ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2"436) The bispectrum can then be modelled with the plane 56,6.6) from Figure 17 and a=0."," The bispectrum can then be modelled with the plane $\mathcal{B}_\star(r,\phi)$ from Figure \ref{PivotPlanesN0} and $\alpha=0$."3 Consider now the stresses of the ultra-violet field with ng=—5/2., Consider now the stresses of the ultra-violet field with $n_B=-5/2$.4 These integrals are much more difficult to integrate since the integration volumes are steeply tilted towards poles at the edges of the integration., These integrals are much more difficult to integrate since the integration volumes are steeply tilted towards poles at the edges of the integration.5 While such integrals can be controlled numerically. much longer chains are required if convergence is to be reached: 5x10° samples for the scalar modes. and 5x10° for the tensor auto-correlation. which possesses a significantly more complicated integration surface.," While such integrals can be controlled numerically, much longer chains are required if convergence is to be reached: $5\times 10^7$ samples for the scalar modes, and $5\times 10^8$ for the tensor auto-correlation, which possesses a significantly more complicated integration surface."6 Analytical solutions are difficult to find and may well not exist., Analytical solutions are difficult to find and may well not exist.7 As with the field. @ is sampled once every five degrees. except around the equilateral line for (5j which contains ar interesting feature and is sampled at every half a degree.," As with the white-noise field, $\phi$ is sampled once every five degrees, except around the equilateral line for $\av{\tau_S^3}$ which contains an interesting feature and is sampled at every half a degree."8" The bispectra are expected to scale along lines of constant [ó.r] as 8oc£77, "," The bispectra are expected to scale along lines of constant $\{\phi,r\}$ as $\mathcal{B}\propto k^{3(n_B+1)}$."9This scaling has been observed for colinear (BCOS. BO6. CFPRO9) and equilateral (CFPRO9) bispectra and is naivvely expected to hold throughout the rest of the bulk.," This scaling has been observed for colinear (BC05, B06, CFPR09) and equilateral (CFPR09) bispectra and is naïvvely expected to hold throughout the rest of the bulk."10 Towards the degenerate line. SSO9 and CFPRO9 found divergences 8ocq77— and concluded that this line dominates.," Towards the degenerate line, SS09 and CFPR09 found divergences $\mathcal{B}\propto q^{2n_B+3}$ and concluded that this line dominates."11 In the (4.r.6] coordinates this scaling will be obscured.," In the $\{k,r,\phi\}$ coordinates this scaling will be obscured."12 Specifically. the dominant term found i1," Specifically, the dominant term found in"13different shapes of (he cutoff in the electron spectrum (exponential in the first case ancl super-exponential in the second case) and possibly in different fits to the svnchrotron X-ray [ας and morphology.,different shapes of the cutoff in the electron spectrum (exponential in the first case and super-exponential in the second case) and possibly in different fits to the synchrotron X-ray flux and morphology.14 One note of caution should be issued about the assumption of stationarity that is underline all calculations of this (vpe., One note of caution should be issued about the assumption of stationarity that is underling all calculations of this type.15 Strictly speaking. stationarity can be reached only if the time for energy. losses is shorter than the age of the shock at all energies and the maximum energy is roughly obtained by equating the acceleration (me with the loss time.," Strictly speaking, stationarity can be reached only if the time for energy losses is shorter than the age of the shock at all energies and the maximum energy is roughly obtained by equating the acceleration time with the loss time."16 In a real astrophysical source it 15 usually the case (hat at sulliciently low momenta the loss time is shorter (han the age of the source. so that no stationarity ean be actually reached at (hose momenta.," In a real astrophysical source it is usually the case that at sufficiently low momenta the loss time is shorter than the age of the source, so that no stationarity can be actually reached at those momenta."17" In other words a spectral break can be expected in the volume integrated spectra of accelerated. particles al some momentum p, and the stationary solution found here should be applied only for p>p, (e.g. (Ixardashev 1962))).", In other words a spectral break can be expected in the volume integrated spectra of accelerated particles at some momentum $p_{b}$ and the stationary solution found here should be applied only for $p>p_{b}$ (e.g. \cite[]{karda}) ).18 This reflects in Cie spectra ol the emitted radiation., This reflects in the spectra of the emitted radiation.19 The formalism presented in this paper will be extended to the case of cosmic ray modified shocks in an upcoming paper: this application is crucial in (hat the presence of a precursor mav appreciably flatten the electron spectra at. high energy. and lead to the production of more pronounced spectral bunips., The formalism presented in this paper will be extended to the case of cosmic ray modified shocks in an upcoming paper: this application is crucial in that the presence of a precursor may appreciably flatten the electron spectra at high energy and lead to the production of more pronounced spectral bumps.20 The author is grateful to L. OC. Drury for reading a preliminary version of the manuscript and E. Amato for a useful conversation on (he spatial distribution of accelerated particles., The author is grateful to L. O'C. Drury for reading a preliminary version of the manuscript and E. Amato for a useful conversation on the spatial distribution of accelerated particles.21 This work was partially supported by MIURB (under grant. PRIN-2006) and by ASI through contract ASLINAF L/038/06/0., This work was partially supported by MIUR (under grant PRIN-2006) and by ASI through contract ASI-INAF I/088/06/0.22 This research was also supported in part bv the National science Foundation under Grant No., This research was also supported in part by the National Science Foundation under Grant No.23 PIIYO5-51164. in the context of the ProgramPlasmas. July 26-October 3. 2009 help at the KITP in Santa Barbara.," PHY05-51164, in the context of the Program, July 26-October 3, 2009 help at the KITP in Santa Barbara."24 llere we brielly illustrate the determination of the Green function of the adjoint equation. defined by:," Here we briefly illustrate the determination of the Green function of the adjoint equation, defined by:"25iu the gg—hpp and gq!—qqh(hpp) chaunels. and hence could contribute siguificantly to the discovery potential for a light Higgs scalar with enliauced couplings to leptous.,"in the $gg\rightarrow h\rightarrow \mu\mu$ and $qq'\rightarrow qq'h(h\rightarrow\mu\mu)$ channels, and hence could contribute significantly to the discovery potential for a light Higgs scalar with enhanced couplings to leptons."26 Higgs productiou via tlie processes aud could also potentially play a role in the discovery of a leptophilic Higgs. though the prospects iu these chanuels are uot as favorable as the other. aforementioned ones.," Higgs production via the processes and could also potentially play a role in the discovery of a leptophilic Higgs, though the prospects in these channels are not as favorable as the other, aforementioned ones."27" SAL cross-sectious [for these processes. taking into account the leptonic decay ofthe Higgs boson. are given iu Table 1. for the case in which mm,=120 GeV. These were determined from leading-order results obtained using MADCRAPH [0]. and modified by the appropriate /N-[actors: Ay=1.27 for signal [0].. Ape;=1.7 for background [0].."," SM cross-sections for these processes, taking into account the leptonic decay of the Higgs boson, are given in Table \ref{table:WHZH} for the case in which $m_h=120$ GeV. These were determined from leading-order results obtained using MADGRAPH \cite{Alwall:2007st} and modified by the appropriate $K$ -factors: $K_S=1.27$ for signal \cite{Brein:2003wg}, $K_{BG}=1.7$ for background \cite{Frixione:1992pj}."28 For processes in which the Higes decays to ppi.. the signal is clearly too small to be of any use.," For processes in which the Higgs decays to $\mu^+\mu^-$, the signal is clearly too small to be of any use."29 However. for processes involvingD> decays to 7. the signal is only about a factor of ~25 smaller than the backgrouud.," However, for processes involving decays to $\tau^+\tau^-$, the signal is only about a factor of $\sim 25$ smaller than the background."30 By optimizing cuts to eliminate the SN. backgrouud. this channel might. potentially be of use — particularly if BREA—rr) is enliauced. as in the L2HDMI.," By optimizing cuts to eliminate the SM background, this channel might potentially be of use — particularly if $\mathrm{BR}(h\rightarrow \tau\tau)$ is enhanced, as in the L2HDM."31 Little analysis of these processes exists in the literature. aud we leave the detailed study of these chiaunels for future work.," Little analysis of these processes exists in the literature, and we leave the detailed study of these channels for future work."32 Now that we have discussed (he channels in which one might look lor a leptonically-clecaying Higgs boson at the LHC. let us investigate the prospects for the discovery of such a Higgs boson iu the L2HDM. using the combined results Grom all eliaunels. discussecl above (excepting the WA. Ζ channels. which we have shown do not contribute siguilicautly to the discovery. potential).," Now that we have discussed the channels in which one might look for a leptonically-decaying Higgs boson at the LHC, let us investigate the prospects for the discovery of such a Higgs boson in the L2HDM, using the combined results from all channels discussed above (excepting the $Wh$, $Zh$ channels, which we have shown do not contribute significantly to the discovery potential)."33 lu particular. we focus on the region of sina - tans? parameter space in which i is large aud yy.171.," In particular, we focus on the region of $\sin\alpha$ - $\tan\beta$ parameter space in which $\eta_\ell$ is large and $\eta_q,\eta_V \sim 1$."34 Iu this case. the cross-sectious for processes involving a )couplingaresubstantialliiucreased.whilethiose forprocessesiivoletughhV V.. hliqqq.. or are only slightly reduced.," In this case, the cross-sections for processes involving a coupling are substantially increased, while those for processes involving , or are only slightly reduced."35 As before. for purposes of illustration. we will focus on the benchmark point (sina=0.55. tau= 3). which exemplifies this situation uicelv.," As before, for purposes of illustration, we will focus on the benchmark point $\sin\alpha=0.55$, $\tan\beta=3$ ), which exemplifies this situation nicely."36 In Fig. 9..," In Fig. \ref{fig:SigPlot},"37 we show the ellect of the coupliug-constant. moclilicatious on the discovery. poteutial of a light Higgs boson for this particular beuclimark poiut., we show the effect of the coupling-constant modifications on the discovery potential of a light Higgs boson for this particular benchmark point.38 Iu the right-liaud panel.thestatistical siguilicauce associated with each," In the right-hand panel,thestatistical significance associated with each"39other than the HST bands.,other than the HST bands.40 This object is especially interesting as its SED is extremely red., This object is especially interesting as its SED is extremely red.41 It is excluded from the SED fitting. and is discussed in Section ??..," It is excluded from the SED fitting, and is discussed in Section \ref{number19}."42 For the rest of the sample. the LEGOs are only detected in the HST bands and hence we choose to stack the entire sample of 23 candidates.," For the rest of the sample, the LEGOs are only detected in the HST bands and hence we choose to stack the entire sample of 23 candidates."43 We can then draw conclusions on the general properties of this type of object., We can then draw conclusions on the general properties of this type of object.44" After stacking. we get a faint detection in the A, band."," After stacking, we get a faint detection in the $K_s$ band."45 The stacked magnitudes are given in Table 6.., The stacked magnitudes are given in Table \ref{tabsed}.46 The lackof X-ray. MIPS 24;:m and radio detections (no counterparts to any of our candidates to a 30 limit of 24 ;Jy. Kellermann et al.," The lackof X-ray, MIPS $\mu$ m and radio detections (no counterparts to any of our candidates to a $\sigma$ limit of 24 $\mu$ Jy, Kellermann et al."47 in preparation) indicates that the AGN fraction among these objects is low., in preparation) indicates that the AGN fraction among these objects is low.48 We used the GALAXEV code (Bruzual Charlot. 2003) to simulate composite stellar populations. in order to fit the stacked SED of the LEGOs.," We used the GALAXEV code (Bruzual Charlot, 2003) to simulate composite stellar populations, in order to fit the stacked SED of the LEGOs."49 The fitting was performed according to à Monte Carlo Markov Chain method (see e.g. Gilks et al., The fitting was performed according to a Monte Carlo Markov Chain method (see e.g. Gilks et al.50 1995 for an introduction)., 1995 for an introduction).51 In outline. the method works as follows: an initial set of parameter values is chosen according to a uniform. random and logarithmic distribution within the allowed parameter space.," In outline, the method works as follows; an initial set of parameter values is chosen according to a uniform, random and logarithmic distribution within the allowed parameter space."52 A summary of the parameter space Is given in reftabsedpars.., A summary of the parameter space is given in \\ref{tabsedpars}. .53" Given the set of parameters. a corresponding 4? value is calculated by running the GALAXEV code. creating a high-resolution spectrum with 6900 wavelength points from 91 to 160 ym. To obtain the magnitudes in each band. we apply the transmission curves for the filters of the various observed wavebands; U. DB. V. ἐν τν J. IT. Iv, and the four Spitzer bands. Cl— Chl. In this analysis.we exclude the Spitzer MIP5 band as it ts very difficult to stack images in"," Given the set of parameters, a corresponding $\chi^2$ value is calculated by running the GALAXEV code, creating a high-resolution spectrum with 6900 wavelength points from 91 to 160 $\mu$ m. To obtain the magnitudes in each band, we apply the transmission curves for the filters of the various observed wavebands; $U$, $B$, $V$, $i$, $z'$, $J$, $H$, $K_s$ and the four Spitzer bands, $Ch1 - Ch4$ , In this analysis,we exclude the Spitzer $MIPS$ band as it is very difficult to stack images in"54fainter galaxies.,fainter galaxies.55 For the total SDSS sample (Black Dots). we observe the same behaviour.," For the total SDSS sample (Black Dots), we observe the same behaviour."56 We apply a non parametric statistical test (run test) in order to check a randomness hypothesis for our data sequence (see Nigoche-Netroetal. 2009))., We apply a non parametric statistical test (run test) in order to check a randomness hypothesis for our data sequence (see \cite{nig09}) ).57 More precisely. it can be used to test the hypothesis that the data of the intrinsic dispersion of the EJR are mutually independent.," More precisely, it can be used to test the hypothesis that the data of the intrinsic dispersion of the FJR are mutually independent."58 With this test we find that there are reasons to affirm. with a level of confidence. that there is an underlying trend for the values of the intrinsic dispersion as a function of luminosity.," With this test we find that there are reasons to affirm, with a level of confidence, that there is an underlying trend for the values of the intrinsic dispersion as a function of luminosity."59" In. order to characterise the behaviour of the intrinsic dispersion as a function of luminosity. we have fitted a straight line to those points in Figure | that correspond to the homogeneous sample at M,€—20.0."," In order to characterise the behaviour of the intrinsic dispersion as a function of luminosity, we have fitted a straight line to those points in Figure 1 that correspond to the homogeneous sample at $M_{g} \le -20.0$."60 The resulting equation Is: The previous equation was obtained from a fit made with the (BCES py.) (Isobeetal.(900: Akritas&Bershady 1996)) method., The resulting equation is: The previous equation was obtained from a fit made with the $BCES_{Bis}$ ) \cite{iso90}; \cite{akr96}) ) method.61 This method takes into consideration the errors in the variables. the error correlation. the data dispersion and both variables as dependent variables.," This method takes into consideration the errors in the variables, the error correlation, the data dispersion and both variables as dependent variables."62 This method is used for all the fits in this paper., This method is used for all the fits in this paper.63 In this section. we analyse the behaviour of the intrinsic dispersion of the FJR as a function of the mass.," In this section, we analyse the behaviour of the intrinsic dispersion of the FJR as a function of the mass."64 We shall be using two different methods to calculate the mass of galaxies., We shall be using two different methods to calculate the mass of galaxies.65 The first method requires the galaxies’ luminosity and colour indices and the following equation (see Belletal. 2003))., The first method requires the galaxies' luminosity and colour indices and the following equation (see \cite{bel03}) ).66" where M, is the mass obtained from the luminosity in the g filter (L.). M. and M, are the magnitudes in the e and r filters. ας and b, are scale factors (see Table 7 from Belletal. 2003))."," where ${\bf M_{g}}$ is the mass obtained from the luminosity in the $g$ filter $L_{g}$ ), $M_{g}$ and $M_{r}$ are the magnitudes in the $g$ and $r$ filters, $a_{g}$ and $b_{g}$ are scale factors (see Table 7 from \cite{bel03}) )."67 From now on. the mass which we obtain from the luminosity shall be called the stellar mass.," From now on, the mass which we obtain from the luminosity shall be called the stellar mass."68" The second method requires knowledge of the velocity dispersion. it also assumes that the galaxies are in virial equilibrium and utilises the following equation: where MyjirighG 18 the virial mass. 7, is the effective radius. oq is the central velocity dispersion and G is the gravitational constant."," The second method requires knowledge of the velocity dispersion, it also assumes that the galaxies are in virial equilibrium and utilises the following equation: where ${\bf M_{virial}}$ is the virial mass, $r_{e}$ is the effective radius, $\sigma_{0}$ is the central velocity dispersion and $G$ is the gravitational constant."69 In Figure 2 we present a comparison of the mass obtained using both methods., In Figure 2 we present a comparison of the mass obtained using both methods.70 In Figures 3 and 4 we see the relation between the mass and the velocity dispersion for the masses obtained with both methods., In Figures 3 and 4 we see the relation between the mass and the velocity dispersion for the masses obtained with both methods.71 For a detailed discussion of Figs., For a detailed discussion of Figs.72" 2, 3 and 4 see section 2.3.3."," 2, 3 and 4 see section 2.3.3."73 In Figure 5. we show the behaviour of the virial mass as a function of redshift for galaxies contained in the SDSS total sample.," In Figure 5, we show the behaviour of the virial mass as a function of redshift for galaxies contained in the SDSS total sample."74 Vertical lines represent the limits of the 0.04<zx 0.08 redshift interval where the homogeneous sample of the SDSS is contained., Vertical lines represent the limits of the $0.04 \leq\;z\;\leq$ 0.08 redshift interval where the homogeneous sample of the SDSS is contained.75 We note that within these limits there Is a deficiency of galaxies for log(Myiria/Mi)<10.5 (M ts the solar mass). so we may affirm that log(Myria/Mi)=10.5 represents the approximate completeness limit of the homogeneous SDSS sample.," We note that within these limits there is a deficiency of galaxies for ${\bf M_{virial}}/{\bf M_{\odot}}) \lesssim 10.5$ ${\bf M_{\odot}}$ is the solar mass), so we may affirm that ${\bf M_{virial}}/{\bf M_{\odot}}) = 10.5$ represents the approximate completeness limit of the homogeneous SDSS sample."76 On the other hand. the behaviour of the stellar mass as function of the redshift is similar to that of the virial mass. so that the approximate completeness limit for the homogeneous sample is. in this case. also log(My/MLs)=10.5 In studying the intrinsic dispersion as function of the mass. we require calculation of the intrinsic. dispersion at constar= mass in order to avoid the geometrical effect.," On the other hand, the behaviour of the stellar mass as function of the redshift is similar to that of the virial mass, so that the approximate completeness limit for the homogeneous sample is, in this case, also ${\bf M_{g}}/{\bf M_{\odot}}) = 10.5$ In studying the intrinsic dispersion as function of the mass, we require calculation of the intrinsic dispersion at constant mass in order to avoid the geometrical effect."77 In Figure 6 w[7 show the behaviour of the intrinsic. dispersion of the FJR 1 very narrow mass ranges Magia/ M.) wide intervals for the homogeneous and total samples from the SDSS., In Figure 6 we show the behaviour of the intrinsic dispersion of the FJR in very narrow mass ranges ${\bf M_{virial}}/{\bf M_{\odot}}$ ) wide intervals) for the homogeneous and total samples from the SDSS.78 In this figure we see that the values of the FJR intrinsic. dispersio depend on the virial mass. however. this mass was obtainec from equation 3 which involves both the effective radius as well as the velocity dispersion. that is to say. there is a correlatio between virial mass and the velocity dispersion which might affect the intrinsic dispersion estimate (see section 2.3.3 for more details).," In this figure we see that the values of the FJR intrinsic dispersion depend on the virial mass, however, this mass was obtained from equation 3 which involves both the effective radius as well as the velocity dispersion, that is to say, there is a correlation between virial mass and the velocity dispersion which might affect the intrinsic dispersion estimate (see section 2.3.3 for more details)."79 In order to avoid this possible bias. it is necessary to use the stellar mass.," In order to avoid this possible bias, it is necessary to use the stellar mass."80 In Figure 7 we present the values of the FJR intrinsic dispersion as function of the stellar mass., In Figure 7 we present the values of the FJR intrinsic dispersion as function of the stellar mass.81 This figure shows that the behaviour of the intrinsic dispersion as function of the stellar mass is similar to the behaviour of the intrinsic dispersion as function of the virial mass. in the sense that. the intrinsic dispersion value changes systematically as we consider more massive galaxies. and that more massive galaxies present a lower value for the intrinsic dispersion than the value for less massive galaxies.," This figure shows that the behaviour of the intrinsic dispersion as function of the stellar mass is similar to the behaviour of the intrinsic dispersion as function of the virial mass, in the sense that, the intrinsic dispersion value changes systematically as we consider more massive galaxies, and that more massive galaxies present a lower value for the intrinsic dispersion than the value for less massive galaxies."82 The run test confirms an underlying trend between the stellar mass and the intrinsic dispersion with a confidence level of approximately 99%., The run test confirms an underlying trend between the stellar mass and the intrinsic dispersion with a confidence level of approximately .83". In order to characterise the behaviour of the intrinsic dispersion as a function of the virial mass. we have fitted the points of the homogeneous sample for Myiria/Mb)=10.5 in Figure 6 to a straight line whose equation 1s: Similarly. in the case for stellar mass (Figure 7). we have fitted the homogeneous sample points for log(M,/M.)>10.5 to a straight line whose equation is: Equation 5 confirms that the correlation between virial mass and the velocity dispersion does not cause the behaviour of the intrinsic dispersion described by equation 4+."," In order to characterise the behaviour of the intrinsic dispersion as a function of the virial mass, we have fitted the points of the homogeneous sample for ${\bf M_{virial}}/{\bf M_{\odot}}) \ge 10.5$ in Figure 6 to a straight line whose equation is: Similarly, in the case for stellar mass (Figure 7), we have fitted the homogeneous sample points for ${\bf M_{g}}/{\bf M_{\odot}}) \ge 10.5$ to a straight line whose equation is: Equation 5 confirms that the correlation between virial mass and the velocity dispersion does not cause the behaviour of the intrinsic dispersion described by equation 4."84 Although this correlation could be behind the differences observed between the coefficients of both equations., Although this correlation could be behind the differences observed between the coefficients of both equations.85 In the following section we shall make an analysis of the possible origin of these differences., In the following section we shall make an analysis of the possible origin of these differences.86 The difference between the coefficients in equations 4 and 5 may be due to various factors., The difference between the coefficients in equations 4 and 5 may be due to various factors.87 One such factor is that virial and stellar mass might be intrinsically different (1-e. that the fit slope to both masses may be different from 1) andother factors wouldbe associated with elements that would make, One such factor is that virial and stellar mass might be intrinsically different (i.e. that the fit slope to both masses may be different from 1) andother factors wouldbe associated with elements that would make88hat implied by the MOND fundamental plane 55).,that implied by the MOND fundamental plane 5).89 The difference between total (ALOND) acceleration and the rewtonian acceleration (jg gx|) then allows us estimate he censity distribution of the phantom dark. halo., The difference between total (MOND) acceleration and the Newtonian acceleration $|g-g_N|$ ) then allows us estimate the density distribution of the phantom dark halo.90" The ojected ALOND FP mass (X-axis in 22). presumably he visible mass of the galaxy. is then ""corrected"" by adding in the projected phantom dark mass."," The projected MOND FP mass (X-axis in 2), presumably the visible mass of the galaxy, is then “corrected” by adding in the projected phantom dark mass."91 The result is shown in 55 which again shows the lensing mass vs. the MOND FP mass including the phantom dark matter., The result is shown in 5 which again shows the lensing mass vs. the MOND FP mass including the phantom dark matter.92 We see that a lensing mass which is higher than the MOND mass is explained by the contribution of moclilied gravity to photon dellection., We see that a lensing mass which is higher than the MOND mass is explained by the contribution of modified gravity to photon deflection.93 We should. note. however. that the Zhao-Famaev interpolating function favours the appearance of phantom dark mass within the optical image of the galaxy.," We should note, however, that the Zhao-Famaey interpolating function favours the appearance of phantom dark mass within the optical image of the galaxy."94 This is because the transition from Newton to MOND is rather more gradual than for the often assumed (standard) form of pr applied to caleulation of galaxy rotation curves (μμ)=wl lat)., This is because the transition from Newton to MOND is rather more gradual than for the often assumed ('standard') form of $\mu$ applied to calculation of galaxy rotation curves $\mu(x)=x/\sqrt{1+x^2}$ ).95 Applying the standard form would result in à reduction in the projected phantom dark mass. so the appearance of 55. and the conclusions we draw from it. would not be altered.," Applying the standard form would result in a reduction in the projected phantom dark mass, so the appearance of 5, and the conclusions we draw from it, would not be altered."96 With MOND. the barvonic mass-rotation velocity relation for spiral galaxies. which forms the basis of the Fisher law. is exact in so far as it relates to the asvmptotic rotation velocity measured. far. from the luminous galaxy.," With MOND, the baryonic mass-rotation velocity relation for spiral galaxies, which forms the basis of the Tully-Fisher law, is exact in so far as it relates to the asymptotic rotation velocity measured far from the luminous galaxy."97 On the other hand. the mass-velocity clispersion relation for pressure supported systems. the basis of the Faber-Jackson law. is only exact for homologous models: the scaling of the relation. depends upon the detailed: characteristics of the object.," On the other hand, the mass-velocity dispersion relation for pressure supported systems, the basis of the Faber-Jackson law, is only exact for homologous models; the scaling of the relation depends upon the detailed characteristics of the object."98 Actual elliptica ealaxies exhibit a range of properties various. shapes. varving degrees of deviation [rom an isothermal— state and. no doubt. isotropy οἱ the velocity dispersion au cannot be represented. by a single homologous sequence— o models.," Actual elliptical galaxies exhibit a range of properties– various shapes, varying degrees of deviation from an isothermal state and, no doubt, isotropy of the velocity dispersion– and cannot be represented by a single homologous sequence of models."99 Eherefore. spheroidal galaxies will inevitably present a Faber-Jackson law with considerable: scatter.," Therefore, spheroidal galaxies will inevitably present a Faber-Jackson law with considerable scatter."100 None-the-less. MOND provides an explanation for the remarkable fact that self-eravitating.| pressure-supported quasi-isothermal objects with a velocity dispersion of a few hundred  will have a mass in the range of galaxies or objects with a velocity dispersion «10 kms| will have the mass of globular clusters or objects with 1000 knis“will have the mass of a cluster of galaxies.," None-the-less, MOND provides an explanation for the remarkable fact that self-gravitating, pressure-supported quasi-isothermal objects with a velocity dispersion of a few hundred $^{-1}$ will have a mass in the range of galaxies– or objects with a velocity dispersion $<10$ $^{-1}$ will have the mass of globular clusters– or objects with 1000 $^{-1}$ will have the mass of a cluster of galaxies."101 In spite of the scatter in the mass-velocity. dispersion relation. when an aclelitional parameter is added. such as ellective radius or surface brightness. MOND moclels [or elliptical galaxies define a narrow fundamental plane which is close to that implied by the Newtonian virial relation for homologous objects (isotropic Jalle models).," In spite of the scatter in the mass-velocity dispersion relation, when an additional parameter is added, such as effective radius or surface brightness, MOND models for elliptical galaxies define a narrow fundamental plane which is close to that implied by the Newtonian virial relation for homologous objects (isotropic Jaffe models)."102 This was not part of the original set of MOND predictions but. became apparent when it was realized that normal elliptical galaxies are essentially Newtonian svstems within the elfective radius and exhibit a wide dispersion in the elfective racius-velocity dispersion relation., This was not part of the original set of MOND predictions but became apparent when it was realized that normal elliptical galaxies are essentially Newtonian systems within the effective radius and exhibit a wide dispersion in the effective radius-velocity dispersion relation.103 The properties of this. fundamental plane were outlined by a set of 360 [aree 9 polvtropic spheres with racially dependent anisotropy chosen to match the observed. joint. distribution of ellipticals by cllective radius and velocity dispersion (Sanders 2000)., The properties of this fundamental plane were outlined by a set of 360 large $n$ polytropic spheres with radially dependent anisotropy chosen to match the observed joint distribution of ellipticals by effective radius and velocity dispersion (Sanders 2000).104 Applying this fundamental plane relation to determine the mass of those ellipticals in the sample of Jorgenson et al. (, Applying this fundamental plane relation to determine the mass of those ellipticals in the sample of rgenson et al. (1051995) vielded reasonable values for the mass-to-light ratios.,1995) yielded reasonable values for the mass-to-light ratios.106 Now. thanks to the work of Dolton et al. (," Now, thanks to the work of Bolton et al. ("1072007) we can compare this mass-based MOND fundamental plane directIv o the observed mass-based. fundamental plane as defined w this set. of 36 strong gravitational lenses.,2007) we can compare this mass-based MOND fundamental plane directly to the observed mass-based fundamental plane as defined by this set of 36 strong gravitational lenses.108 Figs., Figs.109 1 and 2 illustrate that the two coincide apart from a systematic ollset of about30., 1 and 2 illustrate that the two coincide apart from a systematic offset of about.110.. Indeed. the implied MOND mass-o-light ratios are completely consistent. with population svnthesis models 33). and the small cliscrepancy xtween the lensing mass and the MOND FP mass can be unclerstoocl in terms of the contribution of modified. gravity o the deflection of photons 55).," Indeed, the implied MOND mass-to-light ratios are completely consistent with population synthesis models 3), and the small discrepancy between the lensing mass and the MOND FP mass can be understood in terms of the contribution of modified gravity to the deflection of photons 5)."111 It is important to recall that the properties of the MOND fundamental plane (Sanders 2000) were defined well before those of observed mass-basecl fundamental plane (Bolton et al., It is important to recall that the properties of the MOND fundamental plane (Sanders 2000) were defined well before those of observed mass-based fundamental plane (Bolton et al.112 2007). so this does. properly speaking. constitute a. prediction that has on subsequently confirmed.," 2007), so this does, properly speaking, constitute a prediction that has been subsequently confirmed."113 Most significantly. there is no evidence from strong eravitational lensing for a significant mass ciscrepancy within these high surface density systems as MOND would: robustly predict.," Most significantly, there is no evidence from strong gravitational lensing for a significant mass discrepancy within these high surface density systems– as MOND would robustly predict."114 This is in contrast to a recent claim by Ferreras et. al. (, This is in contrast to a recent claim by Ferreras et al. (1152008). based: upon lensing by six carly type galaxies.,2008) based upon lensing by six early type galaxies.116 Fhev note that the lensing mass. as determined either by General Relativity or MOND (as extended by TeVes). is significantly greater than the stellar miss estimated: via population svnthesis models.," They note that the lensing mass, as determined either by General Relativity or MOND (as extended by TeVeS), is significantly greater than the stellar mass estimated via population synthesis models."117 However. this conclusion appears to give much weight to the precision of such models: the mass difference is generally smaller than the cilferences due to the assumption of different initial mass functions (z0.2.0.3 dex).," However, this conclusion appears to give much weight to the precision of such models; the mass difference is generally smaller than the differences due to the assumption of different initial mass functions $\approx 0.2-0.3$ dex)."118 Moreover. in the near infrared. the scatter induced by metallicity effects can be comparable (Bell et al.," Moreover, in the near infrared, the scatter induced by metallicity effects can be comparable (Bell et al."119 2003)., 2003).120 Overall it is cillicult to argue that implied, Overall it is difficult to argue that implied121"grounds, the time scale for the (gradual) cluster disruption is expected to be mass-dependent, owing to tidal shocks and evaporation that follows early gas expulsion (e.g.?),, assuming there is no strong relation between cluster mass and radius.","grounds, the time scale for the (gradual) cluster disruption is expected to be mass-dependent, owing to tidal shocks and evaporation that follows early gas expulsion \citep[e.g.][]{gieles06}, assuming there is no strong relation between cluster mass and radius."122" In this description, the dissolution time tai; of a cluster scales with cluster mass as tais=t4(M/10*ΛΜ), where t4 is the lifetime of a 104 Mo cluster (see??).."," In this description, the dissolution time $t_{\rm dis}$ of a cluster scales with cluster mass as $t_{\rm dis} = t_4 (M/10^4 M_\odot)^\gamma$, where $t_4$ is the lifetime of a $10^4$ $_\odot$ cluster \citep[see][]{BL03,lamers05}."123" The time scale on which clusters dissolve may also depend on external factors, such as the tidal field strength, density of molecular gas, passages near/through giant molecular clouds, or through spiral arms, etc. (seee.g.??).."," The time scale on which clusters dissolve may also depend on external factors, such as the tidal field strength, density of molecular gas, passages near/through giant molecular clouds, or through spiral arms, etc. \citep[see e.g.][]{gieles06,gieleslamers07}."124 This scenario attempts to compile in one single formula all the possible processes that affect cluster disruption., This scenario attempts to compile in one single formula all the possible processes that affect cluster disruption.125 See ? for a description of the different models for cluster dissolution., See \citet{lamers09} for a description of the different models for cluster dissolution.126 Determining the extent to which cluster dissolution is a mass-dependent process has turned out to be difficult., Determining the extent to which cluster dissolution is a mass-dependent process has turned out to be difficult.127" Estimations of cluster parameters based on observations are affected by stochastic effects, degeneracies, and observational uncertainties."," Estimations of cluster parameters based on observations are affected by stochastic effects, degeneracies, and observational uncertainties."128" For example, ? used Monte Carlo simulations to estimate how stochastic effects coming from the random sampling of the stellar initial mass function influence the determination of ages and masses, which are derived from broadband photometry."," For example, \citet{maizapellaniz09} used Monte Carlo simulations to estimate how stochastic effects coming from the random sampling of the stellar initial mass function influence the determination of ages and masses, which are derived from broadband photometry."129 ? show how the consideration of the discreteness of the stellar initial mass function (IMF) can explain features observed in the color-age relation and can improve the fit between models and observations., \citet{piskunov09} show how the consideration of the discreteness of the stellar initial mass function (IMF) can explain features observed in the color-age relation and can improve the fit between models and observations.130" They conclude that the large number of red outliers can be explained as a systematic offset coming from the difference between discrete- and continuous-IMF at low masses (Μ.--103 Μο) and young ages (log(7)[yr] 7), reaching up to ~0.5 magnitudes, and decreases down to ~0.04 magnitudes at higher masses (Μ.