ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Phe effect of non-linear motions on the recshilt distortion must be properly modelled. in order to measure the dynamical quantity and the cosmological parameters from the redshift distortion of extragalactic objects., The effect of non-linear motions on the redshift distortion must be properly modelled in order to measure the dynamical quantity and the cosmological parameters from the redshift distortion of extragalactic objects.3 Recent results (Peacock et al., Recent results (Peacock et al.4 2001) from the redshift distortion of, 2001) from the redshift distortion of5The Fisher matrix for information from a single moce follows the standard form for multivariate. zero-mean Gaussian data (2): The total Fisher matrix is then the sum over all independent k modes in the survey volume.,"The Fisher matrix for information from a single mode follows the standard form for multivariate, zero-mean Gaussian data \citep{TTH}: The total Fisher matrix is then the sum over all independent ${\bf k}$ modes in the survey volume."6 The total Fisher matrix is then used το predict. the covariance matrix of Inf and InC after marginalization over all other parameters. namely. the biases.," The total Fisher matrix is then used to predict the covariance matrix of $\ln f$ and $\ln G$ after marginalization over all other parameters, namely the biases."7 Marginalization and mapping to new parameters are done with standard techniques. as summarized by 2)..," Marginalization and mapping to new parameters are done with standard techniques, as summarized by \citet{FoMSWG}."8 We will forecast uncertainties on the growth parameters for he following tvpes of experiments: Algebraic expressions For the Fisher and covariance matrices in these cases are available. because the matrix. Cis invertible via the Sherman-Morrison. formula.," We will forecast uncertainties on the growth parameters for the following types of experiments: Algebraic expressions for the Fisher and covariance matrices in these cases are available, because the matrix $C$ is invertible via the Sherman-Morrison formula."9 Defining a vector u with i;=b;|fp. we have In the Poisson case. £+=diag(n;) and the matrix elements all can be expressed in terms of number-weighted sums over the halo population.," Defining a vector ${\bf u}$ with $u_i = b_i + f\mu^2$, we have In the Poisson case, ${\cal E}^{-1}={\rm diag}(n_i)$ and the Fisher-matrix elements all can be expressed in terms of number-weighted sums over the halo population."10 These results are stable under change in bin size as long as the bias values do not vary widely within any given bin., These results are stable under change in bin size as long as the bias values do not vary widely within any given bin.11 Marginalizing over bias and summing over the distribution of ye for all the modes leads to rather lengthy. opaque expressions for the final uncertainties.," Marginalizing over bias and summing over the distribution of $\mu$ for all the modes leads to rather lengthy, opaque expressions for the final uncertainties."12 Llowever in the case of a single mocle at fixed pi with known biases. the uncertainties in C ancl f can be derived in an illuminating form.," However in the case of a single mode at fixed $\mu$ with known biases, the uncertainties in $G$ and $f$ can be derived in an illuminating form."13 Lowe define η=»n; as the total space density of halos surveyed. we obtain The averages and variance in this expression are taken over the targets of the redshift survey.," If we define $n=\sum n_i$ as the total space density of halos surveyed, we obtain The averages and variance in this expression are taken over the targets of the redshift survey."14 This sealing is understood. from examination of Figure 1. illustrating the AIS method.," This scaling is understood from examination of Figure \ref{msfig}, illustrating the MS method."15 “Phe quantity of interest. fy. is equal to the d-intereept of the linear regression of the fluctuation amplitudes 9; againstthe bias values 6;.," The quantity of interest, $f\mu^2$, is equal to the $b$ -intercept of the linear regression of the fluctuation amplitudes $\delta_i$ againstthe bias values $b_i$ ."16 Phe main uncertainty ACT) in the location of this intercept. come from statistical Fluctuations Am in the fitted slope m of 6; vs bi: The uncertainty Am in the slope will be roughly (noise in 6;)/(span of observed b values). or (GNin)7~nVar(b)]i since the Poisson variance in 3; is 1/0.," The main uncertainty $\Delta(f\mu^2)$ in the location of this intercept come from statistical fluctuations $\Delta m$ in the fitted slope $m$ of $\delta_i$ vs $b_i$ : The uncertainty $\Delta m$ in the slope will be roughly (noise in $\delta_i$ )/(span of observed $b$ values), or $(\Delta m)^2 \sim [n{\rm Var}(b)]^{-1}$, since the Poisson variance in $\delta_i$ is $1/n$."17 Also we note that m)4=P since 9 is the slope of the line., Also we note that $\langle m^2 \rangle = P$ since $\delta$ is the slope of the line.18 Putting these together. which is very similar to (17)).," Putting these together, which is very similar to \ref{sigmaf}) )."19 We see that a small value of Var()) in the target population will lead to a laree lever-arm in determining the b-intereept that defines f. hence a narrow range of biases will produce poor constraints on. f.," We see that a small value of ${\rm Var}(b)$ in the target population will lead to a large lever-arm in determining the $b$ -intercept that defines $f$, hence a narrow range of biases will produce poor constraints on $f$."20 Equation (17)) also exhibits the expected characteristic of a sample-variance-free. measurement. namely that. mr drops without bound. as the measurement noise is driven to zero (ne o).," Equation \ref{sigmaf}) ) also exhibits the expected characteristic of a sample-variance-free measurement, namely that $\sigma_f$ drops without bound as the measurement noise is driven to zero $(n\rightarrow\infty)$ ."21 We willsee. however. that this gain isnot realized. because a real halo population has Var(b)280 as we seek large nnby going to ever-Iower halo masses.," We willsee, however, that this gain isnot realized, because a real halo population has ${\rm Var}(b)\rightarrow 0$ as we seek large $n$by going to ever-lower halo masses."22this: at By>LS. significant numbers of chwarls have surface-brightnesses so low and scale-Iengths so large that they were not detectable above the night sky in the photographic images used to compile the VCC.,"this: at $B_{T} > 18$, significant numbers of dwarfs have surface-brightnesses so low and scale-lengths so large that they were not detectable above the night sky in the photographic images used to compile the VCC."23 Following this work. Impev. Bothun Alalin (1988) discovered. a number of low surface-brightness galaxies with By«20 missng from the VCC.," Following this work, Impey, Bothun Malin (1988) discovered a number of low surface-brightness galaxies with $B_T < 20$ missing from the VCC."24 They suggested that incompleteness at the faint end of the VCC might be very severe and that the LE could. be as steep as à=1.7., They suggested that incompleteness at the faint end of the VCC might be very severe and that the LF could be as steep as $\alpha = -1.7$.25 In à more recent development. Phillipps et al. (," In a more recent development, Phillipps et al. ("2619988). present evidence for large numbers of luminosity galaxies in the Virgo Cluster.,1998a) present evidence for large numbers of low-luminosity galaxies in the Virgo Cluster.27" They measure à~2.2 fainter than an absolute # magnitude of Alp,19.", They measure $\alpha \sim -2.2$ fainter than an absolute $R$ magnitude of $M_R=-13$.28 Ifthe LE was this steep. Sandage et al.," If the LF was this steep, Sandage et al."29 would have missed the vast majority of cluster members at the faint end. even after imposing their completeness corrections.," would have missed the vast majority of cluster members at the faint end, even after imposing their completeness corrections."30 All these results suggest that the LE. is very. likely steeper in the Virgo Cluster than in dilfuse spiral-rich groups and clusters., All these results suggest that the LF is very likely steeper in the Virgo Cluster than in diffuse spiral-rich groups and clusters.31 In the Local Group. where very faint. absolute magnitudes (Ale 8) can be reached. the faint-end slope jsa-—-L (van den Bergh 1992. 2000).," In the Local Group, where very faint absolute magnitudes $M_B \sim -8$ ) can be reached, the faint-end slope is $\alpha = -1.1$ (van den Bergh 1992, 2000)."32 In the Ursa Major Cluster. a diffuse spiral-rich. group at a similar distance to the Vireo Cluster. less faint absolute magnitudes can be reached. but large enough. numbers of galaxies are present that a statistically robust LE can be computed.," In the Ursa Major Cluster, a diffuse spiral-rich group at a similar distance to the Virgo Cluster, less faint absolute magnitudes can be reached, but large enough numbers of galaxies are present that a statistically robust LF can be computed."33 Here a=1.1 as well (Prentham. Tully Verheijen 2001a).," Here $\alpha = -1.1$ as well (Trentham, Tully Verheijen 2001a)."34 Evidence is therefore accumulating that low-Iuminosity galaxies are very much more numerous per luminous galaxies in dense environments than in cilluse ones., Evidence is therefore accumulating that low-luminosity galaxies are very much more numerous per luminous galaxies in dense environments than in diffuse ones.35 Values of à~—2 are of particular interest since this is the logarithmic slope of the low-mass galaxy. mass function predicted by theory if the primordial Uuetuation spectrum. is a power law with index n=2. as appropriate for cold dark matter (Press Schechter 1974. White Rees 1978. Lee Shandarin 1999. IxIvpin et al.," Values of $\alpha \sim -2$ are of particular interest since this is the logarithmic slope of the low-mass galaxy mass function predicted by theory if the primordial fluctuation spectrum is a power law with index $n=-2$, as appropriate for cold dark matter (Press Schechter 1974, White Rees 1978, Lee Shandarin 1999, Klypin et al."36 1999)., 1999).37 HE this value of à is appropriate for the Virgo Cluster. this would suggest that in this environment the ellicieney of star formation in small galaxies does not depend on the galaxy mass. assuming cold dark matter theory (the problem of reproducing the shallow LE slope à—1 in the diffuse environments still remains: Moore et al.," If this value of $\alpha$ is appropriate for the Virgo Cluster, this would suggest that in this environment the efficiency of star formation in small galaxies does not depend on the galaxy mass, assuming cold dark matter theory (the problem of reproducing the shallow LF slope $\alpha \sim -1$ in the diffuse environments still remains; Moore et al."38 1999: IxIvpin et al., 1999; Klypin et al.39 1999)., 1999).40 We now present the results of a survey of 25 square degrees of the Virgo Cluster (about one-tenth of the total area οἱ the cluster) observed through the D filter using the Wide Field Camera on the Isaac Newton Telescope on La Palma. taken as part of the INT Wide Field Survey.," We now present the results of a survey of 25 square degrees of the Virgo Cluster (about one-tenth of the total area of the cluster) observed through the $B$ filter using the Wide Field Camera on the Isaac Newton Telescope on La Palma, taken as part of the INT Wide Field Survey."41 The intention is to ect à reasonably complete (at least to the surface-brightness levels defined. in the studies mentioned above) inventory of Virgo Cluster members., The intention is to get a reasonably complete (at least to the surface-brightness levels defined in the studies mentioned above) inventory of Virgo Cluster members.42 We can then construct a luminosity function. from Ale=22 (the brightest galaxy in our sample was AIST with Ade= 21.5) down to Ade=11., We can then construct a luminosity function from $M_B = -22$ (the brightest galaxy in our sample was M87 with $M_B = -21.5$ ) down to $M_B = -11$.43 This will permit us to address the following questions: Ipt (i) what is the value ofa. and does this vary significantly with absolute magnitude ie. over what magnitude range can we approximate the LE by a power law?," This will permit us to address the following questions: 1pt (i) what is the value of $\alpha$, and does this vary significantly with absolute magnitude i.e. over what magnitude range can we approximate the LF by a power law?"44 Llow sensitive is the answer to our ability to recognize cluster members based on surface-brightness: could we be missing many hieh surface-brightness members because we think that they are background galaxies or many low surface-brightness galaxies whose contrast against the sky is too low to allow us to identify them?, How sensitive is the answer to our ability to recognize cluster members based on surface-brightness: could we be missing many high surface-brightness members because we think that they are background galaxies or many low surface-brightness galaxies whose contrast against the sky is too low to allow us to identify them?45 Ipt (ii) what are the morphologies of the faintest. galaxies?, 1pt (ii) what are the morphologies of the faintest galaxies?46 Alost previous work (Sancdage et al., Most previous work (Sandage et al.47 1985. Phillipps et al.," 1985, Phillipps et al."48 1998a). suggests. that they are. dwarf. elliptical (alternatively called. chwarl spheroidal) galaxies., 1998a) suggests that they are dwarf elliptical (alternatively called dwarf spheroidal) galaxies.49 This would imply that. low surface-brightness. irregular. star-forming ealaxies do not contribute significantly to the LE at the [aint end as they do in the Ursa Major Cluster (Prentham et al., This would imply that low surface-brightness irregular star-forming galaxies do not contribute significantly to the LF at the faint end as they do in the Ursa Major Cluster (Trentham et al.50 2001a): Ipt (iii) do the results depend on the colour of the galaxies and the filter used?, 2001a); 1pt (iii) do the results depend on the colour of the galaxies and the filter used?51 We. like Sandage et ab.," We, like Sandage et al.,"52 are using a D filter., are using a $B$ filter.53 Phillipps ct al., Phillipps et al.54 used a red & filter., used a red $R$ filter.55 How. much of he very substantial excess of galaxies they found. could. be due do this. given that dSph/dl galaxies tend to be red (Caldwell 1983)?," How much of the very substantial excess of galaxies they found could be due do this, given that dSph/dE galaxies tend to be red (Caldwell 1983)?"56 Ipt (iv) are there substantial numbers of very low surface rightness (WLSB) galaxies. as seen in the Fornax cluster w Ixambas ct al. (," 1pt (iv) are there substantial numbers of very low surface brightness (VLSB) galaxies, as seen in the Fornax cluster by Kambas et al. ("572000)?,2000)?58 In particular. as we approach the imiting surface brightness at which we can detect objects in our data. do we find more and more VLSB galaxies. ancl what is the their contribution to the total LE?," In particular, as we approach the limiting surface brightness at which we can detect objects in our data, do we find more and more VLSB galaxies, and what is the their contribution to the total LF?"59 We will need o quantify this in order to address the questions posed in (1) above: Ipt (*) how does the galaxy luminosity function depend on environment?, We will need to quantify this in order to address the questions posed in (i) above; 1pt (v) how does the galaxy luminosity function depend on environment?60 We will compare our Virgo Cluster luminosity function to the J-bancl luminosity functions of the Local Group. the Ursa Major Cluster. and the rich Coma Cluster abi a distance of 90 Mpc.," We will compare our Virgo Cluster luminosity function to the $B$ -band luminosity functions of the Local Group, the Ursa Major Cluster, and the rich Coma Cluster at a distance of 90 Mpc."61 We will then have measurements of the LE in four very cüfferent. environments., We will then have measurements of the LF in four very different environments.62 In the case of the Local Ciroup. the LE. has large uncertainties due to Poisson statistics.," In the case of the Local Group, the LF has large uncertainties due to Poisson statistics."63 In the Coma Cluster the LE has large uncertainties due to the need to do a background subtraction., In the Coma Cluster the LF has large uncertainties due to the need to do a background subtraction.64 Lt is well-known (Dressler 1980). that the morphologies of galaxies depend on environment. specifically on the galaxy. density.," It is well-known (Dressler 1980) that the morphologies of galaxies depend on environment, specifically on the galaxy density."65 Our results will indicate whether or not the LE does too. over a large magnitude range.," Our results will indicate whether or not the LF does too, over a large magnitude range."66" The data used. here were taken on various observing runs during Spring 1999 and Spring 2000 as part of the INTE Wide Field: Survey (WES: ""wfesur: AleMahon et al.", The data used here were taken on various observing runs during Spring 1999 and Spring 2000 as part of the INT Wide Field Survey (WFS; $^{\sim}$ wfcsur; McMahon et al.67 2001)., 2001).68 This is à digital survey covering about 100 deg? of sky carried out using the Wide Field Camera (a⇉↓∖⋡∣⊲⇀⊲∣⊲⇀⊲∖≱≺⊲≺⊲∐∖⋡ mosaic of four tly pixel scale 0.33. aresec field of view 0.29 E 7," This is a digital survey covering about 100 $^{2}$ of sky carried out using the Wide Field Camera (a mosaic of four 4K $\times$ 2K EEV CCDs, pixel scale 0.33 arcsec $^{-1}$ , field of view 0.29 $^{-2}$ ;"69 This is à digital survey covering about 100 deg? of sky carried out using the Wide Field Camera (a⇉↓∖⋡∣⊲⇀⊲∣⊲⇀⊲∖≱≺⊲≺⊲∐∖⋡ mosaic of four tly pixel scale 0.33. aresec field of view 0.29 E 7:," This is a digital survey covering about 100 $^{2}$ of sky carried out using the Wide Field Camera (a mosaic of four 4K $\times$ 2K EEV CCDs, pixel scale 0.33 arcsec $^{-1}$ , field of view 0.29 $^{-2}$ ;"70All of the techniques used in this paper are faulliar to the unage-analysis comuinunity and many of the elements are discussecl in the above ancl other references.,All of the techniques used in this paper are familiar to the image-analysis community and many of the elements are discussed in the above and other references.71 But I have not found iu the astronomical literature: au application ofthe Fisher information matrix to poiut-source photometry in the presence of cosmic rays: a quantitative cliscussiou of the effects of pixel size on weak lensiug iueastrements: or a quantitative derivation of the required amount of dithering., But I have not found in the astronomical literature: an application of the Fisher information matrix to point-source photometry in the presence of cosmic rays; a quantitative discussion of the effects of pixel size on weak lensing measurements; or a quantitative derivation of the required amount of dithering.72 More importantly. there is not to my knowledge a publication or softwa'e tool which combines all of these important effects to make detailed exposure-time estimates.," More importantly, there is not to my knowledge a publication or software tool which combines all of these important effects to make detailed exposure-time estimates."73 That is the goal of this publication., That is the goal of this publication.74 Following this Introduction is a general discussii1 of pixelization aud sampling upon imagine observations. giving the analytical framework lor the ¢aleulations.," Following this Introduction is a general discussion of pixelization and sampling upon imaging observations, giving the analytical framework for the calculations."75 The next section briefly describes the implemeutation of these ideas in the soltware package., The next section briefly describes the implementation of these ideas in the software package.76 velvesults cdemoustrates the capabilities of the iuethods aud software by providiug euantitative alswers {ο some general questions: what is the S/N penalty for oversized pixels?, \\ref{results} demonstrates the capabilities of the methods and software by providing quantitative answers to some general questions: what is the $S/N$ penalty for oversized pixels?77 What amount ol dithering is required to reach optimal S/V?, What amount of dithering is required to reach optimal $S/N$?78 Then I address some more specific questions about optimizing camera coulfiguratious. aud comparing the performance of state-ol-the art space-based lunaging vs ground-based imagiug.," Then I address some more specific questions about optimizing camera configurations, and comparing the performance of state-of-the art space-based imaging vs ground-based imaging."79effect induced by its rapid rotation.,effect induced by its rapid rotation.80" According to the latest model based on interferometric results (Yoonetal.,2008),, the equatorial velocity of Vega is 274 kmss™! and the effective temperature and the gravity decrease from 9988 K and 4.07 at the pole to 7600 K and logg=3.5 at the equator."," According to the latest model based on interferometric results \citep{Yo08}, the equatorial velocity of Vega is 274 $^{-1}$ and the effective temperature and the gravity decrease from 9988 K and $\log g = 4.07$ at the pole to 7600 K and $\log g = 3.5$ at the equator."81" There is a significant discrepancy with the spectroscopic analysis of Takedaetal.(2008), who find that the polar to equator temperature difference is only ~900 K while the equatorial velocity is reduced to 175 kmss~!."," There is a significant discrepancy with the spectroscopic analysis of \citet{Ta08}, who find that the polar to equator temperature difference is only $\sim\!900$ K while the equatorial velocity is reduced to 175 $^{-1}$."82" Taking the extreme case of a Teg=7500 K and logg = 3.5 stellar atmosphere, we computed the LSD line profiles (not shown here) for the associated line mask and this time obtained a false-alarm probability of 107!."," Taking the extreme case of a $_{\rm eff}$ =7500 K and $\log g$ = 3.5 stellar atmosphere, we computed the LSD line profiles (not shown here) for the associated line mask and this time obtained a false-alarm probability of $10^{-1}$."83 The polarized signal is consistent with the one derived from our previous (hotter) atmospheric model but the low significance of the detection is due to the inadequacy of the line mask that results in a much higher noise level., The polarized signal is consistent with the one derived from our previous (hotter) atmospheric model but the low significance of the detection is due to the inadequacy of the line mask that results in a much higher noise level.84 These tests strongly support that the signal is of stellar origin and therefore that Vega possesses a magnetic field., These tests strongly support that the signal is of stellar origin and therefore that Vega possesses a magnetic field.85 The circularly polarized signal has the typical anti-symmetric shape of a Zeeman signature (Fig. 1))., The circularly polarized signal has the typical anti-symmetric shape of a Zeeman signature (Fig. \ref{fig:stokesv}) ).86" However, as compared to the width of the Stokes I line profile, it only shows up within a limited range of radial velocities about the line-center."," However, as compared to the width of the Stokes I line profile, it only shows up within a limited range of radial velocities about the line-center."87 This suggests that the magnetic field distribution is axisymmetric and confined in the polar region., This suggests that the magnetic field distribution is axisymmetric and confined in the polar region.88" However, a more detailed analysis will be needed to specify the surface field distribution of Vega."," However, a more detailed analysis will be needed to specify the surface field distribution of Vega."89" First, as the 257 spectra at our disposal cover a range of rotation phases, Zeeman signatures from non-axisymmetric magnetic features, if any, are mostly averaged out from the time-averaged line profile."," First, as the 257 spectra at our disposal cover a range of rotation phases, Zeeman signatures from non-axisymmetric magnetic features, if any, are mostly averaged out from the time-averaged line profile."90" Second, due to Vega's temperature inhomogeneities, the weak line profiles range from flat-bottomed to ""V"" shapes (Yoonetal.,2008;Takedaetal.2008)."," Second, due to Vega's temperature inhomogeneities, the weak line profiles range from flat-bottomed to ""V"" shapes \citep{Yo08,Ta08}."91" As the LSD profile is obtained by assuming that all lines have a common profile, its interpretation in terms of the surface field distribution is not straightforward in the present context."," As the LSD profile is obtained by assuming that all lines have a common profile, its interpretation in terms of the surface field distribution is not straightforward in the present context."92" We use the center-of-gravity method (Rees& to estimate the longitudinal magnetic field B,: where v (kmss!) is the radial velocity, Ay (nm) the mean wavelength of the line-list used to compute the LSD profiles, &m the mean Landé factor and c ss!) the light velocity."," We use the center-of-gravity method \citep{Ree79} to estimate the longitudinal magnetic field $B_l$: where $v$ $^{-1}$ ) is the radial velocity, $\lambda_0$ (nm) the mean wavelength of the line-list used to compute the LSD profiles, $g_m$ the mean Landé factor and $c$ $^{-1}$ ) the light velocity."93 The integration limits cover a +30 kmss! velocity range around the line centroid., The integration limits cover a $\pm30$ $^{-1}$ velocity range around the line centroid.94" Using this equation, we obtain B;=—0.6+0.3 G. Three basic features distinguish the present detection from previous measurements of magnetic fields in main-sequence stars of intermediate mass: (1) It is the first time a magnetic field is detected in an A-type star which is not an Ap/Bp chemically peculiar star (if we exclude the debated field detections in a few Am and HgMn stars (Lanz&Mathys,1993;Mathys&Hubrig,1995) discussed in Shorlinetal. (2002))). ("," Using this equation, we obtain $B_l = -0.6 \pm 0.3$ G. Three basic features distinguish the present detection from previous measurements of magnetic fields in main-sequence stars of intermediate mass: (i) It is the first time a magnetic field is detected in an A-type star which is not an Ap/Bp chemically peculiar star (if we exclude the debated field detections in a few Am and HgMn stars \citep{Ma93,Ma95} discussed in \citet{Shor02}) ). ("95ii) The longitudinal magnetic field of Vega is smaller by about two orders of magnitude than the field of the most weakly magnetic Ap/Bp stars.,ii) The longitudinal magnetic field of Vega is smaller by about two orders of magnitude than the field of the most weakly magnetic Ap/Bp stars.96" Indeed, the longitudinal field of a 300 G dipolar field aligned with the stellar rotation axis and viewed pole-on is close to 100 G, that is about two orders of magnitude larger than the 0.6 G field of Vega."," Indeed, the longitudinal field of a 300 G dipolar field aligned with the stellar rotation axis and viewed pole-on is close to 100 G, that is about two orders of magnitude larger than the $0.6$ G field of Vega."97 The longitudinal component of a dipolar field actually depends on its angle with respect to the rotation axis., The longitudinal component of a dipolar field actually depends on its angle with respect to the rotation axis.98" But, whatever this angle, the amplitude of the circular polarization in the LSD Stokes V profile of a 300 G dipolar field will be more than one order of magnitude larger than that of Vega. ("," But, whatever this angle, the amplitude of the circular polarization in the LSD Stokes V profile of a 300 G dipolar field will be more than one order of magnitude larger than that of Vega. ("99iii) The LSD Stokes V profile of Vega is also qualitatively distinct from LSD Stokes V profiles of Ap/Bp stars since the polarized signal of Vega is concentrated in the weakly Doppler shifted regions of the projected stellar disk.,iii) The LSD Stokes V profile of Vega is also qualitatively distinct from LSD Stokes V profiles of Ap/Bp stars since the polarized signal of Vega is concentrated in the weakly Doppler shifted regions of the projected stellar disk.100 These marked observational differences between Vega and the Ap/Bp magnetic stars suggest that we should consider Vega as a new type of magnetic A-type star., These marked observational differences between Vega and the Ap/Bp magnetic stars suggest that we should consider Vega as a new type of magnetic A-type star.101" As there is no reason to believe Vega is unique among A-type stars, Vega should be considered as the first member of a new class of magnetic stars."," As there is no reason to believe Vega is unique among A-type stars, Vega should be considered as the first member of a new class of magnetic A-type stars."102eeometrically thin as well.,geometrically thin as well.103 For densities greater than neutrou drip. however. the electrons no longer support the crust. aud Ej need uot increase with depth.," For densities greater than neutron drip, however, the electrons no longer support the crust, and $\EF$ need not increase with depth."104 In fact. Ej is actually less following t1 electron capture layer if the interface between layers of different Composition is treated as a infinitely-— thin plane.," In fact, $\EF$ is actually less following an electron capture layer if the interface between layers of different composition is treated as a infinitely thin plane."105 The layers. although thin with respect to Bye. are then geometrically thick.," The layers, although thin with respect to $\EF$, are then geometrically thick."106 Iu actuality. thermal broadening of the electron Fermi surface causes many of the captures to occur pre-threshold. aud the capture layers are thickened to nearly the width between layers 1999)..," In actuality, thermal broadening of the electron Fermi surface causes many of the captures to occur pre-threshold, and the capture layers are thickened to nearly the width between layers \citep{ushomirsky00:_crust}."107 Should the capture layers overlap. then Q iu the mixed layer can become larger tliau unity.," Should the capture layers overlap, then $Q$ in the mixed layer can become larger than unity."108 The impurities manulacttred within the capture lavers are probably a small perturbation compared to those already preseut iu the mixture entering the top of the crust., The impurities manufactured within the capture layers are probably a small perturbation compared to those already present in the mixture entering the top of the crust.109 found that Q~100 inumnectiateaa ollowing the end of stable hydrogen burning., \citet{schatz99} found that $Q\sim 100$ immediately following the end of stable hydrogen burning.110 An accurate assessinent of CQ. throughout the crust. requires evolving the composition of an accreted fluid element ou its journey through the crust.," An accurate assessment of $Q$, throughout the crust, requires evolving the composition of an accreted fluid element on its journey through the crust."111 This task is beyoud the scope of this initial survey. aud [ instead set upper aud lower bounds ou the conductivity.," This task is beyond the scope of this initial survey, and I instead set upper and lower bounds on the conductivity."112 The upper bound to the conductivity is that of a pure crystal (electron-pliouou scattering)., The upper bound to the conductivity is that of a pure crystal (electron-phonon scattering).113 To set the lower bound. first note that electrou-impurity scattering dominates the conductivity wherever το<Τρ with 7 being the electron-phonon relaxation time (Baiko&Yakovlev1995) Here a is the fine structure constant. and Ac&13 comes from integrating over the phonon spectrum.," To set the lower bound, first note that electron-impurity scattering dominates the conductivity wherever $\tau_{eQ}<\tau_{ep}$, with $\tau_{ep}$ being the electron-phonon relaxation time \citep{baiko95}114 Here $\alpha$ is the fine structure constant, and $\Lambda_{ep}\approx11513$ comes from integrating over the phonon spectrum."116 Equations (11)) aud (16)) imply that for Qo>0.66(30MeV/Eye)Z/26)UgT/0.05MeV) electron-impurity scattering determines the thermal conductivity iu the crust., Equations \ref{eq:eQ-scattering}) ) and \ref{eq:ep-scattering}) ) imply that for $Q \gtrsim 0.66(30\MeV/\EF) (Z/26) (\kB T/0.05\MeV)$ electron-impurity scattering determines the thermal conductivity in the crust.117 IC the reactions in the crust do not significantly reduce Q from its large value at the base of the hydrogen/helium burnii1g shell. then IfH Q isη very large (rp? Z). then the impurity.H relaxationH timeH isH roughly that ofH electron-ionH scattering for a pure crystal (Yakovlev&Urpin1980).. with Ay;=In[(22Z/3)771.5+3/P]-1.," If the reactions in the crust do not significantly reduce $Q$ from its large value at the base of the hydrogen/helium burning shell, then If $Q$ is very large $\sim Z^2$ ), then the impurity relaxation time is roughly that of electron-ion scattering for a pure crystal \citep{yakovlev80:_therm}, with $\Lambda_{ei}=\ln[(2\pi Z/3)^{1/3}\sqrt{1.5+3/\Gamma}]-1$."118 Basically. the phonon spectrum is extremely disordered in this case.," Basically, the phonon spectrum is extremely disordered in this case."119 E therefore set a lower lunit to the couductivity by using electron-ion scattering. ie.. by treating the ious as if they were liquefied.," I therefore set a lower limit to the conductivity by using electron-ion scattering, i.e., by treating the ions as if they were liquefied."120 For cousistency. [ also use the liquid-state neutrino bremsstrahlung emissivity (Haenseletal.1996) in conjunction with the electrou-iou conductivity.," For consistency, I also use the liquid-state neutrino bremsstrahlung emissivity \citep{haensel96b} in conjunction with the electron-ion conductivity."121 The impurities in the crust reduce the couductivity but increase the ueutrino emissivity., The impurities in the crust reduce the conductivity but increase the neutrino emissivity.122 Iu the core. heat is mostly carried by electrous. with neutrous contributing if they are uormal (Flowers&Itoh1979).," In the core, heat is mostly carried by electrons, with neutrons contributing if they are normal \citep{flowers79}."123. I neglect here the ueutron conductivity., I neglect here the neutron conductivity.124 This is a good approximation. as the core is practically isotherinal (see 22)).," This is a good approximation, as the core is practically isothermal (see \ref{s:results}) )."125 In evaluating the electrou-proton scattering teris.," In evaluating the electron-proton scattering terms,"126"profile and photometric variations of HR 7355, we intend to undertake, in a future study, a more physically realistic line profile analysis, taking into account rotational deformation and gravity darkening, to provide a consistent solution for stellar parameters and evolution.","profile and photometric variations of HR 7355, we intend to undertake, in a future study, a more physically realistic line profile analysis, taking into account rotational deformation and gravity darkening, to provide a consistent solution for stellar parameters and evolution."127 GAW acknowledges support from a Natural Science and Engineering Research Council of Canada (NSERC) Discovery Grant and a Department of National Defense ARP grant., GAW acknowledges support from a Natural Science and Engineering Research Council of Canada (NSERC) Discovery Grant and a Department of National Defense ARP grant.128 RHDT acknowledges support from NASA / LTSA grant NNG05GC36G., RHDT acknowledges support from NASA / LTSA grant NNG05GC36G.129during the second phase of the evolution. and (his timescale may be comparable to the age ol the source in the case of large-scale outer lobes of GRGs and DDIBRGs.,"during the second phase of the evolution, and this timescale may be comparable to the age of the source in the case of large-scale outer lobes of GRGs and DDRGs."130 Following the above argument. in our filling procedure we neglect the effect οἱ a slower expansion phase when evaluating the dynamical parameters of a source.," Following the above argument, in our fitting procedure we neglect the effect of a slower expansion phase when evaluating the dynamical parameters of a source."131 This allows us in parücular to estimate the length of a jet as and the longitudinal expansion velocity of a cocoon as In the above e4 is a numerical constant depending on a value of Ze. ay is the radius of the central plateau in (he density distribution of the surrounding gas. and ;? is the exponent in the anticipated ambient density profile p(r)=py(r/ay).," This allows us in particular to estimate the length of a jet as and the longitudinal expansion velocity of a cocoon as In the above $c_{1}$ is a numerical constant depending on a value of $R_{\rm T}$, $a_{0}$ is the radius of the central plateau in the density distribution of the surrounding gas, and $\beta$ is the exponent in the anticipated ambient density profile $\rho(r)=\rho_{0}\,(r/a_{0})^{-\beta}$."132 The total projected length of the entire structure is D=26.," The total projected length of the entire structure is $D=2\, \ell_{\rm j}$."133" The ratio of the pressure within the lobes” heads to that within (he rest of the cocoon. y.=py/pe. is taken as Py.=(2.14—0.525)ny""om following IXaiser (2000).."," The ratio of the pressure within the lobes' heads to that within the rest of the cocoon, ${\cal P}_{\rm hc}\equiv p_{\rm h}/p_{\rm c}$, is taken as ${\cal P}_{\rm hc}=(2.14-0.52\,\beta)\,R_{\rm T}^{2.04-0.25\,\beta}$ following \citet{k00}. ."134 We note that only if /; is shorter than /. thus evaluated model parameters would correspond to the on the ratio Q;/po.," We note that only if $t_{\rm j}$ is shorter than $t$, thus evaluated model parameters would correspond to the on the ratio $Q_{\rm j}/\rho_{0}$."135 But since in our discussion below 44) we emphasize large jet. kinetic powers and low ambient medium densities required. (o fit the observed spectrum of (and of the other giant sources). equations 12 constitute a very conservalive choice indeed.," But since in our discussion below 4) we emphasize large jet kinetic powers and low ambient medium densities required to fit the observed spectrum of (and of the other giant sources), equations 1–2 constitute a very conservative choice indeed."136 Desides. in (he presented model fitting the jet lifetimes are never less than τος of the source ages.," Besides, in the presented model fitting the jet lifetimes are never less than $70\%$ of the source ages."137 Importantly. the evaluation of the lobes’ huninosities is done taking into account only Chose relativistic particles which are injected into the lobes during the first phase of (he evolution. corresponding to the ongoing jel activity.," Importantly, the evaluation of the lobes' luminosities is done taking into account only those relativistic particles which are injected into the lobes during the first phase of the evolution, corresponding to the ongoing jet activity."138 The integration over the source spectrin is performed following the description provided in aser&Cotter(2002) in the context of relict radio sources., The integration over the source spectrum is performed following the description provided in \citet{kai02} in the context of relict radio sources.139 In the KDA model the minimum-energv condition is applied. being determined by accounüng for the energies stored in the lobes’ magnetic field and in relativistic radiating particles only.," In the KDA model the minimum-energy condition is applied, being determined by accounting for the energies stored in the lobes' magnetic field and in relativistic radiating particles only."140 However. the extended lobes of luminous radio galaxies max not fulfill exactly (he minimunr-energy condition. and may contain — especially at laree stages of their evolution a significant Iraction of non-radiating (possibly mildlv-relativistic) particles. as indicated by the recent. N-ray observations of a munber of such svstems as wellas by some theoretical," However, the extended lobes of luminous radio galaxies may not fulfill exactly the minimum-energy condition, and may contain — especially at large stages of their evolution — a significant fraction of non-radiating (possibly mildly-relativistic) particles, as indicated by the recent X-ray observations of a number of such systems as wellas by some theoretical"141The radial surface brightuess profiles in the high-quality VR aud [απ images appear to be well represeuted by an exponenutial-like profile.,The radial surface brightness profiles in the high-quality $VR-$ and $I$ -band images appear to be well represented by an exponential-like profile.142 Such profiles are often observed in dwart elliptical galaxies (Faber Lin 1983: Ichikawa et al., Such profiles are often observed in dwarf elliptical galaxies (Faber Lin 1983; Ichikawa et al.143 19862: 19865). aud also in the tidal dwarf galaxy Arp 215N (Duc et al.," 1986a; 1986b), and also in the tidal dwarf galaxy Arp 245N (Duc et al."144 2000)., 2000).145 Iu order to investigate the stellar conteut of TDSS. we now investigate its photometric properties.," In order to investigate the stellar content of TDSS, we now investigate its photometric properties."146 We first smear the F336W ΕΟΟ. F555VW V-. V Πο I-. Pali. K'-baud images-. to match the seeiug-. of our R-banud image. eiven that the A-baud image has the largest secius value in our image set.," We first smear the $F336W$ -, $F439W$ -, $F555W$ -, $V$ -, $VR$ -, $I$ -, $F814W$ -, $K^{\prime}$ -band images to match the seeing of our $R$ -band image, given that the $R$ -band image has the largest seeing value in our image set."147 Since a point spread function(PSF) of IONIC is undesirably exteuded (Yanagisawa ct al., Since a point spread function(PSF) of KONIC is undesirably extended (Yanagisawa et al.148 1996). for the ./ and ff nuages after the PSF decouvolution were carried out with the Lucy-Richardsous method realize iu the STSDAS packages. we ποσα both images to match the seeing of our R-band image.," 1996), for the $J-$ and $H-$ images after the PSF deconvolution were carried out with the Lucy-Richardsons method realize in the STSDAS packages, we smear both images to match the seeing of our $R$ -band image."149 Then. using the package. we integrated the light within an ellipse which eucloses TDSS iu each baud: the semi-anajor axis = 1075. the ecceutricity = 0.90. and the position auele = 16°.," Then, using the package, we integrated the light within an ellipse which encloses TDSS in each band; the semi-major axis = $\farcs$ 5, the eccentricity = 0.90, and the position angle = $\arcdeg$."150 The results are shown in Table 1., The results are shown in Table 1.151 Unfortunately. In£336W nuage laree noise overlapped with TDSS. we obtained only upper limit of fiux of TDSS.," Unfortunately, in image large noise overlapped with TDSS, we obtained only upper limit of flux of TDSS."152 We compare the coloranaguitude relation found for TDSS with those of other similar objects by using a P.V versus Ap diagerann, We compare the color-magnitude relation found for TDSS with those of other similar objects by using a $B-V$ versus $M_{\rm B}$ diagram.153 We obtain an averaged apparenut magnitude of 17.13 + 0.01 mae (Johnson D) for TDSS after correcting for galactic extinction (de Vaucouleurs et al., We obtain an averaged apparent magnitude of 17.13 $\pm$ 0.01 mag (Johnson ) for TDSS after correcting for galactic extinction (de Vaucouleurs et al.154 1991: Cardelli et al., 1991; Cardelli et al.155 1989: Schlegel et al., 1989; Schlegel et al.156 1998)., 1998).157 We also obtained apparent JohusouV imaguitudes of 16.17 + 0.27 (observed with II-CCD camera) aud of 16.10 4 0.003 mae (observed with WEPC?)