ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 2009)., 2009).3An excess of quasar pairs on small scales naturally follows. [rom a merger origin lor quasar activitv. whether (hese pairs simply (race biased groups where mergers are likely (o occur (ILopkinsetal.2008) or are being excited in merging galaxies (Djorgovski1991:My-ersοἱal.,"An excess of quasar pairs on small scales naturally follows from a merger origin for quasar activity, whether these pairs simply trace biased groups where mergers are likely to occur \citep{Hopkins2007} or are being excited in merging galaxies \citep{Djorgovski, Myers07b}."4 2008).. Hopkinsetal.(2006). have developed a unified. mereer-cdriven [ramework that naturally predicts that quasar environments should be highlv biased (llopkins 2008).," \citet{Hopkins2006} have developed a unified, merger-driven framework that naturally predicts that quasar environments should be highly biased \citep{Hopkins2007}."5. These simulations show that major mergers between gas-rich galaxies are the likely mechanisms to trigger bright quasar activity. and Chat this activity is a phase in (lie evolution massive spheroidal galaxies (Hopkinsetal.2005.2008).," These simulations show that major mergers between gas-rich galaxies are the likely mechanisms to trigger bright quasar activity, and that this activity is a phase in the evolution of massive spheroidal galaxies \citep{Hopkins2005b, Hopkins2007}."6. In contrast. secular mechanisms mav fuel the activity in most low-Iuminosity AGN. implving that the small-scale environments of these objects should have a smaller bias (llopkins&llernquist 2008).," In contrast, secular mechanisms may fuel the activity in most low-luminosity AGN, implying that the small-scale environments of these objects should have a smaller bias \citep{HopkinsHernquist, Hopkins2007}."7. Therefore. we would expect that objects driven by major mergers will have biased environments on small scales. whereas objects Iueled by secular means will reside in less rich environments.," Therefore, we would expect that objects driven by major mergers will have biased environments on small scales, whereas objects fueled by secular means will reside in less rich environments."8 Such a simplification hides many subtleties. however. as secular mechanisms such as harassment ean probably only occur in slightly overdense environments.," Such a simplification hides many subtleties, however, as secular mechanisms such as harassment can probably only occur in slightly overdense environments."9 Further. for objects whose observed characteristics differ purely because of viewing angle or internal structure (Antonueci1993:Elvis2000).. there should be no particular dilference in local environment.," Further, for objects whose observed characteristics differ purely because of viewing angle or internal structure \citep{Antonucci, Elvis}, there should be no particular difference in local environment."10 This. of course. would only be the case if that structure is not correlated with fueling. as could occur. for instance. i£ more Iluminous quasars had strong winds.," This, of course, would only be the case if that structure is not correlated with fueling, as could occur, for instance, if more luminous quasars had strong winds."11 It is (herefore important to understand the relationship between the physical properties of AGN and their local environment. which will in (urn provide insight into what aspects of AGN properties are explained by formation history. feline. or simply by structure and orientation.," It is therefore important to understand the relationship between the physical properties of AGN and their local environment, which will in turn provide insight into what aspects of AGN properties are explained by formation history, fueling, or simply by structure and orientation."12 In this paper. we address this challenge by studying the nature of AGN environments.," In this paper, we address this challenge by studying the nature of AGN environments."13 We improve upon (he most recent SDSS study. Serberetal.(2006).. in several wavs.," We improve upon the most recent SDSS study, \citet{Serber}, in several ways."14" We use larger samples of background photometric galaxies. as well as larger. more recent samples of spectroscopic AGN,"," We use larger samples of background photometric galaxies, as well as larger, more recent samples of spectroscopic AGN."15 Our spectroscopic data is divided into four target samples: Type I and Type H quasars (e.g. AGN with the highest intrinsic huminositv) ancl lower-huninosity Type ] and Type II AGN.," Our spectroscopic data is divided into four target samples: Type I and Type II quasars (e.g., AGN with the highest intrinsic luminosity) and lower-luminosity Type I and Type II AGN."16 The spectra of Type | AGN and quasars are characterized by broad emission lines (FWIIM1000kinsτοις.2007). while the spectra of Type I] AGN and quasars exhibit narrow emission lines (e.g..Haoetal. 2003)..," The spectra of Type I AGN and quasars are characterized by broad emission lines \citep[FWHM $> 1000~\rm{km~s^{-1}}$;, while the spectra of Type II AGN and quasars exhibit narrow emission lines \citep[e.g.,][]{Haoa, Zakamska}."17 We compare (the overcensity of Type I quasars to the overcensily ol Type IL quasars as well as to lower Iuminositv Type I and Type II AGN., We compare the overdensity of Type I quasars to the overdensity of Type II quasars as well as to lower luminosity Type I and Type II AGN.18 Additionally. we include cuts in photometric redshift space around spectroscopic targets ancl the random positions (ο which thev are compared (o minimize interloping foreground or background objects. as well as marginalize over anv redshift evolution of the photometric galaxy sample.," Additionally, we include cuts in photometric redshift space around spectroscopic targets and the random positions to which they are compared to minimize interloping foreground or background objects, as well as marginalize over any redshift evolution of the photometric galaxy sample."19 By using photometric redshift cuts. we obtain more realistic overdensity estimates and errors. and we are able to extend the study of AGN environments in the SDSS to 0.6.," By using photometric redshift cuts, we obtain more realistic overdensity estimates and errors, and we are able to extend the study of AGN environments in the SDSS to $\leqslant$ 0.6."20"By comparison with equations (6)) and 7) one finds that δρυ OW),","By comparison with equations \ref{rho}) ) and \ref{omega}) ) one finds that _0^1 ), and _0^1 )."21 Thus. in general. any model of a rapidly rotating neutron star has an infinite number of mass- and current-multipole moments.," Thus, in general, any model of a rapidly rotating neutron star has an infinite number of mass- and current-multipole moments."22 In order to match an analytic exterior metric to a numerically-computed interior metric and to check the accuracy of the matching procedure. we computed the mass-quadrupole moment M» and the current-octupole moment 53.," In order to match an analytic exterior metric to a numerically-computed interior metric and to check the accuracy of the matching procedure, we computed the mass-quadrupole moment $M_2$ and the current-octupole moment $S_3$."23 An ulternative. asymptotic method. for evaluating the multipole moments was introduced by Laarakkers Poisson (1997).," An alternative, asymptotic method for evaluating the multipole moments was introduced by Laarakkers Poisson (1997)."24 We also used their method in order to cross-check the results obtained from the integral relations (22)) and (225)., We also used their method in order to cross-check the results obtained from the integral relations \ref{Mn}) ) and \ref{Sn}) ).25" The idea. in this case. is to evaluate numerically the coefficient of Pr,(40) in the general expression for (6)) - or analogously. the coefficient of Pl in (173) - at the outermost grid points (.e.. as r eo), and multiply the result by the appropriate factor (containing powers of ry that can be obtained from equations (27)) and (28)."," The idea, in this case, is to evaluate numerically the coefficient of $P_{2n}(\mu)$ in the general expression for \ref{rho}) ) - or analogously, the coefficient of $P_{2n-1}^1$ in \ref{omega}) ) - at the outermost grid points (i.e., as $r\to \infty$ ), and multiply the result by the appropriate factor (containing powers of $r$ ) that can be obtained from equations \ref{rhotilde}) ) and \ref{omegatilde}) )."26 We have checked that the two methods typically agree to better than one part in 107., We have checked that the two methods typically agree to better than one part in $10^3$.27" The equilibrium solutions for a given EOS form a two-parameter ""amily.", The equilibrium solutions for a given EOS form a two-parameter family.28 In particular. equilibrium solutions are bounded by our limit sequences.," In particular, equilibrium solutions are bounded by four limit sequences."29" These limits are shown in Figure l.. which displays the gravitational mass A vs. the central energy density €,. or one the EOSs derived by Akmal. Pandharipande and Ravenhall (1998. henceforth APR)."," These limits are shown in Figure \ref{StaticKepler}, which displays the gravitational mass $M$ vs. the central energy density $\epsilon_c$ for one the EOSs derived by Akmal, Pandharipande and Ravenhall (1998, henceforth APR)."30 As an illustrative example we consider he APR EOS which does not include boost interactions (we refer o the original paper for details)., As an illustrative example we consider the APR EOS which does not include boost interactions (we refer to the original paper for details).31 The qualitative picture does not change when we consider other EOSs (see eg., The qualitative picture does not change when we consider other EOSs (see eg.32 CST. where slots are presented for a representative sample of EOSs).," CST, where plots are presented for a representative sample of EOSs)."33 The solid line is the limit - that is. the sequence of nonrotating solutions to the standard Tolman-Oppenheimer-Volkoff equations.," The solid line is the limit - that is, the sequence of nonrotating solutions to the standard Tolman-Oppenheimer-Volkoff equations."34 The long-dashed line is the (Kepler) limit. which is determined by the condition that the centrifugal force exactly balances the gravitational attraction at the stellar equator. in which case a fluid element on the equator has the same angular velocity as a free particle ina Keplerian orbit at the same location.," The long-dashed line is the (Kepler) limit, which is determined by the condition that the centrifugal force exactly balances the gravitational attraction at the stellar equator, in which case a fluid element on the equator has the same angular velocity as a free particle in a Keplerian orbit at the same location."35 Both sequences terminate at high central density at the limit. where equilibrium solutions are marginally stable to axisymmetric perturbations: and they terminate at low central densities at the limit. below which a neutron star cannot form (not shown in Figure 1).," Both sequences terminate at high central density at the limit, where equilibrium solutions are marginally stable to axisymmetric perturbations; and they terminate at low central densities at the limit, below which a neutron star cannot form (not shown in Figure \ref{StaticKepler}) )."36 Within the class of stable equilibrium solutions. CST pointed out the significance of constant rest-mass sequences. called.sequences. since an isolated neutron star. slowly losing energy and angular momentum via some dissipative process (e.g. electromagnetic emission or gravitational-wave radiation). must evolve conserving the total baryon number. and hence its rest mass Mp.," Within the class of stable equilibrium solutions, CST pointed out the significance of constant rest-mass sequences, called, since an isolated neutron star, slowly losing energy and angular momentum via some dissipative process (e.g. electromagnetic emission or gravitational-wave radiation), must evolve conserving the total baryon number, and hence its rest mass $M_B$."37 An accreting neutron star in a binary system will not evolve along a constant rest-mass sequence: the actual sequence depends on several parameters. such as the magnetic field. accretion rate ete.," An accreting neutron star in a binary system will not evolve along a constant rest-mass sequence: the actual sequence depends on several parameters, such as the magnetic field, accretion rate etc."38 Nevertheless. the constant rest-mass sequences in CST have been used in the past in evaluating the accuracy of analytic exterior solutions and we will also use them here solely for the same reason.," Nevertheless, the constant rest-mass sequences in CST have been used in the past in evaluating the accuracy of analytic exterior solutions and we will also use them here solely for the same reason."39 We compute three constant rest-mass sequences for each EOS: We include the following set of EOSs., We compute three constant rest-mass sequences for each EOS: We include the following set of EOSs.40 For comparison with CST we include EOSs A. AU. FPS and L. We refer to their paper or an extensive discussion of each EOS.," For comparison with CST we include EOSs A, AU, FPS and L. We refer to their paper for an extensive discussion of each EOS."41" We supplement the set of EOSs considered by CST with a relatively new model: the model derived by Akmal. Pandharipande and Ravenhall (1998) rom Hamiltonian many-body theories of nuclear matter. including boost corrections in the Hamiltonian ¢henceforth. we will refer to his model as APR-b. where ""b"" stands for “boosted”)."," We supplement the set of EOSs considered by CST with a relatively new model: the model derived by Akmal, Pandharipande and Ravenhall (1998) from Hamiltonian many-body theories of nuclear matter, including boost corrections in the Hamiltonian (henceforth, we will refer to this model as APR-b, where “b” stands for “boosted”)."42 In Tables (1-—5)) we give numerical results for the structure woperties of the models we have computed., In Tables \ref{EOSA}- \ref{EOSAPRb})) we give numerical results for the structure properties of the models we have computed.43 All models have been computed using a resolution of (301 angular points) x (601 radial »oints). corresponding to a typical accuracy of at least one part in10 in all quantities.," All models have been computed using a resolution of $301$ angular points) $\times$ $601$ radial points), corresponding to a typical accuracy of at least one part in$10^3$ in all quantities."44" Each Table corresponds to a constant rest mass sequence. and lists: the total central energy density ει in units of LO &  the angular velocity €2 in units of 10° I: the moment of inertia / in units of 107? ¢ em?(for rotaing models only): the gravitational mass M in solar masses: the ratio of rotational kinetic energy to gravitational binding energy Z/W: the equatorial circumferential radius of the star A, in km and the height (in. km) of corotating 07 ) and counterrotating Cr} ISCOs from the surface of the star Gf an ISCO does not exist. the corresponding entry is omitted)."," Each Table corresponds to a constant rest mass sequence, and lists: the total central energy density $\epsilon_c$ in units of $10^{15}$ g $^{-3}$; the angular velocity $\Omega$ in units of $10^3$ $^{-1}$; the moment of inertia $I$ in units of $10^{45}$ g $^2$(for rotating models only); the gravitational mass $M$ in solar masses; the ratio of rotational kinetic energy to gravitational binding energy $T/W$; the equatorial circumferential radius of the star $R_e$ in km and the height (in km) of corotating $h_+$ ) and counterrotating $h_-$ ) ISCOs from the surface of the star (if an ISCO does not exist, the corresponding entry is omitted)."45 The height of an ISCO is defined as the difference between the circumferential radius at the ISCO and the circumferential equatorial radius of the star., The height of an ISCO is defined as the difference between the circumferential radius at the ISCO and the circumferential equatorial radius of the star.46 The next three columns give the first few physical multipoles in geometrized units of c=GI: namely. we list the mass quadrupole moment M» Qin km. the angular momentum SJ in km?*. and the current octupole moment 53 in kit.," The next three columns give the first few physical multipoles in geometrized units of $c=G=1$: namely, we list the mass quadrupole moment $M_2\equiv Q$ in $^3$ , the angular momentum $S_1 \equiv J$ in $^2$ , and the current octupole moment $S_3$ in $^4$ ."47 We have checked our code by reproducing the quadrupole moments computed by Laarakkers Poisson and found excellent agreement., We have checked our code by reproducing the quadrupole moments computed by Laarakkers Poisson and found excellent agreement.48 The accuracy in computing, The accuracy in computing49due to the 25 process is expected since the upward process is suppressed by a factor of 1/131.,due to the $\gamma$ process is expected since the upward process is suppressed by a factor of 1/137.50 The change is especially noticeable in Model D. It is at à Lairly low optical depth where the change in the rates observed but this is also the optical depth where the optical depth of the Balmer line is high (?).., The change is especially noticeable in Model B. It is at a fairly low optical depth where the change in the rates observed but this is also the optical depth where the optical depth of the Balmer line is high \citep{soma09}.51 This wavelength regime is similar to what is described in ?.., This wavelength regime is similar to what is described in \citet{soma09}.52" The net photo-onization rate (2?,) does not change signilicantlv between clilferent bound states in both Models A and B (see Figures 8. and 9)).", The net photo-ionization rate $P_{n}$ ) does not change significantly between different bound states in both Models A and B (see Figures \ref{photo_A} and \ref{photo_B}) ).53" Although in the case (case D). 2, increases bv. almost a [actor of 10 [rom the lowest energy bound state to the higher energv bound states (except for the states very. close to the continua) at low optical depths τω«0.01)."," Although in the multi-level case (case B), $P_{n}$ increases by almost a factor of 10 from the lowest energy bound state to the higher energy bound states (except for the states very close to the continuum) at low optical depths $\tau_{std} <0.01$ )."54 Figures I0. and 11. show the escape probability for Models A and D respectively.," Figures \ref{esc_A}55 and \ref{esc_B} show the escape probability for Models A and B respectively."56 The trend is very similar to that of Models C and D. The collisional de-excitation rate increases with increasing optical depths in both the Models € and D To summarize: our findings on Models A and D (pure hydrogen models) 1) For most optical depth regimes. the basic trend in the rates is similar to Models C and D. 2)The 25 process seems (o have a significant effect in both Model A and D (at lower 744).," The trend is very similar to that of Models C and D. The collisional de-excitation rate increases with increasing optical depths in both the Models C and D To summarize: our findings on Models A and B (pure hydrogen models) 1) For most optical depth regimes, the basic trend in the rates is similar to Models C and D. 2)The $\gamma$ process seems to have a significant effect in both Model A and B (at lower $\tau_{std}$ )."57 The elleet is much larger for Model D. This effect was not seen in Models C and D. We observe the following. for almost all optical depths. For Models B and D.," The effect is much larger for Model B. This effect was not seen in Models C and D. We observe the following, for almost all optical depths, For Models B and D,"58Reeall |J] that the dilation group is represented on %by wih f€ 2.7€ Rand x€R.,"Recall \cite{Jen} that the dilation group is represented on $\H$by with $f \in \H$, $\tau \in \R$ and $x \in \R$."59 Its sell-adjoint generator A is formally given by SiVV+VA). where X is the position operator and V—αν.," Its self-adjoint generator $A$ is formally given by $\hbox{$ $}(X\nabla + \nabla X)$, where $X$ is the position operator and $\nabla = \frac{d}{dx}$."60 These operators are all essentially self-adjoint on SUR)., These operators are all essentially self-adjoint on $\SS(\R)$.61 It is easily observed (hat the formal equality FAF*=-A holds., It is easily observed that the formal equality $\F\;\!A\;\!\F^*=-A$ holds.62 More precisely.lor any. essentially bounded. function y on KR. one has ολ=g(—4).," More precisely,for any essentially bounded function $\varphi$ on $\R$ , one has $\F\varphi(A)\F^* = \varphi(-A)$."63" Furthermore. since A acts only on the racial coordinate. the operator (4) leaves ος and %, invariant."," Furthermore, since $A$ acts only on the radial coordinate, the operator $\varphi(A)$ leaves $\H_\e$ and $\H_\o$ invariant."64 For that reason. we can consider a slightly more complicated operator than 42:(1).," For that reason, we can consider a slightly more complicated operator than $\varphi(A)$."65" Let 4. 42, be (vo essentially bounded functions on R."," Let $\varphi_\e$, $\varphi_\o$ be two essentially bounded functions on $\R$ ."66" Then vl):4—2 defined on ος by 42,01) and on 4%, by 45,61). is à bounded operalor.", Then $\varphi(A):\H \to \H$ defined on $\H_\e$ by $\varphi_\e(A)$ and on $\H_\o$ by $\varphi_\o(A)$ is a bounded operator.67 We [ist state a result about the Mellin (transform., We first state a result about the Mellin transform.68It is widely believed that many astrophysical objects are powered by mass accretion on to black holes.,It is widely believed that many astrophysical objects are powered by mass accretion on to black holes.69 The standard geometrically —un. optically thick accretion dise model can successfully explain most of the observational features in active galactic nuclei (AGN) and X-ray binaries (Shakura&Sunyaev1973).," The standard geometrically thin, optically thick accretion disc model can successfully explain most of the observational features in active galactic nuclei (AGN) and X-ray binaries \citep{s1973}."70. In the standard thin model. the motion of the matter in the accretion dise is nearly Keplerian. and the gravitational energy released in the dise is radiated away locally.," In the standard thin model, the motion of the matter in the accretion disc is nearly Keplerian, and the gravitational energy released in the disc is radiated away locally."71 An alternative accretion dise model. namely. the advection-dominated accretion flow (ADAF) model. was suggested for the black holes accreting at very low rates (Iehimaru1977:Narayan&Yi199-4).," An alternative accretion disc model, namely, the advection-dominated accretion flow (ADAF) model, was suggested for the black holes accreting at very low rates \citep{1977ApJ...214..840I,n1994}."72. In the ADAF model. only a small fraction of the gravitational energy released in the accretion flow is radiated away due to inefficient cooling. and most of the energy 1s stored in the accretion flow and advected to the black hole.," In the ADAF model, only a small fraction of the gravitational energy released in the accretion flow is radiated away due to inefficient cooling, and most of the energy is stored in the accretion flow and advected to the black hole."73 The ADAFs are optically thin and hot (comparable with the virial temperature of the gases in the flows). which radiate mostly in X-ray waveband (seeNarayan&McClintock2008.forareviewandreferences therein)...," The ADAFs are optically thin and hot (comparable with the virial temperature of the gases in the flows), which radiate mostly in X-ray waveband \citep*[see][for a review and74references therein]{2008NewAR..51..733N}."75 This model can successfully explain the main observational features of blackhole X-ray binaries and low-luminosity AGN (LLAGN) (e.g...Narayan&Yi1994.995a:Gam-mieetal.1999:QuataertYuan2003:Ho 2005).," This model can successfully explain the main observational features of blackhole X-ray binaries and low-luminosity AGN (LLAGN) \citep*[e.g.,][]{n1994,n1995a,g1999,q1999,y2003,h2008}."76 As the Bernoulli parameter of an ADAF is positive. the ADAF is likely to have an outflow. which was confirmed by numerical simulations and also supported by observations2003).," As the Bernoulli parameter of an ADAF is positive, the ADAF is likely to have an outflow, which was confirmed by numerical simulations and also supported by observations."77. Blandford&Begelman(1999) proposed a self-similar advection-dominated inflow-outflow solution (ADIOS) for the ADAF with winds., \citet{b1999} proposed a self-similar advection-dominated inflow-outflow solution (ADIOS) for the ADAF with winds.78 In ADIOS model. the mass accretion rate is no longer a constant and is assumed to be a power-law dependence of radius 6x(07.0«s 1. which is an important ingredient in most of the follow-up works (e.g.Quataert&Narayan1999: 2005).," In ADIOS model, the mass accretion rate is no longer a constant and is assumed to be a power-law dependence of radius $\dot{m}\propto{r^{s}}, 0<s<1$ ), which is an important ingredient in most of the follow-up works \citep*[e.g.,][]{q1999b,y2003,x2005}."79. Motivated by the results of numerical simulations on accretion discs. Xie&Yuan(2008) investigated the influence of outflows on the accretion flow based on a 1.5-dimensional description of the accretion flow.," Motivated by the results of numerical simulations on accretion discs, \citet{x2008} investigated the influence of outflows on the accretion flow based on a 1.5-dimensional description of the accretion flow."80 They suggested that their solutions can be described by a power-law r- mass accretion rate fairly well., They suggested that their solutions can be described by a power-law $r$ -dependent mass accretion rate fairly well.81 Magnetic fields are believed in accretion flows. and the magnetorotational instability (MRI) provides the source of viscosity in accretion flows (Balbus&Hawley1991.1998).," Magnetic fields are believed in accretion flows, and the magnetorotational instability (MRI) provides the source of viscosity in accretion flows \citep{b1991,b1998}."82. The outflows/Jets can be driven by the large-scale ordered magnetic fields threading the accretion dise (Blandford&Payne1952)., The outflows/jets can be driven by the large-scale ordered magnetic fields threading the accretion disc \citep{b1982}.83. The physics of magnetically accelerated outflows has been extensively explored in many previous works (e.g.Cao&Spruit1994:Narayan 2007a.b)..," The physics of magnetically accelerated outflows has been extensively explored in many previous works \citep*[e.g.,][]{1994A&A...287...80C,c2002a,1995ApJ...452L..41K,841999ApJ...522..727K,2002ApJ...565.1035K,1998ApJ...499..329O,2001ApJ...553..158O,2007MNRAS.375..548N,2007MNRAS.375..513M,2007MNRAS.375..531M}."85 Such outflows/jets magnetically driven from the accretion discs provide an efficient angular momentum loss mechanism for accretion dises (seeSpruit2008.forareviewand therein)...," Such outflows/jets magnetically driven from the accretion discs provide an efficient angular momentum loss mechanism for accretion discs \citep*[see][for a review and references86therein]{2008arXiv0804.3096S}. ."87 The structure of a standard thin disc/ADAF may be altered by the magnetically driven outflows, The structure of a standard thin disc/ADAF may be altered by the magnetically driven outflows88described iu Ruszkowskietal.(2007) and Durs&Pfronuuer (2008). where the draping is caused by subsonic bubble motions.,"described in \citet{ruszkowski07} and \citet{dursi08}, where the draping is caused by subsonic bubble motions."89 Clearly. MIID Njet simulations. which are bevoud the scope of the cure paper. would be very helpful iu understanding the evolutiou of the magnetic field topology near the bubble surface.," Clearly, MHD jet simulations, which are beyond the scope of the current paper, would be very helpful in understanding the evolution of the magnetic field topology near the bubble surface."90 To accurately study CR diffusion during the jet/bubble evolution. we need to rely upou future maenetolvdrodvuamic CMIID) snuulations with anisotropic CR. diffusion.," To accurately study CR diffusion during the jet/bubble evolution, we need to rely upon future magnetohydrodynamic (MHD) simulations with anisotropic CR diffusion."91" ILowever. within our current methodology, we can still explore the role of CR diffusion on the CR distribution poteurialiu the bubble interior."," However, within our current methodology, we can still explore the potential role of CR diffusion on the CR distribution in the bubble interior."92" To this end. here we present three additional runs VOdil. W3-ditts. aud VW3-datt6. im which we luerease the value of diffusivity in the IhTale interior to LN—14105,3 CR«10275 and G«1025 eni? st respectively(see Table 1 for other model parameters)."," To this end, here we present three additional runs V3-diff1, V3-diff3, and V3-diff6, in which we increase the value of CR diffusivity in the bubble interior to $\kappa_{\rm int} =1\times10^{28}$, $3\times10^{28}$ and $6\times10^{28}$ $^{2}$ $^{-1}$ respectively (see Table 1 for other model parameters)."93 We distinguish thebubble interior (p« poc) from the outside regions (p2 Pair) surrounding the expanding bubble bv a deusity criterion. as the CR bubble is SCxwated from the simroundius halo eas through a contact discontinuity. across which thermal gas deusitv increases abruptly (see the bottom of Fig. 1)).," We distinguish the bubble interior $\rho < \rho_{\rm crit}$ ) from the outside regions $\rho \geq \rho_{\rm crit}$ ) surrounding the expanding bubble by a density criterion, as the CR bubble is separated from the surrounding halo gas through a contact discontinuity, across which thermal gas density increases abruptly (see the bottom panel of Fig. \ref{plot1}) )."94 We use page to identify gas inside thepanelbubbles (low p. ugh s) from ambient shocked gas (high p. low &).," We use $\rho_{\rm crit}$ to identify gas inside the bubbles (low $\rho$, high $\kappa$ ) from ambient shocked gas (high $\rho$, low $\kappa$ )."95 Since in our iodel there are esscutially uo CRs outside the nmbbles. the low CR diffusivity there ouly suppress CR diffusion across thebubble surface.," Since in our model there are essentially no CRs outside the bubbles, the low CR diffusivity there only suppresses CR diffusion across the bubble surface."96 As thebubble spans quickly. the thermal gas deusitv within the mbhle drops.," As the bubble expands quickly, the thermal gas density within the bubble drops."97" Therefore. the critical density (ρω) identifving the bubble interior should also drop with iue,"," Therefore, the critical density $\rho_{\rm crit}$ ) identifying the bubble interior should also drop with time."98 We choose pair to be twice the voluue-averaged hermal gas density along the jet Daxis within the CR mbble at any time curing the e evolution., We choose $\rho_{\rm crit}$ to be twice the volume-averaged thermal gas density along the jet axis within the CR bubble at any time during the bubble evolution.99 Such a crude method produces acceptable results. as clearly seen in the top panels of Figure 6.. which shows spatial distributions of CR energw deusitv at tf=tram lu ruus VOR. οαν aud W3-dift6.," Such a crude method produces acceptable results, as clearly seen in the top panels of Figure \ref{plot6}, which shows spatial distributions of CR energy density at $t=t_{\rm Fermi}$ in runs V3-diff1, V3-diff3, and V3-diff6."100 The edges of the resulting bubbles are as sharp as in the low-diffusivity run V3. and thebubble morphology is also simular in all these ruus.," The edges of the resulting bubbles are as sharp as in the low-diffusivity run V3, and the bubble morphology is also similar in all these runs."101 This is consistent with what we would expect. since CR diffusion is only increased in thebubble interior while still significantly suppressed across the bubble surface.," This is consistent with what we would expect, since CR diffusion is only increased in the bubble interior while still significantly suppressed across the bubble surface."102 As the deusity jum across thebubble surfaceis quite large. our results are not sensitive to the specific value of po.," As the density jump across the bubble surface is quite large, our results are not sensitive to the specific value of $\rho_{\rm crit}$."103 CR diffusion transports CRs near bubble edees to the bubble interior. particularly during carly times when the size of the bubbleis all.," CR diffusion transports CRs near bubble edges to the bubble interior, particularly during early times when the size of the bubble is small."104 The typical leneth that CRs diffuse within a duration of £ is P—kt: As lnereascs. the CR distribution within the nibbles .becomes less Bnub-brigliteued aud more ταΓον]. as clearly secu iu the top panels of Figure 6 (frou left o right}.," The typical length that CRs diffuse within a duration of $t$ is $l\sim \sqrt{\kappa t}$: As $\kappa_{\rm int}$ increases, the CR distribution within the bubbles becomes less limb-brightened and more uniform, as clearly seen in the top panels of Figure \ref{plot6} (from left to right)."105 The bottom panels of Figure 6 show the inc-of-ght projected CR energy deusitv in ruus VW3-diffl. W3-ditt3. and W3-ditt m Galactic coordinates at t= fang.," The bottom panels of Figure \ref{plot6} show the line-of-sight projected CR energy density in runs V3-diff1, V3-diff3, and V3-diff6 in Galactic coordinates at $t=t_{\rm Fermi}$ ."106 In run V3-diffl with was=1 ο. he distribution of projected CR energy. deusitv is still nub-brightened. simular to the low-diffusivitv run V3.," In run V3-diff1 with $\kappa_{\rm int} =1\times10^{28}$ $^{2}$ $^{-1}$, the distribution of projected CR energy density is still limb-brightened, similar to the low-diffusivity run V3."107" But in uus V3-dift3 aud V3-diffG with kg=3107 aud S18 cur s| respectively, the projected CR energy density distribution becomes very flat high latitude (b]= 307). consistent with the gamma-ray observations of the Fermbubbles."," But in runs V3-diff3 and V3-diff6 with $\kappa_{\rm int} =3\times10^{28}$ and $6\times10^{28}$ $^{2}$ $^{-1}$ respectively, the projected CR energy density distribution becomes very flat at high latitude $|b|\gtrsim 30^{\circ}$ ), consistent with the gamma-ray observations of the bubbles."108 This can also be seen in Figure 7.. which shows longitudinal variations of the line-of-sight xojected CR energydeusity iun run VOdiff) at f=fgg at three latitudes: b=207. 30°. 107.," This can also be seen in Figure \ref{plot7}, which shows longitudinal variations of the line-of-sight projected CR energy density in run V3-diff3 at $t=t_{\rm Fermi}$ at three latitudes: $b=20^{\circ}$, $30^{\circ}$, $40^{\circ}$."109 At lower latitude. he projected CR energy density is slelthy lower. but ueher ISRF intensities there could boost the σαΤΝ IC cuussivity.," At lower latitude, the projected CR energy density is slightly lower, but higher ISRF intensities there could boost the gamma-ray IC emissivity."110 The fatuess of the gamma rav inteusity with latitude. which ueeds to be further corroborated wo three-vear or longer observations. secs to require a fine-tuning of the latitudinal distribution of CR particles.," The flatness of the gamma ray intensity with latitude, which needs to be further corroborated by three-year or longer observations, seems to require a fine-tuning of the latitudinal distribution of CR particles."111" The effects of non-uniform, ISRF on the xojected. gamma-ray intensity will be explored in future work.", The effects of non-uniform ISRF on the projected gamma-ray intensity will be explored in future work.112 Iu the discussions above. we have mainly considered Cala rav enussious due to CR electrons through IC It," In the discussions above, we have mainly considered gamma ray emissions due to CR electrons through IC scattering."113 CR protons are also preseut in the bubbles. raftertusethey will also produce eamuna ray enissions.," If CR protons are also present in the bubbles, they will also produce gamma ray emissions."114 It vet unclear if the eauna ray emission frou the 5bubbles is dominated by CR clectrous or protons (Dobleretal. 2000: Crocker&Aharonian 2011))., It is yet unclear if the gamma ray emission from the bubbles is dominated by CR electrons or protons \citealt{dobler10}; \citealt{crocker11}) ).115 The lne-of projections of pes at ffg Wa runs V3 and V3-ci3 shown in Fieure 8. judicate that im these viscous ruus (also seen in rus V3-diffl aud V3-«diff6) the eamuna-rav surfacebrielituess contributedby CR protous peaks at thebubble edge. where the jet backflow is located.," The line-of-sight projections of $\rho e_{\rm c}$ at $t=t_{\rm Fermi}$ in runs V3 and V3-diff3 shown in Figure \ref{plot8} indicate that in these viscous runs (also seen in runs V3-diff1 and V3-diff6) the gamma-ray surface brightness contributed by CR protons peaks at the bubble edge, where the jet backflow is located."116 This edge concentration occurs Mcause the thermal gas density in the jet backflow is much higher than that iu he expanding |»bble interior. as seen in the bottom uel of Figure 1..," This edge concentration occurs because the thermal gas density in the jet backflow is much higher than that in the expanding bubble interior, as seen in the bottom panel of Figure \ref{plot1}."117 The sas deusity in the N backflow is mainly deteriuuedby the initial jet density. which is ιο well constrained i our eurreut model(see Section 3.3 aud3.l of Paper D.," The gas density in the jet backflow is mainly determined by the initial jet density, which is not well constrained in our current model (see Section 3.3 and 3.4 of Paper I)."118 But some level of fine-tuning of he initial jet density may be required if the relatively Ha ezunna-ray surface brightness is dominated by CR ootons I our viscous jet scenario., But some level of fine-tuning of the initial jet density may be required if the relatively flat gamma-ray surface brightness is dominated by CR protons in our viscous jet scenario.119 Furtherstudies are required to investigate if the eamuna rav enissionu of the Fornibubbles is dominatedby CR electrons or protons. whichis bevoud the scope of the current paper.," Furtherstudies are required to investigate if the gamma ray emission of the bubbles is dominated by CR electrons or protons, which is beyond the scope of the current paper."120fraction of this radiation leaves host halos or how this radiation is being deposited into the IGM.,fraction of this radiation leaves host halos or how this radiation is being deposited into the IGM.121 In the past [ew vears. a number of diflerent. techniques for practical solution of the 3D RT equation have been suggested.," In the past few years, a number of different techniques for practical solution of the 3D RT equation have been suggested."122 Among the first. filly numerical works. Umenmura. Nakamoto. Susa (1993) calculated reionization of a cosmological volume by a uniform UV backeround from z—9 to z—4. solving the full 3D quasi-static RT equation on a massively parallel architecture at very high numerical resolution. 128*x128? (spatial x angular). using the method of short characteristics.," Among the first fully numerical works, Umemura, Nakamoto, Susa (1998) calculated reionization of a cosmological volume by a uniform UV background from $z\,{=}\,9$ to $z\,{=}\,4$, solving the full 3D quasi-static RT equation on a massively parallel architecture at very high numerical resolution, $128^3\times 128^2$ (spatial $\times$ angular), using the method of short characteristics."123 However. their caleulations show that direct integration al full angular resolution is very costly. requiring as much as ~LOO hours to reconstruct a snele snapshot on 256 processors.," However, their calculations show that direct integration at full angular resolution is very costly, requiring as much as $\sim 100$ hours to reconstruct a single snapshot on 256 processors."124 Abel. Norman. Alaclan (1999) developed a ταν tracing algorithm lor radial RT around point sources which conserves energy explicitlv. ancl (hus eives (he right speed of lonization fronts (hereafter I-Ironts).," Abel, Norman, Madau (1999) developed a ray tracing algorithm for radial RT around point sources which conserves energy explicitly, and thus gives the right speed of Ionization fronts (hereafter I-fronts)."125 However. in its original form (his aleorithim will work only for a small number of sources. since ils operation count goes as OQCNxNa). Where NV is the number of grid cells or particles in the volume. and ιο is the number of sources.," However, in its original form this algorithm will work only for a small number of sources, since its operation count goes as ${\cal O}(N\times N_{\rm src})$, where $N$ is the number of grid cells or particles in the volume, and $N_{\rm src}$ is the number of sources."126 Abel&Wandelt(2001). have modified this algorithm. introducing trees of rax segments which recursively split into sub-seements as one goes larther away Irom the source. resulting in a significant speed up of caleulations.," \citet{abel01} have modified this algorithm, introducing trees of ray segments which recursively split into sub-segments as one goes farther away from the source, resulting in a significant speed up of calculations."127 Razowumov&Scott(1999). have developed a different technique which is essentially à poor mans solution to the 5D (three spatial coordinates and (wo angles) adwection equation designed to work [or both point sources and (he diffuse flux., \citet{razoumov99} have developed a different technique which is essentially a poor man's solution to the 5D (three spatial coordinates and two angles) advection equation designed to work for both point sources and the diffuse flux.128 Unfortunately. it requires one to store the 5D intensity. hence. (his technique is limited to very. low angular resolution making it currently impractical for hieh-resolution cosmological simulations.," Unfortunately, it requires one to store the 5D intensity, hence, this technique is limited to very low angular resolution making it currently impractical for high-resolution cosmological simulations."129 Recently. Ciardietal.