--106 Mo)."," They conclude that the large number of red outliers can be explained as a systematic offset coming from the difference between discrete- and continuous-IMF at low masses $_c$ $10^2$ $_{\odot}$ ) and young ages $(\tau)[yr]\sim$ 7), reaching up to $\sim$ 0.5 magnitudes, and decreases down to $\sim$ 0.04 magnitudes at higher masses $_c$ $10^6$ $_{\odot}$ )."131" To estimate field star formation histories, a different approach is needed than for clusters, because ages cannot in general be determined directly for individual stars."," To estimate field star formation histories, a different approach is needed than for clusters, because ages cannot in general be determined directly for individual stars."132" ? presented a method that takes incompleteness, resolution, depth, and observational errors (among other parameters) into account to construct a synthetic color-magnitude diagram (CMD), which can be used to estimate the star formation history by comparison with observations."," \citet{tosi91} presented a method that takes incompleteness, resolution, depth, and observational errors (among other parameters) into account to construct a synthetic color-magnitude diagram (CMD), which can be used to estimate the star formation history by comparison with observations."133" This method has been developed further by other authors in the past years, e.g. ? and ?,, and has been used for a large number of galaxies, e.g. SMC, LMC (??),, M31 (?),, NGC 1313 (?).."," This method has been developed further by other authors in the past years, e.g. \citet{dolphin97} and \citet{harriszaritsky01}, and has been used for a large number of galaxies, e.g. SMC, LMC \citep{harriszaritsky04,harriszaritsky09}, M31 \citep{brown08}, NGC 1313 \citep{larsen07}."134" In this series of papers, we make use of this method to estimate the field star formation rates of our target galaxies, which we then compare with cluster formation rates to estimate ΤΟ."," In this series of papers, we make use of this method to estimate the field star formation rates of our target galaxies, which we then compare with cluster formation rates to estimate $\Gamma$."135" In ?,hereafterPaperL, we presented the tools needed to study and constrain the Τ value of our set of galaxies, and used NGC 4395 as a testbed galaxy."," In \citet[][hereafter Paper I]{silvavilla10}, we presented the tools needed to study and constrain the $\Gamma$ value of our set of galaxies, and used NGC 4395 as a testbed galaxy."136" As the second paper in a series, this paper aims to estimate I in different environments and compare it with previous work (e.g. ?7),, using the complete set of galaxies."," As the second paper in a series, this paper aims to estimate $\Gamma$ in different environments and compare it with previous work \citep[e.g.][]{gieles09,goddard10}, using the complete set of galaxies."137" To this end, we took advantage of the superb spatial resolution of the (HST) and used images of the galaxies NGC 5236, NGC 7793, NGC 1313, and NGC 45, which are nearby, face-on spiral galaxies that differ in their current star formation rates and morphology."," To this end, we took advantage of the superb spatial resolution of the (HST) and used images of the galaxies NGC 5236, NGC 7793, NGC 1313, and NGC 45, which are nearby, face-on spiral galaxies that differ in their current star formation rates and morphology."138" These galaxies are near enough (z4 Mpc) to allow us to disentangle the cluster system from the field stars, making it possible to estimate cluster and star formation histories separately and simultaneously from the same data."," These galaxies are near enough $\approx 4$ Mpc) to allow us to disentangle the cluster system from the field stars, making it possible to estimate cluster and star formation histories separately and simultaneously from the same data."139 The paper is structured as follows., The paper is structured as follows.140 In Sect., In Sect.141" 2, we present a short overview of previous work on our target galaxies, related to the present study."," 2, we present a short overview of previous work on our target galaxies, related to the present study."142 The basic reduction and characteristics of the observations are described in Sect., The basic reduction and characteristics of the observations are described in Sect.143 3., 3.144 In Sect., In Sect.145 4 we present the photometry procedures applied to the data and describe how completeness tests were carried out., 4 we present the photometry procedures applied to the data and describe how completeness tests were carried out.146 We also discuss the effect of stochastic sampling of the stellar IMF on integrated cluster properties., We also discuss the effect of stochastic sampling of the stellar IMF on integrated cluster properties.147 In Sect., In Sect.148" 5 we present the results of the estimation of ages and masses of clusters, as well as the field star formation histories."," 5 we present the results of the estimation of ages and masses of clusters, as well as the field star formation histories."149 We also estimate the cluster formation rates and use these to determine I’ values., We also estimate the cluster formation rates and use these to determine $\Gamma$ values.150 In Sect., In Sect.151" 6 we discuss our results and finally, we summarize and conclude our work in Sect."," 6 we discuss our results and finally, we summarize and conclude our work in Sect."152 7., 7.153" In this paper we describe results for the remaining four galaxies in our HST/ACS sample: NGC 5236, NGC 7793, NGC 1313, and NGC 45."," In this paper we describe results for the remaining four galaxies in our HST/ACS sample: NGC 5236, NGC 7793, NGC 1313, and NGC 45."154" These four galaxies share the properties of being face-on, nearby spirals; however, they differ in their morphology, star, and cluster formation"," These four galaxies share the properties of being face-on, nearby spirals; however, they differ in their morphology, star, and cluster formation"155because both ionization aud heating timescales decrease as density becomes smaller. they eventually become much less than the dynamical timescale of the eas.,"because both ionization and heating timescales decrease as density becomes smaller, they eventually become much less than the dynamical timescale of the gas."156 Under such conditions. the radiative feedback plays a uceligible role. aud the accretion becomes Boucli-like.," Under such conditions, the radiative feedback plays a negligible role, and the accretion becomes Bondi-like."157" More intriguingly, we repeat the simulations for a DII mass range of 10710NE... and fud that this correlation is universal over a wide range of BIT mass and gas density. with a simple scaling relation between he DII nass aud the critical deusitv. nearly=(2.108fem2010:AL..."," More intriguingly, we repeat the simulations for a BH mass range of $10^2 - 10^9\, \Msun$, and find that this correlation is universal over a wide range of BH mass and gas density, with a simple scaling relation between the BH mass and the critical density, $n_{\rm crit}\MBH=({2\times 10^8}/{\cm^{-3}})({10^2}/{\Msun})$ ."158 This scaling relation ds casy ο understand. as the lydrodvuaimic equations governing he accretion process without sclferavity can be shown o depend onlv ou μμλέω. under the assumption hat the density is sufficicutly hieh so that the loca eas temperature is close to the thermal equilibria determined by the heating and cooling functious.," This scaling relation is easy to understand, as the hydrodynamic equations governing the accretion process without self-gravity can be shown to depend only on $n_0\MBH$, under the assumption that the density is sufficiently high so that the local gas temperature is close to the thermal equilibrium determined by the heating and cooling functions."159 That neans. for a eiven BIT mass. there exists a critica density. above which the accretion rate can reach the Eddington lit.," That means, for a given BH mass, there exists a critical density, above which the accretion rate can reach the Eddington limit."160 This general relation between DII accretion anc aubicut eas densitv has important imuplications ar applications in studies of DII erowth., This general relation between BH accretion and ambient gas density has important implications and applications in studies of BH growth.161 We note that Boudi accretion has been commonly used im simulations of DII erowth (ee. 77777777?7)]).," We note that Bondi accretion has been commonly used in simulations of BH growth (e.g., \citealt{Li2007A, Johnson2007, Alvarez2009, DiMatteo2005, Springel2005B, Hopkins2006A, DiMatteo2008, Sijacki2009, DiMatteo2011}) )."162" ""This siupli&e prescription neglects the effects of radiation feedback auc overestimates the accretion rate bv up to two orders of jiaenitude at some deusities below LOSemi7."," This simplified prescription neglects the effects of radiation feedback and overestimates the accretion rate by up to two orders of magnitude at some densities below $10^8\, \cm^{-3}$."163 Our results and the fitting formula above can serve as a more realistic recipe for DIT accretion. aud can be implemented directly into merical simulations.," Our results and the fitting formula above can serve as a more realistic recipe for BH accretion, and can be implemented directly into numerical simulations."164 To summarize. we have preseuted a set of onc-nueusional ντοςπας simmlations of the accretion of a black hole eiibedded i a primordial gas cloud. using the modified exid-based. VIT-1 code.," To summarize, we have presented a set of one-dimensional hydrodynamic simulations of the accretion of a black hole embedded in a primordial gas cloud, using the modified grid-based VH-1 code."165 We include not only oeuportaut feedback processes frou the accreting black hole. but also sclberavity of the gas.," We include not only important feedback processes from the accreting black hole, but also self-gravity of the gas."166 We achieved au uprecedeutedly Ligh spatial resolution of 1013 cu. aud covered a wide range of gas deusity of 10710Hcu.," We achieved an unprecedentedly high spatial resolution of $10^{11}$ cm, and covered a wide range of gas density of $10^{5} - 10^{11}\, \cm^{-3}$."1675 These advantages allowed us to study the accretion process in regimes not explored by previous work. aud uuveil the following new fiudiues:," These advantages allowed us to study the accretion process in regimes not explored by previous work, and unveil the following new findings:"168 , 169uamely: X—3.QT (yy=23). a3.32 (hereafter 20-up): X=2.53 Oy)=Y2). a=2.27 (herealter 2o—low).,"namely: $X=3.07$ $\eta_0=2.3$ ), $\alpha=3.32$ (hereafter $2\sigma$ -up); $X=2.53$ $\eta_0=75$ ), $\alpha=2.27$ (hereafter $2\sigma-$ low)."170" The distribution fuuctiou for the total columau density Ny/107""fs> 7> can be wrltten as In Figwe 6. in arbitrary scale. the coutinuous lines show log f/Vg). the HI distribution [uuction. for the best-fit values of XN aud à as given in eq. (15))"," The distribution function for the total column density $\tilde 171N_{H\perp}\equiv N_{H\perp}/10^{20}$ $^{-2}$ can be written as In Figure 6, in arbitrary scale, the continuous lines show log $f(N_{HI})$ , the HI distribution function, for the best-fit values of $X$ and $\alpha$ as given in eq. \ref{bestfit1}) )"172 and (16)). aud for the 2o—low andl the 2o-up 1rodels.," and \ref{bestfit2}) ), and for the $2\sigma-$ low and the $2\sigma$ -up models."173 Our data for Nyy>1.6xLOM 7 is in five large bins just for the purpose of presentation., Our data for $N_{HI}>1.6\times 10^{17}$ $^{-2}$ is in five large bins just for the purpose of presentation.174 NyxgiNy_) eau be integrated over a range of Nyy. say between Nyy; and Nyy). το estimate the mass deusity of lvclrogen atoms in gas clouds with au average HI column density along the liue of sight between πι and μμ.," $\tilde N_{H\perp}\times g(\tilde N_{H\perp})$ can be integrated over a range of $\tilde N_{H\perp}$, say between $\tilde N_{H\perp,i}$ and $\tilde N_{H\perp,n}$, to estimate the mass density of hydrogen atoms in gas clouds with an average HI column density along the line of sight between $N_{HI,i}$ and $N_{HI,n}$."175 The comoving cosmological H+Hegas deusity at —2.5 cau be written as: ↙↘⋅≺⇂↩↥↽≻≺↵⊔≼⇂⊳∖∩∐↕∐≺↵∢∙∩⊳∖∐↕∩↥∩∑≟↥∢∙⋜↕↥∐↕⋯⇂≺↵↥⋜↕∐≺⊔⊳∖⋜↕↥∎⋯∐∙⋃∩∐∩↥∎∶⋅≤−∪ .Qa.," The comoving cosmological H+Hegas density at $z=2.5$ can be written as: $\delta$ depends on the cosmological model and is a function of $z,\Omega_M,176\Omega_\Lambda$."177" For a staucdard Friedinauu Universe in which gy=0. 0= Laud we shall use this value for the rest of this sectiou (for Qa,=0.3 aud £4=0.7 instead 9 depends ou z ancl is close to zero at z 2.5)."," For a standard Friedmann Universe in which $q_0=0$, $\delta=1$ and we shall use this value for the rest of this section (for $\Omega_M=0.3$ and $\Omega_\Lambda=0.7$ instead $\delta$ depends on $z$ and is close to zero at $z\sim 2.5$ )."178" In Table 1 we give the values of Oo, (59. for ¢=1.2.3) which is the otal gas deusity iu the Universe at z2.5 due to absorbing clouds whose HI column density xojected along the line of sight is between Nyy; aud 1077 cm7."," In Table 1 we give the values of $\Omega_{gas}(i)h_{60}$ , for $i=1,2,3$ which is the total gas density in the Universe at $z\simeq 2.5$ due to absorbing clouds whose HI column density projected along the line of sight is between $N_{HI,i}$ and $10^{22}$ $^{-2}$."179" We shall consider Nyy=10|l (see section 1.2). Nquo=1.6x10M and INq4a4=1.3x107"" cm7."," We shall consider $N_{HI,1}=10^{14}$ (see section 4.2), $N_{HI,2}=1.6\times 10^{17}$ and $N_{HI,3}=1.3\times 10^{20}$ $^{-2}$."180 For each corresponding valιο ol Nyy; we give Aj. the log ratio of total to neutral gas column density.," For each corresponding value of $N_{H\perp,i}$ we give $X_i$ , the log ratio of total to neutral gas column density."181 Results are given botl for the best fittiug models aud for the two most extreme values of .X ou the >95.5% coulidence evel of Figure {., Results are given both for the best fitting models and for the two most extreme values of $X$ on the $>95.5\%$ confidence level of Figure 4.182" Iu the Table we also show the gas scale heights for μοι1.6xLOM and μις—13x10? 7. aud values of QO4,,4,)."," In the Table we also show the gas scale heights for $N_{HI,2}=1.6\times 10^{17}$ and $N_{HI,3}=1.3\times 10^{20}$ $^{-2}$, and values of $\Omega_{dark}(i)$."183 For ος iu the regions coinciding with the gas tlie factor ¢ to be substituted itto Table 1 is ςcm1. independent of assumptious on cloud size aud ‘elative distribution of dark matter and gas.," For $\Omega_{dark}$ in the regions coinciding with the gas the factor $\zeta$ to be substituted into Table 1 is $\zeta\approx 1$, independent of assumptions on cloud size and relative distribution of dark matter and gas."184 For rotating disks embedcecd tu spherical dark halos οle can compute the contributio1 of the total dark matter surface deusity to tle cosmological matter deusity., For rotating disks embedded in spherical dark halos one can compute the contribution of the total dark matter surface density to the cosmological matter density.185 This coitribution associated with DLS or LLS systems depends on the rotational velocity V aud is given |N Qu usiig 6G8Vfe., This contribution associated with DLS or LLS systems depends on the rotational velocity $V$ and is given by $\Omega_{dark}$ using $\zeta \approx V/\tilde c_s$.186 This factor may be close to one fo ενα ‘Celouds. but àx9] would hokl for giant diskproto-galaxies.," This factor may be close to one for dwarf clouds, but $\zeta\gg 1$ would hold for giant diskproto-galaxies."187 For the range of uncertainties in Table 1. the value o .*$5güs (2). the tota contributior ol LLS plus DLS. varies little but 7p has a largespread.," For the range of uncertainties in Table 1, the value of $\Omega_{gas}(2)$ , the total contribution of LLS plus DLS, varies little but $\eta_0$ has a largespread."188" Conseqiently. 4,5. and the gas scale eight 77also have a large spread."," Consequently, $\Omega_{dark}$ and the gas scale height $h$also have a large spread."189 Note that (3) is particularly simall for the 2o-low Limit., Note that $h(3)$ is particularly small for the $2\sigma$ -low limit.190any complications in the combination of the two arrays arising [rom source variability.,any complications in the combination of the two arrays arising from source variability.191 “Vhis has been successful as the peak brightness in cach map is very similar., This has been successful as the peak brightness in each map is very similar.192 The positions of the peaks are a Little less consistent., The positions of the peaks are a little less consistent.193 Whilst in declination the peaks are coincident to within 1 mas. the right ascension coordinates diller by GO mas.," Whilst in declination the peaks are coincident to within 1 mas, the right ascension coordinates differ by 60 mas."194 Therefore the wo maps are olfset by about one ALERLIN beam., Therefore the two maps are offset by about one MERLIN beam.195 This is not completely surprising as no attempt was made to »erform exact astrometry with the VLA observations., This is not completely surprising as no attempt was made to perform exact astrometry with the VLA observations.196 The »oor resolution of the VLA map may also be a contributing actor., The poor resolution of the VLA map may also be a contributing factor.197 However. as the ollset in position is not unduly large (and removable with self£-calibration) and the flux. scales xoadly consistent. the two data sets were simply. combine with no scaling or removal of model components. (A anc D).," However, as the offset in position is not unduly large (and removable with self-calibration) and the flux scales broadly consistent the two data sets were simply combined with no scaling or removal of model components (A and B)."198 Prior to this the weights of cach visibility of cach array were made approximately the same so that cach data se contributed roughly equally to the resultant image., Prior to this the weights of each visibility of each array were made approximately the same so that each data set contributed roughly equally to the resultant image.199 All maps of the combined clata set were made using the imagine taskIMAGR., All maps of the combined data set were made using the imaging task.200 A value for the parameter (which allows a compromise to be made between the traditional natural and uniform weighting schemes) of 1 was used in all maps which resulted. in a beanmisize of 57«55 mas., A value for the parameter (which allows a compromise to be made between the traditional natural and uniform weighting schemes) of $-1$ was used in all maps which resulted in a beamsize of $57\times55$ mas.201 The initial map of the combined data was very poor. but with several iterations of phase self-calibration subsequent maps were of much higher quality.," The initial map of the combined data was very poor, but with several iterations of phase self-calibration subsequent maps were of much higher quality."202 1n order to make the best. possible map the data were also amplitude self-calibrated. and corrected. for baseline errors., In order to make the best possible map the data were also amplitude self-calibrated and corrected for baseline errors.203 This latter step was particularly successful in removing the sidelobe structure around. component A seen in Fig. 2.., This latter step was particularly successful in removing the sidelobe structure around component A seen in Fig. \ref{mer3}.204 The final image is shown in Fig., The final image is shown in Fig.205 4 and has an rms noise of 5ομονbeam~ and a dynamic range of 100000:1.," \ref{mervla} and has an rms noise of $82\,\mu\mathrm{Jy\,beam}^{-1}$ and a dynamic range of 000:1."206 The dynamic range of a tvpical bright area of the ring is about 10011., The dynamic range of a typical bright area of the ring is about 100:1.207 The final image shown in Fig., The final image shown in Fig.208 4. represents a marked improvement on previous maps mace of the Einstein ring in this lens svstem. combining the sensitivity of the VLA with the resolution of MISIRLIN.," \ref{mervla} represents a marked improvement on previous maps made of the Einstein ring in this lens system, combining the sensitivity of the VLA with the resolution of MERLIN."209 As the dynamic range of he map is greater and the aperture coverage so much better han in previous high-resolution maps. we can also expect here to have been a substantial improvement in the image idelitv. (fractional on-source errors).," As the dynamic range of the map is greater and the aperture coverage so much better than in previous high-resolution maps, we can also expect there to have been a substantial improvement in the image fidelity (fractional on-source errors)."210 Short. of. performing complicated ancl time-consuming simulations of the entire mapping process on a model source it is dillieult to calculate he image fidelity., Short of performing complicated and time-consuming simulations of the entire mapping process on a model source it is difficult to calculate the image fidelity.211 Instead. in the following paragraphs we will consider several wavs in which the theoretical image fidelity could be degraded and show that the magnitudes of these are negligible.," Instead, in the following paragraphs we will consider several ways in which the theoretical image fidelity could be degraded and show that the magnitudes of these are negligible."212 The fundamental problem with MES that. must. be overcome is that source brightness varies with frequency., The fundamental problem with MFS that must be overcome is that source brightness varies with frequency.213 We have compensated for this with the ALERLIN data. as described. in Section. 2.1.. bx removing the [lat-spectrum cores and scaling the remaining emission.," We have compensated for this with the MERLIN data, as described in Section \ref{merlin}, by removing the flat-spectrum cores and scaling the remaining emission."214 In doing so we have assumed that the Einstein ring emission is described by a single value of à., In doing so we have assumed that the Einstein ring emission is described by a single value of $\alpha$.215 As gravitational lensing is an achromatic process this is in general a reasonable approach. providing that the lensed source has a uniform spectral index.," As gravitational lensing is an achromatic process this is in general a reasonable approach, providing that the lensed source has a uniform spectral index."216 Lf this is not the case then errors will result. from. the spectral-index residuals., If this is not the case then errors will result from the spectral-index residuals.217 We believe that the assumption of uniform a holds fairly well in DO218|357 due to the fact that the area of jet imaged into the ring is small (of order 10 mas) ancl because spectral-index eradients along radio jets are shallow (Briclle&Perley1984)., We believe that the assumption of uniform $\alpha$ holds fairly well in B0218+357 due to the fact that the area of jet imaged into the ring is small (of order 10 mas) and because spectral-index gradients along radio jets are shallow \cite{bridle84}.218.. Furthermore. Conway et al. (," Furthermore, Conway et al. ("2191990) have shown that for a knotty jet (of which the ring in 30218|357 could be considered an example. with extreme curvature) observed. with the ALERLIN array with a bandspread of «25 per cent. the spectral errors can usually be ignored when the dynamic range in the map is «1000:1.,"1990) have shown that for a knotty jet (of which the ring in B0218+357 could be considered an example with extreme curvature) observed with the MERLIN array with a bandspread of $<$ 25 per cent, the spectral errors can usually be ignored when the dynamic range in the map is $<$ 1000:1."220 Our observations easily fulfill this criterion as the dvnamic range of the ring emission is «100:1 and the bandspread +7 per cent., Our observations easily fulfill this criterion as the dynamic range of the ring emission is $\sim$ 100:1 and the bandspread $\pm$ 7 per cent.221 The much brighter cores do not contribute to the spectral. sidelobes as after their subtraction at all three frequencies. only those from the central [requeney were subsequently returned to the combined data.," The much brighter cores do not contribute to the spectral sidelobes as after their subtraction at all three frequencies, only those from the central frequency were subsequently returned to the combined data."222 As the average VLA ancl central. MIZRLAN. frequencies differ by less than l per cent and the peak brightnesses in the three-frequeney AMIERLIN map and. VLA map were so similar. it is unlikely that major spectral errors could result. from the addition of the VLA data.," As the average VLA and central MERLIN frequencies differ by less than 1 per cent and the peak brightnesses in the three-frequency MERLIN map and VLA map were so similar, it is unlikely that major spectral errors could result from the addition of the VLA data."223 Another effect. that will reduce. the image fidelity is source [lux density variability., Another effect that will reduce the image fidelity is source flux density variability.224 This needs particular consideration with regards to D0218|357 as the radio core of the background. source is variable. as it had. to be for the time delay to be measured.," This needs particular consideration with regards to B0218+357 as the radio core of the background source is variable, as it had to be for the time delay to be measured."225 Fortunately. the relatively low frequeney. of these observations means that any source variability. should. be. reduced: compared. with the. rapid variations seen at higher frequencies.," Fortunately, the relatively low frequency of these observations means that any source variability should be reduced compared with the rapid variations seen at higher frequencies."226 VLA monitoring data ad. SA and 15 Cllz(Biggsetal.1999). show that although highly variable at the highest. frequency. the variations become much reduced in magnitude (by a factor of about," VLA monitoring data at 8.4 and 15 GHz \cite{biggs99} show that although highly variable at the highest frequency, the variations become much reduced in magnitude (by a factor of about"227Model C resemble a long tubes that is thicker in the direction away from the midplane; there is no resemblance to a mushroom cloud.,Model C resemble a long tubes that is thicker in the direction away from the midplane; there is no resemblance to a mushroom cloud.228" As the magnetic field increases, the bubble gets more elongated in the direction parallel to the magnetic field."," As the magnetic field increases, the bubble gets more elongated in the direction parallel to the magnetic field."229" For Model B, when the bubble has a slight mushroom shape cross section, (the bubble is lower on the edges than at the center in the By=4jsG y-direction."," For Model B, when $\bf{B}_y$ $\mu$ G the bubble has a slight mushroom shape cross section, (the bubble is lower on the edges than at the center in the $\hat{y}$ -direction."230" When By is increased to 7.1 wG, the bubble is further elongated and the edges are tapered."," When $\bf{B}_y$ is increased to 7.1 $\mu$ G, the bubble is further elongated and the edges are tapered."231" Figure 12. shows the temperature for y-z slices for Models having no magnetic field (left), a magnetic field directed parallel to the midplane with a strength of 4 µία (center), and a magnetic field directed parallel to the midplane with a strength of 7.1 j, G "," Figure \ref{By strength} shows the temperature for y-z slices for Models having no magnetic field (left), a magnetic field directed parallel to the midplane with a strength of 4 $\mu$ G (center), and a magnetic field directed parallel to the midplane with a strength of 7.1 $\mu$ G (right)."232"For Model C, when B,=4wG the bubble is fuller in the direction away from the midplane (also the direction of (right).decreasing thermal pressure and density)."," For Model C, when $\bf{B}_z$ $\mu$ G the bubble is fuller in the direction away from the midplane (also the direction of decreasing thermal pressure and density)."233" When Bz is 7.1 µία the bubble is even more elongated, and it is tapered at the ends."," When $\bf{B}_z$ is 7.1 $\mu$ G the bubble is even more elongated, and it is tapered at the ends."234" Figure 13 shows y-z temperature slices for the models having no magnetic field a magnetic field perpendicular to the midplane of 4 µία (center), or a magnetic field perpendicular to the midplane of (left),7.1 ys G (right)."," Figure \ref{Bz strength} shows y-z temperature slices for the models having no magnetic field (left), a magnetic field perpendicular to the midplane of 4 $\mu$ G (center), or a magnetic field perpendicular to the midplane of 7.1 $\mu$ G (right)."235" In the Milky Way, the strength of the ordered component of the magnetic field decreases slightly with distance from the galactic mid-plane."," In the Milky Way, the strength of the ordered component of the magnetic field decreases slightly with distance from the galactic mid-plane."236 T'he resulting gradient in magnetic pressure would allow the bubble to expand preferentially away from the galactic mid-plane., The resulting gradient in magnetic pressure would allow the bubble to expand preferentially away from the galactic mid-plane.237" Computationally, the gradient in magnetic field strength gives rise to a gradient in the magnetic pressure that would be taken into consideration when calculating the ambient thermal pressure for HSE, effectively allowing us to use a temperature distribution having less variation."," Computationally, the gradient in magnetic field strength gives rise to a gradient in the magnetic pressure that would be taken into consideration when calculating the ambient thermal pressure for HSE, effectively allowing us to use a temperature distribution having less variation."238" Furthermore, Tomisaka found that in his superbubble simulations the variation with height of the magnetic field strength was important to (1998)whether the superbubble could “blow out” of the disk."," Furthermore, \cite{tomisaka98} found that in his superbubble simulations the variation with height of the magnetic field strength was important to whether the superbubble could “blow out” of the disk."239 The magnetic field of the galaxy contains random components which are significant with respect to the average field strength., 			 The magnetic field of the galaxy contains random components which are significant with respect to the average field strength.240 The random component of the magnetic field in external galaxies is slightly larger than the mean galactic field and contains about one and a half times the energy 1997).., The random component of the magnetic field in external galaxies is slightly larger than the mean galactic field and contains about one and a half times the energy \citep{Zweibel and Heiles}.241 Adding à random magnetic field would allow for the possibility that gas might be able to (Zweibelescape through regions of lower magnetic field., Adding a random magnetic field would allow for the possibility that gas might be able to escape through regions of lower magnetic field.242" Adding a random magnetic field would also reduce the magnetic tension since the initial magnetic field lines would be longer, and would increase the magnetic pressure in all directions which could change the structure of the bubble and the direction in which the gas preferentially moves."," Adding a random magnetic field would also reduce the magnetic tension since the initial magnetic field lines would be longer, and would increase the magnetic pressure in all directions which could change the structure of the bubble and the direction in which the gas preferentially moves."243 We have examined three magnetic field backgrounds for our SNR explosion born 400 pc above the galactic midplane., We have examined three magnetic field backgrounds for our SNR explosion born 400 pc above the galactic midplane.244 For the case of no magnetic field we see cauliflower-like eddies develop within the bubble in the first several million years., For the case of no magnetic field we see cauliflower-like eddies develop within the bubble in the first several million years.245 We see a modest rise of 59 pc over the 12 Myr simulation time., We see a modest rise of 59 pc over the 12 Myr simulation time.246" A mushroom structure forms by 9 Myrs, with"," A mushroom structure forms by 9 Myrs, with"247asstuption of a constantως1.5 turus out to be approximately correct (feo)21.8c0.1 in Figure 7)). it was not clearly justified a priori and iav uot be as good of an assumption for other ULX sources.,"assumption of a constant$f_{\rm col} \sim 1.7$ turns out to be approximately correct $f_{\rm col} \approx 1.8 \pm 0.1$ in Figure \ref{f:fcol}) ), it was not clearly justified a priori and may not be as good of an assumption for other ULX sources."248 Iu principle. one could improve this analvsis by estimating fey. ji and 6 from BUSPEC (or some similar model). but at that level of sophistication. if secius more seusible to fit the relativistic mocel directly.," In principle, one could improve this analysis by estimating $f_{\rm col}$, $\mu$, and $\delta$ from BHSPEC (or some similar model), but at that level of sophistication, it seems more sensible to fit the relativistic model directly."249 There are a nmnunber of assmuptions present iu the BUSPEC model that could have some mipact ou ζω., There are a number of assumptions present in the BHSPEC model that could have some impact on $f_{\rm col}$.250 Iu particular. magnetic fields (and associated turbulence) may play a role in modifving the disk vertical structure and radiative trausfer2009).," In particular, magnetic fields (and associated turbulence) may play a role in modifying the disk vertical structure and radiative transfer."251 Another assumption of interest is our choice of à=0.01., Another assumption of interest is our choice of $\alpha=0.01$.252 For à=0.01. the models depend very weakly on à. for the paraiueter range relevant to our fit results.," For $\alpha \lesssim 0.01$, the models depend very weakly on $\alpha$ for the parameter range relevant to our fit results."253 For higher values of o. the typical color correction is larger.," For higher values of $\alpha$ , the typical color correction is larger."254 For low to moderate 6 aud e. f; Increases by less than 25 as a inercases from 0.01 to 0.1.," For low to moderate $\ell$ and $a_*$, $f_{\rm col}$ increases by less than 25 as $\alpha$ increases from 0.01 to 0.1."255" Much. larger shifts can occur if both 6 and e, are larger (a.20.8 and (20.3: 2008)). but models iu this range overpredict Z5, and are inrelevaut to our results."," Much larger shifts can occur if both $\ell$ and $a_*$ are larger $a_* \gtrsim 0.8$ and $\ell \gtrsim 0.3$; ), but models in this range overpredict $T_{\rm obs}$ and are irrelevant to our results."256" Ποσο, if the characteristic a associated with real accretion flows dis larger (as some models of dwarf novae and some nunerical παΊος sugeest. 2007)). the effect would be to shift our best-fit contours to higher AM. but only by a modest amount."," Hence, if the characteristic $\alpha$ associated with real accretion flows is larger (as some models of dwarf novae and some numerical simulations suggest, ), the effect would be to shift our best-fit contours to higher $M$, but only by a modest amount."257" For the parameters correspouding to the lower Af limit (/=07. (=0.7. and a,= 1). BUSPEC vields £4~2."," For the parameters corresponding to the lower $M$ limit $i=0^\circ$, $\ell = 0.7$, and $a_* = -1$ ), BHSPEC yields $f_{\rm col} \sim 2$."258" From equation (C1)) we see that reducing feo,=1l (the absolute minima) oulv reduces AY by a factor of Ll. still placing IILX-1 in the IMDITI regio."," From equation \ref{eq:mass}) ) we see that reducing $f_{\rm col}=1$ (the absolute minimum) only reduces $M$ by a factor of 4, still placing HLX-1 in the IMBH regime."259" Alternatively, oue. could make the disk arouud a low AL BIL look cooler by truncating it at larger radius."," Alternatively, one could make the disk around a low $M$ BH look cooler by truncating it at larger radius."260" Equation (1)) suggests that decreasing AL to a value near 30A/.. would require a factor of 100 increase to ry,~900.", Equation \ref{eq:mass}) ) suggests that decreasing $M$ to a value near $30 \Msun$ would require a factor of 100 increase to $r_{\rm in} \sim 900$.261 Such au interpretation would need to explain why the flow does not radiate iude this radius., Such an interpretation would need to explain why the flow does not radiate inside this radius.262 Since the cherey does not come out in the hard X-rays. it cannot be a transition to an advection dominated accretion flow. which is often invoked to explain the low state of Galactic N-ray binarics2001).," Since the energy does not come out in the hard X-rays, it cannot be a transition to an advection dominated accretion flow, which is often invoked to explain the low state of Galactic X-ray binaries."263". Furthermore. since y~Uri. the required AL would increase by a factor of 100 to AL~102AL.sv3, "," Furthermore, since $\eta \sim 1/r_{\rm in}$, the required $\Mdot$ would increase by a factor of 100 to $\Mdot \sim26410^{-2} \; \Msun \; \rm yr^{-1}$."265"For M~101ALLvet, the accretion rate aud time variability of Π.Ν. present a challenge to standard models of mmass trauster2011)."," For $\Mdot \sim 10^{-4} \; \Msun \;266\rm yr^{-1}$, the accretion rate and time variability of HLX-1 present a challenge to standard models of mass transfer."267. Hence. it is unlikely that such a high rate is even feasible iu a binary mass trausfer scenario.," Hence, it is unlikely that such a high rate is even feasible in a binary mass transfer scenario."268" Finally. one could plausibly obey the Edcdinetou limit by assuniue a large beaming factor so that Lon.ὃνLi. which (nu this foxiualisn) is equivalent to increasing µ for sole narrow range of 7,"," Finally, one could plausibly obey the Eddington limit by assuming a large beaming factor so that $L_{\rm269 obs} \gg L_{\rm iso}$, which (in this formalism) is equivalent to increasing $\mu$ for some narrow range of $i$."270 Obeving the Eddington limit with AZ~30A. would require µ~100. but note that this is insufficicut for explaining ρε due to the µ1/2 dependence in equation (1)).," Obeying the Eddington limit with $M \sim 30 \Msun$ would require $\mu \sim 100$, but note that this is insufficient for explaining $T_{\rm obs}$ due to the $\mu^{1/2}$ dependence in equation \ref{eq:mass}) )."271 Fixiug f=1 aud decreasing AL bw a factor of 1060 vields a factor of 23 increase i Zj., Fixing $\ell =1$ and decreasing $M$ by a factor of 100 yields a factor of 3 increase in $T_{\rm obs}$.272" Maintaining agreenient with Ti). requires AL and ( to decrease proportionately, which requires a factor of 1000 increase in p."," Maintaining agreement with $T_{\rm obs}$ requires $M$ and $\ell$ to decrease proportionately, which requires a factor of 1000 increase in $\mu$."273 Auy scenario with such large beaming factors probably requires a relativistic outflow or very different accretion flow geometry so these sinple scaliugs mia not strictly apply., Any scenario with such large beaming factors probably requires a relativistic outflow or very different accretion flow geometry so these simple scalings may not strictly apply.274 Nevertheless. we cluphasize that explaining the soft enussion iu IILX-1 presents a serious challenge to amy beaming model. but is naturally explaimed by the IMDIT interpretation.," Nevertheless, we emphasize that explaining the soft emission in HLX-1 presents a serious challenge to any beaming model, but is naturally explained by the IMBH interpretation."275" Using DIISPEC. a fully-relativistic accretion disk. model. we fit several disk dominated observations of IILX-1 for which the huninositv exceeds 10/2 eresf,"," Using BHSPEC, a fully-relativistic accretion disk model, we fit several disk dominated observations of HLX-1 for which the luminosity exceeds $10^{42}$ $\rm erg \; s^{-1}$."276 Due to degeneracies in the best-fit model parameters. jot confidence uncertainties are rather largo. vielding a factor of LOO uncertainty iu the best-fit DIT uass.," Due to degeneracies in the best-fit model parameters, joint confidence uncertainties are rather large, yielding a factor of 100 uncertainty in the best-fit BH mass."277 For fits to the data. we obtain a ower limit of M.z300042... where the limit correspouds oi =OL αl. aud (=0.7.," For fits to the data, we obtain a lower limit of $M \gtrsim 3000 \Msun$, where the limit corresponds to $i=0^\circ$, $a_*=-1$, and $\ell =0.7$."278 We curphasize hat this lait is driven by the need to reproduce the shape aud peak energv of the thermal component in he spectrun., We emphasize that this limit is driven by the need to reproduce the shape and peak energy of the thermal component in the spectrum.279 IHeuce. the Eddinetou linit plavs no role in this coustrait.," Hence, the Eddington limit plays no role in this constraint."280 Constraints frou fits toSwiftand observations. which correspoud to higher nuninosifies. nonunally offer a more restrictive lower ound of ALzGOOOAL... but this bound is subject to he Eddineton lait because our mocel exid is limited to a παπα hDuuinositv (—I.," Constraints from fits toand observations, which correspond to higher luminosities, nominally offer a more restrictive lower bound of $M \gtrsim 6000281\Msun$, but this bound is subject to the Eddington limit because our model grid is limited to a maximum luminosity $\ell=1$."282 We also find an absolute upper bound of MX3x10AZ.. with both datasets. this limit corresponding to rearly edee-on (=907) disks with near maximal spins αν~ 0.99).," We also find an absolute upper bound of $M \lesssim 3 \times 10^5283\Msun$ with both datasets, this limit corresponding to nearly edge-on $i=90^\circ$ ) disks with near maximal spins $a_* \sim 0.99$ )."284 This upper lait is subject to he uncertainties in the models at very Ligh spin aud Yel inclination Guost notably our neglect of τοπτις radiation and assumption of a razor thin eeometry)., This upper limit is subject to the uncertainties in the models at very high spin and high inclination (most notably our neglect of returning radiation and assumption of a razor thin geometry).285 The lack of X-ray eclipses and the absence of evidence or nearly edee-on X-rav binary svstenis in the Milky Wav imotivate a limit on iX75 and. therefore. AL<107.," The lack of X-ray eclipses and the absence of evidence for nearly edge-on X-ray binary systems in the Milky Way motivate a limit on $i \lesssim28675^\circ$ and, therefore, $M \lesssim 10^5$."287 An aremment agaist /~907 based ou absence of eclipses assunnies that the accretiug matter is being provided by a binary conrpanion. but obscuration bv a flared outer disk may eonerically limit the range of observable ὁ," An argument against $i288\sim 90^\circ$ based on absence of eclipses assumes that the accreting matter is being provided by a binary companion, but obscuration by a flared outer disk may generically limit the range of observable $i$."289 For M=LP AL... TLN-1 would be consistent with the lower cud of the mass distribution mferred iu active ealactic uuclei2007).. but would still be distinctive because of its offuuclear location in ESO 213-19.," For $M \gtrsim 10^5 \Msun$ , HLX-1 would be consistent with the lower end of the mass distribution inferred in active galactic nuclei, but would still be distinctive because of its off-nuclear location in ESO 243-49."290 Other paramcters of interest. such as / and « are essentially unconstrained bv the data. uuless we require that the disk must radiate below the Eddingtou DIuniuositv. in which case αν20 or a.