., We also obtained apparent Johnson magnitudes of 16.17 $\pm$ 0.27 (observed with 1K-CCD camera) and of 16.40 $\pm$ 0.003 mag (observed with ).158 Thus. we obtained a Johusou BV colors for TDSS of O.7340.01 mae aud O.O740.27 nag and au absolute Johuson Diaguitude of 16.11 inae.," Thus, we obtained a Johnson $B-V$ colors for TDSS of $\pm$ 0.01 mag and $\pm$ 0.27 mag and an absolute Johnson magnitude of $-$ 16.14 mag."159 Iu Figure 3. we plot the data points for TDSS together with those of two tidal dwarf ealaxies. Arp 1058 (VeiS5BIN lan ον de Vancouleurs et al.," In Figure 3, we plot the data points for TDSS together with those of two tidal dwarf galaxies, Arp 105S $V_{\rm GSR}=8518$ km $^{-1}$: de Vaucouleurs et al."160 1991) and Arp 215N (Vosg=2175 lan |. which is the average value of the Voag of NGC 2992 and NGC 2993: de Vaucouleurs et al," 1991) and Arp 245N $V_{\rm GSR}=2175$ km $^{-1}$, which is the average value of the $V_{\rm GSR}$ of NGC 2992 and NGC 2993: de Vaucouleurs et al."161 1991: Drame et al., 1991; Braine et al.162 2000). and dwarf ellipticals iu the Virgo cluster (Bothun et al.," 2000), and dwarf ellipticals in the Virgo cluster (Bothun et al."163 1989). the Foruax cluster (Bothun et al.," 1989), the Fornax cluster (Bothun et al."164 1989). the Centaurus cluster (Bothun ct al.," 1989), the Centaurus cluster (Bothun et al."165 1989). aud the NCC 2011 eroup (Cellone 1999).," 1989), and the NGC 5044 group (Cellone 1999)."166 We also show theoretical loci of choemo-plotomietrie evolution models taken from Arianoto Yoshi (1987)., We also show theoretical loci of chemo-photometric evolution models taken from Arimoto Yoshii (1987).167 The D.V and Ap properties of TDSS are different from those of Arp 1058 (p=16.28. B.V= 0.3) αμα Arp 215N (Mp=16.63. BoV— 0.55) (Braine et al.," The $B-V$ and $M_{B}$ properties of TDSS are different from those of Arp 105S $M_{B}=-16.28$, $B-V=0.3$ ) and Arp 245N $M_{B}=-16.63$, $B-V=0.55$ ) (Braine et al."168 2000)., 2000).169 In Figure 3 TDSS is located near the bright cud of the loci of dwarf ellipticals iu nearby clusters., In Figure 3 TDSS is located near the bright end of the loci of dwarf ellipticals in nearby clusters.170 Braine et al. (, Braine et al. (1712000) sugeested that Arp 1055 and Arp 215N have experienced recent (< 1 Cr) bursts of star formation.,2000) suggested that Arp 105S and Arp 245N have experienced recent $<$ 1 Gyr) bursts of star formation.172 However. the data shown in Figure 3 suggests that a recent (< 1 Gyr) star formation burst has uot occurred in TDSS.," However, the data shown in Figure 3 suggests that a recent $<$ 1 Gyr) star formation burst has not occurred in TDSS."173 Schombert et al. (, Schombert et al. (1741990) showed averaged the color of tidal features (tails. bridges. plumes. and cuvelopes)} of 0.51021.,"1990) showed averaged the color of tidal features (tails, bridges, plumes, and envelopes) of $\pm$ 0.24."175 The color of TDSS is similar to or redder than those of these tidalfeatures., The color of TDSS is similar to or redder than those of these tidalfeatures.176The characteristic timescale due to spectral ageing is given by with B the magnetic field at the Bennshock front in Gauss. Beaty the equivalent magnetic field strength of the CMB 1n j/Gauss. and v the observed frequency in MHz.,"The characteristic timescale due to spectral ageing is given by with $B$ the magnetic field at the shock front in $\mu$ Gauss, $B_{\mathrm{CMB}}$ the equivalent magnetic field strength of the CMB in $\mu$ Gauss, and $\nu$ the observed frequency in MHz."177 At z=0.103. Bem is 4.0 Gauss.," At $z=0.103$, $B_{\mathrm{CMB}}$ is $4.0~\mu$ Gauss."178 If v» and @ are known this gives a method for determining the magnetic field strength., If $v_2$ and $\phi$ are known this gives a method for determining the magnetic field strength.179 Even ifà is not known. limits on the magnetic field can be obtained if the observed width (oye) 1s smaller than the maximum width allowed from Eq. 2..," Even if $\phi$ is not known, limits on the magnetic field can be obtained if the observed width $l_{\mathrm{relic}}$ ) is smaller than the maximum width allowed from Eq. \ref{eq:lrelic1}. ."180 To get an estimate of v». We use a temperature in the post- region of 6 keV. re. about twice the average cluster temperature.," To get an estimate of $v_2$, we use a temperature in the post-shock region of 6 keV, i.e, about twice the average cluster temperature."181 This factor of two increase 1s roughly what has been observed in other clusters with shocks (e.g..??)..," This factor of two increase is roughly what has been observed in other clusters with shocks \citep[e.g.,][]{2010arXiv1004.1559R, 2009ApJ...693L..56M}."182 We use Rankine-Hugoniot jump conditions (?).. with an adiabatic index y5/3. and take the Mach number from the injection spectral index.," We use Rankine-Hugoniot jump conditions \citep{1959flme.book.....L}, with an adiabatic index $\gamma =5/3$, and take the Mach number from the injection spectral index."183 This gives with indices | and 2 referring to the pre-shock and shock regions., This gives with indices 1 and 2 referring to the pre-shock and post-shock regions.184 The downstream speed is given by i5Nca /C. with c;4 the pre-shock sound speed. (ykpμμ)!4 with 4j=0.6 the mean molecular weight.," The downstream speed is given by $ v_2= \mathcal{M} c_{s,1} / C$ , with $c_{s,1}$ the pre-shock sound speed, $\left( \gamma k_{\rm{B}} T_1/ m_{\rm{H}} \mu \right)^{1/2}$, with $\mu=0.6$ the mean molecular weight."185 The compression ratio C ts given by FilingΑΔ in the numbers gives. C=2.4 and km s7'.," The compression ratio $C$ is given by Filling in the numbers gives $C=2.4$ and $c_{s,1}=1100$ km $^{-1}$ ."186 We then obtain vs=750 km s'., We then obtain $v_2 = 750$ km $^{-1}$ .187 The downstream velocity depends only weakly on the adopted downstream temperature., The downstream velocity depends only weakly on the adopted downstream temperature.188 For example. using a downstream temperature of 10 keV increases of v5 to about 950 km s7!.," For example, using a downstream temperature of 10 keV increases of $v_2$ to about $950$ km $^{-1}$."189 For the remainder we will adopt vs=750 km s!, For the remainder we will adopt $v_2 = 750$ km $^{-1}$.190 This then gives for the width of the relic (FWHM) observed at 1382 MHz with the magnetic fieldBoy strengths 1n units of j/Gauss., This then gives for the width of the relic (FWHM) observed at 1382 MHz with the magnetic field strengths in units of $\mu$ Gauss.191 For 6O°. the maximum width is 46 kpe. which corresponds to B=2Gauss.," For $\phi=0\degr$, the maximum width is 46 kpc, which corresponds to $B\approx2~\mu$ Gauss."192 This ts smaller than the observed width of about 150 kpe (see Fig. 16)), This is smaller than the observed width of about 150 kpc (see Fig. \ref{fig:relicprofile}) )193 and hence no constraints on the magnetic field can be put since the angle ὁ is not known., and hence no constraints on the magnetic field can be put since the angle $\phi$ is not known.194 It is possible to set limits on @ using the observed polarization fraction (2).., It is possible to set limits on $\phi$ using the observed polarization fraction \citep{1998A&A...332..395E}.195 A polarization fraction implies @<50°., A polarization fraction implies $\phi <50\degr$.196 This limit on e ts not consistent with the observed width which would require @>72°., This limit on $\phi$ is not consistent with the observed width which would require $\phi > 72\degr$.197 Although. for large sections of the relic the polarization fraction is unknown and could be smaller than20%.," Although, for large sections of the relic the polarization fraction is unknown and could be smaller than."198 In the above analysis we assumed that a relic traces a planar shock wave., In the above analysis we assumed that a relic traces a planar shock wave.199 In a more realistic model of a relic would trace a shock wave that forms a part of a sphere., In a more realistic model of a relic would trace a shock wave that forms a part of a sphere.200 This is illustrated by the curved shape of relic RE., This is illustrated by the curved shape of relic RE.201 The observed width is about a factor of three larger than the maximum intrinsic allowed width. max(/eie(@=0.B).," The observed width is about a factor of three larger than the maximum intrinsic allowed width, $\max({l_{\mathrm{relic} }(\phi=0, B)})$."202 This implies that projection effects probably play an important role., This implies that projection effects probably play an important role.203 The questions is then why do we still see a clear spectral index gradient (Fig. 16)), The questions is then why do we still see a clear spectral index gradient (Fig. \ref{fig:relicprofile}) )204 across the relic?, across the relic?205 To answer this questions we use a more realistic model of a shock front., To answer this questions we use a more realistic model of a shock front.206 The spherical shock subtends an angle V into the plane of the sky anc has a radius of curvature Aoi., The spherical shock subtends an angle $\Psi$ into the plane of the sky and has a radius of curvature $R_{\mathrm{projected}}$.207" The total angle subtended by the relic is 2"".", The total angle subtended by the relic is $2\Psi$.208 We compute the radio luminosity profiles at the observed frequencies of 241 and 1382 MHz., We compute the radio luminosity profiles at the observed frequencies of 241 and 1382 MHz.209 The injection spectral index is taken to be —1.0., The injection spectral index is taken to be $-1.0$.210 Synchrotron cooling processes. based on the distance of the emitting radio plasma fron the front of the shock. which in turn depend on the downstream velocity v»=750 km s7!. are taken into account.," Synchrotron cooling processes, based on the distance of the emitting radio plasma from the front of the shock, which in turn depend on the downstream velocity $v_2 = 750$ km $^{-1}$, are taken into account."211 For the magnetic field we assume B=2 jiGauss. which maximizes the intrinsic width of the relic to 46 kpe.," For the magnetic field we assume $B=2~\mu$ Gauss, which maximizes the intrinsic width of the relic to 46 kpc."212 A spectral index profile is computed using the profiles at the two different frequencies., A spectral index profile is computed using the profiles at the two different frequencies.213 The resulting intrinsic luminosity profiles (with intrinsic referring to a planar shock wave without any projection effects) and profiles for Rig=0.75 and 1.0 Mpe. with opening angles V=22.30.40° are shown in Figs.," The resulting intrinsic luminosity profiles (with intrinsic referring to a planar shock wave without any projection effects) and profiles for $R_{\mathrm{projected}}=0.75$ and 1.0 Mpc, with opening angles $\Psi=22,30,40\degr$ are shown in Figs."214 17. and 18.., \ref{fig:profileMH750} and \ref{fig:profileMH1000}.215 For Ry=0.75 Mpe. we find that the profile with an opening angle between 30 and 22°(~ 26°) provides the best match to the observed profile.," For $R_{\mathrm{projected}}=0.75$ Mpc, we find that the profile with an opening angle between 30 and $\sim 26\degr$ ) provides the best match to the observed profile."216 For 1.0 Mpe. we find the best match for V/222°.," For $R_{\mathrm{projected}}=1.0$ Mpc, we find the best match for $\Psi=22\degr$."217 Our computed lumiosity profiles do no provide a very good match to the observed profile at distances of more than 0.85 Mpe from the cluster center., Our computed luminosity profiles do no provide a very good match to the observed profile at distances of more than 0.85 Mpc from the cluster center.218 The observed profile is more symmetric. while the computed profiles are rather asymmetric with a strong luminosity decrease at large radii.," The observed profile is more symmetric, while the computed profiles are rather asymmetric with a strong luminosity decrease at large radii."219 Thismay be caused by the factthatthe actual 3D shape of the shock front differs somewhat from a sphere., Thismay be caused by the factthatthe actual 3D shape of the shock front differs somewhat from a sphere.220 Also. we assumed a uniform surface brightness over the front of the shock surface (which forms part ofa segment of a sphere).," Also, we assumed a uniform surface brightness over the front of the shock surface (which forms part ofa segment of a sphere)."221 At the edges of, At the edges of222and determine the boundaries between cdillerent ionization states of various species.,and determine the boundaries between different ionization states of various species.223 We do so for hydrogen and helium for an adiabatie Population HE model in Fig., We do so for hydrogen and helium for an adiabatic Population II model in Fig.224 5 and for carbon in Fig. 6.., \ref{fig:adihionbnd} and for carbon in Fig. \ref{fig:adicionbnd}.225 We plot boundaries for he same species for an isothermal Population LL model in Figs., We plot boundaries for the same species for an isothermal Population II model in Figs.226 7 and s., \ref{fig:isohionbnd} and \ref{fig:isocionbnd}.227 1n both cases we use AZ=107ke. 74=18)00W and ay=Qm.," In both cases we use $M=10^{18}~{\rm kg}$, $T_{0}=18~000~{\rm K}$ and $a_{0}=10^{8}~{\rm m}$."228 Ata given time. the various icnic species formi onion lavers of increasing ionization on moving outwards [rom the fireball centre.," At a given time, the various ionic species form onion layers of increasing ionization on moving outwards from the fireball centre."229 The dillerent empoerature. evolutions significantly. alter the ionization ονolution., The different temperature evolutions significantly alter the ionization evolution.230 The adiabatic temperature evolution. causes. the| jonization states to alter rapidly throughout the strucures when the fireball passes the appropriate critical tempevatures., The adiabatic temperature evolution causes the ionization states to alter rapidly throughout the structures when the fireball passes the appropriate critical temperatures.231 Phe isothermal evolutions show the gentler depencance οἱ jonization on density., The isothermal evolutions show the gentler dependance of ionization on density.232 The spatial structure remains roughly constant and only evolves slowly as the density. drops., The spatial structure remains roughly constant and only evolves slowly as the density drops.233In order to predict whether a detectable signal (above the three sigma error given by the Monte Carlo culling deseribed above) is to be expected. we have performed the same MST-based spatial analysis on synthetic clusters of sizes and velocity dispersions appropriate for each of the regions listed in Table |.,"In order to predict whether a detectable signal (above the three sigma error given by the Monte Carlo culling described above) is to be expected, we have performed the same MST-based spatial analysis on synthetic clusters of sizes and velocity dispersions appropriate for each of the regions listed in Table 1."234" We populate each cluster assuming that star formation is continuous during the evolutionary timescale of the low-mass YSO discs and stars are ""born! in a three-dimensional fractal distribution.", We populate each cluster assuming that star formation is continuous during the evolutionary timescale of the low-mass YSO discs and stars are `born' in a three-dimensional fractal distribution.235 The simulations presented here used a 3D fractal dimension of 1.7., The simulations presented here used a 3D fractal dimension of 1.7.236 Cartwright Whitworth (2004) estimated fractal dimensions in the range 1.7 (e.g. Taurus) to 2.3 (e.g. Chamaleon)., Cartwright Whitworth (2004) estimated fractal dimensions in the range 1.7 (e.g. Taurus) to 2.3 (e.g. Chamaleon).237 As a comparison the fractal dimension of the Interstellar medium is thought to be 2.3 (Elmegreen Falgarone 1996)., As a comparison the fractal dimension of the Interstellar medium is thought to be 2.3 (Elmegreen Falgarone 1996).238 In general the fractal dimension in young clusters is expected to start off low (clumpy) and increase with age (e.g. Bastian et al 2009. 2011).," In general the fractal dimension in young clusters is expected to start off low (clumpy) and increase with age (e.g. Bastian et al 2009, 2011)."239 We thus use a low fractal dimension to assign the birthplaces of the YSOs., We thus use a low fractal dimension to assign the birthplaces of the YSOs.240" A higher fractal dimension would of course weaken the expected signal. so we have also investigated models with higher (2.3) fractal dimensions and found that this only affects the results Ad, by at most."," A higher fractal dimension would of course weaken the expected signal, so we have also investigated models with higher (2.3) fractal dimensions and found that this only affects the results $\Delta241d_{av}$ by at most."242" Ad, is"," $\Delta243d_{av}$ is"244crossing. defined bv g(z4)=0) zc254044(2/3)ση-- ,"crossing, defined by $\ybar(\zbar_1) = 0$ ): $\zbar_1 \simeq 2 \gamma_0 \theta_0 + (2/3)\, \gamma_0\beta_{\rm rec} \theta_0^2$."245"This allows us to estimate the changes in the orbit parameters. > ancl 0. from one midplane crossing to the next: 04ο—5oPuZp072ssos7 0. and 9|B4|—[0(2,)|&,c(4/3)344,07«0."," This allows us to estimate the changes in the orbit parameters, $\gamma$ and $|\theta_0|$, from one midplane crossing to the next: $\delta \gamma = \gamma(\zbar_1) - \gamma_0 = \beta_{\rm rec}\,\zbar_1 \simeq 2 \beta_{\rm rec}\, \gamma_0 \theta_0 > 0$ , and $\delta |\theta_0| = |\theta(\zbar_1)| - \theta_0 \simeq -\, (4/3) \, \beta_{\rm rec} \, \theta_0^2 < 0 $."246" Thus. as > increases. |U,|decreases. i.e. the trajectory becomes increasingly aligned with the accelerating electric field."," Thus, as $\gamma$ increases, $|\theta_0|$, i.e., the trajectory becomes increasingly aligned with the accelerating electric field."247 The secular evolution of 5 and 100) over many current-sheet crossing cycles (2>>τι) follows from «θα-0|@y|/o52—(2/3)ή. integrating which we get [Mfe4DERο~zyen7," The secular evolution of $\gamma$ and $|\theta_0|$ over many current-sheet crossing cycles $z\gg z_1$ ) follows from $d|\theta_0|/d\gamma \simeq \delta |\theta_0|/\delta\gamma \simeq -(2/3)\, |\theta_0| /\gamma $, integrating which we get $|\theta_0| \sim \gamma^{-2/3} \sim \zbar^{-2/3}$."248" Similarly. we find. =,eoSETS and guscosP7cofD"," Similarly, we find $\zbar_1\sim \gamma^{1/3} \sim \zbar^{1/3}$ and $\ymax \sim \gamma^{-1/3} \sim \zbar^{-1/3}$."249 Thus. the hiehest-energy particles are focused into a narrow beam confined closer and closer to the midplane! (," Thus, the highest-energy particles are focused into a narrow beam confined closer and closer to the midplane! ("250This shrinkage of the trajectory can be interpreted as a result of the ExB drift of the particle's virtual guiding center away from (he midplane. separately in each hall-cycle segment.,"This shrinkage of the trajectory can be interpreted as a result of the ${\bf E\times B}$ drift of the particle's virtual guiding center away from the midplane, separately in each half-cycle segment."251 It can also be interpreted as a result of the conservation of the adiabatic invariant const.)," It can also be interpreted as a result of the conservation of the adiabatic invariant $J_y = \int p_y dy \sim \gamma m_e c\, \theta_0 \,\ymax \propto \gamma^2 \, \theta_0^3={\rm const}$ .)"252s Two factors limit the particle energy., Two factors limit the particle energy.253" First. the finite current-sheet length. /=10/9/44 em. limits the energy to — HCE — e El =F Bol. corresponding to 54,4;= 6xLO?dyeBo.fig and (aao. ecROUO "," First, the finite current-sheet length, $l=10^{16 }l_{16}$ cm, limits the energy to = m_e c^2 = e E_0 l = e l, corresponding to $\gamma_{\rm max} = $ $6 \times 10^9 \, \beta_{\rm rec} \, B_{0,-3} \, l_{16}$ and = (3/2) _c = (3/2) _c ."254Second. radiation reaction may cause the energy (o saturate ala lower value.," Second, radiation reaction may cause the energy to saturate ata lower value."255" If the initial injection values Uinaxnj and inj satisly Yinas.inj/ὸ>(suls//sing)?4 (where 54,4is defined in"," If the initial injection values $y_{\rm max, inj}$ and $\gamma_{\rm inj}$ satisfy $y_{\rm max,inj}/\delta > (\gamma_{\rm rad,*}/\gamma_{\rm inj})^{1/3}$ (where $\gamma_{\rm rad,*}$is defined in"256Our reference model matches the observed abundance of CO (Fig. 12)).,Our reference model matches the observed abundance of $\rm CO$ (Fig. \ref{rad_dens_coup_CO}) ).257" Table 1 shows that CO excitation is also well predicted by the model, although it was not used as a constraint."," Table \ref{tab:XmodXobs} shows that $\rm CO$ excitation is also well predicted by the model, although it was not used as a constraint."258 The rise in the N(CO)/N(H2) ratio at low density and low radiation field is a chemical effect., The rise in the $N({\rm CO})/N({\rm H}_{2})$ ratio at low density and low radiation field is a chemical effect.259 The formation of CO is illustrated in Fig. 13.., The formation of ${\rm CO}$ is illustrated in Fig. \ref{COevolution}.260 The efficiency of CO formation depends on the ionization fraction., The efficiency of $\rm CO$ formation depends on the ionization fraction.261" Photoionisation is proportional to the gas density ng, while recombination proceeds at a rate that is proportional to the square of that quantity."," Photoionisation is proportional to the gas density $n_{\rm H}$, while recombination proceeds at a rate that is proportional to the square of that quantity."262 The degree of ionization therefore increases when the density decreases in a given radiation field., The degree of ionization therefore increases when the density decreases in a given radiation field.263 Enhancing the ionization enhances OT formation via charge exchange with H* and favors the formation of OH and H2O., Enhancing the ionization enhances ${\rm{{O}}}^{+}$ formation via charge exchange with ${\rm H}^{+}$ and favors the formation of $\rm OH$ and $\rm H_2O$.264 Both molecules interact with Ct and lead either directly or indirectly to the formation of CO., Both molecules interact with ${\rm C}^+$ and lead either directly or indirectly to the formation of $\rm CO$.265 The reaction involving OH is dominant., The reaction involving OH is dominant.266 Photodestruction of CO is limited by the weakness of the radiation field., Photodestruction of $\rm CO$ is limited by the weakness of the radiation field.267 We are cautious about the model interpretation of the CO abundance., We are cautious about the model interpretation of the CO abundance.268" It is noticeable that the CO column densities in the J—1 and 2 levels, derived from UV spectra, are significantly smaller by factors 3 and 7, respectively, than the values derived from the emission radio spectra (Nehméetal,2008)."," It is noticeable that the CO column densities in the J=1 and 2 levels, derived from UV spectra, are significantly smaller by factors 3 and 7, respectively, than the values derived from the emission radio spectra \citep{NCI}."269". These differences indicate that the abundance of CO is inhomogeneous, which could be accounted for within the PDR model, by introducing clumps with higher density than the mean value."," These differences indicate that the abundance of $\rm CO$ is inhomogeneous, which could be accounted for within the PDR model, by introducing clumps with higher density than the mean value."270" However, the large CH* abundance favors an alternative explanation, where a small-scale increase in the CO abundance, traces the localized contribution of out-of-equilibrium chemistry to its formation."," However, the large $^+$ abundance favors an alternative explanation, where a small-scale increase in the CO abundance, traces the localized contribution of out-of-equilibrium chemistry to its formation."271 LisztandLucas(2000) have gathered results from UV and radio absorption measurements of CO along diffuse interstellar medium lines of sight., \cite{Liszt00} have gathered results from UV and radio absorption measurements of CO along diffuse interstellar medium lines of sight.272" They relate the CO abundance to that of HCO* measurements, concluding that CO formation through dissociative recombination of HCOT suffice to account for the CO abundance in diffuse molecular clouds."," They relate the CO abundance to that of $^+$ measurements, concluding that CO formation through dissociative recombination of $^+$ suffice to account for the CO abundance in diffuse molecular clouds."273" Falgaroneetal.(2006) show that the observed abundance of HCO* (~2x1079) cannot be accounted by standard PDR chemistry and must be related, like CH*, to warm out-of-equilibrium chemistry."," \cite{Falga06} show that the observed abundance of $^+$ $\sim 2 \times 10^{-9}$ ) cannot be accounted by standard PDR chemistry and must be related, like $^+$, to warm out-of-equilibrium chemistry."274 A significant fraction of CO observed in diffuse molecular clouds may thus be a product of out-of-equilibrium chemistry., A significant fraction of CO observed in diffuse molecular clouds may thus be a product of out-of-equilibrium chemistry.275 This interpretation links CO abundance inhomogeneities to the CH* chemistry but it is not specifically the CH? rich gas that has an enhanced CO abundance., This interpretation links CO abundance inhomogeneities to the $^+$ chemistry but it is not specifically the $^+$ rich gas that has an enhanced CO abundance.276" It is not ruled out by the observed velocity difference between CHt and CO (Nehméetal.,2008).", It is not ruled out by the observed velocity difference between $^+$ and CO \citep{NCI}.277". CO, unlike CH*, is observed to be concentrated in the intermediate velocity component C. This component may correspond to shielded sections of the cloud where the CO photo-dissociation rate is reduced."," CO, unlike $^+$, is observed to be concentrated in the intermediate velocity component C. This component may correspond to shielded sections of the cloud where the CO photo-dissociation rate is reduced."278" In Nehmé (2008),, we propose that the line of sight to HD 102065 samples material ablated from the Dcld 300.2-16.9 cloud by a cloud-supernova shock interaction."," In \cite{NCI}, we propose that the line of sight to HD 102065 samples material ablated from the Dcld 300.2-16.9 cloud by a cloud-supernova shock interaction."279" In this scenario, the matter flowing out of the cloud is expected to be very turbulent (Nakamuraetal."," In this scenario, the matter flowing out of the cloud is expected to be very turbulent \citep{Nakamura06}."280",2006).. In Fig. 14,"," In Fig. \ref{Fig:ch_ch},"281 we show that the CH abundance (N(CH)/N(H2)) computed by the model depends linearly on the ratio ng/G., we show that the CH abundance ${\rm{{N(CH)}}}/{\rm{{N(H_2)}}}$ ) computed by the model depends linearly on the ratio $n_{\rm H}/G$.282 The value for our reference model is a factor of two lower than observations., The value for our reference model is a factor of two lower than observations.283" This mismatch between model and observations, might be an additional manifestation of the out-of-equilibrium chemistry, as already proposed by e.g. Zsargó&Federman(2003) and Ritcheyetal.(2006)."," This mismatch between model and observations, might be an additional manifestation of the out-of-equilibrium chemistry, as already proposed by e.g. \cite{Zsargo} and \cite{Ritchey06}."284. The “excess” of CH abundance may be the product of CHT recombination with H5., The “excess” of $\rm CH$ abundance may be the product of $\rm CH^+$ recombination with $_2$.285" Finally, we note that the model is consistent with the upper limits on CN and C» abundances (Table 1))."," Finally, we note that the model is consistent with the upper limits on CN and $_2$ abundances (Table \ref{tab:XmodXobs}) )."286 The Ἡο excitation diagram (Fig. 9)), The $\rm H_2$ excitation diagram (Fig. \ref{Excdiag}) )287 shows that the observed column densities at J 2 lie far above the single temperature fit to the low J column densities., shows that the observed column densities at $J>$ 2 lie far above the single temperature fit to the low $J$ column densities.288" This is commonly observed, towards many stars by"," This is commonly observed, towards many stars by"289Very. laree surveys are plaving an increasingly important role in the progress of observational astronomy. with all-skv photometric ancl spectroscopic datasets. particularly prominent.,"Very large surveys are playing an increasingly important role in the progress of observational astronomy, with all-sky photometric and spectroscopic data–sets particularly prominent."290 The most advanced surveys in the latter category are the 2db Galaxy Redshift Survey (20bCRS: Colless 22001) and the Sloan Digital Sky Survey (SDSS: York 22000). both of which already include well over 107 spectra.," The most advanced surveys in the latter category are the 2dF Galaxy Redshift Survey (2dFGRS; Colless 2001) and the Sloan Digital Sky Survey (SDSS; York 2000), both of which already include well over $10^5$ spectra."291 A feature of many of the most ambitious surveys is the incorporation of the rapid release of survey data to the astronomical community. together with user-friendly tools and interfaces that allow exploitation of this resource.," A feature of many of the most ambitious surveys is the incorporation of the rapid release of survey data to the astronomical community, together with user-friendly tools and interfaces that allow exploitation of this resource."292 Indeed the 2d4EGRS's release of 101 is the largest catalogue of galaxy spectra available., Indeed the 2dFGRS's release of $10^5$ is the largest catalogue of galaxy spectra available.293 The 2dECGIUS 100k Data Release has already. formed the basis for investigations key to the primary goals of the survey. including constraints on the luminosity function of local galaxies (Sadler 22001: Magliocchetti 109: Alaclewick 102) and their correlation properties (Peacock 22001: Pereival 102: Norberg VOL). as well as studies of the local cluster population (cle Propris 22001).," The 2dFGRS 100k Data Release has already formed the basis for investigations key to the primary goals of the survey, including constraints on the luminosity function of local galaxies (Sadler 2001; Magliocchetti 2002; Madgwick 2002) and their correlation properties (Peacock 2001; Percival 2002; Norberg 2001), as well as studies of the local cluster population (de Propris 2001)."294 Comparable results have also been obtained. from the SDSS (e.g. Blanton, Comparable results have also been obtained from the SDSS (e.g. Blanton295Stone. 2009).,"Stone, 2009)."296 Sehekochibin ancl co-workers (ο. Schekochihin et al..," Schekochihin and co-workers (e.g. Schekochihin et al.,"297 2004. 2005) have also argued that. the structure of a magnetic field in a turbulent Low at such high Itevnolds numbers can depend critically on the Prandtl number. and that this has implications for dvnamos under such conditions.," 2004, 2005) have also argued that the structure of a magnetic field in a turbulent flow at such high Reynolds numbers can depend critically on the Prandtl number, and that this has implications for dynamos under such conditions."298 Ln addition. Lleitsch et al. (," In addition, Heitsch et al. ("2992008) and Zweibel Leitsch (2008) have discussed the implications for magnetic growth and structure in turbulent media where ambipolar diffusion plavs a significant role.,2008) and Zweibel Heitsch (2008) have discussed the implications for magnetic growth and structure in turbulent media where ambipolar diffusion plays a significant role.300 In the light of the above. we speculate how an aceretion disc dvnamo might produce the intermittent highenergy events which appear to be demanded. by ehondrule formation.," In the light of the above, we speculate how an accretion disc dynamo might produce the intermittent high–energy events which appear to be demanded by chondrule formation."301 As an example we consider a new model for à dvnamo in a turbulent medium suggested by. Daggaley et al. (, As an example we consider a new model for a dynamo in a turbulent medium suggested by Baggaley et al. (3022009a.b).,"2009a,b)."303 The extent to which such a model is applicable to cooler accretion disces. such as the solar nebula. is. somewhat uncertain. and we introduce it here because it is able to illustrate the kind of properties with regard to energy release that we are looking for to facilitate hondrule formation.," The extent to which such a model is applicable to cooler accretion discs, such as the solar nebula, is somewhat uncertain, and we introduce it here because it is able to illustrate the kind of properties with regard to energy release that we are looking for to facilitate chondrule formation."304 In this model the magnetic field is mainly confined to thin Lux ropes which are advected by the How., In this model the magnetic field is mainly confined to thin flux ropes which are advected by the flow.305 Magnetic dissipation only occurs via reconnections of the [lux ropes. and. so the magnetic dissipation is highlv localised.," Magnetic dissipation only occurs via reconnections of the flux ropes, and so the magnetic dissipation is highly localised."306 This model can be viewed as an implementation of the limiting regime of infinitely large. magnetic Revnolds number: magnetic dissipation can be safely. neglected at all scales. but plavs à crucial role through reconnection of field lines in permitting rearrangement of the field topology.," This model can be viewed as an implementation of the limiting regime of infinitely large magnetic Reynolds number: magnetic dissipation can be safely neglected at all scales, but plays a crucial role through reconnection of field lines in permitting rearrangement of the field topology."307 Such rearrangements of the field topology result. in conversion of magnetic energy into kinetic energy of the Duid. and thence to dissipation as heat.," Such rearrangements of the field topology result in conversion of magnetic energy into kinetic energy of the fluid, and thence to dissipation as heat."308 This contrasts to the usual models in which magnetic cilfusivity converts magnetic energy to heat directly., This contrasts to the usual models in which magnetic diffusivity converts magnetic energy to heat directly.309 With this in mind. the picture we propose is that the magnetic field. in. the disc can be thought of as a collection of loops of Lux ropes.," With this in mind, the picture we propose is that the magnetic field in the disc can be thought of as a collection of loops of flux ropes."310 These loops are continually stretehed by the azimuthal shear low., These loops are continually stretched by the azimuthal shear flow.311 The stretching increases the magnetic cnerey associated: with the loop and at constant total (gas plus magnetic) pressure decreases the mass density along the Ποιά line. ancl so increases the Alfvénn speed along the loop.," The stretching increases the magnetic energy associated with the loop and at constant total (gas plus magnetic) pressure decreases the mass density along the field line, and so increases the Alfvénn speed along the loop."312 To maintain an equilibritun distribution of loop properties. the loops must also continually undergo reconnection events.," To maintain an equilibrium distribution of loop properties, the loops must also continually undergo reconnection events."313 The crucial property of these events is that while cach reconnection event in itself releases a negligible amount of energy. it does release the magnetic field. which is then able to reconfigure itself (at the Alfvénn speed) and. in so doing. heat the eas.," The crucial property of these events is that while each reconnection event in itself releases a negligible amount of energy, it does release the magnetic field, which is then able to reconfigure itself (at the Alfvénn speed) and in so doing, heat the gas."314 The picture here thus cdillers fundamentally from that oesented by Sonett (1979) ane Levy Araki (1989)., The picture here thus differs fundamentally from that presented by Sonett (1979) and Levy Araki (1989).315 They considered. magnetic reconnection in low density regions zw from the disc plane (in the disc corona) and took only the magnetic energy. dissipated by the reconnection events into account., They considered magnetic reconnection in low density regions far from the disc plane (in the disc corona) and took only the magnetic energy dissipated by the reconnection events into account.316 We are assuming here that most. of he accretion cnerey is released in the bulk of the disc., We are assuming here that most of the accretion energy is released in the bulk of the disc.317 We should note. however. that some authors have suggested hat a substantial fraction of the accretion energy might »e released. in such low clensity regions (lout Pringle. 1990: Uzdensky Goodman. 