ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" This backreaction leads to several important effects: on one hand the spectra of accelerated particles become concave, and concentrate the bulk of the energy in the form of accelerated particles at the maximum momentum."," This backreaction leads to several important effects: on one hand the spectra of accelerated particles become concave, and concentrate the bulk of the energy in the form of accelerated particles at the maximum momentum."3" On the other hand, the efficiently amplified magnetic field also exerts a strong dynamical reaction on the system, provided the magnetic pressure exceeds the gas pressure in the shock region (??))."," On the other hand, the efficiently amplified magnetic field also exerts a strong dynamical reaction on the system, provided the magnetic pressure exceeds the gas pressure in the shock region \cite{apjlett,long}) )."4 This second effect results in an enhanced acceleration efficiency (due to large B-fields) but weaker shock modification (spectra closer to power laws) due to the reduced compressibility of the plasma in the presence of the amplified magnetic field., This second effect results in an enhanced acceleration efficiency (due to large B-fields) but weaker shock modification (spectra closer to power laws) due to the reduced compressibility of the plasma in the presence of the amplified magnetic field.5" These non-linear effects cannot be taken into account in the type of calculations presented here, although we do not expect the qualitative character of our conclusions to be affected protoundly by them."," These non-linear effects cannot be taken into account in the type of calculations presented here, although we do not expect the qualitative character of our conclusions to be affected profoundly by them."6" Nevertheless it is useful to go through the possible consequences of the non-linear effects in à somewhat deeper detail: one can expect two types of complications, one of principle and the other in the numericalvalues of the growth rates."," Nevertheless it is useful to go through the possible consequences of the non-linear effects in a somewhat deeper detail: one can expect two types of complications, one of principle and the other in the numericalvalues of the growth rates."7 The latter simply derives trom the approximations, The latter simply derives from the approximations8Where T(z2) is the look-back time and 7 is à constant in (he approximate range of 0.1-0.5 that determines the degree of evolution.,Where $T(z)$ is the look-back time and $\tau$ is a constant in the approximate range of 0.1-0.5 that determines the degree of evolution.9 We have also assumed a distribution of Lorentz [actors for which: valid between D4 and E» and a linear model connecting ganuna-ray and radio luminosities. ie. (he inverse Compton moclels discussed above. (o generate a simulated sample with Monte Carlo techniques and then use (he corresponding distributions (luminositv. recshift.flux density. ete.)," We have also assumed a distribution of Lorentz factors for which: valid between $\Gamma_1$ and $\Gamma_2$ and a linear model connecting gamma-ray and radio luminosities, i.e., the inverse Compton models discussed above, to generate a simulated sample with Monte Carlo techniques and then use the corresponding distributions (luminosity, redshift,flux density, etc.)"10 and correlation diagrams {ο assess the validity of the model., and correlation diagrams to assess the validity of the model.11" We express these models using the lollowing equations: llere. L4... and Leges refer to the predicted gamma-ray Iuminosities in (he observer's frame. using the SSC and ECS models respectively,"," We express these models using the following equations: Here, $L_{\gamma,o,ssc}$ and $L_{\gamma,o,ecs}$ refer to the predicted gamma-ray luminosities in the observer's frame, using the SSC and ECS models respectively."12" The IX constants depend on the parameters discussed above. £,; refers to the intrinsic radio luminosity. and the remaining [actors are the appropriate functions of Doppler factors for SSC or ECS assuming that the radiation is [rom discrete blobs (Lister1999).."," The K constants depend on the parameters discussed above, $L_{r,i}$ refers to the intrinsic radio luminosity, and the remaining factors are the appropriate functions of Doppler factors for SSC or ECS assuming that the radiation is from discrete blobs \citep{lis99a}."13 As mentioned above. the powers in each case are reduced by one for the case of a continuous jet.," As mentioned above, the powers in each case are reduced by one for the case of a continuous jet."14" Lister&Marscher(1997) rigorously determines radio luminosity fiction parameters based on siniulations of (he Caltech-Jodrell Bank sample (CJ-F. as labeled by Lister (1997))). taking into account distributions of bulk Lorentz factors. redshifts. and luminosities,"," \citet{lis97} rigorously determines radio luminosity function parameters based on simulations of the Caltech-Jodrell Bank sample (CJ-F, as labeled by \citet{lis97}) ), taking into account distributions of bulk Lorentz factors, redshifts, and luminosities."15 Cara&Lister(2007) have recently arrivecl al comparable results for the similar MOJAVE sample (though the huminosity ancl redshift ranges differ somewhat)., \citet{car07} have recently arrived at comparable results for the similar MOJAVE sample (though the luminosity and redshift ranges differ somewhat).16 We begin by adopting the parameters Chat Lister&Alarscher(1997). derived for the CJ-F sample., We begin by adopting the parameters that \citet{lis97} derived for the CJ-F sample.17 We expect the CJ-F parent. population to be verv similar to that of our sample. because il is selected. for flat spectrum. compact structure and 5 αν total flux density. > 0.35 Jy.," We expect the CJ-F parent population to be very similar to that of our sample, because it is selected for flat spectrum, compact structure and 5 GHz total flux density $>$ 0.35 Jy."18 Additionally we take into account beaming effects appropriate for the SSC or ECS model., Additionally we take into account beaming effects appropriate for the SSC or ECS model.19 Then. assuming both SSC and ECS in (urn. the gamma-ray huminositv. ancl [Iux. density is determined [or each source.," Then, assuming both SSC and ECS in turn, the gamma-ray luminosity and flux density is determined for each source."20 In generating the gamma-ray. Iluninosities from the intrinsic, In generating the gamma-ray luminosities from the intrinsic21largest voids leave the strongest visual impression in images like Figure 4.. they only account for a small fraction of the total void volume.,"largest voids leave the strongest visual impression in images like Figure \ref{GIF2slice}, they only account for a small fraction of the total void volume."22 Lt is not straightforward to compare these findings with results [rom investigations of voids in galaxy catalogues., It is not straightforward to compare these findings with results from investigations of voids in galaxy catalogues.23 This is partly. because of the dillerence in the void. finding algorithms and mainly. because of the fact that galaxies are quite sparse tracers of the underlving density field., This is partly because of the difference in the void finding algorithms and mainly because of the fact that galaxies are quite sparse tracers of the underlying density field.24 On a qualitative level. our void size distribution agrees well with observed. voids.," On a qualitative level, our void size distribution agrees well with observed voids."25 For example. Hovle Vogcley 2004 report vold sizes comparable to our largest. voids (the smallest voids they construct have radii of 10h.+ AIAIpe). with the numbers of voids steeply dropping with increasing racius.," For example, Hoyle Vogeley 2004 report void sizes comparable to our largest voids (the smallest voids they construct have radii of $h^{-1}$ Mpc), with the numbers of voids steeply dropping with increasing radius."26 Massive haloes in simulations are associated with higher peaks in the (smoothed) initial density field (Bardeen ct al 1986: Colberg et al 2000: Sheth Dialerio 2001)., Massive haloes in simulations are associated with higher peaks in the (smoothed) initial density field (Bardeen et al 1986; Colberg et al 2000; Sheth Diaferio 2001).27 Voids are expected to form from initially uncderdense: regions analogously to how clusters or haloes form from. initially. overdense regions., Voids are expected to form from initially underdense regions analogously to how clusters or haloes form from initially overdense regions.28 One might thus wonder if a similar correlation exists between voids anc minima in the initial density field., One might thus wonder if a similar correlation exists between voids and minima in the initial density field.29 We used the Clk simulations to study. this correlation as follows., We used the GIF simulations to study this correlation as follows.30 In the spherical evolution mocel. the mass associated with a void is a measure of the initial comoving radius of the region from which it formed: 2=(3mfAzp)!7.," In the spherical evolution model, the mass associated with a void is a measure of the initial comoving radius of the region from which it formed: $R = (3m/4\pi\bar\rho)^{1/3}$."31 Vherelore. one might expect the voic mass to correlate most. strongly with the depth. of the initial. underdensity. from which it [ormed. when the initial field is smoothed on a scale (m).," Therefore, one might expect the void mass to correlate most strongly with the depth of the initial underdensity from which it formed, when the initial field is smoothed on a scale $R(m)$."32 Since the voids in our sample enclose a large range of masses. we smoothed the initial (2=49) density field using a set of ‘Top Lat filters: 2.5. 5.0. 7.5. 10.0h* ALNpe.," Since the voids in our sample enclose a large range of masses, we smoothed the initial $z=49)$ density field using a set of Top Hat filters: 2.5, 5.0, 7.5, $h^{-1}$ Mpc."33 We identified the minima in cach smoothed field., We identified the minima in each smoothed field.34 Phat is. we identified those erid cells which were less dense than all twenty six of their neighbouring cells.," That is, we identified those grid cells which were less dense than all twenty six of their neighbouring cells."35 We then compared the comoving positions of the minima identified on a smoothing scale with the locations of those voids whose z=0 sizes correspond to Rom) recall how initially. underdense regions grow. bv a [factor of 1.7 until present time., We then compared the comoving positions of the minima identified on a smoothing scale with the locations of those voids whose $z=0$ sizes correspond to $R(m)$ – recall how initially underdense regions grow by a factor of 1.7 until present time.36 1 there was more than one mininiunr inside a void we picked the deepest one., If there was more than one minimum inside a void we picked the deepest one.37 The density inside that cell was identified with the overdensity σ of the trough., The density inside that cell was identified with the overdensity $\sigma$ of the trough.38 This method is analogous to how Colboerg et al 2000 located peaks for clusters., This method is analogous to how Colberg et al 2000 located peaks for clusters.39 What is more. voids evolve by expanding but not by moving.," What is more, voids evolve by expanding but not by moving."40 Thus. one expects to find the void centers in the initial conditions close to the void centers at present time.," Thus, one expects to find the void centers in the initial conditions close to the void centers at present time."41 In this way. we associated voids with minima in the initial field.," In this way, we associated voids with minima in the initial field."42 As it turns out. all voids larger than 425h1 MMpec could be associated with a density minimum.," As it turns out, all voids larger than $h^{-1}$ Mpc could be associated with a density minimum."43 It is interesting that associating a void with an initially uncerdense region does thus work much better than finding a peak for a cluster (sce Colbere et al 2000)., It is interesting that associating a void with an initially underdense region does thus work much better than finding a peak for a cluster (see Colberg et al 2000).44 1n the leftmost panel of Figure 10. we plot the void volumes at >=0 as a function of the void overdensities at 2=0., In the left–most panel of Figure \ref{VoidDelta} we plot the void volumes at $z=0$ as a function of the void overdensities at $z=0$.45 The void overdensities scatter around the value of -0.5., The void overdensities scatter around the value of -0.8.46 Larger voids tend to be slightly less uncderdense., Larger voids tend to be slightly less underdense.47 This is mainly due to the process of the merging of proto.voids., This is mainly due to the process of the merging of proto–voids.48 As will be seen in the following section. void density profiles rise very sharply towards the edges of the voids (see Figure 14)).," As will be seen in the following section, void density profiles rise very sharply towards the edges of the voids (see Figure \ref{LargeDensityProfilesGIF}) )."49 Thus. when a smaller void. is merged onto a larger one Following the criteria outlines above — one basically adds mainly parts of the outer region of the smaller void.," Thus, when a smaller void is merged onto a larger one -- following the criteria outlines above – one basically adds mainly parts of the outer region of the smaller void."50 Once the overdendity of the resulting void is computed this void will have a slightly higher overdensity than the two original volds., Once the overdendity of the resulting void is computed this void will have a slightly higher overdensity than the two original voids.51 The center panel of Figure 10. shows the z=0 void volume as a function of the overdensities of the associated roughs in the initial conditions., The center panel of Figure \ref{VoidDelta} shows the $z=0$ void volume as a function of the overdensities of the associated troughs in the initial conditions.52 As discussed. above. we used. a set. of smoothing scales and. grouped the voids into categories covered by the corresponding scale.," As discussed above, we used a set of smoothing scales and grouped the voids into categories covered by the corresponding scale."53 In. principle. or cach void one would want to apply a smoothing scale hat corresponds exactlv to the void. volume.," In principle, for each void one would want to apply a smoothing scale that corresponds exactly to the void volume."54 Since we cid not do that we end up with clearly visible steps in the plot., Since we did not do that we end up with clearly visible steps in the plot.55 If one rescales overdensities of the associated troughs (compare Sheth Dialerio 2001 for the analogous procedure or haloes) the plot σος tighter., If one re–scales overdensities of the associated troughs (compare Sheth Diaferio 2001 for the analogous procedure for haloes) the plot gets tighter.56 The rightmost panel of Figure 10. shows the z=0 void volume as a function of ofa of the associated troughs., The right–most panel of Figure \ref{VoidDelta} shows the $z=0$ void volume as a function of $\delta/\sigma$ of the associated troughs.57 The dillerent sets are still visible »i now they lie on top of each other., The different sets are still visible but now they lie on top of each other.58criteria at greater than 30 significance.,criteria at greater than $3\sigma$ significance.59 For groups with exactly four members the rejection of a single galaxy pairing is sufficient to remove the group from our final CG sample as it fails to meet the CG richness criterion discussed above., For groups with exactly four members the rejection of a single galaxy pairing is sufficient to remove the group from our final CG sample as it fails to meet the CG richness criterion discussed above.60" In groups with more than four members, we remove the galaxy that results in the highest minimum pairwise likelihood among remaining group members."," In groups with more than four members, we remove the galaxy that results in the highest minimum pairwise likelihood among remaining group members."61 This removal process is iterated until the minimum pairwise likelihood is greater than 0.0027 or the number of remaining CG members falls below four., This removal process is iterated until the minimum pairwise likelihood is greater than 0.0027 or the number of remaining CG members falls below four.62 We gauge the reliability of this removal process using the subset of 154 four-member CGs where all members have spectroscopic redshifts available — hereafter referred to as spectroscopic groups., We gauge the reliability of this removal process using the subset of 154 four-member CGs where all members have spectroscopic redshifts available – hereafter referred to as spectroscopic groups.63" Four-member groups make up the majority (83 per cent) of the Catalogue A sample, and we choose to focus on these CGs for our reliability estimates as the presence of a single interloping galaxy removes these systems from our final sample, allowing for a straight-forward interpretation of the contamination rate."," Four-member groups make up the majority (83 per cent) of the Catalogue A sample, and we choose to focus on these CGs for our reliability estimates as the presence of a single interloping galaxy removes these systems from our final sample, allowing for a straight-forward interpretation of the contamination rate."64 For each spectroscopic group we first assess the likelihood of it being a genuine association following the probabilistic procedure described above., For each spectroscopic group we first assess the likelihood of it being a genuine association following the probabilistic procedure described above.65 Given the small redshift error relative to our expected velocity spread of !(the median spectroscopic redshift error for the CG sample corresponds to cAzz:50 s!)) this measurement is unambiguous for the majority of groups., Given the small redshift error relative to our expected velocity spread of (the median spectroscopic redshift error for the CG sample corresponds to $c\Delta z \approx 50$ ) this measurement is unambiguous for the majority of groups.66" Using this initial likelihood to separate genuine and projected groups, we then randomly replace some number of group members! spectroscopic redshifts with their corresponding photometric redshifts and recompute the distribution of pairwise likelihoods."," Using this initial likelihood to separate genuine and projected groups, we then randomly replace some number of group members' spectroscopic redshifts with their corresponding photometric redshifts and recompute the distribution of pairwise likelihoods."67" In this way we can estimate the probability that a genuine group will be rejected by our interloper removal scheme (false negative), or alternatively that a projected 'group' will be wrongly accepted (false positive), given some arbitrary mix of spectroscopic and photometric redshifts."," In this way we can estimate the probability that a genuine group will be rejected by our interloper removal scheme (false negative), or alternatively that a projected `group' will be wrongly accepted (false positive), given some arbitrary mix of spectroscopic and photometric redshifts."68 We also recompute the CG catalogue using several different redshift likelihood cuts to assess the robustness of our adopted limits., We also recompute the CG catalogue using several different redshift likelihood cuts to assess the robustness of our adopted limits.69 The results of this comparison are summarised in Table [I]., The results of this comparison are summarised in Table \ref{tab:cont_fraction}.70" In general, our relatively tolerant likelihood requirements mean that we reject a minimum of genuine"," In general, our relatively tolerant likelihood requirements mean that we reject a minimum of genuine"71 (Savage&Wakker2009:Yaoctal.2009) 2010).. (Shapiro&Field1976) (Joung&MacLow2006:deAvillez (Sheltonetal.2007).. (Trippctal.2003).. Rasmussenetal.20001)," \citep{savage_wakker_09,yao_etal_09}72 \citep{rueff_howk_10}, \citep{shapiro_field_76}73 \citep{joung_maclow_06,deavillez_breitschwerdt_07}, \citep{shelton_etal_07}. \citep{tripp_etal_03}, \citealt{rasmussen_etal_09})"74. Most of the volume within a few kpe of the midplane is filled with very hot eas having temperatures iu excess of 109 Ts (see pathleugth estimates in Sheltouetal.(2007) or scale height estimates in Yao&Wang2007))., Most of the volume within a few kpc of the midplane is filled with very hot gas having temperatures in excess of $10^6$ K (see pathlength estimates in \citet{shelton_etal_07} or scale height estimates in \citealt{yao_wang_07}) ).75" This eas is traced by ions and Hous having collisional ionization equilibrium (CIE) cluperatures. Tege. of ~1«10° I& and ~3\109 Is. respectively,"," This gas is traced by ions and ions having collisional ionization equilibrium (CIE) temperatures, $T_{CIE}$, of $\sim 1 \times 10^6$ K and $\sim 3 \times10^6$ K, respectively."76 Somewhat cooler. but still hot. eas is traced xw iious (Teqg1s10? K) aud tious (Tepe~3x10° K).," Somewhat cooler, but still hot, gas is traced by ions $T_{CIE} \sim 1 \times 10^5$ K) and ions $T_{CIE} \sim 3 \times 10^5$ K)."77 It fills a lesser fraction of he space (see pathleugths in Sheltonetal. 2007)) but accounts for more radiative energv loss than does the totter gas., It fills a lesser fraction of the space (see pathlengths in \citealt{shelton_etal_07}) ) but accounts for more radiative energy loss than does the hotter gas.78 Because gas in this temperature regine cools rapidly. it iust be replenished from a ucarby reservoir of otter gas.," Because gas in this temperature regime cools rapidly, it must be replenished from a nearby reservoir of hotter gas."79 For this reason. a coumiou conception of the vot interstellar medimu (ISAD is one in which 1 to 3«10? K eas resides in transition zones between hotter aud cooler gas.," For this reason, a common conception of the hot interstellar medium (ISM) is one in which 1 to $3 \times 10^5$ K gas resides in transition zones between hotter and cooler gas."80" Some authors (e.g. Savage&Wakker 20093) rave begun to call the 1 to 3:107 I material ""trausition eniperature gas."," Some authors (e.g., \citealt{savage_wakker_09}) ) have begun to call the 1 to $3 \times 10^5$ K material “transition temperature” gas."81" Here. for simplicity. however. we use ho tevin ""hot eas” for the eutire ~1«10? to ~3«109 I regne."," Here, for simplicity, however, we use the term “hot gas” for the entire $\sim 1 \times 10^5$ to $\sim 3 \times 10^6$ K regime."82 The tracers of hot gas are observed by UV aud X-ray iustruinents., The tracers of hot gas are observed by UV and X-ray instruments.83" Ultraviolet instruieuts are used to observe the strong resonance line transitions (28 784,5 - 2p αυ and 28 784,5 - 2p 2P4 4) of aandVL.", Ultraviolet instruments are used to observe the strong resonance line transitions (2s $^2$ $_{1/2}$ - 2p $^2$ $_{3/2}$ and 2s $^2$ $_{1/2}$ - 2p $^2$ $_{1/2}$ ) of and.84 Owing to the excellent spectral resolution of recent UV instruments. interstellar aand hhave been stucied well via absorption line spectroscopy (Savagectal.2003:Bowenet2008:Savage& 2009).," Owing to the excellent spectral resolution of recent UV instruments, interstellar and have been studied well via absorption line spectroscopy \citep{savage_etal_03,bowen_etal_08,savage_wakker_09}."85..Thevhave also been ποσα via enüssion spectroscopy. but along fewer sight lues (0...," .Theyhave also been seen via emission spectroscopy, but along fewer sight lines (e.g.,"86The disc is described by the equation of motion: the equation of continuity: and the induction equation in the ideal. MIED approximation: where is the Lorentz force per unit volume. P? the pressure. p the mass density. v the How velocity. V. the gravitational potential ancl B the magnetic field (ji is the permeability of vacuum).,"The disc is described by the equation of motion: the equation of continuity: and the induction equation in the ideal MHD approximation: where is the Lorentz force per unit volume, $P$ the pressure, $\rho$ the mass density, ${\bf v}$ the flow velocity, $\Psi$ the gravitational potential and ${\bf B}$ the magnetic field $\mu_0$ is the permeability of vacuum)."87 SL units are used throughout the paper., SI units are used throughout the paper.88 Here we neglect self gravity so that the gravitational potential W is assumed to be due to a central mass Mi., Here we neglect self gravity so that the gravitational potential $\Psi$ is assumed to be due to a central mass $M_{\ast}$.89 We consider a thin disc. so that the above equations can be averaged over the disc thickness.," We consider a thin disc, so that the above equations can be averaged over the disc thickness."90 To first order we neglect the z dependence of v anc V. so thatthe vertically averaged equation of motion and continuity are. respectively: where X is the surface mass density and the brackets denote averaging over the disc thickness.," To first order we neglect the $z$ –dependence of ${\bf v}$ and $\Psi$, so thatthe vertically averaged equation of motion and continuity are, respectively: where $\Sigma$ is the surface mass density and the brackets denote averaging over the disc thickness."91 To close the system of equations. we adopt a barotropic equation of state: The sound speed e is then given by: We adopt a nonrotating evlindrical polar coordinate system (7545.2) with origin at the central mass.," To close the system of equations, we adopt a barotropic equation of state: The sound speed $c$ is then given by: We adopt a nonrotating cylindrical polar coordinate system $(r,92\varphi, z)$ with origin at the central mass."93" We denote (e,e... the associated unit vectors."," We denote $({\bf e}_r,94{\bf e}_{\varphi}, {\bf e}_z)$ the associated unit vectors."95 We suppose that at equilibrium the disce is axisvmnmoetrie and in rotation around a central mass.e.) so that v=(0.Ον0) where © is the angular velocity.," We suppose that at equilibrium the disc is axisymmetric and in rotation around a central mass, so that ${\bf v} = (0, r \Omega(r), 0)$, where $\Omega$ is the angular velocity."96 Furthermore. we assume that the equilibrium configuration contains only a toroidal magnetic field. i.e. B=(0.D(r.2).0).," Furthermore, we assume that the equilibrium configuration contains only a toroidal magnetic field, i.e. ${\bf B} = (0, B(r,z), 0)$."97" The Lorentz force per unit volume is then: If we assume reflection with respect to the disc midplane and that 2 vanishes at the dise surface. this leads to: We consider a planet of mass Ad,«AL on a circular orbit with radius +, and angular velocity O,=VC.ri."," The Lorentz force per unit volume is then: If we assume reflection with respect to the disc midplane and that $B$ vanishes at the disc surface, this leads to: We consider a planet of mass $M_p \ll M_{\ast}$ on a circular orbit with radius $r_p$ and angular velocity $\Omega_p =98\sqrt{GM_{\ast}/r_p^3}$."99" At the location (7.4); in the disc. it exerts the5gravitational potential: where óστιςQ,f and we have introduced a softening length ro."," At the location $(r, \varphi)$ in the disc, it exerts thegravitational potential: where $\phi= \varphi - \Omega_p t$ and we have introduced a softening length $r_0$ ."100" We now expand V,, in a Fourier series with respect to the variable o:", We now expand $\Psi'_p$ in a Fourier series with respect to the variable $\phi$ :101and to follow the complex dynamics of cooling/heating of σας during the process of cluster formation.,and to follow the complex dynamics of cooling/heating of gas during the process of cluster formation.102 Aluanwong et al. (, Muanwong et al. (1032002) and Way. Phomas Vheuns (2002) used hverodyvnamical simulations within a cosmological box to study the interplay of gas cooling and a few prescriptions for nongravitational heating.,"2002) and Kay, Thomas Theuns (2002) used hydrodynamical simulations within a cosmological box to study the interplay of gas cooling and a few prescriptions for non–gravitational heating."104 As a e&eneral result. they found that increasing the heating can suppress the amount of cooled gas.," As a general result, they found that increasing the heating can suppress the amount of cooled gas."105 While the choice of simulating a whole cosmological box has the advantage of ooviding a large statistics of groups ancl clusters. it also severelv limits the available mass ancl force resolution.," While the choice of simulating a whole cosmological box has the advantage of providing a large statistics of groups and clusters, it also severely limits the available mass and force resolution."106 On he other hand. by the very nature of cooling. increasing the mass resolution allows to follow the formation of smaller iios at progressively larger redshift. where cooling and. »otentiallv. star formation are particularly efficient.," On the other hand, by the very nature of cooling, increasing the mass resolution allows to follow the formation of smaller halos at progressively larger redshift, where cooling and, potentially, star formation are particularly efficient."107 As a consequence. unless very high mass resolution is achieved. cooling in simulations can be significantly. uncderestimated (c.g.. Balogh οἱ al.," As a consequence, unless very high mass resolution is achieved, cooling in simulations can be significantly underestimated (e.g., Balogh et al."108 2001)., 2001).109 In this paper. we follow the alternative approach of simulating at verv high resolution a limited number of eroup and clustersized halos selected from a cosmological box. and we widen the explored range of possible patterns for nongravitational heating (see also BOA).," In this paper, we follow the alternative approach of simulating at very high resolution a limited number of group– and cluster–sized halos selected from a cosmological box, and we widen the explored range of possible patterns for non–gravitational heating (see also BGW)."110 While this limits our ability to precisely calibrate shape ancl scatter of NV rav scaling relations. we are able to increase the resolution in the most interesting regions of the eas clistribution.," While this limits our ability to precisely calibrate shape and scatter of $X$ --ray scaling relations, we are able to increase the resolution in the most interesting regions of the gas distribution."111 Indeed. the simulations presented in this paper are among the highest. resolution attempts realized: so far to. follow the structure of gas cooling within groups ancl clusters in the presence of a variety of schemes for extra gas heating.," Indeed, the simulations presented in this paper are among the highest resolution attempts realized so far to follow the structure of gas cooling within groups and clusters in the presence of a variety of schemes for extra gas heating."112 Furthermore. we also investigate how the cooling elliciency depends both on numerical resolution and on details of the SPILL implementation.," Furthermore, we also investigate how the cooling efficiency depends both on numerical resolution and on details of the SPH implementation."113 The structure of this paper is as follows., The structure of this paper is as follows.114 Alter providing a short description of the code. we present in Section 2 the procedure to simulate incividual halos at high resolution aud discuss the main characteristics of the four selected halos.," After providing a short description of the code, we present in Section 2 the procedure to simulate individual halos at high resolution and discuss the main characteristics of the four selected halos."115 In Section 3.λ we discuss the results on the cold fraction.," In Section 3, we discuss the results on the cold fraction."116 Hore we will concentrate on showing how this fraction depends on numerical resolution. integration scheme and removal of cold. dense particles from the SPII computation (star formation).," Here we will concentrate on showing how this fraction depends on numerical resolution, integration scheme and removal of cold dense particles from the SPH computation (star formation)."117 Finally. we present the adopted. schemes. for nongravitational gas heating and discuss their impact on the resulting cold fraction and pattern of star formation.," Finally, we present the adopted schemes for non–gravitational gas heating and discuss their impact on the resulting cold fraction and pattern of star formation."118 In Section 4. we present the predictions on X. ray. properties of clusters and. groups from our simulations. namely the entropytemperature. the luminositytemperature ancl the masstemperature relations.," In Section 4, we present the predictions on $X$ –ray properties of clusters and groups from our simulations, namely the entropy–temperature, the luminosity–temperature and the mass–temperature relations."119 Finally. we discuss our main results and craw conclusions in Section 5.," Finally, we discuss our main results and draw conclusions in Section 5."120 Our simulations are realized. withGADGET’. a parallel ree IN.body/SPI code (Springel. Yoshida White 2001). with fully aclaptive timestep integration.," Our simulations are realized with, a parallel tree N–body/SPH code (Springel, Yoshida White 2001), with fully adaptive time–step integration."121 Gas cooling in he SPILL part of the code is implemented. following Ixatz. Weinberg Lernquist (1996. KAVLE hereafter).," Gas cooling in the SPH part of the code is implemented following Katz, Weinberg Hernquist (1996, KWH hereafter)."122 Specifically. he abundances of ionic species are computed by assuming collisional equilibrium for a gas of primordial composition (massfraction V=0.76 of hydrogen and 1NX=0.24 of wlitun).," Specifically, the abundances of ionic species are computed by assuming collisional equilibrium for a gas of primordial composition (mass–fraction $X=0.76$ of hydrogen and $1-X=0.24$ of helium)."123 Since we not follow metal production from starormation. we do not include the elect of metals on the cooling function.," Since we not follow metal production from star--formation, we do not include the effect of metals on the cooling function."124 We include the elleet of a timedependent uniform UY background. (c.g. Llaardt Aladau 1999). although its elfect is only very small for the massive objects we focus on in this study.," We include the effect of a time–dependent uniform UV background (e.g., Haardt Madau 1999), although its effect is only very small for the massive objects we focus on in this study."125 We set the number of neighbors for SPL computations to 32. allowing the SPILL smoothing length to drop at most to the value of the gravitational softening length of the gas particles.," We set the number of neighbors for SPH computations to 32, allowing the SPH smoothing length to drop at most to the value of the gravitational softening length of the gas particles."126" We simulate four halos at high. resolution. which are extracted from a lowresolution DM only simulation within ἃ box of 70hMpe on a side. for a cosmological model with ©,,=0.3. QO,=0.7. Llubble constant Jf,=310 uus * and normalization as,=O.S. consistent with recent determinations of the number density of nearby clusters (Pierpaoli ct al."," We simulate four halos at high resolution, which are extracted from a low–resolution DM only simulation within a box of $70\hm$ on a side, for a cosmological model with $\Omega_m=0.3$, $\Omega_\Lambda=0.7$, Hubble constant $H_0=70$ km $^{-1}$ $^{-1}$ and normalization $\sigma_8=0.8$, consistent with recent determinations of the number density of nearby clusters (Pierpaoli et al."127 2002. ancl references therein)," 2002, and references therein)."128 As or the barvon content. we assume Que=0.01957 (og. Durles Tytler 1998).," As for the baryon content, we assume $\Omega_{\rm129bar}=0.019\,h^{-2}$ (e.g., Burles Tytler 1998)."130 This choice of Quay corresponds to fine&0.13 for the cosmic barvon fraction. which. for the assumed. Cosmology. is consistent. with the value measured rom cluster observations (οι. Ettori 2002. ancl references herein).," This choice of $\Omega_{\rm bar}$ corresponds to $f_{\rm bar}\simeq 0.13$ for the cosmic baryon fraction, which, for the assumed cosmology, is consistent with the value measured from cluster observations (e.g., Ettori 2002, and references therein)."131 The most massive halo we selected corresponds to a Virgolike cluster. with virial mass of about 410H. (as usual. we call “virial” the mass within the radius encompassing the virial overdensity. computed for. the simulated cosmology: e.g. Eke et al.," The most massive halo we selected corresponds to a Virgo–like cluster, with virial mass of about $4\times 10^{14}M_\odot$ (as usual, we call “virial” the mass within the radius encompassing the virial overdensity computed for the simulated cosmology; e.g. Eke et al."132 19982a)., 1998a).133 This turns out to x the most massive system extracted from the simulation xxx., This turns out to be the most massive system extracted from the simulation box.134 In the following. we will refer to this system as the “Virgo” cluster.," In the following, we will refer to this system as the “Virgo” cluster."135 The other three halos. which have been extracted. from a single Lagrangian region. correspond to groups in the mass range 1077..," The other three halos, which have been extracted from a single Lagrangian region, correspond to groups in the mass range $\times 10^{13}M_\odot$."136" In the following. we will refer to these three structures as 7Ciroup-17. ""Ciroup-27"" and “πομον"," In the following, we will refer to these three structures as “Group-1”, ``Group-2'' and “Group-3”."137 We provide in Table 1 the main characteristics of the sipulated structures., We provide in Table \ref{t:simul} the main characteristics of the simulated structures.138 We follow the technique originally presented by Ixatz White (1993) to increase the mass resolution and to add short. wavelength modes. within Lagrangian regions that contain the structures of interest., We follow the technique originally presented by Katz White (1993) to increase the mass resolution and to add short wavelength modes within Lagrangian regions that contain the structures of interest.139 1n these hish regions. particles are split into a dark matter," In these high--resolution regions, particles are split into a dark matter"140Nearby dwarf galaxies provide an excellent test bed for understanding how the Local Universe has evolved with cosimic time.,Nearby dwarf galaxies provide an excellent test bed for understanding how the Local Universe has evolved with cosmic time.141 This has been made feasible by ὃ-niclass telescopes. which cau access individual stars iu nearby dwart spheroidal (4511) galaxies (Tolstovctal.2009) as well as in the Magellanic Clouds (Till2001).," This has been made feasible by 8-m-class telescopes, which can access individual stars in nearby dwarf spheroidal (dSph) galaxies \citep{Tolstoy_09} as well as in the Magellanic Clouds \citep{Hill_04}."142. The detailed abundance data accumulated to date frou a siguificant sample of stars cnables us to chemically tae what occured iu these dwarf galaxies based onour knowledge of Galactic archacoloey (6...Freeman&Blaud-Uawthoru 2002).," The detailed abundance data accumulated to date from a significant sample of stars enables us to chemically tag what occurred in these dwarf galaxies based onour knowledge of Galactic archaeology \citep[e.g.,][]{Freeman_02}."143. A wel-kuown chemical feature observed in dSphs is a lower a/Fe ratio compared with that iu the Calactic halo starsstudies(e.@..Shetronectal.2001:Vennet2001).," A well-known chemical feature observed in dSphs is a lower $\alpha$ /Fe ratio compared with that in the Galactic halo stars \citep[e.g.,][]{Shetrone_01,Venn_04}."144" Recent fonnd the same level of [o /Fo] iu stars close to the lowest metallicity(c.g.../πιFrebelet and a knee in the vs. Fc diagramsupport(ο,οι,Co-hen&Tang 2009):: ja/Fe}these studies seen to that the contribution of Fe from type Ia supernovac (SNe Ta). starting from a very low metallicity ([Fe/T] <-1) results in the observed stars (c.g..Lan-frauchi&Matteuccilow-[Fe/TI].2003:Iirbylow-la/Fe|etal. 2011)."," Recent studies found the same level of $\alpha$ /Fe] in stars close to the lowest metallicity \citep[e.g.,][]{Frebel_10a} and a knee in the $\alpha$ /Fe] vs. [Fe/H] diagram \citep[e.g.,][]{Cohen_09}; these studies seem to support that the contribution of Fe from type Ia supernovae (SNe Ia), starting from a very low metallicity ([Fe/H] $\ll$ -1) results in the observed low-[Fe/H], $\alpha$ /Fe] stars \citep[e.g.,][]{Lanfranchi_03, Kirby_11}."145. However. uo clear signature of an SN Ia eurichiueut for other elements. such as Mu/Foe aud io-capture/Eoe. casts doubt ou this scheme (Tsujimoto2006).," However, no clear signature of an SN Ia enrichment for other elements, such as Mn/Fe and $n$ -capture/Fe, casts doubt on this scheme \citep{Tsujimoto_06}."146. Moreover. a low-a /Fe ratio hasbeen detected for very low-inetallicitv stars (Aokietal.2009).. and was also found in the Large Magellanic Cloud (LAIC) (Poupéiactal.2008).," Moreover, a $\alpha$ /Fe ratio has been detected for very low-metallicity stars \citep{Aoki_09}, and was also found in the Large Magellanic Cloud (LMC) \citep{Pompeia_08}."147.. This observational fact seecnmis to couflict with the presence of low-inetallicity stars exhibiting high |a/Fe] in some dsphs ((Nochetal.2008:Χαν&TallFrebel2010b:blemLetartectal. 