>L5 are required bv theοι aud data. respectively.," Other parameters of interest, such as $i$ and $a_*$, are essentially unconstrained by the data, unless we require that the disk must radiate below the Eddington luminosity, in which case $a_* > 0$ or $a_* > -0.5$ are required by the and data, respectively."291 Observations with improved signal-to-noise are uulikely to siguificauth tighten these AZ constraints. as the allowed AL range is set primarily bw uncertainties in / and 64.," Observations with improved signal-to-noise are unlikely to significantly tighten these $M$ constraints, as the allowed $M$ range is set primarily by uncertainties in $i$ and $a_*$ ."292 Independent estimates for a. and / are ultimately needed toimprove our AL coustraiuts. aud could plausibly be provided by modeling of broad Fe Ka lines or N-rav polarization if such data became available.," Independent estimates for $a_*$ and $i$ are ultimately needed toimprove our $M$ constraints, and could plausibly be provided by modeling of broad Fe $\alpha$ lines or X-ray polarization if such data became available."293 If a broad Fe line is preseut iu. IILX- obtaining the signal-to-noise uecessary to resolve it would require unteasibly long exposure tines with aud other existing X-ray missions.," If a broad Fe line is present in HLX-1, obtaining the signal-to-noise necessary to resolve it would require unfeasibly long exposure times with and other existing X-ray missions."294 However. such constraints iav be possible for future iissious with larger collecting areas.," However, such constraints may be possible for future missions with larger collecting areas."295 Tn sununiuw. despite the rather large range of AL ," In summary, despite the rather large range of $M$ "296The linear result given by equation (21) is thus the appropriate lorm for the statie deusity However. pi wakes no contribution to the angular momentum trausport.,"The linear result given by equation (24) is thus the appropriate form for the static density However, $\rho_1^s$ makes no contribution to the angular momentum transport."297 Iu calculating the latter. we shall be multiplying the deusity by the induced. azimuthal velocity.," In calculating the latter, we shall be multiplying the density by the induced, azimuthal velocity."298 Since the latter oscillates sinusoidally. the product vanishes over a period.," Since the latter oscillates sinusoidally, the product vanishes over a period."299 We therefore turn to the oscillating deusity perturbation., We therefore turn to the oscillating density perturbation.300" From now on. we may onit pp, when consideriug the equivalent density."," From now on, we may omit $\rho_{10}^\ast$ when considering the equivalent density."301 The time-varying density perturbation. which we shall continue to denote simply as py. obeys where pfs is given by equations (20)-(21).," The time-varying density perturbation, which we shall continue to denote simply as $\rho_1$ , obeys where $\rho_{12}^\ast$ is given by equations (20)-(21)."302" We proceed by finding those parts of p, (denoted pa. ete.)"," We proceed by finding those parts of $\rho_1$ (denoted $\rho_A$, etc.)"303 generated by each additive component of pt., generated by each additive component of $\rho_{12}^\ast$.304 Linearity of the wave equation eusures that we can add these individual solutious to obtain the full oue., Linearity of the wave equation ensures that we can add these individual solutions to obtain the full one.305 Cousider first the fuuctious 24. Dy. aud De obeying [If we cau find these three Cuuctious. then differentiation oftheir governing wave equatious reveals that," Consider first the functions ${\cal D}_A$, ${\cal D}_B$, and ${\cal D}_C$ obeying If we can find these three functions, then differentiation oftheir governing wave equations reveals that"306"the M-dwarf (?) log-normal distribution, which are the functions used to generate the initial binary populations.","the M-dwarf \citep{Fischer92} log-normal distribution, which are the functions used to generate the initial binary populations."307 The open circles in Fig., The open circles in Fig.308" 2(a) show the binary fractions generated by the initial conditions (there is a deviation from the generating function at low separations due to the effect of eigenevolution, however, as we shall see later this is unimportant as these binaries are hard)."," \ref{field_evol_p1} show the binary fractions generated by the initial conditions (there is a deviation from the generating function at low separations due to the effect of eigenevolution, however, as we shall see later this is unimportant as these binaries are hard)."309" The open histograms show the distribution of binary fractions found by our binary finding algorithm, which are clearly different."," The open histograms show the distribution of binary fractions found by our binary finding algorithm, which are clearly different."310 In Fig., In Fig.311" 2 we also compare the separation distributions of binaries generated with a field binary fraction found by our binary finder at time zero (open histogram), and (hatched histogram) at 1 Myr."," \ref{field_evol} we also compare the separation distributions of binaries generated with a field binary fraction found by our binary finder at time zero (open histogram), and (hatched histogram) at 1 Myr."312" Quite clearly there has been significant dynamical destruction of binaries with separations of ~100 — 1000 AU, whilst binaries with separations «50 — 100 AU are almost unchanged."," Quite clearly there has been significant dynamical destruction of binaries with separations of $\sim100$ – $1000$ AU, whilst binaries with separations $<50$ – $100$ AU are almost unchanged."313 This is the Heggie-Hills law (???) in action: the hard-soft boundary in our clusters is at a few hundred AU (this is also seen by e.g. ??? and described in detail by ?)).," This is the Heggie-Hills law \citep{Heggie75,Hills75a,Hills75b} in action: the hard-soft boundary in our clusters is at a few hundred AU (this is also seen by e.g. \citealt{Kroupa95a,Kroupa95b,Kroupa99} and described in detail by \citealt{Kroupa08}) )."314 Even the binary fraction of very hard systems is reduced by the destruction of wide binaries., Even the binary fraction of very hard systems is reduced by the destruction of wide binaries.315 There isvery little evolution in the number of systems with separations below 1 AU; however the binary fraction of those systems decreases due to the increase in thetotal number of systems due to the destruction of wider binaries., There is little evolution in the number of systems with separations below $1$ AU; however the binary fraction of those systems decreases due to the increase in the number of systems due to the destruction of wider binaries.316" For example, in a cluster with 100 binary systems, 20 of these may be very hard."," For example, in a cluster with 100 binary systems, 20 of these may be very hard."317 The initial binary fraction of these hard systems would be 20/100 =20%.., The initial binary fraction of these hard systems would be 20/100 =.318" However, after the destruction of 20 wider systems, each wider system becomes 40 single stars, and so the binary fraction of very hard systems would be 20/120 =17%,, despite none of them having been destroyed."," However, after the destruction of 20 wider systems, each wider system becomes 40 single stars, and so the binary fraction of very hard systems would be 20/120 =, despite none of them having been destroyed."319 There is very little dynamical processing of initially hard systems., There is very little dynamical processing of initially hard systems.320" In each cluster a few (0 — 5) systems with initial separations «50 AU are significantly altered or destroyed, but most systems retain virtually unchanged separations from formation."," In each cluster a few $0$ – $5$ ) systems with initial separations $\ll\,50$ AU are significantly altered or destroyed, but most systems retain virtually unchanged separations from formation."321" We conclude, in common with other authors, that A cluster in which the average separation between systems is a few thousand AU cannot possibly form systems with separations greater than this."," We conclude, in common with other authors, that A cluster in which the average separation between systems is a few thousand AU cannot possibly form systems with separations greater than this."322" Indeed, ? find only 3 possible binaries in Orion with separations of 1000 — 5000 AU (they also note that the origin of wide binaries cannot be in Orion-like clusters)."," Indeed, \citet*{Scally99} find only $3$ possible binaries in Orion with separations of $1000$ – $5000$ AU (they also note that the origin of wide binaries cannot be in Orion-like clusters)."323 Fig., Fig.324" 1(b) appears to show that if the initial binary fraction is unity in dense clusters, then the effect of dynamical evolution is to lower the binary fraction to close to the field values (actually slightly too high for M-dwarfs)."," \ref{fmult-b} appears to show that if the initial binary fraction is unity in dense clusters, then the effect of dynamical evolution is to lower the binary fraction to close to the field values (actually slightly too high for M-dwarfs)."325" This might suggest that in dense clusters stars form with a field-like separation distribution, but with a higher binary fraction (e.g. unity)."," This might suggest that in dense clusters stars form with a field-like separation distribution, but with a higher binary fraction (e.g. unity)."326" However, as we show in Fig."," However, as we show in Fig."327 3 (c.f., \ref{100_sep_dists} (c.f.328" Fig. 2)),"," Fig. \ref{field_evol}) ),"329 exactly the same effects occur with a binary fraction of unity as with a field binary fraction., exactly the same effects occur with a binary fraction of unity as with a field binary fraction.330" Firstly, many of our generated binaries are unphysically wide, given the cluster’s size, and are not identified as binaries even before the start of the simulations."," Firstly, many of our generated binaries are unphysically wide, given the cluster's size, and are not identified as binaries even before the start of the simulations."331" Secondly, the hard-soft boundary is in exactly the same place and so many binaries with separations >50 to a few hundred AU are dynamically disrupted."," Secondly, the hard-soft boundary is in exactly the same place and so many binaries with separations $>50$ to a few hundred AU are dynamically disrupted."332 Our initial conditions also produce too many, Our initial conditions also produce too many333the svunuetiy between positive aud negative values of the axial wavevector q iu Eq. (,the symmetry between positive and negative values of the axial wavevector $q$ in Eq. (33413) even if D. is small compared to D...,13) even if $B_z$ is small compared to $B_{\varphi}$.335 However. Eq. (," However, Eq. ("33613) still coutaius some degeneracy because itis invariant cunder (2.4)>(oaq) or (i.»(oan.z) transformation.,"13) still contains some degeneracy because itis invariant under $(m, q) \rightarrow (-m, -q)$ or $(m, \varepsilon) \rightarrow (-m, 337-\varepsilon)$ transformation."338 The mstabilitv occurs ouly for perturbations with 4 within a narrow range that depends ou the azimuthal wavenumber ma., The instability occurs only for perturbations with $q$ within a narrow range that depends on the azimuthal wavenumber $m$.339" For example. verturbations with im=1l and m=6 are unstable if σαςτη πιά ο>42200. respectively,"," For example, perturbations with $m=1$ and $m=6$ are unstable if $0 > q > -70$ and $-60 > q > -200$, respectively."340 Note hat the unstable perturbations with positive i» should lave negative q auc. on the contrarv. if a is negativo. instability occurs only for perturbations with positive q.," Note that the unstable perturbations with positive $m$ should have negative $q$ and, on the contrary, if $m$ is negative, instability occurs only for perturbations with positive $q$."341 The growth rate das two clear maxima with the highest uaxinmni corresponding to q—in, The growth rate has two clear maxima with the highest maximum corresponding to $q \sim - m/ \varepsilon$.342 By the order of magnitude. the axial wave-vector of the most rapidly erowiue perturbation cau be estimated from the couditiou of iiagnetic resonance Tudeed. this equation inuplies wyxgeμα)20.," By the order of magnitude, the axial wave-vector of the most rapidly growing perturbation can be estimated from the condition of magnetic resonance Indeed, this equation implies $\omega_A \propto q 343\varepsilon + m \psi(x) \approx 0$."344 Since cGe)~ Lin our model. the condition wi=0 corresponds to The most rapidly growing modes turn out to be highly anisotropic if the axial feld is weak compared to the toroidal oue: their axial waveleneth A.=οπή.—272s is much shorter than the radial and azimuthal lenetlscale.," Since $\psi(x) \sim 1$ in our model, the condition $\omega_A = 0$ corresponds to The most rapidly growing modes turn out to be highly anisotropic if the axial field is weak compared to the toroidal one: their axial wavelength $\lambda_z = 2 \pi/k_z \sim 2 \pi \varepsilon s$ is much shorter than the radial and azimuthal lengthscale."345 The growth rate is fairly high aud is of the order of the inverse Alfveu time scale., The growth rate is fairly high and is of the order of the inverse Alfven time scale.346 The erowth rate slowly increases with a aud perturbations with a shorter azimuthal scale erow faster., The growth rate slowly increases with $m$ and perturbations with a shorter azimuthal scale grow faster.347 Tle axisvunmetric mode (#7= 0) turus out to be the most slowly erowiug., The axisymmetric mode $m=0$ ) turns out to be the most slowly growing.348 The model with p—lu=2 exhibits a siauillar behaviour of perturbatious (seo Fie.," The model with $p=1, n=2$ exhibits a similar behaviour of perturbations (see Fig."349 1)., 4).350 As nentioned. electric currents are more concentrated near i6 outer boundary in this model.," As mentioned, electric currents are more concentrated near the outer boundary in this model."351 The values of 4 vat allow the imstabilitv are smaller im this case and rerefore the corresponing vertical wavelengths are ouger. but the ranec of unstable 4 is narrower.," The values of $q$ that allow the instability are smaller in this case and therefore the corresponding vertical wavelengths are longer, but the range of unstable $q$ is narrower."352 For ιο consklered values of n. the growth rate is lower pproxinatelv by a factor 2.," For the considered values of $m$, the growth rate is lower approximately by a factor 2."353 The general mipression is iif the configuration with currents concentrated closer o the outer boundary is more stable than that with nore unuiformlv distribued currents., The general impression is that the configuration with currents concentrated closer to the outer boundary is more stable than that with more uniformly distributed currents.354 This couclusiou qualitatively agrees with the result obtain by Robinson (1971) from the lydromagnuetic οποίος. principle., This conclusion qualitatively agrees with the result obtained by Robinson (1971) from the hydromagnetic energy principle.355 The author considers a pinch configuration with laree ο) aud fuds that the coufieurationC» ix more stable if lareeOo axial currents flow outside the main plasima colin., The author considers a pinch configuration with large $\beta$ and finds that the configuration is more stable if large axial currents flow outside the main plasma column.356 Note that the ecquilibriuni state of both the configurations considered in Fie., Note that the equilibrium state of both the configurations considered in Fig.357 3 aud lis characterized bv thenegative pressure eracdicut that is required for the development of instability (Longaretti 2008)., 3 and 4 is characterized by thenegative pressure gradient that is required for the development of instability (Longaretti 2008).358 Iudeed. using Eq. (," Indeed, using Eq. ("3595) aud expression (15) for the toroidal field. we obtain Evidently dP/ds«0 evervwhere within the rauge L>r> Oifp = Landy =1.2.,"5) and expression (15) for the toroidal field, we obtain Evidently $d P/d s < 0$ everywhere within the range $1 > x > 0$ if $p=1$ and $n=1,2$."360 The sign of the pressure eradient is important because it determines the destabilizing effect in the so called Suvdans criterion., The sign of the pressure gradient is important because it determines the destabilizing effect in the so called Suydam's criterion.361 This criterion represeuts a necessary condition for stability (see. c.g. Lougaretti 2003) and reads iu our notations where 5=SD./D. is the maguetic shear.," This criterion represents a necessary condition for stability (see, e.g., Longaretti 2003) and reads in our notations where $h = s B_z / B_{\varphi}$ is the magnetic shear."362 For the equilibrimu configuration with the toroidal field given by Eq. (, For the equilibrium configuration with the toroidal field given by Eq. (36315). this criterion can be rewritten as For the chosen paramcters (p=].» 1.2). the necessary condition for stability is uot satisfied. 1n some fraction of the jet volume (for example. near the outer boundary). and the corresponding configurations can eonorally be mustable.,"15), this criterion can be rewritten as For the chosen parameters $p=1, n=1,2$ ), the necessary condition for stability is not satisfied in some fraction of the jet volume (for example, near the outer boundary), and the corresponding configurations can generally be unstable."364 Figure 5 shows t1e dependence of the erowth rate on q for the model with p=2.01.," Figure 5 shows the dependence of the growth rate on $q$ for the model with $p=2, n=1$."365" Iu this case. the Παππια of the azimuthal field is located within the jet ποιο, at 1=0.5."," In this case, the maximum of the azimuthal field is located within the jet volume, at $x=0.5$."366 The masini value is approximatcly 1.3 times hieher than the boundary ouc., The maximum value is approximately 1.3 times higher than the boundary one.367 It appears that he instability grows slirbitlv faster iu lis type of nnagnetic configurations. but all the main qualitative features of the instability are uuchauged.," It appears that the instability grows slightly faster in this type of magnetic configurations, but all the main qualitative features of the instability are unchanged."368 Because D. is stronger in this uodel. the instability occurs for larger q as follows frou Eq. (," Because $B_{\varphi}$ is stronger in this model, the instability occurs for larger $q$ as follows from Eq. ("36916).,16).370 Note that we calculate P oulv for àx23 because of computationalproblems at larger m., Note that we calculate $\Gamma$ only for $m \leq 3$ because of computationalproblems at larger $m$ .371 Iu Fie.6 we plot the growth rate of instability for the configuration with the axial field wich weaker than the toroidal one. ¢= 0.01.," In Fig.6 we plot the growth rate of instability for the configuration with the axial field much weaker than the toroidal one, $\varepsilon = 0.01$ ."372 The distribution of the toroidal field is eiven by Eq. (, The distribution of the toroidal field is given by Eq. (373"15) with p=1 aud = no2,",15) with $p=1$ and $n=2$ .374and to better determine the continuum level).,and to better determine the continuum level).375" An emission line template is added visually to the top panel and carried over to the higher flux level profile in the middle panel, the primary aim here being to show that the CVI RRC is well resolved."," An emission line template is added visually to the top panel and carried over to the higher flux level profile in the middle panel, the primary aim here being to show that the CVI RRC is well resolved."376" As with the NVII RRC, the peak CVI RRC flux is seen to shift to the blue as the continuum level increases, and in this case there are no likely absorption lines to affect the RRC profile close to the threshold wavelength."," As with the NVII RRC, the peak CVI RRC flux is seen to shift to the blue as the continuum level increases, and in this case there are no likely absorption lines to affect the RRC profile close to the threshold wavelength."377 The similarity in the CVI and NVII RRC blue shifts at higher continuum levels strengthens a direct association of the recombining plasma with the strong intermediate velocity absorption (~3500-5000 km !) observed in the same higher level ions (Paper I)., The similarity in the CVI and NVII RRC blue shifts at higher continuum levels strengthens a direct association of the recombining plasma with the strong intermediate velocity absorption $\sim$ 3500-5000 km $^{-1}$ ) observed in the same higher level ions (Paper I).378" Furthermore, tracking the CVI RRC through individual orbits shows a similar pattern to the NVII RRC, again indicating a response time for the intermediate velocity gas of a few days."," Furthermore, tracking the CVI RRC through individual orbits shows a similar pattern to the NVII RRC, again indicating a response time for the intermediate velocity gas of a few days."379" In contrast, the lower level CV RRC (31.63 shown in figure 7 (lower panel) only appears at the A))zero velocity threshold, consistent with the low absorption velocities characteristic for that ion."," In contrast, the lower level CV RRC (31.63 ) shown in figure 7 (lower panel) only appears at the zero velocity threshold, consistent with the low absorption velocities characteristic for that ion."380" In summary, we find RRC of NVII and CVI to vary in strength and velocity profile over several days and in a manner apparently dependent on the continuum flux level."," In summary, we find RRC of NVII and CVI to vary in strength and velocity profile over several days and in a manner apparently dependent on the continuum flux level."381" We interpret the variability as from enhanced photoionisation of the high velocity flow when the continuum flux level is high, being followed by strong recombination over the following days of reduced flux level."," We interpret the variability as from enhanced photoionisation of the high velocity flow when the continuum flux level is high, being followed by strong recombination over the following days of reduced flux level."382" The velocity and ionisation gradients found in the absorption spectra (Paper I) then explain the differences between the RRC of NVII, CVI and the lower ionisation state of CV."," The velocity and ionisation gradients found in the absorption spectra (Paper I) then explain the differences between the RRC of NVII, CVI and the lower ionisation state of CV."383" The best determined RRC profiles all indicate a relatively low temperature of ~7+2 eV. In Paper I we reported a rich absorption line spectrum from the 2009 oobservation of4051,, revealing the presence of an ionised outflow with a wide range of velocities and ionisation parameter."," The best determined RRC profiles all indicate a relatively low temperature of $\sim$ $\pm$ 2 eV. In Paper I we reported a rich absorption line spectrum from the 2009 observation of, revealing the presence of an ionised outflow with a wide range of velocities and ionisation parameter."384" The absorption line velocity structure and a broad correlation of velocity with ionisation parameter were shown there to be consistent with an outflow scenario where a highly ionised, high velocity wind runs into the interstellar medium or previous ejecta, losing much of its kinetic energy in the resultant strong shock (King 2010)."," The absorption line velocity structure and a broad correlation of velocity with ionisation parameter were shown there to be consistent with an outflow scenario where a highly ionised, high velocity wind runs into the interstellar medium or previous ejecta, losing much of its kinetic energy in the resultant strong shock (King 2010)."385" With the strong immediate post-shock cooling likely to be dominated by Compton scattering of the AGN thermal continuum (King 2003), we also noted that a quasi-constant soft X-ray emission component might be evidence of further energy loss as the post-shock gas slowed and recombined ahead of the contact discontinuity."," With the strong immediate post-shock cooling likely to be dominated by Compton scattering of the AGN thermal continuum (King 2003), we also noted that a quasi-constant soft X-ray emission component might be evidence of further energy loss as the post-shock gas slowed and recombined ahead of the contact discontinuity."386" A second outstanding feature of the soft X-ray data from the 2009 observation was a complex emission line spectrum, particularly evident at low continuum flux levels, with velocity-broadened emission from several H- and He-like resonance lines, as well as a number of strong RRC."," A second outstanding feature of the soft X-ray data from the 2009 observation was a complex emission line spectrum, particularly evident at low continuum flux levels, with velocity-broadened emission from several H- and He-like resonance lines, as well as a number of strong RRC."387" Broad emission lines of OVII and OVIII have been reported previously from ((Ogle 2004, Steenbrugge 2009), and attributed to scattering of the AGN X-ray continuum from high velocity clouds in the BLR."," Broad emission lines of OVII and OVIII have been reported previously from (Ogle 2004, Steenbrugge 2009), and attributed to scattering of the AGN X-ray continuum from high velocity clouds in the BLR."388" An alternative interpretation, outlined here, envisages the broad emission lines arising from the limb-brightened shell of shocked gas building up ahead of the contact discontinuity."," An alternative interpretation, outlined here, envisages the broad emission lines arising from the limb-brightened shell of shocked gas building up ahead of the contact discontinuity."389 On this alternative picture the line broadening primarily arises from the angular divergence of the flow at the bright limb of the expanding spherical shell., On this alternative picture the line broadening primarily arises from the angular divergence of the flow at the bright limb of the expanding spherical shell.390 An optically thin spherical shell would produce an, An optically thin spherical shell would produce an391"The starting asstuuptious in this analysis are that the motious of the natter now concentrated around the LMC. M31 and the MW may be adequately represented by tje patlis of tnass tracers: the peculiar velocities of the mass tracers at redshift ziii10 are xiiall. Consistent with the eravitatioual tustability picture lor structure formation: the influence of natter outside the Local Group may be adequately represented by the gravitational field of an appropriaely placed third massive body: aud the Magellanic €'""louds have returuec tothe ΝW for te first time since moving away [rom it at high recdshilt.","The starting assumptions in this analysis are that the motions of the matter now concentrated around the LMC, M31 and the MW may be adequately represented by the paths of mass tracers; the peculiar velocities of the mass tracers at redshift $z_{\rm init}\sim 10$ are small, consistent with the gravitational instability picture for structure formation; the influence of matter outside the Local Group may be adequately represented by the gravitational field of an appropriately placed third massive body; and the Magellanic Clouds have returned to the MW for the first time since moving away from it at high redshift."392 Several cousicleratious iu acdition to those mentioned iu Section bear ou these assumptions aud ou the credibility of the resulti& dyuamiueal mocel for the Local Croup., Several considerations in addition to those mentioned in Section \ref{sec:sec1a} bear on these assumptions and on the credibility of the resulting dynamical model for the Local Group.393 Lt is worth emphasizinge againe tiat the mass tracer moclel in liis analysis does uo require t the galaxies had their prese1| coimnpact sirictures at high recsift., It is worth emphasizing again that the mass tracer model in this analysis does not require that the galaxies had their present compact structures at high redshift.394 It. does require that mergi histories since zigLO have beet local eiough that the momentum aud center o“tnass of pieces of a p‘ologalaxy are welully represewed by a single mass tracer., It does require that merging histories since $z_{\rm init}\sim 10$ have been local enough that the momentum and center of mass of the pieces of a protogalaxy are usefully represented by a single mass tracer.395 We have au example the motious ol the Magellanic Cloids in Figure L., We have an example in the motions of the Magellanic Clouds in Figure \ref{figure:4}.396 IL in tve future the Clouds me'ged a fut analysis of tlis sort would moclel t1e Clouds as a single bocly., If in the future the Clouds merged a future analysis of this sort would model the Clouds as a single body.397 Tracing that situation back in time would iiss the earlier presence two Dass concentrations. bttit would give a reasonade indicatjon . where the matter in the merged galaxy. came [rou," Tracing that situation back in time would miss the earlier presence two mass concentrations, but it would give a reasonable indication of where the matter in the merged galaxy came from."398 The second o “the startilg assumptions is tha the peculiar velocities of he mass tracers al tin~LO are €Ousistent with what would be produced by the gravitational interactious witli ieiehibors ad. in le Case o “tle Clouds. with the higler multipoles of tle mass distributions within lie nearest )asslve protogaies.," The second of the starting assumptions is that the peculiar velocities of the mass tracers at $z_{\rm init}\sim 10$ are consistent with what would be produced by the gravitational interactions with neighbors and, in the case of the Clouds, with the higher multipoles of the mass distributions within the nearest massive protogalaxies."399 A measure of the former situation is presented ir equation (2))., A measure of the former situation is presented in equation \ref{eq:pec_vel}) ).400 A nore clirect Least‘e is show in Table {., A more direct measure is shown in Table 4.401 Under the |eader for each Caresiau velocity componeut. he first colina Lists the initi values of the peculiar velocity Components for eacl LC protogalaxy lu uunmerlca solulon 220a.," Under the header for each Cartesian velocity component, the first column lists the initial values of the peculiar velocity components for each LG protogalaxy in numerical solution 220a."402 he second columu uier each header is he preciction from linear »erturbatio theory applied a init to a comtinuois pressureless [luid. v=/dg (eq. [3.2]]).," The second column under each header is the prediction from linear perturbation theory applied at $z_{\rm init}$ to a continuous pressureless fluid, $\vv = t\delta\gv$ (eq. \ref{eq:eomi}] ]),"403 where he peculiar gravitational accele‘allol dg; of bocv d is computed [ror1 the positions at σι di solution 220:1., where the peculiar gravitational acceleration $\delta\gv_i$ of body $i$ is computed from the positions at $z_{\rm init}$ in solution 220a.404 The numerical aud perturbajon tleory velociy components in Tabe [ are correlated. thougl with considerable scatter.," The numerical and perturbation theory velocity components in Table 4 are correlated, though with considerable scatter."405 The sc: uteriay be in part au ellect of the nonlinear growth of clustering. but almost certainly a large coitribuing [actor is that a four-body system is uot a very goo. approximation to a coutiuuous fuid.," The scatter may be in part an effect of the nonlinear growth of clustering, but almost certainly a large contributing factor is that a four-body system is not a very good approximation to a continuous fluid."406 But the important poiut for our purpose is that the initia, But the important point for our purpose is that the initial407Wr) = 22) The upper panels of Fig.,(r) = ( 1 + ) The upper panels of Fig.408 1. show the LOSVD as a function of projected radius and the tangential velocity. distribution as a function. of radius for this model., \ref{losvd} show the LOSVD as a function of projected radius and the tangential velocity distribution as a function of radius for this model.409 The model does. indeed. look very similar to the LOSVDs seen in the stellar kinematies of real edge-on disk galaxies (c.g. Ixuijken. Fisher Alerrifield 1996).," The model does, indeed, look very similar to the LOSVDs seen in the stellar kinematics of real edge-on disk galaxies (e.g. Kuijken, Fisher Merrifield 1996)."410" “Phe lower panels show the parts of these two functions that lic ""above the rotation curve.", The lower panels show the parts of these two functions that lie “above” the rotation curve.411 For the reasons discussed in Section 3.. these two plots appear similar. allowing us to use the bottom right panel as our initial approximation for the bottom left panel.," For the reasons discussed in Section \ref{edgeonsec}, these two plots appear similar, allowing us to use the bottom right panel as our initial approximation for the bottom left panel."412 We have applied the algorithm. described in Section 3. to a model of the form given by Eqs. (19)). (200). (21))," We have applied the algorithm described in Section \ref{edgeonsec} to a model of the form given by Eqs. \ref{dfdef}) ), \ref{betadef}) ), \ref{gdef}) )"413 and (22)) for à variety of sets of parameters., and \ref{Psidef}) ) for a variety of sets of parameters.414 Figure 2. illustrates he case for parameters Ly=1.6. ry=0.2. ry=2.0.," Figure \ref{approxlosvd} illustrates the case for parameters $L_0 =4151.6$, $r_0=0.2$, $v_0=2.0$."416 As this figure shows. the iterative algorithm. recovers the DI verv closely.," As this figure shows, the iterative algorithm recovers the DF very closely."417 1n. fact. convergence occurs in a small number of steps.," In fact, convergence occurs in a small number of steps."418" The only remaining discrepancies between he ""observed"" LOSVDs and those produced by projecting he recovered. DE occur at. very small values of ον. due to numerical noise in the integration process."," The only remaining discrepancies between the “observed” LOSVDs and those produced by projecting the recovered DF occur at very small values of $r_p$, due to numerical noise in the integration process."419 ‘Thus Far. we have assumed that we know the gravitational xotential in our reconstruction of the DE.," Thus far, we have assumed that we know the gravitational potential in our reconstruction of the DF."420 Such an assumption is reasonable if modelling a cisk galaxy containing gas [rom which an emission-line rotation curve can be obtained., Such an assumption is reasonable if modelling a disk galaxy containing gas from which an emission-line rotation curve can be obtained.421 However. such information would not be available for a purely stellar system such as an SO ealaxy.," However, such information would not be available for a purely stellar system such as an S0 galaxy."422 Further. we are also interested in addressing the more general question of whether the gravitational potential is uniquely specified by the observable stellar. kinematics. or whether one can derive ecually-plausible distribution functions using cilfercnt assumptions about the form of the potential.," Further, we are also interested in addressing the more general question of whether the gravitational potential is uniquely specified by the observable stellar kinematics, or whether one can derive equally-plausible distribution functions using different assumptions about the form of the potential."423 ]t is apparent from Fig., It is apparent from Fig.424 1. that there is no obvious way to estimate the rotation curve from the observed LOSVDs: the combination of asvmmetric drift in the stellar kinematics and the elfects of projection along the line of sight means that the local circular speed. does not. correspond. to any simple property of the stellar kinematies such as the peak of the LOSVD or the mean line-of-sight velocity of the stars., \ref{losvd} that there is no obvious way to estimate the rotation curve from the observed LOSVDs: the combination of asymmetric drift in the stellar kinematics and the effects of projection along the line of sight means that the local circular speed does not correspond to any simple property of the stellar kinematics such as the peak of the LOSVD or the mean line-of-sight velocity of the stars.425 We are therefore. in principle. free to choose a. clillerent rotation curve and hence gravitational potential.," We are therefore, in principle, free to choose a different rotation curve and hence gravitational potential."426 Figures 3. and 4. show what happens in. practice if we clo so., Figures \ref{v2.1} and \ref{v1.9} show what happens in practice if we do so.427 For these model calculations. we have adopted a vyvittattionnal potential that dillers only fairly marginally rom the true form.," For these model calculations, we have adopted a nal potential that differs only fairly marginally from the true form."428 The iterative process again converges rapidlv to a plausible DE. which reproduces the LOSVDs exactly for [enstrolru).," The iterative process again converges rapidly to a plausible DF, which reproduces the LOSVDs exactly for $|v_{los}| > v_c(r_p)$."429 Mowever. the LOSVDs that one xediets from the derived. DE for οςΟρ) bear little resemblance to those of the original galaxy. model.," However, the LOSVDs that one predicts from the derived DF for $|v_{los}| <430v_c(r_p)$ bear little resemblance to those of the original galaxy model."431 Thus. it would appear that the exact form of the gravitational »otential is tightly. constrained by the observations: using just the high-velocity kinematics. one can reconstruct the ull DE consistent with any given gravitational potential. but he low-velocity tails of the LOSVDs will only be correctly reproduced if the correct. potential is adopted.," Thus, it would appear that the exact form of the gravitational potential is tightly constrained by the observations: using just the high-velocity kinematics, one can reconstruct the full DF consistent with any given gravitational potential, but the low-velocity tails of the LOSVDs will only be correctly reproduced if the correct potential is adopted."432 The ultimate goal of dynamical astronomy is the derivation ofall that there is to know about a galaxys dynamics [rom its observable kinematics., The ultimate goal of dynamical astronomy is the derivation of all that there is to know about a galaxy's dynamics from its observable kinematics.433 We are still clearly a long way from attaining this “holy erail.” but the analysis of this paper does provide some cause for optimism.," We are still clearly a long way from attaining this “holy grail,” but the analysis of this paper does provide some cause for optimism."434 Specifically. we have shown how the distribution function of a relatively simple model galaxv can be estimated. directly from. its observed. kinematics. using a straightforward. iterative scheme.," Specifically, we have shown how the distribution function of a relatively simple model galaxy can be estimated directly from its observed kinematics, using a straightforward iterative scheme."435 Further. the redundancy of information in the kinematics means that one can readily rule out models in which the wrong gravitational potential has been adopted.," Further, the redundancy of information in the kinematics means that one can readily rule out models in which the wrong gravitational potential has been adopted."436 The success of this iterative scheme seems to derive [rom the fact that the information available from the LOSVD of an edge-on disk is very similar to that available for inclined. disks. for which the inversion to the DE. is already well established. (Alerrificll Ixuijken. 1994. Pichon Thichbaut 1998).," The success of this iterative scheme seems to derive from the fact that the information available from the LOSVD of an edge-on disk is very similar to that available for inclined disks, for which the inversion to the DF is already well established (Merrifield Kuijken 1994, Pichon Thiébbaut 1998)."437 Thus. perhaps rather surprisingly. this problem. does not appear significantly more ill-conditioned than the simpler case of the inclined. disk. even though an extra integral is involved.," Thus, perhaps rather surprisingly, this problem does not appear significantly more ill-conditioned than the simpler case of the inclined disk, even though an extra integral is involved."438 The most tempting practical application for this technique is the study. of cdge-on SO galaxies. since such objects are fairly pure stellar disks. which are believed to contain little by wav of obscuration by There are. however.," The most tempting practical application for this technique is the study of edge-on S0 galaxies, since such objects are fairly pure stellar disks, which are believed to contain little by way of obscuration by There are, however,"439 las a function of 2-10 keV luminosity.,1 as a function of 2-10 keV luminosity.440 Note that the variance computed from several observations of M51. ASL. and NGC 3310 are preseuted. where the typical separation of cach observation was ou the order of several mouths (a more detailed analysis of the multiple M81 observations will be preseuted iu future work).," Note that the variance computed from several observations of M51, M81, and NGC 3310 are presented, where the typical separation of each observation was on the order of several months (a more detailed analysis of the multiple M81 observations will be presented in future work)."441 The motivation for Πιοπιοο multiple observations. when available. is that variance is observed to vary in Sevtert 1 ealaxies (ef.," The motivation for including multiple observations, when available, is that variance is observed to vary in Seyfert 1 galaxies (c.f.,"442 NGC 3227 in Georgeetal. 1998))., NGC 3227 in \cite{george98}) ).443 Also plotted are the variances computed in Noaudra et al. (, Also plotted are the variances computed in Nandra et al. (4441997) for Sevtert 1 galaxies. and it ds obvious hat variance increases with decreasing huninosity in Sevfert 1 galaxies (see Naudraetal. 1997)).,"1997) for Seyfert 1 galaxies, and it is obvious that variance increases with decreasing luminosity in Seyfert 1 galaxies (see \cite{Nandra97}) )."445 Tt is evident from this figure that the same trend docs 10 extend down to the LINER aud LLAGN ealaxies., It is evident from this figure that the same trend does not extend down to the LINER and LLAGN galaxies.446 In addition. simulations were performed to eusure that the lack of variability was not due to the relatively poor statistics of the LLACUN observatious (see Ptak 1997).," In addition, simulations were performed to ensure that the lack of variability was not due to the relatively poor statistics of the LLAGN observations (see Ptak 1997)."447 Note that he variance observed iui the starburst M82 is non-zero and statistically similar to the variance computed from M81., Note that the variance observed in the starburst M82 is non-zero and statistically similar to the variance computed from M81.448 The implications of these results are discussecl below., The implications of these results are discussed below.449 For some of the galaxies iu this sample. the lack of variability is probably due to either the prescuce of anultiple sources of the 2-10. keV cmussion or the fact that the hard emission is scattered at distances ereater than a light-day from the nucleus.," For some of the galaxies in this sample, the lack of variability is probably due to either the presence of multiple sources of the 2-10 keV emission or the fact that the hard emission is scattered at distances greater than a light-day from the nucleus."450 The former case is nost likely the situation for the starburst ealaxies. where while some of the hard flax may he due to “hidden” mucro-ACN. uch of lard fux may to be due to multiple poiut-sources (supernovac aud A-rav binaries) or hot gas (although as mentioned above M82 is similar to AISI in ---s variance).," The former case is most likely the situation for the starburst galaxies, where while some of the hard flux may be due to “hidden” micro-AGN, much of hard flux may to be due to multiple point-sources (supernovae and X-ray binaries) or hot gas (although as mentioned above M82 is similar to M81 in its variance)."451 The latter case is most likely to be true for the Seyfert 2 ealaxies NGC 3117. NCC 1258. and M51. as suggested in Ptaketal(1996).," The latter case is most likely to be true for the Seyfert 2 galaxies NGC 3147, NGC 4258, and M51, as suggested in \cite{Ptak96}."452. Ilowever. vote that in the case of NCC 1258. the observed colt deusitv is on the order of 10°?cuο which is cousistent with the column deusities in Seyfert 2 galaxies observed by (Awaki 1992)) and (Turnerctal. 1997)).," However, note that in the case of NGC 4258, the observed column density is on the order of $10^{23} \rm \ cm^{-2}$ which is consistent with the column densities in Seyfert 2 galaxies observed by \cite{Awaki92}) ) and \cite{turner97}) )."453 While it is possible that the hard X-ray fiux from NGC ⊇⋅↱⊐≺∖∖↕↴∖↴↴∖↴↸⊳⋜↧⇈↸∖↥⋅↸∖≼↧⋜∐⋅∪∏∐≼↧⋯⋜↧↑↸∖↥⋅↕⋜↧↕↖↖⇁↕↑∐⋜↧ BM> ⋯↕∏⋯∐∪∐↑∐∖∪↥⋅≼∐∖↥⋅∪↕↓∩−↓↸⊳⋯−∪↥⋅⋯∪↥⋅↸∖∙↕↑↕↴∖↴⋯∪↴∖↴↑ ⋅⋅ ↕∐↘↽↸∖↕⋅↖⇁↑∐⋜↧↑↑∐∖⊇≓∐⊔↘↽↸∖∖⊽∏∏↘↖↖↽↸∖⋜∐⋅↸∖∪↴⋝↴∖↴↸∖↥⋅↖⇁↕∐∶↴∙⊾↕↴∖↴↑↕∐∖ ≼∐↥⋅↸∖↸⊳↑∐⋯⊳↕↸∖⋜∐⋅↸⊳∪∐↑↕∐⋯∐⊔≺∐∪↑↸∖↑∐⋜↧↑↑∐↕↴∖↴⋜∐⋅∶↴⋁⋯⊔↸∖∐↑↕↴∖↴ streugtheued by the classification of NGC 1258 as a Sevtert 1.9 iu Ποetal. 1997a)).," While it is possible that the hard X-ray flux from NGC 4258 is scattered around material with a column on the order of $10^{24} \rm \ cm^{-2}$ or more, it is most likely that the 2-10 keV flux we are observing is the direct nuclear continuum (note that this argument is strengthened by the classification of NGC 4258 as a Seyfert 1.9 in \cite{Ho97a}) )."454" None of the above considerations are likely to be rue for the brighter LINERs in this sample. M81. NGC 3998. and NGC 1579 suce cach of these has cen observed to exhibit broad ZZe emission (IIoetal.1997b3). nuudug them ""Twpe-I LINERs. analogues o the higher-liuminosity Sevfert 1 galaxies."," None of the above considerations are likely to be true for the brighter LINERs in this sample, M81, NGC 3998, and NGC 4579 since each of these has been observed to exhibit broad $H\alpha$ emission \cite{Ho97b}) ), making them “Type-I” LINERs, analogues to the higher-luminosity Seyfert 1 galaxies."455 Iu the cases of ADSL (καλαetal.1996)). NGC 1579 (Serleiuitsos.Ptals&Yaqool1996)) and. interestingly. he “transition” starburst-LINER ealaxy NCC 3628 (Dahlem.Heckiian.