2008). arguing that magnetic »uovancy can advect energy. clliciently away from the disc lane.," We should note, however, that some authors have suggested that a substantial fraction of the accretion energy might be released in such low density regions (Tout Pringle, 1990; Uzdensky Goodman, 2008), arguing that magnetic buoyancy can advect energy efficiently away from the disc plane."318 For our picture to work. however. we require that a significant amount of reconnection occurs close to the disc plane. so that the bulk of the energy release occurs there and disc gas. along with the ehondrule. can be cllicienthy shock heated.," For our picture to work, however, we require that a significant amount of reconnection occurs close to the disc plane, so that the bulk of the energy release occurs there and disc gas, along with the chondrule, can be efficiently shock heated."319 What we therefore. require for. choncrule formation is that. reconnection events occur in regions with sullicientlv high Alfvénn speeds. that shock velocities. of Ἐνom6c. can be generated., What we therefore require for chondrule formation is that reconnection events occur in regions with sufficiently high Alfvénn speeds that shock velocities of $V_s \approx 6 c_s$ can be generated.320" For this to occur we require that a minority of Dux tubes have field strengths of order D, and loop mass densities around 40 times lower than the mean clisc density before reconnection occurs.", For this to occur we require that a minority of flux tubes have field strengths of order $B_{\rm eq}$ and loop mass densities around 40 times lower than the mean disc density before reconnection occurs.321 Unfortunately the E[iuctuation dynamo’ model of Daggaley et al (2009a. b) is currently computed. only in an incompressible medium.," Unfortunately the `fluctuation dynamo' model of Baggaley et al (2009a, b) is currently computed only in an incompressible medium."322 Further consideration of the model will be required. before it is possible to establish whether or not such highenergy reconnection events are likely in an accretion disc., Further consideration of the model will be required before it is possible to establish whether or not such high–energy reconnection events are likely in an accretion disc.323 In this picture we suppose that from time to time a reconnection event occurs which causes a sullicicntly large ancl rapicl adjustment of field topology that a region of disc gas of size fis subject to shock heating. with velocity Vy7 km s+.," In this picture we suppose that from time to time a reconnection event occurs which causes a sufficiently large and rapid adjustment of field topology that a region of disc gas of size $h$ is subject to shock heating, with velocity $V_s \approx 7$ km $^{-1}$."324 We need this heated region to stay sullicientlv hot for a time foonp&107 s. We can use this information to deduce requirements for the properties of the magnetic loops.," We need this heated region to stay sufficiently hot for a time $t_{\rm cool}325\approx 10^5$ s. We can use this information to deduce requirements for the properties of the magnetic loops."326 We expect the cooling timescale 7 for a region of size / and temperature 7 to be given by We expect that the heat content is simply where p is the gas density., We expect the cooling timescale $\tau$ for a region of size $h$ and temperature $T$ to be given by We expect that the heat content is simply where $\rho$ is the gas density.327 HE the region is optically thick. so that heat [oss is mainly by radiative transfer. then we expect where & is the opacity.," If the region is optically thick, so that heat loss is mainly by radiative transfer, then we expect where $\kappa$ is the opacity."328 Thus we expect For an aceretion disc in thermal equilibrium. the relevant lengthscale is the disc thickness Jf. and the cooling timescale is the thermal timescale η. given by (Pringle 1981) Using this we can obtain a very rough estimate of the size required. for the shockheated. regions.," Thus we expect For an accretion disc in thermal equilibrium, the relevant lengthscale is the disc thickness $H$, and the cooling timescale is the thermal timescale $t_{\rm th}$, given by (Pringle 1981) Using this we can obtain a very rough estimate of the size required for the shock–heated regions."329 To keep things simple we assume that the opacity &z const. (, To keep things simple we assume that the opacity $\kappa \approx$ const. (330e.g. Bell et al..,"e.g. Bell et al.,"331 1997). although if some chondritie material is vaporised and/or I» is signilicantlv cissociatecl. this might not be the case.," 1997), although if some chondritic material is vaporised and/or $_2$ is significantly dissociated, this might not be the case."332 Then from the computations of Deschl Connolly, Then from the computations of Deschl Connolly333Figure 2 shows the axial ratios of the halo isopoteutial contours nieasureddisk. foy various experiments.,"Figure \ref{fig2} shows the axial ratios of the halo isopotential contours measured, for various experiments."334 The growth of the disk modifies the halo shape. making if more axisvnuuetrie.," The growth of the disk modifies the halo shape, making it more axisymmetric."335 Halo A is nearly prolate so placing the disk plane perpendicular to the major axis has little effect ou the shape of the 2D potential on the disk plane., Halo A is nearly prolate so placing the disk plane perpendicular to the major axis has little effect on the shape of the 2D potential on the disk plane.336 When the disk plane contains the major axis the poteutial is strongly non-axisviunietric. but becomes rounder after the disk is added.," When the disk plane contains the major axis the potential is strongly non-axisymmetric, but becomes rounder after the disk is added."337 The effect. however. is minor for the case of the LSB aud ISB disk: ouly the ISB ealaxy is able to moclity substantially the halo shape. increasing the immer axial ratio from 0.6 to ~0.8.," The effect, however, is minor for the case of the LSB and ISB disk; only the HSB galaxy is able to modify substantially the halo shape, increasing the inner axial ratio from $\sim 0.6$ to $\sim 0.8$."338 Before adding the disk. halo D is rather triaxial. with biaονefb~OS in the iuner regions.," Before adding the disk, halo B is rather triaxial, with $b/a \sim c/b339\sim 0.8$ in the inner regions."340 In the case of the IISD disk. placing the disk plaue perpendicular to the halo minor axis renders the halo poteutial almost pertectly axisvnuuetric Gueasured in the plane of the disk).," In the case of the HSB disk, placing the disk plane perpendicular to the halo minor axis renders the halo potential almost perfectly axisymmetric (measured in the plane of the disk)."341 Ou the other laud. the LSB and the ISB galaxies are again barely able to modifv the shape of the halo.," On the other hand, the LSB and the ISB galaxies are again barely able to modify the shape of the halo."342 When the disk plane is perpendicular to the halo major axis the results are simular. although iu this case the halo response to the ISB aud ISB ealaxies are comparable.," When the disk plane is perpendicular to the halo major axis the results are similar, although in this case the halo response to the ISB and HSB galaxies are comparable."343 Except very ucar the center. the potential remains far from axisviuuctric iu all cases;," Except very near the center, the potential remains far from axisymmetric in all cases."344 We note that the chanec in shape iu the case of the USB disk is noticeable out to ~ 30-50 kpe. well outside the region where the disk is eravitationally important.," We note that the change in shape in the case of the HSB disk is noticeable out to $\sim 30$ $50$ kpc, well outside the region where the disk is gravitationally important."345 Figure 3. shows how the 3D halo shape changes iu response to the disk growth., Figure \ref{fig3} shows how the 3D halo shape changes in response to the disk growth.346 The axial ratios of the immer eravitational potential are preseuted as a function of the peak coutribution of the disk to the circular velocity., The axial ratios of the inner gravitational potential are presented as a function of the peak contribution of the disk to the circular velocity.347" This is measured by the paramcter 4ViVere. computed at r=2.2R,. the radius where the exponcutial disk contribution to the circular velocity is maximal."," This is measured by the parameter $\eta = V_d /348V_{\rm circ}$, computed at $r=2.2 R_d$, the radius where the exponential disk contribution to the circular velocity is maximal."349 The shape of the potential is not exactly coustaut iu the ΠΙΟ: reelons (see Fig. 21).," The shape of the potential is not exactly constant in the inner regions (see Fig. \ref{fig2}) ),"350 aud therefore we show the shape of the potential averaged inside 30 kpc., and therefore we show the shape of the potential averaged inside $30$ kpc.351 The trends we discuss are robust to reasonable chanecs in the averaeiug procedure., The trends we discuss are robust to reasonable changes in the averaging procedure.352 Results are preseuted for the “adiabatic” (7;=10 Cx) disk growth aud for both oricutatious of the disk plane relative to the halo principal axis., Results are presented for the “adiabatic” $\tau_d=10$ Gyr) disk growth and for both orientations of the disk plane relative to the halo principal axis.353 jj varies from ~0.25 for the LSB ealaxy to 0.7 for the TSB model., $\eta$ varies from $\sim 0.25$ for the LSB galaxy to $\sim 0.7$ for the HSB model.354 Figure 3 , Figure \ref{fig3} 355"Figure 10 shows the performance of this procedure at a redshift ~0.6, for the two radio sky models used here: GSM/Model-I and Haslam+NVSS/Model-H.","Figure \ref{extlsspk} shows the performance of this procedure at a redshift $\sim 0.6$, for the two radio sky models used here: GSM/Model-I and Haslam+NVSS/Model-II."356" The 21 cm LSS power spectrum, as seen by a perfect instrument with a 25 arcmin (FWHM) gaussian frequency independent beam is shown in orange (solid line), and the extracted power spectrum, after beam and foreground separation with second order polynomial fit (P2) is shown in red (circle markers)."," The 21 cm LSS power spectrum, as seen by a perfect instrument with a 25 arcmin (FWHM) gaussian frequency independent beam is shown in orange (solid line), and the extracted power spectrum, after beam and foreground separation with second order polynomial fit (P2) is shown in red (circle markers)."357" We have also represented the obtained power spectrum without applying the beam correction (step 1 above), or with the first order polynomial fit (P1)."," We have also represented the obtained power spectrum without applying the beam correction (step 1 above), or with the first order polynomial fit (P1)."358" Figure 11 shows a comparison of the original 21 cm brightness temperature map at 884 MHz with the recovered 21 cm map, after subtraction of the radio continuum component."," Figure \ref{extlssmap} shows a comparison of the original 21 cm brightness temperature map at 884 MHz with the recovered 21 cm map, after subtraction of the radio continuum component."359" It can be seen that structures present in the original map have been correctly recovered, although the amplitude of the temperature fluctuations on the recovered map is significantly smaller (factor ~5) than in the original map."," It can be seen that structures present in the original map have been correctly recovered, although the amplitude of the temperature fluctuations on the recovered map is significantly smaller (factor $\sim 5$ ) than in the original map."360 This is mostly due to the damping of the large scale (k€0.04/Mpc!) due the poor interferometer response at large angle (0=4°)., This is mostly due to the damping of the large scale $k \lesssim 0.04 h \mathrm{Mpc^{-1}} $ ) due the poor interferometer response at large angle $\theta \gtrsim 4^\circ $ ).361" We have shown that it should be possible to measure the red shifted 21 cm emission fluctuations in the presence of the strong radio continuum signal, provided that this latter has a smooth frequency dependence."," We have shown that it should be possible to measure the red shifted 21 cm emission fluctuations in the presence of the strong radio continuum signal, provided that this latter has a smooth frequency dependence."362" However, a rather precise knowledge of the instrument beam and the beam or smearing procedure described here are key ingredient for recovering the 21 cm LSS power spectrum."," However, a rather precise knowledge of the instrument beam and the beam or smearing procedure described here are key ingredient for recovering the 21 cm LSS power spectrum."363" It is also important to note that while it is enough to correct the beam to the lowest resolution instrument beam (~30’ or D~50 meter 820 MHZ) for the GSM sky model, a stronger beam correction has to be applied ((~36’ or D~40 meter @ 820 MHz) for the Model-II to reduce significantly the ripples from bright radio sources."," It is also important to note that while it is enough to correct the beam to the lowest resolution instrument beam $\sim 30'$ or $D \sim 50$ meter  820 MHz) for the GSM sky model, a stronger beam correction has to be applied $\sim 36'$ or $D \sim 40$ meter  820 MHz) for the Model-II to reduce significantly the ripples from bright radio sources."364 We have also applied the same procedure to simulate observations and LSS signal extraction for an instrument with a frequency dependent gaussian beam shape., We have also applied the same procedure to simulate observations and LSS signal extraction for an instrument with a frequency dependent gaussian beam shape.365" The mode mixing effect is greatly reduced for such a smooth beam, compared to the more complex instrument response R(u,v,A) used for the results shown in figure 10.."," The mode mixing effect is greatly reduced for such a smooth beam, compared to the more complex instrument response ${\cal R}(u,v,\lambda)$ used for the results shown in figure \ref{extlsspk}."366" The recovered red shifted 21 cm emission power spectrum Ροή(k) suffers a number of distortions, mostly damping, compared to the original P5;(Kk) due to the instrument response and the component separation procedure."," The recovered red shifted 21 cm emission power spectrum $P_{21}^{rec}(k)$ suffers a number of distortions, mostly damping, compared to the original $P_{21}(k)$ due to the instrument response and the component separation procedure."367" We expect damping at small scales, or larges k, due to the finite instrument size, but also at large scales, small k, if total power measurements (auto-correlations) are not used in the case of interferometers."," We expect damping at small scales, or larges $k$, due to the finite instrument size, but also at large scales, small $k$, if total power measurements (auto-correlations) are not used in the case of interferometers."368 The sky reconstruction and the component separation introduce additional filtering and distortions., The sky reconstruction and the component separation introduce additional filtering and distortions.369" Ideally, one has to define a power spectrum measurement response or in the radial direction, (A or redshift, T(kj)) and in the transverse plane ( T(k,) )."," Ideally, one has to define a power spectrum measurement response or in the radial direction, $\lambda$ or redshift, $\TrF(k_\parallel)$ ) and in the transverse plane ( $\TrF(k_\perp)$ )."370 The real transverse plane transfer function might even be anisotropic., The real transverse plane transfer function might even be anisotropic.371" However, in the scope of the present study, we define an overall transfer function T(K) as the ratio of the recovered 3D power spectrum P5f(k) to the original P21(k): Figure 12 shows this overall transfer function for the simulations and component separation performed here, around z~0.6, for the instrumental setup (a), a filled array of 121 Dai;=5 m dishes."," However, in the scope of the present study, we define an overall transfer function $\TrF(k)$ as the ratio of the recovered 3D power spectrum $P_{21}^{rec}(k)$ to the original $P_{21}(k)$: Figure \ref{extlssratio} shows this overall transfer function for the simulations and component separation performed here, around $z \sim 0.6$, for the instrumental setup (a), a filled array of 121 $D_{dish}=5$ m dishes."372" The orange/yellow curve shows the ratio pymoothed(k)/P21(k) of the computed to the original power spectrum, if the original LSS temperature cube is smoothed"," The orange/yellow curve shows the ratio $P_{21}^{smoothed}(k)/P_{21}(k)$ of the computed to the original power spectrum, if the original LSS temperature cube is smoothed"373"The small-scale structure of the fforest, as measured by the curvature or any other method, will depend on the thermal broadening of the absorption features as well as on the Hubble broadening and any turbulent broadening.","The small-scale structure of the forest, as measured by the curvature or any other method, will depend on the thermal broadening of the absorption features as well as on the Hubble broadening and any turbulent broadening."374" Heating the gas will increase not only the thermal broadening but also the characteristic physical size of absorbers, an effect known as Jeans smoothing."," Heating the gas will increase not only the thermal broadening but also the characteristic physical size of absorbers, an effect known as Jeans smoothing."375 The result is an additional smoothing of the fforest due to greater Hubble broadening across individual absorbers., The result is an additional smoothing of the forest due to greater Hubble broadening across individual absorbers.376" In principle, therefore, the small-scale structure of the fforest will depend both on the instantaneous temperature of the gas and on its integrated thermal history (e.g.,?).."," In principle, therefore, the small-scale structure of the forest will depend both on the instantaneous temperature of the gas and on its integrated thermal history \citep[e.g.,][]{pawlik2009}."377" In order to test the sensitivity of our method to the thermal history of the IGM, we applied our analysis to a set of spectra drawn from simulations whose thermal histories included simple scenarios for hydrogen and helium reionization."," In order to test the sensitivity of our method to the thermal history of the IGM, we applied our analysis to a set of spectra drawn from simulations whose thermal histories included simple scenarios for hydrogen and helium reionization."378" The test runs, T15slow and T15fast, include heating meant to mimic rreionization at z=9, and either an extended rreionization spanning 3«z<5 (T15slow) or a rapid rreionization over 3«z3.5 (T15fast)."," The test runs, T15slow and T15fast, include heating meant to mimic reionization at $z = 9$, and either an extended reionization spanning $3 < z < 5$ (T15slow) or a rapid reionization over $3 < z < 3.5$ (T15fast)."379" Current estimates of the ionizing emissivity from QSOs suggest that rreionization should be a patchy and extended process, producing a gradual evolution in the volume-averaged temperature (e.g.,??).."," Current estimates of the ionizing emissivity from QSOs suggest that reionization should be a patchy and extended process, producing a gradual evolution in the volume-averaged temperature \citep[e.g.,][]{boltonohfur2009a,mcquinn2009a}."380" Nevertheless, we include the T15fast model in order to demonstrate that our method is sensitive to rapid changes in temperature, despite the fact that the temperatures of the comparison models evolve slowly."," Nevertheless, we include the T15fast model in order to demonstrate that our method is sensitive to rapid changes in temperature, despite the fact that the temperatures of the comparison models evolve slowly."381" For the sake of simplicity, the slope of the temperature-density relation is held to the fiducial value (~1.5) in these runs."," For the sake of simplicity, the slope of the temperature-density relation is held to the fiducial value $\gamma \sim 1.5$ ) in these runs."382 The temperature histories of the test runs are compared to runs A15-E15 in Figure 8.., The temperature histories of the test runs are compared to runs A15-E15 in Figure \ref{fig:histories}.383" Artificial data were generated using similar redshifts, noise levels, instrumental resolutions, and sample sizes as the real data."," Artificial data were generated using similar redshifts, noise levels, instrumental resolutions, and sample sizes as the real data."384" The curvature was then measured using the same procedure described in Section ??,, with the exception that no metal masking was performed."," The curvature was then measured using the same procedure described in Section \ref{sec:method}, with the exception that no metal masking was performed."385 'The temperatures recovered from the test simulations are plotted in Figure 9.., The temperatures recovered from the test simulations are plotted in Figure \ref{fig:test_run}.386" The top panels shows the temperature at the optimal overdensity,T(A),, with the value of A at each redshift printed along the bottom of each plot."," The top panels shows the temperature at the optimal overdensity, with the value of $\bar{\Delta}$ at each redshift printed along the bottom of each plot."387" The bottom panels showsTo,, which we have computed using the values of mmeasured in the simulations."," The bottom panels shows, which we have computed using the values of measured in the simulations."388" In all panels the recovered temperatures are plotted using filled symbols, while the actual temperature measured directly from the simulations is shown with a solid line."," In all panels the recovered temperatures are plotted using filled symbols, while the actual temperature measured directly from the simulations is shown with a solid line."389 We also show the values of tthat would be recovered from noise-free spectra., We also show the values of that would be recovered from noise-free spectra.390" The results at HIRES (6.7 !)) and MIKE (13.6 s~')) resolution are plotted using dashed and dotted lines, respectively, where the smoothing has been applied to both the test simulations and the comparison runs."," The results at HIRES (6.7 ) and MIKE (13.6 ) resolution are plotted using dashed and dotted lines, respectively, where the smoothing has been applied to both the test simulations and the comparison runs."391" In general, the curvature method recovers the true values very well."," In general, the curvature method recovers the true values very well."392" Notably, a gradual increase in ffrom z~5 to 3 is correctly recovered for T15slow, while a sudden jump in aat z~3.5 is recovered for T15fast."," Notably, a gradual increase in from $z \simeq 5$ to 3 is correctly recovered for T15slow, while a sudden jump in at $ z \sim 3.5$ is recovered for T15fast."393" In both cases, however, the measured temperatures show some deviation from the true values."," In both cases, however, the measured temperatures show some deviation from the true values."394" At z~5, iis overestimated by 2 KK, while at z~3, iis underestimated by ~30000KK for both T15slow and T15fast."," At $z \sim 5$, is overestimated by $\sim$ K, while at $z \sim 3$, is underestimated by $\sim$ K for both T15slow and T15fast."395" The corresponding net rise in iis underestimated by ~40000 KK. The errors in the recovered temperatures can be understood in terms of the differences in thermal history between the test runs and runs A15-G15, which were used to calibrate the conversion from ttoT"," The corresponding net rise in is underestimated by $\sim$ K. The errors in the recovered temperatures can be understood in terms of the differences in thermal history between the test runs and runs A15-G15, which were used to calibrate the conversion from to."396"(A).. At z~5, the T15 runs (which are identical at z> 5) and run B15 have similar values ofTo."," At $z \sim 5$, the T15 runs (which are identical at $z > 5$ ) and run B15 have similar values of."397". Since the T15 runs included a heat injection at z~9, however, the Jean smoothing in these runs will be substantially higher than in run B15."," Since the T15 runs included a heat injection at $z \sim 9$, however, the Jean smoothing in these runs will be substantially higher than in run B15."398" This should cause the T15 runs to have a comparatively lower overall curvature at z~5, leading to a higher estimate of the instantaneous temperature."," This should cause the T15 runs to have a comparatively lower overall curvature at $z \sim 5$, leading to a higher estimate of the instantaneous temperature."399" We note, however, that at z~5 the impact of the thermal history on the measured temperature depends partially on the properties of the data."," We note, however, that at $z \sim 5$ the impact of the thermal history on the measured temperature depends partially on the properties of the data."400" The recovered value of iin the highest-redshift bin is very near the true value (solid line) for noise-free HIRES data (dashed line), but increases at MIKE resolution (dotted line) or when noise is added (filled point, for which 90 per cent of the spectra are at HIRES resolution)."," The recovered value of in the highest-redshift bin is very near the true value (solid line) for noise-free HIRES data (dashed line), but increases at MIKE resolution (dotted line) or when noise is added (filled point, for which 90 per cent of the spectra are at HIRES resolution)."401 These effects relate to properties of the fforest that are sensitive to the amount of Jeans smoothing., These effects relate to properties of the forest that are sensitive to the amount of Jeans smoothing.402" For a given overall mean flux, a lower amount of Jeans smoothing at z~5 will tend to produce sharper and more distinct transmission peaks, which will dominate the"," For a given overall mean flux, a lower amount of Jeans smoothing at $z \sim 5$ will tend to produce sharper and more distinct transmission peaks, which will dominate the"403"by Dravinsetal.(1997b),, where Υ is the zenith angle.","by \citet{Dravins1997b}, where $\gamma$ is the zenith angle."404 The scintillation index is then independent of wavelength and proportional to the altitude of the turbulent layer squared and the strength of the turbulent layer., The scintillation index is then independent of wavelength and proportional to the altitude of the turbulent layer squared and the strength of the turbulent layer.405" We can calculate the scintillation index due to all of the turbulent layers assuming the pupil is conjugate to an altitude, zo."," We can calculate the scintillation index due to all of the turbulent layers assuming the pupil is conjugate to an altitude, $z_{0}$."406" In this case the scintillation index, 92, at a given altitude can be calculated using a modification to the scintillation index equation (equation 5)), where (h—zo) is the separation between the layer altitude and the conjugate altitude, ignoring the surface layer as this will be dealt with separately."," In this case the scintillation index, $\sigma_{\mathrm{z_{0}}}^{2}$, at a given altitude can be calculated using a modification to the scintillation index equation (equation \ref{eqn:scint_var}) ), where $(h-z_{0})$ is the separation between the layer altitude and the conjugate altitude, ignoring the surface layer as this will be dealt with separately."407" The corrected residual scintillation variance, 02,,,, will be dominated by this but we also add noise terms due to the pupil diffraction and the surface layer."," The corrected residual scintillation variance, $\sigma^{2}_{\mathrm{corr}}$, will be dominated by this but we also add noise terms due to the pupil diffraction and the surface layer."408" These noise sources are independent but the total is modulated by the original scintillation variance (equation 4)) and so the total residual scintillation variance can be modelled by, where σξι, is the scintillation index due to the surface layer, F is the Fresnel number used to quantify the ‘amount’ of diffraction and is given by F=D?/4Az, and 1, k and 1 are solved empirically from the simulation results and are found to be j=k=2/3, |=—1.4."," These noise sources are independent but the total is modulated by the original scintillation variance (equation \ref{eqn:Fresnel_prop}) ) and so the total residual scintillation variance can be modelled by, where $\sigma_{\mathrm{SL}}^{2}$ is the scintillation index due to the surface layer, $F$ is the Fresnel number used to quantify the `amount' of diffraction and is given by $F=D^2/4\lambda z$, and $j$, $k$ and $l$ are solved empirically from the simulation results and are found to be $j = k = 2/3$, $l=-1.4$."409 Using high-resolution generalized SCIDAR turbulence profile data from San Pedro Martir (Avilaetal.2006) and the model developed from the simulation results we can estimate the expected improvement in intensity variance., Using high-resolution generalized SCIDAR turbulence profile data from San Pedro $\acute{\mathrm{a}}$ rtir \citep{Avila06} and the model developed from the simulation results we can estimate the expected improvement in intensity variance.410 The SCIDAR profile shown in figure 10 was recorded on 2000 May 19 and shows a strong turbulent layer at approximately 10 km throughout the night., The SCIDAR profile shown in figure \ref{fig:scidar_prof_2000_05_19} was recorded on 2000 May 19 and shows a strong turbulent layer at approximately 10 km throughout the night.411 Figure 11 shows the expected improvement factor in intensity variance as a function of time for the same night., Figure \ref{fig:scidar_improvement} shows the expected improvement factor in intensity variance as a function of time for the same night.412 The median improvement ratio is 11.5 for this example., The median improvement ratio is 11.5 for this example.413 When calculating expected performance for real experiments it is also necessary to include the exposure time, When calculating expected performance for real experiments it is also necessary to include the exposure time414Most of the X-ray binary pulsars (XBPs) are High MassΧ--Ray Binaries (HMXRBs) in which à Neutron Star (NS) with magnetic field B 107? G is acereting matter from a mass early-type star. either an OB supergiant or a Be star.,"Most of the X–ray binary pulsars (XBPs) are High MassX--Ray Binaries (HMXRBs) in which a Neutron Star (NS) with magnetic field B $\sim 10^{12}$ G is accreting matter from a high--mass early–type star, either an OB supergiant or a Be star."415 They can be persistently bright. with luminosities in excess of 10°! eres +. or transient sources characterized by quiescent phases. with emission around 10°! eres. ? or less. interrupted by bright outbursts reaching Lx~10° Sere 1(222)..," They can be persistently bright, with luminosities in excess of $^{34}$ erg $^{-1}$, or transient sources characterized by quiescent phases, with emission around $^{34}$ erg $^{-1}$ or less, interrupted by bright outbursts reaching $L_{\rm X} \sim 10^{36-38}$ erg $^{-1}$ \citep{Negueruela98,Reig07,Sidoli10}."416 In these sources the X-ray spectra between 0.1] and 10 keV are usually described by a rather flat power-law. with photon index ~ 1. but severalXBPs have shown a marked 'soff X-ray excess above the main power-law component (see?forareview): it is well described by a thermal emission model (either blackbody. bremsstrahlung or mekal) with low temperature (kTar« 0.5 keV) and large emission area (lap= a few hundred km).," In these sources the X–ray spectra between 0.1 and 10 keV are usually described by a rather flat power–law, with photon index $\sim$ 1, but severalXBPs have shown a marked ' X–ray excess above the main power–law component \citep[see][ for a review]{LaPalombara&Mereghetti06}; it is well described by a thermal emission model (either blackbody, bremsstrahlung or mekal) with low temperature $kT_{\rm SE} <$ 0.5 keV) and large emission area $R_{\rm SE} \ge$ a few hundred km)."417 This feature has been detected not only in the high-luminosity sources (with Lx~107 eres 1) but also in several low-luminosity (Lx.~107°° erg 1) XBPs observed in the Small Magellanic Cloud (SMC). where its detection is favoured by the low interstellar absorption (22222)..," This feature has been detected not only in the high–luminosity sources (with $L_{\rm X} \sim 10^{37-38}$ erg $^{-1}$ ) but also in several low–luminosity $L_{\rm X} \sim 10^{35-36}$ erg $^{-1}$ ) XBPs observed in the Small Magellanic Cloud (SMC), where its detection is favoured by the low interstellar absorption \citep{Sasaki+03,Ueno+04,Majid+04,Haberl&Pietsch05,Haberl+08}."418 Only in a few cases this low-energy component showed coherent pulses and the debate over its origin remains open., Only in a few cases this low–energy component showed coherent pulses and the debate over its origin remains open.419 ? have shown that a soft spectral component could be a very common. 1f not ubiquitous. feature intrinsic to X-ray pulsars: it is visible in all sources with a sufficiently high flux and small absorption. and its origin is related to the source total luminosity.," \citet{Hickox+04} have shown that a soft spectral component could be a very common, if not ubiquitous, feature intrinsic to X–ray pulsars: it is visible in all sources with a sufficiently high flux and small absorption, and its origin is related to the source total luminosity."420 Recently. based on ddata. we have observed a clear thermal excess also in three of the four Be pulsars originally identified by ?.. Le. (?).. (2).. and (?)..," Recently, based on data, we have observed a clear thermal excess also in three of the four Be pulsars originally identified by \citet{Reig&Roche99}, , i.e. \citep{LaPalombara&Mereghetti06}, \citep{LaPalombara&Mereghetti07}, and \citep{LaPalombara+09}."421 These three sources are characterized by a persistently low luminosity 1057 eres. 1) and a long pulse period (P.> 100 s)., These three sources are characterized by a persistently low luminosity $L_{\rm X} \sim 10^{34-35}$ erg $^{-1}$ ) and a long pulse period $P >$ 100 s).422 These properties suggest that the NS orbits the Be star in a wide and nearly circular orbit. continuously accreting material from the low-density outer regions of the circumstellar envelope: in the case of 4U 03524309 this picture is supported by the long orbital period of 250.3 days (?)..," These properties suggest that the NS orbits the Be star in a wide and nearly circular orbit, continuously accreting material from the low–density outer regions of the circumstellar envelope; in the case of 4U 0352+309 this picture is supported by the long orbital period of 250.3 days \citep{Delgado-Marti+01}."423 For these sources the detection of the thermal component was favoured by the small distance (d<5 kpe) and interstellar absorption CNjj~107! 7)., For these sources the detection of the thermal component was favoured by the small distance $d \le$ 5 kpc) and interstellar absorption $N_{\rm H} \sim 10^{21}$ $^{-2}$ ).424" We found that their soft excess can be fitted only with a blackbody (other simple models are rejected). which contributes for 30-40 of the total flux: interestingly. in comparison with the other. more luminous sources. their blackbody component is characterized by a higher temperature (τον> 1 keV) anda much smaller emission radius (Ποx 0,5 km)."," We found that their soft excess can be fitted only with a blackbody (other simple models are rejected), which contributes for 30-40 of the total flux; interestingly, in comparison with the other, more luminous sources, their blackbody component is characterized by a higher temperature $kT_{\rm BB} >$ 1 keV) and a much smaller emission radius $R_{\rm BB} <$ 0.5 km)."425 This spectral component sets these low-lIuminosity and long-period sources apart from all the other pulsars. strongly suggesting that they form a distinet class.," This spectral component sets these low–luminosity and long–period sources apart from all the other pulsars, strongly suggesting that they form a distinct class."426 In. their case the thermal component could be due to a different emission mechanism than in the high-luminosity pulsars., In their case the thermal component could be due to a different emission mechanism than in the high–luminosity pulsars.427 Based on the work of ?.. it can be attributed to emission from the neutron-star polar caps.," Based on the work of \citet{Hickox+04}, it can be attributed to emission from the neutron–star polar caps."428 This is supported by the emission area of the blackbody component. which ts consistent with the estimated polar cap size. and by the fact that the low energy part of the spectrum Is clearly pulsed.," This is supported by the emission area of the blackbody component, which is consistent with the estimated polar cap size, and by the fact that the low energy part of the spectrum is clearly pulsed."429 In thispaper we present the results of a recent oobservation of1.. the remaining member of this class of Be/NS pulsars.," In thispaper we present the results of a recent observation of, the remaining member of this class of Be/NS pulsars."430 This system was discovered during the GGalactie plane survey (?) and identified with LS V +44 17. a moderately reddened (E(BV)= 0.650.05) BO.2 Ve star at ~ 3.3 kpe (?)..," This system was discovered during the Galactic plane survey \citep{Motch+97} and identified with LS V +44 17, a moderately reddened $E(B-V)=0.65\pm0.0$ 5) B0.2 Ve star at $\sim$ 3.3 kpc \citep{Reig11}."431 Thanks to observations with the PCA instrument on boardRossiXTE.. ? performed the first detailed. timing and spectral analysis. and discovered a pulsation with period P=202.5x0.5 s. Its spectrum was well fitted with different models (power-law. power-law plus blackbody. two black-bodies. cut-off power-law) and the measured flux implied a source luminosity of « 10°! ere + between 3 and 30 keV. hhas been detected also in the hard X-ray range: it is reported (as source PBC JO440.9--4432) in the PalermoSwift--BAT hard X-ray catalogue (?).. with a 15-150 keV flux of (2.0+ ergem 7s +. and in the catalogue obtained with the 7-year All-Sky Hard X-ray Survey (?).. with a 17-60 keV flux of (1.36£0.22)ς10 thergem 7s |.," Thanks to observations with the PCA instrument on board, \citet{Reig&Roche99} performed the first detailed timing and spectral analysis, and discovered a pulsation with period $P = 202.5 \pm 0.5$ s. Its spectrum was well fitted with different models (power–law, power–law plus blackbody, two black--bodies, cut–off power–law) and the measured flux implied a source luminosity of $\times$ $^{34}$ erg $^{-1}$ between 3 and 30 keV. has been detected also in the hard X–ray range: it is reported (as source PBC J0440.9+4432) in the Palermo-BAT hard X–ray catalogue \citep{Cusumano+10}, , with a 15-150 keV flux of $(2.0\pm1.1)\times10^{-11}$ erg $^{-2}$ $^{-1}$ , and in the catalogue obtained with the 7–year All–Sky Hard X–ray Survey \citep{Krivonos+10a}, , with a 17-60 keV flux of $(1.36\pm0.22)\times10^{-11}$ erg $^{-2}$ $^{-1}$ ."432then move ballistically up into the halo ancl back down to the disk.,then move ballistically up into the halo and back down to the disk.433 Livelroclhynamical ellects are essentially neglected in these mocels., Hydrodynamical effects are essentially neglected in these models.434 In this paper we would like to study the motion of the eas on large scales in order to understand. the observed. kinematic of the EPC: and the possible influence in shaping the metallicity gradient in the disk., In this paper we would like to study the motion of the gas on large scales in order to understand the observed kinematic of the EPG and the possible influence in shaping the metallicity gradient in the disk.435 To this aim. we need different kind. of simulations with respect to the aforementioned papers (222).," To this aim, we need different kind of simulations with respect to the aforementioned papers \citep{kor99,deav00,deav01}."436 In fact. although ? take into account the Galactic rotation. the simulated volume is to small to follow the gas circulation over large distances.," In fact, although \citet{kor99} take into account the Galactic rotation, the simulated volume is to small to follow the gas circulation over large distances."437 The volumes considered by ? and ? are larecr. but in this case the rotation is neglected. and. any racial dependence is absent.," The volumes considered by \citet{deav00} and \citet{deav01} are larger, but in this case the rotation is neglected and any radial dependence is absent."438 On the other hand. ? take into account the whole Galaxy. but their approach is purely ballistic.," On the other hand, \citet{frbi06} take into account the whole Galaxy, but their approach is purely ballistic."439 Our approach is to consider the whole Galaxy and run 3D hvedrodynamical simulations of the fountains., Our approach is to consider the whole Galaxy and run 3D hydrodynamical simulations of the fountains.440 While the numerical grid. used here includes the whole rotating Galaxy. our adaptive mesh scheme allow us to follow in cetail only a limited volume of it. the remaining galactic volume being mapped at a lower resolution.," While the numerical grid used here includes the whole rotating Galaxy, our adaptive mesh scheme allow us to follow in detail only a limited volume of it, the remaining galactic volume being mapped at a lower resolution."441 Although a detailed description of the cillerent phases of the ISM is hampered by this limited resolution. the large scale dynamic and thermal evolution of the fountains can be satisfactorily followed.," Although a detailed description of the different phases of the ISM is hampered by this limited resolution, the large scale dynamic and thermal evolution of the fountains can be satisfactorily followed."442 Llere we present. simulations of single fountains. ic. generated by a single OB association.," Here we present simulations of single fountains, i.e. generated by a single OB association."443 We shall describe simulations of multiple fountains in a companion paper., We shall describe simulations of multiple fountains in a companion paper.444 The ISM in our model is made up of three components. namely molecular (H2). neutral (1 1) and ionized (1 11) hydrogen.," The ISM in our model is made up of three components, namely molecular $_2$ ), neutral (H ) and ionized (H ) hydrogen."445 Following ?.. cach density component in the disk is assumed to be of the form: where 2? is the cevlindrical racius. zi is the vertical scale height anc fy is the radial scale length of the cisk.," Following \citet{wolf03}, each density component in the disk is assumed to be of the form: where $R$ is the cylindrical radius, $z_{\rm d}$ is the vertical scale height and $R_{\rm d}$ is the radial scale length of the disk."446" The parameter. Z4, allows for the depression in the gas density. observed. in the inner several kiloparsees of. the Galaxy.", The parameter $R_{\rm m}$ allows for the depression in the gas density observed in the inner several kiloparsecs of the Galaxy.447 X4 represents the superficial density of the cdillerent components.," $\Sigma_{\rm448d}$ represents the superficial density of the different components."449 The values of the parameters are summarized in Table 1.., The values of the parameters are summarized in Table \ref{tab:ism}.450 The 18M is initially set in rotational equilibrium in the Galactic gravitational potential given by the summation of dark matter halo. bulge and disk contributions.," The ISM is initially set in rotational equilibrium in the Galactic gravitational potential given by the summation of dark matter halo, bulge and disk contributions."451 The dark matterhalo gravitational potential is assunied to follow the Navarro. Erenk ancl White profile (?) where panos is a reference density. rin ds a scale radius. .r=r£rqo and r is the spherical radius.," The dark matterhalo gravitational potential is assumed to follow the Navarro, Frenk and White profile \citep{nfw96}452 where $\rho_{\rm dm,0}$ is a reference density, $r_{\rm dm,0}$ is a scale radius, $x=r/r_{\rm dm,0}$ and $r$ is the spherical radius."453 The halo is truncated. at à radius Man. beyond. which its potential follows the L/r profile.," The halo is truncated at a radius $r_{\rm dm,t}$ beyond which its potential follows the $1/r$ profile."454 See Table 2 for the numerical values of these parameters., See Table 2 for the numerical values of these parameters.455" The bulge gravitational potential is given by (2): where rio is a scale racius ancl Adi, is the bulge mass."," The bulge gravitational potential is given by \citep{her90}: where $r_{\rm b,0}$ is a scale radius and $M_{\rm b}$ is the bulge mass."456" Finally. the gravitational potential of the clisk is assumed to be generated. ον a stellar distribution following a flattened Wing profile Llere pou is the central density of the stars. and fy. and z,, are the core radii. whose ratio is 0=z,I, In order toavoid an unbounded growth of the stellar mass with radius the stellar profile is truncated wherever VikRoo|(nfo?mReafeStafee with Ly and σι tidal lengths whose ratio is 2,4/43,= 9."," Finally, the gravitational potential of the disk is assumed to be generated by a stellar distribution following a flattened King profile Here $\rho_{\star,0}$ is the central density of the stars, and $R_{\star,{\rm c}}$ and $z_{\star,{\rm c}}$ are the core radii, whose ratio is $\delta=z_{\star,{\rm c}}/R_{\star,{\rm c}}=0.03$ In order toavoid an unbounded growth of the stellar mass with radius the stellar profile is truncated wherever $\sqrt{(R/R_{\star,{\rm457c}})^2+(z/z_{\star,{\rm c}})^2}> R_{\star,{\rm t}}/ R_{\star,{\rm458c}}\equiv z_{\star,{\rm t}}/z_{\star,{\rm c}}$, with $R_{\star,{\rm459t}}$ and $z_{\star,{\rm t}}$ tidal lengths whose ratio is $z_{\star,{\rm t}}/R_{\star,{\rm t}}=\delta$ ."460" Ehe stellar potential , is computed numerically following the method described in. ?..", The stellar potential $\Phi _{\star}$ is computed numerically following the method described in \citet{brma96}.461 Table 20 gives the values of all the parameters concerning the Galaxy model., Table \ref{tab:gal} gives the values of all the parameters concerning the Galaxy model.462 With such values we obtain Align=13107 AML Αν=355107 M. and AL=9.6«LOM NI. for the dark matter halo. the bulge and the stellar disk. respectively.," With such values we obtain $M_{\rm dm}=1.3\times46310^{12}$ $_{\odot}$, $M_{\rm b}=3.5\times 10^{10}$ $_{\odot}$ and $M_{\star}=9.6\times 10^{10}$ $_{\odot}$ for the dark matter halo, the bulge and the stellar disk, respectively."464 