(2001) implemented a [fast Monte Carlo RT method (ο study propagation of E-fronts around a proto-galaxv al 2=12 showing that reasonable integration limes are possible [ου a single source.," Recently, \citet{ciardi01} implemented a fast Monte Carlo RT method to study propagation of I-fronts around a proto-galaxy at $z=12$ showing that reasonable integration times are possible for a single source."130 Further numerical and analytical studies of reionization are discussed in a comprehensive review by Loeb Barkana (2001)., Further numerical and analytical studies of reionization are discussed in a comprehensive review by Loeb Barkana (2001).131 since all of these techniques (av (to use a lair sampling of the multidimensional phase space to directly solve the 3D RT problem. thev tend to take at least O(.N7) operations.," Since all of these techniques try to use a fair sampling of the multidimensional phase space to directly solve the 3D RT problem, they tend to take at least ${\cal O}(N^2)$ operations."132 Two notable exceptions are the local optical depth approximation (Gnedin Ostriker 1997). requiring QN) operations. aud (he explicit moment solverOTVET (optically thin variable Eddington tensor formalism) of Gnedin Abel (2001). reducing the operation count to O(Nlog.N).," Two notable exceptions are the local optical depth approximation (Gnedin Ostriker 1997), requiring ${\cal O} (N)$ operations, and the explicit moment solver (optically thin variable Eddington tensor formalism) of Gnedin Abel (2001), reducing the operation count to ${\cal O}(N\log N)$."133 The local optical depth approximation. however. does not calculate the optical depth between (wo points (the emitter and the point where the radiation fiekl is to be computed). replacing it instead with local quantities. and (hus making it possible to compute the radiation field with a [ast gravity solver. in (his drastic approximation at least.," The local optical depth approximation, however, does not calculate the optical depth between two points (the emitter and the point where the radiation field is to be computed), replacing it instead with local quantities, and thus making it possible to compute the radiation field with a fast gravity solver, in this drastic approximation at least."134 The explicit moment solver (Gnecin Abel 2001) retains the time derivative of the RT equation and solves lLvperbolic (advection) moment equations. assuming that the geometry of the," The explicit moment solver (Gnedin Abel 2001) retains the time derivative of the RT equation and solves hyperbolic (advection) moment equations, assuming that the geometry of the"135We have adopted the Abia.Isern&Canal(1995) chemical evolution package. in order to follow the evolution of some isotopes over time.,"We have adopted the \citet{abi95} chemical evolution package, in order to follow the evolution of some isotopes over time."136 Current knowledge of star formation history al very early epochs in the evolution of the universe is very. limited (Steideletal.1996:Hopkins.Connolly&Szalay 2000).," Current knowledge of star formation history at very early epochs in the evolution of the universe is very limited \citep{ste99, mad96, hop00}."137. The best estimate available al present indicates a roughly constant star formation activity between z~1—4 but no data exists for z>5., The best estimate available at present indicates a roughly constant star formation activity between $z\sim 1-4$ but no data exists for $z>5$.138 Therefore. as it is usually done. we have assumed a star lormation rate proportional to the comoving gas density c0)=aptgasυπ(1). where a=2 Lis the aslration parameter anc =1.," Therefore, as it is usually done, we have assumed a star formation rate proportional to the comoving gas density $\psi(t)=\alpha \rho_{gas}^n(t)$, where $\alpha= 2$ $^{-1}$ is the astration parameter and $n=1$."139 Note that the computed abundance ratios [N/Y] are nearly insensitive to the adopted star formation rate but (μον do depend upon the stellar vields and ou (he IMF adopted., Note that the computed abundance ratios [X/Y] are nearly insensitive to the adopted star formation rate but they do depend upon the stellar yields and on the IMF adopted.140 In fact. parallel caleulations with other a and 7 values were made io ensure that our calculations were not dependent upon these parameters.," In fact, parallel calculations with other $\alpha$ and $n$ values were made to ensure that our calculations were not dependent upon these parameters."141 As mentioned previously. we have followed the evolution of the abundance ratios for 10 vr [rom the onset of the primordial star formation.," As mentioned previously, we have followed the evolution of the abundance ratios for $10^8$ yr from the onset of the primordial star formation."142 We have not considered (he role plaved by tvpe Ia supernovae since these objects are usually thought to come from longer lifetime progenitors., We have not considered the role played by type Ia supernovae since these objects are usually thought to come from longer lifetime progenitors.143 In any case. decisions regarding of the IMF and the law for the star formation rate have. however. important consequences for the present-day (pe Ia SN rate (see Canal. Isern ]tuiz-Lapuente 1997).," In any case, decisions regarding of the IMF and the law for the star formation rate have, however, important consequences for the present-day type Ia SN rate (see Canal, Isern Ruiz-Lapuente 1997)."144 The stellar lifetimes have been obtained bv means of the same models used to derive the stellar vields., The stellar lifetimes have been obtained by means of the same models used to derive the stellar yields.145 The computed stellar models extend [rom the pre-main sequence until the thermally pulsing AGB phase for the IMS. or until the Si-melting in {he massive star range.," The computed stellar models extend from the pre-main sequence until the thermally pulsing AGB phase for the IMS, or until the Si-melting in the massive star range."146 For VMOs we have extrapolated our numerical lifetime-stellar mass relation (o the corresponding mass range., For VMOs we have extrapolated our numerical lifetime-stellar mass relation to the corresponding mass range.147 For example. the lifetimes of stars with initial masses of 4. 25 and 120 M. are 114. 7.8 and 1 Myr. respectively.," For example, the lifetimes of stars with initial masses of 4, 25 and 120 $_\odot$ are 114, 7.8 and 1 Myr, respectively."148 Due to the very, Due to the very149ol state αἱ las well as uw«] we start with the Lagrangian (Carrollοἱal.2003) pud2 apd. where the positive sign in front of the kinetic term. corresponds to dwl solutions and the negative sign to [E1. DIESE V. ? valo aud dots denote normal time derivatives.,"of state $w>-1$ as well as $w<-1$ we start with the Lagrangian \citep{Carroll:2003st}150 = )^2 -, where the positive sign in front of the kinetic term corresponds to $w>-1$ solutions and the negative sign to $w<-1$, = ^2 +, = ^2 -, and dots denote normal time derivatives."151 Phe equations [or the perturbations are therefore where cl is the acceleration., The equations for the perturbations are therefore where $A$ is the acceleration.152 In the frame in which the scalar field is unperturbecl (the frame comoving with the dark energy. denoted by a hat). 04;=0 and so ὃς2=opjoàp 1.," In the frame in which the scalar field is unperturbed (the frame comoving with the dark energy, denoted by a hat), $\widehat{\delta\varphi}=0$ and so $\hat{c}_s^2 \equiv \widehat{\delta153 p}/\widehat{\delta\rho} = 1$ ."154 If the equation of state pas=wpe is constant. the dark energy. density evolves like pus=pasotGo)," If the equation of state $\pde=w\rde$ is constant, the dark energy density evolves like $\rde = \rho_{{\rm155de},0}\;a^{-3(1+w)}$."156 wv can then identify this solution with a scalar field and. its potential Clearly a constant equation of state makes a very unnatural quintessence model., We can then identify this solution with a scalar field and its potential Clearly a constant equation of state makes a very unnatural quintessence model.157 llowever a large class of models are expected. to be well described. (at. least as [ar as the CAIB anisotropy is concerned) by an effective constant equation of state parameter., However a large class of models are expected to be well described (at least as far as the CMB anisotropy is concerned) by an effective constant equation of state parameter.158 In this paper we clo not explicitly consider dark energy models with an evolving equation of state., In this paper we do not explicitly consider dark energy models with an evolving equation of state.159 In order to analyse the impact of the equation of state parameter of the dark energy. component on the cosmic microwave background. anisotropies we will first look into primary degeneracies originating [rom smaller scales in the teniperature anisotropy power spectrum., In order to analyse the impact of the equation of state parameter of the dark energy component on the cosmic microwave background anisotropies we will first look into primary degeneracies originating from smaller scales in the temperature anisotropy power spectrum.160 (Xs. discussed. in Alelehiorrietal.(2002) the main impact is due to the change in the angular diameter distance toward the last scattering surface., As discussed in \citet{Melchiorri:2002ux} the main impact is due to the change in the angular diameter distance toward the last scattering surface.161" The small scale. CALB anisotropies in a Uat universe are mainly sensitive to the physical cold dark matter anc barvon densities and the angular diameter distance dixf8,0LS)LOOPS3‘|L7"," The small scale CMB anisotropies in a flat universe are mainly sensitive to the physical cold dark matter and baryon densities and the angular diameter distance $d_A \propto \int [\Omega_m(1+z)^3+\Omega_{\rm162de}(1+z)^{3(1+w)}]^{-1/2}$."163" ence if ew is decreasing. we need to inercase (4, and for a Lat universe decrease O4, and therefore increase. the Hubble xwameter Z4, and therefore decrease OQ; in order to obtain he same CMD anisotropy power spectrum."," Hence if $w$ is decreasing, we need to increase $\Omega_{\rm de}$ and for a flat universe decrease $\Omega_{\rm m}$ and therefore increase the Hubble parameter $H_0$ and therefore decrease $\Omega_b$ in order to obtain the same CMB anisotropy power spectrum."164 Let us assume that we can by some artificial mechanism. suppress the fluctuations in the dark energy. component., Let us assume that we can by some artificial mechanism suppress the fluctuations in the dark energy component.165 ote that in general this is consistent with the equations of general. relativity., Note that in general this is consistent with the equations of general relativity.166 Only in the case of a cosmological constant with we=1 we recognise from Eqn., Only in the case of a cosmological constant with $w=-1$ we recognise from Eqn.167 7 that dpa.=) js a solution., \ref{eqn:pertrho} that $\delta\rho_{\rm de} =0$ is a solution.168 We implement the equations in the [rame comoving with the dark matter (synchronous gauge). and allow for a changing background equation of state but fix the dark energy. perturbations to zero.," We implement the equations in the frame comoving with the dark matter (synchronous gauge), and allow for a changing background equation of state but fix the dark energy perturbations to zero."169 We compare results from applying this (incorrect) recipe with those obtained using the full equations consistent with linear general relativity., We compare results from applying this (incorrect) recipe with those obtained using the full equations consistent with linear general relativity.170" In their rest frame the matter perturbations evolve Like uocasado which for matter domination (i6= 0) results in 3, e."," In their rest frame the matter perturbations evolve like _m' = G a^2 _m = 0), which for matter domination $w=0$ ) results in $\delta_m \propto a$ ."171 lU we eradually: decrease. w starting from «e=0. the transition between matter and dark. energy domination happens later ancl later. but more and more rapidly. aud with a larger overall change in the equation of state.," If we gradually decrease $w$ starting from $w=0$, the transition between matter and dark energy domination happens later and later, but more and more rapidly, and with a larger overall change in the equation of state."172 So we expect a smaller contribution to the ISW for values of w closer to zero., So we expect a smaller contribution to the ISW for values of $w$ closer to zero.173 In Fig., In Fig.174 1 we show the quadrupole contribution AE(4) to the ISW., \ref{fig:ISW2} we show the quadrupole contribution $\Delta_2^{\rm ISW}(k)$ to the ISW.175" The solid. line is for a ACDAL universe with w= 10,=03. 0,=0.05. Mo=65kms1Mpe the thin dashed. line is for a=0.6. O,,=O44. OQ,= 0.073. Hy=54kms.!Mpe.| and the thin dot-dashed. for w= 0200,—047. O,=00027. My=SAkms!Mpe.|."," The solid line is for a $\Lambda$ CDM universe with $w=-1$ , $\Omega_m=0.3$, $\Omega_b=0.05$, $H_0=65 \Hunit$, the thin dashed line is for $w=-0.6$, $\Omega_m=0.44$, $\Omega_b=0.073$ , $H_0=54 \Hunit$ and the thin dot-dashed for $w=-2$, $\Omega_m=0.17$, $\Omega_b=0.027$, $H_0=84 \Hunit$."176 For all three models the spectral index is fixed to n;=1.0 and the redshift of instantaneous complete reionization 1s nec17., For all three models the spectral index is fixed to $n_s=1.0$ and the redshift of instantaneous complete reionization is $z_{\rm re} =17$.177 Without dark energy perturbations we clearly see that for we=0.6 there is only a small contribution to the quadrupole from the ISW. while there is a large contribution fore=2.," Without dark energy perturbations we clearly see that for $w=-0.6$ there is only a small contribution to the quadrupole from the ISW, while there is a large contribution for $w=-2$."178" In the case of no dark energy. perturbations for there is a smaller ISW contribution than for a .XC'DM universe. ancl subsequentlv for w=2 a lager [SW contribution,"," In the case of no dark energy perturbations for $w=-0.6$ there is a smaller ISW contribution than for a $\Lambda$ CDM universe, and subsequently for $w=-2$ a larger ISW contribution."179 In Fig., In Fig.180 2 we show the entire temperature anisotropy power spectrum for the three degenerate models., \ref{fig:Clno} we show the entire temperature anisotropy power spectrum for the three degenerate models.181 We can see the increase in power on large scales by moving from the w=0.6 over the w= CXCDALD to the w=2 mocel., We can see the increase in power on large scales by moving from the $w=-0.6$ over the $w=-1$ $\Lambda$ CDM) to the $w=-2$ model.182 If these were the true signaturesof dark energy models on large scales we might be hopeful that by cross correlating large scale. CALB anisotropies with x-ray or radio source, If these were the true signaturesof dark energy models on large scales we might be hopeful that by cross correlating large scale CMB anisotropies with x-ray or radio source183"a reflection of the assumption, implicit in our model, of conditions close to equipartition inside the lobes.","a reflection of the assumption, implicit in our model, of conditions close to equipartition inside the lobes."184 A given radio luminosity originating in a given lobe volume fully determines the strength of the magnetic field (e.g.?).., A given radio luminosity originating in a given lobe volume fully determines the strength of the magnetic field \citep[e.g.][]{ml94}.185" The magnetic field and the synchrotron emitting electrons both contribute to the lobe pressure, pi, but for k=100, m is dominated by the energy density of the non-radiating particles."," The magnetic field and the synchrotron emitting electrons both contribute to the lobe pressure, $p_{\rm l}$, but for $k=100$, $p_{\rm l}$ is dominated by the energy density of the non-radiating particles."186 The uncertainties in the flux measurements at the frequencies used to fit the model spectra give rise to uncertainties in the free model parameters., The uncertainties in the flux measurements at the frequencies used to fit the model spectra give rise to uncertainties in the free model parameters.187 The density in the host galaxy environment is associated with the largest uncertainty., The density in the host galaxy environment is associated with the largest uncertainty.188 Fig., Fig.189 7 shows the confidence contours in the jet power — density model plane., \ref{1450powerdensity} shows the confidence contours in the jet power – density model plane.190" The contours for the outer lobes overlap considerably with respect to the range in jet power preferred by the model, but the model indicates a higher density to the north of the host galaxy."," The contours for the outer lobes overlap considerably with respect to the range in jet power preferred by the model, but the model indicates a higher density to the north of the host galaxy."191 Note that in this and the following figures the confidence contours would cover smaller ranges for the smaller errors on the flux measurements suggested above., Note that in this and the following figures the confidence contours would cover smaller ranges for the smaller errors on the flux measurements suggested above.192" The quality of the data makes it particularly difficult to constrain the source parameters; however, for further discussion of the discrepancies between model parameters for each pair of lobes, see ?.."," The quality of the data makes it particularly difficult to constrain the source parameters; however, for further discussion of the discrepancies between model parameters for each pair of lobes, see \citet{mjs09}."193 Fig., Fig.194 8 shows the confidence contours in the jet power — source age plane., \ref{1450powertime} shows the confidence contours in the jet power – source age plane.195 Both Q and t should be the same for both lobes and it is reassuring that the overlap of the confidence contours in this plane is large., Both $Q$ and $t$ should be the same for both lobes and it is reassuring that the overlap of the confidence contours in this plane is large.196 The model constrains the source age and the jet power roughly to within a factor three., The model constrains the source age and the jet power roughly to within a factor three.197" Finally, the confidence contours in the jet power magnetic field strength plane are shown in Fig. 9.."," Finally, the confidence contours in the jet power -- magnetic field strength plane are shown in Fig. \ref{1450powerfield}."198" As mentioned above, the model strongly constrains the strength of the magnetic field in the lobes."," As mentioned above, the model strongly constrains the strength of the magnetic field in the lobes."199 This demonstrates that the strength of the magnetic field and hence the pressures in the lobes are the best constrained parameters of the model., This demonstrates that the strength of the magnetic field and hence the pressures in the lobes are the best constrained parameters of the model.200" The values of Bj and p, do not change much even for the assumption of 6=0 or for changes of the other set model parameters.", The values of $B_{\rm l}$ and $p_{\rm l}$ do not change much even for the assumption of $\beta =0$ or for changes of the other set model parameters.201 The observed radio spectra of the inner lobes of 11450--333 are well described by the power-laws for the northern inner lobe and for the southern inner lobe., The observed radio spectra of the inner lobes of 1450+333 are well described by the power-laws for the northern inner lobe and for the southern inner lobe.202 Fig., Fig.203 6 shows these fits translated to the source restframe., \ref{1450spec} shows these fits translated to the source restframe.204 We can now apply the modified standard FRII model described in section 6.1 to the observations by setting m—2.42 for the northern inner, We can now apply the modified standard FRII model described in section \ref{stand} to the observations by setting $m=2.42$ for the northern inner205take the Tragments directly into to star.,take the fragments directly into to star.206 Secoudls. the collision might be expected to also produce SLtaller fraginents which would be slowed by motion through the gas in the circuumstellar disc. aud Wwuch would spiral into to star slowly by the mechanism described by Weidenschilling(1977).," Secondly, the collision might be expected to also produce smaller fragments which would be slowed by motion through the gas in the circumstellar disc, and which would spiral into to star slowly by the mechanism described by \cite{Wei77}."207. We 1Xe that the typical rise time of the outbursts (1—10 years) is cousisteut with the former process. Wwiereas the decay time (10—100 years) is cousisteut with the timescale for smaller objects spiralling into the star.," We note that the typical rise time of the outbursts $1-10$ years) is consistent with the former process, whereas the decay time $10-100$ years) is consistent with the timescale for smaller objects spiralling into the star."208 We can also estimate the increase in lumii0slty due to this mechanisin. which is due to material iling iuto tje star.," We can also estimate the increase in luminosity due to this mechanism, which is due to material falling into the star."209 TIje Inass of material which falls iuto tle star will be very variable. depeucing ipou tlie colision parameters as well as the masses of the αςicing objects.," The mass of material which falls into the star will be very variable, depending upon the collision parameters as well as the masses of the colliding objects."210 This is consistent with he very wide raige of luminosities of outbursts., This is consistent with the very wide range of luminosities of outbursts.211 Let us esinate the luminosity of au extremely intense outburst. csed by a iuass of material comparable with the mass of a laree planet (10oE solar masses. say) spiralling into the star over a period of perlaps LOvrs.," Let us estimate the luminosity of an extremely intense outburst, caused by a mass of material comparable with the mass of a large planet $10^{-3}$ solar masses, say) spiralling into the star over a period of perhaps $10\,{\rm yrs}$."212 TIIs accretion rate exc‘eects he commonN asseL baseline lumiuosity resulting from an accretion 1vue of 10i solar masses yer year (PapaloiLOLL&Terquem2006). by a factor of 107., This accretion rate exceeds the commonly assumed baseline luminosity resulting from an accretion rate of $10^{-7}$ solar masses per year \citep{Pap+06} by a factor of $10^3$.213 This is sullicient to explain the 1nost xonounced oubLs events. which involve au increase of luminosity of ip to six magnitudes.," This is sufficient to explain the most pronounced outburst events, which involve an increase of luminosity of up to six magnitudes."214 Iu nost cases the COlision will scatter only a small fraction of the planetary 1jass into the star. which is colsistent Wwith te [act that FU Oriouis outbursts are less intense tla this estinate. and vary widely in mae.itucle.," In most cases the collision will scatter only a small fraction of the planetary mass into the star, which is consistent with the fact that FU Orionis outbursts are less intense that this estmate, and vary widely in magnitude."215 We couchde that a mechanisin based on collisions between juvenile planets is capable of explaining the order of magnitude of the timescales aud strengths of FU Oriouis outburst events. as well as giving an iusight iuto the diversity of these phenomena.," We conclude that a mechanism based on collisions between juvenile planets is capable of explaining the order of magnitude of the timescales and strengths of FU Orionis outburst events, as well as giving an insight into the diversity of these phenomena."216 5.2 In section £3 we suggestedMOD that small rocky planets could be produced by ablation of light elements [rom a juvenile planet. leaving behiud a rocky core.," 5.2 In section 4.3 we suggested that small rocky planets could be produced by ablation of light elements from a juvenile planet, leaving behind a rocky core."217 We also argued tiat the high eniperatures required to produce clioudrules could be produced by frictional heating clue a planet uoviug through the accretion disc at high speed., We also argued that the high temperatures required to produce chondrules could be produced by frictional heating due a planet moving through the accretion disc at high speed.218 Here we propose auotler mechanisia or prociicing ‘rocky planets auc choucdrules., Here we propose another mechanism for producing rocky planets and chondrules.219 I the juvenile planets form rocky cores. aud two of heim were to uxlergo a collision. rocky debris would be widely scattered.," If the juvenile planets form rocky cores, and two of them were to undergo a collision, rocky debris would be widely scattered."220 In the following we cliscuss whether his debris could coalesce to Dorm rocky planets. aud whether the debris could iucide paricles 'esembliug choucrules.," In the following we discuss whether this debris could coalesce to form rocky planets, and whether the debris could include particles resembling chondrules."221 The most severe clifficulty with the standard model for planet foruation lies iu the [γαρ] aggregates οἱ dust., The most severe difficulty with the standard model for planet formation lies in the fragility of aggregates of dust.222 If tje. eircuimstellar dise contained larger pieces of ‘rocky material. which w be much less easily [πιiemented by collisious aud which would. avok spiralling iu. the star moclel would be much uore tenable.," If the circumstellar disc contained larger pieces of rocky material, which would be much less easily fragmented by collisions and which would avoid spiralling in, the standard model would be much more tenable."223 Iu particular. the largest fragmeuts would play the role o plauetisimals of the st:uxdard theory. auc rocky planets could be [orued by coalescence of bodies aud by sweepiiD>oO up stnaller bodies. as is envisaged in the stancdard model.," In particular, the largest fragments would play the role of the planetisimals of the standard theory, and rocky planets could be formed by coalescence of these bodies and by sweeping up smaller bodies, as is envisaged in the standard model."224 Most of difficulties of growing arge bodies are avoided. aud rocky planets oi uear-circular and. copl orbits could be formed from collision debris.," Most of the difficulties of growing large bodies are avoided, and rocky planets on near-circular and coplanar orbits could be formed from collision debris."225"VP| then the subsonic case,",$|\nabla \textbf{P}|$ then the subsonic case.226" Case three js unique to supersonic turbulence in that it represents a very sharp spikeinv, and/or D across a shock frout.", Case three is unique to supersonic turbulence in that it represents a very sharp spikein $n_e$ and/or B across a shock front.227 The ciffereuce οσοι this case aud what might be seen m case two is that here we are dealing with interactions of strong shock frouts. which are known to create delta fiction ike distributions iu density (sim Ryu 2005).," The difference between this case and what might be seen in case two is that here we are dealing with interactions of strong shock fronts, which are known to create delta function like distributions in density (Kim Ryu 2005)."228 Iu this case. the derivative of case three is has a distinctly liffereut profile with respect to case one and two.," In this case, the derivative of case three is has a distinctly different profile with respect to case one and two."229 Case wee shows a “double jump profile across the shock ront. which can be seen in Figure 3. in the top right xul for LOS density and the bottom right panel for VP|.," Case three shows a 'double jump' profile across the shock front, which can be seen in Figure \ref{fig:RM2}230 in the top right panel for LOS density and the bottom right panel for $|\nabla \textbf{P}|$."231 This morphological distinction cuu be used to determine if one is dealing with turbulence that is ina shock dominated regime (.c. 53upersonic) aud can provide researchers with a pronusing new aveuue of obtainiug he souic Mach umuubers frou polarimetric data., This morphological distinction can be used to determine if one is dealing with turbulence that is in a shock dominated regime (i.e. supersonic) and can provide researchers with a promising new avenue of obtaining the sonic Mach numbers from polarimetric data.232 In the case of the Alfvénnic Mach muuber. the morphological difference is less clear. however eradicuts will tend to align along the field lines in the case of stroug field (sub-Alfvónuic turbulence).," In the case of the Alfvénnic Mach number, the morphological difference is less clear, however gradients will tend to align along the field lines in the case of strong field (sub-Alfv\'ennic turbulence)."233 Also of interest is the question of which quantity is wovidine the dominate contribution to the structures in |VP| or |VRM[: Vn. VBros or both equally?," Also of interest is the question of which quantity is providing the dominate contribution to the structures in $|\nabla \textbf{P}|$ or $|\nabla RM|$: $\nabla n_e$, $\nabla B_{LOS}$ or both equally?"234 Especially in the case of compressible turbulence. the uaenetic energv is correlated with density. παλιο]. denser regions contain stronger nmaguetie fields. which is due to the compressibility of the gas (Burkhart ct al.," Especially in the case of compressible turbulence, the magnetic energy is correlated with density, namely, denser regions contain stronger magnetic fields, which is due to the compressibility of the gas (Burkhart et al."235 2009)., 2009).236 This causes the maguetic field to follow the flow of plasma if the maeuectic tension is uceligible., This causes the magnetic field to follow the flow of plasma if the magnetic tension is negligible.237 The compressed regions are dense enough to distort the maeguetic fleld lines. enhance the maguetic field intensity. aud effectively trap the magnetic energy due to the frozen-in condition.," The compressed regions are dense enough to distort the magnetic field lines, enhance the magnetic field intensity, and effectively trap the magnetic energy due to the frozen-in condition."238 Thus. for the supersouic cases. the iuteusitv of the structures seen in VP απο more pronounced then in the subsonic case. which is observed when comparing Figures 2. aud 3..," Thus, for the supersonic cases, the intensity of the structures seen in $\nabla \textbf{P}$ are more pronounced then in the subsonic case, which is observed when comparing Figures \ref{fig:RM1} and \ref{fig:RM2}."239 However. in the case of subsonic turbulence. there are no colpressive motions.," However, in the case of subsonic turbulence, there are no compressive motions."240 In this case. random fluctuations in density and maenetic fold will create structures in [VP] aud |VA.," In this case, random fluctuations in density and magnetic field will create structures in $|\nabla \textbf{P}|$ and $|\nabla RM|$."241 Due to these effects. we night expect ciffereut trends iu the correlationof supersonic aud subsonic |VP] with VV or VEM (the exadieut of the emission nicasure) aud VD.," Due to these effects, we might expect different trends in the correlation of supersonic and subsonic $|\nabla \textbf{P}|$ with $\nabla N$ or $\nabla EM$ (the gradient of the emission measure) and $\nabla B$."242 We test this bv plotting the pixel bv pixel correlation coefficieut of [VP] with the eradients of EM. N. aud LOS D iu Figure 5..," We test this by plotting the pixel by pixel correlation coefficient of $|\nabla \textbf{P}|$ with the gradients of EM, N, and LOS B in Figure \ref{fig:corav}."243 In the case of subsonic turbulence. VP| better traces out the fluctuations iu VB (blue line). while the supersonic cases are dominated bv deusitv fluctuations.," In the case of subsonic turbulence, $|\nabla \textbf{P}|$ better traces out the fluctuations in $\nabla B$ (blue line), while the supersonic cases are dominated by density fluctuations."244 This is because density enhancements are dominate due to shock frouts in the case of supersouic urbuleuce. while in subsonic turbulence deusity is Helly incompressible.," This is because density enhancements are dominate due to shock fronts in the case of supersonic turbulence, while in subsonic turbulence density is highly incompressible."245 Ta this case. the magnetic field will dominate the topology of the rotation mcasure and |VP]|.," In this case, the magnetic field will dominate the topology of the rotation measure and $|\nabla \textbf{P}|$."246 This behavior is analogous to velocity in jeutral hydrogen radio positiou-position-velocitv cubes of turbulence. where density dominates the power spectrum for the case of supersonic turbulence ar velocity dominates the spectrum for subsonic turbulence (see Lazariau Poeosvan 2006. Burkhart ct al.," This behavior is analogous to velocity in neutral hydrogen radio position-position-velocity cubes of turbulence, where density dominates the power spectrum for the case of supersonic turbulence and velocity dominates the spectrum for subsonic turbulence (see Lazarian Pogosyan 2006, Burkhart et al."247 2011a)., 2011a).248 This difference in correlation provides vet another way of eaugiug the Mach ummbers if one has both the emission measure and the linear polarization map., This difference in correlation provides yet another way of gauging the Mach numbers if one has both the emission measure and the linear polarization map.249 Correlate: spatial eracdicuts between the two should indicate regions of shocks., Correlated spatial gradients between the two should indicate regions of shocks.250 Tn the next section we will explore the utility of eracdieuts of poluduetzüue data for the deteriuination of the Mach umubers by investigating two differcut statistical measures of looking at the distribution auk topology of the |VP| maps: PDF moments and. genus function., In the next section we will explore the utility of gradients of polarimetric data for the determination of the Mach numbers by investigating two different statistical measures of looking at the distribution and topology of the $|\nabla \textbf{P}|$ maps: PDF moments and genus function.251" The previous section provided some theoretical discussion for why we expect |VP| data to be useful for deteriiuiue the sonic Mach προς,", The previous section provided some theoretical discussion for why we expect $|\nabla \textbf{P}|$ data to be useful for determining the sonic Mach number.252 Iu. this section we will attempt to statistically quanutifv the differences secu in both the morphology aud the distribution of maps of [VP|., In this section we will attempt to statistically quantify the differences seen in both the morphology and the distribution of maps of $|\nabla \textbf{P}|$.253 We again note our assunption for the simulations of |P|=1 thus giving a trivial scaling relationship between |VP| and |VRAL| as: ΠΑΛΙ=|VP|/2., We again note our assumption for the simulations of $|P|=1$ thus giving a trivial scaling relationship between $|\nabla \textbf{P}|$ and $|\nabla RM|$ as: $|\nabla RM|=|\nabla \textbf{P}|/2 $.254 We also provide an observational comparison for both statistics with the SGPS test region shown in Figure 1.., We also provide an observational comparison for both statistics with the SGPS test region shown in Figure \ref{fig:RM}. .255 A probability distribution function (PDF) is the function describing the frequency of occurrence of values in the distribution of intensities., A probability distribution function (PDF) is the function describing the frequency of occurrence of values in the distribution of intensities.256 PDFs aud their quantitative descriptors have been used to study, PDFs and their quantitative descriptors have been used to study257become less strong in Zform>1.5 galaxies.,become less strong in $z_{form}>1.5$ galaxies.258 We discuss this further in the next Section., We discuss this further in the next Section.259inner regions of the disk the mass available in the disk is smallest. and the energv budget potentially available for evaporation largest.,"inner regions of the disk the mass available in the disk is smallest, and the energy budget potentially available for evaporation largest."260 Lf the mass flow. from disk into torus increases with the energy. dissipation rate. and if a steady state develops. one could. therefore. envisage a structure consisting of three regions: an outer one in which only a geometrically thin optically thick disk is present. inside this a composite region with an evaporating disk inside a hot ion supported. advection torus. ancl inside this a region in which only an ion supported. flow exists because all disk mass has evaporated (Meyer ancl Mever-Hofmeister. 1994. Moever-Hofmoeister and. Meyer 1999).," If the mass flow from disk into torus increases with the energy dissipation rate, and if a steady state develops, one could therefore envisage a structure consisting of three regions: an outer one in which only a geometrically thin optically thick disk is present, inside this a composite region with an evaporating disk inside a hot ion supported advection torus, and inside this a region in which only an ion supported flow exists because all disk mass has evaporated (Meyer and Meyer-Hofmeister 1994, Meyer-Hofmeister and Meyer 1999)."261 Depending on details of the processes of mass and energv exchange between disk and torus. the boundaries between these regions may vary.," Depending on details of the processes of mass and energy exchange between disk and torus, the boundaries between these regions may vary."262 IH is not necessary that the structure is steady., It is not necessary that the structure is steady.263 The model has. in. principle. sullicient ingredients to allow for variability and may perhaps be developed further in the context of the various forms of variability seen in BIIC.," The model has, in principle, sufficient ingredients to allow for variability and may perhaps be developed further in the context of the various forms of variability seen in BHC."264 Iinergv exchange between disk and torus may be mecliatec by. particles or bv radiation.disk (, Energy exchange between disk and torus may be mediated by particles or by radiation. (265this assumption can easily be relaxed).,this assumption can easily be relaxed).266 The radiation produced. by the torus illuminates the disk below. which thermalizes it into an approximate blackbody spectrum.," The radiation produced by the torus illuminates the disk below, which thermalizes it into an approximate blackbody spectrum."267 These (soft) photons are Comptonized in the hot torus., These (soft) photons are Comptonized in the hot torus.268 In this model. approximately half the energy. comes out as soft radiation and half as Comptonized photons.," In this model, approximately half the energy comes out as soft radiation and half as Comptonized photons."269 It correctly predicts the slope of the spectrum.temperatures.," It correctly predicts the slope of the spectrum,."270 For further developments of this model see Eraardt (1997)., For further developments of this model see Haardt (1997).271" A second channel of energetic interaction is the hot o»otons in the torus with temperature near the virial emperature. 7j2d.cl160r,/r MeV. At the distance dominating the energy release. reTre. the protons thus lave a temperature around. 20 MeV. At this energy. they lave a significant penetration. depth into the cool di:"," A second channel of energetic interaction is the hot protons in the torus with temperature near the virial temperature, $T_{\mathrm p}\approx T_{\mathrm v}\approx 272160 273r_{\mathrm g}/r$ MeV. At the distance dominating the energy release, $r\approx 2747r_{\mathrm 275g}$, the protons thus have a temperature around 20 MeV. At this energy, they have a significant penetration depth into the cool disk."276 μον are slowed down mainly by Coulomb interactions with he ensemble of electrons. inside their Debye sphere., They are slowed down mainly by Coulomb interactions with the ensemble of electrons inside their Debye sphere.277 The ‘stopping depth’. expressed. in terms of the corresponding Thomson optical depth. is (c.g. liter et al.," The `stopping depth', expressed in terms of the corresponding Thomson optical depth, is, (e.g. Ryter et al.,"278 1970) where 3=οὁmGum)? is the vertical component of the proton velocity. 06=ηE is à measure of the temperature of the heated. laver. In.Az20 is a Coulomb logarithm. 