&Fabbiano1995: Yaqoobctal.1995)). significant variability has been observed tween the aud observations. indicating hat the nuclear sources are dominating the enission.," In the cases of M81 \cite{ishi96}) ), NGC 4579 \cite{S96}) ) and, interestingly, the “transition” starburst-LINER galaxy NGC 3628 \cite{d95}; \cite{y95}) ), significant variability has been observed between the and observations, indicating that the nuclear sources are dominating the emission."456 It is therefore likely hat inamost of these galaxies the domunant mode of accretion is fundamentally different roni that in Sevtert galaxies. since it Is accretion that is driving the N-rav unuimositv aud. by extension. the N-rav variability.," It is therefore likely that in most of these galaxies the dominant mode of accretion is fundamentally different from that in Seyfert galaxies, since it is accretion that is driving the X-ray luminosity and, by extension, the X-ray variability."457 A fundamental difference between an ADAF aud an optically-thick accretion disk is that in an ADAF it is the flow itself that is producing the N-ravs., A fundamental difference between an ADAF and an optically-thick accretion disk is that in an ADAF it is the flow itself that is producing the X-rays.458 The a-disk solution predicts a temperature of less than 109 for Afyp>LOTM. (Shakura&Sunvacy1973: see Frank.King.&Raine1992 for a review)., The $\alpha$ -disk solution predicts a temperature of less than $10^{6}$ for $M_{BH} > 10^{7} \ \rm M_{\odot}$ \cite{ss73}; see \cite{frank92} for a review).459" Iu this case (ic.. “normal” Sevfer ealaxies). the N-rav contimmiun is most Likely produced by the iuverse-Compton scattering of UV photons from the ""cold? accretion disk by energetic electrons. possibly in a ""corona above the disk (c£. Taardt&Alaraschi 1991)."," In this case (i.e., “normal” Seyfert galaxies), the X-ray continuum is most likely produced by the inverse-Compton scattering of UV photons from the “cold” accretion disk by energetic electrons, possibly in a “corona” above the disk (c.f., \cite{HM91}) )."460 In an ADAF. the N-ravs are produced. by either the Comptonization of svuchrotron radiation bv the electrons in the flow or by Dronmsstrahluug Cluission from the electron themselves.," In an ADAF, the X-rays are produced by either the Comptonization of synchrotron radiation by the electrons in the flow or by Bremsstrahlung emission from the electron themselves."461 In either case. the esseuce of the ADAF solution is that the cmissiou mechanisin ids inefficieut (on accretion time-scales) ancl a πιstantial vobluue coutributes to the N-ray CLUISSIOL.," In either case, the essence of the ADAF solution is that the emission mechanism is inefficient (on accretion time-scales) and a substantial volume contributes to the X-ray emission."462" Since the ADAF is likely ta le ucarly spherical. most of the N-rav. cluission originates in a ποιο that is probably a spherical anuulus extending from kr5.r10R4,"" da the case of a stationary blackhole or r—3.T in the case of a maxinallv-rotating blackhole."," Since the ADAF is likely to be nearly spherical, most of the X-ray emission originates in a volume that is probably a spherical annulus extending from $r \sim 5-10 \ R_{Schw}$ in the case of a stationary blackhole or $r \sim 3-7$ in the case of a maximally-rotating blackhole."463" If variability is due to a change iu ib. then the time for the ADAF to respond is on the order of πιστό where r=fbxtrirde! LxyGr) is the huniuositv of the ADAF in the 2-10 keV bandpass at r aud 2, isthe gravitational tine dilation (5,[15 ⋅"," If variability is due to a change in $\dot{m}$, then the time for the ADAF to respond is on the order of $\pi\bar{r}\gamma_g/c$, where $\bar{r} = \frac{\int L_X(r)rdr}{\int L_X(r)dr}$, $L_X(r)$ is the luminosity of the ADAF in the 2-10 keV bandpass at $r$ and $\gamma_g$ isthe gravitational time dilation $\gamma_g \sim [1-R_{Schw}/r]^{-1/2}$ )."464" the order of 2 aud 6 Rs4,,fe (1.0. near the iner-1ost ↴∖↴↑⋜∏⋝↕↸∖∪↥⋅↴⋝↕↑↴∖↴⋟∙↸⊳∪↥⋅↥⋅↸∖↴∖↴↻∪⋯∐∐∶↴⋁↑∪∿↓⋜⋯≼↧∐≱⋝⊽↴⊥⊍⊤∖↓ "," $\bar{r}/c$ is probably on the order of 2 and 6 $R_{Schw}/c$ (i.e., near the inner-most stable orbits), corresponding to $\sim 4$ and $11\frac{M_{BH}}{3.5 \times 10^{7} \rm \465M_{\odot}}$ "466Dwarf elliptical galaxies (dEs) are small. low-luminosity galaxies with diffuse. exponentially declining surface- profiles (Ferguson&Binggeli (1994))).,"Dwarf elliptical galaxies (dEs) are small, low-luminosity galaxies with diffuse, exponentially declining surface-brightness profiles \cite{fb}) )."467 They are a gregarious species and are found abundantly in clusters and groups of galaxies (although they seem to avoid the very cluster center where the tidal forces exerted by the cluster potential are strong enough to disrupt them (Trujilloefa£. (2002))))., They are a gregarious species and are found abundantly in clusters and groups of galaxies (although they seem to avoid the very cluster center where the tidal forces exerted by the cluster potential are strong enough to disrupt them \cite{tru}) )).468 According to one model for dE evolution. they are primordial objects.," According to one model for dE evolution, they are primordial objects."469 Supernova explosions heat the interstellar gas to temperatures exceeding the escape velocity. expelling gas from the galaxy (Dekel&Silk(1986)...MoriYoshii (1999))).," Supernova explosions heat the interstellar gas to temperatures exceeding the escape velocity, expelling gas from the galaxy \cite{ds,my}) )."470 This scenario. explains the diffuse appearance of dEs with enhanced star formation at larger radii., This scenario explains the diffuse appearance of dEs with enhanced star formation at larger radii.471 They are expected to form a homogeneous class and to have properties that correlate tightly with mass., They are expected to form a homogeneous class and to have properties that correlate tightly with mass.472 Alternatively. dEs could stem from late-type disk galaxies that entered the clusters and groups of galaxies about 5 Gyr ago (Conseliceeral.," Alternatively, dEs could stem from late-type disk galaxies that entered the clusters and groups of galaxies about 5 Gyr ago \cite{co}) )."473(2001)) N-body simulations show that high-speed gravitational interactions trigger bar-formation in any small disk galaxy orbiting in a cluster (Mooreefaf. (1996))) or around a massive galaxy in a group environment (Mayeretaf. (2001))) and strip large amounts of stars. gas. and dark matter from it by tidal forces.," $N$ -body simulations show that high-speed gravitational interactions trigger bar-formation in any small disk galaxy orbiting in a cluster \cite{mkldo}) ) or around a massive galaxy in a group environment \cite{ma}) ) and strip large amounts of stars, gas, and dark matter from it by tidal forces."474 Internal dynamical processes subsequently transform a disk galaxy into a dynamically hot spheriodal£2 dE within a timespan of about 5 Gyr., Internal dynamical processes subsequently transform a disk galaxy into a dynamically hot spheriodal dE within a timespan of about 5 Gyr.475 Some dEs might still. contain a memory of their former state., Some dEs might still contain a memory of their former state.476 Examples are dEs with embedded stellar disks. bars. and spiral structure (Barazzaetal.(2002).DeRijcke(2003).Grahameraf. (2003))) and with sizable amounts of warm gas. suggesting recent. star formation in. some dEs (DeRijckeefaf.(2003b).—Michielsenοἱ (2004))).," Examples are dEs with embedded stellar disks, bars, and spiral structure \cite{ba,dr2,gr03}) ) and with sizable amounts of warm gas, suggesting recent star formation in some dEs \cite{dr3,dm}) )."477 Moreover. rotationally flattened dEs have been discovered (DeRiekeetal.(20010.Simien&Prugniel (2002))).," Moreover, rotationally flattened dEs have been discovered \cite{dr1,sp}) )."478 The harassment model also offers a natural explanation for the Butcher-Oemler effect (Butcher&Oemler (1978))) and. the morphology-density relation (Mayereta£. (2001)))., The harassment model also offers a natural explanation for the Butcher-Oemler effect \cite{bo}) ) and the morphology-density relation \cite{ma}) ).479 In. this paper. we present photometric and kinematical evidence for the presence of kinematically decoupled cores (KDCs) in two dEs in a group environment: FS373 and FS76 (we use the galaxy identification numbers introduced by Ferguson&Sandage (1990))).," In this paper, we present photometric and kinematical evidence for the presence of kinematically decoupled cores (KDCs) in two dEs in a group environment: FS373 and FS76 (we use the galaxy identification numbers introduced by \cite{fe90}) )."480 FS373 (Fig. 15) , FS373 (Fig. \ref{ima373}) )481is a nucleated dwarf elliptical (dE2.N) in the NGC3258 group at a distance of41 Mpe (we use Ho=70 km/s/Mpe throughout the paper).," is a nucleated dwarf elliptical (dE2,N) in the NGC3258 group at a distance of 41 Mpc (we use $H_0=70$ km/s/Mpc throughout the paper)."482 FS76 (Fig. 2) , FS76 (Fig. \ref{ima76}) )483is a dEO in the NGC5044 group. at a distance of 36 Mpe.," is a dE0 in the NGC5044 group, at a distance of 36 Mpc."484The pronounced bump in the rotation velocity profiles signals the presence of a dynamically peculiar component in corotation with the main body of these galaxies.,The pronounced bump in the rotation velocity profiles signals the presence of a dynamically peculiar component in corotation with the main body of these galaxies.485" Both in FS76 and FS373. the KDC dominates the kinematies out to a radius of 1.5""—2"", which is well outside the nucleus or the central density cusp."," Both in FS76 and FS373, the KDC dominates the kinematics out to a radius of $~1.5''-2''$, which is well outside the nucleus or the central density cusp."486 Hence. the KDC should not be associated with the nucleus in the center of the host dE. It is the first time that," Hence, the KDC should not be associated with the nucleus in the center of the host dE. It is the first time that"487The Galaxy was assumed (o have an axisvinmetric magnetic field based on theory (Ruzmaikinetal.1983:Branclenbure1990:Moss&Brandenburg1992). and observational evidence (Rand&Ixulkarni1989:RandLyne1994:Sun]tuiz-Granadosοἱal. 2010).. but there is some evidencein other galaxies (particularlyAISI.Krauseοἱal.1939a;Sokoloff1992). that bisvnunetric fields max exist.,"The Galaxy was assumed to have an axisymmetric magnetic field based on theory \citep{Ruz88,B90,MB92} and observational evidence \citep{RK89,RL94,Sun08,R10}, but there is some evidencein other galaxies \citep[particularly in M81,][]{K89,S92} that bisymmetric fields may exist."488 al.(1996) indicate that many of the galaxies showing evidence for bisvimetrie magnetic fields also show evidence lor galaxy interactions. so we might not expect this magnetic field structure for the Milkv. Way (based on a lack of major merger events: Gilmoreetal.2002)) and the axisvimnnietric assumption max hold.," \citet{B96} indicate that many of the galaxies showing evidence for bisymmetric magnetic fields also show evidence for galaxy interactions, so we might not expect this magnetic field structure for the Milky Way (based on a lack of major merger events; \citealt{GWN02}) ) and the axisymmetric assumption may hold."489 Hieher order azimuthal svanmnetries might. also be possible. but their amplitudes should be relatively small (Becketal.1996).," Higher order azimuthal symmetries might also be possible, but their amplitudes should be relatively small \citep{B96}."490. The measurements needed to distinguish among the various model simulations are well suited to NIB stellar polarimetry., The measurements needed to distinguish among the various model simulations are well suited to NIR stellar polarimetry.491 The polarization mechanism used in (he simulations works from the NIR through near-UV wavelengths (Serkowskietal.1975:Codina-Landaberry&Magalhaes1976:Whittetetal. 1992).," The polarization mechanism used in the simulations works from the NIR through near-UV wavelengths \citep{SMF75,CM76,W92}."492. ILowever. NIR light is less attenuated by interstellar dust and can probe magnetic fields along multi-kpc scales. while the shorter wavelengths only probe within about 1 kpe (Fosalbaetal.2002).," However, NIR light is less attenuated by interstellar dust and can probe magnetic fields along multi-kpc scales, while the shorter wavelengths only probe within about 1 kpc \citep{F02}."493.. As described by (19175).. the polarization signal in the NI. is weaker (han (he visible bx a factor of four or more.," As described by \citet{SMF75}, the polarization signal in the NIR is weaker than the visible by a factor of four or more."494 However. NIR. polarimetric observations at (his level are possible with recent insirumentation (Ixandoriοἱal.2006:Clemenset2007) ancl should soon provide data able to test models of the large-scale structure of the Galactic magnetic field.," However, NIR polarimetric observations at this level are possible with recent instrumentation \citep{K06,C07} and should soon provide data able to test models of the large-scale structure of the Galactic magnetic field."495 The simplest comparison may be (hrough collecting the polarization behavior exhibited through a set of samples of all Galactic latitudes al à single Galactic longitude. as shown in Figs.," The simplest comparison may be through collecting the polarization behavior exhibited through a set of samples of all Galactic latitudes at a single Galactic longitude, as shown in Figs."496 20 through 30.., \ref{S0_cut} through \ref{AA_cut}.497 To best understand (the poloidal component of the Galactic magnetic field. these observations should be made in the outer Galaxy longitude ranges ol €=110—160° or (=200— 250°.," To best understand the poloidal component of the Galactic magnetic field, these observations should be made in the outer Galaxy longitude ranges of $\ell=110-160\degr$ or $\ell=200-250\degr$ ."498 These ranges avoid the degenerate regions that, These ranges avoid the degenerate regions that499for three sets of thermal plasma parameters.,for three sets of thermal plasma parameters.500 In the first and second set. we assume parameters relevant for luminous BUBs. rp=l. R23.101 em. B=10' €. and O=0.1 and 0.2. respectivelv.," In the first and second set, we assume parameters relevant for luminous BHBs, $\tau_{\rm T}$ =1, $R=3 \times 10^7$ cm, $B=10^{7}$ G, and $\Theta=0.1$ and 0.2, respectively."501 In the third. set. we assume parameters relevant to AGNs.rp=l. R=35101 em. B=105 G and ΟΞ0.1.," In the third set, we assume parameters relevant to AGNs,$\tau_{\rm T}$ =1, $R=3\times 10^{14}$ cm, $B=10^{3}$ G and $\Theta=0.1$."502" For each set. we consider two different slopes of the non-thermal tail. p=3 and 4 and 5,=30."," For each set, we consider two different slopes of the non-thermal tail, $p=3$ and 4 and $\gamma_{\rm f}=30$ ."503 Xdditionallv. we consider the cases of +;=10 and 100 for p=3 (for pz3 the influence of the cut-olf is much weaker).," Additionally, we consider the cases of $\gamma_{\rm504f}=10$ and 100 for $p=3$ (for $p>3$ the influence of the cut-off is much weaker)."505 We see that even a weak non-thermal component. with (sun)/O~12 (which corresponds to only 1 per cent of the total energy density of the electrons in the non-thermal tail) can lead to an increase of the turnover [requeney by à factor of ~1.5 2 or DILIDs and ~10 for ACGNs.," We see that even a weak non-thermal component, with $(\gamma_{\rm506nth}-1)/\Theta \sim 12$ (which corresponds to only $\sim 1$ per cent of the total energy density of the electrons in the non-thermal tail) can lead to an increase of the turnover frequency by a factor of $\sim 1.5$ –2 for BHBs and $\sim 10$ for AGNs."507 The dependence of the relative increase of the turnover requency on p and ; is relatively weak., The dependence of the relative increase of the turnover frequency on $p$ and $\gamma_{\rm f}$ is relatively weak.508" This rellects the fact hat the turnover frequeney. depends mostly on the number of electrons at 54, and since for small values of 9. οι is only slightly larger than sain. Ποστ) depends weakly on either poor 5."," This reflects the fact that the turnover frequency depends mostly on the number of electrons at $\gamma_{\rm t}$ and since for small values of $\delta$, $\gamma_{\rm t}$ is only slightly larger than $\gamma_{\rm nth}$, $n_{\rm e}(\gamma_{\rm t})$ depends weakly on either $p$ or $\gamma_{\rm f}$."509" This suggests that the degree of the dependence on p and , should increase with increasing (4/4uthALe in agreement with our results."," This suggests that the degree of the dependence on $p$ and $\gamma_{\rm f}$ should increase with increasing $\nnth/\ntth$, in agreement with our results."510 Ht is important to note that weak dependence of viet on the shape of the non-thermal tail makes our results weakly dependent on details of the acceleration mechanism., It is important to note that weak dependence of $\nnth/\ntth$ on the shape of the non-thermal tail makes our results weakly dependent on details of the acceleration mechanism.511 For Comptonization by a thermal plasma. we cmplov here a simple treatment of this process of Zdziarski (1985. 1986).," For Comptonization by a thermal plasma, we employ here a simple treatment of this process of Zdziarski (1985, 1986)."512 In that approximation. the Comptonization spectrum above the frequency. fij. at which soft seed. photons are injected (which. in the case of the CS process. zm £P). can be approximated as a sum of an e-folded power-law with energy index o and a Wien spectrum. ∖∖⋎↓↥∢⊾↓⋅⋖⋅⊽≀⋅↕∣∣∕∕⊔∣∣⊽∠⋅∶↿∖↓↕∢⋅↓⋅⋖⊾⋜↧∐∢⋅↓⋅⋜↧∐⊀⊔∐⇂⊀⊔⇍⋖⋅⊳∖∪⇂⋅⇁≀⋅↓⋯∖⇁⋖⋅↿↓↥∢⊾ ⊳∖⋜⋯↓∢⊾⊔↓∢⊾⋜⋯⊲↓⊔⋏∙≟⋜↧⊳∖↿↓↕∪⊳∖⋖⋅∪⇂⋅∕∕⊐⋜⋯∠⇂∫↗∖⋅⊲↓⊳∖↿↓↕∢⊾∖⇁⋖⋟↓⊔⊔↓∢⊾−⋜↧∖⇁⋖⊾↓⋅⋜↧⋏∙≟⋖⋅∠⇂ ≱∖≼∙⋜⊔↿⋖⋅↓⋰↓⊔⋏∙≟↓≻↓⋅⋖⋟∣," In that approximation, the Comptonization spectrum above the frequency, $\nu_{\rm inj}$, at which soft seed photons are injected (which, in the case of the CS process, $\approx513\ntth$ ), can be approximated as a sum of an e-folded power-law with energy index $\alpha$ and a Wien spectrum, where $x\equiv h\nu/m_{\rm e}c^2$ (hereafter all indices of $x$ have the same meaning as those of $\nu$ ) and $P_{\rm sc}$ is the volume-averaged scattering probability."514⋡⋜↧∣⋡↕↓↕↿∙∖⇁⋡↓↿≱∖⋠↓⊔↿⋖⋅⋏∙≟↓⋅⋜⊔⊲↓∪⊔∙∖⋰↓⋖⋅⇂∠⇂⊳∖⇂↓↥∢⊾↿⇂↥⋖⊾↓⋅⊔⋯↓− Compton luminosity. which. in the case of a spherical source. is ∖∖⋎↓↥∢⊾↓⋅⋖⋅⋃⊀↓⊳∖⋜↧≼∙∪⊔≱∖⇂⋜⋯↿∠⇂⋖⊾↓≻∢⊾⊔∠⇂⊀↓⊔⋏∙≟∪⊔↿↓↕∢⊾∐⇂∟∖∪⇂⋅↿∐∢⊾ injected seed. photons. (we calculate C in Section 5.2. for the case of svnchrotron seed. photons).," Its integration yields the thermal-Compton luminosity, which, in the case of a spherical source, is where ${\cal C}$ is a constant depending on the flux of the injected seed photons (we calculate ${\cal C}$ in Section \ref{s:cs} for the case of synchrotron seed photons)."515" The presence of non-thermal electrons. mocifíies. the Comptonization spectrum and. since. [or the electron distributions we consider (Loc. TpLl and 9 1) the ""Thomson optical depth for scattering. olf non-thermal electrons. is <<1. the resulting spectrum can be approximated. as a convolution of the thermal Comptonization spectrum with a spectrum resulting from sinele scattering. of photons olf non-thermal electrons."," The presence of non-thermal electrons modifies the Comptonization spectrum and since for the electron distributions we consider (i.e. $\tau_{\rm T}\sim 1$ and $\delta \ll 1$ ) the Thomson optical depth for scattering off non-thermal electrons is $\ll 1$, the resulting spectrum can be approximated as a convolution of the thermal Comptonization spectrum with a spectrum resulting from single scattering of photons off non-thermal electrons."516" ""Therefore. lor aSO. the Comptonization spectrum becomes harder. while for. 2»O. above the thermal eut-olL. a power-law tail in the spectrum develops."," Therefore, for $x517\la \Theta$, the Comptonization spectrum becomes harder, while for $x \gg518\Theta$, above the thermal cut-off, a power-law tail in the spectrum develops."519 As a result. the overall luminosity produced by Comptonization increases.," As a result, the overall luminosity produced by Comptonization increases."520" In calculations of the luminosity [rom Comptonization on non-thermal clectrons. LU.1 where the WKlein-Nishina-.EM ellect has to be taken into account. we use the approximation for the rate of energy. change. ασ/edé. ofa single electron via Compton interaction with isotropic photons of energy density. (jy. and mean energy. Cr where the IxIein-Nishina CLOSS-SCCLLOL was approximated using the first-order correction to. the '""Phomson-linit cross-section (Rwvbicki Lightman 1979)."," In calculations of the luminosity from Comptonization on non-thermal electrons, $L_{\rm C}^{\rm pl}$, where the Klein-Nishina effect has to be taken into account, we use the approximation for the rate of energy change, ${\rm d}\gamma521/{\rm d}t$, ofa single electron via Compton interaction with isotropic photons of energy density, $U_{\rm ph}$, and mean energy, $\langle x\rangle$, where the Klein-Nishina cross-section was approximated using the first-order correction to the Thomson-limit cross-section (Rybicki Lightman 1979)."522 We assume. that the photons undergoing scattering olf non-thermal electrons are those. from. the thermal Comptonization spectrum above wring., We assume that the photons undergoing scattering off non-thermal electrons are those from the thermal Comptonization spectrum above $x_{\rm inj}$.523 Phen where the [actor (3/4|7p/5) accounts for the change of the escape time due to scatterings in the source. and is à matching formula between the optically thin case (where the escape time is 9110) and the optically thick one (rrp /de. Sunvaev Titarchuk 1980)., Then where the factor $\left(3/4+\tau_{\rm T}/5\right)$ accounts for the change of the escape time due to scatterings in the source and is a matching formula between the optically thin case (where the escape time is $3R/4c$ ) and the optically thick one $\tau_{\rm T} R/5c$ Sunyaev Titarchuk 1980).524 Wecan further simplify the calculations assuming that the spectrum. of photons undergoing non-thermal Comptonization is a pure power-law and then neglect scatterings in the IxIein-Nishina limit (see below)., Wecan further simplify the calculations assuming that the spectrum of photons undergoing non-thermal Comptonization is a pure power-law and then neglect scatterings in the Klein-Nishina limit (see below).525 Now. for each > we calculate (yn. Cr? and Gro)2 as an integral over the power-law spectrum from wing up to the," Now, for each $\gamma$ we calculate $U_{\rm ph}$ , $\langle x\rangle$ and $\langle x^2\rangle$ as an integral over the power-law spectrum from $x_{\rm526inj}$ up to the"527Type IIn SNe is inconsistent with pοςr-?.,Type IIn SNe is inconsistent with $\rho\propto r^{-2}$.528 They show that Type IIn SNe do not usually come from the steady wind with pcr-?., They show that Type IIn SNe do not usually come from the steady wind with $\rho\propto r^{-2}$.529 X-ray luminous Type IIn SNe are presumed to be originated from relatively dense winds with high mass-loss rates., X-ray luminous Type IIn SNe are presumed to be originated from relatively dense winds with high mass-loss rates.530" Although the wind densities of these SNe are not high enough to be LSNe, it is highly possible that the dense winds from higher mass-loss rates also result in flat or steep density slopes."," Although the wind densities of these SNe are not high enough to be LSNe, it is highly possible that the dense winds from higher mass-loss rates also result in flat or steep density slopes."531 The presence of the two kinds of slopes can end up with two different kinds of Type II LSNe., The presence of the two kinds of slopes can end up with two different kinds of Type II LSNe.532" So far, we just consider a single slope for the dense wind."," So far, we just consider a single slope for the dense wind."533 One essential difference between Type IIn and Type IIL LSNe is the existence of the spatially-large optically-thin region in the wind of Type IIn LSNe which can make narrow P-Cygni profiles., One essential difference between Type IIn and Type IIL LSNe is the existence of the spatially-large optically-thin region in the wind of Type IIn LSNe which can make narrow P-Cygni profiles.534" Although we show that large w can make such spatially-large optically-thin region with the optically thick region inside, the similar condition can also be achieved by assuming the two components in the wind, i.e., optically thick (inside) and thin (outside) regions with any density slopes."," Although we show that large $w$ can make such spatially-large optically-thin region with the optically thick region inside, the similar condition can also be achieved by assuming the two components in the wind, i.e., optically thick (inside) and thin (outside) regions with any density slopes."535" The two-component wind configuration is suggested for, e.g., Type IIn SN 1998S2001).. Both models can explain Type IIn LSNe."," The two-component wind configuration is suggested for, e.g., Type IIn SN 1998S. Both models can explain Type IIn LSNe."536" (ChugaiIn either case, the P-Cygni profiles can be observed not only after but also before the LC peak."," In either case, the P-Cygni profiles can be observed not only after but also before the LC peak."537" Currently, there are no spectral observations of Type IIn LSNe before the LC peak with resolutions sufficient to resolve the narrow P-Cygni profile and the high resolution spectroscopic observations before the LC peak are important to reveal the wind surrounding LSNe."," Currently, there are no spectral observations of Type IIn LSNe before the LC peak with resolutions sufficient to resolve the narrow P-Cygni profile and the high resolution spectroscopic observations before the LC peak are important to reveal the wind surrounding LSNe."538 Our model cannot be simply extended to the spectral evolution of other kinds of LSNe without H lines., Our model cannot be simply extended to the spectral evolution of other kinds of LSNe without H lines.539" Especially, Type Ic LSNe with fast LC decline show, e.g., Si and O lines which are not seen in Types II LSNe2011)."," Especially, Type Ic LSNe with fast LC decline show, e.g., Si and O lines which are not seen in Types II LSNe."540". Although it is possible that the shock breakout in a dense wind also occurs in Type Ic LSNe as is suggested by it seems to be difficult to attribute the difference (2011),,between Type Ic LSNe and Type II LSNe only to the density slope of the dense wind."," Although it is possible that the shock breakout in a dense wind also occurs in Type Ic LSNe as is suggested by, it seems to be difficult to attribute the difference between Type Ic LSNe and Type II LSNe only to the density slope of the dense wind."541" For example, the composition of the wind is presumed to be quite different between Type Ic and Type II LSNe."," For example, the composition of the wind is presumed to be quite different between Type Ic and Type II LSNe."542" If the shock breakout in the dense wind is also taking place in Type Ic LSNe, narrow spectral lines from the materials other than H may be observed."," If the shock breakout in the dense wind is also taking place in Type Ic LSNe, narrow spectral lines from the materials other than H may be observed."543" While we focus on the origin of Type IIL LSNe in this paper, the understanding of other Type IIL SNe, i.e., less-Iuminous Type IIL SNe, is also lacking."," While we focus on the origin of Type IIL LSNe in this paper, the understanding of other Type IIL SNe, i.e., less-luminous Type IIL SNe, is also lacking."544" Currently, there are many models for Type IIn SNe but only a few models exist for Type IIL SNe1991)."," Currently, there are many models for Type IIn SNe but only a few models exist for Type IIL SNe."545". (e.g.,Although the diversity in the wind condition may be related to other Type IIL SNe, there can be other important, but currently ignored, ingredients for the full understanding of Type IIL SNe."," Although the diversity in the wind condition may be related to other Type IIL SNe, there can be other important, but currently ignored, ingredients for the full understanding of Type IIL SNe."546 We investigate the effect of the non-steady mass loss on the shock breakout in the dense wind., We investigate the effect of the non-steady mass loss on the shock breakout in the dense wind.547" The non-steady mass loss varies the density slope of the wind (pe and the density slope alters the ratio of the diffusion r~”)timescale in the optically thick wind (tq) and the shock propagation timescale of the entire wind (t,) after the shock breakout in the wind.", The non-steady mass loss varies the density slope of the wind $(\rho\propto r^{-w})$ and the density slope alters the ratio of the diffusion timescale in the optically thick wind $t_d$ ) and the shock propagation timescale of the entire wind $t_s$ ) after the shock breakout in the wind.548" Both timescales are comparable (ta/t; for <,1~1)w and ta/ts becomes smaller as w gets larger.", Both timescales are comparable $(t_d/t_s\simeq 1)$ for $}\hspace{-0.75em}\raisebox{-.7ex}{$ and $t_d/t_s$ becomes smaller as $w$ gets larger.549 This is because the last scattering surface of the dense wind locates farther inside from the wind surface for the wind with the steeper density gradient , This is because the last scattering surface of the dense wind locates farther inside from the wind surface for the wind with the steeper density gradient (Figure \ref{fig2}) ).550The difference can only be obtained by the careful (Figuretreatment2)). of the shock breakout condition in the dense wind (Section ??;; Equation (3)))., The difference can only be obtained by the careful treatment of the shock breakout condition in the dense wind (Section \ref{sec2}; Equation \ref{breakout}) )).551" If the two timescales are comparable (ta/ts~ 1), the forward shock goes through the entire wind just after the LC reaches the peak with the timescale tg."," If the two timescales are comparable $(t_d/t_s\simeq 1)$ , the forward shock goes through the entire wind just after the LC reaches the peak with the timescale $t_d$."552" In this case, no signature on the spectra from the wind is expected to be observed especially after the LC peak because the entire wind is already shocked after the LC peak."," In this case, no signature on the spectra from the wind is expected to be observed especially after the LC peak because the entire wind is already shocked after the LC peak."553" On the other hand, if the two timescales are different (t4/t,< 1), the shock continues to propagate in the wind after the LC peak and the unshocked wind remains after the LC peak."," On the other hand, if the two timescales are different $t_d/t_s< 1$ ), the shock continues to propagate in the wind after the LC peak and the unshocked wind remains after the LC peak."554" Thus, narrow P-Cygni profiles from the wind are expected to be observed even after the LC peak."," Thus, narrow P-Cygni profiles from the wind are expected to be observed even after the LC peak."555 The former case corresponds to Type IIL LSNe and the latter to Type IIn LSNe., The former case corresponds to Type IIL LSNe and the latter to Type IIn LSNe.556 The difference in the density slope can also account for thelack of the Lorentzian emission profiles in Type IIL LSNe., The difference in the density slope can also account for thelack of the Lorentzian emission profiles in Type IIL LSNe.557(Steson1987)).,\citealt{stetson}) ).558 Positions for stars iu the field were derived by fitting a plae model to 3t) USNO A2.0 stars (Monete|al.1996)): the fit had an RAIS error of 0.37 arcsec., Positions for stars in the field were derived by fitting a plate model to 39 USNO A2.0 stars \citealt{USNOA2.0}) ); the fit had an RMS error of 0.37 arcsec.559 Tae 2 shows le celestial positious. maguit(udes. ad colors of RS80532+62 aud the field stars.," Table 2 shows the celestial positions, magnitudes, and colors of RX0532+62 and the field stars."560 Fietre 1 shows the field arotud RXO532+62 aoneOm with the measured V inagnituedes., Figure 1 shows the field around RX0532+62 along with the measured V magnitudes.561 We duced. the spectra. uslϱ standard IRAF routines. except [or the ext‘action of spectra [rom the two«limensional images.," We reduced the spectra using standard IRAF routines, except for the extraction of one-dimensional spectra from the two-dimensional images."562 For this. we used au origina iiplementati of the optimal extraction algoritlu developed by Horne(1986):: the primary advtage over IRAF apsum routine was a1 unproved rejection of bad pixels.," For this, we used an original implementation of the optimal extraction algorithm developed by \citet{horne}; the primary advantage over the IRAF ${\it apsum}$ routine was an improved rejection of bad pixels."563 The time average al ux-calibra spectrum of RN0532+62 is shown inFigure 2., The time averaged and flux-calibrated spectrum of RX0532+62 is shown in Figure 2.564 The spectrum aypears typical of dwar ovae. sliowi strong broad emission lines.," The spectrum appears typical of dwarf novae, showing strong broad emission lines."565 The double peaks iu tle emissiou lines imply that tleo jtal iuclinati is not too [ar from edge-on., The double peaks in the emission lines imply that the orbital inclination is not too far from edge-on.566 To measure the eiuission line radial velocities we tSC the convoluti methocl described by Schueider&Young(1980)., To measure the emission line radial velocities we used the convolution method described by \citet{sy80}.567. The steep sides of tie line profile were nieasu“eC by convolving the line with a fuuctiou consisting of positive axd uegative eausslalls ¢isplaced by ai adjustable separation., The steep sides of the line profile were measured by convolving the line with a function consisting of positive and negative gaussians displaced by an adjustable separation.568 The emission lines’ widths aud streugtIn were 1jeasurecd ii the time-average spectra: the results are eiven in Table 3., The emission lines' widths and strengths were measured in the time-average spectra; the results are given in Table 3.569"+) To search for {2orp in the radial velocities. we used the :""yesiduaeral mehod as descjbed by TIorsteusenetal.(19096)."," To search for $P_{\rm orb}$ in the radial velocities, we used the “residualgram” method as described by \citet{thor96}."570. Fiewe 3 shows the resu| for he 20(JS Septemyer data., Figure 3 shows the result for the 2005 September data.571 Tadle 1 gives 1he parameters of the best sitefits of the form ef+dvsin/P]. and the rms scatte: 8 around the best fits.," Table 4 gives the parameters of the best sinefits of the form $v(t) = \gamma + K\sin[2\pi(t-T_{o})/P]$, and the rms scatter $\sigma$ around the best fits."572 Figure | shows the velocities folced ou the period adopted froi1 the combi1ος. (2005 September. 2006 Jzuuary) data. together with the best-fitting sinusoid.," Figure 4 shows the velocities folded on the period adopted from the combined (2005 September, 2006 January) data, together with the best-fitting sinusoid."573 The 2005 septetiber data did not uiambiguously cletermine the co‘rect cloice of daily eycle count )ecatse of he limitecl hour angleOm coveragee available early in the observineOm Season., The 2005 September data did not unambiguously determine the correct choice of daily cycle count because of the limited hour angle coverage available early in the observing season.574 The 2006 January data were aken in order to resolve the ambiguity. but [or uukuown reaxdLs the velocities had greaer scalter hau the 2005 September data.," The 2006 January data were taken in order to resolve the ambiguity, but for unknown reasons the velocities had greater scatter than the 2005 September data."575 We also measured. velociies of the Hj emission in au aitempt to resolve the daily cycle couu., We also measured velocities of the $\beta$ emission in an attempt to resolve the daily cycle count.576 TheHj velocities co‘roboraed the Ha measurements. but he period ΘΕΟΙecd ambiguous.," The$\beta$ velocities corroborated the $\alpha$ measurements, but the period remained ambiguous."577" However. we kuow fj. aie that he Poy, of au SU UMa-type slould be a ew yercent less than Pa."," However, we know $P_{\rm578sh}$ , and that the $P_{\rm orb}$ of an SU UMa-type should be a few percent less than $P_{\rm sh}$."579 This guides our choice of cycle count. which vields 0.0562061 d for the 2005 September data.," This guides our choice of cycle count, which yields 0.05620(4) d for the 2005 September data."580 The run-to-run cycle couut is ambiguors. but periods consistent with all the data are given by where the nuumerator is the meastrecl interval between blue-to-red. erossings of the Ha emission velocities deteriniued from our two observing ruus. aud the «euoninator is constraiued to integer values.," The run-to-run cycle count is ambiguous, but periods consistent with all the data are given by where the numerator is the measured interval between blue-to-red crossings of the $\alpha$ emission velocities determined from our two observing runs, and the denominator is constrained to integer values."581" Combining our 2,4, with the previously measured P4. we find e= 0.016(1)."," Combining our $P_{\rm orb}$ with the previously measured $P_{\rm sh}$ , we find $\epsilon = 0.016(4)$ ."582 plot log(e) against οσον) for a large number of systems with lycdrogen-rich secoucaries.," \citet{patt03} plot $\epsilon$ ) against $P_{\rm583orb}$ ) for a large number of systems with hydrogen-rich secondaries."584caustics induced by close or wide binaries.,caustics induced by close or wide binaries.585 The lensing behavior of a wide binary withs>1 is well described by the Chang-Refsdal lensing., The lensing behavior of a wide binary with$s\gg 1$ is well described by the Chang-Refsdal lensing.586" In this regime, the width of the caustic is approximated as Then, for a wide-separation binarywiths=10 and 1.0,the caustic widthis £,~0.02 as measured byOg."," In this regime, the width of the caustic is approximated as Then, for a wide-separation binarywith$s=10$ and $q=1.0$ ,the caustic widthis $\xi_{\rm c} \sim 0.02$ as measured by$\theta_{\rm E}$."587" This corresponds to the £~0.03 as measured by the Einstein radius corresponding to the mass of the binary component towhich the source trajectory approaches more closely, 0g."," This corresponds to the $\hat{\xi} \sim 0.03$ as measured by the Einstein radius corresponding to the mass of the binary component towhich the source trajectory approaches more closely, $\hat{\theta}_{\rm E}$."588 The perturbation extends outside the caustic., The perturbation extends outside the caustic.589" Assuming that the of detectable extends twice of the caustic size, regionit is foundthat perturbationperturbations can be detected for events with A=30."," Assuming that the region of detectable perturbation extends twice of the caustic size, it is foundthat perturbations can be detected for events with $A\gtrsim 30$."590" For close binaries,the caustic size of a binary with a separation s is equivalent tothe caustic size of a wide binary with a separation s~!."," For close binaries,the caustic size of a binary with a separation $s$ is equivalent tothe caustic size of a wide binary with a separation $s^{-1}$."591" Therefore, the lower limit of the separation range roughly corresponds to the inverse of the upper lensingsurveys high-magnification byfollow-up magnification simple (Leeetal.2008)..planetorbitingbinary system 2008).. (Konacki2005;Eggenbergeretal.2006)."," Therefore, the lower limit of the separation range roughly corresponds to the inverse of the upper \citep{lee08}. \citep{han08}. \citep{konacki05, eggenberger06}."592. type efficiencyhigh-magnification through1.high-magnification , \ref{table:one} 593of these two classes of object might be ambiguous.,of these two classes of object might be ambiguous.594" At the present day GCs are strongly concentrated around central galaxies (more so than the overall subhalo populations in simulated CDM haloes) and their survival is known to be subject to many factors, including evaporation and tidal disruption."," At the present day GCs are strongly concentrated around central galaxies (more so than the overall subhalo populations in simulated CDM haloes) and their survival is known to be subject to many factors, including evaporation and tidal disruption."595" GCs are likely to be present in lensing galaxies in large numbers and may perturb the gravitational potentials in the inner regions, causing cusp-caustic violations."," GCs are likely to be present in lensing galaxies in large numbers and may perturb the gravitational potentials in the inner regions, causing cusp-caustic violations."596" A simple estimate of their contribution was made by ?,, who concluded that a surface density fluctuation of a few per cent (6%~ 0.01) from GCs would be enough to cause the observed flux-ratio anomaly in B1422+231."," A simple estimate of their contribution was made by \citet{MS1998mn}, who concluded that a surface density fluctuation of a few per cent $\delta\kappa\sim5970.01$ ) from GCs would be enough to cause the observed flux-ratio anomaly in B1422+231."598 This conclusion has been re-examined in this work., This conclusion has been re-examined in this work.599 Here we adopt an empirical approach to the effects of GCs on the lensing potential., Here we adopt an empirical approach to the effects of GCs on the lensing potential.600" We use the catalogue of Milky-Way GCs from ?,, which provides their spatial distribution, V-band luminosities L, and half-mass radii ry."," We use the catalogue of Milky-Way GCs from \citet{HarrisGC1996}, which provides their spatial distribution, V-band luminosities $L_{\rm v}$ and half-mass radii $r_{\rm601 h}$."602" Although the Milky-Way GC distribution is slightly flattened within the central ~10A! kpc, the choice of projection does not affect our results."," Although the Milky-Way GC distribution is slightly flattened within the central $\sim 10 h^{-1}$ kpc, the choice of projection does not affect our results."603 It is interesting to ask whether a proportion of the ‘satellite galaxies’ in Aquarius should in fact be identified with a population of ‘primordial’ galaxy-like objects or with the ‘cores’ of galaxies that have been heavily stripped., It is interesting to ask whether a proportion of the `satellite galaxies' in Aquarius should in fact be identified with a population of `primordial' galaxy-like objects or with the `cores' of galaxies that have been heavily stripped.604" We have already included satellites in our calculation, so our approach to GCs risks double-counting some objects if either of these cases is true."," We have already included satellites in our calculation, so our approach to GCs risks double-counting some objects if either of these cases is true."605" However, a detailed investigation of this issue is beyond the scope of this paper, and we will assume that most GCs are not already represented as ‘satellites’ in our semi-analytic model."," However, a detailed investigation of this issue is beyond the scope of this paper, and we will assume that most GCs are not already represented as `satellites' in our semi-analytic model."606" As we state above, the LF of bright satellite galaxies in our model matches the shape of the Milky-Way satellite LF."," As we state above, the LF of bright satellite galaxies in our model matches the shape of the Milky-Way satellite LF."607" This observed LF does not include the many equally bright but structurally distinct Milky-Way GCs: this in turn suggests that these bright GCs are not represented by some of the existing 'satellites in our model, stripped or otherwise."," This observed LF does not include the many equally bright but structurally distinct Milky-Way GCs: this in turn suggests that these bright GCs are not represented by some of the existing `satellites' in our model, stripped or otherwise."608 Fainter than My~—5 the distinction between galaxies and clusters is much less certain and the interpretation of the current data is not at all clear., Fainter than $M_{V}\sim-5$ the distinction between galaxies and clusters is much less certain and the interpretation of the current data is not at all clear.609" However, these low-mass objects are not significant for lensing."," However, these low-mass objects are not significant for lensing."610The observations have been fitted (o a grid of svnthetic spectra based on photospheric models described by Allardetal.