixel size of 1.61 arcsec."1055 The observing technique was identical to that used in previous WO band observations of late-tvpe galaxies at Calar Alto. as described in Boselli et al. (," The observing technique was identical to that used in previous K' band observations of late-type galaxies at Calar Alto, as described in Boselli et al. ("10561997).,1997).1057 Galaxies with optical diameter larger than half of the size of the field. of view of the array were observed. using a pointing sequence in which 8 frames are taken. centred on the target. alternated with S sky. frames. positioned along a circular path around the galaxy. (oll-set by a field of view from the centre).," Galaxies with optical diameter larger than half of the size of the field of view of the array were observed using a pointing sequence in which 8 frames are taken, centred on the target, alternated with 8 sky frames, positioned along a circular path around the galaxy (off-set by a field of view from the centre)."1058 The S on-target fields were dithered by 10 aresee in order to help the elimination of bad pixels., The 8 on-target fields were dithered by 10 arcsec in order to help the elimination of bad pixels.1059 Galaxies with optical diameter. smaller than half. of the size of the Ποιά of view of the array were observed with a pointing sequence consisting of 9 pointings along a circular path and. displaced. from one-another by 2 arcmin such that the target galaxy is always in the field., Galaxies with optical diameter smaller than half of the size of the field of view of the array were observed with a pointing sequence consisting of 9 pointings along a circular path and displaced from one-another by 2 arcmin such that the target galaxy is always in the field.1060 Galaxies with angular sizes larger than the dimension of the detector were mapped using pointing sequences expressly prepared according to the shape and orientation of the galaxy in the skv. in order to cover with a mosaic the entire surface of the target.," Galaxies with angular sizes larger than the dimension of the detector were mapped using pointing sequences expressly prepared according to the shape and orientation of the galaxy in the sky, in order to cover with a mosaic the entire surface of the target."1061 Typical integration times were of 256-28N seconds., Typical integration times were of 256-288 seconds.1062 This corresponds to the product of the exposure time of the elementary integration (1 sec) the number of elementary integrations (32) the number of pointings used in each mosaic (S or 9)., This corresponds to the product of the exposure time of the elementary integration (1 sec) $\times$ the number of elementary integrations (32) $\times$ the number of pointings used in each mosaic (8 or 9).1063 The observations were calibrated and the Duxes transformed. into the LE banc photometric system. using the standard stars in Elias ct al. (, The observations were calibrated and the fluxes transformed into the H band photometric system using the standard stars in Elias et al. (10641982). observed. hourly throughout the night.,"1982), observed hourly throughout the night."1065 The typical uncertainty of the measurements is 0.05 Details on the image analysis and extraction. of the photometric parameters can also be found in Boselli et al. (, The typical uncertainty of the measurements is 0.05 Details on the image analysis and extraction of the photometric parameters can also be found in Boselli et al. (10661997).,1997).1067" Llere it is sullicient to say that the LE magnitudes used in the present analysis were derived: by simulating iverture photometry. Following the method. of Gavazzi Doselli (1906): the counts are integrated in concentric circular rings around the galaxy. centres to provide curves of growth up to the galaxy. optical diameter. (determined in the Bat the 25""nag.aresee 7)."," Here it is sufficient to say that the H magnitudes used in the present analysis were derived by simulating aperture photometry, following the method of Gavazzi Boselli (1996): the counts are integrated in concentric circular rings around the galaxy centres to provide curves of growth up to the galaxy optical diameter (determined in the B at the $25^{th} mag~1068arcsec^{-2}$ )."1069 The LL magnitudes used in this work are corrected for internal extinction using the prescriptions of Gavazzi Bosclli (1996)., The H magnitudes used in this work are corrected for internal extinction using the prescriptions of Gavazzi Boselli (1996).1070 For 1053 ealaxies (not necessarily included in this work) for which an image is available in LL band we compare the corresponding LL magnitudes with those obtained. by ce Vaucouleurs | exponential decomposition of the ligth profiles obtained along elliptical annuli., For 1053 galaxies (not necessarily included in this work) for which an image is available in H band we compare the corresponding H magnitudes with those obtained by de Vaucouleurs + exponential decomposition of the ligth profiles obtained along elliptical annuli.1071 We find that on average IL are 0.10+0.21 mag fainter than the total (extrapolated to infinity) maenitucles., We find that on average H are $0.10 \pm 0.21$ mag fainter than the total (extrapolated to infinity) magnitudes.1072 NIB images are available for SO carky-type galaxies: 83 at II band. and 6 at WO band.," NIR images are available for 89 early-type galaxies: 83 at H band, and 6 at K' band."1073 The Ko band. observations were taken with the