In order to set the ISM given by Eq., In order to set the ISM given by Eq.465 1. in a rotating configuration in equilibrium in the general potential well of the Galaxy. we proceed as follows.," \ref{eq:ism} in a rotating configuration in equilibrium in the general potential well of the Galaxy, we proceed as follows."466 The pressure at any point is found integrating the z-component. of the hyelrostatic equilibrium equation for any value of the disk radius £2., The pressure at any point is found integrating the $z$ -component of the hydrostatic equilibrium equation for any value of the disk radius $R$ .467 Phe inteegratjon starts at the outermost values of z (where we can assume the pressure Z= 0) and proceeds inward to reach the ealactic plane z= 0., The integration starts at the outermost values of $z$ (where we can assume the pressure $P=0$ ) and proceeds inward to reach the galactic plane $z=0$ .468" We then obtain the rotationvelocity [rom where oe(Ros)=VRP10.DAR)econ ds the circular velocity.and e is the total potential of the Galaxy: b=dau,|dg d."," We then obtain the rotationvelocity from where $v_{\rm c}(R,z)=\sqrt {R(d\Phi(R,z) /dR)_{z={\rm cost}}}$ is the circular velocity,and $\Phi$ is the total potential of the Galaxy: $\Phi=\Phi_{\rm dm}+\Phi_{\rm b}+\Phi_{\star}$ ."469 The values 11.0) obtained in this," The values $v_{\phi}(R,0)$ obtained in this"470to PRE bursts while the small (black) points show all other thermonuclear bursts from that source.,to PRE bursts while the small (black) points show all other thermonuclear bursts from that source.471 The PRE bursts appear to occur predominantly when the sources lie near the soft vertices of their color-color diagrams (see also Muno et , The PRE bursts appear to occur predominantly when the sources lie near the soft vertices of their color-color diagrams (see also Muno et 2000).472"However, the regions with PRE bursts still extend across ~1/2 of the lengths of the color-color tracks."," However, the regions with PRE bursts still extend across $\simeq 1/2$ of the lengths of the color-color tracks."473 This minimizes22000). the possibility that the reproducibility of the inferred touchdown fluxes simply reflects the fact we are considering only very similar X-ray bursts in a very narrow range of accretion rates., This minimizes the possibility that the reproducibility of the inferred touchdown fluxes simply reflects the fact we are considering only very similar X-ray bursts in a very narrow range of accretion rates.474" Our limit on the pre-burst flux, i.e., the requirement that y<0.1, excludes the brightest regions of the color-color diagram of each source and may also introduce a bias in our selection of only particular PRE bursts."," Our limit on the pre-burst flux, i.e., the requirement that $\gamma<0.1$, excludes the brightest regions of the color-color diagram of each source and may also introduce a bias in our selection of only particular PRE bursts."475" This is not the case here, however, as only a very small fraction of the color-color diagram of each source corresponds to y>0.1 (compare, for example, the color-color diagram in Figure 3 to the entire color-color diagram of 4U 1728—34 in Figure 1 of Muno et al."," This is not the case here, however, as only a very small fraction of the color-color diagram of each source corresponds to $\gamma>0.1$ (compare, for example, the color-color diagram in Figure \ref{ccfig} to the entire color-color diagram of 4U $-$ 34 in Figure 1 of Muno et al."476 2002)., 2002).477 We now discuss the determination of the touchdown moment and the measurement of the touchdown flux for the PRE bursts in our sample., We now discuss the determination of the touchdown moment and the measurement of the touchdown flux for the PRE bursts in our sample.478" We present here the details of the analysis for 4U 1636—536 and 4U 1728—34, which are the sources with the highest number of PRE events."," We present here the details of the analysis for 4U $-$ 536 and 4U $-$ 34, which are the sources with the highest number of PRE events."479" 'The touchdown moment is defined as the moment when the photosphere falls back onto the neutron star, which is thought to occur when the observed blackbody normalization reaches its lowest and the temperature its highest value."," The touchdown moment is defined as the moment when the photosphere falls back onto the neutron star, which is thought to occur when the observed blackbody normalization reaches its lowest and the temperature its highest value."480" In a very small number of X-ray bursts, however, a statistically insignificant temperature maximum can occur several seconds past the peak flux, as in the example of the PRE burst from 4U 1636—536 shown in Figure 4.."," In a very small number of X-ray bursts, however, a statistically insignificant temperature maximum can occur several seconds past the peak flux, as in the example of the PRE burst from 4U $-$ 536 shown in Figure \ref{examples2}."481" In these cases, we selected the first temperature maximum (and normalization minimum) past the peak flux, ensuring that the temperature at this point is within 1—c of its global maximum."," In these cases, we selected the first temperature maximum (and normalization minimum) past the peak flux, ensuring that the temperature at this point is within $-\sigma$ of its global maximum."482 The touchdown moments in a total of 6 out of 83 bursts from all of the sources were selected in this way., The touchdown moments in a total of 6 out of 83 bursts from all of the sources were selected in this way.483 The precise determination of the touchdown moment can also be affected by data gaps that are present in the science event mode data in some burst observations., The precise determination of the touchdown moment can also be affected by data gaps that are present in the science event mode data in some burst observations.484" In these cases, where a gap may have an effect on the determination of the touchdown moment, we checked whether a *burst catcher"" mode with spectral information (e.g., mode CB.88ms.664M.00.2249HH) was used."," In these cases, where a gap may have an effect on the determination of the touchdown moment, we checked whether a “burst catcher” mode with spectral information (e.g., mode H) was used."485" We found that only in 6 cases, there were no burst catcher mode data with spectral information."," We found that only in 6 cases, there were no burst catcher mode data with spectral information."486" For the rest of the X-ray bursts, we made use of the data in the burst catcher mode to determine the exact touchdown moments."," For the rest of the X-ray bursts, we made use of the data in the burst catcher mode to determine the exact touchdown moments."487 We fit the spectrum that we extracted at the touchdown moment for each PRE event as described in Section 2., We fit the spectrum that we extracted at the touchdown moment for each PRE event as described in Section 2.488 The resulting X?/dof histograms for 4U 1636—536 and 4U 1728—34 are shown in Figure 5 (see Paper I for the definition of this statistic)., The resulting $X^2$ /dof histograms for 4U $-$ 536 and 4U $-$ 34 are shown in Figure \ref{chi2} (see Paper I for the definition of this statistic).489" Using the limits determined in Paper I, we can determine whether a particular fit is statistically acceptable or it should be X?/dofexcluded from further analysis."," Using the $X^2$ /dof limits determined in Paper I, we can determine whether a particular fit is statistically acceptable or it should be excluded from further analysis."490" The X-ray spectra at the touchdown moments were well described with blackbody functions, leading in general to small X?/dof values."," The X-ray spectra at the touchdown moments were well described with blackbody functions, leading in general to small $X^2$ /dof values."491" Therefore, applying the X?/dof limits forced us to exclude only one X-ray burst from 4U 1705—44 (burst 1) and two X-ray bursts from 4U 1636—536 (bursts 3 and 9)."," Therefore, applying the $X^{2}$ /dof limits forced us to exclude only one X-ray burst from 4U $-$ 44 (burst 1) and two X-ray bursts from 4U $-$ 536 (bursts 3 and 9)."492" In this section, we will address the formal and systematic uncertainties in the touchdown fluxes obtained from the PRE bursts of each source."," In this section, we will address the formal and systematic uncertainties in the touchdown fluxes obtained from the PRE bursts of each source."493" As before, we will first focus on the two sources with the highest number of bursts to present the details of the method and then extend our analysis to the rest of the sample."," As before, we will first focus on the two sources with the highest number of bursts to present the details of the method and then extend our analysis to the rest of the sample."494 We will start by discussing our determination of the bolometric flux at touchdown and its formal uncertainty., We will start by discussing our determination of the bolometric flux at touchdown and its formal uncertainty.495 We will then explore whether the different PRE bursts from the same source reach a touchdown flux that remains statistically constant between bursts., We will then explore whether the different PRE bursts from the same source reach a touchdown flux that remains statistically constant between bursts.496" For each burst, the bolometric flux at touchdown is obtained from the combination of the blackbody temperature and normalization."," For each burst, the bolometric flux at touchdown is obtained from the combination of the blackbody temperature and normalization."497 Figure 6 shows the and confidence contours of the blackbody normalization and temperature, Figure 6 shows the and confidence contours of the blackbody normalization and temperature498(he inverse Compton mechanism wilh such a high central magnetic field.,the inverse Compton mechanism with such a high central magnetic field.499 Nonetheless. some uncertainties in both methods max lead to the discrepaney (Newman.2002).," Nonetheless, some uncertainties in both methods may lead to the discrepancy \citep*{new02}."500. An alternative interpretation of the INR excess is non-thermal bremsstrahlung from supra-(hermal electrons (Enblin.Lieu.&Biermann1999:Blasi2000:&kempner 2000).," An alternative interpretation of the HXR excess is non-thermal bremsstrahlung from supra-thermal electrons \citep*{ens99,bla00,dog00,sar00}."501. ILowever. a huge amount of energy is necessary in (this model to produce ihe observed ΗΝ excess (Petrosian2001:Blasi2000).," However, a huge amount of energy is necessary in this model to produce the observed HXR excess \citep{pet01,bla00}."502. Drunettietal.(2001) proposed a two-phase model to interpret the radial steepening of the spectral-index distribution in Coma C. In this two-phase moclel. the relativistic electrons were injected during a first phase in the past and re-accelerated during a second phase up to present (ime.," \citet{bru01} proposed a two-phase model to interpret the radial steepening of the spectral-index distribution in Coma C. In this two-phase model, the relativistic electrons were injected during a first phase in the past and re-accelerated during a second phase up to present time."503 In such a re-acceleration model. there must be a cutoff in the electron spectrum because of the balance between the loss and the gain of the electron energv.," In such a re-acceleration model, there must be a cutoff in the electron spectrum because of the balance between the loss and the gain of the electron energy."504 A cutoff in the electron. spectrum should lead to a cutoff in the emissivity of svnchrotron radiation and then in the integrated radio spectrum., A cutoff in the electron spectrum should lead to a cutoff in the emissivity of synchrotron radiation and then in the integrated radio spectrum.505 If the magnetic fields have a profile. the eutolf Irecuencies will decrease with (he increasing radius.," If the magnetic fields have a radial-decrease profile, the cutoff frequencies will decrease with the increasing radius."506 Consequently. a racial steepening of (he spectral index between (wo fixed [requencies will appear.," Consequently, a radial steepening of the spectral index between two fixed frequencies will appear."507" Brunetti successfully reproduced (he radial steepening of the spectral index. the radio spectrum steepening at high frequencies. and the ILA excess in (he Coma cluster: however. the central ""plateau in the spectral-index distribution was not well explained."," \citet{bru01}508 successfully reproduced the radial steepening of the spectral index, the radio spectrum steepening at high frequencies, and the HXR excess in the Coma cluster; however, the central “plateau"" in the spectral-index distribution was not well explained."509 The authors adopted a central field strength of <3 iG in their models.," The authors adopted a central field strength of $\lesssim5103\ \mu$ G in their models."511 As pointed in their work. the spectral index would be very steep in low magnetic fields and flat in moderate ones.," As pointed in their work, the spectral index would be very steep in low magnetic fields and flat in moderate ones."512" It would be important to know whether a stronger central magnetic field can reproduce the central ""plateau in the spectral-index distribution without violating the observational constraints from the radio and IIXBR. emission."," It would be important to know whether a stronger central magnetic field can reproduce the central “plateau"" in the spectral-index distribution without violating the observational constraints from the radio and HXR emission."513 Cluster mergers are very violent events and release a large amount of energv. (10! eres)., Cluster mergers are very violent events and release a large amount of energy $\sim10^{64}$ ergs).514 Merger shocks and violent turbulence must plav an important role in the generation and re-acceleration of relativistic electrons (Sarazin2001)., Merger shocks and violent turbulence must play an important role in the generation and re-acceleration of relativistic electrons \citep{sar01}.515. Nonetheless. Gabicei(2003) claimed that the shocks generated bv major mergers. mergers between clusters with comparable mass. is {ου weak (o account for the spectral slopes of the non-thermal emission.," Nonetheless, \citet{gab03} claimed that the shocks generated by major mergers, mergers between clusters with comparable mass, is too weak to account for the spectral slopes of the non-thermal emission."516 The Mach numbers of the shocks in major mergers are of order of unity in their simulations and roughly consistent with the Mach mumber ~ 2 observed in Cvgnus A (Alarkevitch. 1999)., The Mach numbers of the shocks in major mergers are of order of unity in their simulations and roughly consistent with the Mach number $\sim$ 2 observed in Cygnus A \citep*{mar99}.517. However. if a significant level of re-acceleration is involved. the evolved spectra of relativistic electrons may be able to account for the observed spectra of non-thermal emission.," However, if a significant level of re-acceleration is involved, the evolved spectra of relativistic electrons may be able to account for the observed spectra of non-thermal emission."518 In (his paper. we investigate the radio ancl INR excess emission in (ie Coma cluster assuming the magnetic fields possessing a central field strength of 6 iG and a radial-decrease profile.," In this paper, we investigate the radio and HXR excess emission in the Coma cluster assuming the magnetic fields possessing a central field strength of $6\519\mu$ G and a radial-decrease profile."520 The effects of different Mach numbers of merger shocks on the Formation of radio halos, The effects of different Mach numbers of merger shocks on the formation of radio halos521clusters near the Galactic center (Krumholz&Matzner 2009).,clusters near the Galactic center \citep{krummatzner09}.522. The situation is different when the disk can fragment and form multiple sink particles., The situation is different when the disk can fragment and form multiple sink particles.523" Initially the mass growth of the central protostar in runs B and D is comparable to the one in run A. As soon as further protostars form in the gravitationally unstable disk, they begin to compete with the central object for accretion of disk material."," Initially the mass growth of the central protostar in runs B and D is comparable to the one in run A. As soon as further protostars form in the gravitationally unstable disk, they begin to compete with the central object for accretion of disk material."524" However, unlike in the classical competitive accretion picture (Bonnelletal.2001a,2004),, it is not the most massive object that dominates and grows disproportionately fast."," However, unlike in the classical competitive accretion picture \citep{bonnell01a,bonetal04}, it is not the most massive object that dominates and grows disproportionately fast."525" Figure 1 shows that, although the accretion rates of the most massive stars (M>10M) steadily decrease, the low-mass stars (M<10Mo), keep accreting at the same rate."," Figure \ref{fig:accretion} shows that, although the accretion rates of the most massive stars $M \geq52610\,$ $_\odot$ ) steadily decrease, the low-mass stars $M <52710\,$ $_\odot$ ), keep accreting at the same rate."528" Although the detailed mass distribution of the low-mass stars depends on numerical resolution (Federrathetal.2010),, the net effect of their accretion should not, so long as they can form at all."," Although the detailed mass distribution of the low-mass stars depends on numerical resolution \citep{federrathetal10}, the net effect of their accretion should not, so long as they can form at all."529 The successive formation of low-mass objects in the disk at increasing radii limits subsequent growth of the more massive objects in the inner disk., The successive formation of low-mass objects in the disk at increasing radii limits subsequent growth of the more massive objects in the inner disk.530 Material that moves inwards through the disk accretes preferentially onto the sinks at larger radii., Material that moves inwards through the disk accretes preferentially onto the sinks at larger radii.531" The key to the process, as already discussed by Bate(2000),, is that fragments that form later at larger radii will preferentially accrete larger-angular momentum material."," The key to the process, as already discussed by \citet{bate00}, is that fragments that form later at larger radii will preferentially accrete larger-angular momentum material."532 This will happen on a much shorter time than the timescales required to redistribute this angular momentum to other parts of the disk at larger radii by viscous or gravitational torques., This will happen on a much shorter time than the timescales required to redistribute this angular momentum to other parts of the disk at larger radii by viscous or gravitational torques.533 Similar effects are discussed in the disk fragmentation studies by Kratteretal. (2010)., Similar effects are discussed in the disk fragmentation studies by \citet{kratteretal10}.534". This behavior is found in models of low-mass protobinary disks, where again the secondary accretes at a higher rate than the primary."," This behavior is found in models of low-mass protobinary disks, where again the secondary accretes at a higher rate than the primary."535 Its orbit around the common center of gravity scans larger radii and hence it encounters material that moves inwards through the disk before the primary star., Its orbit around the common center of gravity scans larger radii and hence it encounters material that moves inwards through the disk before the primary star.536 This drives the system towards equal masses and circular orbits (Bate&Bonnell1997;Bate 2000).," This drives the system towards equal masses and circular orbits \citep{bateetal97,bate00}."537". In our simulations, after a certain transition period hardly any gas makes it all the way to the center and the accretion rate of the first sink particle drops to almost zero."," In our simulations, after a certain transition period hardly any gas makes it all the way to the center and the accretion rate of the first sink particle drops to almost zero."538 This is the essence of the fragmentation-induced starvation process., This is the essence of the fragmentation-induced starvation process.539" In run B, it prevents any star from reaching a mass larger than 25 Mo."," In run B, it prevents any star from reaching a mass larger than $25\,$ $_\odot$."540" The Jeans mass in run D is smaller than in run B because of the lack of accretion heating, and consequently the highest mass star in run D grows to less than 15 "," The Jeans mass in run D is smaller than in run B because of the lack of accretion heating, and consequently the highest mass star in run D grows to less than $15\,$ $_\odot$."541"In comparison, Krumholzetal. described Mo.simulations starting with a ten times less (2007b)massive core than ours, using both an isothermal equation of state and including accretion heating."," In comparison, \citet{krumkleinmckee07} described simulations starting with a ten times less massive core than ours, using both an isothermal equation of state and including accretion heating."542" In both cases, objects with roughly half the mass of our most massive object formed."," In both cases, objects with roughly half the mass of our most massive object formed."543" The isothermal case formed an only slightly less massive object than the one including accretion heating, just as in our models."," The isothermal case formed an only slightly less massive object than the one including accretion heating, just as in our models."544 The smaller final masses of their objects compared to ours seems mainly just to be a result of their smaller initial core masses., The smaller final masses of their objects compared to ours seems mainly just to be a result of their smaller initial core masses.545 Inspection of Figure 1 reveals additional aspects of the, Inspection of Figure \ref{fig:accretion} reveals additional aspects of the546hird of the simulations correspond to the low noise zone and two thirds to the high noise zone.,third of the simulations correspond to the low noise zone and two thirds to the high noise zone.547 Then. we generate 1000 simulations including CMD. anisotropic noise. Galactic oregrounds and. point sources for each of the following Dux imits: LJy. 0.9 Jy. OS Jv. 0.1 Jv. Le. we remove all the sources above the given flux limit (the third order and fourth order eumulants of the dillerent simulated components can » seen in Table 2).," Then, we generate 1000 simulations including CMB, anisotropic noise, Galactic foregrounds and point sources for each of the following flux limits: 1Jy, 0.9 Jy, 0.8 Jy,......., 0.1 Jy, i.e. we remove all the sources above the given flux limit (the third order and fourth order cumulants of the different simulated components can be seen in Table 2)."548 We filter. all the simulations with he MIINI. MIIN2 and. MIIW3 at the optimal scales (obtained by maximizing the amplification) ancl calculate heir skewness and. kurtosis.," We filter all the simulations with the MHW1, MHW2 and MHW3 at the optimal scales (obtained by maximizing the amplification) and calculate their skewness and kurtosis."549" Then. taking into account the skewness. we perform the ollowing hypothesis test: we consider the null hypothesis. Ha. the simulation is Gaussian. against the alternative ivpothesis. //,. it is non-Gaussian."," Then, taking into account the skewness, we perform the following hypothesis test: we consider the null hypothesis, $H_0$, the simulation is Gaussian, against the alternative hypothesis, $H_1$, it is non-Gaussian."550 We set a significance evel a=0.05. this means that we reject the null hypothesis when a simulation with point sources has a skewness higher han a value 55. which corresponds to that of the 95% of the Gaussian simulations.," We set a significance level $ \alpha =0.05 $, this means that we reject the null hypothesis when a simulation with point sources has a skewness higher than a value $s_{5}$, which corresponds to that of the $95\%$ of the Gaussian simulations."551 The test is one-sided to the right. since the simulations with point sources have positive skewness.," The test is one-sided to the right, since the simulations with point sources have positive skewness."552 We deline the power of the test as 1.0. with a the probability of accepting the null hypothesis when it is false. i.c. the power is the proportion of non-Gaussian simulations with a skewness higher than that of 95% of the Caussian ones.," We define the power of the test as $1-\delta$, with $\delta$ the probability of accepting the null hypothesis when it is false, i.e. the power is the proportion of non-Gaussian simulations with a skewness higher than that of $95\%$ of the Gaussian ones."553 The higher the power. the more ellicient the method in detecting non-Ciaussianity.," The higher the power, the more efficient the method in detecting non-Gaussianity."554 We perform the same test with the kurtosis. setting a kurtosis limit A>: it is also once-sided to the right. since the kurtosis of point sources is higher than 3.," We perform the same test with the kurtosis, setting a kurtosis limit $k_{5}$; it is also one-sided to the right, since the kurtosis of point sources is higher than 3."555 The power of these tests for the dillerent. Dux. limits are shown in Table 1. they are also plotted in. Figure 2.," The power of these tests for the different flux limits are shown in Table 1, they are also plotted in Figure 2."556 At το CGllz the power of the skewness test with a [lux limit of OA Jv is SX CMIIWI). 9% (MEIN2) and 10% (MEIN).," At 70 GHz the power of the skewness test with a flux limit of 0.4 Jy is $8\%$ (MHW1), $9\%$ (MHW2) and $10\%$ (MHW3)."557 The power is higher for the kurtosis test: 11% (MIINID 13:4 (MIIW2) and. 114. (MIIN3) at Q4. Jy.," The power is higher for the kurtosis test: $11\%$ (MHW1), $13\%$ (MHW2) and $11\%$ (MHW3) at 0.4 Jy."558 Therefore. for the MIIN2 the probability that a patct with this llux limit has a kurtosis higher than that of 95% of the Gaussian simulations is 0.13.," Therefore, for the MHW2 the probability that a patch with this flux limit has a kurtosis higher than that of $95\%$ of the Gaussian simulations is 0.13."559 In. practice. we could consider 126 patches (half sky) with the size of the simulated ones. if they are Gaussian the probability of finding more than 10 with a kurtosis higher than Az is 0.05. if we had point sources up to Q4 Jv. this probability would. be 0.95. (this can be calculated. by using the binomial distribution with probabilities 0.05 and 0.13 in the Gaussian and. non-Gaussian case. respectively).," In practice, we could consider 126 patches (half sky) with the size of the simulated ones, if they are Gaussian the probability of finding more than 10 with a kurtosis higher than $k_{5}$ is 0.05, if we had point sources up to 0.4 Jy, this probability would be 0.95, (this can be calculated by using the binomial distribution with probabilities 0.05 and 0.13 in the Gaussian and non-Gaussian case, respectively)."560 Therefore. the detection. of non-Gaussianity would be possible for this lux limit.," Therefore, the detection of non-Gaussianity would be possible for this flux limit."561 For the 100 CGllz channel. the results of the skewness test can also be seen in Table 1. for instance the power at 0.3 Jv ds s& (ΛΗΛ 18% CMEIIW2) and. 12% (ΛΗΛ).," For the 100 GHz channel, the results of the skewness test can also be seen in Table 1, for instance the power at 0.3 Jy is $8\%$ (MHW1), $13\%$ (MHW2) and $12\%$ (MHW3)."562 The power is higher for D).the kurtosis test: 9% (ALLIW 18/4 (MEIN2). 2274 (MEI at 0.3 Jy. making detection possibleD). down to this Εικ.," The power is higher for the kurtosis test: $9\%$ (MHW1), $18\%$ (MHW2), $22\%$ (MHW3) at 0.3 Jy, making detection possible down to this flux."563 The 23)kurtosis test allows the cetection of non-Caussianity at 100 6112 for lower [Huxes than at 70 Cillz., The kurtosis test allows the detection of non-Gaussianity at 100 GHz for lower fluxes than at 70 GHz.564 We would like to comment that point sources could be detected in these channels. accepting a 5% of spurious detections. down to 0.47 Jv (70 12) and 0.25 Jv. (100 CGllZ)(López-Caniegoetal.2006).," We would like to comment that point sources could be detected in these channels, accepting a $5\%$ of spurious detections, down to $0.47$ Jy (70 GHz) and $0.25$ Jy (100 \citep{lop06}."565.. Therefore. even if we were able to perform a perfect subtraction (or masking) of the point sources above these detection Huxes. we would still clearly detect a non-Gaussian signal due to unsubtracted point sources in the 70 11 channel.," Therefore, even if we were able to perform a perfect subtraction (or masking) of the point sources above these detection fluxes, we would still clearly detect a non-Gaussian signal due to unsubtracted point sources in the 70 GHz channel."566 For 100 11. at the flux cut of 0.2 Jy (Le below the theoretical detection limit). the highest. found. power is 114. (corresponding to the kurtosis of the MIIW3).," For 100 GHz, at the flux cut of 0.2 Jy (i.e below the theoretical detection limit), the highest found power is $11\%$ (corresponding to the kurtosis of the MHW3)."567 Thus. it is likely that a non-Gaussian signal due to residual point sources is still present when analysing a presumably clean CALB map.," Thus, it is likely that a non-Gaussian signal due to residual point sources is still present when analysing a presumably clean CMB map."568 These results show the importance of studying ancl characterising the non-Gaussianity due to. residual point sources (or. other oregrounds) in order to avoid its misidentification as intrinsic non-Ciaussianityv., These results show the importance of studying and characterising the non-Gaussianity due to residual point sources (or other foregrounds) in order to avoid its misidentification as intrinsic non-Gaussianity.569 In general the MIINW2 and MEIN perform better than he MIIWI. producing higher powers: the kurtosis test. is more powerful than the skewness one and the tests are more xowerful at. 100 Gllz than at 70 Cillz. (see Table 1 and Figure 2).," In general the MHW2 and MHW3 perform better than the MHW1, producing higher powers; the kurtosis test is more powerful than the skewness one and the tests are more powerful at 100 GHz than at 70 GHz, (see Table 1 and Figure 2)."570 In order to assess the influence of the Galactic oregrounds. we have also carried. out 1000. simulations without point sources but. including the Galactic oregrounds.," In order to assess the influence of the Galactic foregrounds, we have also carried out 1000 simulations without point sources but including the Galactic foregrounds."571 The power in this case is always below 6% (see the no sources case in Table 1). confirming hat these foregrounds contribute very Little to the non-CGaussianitv.. when we filter with these wavelets at. the optimal scales.," The power in this case is always below $6\%$ (see the no sources case in Table 1), confirming that these foregrounds contribute very little to the non-Gaussianity, when we filter with these wavelets at the optimal scales."572 We have also performed. similar tests by filtering the maps with the Daubechies 4 wavelet. this wavelet. has been already used in the study of the non-CGaussianity of CAB maps (BarreivoandHobson2001).," We have also performed similar tests by filtering the maps with the Daubechies 4 wavelet, this wavelet has been already used in the study of the non-Gaussianity of CMB maps \citep{bar01}."573. The power of the skewness and kurtosis tests with this wavelet is never higher than 50%. even for Huxes as high as 1 Jy and is always much lower than the power obtained with the MEINE. as can be seen in Figure 2.," The power of the skewness and kurtosis tests with this wavelet is never higher than $50\%$, even for fluxes as high as 1 Jy and is always much lower than the power obtained with the MHWF, as can be seen in Figure 2."574 We have considered skewness and kurtosis of dillerent detail coellicients (horizontal. vertical. diagonal) ab different resolution levels and. plotted. in Figure 2 the power obtained for the detail coefficients which produce the highest power.," We have considered skewness and kurtosis of different detail coefficients (horizontal, vertical, diagonal) at different resolution levels and plotted in Figure 2 the power obtained for the detail coefficients which produce the highest power."575 It is clear that. whereas the members of the MIIWE are adapted to the detection of point sources and the non-Gaussian signal they produce. this is not the case for the Daubechies family.," It is clear that, whereas the members of the MHWF are adapted to the detection of point sources and the non-Gaussian signal they produce, this is not the case for the Daubechies family."576 In the previous section. we have performed: Giaussianity tests in order to detect the non-Gaussian signal generated bv point sources in CAIB maps.," In the previous section, we have performed Gaussianity tests in order to detect the non-Gaussian signal generated by point sources in CMB maps."577 The. estimation of the level of this signal is also of great. interest., The estimation of the level of this signal is also of great interest.578 Therefore. it is worthwhile calculating the third. order. cumulant. Av. and the fourth order cumulant. να. produced. by. point sources.," Therefore, it is worthwhile calculating the third order cumulant, $K_3$, and the fourth order cumulant, $K_4$, produced by point sources."579 The problem is that we could only know directly the values of Avy and Aa of CMD maps including CAIB. noise. point sources ancl other foregrounds. but not of the point source maps.," The problem is that we could only know directly the values of $K_{3}$ and $K_{4}$ of CMB maps including CMB, noise, point sources and other foregrounds, but not of the point source maps."580 A possible solution would be to filter the maps with suitable wavelets so that the main contribution to the eumulants would be that of point sources., A possible solution would be to filter the maps with suitable wavelets so that the main contribution to the cumulants would be that of point sources.581 As we have seen before. the MEINE at the optimal scales could perform well in this respect.," As we have seen before, the MHWF at the optimal scales could perform well in this respect."582 Therefore. our idea is to filter CMD maps with the MIINE and to try to extract the parameters Ava and A4.," Therefore, our idea is to filter CMB maps with the MHWF and to try to extract the parameters $K_3$ and $K_4$."583 However. we should first relate the eumulants of a wavelet filtered. map to the cumulants of the original map. this can be done by using eqs. (," However, we should first relate the cumulants of a wavelet filtered map to the cumulants of the original map, this can be done by using eqs. ("58414) and (15).,14) and (15).585 These equations for the MIIW MIIW2 and. MEIN give us the relation between the originalI. cumulants due to point sources and the wavelet filtered. eumulants.," These equations for the MHW1, MHW2 and MHW3 give us the relation between the original cumulants due to point sources and the wavelet filtered cumulants."586and response matrices used to find the upper limits found in our study (last paragraph of Section 3 in that article).,and response matrices used to find the upper limits found in our study (last paragraph of Section 3 in that article).587 As should be clear from our Section 3 we have consistently used. the black-body temperature to calculate our X-ray to bolometric luminosity conversion factors., As should be clear from our Section \ref{Sect:Data.Reduction} we have consistently used the black-body temperature to calculate our X-ray to bolometric luminosity conversion factors.588 Also. the fact that the ACIS-S detector is unreliable below 300 eV has no inipact on our results. because we only use observed photons with energies above this threshold.," Also, the fact that the ACIS-S detector is unreliable below 300 eV has no impact on our results, because we only use observed photons with energies above this threshold."589 As mentioned in the introduction. DiStefano(2010) showed that the number of observed SSSs in nearby galaxies is one to two orders of magnitude too small compared. with the estimated number of expected. SSSs if these were the progenitors of type la SNe.," As mentioned in the introduction, \citet{DiStefano.2010a} showed that the number of observed SSSs in nearby galaxies is one to two orders of magnitude too small compared with the estimated number of expected SSSs if these were the progenitors of type Ia SNe."590 A similar result. was found. by Cilfanov&Bogdan(2010) who showed that the integrated super-soft N-rav. luminosity of elliptical galaxies is roughly two orders of magnitude too low to account for the SN Ia rate., A similar result was found by \citet{Gilfanov.Bogdan.2010} who showed that the integrated super-soft X-ray luminosity of elliptical galaxies is roughly two orders of magnitude too low to account for the SN Ia rate.591 Although our constraints are not as strong as those found in the two above-mentioned: studies our results are consistent. with them., Although our constraints are not as strong as those found in the two above-mentioned studies our results are consistent with them.592 The search for archival images was initially unelertaken in an attempt to solve the SD vs. DD question. since at least in the naivve picture the SD. progenitors were expected to be X-ray bright. while the DD progenitors were not.," The search for archival images was initially undertaken in an attempt to solve the SD vs. DD question, since at least in the ve picture the SD progenitors were expected to be X-ray bright, while the DD progenitors were not."593 However. as a number of recent studies show the question of X-ray brightness of Ia progenitors has turned out to be somewhat more complicated than this: and other current X-ray satellites are only sensitive at photon energies consicerably above the AZgg of SSS. above ~ 300 eV or so.," However, as a number of recent studies show the question of X-ray brightness of Ia progenitors has turned out to be somewhat more complicated than this: and other current X-ray satellites are only sensitive at photon energies considerably above the $kT_{BB}$ of SSS, above $\sim$ 300 eV or so."594 The corrections applied in Eq. (2)), The corrections applied in Eq. \ref{Eq:Bolometric.Correction}) )595 illustrate that a small change in Ape hasa drastic cllect on the correctional constant € for kTpp sources., illustrate that a small change in $kT_{BB}$ hasa drastic effect on the correctional constant $C$ for $kT_{BB}$ sources.596 The cllective temperature of a SD progenitor depends crucially on the extent of the emitting region. and the radius of an actual SD accretor therefore does not have to diverge much from that of the theoretical model to make the system unobservable toChandra.," The effective temperature of a SD progenitor depends crucially on the extent of the emitting region, and the radius of an actual SD accretor therefore does not have to diverge much from that of the theoretical model to make the system unobservable to."597 For such lower Aee-sources. UV observations should be more useful than X-rays.," For such lower $kT_{BB}$ -sources, UV observations should be more useful than X-rays."598 However. UV observations of these sources are problematic for other reasons. such as interstellar extinction.," However, UV observations of these sources are problematic for other reasons, such as interstellar extinction."599 eAs discussed by Hachisuetal.(2010).. a significant fraction of the progenitors of SD SNe Ia may spend the final phase of their aceretion towards going SN in the nova regime where their accretion and associated. X-ray. emission will be periodic instead. of continuous.," As discussed by \citet{Hachisu.et.al.2010}, a significant fraction of the progenitors of SD SNe Ia may spend the final phase of their accretion towards going SN in the nova regime where their accretion and associated X-ray emission will be periodic instead of continuous."600 For recent. observations of super-soft. X-ray emissions from novae see Llenzeetal. (2010).. Henzeοἱal. (2011).. Schaefer&Collazzi(2010) ancl Vossetal.(2008).," For recent observations of super-soft X-ray emissions from novae see \citet{Henze.et.al.2010}, \citet{Henze.et.al.2011}, \citet{Schaefer.Collazzi.2010} and \citet{Voss.et.al.2008}."601. elven a steacdilv-accreting massive WD consistent with a naked. canonical SSS may be obseured. by local matter lost from the svstem. sec Nielsenetal. (2011)...," Even a steadily-accreting massive WD consistent with a naked, canonical SSS may be obscured by local matter lost from the system, see \citet{Nielsen.et.al.2011}. ."602 Several recent studies have found indications of the presence. of circumstellar matter. e.g. Gorardyetal.(2004)... Lomailerοἱal. (2006).. Borkowskietal. (2006).. Patatetal. (2007).. Chiotellisetal. (2011).. Sternbergetal. (2011).," Several recent studies have found indications of the presence of circumstellar matter, e.g. \citet{Gerardy.et.al.2004}, \citet{Immler.et.al.2006}, \citet{Borkowski.et.al.2006}, \citet{Patat.et.al.2007}, \citet{Chiotellis.et.al.2011}, \citet{Sternberg.et.al.2011}."603. elf the progenitor is a rapidly rotating WD of the type suggested in DiStefanoetal(2011). the X-ray emission of he progenitor would have ceased long before the explosion itself., If the progenitor is a rapidly rotating WD of the type suggested in \citet{DiStefano.et.al.2011} the X-ray emission of the progenitor would have ceased long before the explosion itself.604 elho detailed spectral shape of the SSS is uncertain (Orio2006).. and the assumption of a black-body spectrum. used in this study may therefore be inaccurate.," The detailed spectral shape of the SSS is uncertain \citep{Orio.2006}, and the assumption of a black-body spectrum used in this study may therefore be inaccurate."605 Due to the uigher sensitivity of Chandra above | keV the upper limits are more constraining forharder spectra., Due to the higher sensitivity of Chandra above 1 keV the upper limits are more constraining forharder spectra.606 This is at most an order of magnitude cdillerent compared to our 150 eV data »oints. for the unrealistic assumption of a powerlaw with whoton index P=2. tvpical of X-ray binaries (c£.," This is at most an order of magnitude different compared to our 150 eV data points, for the unrealistic assumption of a powerlaw with photon index $\Gamma=2$, typical of X-ray binaries (c.f."607 the limits or power Law and black-bods in Lietal.