(2001.2003). and. Iauschildtetal.(1999)... and downloaded [rom the Lyon group'swebsite!.,"The observations have been fitted to a grid of synthetic spectra based on photospheric models described by \citet{all01,all03} and \citet{haus99}, and downloaded from the Lyon group's."611. The grid covers the range Ty=100 10.000 Ix in effective temperature and logg=2.5 6.0 ems 7 in surface eravily: we have asstuned solar metallicitv.," The grid covers the range $T_{\rm eff}=100$ –10,000 K in effective temperature and $\log g=2.5$ –6.0 cm $^{-2}$ in surface gravity; we have assumed solar metallicity."612 The temperature range is spannecl bv [our models (COND. SETTL. DUSTY and NextGen). each of which covers a particular regime with respect to dust grain formation: the COND model is applicable to methane cdwarls (7=1500 Ix}.," The temperature range is spanned by four models (COND, SETTL, DUSTY and NextGen), each of which covers a particular regime with respect to dust grain formation; the COND model is applicable to methane dwarfs $T\stackrel{<}{_\sim}1500$ K)."613 For each of these models we have calculated (the inverse-varliance weighted sum of squares of residuals between the model (smoothed to the resolution of the observations) ancl the observed spectrum of a given object., For each of these models we have calculated the inverse-variance weighted sum of squares of residuals between the model (smoothed to the resolution of the observations) and the observed spectrum of a given object.614 During (his procedure it was necessary {ο redden the model spectra since objects in the p Oph cloud are seen through a substantial amount of extinction: lor this purpose the Cardellietal.(1989). reddening law was used.," During this procedure it was necessary to redden the model spectra since objects in the $\rho$ Oph cloud are seen through a substantial amount of extinction; for this purpose the \citet{car89}615 reddening law was used."616 Foreach object. the unknowns were therefore: Zar. logg. Ao. aud the model type.," Foreach object, the unknowns were therefore: $T_{\rm eff}$, $\log g$, $A_V$, and the model type."617 Maximum likelihood estimates of these parameters were obtained by minimizing (he mean square residual over the wavelength range 1.52.4 jan (excluding 1.72.0 yan to avoid the deep telluric absorption bands). aud (he results are presented in the last four columns of Table 1..," Maximum likelihood estimates of these parameters were obtained by minimizing the mean square residual over the wavelength range 1.5–2.4 $\mu$ m (excluding 1.7–2.0 $\mu$ m to avoid the deep telluric absorption bands), and the results are presented in the last four columns of Table \ref{tbl-1}."618 The corresponding model spectra are plotted as dashed lines in Figures |. and 2.., The corresponding model spectra are plotted as dashed lines in Figures \ref{fig1} and \ref{fig2}.619 One of the objects (2244450) has a spectrum which resembles a reddenecl version of SDSS 1254-0122 (T2). and the model fitting results confirm its identity as a moderately cool brown dwarf.," One of the objects 4450) has a spectrum which resembles a reddened version of SDSS 1254-0122 (T2), and the model fitting results confirm its identity as a moderately cool brown dwarf."620 The spectrum is suggestive of a low gravity object. as evidenced by the steeper Fallolf on the short wavelength side of the Z/-band peak with respect to that of the field dwarls in Figure 2.. aud (he displacement of the A-band peak to a longer," The spectrum is suggestive of a low gravity object, as evidenced by the steeper falloff on the short wavelength side of the $H$ -band peak with respect to that of the field dwarfs in Figure \ref{fig2}, , and the displacement of the $K$ -band peak to a longer"621In order to verily that the observed evidence for evolution of environment overdensity is not due to the 7<19.1 (zS3.0) limit imposed on Type I quasar selection in the SDSS (Schneiderοἱal.2007).. we perform several tests in which we vary (the apparent magnitude limit of the cata.,"In order to verify that the observed evidence for evolution of environment overdensity is not due to the $i \leqslant 19.1$ $z \lesssim 3.0$ ) limit imposed on Type I quasar selection in the SDSS \citep{Schneider}, we perform several tests in which we vary the apparent magnitude limit of the data."622 We consider (wo quasar samples limited (ο /<18.9 and to the? x19.1 5D55 limit (see inset of Figure 1))., We consider two quasar samples limited to $i \leqslant 18.9$ and to the $i \leqslant 19.1$ SDSS limit (see inset of Figure \ref{histogram_Nofz}) ).623 The wo maegnitude-Imited samples were each then separated into (wo luminosity bins., The two magnitude-limited samples were each then separated into two luminosity bins.624 We compared environment overdensitv measurements of bright or dim quasars in each of the maegnitude-Imited samples and found πο appreciable difference., We compared environment overdensity measurements of bright or dim quasars in each of the magnitude-limited samples and found no appreciable difference.625 Additionally. no difference was observed when different absolute magnitude values were used to define the bright and dim samples.," Additionally, no difference was observed when different absolute magnitude values were used to define the bright and dim samples."626 In order to ensure that there is no difference between environments of quasars with />19.1. which were selected by the hieh-recdshilt Largeting algorithm. and the rest of the apparent magnitude-selected sample. we performed similar tests comparing the environment overdensity of the entire quasar sample to that of the subset of quasars with 7<18.9 or 7>19.1.," In order to ensure that there is no difference between environments of quasars with $i > 19.1$, which were selected by the high-redshift targeting algorithm, and the rest of the apparent magnitude-selected sample, we performed similar tests comparing the environment overdensity of the entire quasar sample to that of the subset of quasars with $i\leqslant 18.9$ or $i > 19.1$."627 In all cases. there was no appreciable change in the observed overdensity.," In all cases, there was no appreciable change in the observed overdensity."628 We compare the environment overdensities of Type I quasars in (wo luminosity bins {ο (he other target samples without redshift cuts in Figure 10.., We compare the environment overdensities of Type I quasars in two luminosity bins to the other target samples without redshift cuts in Figure \ref{scale_spectargs_M}.629 The threshold value A;=—23.2 is chosen to eive roughly equal numbers of Type I quasars in each huninosity bin: (here are 2.190 (2.044) quasars with —27.5xAM;€—23.2 (-23.2«M;< —22.0).," The threshold value $M_{i}=-23.2$ is chosen to give roughly equal numbers of Type I quasars in each luminosity bin: there are 2,190 (2,044) quasars with $-27.5 \leqslant M_{i} \leqslant -23.2$ $-23.2 < M_{i} \leqslant -22.0$ )."630 The average magnitude of the brighter (fainter) bin is M;=—23.83 M;=—22.10)., The average magnitude of the brighter (fainter) bin is $\overline{M_{i}} = -23.83$ $\overline{M_{i}} = -22.70$ ).631 Type IL quasars and the brighter Type I quasars are located in similarly overdense environments consistentlv at all scales. while the dimmer Type I quasars are located in environments slightly less overdense than the Type II quasars.," Type II quasars and the brighter Type I quasars are located in similarly overdense environments consistently at all scales, while the dimmer Type I quasars are located in environments slightly less overdense than the Type II quasars."632 At a seale 222500htkpe. the cumulative overdensity of Type ILE quasar environment is 1.06 (mes that of the brighter Type I quasars. but 1.3 limes as the dimmer Type I quasars.," At a scale $R\approx500\kpchseventy$, the cumulative overdensity of Type II quasar environment is 1.06 times that of the brighter Type I quasars, but 1.3 times as the dimmer Type I quasars."633 At the scale of Rz1.0izMpe. Type Il quasars have environment overdensities 1.2 Uimes (he environment overdensity of brighter Type I quasars but 1.5 times that of dimmer Type I quasars.," At the scale of $R\approx1.0\Mpchseventy$, Type II quasars have environment overdensities 1.2 times the environment overdensity of brighter Type I quasars but 1.5 times that of dimmer Type I quasars."634 Again we note that the large error bars nearly overlap with unitv and prevent strong conclusions., Again we note that the large error bars nearly overlap with unity and prevent strong conclusions.635 The more luminous Type I quasars are located in environments more overdense (han Type | AGN. while there is less dilference in the overdensities of dimmer Type I euasars and Type I AGN.," The more luminous Type I quasars are located in environments more overdense than Type I AGN, while there is less difference in the overdensities of dimmer Type I quasars and Type I AGN."636 The environment overdensity ratio increases with decreasing scale for both brighter and dimmer Type I quasars., The environment overdensity ratio increases with decreasing scale for both brighter and dimmer Type I quasars.637 At a scale £222500hlkpe. brighter Type I quasar environments have an overdensity 1.6 times the overdensity of Type I AGN environments wilh significance 30. and dimmer Type I quasar environments have an overdensity 1.3 times the overclensity of Type LAGN environments with significance £z20.," At a scale $R\approx500\kpchseventy$, brighter Type I quasar environments have an overdensity 1.6 times the overdensity of Type I AGN environments with significance $\approx3\sigma$, and dimmer Type I quasar environments have an overdensity 1.3 times the overdensity of Type I AGN environments with significance $\approx2\sigma$."638 At HR22150hlkpe. ihe environments of brighter Type I quasars are 2.1 limes as overdense (2.40). and the environments of dimmer Type I quasars are 1.6 limes as overdense as (he environments of," At $R\approx150\kpchseventy$, the environments of brighter Type I quasars are 2.1 times as overdense $2.4\sigma$ ), and the environments of dimmer Type I quasars are 1.6 times as overdense as the environments of"639We show that as far as rotaional curve of gas aud plasina of the Milky Way is concerned. iuclusiou of jxB force ouly provides a tolerable fit to the rotational curve of the Galaxy for r>15 kpe from the centre. but fails i the intermediate rauge 6—12 kpc.,"We show that as far as rotational curve of gas and plasma of the Milky Way is concerned, inclusion of $\vec j \times \vec B$ force only provides a tolerable fit to the rotational curve of the Galaxy for $r>15$ kpc from the centre, but fails in the intermediate range $6-12$ kpc."640 Iu principle. a tolerable fit cau be obtained for all radii with the stronger magnetic field of By>11 µία but such high values are not observed.," In principle, a tolerable fit can be obtained for all radii with the stronger magnetic field of $B_0 \geq 11 $ $\mu$ G, but such high values are not observed."641 Further study is eecded to clarify whether the model formulated in this work cau be used to fit rotational curves of oher known galaxies where the iuaguetie fields are strouger., Further study is needed to clarify whether the model formulated in this work can be used to fit rotational curves of other known galaxies where the magnetic fields are stronger.642 Other weaknesses of tis mocel inelucle: (i) How well galactic pasina couples to the magnetic field (for jxB to be effective)., Other weaknesses of this model include: (i) How well galactic plasma couples to the magnetic field (for $\vec j \times \vec B$ to be effective).643 Naturaly this coupling is prescribed bv the degree of ionisation of the imecdium. which in turni. is prescribed by the Saha equatiou aud is sensitive to the temperature.," Naturally this coupling is prescribed by the degree of ionisation of the medium, which in turn, is prescribed by the Saha equation and is sensitive to the temperature."644 Iu general. initial temperatures of galaxies are expected to be high beeause so called virlal temperature (page 557 [roin (Cilinore et al.," In general, initial temperatures of galaxies are expected to be high because so called virial temperature (page 557 from (Gilmore et al."645 1980)) TuasστGMinpCEU). where symbols have usual meaning. for a typical size galaxy is of the order of 109 K. However. after coing phase ealactic discs are much cooler at about 210 Ix. Quireza et al. (," 1989)) $T_{\rm virial} \simeq G M m_p /(k R)$, where symbols have usual meaning, for a typical size galaxy is of the order of $10^6$ K. However, after cooling phase galactic discs are much cooler at about $\simeq 10^4$ K. Quireza et al. ("6462006) quote electron teiuperatures in the dise of galaxy of the order of 107 IX. which means that degree of ionisation of the galactic dise is sullicieut to couple plasma to tlie magnetic field aud jxB force.,2006) quote electron temperatures in the disc of galaxy of the order of $10^4$ K which means that degree of ionisation of the galactic disc is sufficient to couple plasma to the magnetic field and $\vec j \times \vec B$ force.647 After all. solar photosphere which is at temperature of only 6000Ix. is commonly described by MHD approximation. despite low degree of ionisation and the presence of large coucentration of neutrals.," After all, solar photosphere which is at temperature of only 6000K is commonly described by MHD approximation, despite low degree of ionisation and the presence of large concentration of neutrals."648 Also. iu additiou to thermal collisious some significant ionisation may be provided by the cosmic rays (1nostly srotons) that are accelerated at the bow and termination shocks.," Also, in addition to thermal collisions some significant ionisation may be provided by the cosmic rays (mostly protons) that are accelerated at the bow and termination shocks."649 A substantial [lux of cosmic rays is produced in a shock at Galactic uorth. a direction toward which our Galaxy has long been kuown to be moving in the Local Supercluster with the velocity of 200 kins {Nleclvecley Melott 2007). (," A substantial flux of cosmic rays is produced in a shock at Galactic north, a direction toward which our Galaxy has long been known to be moving in the Local Supercluster with the velocity of 200 km $^{-1}$ (Medvedev Melott 2007). ("650ii) The origin of the 1uaguetic field in the galaxy itself is deeply. coupled with the Cialaxys dynamics and MAD via the dynamo mechanism.,ii) The origin of the magnetic field in the galaxy itself is deeply coupled with the Galaxy's dynamics and MHD via the dynamo mechanism.651 The field streneth aud morphology are dependent ou the dyuaimics of the plasma. which is a function of ceusity. temperature. turbulent velocity. and ealactic rotation.," The field strength and morphology are dependent on the dynamics of the plasma, which is a function of density, temperature, turbulent velocity, and galactic rotation."652 Therefore. the ceutrifugalOm force due to egalactic rotation acts both ou the plasina aud inagnetic fiekl. and not ou the plasma alone.," Therefore, the centrifugal force due to galactic rotation acts both on the plasma and magnetic field, and not on the plasma alone."653 Such advanced topics are uatπαν bevoud the scope of the situple moclel presented here., Such advanced topics are naturally beyond the scope of the simple model presented here.654 The overall conclusion of this work is that jxB does not play an importaut role in the plasina dynamics in the intermedi:e range of distances 6—12 kpe from the centre. whilst the effect. is considerable for larger r (r>15 kpe).," The overall conclusion of this work is that $\vec j \times \vec B$ does not play an important role in the plasma dynamics in the intermediate range of distances $6-12$ kpc from the centre, whilst the effect is considerable for larger $r$ $r \geq 15$ kpc)."655 Author would like to thauk: J.R. Browustein for providing observational data of Milky Way rotational curve: T. Stanev :uid J. Alvarez-Muniz for clarifying some aspects of the galactic magnetic field inocel., Author would like to thank: J.R. Brownstein for providing observational data of Milky Way rotational curve; T. Stanev and J. Alvarez-Muniz for clarifying some aspects of the galactic magnetic field model.656from random populations which have the relevant distributions set out in the previous sections.,from random populations which have the relevant distributions set out in the previous sections.657 Implicit in such a reconstruction is the assumption that the dynamo has operated in a similar way from 1700 onwards., Implicit in such a reconstruction is the assumption that the dynamo has operated in a similar way from 1700 onwards.658" The very limited records of observations during the earlier part of the 18th century indicate that some of the early cycles might be anomalous in having stronger activity near the equator than those of the better observed later cycles (e.g.,see??).."," The very limited records of observations during the earlier part of the 18th century indicate that some of the early cycles might be anomalous in having stronger activity near the equator than those of the better observed later cycles \citep[\egc , see][]{Ribes93, Arlt09}."659 This could indicate that the dynamo was operating in a not purely dipole mode during this period., This could indicate that the dynamo was operating in a not purely dipole mode during this period.660 We first present an example semi-synthetic butterfly diagram for the period from the start of the RGO records to 2010., We first present an example semi-synthetic butterfly diagram for the period from the start of the RGO records to 2010.661 This allows us to directly compare the semi-synthetic and observed butterfly diagrams in Figure 13.., This allows us to directly compare the semi-synthetic and observed butterfly diagrams in Figure \ref{fig:butterly_tmin}.662" As expected, the two diagrams have similar appearances."," As expected, the two diagrams have similar appearances."663 A more detailed comparison of the weakest and strongest cycles is shown in Figure 14.., A more detailed comparison of the weakest and strongest cycles is shown in Figure \ref{fig:butterly_tmin2}.664 Again the observed and semi-synthetic butterfly wings look similar., Again the observed and semi-synthetic butterfly wings look similar.665 This validates the use of the semi-synthetic reconstruction for periods when we only have the sunspot numbers., This validates the use of the semi-synthetic reconstruction for periods when we only have the sunspot numbers.666 The semi-synthetic model shown in Figures 13 and 14 was based on the group sunspot number Rg., The semi-synthetic model shown in Figures \ref{fig:butterly_tmin} and \ref{fig:butterly_tmin2} was based on the group sunspot number $R_G$.667 Prior to 1874 Rz and Rg have substantial differences which affect the reconstructed butterfly diagrams., Prior to 1874 $R_Z$ and $R_G$ have substantial differences which affect the reconstructed butterfly diagrams.668" Figure 15 shows the reconstructed butterfly diagram during 1700-1874 with Rg and Rz, respectively."," Figure \ref{fig:butterly_both}669 shows the reconstructed butterfly diagram during 1700–1874 with $R_G$ and $R_Z$, respectively."670 It will be very interesting to compare both semi-synthetic butterfly diagrams with those being obtained by ?.., It will be very interesting to compare both semi-synthetic butterfly diagrams with those being obtained by \cite{Arlt10}.671 We comment that there is no reason emerging from this study to prefer one data set over the other., We comment that there is no reason emerging from this study to prefer one data set over the other.672 To give another indication of the differences in the reconstructions based on Rg and Rz Figure 16 shows the reconstructed mean latitudes during 1700-1874., To give another indication of the differences in the reconstructions based on $R_G$ and $R_Z$ Figure \ref{fig:lati_analy_wolfgroup} shows the reconstructed mean latitudes during 1700–1874.673 The different cycle strengths derived from the two sets of sunspot numbers produce small differences which differ in strength from cycle to cycle., The different cycle strengths derived from the two sets of sunspot numbers produce small differences which differ in strength from cycle to cycle.674 The extent to which these differences affect the results of surface flux transport simulations and the open flux calculated therefrom will be investigated in Paper II., The extent to which these differences affect the results of surface flux transport simulations and the open flux calculated therefrom will be investigated in Paper II.675" Using the group sunspot number Rg and RGO, MWO and Kodaikanal data sets, we studied the phase dependence and cycle dependence of latitude, area and tilt angle distribution properties of sunspot group emergence."," Using the group sunspot number $R_G$ and RGO, MWO and Kodaikanal data sets, we studied the phase dependence and cycle dependence of latitude, area and tilt angle distribution properties of sunspot group emergence."676 The main correlations found are: 1., The main correlations found are: 1.677 The mean latitude at which sunspots emerge can be modeled using a second order polynomial of cycle phase., The mean latitude at which sunspots emerge can be modeled using a second order polynomial of cycle phase.678Fie.,Fig.679 1 shows the 1 MIIZ GMBRT. spectrum of the absorber towards PISS 0952|179., \ref{fig:0952} shows the 1 MHz GMRT spectrum of the absorber towards PKS 0952+179.680 The spectruui has been TWaunine Ἡnoothed aud has an RAIS noise level of ~ 2.9 uJv per tL kin 1 resolution clement., The spectrum has been Hanning smoothed and has an RMS noise level of $\sim$ 2.9 mJy per 4 km $^{-1}$ resolution element.681 Absorption was detected on all three observing ruus. with the correct Doppler shift.," Absorption was detected on all three observing runs, with the correct Doppler shift."682 The measured quasar flux is ll Jv: the reals Ine «epth is ~ 18.8 indy and occurs at a heliocentric requency of 1117.522 MIIz. ie. 2=0.23780+0.00002.," The measured quasar flux is 1.4 Jy; the peak line depth is $\sim$ 18.8 mJy and occurs at a heliocentric frequency of 1147.522 MHz, i.e. $z = 0.23780 \pm 0.00002$."683 The peak optical depth is ~ 0.012., The peak optical depth is $\sim$ 0.013.684 The fiiid Tanning smoothed spectru of the :=15247 absorber towards B2 0827|213 is shown in Fig. 211, The final Hanning smoothed spectrum of the $z = 0.5247$ absorber towards B2 0827+243 is shown in Fig. \ref{fig:0827};685 he resoluion is ~ 10 jin |., the resolution is $\sim$ 10 km $^{-1}$.686 The RMS noise ou the spectrum is 1.15 10Jv while the peak line depth is ~ ὅταν. Le. a 5.20 resIt.," The RMS noise on the spectrum is 1.15 mJy while the peak line depth is $\sim$ 6 mJy, i.e. a $5.2\sigma$ result."687 The measured line depth is cousistcut with the reported non-deection by Briges Wolfe (1983): their 30 upper limit ou he line depth was ~7 undy., The measured line depth is consistent with the reported non-detection by Briggs Wolfe (1983); their $3\sigma$ upper limit on the line depth was $\sim 7$ mJy.688 We note that the asorption was again secu ou both obscrving runs: however. the Doppler shift between the two epochs was slightly less than aciumel aud heuce cannot be used as a test for fιο reality of the feature.," We note that the absorption was again seen on both observing runs; however, the Doppler shift between the two epochs was slightly less than a channel and hence cannot be used as a test for the reality of the feature."689 No evideuce for interference was seen iu he data. on either the source or the calibrators.," No evidence for interference was seen in the data, on either the source or the calibrators."690 The absorption is quite wide. with a full width between nulls of  50 kins land a peak optical depth of ~0.0067. at a frequency of 93]5462 MIIz. ic. 2=0.52476dE0.00005.," The absorption is quite wide, with a full width between nulls of $\sim$ 50 km $^{-1}$, and a peak optical depth of $\sim 0.0067$, at a frequency of 931.562 MHz, i.e. $z = 0.52476 \pm 0.00005$."691" Finally, uo absorption was detected iu the :=0.5579 absorber towards PISS 0115-272."," Finally, no absorption was detected in the $z = 0.5579$ absorber towards PKS 0118-272."692 The RAS noise on the final Manning simoothecd spectrum (resolution 10 kin +t: not shown hero) is ~2. L1nJsy: this vields a 36 upper limit of τς0.0065 on the optical depth o the absorber., The RMS noise on the final Hanning smoothed spectrum (resolution $\sim 10$ km $^{-1}$; not shown here) is $\sim 2.4$ mJy; this yields a $3\sigma$ upper limit of $\tau < 0.0065$ on the optical depth of the absorber.693" The 21 «anu optical depth. τοι. of an optically thin. homogeneous cloud is related to the column deusitv of the absorbing eas Nyy and the spin temperature T, by the expression (es. Rohllfs 1986)) where f is the covering factor of the absorber."," The 21 cm optical depth, $\tau_{21}$, of an optically thin, homogeneous cloud is related to the column density of the absorbing gas $N_{\rm HI}$ and the spin temperature ${\rm T_s}$ by the expression (e.g. \cite{rohlfs86}) ) where $f$ is the covering factor of the absorber."694 In the above equation.⋅ Nyp is ⇁⋅⋅dmi 57. T. in K aud dV in hans Hi.," In the above equation, $N_{\rm HI} $ is in $^{-2}$, ${\rm T_s}$ in K and $\mathrm{d}V$ in km $^{-1}$."695 For a ΜΜ absorber the spin teniperature erived using the above expression is the colin density weighted harmonic mean of the spin temperatures of the oeidividual phases., For a multi-phase absorber the spin temperature derived using the above expression is the column density weighted harmonic mean of the spin temperatures of the individual phases.696 In the case of «auped systems. the column density can be estimated frou the equivalent width of the Lvuuuro profile: a measurement of τοι jen vields the spin teniperaureif he covering factor is shown.," In the case of damped systems, the column density can be estimated from the equivalent width of the $\alpha$ profile; a measurement of $\tau_{\rm 21}$ then yields the spin temperature the covering factor is known."697 T16 latter is frequenlv uncertain since the radio chussion from quasars is οton extended while the UV continmuni arises csscutially from a point source., The latter is frequently uncertain since the radio emission from quasars is often extended while the UV continuum arises essentially from a point source.698 Thus. 16 line of sight along which the HII colunu density has )ocn estimated need uot be the same as the one for which re the 2] cni optical depth has been measured.," Thus, the line of sight along which the HI column density has been estimated need not be the same as the one for which the the 21 cm optical depth has been measured."699 VLBI observations. when available. can be usec to estimate 16 ilnou woof radio cluission cluanating from conroct coniponenuts spatially coimckeut with the UV point sotree: oue can then estimate f and thus. the spin cluperature.," VLBI observations, when available, can be used to estimate the amount of radio emission emanating from compact components spatially coincident with the UV point source; one can then estimate $f$ and thus, the spin temperature."700collinear points. an algebraic equation of the filth degree is solved numerically with initial approximations to the Tavlor-series as: T1e solution of differential equations (1)) aud (2)) is presented as iiterpolation function which is plotted [or various integration intervals by substituting specific values ofthe time / and initial conditions i.e. (0)—àCL;).y(0)=0 where /=1—3 and (0)=i-gna(0)xστ (for the Griangular equilibrium points).,"collinear points, an algebraic equation of the fifth degree is solved numerically with initial approximations to the Taylor-series as: The solution of differential equations \ref{eq:Omegax}) ) and \ref{eq:Omegay}) ) is presented as interpolation function which is plotted for various integration intervals by substituting specific values ofthe time $t$ and initial conditions i.e. $x(0)=x(L_i),y(0)=0$ where $i=1-3$ and $x(0)= \frac{1}{2}-\mu,701y(0)=\pm\frac{\sqrt{3}}{2}$ (for the triangular equilibrium points)."702 Tje equilibrium points are shown in figure 1. in which two panes Le. (I) pink points COLTES]»ond to the collinear points ancl black points correspond to the (riangular points Lor the Sun-Earth svstem. whereas panel (I1) show the zoom of the neigeiborhood of L5.," The equilibrium points are shown in figure \ref{fig:lpoints} in which two panels i.e. (I) pink points correspond to the collinear points and black points correspond to the triangular points for the Sun-Earth system, whereas panel (II) show the zoom of the neighborhood of $L_2$."703 The inuuerical values of (hese points are presented in Table 1.., The numerical values of these points are presented in Table \ref{tab:lpts}.704 IU is seen that the positions ol L4.L4 ave shifted to rightward: Ls.L; are shilted to leftward: and L4 is also shifted to downward with respect to their positions in the classical problem.," It is seen that the positions of $L_1, L_3$ are shifted to rightward; $L_2, L_4$ are shifted to leftward; and $L_4$ is also shifted to downward with respect to their positions in the classical problem."705" The nature of the L5 is nol discussed in present model because it is same as (he nature of L,.", The nature of the $L_5$ is not discussed in present model because it is same as the nature of $L_4$ .706 But the detail behavior ol the Le with stability regions is discussed in sections 3. 4.., But the detail behavior of the $L_2$ with stability regions is discussed in sections \ref{sec:TrjL2} \ref{sec:stbL2}.707 llowever.in general. it mieht be dillicult to know the critical values of the parameters. but thev could be obtained with the help of Interval Arithmetic(LÀ). which was introduced by Moore (1963)...," However,in general, it might be difficult to know the critical values of the parameters, but they could be obtained with the help of Interval Arithmetic(IA), which was introduced by \cite{mooreRE}. ."708" As per the LX. if £,=fay.ds).£j(by.be} be (vo intervals. then four basic arithmetic operations can be definedas:"," As per the IA, if $I_a=[a_1,a_2],I_b=[b_1,b_2]$ be two intervals, then four basic arithmetic operations can be definedas:"709The dimensionless plhivsical constants like the clectrou-to-proton ness ratio. ff=ηςWy. OF the fine-structure constant. àChe). ave expected to be. dviaunuica quantities in modern extensions of the standard mode of particle plysics (Uzan 2003: Carcia-Berro 22007: Martius 2008: Ianekar 2008: Cin 22009).,"The dimensionless physical constants like the electron-to-proton mass ratio, $\mu = m_{\rm e}/m_{\rm p}$, or the fine-structure constant, $\alpha = e^2/(\hbar c)$, are expected to be dynamical quantities in modern extensions of the standard model of particle physics (Uzan 2003; Garcia-Berro 2007; Martins 2008; Kanekar 2008; Chin 2009)."710 Exploring these predictions is a subject of many high precision nmeasuremeuts iun conteniporary laboratory and astrophysical cexperiuents., Exploring these predictions is a subject of many high precision measurements in contemporary laboratory and astrophysical experiments.711 The S accurate laboratory constraints on temporal a- aud µ- variatious of àο1642.3)«10tyr te and fr/p(1.6c1.7)«1015 1 were obtained by Boseubaud ((2008). aud Blatt ((2008). respectively.," The most accurate laboratory constraints on temporal $\alpha$ - and $\mu$ -variations of $\dot{\alpha}/\alpha = (-1.6\pm2.3)\times10^{-17}$ $^{-1}$, and $\dot{\mu}/\mu = (1.6\pm1.7)\times10^{-15}$ $^{-1}$ were obtained by Rosenband (2008), and Blatt (2008), respectively."712 Iu case of monotonic depeudence of a(t) aud p(t) on cosmic time. at redshift 2~ (correspouding look-back time is At1079 yr) the changes of à and qi would be restricted at the level of [Aofal&E10.* and 310 7.," In case of monotonic dependence of $\alpha(t)$ and $\mu(t)$ on cosmic time, at redshift $z \sim 2$ (corresponding look-back time is $\Delta t \sim 10^{10}$ yr) the changes of $\alpha$ and $\mu$ would be restricted at the level of $|\Delta\alpha/\alpha| < 4\times10^{-7}$ and $|\Delta\mu/\mu| < 3\times10^{-5}$ ."713" Here (Gor Aqgpfp)) isa fractional change in à between a reference value ay, and a given measurement o» obtained at different epochs or at differeut spatial coordinates: Aa/a=(a2 O1.", Here (or ) is a fractional change in $\alpha$ between a reference value $\alpha_1$ and a given measurement $\alpha_2$ obtained at different epochs or at different spatial coordinates: $\Delta\alpha/\alpha = (\alpha_2 - \alpha_1)/\alpha_1$ .714 These constraints are in. line with ecological nieasurenmients of relative isotopic abuidances in the Oklo natural fission reactor which allows us to probe a(t) at At~ὃς10) wl.~0. ), These constraints are in line with geological measurements of relative isotopic abundances in the Oklo natural fission reactor which allows us to probe $\alpha(t)$ at $\Delta t \sim 2\times10^9$ yr $z \sim 0.4$ ).715 Asstunine possible changes ouly in the electromagnetic coupling constant. Gould ((2006) obtained a model dependent coustraint on [Aonfal«2«107.," Assuming possible changes only in the electromagnetic coupling constant, Gould (2006) obtained a model dependent constraint on $|\Delta\alpha/\alpha| < 2\times10^{-8}$."716 However. when the streugth of the stroug interaction. — the panuueter Xocep. is also sugeested to be variable. the Oklo data does not provide anv bound on the variation of à. (Flambaum Shurvak 2002: Clin 22009).," However, when the strength of the strong interaction, – the parameter $\Lambda_{QCD}$, – is also suggested to be variable, the Oklo data does not provide any bound on the variation of $\alpha$ (Flambaum Shuryak 2002; Chin 2009)."717 Current astroplhivsical measurements at higher redshifts are as follows., Current astrophysical measurements at higher redshifts are as follows.718 There was a claim for a variability of a at the 5e confidence level: Aafa=5.5rn;dx1.1 ppm (Murphy 22001)1.. but this was not coufirmed in other ineasureinents whichled to the upper bound [Aafa]«2 ppl (Quast 22001: Levshakov 22005: Srianaud 22008: Molaro 22008a).," There was a claim for a variability of $\alpha$ at the $\sigma$ confidence level: $\Delta\alpha/\alpha = -5.7\pm1.1$ ppm (Murphy , but this was not confirmed in other measurements whichled to the upper bound $|\Delta\alpha/\alpha| < 2$ ppm (Quast 2004; Levshakov 2005; Srianand 2008; Molaro 2008a)."719" AMoeasureimenuts of the cosinological p-variatiou exhibit a similar tendency,", Measurements of the cosmological $\mu$ -variation exhibit a similar tendency.720 Nou-zero values of Ajpi/p=30.5437.5 ppui. App=16.5437.1 οι (Ivauchik 22005). and Αμημς2L46 ppm (Reinhold 22006) found at 2=2.595 (Q 0105113) and 2=3.025 (Q 0317.383) from the Werner and Lyinan bauds of Πο were later refuted by Wendt Reimers (2008). Nine ((2008) aud Thompson ((2009) who used the same optical absorptiou-line spectra of quasars aud restricted changes in yr at the level of [App]<6 ppm.," Non-zero values of $\Delta\mu/\mu = -30.5\pm7.5$ ppm, $\Delta\mu/\mu = -16.5\pm7.4$ ppm (Ivanchik 2005), and $\Delta\mu/\mu = -24\pm6$ ppm (Reinhold 2006) found at $z = 2.595$ (Q 0405–443) and $z = 3.025$ (Q 0347–383) from the Werner and Lyman bands of $_2$ were later refuted by Wendt Reimers (2008), King (2008) and Thompson (2009) who used the same optical absorption-line spectra of quasars and restricted changes in $\mu$ at the level of $|\Delta\mu/\mu| < 6$ ppm."721 The third Uy system at 2=2.059 towards the quasar J21230050 also docs not show aux evidence for cosmological variation iu ps Agespe=5.64DoarE294. ppm (Malec 22010)., The third $_2$ system at $z = 2.059$ towards the quasar J2123–0050 also does not show any evidence for cosmological variation in $\mu$ : $\Delta\mu/\mu = -5.6\pm5.5_{\rm stat}\pm2.9_{\rm sys}$ ppm (Malec 2010).722 More stringent constraints were obtained at lower redshifts from radio observations of the absorption lines of NIL; aud other molecules: Apfy]<1.8 ppii at 2=0.68 (Murphy 22008). aud [Apfet]<0.6 ppii at c=0.89 (Henkel 22009).," More stringent constraints were obtained at lower redshifts from radio observations of the absorption lines of $_3$ and other molecules: $|\Delta \mu/\mu| < 1.8$ ppm at $z = 0.68$ (Murphy 2008), and $|\Delta \mu/\mu| < 0.6$ ppm at $z = 0.89$ (Henkel 2009)."723 Two cool gas absorbers at 2=1.36 (Q 2337 aud :=1.56 (OQ 0158020) were recently studiedin the 21« and Ci1AA1560.1657 absorption lines providing a constraint on the variation of the product Y=ο(here gy is the protou evromaguetic ratio): AN/N=6.8l.0ae£6.7avs opui (Ikanekar 22010).," Two cool gas absorbers at $z = 1.36$ (Q 2337--011) and $z = 1.56$ (Q 0458–020) were recently studiedin the 21cm and $\lambda\lambda1560, 1657$ absorption lines providing a constraint on the variation of the product $X = g_{\rm p}\alpha^2\mu$(here $g_{\rm p}$ is the proton gyromagnetic ratio): $\Delta X/X = -6.8\pm1.0_{\rm stat}\pm6.7_{\rm sys}$ ppm (Kanekar 2010)."724 Thus. t16 nuosf acctrate astronomical estimates," Thus, the most accurate astronomical estimates"725are advected: downstream to be accelerated further by the internal shock Clammi&Dempsey.(2007):PopeAlel-rose(1994))).,"are advected downstream to be accelerated further by the internal shock \cite{tammi,pope}) )."726 Xn internal shock description for the knots in AGN jets has alreacky been discussed in literature (Rees(1978):Sahavanathan&Misra (2005))).," An internal shock description for the knots in AGN jets has already been discussed in literature \cite{rees,saha05}) )."727 Alternatively. reacceleration of power law electron. distribution bv turbulence at. boundary. shear lavers can also be another possible scenario (DeYoung(1986):Stawarz&Ostrowski (2003)3).," Alternatively, reacceleration of power law electron distribution by turbulence at boundary shear layers can also be another possible scenario \cite{young,staw03}) )."728 Inclusion. of these scenario in its exact form into the present model will make it more complex and is beyond the scope of the present work., Inclusion of these scenario in its exact form into the present model will make it more complex and is beyond the scope of the present work.729 Perlman&Wilson(2005) proposed a modified. CL model where the volume within which particle acceleration occurs is energv-dependent., \cite{perl05} proposed a modified CI model where the volume within which particle acceleration occurs is energy-dependent.730 This is expressed in terms of a filling factor which is the ratio between the observed Hux to the Dux. predicted by the simple CL mocelο, This is expressed in terms of a filling factor which is the ratio between the observed flux to the flux predicted by the simple CI model.731 Ἔπον found. declining with increasing distance [ron the nucleus suggesting particle acceleration. taking place in larger fraction of the jet. volume in the inner jet than the outer jet., They found declining with increasing distance from the nucleus suggesting particle acceleration taking place in larger fraction of the jet volume in the inner jet than the outer jet.732 The energy dependence of also indicates that particle acceleration regions occupy a smaller fraction of jet volume at higher energies., The energy dependence of also indicates that particle acceleration regions occupy a smaller fraction of jet volume at higher energies.733 Even though the moclel is phenomenological. it indicates that the process of high enerey emission from the knots are as complicated as their physical region.," Even though the model is phenomenological, it indicates that the process of high energy emission from the knots are as complicated as their physical region."734 However the mechanism responsible for the illine factor is not explained., However the mechanism responsible for the filling factor is not explained.735 Stawarzetal.