Calar Alto 2.2 m telescope. anc are published in Boselli et al. (," The K' band observations were taken with the Calar Alto 2.2 m telescope, and are published in Boselli et al. ("10741997).,1997).1075We now analyze these spectra to coustrain the veilines aid pliysical uatures of these sources.,We now analyze these spectra to constrain the veilings and physical natures of these sources.1076 Our previous high resolution study (Paper H) showed that late-type Class IL Y5Os stars) rotate slowly. (esin’)<20 kins +. ο ones rotate quickly. an +.," Our previous high resolution study (Paper II) showed that late-type Class II YSOs (pre-main-sequence stars) rotate slowly, $\langle v {\rm sin} i \rangle < 20$ km $^{-1}$, while flat-spectrum ones rotate quickly, $\langle v {\rm sin} i \rangle > 107720$ km $^{-1}$."1078 This study also showed that in addition to Yoadeuiug ihe baud lead. bieh rotation also decreased the maximum absorption depth of the bad head aud adjacent iucdividual lines.," This study also showed that in addition to broadening the band head, high rotation also decreased the maximum absorption depth of the band head and adjacent individual rotation-vibration lines."1079 Thus rotation as well as veiling cau redce tle detectability of CO absorption iu [iuie signal-to-noise spectra., Thus rotation as well as veiling can reduce the detectability of CO absorption in finite signal-to-noise spectra.1080 We now explore the limits of A-baud. veiling aud rotation iu our uew protostar sample by comparing their spectra to those of flat-speetruum aud Class IE YSOs to which we have artificially added: continuum veiling., We now explore the limits of $K$ -band veiling and rotation in our new protostar sample by comparing their spectra to those of flat-spectrum and Class II YSOs to which we have artificially added continuum veiling.1081" We chose VSSC 25 to be representative of a slowly rotating Class II YSO ο οι {=5 xls 1) and VSSG 17 to be representative of a quickly rotating (e sin i=4T kin 1j [Iat-spect""un source (see Paper II).", We chose VSSG 25 to be representative of a slowly rotating Class II YSO $v$ sin $i = 5$ km $^{-1}$ ) and VSSG 17 to be representative of a quickly rotating $v$ sin $i = 47$ km $^{-1}$ ) flat-spectrum source (see Paper II).1082 The spectral types and. A-baud. veiliigs Lave beei ineasured for both ol these objects., The spectral types and $K$ -band veilings have been measured for both of these objects.1083 VSSC 25 has a spectral type MOIV/V with rj 0.25 while VSSQ 17 is MOIV/V with rj 0.9 (Luhman&Itieke:: Paper I., VSSG 25 has a spectral type M0IV/V with $r_{k}$ = 0.25 \citep{LR99} while VSSG 17 is M0IV/V with $r_{k}$ = 0.9 \citeauthor{LR99}; Paper I).1084 Tle fy-bar veiling is defined as ry.=Fiver/Fig. where Fi; is the A baud excess flux. at4 FkÁ is 11e dy bane stellar flux.," The $K$ -band veiling is defined as $r_{k} = F_{Kex}/F_{K*}$ where $F_{Kex}$ is the $K$ band excess flux, and $F_{K*}$ is the $K$ band stellar flux."1085 We acded. veiling (a coustait positive offset) to the template s»ectruliiof VSSC IT (taken [rom Paper IL) aud degraded its sienal-to-u«)se so hat its CO absorpion eqlivaent widtl aud cletectability were weakened., We added veiling (a constant positive offset) to the template spectrum of VSSG 17 (taken from Paper II) and degraded its signal-to-noise so that its CO absorption equivalent width and detectability were weakened.1086 We thebn used a series o ‘these VSSCi 17 teumiplates with various veilines aud sigual-to-noise ratios to estiiate the veiliugs of our observed soiJCes., We then used a series of these VSSG 17 templates with various veilings and signal-to-noise ratios to estimate the veilings of our observed sources.1087 We estimated the veiliug [or sources which show CO xuid head. absorptious (IRS 51 aud IRS 63) by matchine their spectra to veiled teuplates witl ποtical signual-to-nolse and similar features (CO baud head depth aud slope)., We estimated the veiling for sources which show CO band head absorptions (IRS 51 and IRS 63) by matching their spectra to veiled templates with identical signal-to-noise and similar features (CO band head depth and slope).1088 The baud lieacd profiles o ‘these objects also matchec tlie shape of VSSG 17 aud matched those of observed slowly rotatiug late-type sta* which had been artificially broadened with a stelar rotation prolile of e siu 720 dus! (see Paper ID)., The band head profiles of these objects also matched the shape of VSSG 17 and matched those of observed slowly rotating late-type stars which had been artificially broadened with a stellar rotation profile of $v$ sin $i = 50$ km $^{-1}$ (see Paper II).1089 This it is likely that their CO absor)ious arise in rapidly rotating ellar photosphe‘es., Thus it is likely that their CO absorptions arise in rapidly rotating stellar photospheres.1090 However. the absorptiou features of tese highly veiled sources are very weaz aud this limits tje clerivecdl rotatlou velocities to uncertalnties of aporoximately and the derived veilings to uu'ertaluties of at least.," However, the absorption features of these highly veiled sources are very weak, and this limits the derived rotation velocities to uncertainties of approximately and the derived veilings to uncertainties of at least."1091. The iniinui likely veiliugs of tle Class I anc| fIat-spectrum sowces without detectable CO absorplous wele esiuated by assuming that their CO absorptious were intrinsically similar to VSSC 1T lx had inc'eased