(2011) for 2011£fo)., the limits for power law and black-body in \citet{Li.et.al.2011} for 2011fe).608 elo make things more dillicult. a DD progenitor may also emit soft. N-ravs for a significant period. of time. see Yoonetal.(2007).," To make things more difficult, a DD progenitor may also emit soft X-rays for a significant period of time, see \citet{Yoon.et.al.2007}."609. However. the luminosities expected in this scenario are approximately an order of magnitude lower than for the steaclily-accreting SD progenitor.," However, the luminosities expected in this scenario are approximately an order of magnitude lower than for the steadily-accreting SD progenitor."610 In any case. the detailed: workings of the DD merger are still not fully unclerstoocl (cf. Pakmorctal. 2010.. Lorén-Aguilarctal. 2009.. vanIxerkwijketal. 2010)).," In any case, the detailed workings of the DD merger are still not fully understood (cf. \citealt{Pakmor.et.al.2010}, , \citealt{Loren-Aguilar.et.al.2009}, , \citealt{van.Kerkwijk.et.al.2010}) )."611 Ht is currently unclear if the lighter WD forms a disk aroundthe more massive companion. or if both WDs are disrupted in the course of," It is currently unclear if the lighter WD forms a disk aroundthe more massive companion, or if both WDs are disrupted in the course of"612 (e.g.277???2).. oft (6.5222 ," \citep[e.g.][]{TG78,Davis82,CfaSurvey,Sathy98, 2dF, SloanGreatWall}. \citep[e.g.][]{CosmicWeb, Sathy96, MMF, Hahn07a},"613"(e.g.7?) οολ), (??).. (e.c.7?"," \citep[e.g.][]{CL0016} \citep{Hahn07a,Hahn07b,Hahn09}. \citep{LensingFils2, LensingFils}. \citep[e.g.][]{Kaiser98,LensingFils2,LensingFils},"614 eto (7). 2=0 (e$.?).. (FOF.?).. (7)...," \citep{Dolag06} $z=0$ \citep[e.g.][]{CO99}. \citep[FOF,][]{FOF}, \citep{Shapefinders}."615 ? algorithin for computing the Shapefinders ou structures at an arbitrary deusitv threshold., \citet{SURFGEN} algorithm for computing the Shapefinders on structures at an arbitrary density threshold.616 Miu of those fouud in data aud siaulatious are indeed filamentary. but FOF aleorithnis are optimized for structures that lie above a set density threshold. a condition approximately mot by clusters at the present epoch.," Many of those found in data and simulations are indeed filamentary, but FOF algorithms are optimized for structures that lie above a set density threshold, a condition approximately met by clusters at the present epoch."617 Filaments and walls. however. are not bound and a strict density cut alone would not provide clean samples of such structures.," Filaments and walls, however, are not bound and a strict density cut alone would not provide clean samples of such structures."618 Another aleorithim. called the Skeleton (???).. identifies filaments by searching for saddle poiuts iu a density field aud then followine the deusitv eracicut along the filament πι] it reaches a local πιαπια.," Another algorithm, called the Skeleton \citep{Skeleton,SkeletonData,Skeleton3D}, identifies filaments by searching for saddle points in a density field and then following the density gradient along the filament until it reaches a local maximum."619 Although it appears to be effective at making an outline of the cosmic network. it lacks an intuitive definition of filament euds.," Although it appears to be effective at making an outline of the cosmic network, it lacks an intuitive definition of filament ends."620 ο also lacks such definition. but has been successful at tracing the filament uetwork in cosmological siauulations using watershed scemeutation (seealso7) aud a Delaunay tessellation deusitv estimator (?7)..," \citet{SpineWeb} also lacks such definition, but has been successful at tracing the filament network in cosmological simulations using watershed segmentation \citep[see also][]{Platen07} and a Delaunay tessellation density estimator \citep{Schaap00}."621 If we wish to analyze filamcut leugth distributions or their spatial relationship to clusters. it is iniportant to separate individual filaments iu the cosmic web.," If we wish to analyze filament length distributions or their spatial relationship to clusters, it is important to separate individual filaments in the cosmic web."622 Structure-finding techniques that onlv detect filaments between galaxy cluster pairs (e.g.777) would preseut a biased view of the flameut-clister relationship.," Structure-finding techniques that only detect filaments between galaxy cluster pairs \citep[e.g.][]{Pimbblet05a,Colberg05,GP09} would present a biased view of the filament-cluster relationship."623— An carly technique for ideutifving filaments iu two-dimensional data was developed by ? that works onu a similar principle to the algorithu described iu this paper., An early technique for identifying filaments in two-dimensional data was developed by \citet{GottFil} that works on a similar principle to the algorithm described in this paper.624 It divides the density ficld iuto a pixelized erid and ideutifics as fllameut clements any ericd cell that has a larecr deusity than its imaueciate neighbors along two of the four axes (includiug thetwo coordinate axes and two axes at 15? angeles to theerid)throughthegrid cell., It divides the density field into a pixelized grid and identifies as filament elements any grid cell that has a larger density than its immediate neighbors along two of the four axes (including thetwo coordinate axes and two axes at $45^\circ$ angles to thegrid)throughthegrid cell.625Thealgorithmwasrunon the Shanc- galaxy count catalogue (?).. but has uot,"Thealgorithmwasrunon the Shane-Wirtanen galaxy count catalogue \citep{ShaneWirtanen}, , but has not"626Foreground uncertainties are always a concern at large aneular scales for CAIB experiments aud a most natural first candidate to consider.,Foreground uncertainties are always a concern at large angular scales for CMB experiments and a most natural first candidate to consider.627 First. we note that the four spectra shown in Figure d. are computed from slightly differcut data sets: The spectrum is based ou the ILC imap with a directly downgraded (1.6.. not expauded) Wp? mask for (<12 and on the template-corrected V- and W-bands with the hieliesolution I&p2 cut at (6>12: the Cübbs spectra are based ou the template-corrected V-bands and the full-resolution Ip2 cut at all scales: the AIL estimate is computed from the degraded. teiiplate-corrected. V-baud. cut with the expanded I&p2 mask.," First, we note that the four spectra shown in Figure \ref{fig:powspec_lowl} are computed from slightly different data sets: The spectrum is based on the ILC map with a directly downgraded (i.e., not expanded) Kp2 mask for $\ell \le 12$ and on the template-corrected V- and W-bands with the high-resolution Kp2 cut at $\ell > 12$; the Gibbs spectra are based on the template-corrected V-bands and the full-resolution Kp2 cut at all scales; the ML estimate is computed from the degraded template-corrected V-band, cut with the expanded Kp2 mask."628 To assess the πηρα of residual foreerounds in the f power spectra. we show in Figure 2. the ML power spectra computed from the ILC aud template-corrected V-band maps. with both the original Ip2 aud extended Kp2e sky cuts.," To assess the impact of residual foregrounds in the $\ell$ power spectra, we show in Figure \ref{fig:powspec_lowl_cut} the ML power spectra computed from the ILC and template-corrected V-band maps, with both the original Kp2 and extended Kp2e sky cuts."629 A noticable trend is clearly visible in this range. in that there is a significant loss of power between he Ip2 aud Ip2e cut for both the ILC and V-baud naps.," A noticable trend is clearly visible in this range, in that there is a significant loss of power between the Kp2 and Kp2e cut for both the ILC and V-band maps."630" This implies that there is considerable additional over tn the uecar-ealactic pixels in tle Kp2 slaw cut relative to the 7%I&p2e cut for both maps. and both maps are most likely coutamunated at some level near the mask vomdlaries,"," This implies that there is considerable additional power in the near-galactic pixels in the Kp2 sky cut relative to the Kp2e cut for both maps, and both maps are most likely contaminated at some level near the mask boundaries."631 Ou the other laud. after expanding the mask he two spectra are quite similar. possibly indicating that one is fairly safe after expanucing the mask. aud that the Hel latitude residuals are small compared to the CMD Huctuatious.," On the other hand, after expanding the mask the two spectra are quite similar, possibly indicating that one is fairly safe after expanding the mask, and that the high latitude residuals are small compared to the CMB fluctuations."632 While the mask explanation can account for some of he discrepaucics secu in Figure 1. it only docs so at ες12 where a pixel-based likelihood evaluation is used wv the team.," While the mask explanation can account for some of the discrepancies seen in Figure \ref{fig:powspec_lowl}, it only does so at $\ell \le63312$ where a pixel-based likelihood evaluation is used by the team."634 For (>12 a MASTER-based ikchhood is used which is based on the full-resolution cluplate-corrected data., For $\ell > 12$ a MASTER-based likelihood is used which is based on the full-resolution template-corrected data.635 The small discrepancies seeu in the range between 12«(X30 is therefore due o differeuces dn statistical treatiment. and not data selection.," The small discrepancies seen in the range between $12 < \ell \lesssim 30$ is therefore due to differences in statistical treatment, and not data selection."636 A αι question is therefore the following: For what (- docs the MASTER-based likelihood approximation provide anu acceptable fit to the exact likelihood?, A main question is therefore the following: For what $\ell$ -range does the MASTER-based likelihood approximation provide an acceptable fit to the exact likelihood?637 Frou Figure d it secs clear that (a4<12 is uot sufiicicut. while οςx50 is quite likely more than enough.," From Figure \ref{fig:powspec_lowl} it seems clear that $\ell_{\textrm{exact}} \le 12$ is not sufficient, while $\ell_{\textrm{exact}} \le 50$ is quite likely more than enough."638 It is difheult to answer this question based on a power spectrin plot alouc. and we will therefore return to this question in Section 6 where we estimate cosmological parameters with various likelihoods.," It is difficult to answer this question based on a power spectrum plot alone, and we will therefore return to this question in Section \ref{sec:parameters} where we estimate cosmological parameters with various likelihoods."639 Iu order to further illuniuate the above sues. we show in Figure 3) a set of different likelihood (and posterior) distributions computed from the data.," In order to further illuminate the above issues, we show in Figure \ref{fig:likelihoods} a set of different likelihood (and posterior) distributions computed from the data."640" The vertical dashed lines show the biuned best-fit ACDM spectrui aud the curves show the likelihoods (black). Gibbs | Dlackwell--Rao posterior distributions (red/orauge) and MCMC posterior distributions (blue/ereen). respectively,"," The vertical dashed lines show the binned best-fit $\Lambda$ CDM spectrum and the curves show the likelihoods (black), Gibbs + Blackwell-Rao posterior distributions (red/orange) and MCMC posterior distributions (blue/green), respectively."641— Two sigma coufideuce— regious relative to the Cübbs distributions with uniforiu priors (red curves) are indicated by horizontal dotted lines., Two sigma confidence regions relative to the Gibbs distributions with uniform priors (red curves) are indicated by horizontal dotted lines.642 Many interesting poiuts may be seen in this figure: We now consider the iuterinediate- and sinall-scale parts of the power spectrum., Many interesting points may be seen in this figure: We now consider the intermediate- and small-scale parts of the power spectrum.643 Since we study fullresolutiou data in this section. the direct likelihood evaluation techniques are no longer available to us.," Since we study full-resolution data in this section, the direct likelihood evaluation techniques are no longer available to us."644 However. ou these scales the MASTER aleorithius are applicable. aud we once again have multiple methods available for eross-checkiug purposes.," However, on these scales the MASTER algorithms are applicable, and we once again have multiple methods available for cross-checking purposes."645 In total four different codes are used. namely Conunander (Cabbs sampling: uniform prior). MAGIC (Cabbs sampling: Jeffrews prior) ALTASTERest and \IASTERint.," In total four different codes are used, namely Commander (Gibbs sampling; uniform prior), MAGIC (Gibbs sampling; Jeffrey's prior), MASTERext and MASTERint."646 For the Cübbs analyses we consider oulv the V-baud data: the Q-band is considered to be too foreground contaminated for reliable analysis. aud the W-banud exhibits strong correlated noise that significantly biases auv auto-correlation iuethod (Ilhushawetal.2006).," For the Gibbs analyses we consider only the V-band data; the Q-band is considered to be too foreground contaminated for reliable analysis, and the W-band exhibits strong correlated noise that significantly biases any auto-correlation method \citep{hinshaw:2006}."647. This has been verified i our analyses. iud we exclude these hands eutirelv. from the Cübbs analyses.," This has been verified in our analyses, and we exclude these bands entirely from the Gibbs analyses."648 Next. we analyzed the data with both Commander aud MAGIC. and obtained identical results (up to convergence) ou," Next, we analyzed the data with both Commander and MAGIC, and obtained identical results (up to convergence) on"649The A-band nuage was registered to theZZ9T optical image on the APM coordinate systeii using the galaxies AIL and ALS.,The $K$ -band image was registered to the optical image on the APM coordinate system using the galaxies M1 and M8.650 The optical astrometry in theZ/9 iuaee las an rns uncertainty of only 072., The optical astrometry in the image has an rms uncertainty of only $0\farcs2$.651 Tlowever. the doimiuaut source of registration eror iu comparing the A-banud data with the radio and ΕΕ data is due to the svsteimatic offsets between the APM svstem aud the radio reference fine (Joliuston et al.," However, the dominant source of registration error in comparing the $K$ -band data with the radio and mm data is due to the systematic offsets between the APM system and the radio reference frame (Johnston et al."652 1995)., 1995).653" These offsets may be as large as 1"" which we adopt as a conservative estimate of the total error iu the A-band position.", These offsets may be as large as $1\arcsec$ which we adopt as a conservative estimate of the total error in the $K$ -band position.654 The positional error for the uum source is 075., The positional error for the mm source is $0\farcs5$.655" This includes a systematic astromietrv certainty of 073 frou, calibration combined in quadrature with the statistical error related to the signaltonoise (S/N) of approximately OL (05/|5/N |).", This includes a systematic astrometry uncertainty of $0\farcs3$ from calibration combined in quadrature with the statistical error related to the signal–to–noise (S/N) of approximately $0\farcs4$ $\theta_{b}/[S/N]$ ).656" The ccn radio data lave a svuthesize beam size of 5"" and a positional error of about (75 (05/|S/N]Y.", The cm radio data have a synthesize beam size of $5\arcsec$ and a positional error of about $0\farcs8$ $\theta_{b}/[S/N]$ ).657 The 850j1n source detected by SCUBA has a positional accuracy of approximately 37 (Saul et al., The $\mu$ m source detected by SCUBA has a positional accuracy of approximately $3\arcsec$ (Smail et al.658 1998)., 1998).659" The positions. of JJ00266|1708. measured at ccm. 1.2. 850542. and 2.2,0u are all consisteut with each other within the errors (Table 1)."," The positions of J00266+1708 measured at cm, mm, $\mu$ m, and $2.2\mu$ m are all consistent with each other within the errors (Table 1)."660 The positional coincidence alone suggests an association between the sources af different wavelcneths., The positional coincidence alone suggests an association between the sources at different wavelengths.661 The probability of raudomly finding a 22.5 mag A-band galaxy within a 1 square-aresee box is oulw1%.. based on the observed. A-baud surface densities of galaxies (Djorgovski et 11995: Aloustakas et 11997).," The probability of randomly finding a 22.5 mag $K$ -band galaxy within a 1 square-arcsec box is only, based on the observed $K$ -band surface densities of galaxies (Djorgovski et 1995; Moustakas et 1997)."662 By taking iuto account the red nature of the galaxv (foAK 36). the likelihood of a raudon association decreases evel more.," By taking into account the red nature of the galaxy $I-K>3.6$ ), the likelihood of a random association decreases even more."663 Oulv about Q faint galaxies (22.0<AKx 22.9) have (IZ.Iv)23.5 (Mkmstakas et 11997)., Only about of faint galaxies $22.0 \leq K \leq 22.9$ ) have $(I-K)>3.5$ (Moustakas et 1997).664 Hence. the probability of a chiaice association of such a faint red galaxw with the uuu source is only 107.," Hence, the probability of a chance association of such a faint red galaxy with the mm source is only $10^{-3}$."665 An even stronger case cul be made on the association between the radio source aud the 1.2nuuu source., An even stronger case can be made on the association between the radio source and the mm source.666 Badio source counts (Richards et 11999: Richards 2000) imply the probability of ταςοι] finding such a strong radio source within 1 square arcsec of the uum source is ouly about 10.7., Radio source counts (Richards et 1999; Richards 2000) imply the probability of randomly finding such a strong radio source within 1 square arcsec of the mm source is only about $10^{-5}$.667 We conclude the sources detected at 210012. 1.21. 85042. and. 2.2/0 are all likely associated with each other.," We conclude the sources detected at cm, mm, $\mu$ m, and $2.2\mu$ m are all likely associated with each other."668 Table 1 preseuts the flux density micasurements and upper-limits observed for JJ00266|1708., Table 1 presents the flux density measurements and upper-limits observed for J00266+1708.669 The ccm radio data are preseuted by Simail et ((2000a)., The cm radio data are presented by Smail et (2000a).670 We measure a flix deusity of 91+15μ.]ν fex the ccm radio ποιος bv fittiis a Cuussian to the unresolved. eissiou., We measure a flux density of $94\pm15 \muJy$ for the cm radio source by fitting a Gaussian to the unresolved emission.671 We also report a ccm upper-limit forthe galaxy based οι Selsitive oervatious of the cluster (A. R. Cooray. private comnication).," We also report a cm upper-limit for the galaxy based on sensitive observations of the cluster (A. R. Cooray, private communication)."672 The sub-nuu flux at 8S5Ojan has been previously tabulaed by Barger et ((1999). and the 1504i upper nuit is diseussed by στα] et (20000).," The sub-mm flux at $\mu$ m has been previously tabulated by Barger et (1999), and the $\mu$ m upper limit is discussed by Smail et (2000b)."673 The optical Z-baud Hluit of µας is derived from the olservatiois preseuted by Suudl et ((1998)., The optical $I$ -band limit of mag is derived from the observations presented by Smail et (1998).674. The l.1121ü and A-bouk nueasurenmentas ire based on the observations preseuted in this paper., The mm and $K$ -band measurements are based on the observations presented in this paper.675 As stated eurlier (82lL). 00566|1708 is thought o lie at a high redsuft of;>2 used on the sub-un/radio spectral uklex of the ealaxy (Cil Yun 1999: Snail et 2200Ja).," As stated earlier 2.1), J00266+1708 is thought to lie at a high redshift of $z\ga2$ based on the sub-mm/radio spectral index of the galaxy (Carilli Yun 1999; Smail et 2000a)."676 High redshifts are also required Q acccount for the low £50410/8504 n ratio. assuniues dust «ημοι. with properties simular to that found iu QW-1edshitt hunuinous starbursts (Dume et 22000).," High redshifts are also required to account for the low $\mu$ $\mu$ m ratio, assuming dust emission with properties similar to that found in low-redshift luminous starbursts (Dunne et 2000)."677 The ootical aud NIR iaagiug data by hemselves provide ittle COistradnt on the redshift of JJO00266|1708 eiven the wide rauge of optical/NIR properties found for he sbau population (e.g.. Ivison e 220002).," The optical and NIR imaging data by themselves provide little constraint on the redshift of J00266+1708 given the wide range of optical/NIR properties found for the sub-mm population (e.g., Ivison et 2000a)."678 The Ost oredshift constraints for JJ0266|1708. come yw fitine the spectral energy distribuion (SED) of the ealaxy frou radio to sub-uuu waveloneths., The best redshift constraints for J00266+1708 come by fitting the spectral energy distribution (SED) of the galaxy from radio to sub-mm wavelengths.679 Figure 3 slows he olserved SEDs of the low redshift ULIGs 2220 aud 2231 (Rigopoulou. Lawrence. Rowau-Bobiuson 1996). as πο as the +=1.11 extremely red galaxy. (ERO) IIR10 (Dey et 11999). the relativelv blue sub-uuau starbrst SAIALTJIL4011|0252 Uvison ¢t 220002). ancl the sub-uun galaxy JJ02399-0136 which contains au AGN (Ivison et 11998).," Figure 3 shows the observed SEDs of the low redshift ULIGs 220 and 231 (Rigopoulou, Lawrence, Rowan-Robinson 1996), as well as the $z=1.44$ extremely red galaxy (ERO) HR10 (Dey et 1999), the relatively blue sub-mm starburst J14011+0252 (Ivison et 2000a), and the sub-mm galaxy J02399-0136 which contains an AGN (Ivison et 1998)."680 These ULIC svstenis are choseu for couparison since they represent the reasonable range of possible SEDs expected for the sub-nuu. population., These ULIG systems are chosen for comparison since they represent the reasonable range of possible SEDs expected for the sub-mm population.681 Asstune a likely range of dust teiiper‘atures ITI) aud füting all the data to the nearest 05 vedshitt unit. we," Assuming a likely range of dust temperatures K) and fitting all the data to the nearest 0.5 redshift unit, we"682"T>5x10°K ina fully ionized plasma, the scaling quantities are found to be connected by the following relations: Εα.","$T \geq6835\times10^{6}\, \rm{K}\,$ in a fully ionized plasma, the scaling quantities are found to be connected by the following relations: Eq."684" [ΑδΙ was derived from the scaling of the cooling term, and the final equation (eq.[A9))"," \ref{eq:cool} was derived from the scaling of the cooling term, and the final equation (eq. \ref{eq:pjet}) )"685 derives assuming the following scaling of jet’s power: JοςJoQ. Note that Eq., derives assuming the following scaling of jet's power: $J \propto J_{0} Q^{i_{\mathrm{J}}}$ Note that Eq.686[A8] is different from Eq. (, \ref{eq:cool} is different from Eq. (68715) of Tang Wang (2009).,15) of Tang Wang (2009).688" The latter reads: iy=—3i,+SizO.5ir."," The latter reads: $i_{M} = -3i_{t} + 5i_{L} +6890.5i_{T}$."690" Our derivation is obtained starting from the scaling of the right-hand side terms: O(pe)/Ot~iptie—=im—3i;+2(iji)ij=iyi, 3i, where the symbol “~” denotes the power law scaling index."," Our derivation is obtained starting from the scaling of the right-hand side terms: $\partial\left(\rho e\right)/\partial t691\sim i_{\rho} + i_{e} - i_{t} = i_{M} -3i_{L} + 2(i_{L} - i_{t}) -692i_{t} = i_{M} - i_{L} - 3i_{t}$ , where the symbol $\sim$ ” denotes the power law scaling index."693" The number density scales as n~p and, therefore, the cooling term scales as L—2iy6i;+0.5ir."," The number density scales as $n\sim\rho$ and, therefore, the cooling term scales as $L \sim6942i_{M}-6i_{L} + 0.5i_{T}$."695" Thus, by equating the two terms, we have: iy—ij3i;=2iy6ἱι+0.5ir, which gives Eq. [A8]."," Thus, by equating the two terms, we have: $i_{M} - i_{L} - 3i_{t} =2i_{M}-6i_{L} + 0.5i_{T}$, which gives Eq. \ref{eq:cool}."696" As described by Tang Wang (2009), this linear system is completely specified after the choice of 2 of the coefficients."," As described by Tang Wang (2009), this linear system is completely specified after the choice of 2 of the coefficients."697" We choose to fix the scaling coefficients for length and time, i, and i;, and find Thus, a given solution (also numerical) can be rescaled by means of Eqs. (A10))"," We choose to fix the scaling coefficients for length and time, $i_{L}$ and $i_{t}$, and find Thus, a given solution (also numerical) can be rescaled by means of Eqs. \ref{sys}) )"698 to a different jet’s power using scalings coefficients., to a different jet's power using scalings coefficients.699" To produce an intensity map of the SZ effect by a cocoon surrounding a less powerful jet using the dynamical scaling of cocoon we choose scaling parameters equaled: Q=10, i,=—0.2, and i,= —0.05."," To produce an intensity map of the SZ effect by a cocoon surrounding a less powerful jet using the dynamical scaling of cocoon we choose scaling parameters equaled: $Q=10$, $i_L=-0.2$, and $i_t=-0.05$ ."700" The scaled power injected by the jet is 10435 erg/s and the scaled size of the simulation box is 25h.., kpc.", The scaled power injected by the jet is $10^{45}$ erg/s and the scaled size of the simulation box is $h_{-1}$ kpc.701 The intensity map of the SZ effect at a frequency 217 GHz derived from the scaling of the simulation maps of the gas pressure and temperature is plotted in Fig. [Al]., The intensity map of the SZ effect at a frequency 217 GHz derived from the scaling of the simulation maps of the gas pressure and temperature is plotted in Fig. \ref{sz-scaling}.702 Thus a new intensity map of the SZ effect can be found for cocoons evolving in different ISM by means of one particular simulation and of the dynamical scaling., Thus a new intensity map of the SZ effect can be found for cocoons evolving in different ISM by means of one particular simulation and of the dynamical scaling.703" Therefore, the dynamical scaling is a promising method to produce the intensity maps of the SZ effect by hot gas residing in AGN cocoons in different ISM."," Therefore, the dynamical scaling is a promising method to produce the intensity maps of the SZ effect by hot gas residing in AGN cocoons in different ISM."704 In Appendix B we show how the broad detector spectral response impacts on the possibility of an analysis of high temperature plasmas., In Appendix B we show how the broad detector spectral response impacts on the possibility of an analysis of high temperature plasmas.705 We convolve the spectral function g(x) over a Gaussian detector response centered at 217 GHz as it was done by Shimon Rephaeli (2003)., We convolve the spectral function $g(x)$ over a Gaussian detector response centered at 217 GHz as it was done by Shimon Rephaeli (2003).706 The signal at a frequency of 217 GHz from a low-temperature plasma which arises due to the convolution over a spectral response is shown in Fig., The signal at a frequency of 217 GHz from a low-temperature plasma which arises due to the convolution over a spectral response is shown in Fig.707 B.1 as a function of the FWHM of the Gaussian detector response., B.1 as a function of the FWHM of the Gaussian detector response.708 The contribution of the SZ signal at a frequency of 217 GHz due to the convolution over a spectral response with the FWHM <30 GHz is far smaller than the SZ signal due to the presence of high temperature plasmas (see Fig. [2)), The contribution of the SZ signal at a frequency of 217 GHz due to the convolution over a spectral response with the FWHM $<30$ GHz is far smaller than the SZ signal due to the presence of high temperature plasmas (see Fig. \ref{Fig217}) )709" and, therefore, the SZ effect at frequency of 217 GHz is a promising tool for analyzing the hot electron component in an AGN cocoon ifthe FWHM of a spectral response is smaller than 30 GHz."," and, therefore, the SZ effect at frequency of 217 GHz is a promising tool for analyzing the hot electron component in an AGN cocoon ifthe FWHM of a spectral response is smaller than 30 GHz."710Infrared polarimetric studies of low-mass X-ray. binaries (LAINBs: where a compact object a black hole or a neutron star accretes from a companion star due to Roche lobe overllow)— are few and far between.,Infrared polarimetric studies of low-mass X-ray binaries (LMXBs; where a compact object – a black hole or a neutron star – accretes from a companion star due to Roche lobe overflow) are few and far between.711 However. such studies can provide information about the physical conditions of the svstem and inner accretion How.," However, such studies can provide information about the physical conditions of the system and inner accretion flow."712 Most. raciation from LMXDs is expected to be unpolarised. for example therma blackbody radiation from the accretion disc or companion star.," Most radiation from LMXBs is expected to be unpolarised, for example thermal blackbody radiation from the accretion disc or companion star."713 The scattering. of unpolarisecl photons could. resul in a small degree of net polarisation in certain. geonietries (e.g.Dolan1984)., The scattering of unpolarised photons could result in a small degree of net polarisation in certain geometries \citep[e.g.][]{dola84}.714. Phere is one emission mechanism presen in LAINBs (that. intrinsically produces. polarised light svnchrotron emission., There is one emission mechanism present in LMXBs that intrinsically produces polarised light – synchrotron emission.715 It has been known for decades tha optically thin svnchrotron radiation can produce a high leve (tens of percent) of linear. polarisation if the magnetic fiel structure is ordered. (c.g.Westlolel1959:Ijórnsson&Blu-menthal 1982).," It has been known for decades that optically thin synchrotron radiation can produce a high level (tens of percent) of linear polarisation if the magnetic field structure is ordered \citep[e.g.][]{west59,bjorbl82}."716. Linear polarisation (LP) of black hole X-ray binaries (DILXNDs) is measured at racio frequencies at à level of ~1 in a number of sources in an X-ray lowhard state. anc up to 30% during transient radio events associated with X-ray state transitions and jet ejections (for à review see Fender2006 and see e.g. Homan&Belloni2005— anc AMeClintock&ltemillard2006/— for. the definitions of X-pav states).," Linear polarisation (LP) of black hole X-ray binaries (BHXBs) is measured at radio frequencies at a level of $\sim 1$ in a number of sources in an X-ray low/hard state, and up to $\sim 30$ during transient radio events associated with X-ray state transitions and jet ejections (for a review see \citealt{fend06} and see e.g. \citealt{homabe05} and \citealt{mcclet06} for the definitions of X-ray states)."717 The radio emission of LAINBs is svnchrotron in nature and ubiquitously originates in their collimatec jets in both black hole ancl neutron star systems. (e.g.Fender2006:Migliari&Fender. 2006).," The radio emission of LMXBs is synchrotron in nature and ubiquitously originates in their collimated jets in both black hole and neutron star systems \citep[e.g.][]{fend06,miglfe06}."718. During transien jetejections the svnchrotron spectrum is optically thin. with a negative spectral index a (where [5x 607).," During transient jetejections the synchrotron spectrum is optically thin, with a negative spectral index $\alpha$ (where $F_{\nu} \propto \nu^{\alpha}$ )."719 For optically thin svnchrotron emission. a strong LP signal is expected. of order f. where f can be considered to crucely parameterise the degree of ordering of the large scale magnetic field (Itvbicki&Lightman1979:DBjórnssonBlu- 1982)..," For optically thin synchrotron emission, a strong LP signal is expected, of order $\times$ $f$, where $f$ can be considered to crudely parameterise the degree of ordering of the large scale magnetic field \citep{rybili79,bjorbl82}. ."720 Phe high polarisation levels measured in the radio from these optically thin ejections have indicated that, The high polarisation levels measured in the radio from these optically thin ejections have indicated that721sublialo distribution of cluster galaxies in simulations docs uot match the observed distributions of cluster galaxies: veal cluster galaxies trace the dark matter profile. while siauulated cluster galaxies are siguificautly autibiased in cluster centers. likely due to the resilience of the stellar conrponeut of a subhalo against tidal disruption relative to the total sublalo (e.g..?2?3..,"subhalo distribution of cluster galaxies in simulations does not match the observed distributions of cluster galaxies: real cluster galaxies trace the dark matter profile, while simulated cluster galaxies are significantly antibiased in cluster centers, likely due to the resilience of the stellar component of a subhalo against tidal disruption relative to the total subhalo \citep[e.g.,][]{diemand04,722faltenbacher06}."723 The details of velocity bias depend also on the selection used to ideutify subhlalooes. e.g.. Whether sublialo mass is 11easured prior to or after a subhalo euters the cluster (2)..," The details of velocity bias depend also on the selection used to identify subhaloes, e.g., whether subhalo mass is measured prior to or after a subhalo enters the cluster \citep{faltenbacher06}."724 The amount of velocity bias in Simulations is typically —1056 for cluster-size haloes. although disaerecnieut remains on whether this bias is oositive or negative.," The amount of velocity bias in simulations is typically $\sim$ for cluster-size haloes, although disagreement remains on whether this bias is positive or negative."725 Velocity bias of this size would cad to virial masses overestimated or muclerestimated by ~20%.., Velocity bias of this size would lead to virial masses overestimated or underestimated by $\sim$.726" Future work is clearly needed to muderstand the lature and significance of velocity bias for cluster mass estimates,", Future work is clearly needed to understand the nature and significance of velocity bias for cluster mass estimates.727 There is no clear evidence from observatious in favor of or against velocity bias iu clusters. although he generally good agreemieut between X-ray. leuxiug. aud vial mass estinates sugeests that anv velocity bias is rot large (5οἱ[IMce.222).," There is no clear evidence from observations in favor of or against velocity bias in clusters, although the generally good agreement between X-ray, lensing, and virial mass estimates suggests that any velocity bias is not large \citep[$\lesssim$20\%;728e.g.,][]{girardi98,popesso04,diaferio05}."729 Because siguificaut velocity jas would produce incorrect virial mass estimates; the agreement between virial and caustic mass estimates 15 no euarantee that the caustic mass estimates are accurate.," Because significant velocity bias would produce incorrect virial mass estimates, the agreement between virial and caustic mass estimates is no guarantee that the caustic mass estimates are accurate."730 However. the mechanisms which cause velocity bias are less effective in the outskirts of clusters. so the caustic technique should be less affected by velocity bias thau estimates based on σαν analysis.," However, the mechanisms which cause velocity bias are less effective in the outskirts of clusters, so the caustic technique should be less affected by velocity bias than estimates based on Jeans' analysis."731 Analysis of simulatious of laree-scale structure with very large dviuuic range (2) or of individual clusters (7) lay provide a clearer uuderstanding of the poteutial iupact of velocity bias on cluster niass estimates from galaxy kinematics., Analysis of simulations of large-scale structure with very large dynamic range \citep{springel05} or of individual clusters \citep{borgani06} may provide a clearer understanding of the potential impact of velocity bias on cluster mass estimates from galaxy kinematics.732 Another common assunption is that the kinenities of galaxies are independent of thei luminosities., Another common assumption is that the kinematics of galaxies are independent of their luminosities.733 The consistency of CAIRNS ass profiles and velocity dispersion profiles for A-baud hunuinositv-luuited. aud deeper samples indicates that this is a reasonable approximation (?).. but theoretical models of subhalocs sugeest that velocity bias should depend on luuinosity (?)..," The consistency of CAIRNS mass profiles and velocity dispersion profiles for $K_s$ -band luminosity-limited and deeper samples indicates that this is a reasonable approximation \citep{cairnsii}, but theoretical models of subhaloes suggest that velocity bias should depend on luminosity \citep{2006MNRAS.366.1455S}."734 We plan to use the CIRS sample to test this assunptiou iu future work bv studviug the hwuninositv dependence of the kinematic distribution of gulaxies., We plan to use the CIRS sample to test this assumption in future work by studying the luminosity dependence of the kinematic distribution of galaxies.735 Note that the CIRS clusters are sampled to depths of ~AL* |1 for the most distaut clusters to ~AL° |7 for Virgo. so the CIRS caustics sample a wide range of hDwunuinositv Iunits.," Note that the CIRS clusters are sampled to depths of $\sim$$M^*$ +1 for the most distant clusters to $\sim$$M^*$ +7 for Virgo, so the CIRS caustics sample a wide range of luminosity limits."736 We coufirim that the ratio of virial to caustic mass estimates in an N-rav huuinositv-liuüted sample shows uo significant trend with redshift. iudicatius that the different spectroscopic sampling limits do not affect these conrparisous.," We confirm that the ratio of virial to caustic mass estimates in an X-ray luminosity-limited sample shows no significant trend with redshift, indicating that the different spectroscopic sampling limits do not affect these comparisons."737 Simularly. the ratio of caustic masses to rav luminosities is not significantlv differeut for au N-rav hunimositv-Dnuuited sample.," Similarly, the ratio of caustic masses to X-ray luminosities is not significantly different for an X-ray luminosity-limited sample."738 These results sugeest that any velocity bias does not depend strouglv on galaxy DIuniuositv., These results suggest that any velocity bias does not depend strongly on galaxy luminosity.739 We defer further discussion to future work., We defer further discussion to future work.740 We apply the virial mass aud projected mass estimators (?) to the CIRS clusters., We apply the virial mass and projected mass estimators \citep{htb} to the CIRS clusters.741 For the latter. we assume the ealaxies are on isotropic orbits.," For the latter, we assume the galaxies are on isotropic orbits."742 We iust defiue a radius of virialization within which the galaxies are relaxed., We must define a radius of virialization within which the galaxies are relaxed.743 We use rogg (Table 9)) and include ouly galaxies withiu the caustics., We use $r_{200}$ (Table \ref{radii}) ) and include only galaxies within the caustics.744 We thus assune that the caustics provide a eood division between cluster galaxies aud iuterlopers (see Figures ??—71))., We thus assume that the caustics provide a good division between cluster galaxies and interlopers (see Figures \ref{allcirs1}- \ref{allcirs6}) ).745" We calculate the virial mass according to where Rpy=2N(ND/Sκ»,LSE ds the projected virial radius aud =Mtο(ΑΔ1)."," We calculate the virial mass according to where $R_{PV} = 2N(N-1)/\sum_{i,j>i}R_{ij}^{-1}$ is the projected virial radius and $\sigma_p^2 = \sum_i (v_i-\bar v)^2/(N-1)$."746 IE the system does not lie eutirelv0. within rogg. a surface pressure terni 3PV should be added to the usual virial theoreia so that OT|U—3PV.," If the system does not lie entirely within $r_{200}$, a surface pressure term 3PV should be added to the usual virial theorem so that $2T + U = 3PV$."747" The virial mass is then an overestimate of the mass within roy) by the fractional amount where 9,(rogo) Is the radial velocity dispersion at rogo and eo(rogo) is the euclosed total velocity dispersion within r)oo (em.7)."," The virial mass is then an overestimate of the mass within $r_{200}$ by the fractional amount where $\sigma_r (r_{200})$ is the radial velocity dispersion at $r_{200}$ and $\sigma (<r_{200})$ is the enclosed total velocity dispersion within $r_{200}$ \citep[e.g.,][]{girardi98}."748" Iu the limiting cases of circular. isotropic. and radial orbits. the maxima value of the term involving the velocity dispersion is 0. 1/3. aud 1 respectively,"," In the limiting cases of circular, isotropic, and radial orbits, the maximum value of the term involving the velocity dispersion is 0, 1/3, and 1 respectively."749 The projected mass estimator is more robust in the presence of close pairs., The projected mass estimator is more robust in the presence of close pairs.750 The projected mass is where we assune isotropic orbits and ao continuous mass distribution., The projected mass is where we assume isotropic orbits and a continuous mass distribution.751" If the orbits are purele radial or purely οποίαν, the factor 32 becomes 61 or 16 respectively,"," If the orbits are purely radial or purely circular, the factor 32 becomes 64 or 16 respectively."752 We estimate the uncertainties using the Dluitiug fractional wncertaiutics 7loNyenU? foy the virial theorem aud zLLN7 for the projected nase.," We estimate the uncertainties using the limiting fractional uncertainties $\pi^{-1} (2 \mbox{ln}753N)^{1/2}N^{-1/2}$ for the virial theorem and $\approx 1.4 N^{-1/2}$ for the projected mass."754 These uncertednties do not inclide systematic uucertainties due to membership determination or the asstuuption of isotropic orbits in the projected mass estimator., These uncertainties do not include systematic uncertainties due to membership determination or the assumption of isotropic orbits in the projected mass estimator.755" Table 12. lists the virial and projected mass estimates,", Table \ref{virial} lists the virial and projected mass estimates.756 Figure ?? compare the virial aud caustic mass estimates at rogg., Figure \ref{cirsvc} compare the virial and caustic mass estimates at $r_{200}$.757" The mean ratios of these estimates are AL./AL,.