(2006) explained the knot LIST-1 of MST jet as a region when the reconfinement shock reaches the jet axis., \cite{staw06} explained the knot HST-1 of M87 jet as a region when the reconfinement shock reaches the jet axis.736 They. considered at the initial stage of AIST jet. he particles expand. freely. decreasing the pressure rapiclly han the ambient gas pressure.," They considered at the initial stage of M87 jet, the particles expand freely decreasing the pressure rapidly than the ambient gas pressure."737 This will develop (in case of AIST) a reconfinement shock which reaches the jet axis at à ocation which coincide with that of the knot HST-I1., This will develop (in case of M87) a reconfinement shock which reaches the jet axis at a location which coincide with that of the knot HST-1.738 Thev xostulate this location as the beginning of LIS'T-1 and while its outer parts are identified as stationary rellected shock ormed when the recontinement shock reaches the jet axis., They postulate this location as the beginning of HST-1 and while its outer parts are identified as stationary reflected shock formed when the reconfinement shock reaches the jet axis.739 Also they evaluated the ambient raciation field along the jet axis and estimated the TeV eamama-ray emission from LS'T-l initiated. by an outburst experienced. at the core., Also they evaluated the ambient radiation field along the jet axis and estimated the TeV gamma-ray emission from HST-1 initiated by an outburst experienced at the core.740 Since he reconfinement shock requires an initial free expansion. he knots downstream ΕΤ. cannot be explained hy this niocel.," Since the reconfinement shock requires an initial free expansion, the knots downstream HST-1 cannot be explained by this model."741 Fleishman(2006) explained the Uattening of non-hermal spectra in the ultraviolet ancl X-ray bands observed rom the knots of AIST and 3€273 jets through dilfusive svnchrotron raciation(DSR) in random small-scale magnetic icles., \cite{fleishman} explained the flattening of non-thermal spectra in the ultraviolet and X-ray bands observed from the knots of M87 and 3C273 jets through diffusive synchrotron radiation(DSR) in random small-scale magnetic fields.742 Whereas the syncehrotron. spectrum. from. regular arge-scale magnetic field. dominates the spectra at. low encrey band., Whereas the synchrotron spectrum from regular large-scale magnetic field dominates the spectra at low energy band.743 The DSR spectrum at high energy is χωο where go ids the observed. photon frequency and i is. the spectral index of the random magnetic field assumed to bea »ower-Iaw., The DSR spectrum at high energy is $\propto \omega^{-\nu}$ where $\omega$ is the observed photon frequency and $\nu$ is the spectral index of the random magnetic field assumed to be a power-law.744 Honda&(2007). proposed a filamentary jet. model to explain the observed. X-ray spectral index., \cite{honda} proposed a filamentary jet model to explain the observed X-ray spectral index.745 In their model. the jet. comprises magnetic filaments. of ransverse size A anc particles trapped in this filaments are accelerated by diffusive shock acceleration.," In their model, the jet comprises magnetic filaments of transverse size $\lambda$ and particles trapped in this filaments are accelerated by diffusive shock acceleration."746 Phe acceleration of the electrons bound to a large filament are controlled bv he racliative losses before escape from the filament., The acceleration of the electrons bound to a large filament are controlled by the radiative losses before escape from the filament.747 Whereas he electrons trapped in smaller filaments escape via energization., Whereas the electrons trapped in smaller filaments escape via energization.748" A critical scale. A, discriminates between the arge and small scale filaments.", A critical scale $\lambda_c$ discriminates between the large and small scale filaments.749 They considered a situation where the magnetic field is larger lor filaments with larger size ancl found the electron energy. peaks when trapped in the filament of size Ac., They considered a situation where the magnetic field is larger for filaments with larger size and found the electron energy peaks when trapped in the filament of size $\lambda_c$.750" The X-ray spectrum. is explained by the svnchrotron radiation of the electrons. accelerated in the filaments of size Ax»A,.", The X-ray spectrum is explained by the synchrotron radiation of the electrons accelerated in the filaments of size $\lambda>\lambda_c$.751 However. svnchrotron radiation from Large-scale magnetic field itself ean reproduce the observed. X-ray spectrum (present model) involving less number of parameters and/or ΠΩ," However, synchrotron radiation from large-scale magnetic field itself can reproduce the observed X-ray spectrum (present model) involving less number of parameters and/or 2)."752 Recently Lin&Shen(2007) proposed à two zone model to explain the observed. spectra of the knots of AIST jet., Recently \cite{liu} proposed a two zone model to explain the observed spectra of the knots of M87 jet.753 In their model electrons are accelerated: to. relativistic energies in acceleration region (AIL) and loose most of their energies in cooling region (CR) through svnchrotron process., In their model electrons are accelerated to relativistic energies in acceleration region (AR) and loose most of their energies in cooling region (CR) through synchrotron process.754 They considered. Al and CR are spatially separated: and introduced a break in the particle spectrum injected in CR through the advection of particles from AR to CR., They considered AR and CR are spatially separated and introduced a break in the particle spectrum injected in CR through the advection of particles from AR to CR.755 This along with the cooling break in CR produce a double broken power-law with indices op. (p|1)and (p|2) which is then used to fit the observed spectra.," This along with the cooling break in CR produce a double broken power-law with indices $-p$, $-(p+1)$ and $-(p+2)$ which is then used to fit the observed spectra."756 Llowever the present model assumes Alt and CR are co-spatial supporting a more physical scenario where electrons accelerated by the shock. cools in its vicinitv.," However the present model assumes AR and CR are co-spatial supporting a more physical scenario where electrons accelerated by the shock, cools in its vicinity."757 The observed radio-optical-X-ray. spectra from the knots in the jets of the FRI radio galaxy MS are explained within the framework of two zone model., The observed radio-optical-X-ray spectra from the knots in the jets of the FRI radio galaxy M87 are explained within the framework of two zone model.758 We considered à power-law electron distribution which are further accelerated in an acceleration region and are injected into a cooling region where they lose their energy through svnchrotron radiation., We considered a power-law electron distribution which are further accelerated in an acceleration region and are injected into a cooling region where they lose their energy through synchrotron radiation.759 In its simplest form. the ΠΟΟἱ does not consider any specific acceleration process but assumes an energy independen acceleration timescale.," In its simplest form, the model does not consider any specific acceleration process but assumes an energy independent acceleration timescale."760 Future observations of AIST knots in UNV-to-N-ray. photon energies will confirm the present moce and constrain the parameters involved., Future observations of M87 knots in UV-to-X-ray photon energies will confirm the present model and constrain the parameters involved.761 We explored the possibility. of the present. model to reproduce the X-ray. Dux of other FRI galaxies (detectec by Chandra) which are observed to have lower radio luminosity ancl relatively smaller jets when compared with PRIL galaxies., We explored the possibility of the present model to reproduce the X-ray flux of other FRI galaxies (detected by ) which are observed to have lower radio luminosity and relatively smaller jets when compared with FRII galaxies.762 Phe X-ray emission from FRI jet is quite wel accepted to be of svnchrotron origin whereas for FRILL anc quasars it may be due to IC/CMDB., The X-ray emission from FRI jet is quite well accepted to be of synchrotron origin whereas for FRII and quasars it may be due to IC/CMBR.763 However the latter is still under debate (see Harris&WKrawezyvnski(2006) for a review about the X-ray emission. from extragalactic jets)., However the latter is still under debate (see \cite{harris} for a review about the X-ray emission from extragalactic jets).764 The X-ray emission from the knots and/or the jets of the FRI galaxies viz., The X-ray emission from the knots and/or the jets of the FRI galaxies viz.765 3€ 66D(Llardcastleetal. (2001))). 3€ Worrall&Birkinshaw (2005))). Cen (Llarcleastleetal. (2006))) and 3€ 296 (Llarceastleetal.(2005). listed in the online catalog of extragalactic N-rav jets ΧΙΟ7. whieh are not explained by synchrotron emission from simple one zone models. can be reproduced by the present mocel.," 3C \cite{hardcastle}) ), 3C \cite{worall}) ), CenA \cite{hardcastle06}) ) and 3C 296 \cite{hardcastle05} listed in the online catalog of extragalactic X-ray jets XJET, which are not explained by synchrotron emission from simple one zone models, can be reproduced by the present model."766 The author thanks S. Bhattacharvva. N. Bhatt and M. Choudhury for the useful discussions and suggestions.," The author thanks S. Bhattacharyya, N. Bhatt and M. Choudhury for the useful discussions and suggestions."767 The author is grateful to referee IE. Perlman for useful comments and suggestions., The author is grateful to referee E. Perlman for useful comments and suggestions.768 This work has made use of the AJET website., This work has made use of the XJET website.769or eroup are then estimated.,or group are then estimated.770 Iu particular. thev find that Δον<6⋅«E1015cmDi7. consistentB with. the constraints for the COAL around our Galaxy.," In particular, they find that $N_{\rm OVII}\le 6 \times 10^{14}~{\rm cm^{-2}}$, consistent with the constraints for the CGM around our Galaxy."771" They. have estimated the total mass coutaimecd in the COAL as Εμ...fovυ.:)E0.1.i}{SpoRkxj2.101011AL. t where Γον. A. aud & are the ionization fraction ofVIL. metal abundance, and the radius of the hot CCM. respectively,"," They have estimated the total mass contained in the CGM as $M_{\rm CGM}\lsim 0.6 \times(\frac{0.5}{f_{\rm772 OVII}})\times(\frac{0.3A_\odot}{A})\times(\frac{R}{500~773 {\rm kpc}})^2\times10^{11}M_\odot$ , where $f_{\rm OVII}$ , $A$, and $R$ are the ionization fraction of, metal abundance, and the radius of the hot CGM, respectively."774 This is in contrast to the expected barvon mass 22<1013AZ. for the halo of a Milly Wav-tvpe galaxy or a typical galaxy eroup (25).., This is in contrast to the expected baryon mass $\gsim2\times10^{11}~M_\odot$ for the halo of a Milky Way-type galaxy or a typical galaxy group \cite{mcg09}.775 Thus the bulk of the CGAL uulikely resides in such a chemically enriched waru-hot pliase at teniperatures raneine from 1077109 K (Fie., Thus the bulk of the CGM unlikely resides in such a chemically enriched warm-hot phase at temperatures ranging from $10^{5.5}-10^{6.5}$ K (Fig.776 1 1)). which our X-ray absorption line spectroscopy is scusitive to.," 1 \ref{fig:f1}) ), which our X-ray absorption line spectroscopy is sensitive to."777 This conclusion has strone implications for understaudiue the accumulated effect. of the stellar aud ACN feedback on the eaOs:actic ecosystem (see the discussion section)., This conclusion has strong implications for understanding the accumulated effect of the stellar and AGN feedback on the galactic ecosystem (see the discussion section).778 To study the effect of ongoing stellar aud ACN feedback. oue cam map out diffuse N-ray. cussion from hot eas in and around nearby galaxies of various masses and star formation rates;," To study the effect of ongoing stellar and AGN feedback, one can map out diffuse X-ray emission from hot gas in and around nearby galaxies of various masses and star formation rates."779 Much atteution has been paid to the feedback in starburst aud massive clliptical galaxies. which are relatively. bright in diffuse X-ray cussion.," Much attention has been paid to the feedback in starburst and massive elliptical galaxies, which are relatively bright in diffuse X-ray emission."780 oobservatious have shown couviuciuglv that the AGN feeback is inportaut in shaping the iiorphology aud tlic1aal evolution of hot σας in massive elliptica ealaxies. particularly those at centers of galaxy eroups and chsters ((26) and references therein).," observations have shown convincingly that the AGN feedback is important in shaping the morphology and thermal evolution of hot gas in massive elliptical galaxies, particularly those at centers of galaxy groups and clusters \cite{mn07} and references therein)."781 The asvunuetry in the global diffuse X-ray morphology is correlated wih radio aud N-rav luuinosities of ACNs in elliptical galaxies. even in rather N-rav-faint ones (27)..," The asymmetry in the global diffuse X-ray morphology is correlated with radio and X-ray luminosities of AGNs in elliptical galaxies, even in rather X-ray-faint ones \cite{die08}."782 This calls iuto question the hydrostatic assuuption commonly used in order to infer the eravitational mass distribution in such galaxies., This calls into question the hydrostatic assumption commonly used in order to infer the gravitational mass distribution in such galaxies.783 Nevertheless. the wdrostatic assuniption may hold approximately for hot gas around the ceutral supermassive black holes (SADII). ifthey are ina sufficiently quiescent state.," Nevertheless, the hydrostatic assumption may hold approximately for hot gas around the central supermassive black holes (SMBHs), if they are in a sufficiently quiescent state."784 The SMDIT lnasses nav then be measured from spatially resolved X-ray spectroscopy of the hot eas., The SMBH masses may then be measured from spatially resolved X-ray spectroscopy of the hot gas.785 Tuuphrey ct al., Humphrey et al.786 have mace such mass measurements for four SMDIIS with ddata (2s)..., have made such mass measurements for four SMBHs with data \cite{hum09}.787 Twee of them already lave mass determinations from the kinematics of either stars or a central eas disk., Three of them already have mass determinations from the kinematics of either stars or a central gas disk.788" It is ¢""ucouraeine to find a eood agreement between the measurements using the differeut methods.", It is encouraging to find a good agreement between the measurements using the different methods.789 From this aerecient.C» they further inter that no more than —1KK20 of the ΤΟΝΤ pressure around the SAIBUs should be nonthermal.," From this agreement, they further infer that no more than $\sim 10\%-20\%$ of the ISM pressure around the SMBHs should be nonthermal."790 Tie feedback in unclear starburst galaxies is manifested iu the so-called galactic superwinds driven by the mechaucal energv injection frou fast stellar winds and superuovae (SNe) of massive stars (¢.e.. (20:30: 31))).," The feedback in nuclear starburst galaxies is manifested in the so-called galactic superwinds driven by the mechanical energy injection from fast stellar winds and supernovae (SNe) of massive stars (e.g., \cite{str04a,str04b,sh09}) )."791 The observed soft X-ray cluission frou a superwind typically has au clongated morphology along the murinex axis of such a galaxy aud is correlated well with extraplanuar We-cuutting features., The observed soft X-ray emission from a superwind typically has an elongated morphology along the minor axis of such a galaxy and is correlated well with extraplanar $\alpha$ -emitting features.792 This indicates that he detected ho cus ALISCS priniariv from the interaction between the superwiud aud cool eas., This indicates that the detected hot gas arises primarily from the interaction between the superwind and cool gas.793" The 3perwiiu itself, believed to be very lot aux low in deusity. is much cüiffieult to detect."," The superwind itself, believed to be very hot and low in density, is much difficult to detect."794" From a detailed comparison beween ddata and liserodvuamic simmlatious. Strickland Teckiman infer that the superwiud of M82 has a mean teniperature o DESIO"" K aud amass outfowing rate of ~2M.vr| (31).."," From a detailed comparison between data and hydrodynamic simulations, Strickland Heckman infer that the superwind of M82 has a mean temperature of $3-8 \times 10^7$ K and a mass outflowing rate of $\sim 2 {\rm~M_\odot~yr^{-1}}$ \cite{sh09}. ."795 Such energetie superwinds with little radiative euergy loss ust have profotud effects on the large-scale CGAL (e.g. 030))).," Such energetic superwinds with little radiative energy loss must have profound effects on the large-scale CGM (e.g., \cite{str04b}) )."796" Recent. A-vav observations have further shown the portance of the feeback in uuderstaudiug even ""normal iutermediate-amass galaxies (similar to the Milkv Way and ALS: οOO.n (29:«3Mi30:à 10))).Chaudra.."," Recent X-ray observations have further shown the importance of the feedback in understanding even “normal” intermediate-mass galaxies (similar to the Milky Way and M31; e.g., \cite{str04a,str04b,wan03,tyl03,doa04,tul06a,tul06b,lw07,lij08,bg08,yam09}) ).,"797 im particular. has unambiguously detected diffuse hot eas im aud around normal disk galaxies.," in particular, has unambiguously detected diffuse hot gas in and around normal disk galaxies."798 The total N-rav luuinosity of the eas is well correlated with the star formation rate for such galaxies., The total X-ray luminosity of the gas is well correlated with the star formation rate for such galaxies.799 The diffuse soft N-rav enission is shown to be strongly euliuiced in recent star formine regions or spiral axius within an individual ealaxy viewed face-on aud is only sightly more diffuse than IIa cluission (e.g.. (33: 31))).," The diffuse soft X-ray emission is shown to be strongly enhanced in recent star forming regions or spiral arms within an individual galaxy viewed face-on and is only slightly more diffuse than $\alpha$ emission (e.g., \cite{tyl03,doa04}) )."800 This narrow appearance of spiral aruis in Naracouflicts theexpectation from. population svuthesis models: the mechanical energy output rate from: SNe shotld be nearlyconstant over a, This narrow appearance of spiral arms in X-rayconflicts theexpectation from population synthesis models: the mechanical energy output rate from SNe should be nearlyconstant over a801along the iinto the IGM density field.,along the into the IGM density field.802" A boost in the signal of the Cross CF between two iis due to the presence in redshift space of two aligned, or very close, llines belonging to the two considered spectra."," A boost in the signal of the Cross CF between two is due to the presence in redshift space of two aligned, or very close, lines belonging to the two considered spectra."803" On this basis, we can provide a measure of the cross correlation between three fforests by searching for triplets of llines, belonging to three different spectra, aligned in redshift space within a given velocity window."," On this basis, we can provide a measure of the cross correlation between three forests by searching for triplets of lines, belonging to three different spectra, aligned in redshift space within a given velocity window."804 This kind of analysis has been applied to the Triplet and to all the combinations of 3 QSOs that could be formed with the Sextet., This kind of analysis has been applied to the Triplet and to all the combinations of 3 QSOs that could be formed with the Sextet.805 The adopted procedure has been the following: 1., The adopted procedure has been the following: 1.806" The lists of llines compiled for the QSOs in our sample were considered in the redshift range between the eemission (or the shortest observed wavelength, when the wwas not included in the spectrum) and 5000 ffrom the eemission (to avoid proximity effect due to the QSO)."," The lists of lines compiled for the QSOs in our sample were considered in the redshift range between the emission (or the shortest observed wavelength, when the was not included in the spectrum) and 5000 from the emission (to avoid proximity effect due to the QSO)."807 2., 2.808 Each pair of lines with a velocity separation Av<100 hhas been replaced by a single line with central wavelength equal to the average value of the parent lines weighted on the EW., Each pair of lines with a velocity separation $\Delta v \le 100$ has been replaced by a single line with central wavelength equal to the average value of the parent lines weighted on the EW.809" This velocity threshold has been chosen on the basis of the characteristic width of lines, ~25—30 km/s (seee.g.Kimetal.2002)."," This velocity threshold has been chosen on the basis of the characteristic width of lines, $\sim 25-30$ km/s \citep[see e.g.][]{kim02}."810" Furthermore, this is also the velocity scale corresponding to the Jeans length, which sets the characteristic dimension of aabsorbers."," Furthermore, this is also the velocity scale corresponding to the Jeans length, which sets the characteristic dimension of absorbers."811 3., 3.812" Triplets of lines, each one belonging to a differentsight, have been considered and the velocity difference between the largest and smallest redshift has been computed."," Triplets of lines, each one belonging to a different, have been considered and the velocity difference between the largest and smallest redshift has been computed."813 This operation has been done for the llines in the three oof the Triplet and in all the triplets of ((20 possible combinations) provided by the Sextet., This operation has been done for the lines in the three of the Triplet and in all the triplets of (20 possible combinations) provided by the Sextet.814" Then, all the measures of velocity difference lower than 1000 hhave been divided into velocity bins of 100 aand the related histogram with the number of occurrences for each bin has been computed."," Then, all the measures of velocity difference lower than 1000 have been divided into velocity bins of 100 and the related histogram with the number of occurrences for each bin has been computed."815 4., 4.816" Next, the previous three steps have been repeated for a sample of 10? mock lists of lines built in the following way."," Next, the previous three steps have been repeated for a sample of $10^3$ mock lists of lines built in the following way."817" In order to take into account the varying number density of detectable lines along the fforests, due to the varying SNR, each forest has been simulated in chunks of about 200A.."," In order to take into account the varying number density of detectable lines along the forests, due to the varying SNR, each forest has been simulated in chunks of about 200."818" In each mock chunk, the number of simulated lines has been determined from a Poissonian distribution centred on the number of observed lines in that chunk, while the positions of the mock lines have been randomly generated following a uniform distribution within the related wavelength range of each chunk."," In each mock chunk, the number of simulated lines has been determined from a Poissonian distribution centred on the number of observed lines in that chunk, while the positions of the mock lines have been randomly generated following a uniform distribution within the related wavelength range of each chunk."819 The redshift intervals masked in the observed spectra were masked also in the simulated ones., The redshift intervals masked in the observed spectra were masked also in the simulated ones.820 The EWs of the mock lines have been randomly chosen among all the EWs measured by the fit of the lines in the observed spectra., The EWs of the mock lines have been randomly chosen among all the EWs measured by the fit of the lines in the observed spectra.821" In this way it has been possible, for each velocity bin, to compute the mean and the standard deviation of the number of occurrences for synthetic lists of lines."," In this way it has been possible, for each velocity bin, to compute the mean and the standard deviation of the number of occurrences for synthetic lists of lines."822 5., 5.823" Finally, we have defined the three point probability excess (PE3) as a function of the velocity difference, Av, according to the following formula: The resulting PE3 is reported in Fig. 7,,"," Finally, we have defined the three point probability excess (PE3) as a function of the velocity difference, $\Delta\,v$, according to the following formula: The resulting PE3 is reported in Fig. \ref{fig:PE3},"824" together with the 1, 2 and 3 o confidence levels."," together with the 1, 2 and 3 $\sigma$ confidence levels."825 The PE3 is non-zero at a 2 σ level up to a velocity difference of ~250s~!., The PE3 is non-zero at a 2 $\sigma$ level up to a velocity difference of $\sim 250$.826. Most of the signal of the PE3 is due to the large number (26) of coincidences produced by the 83-85-86 QSOs triplet which is also the closesttriplet (mean angularseparation of 2.02 arcmin corresponding to ~2 ! comoving Mpc)., Most of the signal of the PE3 is due to the large number (26) of coincidences produced by the S3-S5-S6 QSOs triplet which is also the closesttriplet (mean angularseparation of 2.02 arcmin corresponding to $\sim 2$ $h^{-1}$ comoving Mpc).827 Fig., Fig.828 8 shows the probabilityexcess considering quadruplets of llines., \ref{fig:PE4} shows the probabilityexcess considering quadruplets of lines.829 A significant signal atmore than 3 σ level is measured up to a velocity difference of ~250s~'., A significant signal atmore than 3 $\sigma$ level is measured up to a velocity difference of $\sim 250$.830". Besides, one group of five coincident lines within 100 iin the $2-83-84-85-S6 QSOs is observed at a mean redshift of 1.825, an occurrence that has a probability P—0.013 to arise from a random distribution of lines."," Besides, one group of five coincident lines within 100 in the S2-S3-S4-S5-S6 QSOs is observed at a mean redshift of 1.825, an occurrence that has a probability P=0.013 to arise from a random distribution of lines."831 The portion of spectra where these five lines fall are reported in Fig. 9.., The portion of spectra where these five lines fall are reported in Fig. \ref{fig:Filament}.832" In particular, it is possible to observe in the spectrum of the $3 QSO the presenceof a Damped ssystem (DLA): the fitted Voigt profile gives a column density value of log — 20.6."," In particular, it is possible to observe in the spectrum of the S3 QSO the presenceof a Damped system (DLA): the fitted Voigt profile gives a column density value of $\log N$ = 20.6."833 This DLA is associated with several metallic ion absorptionN lines found in the redder part of the spectrum., This DLA is associated with several metallic ion absorption lines found in the redder part of the spectrum.834" Indeed at the same redshift we have found evidence of Iv,,Ferr, Silv,, Siri, Sim, aand Alrm.."," Indeed at the same redshift we have found evidence of , , , , and ."835 This correlated, This correlated836in Section 3.1.,in Section 3.1.837" In Figure 1, the initial conditions for the x2 loops come from the darkest spine of the inner arch, and therefore the loops can be ordered into a sequence along this arch."," In Figure 1, the initial conditions for the $x_2$ loops come from the darkest spine of the inner arch, and therefore the loops can be ordered into a sequence along this arch."838 This sequence is reflected in Figure 3 by lines which connect points marking individual loops., This sequence is reflected in Figure 3 by lines which connect points marking individual loops.839" We determine the last loop supporting the inner bar as the last of the loops that maintain a consistent PA, which varies in accordance with the PA of the inner bar in the imposed potential."," We determine the last loop supporting the inner bar as the last of the loops that maintain a consistent PA, which varies in accordance with the PA of the inner bar in the imposed potential."840" 'Then among the loops supporting the inner bar we find the one whose major axis is longest, and the length of the bar is defined as the length of this major axis."," Then among the loops supporting the inner bar we find the one whose major axis is longest, and the length of the bar is defined as the length of this major axis."841 Note that the loop with the longest major axis does not have to be the last one in the sequence of loops supporting the bar., Note that the loop with the longest major axis does not have to be the last one in the sequence of loops supporting the bar.842" As can be seen in Figure 3, in models with lower angular velocity of the inner bar (lower panels), the semi-major axis of the loops which support that bar initially increases along the sequence defined by the arch in Figure 1, but then reaches a maximum and decreases, so that the last of the loops supporting the bar is not the loop of the longest semi-major axis."," As can be seen in Figure 3, in models with lower angular velocity of the inner bar (lower panels), the semi-major axis of the loops which support that bar initially increases along the sequence defined by the arch in Figure 1, but then reaches a maximum and decreases, so that the last of the loops supporting the bar is not the loop of the longest semi-major axis."843" Since the loops presented here are only a representative sample of the x2 orbital family, the definition formulated above underestimates the length of the inner bar."," Since the loops presented here are only a representative sample of the $x_2$ orbital family, the definition formulated above underestimates the length of the inner bar."844 The, The845place them close to the major axis of the lens. and >(09) is the angular clependenee of the mean tangential shear experienced: by sources whose azimuthal coordinates place them close to the minor axis of the lens.,"place them close to the major axis of the lens, and $\gamma^- (\theta)$ is the angular dependence of the mean tangential shear experienced by sources whose azimuthal coordinates place them close to the minor axis of the lens."846 Using an observational data set (observed. coordinates and /-band apparent magnitudes) as a framework for a set of. Monte. Carlo simulations. we have demonstrated that the actual signature that one should. expect to observe for anisotropic galaxv-galaxy lensine is far [rom the above idealised case.," Using an observational data set (observed coordinates and $I$ -band apparent magnitudes) as a framework for a set of Monte Carlo simulations, we have demonstrated that the actual signature that one should expect to observe for anisotropic galaxy-galaxy lensing is far from the above idealised case."847" Because galaxies. are broadly distributed. in redshift space. it is common for a clistant source galaxw located at recdshilt ον to be lensed by another galaxy located at redshift 2),<ταν"," Because galaxies are broadly distributed in redshift space, it is common for a distant source galaxy located at redshift $z_s$ to be lensed by another galaxy located at redshift $z_{l1} < z_{s}$."848 In turn. this original lens-source pair may then be lensed by vet another galaxy (or galaxies) located at redshift σος naQ.," In turn, this original lens-source pair may then be lensed by yet another galaxy (or galaxies) located at redshift $z_{l2} < z_{l1}$ ."849" Such instances of cmultiple dellections"" cause the observed. signature of anisotropic ealaxv-galaxy lensing to deviate from the expected. signature.", Such instances of “multiple deflections” cause the observed signature of anisotropic galaxy-galaxy lensing to deviate from the expected signature.850 The degree to which the observed signature. of ealaxy-galaxy lensing cleviates from the expected. signature is a strong function. of the characteristic velocity cispersion of the haloes of galaxies., The degree to which the observed signature of galaxy-galaxy lensing deviates from the expected signature is a strong function of the characteristic velocity dispersion of the haloes of $L^\ast$ galaxies.851 In the case of low characteristic velocity. clispersions.L 9;=100 km +. the observed ratio of mean tangential shears. *(8)/4(0). exceeds a value of unity on all scales 6<100 and is only slightly lower than the function one would obtain if the intrinsic svmmetry axes of the foreground: galaxies were used to perform the caleulation.," In the case of low characteristic velocity dispersions, $\sigma_v^\ast = 100$ km $^{-1}$, the observed ratio of mean tangential shears, $\gamma^+ (\theta) / \gamma^- (\theta)$, exceeds a value of unity on all scales $\theta < 100''$ and is only slightly lower than the function one would obtain if the intrinsic symmetry axes of the foreground galaxies were used to perform the calculation."852 In the case of moderate velocity cispersions. 0;=150 ki +. the observed ratio of mean tangential shears shows little to no anisotropy on scales @>20.," In the case of moderate velocity dispersions, $\sigma_v^\ast = 150$ km $^{-1}$, the observed ratio of mean tangential shears shows little to no anisotropy on scales $\theta > 20''$."853" In the case of high. velocity. dispersions. 0;=200 km the observed function. is actually reversed from the expected funetion (Le. (0)κ(@)) on scales 207<@YO"". and is consistent with no anisotropy on scales 707«8<120""."," In the case of high velocity dispersions, $\sigma_v^\ast = 200$ km $^{-1}$, the observed function is actually reversed from the expected function (i.e., $\gamma^+ (\theta) <854\gamma^- (\theta)$ ) on scales $20'' < \theta < 70''$ , and is consistent with no anisotropy on scales $70'' < \theta < 120''$."855 ln summary. our simulations show that if one observes ~(8)—*5(6) ina large galaxv-galaxy lensing clata set. the observation cannot be simply interpreted as proof that the haloes of the lens galaxies are sphericallv-svmmetric.," In summary, our simulations show that if one observes $\gamma^+ (\theta) = 856\gamma^- (\theta)$ in a large galaxy-galaxy lensing data set, the observation cannot be simply interpreted as proof that the haloes of the lens galaxies are spherically-symmetric."857 That is. although the measured signal appears to be isotropic. it is entirely possible that anisotropic galaxv-galaxy lensing by non-spherical haloes may have taken place.," That is, although the measured signal appears to be isotropic, it is entirely possible that anisotropic galaxy-galaxy lensing by non-spherical haloes may have taken place."858" Further. our simulations show that if one observes ~(6)<54 ina large galaxy-galaxy lensing cata set. the observation cannot be simply interpreted as proof that mass and light are 7anti-aligned"" in the lens galaxies."," Further, our simulations show that if one observes $\gamma^+ (\theta) <859\gamma^- (\theta)$ in a large galaxy-galaxy lensing data set, the observation cannot be simply interpreted as proof that mass and light are ``anti-aligned'' in the lens galaxies."860 That is. although the measured signal appears to be reversed. from the expected signal. the reversal may occur when mass and light are. in fact. perfectly aligned within the lens galaxies.," That is, although the measured signal appears to be reversed from the expected signal, the reversal may occur when mass and light are, in fact, perfectly aligned within the lens galaxies."861 The primary reason that the observed. signature of anisotropic ealaxv-galaxy lensing cilfers from the expected signature is that the foreground. galaxies that are used as centres to compute the mean tangential shear have. themselves. been weakly Iensed.," The primary reason that the observed signature of anisotropic galaxy-galaxy lensing differs from the expected signature is that the foreground galaxies that are used as centres to compute the mean tangential shear have, themselves, been weakly lensed."862 Phe expectation that >(06) will exceed 5.(8) over a wide range of angular scales is basecl upon a picture in whieh the observed svmmetry axes of the lenses are identical to the intrinsic svmmetrv axes of their projected. dark matter haloes., The expectation that $\gamma^+ (\theta)$ will exceed $\gamma^- (\theta)$ over a wide range of angular scales is based upon a picture in which the observed symmetry axes of the lenses are identical to the intrinsic symmetry axes of their projected dark matter haloes.863 However. when one computes 5.(6) and *(8) in an observational data set. one cannot directly view the intrinsic svmmoetrv axes of the bright. central galaxies.," However, when one computes $\gamma^+ (\theta)$ and $\gamma^- (\theta)$ in an observational data set, one cannot directly view the intrinsic symmetry axes of the bright, central galaxies."864 Instead. one is forced to use their observed. svmmetry axes and. in general. these will düller from the intrinsic svmnmietry axes.," Instead, one is forced to use their observed symmetry axes and, in general, these will differ from the intrinsic symmetry axes."865 Our simulations show that. even in the limit of multiple dellections being experienced by the distant source galaxies. if one could. use the intrinsic symmetry axes of the lenses to define the geometry of the problem. one would. expect to observe 5.(0)c5(8).," Our simulations show that, even in the limit of multiple deflections being experienced by the distant source galaxies, if one could use the intrinsic symmetry axes of the lenses to define the geometry of the problem, one would expect to observe $\gamma^+ (\theta)866 > \gamma^- (\theta)$."867 That is. multiple dellections experienced by the source galaxies have little effect on the intrinsic signature of anisotropic galaxv-galaxy lensing by non-spherical haloes.," That is, multiple deflections experienced by the source galaxies have little effect on the intrinsic signature of anisotropic galaxy-galaxy lensing by non-spherical haloes."868 However. weak lensing of the bright. central foreground galaxies causes their observed symmetry axes (which are used to define the geometry for the calculation o£ 4.(6) and  (6)) to diller Crom their intrinsic svmmetryv axes (Le. the unlensed. svmmetry. axes. which deline the geometry for the actual lensine of the distant ealaxies).," However, weak lensing of the bright, central foreground galaxies causes their observed symmetry axes (which are used to define the geometry for the calculation of $\gamma^+ (\theta)$ and $\gamma^- (\theta)$ ) to differ from their intrinsic symmetry axes (i.e., the unlensed symmetry axes, which define the geometry for the actual lensing of the distant galaxies)."869 lt is this change in the svmmetry axes of the right. foreground galaxies that gives rise to the suppression of the observed. function. 5.(01(0). compared. to the unction that would be obtained if the intrinsic symmetry axes were used for the calculation.," It is this change in the symmetry axes of the bright, foreground galaxies that gives rise to the suppression of the observed function, $\gamma^+ (\theta) / \gamma^- (\theta)$, compared to the function that would be obtained if the intrinsic symmetry axes were used for the calculation."870 The effects. of weak ensing of the bright. foreground galaxies on an observation of 5(0)/5(8) cannot be eliminated. simply by. rejecting oreground galaxies with very small image ellipticities. or yw using sources that are particularly close to the observed symmetry axes of the foreground. galaxies.," The effects of weak lensing of the bright, foreground galaxies on an observation of $\gamma^+ (\theta) / \gamma^- (\theta)$ cannot be eliminated simply by rejecting foreground galaxies with very small image ellipticities, or by using sources that are particularly close to the observed symmetry axes of the foreground galaxies."871We conclude. therefore. that in order to. properly interpret any observed. galaxv-galaxy lensing signal (be it,"We conclude, therefore, that in order to properly interpret any observed galaxy-galaxy lensing signal (be it"872IL98).. aud have simulated the evolution of the Ser dSphli over several orbital periods (P. ~1 Cir). computing the orbit of the galaxy as well as the phase-space distribution of the debris under different assunuptious about the flattening of the CDAL halo.,", and have simulated the evolution of the Sgr dSph over several orbital periods (P $\sim 1$ Gyr), computing the orbit of the galaxy as well as the phase-space distribution of the debris under different assumptions about the flattening of the CDM halo."873 The initial conditious of the simulations were based on the known position and radial velocity of Ser dSph aud on its proper motion as estinated bv2001a)., The initial conditions of the simulations were based on the known position and radial velocity of Sgr dSph and on its proper motion as estimated by.874". The orbit has a planar rosette structure, with the pole of the orbit located at [f=907. b= 13°] (ic. a nearly polar orbit). aud peri- and apo-Galactic distances of 15kpc aud 6O0kpe respectively:"," The orbit has a planar rosette structure, with the pole of the orbit located at $\ell=90^\circ$, $b=-13^\circ$ ] (i.e. a nearly polar orbit), and peri- and apo-Galactic distances of $15\kpc$ and $60\kpc$ respectively."875 The derived orbit has been successfully compared with the observed position of the Ser Stream2001a.).. providing also remarkable incications that the dark halo of the Ailky Wav is nearly spherical.," The derived orbit has been successfully compared with the observed position of the Sgr Stream, providing also remarkable indications that the dark halo of the Milky Way is nearly spherical."876 Iu this framework it is a tantalizing application to look for other halo globulars that may be correlated with the orbital path of the Ser dwarf. aud which could be lying iu the Ser Stream.," In this framework it is a tantalizing application to look for other halo globulars that may be correlated with the orbital path of the Sgr dwarf, and which could be lying in the Sgr Stream."877 Iu particular. we look for the phase-space coincidence of outer halo globulus with the computed orbit of the Ser dSph from 1. Car ago up to the present dav. searchiug for the most receut episodes of globular cluster loss. Le. the ones whose traces are most likely to be still detectable.," In particular, we look for the phase-space coincidence of outer halo globulars with the computed orbit of the Sgr dSph from 1 Gyr ago up to the present day, searching for the most recent episodes of globular cluster loss, i.e. the ones whose traces are most likely to be still detectable."878 For our comparison we selected from the catalogue by the 35 elobular clusters in the range of ealactocentrie distance LOkpexReeLokpe.Among these. 