47237/(20). and c the error function adir. This formulaJz holds lor nonrelativistic temperatures: the relativistic eencralization has been given by Stepney (1983) ancl Stepney anc Culbert (1983).," 1970) where $\beta=v_{\mathrm z}/c\approx (kT_{\mathrm 279p}/m_{\mathrm 280p}c^2)^{1/2}$ is the vertical component of the proton velocity, $\theta=kT/m_{\mathrm 281e}c^2$ is a measure of the temperature of the heated layer, $\ln\Lambda\approx 20$ is a Coulomb logarithm, $x^2=\beta^2/(2\theta)$, and $\psi$ the error function x. This formula holds for nonrelativistic temperatures; the relativistic generalization has been given by Stepney (1983) and Stepney and Guilbert (1983)."282 At low temperature ΑκΠοΠρhd. or is small and the factor involving the error function can be expanclecl.," At low temperature $kT<m_{\mathrm e}/m_{\mathrm 283p}\,kT_{\mathrm p}$, $x$ is small and the factor involving the error function can be expanded."284" This vields3/2. EDUET, (uev)EI ]leating by protons vields à Comptonizing laver of thickness equal to the stopping depth 7."," This yields, 50 50 Heating by protons yields a Comptonizing layer of thickness equal to the stopping depth $\tau_{\mathrm s}$."285 This depth is a function of 1e temperature in the laver. by (01).," This depth is a function of the temperature in the layer, by \ref{lsr}) )."286 The temperature on 16 other hand is determined by the heating ancl cooling processes. so that a consistent. calculation of heating and cooling will vield. both the temperature and. the optical epth of the laver.," The temperature on the other hand is determined by the heating and cooling processes, so that a consistent calculation of heating and cooling will yield both the temperature and the optical depth of the layer."287 With a simple estimate. we can now show jut this will vield 7; and ZY in roughly the right range.," With a simple estimate, we can now show that this will yield $\tau_{\mathrm s}$ and $T$ in roughly the right range."288 The cooling process in the laver is the inverse Compton process. Le. the energy [oss electrons experience as they scatter the soft photons from the cool disk below.," The cooling process in the layer is the inverse Compton process, i.e. the energy loss electrons experience as they scatter the soft photons from the cool disk below."289 We assume that these soft photons are all (or mostly) sroclucecl by thermalization of Comptonized photons from. 10 heated. laver. as in the model of Llaardt anc p»laraschi (1991. hereafter LEM).," We assume that these soft photons are all (or mostly) produced by thermalization of Comptonized photons from the heated layer, as in the model of Haardt and Maraschi (1991, hereafter HM)."290 Since approximately half the ο.‘omptonized photons escape and the other half illuminates 1e thermalizing laver. the energy Dux in the soft photons a 10 base of the laver must be about the same as that in the scaping Comptonized photons.," Since approximately half the Comptonized photons escape and the other half illuminates the thermalizing layer, the energy flux in the soft photons at the base of the layer must be about the same as that in the escaping Comptonized photons."291 Such a balance is possible nly if the Comptonization is sullicientIy strong., Such a balance is possible only if the Comptonization is sufficiently strong.292 In terms of 16 Compton j-parameter y7467. it requires that jez1.," In terms of the Compton $y$ -parameter $y\approx 4\theta\tau_{\mathrm s}$, it requires that $y\approx 1$."293 If the temperature is too low. the energy transfer from the lectrons to the soft photons is too low and the laver heats up until jz1. and vice versa.," If the temperature is too low, the energy transfer from the electrons to the soft photons is too low and the layer heats up until $y\approx 1$, and vice versa."294 Since the j-parameter also etermines the slope of the X-ray spectrum. the mocel vields a fixed spectral slope. which is in the range of the observed," Since the $y$ -parameter also determines the slope of the X-ray spectrum, the model yields a fixed spectral slope, which is in the range of the observed"295This image is one of the highest-resolutiou images to date of the more extended structures in the complex GC region. with excellent seusitivity to both point-like aud diffuse features.,"This image is one of the highest-resolution images to date of the more extended structures in the complex GC region, with excellent sensitivity to both point-like and diffuse features."296 Figure 2 is a contour version of the continuum image in Figure I. with the major GC sources labeled.," Figure 2 is a contour version of the continuum image in Figure 1, with the major GC sources labeled."297 Iu adcditiou. wenty-eiglit sources have been detected in this image and are listed in Table 3.," In addition, twenty-eight sources have been detected in this image and are listed in Table 3."298 These sources are categorized as compact or extended. aud for each source. the positiou. peak inteusity. integrated lux deusity (Gf resolved). major axes (if resolved). aucl geometric size (square root of major x ulnor axis) are given.," These sources are categorized as 'compact' or 'extended' and for each source, the position, peak intensity, integrated flux density (if resolved), major axes (if resolved), and geometric size (square root of major $\times$ minor axis) are given."299 These parameters were obtained by fitting the sources with Gaussian profiles wing JMEIT in AIPS., These parameters were obtained by fitting the sources with Gaussian profiles using JMFIT in AIPS.300 Of the 28 continuum sources detected. 16 are classifed as compact! aud 12 as extended.," Of the 28 continuum sources detected, 16 are classifed as 'compact' and 12 as 'extended'."301 Four of the sources (C0.60-0.20.. CO.[8270.0T. 10.32-0.19 and G359.87+0.18) are iresolved and likely to be point sources.," Four of the sources (G0.60-0.20, G0.48+0.07, G0.32-0.19 and G359.87+0.18) are unresolved and likely to be point sources."302 We also searched the compact source catalogs of et al. (, We also searched the compact source catalogs of Yusef-Zadeh et al. (3032001) at 1.1 GHz aud Becker et al. (,2004) at 1.4 GHz and Becker et al. (3041991) at. L.9 GHz in order to identify counterparts.,1994) at 4.9 GHz in order to identify counterparts.305 Sixteen sources in our image that have couuterparts iu oue of these two catalogs are listed tn Table I with their [lux density [rom our image (1.[-Laug). Yusef-Zadehl et al. (," Sixteen sources in our image that have counterparts in one of these two catalogs are listed in Table 4 with their flux density from our image (1.4-Lang), Yusef-Zadeh et al. ("3062004: 1.I-EYZ) and Becker et al. (,2004; 1.4-FYZ) and Becker et al. (307199I: 5-Becker).,1994; 5-Becker).308 Continuum-weighted. line-to-continuum HI absorption integrated spectra were produced towards ~ [0 of the brightest continuum sources in the field.," Continuum-weighted, line-to-continuum HI absorption integrated spectra were produced towards $\sim$ 40 of the brightest continuum sources in the field."309 The profiles were mace to characterize the HI absorption features toward these well-known sources., The profiles were made to characterize the HI absorption features toward these well-known sources.310 In very crowded regions. (e.g.. the HII regions iu the Badio Are region and SerA East and West) the AIPS task BLÀANI was used interactively to select the region of interest using a signal-to-noise cut olf in the continuum unage.," In very crowded regions, (e.g., the HII regions in the Radio Arc region and SgrA East and West) the AIPS task BLANK was used interactively to select the region of interest using a signal-to-noise cut off in the continuum image."311 The GIPSY taskprofil was used to produce integrated. continuum-weighted. line-to-coutinuum spectra towards each of the LO coutiuuunm features (vau der Hulst et al.," The GIPSY task was used to produce integrated, continuum-weighted, line-to-continuum spectra towards each of the 40 continuum features (van der Hulst et al."312 1992)., 1992).313 A continuum cutoll of οσο]5puum was usec inprofi to obtain optimal signal-to-noise in the iutegrated spectra., A continuum cutoff of $\sigma_{continuum}$ was used in to obtain optimal signal-to-noise in the integrated spectra.314 Since the ruis noise varies across the mosaic. a value [or σερμυ Was determined locally for each object.," Since the rms noise varies across the mosaic, a value for $\sigma_{continuum}$ was determined locally for each object."315 Typical rius noise for the spectra are in the range of 0.01-0.05. where the units are line-to-continuunm ratio.," Typical rms noise for the spectra are in the range of 0.01-0.05, where the units are line-to-continuum ratio."316 These profiles were then converted to profiles of optical depth using the formula 7—-In(12-(L/C)). where L/C represents the line-to-continuum profile integrated over a region.," These profiles were then converted to profiles of optical depth using the formula $\tau$ =-ln(1+(L/C)), where L/C represents the line-to-continuum profile integrated over a region."317 Multiple Gaussian fits were applied to each of the profiles (using the GIPSY task ντο). aud Table 5 lists the parameters of the resulting fits and errors when they can be reliably determined (central velocity (νε). Fall-width half maximum line width (AVey yas). and peak opacity 74/7).," Multiple Gaussian fits were applied to each of the profiles (using the GIPSY task ), and Table 5 lists the parameters of the resulting fits and errors when they can be reliably determined (central velocity $_{LSR}$ ), full-width half maximum line width $\Delta$ $_{FWHM}$ ), and peak opacity $\tau$$_{HI}$ )."318 A number ofthe HI components toward the Ser B aud Ser A complexes are highly saturated., A number of the HI components toward the Sgr B and Sgr A complexes are highly saturated.319 Saturated. channels will have an unclelinecl optical depth and occur at the continuum. peaks of SerB aud SerA (Le. 1-1 Jv/beam respectively) aud in other regions where the liue-to-continuum levels are particularly high.," Saturated channels will have an undefined optical depth and occur at the continuum peaks of SgrB and SgrA (i.e., 1-4 Jy/beam respectively) and in other regions where the line-to-continuum levels are particularly high."320 Figures 9 show a representative sample of 10 HI absorption profiles toward some of the sources in the CC reeion: Ser Bl and B2. Ser A East ancl West. the Arched Filaments. Sickle and Badio Are. the Ser C nonthermal filament (NTF) and HID region. aud two point-like," Figures 4-9 show a representative sample of 10 HI absorption profiles toward some of the well-known sources in the GC region: Sgr B1 and B2, Sgr A East and West, the Arched Filaments, Sickle and Radio Arc, the Sgr C nonthermal filament (NTF) and HII region, and two point-like"321CCD photometry of a subsample of our C\WD sample was obtained. between 29th of July ancl the Η of August 1997 on the lm telescope of the South African Astronomical Observatory in Sutherland.,CCD photometry of a subsample of our CWD sample was obtained between 29th of July and the 4th of August 1997 on the 1m telescope of the South African Astronomical Observatory in Sutherland.322 Johnson-Cousins VOR. Lb photometry was obtained for all program stars on the Tek (512x512). CCD. with B measures also acquired for sullicienthy bright objects.," Johnson-Cousins V, R, I photometry was obtained for all program stars on the Tek (512x512) CCD, with B measures also acquired for sufficiently bright objects."323 E-region standards. were observed continuously through cach usable night., E-region standards were observed continuously through each usable night.324 Observed magnitudes with associated errors are clisplaved in Table 3.., Observed magnitudes with associated errors are displayed in Table \ref{saaophot}.325 These observed magnitudes. provide an independent check on the accuracy of the SuperCOSALOS photographic photometry. and we use the deviations of minotesrpie from niccp to obtain errors on the D. V. I. Lb photographic photometry of 0.17. 0.14. 0.13 ancl 0.16 respectively.," These observed magnitudes provide an independent check on the accuracy of the SuperCOSMOS photographic photometry, and we use the deviations of $\rm m_{photographic}$ from $\rm m_{CCD}$ to obtain errors on the B, V, R, I photographic photometry of 0.17, 0.14, 0.13 and 0.16 respectively."326 The CCD photometry also allowed tighter estimates of effective temperature to be derived. for observed. objects. although they did not provide the hoped for useful constraints on log g.In Previous studies of οΑΛ samples. (eg LDAL BRL) have often. benefited. from a comprehensive. and wide ranging observational database. including high quality spectra. optical ancl Ht photometry ancl parallaxes.," The CCD photometry also allowed tighter estimates of effective temperature to be derived for observed objects, although they did not provide the hoped for useful constraints on log g. Previous studies of CWD samples (eg LDM, BRL) have often benefited from a comprehensive and wide ranging observational database, including high quality spectra, optical and IR photometry and parallaxes."327 These observations. in conjunction with detailed. WD models. allow determinations of stellar parameters such as effective temperature. log ο. atmospheric composition. mass an bolometric Iuminositv.," These observations, in conjunction with detailed WD models, allow determinations of stellar parameters such as effective temperature, log g, atmospheric composition, mass and bolometric luminosity."328 However. since this is a relatively new project and is concerned. with stars of unusually fain apparent magnitude. such a database does not vet exist for this sample.," However, since this is a relatively new project and is concerned with stars of unusually faint apparent magnitude, such a database does not yet exist for this sample."329 Lt is therefore necessary [or us to restrict. our analysis. in the first place by exploiting the homogeneity of WD masses by assuming a common typical log ο for our entire CWD sample (the 60 stars with measured log ο in BRL have a mean surface gravity logg=S.099+0.044). anc secondly by treating the atmospheric constituent of cach star as an unknown parameter whose influence on the resulting WDLE must be determined later.," It is therefore necessary for us to restrict our analysis, in the first place by exploiting the homogeneity of WD masses by assuming a common typical log g for our entire CWD sample (the 60 stars with measured log g in BRL have a mean surface gravity $\overline{\log{g}} =330 8.099\pm0.044$ ), and secondly by treating the atmospheric constituent of each star as an unknown parameter whose influence on the resulting WDLF must be determined later."331 3erecron οἱ al. (, Bergeron et al. (3321995) have published a detailed οἱ of model predictions for Johnson-Cousins U. D. V. R. E (and 11) photometry and bolometric corrections as a function of ellective temperature and log e. Making our assumption that log ο is always equal to S. values for cllective temperature and bolometric Luminosity assuming both a Ll and Ie atmosphere can be caleulated for every sample object.,"1995) have published a detailed grid of model predictions for Johnson-Cousins U, B, V, R, I (and IR) photometry and bolometric corrections as a function of effective temperature and log g. Making our assumption that log g is always equal to 8, values for effective temperature and bolometric luminosity assuming both a H and He atmosphere can be calculated for every sample object."333 Fitting for Yay is achieved by interpolating the moclel eric at. LOIS intervals for the colour indices (0.D). (D.HD). (VoH) and (V.1).," Fitting for $T_{\rm eff}$ is achieved by interpolating the model grid at 10K intervals for the colour indices $(U-B)$, $(B-R)$, $(V-R)$ and $(V-I)$."334 We then evaluate v at each. Zir interval using all available colour indices for the object in, We then evaluate $\chi^{2}$ at each $T_{\rm eff}$ interval using all available colour indices for the object in335representatives of the present escape plutinos and performed a second integration.,representatives of the present escape plutinos and performed a second integration.336 From this last integration we obtained the dynamical evolution of plutinos once they escape from the resonance., From this last integration we obtained the dynamical evolution of plutinos once they escape from the resonance.337 From the 1183 initial particles. 1179 were removed from the integration and 4 remain in it.," From the 1183 initial particles, 1179 were removed from the integration and 4 remain in it."338 From the 1179 removed particles. 787 are ejected. 385 reached the Jupiter's zone and 4 collide with the planets.," From the 1179 removed particles, 787 are ejected, 385 reached the Jupiter's zone and 4 collide with the planets."339 We found that the great najority of escaped plutinos have encounters with Neptune. and this planet governs their dynamical evolution.," We found that the great majority of escaped plutinos have encounters with Neptune, and this planet governs their dynamical evolution."340 When a plutino escape from the resonance. it is transferred to the SD zone (>30 AU) or to the Centaur zone (y«30 AU) but it eventually switches to those population. due to the dynamical influence of Neptune.," When a plutino escape from the resonance, it is transferred to the SD zone $q>30$ AU) or to the Centaur zone $q<30$ AU) but it eventually switches to those population, due to the dynamical influence of Neptune."341 The densest zone in the orbital element space of escaped plutinos corresponds to the ranges 30.«a100 AU and 5*«i40° and perihelions near the orbit of Neptune., The densest zone in the orbital element space of escaped plutinos corresponds to the ranges $30 < a < 100$ AU and $5^{\circ} < i < 40^{\circ}$ and perihelions near the orbit of Neptune.342 When escaped plutinos are transferred to the SD they are quickly locked into à mean motion resonance with. Neptune (similar to the behavior of SDOs analyzed by Fernánndez et al. (2004)), When escaped plutinos are transferred to the SD they are quickly locked into a mean motion resonance with Neptune (similar to the behavior of SDOs analyzed by Fernánndez et al. \cite{Fernandez04}) )343 and Gallardo (2006))., and Gallardo \cite{Gallardo06}) ).344 In the Centaur zone (this 1s the zone of q<30 AU ) the distribution of escaped plutinos is similar to that of SDOs in the Centaur zone obtained by Di Sisto Brunini (2007 ))., In the Centaur zone (this is the zone of $q < 30$ AU ) the distribution of escaped plutinos is similar to that of SDOs in the Centaur zone obtained by Di Sisto Brunini \cite{Disisto07}) ).345 The orbital evolution of escaped plutinos in the Centaur zone can be grouped into the four dynamical classes proposed by Di Sisto Brunini (2007))., The orbital evolution of escaped plutinos in the Centaur zone can be grouped into the four dynamical classes proposed by Di Sisto Brunini \cite{Disisto07}) ).346 There are more particles that have the dynamical behavior of the second class and it is notable the great frequency of the presence of Kozai resonances in all the four classes., There are more particles that have the dynamical behavior of the second class and it is notable the great frequency of the presence of Kozai resonances in all the four classes.347 There are also several mean motion resonances densely populated in the ranges of 30«a<50 AU., There are also several mean motion resonances densely populated in the ranges of $30 < a < 50$ AU.348 The escaped plutinos have a mean lifetime in the Centaur zone of 108 Myr. greater than that of Centaurs from SD of 72 Myr.," The escaped plutinos have a mean lifetime in the Centaur zone of $ 108$ Myr, greater than that of Centaurs from SD of $ 72$ Myr."349 Escaped-plutinos live more time than SDOs in the greater-perihelion Centaur zone. causing a slower diffusion to the inner Solar System of escaped-plutino orbits than of SDOs orbits.," Escaped-plutinos live more time than SDOs in the greater-perihelion Centaur zone, causing a slower diffusion to the inner Solar System of escaped-plutino orbits than of SDOs orbits."350" The present rate of injection of plutinos with radius greater than | km to the Centaur zone is between 1.6 to 16 plutinos every 100 years and the number of plutino-Centaurs with radius greater than 1 km would be between 1.8x109—10"".", The present rate of injection of plutinos with radius greater than 1 km to the Centaur zone is between 1.6 to 16 plutinos every 100 years and the number of plutino-Centaurs with radius greater than 1 km would be between $1.8 \times 10^{6} - 1.8 \times 10^{7}$.351 Both. the rate of injection and the number of Centaurs from plutinos are much less than the contribution from the SD obtained by Di Sisto Brunini (2007)).," Both, the rate of injection and the number of Centaurs from plutinos are much less than the contribution from the SD obtained by Di Sisto Brunini \cite{Disisto07}) )."352 Then. plutinos would represent a secondary source of Centaurs and their contribution would be a fraction of less than 6% of the total Centaur population.," Then, plutinos would represent a secondary source of Centaurs and their contribution would be a fraction of less than $6 \%$ of the total Centaur population."353 We thank Matthew S. Tiscareno who. às referee. made valuable comments that helped to improve this manuscript.," We thank Matthew S. Tiscareno who, as referee, made valuable comments that helped to improve this manuscript."354studies offer independent evidence of a negative-pressure component of the energy density (Riess οἱ 11998. 2001: Perliutter οἱ 11999).,"studies offer independent evidence of a negative-pressure component of the energy density (Riess et 1998, 2001; Perlmutter et 1999)."355 This energy component is described bv the equation of stale p—wp with w«0.," This energy component is described by the equation of state $p = \omega \rho$ with $\omega <3560$."357 The value of wis —1 for the spatially homogeneous cosmological constant A. and i can be larger (han —1 for other tvpes of fields such as the quintessence (e.g.. Frieman et 11995: Turner 11997: Caldwell οἱ 11993).," The value of $\omega$ is $-1$ for the spatially homogeneous cosmological constant $\Lambda$, and $\omega$ can be larger than $-1$ for other types of fields such as the quintessence (e.g., Frieman et 1995; Turner 1997; Caldwell et 1998)."358 The latter clusters spatially on large scales. thereby modifving both the matter density [Iuctuation power spectrum and (he CMD anisotropy (Ma οἱ 11999).," The latter clusters spatially on large scales, thereby modifying both the matter density fluctuation power spectrum and the CMB anisotropy (Ma et 1999)."359 Large-scale structure and supernova observations currently favor —1xw<—0.6 (Perlmutter. Turner White 1999: Wang et al.," Large-scale structure and supernova observations currently favor $-1 \le \omega \la -0.6$ (Perlmutter, Turner White 1999; Wang et al."360 2000)., 2000).361 The constraint can be improved with ongoing and [future surveys based on. for example. the classical method. of measuring the Iuminositw distance or the differential volume element as a function of redshift (e.g.. Newman Davis 2000).," The constraint can be improved with ongoing and future surveys based on, for example, the classical method of measuring the luminosity distance or the differential volume element as a function of redshift (e.g., Newman Davis 2000)."362 In thisLeer we locus on strong gravitational lensing and examine the effect. of the equation of state wou the probabilities of producing multiply lensed svstems., In this we focus on strong gravitational lensing and examine the effect of the equation of state $\omega$ on the probabilities of producing multiply lensed systems.363 The number of expected lenses as a function of image separation provides a potential means of constraining uw because it is determined by [actors such as the angular cliameter distances to the lens and the source. the lensing cross sections. and the number density of the lenses. each of which depends on v.," The number of expected lenses as a function of image separation provides a potential means of constraining $\omega$ because it is determined by factors such as the angular diameter distances to the lens and the source, the lensing cross sections, and the number density of the lenses, each of which depends on $\omega$."364 This tvpe of study is timely in view of the completion of the Jodrell-VLA Asirometrie Survey (JVAS: e.g. Patnaik et 11992: Ixing et 11999) and the Cosmic Lens All-Skv Survey (CLASS: e.g.. Myers et 11999. 2001). which together provide the largest uniformly selected sample of radio lens systems and have vielded 18 new lenses thus far.," This type of study is timely in view of the completion of the Jodrell-VLA Astrometric Survey (JVAS; e.g., Patnaik et 1992; King et 1999) and the Cosmic Lens All-Sky Survey (CLASS; e.g., Myers et 1999, 2001), which together provide the largest uniformly selected sample of radio lens systems and have yielded 18 new lenses thus far."365 The Sloan Digital Sky Survey (SDSS) will further increase (he source population by one to two orders of magnitude., The Sloan Digital Sky Survey (SDSS) will further increase the source population by one to two orders of magnitude.366 since lensing probes the mass and not the light distribution. we model the lenses as a population of dark matter halos with an improved version of the Press-Schechter (1974) mass function.," Since lensing probes the mass and not the light distribution, we model the lenses as a population of dark matter halos with an improved version of the Press-Schechter (1974) mass function."367 For galaxv-size lenses. we follow the tradition in lensing studies and use the singular isothermal spheres (SIS) as the mass prolile (e.g.. Turner et al.," For galaxy-size lenses, we follow the tradition in lensing studies and use the singular isothermal spheres (SIS) as the mass profile (e.g., Turner et al."368 1984: Naravan White 1933: INochanek 1996)., 1984; Narayan White 1988; Kochanek 1996).369 The SIS ensures flat rotation curves and is consistent with constraints on the inner mass profiles of elliptical galaxies (e.g.. Rasin Ma 2001: Ras et al.," The SIS ensures flat rotation curves and is consistent with constraints on the inner mass profiles of elliptical galaxies (e.g., Rusin Ma 2001; Rix et al."370 1997: IXochanek 1995: Cohn et al., 1997; Kochanek 1995; Cohn et al.371 2001)., 2001).372 For cluster-size lenses. however. the mass prolile iV. mostly determined by the dark matter.," For cluster-size lenses, however, the mass profile is mostly determined by the dark matter."373 For (his. we take advantage of the recent progress iΕν hieh resolution N-body simulations aud model (he lenses with the phenomenological prolile of Navarro et al. (," For this, we take advantage of the recent progress in high resolution $N$ -body simulations and model the lenses with the phenomenological profile of Navarro et al. ("374NEW. 1997).,"NFW, 1997)."375 This approach allows us to calculate both small-separatioΕν (oalaxyv-basecl) ancl wide-separation (dark matter-based) lensing phenomena concurrently., This approach allows us to calculate both small-separation (galaxy-based) and wide-separation (dark matter-based) lensing phenomena concurrently.376 It also enables us to relate the lensing probabilities directly to cosmological parameters throug[un (he mass power spectrum Chat governs the number density of lenses. aud the lensing cross sections.," It also enables us to relate the lensing probabilities directly to cosmological parameters through the mass power spectrum that governs the number density of lenses, and the lensing cross sections."377 Approximating lenses with a mixture of SIS and dark matter profiles is supported by simple barvon cooling models (Ixeeton 1993: Ikochanek White 2001) and has been used, Approximating lenses with a mixture of SIS and dark matter profiles is supported by simple baryon cooling models (Keeton 1998; Kochanek White 2001) and has been used3786 we summarize our main conclusions.,\ref{sec:conclusions} we summarize our main conclusions.379 We assume that all stars in our model galaxies formec in clusters. and introduce a framework based on previous empirical and theoretical work for treating the formation. migration and dissolution of these young stellar clusters.," We assume that all stars in our model galaxies formed in clusters, and introduce a framework based on previous empirical and theoretical work for treating the formation, migration and dissolution of these young stellar clusters."380 I Section 2.2. we discuss a theoretically motivated descriptio of cluster migration in spheroidal and disk galaxies. taking into account the dominant form of dynamical friction torque acting on a migrating cluster in each type of galaxy.," In Section \ref{subsec:migration} we discuss a theoretically motivated description of cluster migration in spheroidal and disk galaxies, taking into account the dominant form of dynamical friction torque acting on a migrating cluster in each type of galaxy."381 In Sectio 2.3 we describe an empirically motivated model of cluster disruption based on observations of young clusters m disk galaxies., In Section \ref{subsec:disruption} we describe an empirically motivated model of cluster disruption based on observations of young clusters in disk galaxies.382 In Section 2.1. we introduce the initial cluster mass function. which seems to be generic to star formation in all galaxies. including the Milky Way.," In Section \ref{subsec:icmf} we introduce the initial cluster mass function, which seems to be generic to star formation in all galaxies, including the Milky Way."383" The initial cluster mass function (ICMP) contains about equal mass on all cluster mass scales. 1.e..Srestrm MoM CL) with à—2 (e.g..Biketal. 2010).. where M denotes initial cluster mass and M, and M4, are galaxy-dependent cutoffs."," The initial cluster mass function (ICMF) contains about equal mass on all cluster mass scales, i.e., < M < , with $\alpha\sim 2$ \citep[e.g.,][]{Bik:03,deGrijs:03,Hunter:03,Rafelski:05,Chandar:10}, , where $M$ denotes initial cluster mass and $M_{\rm min}$ and $M_{\rm384 max}$ are galaxy-dependent cutoffs."385 We adopt a=2 and Mj=100M in what follows: our results will depend only weakly on Mj;.. since clusters with masses below ~107M.. are disrupted before they can migrate to the center from larger radii and. if they do reach the center. contribute an insignificant fraction of the total NSC mass.," We adopt $\alpha=2$ and $M_{\rm386 min}=100\,M_\odot$ in what follows; our results will depend only weakly on $M_{\rm min}$ since clusters with masses below $\sim10^4\,M_\odot$ are disrupted before they can migrate to the center from larger radii and, if they do reach the center, contribute an insignificant fraction of the total NSC mass."387 The definition of a high-mass cutoff the ICMF and the statistical significance of observational evidenceof for such a cutoff have been the subject of debate., The definition of a high-mass cutoff of the ICMF and the statistical significance of observational evidence for such a cutoff have been the subject of debate.388" We assume here that the ICMF is indeed subject to high mass truncation. and treat My, as a free parameter that varies over the range 10!M..—10/.. which includes the cutoffs reported for the nearby galaxies."," We assume here that the ICMF is indeed subject to high mass truncation, and treat $M_{\rm max}$ as a free parameter that varies over the range $10^4\,M_\odot-10^7\,M_\odot$, which includes the cutoffs reported for the nearby galaxies."389 We will find in Section 4. that masses of nuclear clusters in our calculations are most sensitive to the truncation mass. and thus the photometry. of spheroidal and disk galaxies.," We will find in Section \ref{sec:results} that masses of nuclear clusters in our calculations are most sensitive to the truncation mass, and thus the photometry, of spheroidal and disk galaxies."390 If combined with a theoretical model of cluster migration and dissolution. this sensitivity can be utilized to indirectly constrain the ICMF truncation mass scale in these galaxies.," If combined with a theoretical model of cluster migration and dissolution, this sensitivity can be utilized to indirectly constrain the ICMF truncation mass scale in these galaxies."391" The maximum cluster mass forming in NGC 6946. MSI. andthe Antennae has been estimated from observations to be Mya,~109M.. (Gielesetal.2006b.c)."," The maximum cluster mass forming in NGC 6946, M51, andthe Antennae has been estimated from observations to be $M_{\rm392 max}\sim10^6\,M_\odot$ \citep{Gieles:06b,Gieles:06c}."393. Frequently. an ICMF with an exponential cutoff dn/dMMe™) is found to adequately approximate the truncation of the ICMF at the high-mass end.," Frequently, an ICMF with an exponential cutoff $dn/dM\propto394M^{-\alpha}e^{-M/M_\star}$ is found to adequately approximate the truncation of the ICMF at the high-mass end."395" In spirals and irregulars the mass truncation scales M, and Mya, are in the range —2«I0?107?M. (see.e.g..Zhang&Fall1999;Biketal.2003:deGrijsal.2003:Dowellet2008:Larsen2009;Gieles 2009)."," In spirals and irregulars the mass truncation scales $M_\star$ and $M_{\rm max}$ are in the range $\sim 2\times 10^5 - 10^{7.5} M_\odot$ \citep[see,396 e.g.,][]{Zhang:99,Bik:03,deGrijs:03,Dowell:08,Larsen:09,Gieles:09}."397". The exponential mass truncation scale. which has typical values of M,2.«410M.. is larger in denser starburst environments (Larsen2009)."," The exponential mass truncation scale, which has typical values of $M_\star\sim 2\times 10^5 M_\odot$, is larger in denser starburst environments \citep{Larsen:09}."398. In the present work. we adopt the abrupt truncation with Mj4;. but we do not anticipate that the results would be substantially different if exponential truncation were used.," In the present work, we adopt the abrupt truncation with $M_{\rm max}$, but we do not anticipate that the results would be substantially different if exponential truncation were used."399 The maximum mass of clusters that formed in the assembly of nucleated spheroidals is unknown. but a brief theoretical speculation may be in order.," The maximum mass of clusters that formed in the assembly of nucleated spheroidals is unknown, but a brief theoretical speculation may be in order."400" In a gas disk with surface density Xa. Close to the critical value ~10M.pc corresponding to the column density N—I0?!em that is required for the presence of a self-shielding cold phase (see.e.g..Schaye2004) and Toomre parameters Q—I. the truncation scale My (or M.) should scale with the Jeans mass of the disk. 4. at where fs=0.1ο""ES is the star formation efficiency and H is the epicyclic frequency (see.e.g..Elmegreenetal.2008)."," In a gas disk with surface density $\Sigma_{\rm gas}$ close to the critical value $\sim 10\, M_\odot\,\textrm{pc}^{-2}$ corresponding to the column density $N\sim 10^{21}\,\textrm{cm}^{-2}$ that is required for the presence of a self-shielding cold phase \citep[see,401 e.g.,][]{Schaye:04} and Toomre parameters $Q\lesssim 1$, the truncation scale $M_{\rm max}$ (or $M_\star$ ) should scale with the Jeans mass of the disk, )^3, where $f_{\rm SF} =0.1 f_{\rm SF,-1}$ is the star formation efficiency and $\kappa$ is the epicyclic frequency \citep[see,402 e.g.,][]{Elmegreen:08b}."403 The reference epicyclic frequency in equation (2)) was selected to correspond to the characteristic average total mass density 0.1M..pe in the inner 300pe of the (largely non-nucleated) dwarf spheroidal satellites of the Milky Way (Strigartetal.2008).. but of course. the proto-spheroidals would have been characterized by larger. radius-dependent values of s.," The reference epicyclic frequency in equation \ref{eq:Jeans_mass}) ) was selected to correspond to the characteristic average total mass density $\sim4040.1\,M_\odot\,\textrm{pc}^{-3}$ in the inner $300\,\textrm{pc}$ of the (largely non-nucleated) dwarf spheroidal satellites of the Milky Way \citep{Strigari:08}, , but of course, the proto-spheroidals would have been characterized by larger, radius-dependent values of $\kappa$."405" If the gas disk mass is a fixed proportion of the total (e.g.. dark matter) enclosed mass. and the vertical ⋋∁∐∣⊖∣↴⊜≣∶↔⊺∣⇈∪↑↴↾∣↴⊜↳∐⋋↥∖⊳≣⋋∣∣⋅⋔⊖∏∕⋅⊳∖ X.h∣7, which would imply a weaker dependence My;Xife on the gas surface density."," If the gas disk mass is a fixed proportion of the total (e.g., dark matter) enclosed mass, and the vertical scale height of the disk is $h$, then $\kappa\propto \Sigma_{\rm gas}^{1/2}\,h^{-1/2}$, which would imply a weaker dependence $M_{\rm max}\propto \Sigma_{\rm gas}406\, h^2$ on the gas surface density."407 It is plausible that proto-spheroidals assembled from an ICMF reaching the cluster mass scale associated with the gas disk Jeans mass estimated in equation (2))., It is plausible that proto-spheroidals assembled from an ICMF reaching the cluster mass scale associated with the gas disk Jeans mass estimated in equation \ref{eq:Jeans_mass}) ).408 A gravitationally-bound star cluster migrates on a time scale =(6) higwhere R tLis a characteristicTor; size of the orbit—the equivalent of the semimajor axis in a non-Keplerian potential. / is the angular momentum of the cluster. and (Το) 1s the orbit-averaged dynamical friction torque.," A gravitationally-bound star cluster migrates on a time scale =, where $R$ is a characteristic size of the orbit—the equivalent of the semimajor axis in a non-Keplerian potential, $J$ is the angular momentum of the cluster, and $\left<T_{\rm DF}\right>$ is the orbit-averaged dynamical friction torque."409 All. galactic mass components (dark matter. gas disk. stars) respond dynamically to the cluster but the mechanism of torque coupling varies.," All galactic mass components (dark matter, gas disk, stars) respond dynamically to the cluster but the mechanism of torque coupling varies."410 We separately consider the dynamical friction torque in spheroidal and disky mass components., We separately consider the dynamical friction torque in spheroidal and disky mass components.411 In spheroidal stellar systems or dark matter halos. N-body simulations have shown that the torque from a nonrotating collisionless halo can be heuristically described with the Chandrasekhar formula for dynamical friction.vecV..(7) where p is the local combined density of stars and dark matter. |V|—OR is the velocity of the cluster. InCV) is the Coulomb logarithm. and 4(V) is the mass fraction of starsordark matter particles with velocities less than V.," In spheroidal stellar systems or dark matter halos, $N$ -body simulations have shown that the torque from a nonrotating collisionless halo can be heuristically described with the Chandrasekhar formula for dynamical friction, where $\rho$ is the local combined density of stars and dark matter, $|\vec{V}|\sim \Omega R$ is the velocity of the cluster, $\ln(\Lambda)$ is the Coulomb logarithm, and $\chi(V)$ is the mass fraction of starsordark matter particles with velocities less than $V$ ."412 Because the kinematic structure of actual halos differs from. the premises of Chandrasekhar's derivation. N-body simulations arenecessary to obtain the correct normalization of the torque amplitude.," Because the kinematic structure of actual halos differs from the premises of Chandrasekhar's derivation, $N$ -body simulations arenecessary to obtain the correct normalization of the torque amplitude."413 The numerically evaluated torques (e.g..Ve- can be modeled with Chandrasekhar's formula if the Coulomb logarithm is treated as an empirically-calibrated," The numerically evaluated torques \citep[e.g.,][]{Velazquez:99,Penarrubia:02,Penarrubia:04,Spinnato:03}414 can be modeled with Chandrasekhar's formula if the Coulomb logarithm is treated as an empirically-calibrated"415Here the speed of light is 1. P=(1—V?)U? is the Lorentz factor of the uuperturbed flow. Wwp25laneslmπια is the square of the plasma frequency. A=ArEV. prime is the z-derivative.,"Here the speed of light is $1$ , $\Gamma \equiv (1-V^2)^{-1/2}$ is the Lorentz factor of the unperturbed flow, $\omega _p^2\equiv {4\pi ne^2\over \Gamma ^3m}$ is the square of the plasma frequency, $\Lambda \equiv \lambda +ikV$ , prime is the $x$ -derivative."416 Maxwell equations with this Olinirs law give the following eigeumocde equation: For tangential discontiuuity. VCr)signGr). nGr)=const. oue gets the erowth rate The eigenmodes with [AV]<& are unstable.," Maxwell equations with this Ohm's law give the following eigenmode equation: For tangential discontinuity, $V(x)=V~sign(x)$, $n(x)=const$, one gets the growth rate The eigenmodes with $|kV|<\omega _p$ are unstable."417The maximal growthrate À=I isachieved at wavenunmber 5=2/21 XX. ,The maximal growthrate $\lambda ={\omega _p\over 2\sqrt{2}}$ isachieved at wavenumber $k={\sqrt{3}\omega _p\over 2\sqrt{2}V}$ 418"values implied by Vi,sin;= 120km/s (from Section 3.6) as à function of mass ratio between 4=0.2 and q=2.0.",values implied by $V_{rot}\sin i=120$ km/s (from Section 3.6) as a function of mass ratio between $q=0.2$ and $q=2.0$.419" The dotted lines show the cllects of changing V,sin; by c20km/s. The dashed lines in Figure 9 represent the [x-Corrected. secondary star velocity às à function of the mass ratio. for the cases NA.=O% and AA= 24%."," The dotted lines show the effects of changing $V_{rot}\sin i$ by $\pm20$ km/s. The dashed lines in Figure \ref{f7b}420 represent the K-corrected secondary star velocity as a function of the mass ratio, for the cases $\Delta K=0\%$ and $\Delta K=24\%$ ."421 We find a sell-consistent. value of q in the range 0.5r0.8 when no correction for possible heating effects is applied (Adv=0% , We find a self-consistent value of $q$ in the range $0.5-0.8$ when no correction for possible heating effects is applied $\Delta K=0\%$ ).422"This does not agree with the mass ratio range derived. for either He HE or UV. A, velocities. which are indicated. in Figure 9.."," This does not agree with the mass ratio range derived for either He II or UV $K_1$ velocities, which are indicated in Figure \ref{f7b}."423 When XA=24 1¢ allowed mass ratio range isg=0.6LI (Figure 9)). and again does not overlap with either the He HL or UV range.," When $\Delta424K=24\%$, the allowed mass ratio range is $q=0.6-1.1$ (Figure \ref{f7b}) ), and again does not overlap with either the He II or UV range."425 This can be more clearly seen in Figure 10 where the derived values of g are expressed as a function of A., This can be more clearly seen in Figure \ref{f7c} where the derived values of $q$ are expressed as a function of $\Delta K$.426 The solid black line in Figure 10. shows the mass ratio at which the AS value implied by Vii;sin?=120 km/s equals the Ix-corrected: value of A» (adopting an observed. value of A» of 221 km/s)., The solid black line in Figure \ref{f7c} shows the mass ratio at which the $K_2$ value implied by $V_{rot}\sin i=120$ km/s equals the K-corrected value of $K_2$ (adopting an observed value of $K_2$ of 221 km/s).427 Again the dotted lines indicate the elect of changing νοsin7 bv x20 km/s. The dashed and thick solid lines represent the mass ratio derived. using the He LL and UV line estimates of A4 in combination with the Ix-corrected value of A». as à function of Adv.," Again the dotted lines indicate the effect of changing $V_{rot}\sin i$ by $\pm 20$ km/s. The dashed and thick solid lines represent the mass ratio derived using the He II and UV line estimates of $K_1$ in combination with the K-corrected value of $K_2$, as a function of $\Delta K$."428" Figure 10. shows that Vusini is consistent with the He LI-based mass ratio range only for Adv>344%. and higher still for the UV-based A, value (cf."," Figure \ref{f7c} shows that $V_{rot}\sin i$ is consistent with the He II-based mass ratio range only for $\Delta K>34\%$, and higher still for the UV-based $K_1$ value (cf."429 our best estimate of Ady~24! 