= LOLEO.OL.", The mean ratios of these estimates are $M_c/M_v = 1.01 \pm 0.04$ .758" The caustic mass estimates are consistent with viral nmaass estimates even assumuue a correction factor C5ο024,4, Consistent with the best-fit NEW profiles (scealso?"," The caustic mass estimates are consistent with virial mass estimates even assuming a correction factor $C\approx 0.1-0.2 M_{vir}$, consistent with the best-fit NFW profiles \citep[see also ][]{cye97,girardi98,kg2000,cairnsi}."759 Figures 77-777 compare the mass profiles estimated from the caustics. virial theorem. and projected mass estimator.," Figures \ref{allcirsm1}- \ref{allcirsm6} compare the mass profiles estimated from the caustics, virial theorem, and projected mass estimator."760 In the caustic technique. errors on the mass profiles are estimated by the inverse of the peak of the ealaxy προ density in the redshift diagrams.," In the caustic technique, errors on the mass profiles are estimated by the inverse of the peak of the galaxy number density in the redshift diagrams."761 The errors derived with this recipe aeree with the typical spread of mass profiles measured in simulated clusters (D99. Diaferio et al 2006. in prep).," The errors derived with this recipe agree with the typical spread of mass profiles measured in simulated clusters (D99, Diaferio et al 2006, in prep)."762 The projected mass estimator consistently overestimates the mass at small radii aud uuderestimates the mass at large radii relative to the other profiles., The projected mass estimator consistently overestimates the mass at small radii and underestimates the mass at large radii relative to the other profiles.763 This behavior sugeests that this estimator is best for estimating virial masses but not mass profiles., This behavior suggests that this estimator is best for estimating virial masses but not mass profiles.764 The virial and caustic mass profiles eecnerally agree although there are many clusters with large disagreenmieuts., The virial and caustic mass profiles generally agree although there are many clusters with large disagreements.765 The caustic mass profiles do uot appear to consisteutlv overestimate or underestimate the mass relative to the virial mass profiles., The caustic mass profiles do not appear to consistently overestimate or underestimate the mass relative to the virial mass profiles.766" This result supports our use of caustic lnass profiles as a tracer of the total cluster mass profile (63.5),", This result supports our use of caustic mass profiles as a tracer of the total cluster mass profile $\S$ \ref{shapes}) ).767 Several authors have explored the use of the velocity dispersion profile (WDP) of clusters as a diagnostic of, Several authors have explored the use of the velocity dispersion profile (VDP) of clusters as a diagnostic of768the simulations.,the simulations.769" Thus, the close agreement between these two works suggests that numerical effects in the simulations are well understood at this level."," Thus, the close agreement between these two works suggests that numerical effects in the simulations are well understood at this level."770" Beyond simple host mass dependence, the size of the cosmological volume modeled by the Bolshoi simulation allows us to perform further detailed studies on properties impacting the satellite abundance distribution."," Beyond simple host mass dependence, the size of the cosmological volume modeled by the Bolshoi simulation allows us to perform further detailed studies on properties impacting the satellite abundance distribution."771" Here, we quantify the environmental dependence of the subhalo population by splitting the sample on local density, defined by Pm where p;, is the Eulerian density of dark matter contained in halos larger than Myi,22x10!M (roughly 1000 particles in Bolshoi) defined in a sphere of size r."," Here, we quantify the environmental dependence of the subhalo population by splitting the sample on local density, defined by =, where $\rho_{h,r}$ is the Eulerian density of dark matter contained in halos larger than $\mvir = 2\times 10^{11}\msol$ (roughly 1000 particles in Bolshoi) defined in a sphere of size $r$."772" In the present analysis, we take r=1.0/7!Mpc; we have performed similar analysis on range of scales and find this to be the range where the galaxya halo distribution is the most sensitive to the presence of massive satellites."," In the present analysis, we take $r = 1.0 \hinv\mpc$; we have performed similar analysis on a range of scales and find this to be the range where the galaxy halo distribution is the most sensitive to the presence of massive satellites."773 We compare the distribution for halos in the top and bottom quartile distributions to the mean relation in Figure 2.., We compare the distribution for halos in the top and bottom quartile distributions to the mean relation in Figure \ref{fig:nsats_dens}.774 There is a clear systematic trend: halos living in overdense (red are more to host massive subhalos than regionsthose in underdensepoints) regions likely(blue points)., There is a clear systematic trend: halos living in overdense regions (red points) are more likely to host massive subhalos than those in underdense regions (blue points).775" This is likely due to the fact that halos in denser environments live in more biased regions, where smaller density perturbations are amplified, making it easier for smaller halos to form and accrete onto intermediate mass hosts."," This is likely due to the fact that halos in denser environments live in more biased regions, where smaller density perturbations are amplified, making it easier for smaller halos to form and accrete onto intermediate mass hosts."776" This makes the deviations from the mean relation in Figure 2 a potentially observable manifestation of assembly bias, which posits that the properties of a given halo may be determined by properties other than mass, such as the halo environment."," This makes the deviations from the mean relation in Figure \ref{fig:nsats_dens} a potentially observable manifestation of assembly bias, which posits that the properties of a given halo may be determined by properties other than mass, such as the halo environment."777" Selecting for objects in a dense environment increases by almost the probability of having Ny»;=2 or more, from to just over1196;; this effect becomes stronger for larger values of N,,5,."," Selecting for objects in a dense environment increases by almost the probability of having $N_{subs} = 2$ or more, from to just over; this effect becomes stronger for larger values of $N_{subs}$."778" The Milky Way is somewhat overdense on this scale, having a massive companion, M31, as well as a number of surrounding dwarf galaxies."," The Milky Way is somewhat overdense on this scale, having a massive companion, M31, as well as a number of surrounding dwarf galaxies."779" Recent estimates put the total mass of the local group at roughly 5x10? (Lietal. 2009),, solidly in a dense environment on theM; — 1 Mpc scale."," Recent estimates put the total mass of the local group at roughly $5\times 10^{12}\msol$ \citep{Li08}, solidly in a dense environment on the $\sim$ 1 Mpc scale."780" Even if we ignore the contribution to the local density from all neighboring objects except M31, the MW lies close to the top quartile of our measured local density distribution in Bolshoi on a ~ 1 Mpc scale."," Even if we ignore the contribution to the local density from all neighboring objects except M31, the MW lies close to the top quartile of our measured local density distribution in Bolshoi on a $\sim$ 1 Mpc scale."781 We can begin to directly quantify the impact of such a massive neighbor on the subhalo population by identifying MW-mass halos which have M31-like neighbors with My;=(1—3)x10°?Mo at a distance of 700-900 kpc., We can begin to directly quantify the impact of such a massive neighbor on the subhalo population by identifying MW-mass halos which have M31-like neighbors with $\mvir = (1-3)\times 10^{12}\msol$ at a distance of 700-900 kpc.782" These systems are represented by the green circles in Figure 2,, which have a N,,5,=2 probability enhanced by 2o relative to the full "," These systems are represented by the green circles in Figure \ref{fig:nsats_dens}, which have a $N_{subs} = 2$ probability enhanced by $\sigma$ relative to the full sample."783"Thus, the local environment around the MW, which is sample.dominated by the presence of M31, boosts the chance of seeing the Magellanic Clouds in the Milky Way."," Thus, the local environment around the MW, which is dominated by the presence of M31, boosts the chance of seeing the Magellanic Clouds in the Milky Way."784our field.,our field.785 Observations of halos of external galaxies (6.9.. Dinuke et 11995) have shown that cel sizes du the Galactic halo are uuch larger than im the disk. from 100 - 1000 pc.," Observations of halos of external galaxies (e.g., Dumke et 1995) have shown that cell sizes in the Galactic halo are much larger than in the disk, from 100 - 1000 pc."786 Even a a distance of 3000 pc. the size of the total Auriga field is ~ LOO pc. so big cells iu he halo could be responsible for a considerable part of what we call the regular component of the magnetic field. as measured im the RALs of the extragalactic sources.," Even at a distance of 3000 pc, the size of the total Auriga field is $\sim$ 400 pc, so big cells in the halo could be responsible for a considerable part of what we call the regular component of the magnetic field, as measured in the $RM$ s of the extragalactic sources."787 We subtracted the gradient of the diffuse emission from the eradicut iu the As of the extragalactic sources. after which a gradient in RAL of ARAL z3.6 lin position angle emains (only deviating by about ffrom the direction perpendicular to the Galactic planc).," We subtracted the gradient of the diffuse emission from the gradient in the $RM$ s of the extragalactic sources, after which a gradient in $RM$ of $\Delta RM$ $\approx 3.6$ in position angle remains (only deviating by about from the direction perpendicular to the Galactic plane)."788 This indicates a regular magnetic field of about LoCo in this direction. assuming that ο and D remain constant over a total line of sight of 3000 pc.," This indicates a regular magnetic field of about 1 $\mu$ G in this direction, assuming that $n_e$ and $B$ remain constant over a total line of sight of 3000 pc."789 The magnetic field streneths actually present in the medimm will be higher if the field varies along the line of sight., The magnetic field strengths actually present in the medium will be higher if the field varies along the line of sight.790 ALulti-frequeuey. polarization observations of the diffuse Galactic background vield information on structure iu the Galactic warn gas and magnetic field., Multi-frequency polarization observations of the diffuse Galactic background yield information on structure in the Galactic warm gas and magnetic field.791" The multi-frequency WSRT observatious of a region of size ~~ 07 aat /= 1617.5216 iiu the coustellation Auriga show a smooth total intensity I. but abuudaut structure in Stokes parameters Q aud Ü on severa scales. with a inaxinnn T5,~ 13 K (about polarization)."," The multi-frequency WSRT observations of a region of size $\sim$ $\times$ at $l = 161$, $b = 16$ in the constellation Auriga show a smooth total intensity $I$ , but abundant structure in Stokes parameters $Q$ and $U$ on several scales, with a maximum $T_{b,pol} \approx$ 13 K (about polarization)."792 Filamentary structure up to many deerees long is preseut in P. sometimes aligned with Galactic latitude.," Filamentary structure up to many degrees long is present in $P$, sometimes aligned with Galactic latitude."793 Iu addition. narrow. one-heamr wide depolarization canals are most likely created by beam depolarization and may well iudicate abrupt RAL changes.," In addition, narrow, one-beam wide depolarization canals are most likely created by beam depolarization and may well indicate abrupt $RM$ changes."794 As the polarization structure is uncorrelated to LF. the structure in 7? cannot be created by variations du svuchrotron enussjon. but has to be due to Faraday rotation aud depolarizatiou moechanisuis.," As the polarization structure is uncorrelated to $I$, the structure in $P$ cannot be created by variations in synchrotron emission, but has to be due to Faraday rotation and depolarization mechanisms."795" Rotation measure maps show abundant structure on many scales. meludiug a near gradient of ~ pper degree in the direction of positive Galactic longitude and an average RALy23.1?,."," Rotation measure maps show abundant structure on many scales, including a linear gradient of $\sim$ 1 per degree in the direction of positive Galactic longitude and an average $RM_0 \approx796-3.4$."797 The eradicut is consistent with the regular Galactic maguetic field if its strength is Brey2 LopG and the field is azinuuthallv oricuted with a pitch angle p5li.," The gradient is consistent with the regular Galactic magnetic field if its strength is $B_{reg} \approx 1~\mu$ G and the field is azimuthally oriented with a pitch angle $p \approx798-14$."799" Ubiquitous structure is present m the RAF map ou beams size scales (59). indicating significant changes in iuagnetic field and/or thermal electron density over very αμα. spatial scales,"," Ubiquitous structure is present in the $RM$ map on beam size scales ), indicating significant changes in magnetic field and/or thermal electron density over very small spatial scales."800 There are two dominant depolarization mechauisuis which create structure in P in the Auriga field., There are two dominant depolarization mechanisms which create structure in $P$ in the Auriga field.801 First. bean depolarization ddepolarization due to averaging out polarization angle structure within one beam width) uost likely creates the canals. and 15 iniportaut iu regions of low P.," First, beam depolarization depolarization due to averaging out polarization angle structure within one beam width) most likely creates the canals, and is important in regions of low $P$."802 Additional depolarization is needed to explain ie observed P distribution. which is ouly possible if 1e medium both Faraday-rotates aud cuits svuchrotrou enission.," Additional depolarization is needed to explain the observed $P$ distribution, which is only possible if the medium both Faraday-rotates and emits synchrotron emission."803 Then. cussion originating iu the medium can © depolarized along its path towards the observer. so-called depth depoluization.," Then, emission originating in the medium can be depolarized along its path towards the observer, so-called depth depolarization."804 The polarization angle along ie path can vary duc to Faraday rotation. or due to varviusarviug intrinsic polarization aneleangleof of the emission.," The polarization angle along the path can vary due to Faraday rotation, or due to varying intrinsic polarization angle of the emission."805cussion. ThiThis oeidicates a varving magnetic field. which however is 'Onstraiue by the upper limit on structure in J.," This indicates a varying magnetic field, which however is constrained by the upper limit on structure in $I$."806 A depth cpolarization model was coustructed of a laver of cells with varving magnetic fields aud a constant backeroun polarization., A depth depolarization model was constructed of a layer of cells with varying magnetic fields and a constant background polarization.807 Constraints from the Auriga observatious eive estimates for several parameters in the ISM., Constraints from the Auriga observations give estimates for several parameters in the ISM.808 The cel size of structure in the ISM is coustrained to ~ 15 pc. iux the ratio of random to regular field is 0.7&0.5.," The cell size of structure in the ISM is constrained to $\sim$ 15 pc, and the ratio of random to regular field is $0.7 \pm8090.5$."810 Thirteen extragalactic sources in the Auriga field also show a egradieut in RAL. but roughly in the direction of Galactic latitude. which is perpeudicular to the eradieu in the diffuse emission.," Thirteen extragalactic sources in the Auriga field also show a gradient in $RM$, but roughly in the direction of Galactic latitude, which is perpendicular to the gradient in the diffuse emission."811 The RAL distributions from diffuse radiation and from extragalactic poiut sources aye so ifercut because the diffuse radiation mostly probes the first few hundred parsecs. whereas RASS frou the poiut sources are built up along the eutire line of sight through the Milkv. Way.," The $RM$ distributions from diffuse radiation and from extragalactic point sources are so different because the diffuse radiation mostly probes the first few hundred parsecs, whereas $RM$ s from the point sources are built up along the entire line of sight through the Milky Way."812 RASS of extragalactic sources change sigu over the field. which indicates a local reversal of the maenetic field.," $RM$ s of extragalactic sources change sign over the field, which indicates a local reversal of the magnetic field."813 We thank BR. Beck. E. Derkhuijseu aud F. IHeitsch for critical reading and useful conuueuts," We thank R. Beck, E. Berkhuijsen and F. Heitsch for critical reading and useful comments."814 The Westerbork Svuthesis Radio Telescope is operated by the Netherlands Fouudatiou for Research in Astronomy (ASTRON) with financial support from the Netherlands Oreanizatiou forScicutific Research (NWO)., The Westerbork Synthesis Radio Telescope is operated by the Netherlands Foundation for Research in Astronomy (ASTRON) with financial support from the Netherlands Organization forScientific Research (NWO).815 The Wisconsin II-Alpha Mapper is funded by the National Science. Foundation., The Wisconsin H-Alpha Mapper is funded by the National Science Foundation.816" MIT is supported by NWO eraut 611-21-006,", MH is supported by NWO grant 614-21-006.817Galaxy clusters. the largest gravitationally-bound structures in the universe. are ideal cosmological tools.,"Galaxy clusters, the largest gravitationally-bound structures in the universe, are ideal cosmological tools."818 Accurate measurements of their masses provide a crucial observational constraint. on cosmological models., Accurate measurements of their masses provide a crucial observational constraint on cosmological models.819 Several dynamical methods have been available to estimate cluster masses. such as (1) optical measurements of the velocity dispersions of cluster galaxies. (2) measurements of the X-ray emitting gas. and (3) gravitational lensing.," Several dynamical methods have been available to estimate cluster masses, such as (1) optical measurements of the velocity dispersions of cluster galaxies, (2) measurements of the X-ray emitting gas, and (3) gravitational lensing."820 Good agreements between these methods have been found on scales larger than cluster cores., Good agreements between these methods have been found on scales larger than cluster cores.821 However. joint measurements of lensing and X-rays often identify large discrepancies in the gravitational masses within the central regions of clusters by the two methods. and the lensing mass has always been found to be 2—4 times higher than the X-ray determined mass.," However, joint measurements of lensing and X-rays often identify large discrepancies in the gravitational masses within the central regions of clusters by the two methods, and the lensing mass has always been found to be $2-4$ times higher than the X-ray determined mass."822" This is the so-called ""Mass Discrepancy Problem"" (Allen 1998: Wu 2000).", This is the so-called “Mass Discrepancy Problem” (Allen 1998; Wu 2000).823 Many plausible explanations have been suggested. e... the triaxiality of galaxy clusters (Morandi et al.," Many plausible explanations have been suggested, e.g., the triaxiality of galaxy clusters (Morandi et al."824 2010). the oversimplitication of the strong lensing model for the central mass distributions of clusters (Bartelmann Steinmetz 1996). the inappropriate application of the hydrostatic equilibrium hypothesis for the central regions of clusters (Wu 1994: Wu Fang 1997). or the magnetic fields in clusters (Loeb Mao 1994).," 2010), the oversimplification of the strong lensing model for the central mass distributions of clusters (Bartelmann Steinmetz 1996), the inappropriate application of the hydrostatic equilibrium hypothesis for the central regions of clusters (Wu 1994; Wu Fang 1997), or the magnetic fields in clusters (Loeb Mao 1994)."825 Recently Richard et al. (, Recently Richard et al. (8262010) present a sample of 20 strong lensing clusters taken from the Local Cluster Substructure Survey (LoCuSS). among which 18 clusters have X-ray data from Chandra observations (Sanderson et al.,"2010) present a sample of $20$ strong lensing clusters taken from the Local Cluster Substructure Survey (LoCuSS), among which $18$ clusters have X-ray data from Chandra observations (Sanderson et al."827 2009)., 2009).828" They show that the X- mass discrepancy is [.3 at 307 significance — clusters with larger substructure fractions show greater mass discrepancies. and thus greater departures from hydrostatic equilibrium,"," They show that the X-ray/lensing mass discrepancy is $1.3$ at $3\sigma$ significance — clusters with larger substructure fractions show greater mass discrepancies, and thus greater departures from hydrostatic equilibrium."829 On the other hand. lensing observations of the bullet cluster IE0657-56 (Clowe et al.," On the other hand, lensing observations of the bullet cluster 1E0657-56 (Clowe et al."830 2006). combined with earlier X-ray measurements (Markeviteh et al.," 2006), combined with earlier X-ray measurements (Markevitch et al."831 2006). clearly indicate that the gravitational center of the cluster has an obvious offset from its baryonic center.," 2006), clearly indicate that the gravitational center of the cluster has an obvious offset from its baryonic center."832 Furthermore. recent studies (Shan et al.," Furthermore, recent studies (Shan et al."833 2010) of lensing galaxy clusters reveal that offset between the lensing center and X-ray center appears to be quite common. especially for unrelaxed clusters.," 2010) of lensing galaxy clusters reveal that offset between the lensing center and X-ray center appears to be quite common, especially for unrelaxed clusters."834 Among the recent sample of 38 clusters of Shan et al. (, Among the recent sample of 38 clusters of Shan et al. (835"2010). 45% have been found to have otfsets greater than 10"". and 5 clusters even have offsets greater than 40”.","2010), $45\%$ have been found to have offsets greater than $10''$, and $5$ clusters even have offsets greater than $40''$."836 Motivated by such observations. we propose to investigate galaxy cluster models where the center of the dark matter (DM) halo does not coincide with the center ofthe X-ray gas (See Figure |).," Motivated by such observations, we propose to investigate galaxy cluster models where the center of the dark matter (DM) halo does not coincide with the center of the X-ray gas (See Figure 1)."837 If the X-ray center of a cluster has an offset from its lensing (gravitational) center. then the X-rays and lensing are indeed measuring different regions of the cluster.," If the X-ray center of a cluster has an offset from its lensing (gravitational) center, then the X-rays and lensing are indeed measuring different regions of the cluster."838 Given the same radius. the lensing is measuring the DM halo centered at the gravitational center (shown by the dark blue sphere in Figure | ). while the are measuring the sphere of the halo that is offset from the gravitational center (shown by the red circle in Figure |).," Given the same radius, the lensing is measuring the DM halo centered at the gravitational center (shown by the dark blue sphere in Figure 1 ), while the X-rays are measuring the sphere of the halo that is offset from the gravitational center (shown by the red circle in Figure 1)."839" In this ease. there will always be a discrepaney between the lensing and X-ray measured masses — or specifically. the X-ray mass will always be lower than the lensing mass. just as the ""mass discrepancy problem"" has indicated."," In this case, there will always be a discrepancy between the lensing and X-ray measured masses — or specifically, the X-ray mass will always be lower than the lensing mass, just as the long-standing “mass discrepancy problem” has indicated."840 In this paper. we investigate the lensing-X-ray mass," In this paper, we investigate the lensing-X-ray mass"841group centre. —,group centre. –842" Estimated redshift of the group, determined from the joint probability of group member — Estimated uncertainty on the group redshift, determined from the 1σ width of the joint redshift — Number of group members in the original photometric group catalogue (i.e. prior to — Number of remaining group members after application of the cleaning algorithm described in Section 2.2.1). —"," Estimated redshift of the group, determined from the joint probability of group member – Estimated uncertainty on the group redshift, determined from the $\sigma$ width of the joint redshift – Number of group members in the original photometric group catalogue (i.e. prior to – Number of remaining group members after application of the cleaning algorithm described in Section \ref{interlopers}. –"843" Distance to the nearest rich group in the catalogue in Mpc, estimated following the descriptionin Section [2.1].hz"," Distance to the nearest rich group in the catalogue in Mpc, estimated following the descriptionin Section \ref{corr}."844" Table lists the properties for each galaxy, with columns as — Galaxy ID in the group catalogue of?."," Table \ref{tab:clean_galaxies} lists the properties for each galaxy, with columns as – Galaxy ID in the group catalogue of."845". Formatting isgroupID.galaxy, wheregroupID corresponds to the Group ID in Table andgalary has a value i—1,...,uoo, corresponding to the galaxies number within the group. —"," Formatting is, where corresponds to the Group ID in Table \ref{tab:clean_groups} and has a value $i = 1,...,n_\mathrm{M09}$, corresponding to the galaxies number within the group. –"846 Galaxy object ID within the SDSS. —, Galaxy object ID within the SDSS. –847 Right Ascension (J2000) of the galaxy. —, Right Ascension (J2000) of the galaxy. –848 Declination (J2000) of the galaxy. —, Declination (J2000) of the galaxy. –849" Spectroscopic redshift and its corresponding uncertainty, when — Photometric redshift and its corresponding uncertainty."," Spectroscopic redshift and its corresponding uncertainty, when – Photometric redshift and its corresponding uncertainty."850 Photometric redshifts from the SDSS table are, Photometric redshifts from the SDSS table are851brightness by ~07. where ὁ is the kinematic Doppler factor of the emitting jel plasma.,"brightness by $\sim\delta^3$, where $\delta$ is the kinematic Doppler factor of the emitting jet plasma."852" To correct lor beaming we use published estimates of Doppler factors from (wo blazar stucies: Ghiselliniefaf(1993).. in which lower limits on the Doppler [actor are caleulated [rom measurements of bulk motion in the radio jet. and Dondi&Ghisellini(1995).. in which lower limits to 9 are calculated [roin measurements of the ratio of 5- to N-ray. photons. assumine a svnchrotron sell-Conmpton moclel,"," To correct for beaming we use published estimates of Doppler factors from two blazar studies: \citet{Ghisellini}, in which lower limits on the Doppler factor are calculated from measurements of bulk motion in the radio jet, and \citet{Dondi}, in which lower limits to $\delta$ are calculated from measurements of the ratio of $\gamma$ - to X-ray photons, assuming a synchrotron self-Compton model."853 These (vo studies give lower limits of Doppler factors for eisht of our 40 DL Lac objects., These two studies give lower limits of Doppler factors for eight of our 40 BL Lac objects.854 To estimate the nuclear brightnesses of the remaining sources we use the median value of ὁ—3.1., To estimate the nuclear brightnesses of the remaining sources we use the median value of $\delta = 3.7$.855 This is both the median of the eieht BL Lacs in this sample aud also the median of the measured Doppler factors for the original IIST-1nmaged. sample of 110 BL Lacs. so is likely to be representative of the class.," This is both the median of the eight BL Lacs in this sample and also the median of the measured Doppler factors for the original HST-imaged sample of 110 BL Lacs, so is likely to be representative of the class."856 Although beaming mar affect the Iuminosities of the RLQ sample (o some degree. its effect will be small in comparison to the BL Lac objects eiven the dominance of the thermal emission associated with the accretion disk in RLQs.," Although beaming may affect the luminosities of the RLQ sample to some degree, its effect will be small in comparison to the BL Lac objects given the dominance of the thermal emission associated with the accretion disk in RLQs."857 Figure 3. shows absolute host galaxy magnitude versus absolute nuclear magnitude [or the low- aud high-power subsamples., Figure \ref{fig3} shows absolute host galaxy magnitude versus absolute nuclear magnitude for the low- and high-power subsamples.858 The BL Lac nuclear magnitudes have been Ix corrected and corrected for beaming. wilh the lower limits in the Doppler factors translating to upper limits in nuclear luminosities.," The BL Lac nuclear magnitudes have been K corrected and corrected for beaming, with the lower limits in the Doppler factors translating to upper limits in nuclear luminosities."859 The median absolute nuclear magnitude for the 8 BL Lacs with measured Doppler factor limits is Mj2—19.23 mag. while for the entire low-power subsample it is Mj2—17.59 mag.," The median absolute nuclear magnitude for the 8 BL Lacs with measured Doppler factor limits is $M_R \gtrsim -19.23$ mag, while for the entire low-power subsample it is $M_R \gtrsim -17.59$ mag."860 For the high-power sources (IN. corrected only) the median absolute magnitude is —24.5 mag., For the high-power sources (K corrected only) the median absolute magnitude is $-24.5$ mag.861 At least four orders of magnitude separate the least powerful DL Lacs (Mj2—17 mag) and the most luminous RLQs (Mj~—27 mag)., At least four orders of magnitude separate the least powerful BL Lacs $M_R \gtrsim -17$ mag) and the most luminous RLQs $M_R \sim -27$ mag).862 Although the host galaxies of the low-power sample span a similar range in magnitude to (hose of the high-power sample. (μον are on average slightly fainter.," Although the host galaxies of the low-power sample span a similar range in magnitude to those of the high-power sample, they are on average slightly fainter."863 This leads (to a shallow ivend between (he host galaxy. ancl nuclear luminosiGes across the combined sample., This leads to a shallow trend between the host galaxy and nuclear luminosities across the combined sample.864 We calculated the Kendall's 7 correlation coefficient. censoring the upper limits in the BL Lac nuclear huminosities (and for four of their host Iuminosities).," We calculated the Kendall's $\tau$ correlation coefficient, censoring the upper limits in the beaming-corrected BL Lac nuclear luminosities (and for four of their host luminosities)."865 The trend was significant for the case where we include (ae entire low-power subsample. beauming-corrected with the median Doppler factor probability of no correlation: IXendall's (7) for 62 points: 0.555). and Lor the case where we include only those of the low-power subsample with measured Doppler factor limits probability of no correlation: Ixendall (7) for 30 points: 0.671).," The trend was significant for the case where we include the entire low-power subsample, beaming-corrected with the median Doppler factor probability of no correlation; Kendall's $\tau$ ) for 62 points: 0.555), and for the case where we include only those of the low-power subsample with measured Doppler factor limits probability of no correlation; Kendall $\tau$ ) for 30 points: 0.671)."866 Although this trend is statistically significant. it is also verv shallow.," Although this trend is statistically significant, it is also very shallow."867 Performing a linear fii with the high-power subsample combined with the non-beamine-correctecl power subsample. we find that the host galaxy Iuminositv increases bv only 1 mag for an increase of T mag in the luminosity of the nucleus.," Performing a linear fit with the high-power subsample combined with the non-beaming-corrected low-power subsample, we find that the host galaxy luminosity increases by only $1$ mag for an increase of $7$ mag in the luminosity of the nucleus."868 Any introduction of beaming correction, Any introduction of beaming correction869where ΕΦ.x) is an arbitrary function of two variables and for some constant ko.,"where $F(\phi,x)$ is an arbitrary function of two variables and for some constant $k_0$."870 Direct substitution of this field into the magnetostatic equations shows that the equilibrium pressure must take the form introducing a constant Po and identifying kj1—kTo/mg as the hydrostatic scale height which is of the order of 300km at the photosphere at a temperature of about 6000., Direct substitution of this field into the magnetostatic equations shows that the equilibrium pressure must take the form introducing a constant $P_0$ and identifying $k_0^{-1}=kT_0/mg$ as the hydrostatic scale height which is of the order of $300 ~km$ at the photosphere at a temperature of about $6000K$.871 This family of solutions is geometrically quite simple although it is three-dimensionally varying., This family of solutions is geometrically quite simple although it is three-dimensionally varying.872" Figure 8 shows the contours of constant $(y,2) on a plane of constant x."," Figure \ref{fig_appendix} shows the contours of constant $\phi(y, z)$ on a plane of constant $x$."873" The lines of force (LOFs) are all geometrically the same on each constant-z plane but the field varies with all three Cartesian coordinates through its amplitude function Ε(Φ,x) which is an arbitrary function to be prescribed."," The lines of force (LOFs) are all geometrically the same on each $x$ plane but the field varies with all three Cartesian coordinates through its amplitude function $F(\phi, x)$ which is an arbitrary function to be prescribed."874" Take any explicit function c(ó,x)."," Take any explicit function $\sigma(\phi, x)$."875" Then, setting o=oo, a constant, generates a magnetic flux surface in 3D space."," Then, setting $\sigma = \sigma_0$, a constant, generates a magnetic flux surface in 3D space."876" To construct a flux tube of a finite cross section, a suitable functional form of σ(φ,x) set to a constant σρ describes a flux-tube boundary."," To construct a flux tube of a finite cross section, a suitable functional form of $\sigma(\phi, x)$ set to a constant $\sigma_0$ describes a flux-tube boundary."877" Then, prescribing F'(¢,x)Z0 inside the tube and F($,x)=0 in the rest of the atmosphere completes the construction."," Then, prescribing $F(\phi, x) \ne 0$ inside the tube and $F(\phi, x)878\equiv 0$ in the rest of the atmosphere completes the construction."879" The atmospheric pressure distribution is then given by Equation (A6)) which can also be expressed in the form External to the flux tube, B=0 so that p=Poexp(—koz), the isothermal pressure of the field-free part of the atmosphere."," The atmospheric pressure distribution is then given by Equation \ref{pressure}) ) which can also be expressed in the form External to the flux tube, ${\bf B} = 0$ so that $p = P_0 \exp(- k_0880z)$, the isothermal pressure of the field-free part of the atmosphere."881" Internal to the flux tube, the atmospheric pressure is reduced and compensated by the magnetic pressure so that the total pressure is stratified in the same manner as the external atmospheric pressure."," Internal to the flux tube, the atmospheric pressure is reduced and compensated by the magnetic pressure so that the total pressure is stratified in the same manner as the external atmospheric pressure."882" This solution is mathematically analogous to the solution describing the equilibrium between a field B=B(x,y)? and fluid pressure in the absence of gravity."," This solution is mathematically analogous to the solution describing the equilibrium between a field ${\bf B} = B(x, y){\hat z}$ and fluid pressure in the absence of gravity."883 Equilibrium in this case is satisfied by requiring the total pressure P=p+B?/87 to be uniform in space.," Equilibrium in this case is satisfied by requiring the total pressure $P884= p + B^2/8\pi$ to be uniform in space."885 We have complete freedom to prescribe the field distribution and use this requirement to obtain the associated equilibrium pressure., We have complete freedom to prescribe the field distribution and use this requirement to obtain the associated equilibrium pressure.886 The static balance of forces may be viewed by writing Equation (A1)) in the form, The static balance of forces may be viewed by writing Equation \ref{mag_stat}) ) in the form887This work is supported in part by NASA contract NÀS8-03060 aud the οποία bIustitution.,This work is supported in part by NASA contract NAS8-03060 and the Smithsonian Institution.888 NEM. acknowledges partial support from the Radcliffe Institute for Advanced Study at. Harvarel University., MEM acknowledges partial support from the Radcliffe Institute for Advanced Study at Harvard University.889 This work has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. uncer contract with the National Aeronautics aud Space Aciuinistration.," This work has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."890 We wish to thank Paul Nulseu for helpful discussils., We wish to thank Paul Nulsen for helpful discussions.891diminution of the coherent radial range with increasing frequency shown in Figure 1H.,diminution of the coherent radial range with increasing frequency shown in Figure \ref{fig:dfdr-phase}.892 Our caleulation for the first time correctly accounts for time delavs while rav-tracing 3D GRAIID simulation data., Our calculation for the first time correctly accounts for time delays while ray-tracing 3D GRMHD simulation data.893 We would therefore like to quantify how our results are allected bv inclusion of this effect., We would therefore like to quantify how our results are affected by inclusion of this effect.894 The light curves ancl power spectra trom calculations with and without time delavs are shown in Figure 15.., The light curves and power spectra from calculations with and without time delays are shown in Figure \ref{fig:light-curves-timedelay}.895 The light curves are identical except (hat the time delay. caleulation shows slightly less short timescale variation., The light curves are identical except that the time delay calculation shows slightly less short timescale variation.896 This [aet is illustrated more Clearly in the power spectra panel of this ligure. which clearly shows that the factuation power at high frequencies is diminished when one includes time delavs.," This fact is illustrated more clearly in the power spectra panel of this figure, which clearly shows that the fluctuation power at high frequencies is diminished when one includes time delays."897 This contrast is easily understood., This contrast is easily understood.898 Delay effects can diminish coherence in the received signal when a region whose light crossing time is A/ varies coherently on (imescales shorter than .N., Delay effects can diminish coherence in the received signal when a region whose light crossing time is $\Delta t$ varies coherently on timescales shorter than $\Delta t$.899 On the other hand. enhancement of coherence by clelay effects. would require remarkable contrivance because spatial and temporal fluctuations in the turbulence would have to be correlated with the rav trajectories for particular observers.," On the other hand, enhancement of coherence by delay effects would require remarkable contrivance because spatial and temporal fluctuations in the turbulence would have to be correlated with the ray trajectories for particular observers."900 Consequently. photon time delavs in general decrease (he [Inctuation power.," Consequently, photon time delays in general decrease the fluctuation power."901 The depression of the [Inctuation power is confimed to the highest [requencies because maintenance of emissivitv coherence requires a coordinating signal propagating across the region. but all signals. whether conveved in bulk fluid motion or by some wave mode. are limited to traveling no faster than e.," The depression of the fluctuation power is confined to the highest frequencies because maintenance of emissivity coherence requires a coordinating signal propagating across the region, but all signals, whether conveyed in bulk fluid motion or by some wave mode, are limited to traveling no faster than $c$."902 It follows that. for light travel time effects to suppress variabilitv. the coordinating signals must. be relativistic.," It follows that, for light travel time effects to suppress variability, the coordinating signals must be relativistic."903 In the context of an accretion flow. relativistic signals are largely confined to the innermost regions. which dominate the generation of high frequency. [Iuctuations.," In the context of an accretion flow, relativistic signals are largely confined to the innermost regions, which dominate the generation of high frequency fluctuations."904 Because the time delay effect depends on the lishts path through the material and the local velocity of the fluid. one expects it to depend on 0 and ii.," Because the time delay effect depends on the light's path through the material and the local velocity of the fluid, one expects it to depend on $\vartheta$ and $\dot{m}$."905 We characterize ils trend over parameter space in Figure 16.. where the difference in power-law exponents between the calculation with (ime delavs and that without time delays is plotted.," We characterize its trend over parameter space in Figure \ref{fig:difference-power-law-exponents-pspace}, where the difference in power-law exponents between the calculation with time delays and that without time delays is plotted."906 In all cases. the time delay calculation vields a steeper PDS.," In all cases, the time delay calculation yields a steeper PDS."907 The contrast depends most strongly on accretion rate. in (he sense Chat it diminishes as the disk becomes more opaque: this trend is consistent with the observation (hat as 72 increases. (he inner portion of the disk becomes progressively more obscured and contributes less to the power spectrum.," The contrast depends most strongly on accretion rate, in the sense that it diminishes as the disk becomes more opaque; this trend is consistent with the observation that as $\dot m$ increases, the inner portion of the disk becomes progressively more obscured and contributes less to the power spectrum."908 Larger 0 produces slightly larger deviations between the two methods., Larger $\vartheta$ produces slightly larger deviations between the two methods.909 As the inclination angle increases. photon ravs become more nearly parallel to the disks orbital velocity.," As the inclination angle increases, photon rays become more nearly parallel to the disk's orbital velocity."910 For those fluid elements with relativistic velocities. (he result is that [hid elements” worldlines move closer to the lighteone. leading io somewhat greater coherence of emissivitv along the ravs.," For those fluid elements with relativistic velocities, the result is that fluid elements' worldlines move closer to the lightcone, leading to somewhat greater coherence of emissivity along the rays."911have not alwavs been sublractecl [rom the cata.,have not always been subtracted from the data.912" This post-recombination contribution was relatively small in some earlier models of reionization (Zaldarriaga 1997: Tegmark Silk 1995) that explored optical clepths of 7.