33 have also measured racial velocity Vj.," For our comparison we selected from the catalogue by the 35 globular clusters in the range of galactocentric distance $10\kpc \le R_{GC}\le 40\kpc$.Among these, 33 have also measured radial velocity $V_r$."879 For sake of brevity and clarity we will call this sample the Outer Talo Sample (OIIS). in the following.," For sake of brevity and clarity we will call this sample the Outer Halo Sample (OHS), in the following."880 With this selection we avoid the ceutral part of the Calactic halo where it is less Likely that ordered structures can survive for a long time. and we leave out ofthe sample the παπαπα of clusters Iwine outside of Ree=GOlkpc. a region that lies hbevou the Ser Stream according to the IL98orbit.," With this selection we avoid the central part of the Galactic halo where it is less likely that ordered structures can survive for a long time, and we leave out of the sample the handful of clusters lying outside of $R_{GC}\ge 60\kpc$, a region that lies beyond the Sgr Stream according to the IL98."881. The adopte OUSglobidars. to avoid the detection of the obvious signal of their clustering aro the center of the Ser ealaxy.," The adopted OHS, to avoid the detection of the obvious signal of their clustering around the center of the Sgr galaxy."882 Iu Fieure Lowe show the ONS clusters (s1uall solic civcles) aud the Ser orbit iu the planes formedby the rectangular Galactoceutrie (N.Y.Z. in kpc) and in the Rees |kpe|] vs. Ἐν [suas aue.," In Figure 1 we show the OHS clusters (small solid circles) and the Sgr orbit in the planes formedby the rectangular Galactocentric $X,Y,Z$, in kpc) and in the $R_{GC}$ [kpc] vs. $V_r$ [km/s] plane."883 The large full circles are the known Ser elobulars. which we also show in the plots for completeness.," The large full circles are the known Sgr globulars, which we also show in the plots for completeness."884 Note that hese clusters lie around the eud ofthe orbit corresponding o the present time (f= 0)., Note that these clusters lie around the end of the orbit corresponding to the present time $t=0$ ).885 We lighlieht (with eucircled solid circles) six more clusters that lie remarkably close o the orbit in all the considered planes., We highlight (with encircled solid circles) six more clusters that lie remarkably close to the orbit in all the considered planes.886 These clusters are: Pal 122002).. NGC ULF. NGC 5631. NGC 5053. Pal 5 aud Ter 3.," These clusters are: Pal 12, NGC 4147, NGC 5634, NGC 5053, Pal 5 and Ter 3."887 Is this associationreel or could it be the uere occurrence of a chance aligumioenut?, Is this association or could it be the mere occurrence of a chance alignment?888 Though chauce alieumieuts in the four-dimensional phase space (N.Y.Z.V;.) are not expected to be very likely. the key point is to quantity the probability that the observed structure could have originated from a statistical fluctuation.," Though chance alignments in the four-dimensional phase space $V_r$ ) are not expected to be very likely, the key point is to quantify the probability that the observed structure could have originated from a statistical fluctuation."889 To do this we will compare the observed distribution - and its phase space distance to the Ser orbit - with svuthetic samples (having the same dimension as the OIIS) extracted from a 1nodoel represeutiug an uustructured parent halo., To do this we will compare the observed distribution - and its phase space distance to the Sgr orbit - with synthetic samples (having the same dimension as the OHS) extracted from a model representing an unstructured parent halo.890 The most conservative comparison that can be made is with a model that closely resembles the observed racial and velocity distribution of the OIIS., The most conservative comparison that can be made is with a model that closely resembles the observed radial and velocity distribution of the OHS.891" Figure 2 (upper panel) shows that the cumulative radial distribution of the OUS is well reproduced by a splierical halo model with a density distribution X8L5, ", Figure 2 (upper panel) shows that the cumulative radial distribution of the OHS is well reproduced by a spherical halo model with a density distribution $\propto R^{-1.6}$.892A Ἱκομποσοτον-Suurnov (ISS) test shows that the probability that the OMS is drawn from the ®xR1% inodel is ~90%., A Kolmogorov-Smirnov (KS) test shows that the probability that the OHS is drawn from the $\Phi \propto R^{-1.6}$ model is $\simeq 90$.893". Ou the other haud. the probability that the same sample is drawn from the other two models shown for comparison (bxRLU, and ὃνRO?) ds xἩ "," On the other hand, the probability that the same sample is drawn from the other two models shown for comparison $\Phi \propto R^{-1.0}$, and $\Phi894\propto R^{-2.5}$ ) is $\le 15$."895Doubts may be cast on the appropriateness of a spherical model., Doubts may be cast on the appropriateness of a spherical model.896 It may be conceived that if the parent halo is flattened. sole excess of clustering of the observed points along au orbit with low inclination may artificially enmierge iu the colparison with a spherical model.," It may be conceived that if the parent halo is flattened, some excess of clustering of the observed points along an orbit with low inclination may artificially emerge in the comparison with a spherical model."897 This is clearly not the case. however. since the IL98 orbit is ucarly polar. Le. it is almost perpendicular to the Calactic Plane (see Figure 1).," This is clearly not the case, however, since the IL98 orbit is nearly polar, i.e. it is almost perpendicular to the Galactic Plane (see Figure 1)."898" In the lower panel of Figure 2 it is shown that the observed distribution of radial velocity of the OIIS is well reproduced by a Caussian distribution with <Vo>=oSslas band ey=Ἱτοιςο,"," In the lower panel of Figure 2 it is shown that the observed distribution of radial velocity of the OHS is well reproduced by a Gaussian distribution with $<V_r> = -38\kms$ and $\sigma_V =899175\kms$."900 According to a WS test the probability that the observed sample is drawn from the model distribution is ~90.., According to a KS test the probability that the observed sample is drawn from the model distribution is $\simeq 90$.901 Iu the following simulations we extract all the svuthetic saluples frou a spherical and isotropic model with Φ(πος)xRec and with the Caussian distribution of radial velocitics shown in Figure 2.," In the following simulations we extract all the synthetic samples from a spherical and isotropic model with $\Phi(R_{GC}) \propto902R_{GC}^{-1.6}$ and with the Gaussian distribution of radial velocities shown in Figure 2."903" For each simulated cluster (as well as for all the OTIS ones) we computed he spatial distance from the nearest point in the Ser orbit (D.,4. iu kpc) aud the difference between their radial velocity and the oue predicted from the computed orbit at hat point (AV.=Vi.(tobs)|| Vi.(orb))."," For each simulated cluster (as well as for all the OHS ones) we computed the spatial distance from the nearest point in the Sgr orbit $D_{orb}$, in kpc) and the difference between their radial velocity and the one predicted from the computed orbit at that point $\Delta V_r = V_r(obs) - V_r(orb)$ )."904 Iu Figure 3. the Γον values of the selected clusters (large filled circles) are plotted against their AV...," In Figure 3, the $D_{orb}$ values of the selected clusters (large filled circles) are plotted against their $\Delta V_r$."905 The eucircled xnts are the six clusters highliehted in Figure 1., The encircled points are the six clusters highlighted in Figure 1.906 A sample of 10000 /svnuthetic clusters (dots) extracted from the adopted model is also shown. for comparison. iu the upper xuiel of Figure 3.," A sample of 10000 synthetic clusters (dots) extracted from the adopted model is also shown, for comparison, in the upper panel of Figure 3."907 The OIIS clusters show a remarkable over-deusitv toward the Ser orbit. that lies in the origiu of the axis in the cousidered plauc.," The OHS clusters show a remarkable over-density toward the Sgr orbit, that lies in the origin of the axis in the considered plane."908 The dashed dotted ines enclose the poiuts whose observed radial velocity is within Εθν+ of the velocity predicted by the ILOs orbit., The dashed dotted lines enclose the points whose observed radial velocity is within $\pm 60\kms$ of the velocity predicted by the IL98 orbit.909 Note that the expected velocity dispersion of tle Ser debris along the Ser Stream is σG0lnis |. according to (2001b3.," Note that the expected velocity dispersion of the Sgr debris along the Sgr Stream is $\sigma \sim 60\kms$ , according to ."910". The continuous vertical segments are placed at D,,4, =6. 12. aud Ls kpc."," The continuous vertical segments are placed at $D_{orb}= $ 6, 12, and 18 kpc."911 The lower panel of FigureOo 3 is arrangedC» in the same, The lower panel of Figure 3 is arranged in the same912These matrices are linked to spherical harmonics via where n; are the components of the radial unit vector m=(sindcoso.sin8Ó. 8). and the orthogonality relation is given by (see. c.e.. Maggiore 2008)).,"These matrices are linked to spherical harmonics via where $n_i$ are the components of the radial unit vector $\bmath{n}=(\sin\theta\cos\phi,\sin\theta\sin\phi,\cos\theta)$ , and the orthogonality relation is given by (see, e.g., \citealt{Mag}) )."913 For later use we mention two additional important relations., For later use we mention two additional important relations.914 Multiplving equation (2)) by n;nj. summing over i and j and inserting equation (3)). we obtain and inverting equation (3)) with the help of equation (4)) vields where the factor of 1/3 is fixed by the requirement that the left hand. side be traceless. since the coellicients c7; are given by οSEos," Multiplying equation \ref{eq:expan.sph.harm.}) ) by $n_in_j$, summing over $i$ and $j$ and inserting equation \ref{eq:sph.harm}) ), we obtain and inverting equation \ref{eq:sph.harm}) ) with the help of equation \ref{eq:orth.rel}) ) yields where the factor of 1/3 is fixed by the requirement that the left hand side be traceless, since the coefficients $c_{ij}^m$ are given by $c_{ij}^m=\frac{8\pi}{15}(\mathcal{Y}_{ij}^{2m})^*$."915" In order to derive the equation of motion for the internal velocity. field. of a star under the influence of. external gravitational waves. we start with the Pull field equations of general relativity and the Bianchi identities. which together imply the conservation equations of energy and momentum. where 27"" are the components of the stress-energvye tensor of the star under consideration."," In order to derive the equation of motion for the internal velocity field of a star under the influence of external gravitational waves, we start with the full field equations of general relativity and the Bianchi identities, which together imply the conservation equations of energy and momentum, where $T^{\mu\nu}$ are the components of the stress-energy tensor of the star under consideration."916 Ehe equation. of motion is obtained from the spatial components of equation G0) Since the centre of mass of the star. will move on a geodesic in spacetime. it proves useful to work in. Ferm normal coordinates with the origin at the centre of mass at all times.," The equation of motion is obtained from the spatial components of equation \ref{eq:EMC}) ): Since the centre of mass of the star will move on a geodesic in space–time, it proves useful to work in Fermi normal coordinates with the origin at the centre of mass at all times."917 In this reference frame where (0) denotes the centre of mass at time /., In this reference frame where $P(t)$ denotes the centre of mass at time $t$.918 Using these expressions one finds for the Riemann tensor Alternatively. within the framework of the linearized theory which we assume is valid here the Hiemann tensor is invariant. rather than just covariant. ancl thus can be evaluated in any preferred. frame.," Using these expressions one finds for the Riemann tensor Alternatively, within the framework of the linearized theory – which we assume is valid here – the Riemann tensor is invariant, rather than just covariant, and thus can be evaluated in any preferred frame."919 Consequently. choosing the PP frame for convenience one has from the linearized theory the following expression for the components {ιο of the Riemann tensor in terms of the metric: where fj; are the gravitational wave components of the metric in TP eauge.," Consequently, choosing the TT frame for convenience one has from the linearized theory the following expression for the components $R^i_{\phantom{i}0j0}$ of the Riemann tensor in terms of the metric: where $h_{ij}$ are the gravitational wave components of the metric in TT gauge."920 ]t is now assumed that the diameter d of the star is much smaller than the tvpical length scale A/27 over which the incident gravitational radiation changes substantially., It is now assumed that the diameter $d$ of the star is much smaller than the typical length scale $\lambda/2\pi$ over which the incident gravitational radiation changes substantially.921 Clearly. this is an assumption that in practice has to be checked case by case.," Clearly, this is an assumption that in practice has to be checked case by case."922 Due to the fact that under. this assumption the components /;; have essentially no spatial dependence over the volume of the star. we obtain the following relation which can be integrated to give Aloreover. we assume that the internal motions of the star are non-relativistic.," Due to the fact that under this assumption the components $h_{ij}$ have essentially no spatial dependence over the volume of the star, we obtain the following relation which can be integrated to give Moreover, we assume that the internal motions of the star are non-relativistic."923" In this Newtonian approximation. onlv """"27? terms need. be retained. on the right-hand.. side. of equationRn (8)) anc “pO:7 is givenR by2 puo7=pct.2 where. p isτ the equilibrium proper mass density of the star."," In this Newtonian approximation, only $T^{00}$ terms need be retained on the right-hand side of equation \ref{eq:EOM1}) ) and $T^{00}$ is given by $T^{00}=\rho c^2$, where $\rho$ is the equilibrium proper mass density of the star."924" Elentifving T""fe as the non-relativistic momentuni density given by pv. and 27 as the negative non-relativistic stress. tensor. TP!=a we arrive at where v with components ο denotes the internal velocity [field of the star."," Identifying $T^{0i}/c$ as the non-relativistic momentum density given by $\rho \bmath{v}$, and $T^{ij}$ as the negative non-relativistic stress tensor, $T^{ij}=-\sigma^{ij}$, we arrive at where $\bmath{v}$ with components $v_i$ denotes the internal velocity field of the star."925 For the reasons stated above in Section 1. the star is treatecl as an isotropic clastic sphere.," For the reasons stated above in Section 1, the star is treated as an isotropic elastic sphere."926 This requires pla)= por)., This requires $\rho(\bmath{x})=\rho(r)$ .927 Due to the external force exerted by the gravitational waves. an infinitesimal volume element of the clastic sphere centred. at position a will be displaced. according to a| ula.) where we assume the displacements to be sulliciently small such that the linear theory of elasticity is appropriato.," Due to the external force exerted by the gravitational waves, an infinitesimal volume element of the elastic sphere centred at position $\bmath{x}$ will be displaced according to $\bmath{x}+\bmath{u}(\bmath{x},t)$ , where we assume the displacements to be sufficiently small such that the linear theory of elasticity is appropriate."928" ‘To this approximation ancl neglecting self-stresses. caused by the intrinsic gravitational field. (see also the cliscussion in Section 4). the elastic stress tensor for isotropic mecia is eiven by where ij,=(1/2)(0n,|Ont) and A and ficare the usual Lamé cocllicicnts (Landau&Lifshitz1963)."," To this approximation and neglecting self-stresses caused by the intrinsic gravitational field (see also the discussion in Section 4), the elastic stress tensor for isotropic media is given by where $u_{lm}\equiv (1/2)(\partial_l u_m+\partial_m u_l)$ and $\lambda$ and $\mu$ are the usual Lamé coefficients \citep{LanLif}."929. Phe positive constants A. and. ye parametrize the viscous properties of the clastic sphere., The positive constants $\lambda'$ and $\mu'$ parametrize the viscous properties of the elastic sphere.930 Note that equation (10)) only holds in Forni normal coordinates., Note that equation \ref{eq:stress_ten}) ) only holds in Fermi normal coordinates.931 Since the velocity field ofa star is the easier measurable quantity than the cisplacements themselves. eg. by Doppler techniques. we dilferentiate equation (9)) with respect to time in order to obtain the equation of motion in terms of the velocity Geld: where f(x./). with components given by," Since the velocity field of a star is the easier measurable quantity than the displacements themselves, e.g. by Doppler techniques, we differentiate equation \ref{eq:EOM2}) ) with respect to time in order to obtain the equation of motion in terms of the velocity field: where $\bmath{f}(\bmath{x},t)$ , with components given by"932"These estimates are all the same order of magnitude, and suggest that the gas mass in the central arcsec is of order 4x105 MMo.","These estimates are all the same order of magnitude, and suggest that the gas mass in the central arcsec is of order $4\times10^6$ $_\odot$."933 Hence we can estimate the mean density to be (nj)=6x10? cem., Hence we can estimate the mean density to be $\langle n_{H_2}\rangle \gtrsim 6 \times10^3$ $^{-3}$.934 Comparing this to the cloud densities above yields volume filling factors in the range 1—0.01., Comparing this to the cloud densities above yields volume filling factors in the range 1–0.01.935" In this range, a lower filling factor is more physically plausible, which would tend to favour the solutions with higher cloud densities."," In this range, a lower filling factor is more physically plausible, which would tend to favour the solutions with higher cloud densities."936 Fig., Fig.937 2 shows these have either higher temperature or less extreme HCN abundance., \ref{fig:lvg} shows these have either higher temperature or less extreme HCN abundance.938 11068 and 66951 are two other galaxies for which the HCN(1-0)/CO(2-1) ratio has been measured on comparable 100 ppc scales., 1068 and 6951 are two other galaxies for which the HCN(1-0)/CO(2-1) ratio has been measured on comparable $\sim100$ pc scales.939" We use flux densities reported by Kripsetal.(2007) for the nuclear region (denoted ‘C’ in their Table 1) of 66951; and also the values for the circumnuclear disk of 11068, as the sum of the red and blue channels reported in Table 3 of Useroetal. (2004).."," We use flux densities reported by \cite{kri07} for the nuclear region (denoted `C' in their Table 1) of 6951; and also the values for the circumnuclear disk of 1068, as the sum of the red and blue channels reported in Table 3 of \cite{use04}. ."940" These yield line ratios (for line fluxes in ss!) of 0.37+0.05 and 0.214+0.002 respectively, and are denoted by the solid magenta lines on Fig. 2.."," These yield line ratios (for line fluxes in $^{-1}$ ) of $0.37\pm0.05$ and $0.214\pm0.002$ respectively, and are denoted by the solid magenta lines on Fig. \ref{fig:lvg}."941" These lines appear almost exclusively in the panels corresponding to the highest HCN abundance we have considered, Xycv/Xco=107."," These lines appear almost exclusively in the panels corresponding to the highest HCN abundance we have considered, $X_{HCN}/X_{CO}=10^{-2}$."942" In contrast to 33227, in which the line emission appears to be optically thick, the loci of the magenta lines for 11068 and NGC66951 are toward the optically thin (left) side of the panels."," In contrast to 3227, in which the line emission appears to be optically thick, the loci of the magenta lines for 1068 and 6951 are toward the optically thin (left) side of the panels."943" Despite this, it is notable that there are regions of the parameter space where the contours corresponding to all 3 objects lie close together, running from lower left to upper right."," Despite this, it is notable that there are regions of the parameter space where the contours corresponding to all 3 objects lie close together, running from lower left to upper right."944" The region extends from πμ,= lO0*'ccm? and Ny,/dV=1012 ?/(kmss!) to πμ,= 10°ccm™.", The region extends from $n_{H_2}=10^{4}$ $^{-3}$ and $N_{H_2}/dV=10^{19}$ $^{-2}$ $^{-1}$ ) to $n_{H_2}=10^{6}$ $^{-3}$.945 It is precisely because one can attribute the observed line ratios — with different optical depths for the 3 galaxies — to similar physical properties of the gas in all these 3 objects that this locus is appealing., It is precisely because one can attribute the observed line ratios – with different optical depths for the 3 galaxies – to similar physical properties of the gas in all these 3 objects that this locus is appealing.946 Why this occurs can be seen in Fig., Why this occurs can be seen in Fig.947 2 which shows the optical depths 7 for the HCN(1-0) and CO(2-1) transitions., \ref{fig:tau} which shows the optical depths $\tau$ for the HCN(1-0) and CO(2-1) transitions.948 The gas properties of both these panels correspond to the bottom left panel in Fig., The gas properties of both these panels correspond to the bottom left panel in Fig.949" 2 (300KK and Xycn/Xco= 10:32), and cover the same range of density and velocity gradient."," \ref{fig:lvg} K and $X_{HCN}/X_{CO}=10^{-2}$ ), and cover the same range of density and velocity gradient."950" These plots show clearly the characterisation of the different regions: in the lower half the HCN(1-0) line is optically thick because the density is low enough that it is sub-thermal; above the critical density, the line is in LTE and thus optically thin at low columns and optically thick at high columns."," These plots show clearly the characterisation of the different regions: in the lower half the HCN(1-0) line is optically thick because the density is low enough that it is sub-thermal; above the critical density, the line is in LTE and thus optically thin at low columns and optically thick at high columns."951 The locus where all the contours for the 3 galaxies are close together and parallel follows approximately the boundary where the HCN(1-0) line becomes optically thick., The locus where all the contours for the 3 galaxies are close together and parallel follows approximately the boundary where the HCN(1-0) line becomes optically thick.952" Here, a small change in physical conditions (column or density) can result in the HCN(1-0) emission switching from optically thin to optically thick."," Here, a small change in physical conditions (column or density) can result in the HCN(1-0) emission switching from optically thin to optically thick."953" This regime is, however, also associated with very large velocity gradients."," This regime is, however, also associated with very large velocity gradients."954" It is dV/dr~ lO0*kkmss! ppc! at T=30K, but reduces as the temperature increases."," It is $dV/dr\sim10^4$ $^{-1}$ $^{-1}$ at $T=30\,K$, but reduces as the temperature increases."955 Velocity gradients were not discussed explicitly by Sternbergetal. or Useroetal.(2004) in their T= 50KK LVG calculations for 11068., Velocity gradients were not discussed explicitly by \cite{ste94} or \cite{use04} in their $T=50$ K LVG calculations for 1068.956 But their analyses also associate the observed properties with similarly extreme velocity gradients., But their analyses also associate the observed properties with similarly extreme velocity gradients.957" Indeed, one of the main conclusions of Sternbergetal.(1994) was that Xycw/Xcoz107 in NGC1068."," Indeed, one of the main conclusions of \cite{ste94} was that $X_{HCN}/X_{CO} \gtrsim 10^{-2}$ in NGC1068."958" For the temperature they considered, this would lead to dV/dr~ 10*kkmss'! ppc! (matching the top left panel of Fig."," For the temperature they considered, this would lead to $dV/dr\sim10^4$ $^{-1}$ $^{-1}$ (matching the top left panel of Fig."959 2 here)., \ref{fig:lvg} here).960" However, our LVG calculations shows that dV/dr is reduced as both the temperature and density increase."," However, our LVG calculations shows that $dV/dr$ is reduced as both the temperature and density increase."961" When considering all 3 galaxies together, the smallest — and therefore arguably the most physically plausible value in the parameter space we have covered is dV/dr~ ss“! ppc! at T= 300KK and ny,~105? ccm."," When considering all 3 galaxies together, the smallest – and therefore arguably the most physically plausible -- value in the parameter space we have covered is $dV/dr\sim100$ $^{-1}$ $^{-1}$ at $T=300$ K and $n_{H_2}\sim10^{5.5}$ $^{-3}$."962" This 100kkmlocation is not far from the boundary of the optically thick LTE regime discussed previously, but due to the high velocity gradient represents clouds that are either pressureconfined or unbound."," This location is not far from the boundary of the optically thick LTE regime discussed previously, but due to the high velocity gradient represents clouds that are either pressureconfined or unbound."963" Interestingly, there is evidence in 11068 from recent Herschel observations with PACS of high rotational CO transitions, for a significant mass of molecular gas in the central ~100 ppc at temperatures of KK and KK and densities of ~109? ccm? (Hailey-Dunsheathetal., 2011).."," Interestingly, there is evidence in 1068 from recent Herschel observations with PACS of high rotational CO transitions, for a significant mass of molecular gas in the central $\sim100$ pc at temperatures of K and K and densities of $\sim10^{6.5}$ $^{-3}$ \citep{hai11}. ."964" Similarly, in"," Similarly, in"965 clusters appear to be less cuspy than expected. which jas prompted theoretical work m alternative dark matter uodels (see discussion in Covernato et al.," clusters appear to be less cuspy than expected, which has prompted theoretical work in alternative dark matter models (see discussion in Governato et al."966 2001)., 2001).967 The dark matter deusitv profile has vet to be measured or galaxw groups., The dark matter density profile has yet to be measured for galaxy groups.968 Dynamical studies of eroups are difficult because kinematic iuforiunation is kuown for very ew. ealaxies. aud because equilibrimim assumptions nieht iof be valid.," Dynamical studies of groups are difficult because kinematic information is known for very few galaxies, and because equilibrium assumptions might not be valid."969 Furthermore. these difficulties merease at aree radi from the eroup ceuter.," Furthermore, these difficulties increase at large radii from the group center."970 Weak gravitational chasing has proven invaluable iu the analysis of sinele nassive objects such as galaxy clusters (IHockstra ct al., Weak gravitational lensing has proven invaluable in the analysis of single massive objects such as galaxy clusters (Hoekstra et al.971 1998: Mellier 1999) as well as in the statistical studies of individual galaxies (Brainerd. Blandford σπα]. 1996: Tidson et al.," 1998; Mellier 1999) as well as in the statistical studies of individual galaxies (Brainerd, Blandford Smail, 1996; Hudson et al."972 1998: Fischer et al., 1998; Fischer et al.973 2000: Sheldon et al., 2000; Sheldon et al.974 2001: Tloekstra et al., 2001; Hoekstra et al.975 2001)., 2004).976 To date there has been oulv one weak lensing measurcient of ealaxy groups (Iloeckstra οἳ al., To date there has been only one weak lensing measurement of galaxy groups (Hoekstra et al.977 2001) using a small subsiuple of the total CNOC?2 ealaxy eroup catalog., 2001) using a small subsample of the total CNOC2 galaxy group catalog.978 Asstuning that the dark matter halos of eroups are well described by an isothermal sphere. we expect a taugeutial shear signal as follows where 7 is the velocity dispersion of the halo. aud Da and Ds are the augular diaueter distances to the source and between leus aud source. respectively.," Assuming that the dark matter halos of groups are well described by an isothermal sphere, we expect a tangential shear signal as follows where $\sigma$ is the velocity dispersion of the halo, and $_S$ and $_{LS}$ are the angular diameter distances to the source and between lens and source, respectively."979 The intent of this paper is to present the results of our weak lensing studv of CNOC2 ealaxy groups. aud to compare these results with those found from the dynamical measurements (Carlbere et al., The intent of this paper is to present the results of our weak lensing study of CNOC2 galaxy groups and to compare these results with those found from the dynamical measurements (Carlberg et al.980 2001) aud the, 2001) and the981the spatial profile in order to obtain the maximum signal-to-noise ratio (llorne 1986): wavelength calibration was performed. using the MOLLY package.,the spatial profile in order to obtain the maximum signal-to-noise ratio (Horne 1986); wavelength calibration was performed using the MOLLY package.982 The ΗΝ Al-Sky Monitor. (ASAL) has been operating more or less Continuously since 1996 February 21. providing roughly five to ten scans of a given source per day in the 2-12 keV energy range.," The $RXTE$ All-Sky Monitor (ASM) has been operating more or less continuously since 1996 February 21, providing roughly five to ten scans of a given source per day in the 2-12 keV energy range."983 We obtained the one-day. average X-rav data for λα X1 from the public archive maintained bv the AXTE Guest Observers Facility., We obtained the one-day average X-ray data for Aql X–1 from the public archive maintained by the $RXTE$ Guest Observers Facility.984 For further details about the instrument and the methods used in the ASAL data reduction and error caleulations. see Levine (1996).," For further details about the instrument and the methods used in the ASM data reduction and error calculations, see Levine (1996)."985 The distance to Aql X.1 can be derived using the apparent A-band magnitude and the surface. brightnes Sy of the companion star (Bailey 1981)., The distance to Aql X–1 can be derived using the apparent $K$ -band magnitude and the surface brightnes $S_{K}$ of the companion star (Bailey 1981).986 Using V —19.2 (Thorstensen et al., Using $V$ =19.2 (Thorstensen et al.987 LOTS) and allowing for an accretion disc Contamination in the range 050 per cent ancl reddening of Lp4: 0.35 mags (Shahbaz et al., 1978) and allowing for an accretion disc contamination in the range 0–50 per cent and reddening of $E_{B-V}$ =0.35 mags (Shahbaz et al.988" 1996). we obtain V, in the range 18.1"," 1996), we obtain $V_{o}$ in the range 18.1--18.9."989" Using our ΕΙΝ A-band magnitude of A —15.9 (section 2.1.2) and assuming no disc contamination in the IR. (the clise contamination at iis only 6 per cent: Shahbaz. Casares Charles 1997). we [lind A,-—15.8."," Using our UKIRT $K$ -band magnitude of $K$ =15.9 (section 2.1.2) and assuming no disc contamination in the IR (the disc contamination at is only 6 per cent: Shahbaz, Casares Charles 1997) we find $K_{o}$ =15.8."990" Given the limits for the intrinsic colour of the secondary star and its surface brigthnes. (VA ),-2.303.05 and Sy 23.58.3.83 respectively (Ramsever 1994). and using a secondary star mass of 0.15 (by comparison with Con X.4: Shahbaz. Navlor Charles 1997). we find distance values of 2.22.4 kpe (note that the range quoted is due to the uncertainty in the disc contamination in the Y -band)."," Given the limits for the intrinsic colour of the secondary star and its surface brigthnes, $(V-K)_{o}$ =2.30--3.05 and $S_{K}$ =3.58–3.83 respectively (Ramseyer 1994), and using a secondary star mass of 0.15 (by comparison with Cen X–4; Shahbaz, Naylor Charles 1997), we find distance values of 2.2–2.4 kpc (note that the range quoted is due to the uncertainty in the disc contamination in the $V$ -band)."991 We conclude that the clistanee to Aql N.1 is 2.30.1 kpe. which is consistent with the previous distance estimate of 2.5 kpe (Charles et al.," We conclude that the distance to Aql X–1 is $\pm$ 0.1 kpc, which is consistent with the previous distance estimate of 2.5 kpc (Charles et al."992 1980)., 1980).993 Figure 1 shows the optical outburst spectrum of Aql X.1. which exhibits emission. features of Ho (EW=5.040.5A)). Ilo) (EW=2.S+0.5A)). Le (EWS4.240.5A)). He 46SG6A(EW=S=3.3404A)) and. the Bowen blend —2.040.3A)).," Figure 1 shows the optical outburst spectrum of Aql X–1, which exhibits emission features of $\alpha$ $\pm$ ), $\beta$ $\pm$ ), $\gamma$ $\pm$ ), $\sc ii$ $\pm$ ) and the Bowen blend $\pm$ )."994 There is also some evidence for an itflow in the system. presumably arising from an accretion ise wind. as the 11 emission line has a P-Cvegni type profile. where the blue side of the line profile is absorbed.," There is also some evidence for an outflow in the system, presumably arising from an accretion disc wind, as the $\beta$ emission line has a P-Cygni type profile, where the blue side of the line profile is absorbed."995 Finally. the emission. lines are. single-peaked. sugeesting alt the binary inclination is low.," Finally, the emission lines are single-peaked, suggesting that the binary inclination is low."996 The August X-ray outburst light curve of Λα X1 has three distinct sections (see Fig 2)., The August X-ray outburst light curve of Aql X–1 has three distinct sections (see Fig 2).997 Initially. the X-rays are constant while the source is quiescent.," Initially, the X-rays are constant while the source is quiescent."998 The X-rays then rise linearly to maximum: the subsequent decay is also linear., The X-rays then rise linearly to maximum; the subsequent decay is also linear.999 Phe three boundaries on the curve are the time of the initial rise. the time of maximum. and the end of the decay.," The three boundaries on the curve are the time of the initial rise, the time of maximum, and the end of the decay."1000 Using these three boundaries. we simultaneously fitted the data with a three component model: the resultant. parameters are given in Table 2.," Using these three boundaries, we simultaneously fitted the data with a three component model; the resultant parameters are given in Table 2."1001 The secondary. maximum feature present. ~22 days after the outburst is also seen in other SNTs (Chen. Shrader. Livio 1997) and was removed from the fitting procedure.," The secondary maximum feature present $\sim$ 22 days after the outburst is also seen in other SXTs (Chen, Shrader, Livio 1997) and was removed from the fitting procedure."1002 AX detailed. discussion of the secondary. maxima will be presented in Shahbaz. Charles Ixing (19958).," A detailed discussion of the secondary maxima will be presented in Shahbaz, Charles King (1998)."1003 The V- ancl D-band light curves of Aql X1 display three distinct phases (see Fig 2)., The $V$ - and $B$ -band light curves of Aql X–1 display three distinct phases (see Fig 2).1004 At first. the optical [lux rises linearly.," At first, the optical flux rises linearly."1005 Llowever. instead of peaking at X-ray maximum. the V and 2 light curves Hatten when the X-rays have reached slightly less than half of the maximum intensity.," However, instead of peaking at X-ray maximum, the $V$ and $B$ light curves flatten when the X-rays have reached slightly less than half of the maximum intensity."1006 The optical light curve remains in this plateau state until just after the secondary maximum in the X-ray decay (Shahbaz. Charles Wing 1998). at which point both V and 2 begin a linear decay.," The optical light curve remains in this plateau state until just after the secondary maximum in the X-ray decay (Shahbaz, Charles King 1998), at which point both $V$ and $B$ begin a linear decay."1007 By simultaneously fitting the optical light curves with the three-part N-ray. model described above. we determine the slopes of the linear rise and decay. and also the start and end of the plateau region.," By simultaneously fitting the optical light curves with the three-part X-ray model described above, we determine the slopes of the linear rise and decay, and also the start and end of the plateau region."1008 The four C-band observations also show a linear rise similar to that seen in the 2 and V. light curves., The four$U$ -band observations also show a linear rise similar to that seen in the $B$ and $V$ light curves.1009 A2 and £ measurements were also obtained: the (Rt relative magnitudes are given in Table 2., $R$ and $I$ measurements were also obtained; the $URI$ relative magnitudes are given in Table 2.1010 After an initial period of quiescent observations. the A- band light curve shows a linear rise and then a decrease in flux which mayor may not be associated with the decay.," After an initial period of quiescent observations, the $K$ -band light curve shows a linear rise and then a decrease in flux which mayor may not be associated with the decay."1011 We only fit the initial rise of the light curve and determine the slopeand start of the rise., We only fit the initial rise of the light curve and determine the slopeand start of the rise.1012 Lt is interesting to note that the rate of the increase in brightness is largest in V and smallest in A., It is interesting to note that the rate of the increase in brightness is largest in $V$ and smallest in $K$.1013 However. since the time coverage is sparse. there is some uncertainty in this conclusion.," However, since the time coverage is sparse, there is some uncertainty in this conclusion."1014 The fit. parameters determined for the V. D. A. and. X-ray light. curves are listed in Table 2.," The fit parameters determined for the $V$ , $B$ , $K$ , and X-ray light curves are listed in Table 2."1015imposed the redshift eut 0.8<2«0.9 in order to remove the als of the redshift distribution which contain relatively [ow ealaxies.,"imposed the redshift cut $0.3 < z1016< 0.9$ in order to remove the tails of the redshift distribution which contain relatively few galaxies."1017 A total of N=56.159 ealaxy redshifts remained.," A total of $N = 56{,}159$ galaxy redshifts remained."1018 We then split the sample into three redshilt slices 5.0.5«z0.7 and 0.7«z 0.9. We determined the effective redshift) zr of our. power spectrum estimate in each redshift slice by weighting each pixel in our 3D selection function by its contribution to the IOWOL spectrum οτο: where nyGF)=CNUNAMIVGE) is the galaxy number density in each grid. cell and P(A) is the power spectrum amplitude.," We then split the sample into three redshift slices $0.3 < z < 0.5$ , $0.5 < z < 0.7$ and $0.7 < z < 0.9$ We determined the effective redshift $z_{\rm eff}$ of our power spectrum estimate in each redshift slice by weighting each pixel in our 3D selection function by its contribution to the power spectrum error: where $n_g(\vec{x}) = (N_c N / V) W(\vec{x})$ is the galaxy number density in each grid cell and $P(k)$ is the power spectrum amplitude."1019 In each case we used the best-litting model power spectrum determined below., In each case we used the best-fitting model power spectrum determined below.1020 We evaluated this function at Kk=0455h *. although the dependence on scale. is weak.," We evaluated this function at $k = 0.15 \, h$ $^{-1}$, although the dependence on scale is weak."1021 The cllective redshifts of cach slice determined using equation ΕΕ are zr=(0.42.0.59.0.78).," The effective redshifts of each slice determined using equation \ref{eqzeff} are $z_{\rm eff} =1022(0.42, 0.59, 0.78)$."1023 We analyzed the three WigeleZ survey regions independently. resulting in a total of nine power spectrum measurements.," We analyzed the three WiggleZ survey regions independently, resulting in a total of nine power spectrum measurements."1024 We estimated the power spectrum up to a maximum Fourier wavescale A44=0O4f + assuming he value 2)=25005? Alpe? for the weighting factor in Equation 9..," We estimated the power spectrum up to a maximum Fourier wavescale $k_{\rm max} = 0.4 \,1025h$ $^{-1}$, assuming the value $P_0 = 2500 \, h^{-3}$ $^3$ for the weighting factor in Equation \ref{eqweight}. ."1026 This choice is motivated. by our final measurement of the power spectrum amplitude: presented low on scales &2O.15h 5. but. does. not. have a strong influence on our results given that with the survey partially complete the measurements are. limited o» shot noise on most scales.," This choice is motivated by our final measurement of the power spectrum amplitude presented below on scales $k \approx 0.15 \, h$ $^{-1}$, but does not have a strong influence on our results given that with the survey partially complete the measurements are limited by shot noise on most scales."1027" Representative values [ου he other parameters in Section 3.1. are (LL.(600.600.300)A+ Alpe. (n,.nj.n;)=(256.256.128). L.)V.=Vib? Gpet and mg=5«1075? Ape7."," Representative values for the other parameters in Section \ref{secfkp} are $(L_x,L_y,L_z) = (600,600,300) \, h^{-1}$ Mpc, $(n_x,n_y,n_z) = (256,256,128)$, $V = 0.1 \, h^{-3}$ $^3$ and $n_01028= 5 \times 10^{-5} \, h^3$ $^{-3}$."1029 We combined he Fourier amplitudes in angle-averaged bins of width Af=LOLA Ape+.," We combined the Fourier amplitudes in angle-averaged bins of width $\Delta k = 0.01 \, h$ $^{-1}$."1030 The nine power spectrum measurements are plotted in Figure 15. together with a power spectrum mocel derived using a “standard” set of cosmological parameters together with a prescription for redshift-space distortions., The nine power spectrum measurements are plotted in Figure \ref{figpkreg} together with a power spectrum model derived using a “standard” set of cosmological parameters together with a prescription for redshift-space distortions.1031 Ehe details of this model are. described below in Section. 4.1.., The details of this model are described below in Section \ref{secpkmod}.1032 The dashed: and. solid lines illustrate the input. model. and. the model convolved with the selection function for each region. respectively.," The dashed and solid lines illustrate the input model, and the model convolved with the selection function for each region, respectively."1033 The model provides an acceptable statistical fit to the measured power spectrum in each case., The model provides an acceptable statistical fit to the measured power spectrum in each case.1034 The corresponding nine covariance matrices C; are plotted in Figure 160 as à correlation coellicient Figure 16. demonstrates that the amplitude of the oll-diagonal elements of the covariance matrices is small (note the choice of grevscale range)., The corresponding nine covariance matrices $C_{ij}$ are plotted in Figure \ref{figcov} as a correlation coefficient Figure \ref{figcov} demonstrates that the amplitude of the off-diagonal elements of the covariance matrices is small (note the choice of greyscale range).1035 We also measured. power spectra in wavevector bins GossApu) perpendicular and. parallel to the line-of-sight. respectively (we now use Fourier bins of width AA=0.02/ + in each direction to increase the signal-to-noise ratio in cach bin).," We also measured power spectra in wavevector bins $(k_{\rm perp},1036k_{\rm par})$ perpendicular and parallel to the line-of-sight, respectively (we now use Fourier bins of width $\Delta k = 0.02 \, h$ $^{-1}$ in each direction to increase the signal-to-noise ratio in each bin)."1037 Εις 2D power spectrum allows us to recover the redshift-space distortion parameters which produce an anisotropic galaxy power spectrum., This 2D power spectrum allows us to recover the redshift-space distortion parameters which produce an anisotropic galaxy power spectrum.1038 Since in our analysis we orient the .r-axis parallel to the line-of-xsight to the centre of cach survey region. we make the flat-sky approximation IepermEsdAS. uu=|e] in. this. analysis.," Since in our analysis we orient the $x$ -axis parallel to the line-of-sight to the centre of each survey region, we make the flat-sky approximation $k_{\rm perp} = \sqrt{k_y^2 + k_z^2}$, $k_{\rm par} = |k_x|$ in this analysis."1039. We investigated. the dependence. of our power spectrum measurement on potential systematic errors in the survey selection function., We investigated the dependence of our power spectrum measurement on potential systematic errors in the survey selection function.1040 In order to do this we reconstructed four cillerent selection functions for the 9-hr region. analvzing the full redshift range 0.3<z«0.9. with (extreme) variations in the method: In Figure 17 we plot the difference between the resulting power spectra measured. for these four. cllferent selection functions and the fiducial power spectrum. in units of the standard. deviation. of the measurement at each scale.," In order to do this we re-constructed four different selection functions for the 9-hr region, analyzing the full redshift range $0.3 < z <10410.9$, with (extreme) variations in the method: In Figure \ref{figpksys} we plot the difference between the resulting power spectra measured for these four different selection functions and the fiducial power spectrum, in units of the standard deviation of the measurement at each scale."1042 We note that these (extreme) variations in our understancing of the selection function typically cause up to & O5-0 shifts in the power spectrum estimate., We note that these (extreme) variations in our understanding of the selection function typically cause up to $\approx 0.5$ $\sigma$ shifts in the power spectrum estimate.1043 The exception is the parameterization of the. redshif distribution. which causes large deviations in the very larec-scale (&<0.035 +) power spectrum.," The exception is the parameterization of the redshift distribution, which causes large deviations in the very large-scale $k < 0.03 \, h$ $^{-1}$ ) power spectrum."1044 For the example being studied. we noted that the Oth-orcer polynomial Lit was in [act providing a poorer match than the double Gaussian function to the observed: recshilt distributions. causing a spurious increase in nieasured large-scale power.," For the example being studied, we noted that the 9th-order polynomial fit was in fact providing a poorer match than the double Gaussian function to the observed redshift distributions, causing a spurious increase in measured large-scale power."1045 We conclude that our. power spectrum. measurements are likely to be robust. against reasonable svstematic variations in the selection function. methodology., We conclude that our power spectrum measurements are likely to be robust against reasonable systematic variations in the selection function methodology.1046 The selection function. in Fourier space is compact ancl the corrections are onlv significant on the largest scales., The selection function in Fourier space is compact and the corrections are only significant on the largest scales.1047 In this Section we present some initial comparisons between our power spectrum measurements and cosmological models., In this Section we present some initial comparisons between our power spectrum measurements and cosmological models.1048Our aim is to establish whether or not our measurenients areconsistent with the preclictions of the standard ACDAL framework with parameters determined. by observations of the Cosmic Alicrowave Background radiation.,Our aim is to establish whether or not our measurements areconsistent with the predictions of the standard $\Lambda$ CDM framework with parameters determined by observations of the Cosmic Microwave Background radiation.1049 Future papers will perform a more comprehensive analysis., Future papers will perform a more comprehensive analysis.1050" We derived model matter power spectra A,(&) as a function", We derived model matter power spectra $P_{\rm m}(k)$ as a function1051"With the aim of quantifying the orientation-dependence of the observed properties of quasars, we have embarked on multi-wavelength observations of high-redshift (1<z< 2) radio sources withChandra,Herschel and ground-based observatories.","With the aim of quantifying the orientation-dependence of the observed properties of quasars, we have embarked on multi-wavelength observations of high-redshift $\leq z \leq $ 2) radio sources with, and ground-based observatories."1052" Given the known orientation dependence of the emission from quasars and active galactic nuclei (AGN) and the resulting strong selection bias against obscured/edge-on sources, isotropic, low-frequency radio emission provides a rare, unbiased view of the population based on optically thin emission far from the nucleus lobe-selection)."," Given the known orientation dependence of the emission from quasars and active galactic nuclei (AGN) and the resulting strong selection bias against obscured/edge-on sources, isotropic, low-frequency radio emission provides a rare, unbiased view of the population based on optically thin emission far from the nucleus lobe-selection)."1053 We chose high-redshift 3CR (selected at 178 MHz) sources to ensure the sample is largely unbiased and that it comprises powerful radio galaxies and quasars., We chose high-redshift 3CR (selected at 178 MHz) sources to ensure the sample is largely unbiased and that it comprises powerful radio galaxies and quasars.1054" Studies of high-redshift, radio-loud quasars also facilitate more lines of investigation: emission related to radio structure at high-redshift, and thus the interaction of the quasar with its environment, and searches for high-redshift clusters of galaxies."," Studies of high-redshift, radio-loud quasars also facilitate more lines of investigation: X-ray emission related to radio structure at high-redshift, and thus the interaction of the quasar with its environment, and searches for high-redshift clusters of galaxies."1055 X-ray emission is often observed from radio-emitting hotspots and lobes in quasars., X-ray emission is often observed from radio-emitting hotspots and lobes in quasars.1056" It is generally interpreted (??) in terms of direct synchrotron emission from high-energy electrons, inverse-Compton (iC) emission due to up-scattering of radio photons within the radio hotspots (synchrotron self-Compton (SSC), ?)), or inverse-Compton (iC) up-scattering of external radio photons in the extended lobes, most likely from the Cosmic Microwave Background (1C/CMB, ?))