4)., our best estimate of $\Delta K\sim24\%$ ).430 This is greater than the we find in Section 4.2. suggesting that velocities found using the UV and Le IL emission lines may contain non-orbital components.," This is greater than the we find in Section 4.2, suggesting that velocities found using the UV and He II emission lines may contain non-orbital components."431 Using the Roche Lobe geometry. a relationship between the mass ratio (q). orbital inclination angle (7) and eclipse duration was derived by Chanan (1976) and. also by Lorne (1993).," Using the Roche Lobe geometry, a relationship between the mass ratio $q$ ), orbital inclination angle $i$ ) and eclipse duration was derived by Chanan (1976) and also by Horne (1993)."432 Because the temperature of the accretion clisk increases towards its centre. the UV. emission of the disk will be more concentrated around the white dwarf than the optical emission.," Because the temperature of the accretion disk increases towards its centre, the UV emission of the disk will be more concentrated around the white dwarf than the optical emission."433 Thus an eclipse width at hall light measured in the UV is likely to be a better approximation to the white chwarl eclipse duration than one measured. in the optical band., Thus an eclipse width at half light measured in the UV is likely to be a better approximation to the white dwarf eclipse duration than one measured in the optical band.434 Using the relationships of Chanan (1976) and Llorne (1993). he mass ratio. and the eclipse width at half light of 0.07740.002 from the UV light curves of Mason. (1997). a set of inclination angles can be calculated.," Using the relationships of Chanan (1976) and Horne (1993), the mass ratio, and the eclipse width at half light of $0.077\pm0.002$ from the UV light curves of Mason (1997), a set of inclination angles can be calculated."435" These inclination angles range from 73° to 19"" [or mass ratios between 0.5 and 1.1.", These inclination angles range from $73^o$ to $79^o$ for mass ratios between $0.5$ and $1.1$.436 Hence a range of masses for the primary and secondary stars can be derived: using. and. The results derived using the UV and He LE AY velocities are shown in Figure Ll...," Hence a range of masses for the primary and secondary stars can be derived using, and, The results derived using the UV and He II $K_1$ velocities are shown in Figure \ref{f10}. ."437 Using the UV. measurement. both the uncorrected and. Ixk-corrected. mass ratios lie above the critical value of 4/3 (Section. 4.3). in the region of the diagram where mass transfer is unstable.," Using the UV measurement, both the uncorrected and K-corrected mass ratios lie above the critical value of 4/3 (Section 4.3), in the region of the diagram where mass transfer is unstable."438 The upper mass for the primary star exceeds the Chandrasekhar mass limit of 1.434... and the secondary star mass is also very large and inconsistent withthat of à main sequence star.," The upper mass for the primary star exceeds the Chandrasekhar mass limit of $1.44M_{\odot}$, and the secondary star mass is also very large and inconsistent withthat of a main sequence star."439 Εις reinforces our suspicions that the UV. velocities contain a non-orbital component., This reinforces our suspicions that the UV velocities contain a non-orbital component.440 A reduction. of A» below the Ix- value ofI?Skm/s would. decrease the secondary mass. but further increase the mass ratio.," A reduction of $K_2$ below the K-corrected value of178km/s would decrease the secondary mass, but further increase the mass ratio."441dust condensation radius (Waters et al. 1996)).,dust condensation radius (Waters et al. \cite{waters96}) ).442 ISO las also detected hermal enmüssiou aud absorption by water. in both the gaseous and solid (ice) phases (ee. Barlow 1998)). frou O-rich ciremustellar euviromnuenuts.," ISO has also detected thermal emission and absorption by water, in both the gaseous and solid (ice) phases (e.g. Barlow \cite{barlow}) ), from O-rich circumstellar environments."443 Iu this paper we preseut ISO spectra of seven well-known OILI/IR stars covering a rause of mass-loss rates., In this paper we present ISO spectra of seven well-known OH/IR stars covering a range of mass-loss rates.444 The spectrum of the archetypal Mira variable. ο Cet. is presented for comparison.," The spectrum of the archetypal Mira variable, $o$ Cet, is presented for comparison."445 For most of our targets. the spectra cover the complete 197500 spectral range of ISO.," For most of our targets, the spectra cover the complete $\mu$ m spectral range of ISO."446 Sect., Sect.447 2 of the paper describes the observations and data reduction., 2 of the paper describes the observations and data reduction.448 In Sect., In Sect.449 3. the spectra are presented and analyzed. with cuphasis on the determination of the continu aud the features due to ices aud silicates.," 3, the spectra are presented and analyzed, with emphasis on the determination of the continuum and the features due to ices and silicates."450 Concludiug remarks are made in Sect., Concluding remarks are made in Sect.451" 4,", 4.452 Seven of our cight sources were observed with both the SWS aud LWS iustraucuts. while of 0.3 ouly the SWS data were useful.," Seven of our eight sources were observed with both the SWS and LWS instruments, while of $-$ 0.3 only the SWS data were useful."453 Table 1 lists the sources observed. audthe JD dates of the observations (lencefortl we abbreviate the OII/IR star desiguations to OITIO1.9. OM127.8 etc).," Table \ref{obs} lists the sources observed, and the JD dates of the observations (henceforth we abbreviate the OH/IR star designations to OH104.9, OH127.8 etc)."454 Some of our sources (0.5. OITIOL9. OIT26.5) were observed nearly coutcmporancously with the two iustruineuts. while for others. the two spectra were taken nore than 100 davs apart.," Some of our sources (e.g. OH104.9, OH26.5) were observed nearly contemporaneously with the two instruments, while for others, the two spectra were taken more than 100 days apart."455 In the past. modelling work (e.g. Loreuz-Miutius de Aratijjo 1997)) has been uncered to some extent by the non-uuulttaueitv of NIR photometry aud 10-20 μι spectra (usually TRAS LRS data).," In the past, modelling work (e.g. Lorenz-Martins de Araújjo \cite{lorenz}) ) has been hindered to some extent by the non-simultaneity of NIR photometry and 10-20 $\mu$ m spectra (usually IRAS LRS data)."456 The fact that the SWS spectrum covers both hese waveleneth regions at a single epoch will be useful or future modelling of these sources (semper et al. in reparation).," The fact that the SWS spectrum covers both these wavelength regions at a single epoch will be useful for future modelling of these sources (Kemper et al, in preparation)."457 The 2.3815.2 jun part of the spectrum was obtained using the ISO Short Wavelength Spectrometer (SWS)., The 2.38–45.2 $\mu$ m part of the spectrum was obtained using the ISO Short Wavelength Spectrometer (SWS).458 A detailed description of the instrament can be found iu de Can et al. (19963))., A detailed description of the instrument can be found in de Graauw et al. \cite{degraauw}) ).459 Our objects were observed iu AOT 1l mode. speed 2. except for Mira. (speed. 3) aud OIILOLO (speed 1).," Our objects were observed in AOT 1 mode, speed 2, except for Mira (speed 3) and OH104.9 (speed 1)."460 The spectrum scanned with SWS contains 12 subspectra. that each consist of two scans. one in the direction of decreasing wavelength (up) sca) and one iu the increasing wavelength direction (dow scan).," The spectrum scanned with SWS contains 12 subspectra, that each consist of two scans, one in the direction of decreasing wavelength (`up' scan) and one in the increasing wavelength direction (`down' scan)."461 There are sinall regions of overlap iu wavelength between the subspectra., There are small regions of overlap in wavelength between the subspectra.462 Each sub-spectriua is recorded by 12 indepencent detectors., Each sub-spectrum is recorded by 12 independent detectors.463 The data reduction was performed using the ESA SWS package (IA°). together with the calibration files available in January 1999. equivalent to pipe-line version 6.)," The data reduction was performed using the ESA SWS package $^{\rm 3}$ ), together with the calibration files available in January 1999, equivalent to pipe-line version 6.0."464 We started from the Staudard Processed Data (SPD) to determine the final spectrum. according to the steps described im this session.," We started from the Standard Processed Data (SPD) to determine the final spectrum, according to the steps described in this session."465 The observations suffer from severe micimory effects i the LOs12.0 gan and 29.0.15.2 pan wavelength regions., The observations suffer from severe memory effects in the 4.08–12.0 $\mu$ m and 29.0–45.2 $\mu$ m wavelength regions.466 It is possible to correct for the iemoryv effects for the individual detectors. using a combined dark-curreut and mcmory-cttect subtraction iiethod.," It is possible to correct for the memory effects for the individual detectors, using a combined dark-current and memory-effect subtraction method."467 This method was applied assuniug that the fiw levels in these wavelcueth reeious are very high. aud treating the memory effect as eiviug an additive coutribution to the observed signal.," This method was applied assuming that the flux levels in these wavelength regions are very high, and treating the memory effect as giving an additive contribution to the observed signal."468 We also asstumed that the spurious signal from the 111011ΟΥ effect reaches a certain saturation value very quickly after the start of the wp scan. aud then remaius constant throughou the rest of the up scan and the chtire down scan.," We also assumed that the spurious signal from the memory effect reaches a certain saturation value very quickly after the start of the up scan, and then remains constant throughout the rest of the up scan and the entire down scan."469 This memory saturation value is measured mauediatelv :ter the down scan is euded. ancl is subtracted from the wp and down sceau measurements.," This memory saturation value is measured immediately after the down scan is ended, and is subtracted from the up and down scan measurements."470 The spectral shape of the memory-corrected dow sceau is now correct: the error in the spectral shape of the up scan ds corrected bv fitting a polvnonual to the up sca- and adjusting this fit to he down scan. without chaneiuen the detailed structure of the spectrum.," The spectral shape of the memory-corrected down scan is now correct; the error in the spectral shape of the up scan is corrected by fitting a polynomial to the up scan and adjusting this fit to the down scan, without changing the detailed structure of the spectrum."471 The order of the applied polvnomual fit differs per subbaud. but is cliosen to be in agreement with the spectral shape iu that baud.," The order of the applied polynomial fit differs per subband, but is chosen to be in agreement with the spectral shape in that band."472 For band 1 aud [ve mostly used polvnomials of order 1 or 2. for baud 2a. 2b and 3 we predomunautly used order 2 or 3. and for band 2e higher order polvnouials (up to order LO) were required to adjust the up scan to the down sca.," For band 1 and 4 we mostly used polynomials of order 1 or 2, for band 2a, 2b and 3 we predominantly used order 2 or 3, and for band 2c higher order polynomials (up to order 10) were required to adjust the up scan to the down scan."473 The spectra of some of our objects showed fringes iu the 12.029.0 jin wavelength region., The spectra of some of our objects showed fringes in the 12.0–29.0 $\mu$ m wavelength region.474" This was corrected using the defringe procedures of ΙΑ, ", This was corrected using the defringe procedures of $^{\rm 3}$.475Glitches caused by particle hits ou the detector were removed by haud., Glitches caused by particle hits on the detector were removed by hand.476 Clitelies can be casily recognized: they start with a sudden merease m fux level. followed by a tail which decreases exponentially with time.," Glitches can be easily recognized: they start with a sudden increase in flux level, followed by a tail which decreases exponentially with time."477 Anv οἴνοιι elitch affects oulv oue of the two scans., Any given glitch affects only one of the two scans.478 The data were further analvzed by shifting all spectra of the separate detectors to a mean value. followed by signa clipping and rebinuing to a resolution of A/AA= 600. which is reasonable for AOT 1 speed 2 observations.," The data were further analyzed by shifting all spectra of the separate detectors to a mean value, followed by sigma clipping and rebinning to a resolution of $\lambda / \Delta \lambda = 600$ , which is reasonable for AOT 1 speed 2 observations."479 We obtaiue 13197 jun erating spectra using the LWS instrument., We obtained 43–197 $\mu$ m grating spectra using the LWS instrument.480 Details of the instrument and its performance can be found iu Cleee ct al. (1996)), Details of the instrument and its performance can be found in Clegg et al. \cite{clegg}) )481 and Swinvarc ot al. (19963) , and Swinyard et al. \cite{swinyard}) )482respectively., respectively.483" The resolution elemiceu was 0.3 ,un for the the short-waveleneth detectors (Ax95 pau) are 0.6 gan for the long-wavelength detectors {A=SO µια),", The resolution element was 0.3 $\mu$ m for the the short-wavelength detectors $\lambda \leq 93$ $\mu$ m) and 0.6 $\mu$ m for the long-wavelength detectors $\lambda \geq 80$ $\mu$ m).484 Four samples were taken per resolution clement., Four samples were taken per resolution element.485 Between 6 and 26 fast eyating scaus were made of cach tarect. depending ou source brightuess aud scheduliug coustraiuts.," Between 6 and 26 fast grating scans were made of each target, depending on source brightness and scheduling constraints."486 Each scan consisted of a single sec integration per sample., Each scan consisted of a single 0.5-sec integration per sample.487 The data were reduced using the IAVS offline processing software (version 7.0). aud then averaging the scans after sigima-clipping to remove the discrepaut points caused by cosuic-ray hits.," The data were reduced using the LWS off-line processing software (version 7.0), and then averaging the scans after sigma-clipping to remove the discrepant points caused by cosmic-ray hits."488Hot subdwarf (sdB) stars are horizontal branch stars with masses near to 0.5 M. and very thin Gin mass) hydrogen envelopes.,Hot subdwarf (sdB) stars are horizontal branch stars with masses near to 0.5 $_\odot$ and very thin (in mass) hydrogen envelopes.489 Average effective temperatures and surface gravities are about 300000 K and loggy~ 55.5. respectively.," Average effective temperatures and surface gravities are about 000 K and $\log g \sim$ 5.5, respectively."490 Although it is clear that sdB stars will eventually enter the white dwarf cooling track without reaching the AGB phase (Dorman.Rood&OConnell 1993).. their formation as sdB stars is under debate.," Although it is clear that sdB stars will eventually enter the white dwarf cooling track without reaching the AGB phase \citep{dorman93}, their formation as sdB stars is under debate."491 There are several mechanisms that involve single-star or binary evolution (e.g.D'Cruz.Dorman.Roodetal.1996:Han.Podsiadlowski.Maxtedetal.2002. 2003).," There are several mechanisms that involve single-star or binary evolution \citep[e.g.][]{dcruz96,han02,han03}."492. Detection of pulsations in hot sdB stars opened a way to study their interiors and evolution prior to the horizontal branch., Detection of pulsations in hot sdB stars opened a way to study their interiors and evolution prior to the horizontal branch.493 First. short period oscillations were found by Kilkenny.Koen.O'Donoghueetal.(10997). in 114026 (now officially named AHHya).," First, short period oscillations were found by \cite{kilkenny97} in 14026 (now officially named Hya)."494 According to theoretical models these pulsations are attributed to pressure (p. modes and are driven in the outer part of the stars (Charpinet.Fontaine.sardetal. 1997., According to theoretical models these pulsations are attributed to pressure $p-$ )modes and are driven in the outer part of the stars \citep{charp97}.495 Several years after their discovery. Green.Fontaine.Reedetal.(2003) announced another kind of variability in sdB stars.," Several years after their discovery, \cite{green03} announced another kind of variability in sdB stars."496 The longer-period variations were also identified as stellar oscillations., The longer-period variations were also identified as stellar oscillations.497 In this case however. they are attributed to gravity (g. modes and originate deeper within these stars than the (p. modes (Fontaine.Brassard.Charpinetetal.2003).," In this case however, they are attributed to gravity $g-$ )modes and originate deeper within these stars than the $p-$ )modes \citep{fontaine03}."498. Both types share some overlap in the H-R diagram and so the same stellar models are appropriate for studying both kinds of pulsation., Both types share some overlap in the H–R diagram and so the same stellar models are appropriate for studying both kinds of pulsation.499 Of special interest are these rare stars showing both (p. .) and (qg modes since models of these stars can constrain their cores and outer regions simultaneously., Of special interest are these rare stars showing both $p-$ ) and $g-$ )modes since models of these stars can constrain their cores and outer regions simultaneously.500 The first hybrid sdBV star was found by Schuh.Heber.Dreizleretal.(2006) and three more have been discovered using ground-based data. with JJO45541305 being the faintest.," The first hybrid sdBV star was found by \cite{schuh06}501 and three more have been discovered using ground-based data, with J0455+1305 being the faintest."502 The Kepler satellite has also recently discovered several candidate hybrid sdBV stars (Reed.Kawaler.Ostensenetmenetal.2010b) from its survey phase with follow-up data to be obtained over the next several years.," The Kepler satellite has also recently discovered several candidate hybrid sdBV stars \citep{reed10,kawaler10,ostensen10b} from its survey phase with follow-up data to be obtained over the next several years."503 The brightest known pulsating subdwarf B. (sdBV) star has a V magnitude of 11.8. the typical brightness is about 14.5 and the faintest are 17 (Ostensen.Oreiro.Solheimetal.20100).," The brightest known pulsating subdwarf B (sdBV) star has a $V$ magnitude of 11.8, the typical brightness is about 14.5 and the faintest are 17 \citep{ostensen10a}."504 Methods for constraining the pulsation modes include multicolor photometry (Tremblay.Fontaine.Brassardetal.2006). resolution spectroscopy (Telting&Ostensen.2004.2006:Eggen.Harmsetal. 2009). a combination of these two (Baran.Pigulski&O'Toole 2008).. and time-series observations of line oofile variations using high-resolution spectrosocpy (Telting.Geier.Ostensenetal.2008:Telting.Ostensen.Oreiro 2010).," Methods for constraining the pulsation modes include multicolor photometry \citep{tremblay06}, low-resolution spectroscopy \citep{telting04,telting06,reed09}, a combination of these two \citep{baran08}, and time-series observations of line profile variations using high-resolution spectrosocpy \citep{telting08,telting10}."505. This last method requires large telescopes. where it is quite difficult o get time.," This last method requires large telescopes, where it is quite difficult to get time."506 To date. time-series spectroscopy has been obtained or only a few objects. all brighter than mmag.," To date, time-series spectroscopy has been obtained for only a few objects, all brighter than mag."507 Because of the difficulty of obtaining data spanning relatively long periods of time. he faintest stars are usually limited to discovery observations taken in one or no filter at all (so-called white light).," Because of the difficulty of obtaining data spanning relatively long periods of time, the faintest stars are usually limited to discovery observations taken in one or no filter at all (so-called white light)."508 Single-color data. which are typically obtained to increase emporal resolution. are usually not useful for mode identitication. which is necessary for constraining the models.," Single-color data, which are typically obtained to increase temporal resolution, are usually not useful for mode identification, which is necessary for constraining the models."509 To identify modes using broadband single color data one needs to assume trial values or free parameters in models and search for the best fit to observed requencies., To identify modes using broadband single color data one needs to assume trial values for free parameters in models and search for the best fit to observed frequencies.510 The large number of free parameters does not lead © strong constraints on stellar models., The large number of free parameters does not lead to strong constraints on stellar models.511 An exception is when the Tequency spectrum contains specific features. such as frequency," An exception is when the frequency spectrum contains specific features, such as frequency"512star formation iu the ceuter of the cluster cau oulv be seen in the reeular galaxy NOC L127À. At fixed limiting magnitude the ealaxv density y.ronely varies frou field to field.,star formation in the center of the cluster can only be seen in the irregular galaxy NGC 1427A. At fixed limiting magnitude the galaxy density strongly varies from field to field.513 Ou average the density oei most fields is comparable to the one in the absolute background fields., On average the density in most fields is comparable to the one in the absolute background fields.514 South iux cast of NGC 1399 we found a significant excess of galaxies as compared to the other fields., South and east of NGC 1399 we found a significant excess of galaxies as compared to the other fields.515 ILoxcever. an excess of dwarf galaxies surrounding NGC 1399 can be ruled out. since nearly all of these ealaxies belong to a backeround cluster at 2=0.11.," However, an excess of dwarf galaxies surrounding NGC 1399 can be ruled out, since nearly all of these galaxies belong to a background cluster at $z = 0.11$."516 The brightest ealaxy of this background clister possesses a extended ¢D halo aud is located 171 south of NCC 1399., The brightest galaxy of this background cluster possesses an extended cD halo and is located $1\farcm1$ south of NGC 1399.517" The strong backerouud ealaxv fluctuations inake the search for compact diyvarfs by a statistical subtraction of background objects meanineless,", The strong background galaxy fluctuations make the search for compact dwarfs by a statistical subtraction of background objects meaningless.518 The point sources iu he central Foruax fields are not uuiforiulv distributed around NGC 1399., The point sources in the central Fornax fields are not uniformly distributed around NGC 1399.519 The peak of their deustv distribution is displaced about 173 east of the center of the galaxy., The peak of their density distribution is displaced about $1\farcm3$ east of the center of the galaxy.520 Asstuuine hat most of them are no background cluster members. but rather globular clusters. two explanations secnm to be possible: (1) the ceutral elobular cluster svstemi and the bulee of NGC 1399 are discutaneled from cach other and follow different potentials. or (2) tidal tales of accreted globular clusters fron passing Fornax galaxies lave teniporanlv squewed the distribution of eglobular clusters.," Assuming that most of them are no background cluster members, but rather globular clusters, two explanations seem to be possible: (1) the central globular cluster system and the bulge of NGC 1399 are disentangled from each other and follow different potentials, or (2) tidal tales of accreted globular clusters from passing Fornax galaxies have temporarily squewed the distribution of globular clusters."521 The two catalogs given in this Appendix are available in electronic form only at the CDS via anouvmous ftp to cdsaracstrasbe.fr (130.79.128.5) or via http://cedsweb.u-strasbe.fr/Abstract.htinl., The two catalogs given in this Appendix are available in electronic form only at the CDS via anonymous ftp to cdsar.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html.522 The photometric catalog contains observational data for all galaxies (V.< 22.0) in the ceutral Fornax fields., The photometric catalog contains observational data for all galaxies $V < 22.0$ ) in the central Fornax fields.523 The second catalog coutains the paraiueters of fits to the surface brightuess profiles of a subsample of the photometric catalog., The second catalog contains the parameters of fits to the surface brightness profiles of a subsample of the photometric catalog.524 In both catalogs the objects are sorted in order of increasing right ascceension., In both catalogs the objects are sorted in order of increasing right asccension.525 Iu the following we describe the columns of the catalogs., In the following we describe the columns of the catalogs.526 Identification of the object., Identification of the object.527 It is prefixed by the acronvin CGP (Catalog of Galaxies in Fornax) followed by a sequence number of the field and the sequence nunber of the galaxy in this field (ordered with decreasing maguitude)., It is prefixed by the acronym CGF (Catalog of Galaxies in Fornax) followed by a sequence number of the field and the sequence number of the galaxy in this field (ordered with decreasing magnitude).528 For example. CCF 5-12 is the 12th brightest ealaxyv in field 5 (see also Sect.," For example, CGF 5-12 is the 12th brightest galaxy in field 5 (see also Sect."529 2.1)., 2.1).530 Right ascension for the epoch 2000 in hours. minutes aud seconds (...," Right ascension for the epoch 2000 in hours, minutes and seconds $^h$ $^m$ $^s$ )."531" Declination (2000) in degrees. nünutes aud seconds (8.4.77), "," Declination (2000) in degrees, minutes and seconds $\degr,\arcmin,\arcsec$ )."532The positious of all objects were determined relative Oo positions in the Caricle Star Catalog., The positions of all objects were determined relative to positions in the Guide Star Catalog.533 Typically 1 to ὃ catalog positions are found iu cach field., Typically 4 to 8 catalog positions are found in each field.534 Coordinate transformations with 3 plate coustauts have )en obtained., Coordinate transformations with 3 plate constants have been obtained.535 The positional accuracy of the calculated coordinates is in all fields better than0., The positional accuracy of the calculated coordinates is in all fields better than.5363%. Total V. apparent macuitude as determined w SExtractor. see Sect.l.," Total $V$ apparent magnitude as determined by SExtractor, see Sect.4."537 Values with au appended “Ww indicate that ucighboring objects are present within 2 isophotal radii., Values with an appended 'n' indicate that neighboring objects are present within 2 isophotal radii.538 V.peak surface brielitucss i iuag 7 as even by SExtractor (not seeing corrected)., $V$peak surface brightness in mag $^{-2}$ as given by SExtractor (not seeing corrected).539 (V I) colors within au aperture of 3 in ΠΟΤΟ., $V-I$ ) colors within an aperture of $3\arcsec$ in diameter.540" Ellipticity of the galaxy and the used elliptical aperture. defined as εξ1bfa,"," Ellipticity of the galaxy and the used elliptical aperture, defined as $\epsilon = 1 - b/a$."541 Position augle of the major axis of the elliptical aperture., Position angle of the major axis of the elliptical aperture.542 0 degree is in east direction. positive aueles towards the south. and negative aneles towards the north direction.," 0 degree is in east direction, positive angles towards the south, and negative angles towards the north direction."543 Size of the major axis of the elliptical aperture in aresec., Size of the major axis of the elliptical aperture in arcsec.544 Note that the limiting isophote of the ellipse slightly varies from ficld to feld depending ou the secing and sky brightuess., Note that the limiting isophote of the ellipse slightly varies from field to field depending on the seeing and sky brightness.545 Size of the major axis at au isophotal surface brightness of pi=26 imag in aresec. Dag.," Size of the major axis at an isophotal surface brightness of $\mu_V = 26$ mag in arcsec, $D_{26}$."546 Effective scui-imajor axis αμ du arescc., Effective semi-major axis $a_{\rm eff}$ in arcsec.547 Major axis coutaiuiug half of the total light measured in elliptical aperture:4., Major axis containing half of the total light measured in elliptical apertures.548 Effective surface brightness fgg. nean surface brightuess within the effective senianajor axis.," Effective surface brightness $\mu_{\rm eff}$ , mean surface brightness within the effective semi-major axis."549ccan be estimated. using the distance modulus.,can be estimated using the distance modulus.550 For a cde-reddenced apparent. magnitude of V=16.0 and a distance D9.5 kpe (nferred from the peak of the X-ray burst). we find an absolute visual magnitude of Aly1.1 mag.," For a de-reddened apparent magnitude of $V=16.0$ and a distance $D \lesssim 9.5$ kpc (inferred from the peak of the X-ray burst), we find an absolute visual magnitude of $M_V \gtrsim 1.1$ mag."551 For the estimated mass-acerction rate of ((0.1 per cent of Exldington. see Section ??)). the empirical relation derived by. vanParadijs&AleClintock(1994) predicts an absolute visual magnitude of Ady4.8 mag in case the svstem is an UCXD (assuming PuSO min)," For the estimated mass-accretion rate of (0.1 per cent of Eddington, see Section \ref{subsec:burst_ana}) ), the empirical relation derived by \citet{vanparadijs94} predicts an absolute visual magnitude of $M_V \gtrsim 4.8$ mag in case the system is an UCXB (assuming $P_{\mathrm{orb}} \lesssim 80$ min)."552 Unless iis located. at à distance 2Z2 kpe. t is thus too optically bright to be an UCXD.," Unless is located at a distance $D \lesssim 2$ kpc, it is thus too optically bright to be an UCXB."553 To be able to harbour a H-rich companion. mumust have an orbital period. of SO min (e.g...Nelsonal. 1986).," To be able to harbour a H-rich companion, must have an orbital period of $\gtrsim 80$ min \citep[e.g.,][]{nelson86}."554. In such a configuration. it will be challenging to understand how the low X-ray. luminosity can keep the accretion ongoing making the svstem persistent rather than transiont.," In such a configuration, it will be challenging to understand how the low X-ray luminosity can keep the accretion ongoing making the system persistent rather than transient."555 We are grateful to the referee. Craig Heinke. for useful comments that helped improve this manuscript.," We are grateful to the referee, Craig Heinke, for useful comments that helped improve this manuscript."556 This work was based on observations made with ESO Telescopes at the Paranal ancl La Silla Observatories under programme IDs: 281.D-5030CX) ancl 60.X-9700(D) and made use of the public data archive of aanΑΟL.. as well as publie data from the sslew survey.," This work was based on observations made with ESO Telescopes at the Paranal and La Silla Observatories under programme IDs: 281.D-5030(A) and 60.A-9700(D) and made use of the public data archive of and, as well as public data from the slew survey."557 Support for this work was provided hy the Netherlands Organization for Scientific Rescarch (NWO)., Support for this work was provided by the Netherlands Organization for Scientific Research (NWO).558 NR acknowledges support from a Ramon y. Cajal Research position., NR acknowledges support from a Ramon y Cajal Research position.559 EMC gratefully acknowledges support provided by NASA through the FEellowships Program. grant number DPI8-00052.," EMC gratefully acknowledges support provided by NASA through the Fellowships Program, grant number PF8-90052."560 We acknowledge the use of the software package written by Prof. Tom Marsh., We acknowledge the use of the software package written by Prof. Tom Marsh.561or to of the red giant population. depending ou the specific observational sample ,"for to of the red giant population, depending on the specific observational sample ."562t, Fig.563herein). Fig. 2 shows that ~70% of the projected rotational velocities in our standard immersed object population are ercater han l0kkniss5., \ref{fig:vrot-kms_1D_merger} shows that $\sim$ of the projected rotational velocities in our standard merged object population are greater than $^{-1}$.564 Combining this with the wuuber of RGB stars in our iiereed object and nonual single star nodel populations from Table 2.. and assuming a ZAMS ynary fraction of 0.5. we estimate the fraction of rapi rotators in the ROB population due to CE mergers is ~3.1%©.," Combining this with the number of RGB stars in our merged object and normal single star model populations from Table \ref{tab:dependence}, and assuming a ZAMS binary fraction of 0.5, we estimate the fraction of rapid rotators in the RGB population due to CE mergers is $\sim 3.4\%$."565 We note that this estimate ucelects ROB stars in binaries whose orbits are wide euough to avoir lnass transfer. siuce such binaries are excluded from our population of merged objects.," We note that this estimate neglects RGB stars in binaries whose orbits are wide enough to avoid mass transfer, since such binaries are excluded from our population of merged objects."566 Inclusion of these binaries increases the overall αμήν: of ROB stars. which xvouk lower our estinate.," Inclusion of these binaries increases the overall number of RGB stars, which would lower our estimate."567 Towever. it is also true that tida interactions between the RGB star aud its loweranass colupanion can still spin up the eiaut star in some of these detached biuaies.," However, it is also true that tidal interactions between the RGB star and its lower-mass companion can still spin up the giant star in some of these detached binaries."568 Even though such a system retaius its biuaritv. the presence of the companion may be masked by the much brighter RGB star aud the system could be nusidentificd observationally as a solitary RGD rapid rotator.," Even though such a system retains its binarity, the presence of the companion may be masked by the much brighter RGB star and the system could be misidentified observationally as a solitary RGB rapid rotator."569 At the moment. it is uncertain to what exteut such musidentificatious are preseut in the observational estimates above.," At the moment, it is uncertain to what extent such misidentifications are present in the observational estimates above."570 We also point out that estimate that rapid rotators produced by the ingestion of planets by RGB stars. which we do not consider. can account for ~0.6% of the RGB population.," We also point out that estimate that rapid rotators produced by the ingestion of planets by RGB stars, which we do not consider, can account for $\sim 0.6\%$ of the RGB population."571 The subsequent evolution. of rapidly rotating RGD stars can lead to the production of rapidly rotating IB stars as a result of the contraction of stars from the tip of the RGB to the WB when ποτ is ignited iu the core (see refsec:vesults})}., The subsequent evolution of rapidly rotating RGB stars can lead to the production of rapidly rotating HB stars as a result of the contraction of stars from the tip of the RGB to the HB when helium is ignited in the core (see ).572" Although we fud theoretical evidence or the rapid rotation of stars in a chuup on the red xortion of the IID iu our ITR. diagram (see vefiie:hid,,erger)). obsercationalecidence forra pidrotationanongre li"," Although we find theoretical evidence for the rapid rotation of stars in a clump on the red portion of the HB in our HR diagram (see \\ref{fig:hrd_merger}) ), observational evidence for rapid rotation among red HB field stars is lacking (e.g., )."573u st) in several due UB field stars ]Ti111. AN.," However, in a sample of 45 HB field stars, found evidence for rapid rotation $v \sin i 574\gtrsim 30$ km $^{-1}$ ) in several blue HB field stars $< T <$ K)."575" Tesuggeststhattheunderlyiigdistributionofactualy dau +) and a fast population (esini~30 auos 4), similar to the bimodal distribution found in uauv elobular clusters."," He suggests that the underlying distribution of actual rotational velocities in blue HB field stars may be bimodal, consisting of a slow population $v \sin i \sim 10$ km $^{-1}$ ) and a fast population $v \sin i \sim 30$ km $^{-1}$ ), similar to the bimodal distribution found in many globular clusters."576" If a larecr sample of WB field stars confinis the possibility of a bimodal distribution iu rotational velocities. the fast-rotating population nav result from the mergers studied, in this paper."," If a larger sample of HB field stars confirms the possibility of a bimodal distribution in rotational velocities, the fast-rotating population may result from the mergers studied in this paper."577" 0qu »opulation of very rapidly ""OO 3 stars wav eblve under the action of euliaucét SA wind mass tempenaturenofasingkeostarsadoss due to, the reduction of. surtage eravity associate1 | r"," As already pointed out by, the merged population of very rapidly rotating HB stars may evolve under the action of enhanced stellar wind mass loss due to the reduction of surface gravity associated with centrifugal effects."578otating HB stars may lose a significant fraction of heir euvelope. which would cause both a reduction iu he rotation rate of the star because of the associated angular moment loss and ai bilneward movement in the IIR. cliiagram.," As a result, some very rapidly rotating HB stars may lose a significant fraction of their envelope, which would cause both a reduction in the rotation rate of the star because of the associated angular momentum loss, and a blueward movement in the HR diagram."579 Such stars may contribute to the rapid rotation of blue WB stays in the field found bv and. if sufficient mass is lost. provide au evolutionary channel for the formation of suele sdB stars.," Such stars may contribute to the rapid rotation of blue HB stars in the field found by and, if sufficient mass is lost, provide an evolutionary channel for the formation of single sdB stars."580 predict a spectrum of nasses ranging from 0.32 to ~(0.7AL. with a strong oak between 0.17 and O.SLAL.., predict a spectrum of masses ranging from 0.32 to $\sim 0.7\Msun$ with a strong peak between 0.47 and $0.54\Msun$.581 This djs consistent with the small umber of observationally determined uasses for single sdBostars. the majority of which lave masses between 0.16 and O.SLAL.. but can be as πια as 0.39AL.)..," This is consistent with the small number of observationally determined masses for single sdB stars, the majority of which have masses between 0.46 and $0.54\Msun$, but can be as small as $0.39\Msun$."582 We further note that. although our models have solar uetallicitv. if simular rapid rotation and subsequent uass loss ou the IID is found for merger models with ower moetallieities. this may be relevant to the extended IID morphologies found iu globular clusters (e.¢.. 