2010)... anc clear answers to this pro continue to chide us.," This observational fact seems to conflict with the presence of low-metallicity stars exhibiting high $\alpha$ /Fe] in some dSphs \citep{Koch_08, Venn_08, Frebel_10b, Letarte_10}, and clear answers to this problem continue to elude us."148 Iu contrast. the abundance of m-capture elements. Ba aud La. are euhanced in some dSpls.," In contrast, the abundance of $n$ -capture elements, Ba and La, are enhanced in some dSphs."149" Fist. we noticed that Ba (La) is eulauced relative to the rrprocess clement. Eu. dy examining an eusenible of data frou, six dSphs (Vennetal.2001.referencestherein)."," First, we noticed that Ba (La) is enhanced relative to the $r$ -process element, Eu, by examining an ensemble of data from six dSphs \citep[][references therein]{Venn_04}."150 Theoretically. the high |Da/Eu]| ratio eau be explained with a stroug galactic wind model. iu which the + process clemcuts from type II SNe (SNe II) are no longer produced after the onset of the winds (Lanfranchietal. 2008).," Theoretically, the high [Ba/Eu] ratio can be explained with a strong galactic wind model, in which the $r$ -process elements from type II SNe (SNe II) are no longer produced after the onset of the winds \citep{Lanfranchi_08}."151. This issue was remarkably furthered b the abundant data from a high resolution VLT study for the Fornax (Fux) dSph (Letarteetal.2010)., This issue was remarkably furthered by the abundant data from a high resolution VLT study for the Fornax (Fnx) dSph \citep{Letarte_10}.152.. This study revealed. a clear duerease in Ba and La. not ouly iu comparison with Eu but also with Fe or a- eleiieuts in accordance with an increasing Fe/II chiving late evolution.," This study revealed a clear increase in Ba and La, not only in comparison with Eu but also with Fe or $\alpha$ -elements in accordance with an increasing Fe/H during late evolution."153 This feature contrasts with that of the Galaxy and disagrees with current model predictions (Laufrauchietal.2008)., This feature contrasts with that of the Galaxy and disagrees with current model predictions \citep{Lanfranchi_08}.154. A simular feature is seen in some other dSphs. for example in the Sagitarrius dSpli (Sbordoneetal.2007).. and clearly in the LMC (Pompdiaetal. 2008).," A similar feature is seen in some other dSphs, for example in the Sagitarrius dSph \citep{Sbordone_07}, and clearly in the LMC \citep{Pompeia_08}."155". Based on an idea that invoking the initial mass ""nctiou (IAIF) variations may be one of the solutions to explain chemical abundance patterus ίοιο,Pagel1997).. we present a new mechauisn underlvius the observed rends between Da. Eu. and Fe in some dwarf galaxies. with a focus on the Fux dSpl."," Based on an idea that invoking the initial mass function (IMF) variations may be one of the solutions to explain chemical abundance patterns \citep[e.g.,][]{Pagel_97}, we present a new mechanism underlying the observed trends between Ba, Eu, and Fe in some dwarf galaxies, with a focus on the Fnx dSph."156 Our claim is that star orluations lacking very massive stars. such as ο 25Af... observedmapriut an muusual s-process cahancement. which ls in stellar abundance.," Our claim is that star formations lacking very massive stars, such as $\gtsim$ 25, imprint an unusual $s$ -process enhancement, which is observed in stellar abundance."157 The suppression of he formation of massive stars in low surface-brightucss ealaxies is nuplied. from the observed flux ratio of Ila o the fax ultraviolet (Moeureretal.2009)., The suppression of the formation of massive stars in low surface-brightness galaxies is implied from the observed flux ratio of $\alpha$ to the far ultraviolet \citep{Meurer_09}.158". Th addition. roni a theoretical aspect. receut work suggests that a vigh mass end 4, of the IME. depends on the mass of he star clusters. and thus on the plysical propertics of the galaxies where the clusters have formed (I&roupaAltenburg&Kroupa 2008)."," In addition, from a theoretical aspect, recent work suggests that a high mass end $m_{\rm u}$ of the IMF depends on the mass of the star clusters, and thus on the physical properties of the galaxies where the clusters have formed \citep{Kroupa_03, Weidner_05, Pflamm_08}."159. These studies claim that ing would be lower in the low density cuviroument of dwarf ealaxies. iu Which the formation of massive star clusters is suppressed.," These studies claim that $m_{\rm u}$ would be lower in the low density environment of dwarf galaxies, in which the formation of massive star clusters is suppressed."160 Their mocel predictious have been shown to be consistent with the observed treud for the ITa-to-EUV flux ratio (Leeetal. 2009).., Their model predictions have been shown to be consistent with the observed trend for the $\alpha$ -to-FUV flux ratio \citep{Lee_09}. .161 It is wotlavhile to note that. in the Fux dSphl case. the approximate star formation," It is wothwhile to note that, in the Fnx dSph case, the approximate star formation"162Mapping (he mass distribution of matter in (he universe has been a major challenge for modern observational cosmology.,Mapping the mass distribution of matter in the universe has been a major challenge for modern observational cosmology.163 One of the direct procedures to weigh matter in the, One of the direct procedures to weigh matter in the164"evolution of W UMas (Steppien 2006, 2009), they are lived (a few Gy), as for the estimated age of the planet host population, f+1.","evolution of W UMas (Stęppień 2006, 2009), they are long-lived (a few Gy), as for the estimated age of the planet host population, $f\approx 1$."165" On the basis of these numbers, contact binaries thus appear to be a possible progenitor population, although they may not be the only relevant possibility as discussed below."," On the basis of these numbers, contact binaries thus appear to be a possible progenitor population, although they may not be the only relevant possibility as discussed below."166" The outcome of close binary evolution RRitter 1996) is different depending on the mass ratio, total mass, and the evolutionary status of the components."," The outcome of close binary evolution Ritter 1996) is different depending on the mass ratio, total mass, and the evolutionary status of the components."167" The primary star can be brought (or kept) in synchronous rotation with the orbit if the mass ratio q=M2/M, of the secondary is large enough, and the stars close enough for tidal interaction to be effective."," The primary star can be brought (or kept) in synchronous rotation with the orbit if the mass ratio $q=M_2/M_1$ of the secondary is large enough, and the stars close enough for tidal interaction to be effective."168 Ongoing angular momentum loss from the system by magnetic braking narrows the orbit until one of the stars fills its Roche lobe and mass transfer starts., Ongoing angular momentum loss from the system by magnetic braking narrows the orbit until one of the stars fills its Roche lobe and mass transfer starts.169" If, on the other hand, the orbital angular momentum of the secondary is too small to spin the primary up to corotation with the orbit, the orbit will shrink by tidal interaction (even if magnetic braking were ineffective) until one of the stars fills its Roche lobe."," If, on the other hand, the orbital angular momentum of the secondary is too small to spin the primary up to corotation with the orbit, the orbit will shrink by tidal interaction (even if magnetic braking were ineffective) until one of the stars fills its Roche lobe."170" If the mass ratio is below Darwin’s stability limit (‘tidal instability’, DDarwin 1879, Hut 1980), this will happen even if the stars initially rotate in synchrony with the orbit."," If the mass ratio is below Darwin's stability limit (`tidal instability', Darwin 1879, Hut 1980), this will happen even if the stars initially rotate in synchrony with the orbit."171" For low mass main sequence stars, this limit is on the order of g=0.08 (Rasio 1995)."," For low mass main sequence stars, this limit is on the order of $q=0.08$ (Rasio 1995)."172" After the binary orbit has shrunk until one of the stars fills its Roche lobe, the further evolution depends on the nature of the lobe-filling star, since its internal structure determines how its size responds to loss of mass from its surface."," After the binary orbit has shrunk until one of the stars fills its Roche lobe, the further evolution depends on the nature of the lobe-filling star, since its internal structure determines how its size responds to loss of mass from its surface."173 For main sequence stars the star that first fills its lobe is the more massive one., For main sequence stars the star that first fills its lobe is the more massive one.174" The simplest case is when it is a fully convective, low-mass star."," The simplest case is when it is a fully convective, low-mass star."175" Its adiabatic mass-radius exponent is then negative; i.e., sudden mass loss causes it to expand."," Its adiabatic mass-radius exponent is then negative; i.e., sudden mass loss causes it to expand."176" Mass loss then causes it to overfill its Roche lobe, and the mass loss rate increases exponentially, with the final stages happening on a dynamical (orbital) time scale RRitter 1988)."," Mass loss then causes it to overfill its Roche lobe, and the mass loss rate increases exponentially, with the final stages happening on a dynamical (orbital) time scale Ritter 1988)."177" Since the receiving star does not fill its Roche lobe yet and, being of lower mass, is also fully convective with a negative mass-radius exponent, it can receive a large amount of mass from the primary before also filling its Roche lobe."," Since the receiving star does not fill its Roche lobe yet and, being of lower mass, is also fully convective with a negative mass-radius exponent, it can receive a large amount of mass from the primary before also filling its Roche lobe."178 The SPH simulations by Rasio and Shapiro (1995) and grid based simulations (D'Souza et 22006) show that the final merger of such binaries happens on a time scale of some ten orbits., The SPH simulations by Rasio and Shapiro (1995) and grid based simulations (D'Souza et 2006) show that the final merger of such binaries happens on a time scale of some ten orbits.179 The situation is more complicated when the mass-radius exponent of the primary is positive or becomes positive after an initial phase of dynamical mass transfer (Steppien 2006)., The situation is more complicated when the mass-radius exponent of the primary is positive or becomes positive after an initial phase of dynamical mass transfer (Stęppień 2006).180" A longer phase of mass transfer on the thermal time scale then takes place, until the mass ratio of the system has reversed, as in Algol type binaries."," A longer phase of mass transfer on the thermal time scale then takes place, until the mass ratio of the system has reversed, as in Algol type binaries."181" For primary masses on the order of 1Mo, the star is likely to have evolved a (small) helium core during the magnetic braking period that brought the binary into contact."," For primary masses on the order of $1\ M_\odot$, the star is likely to have evolved a (small) helium core during the magnetic braking period that brought the binary into contact."182" Steppien (2006) shows that this allows binaries in the mass range of W UMa stars to settle into a stable contact configuration, which lasts for a few Gy until angular momentum loss by magnetic braking causes the stars to finally merge."," Stęppień (2006) shows that this allows binaries in the mass range of W UMa stars to settle into a stable contact configuration, which lasts for a few Gy until angular momentum loss by magnetic braking causes the stars to finally merge."183 This solves a longstanding puzzle in the theory of contact binaries and explains their high abundance., This solves a longstanding puzzle in the theory of contact binaries and explains their high abundance.184" The nature and abundance of W UMas makes them a plausible candidate population for making hot Jupiters, but they are probably not the only ones."," The nature and abundance of W UMas makes them a plausible candidate population for making hot Jupiters, but they are probably not the only ones."185" The distribution of (total) mass of W UMas in the catalog of Gazeas Steppien (2008) peaks at 1.5—2Mo, the distribution of known host masses of transit planets around 1.1Mo."," The distribution of (total) mass of W UMas in the catalog of Gazeas Stęppień (2008) peaks at $1.5 - 2 M_\odot $ , the distribution of known host masses of transit planets around $1.1 M_\odot $."186 In refmassD we compare the distribution of total masses of W UMa stars with that of transiting hot Jupiter host stars., In \\ref{massD} we compare the distribution of total masses of W UMa stars with that of transiting hot Jupiter host stars.187 The overlap between the distributions is in fact only modest., The overlap between the distributions is in fact only modest.188" The V1309 Sco event shows that some mass can be lost in the final merger, although loss as large as several tenths of a solar mass seems unlikely."," The V1309 Sco event shows that some mass can be lost in the final merger, although loss as large as several tenths of a solar mass seems unlikely."189 It is thus worth exploring other channels., It is thus worth exploring other channels.190 We propose here that the additional channel is in fact the direct merger of low-mass binaries (M1--M2S 1.2Mo) on a dynamical time scale as discussed above., We propose here that the additional channel is in fact the direct merger of low-mass binaries $M1+M2 \la 1.2 M_\odot$ ) on a dynamical time scale as discussed above.191" There is no obvious reason why such systems, at masses of 0.8—1.2Mo, would be formed at rates much less than the 1—2.5Mo binaries that end up becoming W UMas."," There is no obvious reason why such systems, at masses of $0.8 - 1.2 M_\odot $, would be formed at rates much less than the $1- 2.5 M_\odot $ binaries that end up becoming W UMas."192" Their lower luminosity, and the absence of the extended contact phase that makes W UMas stand out, would make them a much less prominent population."," Their lower luminosity, and the absence of the extended contact phase that makes W UMas stand out, would make them a much less prominent population."193 Detached binary systems that could be such progenitors are known CCoughlin et 2011)., Detached binary systems that could be such progenitors are known Coughlin et 2011).194" Inflated hot Jupiters orbit at distances close to their host star, typically within 0.05 AU reforb))."," Inflated hot Jupiters orbit at distances close to their host star, typically within 0.05 AU \\ref{orb}) )."195" At such distances, friction in the tides they raise on the star cause their orbits to circularize."," At such distances, friction in the tides they raise on the star cause their orbits to circularize."196 T'he functional dependence of this processon system parameters is well established (Goldreich 1963; Jackson et al., The functional dependence of this processon system parameters is well established (Goldreich 1963; Jackson et al.197 2009)., 2009).198 The, The199"In Section +., we have shown that our preferred observational sample, sample T2, exhibits a reversal in the dependence of inetallicity on star formation rate from low to high stellar amass.","In Section \ref{sec:The FMR in observations}, we have shown that our preferred observational sample, Sample T2, exhibits a reversal in the dependence of metallicity on star formation rate from low to high stellar mass."200" At low iasses, low-SER galaxies have higher moetallicities compared το more star forming galaxies."," At low masses, low-SFR galaxies have higher metallicities compared to more star forming galaxies."201" At high masses, they have lower inctallicities."," At high masses, they have lower metallicities."202" This observation alone could be explained by considering inass-dependenut, metal-rich outflows."," This observation alone could be explained by considering mass-dependent, metal-rich outflows."203" At lower masses (c 10?M.). where outflows are more effective, low-SER galaxies produce relatively fewer SNe, disrupting the ISM less and blowing away inctals less efficiently (c.g. MacLow&Ferrara 1999))."," At lower masses $\sim 10^{9} \textnormal{M}_{\textnormal{\astrosun}}$ ), where outflows are more effective, low-SFR galaxies produce relatively fewer SNe, disrupting the ISM less and blowing away metals less efficiently (e.g. \citealt{MLF99}) )."204" At higher masses (> 10/2ML.), where outflows become increasinely weak, low-SFER galaxies sunply produce less imetals and so uuder-curich the ISM relative to more actively star forming galaxies."," At higher masses $\gtrsim 10^{10.2} \textnormal{M}_{\textnormal{\astrosun}}$ ), where outflows become increasingly weak, low-SFR galaxies simply produce less metals and so under-enrich the ISM relative to more actively star forming galaxies."205" However, our model also shows a decrease in. inctallicity with stellar mass at fixed-SFR above ~LOMIM..."," However, our model also shows a decrease in metallicity with stellar mass at fixed-SFR above $\sim 10^{10.4} \textnormal{M}_{\textnormal{\astrosun}}$."206 Such a feature be explained by inass-dependeut outflows alone., Such a feature be explained by mass-dependent outflows alone.207" If the turnover in the M.-Z relation 1s indeed real, then additional physical mechanisms must be at play."," If the turnover in the $M_{*}$ $Z$ relation is indeed real, then additional physical mechanisms must be at play."208 Our model points to inctal-poor galactic infall at high-inass as an explanation., Our model points to metal-poor galactic infall at high-mass as an explanation.209 Those high-M. galaxies with low gas-phase inctallicitics are known to have undergone gradual dilution of their gas phases after a merger event which shut-down further star formation., Those $M_{*}$ galaxies with low gas-phase metallicities are known to have undergone gradual dilution of their gas phases after a merger event which shut-down further star formation.210" The restriction in the amount of infall by AGN feedback allowed these galaxies to dilute their ISM, without accreting enough gas for star formation to resume."," The restriction in the amount of infall by AGN feedback allowed these galaxies to dilute their ISM, without accreting enough gas for star formation to resume."211" Correlations between these galaxies aud the high-V., low-Z galaxies in our observational sample (namely, their large black hole masses) nnplv that such a dilution process could also be involved in shaping the M.-Z relation in the real Universe (see also Appendix B)."," Correlations between these galaxies and the $M_{*}$, $Z$ galaxies in our observational sample (namely, their large black hole masses) imply that such a dilution process could also be involved in shaping the $M_{*}$ $Z$ relation in the real Universe (see also Appendix B)."212" There are, however, two factors hamperme this interpretation."," There are, however, two factors hampering this interpretation."213" First, the dependence of Z on SER is itself strougly dependent on how these properties are measured (see Section 4))."," First, the dependence of $Z$ on SFR is itself strongly dependent on how these properties are measured (see Section \ref{sec:The FMR in observations}) )."214" Although a high-inass dependence is undeniable im our Sample T2. it is not present in Sample T1, at least not within the range of masses studied."," Although a high-mass dependence is undeniable in our Sample T2, it is not present in Sample T1, at least not within the range of masses studied."215" second, the recipes used to model physical processes inL-GALANIES,, although up-to-date with current theory, are stil rather crude, and this could be affecting the galaxy evolution seen in our model galaxies."," Second, the recipes used to model physical processes in, although up-to-date with current theory, are still rather crude, and this could be affecting the galaxy evolution seen in our model galaxies."216" For example, metals are assumed to fully iix with the ISM galactic outflows are allowed to drive gas out of the galaxy."," For example, metals are assumed to fully mix with the ISM galactic outflows are allowed to drive gas out of the galaxy."217" This means that it is the subsequent cessation of star formation im low-inass galaxies that is causing the relation between A. and Z in the model, rather than explicitly inctal-rich outflows."," This means that it is the subsequent cessation of star formation in low-mass galaxies that is causing the relation between $M_{*}$ and $Z$ in the model, rather than explicitly metal-rich outflows."218 Additionally. aud perhaps relatedlv. there is a lack of evolution in the model M.-Z relation. contrary to observations.," Additionally, and perhaps relatedly, there is a lack of evolution in the model $M_{*}$ $Z$ relation, contrary to observations."219" Despite these two caveats, we believe"," Despite these two caveats, we believe"220Investisation DPR-S-1563-Y. C.D.D. was supported by the Office of Naval Research.,Investigation DPR-S-1563-Y. C.D.D. was supported by the Office of Naval Research.221LSB galaxies. which are the systems for which the most information can be obtained.,"LSB galaxies, which are the systems for which the most information can be obtained."222 In most disk. galaxies the o»wvonie component. is gravitationally dominant in the central regions. which makes estimating the total central matter density a dillieult. problem. necessarily sensitive to he assumed AL ratios and orbital anisotropy.," In most disk galaxies the baryonic component is gravitationally dominant in the central regions, which makes estimating the total central matter density a difficult problem, necessarily sensitive to the assumed $M/L$ ratios and orbital anisotropy."223 In the case of the LSB galaxies. the large disk scale racius vields à very extended barvonic component. (presumably arising from a veh initial angular momentum) such that these. systems ave dark matter dominated. into their innermost regions.," In the case of the LSB galaxies, the large disk scale radius yields a very extended baryonic component (presumably arising from a high initial angular momentum) such that these systems are dark matter dominated into their innermost regions."224 Given this. [rom measurements of the rotation Curves a σοοι estimate of the total central density is available. see Figure (1).," Given this, from measurements of the rotation curves a good estimate of the total central density is available, see Figure (1)."225 Despite this situation. the only available sample of LSB rotation curves (de Blok et al.," Despite this situation, the only available sample of LSB rotation curves (de Blok et al."226 1996) contains only a smal sample of galaxies (16). such that it is hard to distinguish any trend in the LSB galaxy-tvpe (after all. this is a highly empirical definition. resting merely on the observationa detectabilitv limits. which do not necessarily correlate with galactic types.," 1996) contains only a small sample of galaxies (16), such that it is hard to distinguish any trend in the LSB galaxy-type (after all, this is a highly empirical definition, resting merely on the observational detectability limits, which do not necessarily correlate with galactic types."227 It has been pointed out that these are very new measurements. and. that niniv more are expected as the observational situation improves).," It has been pointed out that these are very new measurements, and that many more are expected as the observational situation improves)."228 We further emphasize that the central rotation curves remain not well sampled. and may be further degraded by bean smearing and other finite resolution elfects.," We further emphasize that the central rotation curves remain not well sampled, and may be further degraded by beam smearing and other finite resolution effects."229 Nonetheless. fitting straight lines to the inner regions of the rotation curves published hy de Blok et al. (," Nonetheless, fitting straight lines to the inner regions of the rotation curves published by de Blok et al. ("2301996). we can estimate the total central matter densities of these systems. a plot of which is presented. in Fieure (2).,"1996), we can estimate the total central matter densities of these systems, a plot of which is presented in Figure (2)."231" Xs considerable spread is evident. (at least some ol it observational). and only galaxies within a narrow range ol disk masses are present. rather than attempting to extract a trend [rom these galaxies. we only took the median of the distribution to characterize a “typical” LSB. in terms of a total barvon mass and total central matter density of log(M,)=9.5. log(pu/M.pe7)-L85."," As considerable spread is evident (at least some of it observational), and only galaxies within a narrow range of disk masses are present, rather than attempting to extract a trend from these galaxies, we only took the median of the distribution to characterize a “typical” LSB, in terms of a total baryon mass and total central matter density of $log(M_d)=9.5$, $log(\rho_{0}/M_{\odot} pc^{-3})=-1.85$."232 These will be our first two observational restrictions. used to construct a model of a typical LSB galaxy.," These will be our first two observational restrictions, used to construct a model of a typical LSB galaxy."233 From observations of total luminosity ancl rotation velocity amplitude it appears that LSB galaxies follow the same Tullv-Fisher relation as normal late type spirals e.g. Zwaan et al. (, From observations of total luminosity and rotation velocity amplitude it appears that LSB galaxies follow the same Tully-Fisher relation as normal late type spirals e.g. Zwaan et al. (2341995).,1995).235 We take the recent Tullv-Fisher law determination of Rhee Van Albacla (1995). where a population corrected total disk mass is calculated. from colour information to derive a disk mass vs. maximum rotation velocity “Lully-Fisher relation.," We take the recent Tully-Fisher law determination of Rhee Van Albada (1995), where a population corrected total disk mass is calculated from colour information to derive a disk mass vs. maximum rotation velocity Tully-Fisher relation."236 Vhat study shows that by taking into account the cillerent ML. ratios associated: with dillerent galaxies. the dispersion. in the ‘Tully-Fisher relation can be reduced. to a minimum.," That study shows that by taking into account the different $M/L$ ratios associated with different galaxies, the dispersion in the Tully-Fisher relation can be reduced to a minimum."237" The resulting slope in ALjesVay, is quite similar to that of the ] band Tullv-Fisher relation. but the dispersion goes down by a factor of 2."," The resulting slope in $M_d vs. V_M$ is quite similar to that of the I band Tully-Fisher relation, but the dispersion goes down by a factor of 2."238 Given the greater ease with which this can be compared to our studs; we use this Mass. Tullv-Fisher throughout this work. valid for all ealaxies. This Ἐν relation provides a third constraint. for our typical LSL.," Given the greater ease with which this can be compared to our study, we use this Mass Tully-Fisher throughout this work, valid for all galaxies, This T-F relation provides a third constraint for our typical LSB."239 Combining the samples of MeGaugh Bothun (1994) ancl Spravberry Lmpev (1995). who have studied: the light distribution in LSB galaxies. we compiled a List of LSB galaxies for which a measured total luminosity and luminosity exponential scale radius exist.," Combining the samples of McGaugh Bothun (1994) and Sprayberry Impey (1995), who have studied the light distribution in LSB galaxies, we compiled a list of LSB galaxies for which a measured total luminosity and luminosity exponential scale radius exist."240 These data are, These data are241and peripheral radio relic (12534275: Jaffe Rudnick 1979: Giovannini et al.,and peripheral radio relic (1253+275; Jaffe Rudnick 1979; Giovannini et al.242 1985) and has been used as a test-bed for CR acceleration models (e.g.. Donnert et al.," 1985) and has been used as a test-bed for CR acceleration models (e.g., Donnert et al."243 2009)., 2009).244 The dynamical state of Coma has been well established through optical velocity analysis (Fitchett Webster 1987: Mellier et al., The dynamical state of Coma has been well established through optical velocity analysis (Fitchett Webster 1987; Mellier et al.245 1988: Merritt Trimbley 1994: Colless Dunn 1996: and Adami et al., 1988; Merritt Trimbley 1994; Colless Dunn 1996; and Adami et al.246 2005)., 2005).247 Coma has been extensively observed in the radio., Coma has been extensively observed in the radio.248 Kim et al. (, Kim et al. (2491989) and Venturi et al. (,1989) and Venturi et al. (250"1990). mapped the region with the Westerbork Synthesis Radio Telescope (WSRT) at 326 MHz. finding a diffuse ""bridge"" of emission connecting the halo to the relic.","1990) mapped the region with the Westerbork Synthesis Radio Telescope (WSRT) at 326 MHz, finding a diffuse “bridge"" of emission connecting the halo to the relic."251 Deiss et al. (, Deiss et al. (2521997) also detected the bridge at 1.4 GHz using the Effelsberg 100-m-telescope. and found the radio halo to have a diameter of -80.,"1997) also detected the bridge at 1.4 GHz using the Effelsberg 100-m-telescope, and found the radio halo to have a diameter of $\sim$ $^{\prime}$."253 Using the 300 m Arecibo telescope combined with DRAO data at 408 MHz Kronberg et al. (, Using the 300 m Arecibo telescope combined with DRAO data at 408 MHz Kronberg et al. (254"2007) detected a 7| radio ""cloud"" surrounding both the classical halo and relic source.","2007) detected a $\sim$ $^{\prime}$ radio “cloud"" surrounding both the classical halo and relic source."255 This cloud size corresponds to  Mpe if it is associated with the Coma cluster. and would therefore extend into the Warm-Hot Intergalactic Medium (WHIM).," This cloud size corresponds to $\sim$ 4 Mpc if it is associated with the Coma cluster, and would therefore extend into the Warm-Hot Intergalactic Medium (WHIM)."256 The Coma cluster is also one of the few GRHs to have resolved spectral-index maps (Giovannini et al., The Coma cluster is also one of the few GRHs to have resolved spectral-index maps (Giovannini et al.257 2003). which show a spectral steepening at larger cluster radii.," 2003), which show a spectral steepening at larger cluster radii."258 Recent ~150 MHz observations with the Westerbork Synthesis Radio Telescope (Pizzo 2010) confirm the radial steepening of the spectral index. as well as identifying two new candidate relic features to the East and West of the cluster.," Recent $\sim$ 150 MHz observations with the Westerbork Synthesis Radio Telescope (Pizzo 2010) confirm the radial steepening of the spectral index, as well as identifying two new candidate relic features to the East and West of the cluster."259 Coma has also been the subject of intense X-ray observations., Coma has also been the subject of intense X-ray observations.260 In addition to surveys (e.g. the ROSAT All Sky Survey). mosaic XMM—Newton observations (Briel et al 2001: Neumann et al.," In addition to surveys (e.g. the ROSAT All Sky Survey), mosaic $XMM-Newton$ observations (Briel et al 2001; Neumann et al."261 2003: Schuecker et al., 2003; Schuecker et al.262 2004) have revealed the complex thermal substructure of the X-ray halo., 2004) have revealed the complex thermal substructure of the X-ray halo.263 Detections of non-thermal hard X-ray emission have been claimed. e.g.. using AXVE (tRephaeli Gruber 2002) and BeppoSAX (Fusco-Femiano et al.," Detections of non-thermal hard X-ray emission have been claimed, e.g., using $RXTE$ (Rephaeli Gruber 2002) and $BeppoSAX$ (Fusco-Femiano et al."264" 1999, 2004)."," 1999, 2004)."265 Diffuse hard X-ray emission has been imaged with INTEGRAL (Renaud et al., Diffuse hard X-ray emission has been imaged with $INTEGRAL$ (Renaud et al.266 2006: Eckert et al., 2006; Eckert et al.267 2007: Lutovinov et al., 2007; Lutovinov et al.268 2008) and Suzaku Wik et al., 2008) and $Suzaku$ (Wik et al.269 2009). revealing temperature increases in the Western region of the cluster also seen at lower energies with ASCA (Watanabe et al.," 2009), revealing temperature increases in the Western region of the cluster also seen at lower energies with $ASCA$ (Watanabe et al."270 1999)., 1999).271 We present Green Bank Telescope (GBT) |.41. GHz and (WSRT) 352 MHz observations of the Coma cluster in an attempt to investigate the various CR. acceleration models. as well as confirm the dramatic + Mpe radio cloud seen by Kronberg et al. (," We present Green Bank Telescope (GBT) 1.41 GHz and (WSRT) 352 MHz observations of the Coma cluster in an attempt to investigate the various CR acceleration models, as well as confirm the dramatic 4 Mpc radio cloud seen by Kronberg et al. ("2722007).We present the observations and data reduction in $2. and our observational results in $3.,"2007).We present the observations and data reduction in $\S$ 2, and our observational results in $\S$ 3."273 In $4 we present a discussion of the implications of our results. and summarize our key points in $5.," In $\S$ 4 we present a discussion of the implications of our results, and summarize our key points in $\S$ 5."274" In this paper. we assume A,=70. Q4—0.7. Q4;=0.3."," In this paper, we assume $H_{o}=70$, $\Omega_{\Lambda}=0.7$, $\Omega_{M}=0.3$."275 We observed a χο region around the Coma Cluster with the Green Bank Telescope (GBT) between October 2007 and January 2008., We observed a $^{\circ}$ $^{\circ}$ region around the Coma Cluster with the Green Bank Telescope (GBT) between October 2007 and January 2008.276 We observed with the GBT's Spectrometer with a 50 MHz bandpass centred on [.41 GHz., We observed with the GBT's Spectrometer with a 50 MHz bandpass centred on 1.41 GHz.277 The region was sampled with 150 evenly spaced stripes — 75 with constant RA and 75 with constant Dec. Each stripe was covered by tive 60 second raster scans., The region was sampled with 150 evenly spaced stripes – 75 with constant RA and 75 with constant Dec. Each $^{\circ}$ stripe was covered by five 60 second raster scans.278 We performed these scans immediately one after another in order to identify and edit out those times when the overall power levels were unstable due to either receiver or atmospheric fluctuations., We performed these scans immediately one after another in order to identify and edit out those times when the overall power levels were unstable due to either receiver or atmospheric fluctuations.279 During each night of observations. we scanned across some combination of 3C295. 3C48. 3C138 and 3C?86.," During each night of observations, we scanned across some combination of 3C295, 3C48, 3C138 and 3C286."280 The first two are unpolarized calibrators and the second two are polarized., The first two are unpolarized calibrators and the second two are polarized.281 There were some nights where. for a variety of reasons. we did not observe an unpolarized calibrator.," There were some nights where, for a variety of reasons, we did not observe an unpolarized calibrator."282 An internal correlated calibrator signal (19 K) was used to determine the relative X and Y dipole guins (correcting. for leakage from Stokes I into Stokes Q). as well as the X-Y phase offset.," An internal correlated calibrator signal $\sim$ 19 K) was used to determine the relative X and Y dipole gains (correcting for leakage from Stokes I into Stokes Q), as well as the X-Y phase offset."283" A parallactic angle correction. which rotates Qyetescope and Uy:5, into Qs and Usi. was applied to each integration."," A parallactic angle correction, which rotates $_{Telescope}$ and $_{Telescope}$ into $_{Sky}$ and $_{Sky}$, was applied to each integration."284 Observations of the polarized calibrators over 3 independent parallactic angles allows. in principle. for the determination. of the full Mueller matrix elements (e.g. Mason 2007). which deseribe the conversion of measured Stokes parameters into true source Stokes parameters.," Observations of the polarized calibrators over 3 independent parallactic angles allows, in principle, for the determination of the full Mueller matrix elements (e.g., Mason 2007), which describe the conversion of measured Stokes parameters into true source Stokes parameters."285 We were unable to determine these elements due to insufficient parallactic angle coverage of the polarized calibrators., We were unable to determine these elements due to insufficient parallactic angle coverage of the polarized calibrators.286 This results in the loss of of the U Stokes power through conversion into V. based on fractional polarization measurements of 3C138 3C286.," This results in the loss of $<$ of the U Stokes power through conversion into V, based on fractional polarization measurements of 3C138 3C286."287" Due to radio interference and instabilities in the Spectrometer gains, 35 of the data was unusable."," Due to radio interference and instabilities in the Spectrometer gains, $\sim$ of the data was unusable."288 For this paper. we only used the stripes taken at constant declinations. which were more stable than the constant RA stripes.," For this paper, we only used the stripes taken at constant declinations, which were more stable than the constant RA stripes."289 Fortunately. most of the bad data was in the outer regions of the image.," Fortunately, most of the bad data was in the outer regions of the image."290 In order to isolate the diffuse emission. we subtracted out a convolved version of the corresponding NVSS images.," In order to isolate the diffuse emission, we subtracted out a convolved version of the corresponding NVSS images."291 A linear baseline was then removed from each sean by fitting a straight line to source free regions after the NVSS subtraction., A linear baseline was then removed from each scan by fitting a straight line to source free regions after the NVSS subtraction.292 The resulting map rms is 6 mJy | (which is dominated by diffuse Galactic emission). where the beam is 14.25’ 137.," The resulting map rms is $\sim$ 6 mJy $^{-1}$ (which is dominated by diffuse Galactic emission), where the beam is $^{\prime}\times$ $^{\prime}$."293 Fig., Fig.294 | shows the total intensity map after NVSS subtraction and baseline removal., \ref{gbt} shows the total intensity map after NVSS subtraction and baseline removal.295 The low resolution comes from our rapid on-the-fly mapping of the region. needed in order to mitigate gain fluctuations.," The low resolution comes from our rapid on-the-fly mapping of the region, needed in order to mitigate gain fluctuations."296 Figure 2. shows the polarized intensity colour coded by polarization angle with total intensity contours., Figure \ref{gbt_pol} shows the polarized intensity colour coded by polarization angle with total intensity contours.297 We describe the halo and relic emission in $3., We describe the halo and relic emission in $\S$ 3.298 In both figures. the radiosource Coma A (3C277.3) was fit with a gaussian and subtracted out of the image by hand.," In both figures, the radiosource Coma A (3C277.3) was fit with a gaussian and subtracted out of the image by hand."299 A four-pointing mosaic (pointing centres {2h59m52s+27d58m. I2h5-4mO8s427d58m. 12h59m52s426d42 and |2hS4m08s+26d42m) of the Coma cluster was also observedm. for a total of ~4+8 hours over four nights in P-band (352 MHz) with the Westerbork Synthesis Radio Telescope (WSRT) in November of 2008.," A four-pointing mosaic (pointing centres 12h59m52s+27d58m, 12h54m08s+27d58m, 12h59m52s+26d42m, and 12h54m08s+26d42m) of the Coma cluster was also observed for a total of $\sim$ 48 hours over four nights in P-band (352 MHz) with the Westerbork Synthesis Radio Telescope (WSRT) in November of 2008."300 The array was in the maxi-short configuration. with the shortest baselines of 36m. 54m 72m and 90m. used to optimise imaging of very extended structures.," The array was in the maxi-short configuration, with the shortest baselines of 36m, 54m 72m and 90m, used to optimise imaging of very extended structures."301 One primary flux and one polarized calibrator (as a pair) were observed at the beginning and end of each night., One primary flux and one polarized calibrator (as a pair) were observed at the beginning and end of each night.302 For the primary flux calibrators we observed 3CI47 and 3C295. and for the polarized calibrators we observed DA240 and 3C345.," For the primary flux calibrators we observed 3C147 and 3C295, and for the polarized calibrators we observed DA240 and 3C345."303 We used the WSRT wide band correlator to cover a frequency range from 310-390 MHz with eight 10 MHz wide bands. each with 128 channels and full Stokes parameters.," We used the WSRT wide band correlator to cover a frequency range from 310-390 MHz with eight 10 MHz wide bands, each with 128 channels and full Stokes parameters."304 IFs 3. 