coutinuuum veiling., The minimum likely veilings of the Class I and flat-spectrum sources without detectable CO absorptions were estimated by assuming that their CO absorptions were intrinsically similar to VSSG 17 but had increased continuum veiling.1092 We derived au analytical relation for veiling base on the incdle that au objects CO baic head is uidetectable when its maxiuum absorption depth is less hau 3.0 times the RAMS 1oise over 1 resolutjon elemeit (5 pixels) in the spectrum., We derived an analytical relation for veiling based on the principle that an object's CO band head is undetectable when its maximum absorption depth is less than 3.0 times the RMS noise over 1 resolution element (5 pixels) in the spectrum.1093 This is a robust miuimuu likely veiling critejon because less veiliug would eusure that the baud lieac would e definitely detected. aux consideriug more resolution elements would increase the amount of veiliig derived.," This is a robust minimum likely veiling criterion because less veiling would ensure that the band head would be definitely detected, and considering more resolution elements would increase the amount of veiling derived."1094 The resultant «erived minimum likely rj vaUes thal¢‘hecl those of templates whicl were veiled to the point where tleir CO absorptious just disappeared. visually., The resultant derived minimum likely $r_{k}$ values matched those of templates which were veiled to the point where their CO absorptions just disappeared visually.1095 Possible differences between he actual spectral types of these sources aud the MO template also cause uncertainties in the derived veiliugs of up to about 50%.. but most deviations are expected to," Possible differences between the actual spectral types of these sources and the M0 template also cause uncertainties in the derived veilings of up to about , but most deviations are expected to"1096period. starting at about log 2 = 1.75 (P? = 56 days).,"period, starting at about log $P$ = 1.75 $P$ = 56 days)."1097 This is in agreement with the results of Alard et al (2001) for the 66522 Daade's Window: variables as well as the LMC and SAIC fields of Glass. Schultheis and Cioni ((2004).," This is in agreement with the results of Alard et al (2001) for the 6522 Baade's Window variables as well as the LMC and SMC fields of Glass, Schultheis and Cioni ((2004)."1098 Of the 64 variables listed in Table 2.35 have had their IRAS (10jun region) spectra classified. by Sloan Price (1998).," Of the 64 variables listed in Table 2, 35 have had their IRAS $\mu$ m region) spectra classified by Sloan Price (1998)."1099 Ten of them show snaked” photospheres: i6... dust shells were not. detected.," Ten of them show `naked' photospheres; i.e., dust shells were not detected."1100 They correspond to the shortest-period SRVs., They correspond to the shortest-period SRVs.1101 The remainder are classified as tvpes SEL to SES. according to the strength of their SiO features.," The remainder are classified as types SE1 to SE8, according to the strength of their SiO features."1102 Many are also classified as t. meaning that they show the 13/4 feature.," Many are also classified as `t', meaning that they show the $\mu$ m feature."1103" The SE sub-classes ancl presence or absence of the ""U show no correlation with A 42] colour.", The SE sub-classes and presence or absence of the `t' show no correlation with $K$ – [12] colour.1104 Given the fairly clear dependence of A 12] colour on Al-giant sub-tvpe and log P seen in Figs 6 and 7.. it ds surprising that Ololsson et al (2002). using mass-loss rates lor SlhiVs based on CO radio data. do not see clear correlations with pulsation period or stellar blackbocdvy temperature (their Figs 7 and S).," Given the fairly clear dependence of $K$ – [12] colour on M-giant sub-type and log $P$ seen in Figs \ref{CvsM} and \ref{CvsP}, it is surprising that Olofsson et al (2002), using mass-loss rates for SRVs based on CO radio data, do not see clear correlations with pulsation period or stellar blackbody temperature (their Figs 7 and 8)."1105 The current picture. of SRVs in the solar neighbourhood. though improved in detail. remains sketchy because of the small size ancl haphazare nature of the sample.," The current picture of SRVs in the solar neighbourhood, though improved in detail, remains sketchy because of the small size and haphazard nature of the sample."1106 Enough evidence now exists. however. to show that local Sis occupy the same areas of the A. log P diagram as stars in he 66522 Ποια of the Bulge and that they obey similar A log P relations.," Enough evidence now exists, however, to show that local SRVs occupy the same areas of the $K$, log $P$ diagram as stars in the 6522 field of the Bulge and that they obey similar $K$ – log $P$ relations."1107 The currently. available data. especially at. the short-»eriod. end. are. too sparse.," The currently available data, especially at the short-period end, are too sparse."1108 Llipparcos parallaxes are available. for numerous. carly A-type stars which have not vet been monitored with sullicient accuracy or lor ong cnough times to find their variability properties., Hipparcos parallaxes are available for numerous early M-type stars which have not yet been monitored with sufficient accuracy or for long enough times to find their variability properties.1109 While these stars are usually too bright. to be included in current all-sky monitoring projects. they are suitable or photometric measurements