2008)).," We further note that, although our models have solar metallicity, if similar rapid rotation and subsequent mass loss on the HB is found for merger models with lower metallicities, this may be relevant to the extended HB morphologies found in globular clusters (e.g., )."583 Another class of stars that possibly mav result frou a inerecr during CE evolution are Εν Comac stars., Another class of stars that possibly may result from a merger during CE evolution are FK Comae stars.584 These stars are rapidly rotating giauts with LOO t and spectral types G and K1981)... An origin involving the evolution of a rapidly rotating single AIS star is not a viable oue. since the progenitors of FIX Comac stars would have rapid rotation and be chromospherically active. whereas none have Όσοι discovered.," These stars are rapidly rotating giants with $v \sin i \sim 100$ $^{-1}$ and spectral types G and K. An origin involving the evolution of a rapidly rotating single MS star is not a viable one, since the progenitors of FK Comae stars would have rapid rotation and be chromospherically active, whereas none have been discovered."585 Ou the other hau. the coalescence of evolve: contact binaries remains as a viable evolutionary scenario. aud we sugeest that the merecr of uon-corotatius CE binarics may also contribute to this population.," On the other hand, the coalescence of evolved contact binaries remains as a viable evolutionary scenario, and we suggest that the merger of non-corotating CE binaries may also contribute to this population."586 We note. however. that our current mode population does not contain mereed objects of the correc spectral type. although this may be due to our use of nou- stellar models for these objects.," We note, however, that our current model population does not contain merged objects of the correct spectral type, although this may be due to our use of non-rotating stellar models for these objects."587 Incorporation of stellar models that include rotation would be especially Huportant iu deterimunius the wviabilitv of the imerser scenario for Fly Comaoe stars., Incorporation of stellar models that include rotation would be especially important in determining the viability of the merger scenario for FK Comae stars.588 Asa consequence of the merger process. it is likely that there exists a nouspherical distribution of circumstellar matter surrounding the remmant. either resulting from matter which is not accreted nor ejected from the svstem ΠΠ merecr or from an cuhanced mass-loss phase from the equatorial region of the rapidly rotating star.," As a consequence of the merger process, it is likely that there exists a nonspherical distribution of circumstellar matter surrounding the remnant, either resulting from matter which is not accreted nor ejected from the system during merger or from an enhanced mass-loss phase from the equatorial region of the rapidly rotating star."589 In the, In the590discuss here is relatively insensitive to the bulk Lorentz [actor of the outgoing jet. unlike other proposed sources of multi-GeV GRD neutrinos.,"discuss here is relatively insensitive to the bulk Lorentz factor of the outgoing jet, unlike other proposed sources of multi-GeV GRB neutrinos."591 The mechanism giving rise to the variability in the outgoing jet can be crudely represented as (he closing of a dense door composed of stellar material al some point along the jet axis., The mechanism giving rise to the variability in the outgoing jet can be crudely represented as the closing of a dense door composed of stellar material at some point along the jet axis.592 This results in a forward shock propagating into aud accelerating the stellar material. ancl a reverse shock propagating backwards and slowing the jet.," This results in a forward shock propagating into and accelerating the stellar material, and a reverse shock propagating backwards and slowing the jet."593 Decause the stellar material blocking the passage of the jet is typically verv dense relative to the jet material. the forward shock will only be mildly relativistic ancl uninteresting as [ar as a detectable neutrino signature is concerned.," Because the stellar material blocking the passage of the jet is typically very dense relative to the jet material, the forward shock will only be mildly relativistic and uninteresting as far as a detectable neutrino signature is concerned."594 The top panel of Fig., The top panel of Fig.595" 1 illustrates the shocking ancl structure of the oulgoing, jet.", \ref{blob2} illustrates the shocking and structure of the outgoing jet.596 As particles in the jet traverse the reverse shock. they are decelerated from a Lorentz factor pt to a Lorentz [actor p«r.," As particles in the jet traverse the reverse shock, they are decelerated from a Lorentz factor $\Gamma_j^{(L)}$ to a Lorentz factor $\Gamma_{sh}^{(L)}<\Gamma_j^{(L)}$."597 llere the superscript CL) denotes a quantity as measured in the rest frame of the collapsing star., Here the superscript $(L)$ denotes a quantity as measured in the rest frame of the collapsing star.598 The relative Lorentz [actor across the shock is Dy.&Γιore," The relative Lorentz factor across the shock is $\Gamma_{rel}\approx599\Gamma_j^{(L)}/2\Gamma_{sh}^{(L)}$."600 Numerical simulations of relativistic jets propagating in stars indicate that the typical relative Lorentz factor is substantial., Numerical simulations of relativistic jets propagating in stars indicate that the typical relative Lorentz factor is substantial.601 Zhang et al., Zhang et al.602 studied the propagation of a relativistic jet in à 15.V. star for 3 different initial jet. conditions., studied the propagation of a relativistic jet in a $\Msun$ star for 3 different initial jet conditions.603 Typical values of Tg for their simulations are given in Table 1.., Typical values of $\Gamma_{rel}$ for their simulations are given in Table \ref{thetable}.604 The simulations of Zhang et al..," The simulations of Zhang et al.,"605 as well as observations of many peaks in observed GRB liehteurves. indicate (hat a substantial fraction (half or more) of the jet undergoes a slowing via relativistic shocks.," as well as observations of many peaks in observed GRB lightcurves, indicate that a substantial fraction (half or more) of the jet undergoes a slowing via relativistic shocks."606 The gross properties of the reverse shock slowing the jet are given bv the jump conditions., The gross properties of the reverse shock slowing the jet are given by the Rankine-Hugoniot jump conditions.607" In particular. (e proper barvon nunber densitv in the shocked jet G.e. the barvon number density as measured in a frame comoving with the shocked fIuid) ls n,£2ADun. where n; is the proper barvon number density in the unshocked jet."," In particular, the proper baryon number density in the shocked jet (i.e. the baryon number density as measured in a frame comoving with the shocked fluid) is $n_{sh}\approx6084\Gamma_{rel} n_j$, where $n_j$ is the proper baryon number density in the unshocked jet."609" For radii larger than zzLOTan, which is the region of interest in the present work. the outgoing jet is coasting rather than accelerating (Piran.Shemi.&Naravan1993)."," For radii larger than $\approx 10^6\Gamma_j^{(L)}{\rm610cm}$, which is the region of interest in the present work, the outgoing jet is coasting rather than accelerating \citep{coast}."611. In the coasting regime. n; is. determined. by barvon number conservationB as n;=L/4xr>msc(E3y," In the coasting regime, $n_j$ is determined by baryon number conservation as $n_j=L/4\pi r^2 m_N c^3 (\Gamma_j^{(L)})^2$."612 Observations of GRBs suggest that the isotropic equivalent huninosity L is of order L>I07erg/sec 2001).. and (hat tvpically p=200 (Lithwick&Sari2001)..," Observations of GRBs suggest that the isotropic equivalent luminosity $L$ is of order $L\gtrsim 10^{52}{\rm erg/sec}$ \citep{frail}, and that typically $\Gamma_j^{(L)}\gtrsim 200$ \citep{lith}."613" The energy density in the shocked jet fluid is C,zzDinarivet. provided that the specific enthalpy in the unshocked jet is small (i.e. Chat the jet is in the coasting regime)."," The energy density in the shocked jet fluid is $U_{sh}\approx \Gamma_{rel} n_{sh} m_N c^2$, provided that the specific enthalpy in the unshocked jet is small (i.e. that the jet is in the coasting regime)."614 In the middle panel of Fig., In the middle panel of Fig.615 1. we show the evolution. of: 7; and I; (Lj).in the jet.., \ref{blob2} we show the evolution of $n_j$ and $\Gamma_j^{(L)}$ in the jet.616 Pion production and associated neutrino production in the reverse shock depend in detail, Pion production and associated neutrino production in the reverse shock depend in detail617"upper liit may be obtained without a kuowledge of he full distribution function of the halo model aud of he MACIIOs mass fuuction (hereafter AIF). Le, the julICL density of ATACTIOs with Mass in the rauge (μμddg).","upper limit may be obtained without a knowledge of the full distribution function of the halo model and of the MACHO's mass function (hereafter MF), i.e. the number density of MACHOs with mass in the range $(\mu, \mu + d\mu)$."618 The result obtained |»* Iservins was proved Taccr the hypothesis that all the leuses lave the same nass and assumnne a staudard core isothermal sphere Or he dark halo mass density., The result obtained by Kerins was proved under the hypothesis that all the lenses have the same mass and assuming a standard cored isothermal sphere for the dark halo mass density.619 In this paper we eeneralize he caleulation of πι and analyze a eencral class of rolmogcnous ME., In this paper we generalize the calculation of $\tau_{oble}$ and analyze a general class of homogenous MF.620 Several studies have ECL made Dv may autrors to determine the ME function by mucrolensing data. but thev aro essentiallv devote to the MF of lee lenses (Zhaoetal.1995:: Tan&Could1996 Grenacheretal. 19993) and the work is still in progress.," Several studies have been made by many authors to determine the MF function by microlensing data, but they are essentially devoted to the MF of bulge lenses \cite{Z95}; \cite{HG96}; \cite{Lukas}) ) and the work is still in progress."621 Mao Paczvuski (1996) considered simplified tov nodels and a αν ME aud estimated that ar eliable determination could be achieved oulv if we had 100 or nore events., Mao Paczynski (1996) considered simplified toy models and a law MF and estimated that a reliable determination could be achieved only if we had 100 or more events.622" Their resuts, obtained nuder he asstuptiou hat MACIIOs spatial distribution and kincuiatic ""Were ο have been confinued by Markovic LLarsen (1997) who have also studied. the aect of chareine halo model ou the estimated average uass of eusius objects."," Their results, obtained under the assumption that MACHO's spatial distribution and kinematics were known, have been confirmed by Markovic Larsen (1997) who have also studied the effect of changing halo model on the estimated average mass of lensing objects."623 All these studies ave based ou statistical nuethods. that is why there is weed of a large uuuber of eveits to reduce the error on yaralucters determination.," All these studies are based on statistical methods, that is why there is need of a large number of events to reduce the error on parameters determination."624" Iu this paper WO Use a cffferent technique to got lise""ul informations on the lensing objects AIF.", In this paper we use a different technique to get useful informations on the lensing objects MF.625 Since iiicroleusiug observable quantities. i.c. number of events. observable optical deoath aud mean duration. depend ou the dark halo model aud onu the MF. we av CXpress these quautities as functions of sole models parameters aud of the| slope of he AIF itself.," Since microlensing observable quantities, i.e. number of events, observable optical depth and mean duration, depend on the dark halo model and on the MF, we may express these quantities as functions of some models parameters and of the slope of the MF itself."626 Then a conarison between tworctical expectations and observed quantities will help us to recover the values of he models parameOYs simply iniposiug that theory aud oservations are in good agreement., Then a comparison between theoretical expectations and observed quantities will help us to recover the values of the model's parameters simply imposing that theory and observations are in good agreement.627 This is what we call henerolensing., This is what we call the.628 To be neamuett mr analysis must fake iuto account also tιο detection efficiency aud that is why our theoretical expectations have ο be corrected for this effect too., To be meaningful our analysis must take into account also the detection efficiency and that is why our theoretical expectations have to be corrected for this effect too.629 Iu the following we wi VAiow how this is possib aud will eet some interesting costraints on the dark la lass fraction f composed bv VNACTIOs aud the slope ο| the asstuned homogenous Haw AIF for a wide class of spheroidal uocels., In the following we will show how this is possible and will get some interesting constraints on the dark halo mass fraction $f$ composed by MACHOs and the slope $\alpha$ of the assumed homogenous law MF for a wide class of spheroidal models.630 By t1ο Way our method is AC e to esca2ο the problems comrected to the low umber of observed events and actually our results are stronsSV affectec by errors which do not allow us to coustraiu he slope a of the ME in a narrow ranec., By the way our method is not able to escape the problems connected to the low number of observed events and actually our results are strongly affected by errors which do not allow us to constrain the slope $\alpha$ of the MF in a narrow range.631 Were the errors he reduced byiucreasije the umuber of observed events. OUL metlod s1ould be alde to narrow the uncertainties on he ALACTIOs λF.," Were the errors be reduced by increasing the number of observed events, our method should be able to narrow the uncertainties on the MACHOs MF."632 There is Oone possible source of systematic οἱ connueced to οιv analysis., There is one possible source of systematic error connected to our analysis.633 In the previous discussion. we have nmiplicitlv assimed that all the observed eveuts are due to NACTIOs in he Milkv. Way dark halo. but it should be cousidered aso the possibility that at least part of the events are ¢ue to LAIC self lensing.," In the previous discussion, we have implicitly assumed that all the observed events are due to MACHOs in the Milky Way dark halo, but it should be considered also the possibility that at least part of the events are due to LMC self lensing."634 This hypotresis has been suggesed in mauy papers. but the recent aualvsis bv the NACIIO eroup of the spatial distribution of t1ο events across the oserved LMC fields las shown that tus latter is not compatible with the propose inodoels of self lensing.," This hypothesis has been suggested in many papers, but the recent analysis by the MACHO group of the spatial distribution of the events across the observed LMC fields has shown that this latter is not compatible with the proposed models of self lensing."635 As a further test. NACIIO has also aualvzec ιο CMD (Color Magutude Diagram) of the sources of reir first cight eveuts to see if they reside in tic LMC' csk Qr behiud it.," As a further test, MACHO has also analyzed the CMD (Color Magnitude Diagram) of the sources of their first eight events to see if they reside in the LMC disk or behind it."636 Even if the sample is too small fpect a definitive result. he hvpothesis that all the eight events are die to halo enses is slightly favoured (Alcockοal.20005).," Even if the sample is too small to get a definitive result, the hypothesis that all the eight events are due to halo lenses is slightly favoured \cite {A00c}) )."637 Towever. here is still the possibility tha there are no MNACIIOs a all in the dark halo and that the oserved evens are cuc o the LMC dark halo.," However, there is still the possibility that there are no MACHOs at all in the dark halo and that the observed events are due to the LMC dark halo."638 Iu fact. the maxima liikelihood analysis of the ATACTIO collaboration has shown tha us hypothesis is not compleely excluded. even if the 10οςed LMC model should be somewhat extreme.," In fact, the maximum likelihood analysis of the MACHO collaboration has shown that this hypothesis is not completely excluded, even if the needed LMC model should be somewhat extreme."639 Besides. a recent paper by Alves Nelson (2000) has slwn tha 1ο LAIC rotation curve aud the daaon the kinematics oft 16 Carlynn stars in LMC are best fitted. by a model composed. by a flared aud warped disk aud no cleuk halo.," Besides, a recent paper by Alves Nelson (2000) has shown that the LMC rotation curve and the data on the kinematics of the carbon stars in LMC are best fitted by a model composed by a flared and warped disk and no dark halo."640 If this result will be coufirmed by uture works. will streneliten our asstuuption that the oserved nuücerolensing veuts are due to MACIIOs in Milkv. Way clark. halo.," If this result will be confirmed by future works, it will strenghten our assumption that the observed microlensing events are due to MACHOs in Milky Way dark halo."641 Iu the meautime. we are coustrained to consider the efffects that a possibe contamination by self lousing should have On our results.," In the meantime, we are constrained to consider the effects that a possible contamination by self lensing should have on our results."642 We will dixπως how this will affec our results doing» sole qualitative tests., We will discuss how this will affect our results doing some qualitative tests.643 Iu Sect., In Sect.644 2 we introduce aid evaluate the mucrolensing observables. be. the umuber of events. the olservalle optical dept[um aud the lueali duration. taking iuto account the deection efficiency for mod‘ds with isotropic niaxwelliau ransverse velocity distribution aud 10110801008 aw AIF axd assuniug a wide class of splieroida] non sineular isotlie1aal modes.," 2 we introduce and evaluate the microlensing observables, i.e. the number of events, the observable optical depth and the mean duration, taking into account the detection efficiency for models with isotropic maxwellian transverse velocity distribution and homogenous law MF and assuming a wide class of spheroidal non singular isothermal models."645 The model aaNetCrs 1uid the wavy we fix some of them is dTadled iu Sect., The model parameters and the way we fix some of them is detailed in Sect.646 3 wherο we illusrate the nodels we have cjosen to explore., 3 where we illustrate the models we have chosen to explore.647 Sect., Sect.648 Lis devoted to the analysis o the caiffereut nodels with he simple technique of the iICTS problem nethod to οrot constraints on the slope of the cus ME and the dark halo mass fraction composcc w MACTIOs., 4 is devoted to the analysis of the different models with the simple technique of the inverse problem method to get constraints on the slope of the lens MF and the dark halo mass fraction composed by MACHOs.649 Tow the self lensing could affect our resuts is (IscussccL qualitatively in Sect., How the self lensing could affect our results is discussed qualitatively in Sect.650 5. while a final discussioji of the results is preseuted in the conclusions.," 5, while a final discussion of the results is presented in the conclusions."651 To apply the method we have outlined in the introduction. we have first to calculate the observable quautities in mucrolensing to which we wil compare the observed ones towards LAIC.," To apply the method we have outlined in the introduction, we have first to calculate the observable quantities in microlensing to which we will compare the observed ones towards LMC."652 These quautities are the nuuber of events. the observalde optical depth aud the mean dureion.," These quantities are the number of events, the observable optical depth and the mean duration."653 Iu all this caleulatiou. we will tase luto account the detection efficiency in order to be sure that the comparison betweeu predicted and observed quauitics Is incaninetul.," In all this calculation, we will take into account the detection efficiency in order to be sure that the comparison between predicted and observed quantities is meaningful."654The first code is written in and the burn-in criterion is based on the power spectrum of the single chain (Dunkleyal. 2005).,The first code is written in and the burn-in criterion is based on the power spectrum of the single chain \citep{Dunkley:05}.655.. The first chain step within Alog£=2 of the best- parameters is taken as the start of the converged sampling.," The first chain step within $\Delta \log656\mathcal{L} = 2$ of the best-fit parameters is taken as the start of the converged sampling."657 A Fisher-matrix approximation to the ffit is used for the proposal density., A Fisher-matrix approximation to the fit is used for the proposal density.658 This code interpolates in log space from a moderate number 80) of flux densities to calcluate thePD)., This code interpolates in log space from a moderate number $\sim \! \! 80$ ) of flux densities to calcluate the.659 The other code is written in C++. and is explicitly parallel.," The other code is written in $\mathrm{C}\!\!+\!\!+$, and is explicitly parallel."660 It uses the Gelman-Rubin criterion for burn-in (Gelman&Rubin 1992).. which is based on computing the variance between chains and directly provides the point of convergence.," It uses the Gelman-Rubin criterion for burn-in \citep{Gelman:1992}, which is based on computing the variance between chains and directly provides the point of convergence."661 This code does not use interpolation when computing the(2). but supports a more limited range of models.," This code does not use interpolation when computing the, but supports a more limited range of models."662 The proposal density is a multi-variate Gaussian estimated from the previous fit steps. and is frozen in at burn-in.," The proposal density is a multi-variate Gaussian estimated from the previous fit steps, and is frozen in at burn-in."663 We have checked these codes against each other on simulated data. and find good agreement.," We have checked these codes against each other on simulated data, and find good agreement."664 Our mmethodology is almost identical to that described in POY except as follows., Our methodology is almost identical to that described in P09 except as follows.665 First. POY explicitly fit for the mean of pixel values in the map (0.," First, P09 explicitly fit for the mean of pixel values in the map $\mu$ )."666 Since we can analytically predict the mean of the ffor a given set of model parameters. we simply shift the mean to zero explicitly during construction.," Since we can analytically predict the mean of the for a given set of model parameters, we simply shift the mean to zero explicitly during construction."667 The input map is also mean-subtracted. and the uncertainty in this subtraction contributes negligibly to our error budget.," The input map is also mean-subtracted, and the uncertainty in this subtraction contributes negligibly to our error budget."668 Second. POY fit to the instrument noise explicity for each field except for the deepest section of their map.," Second, P09 fit to the instrument noise explicity for each field except for the deepest section of their map."669 Instead. we marginalize over the noise for all fields in our full fits. but use the measurements of Nguyenetal.(2010). as a prior. assuming an Gaussian uncertainty of5%.," Instead, we marginalize over the noise for all fields in our full fits, but use the measurements of \citet{Nguyen:2010} as a prior, assuming an Gaussian uncertainty of."670. At low flux densities. the number of sources per beam is large. and hence the contribution to he iis almost Gaussian.," At low flux densities, the number of sources per beam is large, and hence the contribution to the is almost Gaussian."671 Therefore. the values of //N/4S for the faintest flux densities probed and the noise level are nearly degenerate. and jencee fixing the noise will tend to under-estimate the uncertainties in the model parameters at the faint end.," Therefore, the values of $dN/dS$ for the faintest flux densities probed and the noise level are nearly degenerate, and hence fixing the noise will tend to under-estimate the uncertainties in the model parameters at the faint end."672 We have developed a simple simulation. framework to test hese codes and their sensitivity to various effects such as. [/f noise., We have developed a simple simulation framework to test these codes and their sensitivity to various effects such as $1/f$ noise.673 As inputs we consider two types of catalogs that should be representative of the sub-mm sky: the PO9 models. and the simulations of Fernandez-Condeetal. (2008).," As inputs we consider two types of catalogs that should be representative of the sub-mm sky: the P09 models, and the simulations of \citet{fer08}. ."674. The fits to the PO9 models are easier to compare with the inputs. but the Condeetal.(2008) models include clustering etfects.," The fits to the P09 models are easier to compare with the inputs, but the \citet{fer08} models include clustering effects."675 A fake sky is generated from the input catalogue. and scanned using the pointing information from the actual SPIRE observations.," A fake sky is generated from the input catalogue, and scanned using the pointing information from the actual SPIRE observations."676 Different noise levels (white and 1/f) can be specitied., Different noise levels (white and $1/f$ ) can be specified.677 These data are then run through the same map-making pipeline as the real data., These data are then run through the same map-making pipeline as the real data.678 In addition to the simulated. science data. we also simulate observations of Neptune using the same framework to determine the beams we use when fitting the simulated data.," In addition to the simulated science data, we also simulate observations of Neptune using the same framework to determine the beams we use when fitting the simulated data."679" These simulations use simple Gaussian beams with FWHMs similar to those measured on-orbit. and account for characteristics of the data introduced by the mapping pipeline. but do not simulate errors in the lower-level SPIRE pipeline (pointing errors. crosstalk-corrections, ete.)."," These simulations use simple Gaussian beams with FWHMs similar to those measured on-orbit, and account for characteristics of the data introduced by the mapping pipeline, but do not simulate errors in the lower-level SPIRE pipeline (pointing errors, crosstalk-corrections, etc.)."680 We use them to quantify the etfects of 1// noise. uneven coverage. clustering. and smoothing by the beam on our maps.," We use them to quantify the effects of $1/f$ noise, uneven coverage, clustering, and smoothing by the beam on our maps."681 The SPIRE |// knee frequency is a few mHz. corresponding to a spatial scale of approximately 3 degrees for a scan speed of 30 areseconds per second. and our map-making algorithm reduces this already small amount as discussed in Levenson et (2010. in prep).," The SPIRE $1/f$ knee frequency is a few mHz, corresponding to a spatial scale of approximately 3 degrees for a scan speed of 30 arcseconds per second, and our map-making algorithm reduces this already small amount as discussed in Levenson et (2010, in prep)."682 We tind that the remaining amount. as well as the uneven coverage. introduces negligible bias in our tits. but that clustering can have measureable effects on our largest maps. as discussed in 33.," We find that the remaining amount, as well as the uneven coverage, introduces negligible bias in our fits, but that clustering can have measureable effects on our largest maps, as discussed in \ref{subsec:filtering}."683 In addition. we have determined the appropriate correction or pixel-pixel correlations using the same framework and a arge number of simulated HerMES datasets.," In addition, we have determined the appropriate correction for pixel-pixel correlations using the same framework and a large number of simulated HerMES datasets."684 We find that the correct normalization factor varies with signal-to-noise ratio of he map. and whether it has been additionally smoothed with he beam.," We find that the correct normalization factor varies with signal-to-noise ratio of the map, and whether it has been additionally smoothed with the beam."685 If the map is beam-smoothed. then the beam area actor is approximately correct. if slightly conservative for deeper fields: note that all of the maps in POY were beam-smoothed.," If the map is beam-smoothed, then the beam area factor is approximately correct, if slightly conservative for deeper fields; note that all of the maps in P09 were beam-smoothed."686 However. for deep. unsmoothed maps. this procedure clearly overestimates the uncertainties (by about a factor of 2 for GOODS-).," However, for deep, unsmoothed maps, this procedure clearly overestimates the uncertainties (by about a factor of 2 for GOODS-N)."687 Rather than derive individual correction factors for each field. we have taken the more conservative approach of tinding the largest correction factor (which therefore increases the uncertainties the most) for all of our fields. and applying it to all un-smoothed data.," Rather than derive individual correction factors for each field, we have taken the more conservative approach of finding the largest correction factor (which therefore increases the uncertainties the most) for all of our fields, and applying it to all un-smoothed data."688 For the GOODS-N and Lockman-North observations. the correct normalization factor (without smoothing)is less than A;/3.," For the GOODS-N and Lockman-North observations, the correct normalization factor (without smoothing)is less than $A_b/3$."689" Because we do not have an exaet formulation for this correction. we conservatively adopt 2A,,/5."," Because we do not have an exact formulation for this correction, we conservatively adopt $2 A_b/5$."690 For the smoothed observations. we adopt the Aj normalization. also conservatively: this means that the two Lockman fields have the same correction factors. but the smoothed) GOODS-N field has a ditferent one.," For the smoothed observations, we adopt the $A_b$ normalization, also conservatively; this means that the two Lockman fields have the same correction factors, but the (un-smoothed) GOODS-N field has a different one."691 Clustering will attect the ddistribution in two ways., Clustering will affect the distribution in two ways.692 First. the presence of clustering implies sample variance effects. so that the SDP fields may not be representative of the all-sky number counts.," First, the presence of clustering implies sample variance effects, so that the SDP fields may not be representative of the all-sky number counts."693 Second. the fact that 1ὸ underlying counts are not Poisson distributed would change the shape of the ddistribution even if we were somehow lucky enough to select a orecisely average region of sky.," Second, the fact that the underlying counts are not Poisson distributed would change the shape of the distribution even if we were somehow lucky enough to select a precisely average region of sky."694 This effect can be modeled if all of le N-point statistics of the source distribution are known 199?, This effect can be modeled if all of the $n$ -point statistics of the source distribution are known \citep{barc92}.695 The etfect on the width of the iis discussed.. in Appendix A of PO9. although clustering is no surely limited to changing the width of the distribution.," The effect on the width of the is discussed in Appendix A of P09, although clustering is not purely limited to changing the width of the distribution."696 Only the 2-point function has been measured for the population sampled by SPIRE. and even this is not known at the flux densities importan ‘or our results.," Only the 2-point function has been measured for the population sampled by SPIRE, and even this is not known at the flux densities important for our results."697 The first issue is discussed in 5.1. and the second re.," The first issue is discussed in \ref{subsec:systematics}, and the second here."698 There are two effects: clustering on small scales between individual SMGs. and clustering on larger scales between groups of SMGs.," There are two effects: clustering on small scales between individual SMGs, and clustering on larger scales between groups of SMGs."699 The framework for the clustering contribution to the is given in) Barcons(1992):Takeuchi&Ishii(20045.," The framework for the clustering contribution to the is given in \citet{barc92,ti04}."700" The contribution to the "" moment is proportional to [P.GObd)""οκ. where. P,dk) is. the power spectrum of the 7-point correlation function. and 5b(ü is the Fourier transform of the beam."," The contribution to the $n^{\mathrm{th}}$ moment is proportional to $\int P_n\left( \mathbf{k} \right) \tilde{b}\left(701\mathbf{k} \right)^n \, d^2 \mathbf{k},$ where $P_n\left( \mathbf{k}702\right)$ is the power spectrum of the $n$ -point correlation function, and $\tilde{b}\left( \mathbf{k} \right)$ is the Fourier transform of the beam."703 P falls rapidly with [kJ (e.g.. an 18 arcsecond FWHM Gaussian beam has a [ο value atk = 1.2 '. and the higher powers fall off even more rapidly).," $\tilde{b}$ falls rapidly with $\left| \mathbf{k} \right|$ (e.g., an 18 arcsecond FWHM Gaussian beam has a 1/e value at k = 1.2 $^{-1}$, and the higher powers fall off even more rapidly)."704 Thus. small scale clustering. which is implied by the measurements of. e.g.. Blainetal.(2004). is filtered out by the beam on seales of less than about one to two areminutes in our data.," Thus, small scale clustering, which is implied by the measurements of, e.g., \citet{Blain:2004}, is filtered out by the beam on scales of less than about one to two arcminutes in our data."705" Generically. P, falls rapidly with |k| . suggesting that high- filtering the maps may mitigate large-scale clustering effects."," Generically, $P_n$ falls rapidly with $\left| \mathbf{k} \right|$ , suggesting that high-pass filtering the maps may mitigate large-scale clustering effects."706" In particular, in the far-IR the power spectrum of the two point correlation function (P>) shows excess power above Poissonian noise at scaleslarger than 10 "," In particular, in the far-IR the power spectrum of the two point correlation function $P_2$ ) shows excess power above Poissonian noise at scaleslarger than $10^{\prime}$ "707at [Fe/H] ~—2.5 (as shown below. this break represents a real discontinuity). which have essentially zero slopes (within the error bars) and very low star-to-star scatter mn their Li abundances.,"at [Fe/H] $\sim-2.5$ (as shown below, this break represents a real discontinuity), which have essentially zero slopes (within the error bars) and very low star-to-star scatter in their Li abundances."708 The first group has —2.5x [Fe/H] <-1.0 and <ALi>) = 2.272 (020.051) dex and a slope of 0.01840.026. Le.. flat within the uncertainties.," The first group has $-2.5 \leq$ [Fe/H] $< -1.0$ and $<$ $_{\rm Li}$$>_1$ = 2.272 $\sigma$ =0.051) dex and a slope of $\pm$ 0.026, i.e., flat within the uncertainties."709" The second group is more metal poor ([Fe/H] «-2.5) and has <A,j>> = 2.184 dex (c= 0.036) dex.", The second group is more metal poor ([Fe/H] $< -2.5)$ and has $<$ $_{\rm Li}$$>_2$ = 2.184 dex $\sigma = 0.036$ ) dex.710 The slope of this second group is also zero (—0.008:0.037)., The slope of this second group is also zero $-$ $\pm$ 0.037).711 Adopting a more conservative exponential cutoff obtained from Y isochrones (Demarque et al., Adopting a more conservative exponential cutoff obtained from $Y^2$ isochrones (Demarque et al.712 2004). which for a 0.79 M. star can be fit by = 6698 -2173 x οΠΕΟΣ we would also recover a flat Spite plateau. although only stars with [Fe/H] > —2.5 are left using this more restrictive cut-off.," 2004), which for a 0.79 $_\odot$ star can be fit by = 6698 $-$ 2173 $\times$ $e^{\rm [Fe/H]/1.021}$, we would also recover a flat Spite plateau, although only stars with [Fe/H] $> -$ 2.5 are left using this more restrictive cut-off."713 Thus. the flatness of the Spite plateau is independent of applying a linear or an exponential cutoff.," Thus, the flatness of the Spite plateau is independent of applying a linear or an exponential cutoff."714 Adopting a constant cutoff in we also find flat plateaus., Adopting a constant cutoff in we also find flat plateaus.715 For example adopting a cutoff of > 6100 K (filled squares in Fig., For example adopting a cutoff of $>$ 6100 K (filled squares in Fig.716" 3) we find in the most metal-rich plateau (|Fe/H] —2.5) no trend between Li and [Fe/H] (slope = 0.01950.025. Spearman rank correlation coefficient. ""span 70.1 and a probability of 0.48 (1.e.. 48%)) of a correlation arising by pure chance for [Fe/H] > —-2.5). while for the most metal-poor plateau ([Fe/H] « —2.5) we also do not find any trend within the errors (slope = 0.05840.072. rspeannan=0.2 and probability of a spurious correlation)."," 3) we find in the most metal-rich plateau ([Fe/H] $\geq -2.5$ ) no trend between Li and [Fe/H] (slope = $\pm$ 0.025, Spearman rank correlation coefficient $r_{\rm Spearman}$ =0.1 and a probability of 0.48 (i.e., ) of a correlation arising by pure chance for [Fe/H] $\geq -$ 2.5), while for the most metal-poor plateau ([Fe/H] $< -$ 2.5) we also do not find any trend within the errors (slope = $\pm$ 0.072, $r_{\rm Spearman}$ =0.2 and probability of a spurious correlation)."717 Using a hotter cutoff > 6350 K. filled triangles in Fig.," Using a hotter cutoff $>$ 6350 K, filled triangles in Fig."718 3) we obtain also two flat plateaus with slope = -0.04040.063 Gs; = 70.2. probability = 60%)) for [Fe/H] > —2.5 and slope = 0.00840.035 ('speanman = 0.1. probability = 68%)) for[Fe/H] < -2.5.," 3) we obtain also two flat plateaus with slope = $\pm$ 0.063 $r_{\rm Spearman}$ = -0.2, probability = ) for [Fe/H] $\geq -$ 2.5 and slope = $\pm$ 0.035 $r_{\rm Spearman}$ = 0.1, probability = ) for[Fe/H] $< -$ 2.5."719 In Fig., In Fig.720 4 we demonstrate that the break at [Fe/H] ~—2.5 is statistically significant., 4 we demonstrate that the break at [Fe/H] $\sim -2.5$ is statistically significant.721" In panel (a) the slope/o in the Aj; vs. [Fe/H] plot for the range X, « [Fe/H] «—1.0 are shown as filled eireles. where μη varies within [-3.50.-1.25]."," In panel (a) the $\sigma$ in the $A_{\rm Li}$ vs. [Fe/H] plot for the range $_{\rm min}$ $<$ [Fe/H] $<-1.0$ are shown as filled circles, where $_{\rm min}$ varies within [-3.50,-1.25]."722" For Xi, > —2.5. the slope is insignificant (<< 3c). and only when stars with [Fe/H] «—2.5 are included a measurable slope is forced in the Aj; vs. [Fe/H relation."," For $_{\rm min}$ $\geq -2.5$ , the slope is insignificant $<<$ $\sigma$ ), and only when stars with [Fe/H] $< -2.5$ are included a measurable slope is forced in the $A_{\rm Li}$ vs. [Fe/H] relation."723" The opposite test is shown by open circles. where we show slope/c for the range —3.25 < [Fe/H] « Xinax. where Xia, changes from [—3.00.—1.00]."," The opposite test is shown by open circles, where we show $\sigma$ for the range $-$ 3.25 $<$ [Fe/H] $<$ $_{\rm max}$, where $_{\rm max}$ changes from $-$ $-$ 1.00]."724" For Xu €—2.5 the slope is negligible (<< 3c). and only when stars with [Fe/H] =>—2.5 are included. a slope is produced between A,; and [Fe/H]."," For $_{\rm max}$ $< -2.5$ the slope is negligible $<<$ $\sigma$ ), and only when stars with [Fe/H] $\geq -2.5$ are included, a slope is produced between $A_{\rm Li}$ and [Fe/H]."725 The correlation coefficient rspeannan and the probability of a correlation between Àj; and [Fe/H] by pure chance are shown in panel (b)., The correlation coefficient $r_{\rm Spearman}$ and the probability of a correlation between $A_{\rm Li}$ and [Fe/H] by pure chance are shown in panel (b).726 Again. this plot shows that no correlation between Aj; and [Fe/H] exists the two groups (-3.5« [Fe/H] <-2.5 and -2.5> [Fe/H] 5 -1.0). and that only when stars the two groups are mixed. significant (probability ~ 0) correlations of Aj; with [Fe/H] are generated.," Again, this plot shows that no correlation between $A_{\rm Li}$ and [Fe/H] exists the two groups $-3.5<$ [Fe/H] $<-2.5$ and $-2.5\geq$ [Fe/H] $\geq-1.0$ ), and that only when stars the two groups are mixed, significant (probability $\sim$ 0) correlations of $A_{\rm Li}$ with [Fe/H] are generated."727 Systematically lower E(B-V) values (by ~0.03 mags) in the most metal-poor plateau ([Fe/H] « -2.5) could produce a more Li-depleted plateau., Systematically lower E(B-V) values (by $\sim$ 0.03 mags) in the most metal-poor plateau ([Fe/H] $< -$ 2.5) could produce a more Li-depleted plateau.728 However. those E(B-V) values (Fig.," However, those E(B-V) values (Fig."729 1) are actually slightly higher (~0.007 mags. 1.e.. ~33 K) than those for [Fe/H] > —2.5 (mainly due to a high number of unreddened nearby more metal-rich stars). thus not explaining the existence of two different plateaus.," 1) are actually slightly higher $\sim$ 0.007 mags, i.e., $\sim$ 33 K) than those for [Fe/H] $\geq -$ 2.5 (mainly due to a high number of unreddened nearby more metal-rich stars), thus not explaining the existence of two different plateaus."730 Previous claims of a steep monotonic decrease in Li abundance with decreasing metallicity (e.g. Ryan et al., Previous claims of a steep monotonic decrease in Li abundance with decreasing metallicity (e.g. Ryan et al.731 1999: A06: BO7; Hosford et al., 1999; A06; B07; Hosford et al.732 2009) are probably due to the mix of stars from the two different groups. forcing a monotonic dependence with metallicity.," 2009) are probably due to the mix of stars from the two different groups, forcing a monotonic dependence with metallicity."733 Our large sample of homogeneous and precise Li abundances that covers a broad metallicity range (-3.5< [Fe/H] < -1.0) does not support these claims., Our large sample of homogeneous and precise Li abundances that covers a broad metallicity range $-3.5 <$ [Fe/H] $< -1.0$ ) does not support these claims.734 Nevertheless. a hint of two different groups in the Spite plateau was already found by A06. who found a change in the slope of the Spite plateau at [Fe/H] = -2.2.," Nevertheless, a hint of two different groups in the Spite plateau was already found by A06, who found a change in the slope of the Spite plateau at [Fe/H] $\approx$ $-$ 2.2."735 Also. in the combined A06-B07 sample (Fig.," Also, in the combined A06+B07 sample (Fig."736" 7 of BO7). there are two different groups: stars with [Fe/H] =—2.6 have A,; > 2.2. while stars with [Fe/H] €—2.6 have A,; « 2.2."," 7 of B07), there are two different groups: stars with [Fe/H] $\gtrsim -2.6$ have $A_{\rm Li}$ $>$ 2.2, while stars with [Fe/H] $\lesssim -2.6$ have $A_{\rm Li}$ $<$ 2.2."737" Although in the study by MRO4 a flat Spite plateau is found in the range -3.4« [Fe/H] «- I. this is due to the overestimation of below [Fe/H] «-2.5. thus overestimating A,;at low metallicities and forcing a flat plateau from [Fe/H] = —3.4 to — I."," Although in the study by MR04 a flat Spite plateau is found in the range $-3.4 <$ [Fe/H] $< -1$ , this is due to the overestimation of below [Fe/H] $< -2.5$, thus overestimating $A_{\rm Li}$at low metallicities and forcing a flat plateau from [Fe/H] = $-3.4$ to $-$ 1."738 Models of Li depletion predict that the least massive stars are the most depleted in Li. but due to the limitations of previous," Models of Li depletion predict that the least massive stars are the most depleted in Li, but due to the limitations of previous"739C-N anticorrelations should appear quite different.,C-N anticorrelations should appear quite different.740 This prediction might be compared with the actual data (see e.g. Briley et al., This prediction might be compared with the actual data (see e.g. Briley et al.741 2004)., 2004).742 The ratio of primordial population/GC cannot be greater than the ratio between the mass of the halo and the mass in GCs. which is ~100.," The ratio of primordial population/GC cannot be greater than the ratio between the mass of the halo and the mass in GCs, which is $\sim 100$."743 In the current framework. this provides a lower limit for a. that is.