4. 6. and 8 were not used due to interference and ealibration problems.," IFs 3, 4, 6, and 8 were not used due to interference and calibration problems."305 After removing the end channels in each band and editing for strong RFT. 400) channels remained in the tinal analysis. for a total bandwidth of 31 MHz.," After removing the end channels in each band and editing for strong RFI, 400 channels remained in the final analysis, for a total bandwidth of 31 MHz."306 The calibration and reduction of the WSRT data were performed using the NRAO’s Astronomical Image Processing System (AIPS)., The calibration and reduction of the WSRT data were performed using the NRAO's Astronomical Image Processing System (AIPS).307 The total intensity in each of the 4 bands was calibrated independently using standard procedures and the fluxes in the VLA calibrator manual for 3C147 and 2603295., The total intensity in each of the 4 bands was calibrated independently using standard procedures and the fluxes in the VLA calibrator manual for 3C147 and 3C295.308 We did several iterations of amplitude and phase self-calibration on each data set., We did several iterations of amplitude and phase self-calibration on each data set.309 Fig., Fig.310 3 shows the total intensity image which is a combination of the 4 IF images with an average frequency of 352 MHz., \ref{wsrt_mos} shows the total intensity image which is a combination of the 4 IF images with an average frequency of 352 MHz.311" In order to see the diffuse emission more clearly. we imaged the point sources by using only UV data 7 700 A. then subtracted their clean components out of the original UV data and reimaged the residuals at a resolution of 4x 2"". matching that of Kim et al. ("," In order to see the diffuse emission more clearly, we imaged the point sources by using only UV data $>$ 700 $\lambda$ , then subtracted their clean components out of the original UV data and reimaged the residuals at a resolution of $4^{\prime}\times2^{\prime}$ , matching that of Kim et al. ("3121989).,1989).313 Fig., Fig.314The coutribute of violin resonances is giveu by Sf) = bL fyc where we take into account the different masses of close and far muürrors. beiue C=3.22-10 Cy =2:82.10 O2 -Itruecun We need a pre-filterius of the low-frequency part of the spectrum. because the pendulum mode dominates the autocorrelation function.,"The contribute of violin resonances is given by S_v(f) = + f) where we take into account the different masses of close and far mirrors, being = n = n C_c = C_f = _n^2 = -1truecm We need a pre-filtering of the low-frequency part of the spectrum, because the pendulum mode dominates the autocorrelation function."315 If we used adaptive algorithius to find the parameters of our spectruni model in such a way to follow the slow uou stationarity of the noise. we would need a short learning tine for the algorithius.," If we used adaptive algorithms to find the parameters of our spectrum model in such a way to follow the slow non stationarity of the noise, we would need a short learning time for the algorithms."316 This is an impossible task if we analyze a noise characterized by a long autocorrelation time., This is an impossible task if we analyze a noise characterized by a long autocorrelation time.317quiescence.,quiescence.318 Iu coutrast. the highest liminosity observed roni wwith was oulv dos1075," In contrast, the highest luminosity observed from with was only $4 \times 10^{34}$."319 This huuimositv is well low those at which transient LAINBs are typically detected in outburst (e.e.Campanactal.1998)., This luminosity is well below those at which transient LMXBs are typically detected in outburst \citep[e.g.][]{cam98}.320. The ow luninositv is surprising iu the context of the disk-instability models that are typically used to explain he outbursts of LAINBs. which predict that the entire accretion. disk is be disrupted. leading to an outburst with Zx>10% citep|e.g..|[]yrO8..," The low luminosity is surprising in the context of the disk-instability models that are typically used to explain the outbursts of LMXBs, which predict that the entire accretion disk is be disrupted, leading to an outburst with $L_{\rm X} > 10^{37}$ \\citep[e.g.,][]{kr98}."321 However. three observational selection effects could contribute to the low peak hunuinositv of290031.," However, three observational selection effects could contribute to the low peak luminosity of."322. Fist. trausicut LAINBs have traditionally been identified with wide-field monitoring iustrunieuts that onlv have seusitivitics of >1019 citeplev96.jag97.. or 1076 lor the Galactic center distance.," First, transient LMXBs have traditionally been identified with wide-field monitoring instruments that only have sensitivities of $\ga 10^{-10}$ \\citep{lev96,jag97}, or $10^{36}$ for the Galactic center distance."323 There are few accreting black holes aud neutron stars within 2 kpe of Earth. so there is a strong selection effect against finding trausieuts this faint.," There are few accreting black holes and neutron stars within 2 kpc of Earth, so there is a strong selection effect against finding transients this faint."324 Second. oulv a few scusitive X-ray observatious of the Galactic ceuter have been obtained within the last vear. so we nav lave missed the peak of the outburst.," Second, only a few sensitive X-ray observations of the Galactic center have been obtained within the last year, so we may have missed the peak of the outburst."325 The first observation of the source in outburst was taken by in[η 2001 March (Bélangeretal.2005.D.Porquetal..in prep)..," The first observation of the source in outburst was taken by in 2004 March \citep[][D. Porquet \etal, in prep]{bel05}."326 They report that the source had a comparable DIuuiuositv to that at which we detected the source with jin 2001 July iud August., They report that the source had a comparable luminosity to that at which we detected the source with in 2004 July and August.327 In between time. the Ecplorer carvicd out scamming observations of the Galactic center with Proportional Counter Array (Alarkwardtetal.2002).," In between time, the carried out scanning observations of the Galactic center with Proportional Counter Array \citep{mar02}."328.. These allow us to put an upper limit of 3«1079 oon the intensity of the source during 2005., These allow us to put an upper limit of $3 \times 10^{36}$ on the intensity of the source during 2005.329 This upper limit is at the low end of the Iuniuosities of outbursts often scen frou LAINBs., This upper limit is at the low end of the luminosities of outbursts often seen from LMXBs.330 Finally. as mentioned above. we observe aaloug the plane of its binary orbit. so it is likely that the outer aceretion disk obscures most of the N-ray cluitting region.," Finally, as mentioned above, we observe along the plane of its binary orbit, so it is likely that the outer accretion disk obscures most of the X-ray emitting region."331 These facts motivate us to search for au independent constraint on the X-rav hmuuinositv of the transient outburst., These facts motivate us to search for an independent constraint on the X-ray luminosity of the transient outburst.332 Fortunately. the apparent detection of scattered X-ray cnussion from the transient outburst in Fieure d provides us with just such a constraint.," Fortunately, the apparent detection of scattered X-ray emission from the transient outburst in Figure \ref{fig:img} provides us with just such a constraint."333" The cuhancement in the diffuse X-ray emission is coincident with part of a well-dsnown ridge of dust aud ionized gas. referred to as the ""Minispiral, (Fig."," The enhancement in the diffuse X-ray emission is coincident with part of a well-known ridge of dust and ionized gas, referred to as the “Minispiral” (Fig."334 9. and S))., \ref{fig:midir} and \ref{fig:paalpha}) ).335" Although the brightening in diffuse N-ravs could represcut either scattered X-rays or a mechanical outflow shocking against the surrounding imterstellay inediun. the morphology and cnerectics of the observed XN-ravs makes the first mechauisu, appear more likely."," Although the brightening in diffuse X-rays could represent either scattered X-rays or a mechanical outflow shocking against the surrounding interstellar medium, the morphology and energetics of the observed X-rays makes the first mechanism appear more likely."336 First. the diffuse region is separated from the central source bv at least 1| Ποιος aud the outburst of started after June 2003. so anv material that mipacted the Miuispiral iust have been traveling faster than 0.36.," First, the diffuse region is separated from the central source by at least 4 light-months and the outburst of started after June 2003, so any material that impacted the Minispiral must have been traveling faster than $0.3c$."337 Second. if we interpret the brighteuiug of the diffuse X-rave as an increase in the deusitv of the emitting plasia. then the implied euergv input is AU=(An)kT~LO” eye (Table 3)).," Second, if we interpret the brightening of the diffuse X-rays as an increase in the density of the emitting plasma, then the implied energy input is $\Delta U = (\Delta n) kT \sim 10^{42}$ erg (Table \ref{tab:diff}) )."338 Therefore. the power required over six mouths is LO1.," Therefore, the power required over six months is $10^{35}$."339 Both of these conditions could be fulfilled by a radio jet (see81.2andBowerctal.2005)., Both of these conditions could be fulfilled by a radio jet \citep[see \S4.2 and][]{bow05}.340. However. the axis of the observed jet is oriented about ffrom the ceuter of the brightening ofthe diffuse emission.," However, the axis of the observed jet is oriented about from the center of the brightening of the diffuse emission."341" Moreover. the diffuse emission has an extent of z3"".. which is vastly more extended than the radio features."," Moreover, the diffuse emission has an extent of $\approx$, which is vastly more extended than the radio features."342 These facts ake it secur unlikely that the jet is responsible for the diffuse N-raw cussion., These facts make it seem unlikely that the jet is responsible for the diffuse X-ray emission.343 lustead. we propose that the enlianceinent in the diffuse enission is produced by. N-vavs from tthat are scattered by electrons in the Minispiral.," Instead, we propose that the enhancement in the diffuse emission is produced by X-rays from that are scattered by electrons in the Minispiral."344 The ionized gas from this ridge has been exteusivelv studied in radio continuum at 12 nuu (Zhao&Coss1905) and ὅσα (Lo&Claussen1983): livdrogen cluission from the W920 (3.6cmRoberts&Coss1993).. Pan (LSTjunScovilleetal.2003).. aud Drs; (2.16janPaunuardetal.2004)/ clectrouic transitions: and [Ne TI] cunission (12.5jaaLacy.Achteruniann.&Seri»u1991:Vollmer&Duschl 2000).," The ionized gas from this ridge has been extensively studied in radio continuum at 13 mm \citep{zg98} and 6cm \citep{lc83}; hydrogen emission from the $\alpha$ \citep[3.6 cm][]{rg93}, $\alpha$ \citep[1.87 $\mu$m][]{sco03}, and $\gamma$ \citep[2.16 $\mu$m][]{pau04} electronic transitions; and [Ne II] emission \citep[12.8 $\mu$m][]{las91,vd00}."345.. The ridge is obviously more extended than the brighteuiug of the diffuse emission (Fie. 8)).," The ridge is obviously more extended than the brightening of the diffuse emission (Fig. \ref{fig:paalpha}) ),"346 which raises the question of why only a small fraction of it has been ilbuuinated., which raises the question of why only a small fraction of it has been illuminated.347 Careful studies of the velocity of the gas in the Minispiral have indicated that it is composed of several kinematic features (Vollmer&Duschl2000.Patmard.Maillard.&Morris 2001)..," Careful studies of the velocity of the gas in the Minispiral have indicated that it is composed of several kinematic features \citep[][Paumard, Maillard, \& Morris 2004]{vd00}."348 Although the complexity of the region precludes any conclusive associations. the eunliancemenut in N-ray flux is coincident witli a section of the “Northern Arii that has a hieh velocity toward us (200Jans rsee2001).," Although the complexity of the region precludes any conclusive associations, the enhancement in X-ray flux is coincident with a section of the “Northern Arm” that has a high velocity toward us \citep[200 km s$^{-}$ ;."349 We suggest that this is the ouly region that has brightened because it is closest to 290031., We suggest that this is the only region that has brightened because it is closest to .350 The scattered flux (PS) associated with the outburst of ddepenuds ou the Iuuimositv (Lx) aud distance (D) of the source. the solid angle (Q) aud optical depth (7) of the scattering region. aud the angle (0) through which photons are scattered: The function f(0) depends on the scattering process: for Thompson scattering f(0)=(.75(1|cos? A).," The scattered flux $F_{\rm scat}$ ) associated with the outburst of depends on the luminosity $L_{\rm X}$ ) and distance $D$ ) of the source, the solid angle $\Omega$ ) and optical depth $\tau$ ) of the scattering region, and the angle $\theta$ ) through which photons are scattered: The function $f(\theta)$ depends on the scattering process; for Thompson scattering $f(\theta) = 0.75(1+\cos^2\theta)$ ."351 The solid angle O depends ou the distance between the source and the scattering region. aud the size of the scatterer.," The solid angle $\Omega$ depends on the distance between the source and the scattering region, and the size of the scatterer."352" The projected separation between the two is z2"".. πο if 0 isthe angle between our line of sight aud the line connecting the source aud the scatterer. the true distance isdσε(μπι).5 pe."," The projected separation between the two is $\approx$, so if $\theta$ isthe angle between our line of sight and the line connecting the source and the scatterer, the true distance is $d \approx 0.1 (\sin\theta)^{-1}$ pc."353 The brightening of the diffuse flux is contained ina roughly elliptical region no larecr thu 1766. so we estimate that theprojected area of the scatteringregion with respect to the source is 4X pc?. ," The brightening of the diffuse flux is contained in a roughly elliptical region no larger than $\times$ 6, so we estimate that theprojected area of the scatteringregion with respect to the source is $A \la 0.02$ $^{2}$."354Therefore. the solid anele of the scatterer is Ofla=Af(lid?)©0.2sin? 0.," Therefore, the solid angle of the scatterer is $\Omega/4\pi = A/(4\pi d^2) \approx 0.2 \sin^2\theta$ ."355 The scattering is 1nost likely caused by The electron density in the region of chhanced diffuse X-ray, The scattering is most likely caused by The electron density in the region of enhanced diffuse X-ray356turn similar.,turn similar.357 In Table 2.. the intrinsic dispersion is determined by assuming that the reduced chi-squared is unity.," In Table \ref{tab:sn4}, the intrinsic dispersion is determined by assuming that the reduced chi-squared is unity."358 The value of the intrinsic dispersion required to renormalize the reducec v of the EdS model to unity is here again much larger thar those required for the other two models., The value of the intrinsic dispersion required to renormalize the reduced $\chi^2$ of the EdS model to unity is here again much larger than those required for the other two models.359 The conclusion of this first analysis is twofold., The conclusion of this first analysis is twofold.360 First. we confirm that the decelerating Einstein-de Sitter model is extremely unlikely. which should come as no surprise.," First, we confirm that the decelerating Einstein-de Sitter model is extremely unlikely, which should come as no surprise."361 Second. the Dirac-Milne and the flat ACDM models are almost identical. Dirac-Milne being in ever closer agreement with the data than the flat ACDM model.," Second, the Dirac-Milne and the flat $\Lambda$ CDM models are almost identical, Dirac-Milne being in even closer agreement with the data than the flat $\Lambda$ CDM model."362 Our analysis stresses that all SNe Ia analysis depend strongly on the use of low-z data to anchor the Hubble diagram., Our analysis stresses that all SNe Ia analysis depend strongly on the use of low-z data to anchor the Hubble diagram.363 Similarly. we proceeded with our analysis of the full data sample used by SNLS in its one-year analysis. re. using an heterogeneous sample of low-z SNe Ia. Our results are given in4.," Similarly, we proceeded with our analysis of the full data sample used by SNLS in its one-year analysis, i.e. using an heterogeneous sample of $z$ SNe Ia. Our results are given in."364. In this case. as expected. the flat ACDM provides a closer fit to the data than the Dirac-Milne universe.," In this case, as expected, the flat $\Lambda$ CDM provides a closer fit to the data than the Dirac-Milne universe."365 In Fig. 9..," In Fig. \ref{res_sn},"366 we present the residuals of the Hubble diagram for the Dirac-Milne. the flat ACDM. and Einstein-de Sitter models.," we present the residuals of the Hubble diagram for the Dirac-Milne, the flat $\Lambda$ CDM, and Einstein-de Sitter models."367 The left-hand column represents the residuals when the value of the intrinsic dispersion was adjusted to normalize the y to | per degree of freedom., The left-hand column represents the residuals when the value of the intrinsic dispersion was adjusted to normalize the $\chi^2$ to 1 per degree of freedom.368 In the right-hand column.," In the right-hand column,"369The results for TR 5138 aud UR 5717 were arrived at after 350 iterations.,The results for HR 5138 and HR 5747 were arrived at after 350 iterations.370 Since the iuteusitv of the stars were different. the value of the Weiner filter paralcters also had to be chosen accordingly.," Since the intensity of the stars were different, the value of the Weiner filter parameters also had to be chosen accordingly."371 Figures l(a). 105). ο) show the speckle tage. PSF. aud deconvolved tuage of IIR. 5138 respectively.," Figures 1(a), 1(b), 1(c) show the speckle image, PSF, and deconvolved image of HR 5138 respectively."372 Figures 2(a). 20). 2(c) are for IIR 5717 respectively.," Figures 2(a), 2(b), 2(c) are for HR 5747 respectively."373 The companions of IIR 5138 aud IIR 5717 are separated by and aresecouds respectively., The companions of HR 5138 and HR 5747 are separated by and arcseconds respectively.374 Measureimoeuts of position angle (235 aud 110 degrees for TR 5138 aud UR 5717 respectively) and separation were compatible with the values published iu the CIARA catalogue (AcAlister aud Hartkopf. 1988).," Measurements of position angle (235 and 110 degrees for HR 5138 and HR 5747 respectively) and separation were compatible with the values published in the CHARA catalogue (McAlister and Hartkopf, 1988)."375 Torch (1991). too found similay results.," Horch (1994), too found similar results."376 The magnitude difference for the reconstructed objects were 0.01 aud 1.65 respectively for IIR 5138 aud IIR 5717., The magnitude difference for the reconstructed objects were 0.04 and 1.65 respectively for HR 5138 and HR 5747.377 Although these values compare quite well with those published iu the Bright Star Catalogue (Wofieit aud Jaschek. 1982) one needs to treat many more objects before oue can characterise the photometric quality of the recoustructions.," Although these values compare quite well with those published in the Bright Star Catalogue (Hoffleit and Jaschek, 1982) one needs to treat many more objects before one can characterise the photometric quality of the reconstructions."378 The preseut scheme of DID has the chief problem of convergence., The present scheme of BID has the chief problem of convergence.379 It is indeed an art to decide when to stop the iterations., It is indeed an art to decide when to stop the iterations.380 The results are also vulnerable o the choice of various parameters like the support radius. the level of high yequency suppression duriug the Wiener filtering. ete.," The results are also vulnerable to the choice of various parameters like the support radius, the level of high frequency suppression during the Wiener filtering, etc."381 The availability of prior shnowledge on the object through autocorrelation of the degraded image was ound to be very useful for specifving the object support radius., The availability of prior knowledge on the object through autocorrelation of the degraded image was found to be very useful for specifying the object support radius.382 Iu spite of this care taken in the choice of the support radius. the pst for each star contaius residual signatures of the binary sources.," In spite of this care taken in the choice of the support radius, the psf for each star contains residual signatures of the binary sources."383 Although sugeestions have been iade or iuproviue the convergence JJefferies aud Christou. 1993). these improved algorithius require more than a single speckle frame.," Although suggestions have been made for improving the convergence Jefferies and Christou, 1993), these improved algorithms require more than a single speckle frame."384 For the present. it is noteworthy that useful reconstructious are possible using sinele speckle frames.," For the present, it is noteworthy that useful reconstructions are possible using single speckle frames."385 Questions regarding their dvuamic range and linearity can be answered onlv after cxamiuing a wide range of reconstructions., Questions regarding their dynamic range and linearity can be answered only after examining a wide range of reconstructions.386 The iterative nature of the algorithm does uot lend to an explicit estimation of these paralucters from a limited sample., The iterative nature of the algorithm does not lend to an explicit estimation of these parameters from a limited sample.387 New developiuents iu camera electronics promise the capability to acquire several images within a short time., New developments in camera electronics promise the capability to acquire several images within a short time.388 This will also reduce the level of artifacts., This will also reduce the level of artifacts.389 The chief achievement in this paper is a demonstration of the scieutific potential of DID for resolving bright objects acquired using simple apparatus., The chief achievement in this paper is a demonstration of the scientific potential of BID for resolving bright objects acquired using simple apparatus.390 The authors are grateful to Dr. P. Niseusou of Ceuter for Astroplivsics. Cambridge. USA. for the BID code as well as for useful discussions.," The authors are grateful to Dr. P. Nisenson of Center for Astrophysics, Cambridge, USA, for the BID code as well as for useful discussions."391Collinder 110 is a poorly populated cluster. even less studied (han Trumpler 5.,"Collinder 110 is a poorly populated cluster, even less studied than Trumpler 5."392 Only two photometric studies can be found in the literature for the last (ηχου decades., Only two photometric studies can be found in the literature for the last three decades.393 Using synthetic colourmagnitude diagrams. Bragaglia&Tosi(2003) have estimated a recddening of 0.38 «E(DB—V)<0.45 and distance modulus (n-M)4 between 11.3 and 11.9.," Using synthetic colour–magnitude diagrams, \citet{bragagliatosi03} have estimated a reddening of 0.38 $\leq E(B-V) \leq 0.45$ and distance modulus $_0$ between 11.8 and 11.9."394 From these values thev derived an age between 1.1 and 1.5 Gyr., From these values they derived an age between 1.1 and 1.5 Gyr.395 Similar values were found by (1993)., Similar values were found by \citet{dawson98}.396. There are no metallicity determinations for this cluster in the literature., There are no metallicity determinations for this cluster in the literature.397 tried to derive the metallicity of this cluster [rom different stellar evolution models. but concluded Chat the final result vary. wiclely depending on Cie mocels.," \citet{bragagliatosi03} tried to derive the metallicity of this cluster from different stellar evolution models, but concluded that the final result vary widely depending on the models."398 The metallicity derived. from Equation 5. is |Fe/I]ecsz = —0.01+0.07., The metallicity derived from Equation \ref{cg97i} is $_{CG97}$ = $-0.01 \pm 0.07$.399 If. we use Equations 7a and 8b. on INI03 and ZW84 metallicity scales we find y75; = —0.192£0.21 and [Fe/H]zis; = 0.00 = 0.30., If we use Equations \ref{ki03im} and \ref{zw84i} on KI03 and ZW84 metallicity scales we find $_{KI03}$ = $-0.19 \pm 0.21$ and $_{ZW84}$ = 0.00 $\pm$ 0.30.400" From our data we can also provide the first determination of ils radial velocity. V, = 45 x 8 km 1"," From our data we can also provide the first determination of its radial velocity, $_r$ = 45 $\pm$ 8 km $^{-1}$."401 We have observed the CaT lines in RGB stars in a sample of 29 clusters of the Milky Wav., We have observed the CaT lines in RGB stars in a sample of 29 clusters of the Milky Way.402 This sample covers an age range of (13 € Age/Gvr € 0.25) ancl metallicity range of (—2.2€ |Fe/I] < +047)., This sample covers an age range of (13 $\leq$ Age/Gyr $\leq$ 0.25) and metallicity range of $-2.2\leq$ [Fe/H] $\leq$ +0.47).403 These are the widest ranges of ages and metallicities in which the behaviour of the CaT has been investigated in a homogeneous way until now., These are the widest ranges of ages and metallicities in which the behaviour of the CaT has been investigated in a homogeneous way until now.404 We have obtained relationships between (he CaT equivalent widths and metallicities on (he scales of Zinn&West(1984).. Carretta&Gratton(1997). and Ixraft&Ives(2003).," We have obtained relationships between the CaT equivalent widths and metallicities on the scales of \citet{zw84}, \citet{cg97} and \citet{ki03}."405. The influence of other parameters. such as age and [Ca/Fe] ratio. has been investigated.," The influence of other parameters, such as age and [Ca/Fe] ratio, has been investigated."406 Moreover. for the first time. the behaviour of the CaT lines as a fincetion of Iuminositv along the RGB has been studied for the whole range of metalliciGes in our sample.," Moreover, for the first time, the behaviour of the CaT lines as a function of luminosity along the RGB has been studied for the whole range of metallicities in our sample."407 The main results of this work are:, The main results of this work are:408llere we report preliminary statistical analysis for Cae observed sample.,Here we report preliminary statistical analysis for the observed sample.409" More detailed analvsis and conclusions will be presented after completion of the full survey with all 532 galaxies,", More detailed analysis and conclusions will be presented after completion of the full survey with all 582 galaxies.410 Figure 5 (fop) shows the well established radioFIR correlation through a logarithmic plot of the 1.4 GlIlz continuum huninosities versus (he FIR. luminosities for the galaxies in our sample., Figure 5 ) shows the well established radio–FIR correlation through a logarithmic plot of the 1.4 GHz continuum luminosities versus the FIR luminosities for the galaxies in our sample.411 The derived correlation coefficient is88%., The derived correlation coefficient is.412.. Figure 5 (boltom) shows a logarithmic plot of the 1.4 GlIz continuum Iuminosities versus the total I. luminosities., Figure 5 ) shows a logarithmic plot of the 1.4 GHz continuum luminosities versus the total IR luminosities.413 The correlatioΕν coeíficient here is8914., The correlation coefficient here is.414.. This remarkably tight linear correlation between the (otal radio continuum emission and the IR. (or FIR) luminosities is well known for “normal” galaxies where the main enereyv source is not due (ο a supermassive black hole (Condon1992)., This remarkably tight linear correlation between the total radio continuum emission and the IR (or FIR) luminosities is well known for “normal” galaxies where the main energy source is not due to a supermassive black hole \citep{CON92}.415. The most obvious interpretation of this correlation is (he presence of massive stars that provide both relativistic parücles via subsequent supernova events. aud heat the interstellar dust which radiates al IR (or FIR) wavelengths (Helou.Soifer&Rowan-Robinson1935:Condon 1992).," The most obvious interpretation of this correlation is the presence of massive stars that provide both relativistic particles via subsequent supernova events, and heat the interstellar dust which radiates at IR (or FIR) wavelengths \citep{HSR85,WK88,CON92}."416. Fieure 6 shows logarithmic plots of the mass versus the FIR (/op) ancl IR. (bot/eim) luminosities Lor the observed sample., Figure 6 shows logarithmic plots of the mass versus the FIR ) and IR ) luminosities for the observed sample.417 Both plots show extremely weak correlations wilh coeíficients of in each., Both plots show extremely weak correlations with coefficients of in each.418 Figure 7 shows a logarithmic plot of the mass versus the 1.4 GlIIz radio luminosity., Figure 7 shows a logarithmic plot of the mass versus the 1.4 GHz radio luminosity.419 The correlation coellicient here is53%., The correlation coefficient here is.420. These plots suggest that the total neutral eas content and star formation activily traced through the radio luminosities or the IR luminosities are only weakly correlated for (his sample., These plots suggest that the total neutral gas content and star formation activity traced through the radio luminosities or the IR luminosities are only weakly correlated for this sample.421 This is consistent with the scenario that atomic gas has first to be converted into molecular gas (ο form stars. and that the molecular gas content itself correlates well with star formation (Wong&Blitz2002).," This is consistent with the scenario that atomic gas has first to be converted into molecular gas to form stars, and that the molecular gas content itself correlates well with star formation \citep{WB02}."422. In Table 7. we present the mean and median mass values of galaxies with 21 cm enission as a function of total-IB. luminosity bins.," In Table 7, we present the mean and median mass values of galaxies with 21 cm emission as a function of total-IR luminosity bins."423 The numbers reflect a general trend of higher mass values at higher I. luminosities. consistent with the weak correlation seen in Figure6-5bo!lom.," The numbers reflect a general trend of higher mass values at higher IR luminosities, consistent with the weak correlation seen in Figure."424 We utilize the values presented in Chis table in our notes on individual objects in 36., We utilize the values presented in this table in our notes on individual objects in 6.425 In our observed sample. several galaxies show either absorption or both emission and absorption.," In our observed sample, several galaxies show either absorption or both emission and absorption."426" Binnine the sample in Ly, (Table δα) reveals that sources with higher Ih luminosities have the greater likelihood of showing absorption.", Binning the sample in $L_{\rm IR}$ (Table 8a) reveals that sources with higher IR luminosities have the greater likelihood of showing absorption.427" For instance. of the sources with Ly;>10H""L. show"," For instance, of the sources with $L_{\rm IR} \geq 10^{11.50}~L_{\odot}$ show"428distributions that are uncorrelated with cluster. position going into the stellar dominated phase result in mass spectra olsz2 whereas those that are mass segregated initially will have slightly steeper mass spectra ον2.5.,distributions that are uncorrelated with cluster position going into the stellar dominated phase result in mass spectra of $\gamma \approx -2$ whereas those that are mass segregated initially will have slightly steeper mass spectra $\gamma \approx -2.5$.429 ]t is important to note that the above derivation relies upon all the stars stopping their aceretion at. the same time. as the final masses are a strong function of the time (equation 28)).," It is important to note that the above derivation relies upon all the stars stopping their accretion at the same time, as the final masses are a strong function of the time (equation \ref{maccbhsol}) )."430 This should not be too strong a limitation as in the stellar dominated potential the accretion timescale must be much longer than the local crossing time as Maus<<Alias., This should not be too strong a limitation as in the stellar dominated potential the accretion timescale must be much longer than the local crossing time as $\mgas << \mstars$.431 In a rich voung stellar cluster. gas removal is due to the presence of massive stars.," In a rich young stellar cluster, gas removal is due to the presence of massive stars."432 These stars ionise the gas such that the sound speed (2210. km/s) is comparable to or greater than the velocity dispersion., These stars ionise the gas such that the sound speed $\approx 10$ km/s) is comparable to or greater than the velocity dispersion.433 Thus the eas should be removed on a timescale shorter than or comparable to the crossing time. and all the stars in the core should stop accreting quasi-simultancously.," Thus the gas should be removed on a timescale shorter than or comparable to the crossing time, and all the stars in the core should stop accreting quasi-simultaneously."434 H this is not the case. then the resulting mass spectrum will exhibit a local niàximunm. corresponding to stars that are just outside the cleared region.," If this is not the case, then the resulting mass spectrum will exhibit a local maximum corresponding to stars that are just outside the cleared region."435 In summary. we expect that the combination of a gas dominated and a stellar dominated regimes and the dilferent accretion physics operating in each. results in à two power-law LME.," In summary, we expect that the combination of a gas dominated and a stellar dominated regimes and the different accretion physics operating in each, results in a two power-law IMF."436 The lower-mass stars have a shallower (5=— 1.5) slope as their mass accumulation is dominated by tidal-Lobe accretion wheras the higher mass stars have a steeper (2> 2.5) slope as their mass accumulation is dominated by Aondi-IHlovlIe accretion in the stellar dominated core., The lower-mass stars have a shallower $\gamma \approx -1.5$ ) slope as their mass accumulation is dominated by tidal-lobe accretion wheras the higher mass stars have a steeper $-2 \ge \gamma\simless -2.5$ ) slope as their mass accumulation is dominated by Bondi-Hoyle accretion in the stellar dominated core.437 In order to explore the relevance of the asymptotic limits for the mass spectrum. we performed a number of simulations of accretion onto a cluster of 1000 stars.," In order to explore the relevance of the asymptotic limits for the mass spectrum, we performed a number of simulations of accretion onto a cluster of 1000 stars."438 The stars are initially of equal. mass (0.137.) anc are embedded: in gas which comprises 91 per cent of the total cluster mass The gas is cold such that it contains 1000 Jeans masses. where p is the gas density. Z/ is the gas temperature. Ly is the gas constant. G is the gravitational constant. and fois the mean molecular weight.," The stars are initially of equal mass $0.1 \solm$ ) and are embedded in gas which comprises 91 per cent of the total cluster mass The gas is cold such that it contains 1000 Jeans masses, where $\rho$ is the gas density, $T$ is the gas temperature, $R_g$ is the gas constant, $G$ is the gravitational constant, and $\mu$ is the mean molecular weight."439 The simulations were performed with a hybricl N-body SPL code (Bate. Bonnell Price 1995) which uses standard SPL particles to model the gas and sink-particles to nioclel the stars (for more details see also Bonnell 2000).," The simulations were performed with a hybrid N-body SPH code (Bate, Bonnell Price 1995) which uses standard SPH particles to model the gas and sink-particles to model the stars (for more details see also Bonnell 2000)."440 Phese sink-particles interact only eravitationally with the rest of the cluster and by accreting gas particles that come within their sink radius., These sink-particles interact only gravitationally with the rest of the cluster and by accreting gas particles that come within their sink radius.441 This sink or accretion radius was taken to be the smaller of the tidal-Iobe radius. the Boncli-Llovle radius or the stellar separation.," This sink or accretion radius was taken to be the smaller of the tidal-lobe radius, the Bondi-Hoyle radius or the stellar separation."442 In addition. gas particles can only be accreted if they are bound to the star.," In addition, gas particles can only be accreted if they are bound to the star."443 The simulations were performed with either 9000 or 90000 SPL particles., The simulations were performed with either 9000 or 90000 SPH particles.444 Phe low-resolution simulations resulted. in an excess of stars in the lowest (initial) mass bins as they were not able to resolve the low accretion rates involved., The low-resolution simulations resulted in an excess of stars in the lowest (initial) mass bins as they were not able to resolve the low accretion rates involved.445 The higher-resolution. simulations resolved the accretion onto all stars and both low and high-resolution simulations resulted in similar high-mass mass-spectra., The higher-resolution simulations resolved the accretion onto all stars and both low and high-resolution simulations resulted in similar high-mass mass-spectra.446 Both the stellar ancl eas distribution. are initially uniform but collapse down towards a centrally condensed clistribution., Both the stellar and gas distribution are initially uniform but collapse down towards a centrally condensed distribution.447 Gas is accreted by the stars and removed from the simulation., Gas is accreted by the stars and removed from the simulation.448 As the eas is aceretec preferentially near the centre once a power-law density profile is established (pxH 7) the stars soon dominate the potential there.," As the gas is accreted preferentially near the centre once a power-law density profile is established $\rho\propto R^{-2}$ ), the stars soon dominate the potential there."449 The gas must then infall from further out in the cluster., The gas must then infall from further out in the cluster.450 The simulations result. in mass spectra that are broadly consistent with our analytical expectations., The simulations result in mass spectra that are broadly consistent with our analytical expectations.451 The low-mass stars that accrete their mass during the gas dominated phase display shallow (ο= 3/2) mass spectra whereas the hieh-miss stars that accrete the majority of their mass during the stellar dominated. phase displav steeper 2.5£55x— 2) mass spectra., The low-mass stars that accrete their mass during the gas dominated phase display shallow $\gamma \approx -3/2$ ) mass spectra whereas the high-mass stars that accrete the majority of their mass during the stellar dominated phase display steeper $-2.5 \simless\gamma \le -2$ ) mass spectra.452 As the clusters are initially uniform ancl cold. only the enc of the simulations develop a power-law density profile ancl that just before entering the stellar dominated regime.," As the clusters are initially uniform and cold, only the end of the simulations develop a power-law density profile and that just before entering the stellar dominated regime."453 Because of this. the expected. low-mass mass spectrum does not extend over a large mass range.," Because of this, the expected low-mass mass spectrum does not extend over a large mass range."454 In Figure 3.. we plot the resultant mass function for one of the higher resolution simulations. (performed. with 90000 SPILL particles) at three dillerent. times during the evolution.," In Figure \ref{simimf}, we plot the resultant mass function for one of the higher resolution simulations, (performed with 90000 SPH particles) at three different times during