source,target "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 $\alpha=0$." Consider now the stresses of the ultra-violet field with ng=—5/2., Consider now the stresses of the ultra-violet field with $n_B=-5/2$. 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. 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." Analytical solutions are difficult to find and may well not exist., Analytical solutions are difficult to find and may well not exist. 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." " 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 $\mathcal{B}\propto k^{3(n_B+1)}$." This 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." 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." In the (4.r.6] coordinates this scaling will be obscured.," In the $\{k,r,\phi\}$ coordinates this scaling will be obscured." Specifically. the dominant term found i1," Specifically, the dominant term found in" different 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. 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. 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." 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." " 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}) ). This reflects in Cie spectra ol the emitted radiation., This reflects in the spectra of the emitted radiation. 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. 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. 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. 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. 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." 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:" iu 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." 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." " 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}." 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." 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." 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." 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." 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)." 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 $\eta_q,\eta_V \sim 1$." 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." 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." In Fig. 9..," In Fig. \ref{fig:SigPlot}," 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. Iu the right-liaud panel.thestatistical siguilicauce associated with each," In the right-hand panel,thestatistical significance associated with each" other than the HST bands.,other than the HST bands. This object is especially interesting as its SED is extremely red., This object is especially interesting as its SED is extremely red. 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}." 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." 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. " After stacking. we get a faint detection in the A, band."," After stacking, we get a faint detection in the $K_s$ band." The stacked magnitudes are given in Table 6.., The stacked magnitudes are given in Table \ref{tabsed}. 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." in preparation) indicates that the AGN fraction among these objects is low., in preparation) indicates that the AGN fraction among these objects is low. 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." 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. 1995 for an introduction)., 1995 for an introduction). 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." A summary of the parameter space Is given in reftabsedpars.., A summary of the parameter space is given in \\ref{tabsedpars}. . " 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" fainter galaxies.,fainter galaxies. For the total SDSS sample (Black Dots). we observe the same behaviour.," For the total SDSS sample (Black Dots), we observe the same behaviour." 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}) ). 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." 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." " 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 $M_{g} \le -20.0$." 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. 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." This method is used for all the fits in this paper., This method is used for all the fits in this paper. 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." 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. 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}) ). " 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}) )." 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." " 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." 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. 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. For a detailed discussion of Figs., For a detailed discussion of Figs. " 2, 3 and 4 see section 2.3.3."," 2, 3 and 4 see section 2.3.3." 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." Vertical lines represent the limits of the 0.0410.5 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." 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. 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. 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. 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 make hat implied by the MOND fundamental plane 55).,that implied by the MOND fundamental plane 5). 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. " 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." 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. 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. 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." 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 $\mu(x)=x/\sqrt{1+x^2}$ ). 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." 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." 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." 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." 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." 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." 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)." 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. 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). 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. ( 1995) vielded reasonable values for the mass-to-light ratios.,1995) yielded reasonable values for the mass-to-light ratios. Now. thanks to the work of Dolton et al. (," Now, thanks to the work of Bolton et al. (" 2007) 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. Figs., Figs. 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. .. 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)." 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. 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." 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." This is in contrast to a recent claim by Ferreras et. al. (, This is in contrast to a recent claim by Ferreras et al. ( 2008). based: upon lensing by six carly type galaxies.,2008) based upon lensing by six early type galaxies. 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." 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)." 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." 2003)., 2003). Overall it is cillicult to argue that implied, Overall it is difficult to argue that implied "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." " 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}." " 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}." 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. See ? for a description of the different models for cluster dissolution., See \citet{lamers09} for a description of the different models for cluster dissolution. 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. " 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." " 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." ? 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. " 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 $_c$ $10^6$ $_{\odot}$ )." " 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." " ? 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." " 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}." " 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 $\Gamma$." " 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." " 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." " 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." " 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." The paper is structured as follows., The paper is structured as follows. In Sect., In Sect. " 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." The basic reduction and characteristics of the observations are described in Sect., The basic reduction and characteristics of the observations are described in Sect. 3., 3. In Sect., In Sect. 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. 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. In Sect., In Sect. " 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." 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. In Sect., In Sect. " 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." 7., 7. " 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." " 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" because 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." 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." " 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, $n_{\rm crit}\MBH=({2\times 10^8}/{\cm^{-3}})({10^2}/{\Msun})$ ." 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." 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." 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. 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}) )." " ""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 $10^8\, \cm^{-3}$." 