=0.5—1.0 ancl suggested reionization epochs up to z,~100.", This post-recombination contribution was relatively small in some earlier models of reionization (Zaldarriaga 1997; Tegmark Silk 1995) that explored optical depths of $\tau_e = 0.5-1.0$ and suggested reionization epochs up to $z_r \sim 100$.913 However. with current. data indicating late reionization. it becomes particularly important to consider contributions (to 7. prior to the first sources of light.," However, with current data indicating late reionization, it becomes particularly important to consider contributions to $\tau_e$ prior to the first sources of light."914" The new WAIAP-3 results find a lower z.. but thev also suggest less small-scale power available:. [orj reionizing:−∙↽ sources. owing−↽ to lower normalization∙ parameters.↽ os20.74.=0.054 and OQ,h?zm0.12tras."," The new WMAP-3 results find a lower $\tau_e$, but they also suggest less small-scale power available for reionizing sources, owing to lower normalization parameters, $\sigma_8 \approx 0.74^{+0.05}_{-0.06}$ and $\Omega_m h^2 \approx 0.127^{+0.007}_{-0.013}$."915 This reduction is somewhat offset by the reduction in spectrum tilt from p.=0.99d:0.04. (WMADP-I1) to ne=0.951tulis (NMADP-3).," This reduction is somewhat offset by the reduction in spectrum tilt from $n_s = 0.99 \pm9160.04$ (WMAP-1) to $n_s = 0.951^{+0.015}_{-0.019}$ (WMAP-3)."917 Alvarez (2006) argue. from the lower values of 7. and ox. that both WMAP-3 and WAIAP-1 data require similar (high) stellar ionizing efficiencies.," Alvarez (2006) argue, from the lower values of $\tau_e$ and $\sigma_8$, that both WMAP-3 and WMAP-1 data require similar (high) stellar ionizing efficiencies."918" Haiman Holcler (2003) use the lower 7, (o suggest that massive star formation was suppressed in minihalos.", Haiman Holder (2003) use the lower $\tau_e$ to suggest that massive star formation was suppressed in minihalos.919" Our results on a lower Az, make these requirements even more stringent. as we now cuantilv."," Our results on a lower $\Delta \tau_e$ make these requirements even more stringent, as we now quantify."920" senmi-analviie and numerical models of reionization (licotti. Gnedin. Shull 2002a.b: VTS03. Haiman IHolder 2003) show that the efficiency. of ionizing photon injection into the IGM can be parameterized bv the ""triple product. Nyffu."," Semi-analytic and numerical models of reionization (Ricotti, Gnedin, Shull 2002a,b; VTS03, Haiman Holder 2003) show that the efficiency of ionizing photon injection into the IGM can be parameterized by the “triple product"", $N_{\gamma} f_* f_{\rm esc}$."921 Here. fF. represents the efficiency (the fraction of à halos barvons that ego into stars). A. is (he number of ionizing photons produced per barvon of star formation. ancl fJ is the fraction of these ionizing photons that escape from the halo into the IGM.," Here, $f_*$ represents the star-formation efficiency (the fraction of a halo's baryons that go into stars), $N_{\gamma}$ is the number of ionizing photons produced per baryon of star formation, and $f_{\rm esc}$ is the fraction of these ionizing photons that escape from the halo into the IGM."922" We can now use our calculations to constrain the amount of hieh-z star formation through (the product of these three parameters. jenceforülhi referred. (o as the ""efficiency."," We can now use our calculations to constrain the amount of $z$ star formation through the product of these three parameters, henceforth referred to as the “efficiency""."923" For (hie ionization history in equation (5). we sel welt)=INfsecit)ftz). wheree;(z) is (he space-averaged barvon chunping factor of ionized wdrogen. ο,=Org)>πμ)”."," For the ionization history in equation (5), we set $x_e(z) = N_{\gamma} f_* f_{\rm esc} c_L(z) f_b(z)$, where $c_L(z)$ is the space-averaged baryon clumping factor of ionized hydrogen, $c_L \equiv \langle n^2_{\rm HII} \rangle924\langle n_{\rm HII} \rangle^2$."925 We assume that ej is the same for IE IE and He HI., We assume that $c_L$ is the same for H II and He III.926 The factor fuz) is the fraction of barvons in collapsed. halos. computed. through the Press-Schechter ormalism (as in WTS03) for the cosmological parameters from. WMAP-3.," The factor $f_b (z)$ is the fraction of baryons in collapsed halos, computed through the Press-Schechter formalism (as in VTS03) for the cosmological parameters from WMAP-3."927. We assume that Nofitose is Constant with redshift., We assume that $N_{\gamma} f_* f_{\rm esc}$ is constant with redshift.928 There is surely some dependence of each of these parameters on the halo mass aud environment (ladman Bryan 2006: Ricotti Shull 2000)., There is surely some dependence of each of these parameters on the halo mass and environment (Haiman Bryan 2006; Ricotti Shull 2000).929 Since we have alreacly parameterized (he intrahalo recombinations through. fi. we account Lor the loss of ionizing photons on IGM scales through c; in two forms: (1) a power-law form with slope ο=—2 [rom (he work of Haiman Bryan (2006): and (2) the numerical simulations of Kohler. Gneclin Tamilton (2006). using their case C (overdensity 6~1 for the large-scale IGM) for Cy. the recombination chunping [actor corresponding to our definition of cj.," Since we have already parameterized the intrahalo recombinations through $f_{\rm esc}$, we account for the loss of ionizing photons on IGM scales through $c_L$ in two forms: (1) a power-law form with slope $\beta = -2$ from the semi-analytic work of Haiman Bryan (2006); and (2) the numerical simulations of Kohler, Gnedin Hamilton (2006), using their case C (overdensity $\delta \sim 1$ for the large-scale IGM) for $C_R$, the recombination clumping factor corresponding to our definition of $c_L$."930" In the latter case. the clumpine factor is almost constant (οι,22 6) until the very end of reionization."," In the latter case, the clumping factor is almost constant $c_L \approx 6$ ) until the very end of reionization."931 Together. these two different cases provide bounds on the range of possible values.," Together, these two different cases provide bounds on the range of possible values."932 With these assumptions. we can use equation (5) and the allowed additional optical depth.," With these assumptions, we can use equation (5) and the allowed additional optical depth,"933models given by equations. 1-5 we derive the best. fit xuvameters for cach galaxy ancl overlay the resulting mass model onto each rotation curve in Fig. 1.,models given by equations 1-5 we derive the best fit parameters for each galaxy and overlay the resulting mass model onto each rotation curve in Fig. \ref{fig:rot_curves}.934" In. Table 1 we report the main structural parameters: the disk mass. the ido core radius. po. the optical radius Aap, and eon=Va (Ro). ic. the halo contribution to circular velocity. at he optical radius."," In Table 1 we report the main structural parameters: the disk mass, the halo core radius, $\rho_0$, the optical radius $R_{opt} $ and $ v_{0h}\equiv V_H(R_{opt})$ , i.e. the halo contribution to circular velocity at the optical radius."935 In all our rotation curves the and the ot he stellar disk contribution can not reproduce the observed (C rise between 1.5 Ry and the last measured. raclius., In all our rotation curves the and the of the stellar disk contribution can not reproduce the observed RC rise between 1.5 $R_D $ and the last measured radius.936 This strongly. suggests evidence for the presence. at zz1. of à dark matter component. of mass comparable to that ound for local disk galaxies with similar V5; (see Figures 2. δ and 9 of Persic. Salucei Stel. 1996).," This strongly suggests evidence for the presence, at $z\approx 1$, of a dark matter component of mass comparable to that found for local disk galaxies with similar $V_{opt}$ (see Figures 2, 8 and 9 of Persic, Salucci Stel, 1996)."937 We derive disk masses ranging between 11044. to 2«LOMAL. for ealaxies with reference velocity Vo; between kms+ and 200kms+.," We derive disk masses ranging between $1 \times 10^9 M_\odot $ to $ 2 \times 10^{10}938M_\odot $ for galaxies with reference velocity $V_{opt}$ between $\kms$ and $\kms$."939 These disk masses are smaller by a [actor 2- than those of the local spirals with the same reference velocity which are shown to follow Inner Barvon Dominance (sce Salucci Persie. 1999).," These disk masses are smaller by a factor 2-4 than those of the local spirals with the same reference velocity which are shown to follow Inner Baryon Dominance (see Salucci Persic, 1999)."940" ""Phe high redshift stellar disks are sub-maximal disks.", The high redshift stellar disks are sub-maximal disks.941 Forcing a maximal disk even in the “weak” implementation of Persic ancl Salucci (1990). leacls to unacceptable fits of our high-z ICs.," Forcing a maximal disk even in the ""weak"" implementation of Persic and Salucci (1990) leads to unacceptable fits of our high-z RC's."942 The best fit values for rj is of the order of 1.5/2p. which is larger than usually compatible with a NEW profile. although the error-bars on our data preclude any strong statement.," The best fit values for $r_0$ is of the order of $\sim 1.5 R_D$, which is larger than usually compatible with a NFW profile, although the error-bars on our data preclude any strong statement."943 Since the gravitational lens model alfects the source-plane reconstruction of the galaxies. we must test. for the ellect that this has on the resulting rotation curves.," Since the gravitational lens model affects the source-plane reconstruction of the galaxies, we must test for the effect that this has on the resulting rotation curves."944 We reconstruct the galaxies using the family of lens mocels that inhabit the Ay? contour corresponding to Lo conlidence interval relevant to each cluster., We reconstruct the galaxies using the family of lens models that inhabit the $\Delta \chi^2$ contour corresponding to $1{\sigma}$ confidence interval relevant to each cluster.945 For example. the model of 11745 has five free parameters. and the lens moceling uncertainties are therefore derived. by considering. models within the A\y7=5.89 contour.," For example, the model of 1745 has five free parameters, and the lens modeling uncertainties are therefore derived by considering models within the ${\Delta}{\chi}^2{=}5.89$ contour."946 From each reconstruction we extract the one-dimensional rotation curve and. apply the analysis outlined. above ancl fine the maximum. variations are: AlogMp=0.03. Alog«p>=0.02. Alogi.)xSkims *.," From each reconstruction we extract the one-dimensional rotation curve and apply the analysis outlined above and find the maximum variations are: $\Delta\log \ M_{D}=0.03$, $\Delta\log<\rho>=0.02$, $\Delta\log(V_{opt})\lsim5\kms$ ."947 Thus the uncertainties in the gravitational lens mocelling is negligable compared to the uncertainties in the RC mass modelling., Thus the uncertainties in the gravitational lens modelling is negligable compared to the uncertainties in the RC mass modelling.948 A cosmological significance of our result. is evident in lig 2. where we compare the disk mass. the mean dark matter density within the optical radius and the angular momentunr per unit mass. all as a function. of reference velocity.," A cosmological significance of our result is evident in Fig \ref{fig:MD_rhom} where we compare the disk mass, the mean dark matter density within the optical radius and the angular momentum per unit mass, all as a function of reference velocity."949 These are compared. to similar properties of the local objects (Shankaretal., These are compared to similar properties of the local objects \citep{Shankar06}.950"2006).. Figure 2) strikinely shows that high redshift spirals. modulo an olfset of 0.6OLOLS dex. are on the same fogAly versus {ο relationship founcl for local spirals arising from the systematic structural properties of their mass distribution (""oninietal.2006).. see also (Saluceietal.1993) "," Figure \ref{fig:MD_rhom} strikingly shows that high redshift spirals, modulo an offset of $0.6^{+0.1}_{-0.15}$ dex, are on the same $log M_D951$ versus $log V_{opt}$ relationship found for local spirals arising from the systematic structural properties of their mass distribution \citep{Tonini}, see also \citep{Salucci93} ."952In Fig 2. from the values of «&p a quantity that differently from. po is weakly alleeted by the RC 1-7 fitting uncertainties. ib is apparent that the DM halos of ς=1 disk galaxies are denser by 0.7UlN dex than those around similarly luminous +=0 spirals.," In Fig 2, from the values of $<\rho>$, a quantity that differently from $\rho_0$ is weakly affected by the RC $\sigma$ fitting uncertainties, it is apparent that the DM halos of $z=1$ disk galaxies are denser by $0.7^{+0.1}_{-0.2}$ dex than those around similarly luminous $z$ =0 spirals."953 The evidence that spiral disks at >=0 and z=] have the same structural relationships is further supported by observations of the evolution of the Tully-Fisher relation (which correlates the disk mass with Vou)., The evidence that spiral disks at $z$ =0 and $z$ =1 have the same structural relationships is further supported by observations of the evolution of the Tully-Fisher relation (which correlates the disk mass with $V_{opt}$ ).954 In our and in other independent samples (Swinbank et al 2006.. Vogt et al 1996. Bamfordet al2005) the galaxies ab 2=d show a FE relation with a slope similar to that of the local TE. but with an olfset compatible with that found in the present work from the disk masses rotation velocity.," In our and in other independent samples (Swinbank et al 2006, Vogt et al 1996, Bamford et al2005) the galaxies at $z=1$ show a TF relation with a slope similar to that of the local TF, but with an offset compatible with that found in the present work from the disk mass rotation velocity."955 ‘This suggests that from 2=1 to 2=0. the stellar clisk masses Alp of a spiral has grown by a factor ~44. that leads to just a modest increase in the DM dominated quantity 15;," This suggests that from $z$ =1 to $z$ =0, the stellar disk masses $M_{D}$ of a spiral has grown by a factor $\sim 4^{+1}_{-2}$, that leads to just a modest increase in the DM dominated quantity $V_{opt}$."956 Further evidence that z=1 disk galaxies are related to present day spirals is) provided. by the. relationship between angular momentum per unit mass (7) versus the reference velocity. as shown in Fig. 2..," Further evidence that $z=1$ disk galaxies are related to present day spirals is provided by the relationship between angular momentum per unit mass $j$ ) versus the reference velocity, as shown in Fig. \ref{fig:MD_rhom}."957 This well theoretically motivated. relation (e.g. (Voninietal. 2006))) can be considered as the imprint of the process of the formation of isks inside clark matter halos related to the cosmological properties of halo spin parameters., This well theoretically motivated relation (e.g. \citep{Tonini}) ) can be considered as the imprint of the process of the formation of disks inside dark matter halos related to the cosmological properties of halo spin parameters.958 As Figure 2 shows. jore appears to be no evolution in this crucial relationship between the the comological time at which we observe these spirals.z=1./6Cyr and the present time. +=0./ Gyr.," As Figure \ref{fig:MD_rhom} shows, there appears to be no evolution in this crucial relationship between the the comological time at which we observe these spirals,$z=1, t=6 \ Gyr$ and the present time, $z=0, t=13.7\ Gyr$ ."959 This agreement is remarkable: it establishes a link between local anc high redshift disks. supporting the idea iw the angular momentum remains constant during the," This agreement is remarkable: it establishes a link between local and high redshift disks, supporting the idea that the angular momentum remains constant during the"960"andl σερως respectively, we again used error propagation formulae: where fou is the fraction of the total black hole mass in ellipticals. οιο is the total black hole mass in ellipticals. Tota Al mouges are respectively the upper and. lower limit uncertainties in the total black hole mass. ancl Mig is the total black hole mass in all galaxies in our sample.","and $\sigma_{\rm f,ell,low}$, respectively, we again used error propagation formulae: where $f_{\rm ell}$ is the fraction of the total black hole mass in ellipticals, $M_{\rm BH,ell}$ is the total black hole mass in ellipticals, $\sigma_{\rm tot,up}$ and $\sigma_{\rm tot,low}$ are respectively the upper and lower limit uncertainties in the total black hole mass, and $M_{\rm BH,tot}$ is the total black hole mass in all galaxies in our sample."961 Note that Eqs. (, Note that Eqs. (9623) do not take into account the covariance term between Alpyoon anc Mpguos.,"3) do not take into account the covariance term between $M_{\rm BH,ell}$ and $M_{\rm BH,tot}$."963 The οσοι of the covariance term is to lower the estimated: uncertainties., The effect of the covariance term is to lower the estimated uncertainties.964 Similar equations were used to caleulate the uncertainties in the fractions of the total black hole mass that are in classical and. pseudo-bulges., Similar equations were used to calculate the uncertainties in the fractions of the total black hole mass that are in classical and pseudo-bulges.965 We can now quote the fractions we find with the estimated. uncertainties arising from the intrinsic scatter in the relation: 55.1 per cent of the mass in black holes is in elliptical galaxies. 411 per cent in classical bulges and 4(0571 per cent in pseudo-bulges.," We can now quote the fractions we find with the estimated uncertainties arising from the intrinsic scatter in the relation: $55^{+8}_{-4}$ per cent of the mass in black holes is in elliptical galaxies, $41^{+4}_{-2}$ per cent in classical bulges and $4^{+0.9}_{-0.4}$ per cent in pseudo-bulges."966 We note that there is no particular reason why black hole masses obtained using a relation between bulge mass. Apu. and black bole mass awe more correct. than. those obtained through an ApH0 relation.," We note that there is no particular reason why black hole masses obtained using a relation between bulge mass, $M_{\rm{Bulge}}$, and black hole mass are more correct than those obtained through an $M_{\rm{BH}}-\sigma$ relation."967 We could have used as well an AMpgoo relation from the literature to obtain black hole masses., We could have used as well an $M_{\rm{BH}}-\sigma$ relation from the literature to obtain black hole masses.968 We have used the AdpuMise relation to obtain black hole masses for all galaxies simply because we do not have measurements of σ for all our galaxies. and thus this does not imply that the AlgaMisc relation is to be preferred over the AMpg6 relation.," We have used the $M_{\rm{BH}}-M_{\rm{Bulge}}$ relation to obtain black hole masses for all galaxies simply because we do not have measurements of $\sigma$ for all our galaxies, and thus this does not imply that the $M_{\rm{BH}}-M_{\rm{Bulge}}$ relation is to be preferred over the $M_{\rm{BH}}-\sigma$ relation."969 The consequences of this choice are discussed below when necessary., The consequences of this choice are discussed below when necessary.970 and provide extensive discussion on the consequences of using different relations to infer black hole masses?)., and provide extensive discussion on the consequences of using different relations to infer black hole masses.971. Using the a... values. we can also check how bulge mass and black hole mass relate to velocity dispersion in ellipticals. classical bulges and. pseudo-bulges.," Using the $\sigma_{e/8}$ values, we can also check how bulge mass and black hole mass relate to velocity dispersion in ellipticals, classical bulges and pseudo-bulges."972 This is done in Fig. Ll., This is done in Fig. \ref{fig:smbh}.973 One sees that elliptical galaxies follow a well-defined relation between their stellar masses and. aes. as expected [rom the relation.," One sees that elliptical galaxies follow a well-defined relation between their stellar masses and $\sigma_{e/8}$, as expected from the relation."974 Classical. bulges deviate slightly from this relation and follow a somewhat olfset line. with lower masses for the same velocity dispersion.," Classical bulges deviate slightly from this relation and follow a somewhat offset line, with lower masses for the same velocity dispersion."975 Pseudo-bulges tend to fall far oll! the ellipticals’ relation. being on average much less massive than one would expect [rom this relation.," Pseudo-bulges tend to fall far off the ellipticals' relation, being on average much less massive than one would expect from this relation."976 Note also that one cannot see a efeear relation between bulge mass and oe for pseudo-bulges alone., Note also that one cannot see a relation between bulge mass and $\sigma_{e/8}$ for pseudo-bulges alone.977 The fits to the data shown in the left. panels of Fig., The fits to the data shown in the left panels of Fig.978 1. were obtained by minimising x7 as in Eq. (, \ref{fig:smbh} were obtained by minimising $\chi^2$ as in Eq. (9793) of7.. Le. weighting every point by the inverse of its measurement uncertainties.,"3) of, i.e. weighting every point by the inverse of its measurement uncertainties."980" We use the uncertainties in m,;s às provided by the SDSS.", We use the uncertainties in $\sigma_{e/8}$ as provided by the SDSS.981 For the uncertainties in bulge mass we use 0.1 dex. i.e. the same [fractional uncertainty in all bulge mass estimates.," For the uncertainties in bulge mass we use 0.1 dex, i.e. the same fractional uncertainty in all bulge mass estimates."982 Such procedure has also been used by in fitting the AdpHσ relation., Such procedure has also been used by in fitting the $M_{\rm{BH}}-\sigma$ relation.983 We have chosen the value of 0.1 dex because this is the typical uncertainty in the estimates of galaxy masses when one uses colours to derive mass-to-light ratios(22).. as we have done.," We have chosen the value of 0.1 dex because this is the typical uncertainty in the estimates of galaxy masses when one uses colours to derive mass-to-light ratios, as we have done."984 Note. however. that while this value is a safe estimate for the uncertainty in the masses of the ellipticals. it is only a lower limit in the case of bulges. as the uncertainty in bulge luminosity from the image decomposition of disc ealaxies is not taken into account (the current version of the code used to perform the decompositions in Paper I does not provide such estimate).," Note, however, that while this value is a safe estimate for the uncertainty in the masses of the ellipticals, it is only a lower limit in the case of bulges, as the uncertainty in bulge luminosity from the image decomposition of disc galaxies is not taken into account (the current version of the code used to perform the decompositions in Paper I does not provide such estimate)."985 Nevertheless. we have verified hat there is no substantial change in the [its obtained even if no weighting is included. and the cillerence in slope obtained in the relations for ellipticals ancl classical σος is statistically significant at zz95 per cent confidence evel.," Nevertheless, we have verified that there is no substantial change in the fits obtained even if no weighting is included, and the difference in slope obtained in the relations for ellipticals and classical bulges is statistically significant at $\approx95$ per cent confidence level."986 Furthermore. 2D Ixolmogorov-Srmirnov. tests indicate hat the distributions of bulge mass and σ are cdillerent or ellipticals. classical bulges ancl pseudo-bulges at zz99 vcr cent confidence level.," Furthermore, 2D Kolmogorov-Smirnov tests indicate that the distributions of bulge mass and $\sigma$ are different for ellipticals, classical bulges and pseudo-bulges at $\approx99$ per cent confidence level."987" These results might be not too surprising. considering that structural differences between »eudo-bulges. classical bulees and. cllipticals are found. in ""aper L ""These dilferences can have consequences on the Alpyoo relation. since black hole mass is correlated with »ilee mass."," These results might be not too surprising, considering that structural differences between pseudo-bulges, classical bulges and ellipticals are found in Paper I. These differences can have consequences on the $M_{\rm{BH}}-\sigma$ relation, since black hole mass is correlated with bulge mass."988 This is explicitly. shown in the right. panels of Fig. 1.., This is explicitly shown in the right panels of Fig. \ref{fig:smbh}.989 The Alouσ relation we find for ellipticals is eenerallv well described by relations found. with real black role mass measurements(22??).. although our. cllipticals seem to follow a somewhat shallower relation.," The $M_{\rm{BH}}-\sigma$ relation we find for ellipticals is generally well described by relations found with real black hole mass measurements, although our ellipticals seem to follow a somewhat shallower relation."990 Lviclently. Mack holes in classical bulges follow a slightly olfset. line. while those in. pseuclo-bulges are. on average. significantly detached from the ellipticals’ Adpy—0 relation.," Evidently, black holes in classical bulges follow a slightly offset line, while those in pseudo-bulges are, on average, significantly detached from the ellipticals' $M_{\rm{BH}}-\sigma$ relation."991" Despite the small & aperture corrections. it is legitimate to be concerned about the fact that the extrapolation from 70 Vo m,os Is relatively more significant to pseudo-bulges than to classical bulges and ellipticals."," Despite the small $\sigma$ aperture corrections, it is legitimate to be concerned about the fact that the extrapolation from $\sigma$ to $\sigma_{e/8}$ is relatively more significant to pseudo-bulges than to classical bulges and ellipticals."992 In fact. the mean relative difference (σι0)/o is 12 per cent for pseudo-bulges. 9 per cent for classical— bulges and 5 per cent for. elliptical.," In fact, the mean relative difference $(\sigma_{e/8}-\sigma)/\sigma$ is 12 per cent for pseudo-bulges, 9 per cent for classical bulges and 5 per cent for ellipticals."993 Llowever. since these corrections follow a power law. the results in Fig.," However, since these corrections follow a power law, the results in Fig."994 1. do not depend on whether the corrections applied correspond to e at 1/8 of the bulge clleetive radius or at any other fraction of it. as the dillerence in such corrections produces only a constant shift.," \ref{fig:smbh} do not depend on whether the corrections applied correspond to $\sigma$ at 1/8 of the bulge effective radius or at any other fraction of it, as the difference in such corrections produces only a constant shift."995 For instance. we have verified that exactly the same ollsets are seen if we use c at the effective radius. which involves even smaller corrections. instead of σε.," For instance, we have verified that exactly the same offsets are seen if we use $\sigma$ at the effective radius, which involves even smaller corrections, instead of $\sigma_{e/8}$."996 Furthermore. these results are essentially unchanged even. if no aperture correction is applied.," Furthermore, these results are essentially unchanged even if no aperture correction is applied."997 Figure 1 thus shows that we find that the Misa0 relation of classical bulges is latter than that of ellipticals., Figure \ref{fig:smbh} thus shows that we find that the $M_{\rm{Bulge}}-\sigma$ relation of classical bulges is flatter than that of ellipticals.998 Furthermore. the Aga @ relations we find for ellipticals and classical bulges are also Uatter than the relations found in the literature using direct black hole mass measurements.," Furthermore, the $M_{\rm{BH}}-\sigma$ relations we find for ellipticals and classical bulges are also flatter than the relations found in the literature using direct black hole mass measurements."999 One should. thus verify that this Uattening is not caused bv our selection cllects., One should thus verify that this flattening is not caused by our selection effects.1000 In fact. because the scatter around the Anus6 relation is larger at the [ow mass end. a cut in mass could in principle produce such flattening.," In fact, because the scatter around the $M_{\rm{Bulge}}-\sigma$ relation is larger at the low mass end, a cut in mass could in principle produce such flattening."1001 Furthermore. because the uncertainties dn. A4gus; are presumably larger than those in σ. (Ανω could be more allected by such bias than 7]Alpe).," Furthermore, because the uncertainties in $M_{\rm{Bulge}}$ are presumably larger than those in $\sigma$, $\langle M_{\rm{Bulge}}\vert \sigma\rangle$ could be more affected by such bias than $\langle \sigma\vert M_{\rm{Bulge}}\rangle$."1002 However.σὸ we stress that our cut in mass concerns galaxy mass. not bulge mass.," However, we stress that our cut in mass concerns galaxy mass, not bulge mass."1003 Most galaxies at the low mass end have significant disc components. and thus the Misuse0 relations we find are not significantly biased by our mass cut.," Most galaxies at the low mass end have significant disc components, and thus the $M_{\rm{Bulge}}-\sigma$ relations we find are not significantly biased by our mass cut."1004 In fact. the range in bulge mass in our sample &oes as low as more than an order of magnitude below our mass cut. as do the sampleof galaxies with direct. Mpg measurements.," In fact, the range in bulge mass in our sample goes as low as more than an order of magnitude below our mass cut, as do the sampleof galaxies with direct $M_{\rm{BH}}$ measurements."1005 Thus our mass cut. should not have an important effect in. producing the llattening of the relations we find here., Thus our mass cut should not have an important effect in producing the flattening of the relations we find here.1006 These findings thus indicate that ellipticals. classical," These findings thus indicate that ellipticals, classical"1007In this subsection we will derive asymptoties lor in several generalized allocation schemes as defined at the beginning of Section ?2..,In this subsection we will derive asymptotics for in several generalized allocation schemes as defined at the beginning of Section \ref{sec:appl}.1008" As we will see, when nox and N/n—A€(0.x] the order of ES),p] is. n""EAT!ΑΛ+ forany. r=0.1.....- and the order ol. VarSu”? is the same for /> 2."," As we will see, when $n\to \infty$ and $N/n\to\lambda\in(0,\infty]$ the order of $\E\,S_n^{(r)}$ is $n^r/N^{r-1}$ for any $r=0,1,\ldots$, and the order of $\var\,S_n^{(r)}$ is the same for $r\ge2$ ."1009 When À=x and r=O0 or 1 the order of VarSj is? ?/N.," When $\lambda=\infty$ and $r=0$ or $1$ the order of $\var\,S_n^{(r)}$ is $n^2/N$."1010", Consequently. we will derive asymptotic normality of when either and asymptotic normality of when À—x. $>» and r—0.1."," Consequently, we will derive asymptotic normality of when either and asymptotic normality of when $\lambda=\infty$, $\frac{n^2}{N}\to\infty$ and $r=0,1$."1011 Although in all the cases results look literally the same (with dillerent asymptotic expectations and variances and having different prools) for the sake of precision we decided to repeat lormulations of theorems in each of the subsequent cases., Although in all the cases results look literally the same (with different asymptotic expectations and variances and having different proofs) for the sake of precision we decided to repeat formulations of theorems in each of the subsequent cases.1012" Consider a scheme of à random distribution of » indisunguishable balls into .V disünguishable boxes, that alldistributions are⋅⋅⋅ equiprobable."," Consider a scheme of a random distribution of $n$ indistinguishable balls into $N$ distinguishable boxes, such thatall distributions are equiprobable."1013" That⋅ is, if (n)£; —£Pdenotes. the number of balls⋅ which fall.into⋅ thesuch ith box. 7 =1.....;N. then"," That is, if $\xi_i=\xi_i^{(n)}$ denotes the number of balls whichfall into the $i$ th box, $i=1,\ldots,N$ , then"1014also coufinmied by the existence of binaries with flux reversals (Liuetal.2006:Looper2008).,"also confirmed by the existence of binaries with flux reversals \citep{Liu2006, Looper2008}."1015. This brightening is probably best uuderstood απ resulting from the disappearance of dust-beariug clouds from the photosphere. but this temperature interval has proved challenging to describe with a selt-cousisteut ΠΟ model (Marleyetal.2010 and references therein).," This brightening is probably best understood as resulting from the disappearance of dust-bearing clouds from the photosphere, but this temperature interval has proved challenging to describe with a self-consistent atmosphere model \citealt{Marley2010} and references therein)."1016 Binaries. expecially those amenable0 to spatially resolved spectroscopy. provide uuique constraints to these models.," Binaries, especially those amenable to spatially resolved spectroscopy, provide unique constraints to these models."1017 Tighter binaries have orbital periods short enoush for orbital monitorius and provide further constraints on uodels through dynamical masses (Liuetal.2008:Dupuyetal.2009:I&onopacky 2010).," Tighter binaries have orbital periods short enough for orbital monitoring and provide further constraints on models through dynamical masses \citep{Liu2008, Dupuy2009, Konopacky2010}."1018. Iu 2006. we have undertaken a near-infrared proper notion survey - SIMP: Artiganotal. 2009)) with the field near-infrared camera CPAPIR (Artigan at the CTIO 1.5111 and ONAL 1.61un (Racine1975) telescopes aud have covered ~35% of the sky up to row.," In 2006, we have undertaken a near-infrared proper motion survey - SIMP; \citealt{Artigau2009}) ) with the wide-field near-infrared camera CPAPIR \citep{Artigau2004} at the CTIO m and OMM m \citep{Racine1978} telescopes and have covered $\sim35\%$ of the sky up to now."1019 BD candidates were found using both the SIMP aud 2ATASS database obtained at different epochs to identify ugh proper motion sources., BD candidates were found using both the SIMP and 2MASS database obtained at different epochs to identify high proper motion sources.1020 Spectroscopic follow-up of Heh proper motion candidates las been done with CNIRS (Eliasetal.2006)... SpeX (Ravueretal.2003) and NIRI (Ilodappetal.2003) in 2006. 2007 and 2008.," Spectroscopic follow-up of high proper motion candidates has been done with GNIRS \citep{Elias2006}, SpeX \citep{Rayner2003} and NIRI \citep{Hodapp2003} in 2006, 2007 and 2008."1021 More than 80 new L dwarts aud 11 new T cwas (Ανάσα et al.," More than 80 new L dwarfs and 14 new T dwarfs (Artigau et al.,"1022 in prep.), in prep.)1023 were confiruied., were confirmed.1024 We did not expect to detect any resolved biuaries in our siuuple eiven that the binary DDs separation distribution peaks at ~ LAAT (Masted&Jeffries2005:Durgasseretal.2007b) and that all of our observatious were secing-limited.," We did not expect to detect any resolved binaries in our sample given that the binary BDs separation distribution peaks at $\sim4$ AU \citep{Maxted2005, Burgasser2007} and that all of our observations were seeing-limited."1025 We nevertheless searched. svstcmatically through our spectroscopy acquisition nuages and found two partially resolved binarics: ao pair of iid-L dwarts separated by ~1.0% (SIMIPJ1501530-013506. hereafter J1501-0135) aud ai pair of iuid-Ts separated by ~0.7 (SIMPJ1619275|031350. hereafter J1619]0313).," We nevertheless searched systematically through our spectroscopy acquisition images and found two partially resolved binaries: a pair of mid-L dwarfs separated by $\sim1.0\arcsec$ (SIMPJ1501530-013506, hereafter ) and a pair of mid-Ts separated by $\sim0.7\arcsec$ (SIMPJ1619275+031350, hereafter )."1026 Following these discoveries. we obtained a series of observatious to characterize the individual compoucuts of these svstenis.," Following these discoveries, we obtained a series of observations to characterize the individual components of these systems."1027 Ins 2.1 we present the NIBI resolved spectroscopy of both systems., In \ref{spectro} we present the NIRI resolved spectroscopy of both systems.1028" Iu 2.2.. 2.3. 2.1 ands 2.5 we detail resolved aud uuresolved. sccing-lanited. / through A, photometric measurements and Laser Guide Star (LGS) AQ observations of doth binaries."," In \ref{niri_photometry}, \ref{megacam_photometry}, \ref{cpapir_photometry} and \ref{lgs} we detail resolved and unresolved, seeing-limited, $i$ through $K_{\rm s}$ photometric measurements and Laser Guide Star (LGS) AO observations of both binaries."1029 Finallv. the spectral typing of all components is discussed in 3 and 1 details the properties of both svstems.," Finally, the spectral typing of all components is discussed in \ref{typing} and \ref{discussion} details the properties of both systems."1030 Following the discovery of the binary nature of aud we obtained a set of observatious tfo characterize their resolved far-red aud near-infrared (0.7-2.pau) spectral energy distribution (SED)., Following the discovery of the binary nature of and we obtained a set of observations to characterize their resolved far-red and near-infrared $\mu$ m) spectral energy distribution (SED).1031 These observations15 were aimed at putting both systems in the broader context of the existing sample of resolved BD binarics. as they both showed peculiarities worthy of further studs.," These observations were aimed at putting both systems in the broader context of the existing sample of resolved BD binaries, as they both showed peculiarities worthy of further study."1032 The large coutrast ratio of (AIF~ d5anag) suggested a αςΠομα biuarx. of which we know only a handful of examples.0," The large contrast ratio of $\Delta H \sim 1.5\,$ mag) suggested a mid-L/mid-T binary, of which we know only a handful of examples.,"10333123. with a ~T3 blended spectral type. lies at the cooler eud of the J-band brightening aud was seen as likely to provide useful coustraiuts to models telmpting to reproduce this interval.," with a $\sim$ T3 blended spectral type, lies at the cooler end of the $J$ -band brightening and was seen as likely to provide useful constraints to models attempting to reproduce this interval."1034 The characterization was done through resolved optical aud near-infrared plotometry. resolved. infrared spectroscopy. ligh-aneular resolution nuagiug. aud accurate near-infrared blended plotometirv.," The characterization was done through resolved optical and near-infrared photometry, resolved infrared spectroscopy, high-angular resolution imaging, and accurate near-infrared blended photometry."1035 These observations resulted in detailed portraits of the individual components of both systems., These observations resulted in detailed portraits of the individual components of both systems.1036 Alog of all observations is provided in Table 1.., Alog of all observations is provided in Table \ref{tbl-3}.1037 All measurements available at hand. both frou archives aud from the observations presented lere. as well as derived quantities. are conipiled for aand in Tables 2 and 3. respectively.," All measurements available at hand, both from archives and from the observations presented here, as well as derived quantities, are compiled for and in Tables \ref{tbl-1} and \ref{tbl-2} respectively."1038 When applicable. these lucasurements are eiven for the individual componcuts of both svstens.," When applicable, these measurements are given for the individual components of both systems."1039 Seeing linited spectroscopy was obtained at the Comin North telescope with NIBRI for both binaries under excellent secing couditions (FEWIIM.~0.17)., Seeing limited spectroscopy was obtained at the Gemini North telescope with NIRI for both binaries under excellent seeing conditions ${\rm FWHM}\sim0.4\arcsec$ ).1040 For voth binaries. the slit was aligned with the binary axis to include both components in the slit.," For both binaries, the slit was aligned with the binary axis to include both components in the slit."1041 The I-pixel 1097)} wide slit in the blue setup was used in combination witli he £/6 JJ. £/6 II and £/6 Iv exiis for a resolving power of 650 to 825.," The 4-pixel ) wide slit in the blue setup was used in combination with the f/6 $J$, f/6 $H$ and f/6 $K$ grisms for a resolving power of 650 to 825."1042 For cach evista setup. a sot of 10. 