the evolution."455 Phe mass spectrum increases in breadth with time and develops into a power-law for the high-mass stars., The mass spectrum increases in breadth with time and develops into a power-law for the high-mass stars.456 The low-mass mass spectrum. is broadly consistent with tidal-lobe accretion in a mostly uniform cloud. although only over a small range in mass.," The low-mass mass spectrum is broadly consistent with tidal-lobe accretion in a mostly uniform cloud, although only over a small range in mass."457 Due to the uniform initial conditions. only a fraction of the stars experience the power-law density prolile before entering. the stcllar-dominated phase.," Due to the uniform initial conditions, only a fraction of the stars experience the power-law density profile before entering the stellar-dominated phase."458 This region would extend further in mass if the cluster was initially centrally condensed when accretion begins., This region would extend further in mass if the cluster was initially centrally condensed when accretion begins.459 At later, At later460models.,models.461 The same behaviour can be observed for other Lagrangian radii and 10%))., The same behaviour can be observed for other Lagrangian radii and ).462 The reason for such a behaviour is unclear and can be attributed to different mutual strengths of the physical processes which operate during the different phases of cluster evolution., The reason for such a behaviour is unclear and can be attributed to different mutual strengths of the physical processes which operate during the different phases of cluster evolution.463 Faster mass segregation in N-body than in MOCCA can generate more extended cluster., Faster mass segregation in N-body than in MOCCA can generate more extended cluster.464" Stellar evolution responsible for the loss of stellar mass can substantially blow up the cluster, particularly at the initial phases of evolution."," Stellar evolution responsible for the loss of stellar mass can substantially blow up the cluster, particularly at the initial phases of evolution."465" Both N-body and MOCCA models relay on the same stellar evolution prescription (Hurley,Pols,&Tout2000;Hurley,Tout,Pols2002),, so we cannot expect that the amount of mass loss is different in both models."," Both N-body and MOCCA models relay on the same stellar evolution prescription \citep[][]{Hu2000,Hu2002}, so we cannot expect that the amount of mass loss is different in both models."466" However, the mass segregation acting together with the stellar mass loss can substantially amplify the expansion effect."," However, the mass segregation acting together with the stellar mass loss can substantially amplify the expansion effect."467 If the most massive stars lose their envelopes when they are already mass segregated the effect on cluster expansion is largest., If the most massive stars lose their envelopes when they are already mass segregated the effect on cluster expansion is largest.468" Finally, the larger binary energy generation in N-body simulations (see Fig.13 - increase of the total binary binding energy) can be responsible for faster Lagrangian radii expansion."," Finally, the larger binary energy generation in N-body simulations (see \ref{fig:ebin} - increase of the total binary binding energy) can be responsible for faster Lagrangian radii expansion."469 The evolution of the average mass inside Lagrangian radius and evolution of the total binary binding energy for N=200000 are shown on Figs.12 and 13.., The evolution of the average mass inside Lagrangian radius and evolution of the total binary binding energy for $N=200000$ are shown on \ref{fig:am50} and \ref{fig:ebin}.470 These figures are representative for all models and Lagrangian radii., These figures are representative for all models and Lagrangian radii.471" Indeed, it seems that the mass segregation is slightly stronger in N-body than in MOCCA."," Indeed, it seems that the mass segregation is slightly stronger in N-body than in MOCCA."472" This suggests that the larger mass segregation in N-body model can be responsible, at least partially, for the slightly discrepant evolution of the Lagrangian radii."," This suggests that the larger mass segregation in N-body model can be responsible, at least partially, for the slightly discrepant evolution of the Lagrangian radii."473" The evolution of the total binary binding energy, is from the very beginning rather similar, until later time (about 4 Gyr), when more bound binaries are formed in N-body."," The evolution of the total binary binding energy, is from the very beginning rather similar, until later time (about 4 Gyr), when more bound binaries are formed in N-body."474" The final formation of very hard binary is visible in MOCCA and N-body (see discussion in Sec.??)), but not for MOCCA-NoFB."," The final formation of very hard binary is visible in MOCCA and N-body (see discussion in \ref{sec:binary}) ), but not for MOCCA-NoFB."475" When binary is removed from the system, because of interactions, all models again are similar."," When binary is removed from the system, because of interactions, all models again are similar."476 It is worth to note that the results of simulations for MOCCA and NoFB are very similar until the late phases of evolution., It is worth to note that the results of simulations for MOCCA and MOCCA-NoFB are very similar until the late phases of evolution.477 The evolution of the number of binaries was already presented in Sec.?? during discussion about the determination of the free model parameters., The evolution of the number of binaries was already presented in \ref{sec:free} during discussion about the determination of the free model parameters.478 We know that the evolution of the total number of binaries is slightly too slow for MOCCA., We know that the evolution of the total number of binaries is slightly too slow for MOCCA.479 The difference starts to buildup at the time when stellar evolution becomes less and less important (see Fig.6))., The difference starts to buildup at the time when stellar evolution becomes less and less important (see \ref{fig:Nb-rp-100k}) ).480 The average binary mass and the binding energy distributions will be discussed for model N=200000., The average binary mass and the binding energy distributions will be discussed for model $N=200000$.481 The results for this model are representative for other models and additionally shows buildup of the average binary mass and binding energy for massive binaries., The results for this model are representative for other models and additionally shows buildup of the average binary mass and binding energy for massive binaries.482" This buildup is possible only for the model N=200000 for which the distribution of supernova (SN) kicks is uniform between 0 and 100 km/s and lets larger, than in other models (Maxwellian distribution with σ=190km/s for SN kicks), fraction of BHs to be bound to the system."," This buildup is possible only for the model $N=200000$ for which the distribution of supernova (SN) kicks is uniform between $0$ and $100$ km/s and lets larger, than in other models (Maxwellian distribution with $\sigma=190 km/s$ for SN kicks), fraction of BHs to be bound to the system."483" The evolution of the average binary mass for different regions of the system is shown in Figs.14,, 15 and 16.."," The evolution of the average binary mass for different regions of the system is shown in \ref{fig:Mbin_50_t}, \ref{fig:Mbin_10_50} and \ref{fig:Mbin_0_rc}."484 The agreement between N-body and MOCCA results is very good in all regions., The agreement between N-body and MOCCA results is very good in all regions.485" This is despite the fact, that in N-body there is a smaller number of binaries than in MOCCA and Lagrangian radii are slightly different."," This is despite the fact, that in N-body there is a smaller number of binaries than in MOCCA and Lagrangian radii are slightly different."486" It seems that the average binary mass and its distribution does not depend on the number of binaries, which is probably a result of exactly the same binary initial conditions for the both models and similar mass spectrum of removed or destroyed binaries in the models."," It seems that the average binary mass and its distribution does not depend on the number of binaries, which is probably a result of exactly the same binary initial conditions for the both models and similar mass spectrum of removed or destroyed binaries in the models."487" For the region inside the core, the buildup of the mass of binaries is clearly visible."," For the region inside the core, the buildup of the mass of binaries is clearly visible."488" The big fluctuations are connected with the movement of the massive binaries, which because of hard interactions with other stars are kicked out from the core and then because of mass segregation sink again to the centre."," The big fluctuations are connected with the movement of the massive binaries, which because of hard interactions with other stars are kicked out from the core and then because of mass segregation sink again to the centre."489" Finally, they are kicked out of the system and the average mass of binaries starts to become less chaotic and its changes are rather small."," Finally, they are kicked out of the system and the average mass of binaries starts to become less chaotic and its changes are rather small."490 The drop and then increase of the average mass around 14.5Gyr is connected with the core collapse., The drop and then increase of the average mass around 14.5Gyr is connected with the core collapse.491 The high central density makes binary-binary interactions very effective and substantial number of relatively wide and massive binaries are destroyed causing drop of the binary average mass., The high central density makes binary-binary interactions very effective and substantial number of relatively wide and massive binaries are destroyed causing drop of the binary average mass.492 Looking on the average masses in the different cluster regions the mass segregation is clearly visible., Looking on the average masses in the different cluster regions the mass segregation is clearly visible.493 In the centre the mass is about twice as large as in the halo., In the centre the mass is about twice as large as in the halo.494" For the N—200000 model the difference between MOCCA and MOCCA-NOoFB is very small, except in the core when the increase of the average mass is less pronounced for MOCCA-NoFB."," For the $N=200000$ model the difference between MOCCA and MOCCA-NoFB is very small, except in the core when the increase of the average mass is less pronounced for MOCCA-NoFB."495" The sharp increase of the average mass, close to the cluster dissolution time, is connected with the fact that only the most massive binaries"," The sharp increase of the average mass, close to the cluster dissolution time, is connected with the fact that only the most massive binaries"496Ixolpak. M. À.. Jackson. J.M.. Dania. T.M.. ancl Dickey. JAI. 2002. Ap.,"Kolpak, M. A., Jackson, J.M., Bania, T.M., and Dickey, J.M., 2002, Ap."497 J. in, J. in498molecular clouds then produces the luminositw observed rom non-nuclear point sources in other galaxies.,molecular clouds then produces the luminosity observed from non-nuclear point sources in other galaxies.499 Such Mack holes. acereting at less than the Eddington limit. can νοποσο the observed Dux without strong beaming.," Such black holes, accreting at less than the Eddington limit, can produce the observed flux without strong beaming."500 hing et al. (, King et al. (5012001) have proposed instead that the black roles ave of ordinary. stellar mass but are strongly. beanie.,2001) have proposed instead that the black holes are of ordinary stellar mass but are strongly beamed.502 They argue that larger black holes would have cilliculty in »oducing the required high-energy X-rays if the emission is rom blackbocly annuli in the disk. because the characteristic ασκος temperature for an Eddington accretor near the inner edge of the disk is AT220MM.)E! keV. However. we point out that if a hot Compton corona exists. near he black hole. as is usually invoked to explain the highest energy emission. the temperature scales as Ar and is thus independent of mass. so unless the spectrum is clearly of the multicolour blackbody form and has no nonthermal tail the A-ray spectrum does not easily clistinguish between beanie: and unbeaniecl emission.," They argue that larger black holes would have difficulty in producing the required high-energy X-rays if the emission is from blackbody annuli in the disk, because the characteristic blackbody temperature for an Eddington accretor near the inner edge of the disk is $kT\approx 2(M/M_\odot)^{-1/4}$ keV. However, we point out that if a hot Compton corona exists near the black hole, as is usually invoked to explain the highest energy emission, the temperature scales as $M/r$ and is thus independent of mass, so unless the spectrum is clearly of the multicolour blackbody form and has no nonthermal tail the X-ray spectrum does not easily distinguish between beamed and unbeamed emission."503 For example. we note that. the Galactic microquasars GRS 1915|105 and GRO 1655-40 have significantly harder emission than would be expectec from a simple multicolour. blackbocky (Alakishima et al.," For example, we note that the Galactic microquasars GRS 1915+105 and GRO J1655-40 have significantly harder emission than would be expected from a simple multicolour blackbody (Makishima et al."504 2000)., 2000).505 We also point out that blazars. which are believer to have emission beamed towards us. tend to have relatively Hat vi) spectra. varving typically by only a factor 10 from Lot?107 Ly (up to an X-ray to radio ratio of 0 for some Einstein Slew Survey blazars: see Fossati e al.," We also point out that blazars, which are believed to have emission beamed towards us, tend to have relatively flat $\nu F_\nu$ spectra, varying typically by only a factor $\sim 10$ from $10^{10}-10^{18}$ Hz (up to an X-ray to radio ratio of $10^3$ for some Einstein Slew Survey blazars; see Fossati et al."506 1998)., 1998).507 In. contrast. the N-ray to radio vi. ratio lor Galactic microquasars. which are not. beamed us. is much &reater: 1O° for GRS 1915|105 oev et al.," In contrast, the X-ray to radio $\nu F_\nu$ ratio for Galactic microquasars, which are not beamed towards us, is much greater; $10^6$ for GRS 1915+105 (Ogley et al."508 MNm2000 for radio: Rao et al., 2000 for radio; Rao et al.509 2000 for X-rav) and1 nfor GRO 655- (Llannikainen et al., 2000 for X-ray) and $10^5$ for GRO J1655-40 (Hannikainen et al.5102000 for radio: et al., 2000 for radio; Zhang et al.511 1997 [or X-ray)., 1997 for X-ray).512 These latter sources are comparable to the brightest X-ray source in MS2. which has an T to racio ratio of at least 107.(see Matsumoto et isl," These latter sources are comparable to the brightest X-ray source in M82, which has an X-ray to radio ratio of at least $10^5$ (see Matsumoto et al."513 and Exronberg et al., 2001 and Kronberg et al.514 2000 for radio: Ixaaret et al., 2000 for radio; Kaaret et al.5152s01 --X-rav)., 2001 for X-ray).516 blackAlthough this does not. prove that the mass hole candidates are üunbeamecd. it does argue in that direction.," Although this does not prove that the intermediate mass black hole candidates are unbeamed, it does argue in that direction."517 Additional observations would be very helpful in determining whether beamed or unbeamed models. are [avoured., Additional observations would be very helpful in determining whether beamed or unbeamed models are favoured.518 Looking at radio spectra of these sources. al hish angular resolution. will allow a broader sample to be compared with blazar spectra.," Looking at radio spectra of these sources, at high angular resolution, will allow a broader sample to be compared with blazar spectra."519 Another cdilference. is the expected. minimum time scale of variability., Another difference is the expected minimum time scale of variability.520 For an unbeamed black hole of eg. 105Ας. the minimum. time scale would be the light crossing time across the diameter of the minimum stable orbit. or zz0.1 s. The time scale is ikelv to actually be a lew times this: for example. (νο with a black hole mass likely to be 10M.. has a minimum timescale of significant. variability of zz3 ms. hree times the light crossing time (Revnivisey ct al.," For an unbeamed black hole of, e.g., $10^3\,M_\odot$, the minimum time scale would be the light crossing time across the diameter of the minimum stable orbit, or $\approx 0.1$ s. The time scale is likely to actually be a few times this; for example, Cyg X-1, with a black hole mass likely to be $\sim 10\,M_\odot$, has a minimum timescale of significant variability of $\approx 3$ ms, three times the light crossing time (Revnivtsev et al."521 2000)., 2000).522 Above this timescale. the fractional variability increases significantly.," Above this timescale, the fractional variability increases significantly."523 For a beamed. black hole of mass LOAL.. he minimum time scale is decreased. by a factor of ~10 »v relativistic elfects and the smaller size of the hole itself.," For a beamed black hole of mass $\sim 10\,M_\odot$, the minimum time scale is decreased by a factor of $\sim 10^3$ by relativistic effects and the smaller size of the hole itself."524 A long observation with Chandra in continuous clocking mode. with a time resolution of3 ms. would help distinguish »vtween beamecl and unbeamed. models.," A long observation with Chandra in continuous clocking mode, with a time resolution of 3 ms, would help distinguish between beamed and unbeamed models."525 Such observations are important to determine whether the bright sources are the first representatives of a third class of black holes., Such observations are important to determine whether the bright sources are the first representatives of a third class of black holes.526 We thank Sterl Phinney. Derek Richardson. ancl especially Steinn Sigurdsson for discussions.," We thank Sterl Phinney, Derek Richardson, and especially Steinn Sigurdsson for discussions."527 We also thank Andrew Wilson ancl Andy Young for discussions and. comments on a previous version of this manuscript., We also thank Andrew Wilson and Andy Young for discussions and comments on a previous version of this manuscript.528 This work was supported in part by NASA erant NAC 5-9756., This work was supported in part by NASA grant NAG 5-9756.529"The ring orientation for some of these warm Saturns may not be trivial, since it is determined by the competing forces of the planet’s bulge and the stellar tide.","The ring orientation for some of these warm Saturns may not be trivial, since it is determined by the competing forces of the planet's bulge and the stellar tide."530" Because the ratio of these forces varies as a function of the ring’s distance from the planet, r, the ring’s orientation follows the planet’s equator at small r and follows the orbital plane at large r."," Because the ratio of these forces varies as a function of the ring's distance from the planet, $r$, the ring's orientation follows the planet's equator at small $r$ and follows the orbital plane at large $r$."531 The combined effects of the planet's oblateness and the stellar tide in determining the ring orientation was first recognized by Laplace(1805)., The combined effects of the planet's oblateness and the stellar tide in determining the ring orientation was first recognized by \citet{Laplace1805}.532 Here we use the more recent discussion of Tremaineetal.hereafter TTN).., Here we use the more recent discussion of \citet[hereafter TTN]{Tremaine+09}.533" Because the strength of planetary(2009, oblateness and the stellar tide scale differently with the planet ring separation, the ring orientation varies as a function of r."," Because the strength of planetary oblateness and the stellar tide scale differently with the planet ring separation, the ring orientation varies as a function of $r$."534 The plane that this defines is known as the Laplace plane., The plane that this defines is known as the Laplace plane.535" To estimate the magnitude of this effect, we first note that the strength of the quadrupole potential arising from the planet's bulge is (TTN) where @ is the polar angle from the rotation axis of the planet, Jz is the quadrupole gravitational harmonic, and P5 is a Legendre polynomial."," To estimate the magnitude of this effect, we first note that the strength of the quadrupole potential arising from the planet's bulge is (TTN) where $\theta$ is the polar angle from the rotation axis of the planet, $J_2$ is the quadrupole gravitational harmonic, and $P_2$ is a Legendre polynomial."536" The quadrupole potential arising from the star is where e, is the extrasolar planet's eccentricity.", The quadrupole potential arising from the star is where $e_*$ is the extrasolar planet's eccentricity.537" Equating equations (6)) and (7)) and ignoring the Pj we estimate what is known as the Laplace radius, Ry: 'This simple order of magnitude estimate agrees with the exact calculation of Numerically this gives where Ry=71492 km is the radius of Jupiter."," Equating equations \ref{eq:planet quadrupole}) ) and \ref{eq:stellar quadrupole}) ) and ignoring the $P_2$ we estimate what is known as the Laplace radius, $\rL$: This simple order of magnitude estimate agrees with the exact calculation of Numerically this gives where $R_J = 71492$ km is the radius of Jupiter."538" To determine if the rings will lie in the equatorial plane of the planet or in the planet's orbital plane around the host star, we take the ratio of Ry, and Enocae In Figure 6,, we plot this ratio for three different values of Jo, ranging from of 107 to 10-2."," To determine if the rings will lie in the equatorial plane of the planet or in the planet's orbital plane around the host star, we take the ratio of $\rL$ and $\rroche$ In Figure \ref{f:aL}, we plot this ratio for three different values of $J_2$, ranging from of $10^{-4}$ to $10^{-2}$."539" For reference, we note that the giant planets in the Solar System have J3's that vary from +0.003 for Uranus and Neptune to z0.01 for Jupiter and Saturn."," For reference, we note that the giant planets in the Solar System have $J_2$ 's that vary from $\approx 0.003$ for Uranus and Neptune to $\approx 0.01$ for Jupiter and Saturn."540 Rp=Rroche is denoted by the solid line in Figure 6.., $\rL = \rroche$ is denoted by the solid line in Figure \ref{f:aL}.541" Above this line, Rp>Rroche and the rings will mostly lie in the plane defined by the planet’s equator."," Above this line, $\rL>\rroche$ and the rings will mostly lie in the plane defined by the planet's equator."542" Below this line, RL<Rroche and the rings will undergo a transition from lying in the planet’s equatorial plane at small r to lying in the orbital plane at large r."," Below this line, $\rL < \rroche$ and the rings will undergo a transition from lying in the planet's equatorial plane at small $r$ to lying in the orbital plane at large $r$."543" From Figure 6,, it is clear that the fraction of planets with nontrivial Laplacian planes varies with Jo."," From Figure \ref{f:aL}, it is clear that the fraction of planets with nontrivial Laplacian planes varies with $J_2$."544" For JoX107%, most ringed extrasolar planets fall below this line and thus have warped rings such that their rings will lie in the planet’s equatorial plane inside of Ry, but coincide with the orbital plane outside of Ri."," For $J_2 \lesssim 10^{-3}$, most ringed extrasolar planets fall below this line and thus have warped rings such that their rings will lie in the planet's equatorial plane inside of $\rL$, but coincide with the orbital plane outside of $\rL$."545" On the other hand, for Ja=1073, most planets have rings that lie in the plane defined by the exoplanet's equator, much like the planetary rings in the Solar System."," On the other hand, for $J_2 = 10^{-2}$, most planets have rings that lie in the plane defined by the exoplanet's equator, much like the planetary rings in the Solar System."546 The observational signature of warped rings is especially interesting as it provides a means by which the planet’s Jo can be measured directly., The observational signature of warped rings is especially interesting as it provides a means by which the planet's $J_2$ can be measured directly.547 Present constraints on Jz are inferred from transit measurements of the planet's oblateness (Carter&Winn2010a)., Present constraints on $J_2$ are inferred from transit measurements of the planet's oblateness \citep{Carter+10a}.548. The inferred Jz from such oblateness measurements is however model dependent., The inferred $J_2$ from such oblateness measurements is however model dependent.549" Since warped rings provide a direct constraint on the planet's Jo, which in turn relates to the three moments of inertia about the principle axes, the planets internal structure can be probed (Ragozzine&Wolf 2009)."," Since warped rings provide a direct constraint on the planet's $J_2$, which in turn relates to the three moments of inertia about the principle axes, the planet's internal structure can be probed \citep{Ragozzine+09}."550". Furthermore, measurements of an exoplanet's Jo and of its oblateness would together constrain its spin period."," Furthermore, measurements of an exoplanet's $J_2$ and of its oblateness would together constrain its spin period."551 This method was successfully applied in the past to determine the rotation period of Uranus (Dunham&Elliot1979;etal. 1981).," This method was successfully applied in the past to determine the rotation period of Uranus \citep{DE79,EF81}."552. We examined the nature of rings that could exist around extrasolar planets that have orbital periods of about one year or less., We examined the nature of rings that could exist around extrasolar planets that have orbital periods of about one year or less.553" Such systems are ideal targets for the Kepler satellite, whose photometric precision will be able to identify Saturn-like rings around extrasolar planets that are transiting Sun-like stars (Barnes&Fortney2004) (http:keplergo.arc.nasa.gov/CalibrationSN.shtml)."," Such systems are ideal targets for the Kepler satellite, whose photometric precision will be able to identify Saturn-like rings around extrasolar planets that are transiting Sun-like stars \citep{BF04} (http:keplergo.arc.nasa.gov/CalibrationSN.shtml)."554spectrograph SINFONI (?7) on the VLT iu December 2001 uuder excelleut and stable conditions.,"spectrograph SINFONI \citep{eisenhauer03,bonnet04} on the VLT in December 2004 under excellent and stable conditions."555" SINFONT is a οςαιοποίοι, innage-sliciug spectrograph. with «& field of view at a « opixel scale and spectral resolving power AR~1000 i- he IK band."," SINFONI is a medium-resolution, image-slicing integral-fieldspectrograph, with $\times$ field of view at a $\times$ pixel scale and spectral resolving power $R \sim 4000$ in the K band."556 The total observing time was 1LL00s wit[um individual exposure times of GO0s., The total observing time was 14400s with individual exposure times of 600s.557 This corresponds to he ou-source observing tine. since we adopted a dither ρατσι where the galaxy was constantly within the field of view.," This corresponds to the on-source observing time, since we adopted a dither pattern where the galaxy was constantly within the field of view."558 We used the IRAF (2) staudard tools for the reduction of lonegslit-spectra. modified to mect the special requirements of inteeralfield spectroscopy. aud complemented by a dedicated set of IDL routines.," We used the IRAF \citep{tody93} standard tools for the reduction of longslit-spectra, modified to meet the special requirements of integral-field spectroscopy, and complemented by a dedicated set of IDL routines."559 Data are dark-trame subtracted and flat-telded., Data are dark-frame subtracted and flat-fielded.560 The position of each slitlet is measured ;frou a se of standard SINFONI calibration data. measuring the )osition of an artificial point source.," The position of each slitlet is measured from a set of standard SINFONI calibration data, measuring the position of an artificial point source."561 Rectification aloug the spectral dimension and waveleneth calibration are done before night sk subtraction to account for some spectral flexure between the frames., Rectification along the spectral dimension and wavelength calibration are done before night sky subtraction to account for some spectral flexure between the frames.562 Cirvature is measured aud removed usine an are lump. before shifting the spectra to an absolute (vac) waveleneth scale with reference to the ΟΠ lines in the data.," Curvature is measured and removed using an arc lamp, before shifting the spectra to an absolute (vacuum) wavelength scale with reference to the OH lines in the data."563 To account for variations iu the night skv CUSSION. we nonnalize he skv frame to the average of the object frame separately for cach wavelength before sky subtraction. correcting for residuals of the backeroun subtraction and uncertaünuties in the flux calibration bv subsequeutly subtracting the (empty sky} backeroun separately from cach waveleneth plane.," To account for variations in the night sky emission, we normalize the sky frame to the average of the object frame separately for each wavelength before sky subtraction, correcting for residuals of the background subtraction and uncertainties in the flux calibration by subsequently subtracting the (empty sky) background separately from each wavelength plane."564" The three-dimensional data are then recoustructed auk PAwatially aligned using the telescope offsets as recordec oei the header within the same sequence of 6 dithere sxposures (about one hour of exposure). aud by CYoss-correlating the line images from the combined data oel Onci Seqποσο, to eliminate relative offsets between ifereut sequences."," The three-dimensional data are then reconstructed and spatially aligned using the telescope offsets as recorded in the header within the same sequence of 6 dithered exposures (about one hour of exposure), and by cross-correlating the line images from the combined data in each sequence, to eliminate relative offsets between different sequences."565 Tellure correction is applied to cach oeidividual cube before the cube combination., Telluric correction is applied to each individual cube before the cube combination.566 Flux scales are obtained from standard star observations taken every hour at similar position and air mass as the source., Flux scales are obtained from standard star observations taken every hour at similar position and air mass as the source.567" We also used the standard star to carefully monitor the secine diving observations. and we find an effective seems iu the combined cube of FWIHAI 0.55""ο «0. 20.017..."," We also used the standard star to carefully monitor the seeing during observations, and we find an effective seeing in the combined cube of FWHM $\pm0.05$ $\times$ $\pm$."568 The spectral resolution was iieasured from niglit-«ky lines aud is FWIIM- 103 kins | at the wavelength of A5007., The spectral resolution was measured from night-sky lines and is $=$ 103 km $^{-1}$ at the wavelength of $\lambda$ 5007.569 We also obtained WFPC2 F702W imaging of QU31T7-383 C5 from the OST archive. which was originally presented by 2..," We also obtained WFPC2 F702W imaging of Q0347-383 C5 from the HST archive, which was originally presented by \citet{pettini01}."570 We used the ΟΤΕ calibrated data sets. anc followed the standard DRIZZLE procedures eiven iu. e.g. 7.. to remove cosinic ravs and to align and combine the individual frames.," We used the OTFC calibrated data sets, and followed the standard DRIZZLE procedures given in, e.g., \citet{drizzlemanual}, to remove cosmic rays and to align and combine the individual frames."571" It is difficult to accurately alien the SINFONT aud WEPC2 data at sub-arcsecond precision. because of the xinall field of view of SINFONI of only <8” aand the simall source size. which is about similar to the uncertaintv iu the absolute astrometry of both the VET and WEPC?2 (~1"")."," It is difficult to accurately align the SINFONI and WFPC2 data at sub-arcsecond precision, because of the small field of view of SINFONI of only $\times$ and the small source size, which is about similar to the uncertainty in the absolute astrometry of both the VLT and WFPC2 $\sim 1\arcsec$ )."572 Moreover. the morphologies in the WEPC? continuui image aud SINFONI line image are very different.," Moreover, the morphologies in the WFPC2 continuum image and SINFONI line image are very different."573 We therefore base the aligument on astroplivsical areuinents., We therefore base the alignment on astrophysical arguments.574 Overall. the emission line regions will roughly align with the continuum. as typically observed iu blue. star-forming galaxies at redshifts z~2 (777). ," Overall, the emission line regions will roughly align with the continuum, as typically observed in blue, star-forming galaxies at redshifts $\sim5752$ \citep{nmfs06,law07,nesvadba07}. ."576The oulv lugh-redshift salaxies. where the line ancl coutimm£§£_ chussion do nof seen to align well. are radio galaxies in which several 1019 AL... of ionize: eas extend over radii of 30 Ipc. which appear to be eutraiued aud ionized w feedback from the powerful AGN (?)..," The only high-redshift galaxies, where the line and continuum emission do not seem to align well, are radio galaxies in which several $10^{10}$ $_{\odot}$ of ionized gas extend over radii of $\sim 20-30$ kpc, which appear to be entrained and ionized by feedback from the powerful AGN \citep{nesvadba07}."577" But those cau e Good analogs to QU317-383. C5,", But those can hardly be good analogs to Q0347-383 C5.578 If we aligu the unresolved. bright knot in the southern wart of the source with one of the unresolved knots in the OII[AS007 emission line image. the line and continua cuuission are overall well aligned.," If we align the unresolved, bright knot in the southern part of the source with one of the unresolved knots in the $\lambda$ 5007 emission line image, the line and continuum emission are overall well aligned."579 Astrophlysically. this articular choice relies ou the assmuption that the strong Ine cluission and UV continuum originate frou the same region. Which is a reasonable assumption for both star-Orniüne regions. aln AGN.," Astrophysically, this particular choice relies on the assumption that the strong line emission and UV continuum originate from the same region, which is a reasonable assumption for both star-forming regions, and AGN."580 The spatial extent of the ino aud coutimuuni Cluission are well matched. which nay serve as a heuristic justification of the method. aud lis choice does not have a stroug impact on our overall interpretation.," The spatial extent of the line and continuum emission are well matched, which may serve as a heuristic justification of the method, and this choice does not have a strong impact on our overall interpretation."581" We note tha the istance between the wo knots iu the line image does not correspond to the distance between the aunt source towards the north. which is mareinally detectec inthe WFPC?2 image. aud anv part of QU317-383. Ch,"," We note that the distance between the two knots in the line image does not correspond to the distance between the faint source towards the north, which is marginally detected in the WFPC2 image, and any part of Q0347-383 C5."582 QUJ3IT-383. C5 is oue of the largest z~3 LBs. iu particular it is large enough to be spatially resolved with secing-limited observations.," Q0347-383 C5 is one of the largest $\sim 3$ LBGs, in particular it is large enough to be spatially resolved with seeing-limited observations."583 Fig., Fig.584 1. shows the F702W morphology obtained with the IIST., \ref{fig:o3im} shows the F702W morphology obtained with the HST.585 At z223.23. the Έτος baudpass corresponds to rest-frame wavelonetls of ~1170LSO0A..," At z=3.23, the F702W bandpass corresponds to rest-frame wavelengths of $\sim 1470-1800$."586 The brightest cussion comes from a compact. marginally resolved knot. which has au intrinsic size of «0150 ((Q.97kpe « I.9 kpe for our cosmology}.," The brightest emission comes from a compact, marginally resolved knot, which has an intrinsic size of $\times$ (0.97kpc $\times$ 1.49 kpc for our cosmology)."587 We obtained this estimate from assuniug that the observed full width at half maxiunun of the image is a quadratic suni of the intrinsic EWIIM of the source aud. the poiut spread function. « 0.17... which we measured from a nearby star ou the same clip.," We obtained this estimate from assuming that the observed full width at half maximum of the image is a quadratic sum of the intrinsic FWHM of the source and the point spread function, $\times$ , which we measured from a nearby star on the same chip."588 The knotis separated by ~0.67 ((1.5 spe) frou a more diffuse. elongated object.," The knotis separated by $\sim 0.6$ (4.5 kpc) from a more diffuse, elongated object."589 About 1.67(12 kpc) to the north-west from the brightest knot is, About (12 kpc) to the north-west from the brightest knot is590allowed sound velocity of this fluid (which occurs iu the regious where p>p) ix given by να. this condition tuposes a<1.,"allowed sound velocity of this fluid (which occurs in the regions where $p\rightarrow -\rho $ ) is given by $\sqrt{\alpha }$, this condition imposes $\alpha \leq 1$."591 The Chaplvein gas. a=1. is the extreme case. where the sound velocity cau be newly the speed of Leht.," The Chaplygin gas, $\alpha =1$, is the extreme case, where the sound velocity can be nearly the speed of light."592 The case a=0 is equivalent to ACDAL aud is. of course. well motivated.," The case $\alpha =0$ is equivalent to $\Lambda $ CDM and is, of course, well motivated."593 Iu this paper. we discuss the CCC model from a phenomenological point of view.," In this paper, we discuss the GCG model from a phenomenological point of view."594" Hence, although we are aware that most likely 0<ax1. we alsoiuclude in our analysis the region whereà is negative. but larger than 1."," Hence, although we are aware that most likely $0\leq \alpha595\leq 1$, we alsoinclude in our analysis the region where$\alpha $ is negative, but larger than $-1$."596 Ifa 1 we obtain ade Sitter Universe., If $\alpha =-1$ we obtain a de Sitter Universe.597 The situation a<1 secs uuplivsical. since the energy density of UDM would be increasing with the expausion of the Universe.," The situation $\alpha <-1$ seems unphysical, since the energy density of UDM would be increasing with the expansion of the Universe."598 In fact. as we shall sec. age coustraiunts cau safely exclude regions in the parameter space with very negative values of a.," In fact, as we shall see, age constraints can safely exclude regions in the parameter space with very negative values of $\alpha $."599 Iu the forthcoming section we will see what constraiuts to the model described above are set by present aud future SNIa observations., In the forthcoming section we will see what constraints to the model described above are set by present and future SNIa observations.600 Recently. some constraints youn SNIa ou related models where obtained in Ret. [13]..," Recently, some constraints from SNIa on related models where obtained in Ref. \cite601{fabris2}."602 The work presented vere differs from [13]. in the following aspects: a) Following the idea of unification. we have not included an additional dark matter componcut aud we have considered he more general case in which à is not necessarily equal to unitv.," The work presented here differs from \cite{fabris2} in the following aspects: a) Following the idea of unification, we have not included an additional dark matter component and we have considered the more general case in which $\alpha $ is not necessarily equal to unity."603 b) When analyzing current SNIa data we perform a Bayesian approach in which the intercept is mareimalized c) We also investigate the predicted constraints on the nodels from future SNIa observations., b) When analyzing current SNIa data we perform a Bayesian approach in which the intercept is marginalized c) We also investigate the predicted constraints on the models from future SNIa observations.604 The luminosity distance of a light source is defined iu such away as to generalize to an expanding and curved space the iuverse-square law of brightness valid iu a static Enclidean space. Tn (9)) L is the absolute Iuuinositv aud F is the measured fiux.," The luminosity distance of a light source is defined in such a way as to generalize to an expanding and curved space the inverse-square law of brightness valid in a static Euclidean space, In \ref{L}) ) ${L}$ is the absolute luminosity and ${\cal F}$ is the measured flux."605" For a source of absolute magnitude AL. the apparent bolometric iiaguitude mtz) can be expressed as where Dr=Dr(z.o.O3,) is tho huuinosity distance in units of 77, land is the ""zero point” magnitude (or IIubble intercept maguitude)."," For a source of absolute magnitude $M$, the apparent bolometric magnitude $ m(z)$ can be expressed as where $D_{L}=D_{L}(z,\alpha ,\Omega _{M}^*)$ is the luminosity distance in units of $H_{0}^{-1}$, and is the “zero point” magnitude (or Hubble intercept magnitude)."606 Iu our computations we follow the Davesin approach of Drell. Loredo aud Wassermial [1I (sce also [15] )) aud we direct the reader to these references for details.," In our computations we follow the Bayesian approach of Drell, Loredo and Wasserman \cite{drell} (see also \cite{ng}) ) and we direct the reader to these references for details."607 We consider the data of fit C. of Perhuutter |16].. with 16 aud 38 ligh-+vedshift superuovae.," We consider the data of fit C, of Perlmutter \cite{perlmutter}, , with 16 low-redshift and 38 high-redshift supernovae."608 Iu our analysis we use the followine mareial likelihood.," In our analysis we use the following marginal likelihood,"609provide little information about the shape of q(2).,provide little information about the shape of $q(z)$.610 Note that the first mode does not cross zero. and we have chosen its sign to be wholly positive.," Note that the first mode does not cross zero, and we have chosen its sign to be wholly positive."611" As argued by Shapiro&Turner (2006).. this mode is useful since in addition to being well constrained. à, can only be negative if q(2) is negative for some z."," As argued by \citet{2006ApJ...649..563S}, this mode is useful since in addition to being well constrained, $\alpha_1$ can only be negative if $q(z)$ is negative for some $z$."612 Therefore. i£ we fit the model q(z)=arey(s) to the data. and then measure αιUO. dC constitutes paranmeter-independent. evidence that the universe has accelerated. at some redshift.," Therefore, if we fit the model $q(z)=\alpha_1 e_1(z)$ to the data, and then measure $\alpha_1<0$, it constitutes parameter-independent evidence that the universe has accelerated at some redshift."613" We need not consider additional moces since the constraint on à, is. by construction. independent: of the constraints on the other a;."," We need not consider additional modes since the constraint on $\alpha_1$ is, by construction, independent of the constraints on the other $\alpha_i$."614" Marginalizing over fh. we find a,=0.155+0.086 and determine that a,<0 with probability."," Marginalizing over $h$, we find $\alpha_1=-0.155\pm 0.086$ and determine that $\alpha_1<0$ with probability."615 The fact that the error bar from our lit closely matches the Fisher matrix estimate of a(ay)=0.082 demonstrates consistency., The fact that the error bar from our fit closely matches the Fisher matrix estimate of $\sigma(\alpha_1)=0.082$ demonstrates consistency.616 Εις result. is comparable to our qu fit above. while providing robust evidence for an accelerating universe regardless of the model assumptions.," This result is comparable to our $q_0$ fit above, while providing robust evidence for an accelerating universe regardless of the model assumptions."617 The significance of our detection could be enhanced by combining the SDSS-II SNe with other SN datasets., The significance of our detection could be enhanced by combining the SDSS-II SNe with other SN datasets.618 This has already. been done in part by Shapiro&Turner(2006) but could. suller from svstematic uncertainties associated with combining cata from cillerent instruments and surveys., This has already been done in part by \citet{2006ApJ...649..563S} but could suffer from systematic uncertainties associated with combining data from different instruments and surveys.619 Again. the reader is referred to Kesslerctal.