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." 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." 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." 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 $10^{5} - 10^{11}\, \cm^{-3}$." 5 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:" , uamely: 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)." " 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 $\tilde N_{H\perp}\equiv N_{H\perp}/10^{20}$ $^{-2}$ 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}) )" 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." 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. 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 $N_{HI,n}$." 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 $z,\Omega_M, \Omega_\Lambda$." " 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 $z\sim 2.5$ )." " 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 $10^{22}$ $^{-2}$." " 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 $N_{HI,3}=1.3\times 10^{20}$ $^{-2}$." 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." 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. " 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 $\Omega_{dark}(i)$." 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." 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. 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 $\zeta \approx V/\tilde c_s$. 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." 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." " 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." Note that (3) is particularly simall for the 2o-low Limit., Note that $h(3)$ is particularly small for the $2\sigma$ -low limit. any 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. “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. The positions of the peaks are a Little less consistent., The positions of the peaks are a little less consistent. 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." Therefore the wo maps are olfset by about one ALERLIN beam., Therefore the two maps are offset by about one MERLIN beam. 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. 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. 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)." 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. 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. 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. 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." 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. 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}. The final image is shown in Fig., The final image is shown in Fig. 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." 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. The final image shown in Fig., The final image shown in Fig. 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." 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)." 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. 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." 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. 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." 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 $\alpha$. 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." 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. 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}. .. Furthermore. Conway et al. (," Furthermore, Conway et al. (" 1990) 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." 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. 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." 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." 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. 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." 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." 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" Model 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. " 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." " 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." " 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." " 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)." "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)." " 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." " 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)." " 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." 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. " 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." " 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." 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. 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}. 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. " 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." 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. 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. 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. " A mushroom structure forms by 9 Myrs, with"," A mushroom structure forms by 9 Myrs, with" asstuption 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." 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." 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 $f_{\rm col}$. 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." Another assumption of interest is our choice of à=0.01., Another assumption of interest is our choice of $\alpha=0.01$. 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." For higher values of o. the typical color correction is larger.," For higher values of $\alpha$ , the typical color correction is larger." 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." " 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." " 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." " 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 $f_{\rm col} \sim 2$." " 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." " 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." " 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 $r_{\rm in} \sim 900$. 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. 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." ". 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 $\Mdot \sim 10^{-2} \; \Msun \; \rm yr^{-1}$." "For M~101ALLvet, the accretion rate aud time variability of Π.Ν. present a challenge to standard models of mmass trauster2011)."," For $\Mdot \sim 10^{-4} \; \Msun \; \rm yr^{-1}$, the accretion rate and time variability of HLX-1 present a challenge to standard models of mass transfer." . 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." " 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 $L_{\rm obs} \gg L_{\rm iso}$, which (in this formalism) is equivalent to increasing $\mu$ for some narrow range of $i$." 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}) )." 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 $T_{\rm obs}$. " 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 $\mu$." 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. 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." " 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 $10^{42}$ $\rm erg \; s^{-1}$." 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." 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 $\ell =0.7$." 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. IHeuce. the Eddinetou linit plavs no role in this coustrait.," Hence, the Eddington limit plays no role in this constraint." 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 $M \gtrsim 6000 \Msun$, but this bound is subject to the Eddington limit because our model grid is limited to a maximum luminosity $\ell=1$." 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 $M \lesssim 3 \times 10^5 \Msun$ with both datasets, this limit corresponding to nearly edge-on $i=90^\circ$ ) disks with near maximal spins $a_* \sim 0.99$ )." 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). 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 $i \lesssim 75^\circ$ and, therefore, $M \lesssim 10^5$." 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 $i \sim 90^\circ$ 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 $i$." 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." 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." 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 $a_*$ ." 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." 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." 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." Tn sununiuw. despite the rather large range of AL ," In summary, despite the rather large range of $M$ " The 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." 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." Since the latter oscillates sinusoidally. the product vanishes over a period.," Since the latter oscillates sinusoidally, the product vanishes over a period." We therefore turn to the oscillating deusity perturbation., We therefore turn to the oscillating density perturbation. " 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." 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)." " We proceed by finding those parts of p, (denoted pa. ete.)"," We proceed by finding those parts of $\rho_1$ (denoted $\rho_A$, etc.)" generated by each additive component of pt., generated by each additive component of $\rho_{12}^\ast$. 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. 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" "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." The open circles in Fig., The open circles in Fig. " 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)." " 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." In Fig., In Fig. " 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." " 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." 