120-8 exposures was taken with a mod along the slit between exposures.," For each grism setup, a set of 10 120-s exposures was taken with a nod along the slit between exposures."1043 Telluric correction was performed using AQ-Al star spectra (IMP 75230 and TIP 79163 for and1135. respectively).," Telluric correction was performed using A0-A1 star spectra (HIP 75230 and HIP 79463 for and, respectively)."1044 Spectroscopic flats were obtained ax part of the standard calibratious with the CCAL calibration unit., Spectroscopic flats were obtained as part of the standard calibrations with the GCAL calibration unit.1045 Wavelength calibration was performed w oregisteriue brielt telhlurie cussion lues., Wavelength calibration was performed by registering bright telluric emission lines.1046 The spectra were reduced by first pair subtracting wo dithered spectral images., The spectra were reduced by first pair subtracting two dithered spectral images.1047 The resulting positive aud reeative traces showed the spectra of both componcuts with little overlap., The resulting positive and negative traces showed the spectra of both components with little overlap.1048 We extracted the individual spectra o» unge a linear inversion method where. for cach spectral pixel we represented the trace along the spatial direction by the stn of two 1-D Caussians of identical widths. with the same separation as the binary.," We extracted the individual spectra by using a linear inversion method where, for each spectral pixel, we represented the trace along the spatial direction by the sum of two 1-D Gaussians of identical widths, with the same separation as the binary."1049 This linear inversion correctly handles the overlapping spectra., This linear inversion correctly handles the overlapping spectra.1050 Ouce extracted. the final spectrum of cach component was obtained by taking the median of all individual exposures and corrected for telluric absorption.," Once extracted, the final spectrum of each component was obtained by taking the median of all individual exposures and corrected for telluric absorption."1051 The J. fF aud A spectra were scaled. by adjusting svuthetic fiuxes to the NIRI aud CPAPIR photometry 2.2 and 2.1)).," The $J$, $H$ and $K$ spectra were scaled by adjusting synthetic fluxes to the NIRI and CPAPIR photometry \ref{niri_photometry} and \ref{cpapir_photometry}) )."1052 Figure1. shows the resolved spectra of both components of both binarics compared to archival spectra of L1.5. L5.5. T3 aud Tl dwarts.," Figure \ref{fig3} shows the resolved spectra of both components of both binaries compared to archival spectra of L4.5, L5.5, T3 and T4 dwarfs."1053" Iu addition. to the spectroscopic observations. we obtained resolved J. 11. photometry with NIRI for both binaries under excellent secine conditions 0.52""))."," In addition to the spectroscopic observations, we obtained resolved $J$, $H$ , photometry with NIRI for both binaries under excellent seeing conditions )."1054 Iun addition. these observations confinia the differcutial photometry obtained from AO observations 2.5)).," In addition, these observations confirm the differential photometry obtained from AO observations \ref{lgs}) )."1055 Resolved photometry is necessary to accurately reconstruct the near-infrared spectrum of cach binary conrponeutasthe NIRI spectra were obtained piecewise with separate J. ff aud A-egrisui setups.," Resolved photometry is necessary to accurately reconstruct the near-infrared spectrum of each binary componentasthe NIRI spectra were obtained piecewise with separate $J$ , $H$ and $K$ -grism setups."1056 The nuages were reduced in ai standard imanucr., The images were reduced in a standard manner.1057 A sky image was obtained by median combining all, A sky image was obtained by median combining all1058"This is demonstrated in Figure 2,, where we have plotted the density-temperature evolution of protostellar cores of two different metallicities (logZ/Zc;=—2, —3) from ?..","This is demonstrated in Figure \ref{figure:omukai}, where we have plotted the density-temperature evolution of protostellar cores of two different metallicities $\log Z/Z_{\sun} = -2$, $-3$ ) from \citet{omukai-etal05}."1059" In each of the four panels, we have imposed a temperature floor given by aata different redshift."," In each of the four panels, we have imposed a temperature floor given by ata different redshift."1060" At z=3, Temp=10.9 K, which is colder than either core ever reaches, and theCMB has no effect."," At $z=3$, $\TCMB=10.9$ K, which is colder than either core ever reaches, and theCMB has no effect."1061" At z=4.2, Tomp=14.2 K, which is the exact minimum temperature that the logΖ/Ζο=—2 protostar reaches; if the CMB temperature were any higher, it would affect thecore evolution."," At $z=4.2$, $\TCMB=14.2$ K, which is the exact minimum temperature that the $\log Z/Z_{\sun}=-2$ protostar reaches; if the CMB temperature were any higher, it would affect thecore evolution."1062" This can be seen at z= 11.5, when Temp=34.1 K; the log7/Z=—2 core does not cool nearlyas far, and the CMB temperature just reaches the minimum temperature of the logZ/Zc=—3 protostar."," This can be seen at $z=11.5$ , when $\TCMB=34.1$ K; the $\log Z/Z_{\sun}=-2$ core does not cool nearlyas far, and the CMB temperature just reaches the minimum temperature of the $\log Z/Z_{\sun}=-3$ protostar."1063" At z—15, the temperature floor imposed by the CMB clearly affects the evolution of both cores."," At $z=15$, the temperature floor imposed by the CMB clearly affects the evolution of both cores."1064" We therefore adopt Zeug,=43)107?Ze and Zomp(z=11.5)metallicity107% trac", We therefore adopt $\ZCMB(z=4.2) = 10^{-2}~Z_{\sun}$ and $\ZCMB(z=11.5) = 10^{-3}~Z_{\sun}$.1065kWe the same calculation for each ini ? performand plot the relationship as the solid line in Figure 1.., We perform the same calculation for each metallicity track in \citet{omukai-etal05} and plot the relationship as the solid line in Figure \ref{figure:zcmbest}.1066" Fragmentation is only expected to be efficient when the Jeans mass rapidly decreases, i.e. when the tracks move downward."," Fragmentation is only expected to be efficient when the Jeans mass rapidly decreases, i.e. when the tracks move downward."1067 Therefore the characteristic mass scale is the Jeans mass when the core stops cooling(?).., Therefore the characteristic mass scale is the Jeans mass when the core stops cooling\citep{larson05}.1068 Lines of constant Jeans mass are shown as the diagonal dashed gray lines in Figure 2.., Lines of constant Jeans mass are shown as the diagonal dashed gray lines in Figure \ref{figure:omukai}.1069" For the Z—107? track, this characteristic scale is 0.2Mo, but at redshift z—11.5 it rises to 50"," For the $Z=10^{-2}~Z_{\sun}$ track, this characteristic scale is $0.2~M_{\sun}$, but at redshift $z=11.5$ it rises to $50~M_{\sun}$."1070 The top-heavy IMF is a direct consequence of this dramaticMo. change in the characteristic mass scale at the end of fragmentation., The top-heavy IMF is a direct consequence of this dramatic change in the characteristic mass scale at the end of fragmentation.1071" Because the temperature of the protostellar core only just reaches the CMB temperature, it is unlikely that the CMB has much effect at the exact redshift we calculate."," Because the temperature of the protostellar core only just reaches the CMB temperature, it is unlikely that the CMB has much effect at the exact redshift we calculate."1072" The Tomp(z), and therefore z, that we calculate for each metallicity must be a slight underestimate, or correspondingly the tthat we calculate at each redshift must be a slight underestimate."," The $\TCMB(z)$, and therefore $z$, that we calculate for each metallicity must be a slight underestimate, or correspondingly the that we calculate at each redshift must be a slight underestimate."1073" Our estimated mmatches the simulation results of ? very well for their Set 1 initial conditions, mildly underpredicts it for their Set 3 intial conditions, and underpredicts it by about an order of magnitude for their Set 2 initial conditions."," Our estimated matches the simulation results of \citet{stson}1074 very well for their Set 1 initial conditions, mildly underpredicts it for their Set 3 intial conditions, and underpredicts it by about an order of magnitude for their Set 2 initial conditions."1075" We should therefore expect that the transition between a normal and top-heavy IMF occurs at metallicities somewhere between our predicted aand a metallicity ten times larger, with the details depending on the properties and formation history of the individual halos in which the star formation occurs."," We should therefore expect that the transition between a normal and top-heavy IMF occurs at metallicities somewhere between our predicted and a metallicity ten times larger, with the details depending on the properties and formation history of the individual halos in which the star formation occurs."1076" Although our estimate for iis well-defined down to z=0.2, it is unlikely that CMB regulation is truly important at these redshifts."," Although our estimate for is well-defined down to $z\approx 0.2$ , it is unlikely that CMB regulation is truly important at these redshifts."1077" As noted by ?,, gas clouds in the local ISM are not observed to cool below 10 K; therefore, when the CMB drops below this temperature, it can no longer affect the thermal evolution of protostellar gas."," As noted by \citet{stson}, gas clouds in the local ISM are not observed to cool below $10$ K; therefore, when the CMB drops below this temperature, it can no longer affect the thermal evolution of protostellar gas."1078" This occurs at z—2.7, denoted by the vertical dotted line in Figure 1.."," This occurs at $z=2.7$, denoted by the vertical dotted line in Figure \ref{figure:zcmbest}."1079" As discussed earlier, a top-heavy IMF is also expected for Population III stars, with metallicities belowZeit, denoted by the horizontal dot-dashed line in Figure 1.."," As discussed earlier, a top-heavy IMF is also expected for Population III stars, with metallicities below, denoted by the horizontal dot-dashed line in Figure \ref{figure:zcmbest}."1080" A normal IMF is therefore expected in the shaded region of Figure 1; at lower metallicities, cooling is too inefficient for fragmentation to occur, while at higher metallicities, the gas cools immediately to the CMB temperature where it becomes isothermal and does not fragment."," A normal IMF is therefore expected in the shaded region of Figure \ref{figure:zcmbest}; at lower metallicities, cooling is too inefficient for fragmentation to occur, while at higher metallicities, the gas cools immediately to the CMB temperature where it becomes isothermal and does not fragment."1081" Although the estimates of the boundaries of the region are rough, they provide a guideline for the star formation events that would have been influenced by the CMB."," Although the estimates of the boundaries of the region are rough, they provide a guideline for the star formation events that would have been influenced by the CMB."1082 It is interesting that our derived rrises substantially from «10-7?Zo at z>10 to ~10-1? at z~3., It is interesting that our derived rises substantially from $< 10^{-3}~Z_{\sun}$ at $z>10$ to $\sim 10^{-1.5}$ at $z\sim 3$.1083" Such metallicities are typical for old stellar populations, and it is therefore plausible that CMB regulation could have been important for stars formed at these redshifts."," Such metallicities are typical for old stellar populations, and it is therefore plausible that CMB regulation could have been important for stars formed at these redshifts."1084" In order to determine the effects of CMB-regulated star formation, we must estimate, at each redshift z, the fraction of stars that formed with metallicities Z> ZcoMB(z)."," In order to determine the effects of CMB-regulated star formation, we must estimate, at each redshift $z$, the fraction of stars that formed with metallicities $Z > \ZCMB(z)$ ."1085" Observational measurements are available at zS3 from stellar population modelling of the integrated spectra of galaxies from the Sloan Digital Sky Survey (SDSS; ?)), but, as discussed in 2, the effects of the CMB are only likely to be significant at z>3."," Observational measurements are available at $z \la 3$ from stellar population modelling of the integrated spectra of galaxies from the Sloan Digital Sky Survey (SDSS; \citealp{panter-etal08}) ), but, as discussed in \ref{section:estimating-zcmb}, the effects of the CMB are only likely to be significant at $z \ga 3$."1086 We must therefore use theoretical models to estimate the cosmic evolution of the metallicity of star-forming gas., We must therefore use theoretical models to estimate the cosmic evolution of the metallicity of star-forming gas.1087" Our simulations were performed as part of the McMaster Unbiased Galaxy Simulations project a campaign to construct high resolution simulations(MUGS), of a large set of L* galaxies that randomly sample the sites of galaxy formation, including full range of modern galaxy formation physics."," Our simulations were performed as part of the McMaster Unbiased Galaxy Simulations project (MUGS), a campaign to construct high resolution simulations of a large set of $L^*$ galaxies that randomly sample the sites of galaxy formation, including a full range of modern galaxy formation physics."1088 Full detailsa of the MUGS simulations will be presented in Stinson etal. (, Full details of the MUGS simulations will be presented in Stinson etal. (1089in preparation); we provide an overview of the most important properties of the simulations below.,in preparation); we provide an overview of the most important properties of the simulations below.1090" The simulations were performed using a WMAP 3 ACDM cosmology with Ho=τὸkms! Mpc!, Q,,= 0.24 QA,= 0.76, Ώνων= 0.04, and og=0.76 (?).."," The simulations were performed using a WMAP 3 $\Lambda$ CDM cosmology with $H_0 = 73~\mathrm{km~s^{-1}~Mpc^{-1}}$ , $\Omega_m=0.24$ , $\Omega_\Lambda=0.76$ , $\Omega_{\mathrm{bary}}=0.04$ , and $\sigma_8=0.76$ \citep{wmap3}. ."1091 Halos were chosen from a uniform-resolution 256?dark simulation in a box of side 50h! Mpc using the matter-onlyfriends-of-friends algorithm , Halos were chosen from a uniform-resolution $256^3$dark matter-only simulation in a box of side $50~h^{-1}$ Mpc using the friends-of-friends algorithm \citep{defw85}. .1092A random selection of isolated halos with masses (?)..4resimulation.x10!!Mo< were chosen for at higher resolution with full baryonic physics.," A random selection of isolated halos with masses $4 \times 10^{11}~M_{\sun} \le1093M \le 2 \times 10^{12}~M_{\sun}$ were chosen for resimulation at higher resolution with full baryonic physics."1094 The highest, The highest1095(and all CDM) mass density profiles are characterized by steep central cusps.,(and all CDM) mass density profiles are characterized by steep central cusps.1096 This is in coutrast with the other conunonly used “classic” pseudo-isothermal sphere halo model which is characterized by a coustaut deusity core., This is in contrast with the other commonly used “classic” pseudo-isothermal sphere halo model which is characterized by a constant density core.1097 The paramcters of the NEW iass density distribution are related to the mass of the halo aud the deusity of the universe at the time of collapse aud are therefore set bv the cosmology., The parameters of the NFW mass density distribution are related to the mass of the halo and the density of the universe at the time of collapse and are therefore set by the cosmology.1098 As these parameters can be determined from observations. this opens the possibility of testing the NEW CDAL model as well its underline assumptions.," As these parameters can be determined from observations, this opens the possibility of testing the NFW CDM model as well its underlying assumptions."1099 A first analysis of LSB ealaxy rotation curves by deBlok&MeGaueh(1997). indicated that they did not rise as steeply as their USB counterparts of similar Iuninosity. contrary to CDAL predictions.," A first analysis of LSB galaxy rotation curves by \citet{edb_rot}1100 indicated that they did not rise as steeply as their HSB counterparts of similar luminosity, contrary to CDM predictions."1101 The mass distribution iu LSB ealaxics is more exteuded aud of lower density tha in USB ealaxies (deBlok&AlcGangh1996)., The mass distribution in LSB galaxies is more extended and of lower density than in HSB galaxies \citep{edb_hsblsb96}.1102. Other results also indicate that the steep rotation curves nuplied by CDM ave hard to reconcile with the observed shallow rotation curves of dwarf galaxies (Moore1901:uan2001:Coté.Carignan&Freeman 2000).," Other results also indicate that the steep rotation curves implied by CDM are hard to reconcile with the observed shallow rotation curves of dwarf galaxies \citep{moore94,floresprimack94,blais00,cote00}."1103. To explain this discrepancy the possibility of redistribution of the (cuspy) DM due to violent star-formation (thus creating the observed cores) was sometimes raised. but this has been shown to be immconsisteunt with other observational data (MacLow&Ferrara1998).," To explain this discrepancy the possibility of redistribution of the (cuspy) DM due to violent star-formation (thus creating the observed cores) was sometimes raised, but this has been shown to be inconsistent with other observational data \citep{maclow}."1104. MeGanegh&deBlok(1998). argued that the shapes of rotation curves of LSB ealaxies were mconsisteut with those predicted by the NEW prescription., \citet{mcg_nodm98} argued that the shapes of rotation curves of LSB galaxies were inconsistent with those predicted by the NFW prescription.1105 This could uo be explained by the effects of star formation as the larger masses of LSB ealaxies would require large bursts in order to redistribute matter on large scales., This could not be explained by the effects of star formation as the larger masses of LSB galaxies would require large bursts in order to redistribute matter on large scales.1106 Their quiesceu evolutionary history argues stronely against this (vaudeuIIocketal. 2000)., Their quiescent evolutionary history argues strongly against this \citep{vdhoek00}.1107. This comparison with the CDM model is often disiuisse because of the liuited resolution of the observed curves., This comparison with the CDM model is often dismissed because of the limited resolution of the observed curves.1108 The carly LSB rotation curves were obtainc using the and radio svuthesis telescopes., The early LSB rotation curves were obtained using the and radio synthesis telescopes.1109 The relatively large beams of these imstruneuts resulted iu rotation curves with ouly a limited resolution., The relatively large beams of these instruments resulted in rotation curves with only a limited resolution.1110 deBlok&MeCGaugh(1997). did however show that for the best resolved cases the effects of beam siucaring were not strong enough to explain the observed shallow curve as simply the result of a steep NEW inodel curve affected by beausIncaring., \citet{edb_rot} did however show that for the best resolved cases the effects of beam smearing were not strong enough to explain the observed shallow curve as simply the result of a steep NFW model curve affected by beam-smearing.1111" Sinular results were found for more fashionable cosmmologies. suchas ACDAL(Q,,~0.3.Oy, 0.7). though with smaller discrepancies."," Similar results were found for more fashionable cosmologies, such as $\Lambda$ CDM $\Omega_m \sim 0.3,\1112\Omega_{\Lambda}\sim 0.7$ ), though with smaller discrepancies."1113 Even so. the theoretical debate now ποσα» to have settled on halos with cusps even steeper than NEW halos (Mooreetal.1999).. thus worsening the possible conflict between the data and the simulations.," Even so, the theoretical debate now seems to have settled on halos with cusps even steeper than NFW halos \citep{moore99}, thus worsening the possible conflict between the data and the simulations."1114 From the observational point of view the easiest aud least anibigous wav to test the reality of these discrepancies is fo mcasire lüeh-resolutiou rotation curves., From the observational point of view the easiest and least ambigous way to test the reality of these discrepancies is to measure high-resolution rotation curves.1115 Optical Ta rotation curves of five LSB galaxies from the sample of deBlok.MeCiaugh&vauder (DMII) were presented in Swaters.Madore&Trewlholla(2000) (SAIT)., Optical $\alpha$ rotation curves of five LSB galaxies from the sample of \citet{edb_bmh96} (BMH) were presented in \citet{SMT} (SMT).1116 Thouneh SALT found that for two of the five galaxies the imucr slopes of the rotation curves were steeper than derived from the observations. this difference docs not affect the DMIT conchision that LSB rotation curves have shallower slopes than USB rotation curves of simular amplitude.," Though SMT found that for two of the five galaxies the inner slopes of the rotation curves were steeper than derived from the observations, this difference does not affect the BMH conclusion that LSB rotation curves have shallower slopes than HSB rotation curves of similar amplitude."1117 Because of these steeper slopes. SAIT derive higher masximauu-disk vvalues (i sole cases >LO). strenethening one of the conclusious from deBlok&AlcCaugh(1997). that the maximum vvalues in LSB ealaxies are too large to be accomodated by reasonable star formation histories ancl Initial Mass Functions.," Because of these steeper slopes, SMT derive higher maximum-disk values (in some cases $> 10$ ), strengthening one of the conclusions from \citet{edb_rot} that the maximum values in LSB galaxies are too large to be accommodated by reasonable star formation histories and Initial Mass Functions."1118 Such hieh values are inconsistent with the existence of a barvonic TF-relation 2000)., Such high values are inconsistent with the existence of a baryonic TF-relation \citep{mcg_barytf}.1119 A differeut approach was taken by vandeuBoschetal.(20003., A different approach was taken by \citet{frankvdb}.1120. They attempted to apply a rigorous correction for beausimoeariug to the DMIT data. and thus to derive the true “infinite resolution” rotation curve.," They attempted to apply a rigorous correction for beamsmearing to the BMH data, and thus to derive the true “infinite resolution” rotation curve."1121 Thev conclude that the data are not of high enoushl resolution to accept or reject the NEW hypothesis with any significance., They conclude that the data are not of high enough resolution to accept or reject the NFW hypothesis with any significance.1122 However. as they use a niodified NEW profile with the inner slope of the mass-deusity distribution as an (additional) free paralcter. it is not clear how significant this conclusion is.," However, as they use a modified NFW profile with the inner slope of the mass-density distribution as an (additional) free parameter, it is not clear how significant this conclusion is."1123 The usual 3-paraineter rotation curve fits are already nuder-constrained: adding another paramcter does not nuprove the significance of the results., The usual 3-parameter rotation curve fits are already under-constrained; adding another parameter does not improve the significance of the results.1124 Furthermore. in sole cases they find such low values for the immer slope that their NFW-halos effectively become core-dominuated.," Furthermore, in some cases they find such low values for the inner slope that their NFW-halos effectively become core-dominated."1125 These halos do of course fit the data. but do not occur iu CDAL simulations.," These halos do of course fit the data, but do not occur in CDM simulations."1126 The general picture as derived from carly observations of rotation curves of LSB ealaxics therefore still holds: LSB ealaxies are unevolved. low density galaxies. dominated by DM.," The general picture as derived from early observations of rotation curves of LSB galaxies therefore still holds: LSB galaxies are unevolved, low density galaxies, dominated by DM."1127 Their rotation curves have shallower slopes than those of IISD ealaxies of similar amplitude. and the shape of the best-resolved LSB curves are not necessarily consistent with the ΣΕΝ rotation curve shapes.," Their rotation curves have shallower slopes than those of HSB galaxies of similar amplitude, and the shape of the best-resolved LSB curves are not necessarily consistent with the NFW rotation curve shapes."1128 Iu this paper we present au analysis of high-resolution lugh-quality hybrid Io rotation curves of a sample of 30 LSB ealaxies., In this paper we present an analysis of high-resolution high-quality hybrid $\alpha$ rotation curves of a sample of 30 LSB galaxies.1129 Of this sample 26 curves were taken from the large saunple of50 LSB galaxies presented in MeCaugh. Rubin de Blok (2001) Cherafter Paper I).," Of this sample 26 curves were taken from the large sample of 50 LSB galaxies presented in McGaugh, Rubin de Blok (2001) (herafter Paper I)."1130 In that paper an exteusive description is eiven of the data. the sample and recuction method.," In that paper an extensive description is given of the data, the sample and reduction method."1131 We also refer to that paper for a conrparisou of the new Πα data with the DMIT curves., We also refer to that paper for a comparison of the new $\alpha$ data with the BMH curves.1132 We also re-analyse the data for au additional 5 curves taken from Swaters.Madore&Trewhella(2000)., We also re-analyse the data for an additional 5 curves taken from \citet{SMT}.1133. In. this paper we derive mass models uuder various assunrptions for aud fit these models both with NEW halos aud pseudo-isothermal halos., In this paper we derive mass models under various assumptions for and fit these models both with NFW halos and pseudo-isothermal halos.1134 A similar analysis for a differeut set of rotation curves of dwarf aud LSB salaxies is given iu de Blok Bosina (2001)., A similar analysis for a different set of rotation curves of dwarf and LSB galaxies is given in de Blok Bosma (2001).1135 Iu Section 2 we discuss the sample. and discuss the derivation of the rotation curves.," In Section 2 we discuss the sample, and discuss the derivation of the rotation curves."1136 We also show internal and external couparisous of the data and discuss possible systematics., We also show internal and external comparisons of the data and discuss possible systematics.1137 Iu Section 3 we discuss the various lass models., In Section 3 we discuss the various mass models.1138 Section 1 contains the results of the model fitting., Section 4 contains the results of the model fitting.1139 Section 5 discusses the miplicatious for the various halo models., Section 5 discusses the implications for the various halo models.1140 Iu Section 6 we tum our attention to the maxi disk and a sunu ds given in Section 7., In Section 6 we turn our attention to the maximum disk and a summary is given in Section 7.1141uet flux of augular momentum through the disk. 4... is therefore zero.,"net flux of angular momentum through the disk, $\dot J_z$, is therefore zero."1142 We therefore assmne that the :- conrponeut of the net flux. (which is equal to the conrponeut of the uct flux parallel to the axis of the disk. to first order iu the tilt) is zero.," We therefore assume that the $z$ -component of the net flux (which is equal to the component of the net flux parallel to the axis of the disk, to first order in the tilt) is zero."1143 Tu order to simplify the preseutation. the equatious in the remainder of this section assume that the aneular velocity iu the disk is Keplerian in the l/r Nowtouiau-: potential.: (," In order to simplify the presentation, the equations in the remainder of this section assume that the angular velocity in the disk is Keplerian in the $1/r$ Newtonian potential. ("1144The: generalization: to pseudopotentials: is straightforward.),The generalization to pseudopotentials is straightforward.)1145 For Ixepleriau disks with zero net augular moment flux alone the z-axis. eg=G4/0(000/0R)(3/2)04/R) ," For Keplerian disks with zero net angular momentum flux along the $z$ -axis, $v_{\rm R} =1146(\nu_1/\Omega) (\pd\Omega/\pd R) =1147-(3/2)(\nu_1/R)$ everywhere."1148"To facilitate ⋅comparison with. previous: work.then we consider disks with power-huw radial teiuperature B =⋅ πι)!"".wherethe subscript i ATP. |qp! value.+ of the quantityH at theH inner radius 1H ενUl calculation."," To facilitate comparison with previous work, we consider disks with power-law radial temperature profiles $T(R)1149= T_{\rm i} (R/R_{\rm i})^{-\mu}$, where the subscript i indicates the value of the quantity at the inner radius of the calculation."1150". Iu attheàjo]. a-disk model.N a4""P (9Ο⋅ 0)fin,audheuce tour. A= iu the⋅ 6preseut work we take the ratio Bj leFor μονofthe two+ kinematic viscosities fo+AM he»— ICR. ""T radius."," In the $\alpha$ -disk model, $-\rho\nu_1 R(\pd\Omega/\pd1151R) = 2\alpha\rho k_{\rm B}T/m_{\rm p}$ and hence For simplicity, in the present work we take the ratio $\kappa \equiv \nu_2/\nu_1$ of the two kinematic viscosities to be independent of radius."1152 ↽−↽ Lr.10b∣ tilt angles. | z (cos5./sin5.1)aud=f ο disk warp is completely specified locally by the tilt ¢ and twist 5.," For small tilt angles, ${\bf l} \approx1153(\beta\cos\gamma, \beta\sin\gamma, 1)$ and hence the disk warp is completely specified locally by the tilt $\beta$ and twist $\gamma$."1154 Following Uatchett et al. is represeut the warp by the iÀuaginaryqns parts. ofnate the: complex∖⊳ variabk ∖moment ∣j IT—jeos{1=Jel.," Following Hatchett et \\markcite{HBS81}( (1981), we represent the warp by the real and imaginary parts of the complex variable $W \equiv1155\beta\cos\gamma + i\beta\sin\gamma = \beta1156e^{i\gamma}$."1157 Then the componentThe equation. (1)) ↴⋅ perpendicular toη z can be written as ⋅⋅ Papaloizoube ©ap:& 1108311983.o )eq. [," Then the component of equation \ref{AngMomCons}) ) perpendicular to $\hat{\bf z}$ can be written as (compare Papaloizou Pringle \markcite{PP83}1 1983, eq. ["11582.6i [2.6]:efücienev Here where is the characteristic angular frequency associated with the radiation torque at the Ίππο edge of the disk. expressed im terms of the accretion efficiency €.,"2.6]) Here where is the characteristic angular frequency associated with the radiation torque at the inner edge of the disk, expressed in terms of the accretion efficiency $\epsilon$."1159 In writing the last expression on the right iu equation (£L). we have used the mass continuity equation and the expression for the radial velocity.," In writing the last expression on the right in equation \ref{Gamma}) ), we have used the mass continuity equation and the expression for the radial velocity."1160 We now chanee to the new radial variable where Ry—CM/c.4> aud look for. global modes of. the disk⋅ of. the form. W.(f.R);=ο...YGe).," We now change to the new radial variable where $R_g \equiv GM/c^2$, and look for global modes of the disk of the form $W(t,R) = e^{i\eta1161t} W(x)$."1162 Equation⋅ (3)). becomes everywhere. prime denotes differentiation. with respect.of 2nthe pkgT 2y/ ⋅⋅⋅c lex lefrequency sealed byGy. and Suny (GAL) eravitomaguetic frequency at. = 1 scaledby marketellDSs1((1981). we Gy. for a compact object with dimensionless angular = 0J/GM?.Dr," Equation \ref{dWdt}) ) then becomes where the prime denotes differentiation with respect to $x$, is the complex mode frequency scaled by $G_0$, and is the gravitomagnetic frequency at $x=1$ scaled by $G_0$, for a compact object with dimensionless angular momentum $j \equiv1163cJ/GM^2$."1164ealand strong depeudence of B: on the accretion of: ε. and: viscosity ratio. #. is anjp artifact of. comparePavaloi our clioice↴ xef& for ⋅fixed R.," The strong dependence of $B$ on the accretion efficiency $\epsilon$ and viscosity ratio $\kappa$ is an artifact of our choice $x \propto1165\epsilon/\kappa$ for fixed $R$."1166 The⋅ eravitomaguctic precession frequency at a eiven radius A2 is indepeudeut ofe anda. aud the radius at which the eravitomaguetic and radiation torques are comparable therefore depends only weakly on ε and s.," The gravitomagnetic precession frequency at a given radius $R$ is independent of $\epsilon$ and $\kappa$, and the radius at which the gravitomagnetic and radiation torques are comparable therefore depends only weakly on $\epsilon$ and $\kappa$."1167 Note alsothat if s is set to zero. so that the radiation torque is ucelected. equation (7)) becomes independent of e; as it must: in this case ε is simply an arbitrary factor m the conversion from to. aud has no plivsical 1icauing.," Note alsothat if $s$ is set to zero, so that the radiation torque is neglected, equation \ref{WarpEqn}) ) becomes independent of $\epsilon$, as it must; in this case $\epsilon$ is simply an arbitrary factor in the conversion from $R$ to $x$ and has no physical meaning."1168 Equation (7)) is a linear. complex. second-order ordinary differeutial equation with complex frequency AL," Equation \ref{WarpEqn}) ) is a linear, complex, second-order ordinary differential equation with complex frequency $A$."1169 Specifviug a solution of this equation. including the complex frequency. therefore requires six. conditions.," Specifying a solution of this equation, including the complex frequency, therefore requires six conditions."1170 The tilt amplitude and twist angle at the ner οσο of the disk are arbitrary. and hence only four couditious are plivsically meauimeful.," The tilt amplitude and twist angle at the inner edge of the disk are arbitrary, and hence only four conditions are physically meaningful."1171 In general. the plysics iuposes two boundary coucitious at the ππιο edge of the disk. at .j. aud two at the outer edee. at," In general, the physics imposes two boundary conditions at the inner edge of the disk, at $x_{\rm i}$ , and two at the outer edge, at"1172IU we are interested. in the error bars on 5; irrespective of the values of the other variables. we would marginalize over these. with error a;=AL? for the Gaussian case.,"If we are interested in the error bars on $s_i$ irrespective of the values of the other variables, we would marginalize over these, with error $\sigma_i = M_{ii}^{1/2}$ for the Gaussian case."1173 For most of the entries in Table 2 we use no prior at all (no? ). except for Va. where indicated.," For most of the entries in Table \ref{tab:satparams1} we use no prior at all $P$ '), except for $Y_{He}$ where indicated."1174" When priors are used. we adopted a diagonal covariance matrix 7;; with the following values for 725i: 0.3 on the normalization 90,25;1/2οο. 0.5 on ne. 2 on rj. 0.075 on wy. 1 on w,,. lon ων. lon oy. 0.5 on tuns and lon zc."," When priors are used, we adopted a diagonal covariance matrix $T_{ij}$ with the following values for $\sqrt{T_{ii}}$: 0.3 on the normalization $\delta \avrg{{\cal C}_\ell}_B^{1/2}/1175\avrg{{\cal C}_\ell}_B^{1/2}$, 0.5 on $n_s$ , 2 on $r_{ts}$, 0.075 on $\omega_b$, 1 on $\omega_{m}$, 1 on $\omega_{\Lambda}$, 1 on $\omega_{k}$, 0.5 on $\omega_{hdm}$, and 1 on $\tau_C$."1176" Some variables are restricted for physical reasons to lic within a certain range zc: and rj, must be positive.", Some variables are restricted for physical reasons to lie within a certain range $\tau_C$ and $r_{ts}$ must be positive.1177 Such constraints can be incorporated into the prior. out. at the expense of more complicated: expressions after mareginalization over these constrained variables.," Such constraints can be incorporated into the prior, but at the expense of more complicated expressions after marginalization over these constrained variables."1178 In. some cases. imposing physical restrictions can lead to a factor of wo or more improvement in the accuracy of the parameter estimates.," In some cases, imposing physical restrictions can lead to a factor of two or more improvement in the accuracy of the parameter estimates."1179 Generally the errors in the parameters will be correlated hrough nondiagonal components of (F|Τ*) 1., Generally the errors in the parameters will be correlated through nondiagonal components of $({\bf F}+{\bf T}^{-1})^{-1}$ .1180 Linear combinations of the parameters which are uncorrelated can »e found by diagonalizng (F|T+)., Linear combinations of the parameters which are uncorrelated can be found by diagonalizing $({\bf F}+{\bf T}^{-1})$.1181 When the eigenvalues of (F|T+) are rank ordered. from highest to lowest. the variable combinations corresponding to high. values will be very accurately determined. while those for the lowest may be very poorly determined. representing the most degenerate directions in parameter space.," When the eigenvalues of $({\bf F}+{\bf T}^{-1})$ are rank ordered, from highest to lowest, the variable combinations corresponding to high values will be very accurately determined, while those for the lowest may be very poorly determined, representing the most degenerate directions in parameter space."1182 In Tables 2 and 3 below we list the number of parameter combinations that are determined within a £0.01 and £01 accuracy.," In Tables 2 and 3 below we list the number of parameter combinations that are determined within a $\pm11830.01$ and $\pm 0.1$ accuracy."1184 In this section we apply the above machinery to determine the accuracy of cosmological parameter estimation [rom two satellite experiments: the MAP. satellite selected: by NASA (Bennett 1996b). and the Planck. Surveyor Mission. (formerly named CODIUAS/SAMDBDA) selected by ESA (Bersanelli 1996)., In this section we apply the above machinery to determine the accuracy of cosmological parameter estimation from two satellite experiments: the MAP satellite selected by NASA (Bennett 1996b) and the Planck Surveyor Mission (formerly named COBRAS/SAMBA) selected by ESA (Bersanelli 1996).1185 These satellites olfer examples of the best that is likely to be achieved in the next clecace., These satellites offer examples of the best that is likely to be achieved in the next decade.1186 Ground based and balloon borne experiments will certainly continue to provide improved constraints on cosmological »wameters over this timescale. and so we also analyze a sample long duration balloon experiment (LDB).," Ground based and balloon borne experiments will certainly continue to provide improved constraints on cosmological parameters over this timescale, and so we also analyze a sample long duration balloon experiment (LDB)."1187 The specifications adopted for NLAP. and. Planck are istec in. Table 1 and have been computed from the information provided on the respective WWW. pages for he two missions., The specifications adopted for MAP and Planck are listed in Table 1 and have been computed from the information provided on the respective WWW pages for the two missions.1188 Although indicative. of the expected »erformance of each. satellite at the time of writing. these are likely to evolve.," Although indicative of the expected performance of each satellite at the time of writing, these are likely to evolve."1189 OF the 5 LEAT channels for NLAD. we assume that the 3 highest frequency. channels. at 40. 60 and 90 Cllz. will be dominated by the primary cosmological signal.," Of the 5 HEMT channels for MAP, we assume that the 3 highest frequency channels, at 40, 60 and 90 GHz, will be dominated by the primary cosmological signal."1190 We also present the gains that result. from a iniprovement in angular resolution at all frequencies and 2 vears of observing time (we denote these specifications by MAP)., We also present the gains that result from a improvement in angular resolution at all frequencies and 2 years of observing time (we denote these specifications by $^{+}$ ).1191 Such. an improvement is now expected. for ALADP (Page. private communication).," Such an improvement is now expected for MAP (Page, private communication)."1192 Planck will have two detector arravs. à Low Frequeney Instrument. (LET) using IHIZM'Es and a Ligh Frequency Instrument. (HEIL) using bolometers.," Planck will have two detector arrays, a Low Frequency Instrument (LFI) using HEMTs and a High Frequency Instrument (HFI) using bolometers."1193 The current design of the LIL incorporates an aclelitional channel at 100. 6112 in aclelition to channels at 150. 217 and 353 Cillz: we have acoptec parameters as listed in Table 2 for these four channels.," The current design of the HFI incorporates an additional channel at 100 GHz in addition to channels at 150, 217 and 353 GHz; we have adopted parameters as listed in Table 2 for these four channels."1194 We also present results for the 3 highest resolution channels in the current design of the Planck LET whic= ms an expected. performance that is significantly improved over those given by Bersanclli (1996)., We also present results for the 3 highest resolution channels in the current design of the Planck LFI which has an expected performance that is significantly improved over those given by Bersanelli (1996).1195 For each multipole ἐς the computational procedure witomaticallv rotates the channels into a linear combination optimal for the CAB.," For each multipole $\ell$, the computational procedure automatically rotates the channels into a linear combination optimal for the CMB."1196 In practice. a more sophisticated treatment would be required in practice to remove Galactic ancl extragalactic foregrounds.," In practice, a more sophisticated treatment would be required in practice to remove Galactic and extragalactic foregrounds."1197 It is beyond the scope of lis letter to assess the svstematic errors in parameter estimates arising from. inaccurate foreground subtraction., It is beyond the scope of this letter to assess the systematic errors in parameter estimates arising from inaccurate foreground subtraction.1198" We therefore simply assume that Calactic foregrounds are negligible over a fraction of the sky. for,=0.65. similar to he velean’ sky. area adopted in most analyses of the COBL DOWEL spectrunm."," We therefore simply assume that Galactic foregrounds are negligible over a fraction of the sky $f_{sky}=0.65$, similar to the `clean' sky area adopted in most analyses of the COBE power spectrum."1199 Figure 1. shows examples of C; estimates. from one realization of the οςΝΤ and OCDM target models., Figure \ref{fig:CLpower} shows examples of ${\rm C}_\ell$ estimates from one realization of the SCDM and OCDM target models.1200 In this igure. the estimated power spectra have been averaged over 5% wide bands in f£.," In this figure, the estimated power spectra have been averaged over $5\%$ wide bands in $\ell$."

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