(2009). [or a detailed description of such combinations of the SDSS-LL SN Survey with other SN datasets.," Again, the reader is referred to \citet{kessler} for a detailed description of such combinations of the SDSS-II SN Survey with other SN datasets."620 We plan to repeat this analvsis with the full 3.vear ο) SN dataset., We plan to repeat this analysis with the full 3–year SDSS-II SN dataset.621 We next consider the comparison of our SDSS-LL SN distances with other geometrical distance estimates. over he same redshift range., We next consider the comparison of our SDSS-II SN distances with other geometrical distance estimates over the same redshift range.622 This is motivated by the original results of Peorcivaletal.(2007) who noticed some tension (al 2 Bor} between the cosmological constraints derived rom nearby BAQ measurements (2=0.2 and 2= 0.35) and higher redshift SNe of Asticr et al. (, This is motivated by the original results of \citet{2007MNRAS.381.1053P} who noticed some tension (at $>2\sigma$ ) between the cosmological constraints derived from nearby BAO measurements $z=0.2$ and $z=0.35$ ) and higher redshift SNe of Astier et al. (6232006).,2006).624 The BAO oovide a measure of distances in the universe by relating he scale of the sound horizon at last scattering (ης) to the scale of the corresponding correlations seen in the galaxy clistribution., The BAO provide a measure of distances in the universe by relating the scale of the sound horizon at last scattering $r_s$ ) to the scale of the corresponding correlations seen in the galaxy distribution.625 One such measurement of this ratio is given by he cl-parameter in Eisensteinetal. (2005).., One such measurement of this ratio is given by the $A$ -parameter in \citet{2005ApJ...633..560E}. .626 Phis parameter is [frequently used. in combination with SN data to derive constraints on uw (Astieretal.2006:Kowalski 2008).. og. see Ixessleretal.(2009). for the combination of the SDSS-LLSN data with the ;A-parameter.," This parameter is frequently used in combination with SN data to derive constraints on $w$ \citep{2006A&A...447...31A, 2008arXiv0804.4142K}, , e.g., see \citet{kessler} for the combination of the SDSS-II SN data with the $A$ -parameter."627 Llere. we adopt the quantity defined in Eisensteinetal.(2005) where. Da is the co-moving distance.," Here, we adopt the quantity defined in \citet{2005ApJ...633..560E} where $D_M$ is the co-moving distance."628 Percivaletal.(2007) showed by combining measurements of kr;/Dy at redshifts of 0.2 and. 0.35 from both the δα and SDSS galaxy samples. that one can obtain the ratio of the distance between two cilferent redshifts that is independent of both r; and. Zo.," \citet{2007MNRAS.381.1053P} showed by combining measurements of $r_s/D_V$ at redshifts of 0.2 and 0.35 from both the 2dFGRS and SDSS galaxy samples, that one can obtain the ratio of the distance between two different redshifts that is independent of both $r_s$ and $H_0$ ."629" This approach also avoids a large extrapolation between the redshift’ of recombination (sexu,=1090. Komatsu 2008)) and these intermediate-redshift measurements."," This approach also avoids a large extrapolation between the redshift of recombination $z_{\rm CMB}=1090$, \citealt{2008arXiv0803.0547K}) ) and these intermediate-redshift measurements."630 For the analysis presented. in this paper. we have EUlopted the latest value of Dy(2=0.35)/DéΞ0.2)1.73673:E0.065 taken from Percivaletal.(2009)...," For the analysis presented in this paper, we have adopted the latest value of $D_V(z=0.35)/D_V(z=0.2) = 1.736\pm0.065$ taken from \citet{2009arXiv0907.1660P}."631 The inferred value of Dy(2=035)/D4V(022) from Pereival et al. (, The inferred value of $D_V(z=0.35)/D_V(0.2)$ from Percival et al. (6322009) is lower than that of Percival ct al. (,2009) is lower than that of Percival et al. (6332007). bringing it into better agreement with AC DAL.,"2007), bringing it into better agreement with $\Lambda$ CDM."634 This change was caused by a revised error analysis and a change in the methodology adopted. as well as the addition of more data.," This change was caused by a revised error analysis and a change in the methodology adopted, as well as the addition of more data."635 In this paper we do not use constraints on r()/De(z). which depend on the sound horizon at the barvon drag epoch r;(2;).," In this paper we do not use constraints on $r_s(z_d)/D_V(z)$, which depend on the sound horizon at the baryon drag epoch $r_s(z_d)$."636 We therefore avoid. including CAIB data. commonly used. to model the sound horizon.," We therefore avoid including CMB data, commonly used to model the sound horizon."637 In Fie., In Fig.638 1 owe show the Llubble clagram for the SDSS-LL SN data cliseussecl in Section 2 compared with à variety of cosmological and nonparametric models discussed. herein., \ref{fig_sdss_hubble} we show the Hubble diagram for the SDSS-II SN data discussed in Section 2 compared with a variety of cosmological and non–parametric models discussed herein.639 We find a scatter. of 0.14. mag around these moclels independent of the particular. fitting. method., We find a scatter of $0.14$ mag around these models independent of the particular fitting method.640" Ehe. first non-parametric model we consider is a ""sliding window method. which allows us to investigate the general. shape and smoothness of the Llubble diagram: without assuming a cosmological model."," The first non-parametric model we consider is a “sliding window"" method which allows us to investigate the general shape and smoothness of the Hubble diagram without assuming a cosmological model."641 We have thus fit. piecewise Hubble parameters and luminosity distances in different redshift bins using a local redshift window following the approach of Daly&Djorgovski(2003)..., We have thus fit piecewise Hubble parameters and luminosity distances in different redshift bins using a local redshift window following the approach of \citet{2003ApJ...597....9D}.642 At each redshift z. we fit the SNe co-moving distances. Da(z;)=dif(l]z) over a fitting window of z;As<a<a)|At lu by a polynomial of second order given by: The values of 24; are determined. separately via. \7- minimisation in each redshift window. and we slide this window as a function of redshift in increments of 0.01 throughout the entire range.," At each redshift $z$ , we fit the SNe co-moving distances, $\DM(z_i)=\DL/(1+z_i)$, over a fitting window of $z_i-\Delta z <z_i< z_i+\Delta z$ , by a polynomial of second order given by: The values of $A_i$ are determined separately via $\chi^2$ -minimisation in each redshift window, and we slide this window as a function of redshift in increments of 0.01 throughout the entire range."643 The best-it ον ab z ds proportional to chy. while the best-fit ο is proportional to chy. and Dai is related to ENTER?.," The best-fit $\DM$ at $z$ is proportional to $A_0$, while the best-fit $c/H$ is proportional to $A_1$ , and $D_V$ is related to $[ zA^2_0 A_1] ^{1/3}$."644 Our results depend on the size of the redshift window. with a wider window allowing less Uexibility but smaller errors. and. vice versa.," Our results depend on the size of the redshift window, with a wider window allowing less flexibility but smaller errors, and vice versa."645 We show in the resulting nonparametric fit to the SDSS-LLE SN data as an example for a window size of As=0.15 which demonstrates that the SDSS SNe data is fully consistent with the individual BAO measurements at >=02 and 0.35 of Percivalctal.(2009). (the evan and erecn shaded regions indicate the lo and 2e errors. which are highly. correlated as they share the same data points in the overlapping fitting windows).," We show in \ref{fig_sdss_hubble} the resulting non–parametric fit to the SDSS-II SN data as an example for a window size of $\Delta z = 0.15$ which demonstrates that the SDSS SNe data is fully consistent with the individual BAO measurements at $z=0.2$ and $0.35$ of \citet{2009arXiv0907.1660P} (the cyan and green shaded regions indicate the $\sigma$ and $\sigma$ errors, which are highly correlated as they share the same data points in the overlapping fitting windows)."646 Next. we derive the ratio I3(0.35)/D4V(0.2) and determine the covariances between the 21; values within. and between. redshift bins using the observational errors.," Next, we derive the ratio $\DV(0.35)/\DV(0.2)$ and determine the covariances between the $A_i$ values within, and between, redshift bins using the observational errors."647 This is shown in Fig., This is shown in Fig.648 3.for cillerentwindow sizes., \ref{fig_bao} for differentwindow sizes.649" H isinteresting to note that the sliding window method tends to preferlarge values (steeper slopes) for£A comparedto Di: caleulated from a qo fit described in Section 3. or Dy from the best fitting wQO, parametrizations given Table 1."," It isinteresting to note that the sliding window method tends to preferlarge values (steeper slopes) for$\DV$ comparedto $\DV$ calculated from a $q_0$ fit described in Section 3, or $\DV$ from the best fitting $w-\Om$ parametrizations given Table 1."650 We also see that the sliding window method provides values for 2 which are fully consistent with the, We also see that the sliding window method provides values for $\DV$ which are fully consistent with the651since Aeon 15 reached at a smaller κ.,since $k_\mathrm{Coh}$ is reached at a smaller $k$.652 The scale has been truncated to show the increased structure in the pivot plane comparedto the 5=O case., The scale has been truncated to show the increased structure in the pivot plane comparedto the $n_B=0$ case.653 As with those (ri) and (τη) cases. this is unfortunately not immediately amenable to analytic approximation.," As with those $\av{\tau_S^3}$ and $\av{\tau_T^3}$ cases, this is unfortunately not immediately amenable to analytic approximation."654 Modelling the bispectrum with the power law around this plane we recover 0.006(39) which is extremely close to the predicted a=—9/2., Modelling the bispectrum with the power law around this plane we recover 0.006 which is extremely close to the predicted $\alpha=-9/2$.655" Using the 8,(7.Φ) plane with this value of « can then recover the section of the bispectrum relevant to the CMB."," Using the $\mathcal{B}_\star(r,\phi)$ plane with this value of $\alpha$ can then recover the section of the bispectrum relevant to the CMB."656 The extent to which the power piles onto the degenerate line renders diagrams of the full bispectrum at 252—5/2 somewhat unhelpful., The extent to which the power piles onto the degenerate line renders diagrams of the full bispectrum at $n_B=-5/2$ somewhat unhelpful.657 The most useful information can be extracted from the lane presented in Figure 18. and the recovered value of a., The most useful information can be extracted from the lane presented in Figure \ref{PivotPlanesNm25} and the recovered value of $\alpha$.658" It can also be noted that the increase of the error in a can be used to diagnose when keon() has grown through 4,(7): however. given the domination of the degenerate line 1t is not expected that much error will be introduced at high 7 from employing a constant ky."," It can also be noted that the increase of the error in $\alpha$ can be used to diagnose when $k_\mathrm{Coh}(r)$ has grown through $k_\star(r)$; however, given the domination of the degenerate line it is not expected that much error will be introduced at high $r$ from employing a constant $k_\star$."659 As with the previous bispectra (both for ag=0 and ng= —5/2). the r=1 plane can contain features that only exist right on this plane due to the high symmetries that can occur when &=p. the clearest examples being that the degenerate line for 5=0 is positive for (τς) and non-vanishing for (rj). in contrast with the behaviour in the rest of the squeezed plane.," As with the previous bispectra (both for $n_B=0$ and $n_B=-5/2$ ), the $r=1$ plane can contain features that only exist right on this plane due to the high symmetries that can occur when $k=p$, the clearest examples being that the degenerate line for $n_B=0$ is positive for $\av{\tau_S^3}$ and non-vanishing for $\av{\tau_T^3}$, in contrast with the behaviour in the rest of the squeezed plane."660 The (5) bispectrum at 5=—5/2 illustrates this even more dramatically. although it also contains other unique features.," The $\av{\tau_S^3}$ bispectrum at $n_B=-5/2$ illustrates this even more dramatically, although it also contains other unique features."661 Figure 4. shows the colinear. equilateral and near-degenerate lines.," Figure \ref{LinethroughsNm25} shows the colinear, equilateral and near-degenerate lines."662 As with (7) the agreement with realisations for the colinear line is good. with the realisations exhibiting an infra-red damping.," As with $\av{\tau^3}$ the agreement with realisations for the colinear line is good, with the realisations exhibiting an infra-red damping."663 The two scalar signals are indistinguishable from one-another along this line., The two scalar signals are indistinguishable from one-another along this line.664 Along the degenerate line. the signal has become negative. and almost equal in magnitude to (7).," Along the degenerate line, the signal has become negative, and almost equal in magnitude to $\av{\tau^3}$."665 This is in agreement with TSSIO. recalling that their Ny=το. who found that their degenerate line was positive in contrast to the approximate solutions.," This is in agreement with TSS10, recalling that their $\Pi_B=-\tau_S$, who found that their degenerate line was positive in contrast to the approximate solutions."666 The equilateral line is more interesting., The equilateral line is more interesting.667 The signal along this line ts significantly suppressed across much of the range of k before flattening out as &—|., The signal along this line is significantly suppressed across much of the range of $k$ before flattening out as $k\rightarrow 1$.668 Fork>| it is of the same order of magnitude as the other two correlations., For $k>1$ it is of the same order of magnitude as the other two correlations.669 The bispectrum of the anisotropic pressure then exhibits some interesting behaviour in the r=| plane. passing from positive to a negative region near the equilateral line.," The bispectrum of the anisotropic pressure then exhibits some interesting behaviour in the $r=1$ plane, passing from positive to a negative region near the equilateral line."670 It remains negative near the degenerate line., It remains negative near the degenerate line.671 However. the linethroughs at 7=5 in Figure 4.. and the planes in Figure 15 demonstrate that the signal does not remain negative between the equilateral and degenerate lines.," However, the linethroughs at $r=5$ in Figure \ref{LinethroughsNm25}, and the planes in Figure \ref{PlanesNm25TsTsTs} demonstrate that the signal does not remain negative between the equilateral and degenerate lines."672" Instead. there is a negative trough. or ""river"" running between regions of positivity before a strong negative divergence as ὁ—π."," Instead, there is a negative trough, or “river” running between regions of positivity before a strong negative divergence as $\phi\rightarrow\pi$."673 Conversely. the small-scale signal 15 negative for almost all ὁ.," Conversely, the small-scale signal is negative for almost all $\phi$."674 The manner in which this bispectrum changes signs on large scales could potentially lead to very characteristic signatures on the CMB., The manner in which this bispectrum changes signs on large scales could potentially lead to very characteristic signatures on the CMB.675 Furthermore. the fact that the degenerate line possesses a different sign to the scalar signal implies that the magnetic signal — the sum of all possible CMB bispectra. covering auto- and cross-correlations of all the components of the stress tensor — will exhibit cancellations.," Furthermore, the fact that the degenerate line possesses a different sign to the scalar signal implies that the magnetic signal – the sum of all possible CMB bispectra, covering auto- and cross-correlations of all the components of the stress tensor – will exhibit cancellations."676 The planes at r€(2.3.4] demonstrate further oscillations in the signal: a negative region at κ--κ. grows in area and then declines again with increasing +.," The planes at $r\in\{2,3,4\}$ demonstrate further oscillations in the signal; a negative region at $k\rightarrow k_c$ grows in area and then declines again with increasing $r$ ."677 However. these interesting “caves” in the bispectrum are unlikely to leave significant signs on the CMB as the transfer functions and the amplitude of the bispectra close to the damping scale are negligible compared to the largest scales.," However, these interesting “caves” in the bispectrum are unlikely to leave significant signs on the CMB as the transfer functions and the amplitude of the bispectra close to the damping scale are negligible compared to the largest scales."678With the above choices for 2 and /. we find The mass in the ejecta is then and the kinetic energy is The kinetic energy may be overestimated by a [actor of a few because thevelocity of O.le presumably refers only to the surface lavers. while the bulk of the ejecta may be moving substantially slower.,"With the above choices for $R$ and $t$, we find The mass in the ejecta is then and the kinetic energy is The kinetic energy may be overestimated by a factor of a few because thevelocity of $0.1c$ presumably refers only to the surface layers, while the bulk of the ejecta may be moving substantially slower."679 Overall. (he parameters are more reasonable in (his model than in the previous (wo models.," Overall, the parameters are more reasonable in this model than in the previous two models."680 The mass and energy requirements. for instance. are consistent. wilh an underlving supernova.," The mass and energy requirements, for instance, are consistent with an underlying supernova."681 Two issues remain (o be clarified in this model. both of which are discussed in 833.," Two issues remain to be clarified in this model, both of which are discussed in 3."682 First. we need to identilv the nature of the scattering screen.," First, we need to identify the nature of the scattering screen."683 We suggest (that it is a pair plasma cloud which is temporarily created by the GERD radiation itself., We suggest that it is a pair plasma cloud which is temporarily created by the GRB radiation itself.684 Second. we have to check whether (here is enough scattered radiation to power the rather impressive level of line emission seen in GRB 011211.," Second, we have to check whether there is enough scattered radiation to power the rather impressive level of line emission seen in GRB 011211."685 As the pulse of gamma-ray photons from a GRB moves outward. some of the photons will be scattered by. electrons in their path ancl will collide with other outgoing photons to produce electron-positron pairs.," As the pulse of gamma-ray photons from a GRB moves outward, some of the photons will be scattered by electrons in their path and will collide with other outgoing photons to produce electron-positron pairs."686 This process has been considered by a number of authors in the context of GRBs (Thompson Madau 2000; Meszaros et al., This process has been considered by a number of authors in the context of GRBs (Thompson Madau 2000; Meszaros et al.687 2000: Beloborocdoy 2002: ήπια Panaitescu 2002)., 2000; Beloborodov 2002; Kumar Panaitescu 2002).688 An exponential eerowth of pairs occurs when the optical depth for a scattered. GRB photon to pair-produce off outgoing Mev photons is greater than 1., An exponential growth of pairs occurs when the optical depth for a scattered GRB photon to pair-produce off outgoing Mev photons is greater than 1.689" This condition gives an limit on−⋅ the distance of⋅ the⋅ pair screen. [rom the. central explosion: R.= ~10:5""cm.upper "," This condition gives an upper limit on the distance of the pair screen from the central explosion: $R_\pm\sim 10^{15}690E_{52}^{1/2}$ cm."691"llere. E. measures the isotropic equivalent energv in the eamunma-rayv pulse in photons of energy greater than | Mev. where Ess£Peng(2m./hv,)10 eres. Bony is the total"," Here, $E_{52}$ measures the isotropic equivalent energy in the gamma-ray pulse in photons of energy greater than 1 Mev, where $E_{52}\approx E_{GRB} (2m_e c^2/h\nu_p)^{-\beta}/10^{52} ~{\rm692ergs}$ , $E_{GRB}$ is the total"693planets in (he svstem. then the periodic passage of this material closer to ancl further away from the star would change the temperature aud resultant emission from the cust.,"planets in the system, then the periodic passage of this material closer to and further away from the star would change the temperature and resultant emission from the dust."694 For specdicitv. consicer (he possibility that the 38 mJ of excess detected in the IRS peak-up images al 22 jm consists of a constant component of 80 mJv from uniformly distributed. dust. at a semi-major axis of 1 AU plus another in a clamp that moves in an eccentric orbit with semi-major axis of 1 AU and an eccentricity. e.," For specificity, consider the possibility that the $\sim$ 88 mJy of excess detected in the IRS peak-up images at 22 $\mu$ m consists of a constant component of 80 mJy from uniformly distributed dust at a semi-major axis of 1 AU plus another in a clump that moves in an eccentric orbit with semi-major axis of 1 AU and an eccentricity, $\epsilon$."695 A simple model that follows the clump through its orbit vields a time-varyving amount of emission we could compare with the data in Figure 3.., A simple model that follows the clump through its orbit yields a time-varying amount of emission we could compare with the data in Figure \ref{IRSPeakupFig}.696 The model puts the dust clump in a 2:1 resonance with ihe outermost planet seen at a semi-major axis of | AU. a corresponding period of approximately 400 days aud eccentricities of 0.1. 0.3. 0.6 and 0.9.," The model puts the dust clump in a 2:1 resonance with the outermost planet seen at a semi-major axis of 1 AU, a corresponding period of approximately 400 days and eccentricities of 0.1, 0.3, 0.6 and 0.9."697" The small grain temperature follows the radial power-law derived above. 7,,=670RyΛΑ."," The small grain temperature follows the radial power-law derived above, $T_{gr}=670 \, R_{AU}^{-2/5}\, K$."698 Following the clumped. erains through multiple orbits vields the orbital location. temperature ancl total disk emission which can be compared to the Spitzer observations (Figure 10)).," Following the clumped grains through multiple orbits yields the orbital location, temperature and total disk emission which can be compared to the Spitzer observations (Figure \ref{PlanckOrbit}) )."699 The IRAS value is not constraining., The IRAS value is not constraining.700 The maximum variation in the observed excess for the different eccenlricilies ranges [rom (e—0.1) to (e=0.9)., The maximum variation in the observed excess for the different eccentricities ranges from $e$ =0.1) to $e$ =0.9).701 Of course. the orbital location of anv clamp (taken here (to be a point source) is unknown. so to assess (he importance of eccenlricily and cblumpiness requires an average over all possible clump locations.," Of course, the orbital location of any clump (taken here to be a point source) is unknown, so to assess the importance of eccentricity and clumpiness requires an average over all possible clump locations."702 Figure 11 shows (he result of a Monte Carlo simulation comparing the model of variable emission with the observations as à funelion of eccentricity and the fraction of total material carried in an eccentric orbit. averaged over all starting locations.," Figure \ref{PlanckOrbitFluxchi2} shows the result of a Monte Carlo simulation comparing the model of variable emission with the observations as a function of eccentricity and the fraction of total material carried in an eccentric orbit, averaged over all starting locations."703 The contours show that only an extreme range of eccentricity and chlump fraction can be ruled out., The contours show that only an extreme range of eccentricity and clump fraction can be ruled out.704 For simplicity the simulation assumes a point source clump: to the extent that the chump is spread out in orbital phase. (he amount of variation associated with (he inhomogeneity will be reduced.," For simplicity the simulation assumes a point source clump; to the extent that the clump is spread out in orbital phase, the amount of variation associated with the inhomogeneity will be reduced."705 have argued that a highly eccentric swarm of planetesimals 0.9) could be responsible for a long-lived debris disks around stars like HD 698230., have argued that a highly eccentric swarm of planetesimals $\epsilon>>0.9$ ) could be responsible for a long-lived debris disks around stars like HD 69830.706 Without such hieh eccentricities aud in the absence of a rare collisional event. producing a burst of small grains. collisional processes operating over (he presumed [ew Gvr age of ILD 69830 would result in dust levels much closer to what we now see in our own solar svstem2007a).," Without such high eccentricities and in the absence of a rare collisional event producing a burst of small grains, collisional processes operating over the presumed few Gyr age of HD 69830 would result in dust levels much closer to what we now see in our own solar system."707. Ifa high eccentricitv parent population proves to be the explanation For the ILD 69830 disks. then the results here suggest Chat the parent bodies of the emitting dust mist be spread quite uniformly along the orbital path to account for the lack of the variability monitored by Spitzer and IRAS.," If a high eccentricity parent population proves to be the explanation for the HD 69830 disks, then the results here suggest that the parent bodies of the emitting dust must be spread quite uniformly along the orbital path to account for the lack of the variability monitored by Spitzer and IRAS."708The evolution miplied bv the collisional nature of dark matter must not conflict with observations of dark halos over nearly three orders of magnitude in halo circular velocity.,	The evolution implied by the collisional nature of dark matter must not conflict with observations of dark halos over nearly three orders of magnitude in halo circular velocity.709 In (his section we discuss four constraints on the dark matter interaction obtained at different halo mass scales., In this section we discuss four constraints on the dark matter interaction obtained at different halo mass scales.710 First. a minimum cross section per unit mass is required to solve the cuspy halo problem on chwarf galaxy. and low surlace brightness (LSB) galaxy. scales. below which SIDA interpolates smoothly with CDM and is astvophvsically uninteresting.," First, a minimum cross section per unit mass is required to solve the cuspy halo problem on dwarf galaxy and low surface brightness (LSB) galaxy scales, below which SIDM interpolates smoothly with CDM and is astrophysically uninteresting."711 Second. all dark halos observed today must not have undergone core collapse bv (he present. giving a upper limit or core collapse constraint.," Second, all dark halos observed today must not have undergone core collapse by the present, giving a upper limit or core collapse constraint."712 Third. as pointed out by Guedin and Ostriker (2001). an upper limit on the dark matter interaction can be obtained by requiring (hat. galactic subhalos survive until the present in hotter cluster environments.," Third, as pointed out by Gnedin and Ostriker (2001), an upper limit on the dark matter interaction can be obtained by requiring that galactic subhalos survive until the present in hotter cluster environments."713 Finally. an observational upper limit on the core radius of a cluster of galaxies (Arabacljis οἱ al.," Finally, an observational upper limit on the core radius of a cluster of galaxies (Arabadjis et al."714 2001) also gives a strong constraint on the dark matter interaction., 2001) also gives a strong constraint on the dark matter interaction.715 In the regime where SIDAI halos are optically (hin. the dynamics resembles (wo body relaxation in elobular clusters.," 	In the regime where SIDM halos are optically thin, the dynamics resembles two body relaxation in globular clusters."716 Heat will flow inward from the outer halo due to the temperature inversion implied bv the post-collapse prolile (see Figure 2))., Heat will flow inward from the outer halo due to the temperature inversion implied by the post-collapse profile (see Figure \ref{cartoon}) ).717 À flattened core will develop and erow outward. wilh the central density falling and (he velocity rising.," A flattened core will develop and grow outward, with the central density falling and the velocity rising."718 Once the temperature inversion 1s gone. expansion halts.," Once the temperature inversion is gone, expansion halts."719 The direction of heat flow reverses aud core collapse begins., The direction of heat flow reverses and core collapse begins.720 The state of evolution of a dark halo will be determined bv the ratio of the relaxation time ab its characteristic scale to ils age., The state of evolution of a dark halo will be determined by the ratio of the relaxation time at its characteristic scale to its age.721" For example. if core collapse begins after a number Cy relaxation times. then all halos observed today must have where 7, is given by equ. (2-1b))."," For example, if core collapse begins after a number $C_{1}$ relaxation times, then all halos observed today must have ) = - t_f, where $\tau_s$ is given by eqn. \ref{tau_s}) ),"722" fy is the age of the universe. and /, is the halo formation time."," $t_{H}$ is the age of the universe, and $t_{f}$ is the halo formation time."723 Furthermore. if a number C5 relaxation times must pass belore the central density cusp is significantly flattened. then SIDM will not resolve (he cuspy halo problem unless," Furthermore, if a number $C_{2}$ relaxation times must pass before the central density cusp is significantly flattened, then SIDM will not resolve the cuspy halo problem unless"724therein.,therein.725 The remainder of the Letter is organized as follows., The remainder of the Letter is organized as follows.726 Section 2 contains the derivation of the effective dissipation rate of a mean magnetic field with ambipolar daft in 2D. We provide a mean field dvnamo theory in weakly ionized gas in 8323. by deriving the analytic expressions for alpha aud beta effects.," Section 2 contains the derivation of the effective dissipation rate of a mean magnetic field with ambipolar drift in 2D. We provide a mean field dynamo theory in weakly ionized gas in 3, by deriving the analytic expressions for alpha and beta effects."727 Concluding remarks are provided in 84., Concluding remarks are provided in 4.728 In weakly ionized medium. Ohnms law is valid provided that the velocity of ions is used in the caleulation of current.," In weakly ionized medium, Ohm's law is valid provided that the velocity of ions is used in the calculation of current."729 So. (o consistently treat this problem. one needs (o solve ihe momentum equation for ious aud lor neutrals (without Lorentz Force). together with induction equation for magnetic fields.," So, to consistently treat this problem, one needs to solve the momentum equation for ions and for neutrals (without Lorentz Force), together with induction equation for magnetic fields."730" Since Γρ=r,/p; and p;/p,«1 for weakly ionized medium. the neutralzion collision frequency. can be neglected."," Since $\nu_{in}/{\rho_n}= \nu_{ni}/{\rho_i}$ and $\rho_i/\rho_n \ll 1$ for weakly ionized medium, the neutral-ion collision frequency can be neglected."731" Iere. p, and p; are (he densitv of neutrals aud ions. respectively. and νι and v,,; are jon-neutral aid neutral-ion collision Irequency. respectively."," Here, $\rho_n$ and $\rho_i$ are the density of neutrals and ions, respectively, and $\nu_{in}$ and $\nu_{ni}$ are ion-neutral and neutral-ion collision frequency, respectively."732 Thus. the momentum equation for the neutrals is entirely decoupled from that of the ions as well as from the induction equation.," Thus, the momentum equation for the neutrals is entirely decoupled from that of the ions as well as from the induction equation."733 We thus assume that neutral velocity is turbulent with a prescribed statistics. aud then solve the momentum equation for ions. which evolves sell-consistentlv by [frietional coupling to neutrals and by Lorentz force.," We thus assume that neutral velocity is turbulent with a prescribed statistics, and then solve the momentum equation for ions, which evolves self-consistently by frictional coupling to neutrals and by Lorentz force."734 Note that we are not invoking the strong coupling approximation., Note that we are not invoking the strong coupling approximation.735" In 2D. we work with ion vorlicily w (ως=Vx v) and magnetic potential 1 CÀz)). which are governed by the following set of (vo equations (n dimensionless form): llere. v is the ion velocity. /N is the vorticity of neutrals. 5=i7, is the [rietional coupling between ions and neutrals. 7 is Ohmic diffusivity. and X is ion viscosity."," In 2D, we work with ion vorticity $\omega$ $\omega \hat{z} = \nabla \times {\bf v}$ ) and magnetic potential $A$ ${\bf B}=\nabla \times (A \hat{z})$ ), which are governed by the following set of two equations (in dimensionless form): Here, ${\bf v}$ is the ion velocity, ${\N}$ is the vorticity of neutrals, $\gamma=\nu_{in} \tau_n$ is the frictional coupling between ions and neutrals, $\eta$ is Ohmic diffusivity, and $\chi$ is ion viscosity."736 We shall assume unitv magnetic Prandt] number (i.e.. 47= X).," We shall assume unity magnetic Prandtl number (i.e., $\eta = \chi$ )."737 By decomposing fields into large and small scale parts and assuming that there is no large scale displacement of the medium. we lel v—VotvV.wuwydue—dwuN—ON44N-NB-DBo-cb. and A=Ayta.," By decomposing fields into large and small scale parts and assuming that there is no large scale displacement of the medium, we let ${\bf v}={\bf v_0} + {\bf v} = {\bf v}, \omega=\omega_0 + \omega = 738\omega,739N=N_0 + N = N, {\bf B}={\bf B_0} + {\bf b}$, and $A=A_0 + a$."740 llere. subscript ‘O° denotes a mean component. averaged over (he statistics oEN.," Here, subscript $0$ ' denotes a mean component, averaged over the statistics of $N$."741 Using this decomposition. we can separate the svstem ((1)) in large and small scale components {ο obtain Bex ad 5N..