with small telescopes.," While these stars are usually too bright to be included in current all-sky monitoring projects, they are suitable for photometric measurements with small telescopes."1110 Thus. frequent measurements over periods of one νοα or more. though tedious. can certainly be contemplated.," Thus, frequent measurements over periods of one year or more, though tedious, can certainly be contemplated."1111 Because the Lipparcos parallaxes are directly the result. of trigonometrical determinations ane often of high accuracy. an inerease of the number in the sample will vield a sounder absolute calibration of the properties of the SRVs ancl other M-tyvpe giants.," Because the Hipparcos parallaxes are directly the result of trigonometrical determinations and often of high accuracy, an increase of the number in the sample will yield a sounder absolute calibration of the properties of the SRVs and other M-type giants."1112 With a better understanding of the ellects of metallicity and age. they may even prove useful as distance indicators.," With a better understanding of the effects of metallicity and age, they may even prove useful as distance indicators."1113 Finally. we note that fv-bancl observations for bright stars are fortunately still possible.," Finally, we note that $K$ -band observations for bright stars are fortunately still possible."1114 An earlier version of this paper. based on the published Llipparcos parallaxes. was presented at the conference “Why Galaxies Care About AGB Stars”. Vienna. August 611. 2006.," An earlier version of this paper, based on the published Hipparcos parallaxes, was presented at the conference “Why Galaxies Care About AGB Stars"", Vienna, August 6–11, 2006."1115 We wish to acknowledge use of data from the Centre des Donnéees Stellaires. Strasbourg.," We wish to acknowledge use of data from the Centre des Donnéees Stellaires, Strasbourg."1116 Drs T. Llovd Evans. M. Schultheis and A. Zijlstra read drafts of the paper. providing useful comments and some extra data.," Drs T. Lloyd Evans, M. Schultheis and A. Zijlstra read drafts of the paper, providing useful comments and some extra data."1117our models in Figure + we find that single stars predict too low a value because either there are too many RACs. too few BSGs or à combination of these two.,"our models in Figure \ref{blue2red} we find that single stars predict too low a value because either there are too many RSGs, too few BSGs or a combination of these two."1118 Extra BSCGs can be made via stellar mergers., Extra BSGs can be made via stellar mergers.1119 Such stars are seen in globular clusters when the mass of the merged star is greater than the =ass of the cluster turn-olL. these are blue stragelers (Sillsal. 2000)..," Such stars are seen in globular clusters when the mass of the merged star is greater than the mass of the cluster turn-off, these are blue stragglers \citep{bluestrag}."1120 The second binary ellect is that stars below the minimum initial single star mass fora WR. star will lose win hydrogen envelopes to become WR stars because of RLOEF or CEE., The second binary effect is that stars below the minimum initial single star mass for a WR star will lose their hydrogen envelopes to become WR stars because of RLOF or CEE.1121 These are stars that would have been RSCs nd therefore the total number is reduced., These are stars that would have been RSGs and therefore the total number is reduced.1122 In combination dese processes increase the predicted. BSG/RSC ratio as our binary models show., In combination these processes increase the predicted BSG/RSG ratio as our binary models show.1123 The binary model ratio is dependent on how we 'hoose the clistribution of binaries in gq and log(alt.).," The binary model ratio is dependent on how we choose the distribution of binaries in $q$ and $\log \, (a/{\rm R}_{\odot})$."1124 In our binary population we include very wide binaries. low(afl.)z3. which evolve as single stars so our binary population is a mix of interacting binaries and single stars.," In our binary population we include very wide binaries, $\log \, (a/{\rm R}_{\odot}) \ge 3$, which evolve as single stars so our binary population is a mix of interacting binaries and single stars."1125 Approximately one third of our. primary models evolve as single stars., Approximately one third of our primary models evolve as single stars.1126 Therefore. to reproduce observations. two thirds of all stars must be in interacting binaries.," Therefore, to reproduce observations, two thirds of all stars must be in interacting binaries."1127 1 our. binary models are not completely correct something extra. such as rotation. mav decrease the required fraction. of interacting binaries.," If our binary models are not completely correct something extra, such as rotation, may decrease the required fraction of interacting binaries."1128 Maeder&Alevnet(2001). find that rotation has a strong elfect on the BSC to RSG ratio but the trend they Found was that the BSG to RSG ratio decreased rather than The WI to OSG ratio has been studied. for. sometime (Alaeder&Alevnet1994)., \citet{mm2001} find that rotation has a strong effect on the BSG to RSG ratio but the trend they found was that the BSG to RSG ratio decreased rather than The WR to OSG ratio has been studied for sometime \citep{mm1994}.1129.. LO binaries leave the RSCG population to become WR stars therefore this ratio should increase if the DSG to RAG ratio decreases., If binaries