>—0.0097/x.," In the current framework, this provides a lower limit for $\alpha$, that is, $\alpha>-0.0097/x$."744 If we assume av=0.01 aand x»=-2.3. we should expect a mass ratio of primordial population to the GC of ~40.," If we assume $\alpha=0.01$ and $x=-2.3$, we should expect a mass ratio of primordial population to the GC of $\sim 40$."745 In this framework. to produce a cluster with a current mass of 10°M.. (like NGC 2808 or 47 Tuc 4)). one should start with ~410°Ma of gas with a very homogeneous composition (A[Fe/H|<<0.04 dex): possibly a value of ~8107M. for the cloud mass would be more reasonable. considering a reasonable ~0.5 star formation efficiency for the primordial (original) generation.," In this framework, to produce a cluster with a current mass of $10^6~M_\odot$ (like NGC 2808 or 47 Tuc ), one should start with $\sim 4\,10^7~M_\odot$ of gas with a very homogeneous composition $\Delta$ $<<0.04$ dex); possibly a value of $\sim 8\,10^7 746M_\odot$ for the cloud mass would be more reasonable, considering a reasonable $\sim 0.5$ star formation efficiency for the primordial (original) generation."747 Star formation for the primordial generation cannot have lasted very long. or else SNe would have either (1) stopped it or (11) contributed to the nucleosynthesis.," Star formation for the primordial generation cannot have lasted very long, or else SNe would have either (i) stopped it or (ii) contributed to the nucleosynthesis."748 A reasonable upper limit is 10 yr., A reasonable upper limit is $10^7$ yr.749 Such a massive (410’M. stellar mass) star-forming regior should be very luminous (My~ -18).," Such a massive $4\,10^7~M_\odot$, stellar mass) star-forming region should be very luminous $M_V \sim -18$ )."750 Almost all (98.7%)) of the original cluster population would have been lost from the expansion of the cluster after SNe explosion and mass loss., Almost all ) of the original cluster population would have been lost from the expansion of the cluster after SNe explosion and mass loss.751 The second burst of star formation (the one producing the second generation) would then be a much smaller episode., The second burst of star formation (the one producing the second generation) would then be a much smaller episode.752 With a mass of 5JO?M. of stars produced. it should have a luminosity of My=—14 aat peak.," With a mass of $5\,10^5~M_\odot$ of stars produced, it should have a luminosity of $M_V=-14$ at peak."753 At this epoch. the fading original population should still have a luminosity of My=—16. dominating the compact central cluster of second-generation stars.," At this epoch, the fading original population should still have a luminosity of $M_V=-75416$, dominating the compact central cluster of second-generation stars."755 Assuming a ratio M/L=2. all galactic GCs summed up have a mass of 3.4107Ms.," Assuming a ratio $M/L=2$, all galactic GCs summed up have a mass of $3.4\,10^7~M_\odot$."756 The primordial population should then be ~1.410?Ms.," The primordial population should then be $\sim 1.4\,10^9~M_\odot$."757 This requires that roughly half of the halo/thick disk mass comes from GCs (see Gratton et al., This requires that roughly half of the halo/thick disk mass comes from GCs (see Gratton et al.758 2010. in preparation. where we will discuss the metallicity distribution and the element-to-element abundance ratios of the primordial population. which are very similar to that of the halo-thick disk).," 2010, in preparation, where we will discuss the metallicity distribution and the element-to-element abundance ratios of the primordial population, which are very similar to that of the halo-thick disk)."759 Winds from main sequence stars are quite fast. with typical velocities of a few hundred km/s (Neugebauer 1994; Dupree 2005).," Winds from main sequence stars are quite fast, with typical velocities of a few hundred km/s (Neugebauer 1994; Dupree 2005)."760 This is much higher than the escape velocity from a C, This is much higher than the escape velocity from a proto-GC.761ould this wind be contributing to the second generation?, Could this wind be contributing to the second generation?762" To address this issue. we follow the same arguments considered by Smith (1999), who considered the case for dissipation of intracluster gas (lost at low speed by red giants) from the energy injection by the high-velocity wind from the main sequence."," To address this issue, we follow the same arguments considered by Smith (1999), who considered the case for dissipation of intracluster gas (lost at low speed by red giants) from the energy injection by the high-velocity wind from the main sequence."763 We should replace the wind by red giants with the much stronger winds of AGB stars., We should replace the wind by red giants with the much stronger winds of AGB stars.764 The specific mass-loss rate for massive AGB stars is about two orders of, The specific mass-loss rate for massive AGB stars is about two orders of765Figure 1. shows the computed abundances of O in the gas phase as a function of time for the four elemental abundances of oxygen described in section. ?? (left panel) and as a function of the oxygen elemental abundance for different times (right panel).,Figure \ref{fig:O2ab_VS_time_and_O_ElemAb} shows the computed abundances of $\rm O_2$ in the gas phase as a function of time for the four elemental abundances of oxygen described in section \ref{elements} (left panel) and as a function of the oxygen elemental abundance for different times (right panel).766 A decrease in the oxygen elemental abundance produces a general decrease in the O» abundances at any time. although the effect is stronger between 3x10° and 2x10° yr.," A decrease in the oxygen elemental abundance produces a general decrease in the $\rm O_2$ abundances at any time, although the effect is stronger between $3\times 10^5$ and $2\times 10^6$ yr."767 Assuming that Os has been searched for in à variety of clouds with ages across this range. the non-detection of Os. with abundances above 1077 compared to total hydrogen woulc require the elemental abundance of oxygen to be smaller thai 1.6x1077.," Assuming that $_2$ has been searched for in a variety of clouds with ages across this range, the non-detection of $_2$ with abundances above $10^{-7}$ compared to total hydrogen would require the elemental abundance of oxygen to be smaller than $1.6\times 10^{-4}$."768" Figure 2. shows the computed abundances of a selectioi of gas phase species as a function of time. for the extreme ""low"" and “high depletion"" cases."," Figure \ref{fig:paper1_AbX_vs_time} shows the computed abundances of a selection of gas phase species as a function of time, for the extreme ""low"" and ""high depletion"" cases."769" As expected. the abundances of carbon-rich species (such as cyanopolyynes) are higher i the ""high oxygen depletion"" case (higher C/O ratio). whereas the abundance of O-bearing species is lower."," As expected, the abundances of carbon-rich species (such as cyanopolyynes) are higher in the ""high oxygen depletion"" case (higher C/O ratio), whereas the abundance of O-bearing species is lower."770 The various O- spectes are however not influenced to the same extent., The various O-bearing species are however not influenced to the same extent.771 CO. OH. and H:O are changed only slightly.," CO, OH, and $_2$ O are changed only slightly."772 Os and SO» are lower by two orders of magnitude and more than one order of magnitude. respectively. at the peak abundance (~4x10° yr).," $_2$ and $_2$ are lower by two orders of magnitude and more than one order of magnitude, respectively, at the peak abundance $\sim 4\times 10^5$ yr)."773 In our four cases. the elemental C/O ratio varies over a large range.," In our four cases, the elemental C/O ratio varies over a large range."774 Pure gas-phase chemical models would be very sensitive to these variations: for example. ? show that the HC5N abundance can be modified by four orders of magnitude at 107 yr when C/O goes from 0.7 to I.," Pure gas-phase chemical models would be very sensitive to these variations: for example, \citet{2010A&A...517A..21W} show that the $_7$ N abundance can be modified by four orders of magnitude at $10^7$ yr when C/O goes from 0.7 to 1."775 In our present study and at 107 yr. the HC;N abundance does not depend much on the different values of C/O that we adopted. as can be seen in Fig. 2..," In our present study and at $10^{7}$ yr, the $_7$ N abundance does not depend much on the different values of C/O that we adopted, as can be seen in Fig. \ref{fig:paper1_AbX_vs_time}."776" When the C/O ratio increases. this occurs because the available C is mainly used to form C-rich molecules. e.g. C,H». on the grains (seealso?).."," When the C/O ratio increases, this occurs because the available C is mainly used to form C-rich molecules, e.g. $_n$ $_m$, on the grains \citep[see also][]{2007A&A...467.1103G}."777 However. the modeled abundances are not only sensitive to the elemental C/O ratio but also to the elemental abundances themselves.," However, the modeled abundances are not only sensitive to the elemental C/O ratio but also to the elemental abundances themselves."778 Increasing both elemental abundances by a factor of two would for instance increase the CO gas-phase abundance by two orders of magnitude at 5x10° yr in all the models. but the O» abundance at the peak (~4x10° yr) remains unchanged.," Increasing both elemental abundances by a factor of two would for instance increase the CO gas-phase abundance by two orders of magnitude at $5\times 10^6$ yr in all the models, but the $_2$ abundance at the peak $\sim 4\times 10^5$ yr) remains unchanged."779 In this dense cloud modeling. the CO abundance in the gas phase decreases after a few 10° yr because CO sticks onto grains and is then hydrogenated to form H:CO and CH:OH.," In this dense cloud modeling, the CO abundance in the gas phase decreases after a few $10^5$ yr because CO sticks onto grains and is then hydrogenated to form $_2$ CO and $_3$ OH."780 When the C and O elemental abundances are increased. the gas phase CO abundance. and as a consequence the solid CO abundance. increases and takes longer to decrease its abundance.," When the C and O elemental abundances are increased, the gas phase CO abundance, and as a consequence the solid CO abundance, increases and takes longer to decrease its abundance."781 If we allow the system to evolve up to 10* yr. the CO gas phase abundance is only two times larger than the one obtained with our previous elemental abundances.," If we allow the system to evolve up to $10^8$ yr, the CO gas phase abundance is only two times larger than the one obtained with our previous elemental abundances."782 Decreasing C and O elemental abundance by a factor of two would slightly decrease the O» abundance., Decreasing C and O elemental abundance by a factor of two would slightly decrease the $_2$ abundance.783 We started our chemistry assuming that all species were initially atomic. except for hydrogen.," We started our chemistry assuming that all species were initially atomic, except for hydrogen."784 If we instead assume that all carbon is initially in carbon monoxide. the results change drastically before 10° years.," If we instead assume that all carbon is initially in carbon monoxide, the results change drastically before $10^{5}$ years."785 Carbon chains are obviously the most affected species., Carbon chains are obviously the most affected species.786 Using these initial abundances increases the time taken to form the carbon-bearing molecules observed in dense clouds by a factor of between 10° , Using these initial abundances increases the time taken to form the carbon-bearing molecules observed in dense clouds by a factor of between $10^{2}$ \citep[see also][]{2010SSRv..156...13W} 787of hyH4. lor a range of dust-to-gas surface density. ratios and Όροςος=0.1.,"of $k_y H_d$, for a range of dust-to-gas surface density ratios and $v_{0,max}/c_s = 0.1$."788 Both even- and. odd-syaimetry solutions are shown., Both even- and odd-symmetry solutions are shown.789 In a real svstem. the dust will (at least initially) likely settle toward the midplane at a higher rate than the surface density ratio changes.," In a real system, the dust will (at least initially) likely settle toward the midplane at a higher rate than the surface density ratio changes."790 50. we can imagine the disk evolving down along a vertical line in Figure 2.. until it reaches the stability edge at a relevant wavelength.," So, we can imagine the disk evolving down along a vertical line in Figure \ref{sdh_fig}, until it reaches the stability edge at a relevant wavelength."791" On a longer time scale. the disk may then move along that edge towards larger X,/X, values as gas is lost to photoevaporation or the dust component is increased due to radial απ, lor example."," On a longer time scale, the disk may then move along that edge towards larger $\Sigma_d / \Sigma_g$ values as gas is lost to photoevaporation or the dust component is increased due to radial drift, for example."792 The slopes of the critical curves at fixed 1; canbe understood physically., The slopes of the critical curves at fixed $k_y H_d$ canbe understood physically.793" At small Ma/M,. an increase in Mj/YX, increases µ. (hus increasing the velocity shear since p)."," At small $\Sigma_d / \Sigma_g$, an increase in $\Sigma_d / \Sigma_g$ increases $\mu$, thus increasing the velocity shear since $V = v_{0,max} \mu / (1+\mu)$ ."794" This forces an increase in 7/;/11, in order to keep the laver marginally stable: as a consequence. from equation (25)). the critical (I4/H,4)x(X/X,)! ab small ji."," This forces an increase in $H_d / H_g$ in order to keep the layer marginally stable; as a consequence, from equation \ref{instb_eq}) ), the critical $(H_d/H_g) \propto (\Sigma_d / \Sigma_g)^{1/3}$ at small $\mu$."795" For large Xj/X,. jp>1 and the velocity dillerence saturates to c5,;,,: 1n (his case. the dust laver must get thinner (ο remain marginally stable with increasing dust abundance."," For large $\Sigma_d / \Sigma_g$, $\mu \gg 1$ and the velocity difference saturates to $v_{0,max}$; in this case, the dust layer must get thinner to remain marginally stable with increasing dust abundance."796" At large pr. the critical curve therefore follows (H14/11,)xδν) !."," At large $\mu$, the critical curve therefore follows $(H_d / H_g) \propto (\Sigma_d / \Sigma_g)^{-1}$ ."797" These small- and large-4i scalings of (LaΜΕ WU Vy/M,y ave the same as have been identified by", These small- and $\mu$ scalings of $(H_d/H_g)_{crit}$ with $\Sigma_d / \Sigma_g$ are the same as have been identified by798In this paper we analyse properties of the Solar neighbourhood SER. by means of a statistically significant ADF built with 442 star (embedded: and open) clusters closer than kkpe from the Sun.,"In this paper we analyse properties of the Solar neighbourhood SFR, by means of a statistically significant ADF built with 442 star (embedded and open) clusters closer than kpc from the Sun."799 By adopting a simplifying approach. in which the mass evolution of artificial clusters is followed. over time. we reduce the problem: to essentially linding the SER.," By adopting a simplifying approach, in which the mass evolution of artificial clusters is followed over time, we reduce the problem to essentially finding the SFR."800 The artificial clusters embody parameters and conditions expected. to apply to most actual star. clusters orbiting not far from the Solar circle., The artificial clusters embody parameters and conditions expected to apply to most actual star clusters orbiting not far from the Solar circle.801 “To simulate the observed. ADL. we employ semi-analytical descriptions of the mass-loss process responsible Lor cluster. dissolution. and assume that only clusters with a present-day piass above ccan be clleetively observed (ie. take part in the ADI).," To simulate the observed ADF, we employ semi-analytical descriptions of the mass-loss process responsible for cluster dissolution, and assume that only clusters with a present-day mass above can be effectively observed (i.e., take part in the ADF)."802 The best match between observed and simulated ADEs corresponds to a non-constant SER. with enhanced: rates for ages the < 9MMyr. ancl 220 GOOAAIVe (he called. local starburst).," The best match between observed and simulated ADFs corresponds to a non-constant SFR, with enhanced rates for ages the $\le9$ Myr and $220-600$ Myr (the so-called local starburst)."803 The. average rate is SiRzm(2500x500)M.Myr.+ Corresponding to the average density Nsppz(07903160)M.Mar|kpe7.," The average rate is $\overline{SFR}\approx(2500\pm500)\,\mmy$ , corresponding to the average density $\overline{\ssfr}\approx(790\pm160)\,\mmk$."804 These values agree with the formation rate inferred from EC's. but represent only ~16% of the rate implied by field stars.," These values agree with the formation rate inferred from ECs, but represent only $\sim16\%$ of the rate implied by field stars."805 Both the local starburst ancl the recent formation (s:9 MMwr) have ADF amplitudes suggesting periods with a SER about twice the average value., Both the local starburst and the recent formation $\le9$ Myr) have ADF amplitudes suggesting periods with a SFR about twice the average value.806 We also find that 91.202.74 of the clusters created in the Solar neighbourhood cissolve before OMA. which is consistent with the rate ofEC dissolution.," We also find that $91.2\pm2.7\%$ of the clusters created in the Solar neighbourhood dissolve before Myr, which is consistent with the rate of EC dissolution."807 We thank the comments of the referee. Simon Portegies Zwart.," We thank the comments of the referee, Simon Portegies Zwart."808 We acknowledge support) from the Brazilian Institution CNPq., We acknowledge support from the Brazilian Institution CNPq.809 This publication makes use of the WEBDA database. operated at the Institutefor Astronomy of the University of Vienna.," This publication makes use of the WEBDA database, operated at the Institutefor Astronomy of the University of Vienna."810 , 811Iu thereal Universe thelocal temperature of theradiation fluid,"crucial difference to the scenario of heterogeneous nucleation \cite{Christiansen}, where bubbles nucleate at ad hoc impurities."812 fluctuates. Wedecompose the localtemperature the, Let us now investigate bubble nucleation in a Universe with spatially inhomogeneous temperature distribution.813 perturbation T(f. x).The temperature coutrast isdenoted byA= àT/T.Ou subhor, Bubble nucleation effectively takes place while the temperature drops by the tiny amount $\Delta_{\rm nuc}$.814izonscales intheradiation dominated epoch. cachFourier coefficient At.," To determine the mechanism of nucleation, we compare $\Delta_{\rm nuc}$ with the rms temperature fluctuation $\Delta_T^{\rm rms}$: 1."815) oscillates withconstant amplitude. which we denotely Arth).Inflation pre," If $\Delta_T^{\rm rms} < \Delta_{\rm nuc}$, the probability to nucleate a bubble at a given time is in space."816dicts a Gaussian distribution., This is the case of homogeneous nucleation.817 , 2.818p(AjdA = 1 exp LA? dA. (6) V2sAT$e 2(Amy? We find?for COBEnormal," If $\Delta_T^{\rm rms} > \Delta_{\rm nuc}$, the probability to nucleate a bubble at a given time is in space."819ized! temperature fluctuation, We call this inhomogeneous nucleation.820 ofthe (nottheof cold dark matter) rns «10.1for radiatiouILurison-Zeldovichfluid spectrum. The change," The quenched lattice QCD data and a COBE normalized flat spectrum lead to the values $\Delta_{\rm nuc} \sim 10^{-6}$ and $\Delta_T^{\rm rms} \sim 82110^{-5}$."822 Age oftheL0 of statea primordialpriorto OCD transitionmodifies equation, We conclude that the cosmological QCD transition may proceed via inhomogeneous nucleation.823 density relation. A, A sketch of inhomogeneous nucleation is shown in Fig. \ref{fig1}.824 theπόσες.ς| - the temperature-cucrey M temperature since p).atWomay ueglecttheother, The basic idea is that temperature inhomogeneities determine the location of bubble nucleation.825 pressurethep nearof the soundcritical, Bubbles nucleate first in the cold regions.826 eubauces p<eg TnOn haud drop 1/2speed95 the amplitudeof the density fluctuations, The temperature change at a given point is governed by the Hubble expansion and by the temperature fluctuations.827 those effectstogether and allowingfor fluctuationatilt in thepower spectrmu. the CODE normalizedtus temperature reads A smallscale Agscut-offin the spectrumof primordial fluctuations comesfrou collisional," For the fastest changing fluctuations, with angular frequency $c_s/l_{\rm smooth}$, we find The Hubble expansion is the dominant contribution, as typical values are $3 c_s^2 = 0.1$ from quenched lattice QCD and $\Delta_T^{\rm rms}828t_{\rm H}/\delta t \approx 0.01$ from the discussion above."829 dampingby neutrinos L5.temperatureTheinteraction rate of neutrinos is— GET”. This ha," This means that the local temperature does never increase, except by the released latent heat during bubble growth."830sto be comparedwith the aneular frequeucy Cohn of the acoustic oscillations.," To gain some insight in the physics of inhomogeneous nucleation, let us first inspect a simplified case."831" Atthe trausitionneutrinos scales/, zz ες10. Fluctuations QCDbelowthe diffusionscaleof neutrinosfreely are washedout. Pdg. af, 5 lit= / LAtydt]~7<\10-4 ‘dy. (Sj Jy Iu Ret."," We have some randomly distributed cold spheres of diameter $l_{\rm smooth}$ with equal and uniform temperature, which is by the amount $\Delta_T^{\rm rms}T_c$ smaller than the again uniform temperature in the rest of the Universe."832"""the damping scale frou collisional dampingby neutrinos las been calculated"," When the temperature in the cold spots has dropped to $T_{\rm f}$, homogeneous nucleation takes place in them."833tobe 08 = 101 atT=150MeV.The estimate(8)) is consistent with this dampingo scale. We assunie 111 μμ]li= LOαμ.Il The compression, Due to the Hubble expansion the rest of the Universe would need the time $\Delta t_{\rm cool} = t_H \Delta^{\rm rms}_T / 3 c_s^2$ to cool down to $T_{\rm f}$.834" timescalefora homogeneous voluae ~ £25, isOt=RausCsv10 fu. Sinceδὲ <>Aus"," Inside each cold spot there is a large number of tiny hadron bubbles, assumed to grow as deflagrations."835 the temperature fluctuationsare frozen withrespect tothe time scal, They merge within $\Delta t_{\rm cool}$ if $\Delta_{\rm nuc} < (v_{\rm def}/v_{\rm heat}) \Delta^{\rm rms}_T$.836"eof nucleations. As loneas/44,,,4 excecdsthe Fermi", This condition should be clearly fulfilled for our reference set of parameters.837 scale homogeneous bubble uucleation applies within these small homogeucous, Thus the cold spots have fully been transformed into the hadron phase while the rest of the Universe still is in the quark phase.838 volumes.This is a, The latent heat released in a839the r. 7 and ibands)P. which resulted in 65.277 M dwarfs.,"the $r$ , $i$ , and $z$, which resulted in 65,277 M dwarfs."840 While our catalog contains all of the 70.51 visually iuspected AL cdiviuf spectra. the 7GOODPIIOT? and “WDA flags can be used to obtain samples that include good plotometiy aud remove possible WD-dM airs respectively.," While our catalog contains all of the 70,84 visually inspected M dwarf spectra, the “GOODPHOT” and “WDM” flags can be used to obtain samples that include good photometry and remove possible WD-dM pairs respectively."841 Racial velocities (RVs) were measured by cross-correlating cach spectrum with the appropriate Bochauskietal.(2007b) M dwarf template., Radial velocities (RVs) were measured by cross-correlating each spectrum with the appropriate \citet{bootem} M dwarf template.842 This method das been shown to produce uucertainties raneius frou. 7-10 + (Bochanskiotal.20075).., This method has been shown to produce uncertainties ranging from 7-10 $^{-1}$ \citep{bootem}.843. All of the DRT objects were crossmatched to the USNO-D/SDSS proper notion catalog (Muunetal.20014.2008).. ideutifvius 39.151 M dwarfs with &ood proper motioust!.," All of the DR7 objects were cross-matched to the USNO-B/SDSS proper motion catalog \citep{munn04,munn08}, identifying 39,151 M dwarfs with good proper ."844". Distiuces ο cach star were calculated using the M, r-zeolor earh-typeandALSAllaterchwarls.(right).thereWhileisasvstematie inagnituderclationgivceninDBochauskict al.(2010)", Distances to each star were calculated using the $M_r$ $r-z$ color-magnitude relation given in \citet{boo10}.845 Ourcaleaftideetedestunedeg theda nenyctaVid ως gus arising imostly from the intrinsic spread of the main sequence.," Our calculated distances have uncertainties of $\sim$, arising mostly from the intrinsic spread of the main sequence."846 The proper ietions αμα distances were conibined with the RVs to produce 3-dimensioual space motions for the DR? AI dwarfs., The proper motions and distances were combined with the RVs to produce 3-dimensional space motions for the DR7 M dwarfs.847 Although we iuclude the standard C. V. W. space motious in our catalog. we caution that the C. V. W velocities are in a Cartesian coordinate syste that may not be appropriate for stars at appreciable distances frou the Sun.," Although we include the standard $U$, $V$, $W$ space motions in our catalog, we caution that the $U$, $V$, $W$ velocities are in a Cartesian coordinate system that may not be appropriate for stars at appreciable distances from the Sun."848 We therefore also include the Calactic radial (A). tangential (0) and vertical CZ) cvlindrical componcuts of the position and velocity for cach star for which we have 3D space lotious.," We therefore also include the Galactic radial $R$ ), tangential $\Theta$ ) and vertical $Z$ ) cylindrical components of the position and velocity for each star for which we have 3D space motions."849" We also matched our catalog to the 2MÁSS poiut source catalog (Cutrietal.2003).. matching only to unique 2ATASS counterparts within 5"" of the SDSS position that do not fall within the bouudarics of au extended source =0)."," We also matched our catalog to the 2MASS point source catalog \citep{2mass}, matching only to unique 2MASS counterparts within $^{\prime\prime}$ of the SDSS position that do not fall within the boundaries of an extended source $=$ 0)."850 To cusure that we used ouly hieh quality 2\LASS photometric data. we applied. additional cuts to cach of the J. 11. aud As lauds.," To ensure that we used only high quality 2MASS photometric data, we applied additional cuts to each of the $J$, $H$, and $K_S$ bands."851 If the source was not detected =). nomlnally detected —6). was detected but unresolved =9). or had contaminatedconfused photometry 40) in a particular baud. the 2ATASS data were not included.," If the source was not detected $=$ 0), nominally detected $=$ 6), was detected but unresolved $=$ 9), or had contaminated/confused photometry $\neq$ 0) in a particular band, the 2MASS data were not included."852 This resulted in 57.956 2ATASS counterparts with J. T aud Is magnitudes aud their mncertaimtics that were included im the catalog.," This resulted in 57,956 2MASS counterparts with $J$, $H$ and $K_S$ magnitudes and their uncertainties that were included in the catalog."853 We used the 2MASS photometry to investigate αν possible AL eiaut contamination., We used the 2MASS photometry to investigate any possible M giant contamination.854 Dessell&Brett(1955) found that NM eiauts aud AL cawarts separate iu JLT vs. IT color space due to differences in Πο absorption in their atmospheres., \citet{bessell88} found that M giants and M dwarfs separate in $J-H$ vs. $H-K$ color space due to differences in $_2$ O absorption in their atmospheres.855 By comparing the DR? JIT ve. JEK color-color diagrama with that of Bessell&Brett (1988).. we find that πο more than of our siuuple could be giants.," By comparing the DR7 $J-H$ vs. $H-K$ color-color diagram with that of \citet{bessell88}, we find that no more than of our sample could be giants."856 Iu addition. Coveyetal.(200510) conducted a complete magnitude-lamited spectroscopic survey of ILI? field in the SDSS footprint aud concluded that the eiuta contamination rate was less than for stars redder than a spectral type of Ish.," In addition, \citet{covey08} conducted a complete magnitude-limited spectroscopic survey of a $\Box^{\circ}$ field in the SDSS footprint and concluded that the giant contamination rate was less than for stars redder than a spectral type of K5."857 Previous large spectroscopic saeüuples of AL dwarfs have relied ou automated spectral typing due to the quantity of time required to manually inspect tens of thousands of candidate spectra., Previous large spectroscopic samples of M dwarfs have relied on automated spectral typing due to the quantity of time required to manually inspect tens of thousands of candidate spectra.858" Systematic discrepancies were recently identified iu the spectral types from the WWo0s SDSS sample that were deteriined automatically by the ""Ianuner spectral typing algorithm (Coveyetal. 2007).", Systematic discrepancies were recently identified in the spectral types from the \nocite{west08}W W08 SDSS sample that were determined automatically by the “Hammer” spectral typing algorithm \citep{covey07}.859 The bias was detected as a systematic offset for late-type stars. whose automatic classification was often 1 subtype earlier than deteruuned via visua inspection (sce Fieure 1)).," The bias was detected as a systematic offset for late-type stars, whose automatic classification was often 1 subtype earlier than determined via visual inspection (see Figure \ref{hamdiff}) )."860 We thus decided that visua inspection would produce the most reliable aud precise spectroscopic sample., We thus decided that visual inspection would produce the most reliable and precise spectroscopic sample.861 We visually inspected all 116.161 AD dwarf candidates and manually assigned spectra types.," We visually inspected all 116,161 M dwarf candidates and manually assigned spectral types."862" The sample was divided amoug 17 who used the manual ""evecheck mode of the Tamuuer 11.22.55) to assigu spectral types aud remove wou-\ dwazrt iuterlopers.", The sample was divided among 17 who used the manual “eyecheck” mode of the Hammer 5) to assign spectral types and remove non-M dwarf interlopers.863 Figure d. shows the ciffereuce between the spectra types automatically determined by the IHanuner mx the mean visual inspection., Figure \ref{hamdiff} shows the difference between the spectral types automatically determined by the Hammer and the mean visual inspection.864 For early-type AI dwarfs (left panel). the Tamuner aud the spectral tvpers agree most of the time.," For early-type M dwarfs (left panel), the Hammer and the spectral typers agree most of the time."865 However. for ~38% of the late-type ADI dwurfs (nieht panel). the Tamuner assigus spectral types L subtype earlier than the average luna spectral typer.," However, for $\sim$ of the late-type M dwarfs (right panel), the Hammer assigns spectral types 1 subtype earlier than the average human spectral typer."866 This confrxius that while the Ilanuner generates automatic spectral types within the quoted x1 subtype accuracy (Coveyetal.2007).. there is a systematic offset of 1 subtype for the late-type stars. and justifies our effort to manually inspect more than 116.000 candidates.," This confirms that while the Hammer generates automatic spectral types within the quoted $\pm1$ subtype accuracy \citep{covey07}, there is a systematic offset of 1 subtype for the late-type stars, and justifies our effort to manually inspect more than 116,000 candidates."867 Each spectral tvper also examined a control sample of 1000 spectra. of which 638 were AL divarfs.," Each spectral typer also examined a control sample of 1000 spectra, of which 638 were M dwarfs."868 We used this control sample to assess the quality aud reliability of the visually iuspected sample by quantitving the variatious amoug the 17 individual tvpers. and by. comparing the median visual type for cach star to its automatic ΠαΙΟ: type.," We used this control sample to assess the quality and reliability of the visually inspected sample by quantifying the variations among the 17 individual typers, and by comparing the median visual type for each star to its automatic Hammer type."869 The results of the coutrol sample show that there is excellent agreement between all of the spectral tvpers with a laree fraction of the stays beingassigned., The results of the control sample show that there is excellent agreement between all of the spectral typers with a large fraction of the stars beingassigned.870Alinost all of the visual classifications iu the control sample agreed to within +1 subtype of the median value: for most ofthe stars. the dispersion in visual classifications was <0.1 subtypes.,"Almost all of the visual classifications in the control sample agreed to within $\pm$ 1 subtype of the median value; for most ofthe stars, the dispersion in visual classifications was $<0.4$ subtypes."871 To eusure that there were no niajor svstematics in the spectral types assigned by anyindividual. we examined the mean difference between," To ensure that there were no major systematics in the spectral types assigned by anyindividual, we examined the mean difference between"872introduced by the + parameter.,introduced by the $r$ parameter.873 It should have little influence as the J. H and K near-infrared bands strongly constrain the modeled SED in longward bands in wich the stellar emission is dominated by the same populations.," It should have little influence as the J, H and K near-infrared bands strongly constrain the modeled SED in longward bands in wich the stellar emission is dominated by the same populations."874 However. when no near-infrared band is available shortward of 3.6 ym. the r parameter is much harder to constram and the uncertainty in the 3.6 uim and 4.5 um bands ts much higher.," However, when no near-infrared band is available shortward of 3.6 $\mu$ m, the $r$ parameter is much harder to constrain and the uncertainty in the 3.6 $\mu$ m and 4.5 $\mu$ m bands is much higher."875 In this study we have compiled and modeled the spectral energy distribution of a sample of 7 star forming regions in collision debris., In this study we have compiled and modeled the spectral energy distribution of a sample of 7 star forming regions in collision debris.876 We have carried out this study in three steps., We have carried out this study in three steps.877 First. we have adjusted the SED from the ultraviolet to the near-infrared (f available. otherwise ultraviolet to optical) with a photospheric+nebular model. yielding information on the star formation rate. attenuation. and star formation history.," First, we have adjusted the SED from the ultraviolet to the near-infrared (if available, otherwise ultraviolet to optical) with a photospheric+nebular model, yielding information on the star formation rate, attenuation, and star formation history."878 In a second step. we have fitted their UV to near-IR SED with templates of well known galaxies and then compared the mid-infrared part of their SED to infer information on the dust content.," In a second step, we have fitted their UV to near-IR SED with templates of well known galaxies and then compared the mid-infrared part of their SED to infer information on the dust content."879 Finally. a dust model was made to obtain estimates of the dust-to-PAH mass ratios.," Finally, a dust model was made to obtain estimates of the dust-to-PAH mass ratios."880 We have obtained the following main results:, We have obtained the following main results:881contribution from magnetic activity.,contribution from magnetic activity.882 As pointed out by Cram&Mullan(1979).. the onset of chromospheric activitw will first tend to deepen the absorption feature by as much as inrelatively cool and thin ehromospheres. where line formation is dominated by photoionization and not bv collisions.," As pointed out by \citet{1979ApJ...234..579C}, the onset of chromospheric activity will first tend to deepen the absorption feature by as much as in relatively cool and thin chromospheres, where line formation is dominated by photoionization and not by collisions."883 This effect is not seen in our data. πο object shows significantly more absorption than the photospheric values.," This effect is not seen in our data, no object shows significantly more absorption than the photospheric values."884 Thus. objects in transition between essentially non-active chromospheres to the collision-dominated regime are rare.," Thus, objects in transition between essentially non-active chromospheres to the collision-dominated regime are rare."885 The maximum level of magnetic activity aud (he fraction of active objects increases rapidly [rom early IX to mid M spectral types., The maximum level of magnetic activity and the fraction of active objects increases rapidly from early K to mid M spectral types.886 These results can be compared (to studies of older and vounger objects in a similar spectral range., These results can be compared to studies of older and younger objects in a similar spectral range.887 We use three criteria: A) This value was introduced by Lawleyetal.(1999) as an indicator of stellar age. as it is steaclily shilling to later spectral (νρος as the objects get older.," We use three criteria: A) This value was introduced by \citet{1999ASPC..158...63H} as an indicator of stellar age, as it is steadily shifting to later spectral types as the objects get older."888 Ia our sample. the transition is αἱ spectral types IX2.Kd. but it is only accurately defined lor objects in TII.," In our sample, the transition is at spectral types K2–K4, but it is only accurately defined for objects in TH."889 As summarized in Fie., As summarized in Fig.890 5 of Hawleyetal.(1999).. the transition occurs al early M. types in the IHyades (age GGvr). al late IK tvpes in the Pleiades (age MMyr). and at mid Ix. types in 22602/2391 (age MMwyr).," 5 of \citet{1999ASPC..158...63H}, the transition occurs at early M types in the Hyades (age Gyr), at late K types in the Pleiades (age Myr), and at mid K types in 2602/2391 (age Myr)."891 For objects in the MMyr age range vvounger (han our sample). the (Gransition occurs al spectral types earlier than INO (Dakin2005) in fact. objects without IIo. in emission are very rare at these ages (Poneetetal.1998)..," For objects in the Myr age range younger than our sample), the transition occurs at spectral types earlier than K0 \citep{2005AJ....130.1805D} – in fact, objects without $\alpha$ in emission are very rare at these ages \citep{1998ASPC..154.1772P}."892 Thus. the stars in TII fit nicely in the evolutionary sequence defined in the literature. indicating a steady decline of activity in (he pre-main-sequence evolution.," Thus, the stars in TH fit nicely in the evolutionary sequence defined in the literature, indicating a steady decline of activity in the pre-main-sequence evolution."893 Using this criterion as an age indicator. we find that ages in the TIL association are most likely between LO and AIvr. confirming previous estimates by Torresetal.(2000) ancl Songetal.(2004).," Using this criterion as an age indicator, we find that ages in the TH association are most likely between 10 and Myr, confirming previous estimates by \citet{2000AJ....120.1410T} and \citet{2004ApJ...614L.125S}."894 D) In our sample. practically all Ix/M objects are above the photospheric values. indicating activity. which is also (he case for (non-accreting) stars vounger than MMvr.," B) In our sample, practically all K/M objects are above the photospheric values, indicating activity, which is also the case for (non-accreting) stars younger than Myr."895 A close to fraction of active stars is also seen in pre-main-sequence clusters like 22602/2391 with ages of MMwvr. elal. 1997b).., A close to fraction of active stars is also seen in pre-main-sequence clusters like 2602/2391 with ages of Myr \citep{1997ApJ...479..776S}.896 In contrast. only a small fraction of active stars is seen in the IIvades at an age of GGvr CS30%.Reidetal.1995) and in the old field population &Miller 1989)..," In contrast, only a small fraction of active stars is seen in the Hyades at an age of Gyr \citep[$\lesssim 30$\%,][]{1995MNRAS.272..828R} and in the old field population \citep[$\lesssim 10$\%,][]{1989AJ.....97..891H}."897 Criterion D thus confirms the drop in activity [ον objects older MMwi. but some of this effect might be due to the selection bias in our sample towards highly active objects (see above).," Criterion B thus confirms the drop in activity for objects older Myr, but some of this effect might be due to the selection bias in our sample towards highly active objects (see above)."898 C) M stars are the most active objects in our sample with EW ranging from zero toAA., C) M stars are the most active objects in our sample with EW ranging from zero to.899. To avoid being biased too much by a few extremely active objects. we do not take into account the most active of the objects and thus obtain ~9 ," To avoid being biased too much by a few extremely active objects, we do not take into account the most active of the objects and thus obtain $\sim 9$ "900Hot luminous massive stars possess powerful radiatively driven stellar winds 2008).,Hot luminous massive stars possess powerful radiatively driven stellar winds .901. In à binary system consisting of two such stars. the collision of the winds generates a region of high temperature (7.