(2)," Using this decomposition, we can separate the system \ref{syst2D}) ) in large and small scale components to obtain _t - ^2 ] = } ) a + N ,"742intrinsic unabsorbed Luminosity of this object should exceec 107 (assuming that we observe only à. few percent of scattered light alone our line of sight).,intrinsic unabsorbed luminosity of this object should exceed $10^{45}$ (assuming that we observe only a few percent of scattered light alone our line of sight).743 Phe column density garule be above Ny107! em? in order to absorb al transmitted photons with energy up to 7 keV. Such a large 'obumn should: produce a high equivalent. width Fe line as 10 Cold obscuring material is photoionised bv the inciden hard X-ray photons., The column density should be above $N_H>10^{24}$ $\rm cm^{-2}$ in order to absorb all transmitted photons with energy up to 7 keV. Such a large column should produce a high equivalent width Fe line as the cold obscuring material is photoionised by the incident hard X-ray photons.744 For an obseuring column of 1074 em we expect an equivalent width Fe line of ~ 1 keV (see Fig., For an obscuring column of $10^{24}$ $\rm cm^{-2}$ we expect an equivalent width Fe line of $\sim$ 1 keV (see Fig.745 3 of Ptak et al., 3 of Ptak et al.746 1996)., 1996).747 This value is consistent with our 90 per cent upper limit for the Fe line equivalent width (0.9 keV)., This value is consistent with our 90 per cent upper limit for the Fe line equivalent width (0.9 keV).748 Probably the most stringent constraints on the AGN nature come from the X-ray to optical emission line ratios., Probably the most stringent constraints on the AGN nature come from the X-ray to optical emission line ratios.749 \laioline et al. (, Maiolino et al. (7501998) argue that as the ΟΠ emission comes from scales much lzwger than the obscuring torus. the fy/for ratio provides a powerful diagnostic of the nuclear activity.,"1998) argue that as the [OIII] emission comes from scales much larger than the obscuring torus, the $f_x/f_{[OIII]}$ ratio provides a powerful diagnostic of the nuclear activity."751 Hence. an obscured AGN should have very low fe/for ratio as the nuclear X-ray luminosity is obscurec while ethe ΟΠ) is not.," Hence, an obscured AGN should have very low $f_x/f_{[OIII]}$ ratio as the nuclear X-ray luminosity is obscured while ethe [OIII] is not."752 The ratio of the X-ray (2-10 keV) to the OLLI] ας (corrected. for absorption using the formula of Bassani et al., The ratio of the X-ray (2-10 keV) to the [OIII] flux (corrected for absorption using the formula of Bassani et al.753 1999) is about 2.5 for our object., 1999) is about 2.5 for our object.754 This is more typical of unobscured AGN (Maiolino et al., This is more typical of unobscured AGN (Maiolino et al.755 1998) arguing against the obscurecl ACN scenario., 1998) arguing against the obscured AGN scenario.756 Aclelitional constraints on the nature of the AGN could in principle. be provided. by the observed: variability.," Additional constraints on the nature of the AGN could in principle, be provided by the observed variability."757 The σον[ος objects should. present rapid. variability with the amplitude increasing as we go to lower luminosities (eg Nandra et al., The Seyfert-1 objects should present rapid variability with the amplitude increasing as we go to lower luminosities (eg Nandra et al.758.. LOOT. Ptak et al.," 1997, Ptak et al."759 1998)., 1998).760 In. contrast. the obseured AGN show little or no variability as a large [fraction of the X-ray emission comes from re-processed radiation far away [rom the nucleus.," In contrast, the obscured AGN show little or no variability as a large fraction of the X-ray emission comes from re-processed radiation far away from the nucleus."761 Llowever. in our case the light curves have poor photon statistics.," However, in our case the light curves have poor photon statistics."762 Both the CLS and the SIS data (4 ksec bins) cannot rule out a constant count rate even ab the 68 per cent confidence level., Both the GIS and the SIS data (4 ksec bins) cannot rule out a constant count rate even at the 68 per cent confidence level.763 Pherelore it is dilIicult to differentiate. on the basis of variability alone. between a Sevlert-1 and an obscured AGN scenario.," Therefore it is difficult to differentiate, on the basis of variability alone, between a Seyfert-1 and an obscured AGN scenario."764 Reearcless of the X-ray emission origin. the enigmatic composite objects present many similarities with the NLAGs detected. in abundance in deep surveys (eg Doyle et al.," Regardless of the X-ray emission origin, the enigmatic composite objects present many similarities with the NLXGs detected in abundance in deep surveys (eg Boyle et al."765 1995)., 1995).766 Many. of these present clear-cut star-forming galaxy spectra., Many of these present clear-cut star-forming galaxy spectra.767 However. their high X-ray luminosities immediately rule out. a star-forming galaxy origin for the X-ray emission.," However, their high X-ray luminosities immediately rule out a star-forming galaxy origin for the X-ray emission."768 Only data exist for these faint objects and therefore their X-ray spectra remain vet largely unconstrained (eg Almaini et al., Only data exist for these faint objects and therefore their X-ray spectra remain yet largely unconstrained (eg Almaini et al.769 1996)., 1996).770 Thus it is cüllicult to compare the X-ray. properties of NLAGs with those of the ‘composites’., Thus it is difficult to compare the X-ray properties of NLXGs with those of the 'composites'.771 However. it is interesting to note that if the NLNGs have X-ray spectra similar to HUXS00317- then they would make a small contribution to the background.," However, it is interesting to note that if the NLXGs have X-ray spectra similar to IRAS00317-2142, then they would make a small contribution to the X-ray background."772 Indeed. the X-ray spectrum of HUXS003217-2142 in the 2-10 keV. band is much steeper than that of the X-ray background in the same band (Gendreau et al.," Indeed, the X-ray spectrum of IRAS003217-2142 in the 2-10 keV band is much steeper than that of the X-ray background in the same band (Gendreau et al."773 1995)., 1995).774We now eo through the exercise of evaluating the p-mode frequencies of the 75 selected nodels using Guenther's stellar pulsation code (Guenther 1994).,We now go through the exercise of evaluating the -mode frequencies of the 75 selected models using Guenther's stellar pulsation code (Guenther 1994).775 It is important to remember that the theoretical frequencies calculated here should not be expected to match the observed yequencies of 51 Pee very closely., It is important to remember that the theoretical frequencies calculated here should not be expected to match the observed frequencies of 51 Peg very closely.776 To start with. our theoretical models do not match either the radius or mass of 51 Peg precisely.," To start with, our theoretical models do not match either the radius or mass of 51 Peg precisely."777 But even in the hypothetical case in which the nodel radius ancl mass reproduce (he stellar radius aud mass with high precision (as in a calibrated. standard solar models). the caleulated. Lrequencies could still differ appreciably rom the observed frequencies due to the uncertainty in caleulating the sound speed in the outer lavers of the models where non-adiabatic effects become important.," But even in the hypothetical case in which the model radius and mass reproduce the stellar radius and mass with high precision (as in a calibrated standard solar models), the calculated frequencies could still differ appreciably from the observed frequencies due to the uncertainty in calculating the sound speed in the outer layers of the models where non-adiabatic effects become important."778 For instance. in the case of standard solar models constructed under the same physical assumptions as the 51 Peg models we present. this discrepancy. can reach. 10-20: 4472 at the higher frequencies (see Guenther Demarque 1997; Winnick et al.," For instance, in the case of standard solar models constructed under the same physical assumptions as the 51 Peg models we present, this discrepancy can reach 10-20 $\mu Hz$ at the higher frequencies (see Guenther Demarque 1997; Winnick et al."779 2001)., 2001).780 This discrepancy is reduced by a factor of four in standard solar models (hat include à more realistic description of convection in (he atmosphere (Li et al., This discrepancy is reduced by a factor of four in standard solar models that include a more realistic description of convection in the atmosphere (Li et al.781 2002)., 2002).782" Because the discrepancies are themselves a function of frequency, these could also result in a smaller but significant effect on the caleulated large spacings discussed in 83.2 and &4."," Because the discrepancies are themselves a function of frequency, these could also result in a smaller but significant effect on the calculated large spacings discussed in 3.2 and 4."783 On the other hand. (he small spacings. being primarily sensitive to (he central concentration ol the model. are less affected by the details of the surface boundary conditions.," On the other hand, the small spacings, being primarily sensitive to the central concentration of the model, are less affected by the details of the surface boundary conditions."784 The small spacings are sensiüve primarily (0 age and to the size of the convective core when one is present., The small spacings are sensitive primarily to age and to the size of the convective core when one is present.785 Guenther's (1994) pulsation code allows For (he non-adiabatie corrections in the pulsation needed (o account for radiation in the Eddington approximation., Guenther's (1994) pulsation code allows for the non-adiabatic corrections in the pulsation needed to account for radiation in the Eddington approximation.786 The accuracy of these corrections is a function of frequency. such that at high frequencies it is harder to account for non-adiabatic effects due to convection-oscillation interactions and thus errors are larger., The accuracy of these corrections is a function of frequency such that at high frequencies it is harder to account for non-adiabatic effects due to convection-oscillation interactions and thus errors are larger.787" We define (he large spacings )andsmallspacings Yntheusualway.suchlhal.Nv,, and."," We define the large spacings and small spacings in the usual way, such that, and,"788only as good as their initial conditions which. until now. rave been known only rather poorly.,"only as good as their initial conditions which, until now, have been known only rather poorly."789 In this work. we quantify the distribution of orbita xwameters for dark matter halos at the point of merging with their host. (i.c. we proceed in a similar wav as clic Vitvitskactal. 2002)).," In this work, we quantify the distribution of orbital parameters for dark matter halos at the point of merging with their host (i.e. we proceed in a similar way as did \pcite{vitvit02}) )."790 We measure this distribution in a aree number of N-body simulations to attain high statistica orecision and to facilitate checks of our techniques and tests or variations of the distribution of orbital parameters with variables such as redshift. halo mass ete.," We measure this distribution in a large number of N-body simulations to attain high statistical precision and to facilitate checks of our techniques and tests for variations of the distribution of orbital parameters with variables such as redshift, halo mass etc."791 While we wil esent. clistributions of orbital cecentricity and semi-major axis. our focus is on distributions of radial anc tangentia velocities. which we find are more practical when clealing with orbits in non-spherical svstems in which ονπαίσα friction is atwork?.," While we will present distributions of orbital eccentricity and semi-major axis, our focus is on distributions of radial and tangential velocities, which we find are more practical when dealing with orbits in non-spherical systems in which dynamical friction is at."792. We also examine the distribution of infalling substructures as a function of position on the viria sphere. and explore correlations between orbital properties and the spin of the host halo.," We also examine the distribution of infalling substructures as a function of position on the virial sphere, and explore correlations between orbital properties and the spin of the host halo."793 Our aim is to provide a precise and accurate measurement of the distribution of orbital properties of substructures at the time of merging. and to provide fits to this distribution so that it may be used. in. further studies.," Our aim is to provide a precise and accurate measurement of the distribution of orbital properties of substructures at the time of merging, and to provide fits to this distribution so that it may be used in further studies."794 This distribution could. in. principle. depend. on many quantities. such as the masses of the merging halos. redshift. cosmological parameters ete.," This distribution could, in principle, depend on many quantities, such as the masses of the merging halos, redshift, cosmological parameters etc."795 Furthermore. the six parameters. describing cach orbit. (e.g. the position and velocity of the satellite at the time of merging. or anv equivalent. parameter. set) may well be correlated with each other. such that we should. really examine a six-dimensional phase-space clistribution function.," Furthermore, the six parameters describing each orbit (e.g. the position and velocity of the satellite at the time of merging, or any equivalent parameter set) may well be correlated with each other, such that we should really examine a six-dimensional phase-space distribution function."796 With the currently: available N-bock simulations we will limit ourselves to exploring a two-dimensional function. tvpically that of radial and tangential velocities (effectively assuming that infalling satellites are uniformly distributed on a sphere around the halo centre and that their tangential velocities have no preferred. direction). although we will. explore correlations between these quantities ancl the host. halo.," With the currently available N-body simulations we will limit ourselves to exploring a two-dimensional function, typically that of radial and tangential velocities (effectively assuming that infalling satellites are uniformly distributed on a sphere around the halo centre and that their tangential velocities have no preferred direction), although we will explore correlations between these quantities and the host halo."797 We note also that the situation could in principle be more complicated still., We note also that the situation could in principle be more complicated still.798 We are aiming to quantify P(x). where x ave the orbital parameters ancl £? is the distribution of these averaged over all merging events.," We are aiming to quantify $P({\bf x})$ , where ${\bf799x}$ are the orbital parameters and $P$ is the distribution of these averaged over all merging events."800" Llowever. after one merger with parameters x, the relevant distribution function for the next merger may be dilflerent. P(x[x1)."," However, after one merger with parameters ${\bf x}_1$ the relevant distribution function for the next merger may be different, $P({\bf x}|{\bf x}_1)$."801 An example might be infall of halos along a filament., An example might be infall of halos along a filament.802 Ixnowing that one halo [ell in from a particular direction. it becomes more likely that the next halo will fall in from a similar direction.," Knowing that one halo fell in from a particular direction, it becomes more likely that the next halo will fall in from a similar direction."803 We will explore one aspect of this possibility by measuring the distribution of angles between pairs of infalling satellites., We will explore one aspect of this possibility by measuring the distribution of angles between pairs of infalling satellites.804 The remainder of this paper is arranged as follows., The remainder of this paper is arranged as follows.805 In we describe our analysis technique while in we present our results., In \\ref{sec:analysis} we describe our analysis technique while in \\ref{sec:results} we present our results.806 We give our conclusions in& relsee:cliscuss. ., We give our conclusions in \\ref{sec:discuss}.807 ‘To measure satellite orbital parameters. we make use of a large number of N-body simulations carried out by the VIRGO Consortium and which are publich available (see Jenkinsetal.1998:Ixaulfmann1999.:ct2001 for further details). together with one other simulation used. for testing various aspects of our methodology.," To measure satellite orbital parameters we make use of a large number of N-body simulations carried out by the VIRGO Consortium and which are publicly available (see \pcite{jenkins98,kauffmann99,jenkins01}808 for further details), together with one other simulation used for testing various aspects of our methodology."809 These span a range of cosmologies and redshifts., These span a range of cosmologies and redshifts.810 Details of the simulations used are given in “Table 1.., Details of the simulations used are given in Table \ref{tb:sims}.811 Alb of the outputs from these simulations are analysed. but in practise only those at recshifts z provide statistically useful measurcments of orbital parameter distributions.," All of the outputs from these simulations are analysed, but in practise only those at redshifts $z\lsim 2$ provide statistically useful measurements of orbital parameter distributions."812 1n order to find merging dark matter halos in the simulations we must first identifv all dark matter halos., In order to find merging dark matter halos in the simulations we must first identify all dark matter halos.813 To locate dark matter halos in the N-body simulations we emplov two standard. group finders. the friends-of-Eriends (FOE: etal. 1985)) and spherical overdensity (SO: Lacey&Cole19942) algorithms.," To locate dark matter halos in the N-body simulations we employ two standard group finders, the friends-of-friends (FOF; \pcite{defw}) ) and spherical overdensity (SO; \pcite{lc94}) ) algorithms."814 We will compare results for halos found using these two techniques to test for any dependence on he group finding algorithm: used., We will compare results for halos found using these two techniques to test for any dependence on the group finding algorithm used.815 Each algorithm has one tunable parameter. the linking ength. mink. for the FOR algorithm and the mean density contrast inside the sphere. A. for the SO algorithm.," Each algorithm has one tunable parameter, the linking length, $r_{\rm816link}$, for the FOF algorithm and the mean density contrast inside the sphere, $\bar{\Delta}$, for the SO algorithm."817 Both can xf related to the mean density of dark matter halos (once a specific halo density profile has been chosen in the case of he FOE. algorithm), Both can be related to the mean density of dark matter halos (once a specific halo density profile has been chosen in the case of the FOF algorithm).818 We apply cach algorithm twice. once assuming. a mean overdensity ⋠⋅for halos of A=18x72171.3-- (equivalent to rink=020r. assuming an isothermal haloolile?.. where r is the mean inter-particle spacing in the simulation). as expected. from the spherical collapse mocel in a critical density cosmology (e.g. Peebles— 1980)). and once using the mean overdensity expected from the spherical collapse model for the specific cosmology ancl redshift in question (Lacey&Cole1993:Eke.Frenk1996).," We apply each algorithm twice, once assuming a mean overdensity for halos of $\bar{\Delta}=18 \pi^2 \approx 177.7$ (equivalent to $r_{\rm link} =8190.20 \bar{r}$, assuming an isothermal halo, where $\bar{r}$ is the mean inter-particle spacing in the simulation), as expected from the spherical collapse model in a critical density cosmology (e.g. \pcite{peebles80}) ), and once using the mean overdensity expected from the spherical collapse model for the specific cosmology and redshift in question \cite{lc93,eke96}."820" We will refer to these two alternatives as ""fixed. A” and “variable AW respectively. and will compare results from the two."," We will refer to these two alternatives as “fixed $\Delta$ ” and “variable $\Delta$ ” respectively, and will compare results from the two."821 Once halos have been Located. by either algorithm we apply a procedure to remove unbound halos from the resulting catalogue., Once halos have been located by either algorithm we apply a procedure to remove unbound halos from the resulting catalogue.822 Our technique is described: fully by Bensonctal.(2001) and involves repeatedlyremoving the least bound. particle from an unbound halo until the halo either. beeomes bound. or falls below the minimunr mass required to be included in our catalogue.," Our technique is described fully by \scite{benson01} and involves repeatedlyremoving the least bound particle from an unbound halo until the halo either becomes bound, or falls below the minimum mass required to be included in our catalogue."823the action of radiative cooling. which is stronger at higher redshifts.,"the action of radiative cooling, which is stronger at higher redshifts."824 This is illustrated by Fig. 7..," This is illustrated by Fig. \ref{fig:toymodelz100Myr},"825 where the spectra of our models are shown after 100 Myr cooling., where the spectra of our models are shown after 100 Myr cooling.826 With Fig., With Fig.827 8. we demonstrate that the combined SSC and CAIB-IC spectra contain chough information in order to discriminate between models with different cucrev-rich low euergv clectron populations. e.g. power-law aud relativistic \laxwell-Boltzimaun distributions (Eq. AS))," \ref{fig:toymodellEPop} we demonstrate that the combined SSC and CMB-IC spectra contain enough information in order to discriminate between models with different energy-rich low energy electron populations, e.g. power-law and relativistic Maxwell-Boltzmann distributions (Eq. \ref{eq:fth}) )"828 as e.g. sketched in Fig. 2.., as e.g. sketched in Fig. \ref{fig:rgsketch}.829 IC scattering of an anisotropic seed photon field leads to some polarization in the scattered radiation for small electron Lorentz factors (sec e.g. Beechuan et al. (1987)))., IC scattering of an anisotropic seed photon field leads to some polarization in the scattered radiation for small electron Lorentz factors (see e.g. Begelman et al. \cite*{1987ApJ...322..650B}) ).830 Tn our spherically svuuucetrie model the photon feld has a radial anisotropy at off-center locations., In our spherically symmetric model the photon field has a radial anisotropy at off-center locations.831 Therefore the source should exhibit au SSC polarization pattern. which is strongest at the source edge aud has clectric vectors aligned ou circles.," Therefore the source should exhibit an SSC polarization pattern, which is strongest at the source edge and has electric vectors aligned on circles."832 The source averaged polarization is zero in our highly svuumetric tov model., The source averaged polarization is zero in our highly symmetric toy model.833 But in nature. typical sources can be expected to be elongated.," But in nature, typical sources can be expected to be elongated."834 For radio galaxy lobes. elongation bv a factor of two are not unusual. aud rather laree aspect ratios can be attributed to head-tail radio galaxies.," For radio galaxy lobes, elongation by a factor of two are not unusual, and rather large aspect ratios can be attributed to head-tail radio galaxies."835 Thus. we expect radio galaxies to exhibit a stnall level of linearly polarized SSC fux at lowest frequencies due to source elongation. if a substantial ouly iüldlv relativistic electron population is present in the sSOUrCO.," Thus, we expect radio galaxies to exhibit a small level of linearly polarized SSC flux at lowest frequencies due to source elongation, if a substantial only mildly relativistic electron population is present in the source."836 Further. the iutrinsic svuchrotrou polarization of sources with large-scale ordered magnetic fields is conserved to a large fraction iu the IC process (Bonometto&Saeeion.1973:CelottiMatt.199 D).," Further, the intrinsic synchrotron polarization of sources with large-scale ordered magnetic fields is conserved to a large fraction in the IC process \cite{1973A&A....23....9B,1994MNRAS.268..451C}."837. Since many racio ealaxies exhibit polarization. fossil radio galaxies should often have au iutriusicallv polarized SSC flux of up to. 10 »»larization at all frequencies.," Since many radio galaxies exhibit polarization, fossil radio galaxies should often have an intrinsically polarized SSC flux of up to 40 polarization at all frequencies."838 Enviroumenutal infuences ou the radio plasma. like shear flows aud shock compression. can dmerease both oj)larization effects bw increasing the source elongatiou and by aligning the iuterual magnetic fields (Eufbliu&Bitigecn.2001.fortheimpactofshock waves}.," Environmental influences on the radio plasma, like shear flows and shock compression, can increase both polarization effects by increasing the source elongation and by aligning the internal magnetic fields \cite[for the impact of shock waves]{ensslinbrueggen01}."839. Very peculiar »)larization properties can arise around 100 CIIz for sources. where the unpolarized CMD js cdiuiuisled by IC scattering. but polarized SSC chussion contributes to this spectral raneec.," Very peculiar polarization properties can arise around 100 GHz for sources, where the unpolarized CMB is diminished by IC scattering, but polarized SSC emission contributes to this spectral range."840 If the CMD-IC. decrement exceeds the SSC) huuinositv a polarized decreiuent inu the CMD sky can be found at these frequeucies., If the CMB-IC decrement exceeds the SSC luminosity a polarized decrement in the CMB sky can be found at these frequencies.841 This can be of importance for future high precision CMD polarization measurements., This can be of importance for future high precision CMB polarization measurements.842 Several telescopes are uncer development which may be suitable to search for SSC and CALIB-IC signatures of low energv cosnüc rav electrons., Several telescopes are under development which may be suitable to search for SSC and CMB-IC signatures of low energy cosmic ray electrons.843 We list in Tab., We list in Tab.844 1 approxiuate values of expected poiut source scusitivitics Fa of several plaued instruments., \ref{tab:sensitivity} approximate values of expected point source sensitivities $F_{\nu}$ of several planed instruments.845" If a source with surface brightuess 5, and augulu area ος is smaller or comparable to the instrament beam with area zl, then the full seuxitivitv can directly be compared to the source huninosity iu order to estinate the significauce σ of the expected detection: 02S,4/FL."," If a source with surface brightness $S_\nu$ and angular area $A_{\rm s}$ is smaller or comparable to the instrument beam with area $A_{\rm b}$ then the full sensitivity can directly be compared to the source luminosity in order to estimate the significance $\sigma$ of the expected detection: $\sigma \approx S_\nu \,A_{\rm s}/F_{\nu}$."846 If the source appears extended the significance is lower., If the source appears extended the significance is lower.847" For a sinele-dish aud phased array telescopes the significance is approxiuatelv eiven by σzαρ(ALM)DEQ since the signal of the No=ACPA), dmedividual beais should be added like independent mieasurenme-s vieldiug Ororal7Thoam-VP "," For a single-dish and phased array telescopes the significance is approximately given by $\sigma \approx S_\nu \,(A_{\rm s}\,A_{\rm848b})^{1/2}/F_{\nu}$, since the signal of the $N = A_{\rm s}/A_{\rm b}$ individual beams should be added like independent measurements yielding $\sigma_{\rm total} \approx \sigma_{\rm beam} \,849N^{1/2}$."850For interferometers. the detected sigual of an extended source scales with (the square root of) the fraction of the telescope baselines for which the source is still unresolved.," For interferometers, the detected signal of an extended source scales with (the square root of) the fraction of the telescope baselines for which the source is still unresolved."851 This depends strongly on- the iudividual array design aud we therefore do not attempt to estimate it., This depends strongly on the individual array design and we therefore do not attempt to estimate it.852 Often. the interferometers clemeuts are distributed iu a wav that anv more short baselines (which are sensitive to large-scale structures) exist than long baselines (which oulv see small angular sources).," Often, the interferometers elements are distributed in a way that many more short baselines (which are sensitive to large-scale structures) exist than long baselines (which only see small angular sources)."853 For example it is planed that zz25% of the collecting area of LOFAR is within a virtual core of 2 Ian diameter (compared to an mstruneut diaüneter of 300 ku)., For example it is planed that $\approx 25$ of the collecting area of LOFAR is within a virtual core of 2 km diameter (compared to an instrument diameter of 300 km).854 Therefore the virtual core of LOFAR Is quiet sensitive to extended flux on augular scales 60 times larger than the full resolution of the iustrunent., Therefore the virtual core of LOFAR is quiet sensitive to extended flux on angular scales 60 times larger than the full resolution of the instrument.855tests is showed in Fig.,tests is showed in Fig.856 3 as a function of the semimajor axis and perihelion distance.," \ref{figure3}857 as a function of the semimajor axis and perihelion distance."858 For comparison Fig., For comparison Fig.859 4 shows the effect in w given by Eq. (4))., \ref{figure4} shows the effect in $\omega$ given by Eq. \ref{quinnperi}) ).860" If we are interested in computing the relativistic effects due to the Sun on a small body, we could just introduce Eq. (1))"," If we are interested in computing the relativistic effects due to the Sun on a small body, we could just introduce Eq. \ref{quinn}) )"861 into an integrator., into an integrator.862" The problem is that this acceleration depends on both vectors position an velocity of the particle, so the speed of the integrator may be slowed down in order to calculate accurately the vectorial products at small heliocentric distances."," The problem is that this acceleration depends on both vectors position an velocity of the particle, so the speed of the integrator may be slowed down in order to calculate accurately the vectorial products at small heliocentric distances."863" Moreover, it is not a simple task to introduce this perturbation in a sympletic integrator, though it can be done (Saha&Tremaine1994)."," Moreover, it is not a simple task to introduce this perturbation in a sympletic integrator, though it can be done \citep{satre94}."864". In order to overcome this difficulty, some alternative simpler models have been created in the last two decades."," In order to overcome this difficulty, some alternative simpler models have been created in the last two decades."865 The relativistic precession of the argument of perihelion is correctly reproduced defining a radial (T'= 0) acceleration: (Nobili&Roxburgh1986)., The relativistic precession of the argument of perihelion is correctly reproduced defining a radial $T=0$ ) acceleration: \citep{Nob86}.866. Inserting this R in the TAGPE the exact secular drifts generated by Eq. (1)), Inserting this $R$ in the TAGPE the exact secular drifts generated by Eq. \ref{quinn}) )867 are recovered except for mean anomaly., are recovered except for mean anomaly.868 Saha&Tremaine(1992) added one more term into (6)) in order to account for both w and M drifts:, \cite{satre} added one more term into \ref{nob}) ) in order to account for both $\omega$ and $M$ drifts:869will modify this behavior by liwiting the wim possible iuuer disk radius. see figure 5.,"will modify this behavior by limiting the minimum possible inner disk radius, see figure 5."870 Thus. saturation at a nininnmun disk radius for large mass accretion rates is a signature of the mareially stable orbit (Miller. Lamb. Psaltis 1998).," Thus, saturation at a minimum disk radius for large mass accretion rates is a signature of the marginally stable orbit (Miller, Lamb, Psaltis 1998)."871" As described in Ἱναατοῖ, Ford. Chen (1997). when the disk reaches the mareinally stable orbit. the iuner radius will not approach a suele value. but instτας wander over soie range due to the properties of the trausouc flow near the mareially stable orbit."," As described in Kaaret, Ford, Chen (1997), when the disk reaches the marginally stable orbit, the inner radius will not approach a single value, but instead wander over some range due to the properties of the transonic flow near the marginally stable orbit."872 Tf one is willing to accept the assertious made in the previous section that the QPO frequency is determined by the radius of the inner edee of the accretion disk and that the x-ray specval state is au iudicator of mass accretion rate through the disk. then the relation of ΟΡΟ frequency versus spectral state can be used to probe he relation of immer disk racius versus nass accretion rate through the disk.," If one is willing to accept the assertions made in the previous section that the QPO frequency is determined by the radius of the inner edge of the accretion disk and that the x-ray spectral state is an indicator of mass accretion rate through the disk, then the relation of QPO frequency versus spectral state can be used to probe the relation of inner disk radius versus mass accretion rate through the disk."873" Thus he shape of the ΟΡΟ versus spectral state diagram. ic. whether or not the QPO YOquenicy sauates at high mass accretion rates, provides a test for tle preseuce of he mareiaIv stable orbit."," Thus, the shape of the QPO versus spectral state diagram, i.e. whether or not the QPO frequency saturates at high mass accretion rates, provides a test for the presence of the marginally stable orbit."874 The OPO frequency versus spectral stae diagraun for LU 172831. Fig.," The QPO frequency versus spectral state diagram for 4U 1728–34, Fig."875 3. shows 10 evidence or a saturation of QPO frequeucv at lieh mass accretion rates.," 3, shows no evidence for a saturation of QPO frequency at high mass accretion rates."876 This is also true for almost all neutron star binary ‘or Which kIIz QPOs have beeu detected., This is also true for almost all neutron star binary for which kHz QPOs have been detected.877 There is only oue source which does show a clear saturation of ΟΡΟ frequency at Heh inferre lass accretion rates: [IU 152130., There is only one source which does show a clear saturation of QPO frequency at high inferred mass accretion rates: 4U 1820-30.878 Zhane et (1998) demonstrated a saturation of QPO frequency versus X-ray* count rate for LU 1820-30., Zhang et (1998) demonstrated a saturation of QPO frequency versus x-ray count rate for 4U 1820-30.879 Tlowever. as OPO frequeicv is poorly correlated with ccount rate in most sources (the relation ends to look similar to the QPO frequeacy versus fux relation in Fie.," However, as QPO frequency is poorly correlated with count rate in most sources (the relation tends to look similar to the QPO frequency versus flux relation in Fig."880 1). this approach caue under significant criticisun.," 1), this approach came under significant criticism."881 Ikaaret et ((1999) showed that the, Kaaret et (1999) showed that the882In the entire sky. there are regions where both the main-correlation and the can be seen (e.g.. the Galactic plane).,"In the entire sky, there are regions where both the main-correlation and the sub-correlation can be seen (e.g., the Galactic plane)."883 There are (wo methods for determining whether (he main- or sub-correlation is applicable if the best-fit is not used., There are two methods for determining whether the main- or sub-correlation is applicable if the best-fit is not used.884 The first method is the same as that for the Cvenus region., The first method is the same as that for the Cygnus region.885 We can make a color-color diagram in anv area of the skv and choose (he better one., We can make a color-color diagram in any area of the sky and choose the better one.886 The second method involves referring to the radio thermal continuum map that represents the bulk of the ionized gas excited bv the OD stars., The second method involves referring to the radio thermal continuum map that represents the bulk of the ionized gas excited by the OB stars.887 The direction with strong radio continuum should be associated with the region where the ISRF varies on a small scale because of the strong local heating sources., The direction with strong radio continuum should be associated with the region where the ISRF varies on a small scale because of the strong local heating sources.888 Therefore. the FII colors in (he direction with strong radio continuum can be thought to follow the sub-correlation as demonstrated by Ibi et al. (," Therefore, the FIR colors in the direction with strong radio continuum can be thought to follow the sub-correlation as demonstrated by Hibi et al. ("8892006).,2006).890 Figure 1 shows that the sub-correlation is more major than (he main-correlation in (he Cvgnus region., Figure 1 shows that the sub-correlation is more major than the main-correlation in the Cygnus region.891 We estimate the svstematic dillerence arising [rom the selection of either the or (he sub-correlation. since in general] we are unaware a priori which of the two correlations is applicable to a certain region.," We estimate the systematic difference arising from the selection of either the main-correlation or the sub-correlation, since in general we are unaware a priori which of the two correlations is applicable to a certain region."892 We compare Ay caleulated by the and the sub-correlation in Figure 1H., We compare $A_{V}$ calculated by the main-correlation and the sub-correlation in Figure 14.893 The range of the Ay ratio is between | and 2.5 where the range of £(60jun)/Fe(100qon) is between 0.2 and 0.6., The range of the $A_{V}$ ratio is between 1 and 2.5 where the range of $I (60\ \mu m)/I_{C} (100\ \mu m)$ is between 0.2 and 0.6.894 ]libi et al. (, Hibi et al. (8952006) identified the (wo groups in the color-color plot of the DIRDBE data with 42’ resolution.,2006) identified the two groups in the color-color plot of the DIRBE data with $'$ resolution.896 Each group has good correlation expressed by Equations (3) and (4)., Each group has good correlation expressed by Equations (3) and (4).897 These (wo expressions can be applied to the intensity distribution with a hieher spatial resolution such as that of theLRAS map., These two expressions can be applied to the intensity distribution with a higher spatial resolution such as that of the map.898 As indicated by Hibi et al. (, As indicated by Hibi et al. (8992006) and IHirashita et al. (,2006) and Hirashita et al. (9002007). (he main-correlation represents (he lines of sight along which the ISRF is constant. and the sub-correlation represents the lines of sieht along which the ISRF varies greatly.,"2007), the main-correlation represents the lines of sight along which the ISRF is constant, and the sub-correlation represents the lines of sight along which the ISRF varies greatly."901 Obviously. the lines of sight showing the sub-correlation mav also represent (he direction along which ihe ISRF varies within the beam.," Obviously, the lines of sight showing the sub-correlation may also represent the direction along which the ISRF varies within the beam."902 The direction following the main-correlation with the DIRDBE beam does not include regions having strong radiation (Case 1)., The direction following the main-correlation with the DIRBE beam does not include regions having strong radiation (Case 1).903 Otherwise. it must follow the sub-correlation.," Otherwise, it must follow the sub-correlation."904 The ISRE does not vary extensively along the line of sight and over the spatial extent of the DIRBE beam., The ISRF does not vary extensively along the line of sight and over the spatial extent of the DIRBE beam.905 Therefore. all lines of sight of the7/15 beam in à DIRBE beam should follow the main-correlation.," Therefore, all lines of sight of the beam in a DIRBE beam should follow the main-correlation."906 On the other hand. there should be strong ISRF regions in the line of sight indicating the sub-correlation with the DIRBE beam (Case 2).," On the other hand, there should be strong ISRF regions in the line of sight indicating the sub-correlation with the DIRBE beam (Case 2)."907 The strong ISRE region is usually compact. so the spatial extent could be smaller (han the DIRBE beam.," The strong ISRF region is usually compact, so the spatial extent could be smaller than the DIRBE beam."908 A DIRBE beam can be divided into manyZ/215S beams. some indicating (he main-correlation (Case 2-1) and the others the sub-correlation (Case 2-2).," A DIRBE beam can be divided into many beams, some indicating the main-correlation (Case 2-1) and the others the sub-correlation (Case 2-2)."909 The former does not include the strong ISRF regions. and the," The former does not include the strong ISRF regions, and the"910This work was partly supported by the National Natural Science Foundation. of China. grants. 1977300 and 19825109. and the National Climbing Project on Funcamental men,"This work was partly supported by the National Natural Science Foundation of China, grants 19773007 and 19825109, and the National Climbing Project on Fundamental Researches."911magnetic field and dust models are listed. followed by a brief discussion of the properties of (he simulated stellar populations.,"magnetic field and dust models are listed, followed by a brief discussion of the properties of the simulated stellar populations."912" Finally, the Stokes radiative transfer moclel is presented."," Finally, the Stokes radiative transfer model is presented."913 Polarization of background starlisht is thought to arise [rom anisotropic dust erains aligned in magnetic fields (loracomprehensivehistoryof(hisideasee 2003)., Polarization of background starlight is thought to arise from anisotropic dust grains aligned in magnetic fields \citep[for a comprehensive history of this idea see][]{Laz03}.914. Theories for alignment. mechanisms include paramagnetic dissipation (Davis&Greenstein1951:Purcell1975. 