leave the RSG population to become WR stars therefore this ratio should increase if the BSG to RSG ratio decreases.1130 The observed ralio is less certain than the BSG to RSC ratio because there is greater uncertainty in the completeness of the observations (Massey2003)..., The observed ratio is less certain than the BSG to RSG ratio because there is greater uncertainty in the completeness of the observations \citep{massey}.1131 However the trend that. the ratio decreases with metallicity is well established (Crowther 2007)., However the trend that the ratio decreases with metallicity is well established \citep{crowther2007}.1132. Figure 5 shows that our single star models uncderpredict the ratio while our binary models are in better agreement. as are the Geneva rotating models.," Figure \ref{blue2wr} shows that our single star models underpredict the ratio while our binary models are in better agreement, as are the Geneva rotating models."1133 This is because in our models more stars are stripped of their envelopes and become WR. stars., This is because in our models more stars are stripped of their envelopes and become WR stars.1134 There is also a contribution to the OSG population from stellar mergers and secondary accretion as for the BSCG/ISCG ratio above., There is also a contribution to the OSG population from stellar mergers and secondary accretion as for the BSG/RSG ratio above.1135 The trend our binary. mocoels predict with metallicity is a little too shallow but within the uncertainty of the observed ratios., The trend our binary models predict with metallicity is a little too shallow but within the uncertainty of the observed ratios.1136 This again could indicate something extra may need to be included in our mocels., This again could indicate something extra may need to be included in our models.1137 The RSCG to WI ratio compares the relative populations of the two stellar types that have completed. core hydrogen burning and so measures the inlluence of mass loss., The RSG to WR ratio compares the relative populations of the two stellar types that have completed core hydrogen burning and so measures the influence of mass loss.1138 In Table 3. we list the observed populations., In Table \ref{red2wrtable} we list the observed populations.1139 We plot the ratio in Figure 6.. it decreases dramatically with increasing metallicity.," We plot the ratio in Figure \ref{rsg2wr}, it decreases dramatically with increasing metallicity."1140 Such a change would require a stronger scaling of mass loss with metallicity than we currently emplov., Such a change would require a stronger scaling of mass loss with metallicity than we currently employ.1141 Our sinele star models agree with the observations at SAIC metallicity while our binary models agree with the observations around. LAIC metallicity., Our single star models agree with the observations at SMC metallicity while our binary models agree with the observations around LMC metallicity.1142 One way to match the observed trend between these metallicities is to have a metallicity dependent binary fraction., One way to match the observed trend between these metallicities is to have a metallicity dependent binary fraction.1143 However something extra is still required: around: solar metallicity to get an exact agreement., However something extra is still required around solar metallicity to get an exact agreement.1144 At the higher metallicities the ratios are based on a small number of observed stars (see ‘Table 3)) ancl therefore. co not. sample the full binary parameter space., At the higher metallicities the ratios are based on a small number of observed stars (see Table \ref{red2wrtable}) ) and therefore do not sample the full binary parameter space.1145 Furthermore. small numbers mean our assumptions of constant star formation and. LAI become invalid.," Furthermore, small numbers mean our assumptions of constant star formation and IMF become invalid."1146 For example. if all the WIR stars are in very close binaries the RSCGAWR. ratio would be even smaller than we estimate.," For example, if all the WR stars are in very close binaries the RSG/WR ratio would be even smaller than we estimate."1147 A laree number of stars must be observed to calculate the population ratio to ensure the full range of possible binary svstenis is probed., A large number of stars must be observed to calculate the population ratio to ensure the full range of possible binary systems is probed.1148 Finally. we consider a ratio which provides a measure of the relative lifetimes of the two main WIU star types: WN and WC (we include WO with WC).," Finally, we consider a ratio which provides a measure of the relative lifetimes of the two main WR star types: WN and WC (we include WO with WC)."1149 The lifetimes of the two types are determined by the mass-oss rates of WIR stars., The lifetimes of the two types are determined by the mass-loss rates of WR stars.1150 We plot the observations ancl predicted. ratios in Figure 7 it shows our predicted ratios and the most recent Geneva group rotating models (Alevnet&Alacder2005) for comparison., We plot the observations and predicted ratios in Figure \ref{wc2wn} it shows our predicted ratios and the most recent Geneva group rotating models \citep{mm2005} for comparison.1151 The trend of the observations is for the, The trend of the observations is for the1152resolution of the large-scale structure.,resolution of the large-scale structure.1153 The ΕΤΛΑΡΙ survey. with a sampling rate of about 2-in-3. maps a Larger number of galaxies in a smaller volume. thereby sampling the arge-scale structure at à higher resolution and allowing a iner probe of the large-scale structure in the direction of he aanel Lvera cluster. and. better determining the ellects of hese structures upon the Local Group motion.," The FLASH survey, with a sampling rate of about 2-in-3, maps a larger number of galaxies in a smaller volume, thereby sampling the large-scale structure at a higher resolution and allowing a finer probe of the large-scale structure in the direction of the and Hydra cluster, and better determining the effects of these structures upon the Local Group motion."1154" Figure 9 also shows the redshift distribution expected or a homogeneous universe with the same luminosity ""unction parameters (as derived in a subsequent. paper in his series) and selection function as the FLASII survey.", Figure \ref{fig:nz} also shows the redshift distribution expected for a homogeneous universe with the same luminosity function parameters (as derived in a subsequent paper in this series) and selection function as the FLASH survey.1155 In comparison to this homogeneous recdshift. clistribution. he most outstanding features in the observed: recshift distribution are. the strong peaks due to. the many oreground clusters at ~4000 (including the Hydra cluster) and the aat ~ 15000," In comparison to this homogeneous redshift distribution, the most outstanding features in the observed redshift distribution are the strong peaks due to the many foreground clusters at $\sim$ 4000 (including the Hydra cluster) and the at $\sim$ 15000."1156 These structures anc others are clearly visible in. the wedge plot shown in Figure 10.., These structures and others are clearly visible in the wedge plot shown in Figure \ref{fig:wedge_all}.1157 In this figure. the iis the large aat /c310° and czz14000 while the Lvera cluster is the sharply defined aat [oz270° and ezc4000ο.," In this figure, the is the large at $l \approx 310\degr$ and $cz \approx 14000$, while the Hydra cluster is the sharply defined at $l \approx 270\degr$ and $cz \approx 4000$."1158 There are many other clusters in the survey. region. evidenced by the tale iin Figure 10.. most. of which are Abell clusters in the direction of the Figure 8)).," There are many other clusters in the survey region, evidenced by the tell-tale in Figure \ref{fig:wedge_all}, most of which are Abell clusters in the direction of the Figure \ref{fig:skyzplot}) )."1159" Along with the clusters. a number of wall-like structures can be seen. particularly in the vicinity. of theSupercluster.. where they fornia structure similar to the famous '""stick-man! structure associated with the Coma cluster. that was found in the CLA redshilt survey (cleLapparent.CGeller&Lluchra 1986)."," Along with the clusters, a number of wall-like structures can be seen, particularly in the vicinity of the, where they form a structure similar to the famous `stick-man' structure associated with the Coma cluster, that was found in the CfA redshift survey \cite{cfa:1986}."1160. Since the ΕΙΛΑΡΙ survey has morphological information. it 1s possible το examine the properties of cach morphological tvpe separately.," Since the FLASH survey has morphological information, it is possible to examine the properties of each morphological type separately."1161 We choose to divide the sample into two broad. morphological typescarly (I2 and SO) and late (Sp and ler)even though the type information we possess is more detailed., We choose to divide the sample into two broad morphological types—early (E and S0) and late (Sp and Irr)—even though the type information we possess is more detailed.1162 The reason for doing so is parthy to minimize the elfects of classification errors. but mainly so that there are enough objects in each erouping to allow meaningful comparisons.," The reason for doing so is partly to minimize the effects of classification errors, but mainly so that there are enough objects in each grouping to allow meaningful comparisons."1163 The redshift wedge plots of the early and late galaxy tvpes are shown in Figures Ll and 12/— respectively., The redshift wedge plots of the early and late galaxy types are shown in Figures \ref{fig:wedge_early} and \ref{fig:wedge_late} respectively.1164 The ΕΙΛΙ survey contains redshifts for early-tvpe ealaxies. and. Iate-tvpes.," The FLASH survey contains redshifts for early-type galaxies, and late-types."1165 Although similar. the distributions of early and late types show some interesting dilferences.," Although similar, the distributions of early and late types show some interesting differences."1166 Figure 11 shows that the early-tvpe galaxies are found. predominantly within cluster cores. and less frequently within wall-like structures.," Figure \ref{fig:wedge_early} shows that the early-type galaxies are found predominantly within cluster cores, and less frequently within wall-like structures."1167 The late-type galaxies are found in both clusters and wall-like structures. as shown in Figure 12.. and thus can be considered. as more representative tracers of the large-scale structure.," The late-type galaxies are found in both clusters and wall-like structures, as shown in Figure \ref{fig:wedge_late}, and thus can be considered as more representative tracers of the large-scale structure."1168" A good. example of this is the bridge of ealaxies between 10000xez:15000 ""along /=290°. which is almost entirelypopulated: with late-twpe galaxies. and is not visible in Figure 11.."," A good example of this is the bridge of galaxies between $10000 \leq cz1169\leq 15000$ along $l = 290\degr$, which is almost entirelypopulated with late-type galaxies, and is not visible in Figure \ref{fig:wedge_early}. ."1170" The ELASID survey catalogue contains galaxies brighter than 6,;=16.7 within a 0010* region bounded", The FLASH survey catalogue contains galaxies brighter than $\bJ$ =16.7 within a $60\degr \times 10\degr$ region bounded1171calculation. we assume a «etection threshold of S/N>6.5.7 hours per night. systematic error. auc perfect. weather.,"calculation, we assume a detection threshold of $S/N>6.5$, 7 hours per night, systematic error, and perfect weather."1172 We hen cousider the effect of changing each of these fiducial assumptions ou the number of detected jxlanets., We then consider the effect of changing each of these fiducial assumptions on the number of detected planets.1173 Fig., Fig.1174 7 shows the number of detected. planets as a function of radius. uuder the assuimption that every star has a planet of a given radius.," \ref{gaudi} shows the number of detected planets as a function of radius, under the assumption that every star has a planet of a given radius."1175 As mentioned above. NGC 6791 |as a SUper-solar metallicity of [Fe/H]—0.3—0.1 dex. which implies a frequency of hot Jupiters CP?=3—9 days oL ~ (Fische|:&Valenti2005:Santos.Israelian.Mayor2001:Mochejskaetal.2005).. aud a frequency of very hot Jipiters (P=1—3 days) of ~ 2005)... assuiniig the po»ulation «of panets is similar to the local solar neighborhood.," As mentioned above, NGC 6791 has a super-solar metallicity of $=0.3-0.4$ dex, which implies a frequency of hot Jupiters $P=3-9$ days) of $\sim$ \citep{fischer05, santos04b, mochejs05}, and a frequency of very hot Jupiters $P=1-3$ days) of $\sim$ \citep{gaudi05}, assuming the population of planets is similar to the local solar neighborhood."1176 For our ficticial asstluj(tions. these [requeicies vield ~ 5 expected detectious of hot Jupiters aud ~ 3) expected cleectious of very bot Jujters.," For our fiducial assumptions, these frequencies yield $\sim$ 5 expected detections of hot Jupiters and $\sim$ 3 expected detections of very hot Jupiters."1177 One is lllikely to cletect a signiicant number of hot Neptuues in NCC 6791. unless they are considerably more common than their uassive counterparts.," One is unlikely to detect a significant number of hot Neptunes in NGC 6791, unless they are considerably more common than their massive counterparts."1178 However. NCC 6791 is not necessarily ideal lor the «etectiou of Hot Neptutes. aud closer clusters will likely viekl iiiproved. expected detection rates.," However, NGC 6791 is not necessarily ideal for the detection of Hot Neptunes, and closer clusters will likely yield improved expected detection rates."1179 To «eimmoustrate tlis. in Fig.," To demonstrate this, in Fig."1180 7 we also show the number of expected detections for a hypothetical cluster with the same paraneters as NGC 6791. but with ce=2.5kpc. 2500 stars. 10 hours per night. ancl systematic error.," \ref{gaudi} we also show the number of expected detections for a hypothetical cluster with the same parameters as NGC 6791, but with $=2.5$ kpc, 2500 stars, 10 hours per night, and systematic error."1181 I1 this case. one would expect to detect 90/ hot veptunes. ald 2TOf very hot Neptunes. asstmine a [raclion. f of stars have Neptuue-sized planes in the give1 rauge of periods.," In this case, one would expect to detect $\sim 90f$ hot Neptunes, and $\sim 270f$ very hot Neptunes, assuming a fraction $f$ of stars have Neptune-sized planets in the given range of periods."1182 Finally we nention that the weather in Arizona also makes NCC OTOL au uukeal target for the MMT., Finally we mention that the weather in Arizona also makes NGC 6791 an unideal target for the MMT.1183 At 19h21™ of RA. the cluster is best observed in July/Augist and is this subject to the Arizona monsoot season.," At $19^{\rm h}21^{\rm m}$ of RA, the cluster is best observed in July/August and is thus subject to the Arizona monsoon season."1184 We lave aso obtained preliminary data for the open chsters M35 and NGC 2158., We have also obtained preliminary data for the open clusters M35 and NGC 2158.1185 The results from these clusters will be presented in a future contjbutiol., The results from these clusters will be presented in a future contribution.1186clusters.,clusters.1187 The latter AGN feedback ellect has been invoked to explain the correlations between black hole mass ancl host galaxy properties (e.g.Silk&Rees1998:Fabian1999:Alatteoetal.2005:Bower 2006)... as well as the end shape of the galaxy. luminosity function (Bensonctal. 2003).," The latter AGN feedback effect has been invoked to explain the correlations between black hole mass and host galaxy properties \citep[e.g.][]{silk98,fabian99,dimatteo05,bower06}, as well as the high-end shape of the galaxy luminosity function \citep{benson03}."1188. On the other hand. the triggering of ΑΝ activity as a result of evolution-driven gas accretion can provide an explanation for the similarity between the redshift evolution of AGN activity and that of the global star formation rate of the field galaxy population (Dunlop&Peacock1990:Macauetal. 