>107 K) plasma which emits prolifically at X-ray wavelengths1992).," In a binary system consisting of two such stars, the collision of the winds generates a region of high temperature $T > 10^7\;$ K) plasma which emits prolifically at X-ray wavelengths."902. Depending on the parameters of the winds and the orbit. the dynamies of the postshock gas in the WCR can cover a diverse range1992).," Depending on the parameters of the winds and the orbit, the dynamics of the postshock gas in the WCR can cover a diverse range."903. For instance. in long-period binaries (i.e. of the order of years) the postshock gas is expected to be quasi-adiabatic for the most part. whereas in short-period (1.8. a few days) systems the postshock gas is expected to be highly radiative.," For instance, in long-period binaries (i.e. of the order of years) the postshock gas is expected to be quasi-adiabatic for the most part, whereas in short-period (i.e. a few days) systems the postshock gas is expected to be highly radiative."904 As a result. eccentric intermediate period systems (of the order of 1007s of days). such as WR22 (e=0.559. P=80 days - see Tables | and 2)). provide the prospect of transitioning between these two extremes.," As a result, eccentric intermediate period systems (of the order of 100's of days), such as WR22 $e \simeq0.559$, $P\simeq 80\;$ days - see Tables \ref{tab:system_parameters} and \ref{tab:stellar_parameters}) ), provide the prospect of transitioning between these two extremes."905 Such a transition in the state of the postshock gas has also been found in simulations of shorter period eccentric OB star systems by and(2009)., Such a transition in the state of the postshock gas has also been found in simulations of shorter period eccentric OB star systems by and.906 The X-ray emission from a colliding winds binary system acts as a direct observational probe of the postshock winds. and hence an indirect probe of the preshock winds2006).," The X-ray emission from a colliding winds binary system acts as a direct observational probe of the postshock winds, and hence an indirect probe of the preshock winds."907. Recently. an analysis of observations of WR22 by characterised the X-ray emission using à two-component spectrum consisting of a softcomponent at -0.6 keV and a harder component at ~2-4.5 keV. However. difficulties were encountered as wind-wind collision models were found to over-predict the observed X-ray flux by more than two orders of magnitude.," Recently, an analysis of observations of WR22 by characterised the X-ray emission using a two-component spectrum consisting of a softcomponent at $~\sim0.6\;$ keV and a harder component at $\sim908 2-4.5\;$ keV. However, difficulties were encountered as wind-wind collision models were found to over-predict the observed X-ray flux by more than two orders of magnitude."909 Considering the separation of the stars in WR22 (Table 1)). and the dominant WR wind ram pressure characteristic of WR+O binary systems2006).. the WCR will reside in the wind acceleration region of the O star's wind throughout the orbit.," Considering the separation of the stars in WR22 (Table \ref{tab:system_parameters}) ), and the dominant WR wind ram pressure characteristic of WR+O binary systems, the WCR will reside in the wind acceleration region of the O star's wind throughout the orbit."910 Consequently. lower preshock velocities will increase the importance of radiative cooling in the postshock gas. affecting the stability of the WCR.," Consequently, lower preshock velocities will increase the importance of radiative cooling in the postshock gas, affecting the stability of the WCR."911 The interplay between the stellar radiation fields may also significantly reduce the acquired preshock velocities through radiative inhibition. and/or braking1995)maimBodyCitationEnd353]|Gayley:1997., The interplay between the stellar radiation fields may also significantly reduce the acquired preshock velocities through radiative inhibition and/or braking.912 In fact. a stable ram pressure balance may not be established between the winds.," In fact, a stable ram pressure balance may not be established between the winds."913 WR22 - one of the most massive Wolf-Rayet stars currently known - may play host to these interesting phenomena which have the potential to significantly affect the observed X-ray emission., WR22 - one of the most massive Wolf-Rayet stars currently known - may play host to these interesting phenomena which have the potential to significantly affect the observed X-ray emission.914 The influence of orbital motion on the eircumbinary medium may also affect the observed emission., The influence of orbital motion on the circumbinary medium may also affect the observed emission.915 The shape of the wind-wind collision region (WCR) between the stars 15 largely dependent on the ram pressure of the stellar winds., The shape of the wind-wind collision region (WCR) between the stars is largely dependent on the ram pressure of the stellar winds.916 However. orbital motion introduces curvature to the WCR away from the stars 2011).," However, orbital motion introduces curvature to the WCR away from the stars ."917. This results in the spiral-like structure seen in the so-called “pinwheel” nebula2008)., This results in the spiral-like structure seen in the so-called “pinwheel” nebula.918. As such. the resulting highly asymmetric gas distribution introduces a viewing angle dependence to the emergent X-ray spectrum.," As such, the resulting highly asymmetric gas distribution introduces a viewing angle dependence to the emergent X-ray spectrum."919 In this paper the wind-wind collision in. WR22 is investigated using three dimensional adaptive-mesh refinement (AMR) simulations aimed at establishing the importance of the wind acceleration regions. radiative cooling. and orbital motion on the dynamics and resulting X-ray emission.," In this paper the wind-wind collision in WR22 is investigated using three dimensional adaptive-mesh refinement (AMR) simulations aimed at establishing the importance of the wind acceleration regions, radiative cooling, and orbital motion on the dynamics and resulting X-ray emission."920 The remainder of this paper is structured as follows: the hydrodynamical ane X-ray calculations are described in 2.., The remainder of this paper is structured as follows: the hydrodynamical and X-ray calculations are described in \ref{sec:model}.921 The simulation dynamics. resulting X-ray emission. and suggested revisions to model parametersare given in 4 3. ," The simulation dynamics, resulting X-ray emission, and suggested revisions to model parametersare given in \ref{sec:results}. ."922A discussion ts given in 4.. followed by conclusions in 5..," A discussion is given in \ref{sec:discussion}, , followed by conclusions in \ref{sec:conclusions}. ."923The reason [or introducing the stretched horizon has to clo with the dispersion relation w@=—/Dqg?+++.,The reason for introducing the stretched horizon has to do with the dispersion relation $\omega = -iD q^2 +\cdot \cdot \cdot$.924 Although JA)<|B] as r—ry. consideration of verv small but nonvanishing wave-muuber q will result in qiAlcJoD| and eventually g)AlZ9ωή for a fixed value of r as gq—0.," Although $|A| \ll |B|$ as $r \rightarrow r_0$, consideration of very small but nonvanishing wave-number $q$ will result in $q|A| \sim |\omega B|$ and eventually $q|A| \gg |\omega B|$ for a fixed value of $r$ as $q \rightarrow 0$ ."925" The latter can be satisfied sell-consistently ifr, —ry is not too small.", The latter can be satisfied self-consistently if $r_h-r_0$ is not too small.926 A more precise condition will be given below., A more precise condition will be given below.927 The shear mocles are transverse and strongly over-damped., The shear modes are transverse and strongly over-damped.928 At low lrequency and wave-number they have the dispersion relation w=—iDq? where D is a diffusion constant., At low frequency and wave-number they have the dispersion relation $\omega = -iD q^2$ where $D$ is a diffusion constant.929 In terms of the shear viscosity 7) and enthalpy density i0—Ts=P4+pilis D=yf., In terms of the shear viscosity $\eta$ and enthalpy density $w = Ts = P+\rho$ it is $D = \eta/w$.930" Upon inspection. and with the expectation of a diffusive mode. we expand the functions in powers of g asfollows: AQ) = AC""(r) Dr) Lp Όρη]"," Upon inspection, and with the expectation of a diffusive mode, we expand the functions in powers of $q$ asfollows: A(r) = (r), B(r) = (r)."931", From Eqs. (3))", From Eqs. \ref{hyzA}) )932" and (3)) we find the lowest order solutions MOP) —qu tay dift DP) = h, + hy dy! ("," and \ref{hyzB}) ) we find the lowest order solutions (r) = a_0 + a_1 dr', (r) = b_0 + b_1 dr' ."93332) Substitution into Eq. (3)).," Substitution into Eq.\ref{hyzC}) ),"934 together with w=—/Dq. gives the relationship D=ibyfay.," together with $\omega = - i D q^2$, gives the relationship $D = i b_1/a_1$."935 The Dirichlet boundary condition on A and D al infinity gives (Gu=by0., The Dirichlet boundary condition on $A$ and $B$ at infinity gives $a_0 = b_0 = 0$.936 lt is now a straightforward matter to substitute the lowest order solution into the boundary condition on thestretched horizon to obtain the shear diffusion constant. D= dy m," It is now a straightforward matter to substitute the lowest order solution into the boundary condition on thestretched horizon to obtain the shear diffusion constant, D= dr ."937 lt is now a straightforward matter to substitute the lowest order solution into the boundary condition on thestretched horizon to obtain the shear diffusion constant. D= dy mn," It is now a straightforward matter to substitute the lowest order solution into the boundary condition on thestretched horizon to obtain the shear diffusion constant, D= dr ."938 lt is now a straightforward matter to substitute the lowest order solution into the boundary condition on thestretched horizon to obtain the shear diffusion constant. D= dy mno," It is now a straightforward matter to substitute the lowest order solution into the boundary condition on thestretched horizon to obtain the shear diffusion constant, D= dr ."939Iu conclusion. the existing work has demonstrated the power of oobservations in probing the stellar and ACN feedback aud its effect ou galaxy evolution as well as inventorving various kinds of lieh-cncrey sources in galaxies.,"In conclusion, the existing work has demonstrated the power of observations in probing the stellar and AGN feedback and its effect on galaxy evolution as well as inventorying various kinds of high-energy sources in galaxies."940pulsar wind nebulae. which are also capable of producing ligh-cuerey y-ray enission.,"pulsar wind nebulae, which are also capable of producing high-energy $\gamma$ -ray emission."941 Some sources reported by Torresetal.(2003). as potential EGRET counterparts to SNRs have since been associated with other astroplivsical sources., Some sources reported by \citet{torres03} as potential EGRET counterparts to SNRs have since been associated with other astrophysical sources.942 The source 3ECO JLULO-GLIT. coincident with SNR C€312.1-0.1. has receutlv been associated with the voung pulsar JL110-6132 with variability detected by AQGILE (O’Brienotal.2008).," The source 3EG J1410-6147, coincident with SNR G312.4-0.4, has recently been associated with the young pulsar J1410-6132 with variability detected by AGILE \citep{obrien08}."943. The source 3EG J1821-1511 has been confirmed as the mücroquasar LS 5039 (Aharonianetal.2005). ruling out an association with SNR. CH6.5-1.1. (Torresetal.2003).," The source 3EG J1824-1514 has been confirmed as the microquasar LS 5039 \citep{ls5039}, ruling out an association with SNR G16.8-1.1 \citep{torres03}."944" Sources BEG J2016| and 3ECO J2020,|I017.. coincident with SNRs €G71.91|1.23657 and (78.212.1 respectively. are identified as exragalactie blazars (Ivudiuetal.2007)."," Sources 3EG J2016+3657 and 3EG J2020+4017, coincident with SNRs G74.9+1.2 and G78.2+2.1 respectively, are identified as extragalactic blazars \citep{iyudin07}."945". Finally. the ECRET counterparts for SNRs (σιο, 1355.6|0.0. C39.2-0.3 and GrL811.2 (Torresetal. do not appear in the Fermi bright source catalog (Abdoetal.2009).. and we therefore do not include them as detectious ii our analysis."," Finally, the EGRET counterparts for SNRs G180.0-1.7, G355.6+0.0, G39.2-0.3 and G74.8+1.2 \citep{torres03} do not appear in the Fermi bright source catalog \citep{abdo09}, and we therefore do not include them as detections in our analysis."946 We include all remmauts for which au association with the coincideut 5-rav source has not been ruled out., We include all remnants for which an association with the coincident $\gamma$ -ray source has not been ruled out.947 There are 26 identified SNRs with οταν coiucideuces: 7 are young remnants (Z1 kyr). 12 are SNRs with evidence of interaction with deuse clouds. aud 7 are nuclassified remnants.," There are 26 identified SNRs with $\gamma$ -ray coincidences: 7 are young remnants $\la$ 1 kyr), 12 are SNRs with evidence of interaction with dense clouds, and 7 are unclassified remnants."948 Of the 12 ideutified SNRs which are interacting with deuse gas. all but two (AISIT 11-61A and WL9B) have detected SNR imasers.," Of the 12 identified SNRs which are interacting with dense gas, all but two (MSH 11-61A and W49B) have detected SNR masers."949 The presence of masers gives several advantages: (1) masers signpost interaction with dense (10°? 5) clouds. which will chhance the pion decay signature. (2) the velocity of the lmaser gives a kincmatic distance. and (3) an established velocity allows the adjacent cloud. to be isolated from confusing Galactic emission along the line of sight.," The presence of masers gives several advantages: (1) masers signpost interaction with dense $^5$ $^{-3}$ ) clouds, which will enhance the pion decay signature, (2) the velocity of the maser gives a kinematic distance, and (3) an established velocity allows the adjacent cloud to be isolated from confusing Galactic emission along the line of sight."950 Table P. lists all SNRs wiἩ amasers and the properties of potentially associated +- rav cuussion., Table \ref{tbl:list} lists all SNRs with masers and the properties of potentially associated $\gamma$ -ray emission.951 Du the first five columus the Calactic coorinates. name. diameter aud kinematic distance are Listec for each remmant.," In the first five columns the Galactic coordinates, name, diameter and kinematic distance are listed for each remnant."952 The +-rav huninosity for all derived frou. the reported ~LOO 10 GeV and TeV fuxes in colts 6 aud 8., The $\gamma$ -ray luminosity for all derived from the reported $\sim$ 100 MeV--10 GeV and $\gtrsim$ 1 TeV fluxes in columns 6 and 8.953 Spectral indices for are 21given in cols 7 aud 9., Spectral indices for are given in columns 7 and 9.954 References for detections are given in the last column., References for detections are given in the last column.955 The ten SNRs with coincident οταν sources are divided based on the certainty of their association: Group A includes four SNRs for which 5-ravs are established as related to the SNR: Group D includes six SNRs with coincident οταν sources which have uot been attributed to other astrophysical phenomenon (pulsars. blazars. ete.)," The ten SNRs with coincident $\gamma$ -ray sources are divided based on the certainty of their association: Group A includes four SNRs for which $\gamma$ -rays are established as related to the SNR; Group B includes six SNRs with coincident $\gamma$ -ray sources which have not been attributed to other astrophysical phenomenon (pulsars, blazars, etc.)"956 but for which an association with the SNR is less than certain: Group € lists the sixtecn SNRs with mascrs which do not vet have detected 2-rav sources., but for which an association with the SNR is less than certain; Group C lists the sixteen SNRs with masers which do not yet have detected $\gamma$ -ray sources.957 Coven that both masers and 2-rays are detected for onlv LOY of SNRs. the large number of coincident detections makes an association between SNR aasers aud οταν cussiow as tracers of interaction quite plausible.," Given that both masers and $\gamma$ -rays are detected for only $\%$ of SNRs, the large number of coincident detections makes an association between SNR masers and $\gamma$ -ray emission as tracers of interaction quite plausible."958 To explore the correlation between SNR mascers and ~-ray sources. we use a contingency table analysis to test the uull hypothesis that there is uo association between the two groups.," To explore the correlation between SNR masers and $\gamma$ -ray sources, we use a contingency table analysis to test the null hypothesis that there is no association between the two groups."959 Tere we include all roimmauts which have been searched for SNR imasers (Frailctal.1996:Crecu aud those 2-rav sources which have not been clearly identified as hiviug a," Here we include all remnants which have been searched for SNR masers \citep{frail96,green97,koralesky98,fyz99,hewitt09} and those $\gamma$ -ray sources which have not been clearly identified as having a"960<ta Lwweelk) and two transicuts found im rolling 2anouth searches (hereafter. “multi-epoch” sources).,"$<t_{\rm dur}<$ week) and two transients found in rolling 2-month searches (hereafter, “multi-epoch” sources)."961 Deep observations towards these sources were uudertaken at optical. near-IR aud X-ray bands," Deep observations towards these sources were undertaken at optical, near-IR and X-ray bands."962 The most remarkable feature of the BOT sources ds an absence of optical aud near-IR counterparts. despite deep searches (BOT: Ofeketal. 2010)).," The most remarkable feature of the B07 sources is an absence of optical and near-IR counterparts, despite deep searches (B07; \citealt{obg+10}) )."963 As noted by Ofexetal(2010) all extra-galactie trausicuts (regmless of the band at which the transient was discovered) iive detectable optical counterparts. namely. their host ealaxies.," As noted by \citet{obg+10} all extra-galactic transients (regardless of the band at which the transient was discovered) have detectable optical counterparts, namely, their host galaxies."964 Furthermore. remarkably the areal deusitv of ransicuts live at auv given fiue was estimated to be ? (S> O.37unJv).," Furthermore, remarkably the areal density of transients live at any given time was estimated to be $^{-2}$ $S>0.37\,$ mJy)."965 This density exceeds. that 6: all other known radio transieut source populations o» an order of magnitude (or more): soe Table 1. Of, This density exceeds that of all other known radio transient source populations by an order of magnitude (or more); see Table \ref{tab:ListOfTrans}.966eketal.(2010). thus argued that the absence of au optical counterpart meaus that DOT transicuts have to e repeating sources of Calactic origin. and proposed hat BOT trausicuts are old neutron stars (which ιαπαν satisty the requirenent of being optically almost invisible).," \cite{obg+10}967 thus argued that the absence of an optical counterpart means that B07 transients have to be repeating sources of Galactic origin, and proposed that B07 transients are old neutron stars (which naturally satisfy the requirement of being optically almost invisible)."968 Given that the search for trausieut aud strong variables is one of the primary inotivators for the next eeneration radio facilities. (described earlier) it is important to critically investigate the BOT transieuts since this class nonunuallv dominates over all other known classes of radio transicuts (see Table 1))., Given that the search for transient and strong variables is one of the primary motivators for the next generation radio facilities (described earlier) it is important to critically investigate the B07 transients since this class nominally dominates over all other known classes of radio transients (see Table \ref{tab:ListOfTrans}) ).969 To this end. here we report ou are-analysis of the original data of DOT refsec:ObsReana.. retsec:Findines)} aud revisit he transient reported by Ofeketal.20101 refseciOtherSurvevs)).," To this end, here we report on a re-analysis of the original data of B07 \\ref{sec:ObsReana}, \\ref{sec:Findings}) ) and revisit the transient reported by \citealt{ofb+11} \\ref{sec:OtherSurveys}) )."970 In retsec:logNlogS owe present an update of the expected rate of radio trausicuts., In \\ref{sec:logNlogS} we present an update of the expected rate of radio transients.971 In refsec:FutureSurvers we discuss these rates m relation to future svuoptic radio dmaeine surveys aud conclude., In \\ref{sec:FutureSurveys} we discuss these rates in relation to future synoptic radio imaging surveys and conclude.972 The data used by BOF arose from a calibrator program. carricd out during the period 1983.2005., The data used by B07 arose from a calibrator program carried out during the period 1983–2005.973 All observations were made in the standard continuum mode with NMIIz of total bandwidth in each of two adjaccut 5O-MITz bauds (IEx) at center frequencies of CCUz and SLCCz aud iu both hands of circular polarization., All observations were made in the standard continuum mode with MHz of total bandwidth in each of two adjacent 50-MHz bands (IFs) at center frequencies of GHz and GHz and in both hands of circular polarization.974 See DU? for more details about the full data-set., See B07 for more details about the full data-set.975 For the re-analvsis we selected. from the archive. oulv the raw data relevant to the transicuts reported in DOT.," For the re-analysis we selected, from the archive, only the raw data relevant to the transients reported in B07."976 This means the eight epochs from which the sinegle-cpoch transicuts were first found and the 318 data sets from which the two multi-epoch trausieuts were found., This means the eight epochs from which the single-epoch transients were first found and the 3+8 data sets from which the two multi-epoch transients were found.977 Data were taken at other radio frequencies in about half of the cases., Data were taken at other radio frequencies in about half of the cases.978 Some details of the single epoch and ποοι trausients can be found iu Table 2))., Some details of the single epoch and two-month transients can be found in Table \ref{tab:ListOfFields}) ).979 For the re-analvsis we used. (Creiseun2003)., For the re-analysis we used \citep{Greisen03}.980 The data reduction and nuaeiug followed the same path used by Bot with a small exception., The data reduction and imaging followed the same path used by B07 with a small exception.981 BOT enmploved AIPS for the flageine aud analysis of the simele-epoch transients. aud used theAfiriad package (Saultctal.1995). for imaging the two- averages.," B07 employed AIPS for the flagging and analysis of the single-epoch transients, and used the package \citep{stw95} for imaging the two-month averages."982 We eudeavored to make the calibration and the flageiug of UV. data (AIPS task TVFLG)) data for each epoch as uniform wav., We endeavored to make the calibration and the flagging of UV data (AIPS task ) data for each epoch as uniform way.983 Following these steps we ran cach raw visibility data sct through the VLA pipeline (VLARUN))., Following these steps we ran each raw visibility data set through the VLA pipeline ).984 No flux deusitv calibrator was observed daring uu 2ος] of these test observations., No flux density calibrator was observed during any epoch of these test observations.985 Following D07. the flux density of the pliase calibrator (BIS03|781) was fixed to be 2.2JJIv GGIIZ) and 2.5JJv GITz).," Following B07, the flux density of the phase calibrator (B1803+784) was fixed to be Jy GHz) and Jy GHz)."986 For those epochs with €GIIz aud 1.1GITIz observatious the flux deusitv of the phase calibratorC was taken to be JJ and 2JJy. respectively.," For those epochs with GHz and GHz observations the flux density of the phase calibrator was taken to be Jy and Jy, respectively."987 It is evident from the strong various in the radio light curves for that these mean values are only approximate., It is evident from the strong variations in the radio light curves for that these mean values are only approximate.988 Our reinvestigation coufinu that at least curving the period 19811999 the variation was less than, Our reinvestigation confirm that at least during the period 1981–1999 the variation was less than.989 Fortunately. an accurate flux densitv scale is uot crucial for our analysis since we report results iu terms of the signa," Fortunately, an accurate flux density scale is not crucial for our analysis since we report results in terms of the signal-to-noise."990 Following BOF we applied a Gaussian weieliting to the visibility data in order to linüt the effects of bandwidth sncazing., Following B07 we applied a Gaussian weighting to the visibility data in order to limit the effects of bandwidth smearing.991 This was done by applying a L50-kA taper to all visibility data prior to dmaeing (IMAGR))., This was done by applying a $\lambda$ taper to all visibility data prior to imaging ).992 For each field we required that a source be present in both frequency bands (IFs) with similar flux densities aud with similar positions., For each field we required that a source be present in both frequency bands (IFs) with similar flux densities and with similar positions.993 huages were made with extra large felds-of-view., Images were made with extra large fields-of-view.994 The wide field-of-view is necessary to reduce the effect of side-lobes that can mimic sources di narrow fields., The wide field-of-view is necessary to reduce the effect of side-lobes that can mimic sources in narrow fields.995 These final analysis iuages had a size of about. LO- at GGIIz data and 27-arcuinu at GGIIz., These final analysis images had a size of about 40-arcmin at GHz data and 27-arcmin at GHz.996 For euidauce. the fullewidth at half power for VLA auteunas is [5-arciun/rtGIDz). or 9.3-arenin at GGIIz and," For guidance, the full-width at half power for VLA antennas is $\nu$ (GHz), or 9.3-arcmin at GHz and"997"? and ? compare the three models of ?,, ?,, and ?..","\cite{2006MNRAS.372..381B} and \cite{2008MNRAS.388..677W} compare the three models of \cite{1997MNRAS.286..215K}, , \cite{1999AJ....117..677B}, and \cite{1999AJ....117..677B}."998" Monte Carlo simulations for each model are used to predict radio powers, sizes, redshifts and spectral indices of an artificial sample, which are compared to the data of the low-frequency radio survey 3CRR, 6CE and 7CRS."," Monte Carlo simulations for each model are used to predict radio powers, sizes, redshifts and spectral indices of an artificial sample, which are compared to the data of the low-frequency radio survey 3CRR, 6CE and 7CRS."999" ? find that no existing model can give acceptable fits to all the properties of the surveys considered, and the simplest ? model is somewhat better at fitting the data."," \cite{2006MNRAS.372..381B} find that no existing model can give acceptable fits to all the properties of the surveys considered, and the simplest \cite{1997MNRAS.286..215K} model is somewhat better at fitting the data."1000" ? evolve some of the properties of FR II sources with redshift to have the artificial samples to fit the observations, and also finds ? best matches observations."," \cite{2008MNRAS.388..677W} evolve some of the properties of FR II sources with redshift to have the artificial samples to fit the observations, and also finds \cite{1997MNRAS.286..215K} best matches observations."1001 The model of ? is the first to go beyond the stopping of the jet after a time t; and consider the X-ray emission of the lobes from IC scattering of the CMB photons., The model of \cite{2010MNRAS.tmp.1004N} is the first to go beyond the stopping of the jet after a time $t_{\rm j}$ and consider the X-ray emission of the lobes from IC scattering of the CMB photons.1002" The model is a variant of ? and ?,, also assuming a constant axial ratio."," The model is a variant of \cite{1997MNRAS.286..215K} and \cite{1997MNRAS.292..723K}, also assuming a constant axial ratio."1003 The model does not evolve simply according to the self-similar evolution of lobe length determined by the characteristic length scale., The model does not evolve simply according to the self-similar evolution of lobe length determined by the characteristic length scale.1004" The model in the present work also goes beyond the cessation of the jet in the formalism of ? and considers the growth of the lobe as described by ? where a compact hotspot with a pressure distinct from the lobe pressure that determines lobe length growth feeds the lobes, and in which axial ratios grow over time during jet activity."," The model in the present work also goes beyond the cessation of the jet in the formalism of \cite{2010MNRAS.tmp.1004N} and considers the growth of the lobe as described by \cite{1999AJ....117..677B} where a compact hotspot with a pressure distinct from the lobe pressure that determines lobe length growth feeds the lobes, and in which axial ratios grow over time during jet activity."1005 The model is also analytic rather than numeric., The model is also analytic rather than numeric.1006 We are able to go beyond the self-similarity expansion after the jet stops (i.e. no longer rely on a characteristic length scale)., We are able to go beyond the self-similarity expansion after the jet stops (i.e. no longer rely on a characteristic length scale).1007" We are not required to fix a constant axial ratio during jet activity and solve the pairs of differential equations as in equation (6) of to solve for the evolution of length and pressure, which results in the volume evaluated as Vi(t)=vL;(t)?/(4R?) not precisely agreeing with the volume of the lobe determined by integration of volume elements (equation (8) of ?))."," We are not required to fix a constant axial ratio during jet activity and solve the pairs of differential equations as in equation (6) of \cite{2010MNRAS.tmp.1004N} to solve for the evolution of length and pressure, which results in the volume evaluated as $V_{\rm l}(t)=\pi L_{\rm j}(t)^3/(4R^2)$ not precisely agreeing with the volume of the lobe determined by integration of volume elements (equation (8) of \cite{2010MNRAS.tmp.1004N}) )."1008" In this section we discuss the radio luminosity function (RLF) of Fanaroff and Riley Class II radio sources, the inferred birth function of such sources and the empirically-inferred distribution of jet energies which are necessary to find the distribution of the IC ghosts and the completely dark, i.e. observable, radio and X-ray lobes."," In this section we discuss the radio luminosity function (RLF) of Fanaroff and Riley Class II radio sources, the empirically-inferred birth function of such sources and the empirically-inferred distribution of jet energies which are necessary to find the distribution of the IC ghosts and the completely dark, i.e. non-observable, radio and X-ray lobes."1009 An IC ghost refers to a galaxy that has its jets turned off but still emits X-ray radiation due to the upscattering of CMB photons., An IC ghost refers to a galaxy that has its jets turned off but still emits X-ray radiation due to the upscattering of CMB photons.1010 An IC ghost is the term we use to call an IC ghost that radiates above a given X-ray flux limit (but lacks detectable synchrotron radiation)., An IC ghost is the term we use to call an IC ghost that radiates above a given X-ray flux limit (but lacks detectable synchrotron radiation).1011 In 22--?? we use the normative model parameters of case [A]., In \ref{sec:OIDP}- \ref{sec:XLF} we use the normative model parameters of case [A].1012 In ?? we explore model parameter cases [B]-[L]., In \ref{sec:params} we explore model parameter cases [B]-[L].1013" We will use the RLF of high radio power FR II sources determined by ? from the 7CRS, 6CE and 3CRR samples, to aid in predicting the density of radio lobes including IC ghosts and completely non-observable ones."," We will use the RLF of high radio power FR II sources determined by \cite{2001MNRAS.322..536W} from the 7CRS, 6CE and 3CRR samples, to aid in predicting the density of radio lobes including IC ghosts and completely non-observable ones."1014 The radio luminosity function describes the space density per unit comoving volume of sources as afunction of luminosity as derived from the surveys., The radio luminosity function describes the space density per unit comoving volume of sources as afunction of luminosity as derived from the surveys.1015" The luminosity function was converted from the cosmology Πο=50kms! Mpc!, Ow= 0, Q4=0, Ωκ=1 to the cosmology we use in this paper with the relation (?) where the indices refer to a cosmological model, P, is the luminosity derived from the flux density and redshift in model 7 and Vi is comoving volume."," The luminosity function was converted from the cosmology $H_0=50~{\rm km}~{\rm s}^{-1}~{\rm Mpc}^{-1}$ , $\Omega_{\rm M}=0$ , $\Omega_\Lambda=0$, $\Omega_{\rm k}=1$ to the cosmology we use in this paper with the relation \citep{1985MNRAS.217..601P}1016 where the indices refer to a cosmological model, $P_{\rm i}$ is the luminosity derived from the flux density and redshift in model $i$ and $V_{\rm i}$ is comoving volume."1017" The RLF of ? will reflect only those radio galaxies that are above the flux limit (at low radio frequencies ~151MHz) of 0.5Jy (?),, which is the lowest flux limit of the surveys they used to determine the RLF."," The RLF of \cite{2001MNRAS.322..536W} will reflect only those radio galaxies that are above the flux limit (at low radio frequencies $\sim151~{\rm MHz}$ ) of $0.5~{\rm Jy}$ \citep{2001ApJ...560L.115G}, which is the lowest flux limit of the surveys they used to determine the RLF."1018 We assume the empirically-inferred birth function of radio sources given by ?:: with zi;2.2 and Az=0.6., We assume the empirically-inferred birth function of radio sources given by \cite{1999AJ....117..677B}: with $z_1=2.2$ and $\Delta z=0.6$.1019" Most sources are born during the quasar era, z= 1.5-3."," Most sources are born during the quasar era, $z=1.5$ $3$."1020" By ""birth"" we mean jet activity initiates.", By a “birth” we mean jet activity initiates.1021 The birth function was determineda by ? such that simulations of sources best match 3C and 7C data., The birth function was determined by \cite{1999AJ....117..677B} such that simulations of sources best match 3C and 7C data.1022 It is useful to convert the birth function to the probability density function (PDF) for the age of radio sources as a function of redshift., It is useful to convert the birth function to the probability density function (PDF) for the age of radio sources as a function of redshift.1023" This is accomplished through the equation where pa(t,2) gives the probability densitythat a source is age t at redshift z and z; is the redshift of a source at its birth for itto appear age t when observed at a redshift of z."," This is accomplished through the equation where $p_{\rm A}(t,z)$ gives the probability densitythat a source is age $t$ at redshift $z$ and $z_{\rm t}$ is the redshift of a source at its birth for itto appear age $t$ when observed at a redshift of $z$ ."1024" The PDF for the age of radio sources at z=0,1,2,3,4 is presented in Figure 5.."," The PDF for the age of radio sources at $z=0,1,2,3,4$ is presented in Figure \ref{fig:pAge}. ."1025subsequent detailed development of the theory of LAE for highly relativistie particles.,subsequent detailed development of the theory of LAE for highly relativistic particles.1026 Our objective in this paper is to develop the theory of LAE for motion in a large-amplitude electrostatic wave (LAEW). emphasizing the analogy with svnehrotron emission. and the important differences from svnchrotron emission.," Our objective in this paper is to develop the theory of LAE for motion in a large-amplitude electrostatic wave (LAEW), emphasizing the analogy with synchrotron emission, and the important differences from synchrotron emission."1027 Two other emission processes [or hiehlv relativistic particles. inverse Compton emission and emission due to motion in a lzrge-aanplitude (transverse wave (Gunn&Ostriker1971;Arons1972).. have properties that are somewhat analogous to (hose of svuchrotvon emission.," Two other emission processes for highly relativistic particles, inverse Compton emission and emission due to motion in a large-amplitude transverse wave \citep{go71,a72}, have properties that are somewhat analogous to those of synchrotron emission."1028 In particular. all (ree are treated bv making an Airv-integral approximation to a relevant phase integral.," In particular, all three are treated by making an Airy-integral approximation to a relevant phase integral."1029 Our treatment of LAE in à LAEW is based on the assumption that an Airv-integral approximation is also appropriate in (his case., Our treatment of LAE in a LAEW is based on the assumption that an Airy-integral approximation is also appropriate in this case.1030 Our argument for Chis assumption is given in an accompanvine paper (Melrose.Ralat&Luo2009).. hereinalter referred to as paper 1.," Our argument for this assumption is given in an accompanying paper \citep{mrl09}, hereinafter referred to as paper 1."1031 We should emphasize that any treatment of LAE encounters conceptual diffieulties that are not relevant to the other three emission processes mentioned., We should emphasize that any treatment of LAE encounters conceptual difficulties that are not relevant to the other three emission processes mentioned.1032 In particular. Schwinger(1949). showed how the theory of svnchrotron emission reproduces the total power radiated as predicted bv the generalized Larmor formula. and it can be shown that this is also the case for the other {wo mechanisms mentioned.," In particular, \cite{s49} showed how the theory of synchrotron emission reproduces the total power radiated as predicted by the generalized Larmor formula, and it can be shown that this is also the case for the other two mechanisms mentioned."1033 Lowever. it is not the case for LAE.," However, it is not the case for LAE."1034 Moreover. it has been recognized for over a century. (hat there is a conceptual diffieuliv in the treatment of linear acceleration emission itself. and the wnderlving difficulty leads to problems in anv treatment of LAE.," Moreover, it has been recognized for over a century that there is a conceptual difficulty in the treatment of linear acceleration emission itself, and the underlying difficulty leads to problems in any treatment of LAE."1035 The motivation for this investigation relates to possible emission processes that. can occur in an oscillating model for a pulsar (Levinsonοἱal.2005). or magnetar (BeloborodoyThompson2007) magnetosphere., The motivation for this investigation relates to possible emission processes that can occur in an oscillating model for a pulsar \citep{letal05} or magnetar \citep{bt07} magnetosphere.1036" Specilicallv. we pose the question whether LAE in an oscillating model can be important as an emission mechanism. aud whether (the properties ol LAE can lead to observational signatures that are unique to an oscillating model,"," Specifically, we pose the question whether LAE in an oscillating model can be important as an emission mechanism, and whether the properties of LAE can lead to observational signatures that are unique to an oscillating model."1037 LAE is of potential interest in four wavs., LAE is of potential interest in four ways.1038 First. it may be relevant as a high-energyv. emission process. which would require that LAE allow emission up to gamnma-ray. energies.," First, it may be relevant as a high-energy emission process, which would require that LAE allow emission up to gamma-ray energies."1039 Second.," Second,"1040Encouraginely our 4 new associations have bIuminosities ancl redshifts consistent with the rest of the SMG sample.,Encouragingly our 4 new associations have luminosities and redshifts consistent with the rest of the SMG sample.1041 Llowever this does make their. radio-weak nature. all 4 are undetectecl in. deep VLA radio imaging. somewhat mysterious.," However this does make their radio-weak nature, all 4 are undetected in deep VLA radio imaging, somewhat mysterious."1042 To further examine whether we expect these sources to be radio-weak the SbOjm-1.4 Cllz lux redshift correlation is shown in Figure 6.., To further examine whether we expect these sources to be radio-weak the $\mu$ m-1.4 GHz flux ratio-to-redshift correlation is shown in Figure \ref{fig:irradz}.1043 5 SMCGSs in our combined sample have no accompanving radio detection. the + new associations (SXDES50.32. SXDES50.56. SNDES50.65. SNDESD0.70) and ΝΟΤΙ.," 5 SMGs in our combined sample have no accompanying radio detection, the 4 new associations (SXDF850.32, SXDF850.56, SXDF850.65, SXDF850.70) and SXDF850.71."1044 Of these 6. 3 have upper limits on the S5O0jun/1.4 112 lux ratio which are roughly consistent with both the Chapman et al.," Of these 6, 3 have upper limits on the $\mu$ m/1.4 GHz flux ratio which are roughly consistent with both the Chapman et al."1045 relation and the A220 model (SNDES50.50. SADES50.56. SNDESS0.71).," relation and the A220 model (SXDF850.50, SXDF850.56, SXDF850.71)."1046 The other 2 all have upper limits which are higher than both predictions. be. they should have been detected. given the depth of the radio observations.," The other 2 all have upper limits which are higher than both predictions, i.e. they should have been detected given the depth of the radio observations."1047 While this would appear to be a strong argument against the plausibility. of these associations a large number of the LO7/COS sample of SALGS are. also found to have s50y;mny1.4 CGllz flux ratios much higher than expected., While this would appear to be a strong argument against the plausibility of these associations a large number of the I07/C08 sample of SMGs are also found to have $\mu$ m/1.4 GHz flux ratios much higher than expected.1048 While this may. simply be a result. of the large errors on both the SCUBA 85050 ancl 1.4 Cillz radio Iuxes and. possibly erroneous photo-z's. there are still a significant number of discrepant SMCGs even when errors are taken into account.," While this may simply be a result of the large errors on both the SCUBA $\mu$ m and 1.4 GHz radio fluxes and possibly erroneous $z$ 's, there are still a significant number of discrepant SMGs even when errors are taken into account."1049 6 SMCGs from the I07/C08 sample are found to have discrepantly high 850/42/1.4 ας flux ratios here., 6 SMGs from the I07/C08 sample are found to have discrepantly high $\mu$ m/1.4 GHz flux ratios here.1050 Of these one is the incorrect association SNDES5O.10., Of these one is the incorrect association SXDF850.10.1051 Another three are cases where we have found a photometric redshift much less than COS (SXDES50.8. SNDESSO.11. SNDESS0.37).," Another three are cases where we have found a photometric redshift much less than C08 (SXDF850.8, SXDF850.11, SXDF850.37)."1052 In these cases the lux ratio would not be discrepant. if the SAIG is actually at the COS photo-z estimate rather than the one mace bere., In these cases the flux ratio would not be discrepant if the SMG is actually at the C08 photo-z estimate rather than the one made here.1053 This leaves two cases (SNDESD0.96. SXDESS0.119) in which the s50;an/l4 Cllz Εαν ratio is inexplicably cliscrepant.," This leaves two cases (SXDF850.96, SXDF850.119) in which the $\mu$ m/1.4 GHz flux ratio is inexplicably discrepant."1054 Interestingly in these caess the p-statistic for the radio LD which is significant (0.039 0.043. respectively).," Interestingly in these caess the p-statistic for the radio ID which is significant (0.039 0.043, respectively)."1055" However both have fairly significant evidence (In Dj,=9.1 10.0 respectively.", However both have fairly significant evidence (ln $B_{tot}=9.1$ 10.0 respectively.1056 So while we hesitate to further downgrade tie status of these associations. this excreise again demonsrates the diagnostic power of the radio data to discriminate between plausible associations.," So while we hesitate to further downgrade the status of these associations, this exercise again demonstrates the diagnostic power of the radio data to discriminate between plausible associations."1057 Additionally this also. demonstrates the need. for. good. quality redshifts. whether they be spectroscopic or. more practically. well calibrated photometric estimates.," Additionally this also demonstrates the need for good quality redshifts, whether they be spectroscopic or, more practically, well calibrated photometric estimates."1058 lt is. clear. from the discussion above that deep interferometric radio images remain the most elfective way to identify counterparts to sub-nim galaxies., It is clear from the discussion above that deep interferometric radio images remain the most effective way to identify counterparts to sub-mm galaxies.1059 Of the 25 IDs we are able to present with some certainty. only 5 are without racio counterparts.," Of the 25 IDs we are able to present with some certainty, only 5 are without radio counterparts."1060 When considering the practicality of using mid-Lt data o icentify distant. sub-mium sources it is worth noting the expected. ratio between the sub-mnm flux and those in the TRAC ancl MIPS 24/2 bands is significantly greater than he sub-mum to radio Εαν ratio., When considering the practicality of using mid-IR data to identify distant sub-mm sources it is worth noting the expected ratio between the sub-mm flux and those in the IRAC and MIPS $\mu$ m bands is significantly greater than the sub-mm to radio flux ratio.1061" This is emphasised in Figure Ἐν,", This is emphasised in Figure \ref{fig:a220flxrat}.1062 Shown are various expected. Dux ratios for an Arp220 emplate in the Spifzer URAC and. ΑΔΗ bands. ancl also a prediction of the 1.4 Cllz radio from — απ Yun (2000).," Shown are various expected flux ratios for an Arp220 template in the IRAC and MIPS bands, and also a prediction of the 1.4 GHz radio from \nocite{Carilli2000} Carilli Yun (2000)."1063" It is clear that for a tvpical SCUBA 8505 source with Sasoju, 5miJy. and an Arp220 like SED. at 2~2.5 we would expect to detect. it in the müd-IR at 24m at  DO and at Sym ati124]y. while in the"," It is clear that for a typical SCUBA $\mu$ m source with $_{850\mu m}\sim5$ mJy, and an Arp220 like SED, at $z\sim2.5$ we would expect to detect it in the mid-IR at $\mu$ m at $\sim50\mu$ Jy and at $\mu$ m at $\sim1-2\mu$Jy, while in the"1064 (11,)= ^2.1065"7)According to the peak formalism (see Sec. ??)),"," According to the peak formalism (see Sec. \ref{discussion}) ),"1066" the typical (most probable)trajectory ópi(Rr) of peaks evolving into the series of halo ancestors ending in a halo with M at t is the solution of the differential equation (SSb) dRg—-—ze(pc.sigma,R,,, with the boundary condition defined by the halo, that is satisfying the relations οςt and⋅"," the typical (most probable)trajectory $\delta\pk(\R)$ of peaks evolving into the series of halo ancestors ending in a halo with $M$ at $t$ is the solution of the differential equation (SSb) =, with the boundary condition defined by the halo, that is satisfying the relations (t) and."1067"⋅ where G(t) is the cosmic growth factor, q=2.75 is the radius, in units of Rr, of the collapsing cloud with volume equal to M/p;, 6.[t(z)]=1.93+(5.92—0.4722+0.054627)/(10.0005682?) is the critical linearly extrapolated density contrast for halo formation at the redshift z (see Sec."," where $G(t)$ is the cosmic growth factor, $q=2.75$ is the radius, in units of $\R$, of the collapsing cloud with volume equal to $M/\rho\ii$, $\delta\co[t(z)]=1.93+(5.92-0.472 z+0.05461068z^2)/(1+0.000568 z^3)$ is the critical linearly extrapolated density contrast for halo formation at the redshift $z$ (see Sec."1069" ?? for those values of qand 6,[t(z)])."," \ref{peaks}1070 for those values of $q$and $\delta\co[t(z)]$ )."1071" In equation (118)), te(dpx,Rr) is the inverse of the average inverse curvature z (equal to minus the Laplacian over o2) for the distribution of curvatures (BBKS),» at peaks with dp, and Rr, being 51, and o2(R¢) the second order spectral moment, where 7 and x,* are respectivelyPy defined, in terms of the spectralP moments, as a0902) and Ύδρι/σο."," In equation \ref{dmd}) ), $x_{{\rm e}}(\delta\cs,\R)$ is the inverse of the average inverse curvature $x$ (equal to minus the Laplacian over $\sigma_2$ ) for the distribution of curvatures (BBKS), at peaks with $\delta\cs$ and $\R$, being , and $\sigma_2(\R)$ the second order spectral moment, where $\gamma$ and $x_\star$ are respectively defined, in terms of the spectral moments, as $\sigma_1^2/(\sigma_0\sigma_2)$ and $\gamma1072\delta\cs/\sigma_0$."1073" This distribution “-ν NC. quite symmetric, bell-shaped Eungtion.δείdpk) inverse of the ópi(Re) solution of equation"" (118)) is traced by peaks with the average (essentially equal to the most probable) inverse curvature at each Ppoint (px, (óy&,R;)."," This distribution function is a very peaked, quite symmetric, bell-shaped function so that the function$\R(\delta\pk)$ inverse of the $\delta\pk(\R)$ solution of equation \ref{dmd}) ) is traced by peaks with the average (essentially equal to the most probable) inverse curvature at each point $\delta\pk,\R$ )."1074"Re) Note that the slopeP dR:/dépx translates into the typical (average or most probable) accretion rate, dM/dt, of haloes with M(Rr) at t(dpk) evolving from those peaks."," Note that the slope $\der \R/\der \delta\pk$ translates into the typical (average or most probable) accretion rate, $\der M/\der t$, of haloes with $M(\R)$ at $t(\delta\pk)$ evolving from those peaks."1075" In Figure 2,, we show the typical peak trajectories at z—100 leading to typical haloes with current masses equal to 10! M, M, and 10M., where M. is the critical mass for collapseP in the concordance model (3.6x10""? M.)),Given a typical peak trajectory, dpx(Rr), equation (117)) is a Fredholm integral equation of first kind for (6p)(rp)."," In Figure \ref{f1}, we show the typical peak trajectories at $z=100$ leading to typical haloes with current masses equal to $10^{-1}M_\ast$ , $M_\ast$ and $10M_\ast$, where $M_\ast$ is the critical mass for collapse in the concordance model $3.6\times107610^{12}$ ).Given a typical peak trajectory, $\delta\cs(\R)$, equation \ref{Fred}) ) is a Fredholm integral equation of first kind for $\lav\delta\p\rav1077(r\p)$."1078" Through the changes y=τὸ and «= 1/(2R;?), it takes the form of a two-sided Laplace integral transform, —xy, with f(y) and g(z) respectively equal to y!/?(0,)(y!?)and 2/21(2x) ?/26,,[(27)-/?], which can be solved in the standard way."," Through the changes $y=r_p^2$ and $x=1/(2\R^2)$ , it takes the form of a two-sided Laplace integral transform, , with $f(y)$ and $g(x)$ respectively equal to $y^{1/2}\lav\delta\p\rav1079(y^{1/2})$and $2\sqrt{2\pi}(2x)^{-3/2}\delta\pk[(2x)^{-1/2}]$ , which can be solved in the standard way."1080" Extending x to the complexspace and taking x= i2n€, equation (134)) adopts the form of a Fourier Transform, —i2n£y,"," Extending $x$ to the complexspace and taking $x=i2\pi\xi$ , equation \ref{gx}) ) adopts the form of a Fourier Transform, ,"1081eeven AJ transitions.,even $\Delta J$ transitions.1082 vaalid., alid.1083"| Note that 5l sources ave in conuuon between the ""soft"" and “hard” saluple.","$^{1}$ Note that 54 sources are in common between the “soft"" and “hard"" sample."1084" A ""complete"" spectral analysis for all the sources in f1ο NAIAT BSS is in progress: in the meantime a “snapshot” of the N-rav spectral propertics of the ideutified sources obtained using the “harcuess ratio"" method (equivalent to the ""coor-color"" analysis largely used at opical wavecheths) is shown iu fieure 1."," A “complete"" spectral analysis for all the sources in the XMM BSS is in progress; in the meantime a “snapshot"" of the X-ray spectral properties of the identified sources obtained using the “hardness ratio"" method (equivalent to the “color-color"" analysis largely used at optical wavelengths) is shown in figure 1."1085 A fairly shar} yseparation between Calactic and exragalactic sources is visible iu figure 1 (loft panel): 25 out of 29 stars |iive IIR2-< 0.7., A fairly sharp separation between Galactic and extragalactic sources is visible in figure 1 (left panel): 25 out of 29 stars have $<$ –0.7.1086 Moreover it is worth noting that bot rin the hard aud in the sof siuuples Droad Line AGNs jo in the range «Οδ 25 0.3 (except for a few czwes)., Moreover it is worth noting that both in the hard and in the soft samples Broad Line AGNs lie in the range $<$ $<$ –0.3 (except for a few cases).1087" On he contrary Narrow Line ACNs are clistrilted over a larger area in he “hardless ratio"" plot wili the trend ο lave a arecr ΠΑΣ value for the Narrow Line ACNs belougi18o to the XNMM BSS ""hard sample."," On the contrary Narrow Line AGNs are distributed over a larger area in the “hardness ratio"" plot with the trend to have a larger HR2 value for the Narrow Line AGNs belonging to the XMM BSS “hard"" sample."1088 Besides the ticoretical inplications of this segregation. the seusitivitv of the IIR2 value to the optical spectral type of the N-rav sources ca1 offer a powerful tool to increase the efficiency for t1C selection of rave aud interesting classes of objects (e.g. the absorbed ACNs).," Besides the theoretical implications of this segregation, the sensitivity of the HR2 value to the optical spectral type of the X-ray sources can offer a powerful tool to increase the efficiency for the selection of rare and interesting classes of objects (e.g. the absorbed AGNs)."1089 Preliminary results for a first sample of “NAIAL BSS optically dull” galaxies are discussed in Severguini et al. (," Preliminary results for a first sample of “XMM BSS optically dull"" galaxies are discussed in Severgnini et al., ("1090this conference}.,this conference).1091 This work has received financial support from ASIC/BR/037/01) aud from AIURST (Cofiu 00-02-001)., This work has received financial support from ASI(I/R/037/01) and from MURST (Cofin 00-02-004).1092 We thank the ESO. TNC and Calar Alto telescope allocation conunittee for supporting this project.," We thank the ESO, TNG and Calar Alto telescope allocation committee for supporting this project."1093The observation of some hundred cosmic rav events to date with energy above the (οίκοςZatsepin.Ixuzmin cutoll. Ezc10077 00V. T'ukeda et L1998. and references. therein) has sparked: renewed: interest. in heir origin.,"The observation of some hundred cosmic ray events to date with energy above the Greisen–Zatsepin–Kuz'min cutoff, $\Egzk \simeq 10^{19.5}$ eV, Takeda et 1998, and references therein) has sparked renewed interest in their origin."1094 Ultra-high-energv cosmic ravs (ULLECTs). with energies in the range 4—10577 107 60eV. are generally rclicvecl to be extragalactic in origin. based on their harder spectrum. isotropic arrival directions on the sky. and. the act that they are not confined by the Galactic magnetic ield.," Ultra-high-energy cosmic rays (UHECRs), with energies in the range $E \sim 10^{18.5}$ $10^{20.5}$ eV, are generally believed to be extragalactic in origin, based on their harder spectrum, isotropic arrival directions on the sky and the fact that they are not confined by the Galactic magnetic field."1095 One class of models involves. production of ULLECRs at large shocks. such as those associated. with »owerful radio galaxies. or with ongoing large-scale structure ormation in clusters of galaxies NNorman. Melrose Achterberg 1995. and references therein).," One class of models involves production of UHECRs at large shocks, such as those associated with powerful radio galaxies, or with ongoing large-scale structure formation in clusters of galaxies Norman, Melrose Achterberg 1995, and references therein)."1096 A major dilliculty with these models is that the number of possible sources within the volume contributing to the [lux above Liv. which has a radius A44450 100 Mpc. is too small to explain the observed number of independent events.," A major difficulty with these models is that the number of possible sources within the volume contributing to the flux above $\Egzk$, which has a radius $D_{\rm max} \sim 50$ $100$ Mpc, is too small to explain the observed number of independent events."1097 An alternative model (Waxman 1905a:. Vietri 1995: Milerom Usov 1995) considers production in the sources of eamma-ray bursts (GRBs)., An alternative model (Waxman 1995a; Vietri 1995; Milgrom Usov 1995) considers production in the sources of gamma-ray bursts (GRBs).1098 Observations of X-ray ancl optical afterglows of GRBs (van Paradijs et 11997: Metzger et 141997) have confirmed the cosmological origin of the phenomenon: the energy. associated with cach event is then thought to be £uc1075 1075 core., Observations of X-ray and optical afterglows of GRBs (van Paradijs et 1997; Metzger et 1997) have confirmed the cosmological origin of the phenomenon; the energy associated with each event is then thought to be $\Egrb \simeq 10^{51}$ $10^{53}$ erg.1099 Waxman (1995a) and. Vietri (1995) notecl that assuming comparable elliciencies for gamuma-ray ancl ULLECTIU production. the estimated GAB rate. Qon~107 joy ‘implies a flux of ULECRs reaching Earth from within Dias remarkably similar to the one observed.," Waxman (1995a) and Vietri (1995) noted that assuming comparable efficiencies for gamma-ray and UHECR production, the estimated GRB rate, $Q_{\rm GRB} \sim 10^{-8}$ $^{-3}$ $^{-1}$, implies a flux of UHECRs reaching Earth from within $D_{\rm max}$ remarkably similar to the one observed."1100 Another. perhaps more compelling. argument is that the dispersion in CHECK. arrival times due to small-anele deflections in the intergalactic magnetic field implies that at any one time. enough GARB sources contribute to the ULIECTU llux to account for the observed. number of independent: arrival directions (Miralda-Escudé Waxman 1996: Xchterberg et al.," Another, perhaps more compelling, argument is that the dispersion in UHECR arrival times due to small-angle deflections in the intergalactic magnetic field implies that at any one time, enough GRB sources contribute to the UHECR flux to account for the observed number of independent arrival directions (Miralda-Escudé Waxman 1996; Achterberg et al.,"1101 in preparation)., in preparation).1102" Relativistic fireball models for GRBs involve an ultra-relativistic blast wave with Lorentz factor E,2107 107 bouncing the fireball (Rees 11992). and internal milelly relativistic shocks (E,=2 10) due to unsteacly outllows (Rees Alésszarros 1994)."," Relativistic fireball models for GRBs involve an ultra-relativistic blast wave with Lorentz factor $\Gs \simeq 10^{2}$ $10^{3}$ bounding the fireball (Rees 1992), and internal mildly relativistic shocks $\Gs \simeq 2$ $10$ ) due to unsteady outflows (Rees Mésszárros 1994)."1103aud. where Ej>nyc=105.66NeV. muons.,"and, where $\EF>m_\mu c^2=105.66\MeV$, muons."1104 I do not cousicer. [or simplicity. other. possible components (e.g.. hyperous or quark matter) in the EOS.," I do not consider, for simplicity, other possible components (e.g., hyperons or quark matter) in the EOS."1105" To construct a table suitable for interpolating n(p). E caleulate for each à the proton fraction Y=np/i and electron [fraction Y,=nfi [roi the equations for j-equilibrium. p,—ty=fleqiu. aud charge neutrality. ip=ne+ng."," To construct a table suitable for interpolating $n(p)$, I calculate for each $n$ the proton fraction $Y_p=n_p/n$ and electron fraction $Y_e=n_e/n$ from the equations for $\beta$ -equilibrium, $\mu_n-\mu_p = \mu_e = \mu_\mu$, and charge neutrality, $n_p=n_e+n_\mu$."1106 Given (Y.1 Y). E then compute1 the mass density. Ndp and 1pressure 1p—@(—p/+Pndp/dn).," Given $(Y_p,Y_e)$ , I then compute the mass density $\rho$ and pressure $p=c^2(-\rho+n\partial\rho/\partial n)$."1107 There have been many attempts to calculate the density of the phase transition from the inier crust to the core (seePethick&Ravenhall1995.audreferencestherein)..," There have been many attempts to calculate the density of the phase transition from the inner crust to the core \citep[see][and references1108therein]{pethick95:_matter}."1109 E adopt the following approach., I adopt the following approach.1110 The density and pressure of the EEOS equal those of Negele&Vautherin(1973) at n=0.078fin? p=0.39MeVfm.7.," The density and pressure of the EOS equal those of \citet{negele73}1111 at $n = 0.078\fermi^{-3}$, $p=0.39\MeV\fermi^{-3}$."1112 E therefore take this density as the trausition from crust to core: there is uo density discontinuity in this case., I therefore take this density as the transition from crust to core; there is no density discontinuity in this case.1113 For the EEOS. the enerey deusity is always greater than that of Negele&Vautherin(1973).. and so I choose the maximum crust density to be Q.1fn (p=0.60MeVfin 7).," For the EOS, the energy density is always greater than that of \citet{negele73}, and so I choose the maximum crust density to be $0.1\fermi^{-3}$ $p=0.60\MeV\fermi^{-3}$ )."1114 In this case. there is a substantial density jump (from n=0.1fn.* ton—0.13fm 7) between crust aud core.," In this case, there is a substantial density jump (from $n=0.1\fermi^{-3}$ to $n=0.13\fermi^{-3}$ ) between crust and core."1115 The choice ηΞ0.1fn as the upper limit for the crust density reflects recent. detailed caleulations of the phase transitiou., The choice $n=0.1\fermi^{-3}$ as the upper limit for the crust density reflects recent detailed calculations \citep{pethick95} of the phase transition.1116 For equilibrium crust compositious. it becomes enuergetically favorable for nuclei to turi in the inuer crust aud form a pliase with bubbles of neutrou gas eucased iu bouud nuclear matter (Lorenz.Ravenhall.&Pethick1993: Ovamatsu 1993)).," For equilibrium crust compositions, it becomes energetically favorable for nuclei to turn inside-out in the inner crust and form a phase with bubbles of neutron gas encased in bound nuclear matter \citealt*{lorenz93:_neutr}; \citealt{oyamatsu93:_nuclear}) )."1117 Because the charee of nuclei in au acereted crustis less than that of the equilibrium composition. it is possible that the nuclei do uot," Because the charge of nuclei in an accreted crustis less than that of the equilibrium composition, it is possible that the nuclei do not"1118The CMDI constitutes one of the cornerstones of the hot Ae Dang model. which makes three basic quantitative predictions on its properties: Over the past decade. the advent of theCODE satellite has allowed the confirmation of the isotropy (Smootctal.1992) and black-body spectral shape (Alatheretal.1994). to unprecedented.l precision. giving a present day temperature of Ty=2.725+0.001 Ix (1o error) as determined from thePARAS instrument (Alatheretal.1999:Smoot&Scott 2000).,"The CMBR constitutes one of the cornerstones of the hot Big Bang model, which makes three basic quantitative predictions on its properties: Over the past decade, the advent of the satellite has allowed the confirmation of the isotropy \cite{Smoot92} and black-body spectral shape \cite{Mather94} to unprecedented precision, giving a present day temperature of $T_0=2.725\pm 0.001$ K $1\sigma$ error) as determined from the instrument \cite{Mather99,Smoot}."1119. Any direct means of measuring the CAIBR. temperature can just provide us with the value ofits current temperature. orcing us to resort to other indirect. methods to test the emperature-redshift: relation predicted. by the. standard mocel.," Any direct means of measuring the CMBR temperature can just provide us with the value of its current temperature, forcing us to resort to other indirect methods to test the temperature-redshift relation predicted by the standard model."1120 The best alternative is to use atomic and molecular ransitions seen in the spectra of QSO absorbers (Meyer 1904)., The best alternative is to use atomic and molecular transitions seen in the spectra of QSO absorbers \cite{Meyer94}.1121. It is worth noting that the observation of CN absorption lines from) diffuse interstellar clouds: towards wight stars in the Galaxy vielded 5=2.729(151 Ik. in excellent. agreement with theFIRAS result. (oth1992:Roth.Meyer&Hawkins1993:RothAlever 1995).," It is worth noting that the observation of CN absorption lines from diffuse interstellar clouds towards bright stars in the Galaxy yielded $T_0=2.729^{+0.023}_{-0.031}$ K, in excellent agreement with the result \cite{Roth92,Roth93,Roth95}."1122. Unfortunately. molecular transitions are not commonly seen in the spectra of QSO absorbers.," Unfortunately, molecular transitions are not commonly seen in the spectra of QSO absorbers."1123 Apart from ο. so [ar molecules have been identified in just four absorption systems (Wiklind&Combes1994:Wiklind1995:Wiklined&Combes19962: 1996b).," Apart from $_2$, so far molecules have been identified in just four absorption systems \cite{WC94,WC95,WC96a,WC96b}."1124. Surprisingly. in one of them (Wiklind&Combes1996b) he rotational transitions from several molecules indicated an excitation temperature Z54;=432 Ix (3o error). lower han the expected CAIBR temperature 2=5.14 Ix. predicted at the observed. redshift.," Surprisingly, in one of them \cite{WC96b} the rotational transitions from several molecules indicated an excitation temperature $T_{\rmn{exc}}=4\pm 2$ K $3\sigma$ error), lower than the expected CMBR temperature $T=5.14$ K predicted at the observed redshift."1125 Phe low excitation temperature in his object is. nevertheless. due to the elfect ofa microlensing event (Combes 2000. private comm.).," The low excitation temperature in this object is, nevertheless, due to the effect of a microlensing event (Combes 2000, private comm.)."1126 Molecular absorption systems are often. gravitational lenses. since the impact xuvameter to the foreground galaxy must be close to zero in order to allow the detection of molecules.," Molecular absorption systems are often gravitational lenses, since the impact parameter to the foreground galaxy must be close to zero in order to allow the detection of molecules."1127 Hence. we believe hat atomic lines are better suited to study the temperature of the CMDRB at high recdshifts.," Hence, we believe that atomic lines are better suited to study the temperature of the CMBR at high redshifts."1128 We can use the population ratios of the fine-structure evels for the absorption svsterms collected. in table 2 to constrain the temperature of the CAIBR. at their redshifts., We can use the population ratios of the fine-structure levels for the absorption systems collected in table \ref{obsdata} to constrain the temperature of the CMBR at their redshifts.1129 For each observed. ion the excitation temperature will be eiven by with temperatures given in Ix. The excitation temperatures so obtained represent firmi upper Limits to the temperature of the CAIBR. because local excitation mechanisms may also contribute significantly to populate the excited levels.," For each observed ion the excitation temperature will be given by with temperatures given in K. The excitation temperatures so obtained represent firm upper limits to the temperature of the CMBR, because local excitation mechanisms may also contribute significantly to populate the excited levels."1130 In fig., In fig.1131 12 we plot the excitation temperatures along with the expected. temperature of the CMBR. according to the standard model prediction., \ref{figure:Tcmbr} we plot the excitation temperatures along with the expected temperature of the CMBR according to the standard model prediction.1132 For most systems. either the signal to noise ratio of the spectrum was not high enough to detect the excited fine structure Line. or the ground line was strongly saturated.," For most systems, either the signal to noise ratio of the spectrum was not high enough to detect the excited fine structure line, or the ground line was strongly saturated."1133 Therefore for hese systems the excitation temperature itself is also an upper limit. ancl this is indicated in fig.," Therefore for these systems the excitation temperature itself is also an upper limit, and this is indicated in fig."1134 12) by a downward arrow., \ref{figure:Tcmbr} by a downward arrow.1135 The point labelled “molecules” corresponds to the xuzzling observation of Wiklind Combes (19090) discussedabove.," The point labelled ""molecules"" corresponds to the puzzling observation of Wiklind Combes \shortcite{WC96b} discussedabove."1136 Phillips (1994) supports a closed. steads-state moclel hat predicts considerably lower temperatures to the CAIBR compared to the standard model: e.g. for the 2=2.9 system observed by Songaila et al. (1994a):, Phillips \shortcite{Phil94} supports a closed steady-state model that predicts considerably lower temperatures to the CMBR compared to the standard model; e.g. for the $z=2.9$ system observed by Songaila et al. \shortcite{Songa}:1137: Fin.=6.55 Ix. Alternative models in which photon creation takes place as the Universe expands predict a more general redshift relation (Lima.Silva&Viegas2000): where ο ds a parameter to be adjusted. from. the observations. within the range 0.—jx1.," $T_{\rmn{obs}}=6.55$ K. Alternative models in which photon creation takes place as the Universe expands predict a more general temperature-redshift relation \cite{LSV2000}: where $\beta$ is a parameter to be adjusted from the observations, within the range $0\leq\beta\leq 1$."1138 Equation (15)) therefore. gives temperatures lower than predicted. by the standard model (fig. 12))., Equation \ref{Tbeta}) ) therefore gives temperatures lower than predicted by the standard model (fig. \ref{figure:Tcmbr}) ).1139 lt has been stated that any scenario that. does. not preserve the number of photons would. introduce. large distortions in the black-bodsy spectrum of the CAIBR (Steigman 1978)., It has been stated that any scenario that does not preserve the number of photons would introduce large distortions in the black-body spectrum of the CMBR \cite{Steigman}. .1140. However. it was shown that for the class of models that follow the temperature law (15)) the Planckian spectral shape is not destroved as the Universe evolves," However, it was shown that for the class of models that follow the temperature law \ref{Tbeta}) ) the Planckian spectral shape is not destroyed as the Universe evolves"1141As the [low expauds. the local magnetization decreases.,"As the flow expands, the local magnetization = = - ) decreases."1142" At the sonic point o,,.=(0/2)", At the sonic point $ \sigma_{loc} = (\sigma/2)^{2/3}$.1143 [f there is an outside medium with density pe;. we may identify two expausion regimes.," If there is an outside medium with density $ \rho_{\rm ex}$, we may identify two expansion regimes."1144 For relativistically strong forward shocks. so that the post-shock pressure is much larger than deusity. the Lorentz [actor of the CD is (the last approximation assumes oZ 1).," For relativistically strong forward shocks, so that the post-shock pressure is much larger than density, the Lorentz factor of the CD is = (the last approximation assumes $\sigma \gg 1$ )."1145 For weak forward shocks the velocity of the CD approaches the expausion velocity iuto vacuum σος. Eq. (2.1)).," For weak forward shocks the velocity of the CD approaches the expansion velocity into vacuum $\gamma_{vac}$, Eq. \ref{gammavac}) )."1146 The transition between the relativistically strong aud weak shocks occurs for =-va) For o«o4. the forward shock is weak.," The transition between the relativistically strong and weak shocks occurs for = For $\sigma < \sigma_{crit}$, the forward shock is weak."1147 For cold unmaguetized jets the reverse shock always exists: it is weak [or yy.X/————popes aud stroug otherwise (2).., For cold unmagnetized jets the reverse shock always exists; it is weak for $\gamma_w \leq \sqrt{\rho_0 / \rho_{\rm ex}}$ and strong otherwise \citep{Sari95}.1148 For maguetized jets the couditious for existence of a reverse shock are more complicated (seealso?2)..," For magnetized jets the conditions for existence of a reverse shock are more complicated \citep[see also][]{2008A&A...478..747G,Mizuno}."1149 There are. in fact. two somewhat different regimes for the existeuce oL a RS in highly maguetized outflows.," There are, in fact, two somewhat different regimes for the existence of a RS in highly magnetized outflows."1150 First. if ejecta is supersonic with respect to the CD (iu term of," First, if ejecta is supersonic with respect to the CD (in term of"1151"could be performed without much ambiguity. aud the ""exelsed? data are shown in Figs.","could be performed without much ambiguity, and the “excised” data are shown in Figs."1152 E and 2., 1 and 2.1153 For the FLAWO data. no brightening eveuts were obvious to the eve.," For the FLWO data, no brightening events were obvious to the eye."1154 This is probably due to a combination of the lower precision of the FIWO data. and the weaker contrast between the spots aud the photosphere at the longer waveleugtlis," This is probably due to a combination of the lower precision of the FLWO data, and the weaker contrast between the spots and the photosphere at the longer wavelengths"1155seem mildly favored by galaxy density data.,seem mildly favored by galaxy density data.1156 Conversely. models with was high as —0.5 are strongly disfavored by galactic rotation curves coupled with only a weak prior on the normalization of the power spectrum.," Conversely, models with $\wQ$ as high as $\sim -0.5$ are strongly disfavored by galactic rotation curves coupled with only a weak prior on the normalization of the power spectrum."1157 Note that none of the models can easily account for the very low data points., Note that none of the models can easily account for the very low data points.1158 Nevertheless. the scatter in the data is not extremely large compared to the scatter expected from the halo-to-halo variations observed in N-body simulations.," Nevertheless, the scatter in the data is not extremely large compared to the scatter expected from the halo-to-halo variations observed in N-body simulations."1159" For example. at Vig=SO km/s. the lo scatter in N-bocdy simulations is e(log(;N,:;5))2-0.37 while the le scatter inalf. 67 data. points is o(log(zNqu3))=0.41."," For example, at $V_{\rm max} = 80$ km/s, the $1\sigma$ scatter in N-body simulations is $\sigma(\log(\Delta_{V/2})) \simeq 0.37$ while the $1\sigma$ scatter in $67$ data points is $\sigma(\log(\Delta_{V/2})) \simeq11600.41$."1161 This suggests that lowering the median. of the theoretically predicted central densities. perhaps by a reduction in ax or invoking a Ciltecl or running power spectrum that reduces power on ealaxy scales. or as we cliscuss here. by invoking we<1 quintessence. may be sullicient to bring the predictions into &ood agreement with the data.," This suggests that lowering the median of the theoretically predicted central densities, perhaps by a reduction in $\sigma_8$ or invoking a tilted or running power spectrum that reduces power on galaxy scales, or as we discuss here, by invoking $\wQ < -1$ quintessence, may be sufficient to bring the predictions into good agreement with the data."1162 Yet. we must bear in mind that our caleulations are approximate.," Yet, we must bear in mind that our calculations are approximate."1163 The most. obvious omission is that all of our calculations are based: on N-body. simulations that contain no barvons., The most obvious omission is that all of our calculations are based on N-body simulations that contain no baryons.1164 The elfects of barvonie contraction are likely to be small in LSB galaxies de Blok MeCGaugh 1907) and would tend to drive rotation curves to higher values or Ayes and Vinay in the simplest models (Blumenthal ct al., The effects of baryonic contraction are likely to be small in LSB galaxies de Blok McGaugh 1997) and would tend to drive rotation curves to higher values or $\Delta_{V/2}$ and $V_{\rm max}$ in the simplest models (Blumenthal et al.1165 1986)., 1986).1166 This serves only to increase the apparent discrepancy., This serves only to increase the apparent discrepancy.1167 Aclelitionally. rotation curve measurements may vet be subject to poorlv-understood. svstematic effects. in. the reduction. of the observational data (Swaters 2003).," Additionally, rotation curve measurements may yet be subject to poorly-understood systematic effects in the reduction of the observational data (Swaters 2003)."1168 Currently. it is cüllieult to clraw a firm conclusion.," Currently, it is difficult to draw a firm conclusion."1169 Although the nature of dark energy is unknown. its cllects on structure formation can be studied using numerical N-bodvy simulations.," Although the nature of dark energy is unknown, its effects on structure formation can be studied using numerical N-body simulations."1170 We have performed a series of these simulations for a range of dark energyv equation. of state parameters., We have performed a series of these simulations for a range of dark energy equation of state parameters.1171 Confirming previous findings by Linder Jenkins (2003). Ixlvpin (2003). Macció (2003). and. Lokas (2003) we show that the JOL formula provides a good fit to halo mass functions even in the presence of dark energy.," Confirming previous findings by Linder Jenkins (2003), Klypin (2003), Macciò (2003), and okas (2003) we show that the J01 formula provides a good fit to halo mass functions even in the presence of dark energy."1172 We show that this is true for moclels withXC aw< las well., We show that this is true for models with $\wQ<-1$ as well.1173 The density. structure of dark matter haloes is. also allected by dark energy., The density structure of dark matter haloes is also affected by dark energy.1174We have shown how the predictions of the BOL model are modified when dark cnerey with constant w is accounted for.,We have shown how the predictions of the B01 model are modified when dark energy with constant $\wQ$ is accounted for.1175 As structure tends to form earlier in mocdoels with less negative w. halo concentrations tend to be somewhat higher in these models.," As structure tends to form earlier in models with less negative $\wQ$, halo concentrations tend to be somewhat higher in these models."1176 These findings are in agreement with the results of IXIvpin (2003) and qualitatively agree with Dolag (2003). although we probe a different range of masses than the latter.," These findings are in agreement with the results of Klypin (2003) and qualitatively agree with Dolag (2003), although we probe a different range of masses than the latter."1177 The larger number of halocs with NEW profile fits and concentrations in our study allows us to quantitatively test the BOL moclel., The larger number of haloes with NFW profile fits and concentrations in our study allows us to quantitatively test the B01 model.1178 We find that the original (f°=0.01.ἐν 4.0) over-predicts the concentrations of haloes in our simulations by about ~12.IS%.," We find that the original $F=0.01,1179K=4.0$ ) over-predicts the concentrations of haloes in our simulations by about $\sim 12-15\%$."1180 Llowever. the shape of the mass-concentration relation that we find is the same as in BOL. and we find that a slightly. mocified set of the BOL parameters (£=0.01. 3.5) matches our haloes well.," However, the shape of the mass-concentration relation that we find is the same as in B01, and we find that a slightly modified set of the B01 parameters $F=0.01, K=3.5$ ) matches our haloes well."1181 This olfset may likely be caused bv the lower force resolution of our GADGET simulations compared to the adaptive-refinement. code ARTE used. in BOL., This offset may likely be caused by the lower force resolution of our GADGET simulations compared to the adaptive-refinement code ART used in B01.1182 For the haloes in our simulations the adopted. Bol model accurately reproduces the median concentration-mass relation over a range of masses [rom Ada~6»LOM to Alay4o1075PAL.," For the haloes in our simulations the adopted B01 model accurately reproduces the median concentration-mass relation over a range of masses from $M_{\rm vir}1183\sim 6 \times 10^{11}$ to $M_{\rm vir} \sim 4 \times 10^{13}\hinv1184\msun$."1185 We confirm that for a fixed mass halo concentration decrease with redshift as 1/(1|2). at least out to z2.5.," We confirm that for a fixed mass halo concentration decrease with redshift as $1/(1+z)$, at least out to $z \sim 2.5$."1186 Interestingly. we find that halo concentrations are more easily understood. when the halo virial racius is defined in terms of a cosmology-dependent virial overdensity rather than by one that uses a fixed overdensity of pfpos 200. The result’ supports one of the (previouslv-untested) assumptions of the original BOL model.," Interestingly, we find that halo concentrations are more easily understood when the halo virial radius is defined in terms of a cosmology-dependent virial overdensity rather than by one that uses a fixed overdensity of $\rho/\rho_{\rm crit}=200$ The result supports one of the (previously-untested) assumptions of the original B01 model."1187 Specifically. we," Specifically, we"1188fraggmentation of IRDCs.,gmentation of IRDCs.1189" Local temperature minima are strongly correlated with column density peaks. which in a few cases reach Njj,=1x107 επι”. identifying these clouds as candidate massive prestellar cores."," Local temperature minima are strongly correlated with column density peaks, which in a few cases reach $_{H_2} = 1\times 10^{23}$ $^{-2}$, identifying these clouds as candidate massive prestellar cores."1190" Applying this technique to the full Hi-GAL data set will provide important constraints on the fragmentation and thermal properties of IRDCs. and help identify hundreds of massive prestellar core candidates,"," Applying this technique to the full Hi-GAL data set will provide important constraints on the fragmentation and thermal properties of IRDCs, and help identify hundreds of massive prestellar core candidates."1191and magnetic fields is a factor of ten smaller than the pressures required to inflate the bubbles (e.g. Ito et al.,and magnetic fields is a factor of ten smaller than the pressures required to inflate the bubbles (e.g. Ito et al.1192 2008)., 2008).1193 This implies that most of the energy in the cocoon is carried by an invisible component such as high energy thermal electrons (e.g. Ito et al., This implies that most of the energy in the cocoon is carried by an invisible component such as high energy thermal electrons (e.g. Ito et al.1194 2008)., 2008).1195 Observations of the SZ effect were proposed by Pfrommer et al. (, Observations of the SZ effect were proposed by Pfrommer et al. (11962005) to probe the inferred dynamically-dominant component of plasma bubbles associated with X-ray cavities.,2005) to probe the inferred dynamically-dominant component of plasma bubbles associated with X-ray cavities.1197 Pfrommer et al. (, Pfrommer et al. (1198"2005) studied examples of several different physical scenarios concerning the composition of the plasma bubble which is as a whole in pressure equilibrium with the ambient ICM, and derived the SZ effect due to electrons in the plasma bubbles using the Wright formalism.","2005) studied examples of several different physical scenarios concerning the composition of the plasma bubble which is as a whole in pressure equilibrium with the ambient ICM, and derived the SZ effect due to electrons in the plasma bubbles using the Wright formalism."1199" However, cocoons are expected to be over-pressured with respect to the ambient IGM (Begelman Cioffi 1989), and therefore the SZ effect derived under the assumption of pressure balance gives only a lower limit on the true SZ effect produced in the cocoons."," However, cocoons are expected to be over-pressured with respect to the ambient IGM (Begelman Cioffi 1989), and therefore the SZ effect derived under the assumption of pressure balance gives only a lower limit on the true SZ effect produced in the cocoons."1200" To constrain a population of high energy electrons inside AGN cocoons predicted by numerical simulations, we study in this paper the induced CMB distortion as a function of gas temperature."," To constrain a population of high energy electrons inside AGN cocoons predicted by numerical simulations, we study in this paper the induced CMB distortion as a function of gas temperature."

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