1979)..mechanical (gas streaming) alignment (Gold.1952).. superparamaegnetic dissipation (Jones&Spitzer1967).. aud radiative torques (Dolginov&Mvytrophanov1976:DraineWeingartner1996.1997:LazarianIloang 2007).," Theories for alignment mechanisms include paramagnetic dissipation \citep{DG51,P75,P79}, mechanical (gas streaming) alignment \citep{G52}, superparamagnetic dissipation \citep{JS67}, and radiative torques \citep{DM76,DW96,DW97,LH07}."915 With the exception of mechanical alignment. the prediction is that spinning dust grains will preferentially alien with their long axes perpendicular to the local magnetic field.," With the exception of mechanical alignment, the prediction is that spinning dust grains will preferentially align with their long axes perpendicular to the local magnetic field."916 Unpolarized background starlight passing through. a medium with aligned grains will experience a larger extinction cross-section perpendicular to the magnetic field than parallel to it. so that the Gransmitted lisht becomes weakly linearly polarized parallel to the direction of the magnetic field as projected onto the plane of the Two broad classes of Galactic magnetic fields need to be considered: axisviimetric (ASS) and bisvmmetrie (BSS). though higher-order svimnmetries and combinations are possible (Wielebinski&Krause 1993)..," Unpolarized background starlight passing through a medium with aligned grains will experience a larger extinction cross-section perpendicular to the magnetic field than parallel to it, so that the transmitted light becomes weakly linearly polarized parallel to the direction of the magnetic field as projected onto the plane of the Two broad classes of Galactic magnetic fields need to be considered: axisymmetric (ASS) and bisymmetric (BSS), though higher-order symmetries and combinations are possible \citep{WK93}. ."917 ASS and BSS fields are differentiated by their, ASS and BSS fields are differentiated by their918in the dise of NGC 5719 are counter-rotating with respect to the main stellar disc.,in the disc of NGC 5719 are counter-rotating with respect to the main stellar disc.919 The kinematics of the ionized-gas dise and of both the counter-rotating stellar dises are measured out to about 40 (4.3 kpc) from the galaxy centre., The kinematics of the ionized-gas disc and of both the counter-rotating stellar discs are measured out to about $40''$ (4.3 kpc) from the galaxy centre.920 In conclusion. ?. propose a scenario where ffrom the large reservoir available in the galactic surroundings was accreted by NGC 5719 onto a retrograde orbit and subsequently fuelled the formation of the counter-rotating stellar disc.," In conclusion, \citet{Vergani+07} propose a scenario where from the large reservoir available in the galactic surroundings was accreted by NGC 5719 onto a retrograde orbit and subsequently fuelled the formation of the counter-rotating stellar disc."921 In this work. we will address the erucial piece of information which is still missing. i.e. proving that the stellar population of the counter-rotating dise of NGC 5719 is vounger with respect to that of the stars in the galaxy main disc.," In this work, we will address the crucial piece of information which is still missing, i.e. proving that the stellar population of the counter-rotating disc of NGC 5719 is younger with respect to that of the stars in the galaxy main disc."922 The integral-field spectroscopic observations were carried out in service mode with the Very Large Telescope (VLT) at the European Southern Observatory CESO) in Paranal during dark time between 28 April and 16 June 2009., The integral-field spectroscopic observations were carried out in service mode with the Very Large Telescope (VLT) at the European Southern Observatory (ESO) in Paranal during dark time between 28 April and 16 June 2009.923 The Unit Telescope 3 was equipped with the Visible Multi Object Spectrograph (VIMOS) in the Integral Field Unit (FU) configuration., The Unit Telescope 3 was equipped with the Visible Multi Object Spectrograph (VIMOS) in the Integral Field Unit (IFU) configuration.924 The HR blue grism covering the spectral range 4150— 6200 aand the 07667 resolution were used., The HR blue grism covering the spectral range 4150 – 6200 and the 67 $^{-1}$ resolution were used.925 The instrumental spectral resolution measured at 5200 wwas 2.0 (FWHM). equivalent to 115," The instrumental spectral resolution measured at 5200 was $2.0$ (FWHM), equivalent to 115."926 Observations were organised into three dithered on-target exposures of 2950 seconds each. alternated to three offset sky exposures of 280 seconds each.," Observations were organised into three dithered on-target exposures of 2950 seconds each, alternated to three offset sky exposures of 280 seconds each."927" The average seeing measured by the ESO Differential Image Meteo Tonitor was 1"".", The average seeing measured by the ESO Differential Image Meteo Monitor was $1''$.928 Data reduction (bias subtraction. fibre identification and racing. flat fielding. wavelength calibration and correction for instrument transmission) was performed using the VIMOS ESO yipeline version 2.2.1 chttp://Awww.eso.org/sci/software/pipelines/).," Data reduction (bias subtraction, fibre identification and tracing, flat fielding, wavelength calibration and correction for instrument transmission) was performed using the VIMOS ESO pipeline version 2.2.1 (http://www.eso.org/sci/software/pipelines/)."929 The different relative transmission of the VIMOS quadrants was corrected by comparing the intensity of the night-sky emission ines., The different relative transmission of the VIMOS quadrants was corrected by comparing the intensity of the night-sky emission lines.930 The three offset observations were used to construct three sky spectra., The three offset observations were used to construct three sky spectra.931 To compensate for the time variation of the relative intensity of the night-sky emission lines. we compared the fluxes of the sky lines measured in the offset and on-target exposures.," To compensate for the time variation of the relative intensity of the night-sky emission lines, we compared the fluxes of the sky lines measured in the offset and on-target exposures."932 The corrected sky spectra were then subtracted from the corresponding on-target exposures., The corrected sky spectra were then subtracted from the corresponding on-target exposures.933 Each exposure was organised in a data cube using the tabulated correspondence between each fibre and its position in the field of view., Each exposure was organised in a data cube using the tabulated correspondence between each fibre and its position in the field of view.934 The three sky-subtracted data cubes were aligned using the bright galaxy nucleus as reference and added into a single data cube., The three sky-subtracted data cubes were aligned using the bright galaxy nucleus as reference and co-added into a single data cube.935 In order to increase the signal to noise ratio CSN). spectra from fibres mapping adjacent regions in the sky were added together using the Voronoi binning method (2).," In order to increase the signal to noise ratio $S/N$ ), spectra from fibres mapping adjacent regions in the sky were added together using the Voronoi binning method \citep{Cappellari+03}."936 Some of the spatial bins were modified to include only spectra from the regions associated to intense eemission or the dust lanes crossing the galactic disc., Some of the spatial bins were modified to include only spectra from the regions associated to intense emission or the dust lanes crossing the galactic disc.937 This ensured us to minimise the contamination of the Kinematic and. stellar-population properties to be measured from. spectra obtained in regions where stellar counter-rotation was detected and chemical decoupling is expected (2).., This ensured us to minimise the contamination of the kinematic and stellar-population properties to be measured from spectra obtained in regions where stellar counter-rotation was detected and chemical decoupling is expected \citep{Vergani+07}.938 In total. we have 130 spatial bins few areseconds square large.," In total, we have 130 spatial bins few arcseconds square large."939 We tested the robustness of our results using different binning sehemes., We tested the robustness of our results using different binning schemes.940 In order to measure the kinematics and stellar population properties of the two counter-rotating stellar components in NGC 5719. we need to separate their contribution to the observed spectrum in each spatial bin. taking advantage of their different velocities that causes a wavelength shift of their spectra.," In order to measure the kinematics and stellar population properties of the two counter-rotating stellar components in NGC 5719, we need to separate their contribution to the observed spectrum in each spatial bin, taking advantage of their different velocities that causes a wavelength shift of their spectra."941 To do that. we moditied the penalized pixel fitting code (pPXF. ?)) in a similar way to that done by ?..," To do that, we modified the penalized pixel fitting code (pPXF, \citealt{Cappellari+04}) ) in a similar way to that done by \citet{McDermid+06}."942 The code builds two synthetic templates tone for each stellar component) as linear combination of stellar spectra from the MILES library (at I'WIIM=2.54 sspectral resolution. 2)) and convolves them with two Gaussian line-of-sight velocity distributions (LOSVDs) with different radial velocities and the same velocity dispersion o.," The code builds two synthetic templates (one for each stellar component) as linear combination of stellar spectra from the MILES library (at ${\rm943 FWHM}=2.54$ spectral resolution, \citealt{Beifiori+10}) ) and convolves them with two Gaussian line-of-sight velocity distributions (LOSVDs) with different radial velocities and the same velocity dispersion $\sigma$."944 This assumption is in agreement with the findings by ?.., This assumption is in agreement with the findings by \citet{Vergani+07}.945 Results are confirmed if two different velocity dispersions are considered. although the velocity fields and maps of stellar population properties appear more noisy due to the additional degree of freedom that increases the degeneracy between measured parameters.," Results are confirmed if two different velocity dispersions are considered, although the velocity fields and maps of stellar population properties appear more noisy due to the additional degree of freedom that increases the degeneracy between measured parameters."946" Gaussian functions are added to the convolved synthetic templates to account for ionised-gas emission lines 7. 111]AA4959, 5007. and 1]A5198) and tit simultaneously to the observed galaxy spectra."," Gaussian functions are added to the convolved synthetic templates to account for ionised-gas emission lines $\beta$, $\lambda\lambda$ 4959, 5007, and $\lambda$ 5198) and fit simultaneously to the observed galaxy spectra."947" Multiplicative Legendre polynomials are included to match the shape of the galaxy continuum, and are set to be the same for the two synthetic emplates."," Multiplicative Legendre polynomials are included to match the shape of the galaxy continuum, and are set to be the same for the two synthetic templates."948 Our technique represents an improvement with respect o ?:: in fitting the measured LOSVD with a double Gaussian. they assumed that the two counter-rotating components had the same stellar population.," Our technique represents an improvement with respect to \citet{Vergani+07}: in fitting the measured LOSVD with a double Gaussian, they assumed that the two counter-rotating components had the same stellar population."949 On the contrary. our synthetic templates account or different stellar populations sincethey are independently built rom the MILES library.," On the contrary, our synthetic templates account for different stellar populations sincethey are independently built from the MILES library."950 We check the robustness of our results using also the INDO-US Coudé library of stellar spectra (2) and the single stellar population (SSP) synthesis models by ? o build the synthetic templates., We check the robustness of our results using also the INDO-US Coudé library of stellar spectra \citep{Valdes+04} and the single stellar population (SSP) synthesis models by \citet{Vazdekis+10} to build the synthetic templates.951 Figure | shows an example of he decomposition of the galaxy spectrum measured in one of the spatial bins where the two stellar counter-rotating components and ionised gas are observed., Figure \ref{fig:kinem_fit} shows an example of the decomposition of the galaxy spectrum measured in one of the spatial bins where the two stellar counter-rotating components and ionised gas are observed.952 We perform the double stellar component tit only in 73 spatial bins. where the separation of the two kinematic components is reliable. and do the single stellar component fit to he spectra of the other bins.," We perform the double stellar component fit only in 73 spatial bins, where the separation of the two kinematic components is reliable, and do the single stellar component fit to the spectra of the other bins."953 The spectra of outermost spatial bins jive alow S/N. therefore only the ionised-gas emission lines are," The spectra of outermost spatial bins have a low $S/N$ , therefore only the ionised-gas emission lines are"954The minimum value of |o]. fixed by allowing ry.7rye. is therefore zzO.5radians=28° ahead of the pole. at a radius of half the light evlinder. with an absorbing region at the light evlinder at phase c|i=LY.,"The minimum value of $|\psi|$, fixed by allowing $r_{*}\rightarrow{r_{lc}}$, is therefore $\approx{0.5 radians}=28^{o}$ ahead of the pole, at a radius of half the light cylinder, with an absorbing region at the light cylinder at phase $\psi+\frac{1}{4}=-14^{o}$."955 The maximum value of fc} can be determined by constraining the emission to lie on an open fieldline: if the notch emission is located on the last closed ΠοιάΠο then where rj» ds the limiting value of equation (32) and s. à measure of the fieldlines distance from the polar axis. is unity.," The maximum value of $|\psi|$ can be determined by constraining the emission to lie on an open fieldline: if the notch emission is located on the last closed fieldline then where $r_{1,2}$ is the limiting value of equation (32) and s, a measure of the fieldline's distance from the polar axis, is unity."956" In dipole geometry the angle the Leading fieldlines make with the radial vector is b=5. so we have from (32) and (29) Solving (39). (40) and (41) gives cz34"" and 0.977.."," In dipole geometry the angle the leading fieldlines make with the radial vector is $\Phi=\frac{\psi}{2}$, so we have from (32) and (29) Solving (39), (40) and (41) gives $\psi\approx{-34^{o}}$ and $r_{*}\approx{0.9r_{lc}}$ ."957" Thus now the emitting region is now 6"" further from the pole but. (from. (40)) at à somewhat reduced: radius of 0.375. and the absorbing site is still close to the evlinder. leading the pole by. 20°."," Thus now the emitting region is now $6^{o}$ further from the pole but (from (40)) at a somewhat reduced radius of $0.3r_{lc}$, and the absorbing site is still close to the light-cylinder, leading the pole by $20^{o}$."958 Whichever of these not clissimilar extremes is correct. we have to conclude for this pulsar that we are indeed dealing with emission regions well away from the polar cap. possibly linked. to the observed high-cnerey emission.," Whichever of these not dissimilar extremes is correct, we have to conclude for this pulsar that we are indeed dealing with emission regions well away from the polar cap, possibly linked to the observed high-energy emission."959 The observed emission band in which the notches are embedded must cross the observer's spiral in a roughly convex form to acilitate the formation of the notch (bie 3). and extend ina narrow vertical strip (Fig 4) so as to give rise to the observed smooth and slow variation in the position angle.," The observed emission band in which the notches are embedded must cross the observer's spiral in a roughly convex form to facilitate the formation of the notch (Fig 3), and extend in a narrow vertical strip (Fig 4) so as to give rise to the observed smooth and slow variation in the position angle."960" Low this is hen precisely linked to the polarization properties of the full 360"" emission features will be considered in a further paper.", How this is then precisely linked to the polarization properties of the full $360^{o}$ emission features will be considered in a further paper.961 Work by Dyks et al (2003b) shows that emission. strictly vlc to the last elosed. fieldlines will create position angle swings more complex than those observed. so it would seem hat a configuration more like the quasi-racial cigar-shaped emission regions of Fig 4 should be preferred. in keeping with he picture of a relativistic caustic wave described. in the opening discussion of this paper.," Work by Dyks et al (2003b) shows that emission strictly held to the last closed fieldlines will create position angle swings more complex than those observed, so it would seem that a configuration more like the quasi-radial cigar-shaped emission regions of Fig 4 should be preferred, in keeping with the picture of a relativistic caustic wave described in the opening discussion of this paper."962 Only numerical modelling (ος Dvks & Rueda 2003. Dyks et al 2003b) can resolve this »oint.," Only numerical modelling (eg Dyks $\&$ Rudak 2003, Dyks et al 2003b) can resolve this point."963 ‘The absorbing region near the light-cvlinder can have a size no greater than the width of an individual notch. which is &4° or equivalently ΟΕ or 120km.," The absorbing region near the light-cylinder can have a size no greater than the width of an individual notch, which is $\approx{4^{o}}$ or equivalently $.01r_{lc}$ or 120km."964 Since it leads the polar axis it may be identified as a location where particles in à polar beam acquire high Lorentz factors in the rotating frame and. leave fieldlines to avoid. becoming superluminal in the inertial frame., Since it leads the polar axis it may be identified as a location where particles in a polar beam acquire high Lorentz factors in the rotating frame and leave fieldlines to avoid becoming superluminal in the inertial frame.965 The orientation of this pulsar has been subject to much debate over the vears and is far from understood. (Llankins & Cordes 1981. Cil 1983. Lyne & Manchester 1988. Rankin 1993a.b. von lloensbroech & Nilouris 1997. Everett. & Weisherg 2001).," The orientation of this pulsar has been subject to much debate over the years and is far from understood (Hankins $\&$ Cordes 1981, Gil 1983, Lyne $\&$ Manchester 1988, Rankin 1993a,b, von Hoensbroech $\&$ Xilouris 1997, Everett $\&$ Weisberg 2001)."966" In. contrast to PSR 1929|10. its. two principal radio emission components are separated by much less than INO"" and it is cillicult to argue that they are dilerent. poles."," In contrast to PSR 1929+10, its two principal radio emission components are separated by much less than $180^{o}$ and it is difficult to argue that they are different poles."967 However this separation does not vary. with frequeney (Llankins & Fowler 1986) as would be expected of a wide single cone close to alignment. and an intriguing correlation has been found between pulses in the the main component anc the subsequen! pulse in the interpulse component (Llankins & Cordes 1981).," However this separation does not vary with frequency (Hankins $\&$ Fowler 1986) as would be expected of a wide single cone close to alignment, and an intriguing correlation has been found between pulses in the the main component and the $\it{subsequent}$ pulse in the interpulse component (Hankins $\&$ Cordes 1981)."968 Like PSR 1929|10. a double peak periocicity has been detected in the X-ray emission and in our interpretation here we will assume that -- is not near alignment and that the main pulse is at the phase of a magnetic pole.," Like PSR 1929+10, a double peak periodicity has been detected in the X-ray emission and in our interpretation here we will assume that it is not near alignment and that the main pulse is at the phase of a magnetic pole."969 This pulsar has in common with PSR. 1929|10 that — possesses a band of weak emission. extending. between 1e interpulse and main pulse., This pulsar has in common with PSR 1929+10 that it possesses a band of weak emission extending between the interpulse and main pulse.970 Although at first elance the ouble notch feature - located on the leacing edge of the main pulse - seenis not part of us band. on closer inspection -- has been demonstrated to arise in the weak pulse system which generates this band. (reported. by Nowakowski et αἱ 2003 - see MB).," Although at first glance the double notch feature - located on the leading edge of the main pulse - seems not part of this band, on closer inspection it has been demonstrated to arise in the weak pulse system which generates this band (reported by Nowakowski et al 2003 - see MR)."971" The angular separation of the notches is again about 10"". and since the two pulsars have very similar periods this corresponds to à similar physical separation of 1s00km."," The angular separation of the notches is again about $10^{o}$, and since the two pulsars have very similar periods this corresponds to a similar physical separation of 1800km."972 They also have similar individual widths. so the size of the absorber will be again around. θα.," They also have similar individual widths, so the size of the absorber will be again around 400km."973 We thus interpret the weak bridge of emission. and its continuation in the main pulse and interpulse. as being generated in the upper magnetosphere. and we again suggest," We thus interpret the weak bridge of emission, and its continuation in the main pulse and interpulse, as being generated in the upper magnetosphere, and we again suggest"974"with E;«Ej(Li), (Fig.","with $E_j<E_j(L_1)$, (Fig."975" 6b) and for orbits that can explore the whole permissible phase space inside and outside corotation with E;>E;(L1), (Fig."," 6b) and for orbits that can explore the whole permissible phase space inside and outside corotation with $E_j>E_j(L_1)$, (Fig."976 6c)., 6c).977 In Fig., In Fig.978 6a we observe that the pericentres of the orbits outside corotation have smaller velocities than the apocentres., 6a we observe that the pericentres of the orbits outside corotation have smaller velocities than the apocentres.979 Moreover the distribution of the velocity minima gives good agreement with the distribution of the velocities of the pericentres., Moreover the distribution of the velocity minima gives good agreement with the distribution of the velocities of the pericentres.980" At the same time, the distribution of the velocities of the apocentres almost coincide with the distribution of the velocity maxima (not plotted in the panel)."," At the same time, the distribution of the velocities of the apocentres almost coincide with the distribution of the velocity maxima (not plotted in the panel)."981" Therefore, the particles outside corotation spend most of their time near the pericentres of their orbits which is consistent with the description of Fig."," Therefore, the particles outside corotation spend most of their time near the pericentres of their orbits which is consistent with the description of Fig."982 5., 5.983 On the other hand the opposite is true for particles inside corotation (Fig., On the other hand the opposite is true for particles inside corotation (Fig.984 6b)., 6b).985 The particles inside corotation have smaller velocities at their apocentres than at their pericentres., The particles inside corotation have smaller velocities at their apocentres than at their pericentres.986" Moreover, the apocentric velocity distribution almost coincides with the distribution of the velocity minima."," Moreover, the apocentric velocity distribution almost coincides with the distribution of the velocity minima."987 Here again the distribution of the velocity maxima (not plotted in the panel) almost coincides with the distribution of the velocities of the pericentres., Here again the distribution of the velocity maxima (not plotted in the panel) almost coincides with the distribution of the velocities of the pericentres.988 For the orbits having Jacobi constant above E;(L1) (Fig., For the orbits having Jacobi constant above $E_j(L_1)$ (Fig.989" 6c) even though there is not a clear breakoff of the distributions, the pericentres have statistically smaller velocities than the apocentres."," 6c) even though there is not a clear breakoff of the distributions, the pericentres have statistically smaller velocities than the apocentres."990" Both pericentres and apocentres present a peak around the same value of velocity, which also coincides with the peak of the velocity minima distribution."," Both pericentres and apocentres present a peak around the same value of velocity, which also coincides with the peak of the velocity minima distribution."991" The distribution of the apocentres, however, has a second important peak around a somewhat greater value of velocity."," The distribution of the apocentres, however, has a second important peak around a somewhat greater value of velocity."992 In Fig., In Fig.993" 7a we plot, in color scale, the density distribution of the particles of Fig."," 7a we plot, in color scale, the density distribution of the particles of Fig."994" 1 taking each of them at a position corresponding to 7=0, ie. at the apocentre or the pericentre of its orbit."," 1 taking each of them at a position corresponding to $\dot{r}=0$, i.e. at the apocentre or the pericentre of its orbit."995 The black curves correspond to the density contours of the space distribution shown in Fig., The black curves correspond to the density contours of the space distribution shown in Fig.996 1., 1.997" Figure 7b presents, the density distribution of only the apocentres of the orbits."," Figure 7b presents, the density distribution of only the apocentres of the orbits."998" The corresponding density maxima inside corotation support the bar (since they correspond to loci of minimum velocities, see Fig."," The corresponding density maxima inside corotation support the bar (since they correspond to loci of minimum velocities, see Fig."999 6b) as well as a small extension of the bar to the inner parts of the spiral structure., 6b) as well as a small extension of the bar to the inner parts of the spiral structure.1000" However, the density maxima outside corotation, do not correspond to the density contours of the real spiral arms (black curves) but they extend far beyond."," However, the density maxima outside corotation, do not correspond to the density contours of the real spiral arms (black curves) but they extend far beyond."1001 Figure 7c presents the density distribution of only the pericentres of the orbits., Figure 7c presents the density distribution of only the pericentres of the orbits.1002" We see that these density maxima support a spiral structure very close to the real one, but a little more tight, and they do not support the bar."," We see that these density maxima support a spiral structure very close to the real one, but a little more tight, and they do not support the bar."1003" Thus, we conclude that, in general, the apocentres of the orbits support the shape of the bar and the origins of the spirals near corotation, while the pericentres of the orbits better support the spiral structure near and outside corotation."," Thus, we conclude that, in general, the apocentres of the orbits support the shape of the bar and the origins of the spirals near corotation, while the pericentres of the orbits better support the spiral structure near and outside corotation."1004" Figure 8 presents, in gray scale, the density distribution of the particles of Fig."," Figure 8 presents, in gray scale, the density distribution of the particles of Fig."1005 1 at positions corresponding to local minimum values of their rotation plane velocities (vyz= Umin)., 1 at positions corresponding to local minimum values of their rotation plane velocities $v_{yz}=v_{min}$ ).1006" The comparison with the density contours (black curves) of the initial conditions shows that the loci of the velocity minima reveal satisfactorily the features of the galaxy, 1.6. the bar and the spiral arms."," The comparison with the density contours (black curves) of the initial conditions shows that the loci of the velocity minima reveal satisfactorily the features of the galaxy, i.e. the bar and the spiral arms."1007" In this figure, however we have removed the overdensity of the particles along the theoretical locus of Umin (gray elliptical curve) that represents the maximum of the effective potential (Ver;) for Jacobi constants above E;(L4), because it does not correspond to the distribution of the real particles."," In this figure, however we have removed the overdensity of the particles along the theoretical locus of $v_{min}$ (gray elliptical curve) that represents the maximum of the effective potential $V_{eff}$ ) for Jacobi constants above $E_j(L_4)$, because it does not correspond to the distribution of the real particles."1008 Here we note that a density maximum in some area can be produced either by frequent (but not too short-lasting) transits or by long-lasting (but not too rare) transits of the particles through this area., Here we note that a density maximum in some area can be produced either by frequent (but not too short-lasting) transits or by long-lasting (but not too rare) transits of the particles through this area.1009 For Jacobi constant values higher than E;(L4) the locus of the local velocity minima (red curve in Fig., For Jacobi constant values higher than $E_j(L_4)$ the locus of the local velocity minima (red curve in Fig.1010 8) corresponds to velocity values that can be comparable to the mean velocity of the whole orbits., 8) corresponds to velocity values that can be comparable to the mean velocity of the whole orbits.1011 In Fig., In Fig.1012" 9 we have plotted the density distribution of the particles with Jacobi constant values E;>—977000Ej;(L4) corresponding to low and high values of the ratio A=<Umin>/<vy, as indicated on the two panels of Fig.", 9 we have plotted the density distribution of the particles with Jacobi constant values $E_j>-977000>E_j(L_4)$ corresponding to low and high values of the ratio $\lambda=<v_{\min}>/<v_{yz}>$ as indicated on the two panels of Fig.1013 9., 9.1014 We observe that the particles with low A values (Fig., We observe that the particles with low $\lambda$ values (Fig.1015" 9a) form a ring-like density maximum area lying close to the locus of the maximum V.,; (red curve).", 9a) form a ring-like density maximum area lying close to the locus of the maximum $V_{eff}$ (red curve).1016" However the distribution is not uniform along the red curve, but it follows the distribution of the inner parts of the spiral arms."," However the distribution is not uniform along the red curve, but it follows the distribution of the inner parts of the spiral arms."1017 The maximum density area of the particles with high A values (Fig., The maximum density area of the particles with high $\lambda$ values (Fig.1018 9b) is located inside the red curve corresponding to the velocity minima., 9b) is located inside the red curve corresponding to the velocity minima.1019 In this case the density maxima are due to the more frequent transits of the orbits from this area., In this case the density maxima are due to the more frequent transits of the orbits from this area.1020 In Figure 4 the frequency ratio q of the chaotic population is plotted showing preferable concentrations around specific resonant periodic orbits., In Figure 4 the frequency ratio $q$ of the chaotic population is plotted showing preferable concentrations around specific resonant periodic orbits.1021 In order to study the behavior of sticky resonant orbits we find the characteristics of the most important periodic orbits in the 3D case., In order to study the behavior of sticky resonant orbits we find the characteristics of the most important periodic orbits in the 3D case.1022 Figure 10 presents, Figure 10 presents1023at 3a.,at $\sim3\sigma$.1024 Those observations. combined with the first detection of the CO 3.2 line in one of these galaxies (021.21000). allowed ? to perform an analysis of the excitation properties of the molecular gas. finding low excitation conditions. similar to what is secu in local disk ealaxies.," Those observations, combined with the first detection of the CO $3-2$ line in one of these galaxies (BzK-21000), allowed \citet{Dannerbauer2009} to perform an analysis of the excitation properties of the molecular gas, finding low excitation conditions, similar to what is seen in local disk galaxies."1025 This suggests an important difference to what is found in more Iuninous objects at hieh-redslüft. where the CO emission is in LTE up to J CO transitious.," This suggests an important difference to what is found in more luminous objects at high-redshift, where the CO emission is in LTE up to $-J$ CO transitions."1026" Iu this paper. we report individual detections of the CO J—1]0 emission line in a sample of three mear-IR selected star-forming galaxies at 2~1.5 that lave previously been studied in detail by ?:: BzIs-171. BzlIx-21000 and BzIx-16000,"," In this paper, we report individual detections of the CO $J=1-0$ emission line in a sample of three near-IR selected star-forming galaxies at $z\sim1.5$ that have previously been studied in detail by \citet{Daddi2009}: BzK-4171, BzK-21000 and BzK-16000."1027 Iu section 2. we describe our CO 1l0 observations., In section \ref{section:obs} we describe our CO $1-0$ observations.1028 In section 3.. we present our results. eive fluxes aud luminosities.," In section \ref{section:res}, we present our results, give fluxes and luminosities."1029 In section L.. we stuunarize our results and diseuss the average properties of the molecular gas iu our galaxies.," In section \ref{section:diss}, we summarize our results and discuss the average properties of the molecular gas in our galaxies."1030" We assume a concordance cosiiologv with {10=Tl lau + |. Q4=0.73 and Q,,enti=0.27."," We assume a concordance cosmology with $H_0=71$ km $^{-1}$ $^{-1}$, $\Omega_\lambda=0.73$ and $\Omega_m=0.27$."1031 We used the Very Large Array (VLÀ) in its C and D- configuration aud the Q-hand receivers to observe the redshifted CO 1/—0 emission line (pest115.271 CGIIz) in three Dzl galaxies at 2~1.5 iu the GOODS North field., We used the Very Large Array (VLA) in its C and D-array configuration and the Q-band receivers to observe the redshifted CO $1-0$ emission line $\nu_\mathrm{rest}=115.271$ GHz) in three BzK galaxies at $z\sim1.5$ in the GOODS North field.1032" This configurationc» provides [m]good spatial resolution (typical beams of ~1. 2”). with a primary beam of ~60"","," This configuration provides good spatial resolution (typical beams of $\sim1-2\arcsec$ ), with a primary beam of $\sim 60\arcsec$."1033 For two of our sources. Dzh-1171 and BzIx-21000. the observations were done in D-coufiguration between 2009 November 02 and 2009 November 27 uuder very eood weather conditions.," For two of our sources, BzK-4171 and BzK-21000, the observations were done in D-configuration between 2009 November 02 and 2009 November 27 under very good weather conditions."1034 A total of 35 hrs were speut observing each source. over 5 tracks per source.," A total of 35 hrs were spent observing each source, over 5 tracks per source."1035 Since the observations were done diving a transition period to the Expanded VLA (EVLA). many auteuuae were malfiuctioning aud we were only able to reach less than half the sensitivity expected for the whole array (Table 1).," Since the observations were done during a transition period to the Expanded VLA (EVLA), many antennae were malfunctioning and we were only able to reach less than half the sensitivity expected for the whole array (Table \ref{table:1}) )."1036 We used two channels ο HO ΑΠ bandwidth cach and two polarizations per clhauucl, We used two channels of 50 MHz bandwidth each and two polarizations per channel.1037 At ~15 CIIz. 50 AMz correspond to ~330 liu | velocity coverage.," At $\sim45$ GHz, 50 MHz correspond to $\sim330$ km $^{-1}$ velocity coverage."1038 For BDzk-1171. the two channels were centered at. 16.735 16.785 GIIz.," For BzK-4171, the two channels were centered at 46.735 and 46.785 GHz."1039 For BzIx-21000. the two channels were sutered at 15.685 GIIz aud. 15.735 GIIz.," For BzK-21000, the two channels were centered at 45.685 GHz and 45.735 GHz."1040 A fraction of time of cach track was speut observiug these sources 3 GIIz using two non-overlappiug chanuels of 50 MITz bandwidth (1.0. 100 MIIz baudsvidth in total) in order to Otain a lanit for the continuum cussion., A fraction of the time of each track was spent observing these sources at 43 GHz using two non-overlapping channels of 50 MHz bandwidth (i.e. 100 MHz bandwidth in total) in order to obtain a limit for the continuum emission.1041 Iu both cases the phase tracking center was poiuted about ssouth from the target positions., In both cases the phase tracking center was pointed about south from the target positions.1042 The observations of BzIx-16000 were doue in C- and D-confieuration between 2009 July aud 2009 December under mostly good weather conditions., The observations of BzK-16000 were done in C- and D-configuration between 2009 July and 2009 December under mostly good weather conditions.1043 A total of IN hours were used to observe this source., A total of 48 hours were used to observe this source.1044 Spectral line observations were performed using two IEs of 7 channels cach aud two polarizations., Spectral line observations were performed using two IFs of 7 channels each and two polarizations.1045 Both IEs have one channel overlap. leading to a total of 13 independent spectral," Both IFs have one channel overlap, leading to a total of 13 independent spectral"10461n this section we consider a non-evolving binary svstem in a circular orbit as the source of a monochromatic gravitational wave.,In this section we consider a non-evolving binary system in a circular orbit as the source of a monochromatic gravitational wave.1047 Lowe choose the coordinate svstem such that the gravitational wave is in the z-axis and the ascending node along the weaxis(reference frame of the source).the two polarizations can be written as (?) hy isa constant phase shift and + denotes the angle between the orbital angular momentum of the source and the direction from the source to the Earth.," If we choose the coordinate system such that the gravitational wave is in the $z$ -axis and the ascending node along the $x$ -axis (reference frame of the source), the two polarizations can be written as \citep{Blanchet06}1048 $\Phi_0$ is a constant phase shift and $\iota$ denotes the angle between the orbital angular momentum of the source and the direction from the source to the Earth."1049 Phe amplitude fo depends on the binary. parameters ancl distance (see Section 3.1))., The amplitude $h_0$ depends on the binary parameters and distance (see Section \ref{sec:timres}) ).1050 For a pulsar at distance Da. with azimuthal angle c and with polar angle 6. the residuals caused by the gravitational wave are eiven by (2???) where where After dropping constant terms. the timing residuals caused by the gravitational wave reads where ®=dyA/2.," For a pulsar at distance $D_{\rm psr}$ , with azimuthal angle $\psi$ and with polar angle $\theta$, the residuals caused by the gravitational wave are given by \citep{EW75, Detweiler79, Wahlquist87}1051 where where After dropping constant terms, the timing residuals caused by the gravitational wave reads where $\Phi'= \Phi_0 - \Delta\Phi/2$."1052 One can easily convert these results to the representation in ecliptic coordinates as used in the main text., One can easily convert these results to the representation in ecliptic coordinates as used in the main text.1053 The representation here has the merit of clearly presenting the physical pictures., The representation here has the merit of clearly presenting the physical pictures.1054 For example. it looks like a singularity at @=0 in equation. CX13)).," For example, it looks like a singularity at $\theta = 0$ in equation. \ref{eq:redshiftsig}) ),"1055 but the representation here. equation. CX7)).," but the representation here, equation. \ref{eq:2dtim}) ),"1056 clearly shows that the singularity is canceled by geometrical factors of GW polarization., clearly shows that the singularity is canceled by geometrical factors of GW polarization.1057 The amplitucde moduliion (sin(A /2)) and phase modulation. («P can be easily understood using the identity 4!22?—(4=2sin(Ad/2jete!2T/23 where the interference. between two sinusoidal signals with a phase cillerence of A introduces an hee moculation of sin(A@/2) and a phase shift of Ab/?