1996).," On the other hand, the triggering of AGN activity as a result of evolution-driven gas accretion can provide an explanation for the similarity between the redshift evolution of AGN activity and that of the global star formation rate of the field galaxy population \citep{dunlop90,madau96}."1189.. Clearly: if we are to incorporate the ACN Feedback effect accurately into galaxy evolution models. it is important to understand how and when ACN are triggered as their host galaxies evolve.," Clearly, if we are to incorporate the AGN feedback effect accurately into galaxy evolution models, it is important to understand how and when AGN are triggered as their host galaxies evolve."1190 Deep ground-based imaging observations of powerful racio galaxies show morphological evidence (tidal tails. fans. bridges and shells ete.)," Deep ground-based imaging observations of powerful radio galaxies show morphological evidence (tidal tails, fans, bridges and shells etc.)"1191 that a Large fraction are triggered in ealaxy interactions and mergers (Heckmanetal.1986:Smith&lHleckman1989:RamosAlmeidactal. 2010).," that a large fraction are triggered in galaxy interactions and mergers \citep{heckman86,smith89, ramos10}."1192.. A merger origin is also supported by the kinematics of the extended emission line regions in some sources (Tacdhunter.Fosbury&Quinn1989:Baum.lHleckmanvanBreugel 1992).," A merger origin is also supported by the kinematics of the extended emission line regions in some sources \citep{tadhunter89,baum92}."1193. However. the idea that the activity is always triggered. in major galaxy mergers and interactions has been challenged bv high resolution Hubble Space Telescope. (LIEST). images which provide evidence that the host. galaxies of powerful AGN of both racdio-Ioud and racio-quict tvpes are relatively quicscent eiant. elliptical ealaxics (Dunlopetal.2003).," However, the idea that the activity is always triggered in major galaxy mergers and interactions has been challenged by high resolution Hubble Space Telescope (HST) images which provide evidence that the host galaxies of powerful AGN of both radio-loud and radio-quiet types are relatively quiescent giant elliptical galaxies \citep{dunlop03}."1194.. At east part of this apparent. discrepancy. between the LIST and. ground-based results is likely to be a consequence of he fact that shallow LIST observations are sensitive to high surface brightness structures close to the nuclei. while the ower resolution grouncd-based. studies are more sensitive to ower surface brightness structures on larger scales (secclis-cussioninCanalizoetal.2007:Bennert 2008).," At least part of this apparent discrepancy between the HST and ground-based results is likely to be a consequence of the fact that shallow HST observations are sensitive to high surface brightness structures close to the nuclei, while the lower resolution ground-based studies are more sensitive to lower surface brightness structures on larger scales \citep[see discussion in][]{canalizo07,bennert08}."1195. While some radio galaxies show clear evidence Lor rigecring in galaxy interactions and mergers. a significant subset have optical morphologies απ emüssion line kinematics that do not support such a triggering mechanism.," While some radio galaxies show clear evidence for triggering in galaxy interactions and mergers, a significant subset have optical morphologies and emission line kinematics that do not support such a triggering mechanism."1196 Alany such cases are central cluster galaxies surrounded by massive haloes of hot. gas Clacdhunter.Fosbury.&Quinn1989:Baum.lHleckman&vanBreugel 1992).," Many such cases are central cluster galaxies surrounded by massive haloes of hot gas \citep{tadhunter89,baum92}."1197. Therefore the infall of warm/cool gas condensing from the hot X-rav haloes in cooling Lows has been been suggested. as an alternative trigger for the AGN activity (e.g.Bremer.Fabian&Crawford 1997)., Therefore the infall of warm/cool gas condensing from the hot X-ray haloes in cooling flows has been been suggested as an alternative trigger for the AGN activity \citep[e.g.][]{bremer97}.1198. In addition. based both on detailed: X- studies of individual objects and optical studies of large samples of low luminosity radio sources. the direct (Bondi) accretion of thefeof ISAT associated with the X-ray haloes has been proposed to explain the fuelling of weak line racio ealaxies (WLBG) in the local Universe (Bestetal.2005:ton2007:Buttiglioneetal. 2009).," In addition, based both on detailed X-ray studies of individual objects and optical studies of large samples of low luminosity radio sources, the direct (Bondi) accretion of the ISM associated with the X-ray haloes has been proposed to explain the fuelling of weak line radio galaxies (WLRG) in the local Universe \citep{best05,allen06,best06,hardcastle07,buttiglione10}."1199. Although the morphologies anc emission. line kinematics provide important information about the trigecring events. this information is generally. qualitative.," Although the morphologies and emission line kinematics provide important information about the triggering events, this information is generally qualitative."1200 For example. it is clillieult to use. such information to quantify when AGN are triggered in major galaxy mergers relative to the time of coalescence of the merging nuclei.," For example, it is difficult to use such information to quantify when AGN are triggered in major galaxy mergers relative to the time of coalescence of the merging nuclei."

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