."," It is generally interpreted \citep{2002ApJ...565..244H, 10572009A&ARv..17....1W}1058 in terms of direct synchrotron emission from high-energy electrons, inverse-Compton (iC) emission due to up-scattering of radio photons within the radio hotspots (synchrotron self-Compton (SSC), \citet{2004ApJ...612..729H}) ), or inverse-Compton (iC) up-scattering of external radio photons in the extended lobes, most likely from the Cosmic Microwave Background (iC/CMB, \citet{2005ApJ...626..733C}) )."1059 The latter will be more luminous for larger radio-emitting structures and at higher redshift due to the higher energy density of the CMB., The latter will be more luminous for larger radio-emitting structures and at higher redshift due to the higher energy density of the CMB.1060" Luminous high-redshift radio sources occur in massive galaxies and so, according to the hierarchical paradigm, form at peaks in the dark matter density."," Luminous high-redshift radio sources occur in massive galaxies and so, according to the hierarchical paradigm, form at peaks in the dark matter density."1061" Thus they are beacons for high density regions in the early universe and for high-redshift clusters and groups, very few of which are yet known."," Thus they are beacons for high density regions in the early universe and for high-redshift clusters and groups, very few of which are yet known."1062 Finding clusters at these high redshifts is key to the study of both cluster and galaxy formation and will provide critical constraints on theoretical models for cluster and galaxy evolution (???) and the mass distribution of dark matter halos (?)..," Finding clusters at these high redshifts is key to the study of both cluster and galaxy formation and will provide critical constraints on theoretical models for cluster and galaxy evolution \citep{2011MNRAS.tmp...73A,2010ApJ...718..133H,2007A&A...461..823V} and the mass distribution of dark matter halos \citep{2007MNRAS.374.1303C}."1063" The radio-loud quasar 2270.1 (z=1.532) has the double-lobed radio structure characteristic of FR-II (?) radio sources and the strong, broad emission lines of a type 1 quasar."," The radio-loud quasar 270.1 $z$ =1.532) has the double-lobed radio structure characteristic of FR-II \citep{1974MNRAS.167P..31F}1064 radio sources and the strong, broad emission lines of a type 1 quasar."1065 Optical and infrared (IR) data show an excess of galaxies within ~640 kpc (1.33) of the quasar suggesting a surrounding cluster of galaxies (?).., Optical and infrared (IR) data show an excess of galaxies within $\sim 640$ kpc 3) of the quasar suggesting a surrounding cluster of galaxies \citep{2009ApJ...695..724H}.1066" The sky distribution of the cluster galaxy candidates forms a loose concentration centered ~20"" east", The sky distribution of the cluster galaxy candidates forms a loose concentration centered $\sim 20 \arcsec$ east1067and the required suprenimun over partitions is effected.,and the required supremum over partitions is effected.1068 Iu fact. these fiuite-ion. finite-time eutropies.behavior with respect to the systeni parameters are in our view the most significant pliysical quantities.," In fact, these finite-partition, finite-time entropies, with respect to the system parameters are in our view the most significant physical quantities."1069 The ummerical probk310 of computing the quantity 9(4) for svstcms with a finite dimensional Hilbert space has been discussed in [10].., The numerical problem of computing the quantity $S(J)$ for systems with a finite dimensional Hilbert space has been discussed in \cite{etna}.1070 Oue consider a differeut matrix. also iutroduced by ΑΕ. with the same spectral properties as D. but with a size that is independent of the word leusth J.," One consider a different matrix, also introduced by A-F, with the same spectral properties as $D$, but with a size that is independent of the word length $J$."1071 Relvine ou the properties of this latter matrix. derived in [LO].. a general purpose parallel code has been designed aud will be emploved iu this paper.," Relying on the properties of this latter matrix, derived in \cite{etna}, a general purpose parallel code has been designed and will be employed in this paper."1072 Let us now cousider a partition of classical phasespace in four equal cells of rectangular shape. defined by letting the position of the large particle. Q. belong to the sets [hyL(k|1)/4).," Let us now consider a partition of classical phase–space in four equal cells of rectangular shape, defined by letting the position of the large particle, $Q$, belong to the sets $[k/4,(k+1)/4)$."1073 In these cells the momentum 2? of the large particle and the coordinates (positions and momenta) of the small ones take on all the allowed values., In these cells the momentum $P$ of the large particle and the coordinates (positions and momenta) of the small ones take on all the allowed values.1074 This partition cau be easily ecneralized. but there is no ποσα to do that in the preseut context.," This partition can be easily generalized, but there is no need to do that in the present context."1075 Caven this partition. when only the large particle is present. classical theory provides us with INXS eutropy of the Arnold cat map.," Given this partition, when only the large particle is present, classical theory provides us with KS entropy of the Arnol'd cat map."1076 Correspouding to each partition coll. we cau define a projection operator in the Illbert space of the svstem. whose formi is trivially simple when the wavefunction WV is written in the position representation.," Corresponding to each partition cell, we can define a projection operator in the Hilbert space of the system, whose form is trivially simple when the wave–function $\Psi$ is written in the position representation."1077 We can therefore compute the S-A-F eutpies SCJ)., We can therefore compute the S-A-F entropies $S(J)$.1078" Let us start from the singleparticle case. that has already. been described iu |l| and. just for the linear eutropy. a quantity that cau be computed more casily than Shannon's. im 101, Iu."," Let us start from the single–particle case, that has already been described in \cite{etna} and, just for the linear entropy, a quantity that can be computed more easily than Shannon's, in \cite{alimoni}."1079 Fie., In Fig.1080 l1 woe plot these functions for increasing values of jV., \ref{fig-incdim} we plot these functions for increasing values of $N$.1081 We observe that as NV increases. the linear behavior (aud the numerical values) of the classical cat is approached. for a region in J of imereasing size.," We observe that as $N$ increases, the linear behavior (and the numerical values) of the classical cat is approached, for a region in $J$ of increasing size."1082 This region terminates as soon as the linear increase of S(C7) is hampered by the finiteness of Wilbert space. via the bound SCJ)x2loet.A.," This region terminates as soon as the linear increase of $S(J)$ is hampered by the finiteness of Hilbert space, via the bound $S(J) \leq 2 \log({\cal N})$."1083 Here. AX=N.," Here, ${\cal N} = N$."1084 This bounds translates ou the one side the imuniual size of phasespace cells iuplied by quantization aud ou the other side the finite amount of algorithiuic information coutent of the quantum notio-, This bounds translates on the one side the minimal size of phase–space cells implied by quantization and on the other side the finite amount of algorithmic information content of the quantum motion.1085 Therefore. fig.," Therefore, fig."1086 1l is]st another mathematical confirmation of the thesis of ref., \ref{fig-incdim} is just another mathematical confirmation of the thesis of ref.1087 [5] (see also [7]., \cite{physd} (see also \cite{viva}) ).1088 It is there pretended that the correspoudence principle is plvsically irelevaut for this svstem. on the basis of the simple observation that to achieve a lineariawcrease of the time-lag of chaotic behavior (the regiou with information produclon. increasiug 9()). anecponential crease of N (aud therefore of the uass AL. which is proportional to the former. see the formmlac iu Sect. 2))," It is there pretended that the correspondence principle is physically irrelevant for this system, on the basis of the simple observation that to achieve a increase of the time-lag of chaotic behavior (the region with information production, increasing $S(J)$ ), an increase of ${\cal N}$ (and therefore of the mass $M$, which is proportional to the former, see the formulae in Sect. \ref{sec-spac}) )"1089 is required., is required.1090 To the coutrary. for the multiparticle Arnold cat map. the bound is not so stringent: in fact. the ful Illbert spaceHo of the syste is the tensor product," To the contrary, for the multi–particle Arnol'd cat map, the bound is not so stringent: in fact, the full Hilbert space${\cal H}$ of the system is the tensor product"1091most abundant ice (Owenetal.1993).. but sublimated CO is the strongest coolant (Strobel2008). and so should act as the thermostat.,"most abundant ice \citep{owen93}, but sublimated CO is the strongest coolant \citep{strobel07} and so should act as the thermostat."1092 Some evidence for CO includes the brightest patch on Pluto's surface. suggested to be CO ice (Buieetal.2010b.andreferences therein).. and an extinction [aver seen in atmospheric occultation. interpreted as droplets of No or CO (Rannou&Durry2009).," Some evidence for CO includes the brightest patch on Pluto's surface, suggested to be CO ice \citep[and references 1093therein]{buie10b}, and an extinction layer seen in atmospheric occultation, interpreted as droplets of $_2$ or CO \citep{rannou09}."1094. rior searches for gaseous CO have been made with ground- telescopes., Prior searches for gaseous CO have been made with ground-based telescopes.1095 Infrared. absorption spectroscopy has recently Constrained CO:N2 to be «0.55 near the surface (Lellouchetal.2010).. an order of magnitude below an earlier limit (Youngetal.2001).," Infrared absorption spectroscopy has recently constrained $_2$ to be $<$ 0.5 near the surface \citep{lellouch10}, an order of magnitude below an earlier limit \citep{young01}."1096. Phere is also a long history of millimetre-waveleneth searches. looking for rotational ransitions of CO from the higher atmosphere (Barnes1993:Dockélee-Morvanetal. 2001).," There is also a long history of millimetre-wavelength searches, looking for rotational transitions of CO from the higher atmosphere \citep{barnes93,bockelee01}."1097.. As the atmosphere is warmer han the surface. and. extends bevond the planetary. disc. emission lines are predicted.," As the atmosphere is warmer than the surface, and extends beyond the planetary disc, emission lines are predicted."1098 “Phe major cilliculty is that tuto is small ancl distant. subtending less than a percent of the beam solid angle. even for telescopes of 10-30m class.," The major difficulty is that Pluto is small and distant, subtending less than a percent of the beam solid angle, even for telescopes of 10-30m class."1099 An upper limit was first obtained: using the Havstack 37m in 1993. for the CO J—1-0 transition rotational line at. 2.6 mm. wavelength. (Barnes1993).," An upper limit was first obtained using the Haystack 37m in 1993, for the CO J=1-0 transition rotational line at 2.6 mm wavelength \citep{barnes93}."1100.. This limit was improved by the equivalent of eight-fold in 2000. with the LUCAM 30m telescope (Bockélee-Morvanetal.2001).. ancl this group also searched. for the 22-1 transition at 1.3 mm with better sensitivity.," This limit was improved by the equivalent of eight-fold in 2000, with the IRAM 30m telescope \citep{bockelee01}, and this group also searched for the J=2-1 transition at 1.3 mm with better sensitivity."1101 A tentative positive signal was seen. with the brightest spectral channel observed at. 28 mlx. in main-beam brightness temperature. versus la noise of LO mils vcr 0.1 kms spectral channel.," A tentative positive signal was seen, with the brightest spectral channel observed at 28 mK in main-beam brightness temperature, versus $\sigma$ noise of 10 mK per 0.1 km/s spectral channel."1102 However. the observation was severely allected by a strong line from a backerounc Galactic cloud. coming as close as 0.5 km/s to potentia uto emission (Bockéloe-A\lorvanetal.2001).," However, the observation was severely affected by a strong line from a background Galactic cloud, coming as close as 0.5 km/s to potential Pluto emission \citep{bockelee01}."1103. The 2000 data sulferecl from an unfortunate coincidence in skv position with an uncatalogued. Galactic source. bu putos orbit as seen from the Earth has brought it closer o the Galactic Plane over the last couple of vears.," The 2000 data suffered from an unfortunate coincidence in sky position with an uncatalogued Galactic source, but Pluto's orbit as seen from the Earth has brought it closer to the Galactic Plane over the last couple of years."1104 Herc we present results. [rom the 15m James Clerk Alaxwel ‘Telescope. making a new search for the J=2-1 line. a exochs chosen to minimise Galactic contamination behi IEluto.," Here we present results from the 15m James Clerk Maxwell Telescope, making a new search for the J=2-1 line, at epochs chosen to minimise Galactic contamination behind Pluto."1105 The search was motivated bv time availability at an excellent. millimetre-site. ancl the opportunity to examine the evolution of Pluto's atmosphere in the exciting up period to the arrival of New Llorizons (Stern&Spencer Y03)..," The search was motivated by time availability at an excellent millimetre-site, and the opportunity to examine the evolution of Pluto's atmosphere in the exciting run-up period to the arrival of New Horizons \citep{stern03}. ."1106 We report the confirmation of atmospheric CO (alter two decades of searches). making it only the second. phase species to be detected. after methane 1991).," We report the confirmation of atmospheric CO (after two decades of searches), making it only the second gas-phase species to be detected, after methane \citep{young97}."1107. We used the JCNUE at 4000 mi altitude on Alauna Wea. Hawaii. observing over 3 nights in August 2009 and S nights in April to Alay 2010.," We used the JCMT at 4000 m altitude on Mauna Kea, Hawaii, observing over 3 nights in August 2009 and 8 nights in April to May 2010."1108 Conditions were good to average for the site. with zenith sky opacity at 1.3 mim typically around 0.1.," Conditions were good to average for the site, with zenith sky opacity at 1.3 mm typically around 0.1."1109 Phe setup used the ACSIS spectrometer together with the AS receiver (Cunningham (the instrument described. was subsequently rebuilt by the Herzberg Institute of Astrophysics with a 1.3 mm-banemixer)., The setup used the ACSIS spectrometer \citep{buckle09} together with the A3 receiver \citep{cunningham92} (the instrument described was subsequently rebuilt by the Herzberg Institute of Astrophysics with a 1.3 mm-bandmixer).1110 ‘Total on-source integration times, Total on-source integration times1111clusters (hat are more gas-poor.,clusters that are more gas-poor.1112 The primary complication in making this measurement is accounting lor (he presence of cooling cores. which can bias the emission-welghted metallicity upwards by introducing additional flux. [rom the enriched core. usually coincident. with a central galaxy (e.g.. Rasmussen&Ponman 2009)).," The primary complication in making this measurement is accounting for the presence of cooling cores, which can bias the emission-weighted metallicity upwards by introducing additional flux from the enriched core, usually coincident with a central galaxy (e.g., \citealt {rasm09}) )."1113 We therefore present (wo metallicities for each eluster. one emission-weighted over all of the X-ray emission. and one that excludes emission from the core of the cluster. as described below.," We therefore present two metallicities for each cluster, one emission-weighted over all of the X-ray emission, and one that excludes emission from the core of the cluster, as described below."1114 Correctly accounting for a cool core requires careful deprojection of the emission. but we lack the data for such an analvsis in all cases. and so perform a simpler correction.," Correctly accounting for a cool core requires careful deprojection of the emission, but we lack the data for such an analysis in all cases, and so perform a simpler correction."1115 We examined (he universal temperature and abundance profiles of Rasmussen(2007) for galaxy groups and Baleetal.(2007) for hot (T >6 keV) galaxy. clusters., We examined the universal temperature and abundance profiles of \citet{rasm07} for galaxy groups and \citet{bald07} for hot (T $\ge 6$ keV) galaxy clusters.1116 Both groups found temperature profiles that slowly rise towards the core. then decline more sharply starting al Ro745717? kpe. where T is the emission-weighted temperature of the ICM in keV. Most of the objects in our sample have temperatures within the range of values considered in these papers. so the same proliles should also apply.," Both groups found temperature profiles that slowly rise towards the core, then decline more sharply starting at $R \sim 45 T^{1/2}$ kpc, where T is the emission-weighted temperature of the ICM in keV. Most of the objects in our sample have temperatures within the range of values considered in these papers, so the same profiles should also apply."1117 We therefore attempt to exclude emission [rom within a projected radius of 457? kpe in each cluster to produce an emission-welghted iron abundance without the bias of a bright core (T is in keV units)., We therefore attempt to exclude emission from within a projected radius of $45 T^{1/2}$ kpc in each cluster to produce an emission-weighted iron abundance without the bias of a bright core (T is in keV units).1118 This is straightforward for the clusters with measurements [rom Snowclenetal.(2008).. since they provide measurements of the temperature. metallicitv. and {lis in a series of annuli for each cluster. which allows us to verify that a cooling core exists and (hen to remove the inner annuli and recompute (he fIux-weighted metallicity.," This is straightforward for the clusters with measurements from \citet{snow08}, since they provide measurements of the temperature, metallicity, and flux in a series of annuli for each cluster, which allows us to verify that a cooling core exists and then to remove the inner annuli and recompute the flux-weighted metallicity."1119 We perform a similar analysis on BCHAPA. for which we have measurements of temperature ancl metallicity as a [unetion of radius (Sun 2009. private communication). and lor RGIISO. using the single-temperature lits of Xueetal.(2004).," We perform a similar analysis on 3C442A, for which we have measurements of temperature and metallicity as a function of radius (Sun 2009, private communication), and for RGH80, using the single-temperature fits of \citet{xue04}."1120. For these (wo svstems. we estimate the expected flux in each annulus by assuming the IC'M eas density follows a o-mocdel with 3=0.65.," For these two systems, we estimate the expected flux in each annulus by assuming the ICM gas density follows a $\beta$ -model with $\beta = 0.65$."1121 In Abell 1275 ihe metallicities are from our analvsis of the Chandra data., In Abell 1275 the metallicities are from our analysis of the Chandra data.1122 For ALGO. and A2462 2005).. we have only global measurements of the metallicity. so we estimate the effect of a cooling core.," For A160, and A2462 \citep{jeth05}, we have only global measurements of the metallicity, so we estimate the effect of a cooling core."1123 Based on the other clusters in our sample. the the exclusion of a bright core reduces the iron abundance by 254. so we use this correction.," Based on the other clusters in our sample, the the exclusion of a bright core reduces the iron abundance by $25\%$, so we use this correction."1124 The final quantity is the stellar mass. which is obtained bv identilving the galaxies aud measuring their magnitudes to a radius of roy. which inelucles nearly all of the stellar light.," The final quantity is the stellar mass, which is obtained by identifying the galaxies and measuring their magnitudes to a radius of $_{200}$, which includes nearly all of the stellar light."1125 The data set for the galaxies used here is (he 2\TASS data base. so there is a magnitude limit to galaxy identification.," The data set for the galaxies used here is the 2MASS data base, so there is a magnitude limit to galaxy identification."1126 This leads to sampling only part of the galaxy luminosity function. so à Correction is applied (to account for galaxy incompleteness and Poisson bias for a simple halo occupation model. as previously discussed (Ixochaneketal.2003:Linοἱal. 2007).," This leads to sampling only part of the galaxy luminosity function, so a correction is applied to account for galaxy incompleteness and Poisson bias for a simple halo occupation model, as previously discussed \citep{koch03,lin04a,dai07}."1127. The uncertainties assigned are conservative in that they are larger than those eiven in Linetal.(2004).., The uncertainties assigned are conservative in that they are larger than those given in \citet{lin04a}.1128 For some of the analvsis. we include the metals in the stars. so we assumed a solar metallicity for that correction as applied to the total stellar mass.," For some of the analysis, we include the metals in the stars, so we assumed a solar metallicity for that correction as applied to the total stellar mass."1129should be different in the two regions of the disk.,should be different in the two regions of the disk.1130 Iu other words. im this paper we simulate transonic. viscous. rotating fluid around black holes.," In other words, in this paper we simulate transonic, viscous, rotating fluid around black holes."1131 We employ a new code to study the effect of angular momentum transport in the accretion disk., We employ a new code to study the effect of angular momentum transport in the accretion disk.1132 Uulike other purely Eulerian codes. tlis new code is especially developed. to strictly couserve aneular momentum in absence of viscosity.," Unlike other purely Eulerian codes, this new code is especially developed to strictly conserve angular momentum in absence of viscosity."1133 Iu 8&2. governing equations and asstuuptions are preseuted.," In 2, governing equations and assumptions are presented."1134 Iu &3. the code which was built to calculate the evolution of angular monmenutuni as accurately as possible is described. along with tests for a rotating transonic flow and a viscous flow.," In 3, the code which was built to calculate the evolution of angular momentum as accurately as possible is described, along with tests for a rotating transonic flow and a viscous flow."1135" In 5, the structure and the imstabilitv shown iu simulations are presented. along with descriptions on the nature of the instability."," In 4, the structure and the instability shown in simulations are presented, along with descriptions on the nature of the instability."1136 A Sununary and discussion is preseuted iu 85., A summary and discussion is presented in 5.1137 The one-dimensional time-dependent equations for quasi-spherical accretion of viscous flows are eiven bv where p. 6s 7. 0; and ο are the gas density. radial velocity. specific angular momentum. eravitational potential aud specific internal euerex. respectively.," The one-dimensional time-dependent equations for quasi-spherical accretion of viscous flows are given by where $\rho$ , $v_r$ , $l$, $\Phi_i$ and $e$ are the gas density, radial velocity, specific angular momentum, gravitational potential and specific internal energy, respectively."1138 The augulu velocity is defined as Q=ήν., The angular velocity is defined as $\Omega = l/r^2 $.1139 The suffix / in equation (2) denotes N or PN. corresponding to Newtouiau or pseudo-Newtoniau eravitv (Paczvüski&Wita 1980).. respectively. and are given by and where Afpy is the black hole mass aud the Schwarzschild radius is ry2CALByο.," The suffix $i$ in equation (2) denotes ${\rm N}$ or ${\rm PN}$, corresponding to Newtonian or pseudo-Newtonian gravity \citep{pw80}, respectively, and are given by and where $M_{BH}$ is the black hole mass and the Schwarzschild radius is $r_g=2GM_{BH}/c^2$."1140 The pseudo-Newtonian potential is widely used to ninüc the Schwarzschild geometry, The pseudo-Newtonian potential is widely used to mimic the Schwarzschild geometry.1141 For the eas pressure the equation of state for ideal gas is assumed. where 5 is the ratio of specific heats.," For the gas pressure the equation of state for ideal gas is assumed, where $\gamma$ is the ratio of specific heats."1142 For viscosity. the a prescription (Shakira Suuvaev 1973) cau be assumed. tthe dvuauical viscosity coefficient is described by where is the Iseplerian angular velocity. aud the viscosity parameter à is a constant which is generally less than 1.," For viscosity, the $\alpha$ prescription (Shakura Sunyaev 1973) can be assumed, the dynamical viscosity coefficient is described by where is the square of the adiabatic sound speed, and is the Keplerian angular velocity, and the viscosity parameter $\alpha$ is a constant which is generally less than 1."1143 It is to be noted that the actual expression of Oy epeuds on the eravitational oteuntial used., It is to be noted that the actual expression of $\Omega_K$ depends on the gravitational potential used.1144 Finally following NY9L. the parameter f measures the fraction of the viscously generatedo cucrey that is stored as eutropy aud advected along with flows.," Finally following NY94, the parameter $f$ measures the fraction of the viscously generated energy that is stored as entropy and advected along with flows."1145 The value f= lcorespouds to the limit of full advection iil has been used in this paper., The value $f=1$ corresponds to the limit of full advection and has been used in this paper.1146 Iu the following.S we use e aud r£/ as the units of velocity aud leneth. respectively. muless otherwise stated.," In the following, we use $c$ and $r_g$ as the units of velocity and length, respectively, unless otherwise stated."1147 Iu the geometrical units. the unit of time Is Ty=gfe," In the geometrical units, the unit of time is $\tau_g=r_g/c$."1148 Oue of the most demanding tasks in carrviug out nunercal simulations of equations (1) (1) as to calculate the evolution of the angular momenta as accurately as possible., One of the most demanding tasks in carrying out numerical simulations of equations (1) – (4) is to calculate the evolution of the angular momentum as accurately as possible.1149 Capturing shocks sharply should also be important iu resolving structures with clarity. if shocks are involved.," Capturing shocks sharply should also be important in resolving structures with clarity, if shocks are involved."1150 It las been known that the latter cau be achievedby usingcodes based on modern. upwind finite-ditterence schemes ou an Eulerian erid.," It has been known that the latter can be achievedby usingcodes based on modern, upwind finite-difference schemes on an Eulerian grid."1151 However. without viscosity in such Eulerian," However, without viscosity in such Eulerian"1152Fin ‘ zou vf to first order in /.,_0(t) = _c - T_c s_c (1+t) to first order in $t$.1153 The simplest parameterization of the other smooth [unetion is Jed 131032) The parameters α and b are (( ?(104)where An is the discontinuity in the barvon density al Z'=0. , The simplest parameterization of the other smooth function is b_- t^2 The parameters $a_-$ and $b_-$ are a_- = T_c ) b_- = ( where $\Delta n$ is the discontinuity in the baryon density at $T=0$ 1154A constant factor can. in principle. be used to correct. for [NU] contamination.,"A constant factor can, in principle, be used to correct for [NII] contamination."1155 However. ealaxy lo galaxy variations are large enough to compronmise this procedure.," However, galaxy to galaxy variations are large enough to compromise this procedure."1156 examined ratios for 90 nearby galaxies. and. found a median value close to 0.53 (excluding Sevlert galaxies).," \citet{Kennicutt1992} examined ratios for 90 nearby galaxies, and found a median value close to 0.53 (excluding Seyfert galaxies)."1157 However. the mean ratio for 6 non-interacting Sa-Sab galaxies in his sample was 1.24 with ratios ranging Irom 0.45 up-to as high as 2.4.," However, the mean ratio for 6 non-interacting Sa-Sab galaxies in his sample was 1.24 with ratios ranging from 0.48 up-to as high as 2.4."1158 Furthermore. within à particular galaxy. the diffuse ionized gas has a higher value of than regions (GreenawaltL998).," Furthermore, within a particular galaxy, the diffuse ionized gas has a higher value of than regions \citep{Greenawalt1998}."1159. The ratio is especially high in the central regions of galaxies. where absorption is strongest and. [NU] is in emission (Younge£al...1996).," The ratio is especially high in the central regions of galaxies, where absorption is strongest and [NII] is in emission \citep{Young1996}."1160.. Thus we would need precise information about ratio both within and among galaxies to properly correct for [NH] contamination., Thus we would need precise information about ratio both within and among galaxies to properly correct for [NII] contamination.1161 The fluxes presented in (his paper have not been corrected for Galactic or internal ex(ünetion., The fluxes presented in this paper have not been corrected for Galactic or internal extinction.1162 Thus. the fluxes ancl Iuminosiües we measure provide lower limits to the intrinsic κος and bDumninositles. ancl consequently (o massive star [formation rates.," Thus, the fluxes and luminosities we measure provide lower limits to the intrinsic fluxes and luminosities, and consequently to massive star formation rates."1163 lxennicutt&IXent.(1983) estimated. on average. | magnitude of extinction in (heir fluxes.," \citet{KK1983} estimated, on average, 1 magnitude of extinction in their fluxes."1164 llowever. extinction is expected to be higher lor galaxies with high inclinations ancl [or ealaxies with dustv. starbursts.," However, extinction is expected to be higher for galaxies with high inclinations and for galaxies with dusty starbursts."1165 Detailed studies of the hiehlv. disturbed earlv-tvpe spirals. NGC 2146 and NGC 660. estimate 9 and 13 magnitudes of extinction in (he visible. respectively (Young.Nleinmann&Allen1933).," Detailed studies of the highly disturbed early-type spirals, NGC 2146 and NGC 660, estimate 9 and 13 magnitudes of extinction in the visible, respectively \citep{Young1988}."1166. In stich extreme cases. Balmer recombination lines in the inlrared. like Paschen a aud Brackett 5. will be more suitable for determining star formation rales.," In such extreme cases, Balmer recombination lines in the infrared, like Paschen $\alpha$ and Brackett $\gamma$, will be more suitable for determining star formation rates."1167 The continuum image for each galaxy was scaled to (he line plus continuum image bv measuring the integrated fluxes of 10-15 foreground. stars common to both images., The continuum image for each galaxy was scaled to the line plus continuum image by measuring the integrated fluxes of 10-15 foreground stars common to both images.1168 This scale factor. however. offen needs adjustments. since the foreground stars and (the galaxy are sometimes different in color.," This scale factor, however, often needs adjustments, since the foreground stars and the galaxy are sometimes different in color."1169 Adjustments were made iteratively until a satisfactory subtraction was obtained for the majority of the galaxy., Adjustments were made iteratively until a satisfactory subtraction was obtained for the majority of the galaxy.1170 The application of a constant scale [actor across the entire galaxy introduces significant uncertainty. especially if there are large variations in color caused by changes in stellar populations.," The application of a constant scale factor across the entire galaxy introduces significant uncertainty, especially if there are large variations in color caused by changes in stellar populations."1171 Often. the central regions are over-subiracted when the disk is well fit.," Often, the central regions are over-subtracted when the disk is well fit."1172 The uncertzintv in the flux depends sensitively ancl non-lnearly on the continuum, The uncertainty in the flux depends sensitively and non-linearly on the continuum1173made here are actually ejected and contribute to the solar inventory of heavy elements.,made here are actually ejected and contribute to the solar inventory of heavy elements.1174 The study of these is a major goal for nuclear astrophysics experiments of the future. like the hare Isotope Accelerator (httpz//www.anl.gov/ria/index.html).," The study of these is a major goal for nuclear astrophysics experiments of the future, like the Rare Isotope Accelerator (http://www.anl.gov/ria/index.html)."1175 For now. we can only note that these nuclear uncertainties are almost certainly responsible for a large Iraction of the spread in production factors in. e.g. Figs.," For now, we can only note that these nuclear uncertainties are almost certainly responsible for a large fraction of the spread in production factors in, e.g. Figs."1176 1. and 3.., \ref{allFig} and \ref{2sfig}.1177 This study has explored only a relatively limited set of outflow parameter space based upon simple modifications to trajectories found in one particular simulation., This study has explored only a relatively limited set of outflow parameter space based upon simple modifications to trajectories found in one particular simulation.1178" Further studies will surely be carried out by us aud others. but we have identilied a kev physical parameter. A,, (eq."," Further studies will surely be carried out by us and others, but we have identified a key physical parameter, $\Delta_n$ (eq."1179 2). which characterizes the solution for various combinations of time scale. 1. and entropy.," 2), which characterizes the solution for various combinations of time scale, $Y_e$, and entropy."1180" A,, is essentially a dimensionless measure of the number of neutrons produced by neuirino capture on protons compared to the number of heavy seed nuclei.", $\Delta_n$ is essentially a dimensionless measure of the number of neutrons produced by neutrino capture on protons compared to the number of heavy seed nuclei.1181" Survevs on a finer exid of A, than were used here will be interesting.", Surveys on a finer grid of $\Delta_n$ than were used here will be interesting.1182 This work was performed under the auspices of the U.5. Departnent of Energy by the University of California Lawrence Livermore National Laboratory under contract ENG-48., This work was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory under contract W-7405-ENG-48.1183 It was also supported. in part. bv the SciDAC Program of the US Department of Energv CDC-FCO02-01ER41176). the National Science Foundation (AST 02-06111). and NASA (NAG5-12036) and. in Germany. bv the Research Center for. Astroparticle Physics (SFB 375) and the Transregional Collaborative Research Center for Gravitational Wave Astronomy (SFB-Transregio 7).," It was also supported, in part, by the SciDAC Program of the US Department of Energy (DC-FC02-01ER41176), the National Science Foundation (AST 02-06111), and NASA (NAG5-12036) and, in Germany, by the Research Center for Astroparticle Physics (SFB 375) and the Transregional Collaborative Research Center for Gravitational Wave Astronomy (SFB-Transregio 7)."1184error.,error.1185 All spectral channels were combined to maximize the coverage and we obtained two polychromatie images. for the H-band and the K-band. assuming a grey emission within each filter.," All spectral channels were combined to maximize the coverage and we obtained two polychromatic images, for the $H$ -band and the $K$ -band, assuming a grey emission within each filter."1186 We present in Fig., We present in Fig.1187 2. the resulting image in the K band., \ref{fig:image} the resulting image in the $K$ band.1188 The interferometric beam is shown in the lower right corners. and is defined as the maximum angular resolution along the U and V axis (1.8 mas x 2.3 mas in the KX band and 1.6 mas x 1.8 mas in the H band).," The interferometric beam is shown in the lower right corners, and is defined as the maximum angular resolution along the U and V axis (1.8 mas x 2.3 mas in the $K$ band and 1.6 mas x 1.8 mas in the $H$ band)."1189" Using MiRA (or a similar fitting procedure). one can retrieve spatial information at about half the maximum angular resolution of the interferometer (performing. the so-called ""super-resolution?)."," Using MiRA (or a similar fitting procedure), one can retrieve spatial information at about half the maximum angular resolution of the interferometer (performing the so-called 'super-resolution')."1190" The reconstructed image resolves the inner environment around HR 5999, and reveals several features."," The reconstructed image resolves the inner environment around HR 5999, and reveals several features."1191" The ""blobby aspect of the image is probably due to the incomplete coverage.", The 'blobby' aspect of the image is probably due to the incomplete coverage.1192 The K-band image gives indications of a bright spot at the center and an elongated structure in a ring-like shape., The $K$ -band image gives indications of a bright spot at the center and an elongated structure in a ring-like shape.1193 The central spot is  1.8 mas wide. 1.e.. about our limit in resolution.," The central spot is $\sim$ 1.8 mas wide, i.e., about our limit in resolution."1194 Using an ellipse to describe the ring-like structure. we find a major axis at the inner edge of ~5.5-6 mas (1.9. at a distance of 210 pe. « 1.15-1.26 AU). a ratio |width/inner radius] of ~25%.. an inclination of -40-507.. and an orientation of the long axis along PA~130-1407.," Using an ellipse to describe the ring-like structure, we find a major axis at the inner edge of $\sim$ 5.5-6 mas (i.e, at a distance of 210 pc, $\sim$ 1.15-1.26 AU), a ratio [width/inner radius] of $\sim$, an inclination of $\sim$ , and an orientation of the long axis along $\sim$."1195 It provides ~33-38% of the total flux in the image (depending on the regularization). while the large central spot contributes to the rest.," It provides $\sim$ of the total flux in the image (depending on the regularization), while the large central spot contributes to the rest."1196 Betweer these two main features. the image reveals low or zero emission.," Between these two main features, the image reveals low or zero emission."1197 We interpret the elongated structure as the disk emission., We interpret the elongated structure as the disk emission.1198 The central spot is interpreted as the image of the star (of diameter «0.2 mas). and possibly of additional unresolved or partially resolved circumstellar material (~ | to 2 mas wide).," The central spot is interpreted as the image of the star (of diameter $\sim$ 0.2 mas), and possibly of additional unresolved or partially resolved circumstellar material $\sim$ 1 to 2 mas wide)."1199 The H-band emission is more compact than the A-band emission. and the image is of quite low quality because the observations obtained are of much lower signal-to-noise ratio.," The $H$ -band emission is more compact than the $K$ -band emission, and the image is of quite low quality because the observations obtained are of much lower signal-to-noise ratio."1200 The image consists of two blobs (separated by 3.8 mas. which we interpret as tracing the elongated structure seen in the K-band image. ie. a disk) and a central spot (~1.8 mas wide).," The image consists of two blobs (separated by 3.8 mas, which we interpret as tracing the elongated structure seen in the $K$ -band image, i.e., a disk) and a central spot $\sim$ 1.8 mas wide)."

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