πο.," The amplitude modulation $\sin(\Delta 1058\Phi/2)$ ) and phase modulation $\Delta \Phi/2$ ) can be easily understood using the identity $e^{{\rm i}(\omega t + \Delta\Phi)} - e^{ {\rm i}\omega t}1059= 2 \sin(\Delta\Phi/2) e^{{\rm i}(\omega t + \Delta\Phi/2+\pi/2)}$ , where the interference between two sinusoidal signals with a phase difference of $\Delta\Phi$ introduces an amplitude modulation of $\sin(\Delta\Phi/2)$ and a phase shift of $\Delta\Phi/2 + \pi/2$."1060 One can also calculate the results using the observer frame., One can also calculate the results using the observer frame.1061 The waveform of GWs from a SMDIID with a circular orbit at cosmological redshift z and chirp mass .ME is given by(??7) where (μας and iA. are the waveforms of the two polarization modes | and τον respectively.," The waveform of GWs from a SMBHB with a circular orbit at cosmological redshift $z$ and chirp mass $\cal M$ is given by \citep{Wahlquist87, 1062Blanchet06, Hughes09}1063 where the $A_{+}$ and $A_{\times}$ are the waveforms of the two polarization modes `+' and $\times$ ', respectively."1064" “Phe polarization tensors ο), and ο) are (?) where A ancl 3 are the ecliptic longitude and Iatitude of the GAY source."," The polarization tensors $\epsilon_{ij}^{+}$ and $\epsilon_{ij}^{\times}$ are \citep{Wahlquist87}1065 where $\lambda$ and $\beta$ are the ecliptic longitude and latitude of the GW source."1066 For a non-evolving SMDBIID with circular orbit. the CAV waveform et. andzd of the two polarization moces are(?) The angle + is the orbital inclination of the GW binary source. (the angle between orbital angular momentum and the," For a non-evolving SMBHB with circular orbit, the GW waveform $A_{\times}$ and$A_{+}$ of the two polarization modes are\citep{Wahlquist87}1067 The angle $\iota$ is the orbital inclination of the GW binary source, the angle between orbital angular momentum and the"1068et al.,et al.1069 2004 Laursen Stanek 2003) associated with a very well sampled polarisation curve (Gorosabel et al., 2004; Laursen Stanek 2003) associated with a very well sampled polarisation curve (Gorosabel et al.1070 2004) that is characterised by a constant position angle and a smoothly decreasing degree of polarisation., 2004) that is characterised by a constant position angle and a smoothly decreasing degree of polarisation.1071 Εις burst. is thus particularly suited fora proper comparison with data of the models described in this paper., This burst is thus particularly suited for a proper comparison with data of the models described in this paper.1072 Lazzati ct al. (, Lazzati et al. (10732004) has performed the modelling of the polarisation curve according to several models (including all the models considered here) and they find that the structured: model can successtullv reproduce the data and it can predict the jet-break time in agreement with what measured in the lighteurve.,2004) has performed the modelling of the polarisation curve according to several models (including all the models considered here) and they find that the structured model can successfully reproduce the data and it can predict the jet-break time in agreement with what measured in the lightcurve.1074 Further complication can arise from the presence of a second non neeligible coherent component of the magnetic ield in the ISAL, Further complication can arise from the presence of a second non negligible coherent component of the magnetic field in the ISM.1075 Our results have been obtained assuming hat the magnetic [field responsible for the observed svnchrotron emission is the one generated at the shock (thus angled at small scales)., Our results have been obtained assuming that the magnetic field responsible for the observed synchrotron emission is the one generated at the shock (thus tangled at small scales).1076 This is à reasonable assumption since the compression of a standard interstellar field is far oo low to produce the observed. radiation., This is a reasonable assumption since the compression of a standard interstellar field is far too low to produce the observed radiation.1077 However if the ourst. explodes in a pre-magnetised. environment or if the jet is magnetic dominated. and the field advected from the source survives till the afterglow phase. then the polarisation curve will be the result of the relative strength of the two components of the magnetic field.," However if the burst explodes in a pre-magnetised environment or if the jet is magnetic dominated and the field advected from the source survives till the afterglow phase, then the polarisation curve will be the result of the relative strength of the two components of the magnetic field."1078 Cranot Ixónniel (2003) have discussed the polarisation curve in the former case for an homogeneous jet. propagating through a magnetic wind bubble., Granot Könnigl (2003) have discussed the polarisation curve in the former case for an homogeneous jet propagating through a magnetic wind bubble.1079 Finally the intrinsic polarisation curve of the afterelow can be allected by the dust. present both in the Milkv. Way and in the host galaxy., Finally the intrinsic polarisation curve of the afterglow can be affected by the dust present both in the Milky Way and in the host galaxy.1080 Lazzati et al., Lazzati et al.1081 2003 discuss the mocification of the transmitted: polarised vector and. they show that in GRB 021004 a sizable fraction of the observed polarised Lux is likely due to Galactic selective extinction., 2003 discuss the modification of the transmitted polarised vector and they show that in GRB 021004 a sizable fraction of the observed polarised flux is likely due to Galactic selective extinction.1082 Despite the. dilliculties inherent το polarisation observations ancl modelling (Lazzati et al., Despite the difficulties inherent to polarisation observations and modelling (Lazzati et al.1083 2004). we believe that polarimetric studies are of great importance in determining the structure of GRB outllows.," 2004), we believe that polarimetric studies are of great importance in determining the structure of GRB outflows."1084 We thank Martin. J. ees lor useful ancl stimulating discussions and Jonatan Cuanot for numerous. interaction and comparisons between our results., We thank Martin J. Rees for useful and stimulating discussions and Jonatan Granot for numerous interaction and comparisons between our results.1085 ER thanks the Isaac Newton and PPADBC studentships for financial support., ER thanks the Isaac Newton and PPARC studentships for financial support.1086 DL acknowledges support. from the PPARC postdoctoral fellowship PPA/P/S/2001/00268., DL acknowledges support from the PPARC postdoctoral fellowship PPA/P/S/2001/00268.1087"For the optically thick source. 1.8. optical depths 7>>|. the brightness temperature 7), can be constrained by Eq.","For the optically thick source, i.e. optical depths $\tau\gg1$, the brightness temperature $T_{\rm b}$ can be constrained by Eq."1088 3 by using the observed flux density., \ref{eq_fluxtube} by using the observed flux density.1089" In order to see the relation between Τι, and flux density. we rewrite the equation in the form of where S, is the flux density in mJy at the frequency f£ (GHz). d the distance of the radio source from us in pe. Αι the size of the emission region in Jupiter radii (1 Ryyp ~ 0.1 Re = 7x 10° em) (22222)..."," In order to see the relation between $T_{\rm b}$ and flux density, we rewrite the equation in the form of where $S_{f}$ is the flux density in mJy at the frequency $f$ (GHz), $d$ the distance of the radio source from us in pc, $R_{\rm s}$ the size of the emission region in Jupiter radii (1 $R_{\rm Jup}$ $\sim$ 0.1 $R_{\odot}$ $\approx$ 7 $\times$ $^{9}$ cm) \citep{Linsky83,Doyle88,Dorman89,Burrows89,Leto00}."1090 Unfortunately. when we calculate 7). we have to assume the size of the radio-emitting region.," Unfortunately, when we calculate $T_{\rm b}$, we have to assume the size of the radio-emitting region."1091 For example. observations show that the flux density of the pulses of TVLM 513 is about 4 mJy at ~4.9 GHz.," For example, observations show that the flux density of the pulses of TVLM 513 is about 4 mJy at $\sim$ 4.9 GHz."1092" ? obtained the brightness temperature in the range of 10*—10? K by assuming the size of a corona to be 2-4 AR. while ? deduced a value of 2.9x10'"" K if the size of the region is 1 Aj."," \citet{Berger02} obtained the brightness temperature in the range of $10^{8}-10^{9}$ K by assuming the size of a corona to be $2-4$ $R_{\rm Jup}$, while \citet{Hallinan06} deduced a value of $\times10^{10}$ K if the size of the region is 1 $R_{\rm Jup}$."1093" In our model. Ty>Sx10"" K is about the temperature of the quiescent radio emission. assumed to come from a large emission region (<| Rip)."," In our model, $T_{\rm b}\gtrsim5\times10^{10}$ K is about the temperature of the quiescent radio emission, assumed to come from a large emission region $\lesssim1~R_{\rm Jup}$ )."1094 For the radio pulses from magnetic loops. the theoretical temperature of the coherent ECMI emission can be up to 10 K. implying the emissior region for the pulses is much more compact. e.g. 0.007 Ry.," For the radio pulses from magnetic loops, the theoretical temperature of the coherent ECMI emission can be up to $10^{15}$ K, implying the emission region for the pulses is much more compact, e.g. 0.007 $R_{\rm Jup}$."1095 The configuration and topology of magnetic field on UCDs remains unclear., The configuration and topology of magnetic field on UCDs remains unclear.1096 In our model. we only need a simple dipole poloidal-like field to calculate the flux density and explain the high polarisation of the radio pulses.," In our model, we only need a simple dipole poloidal-like field to calculate the flux density and explain the high polarisation of the radio pulses."1097 In the case of TVLM 513. multiple bursts of both left and right circularly polarized emission in regions of opposite magnetic polarity indicate the existence of a dipolar large-scale magnetic field (?) or a few small active regions with scale <<1Rip.," In the case of TVLM 513, multiple bursts of both left and right circularly polarized emission in regions of opposite magnetic polarity indicate the existence of a dipolar large-scale magnetic field \citep{Hallinan07} or a few small active regions with scale $ << 1~R_{\rm Jup}$."1098 Another important parameter. when combined with the magnetic field strength. is the pitch angle 8.," Another important parameter, when combined with the magnetic field strength, is the pitch angle $\beta$."1099 Electrons with small 8 less than a eritical value B.. Le. B<fy. precipitating into the dense atmosphere are lost. while the electrons with P>B. will be reflected back to the flux tube to form an anisotropic velocity distribution.," Electrons with small $\beta$ less than a critical value $\beta_{\rm c}$, i.e. $\beta<\beta_{\rm c}$, precipitating into the dense atmosphere are lost, while the electrons with $\beta>\beta_{\rm c}$ will be reflected back to the flux tube to form an anisotropic velocity distribution."1100 The value of 6. depends on the convergence factor which is determined by the ratio of magnetic field strengths at the top and the foot-points of the flux tube (also called magnetic mirror ratio)., The value of $\beta_{\rm c}$ depends on the convergence factor which is determined by the ratio of magnetic field strengths at the top and the foot-points of the flux tube (also called magnetic mirror ratio).1101" For a symmetric flux tube. we have (?) where B4, and Βίου are the magnetic field strengths at the top and in the foot-point of the magnetic flux tube. respectively."," For a symmetric flux tube, we have \citep{Dulk85}1102 where $B_{\rm top}$ and $B_{\rm foot}$ are the magnetic field strengths at the top and in the foot-point of the magnetic flux tube, respectively."1103 Typical values of Biop/Broo in the Sun are in the range of Ο.Ε to 0.5., Typical values of $B_{\rm top}/B_{\rm foot}$ in the Sun are in the range of 0.1 to 0.5.1104 In the simulation. the pitch angle is approximately equal to 30°. which means we should have 0.5>(Brop/Bia) 7.," In the simulation, the pitch angle is approximately equal to $30^{\circ}$, which means we should have $0.5>\sin \beta_{\rm c}=(B_{\rm top}/B_{\rm foot})^{1/2}$ ."1105 This could give a lower limit on P., This could give a lower limit on $B_{\rm foot}$.1106 Assuming the magnetic field is radial. the field strength of a region can be described by where Bo is the magnetic field at the photosphere. R the height of the radio emitting region measured from the centre of the star and Δ. the photospheric radius.," Assuming the magnetic field is radial, the field strength of a region can be described by where $B_{0}$ is the magnetic field at the photosphere, $R$ the height of the radio emitting region measured from the centre of the star and $R_{\ast}$ the photospheric radius."1107" This was chosen as a compromise between a unipolar-like field B=By(R/R,)7* and the best-fit form for solar coronal magnetic fields above active regions B=0.5|(R/R.)—1||? given by ? for the range 1.01<R/R.« 10.", This was chosen as a compromise between a unipolar-like field $B=B_{0}(R/R_{\ast})^{-2}$ and the best-fit form for solar coronal magnetic fields above active regions $B=0.5[(R/R_{\ast})-1]^{-1.5}$ given by \citet{Dulk78} for the range $1.01<R/R_{\ast}<10$ .1108 This choice makes the field fall off more quickly than either a unipolar magnetic field configuration or that of the solar active region magnetic field (?).., This choice makes the field fall off more quickly than either a unipolar magnetic field configuration or that of the solar active region magnetic field \citep{Gary81}.1109 Figure 7. shows the dependence of magnetic field strength on height of the radio emission region above the photosphere., Figure \ref{fig_b} shows the dependence of magnetic field strength on height of the radio emission region above the photosphere.1110 Combining Eqs., Combining Eqs.1111 9. and 10.. the radio emission region and therefore the magnetosphere can be constrained in the range of 0.56 Α. to 6.75 Α..," \ref{pitchangle} and \ref{geometry}, the radio emission region and therefore the magnetosphere can be constrained in the range of 0.56 $R_{\ast}$ to 6.75 $R_{\ast}$."1112 A possible position for the radio-emitting region m the radio active UCDs at ~4.9 GHz is 1.5 ΔΝ. from their center. 1.06x10? km in the case of TVLM $13.," A possible position for the radio-emitting region in the radio active UCDs at $\sim$ 4.9 GHz is 1.5 $R_{\ast}$ from their center, $\times10^{5}$ km in the case of TVLM 513."1113 This implies that the magnetic field strength at the photosphere or chromosphere would be as large as 7.000 G. More observations in the optical (Zeeman Doppler effect) and infrared bands are needed to constrain the magnetic topology and the behavior of the plasma in the magnetic flux tube and to determine whether such large field strengths exist on these objects.," This implies that the magnetic field strength at the photosphere or chromosphere would be as large as 7,000 G. More observations in the optical (Zeeman Doppler effect) and infrared bands are needed to constrain the magnetic topology and the behavior of the plasma in the magnetic flux tube and to determine whether such large field strengths exist on these objects."1114 In addition. we expect the existence of an enhanced ambient wave energy background by gyroresonance turbulence or gyrosynchoroton radiation and some intense events at other wavelengths. e.g. optical or X-ray emission. which would occur from the process where hot plasma starting from collision-less region collides with the collisional chromosphere or photosphere.," In addition, we expect the existence of an enhanced ambient wave energy background by gyroresonance turbulence or gyrosynchoroton radiation and some intense events at other wavelengths, e.g. optical or X-ray emission, which would occur from the process where hot plasma starting from collision-less region collides with the collisional chromosphere or photosphere."1115 lr the case of X-ray emission. thermal bremsstrahlung emission and inverse Comptor scattering could be the responsible mechanism since there are hot plasmas with Τι up to 105 K and possible low energy photons.," In the case of X-ray emission, thermal bremsstrahlung emission and inverse Compton scattering could be the responsible mechanism since there are hot plasmas with $T_{\rm h}$ up to $10^8$ K and possible low energy photons."1116 However. since the Thomson scattering optical depth of the corona of," However, since the Thomson scattering optical depth of the corona of"1117the CCDs.,the CCDs.1118 Lu all cases. the telescope pointing was offset so that the dwarf elliptical galaxy Lit on a sinele CCD.," In all cases, the telescope pointing was offset so that the dwarf elliptical galaxy fit on a single CCD."1119 The WIYN 3.511 observatious consisted of 2 exposures of 600 sec. 600 sec. 300 sec. aud. 600 sec with the B. V. B. and I filters. respectively.," The WIYN 3.5m observations consisted of 2 exposures of 600 sec, 600 sec, 300 sec, and 600 sec with the B, V, R, and I filters, respectively."1120 R-baucl images were obtained for 13 of the 16 dEs in the sample: additional BVI images were obtaiued for 6 of the 13 galaxies., R-band images were obtained for 13 of the 16 dEs in the sample; additional BVI images were obtained for 6 of the 13 galaxies.1121 All 5 nights were uou-pliotometric so the limiting surface brightness varied significantly [rom exposure to exposure., All 5 nights were non-photometric so the limiting surface brightness varied significantly from exposure to exposure.1122 Typical image qualits for the R-band WIYN images is1-2”., Typical image quality for the R-band WIYN images is.1123 The optical images were reduced aud analvzed with the pack:we., The optical images were reduced and analyzed with the package.1124 The image reductiO1 iucluded. bias suMuraction aud flat fielding., The image reduction included bias subtraction and flat fielding.1125" The VATT images were [lat fielded to high accurac""V lug iwiight [las.", The VATT images were flat fielded to high accuracy using twilight flats.1126 The WIYN 3.5m images were first flat fielded using dome flats taken duriig the afteruoon: slnce hese images had a 'esidtal flat field problem. a secondary flat. Geld was generaed TOLL a οςnbiuaion of the object. [reunes using staudard tasks iu the MSCRED package.," The WIYN 3.5m images were first flat fielded using dome flats taken during the afternoon; since these images had a residual flat field problem, a secondary flat field was generated from a combination of the object frames using standard tasks in the MSCRED package."1127 Boh VATT atd WIY: I-baud images we'e fringe corrected based on a iuge f£ime generated by aki he meclieul of a [-banc ealaxy observations obtained during the night., Both the VATT and WIYN I-band images were fringe corrected based on a fringe frame generated by taking the median of all I-band galaxy observations obtained during the night.1128" For he \X""IN images. cata [ro nthe two CCDs must be projected oWoO à Common coordina sysleln plor urther ¢ata processing."," For the WIYN images, data from the two CCDs must be projected onto a common coordinate system prior to further data processing."1129 For each unage. the WCS was up¢atec using star lists fro the USNC dcaalog aud tve RAF tasks MSCZERO aud MSCCMATCH.," For each image, the WCS was updated using star lists from the USNO catalog and the IRAF tasks MSCZERO and MSCCMATCH."1130 The multi-ecd images wer then projected into siugle images ug the MSCIMACGE task using a coumon coordinate syste for all observations o “tle salue gaAXV., The multi-ccd images were then projected into single images using the MSCIMAGE task using a common coordinate system for all observations of the same galaxy.1131 For oth. tje. VATT aud. WIYN images. sky values were measured as he mode of regious of the 1uages prior to combination of multiple exposures.," For both the VATT and WIYN images, sky values were measured as the mode of galaxy-free regions of the images prior to combination of multiple exposures."1132 Te lnages were then scaled. aligued. aud :weraged logeher to make a final combined image.," The images were then scaled, aligned, and averaged together to make a final combined image."1133 For the non-photoinetdc observatious (WIYN). the iudividlal exposures were scaled to the image with the most counS scale factors were cdeermined based ou the relative inteusity of several stars in each frame.," For the non-photometric observations (WIYN), the individual exposures were scaled to the image with the most counts; scale factors were determined based on the relative intensity of several stars in each frame."1134 T VATT data were photometric aud required no additional scaling before combjuatloi., The VATT data were photometric and required no additional scaling before combination.1135 The VATT and WIYN images were processed independently iu order to provide intern cousistency checks for the derived structural parameters., The VATT and WIYN images were processed independently in order to provide internal consistency checks for the derived structural parameters.1136 Since the VATT images are photometr aud higher quality than the WIYN images. the subsequent analysis will locus on results [roin t VATT observations.," Since the VATT images are photometric and higher quality than the WIYN images, the subsequent analysis will focus on results from the VATT observations."1137To estimate the completeness of our spectroscopic observation we extract galaxies down to /?=19.5 mag using Sextraetor.,To estimate the completeness of our spectroscopic observation we extract galaxies down to $R=19.5$ mag using Sextractor.1138 This gives a total of 48 sources within 0.5755 (the radius used in the definition of fossil systems by Jonesetal... 0003))). of which 9 are classified as stars.," This gives a total of 48 sources within $r_{200}$ (the radius used in the definition of fossil systems by \citet{jones03}) ), of which 9 are classified as stars."1139 From the total of 39 galaxies. only 27 were observed. of which 18 were cluster members with a mean redshift of 0.137 and calculated galaxy velocity dispersion of 120 kms +.," From the total of 39 galaxies, only 27 were observed, of which 18 were cluster members with a mean redshift of 0.137 and calculated galaxy velocity dispersion of $\sigma=700\pm120$ km $^{-1}$."1140" Some of the galaxies (8 in total) have been missed due to the slit configuration,", Some of the galaxies (8 in total) have been missed due to the slit configuration.1141 Four galaxies were know to be foreground galaxies prior to this observation., Four galaxies were know to be foreground galaxies prior to this observation.1142 We estimate the completeness of the sample to be 77 percent within O.Sreq0 and down to 19.5., We estimate the completeness of the sample to be 77 percent within $r_{200}$ and down to $m_R=19.5$ .1143 Based on this calibration. the magnitude of the central galaxy is 15.17 and the second brightest galaxy in the cluster is 17.7.," Based on this calibration, the magnitude of the central galaxy is 15.17 and the second brightest galaxy in the cluster is $m_R=17.7$ ."1144 None of the galaxies missed due to the slit configuration were brighter than /?—17.7. thus the system does meet the formal fossil criteria of Jonesetal.(2003).," None of the galaxies missed due to the slit configuration were brighter than $R=17.7$, thus the system does meet the formal fossil criteria of \citet{jones03}."1145 The luminosity function (LF) of galaxies in this fossil cluster is obtained by selecting the galaxies down to Mj —-18.5., The luminosity function (LF) of galaxies in this fossil cluster is obtained by selecting the galaxies down to $M_R\sim$ -18.5.1146 The cumulative LF is shown in Fig 9. after statistical subtraction of the background galaxies extracted from two fields around the source just outside the ου of the cluster., The cumulative LF is shown in Fig \ref{glf} after statistical subtraction of the background galaxies extracted from two fields around the source just outside the $r_{200}$ of the cluster.1147 In this figure we show the luminosity function of the spectroscopically confirmed cluster members (open red circles) and the luminosity function of galaxies (filled circles) after a statistical subtraction of the field galaxies and the associated error bars., In this figure we show the luminosity function of the spectroscopically confirmed cluster members (open red circles) and the luminosity function of galaxies (filled circles) after a statistical subtraction of the field galaxies and the associated error bars.1148 Fitting a Schecter function to the LF of confirmed members. we obtain ἃ=1.23+0.28 and Ap=—20.40+0.22.," Fitting a Schecter function to the LF of confirmed members, we obtain $\alpha= -1.23\pm0.28$ and $M^\star_R= -20.40\pm0.22$."1149 An independent study of a higher quality galaxy sample for this fossil cluster results in a similar slope (Cypriano.MendesdeOliveira&SodreJr. 2006)., An independent study of a higher quality galaxy sample for this fossil cluster results in a similar slope \citep{mendes06}.1150.. We obtain α=—0.61+0.20 and Alp—20.55+0.40 when we fit a Schecter function to the LF of photometrically selected galaxies (solid curve in the Fig 9).," We obtain $\alpha= -0.61\pm0.20$ and $M^\star_R=1151-20.55 \pm0.40$ when we fit a Schecter function to the LF of photometrically selected galaxies (solid curve in the Fig \ref{glf}) )."1152 As this figure shows. this luminosity function is considerably shallower.," As this figure shows, this luminosity function is considerably shallower."1153 There is an inconsistency in the slopes of the galaxy luminosity functions of the confirmed members and that obtained from statistical background subtraction. which could be due to the fact that the statistical background subtraction is performed based on the galaxy classification. using SExtraetor. in the absence of galaxy colours.," There is an inconsistency in the slopes of the galaxy luminosity functions of the confirmed members and that obtained from statistical background subtraction, which could be due to the fact that the statistical background subtraction is performed based on the galaxy classification, using SExtractor, in the absence of galaxy colours."1154 For RX J1552.24+2013. another fossil with a similar mass to J1416. MendesdeOliveira.Cypriano&SodreJr.(2005). find a slope of à=0.77+0.37 for the spectroscopically selected galaxies anda =0.64+0.30 for the photometrically selected galaxies.," For RX J1552.2+2013, another fossil with a similar mass to J1416, \cite{mendes05} find a slope of $\alpha=-0.77\pm0.37$ for the spectroscopically selected galaxies and $\alpha=-0.64\pm0.30$ for the photometrically selected galaxies."1155 From the study of the GEMS X-ray groups. (2004) tinda —1.0.," From the study of the GEMS X-ray groups, \citet{miles04} find $\alpha=-1.0$."1156 They also report a dip in the luminosity function which is more prominent in poor groups and is argued to be the result of galaxy mergers in groups., They also report a dip in the luminosity function which is more prominent in poor groups and is argued to be the result of galaxy mergers in groups.1157 A similar mechanism is thought to be the origin of the large gap in fossils” luminosity function., A similar mechanism is thought to be the origin of the large gap in fossils' luminosity function.1158 This is discussed in section 5., This is discussed in section 5.1159 Having the total gravitational mass and the optical luminosity of the cluster we are in a position to estimate the mass-to-light ratio of the system., Having the total gravitational mass and the optical luminosity of the cluster we are in a position to estimate the mass-to-light ratio of the system.1160 Thetotal R-band luminosity of the cluster is measured to be 10177 Ες. by accumulating the luminosity of the photometrically identified cluster members within 7500., Thetotal R-band luminosity of the cluster is measured to be $^{11.85}$ $L_{\odot}$ by accumulating the luminosity of the photometrically identified cluster members within $r_{200}$.1161 Thus the total mass-to-light ratio within σου is ~440 AZ.Εν, Thus the total mass-to-light ratio within $r_{200}$ is $\sim 440$ $M_{\odot}/L_{\odot}$.1162 Converting this to the mass-to-light ratio in B-band we find A/Lg~580 AL./L.., Converting this to the mass-to-light ratio in B-band we find $M/L_B\sim 580$ $M_{\odot}/L_{\odot}$.1163 This AMfL. derived assuming B-Rz1.5. is an upper limit because all the cluster galaxies are assumed to be early-types.," This $M/L$, derived assuming B-R=1.5, is an upper limit because all the cluster galaxies are assumed to be early-types."1164 Under a similar assumption MendesdeOliveira.Cypriano&SodreJr.(2005) find a mass-to-light ratio of M/Lg~150 M.££. for another massive fossil based on a dynamical mass estimate., Under a similar assumption \citet{mendes05} find a mass-to-light ratio of $M/L_B\sim 750$ $M_{\odot}/L_{\odot}$ for another massive fossil based on a dynamical mass estimate.1165 These mass to light ratios. ours and that of MendesdeOliveira.Cypriano&SodreJr. (2005)... are relatively high compared to the results of distant clusters A//Lj;2IOAL./L. (Carlbergetal...1996:Girardietal. 2002).," These mass to light ratios, ours and that of \citet{mendes05}, are relatively high compared to the results of distant clusters $M/L_R \sim 210 M_\odot/L_\odot$ \citep{carlberg96,girardi02}."1166 However. higher values of mass to light ratio are also reported (Mohretal.1996).," However, higher values of mass to light ratio are also reported \citep{mohr96}."1167. In comparison to other fossils (Vikhlininetal.1999:Yoshiokaetal.2004) these fossils and NGC 6482 (Khosroshahi.Jones&Ponman2004). have lower mass-to-light ratio and hence difficult to argue whether or not fossils have. in general. higher values of AZ/L.," In comparison to other fossils \citep{vikh99,yoshioka04} these fossils and NGC 6482 \citep{kjp04} have lower mass-to-light ratio and hence difficult to argue whether or not fossils have, in general, higher values of $M/L$."1168 To study the stellar light distribution of the central giant elliptical galaxy we performed an isophotal analysis using the high resolution UIST K-band images of the system., To study the stellar light distribution of the central giant elliptical galaxy we performed an isophotal analysis using the high resolution UIST K-band images of the system.1169 The isophotal analysis using the IRAF task ‘ellipse’ shows a disey nature for the stellar light at an outer radius of r20 Κρο as shown in figure Fig 10.., The isophotal analysis using the IRAF task 'ellipse' shows a discy nature for the stellar light at an outer radius of $r> 20$ kpc as shown in figure Fig \ref{isophot}.1170 The ellipticity of the galaxy increases fo a value of 0.43. overtaking the ellipticity of the X-ray distribution as expected (Buote&Canizares1996).," The ellipticity of the galaxy increases to a value of 0.43, overtaking the ellipticity of the X-ray distribution as expected \citep{buote96}."1171. To tind out if this is a sure elliptical galaxy we fitted a Sersic profile (75 ) to the radial surface brightness protile using a two dimensional decomposition echnique which allows for a possible dise component. with an exponential profile.," To find out if this is a pure elliptical galaxy we fitted a Sersic profile $r^{1/n}$ ) to the radial surface brightness profile using a two dimensional decomposition technique which allows for a possible disc component, with an exponential profile."1172 We find no dise contribution to the total galaxy ight., We find no disc contribution to the total galaxy light.1173 We find a Sersic index of η—3.0 and a half light radius of ~ kpe., We find a Sersic index of $n\sim3.0$ and a half light radius of $\sim 20$ kpc.1174 The giant elliptical galaxies in galaxy clusters often show boxy isophotes (Bender.Burstein&Faber1992). while having arger values of η (Khosroshahietal. 2004., The giant elliptical galaxies in galaxy clusters often show boxy isophotes \citep{bender92} while having larger values of $n$ \citep{habib04}. .1175.. Further discussion should be based on a well defined sample of dominant galaxies in ossils. Which is the subject of a separate study.," Further discussion should be based on a well defined sample of dominant galaxies in fossils, which is the subject of a separate study."1176 The spectrum of the central galaxy is similar to that of a typical elliptical galaxy. with £/.3 and Alg lines marked in Fig 10..," The spectrum of the central galaxy is similar to that of a typical elliptical galaxy, with $H\beta$ and $Mg$ lines marked in Fig \ref{isophot}. ."1177"jam. Since we only have MIPS ""μπι photometry. we have to determine the correction factor required to convert our 247m luminosities to total infrared luminosities.","$\mu$ m. Since we only have MIPS $\mu$ m photometry, we have to determine the correction factor required to convert our $\mu$ m luminosities to total infrared luminosities."1178 To achieve this we assume the correlation between 154/m (corresponding to observed ~ yim at z~0.5) and total-infrared luminosity seen for local infrared galaxies (Chary Elbaz 2001) continues to hold at z~0.5., To achieve this we assume the correlation between $\mu$m (corresponding to observed $\sim$ $\mu$ m at $z\sim0.5$ ) and total-infrared luminosity seen for local infrared galaxies (Chary Elbaz 2001) continues to hold at $z\sim0.5$.1179 We then follow a similar technique to that of Bell et ((2005) and use the spectral energy distribution (SED) templates from Dale Helou (2002) to estimate the ratio of the observed-frame 24-;j;m luminosity to the 1000;:m luminosity., We then follow a similar technique to that of Bell et (2005) and use the spectral energy distribution (SED) templates from Dale Helou (2002) to estimate the ratio of the observed-frame $\mu$ m luminosity to the $\mu$ m luminosity.1180 We calculate the ratio of total-infrared to observed 24-j/m luminosities for each SED template. taking the mean value of all the ratios as our correction factor. and the range from the most active to the most quiescent SEDs às à conservative estimate of the systematic uncertainty.," We calculate the ratio of total-infrared to observed $\mu$ m luminosities for each SED template, taking the mean value of all the ratios as our correction factor, and the range from the most active to the most quiescent SEDs as a conservative estimate of the systematic uncertainty."1181 The correction factors are 1632 and 16+3 for C100024+16 and 00451—03 respectively., The correction factors are $16\pm2$ and $16\pm3$ for 0024+16 and $-$ 03 respectively.1182 We compare our conversion factors to the relation found by Chary Elbaz (2001) by calculating the mid-infrared to total infrared ratio with the (15;:m) filter for the Dale Helou templates at z20.1., We compare our conversion factors to the relation found by Chary Elbaz (2001) by calculating the mid-infrared to total infrared ratio with the $\mu$ m) filter for the Dale Helou templates at $z=0.1$.1183 The Chary Elbaz conversion for local LIRGs corresponds to Lig~VIMs while our estimate gives a prefactor of 7x3 over the full Lisarange of LIRG templates.," The Chary Elbaz conversion for local LIRGs corresponds to $L_{IR} \sim 11^{+6}_{-4}\times L_{\rm 15\mu m}^{0.998}$, while our estimate gives a prefactor of $7\pm 3$ over the full range of LIRG templates."1184 Thus these two calibrations are consistent. although the reader should note our estimates are roughly fainter than would be given by Chary Elbaz (2001).," Thus these two calibrations are consistent, although the reader should note our estimates are roughly fainter than would be given by Chary Elbaz (2001)."1185" Our 24-yjm flux limit of 200;Jy corresponds to average total infrared luminosities of 6«10!"" LL. and 12«10!"" LL. in CL000244+ and 1—03 respectively. hence the bulk of the populations16 we are detecting are Luminous Infrared galaxies (LIRGs) with Lye2IO! LL..."," Our $\sigma$ $\mu$ m flux limit of $\mu$ Jy corresponds to average total infrared luminosities of $6\times10^{10}$ $_\odot$ and $12\times10^{10}$ $_\odot$ in 0024+16 and $-$ 03 respectively, hence the bulk of the populations we are detecting are Luminous Infrared galaxies (LIRGs) with $_{IR}\geq118610^{11}$ $_\odot$."1187 These luminosities translate into SFRs of ~ 1OMM.. yyr! and ~ 20MM. yyr! assuming the far-infrared star-formation calibration given by Kennicutt (1998) with a Salpeter IMF and a mass range of 100MM..., These luminosities translate into SFRs of $\sim10$ $_\odot$ $^{-1}$ and $\sim20 $ $_\odot$ $^{-1}$ assuming the far-infrared star-formation calibration given by Kennicutt (1998) with a Salpeter IMF and a mass range of $_\odot$.1188 In Figure 4 we plot the mid-infrared luminosity function for the C100024+16. based on the color-selected sample out to à radius of MMpe.," In Figure 4 we plot the mid-infrared luminosity function for the 0024+16, based on the color-selected sample out to a radius of Mpc."1189 To field correct the luminosity function in 0002416. we integrate the extrapolated power-law fit to the color-selected 24;:m sources in the SWIRE ELAIS NI field. from $33.2.," To field correct the luminosity function in 0024+16, we integrate the extrapolated power-law fit to the color-selected $\mu$ m sources in the SWIRE ELAIS N1 field, from 3.2."1190 We use the scatter in the normalisation of dN/dS in independent 25«25 regions within the SWIRE field. combined with the counting errors in each bin. to give the uncertainty in the field-correction.," We use the scatter in the normalisation of $dN/dS$ in independent $25'\times 25'$ regions within the SWIRE field, combined with the counting errors in each bin, to give the uncertainty in the field-correction."1191 This plot demonstrates that the field-corrected luminosity function in 00024416 is similar in form to that seen for 60j/m-selected populations at low-redshift (Takeuchi et 22003)., This plot demonstrates that the field-corrected luminosity function in 0024+16 is similar in form to that seen for $\mu$ m-selected populations at low-redshift (Takeuchi et 2003).1192 While there are too few sources in 00451—03 to allow us to make an equivalent plot to Figure 4 for that cluster. we can use the 00024--16 luminosity function to estimate how many sources we would have detected if we place the C]00024+16 population at z= 0.55.," While there are too few sources in $-$ 03 to allow us to make an equivalent plot to Figure 4 for that cluster, we can use the 0024+16 luminosity function to estimate how many sources we would have detected if we place the 0024+16 population at $z=0.55$ ."1193 Applying a factor to scale for the effective areas of our surveys in C100024+16 and 00451—03. we estimate that we would detect 69+21 galaxies above the luminosity limit. 12« 10!LL... of the 00451—03 survey.," Applying a factor to scale for the effective areas of our surveys in 0024+16 and $-$ 03, we estimate that we would detect $69\pm 21$ galaxies above the luminosity limit, $12\times 10^{10}$ $_\odot$, of the $-$ 03 survey."1194 This compares to our estimate of 28+17 from our 00451—03 catalog. indicating à roughly 2-3« difference in the numbers of mid-infrared sources in the two clusters.," This compares to our estimate of $28 \pm 17$ from our $-$ 03 catalog, indicating a roughly $2$ $3\times$ difference in the numbers of mid-infrared sources in the two clusters."1195 This suggests that. although the dearth of mid-infrared sources in. MS00451—03 may be partly due to sensitivity limitations. there may be a real difference in the mid-infrared populations in the two clusters.," This suggests that, although the dearth of mid-infrared sources in $-$ 03 may be partly due to sensitivity limitations, there may be a real difference in the mid-infrared populations in the two clusters."1196 We can also compare the properties of our mid-infrared selected sample in C100024+16 with the Ha survey of this cluster by Kodama et ((2004)., We can also compare the properties of our mid-infrared selected sample in 0024+16 with the $\alpha$ survey of this cluster by Kodama et (2004).1197 Kodama et oobtained a deep image of the cluster in a narrow-band filter centered on redshifted Ho., Kodama et obtained a deep image of the cluster in a narrow-band filter centered on redshifted $\alpha$.1198 Galaxies with excess emission in. this narrow-band filter were identified as cluster members with Hoa emission., Galaxies with excess emission in this narrow-band filter were identified as cluster members with $\alpha$ emission.1199 They estimate their sensitivity limit corresponds to a star formation rate of —1.5 MM. vyr! — significantly below the estimated SER limit of our mid-infrared survey. ~10MM. yyr!.," They estimate their sensitivity limit corresponds to a star formation rate of $\sim 1.5$ $_\odot$ $^{-1}$ – significantly below the estimated SFR limit of our mid-infrared survey, $\sim 10$ $_\odot$ $^{-1}$."1200 To start with. we compare in Figure 3 the cumulative radial profile of the mid-infrared sources with the Ho -emitting galaxies from Kodama et ((2004).," To start with, we compare in Figure 3 the cumulative radial profile of the mid-infrared sources with the $\alpha$ -emitting galaxies from Kodama et (2004)."

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