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}) )." 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. 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. " 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." 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 =. " 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." There is very little dynamical processing of initially hard systems., There is very little dynamical processing of initially hard systems. " 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." " 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." " 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)." Fig., Fig. " 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)." " 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)." " However, as we show in Fig."," However, as we show in Fig." 3 (c.f., \ref{100_sep_dists} (c.f. " Fig. 2)),"," Fig. \ref{field_evol}) )," 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. " 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." " 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." Our initial conditions also produce too many, Our initial conditions also produce too many the 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. ( 13) even if D. is small compared to D...,13) even if $B_z$ is small compared to $B_{\varphi}$. However. Eq. (," However, Eq. (" 13) 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 $(m, \varepsilon) \rightarrow (-m, -\varepsilon)$ transformation." 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 $m$. " 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." 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 $q$." 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 $q \sim - m/ \varepsilon$. 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 $\omega_A \propto q \varepsilon + m \psi(x) \approx 0$." 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." 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. 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. 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. 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." 1)., 4). 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." 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." 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." 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. 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. 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. Note that the ecquilibriuni state of both the configurations considered in Fie., Note that the equilibrium state of both the configurations considered in Fig. 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). Iudeed. using Eq. (," Indeed, using Eq. (" 5) 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 $n=1,2$." 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. 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." For the equilibrimu configuration with the toroidal field given by Eq. (, For the equilibrium configuration with the toroidal field given by Eq. ( 15). 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." 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 $p=2, n=1$." " 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 $x=0.5$." 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. 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." 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. (" 16).,16). 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 $m$ . 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, $\varepsilon = 0.01$ ." The distribution of the toroidal field is eiven by Eq. (, The distribution of the toroidal field is given by Eq. ( "15) with p=1 aud = no2,",15) with $p=1$ and $n=2$ . and to better determine the continuum level).,and to better determine the continuum level). " 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." " 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." 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). " 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." " 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." " 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." " 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." " 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." " 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." " 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)." " 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." " 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." " 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." " 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." 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. An optically thin spherical shell would produce an, An optically thin spherical shell would produce an "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." 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. 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. 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. 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}. 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. 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." 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." 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}) ). A nore clirect Least‘e is show in Table {., A more direct measure is shown in Table 4. 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." 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}] ])," 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. 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." 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." But the important poiut for our purpose is that the initia, But the important point for our purpose is that the initial Wr) = 22) The upper panels of Fig.,(r) = ( 1 + ) The upper panels of Fig. 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. 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)." " “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. 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." 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}) )" and (22)) for à variety of sets of parameters., and \ref{Psidef}) ) for a variety of sets of parameters. Figure 2. illustrates he case for parameters Ly=1.6. ry=0.2. ry=2.0.," Figure \ref{approxlosvd} illustrates the case for parameters $L_0 = 1.6$, $r_0=0.2$, $v_0=2.0$." As this figure shows. the iterative algorithm. recovers the DI verv closely.," As this figure shows, the iterative algorithm recovers the DF very closely." 1n. fact. convergence occurs in a small number of steps.," In fact, convergence occurs in a small number of steps." " 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." ‘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." 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. 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." 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." ]t is apparent from Fig., It is apparent from Fig. 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. 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." 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. 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." 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 $|v_{los}| > v_c(r_p)$." 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 $|v_{los}| < v_c(r_p)$ bear little resemblance to those of the original galaxy model." 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." 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. 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." 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." 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." 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)." 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." 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," las a function of 2-10 keV luminosity.,1 as a function of 2-10 keV luminosity. 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)." 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.," NGC 3227 in Georgeetal. 1998))., NGC 3227 in \cite{george98}) ). Also plotted are the variances computed in Noaudra et al. (, Also plotted are the variances computed in Nandra et al. ( 1997) 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}) )." 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. 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)." 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. The implications of these results are discussecl below., The implications of these results are discussed below. 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." 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)." 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}." . 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}) )." 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}) )." " 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." 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." 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." 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. 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). " 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}) )." 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." 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." " 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." " 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 $\gamma_g \sim [1-R_{Schw}/r]^{-1/2}$ )." " 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 $11\frac{M_{BH}}{3.5 \times 10^{7} \rm \ M_{\odot}}$ " Dwarf 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}) )." 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}) )). According to one model for dE evolution. they are primordial objects.," According to one model for dE evolution, they are primordial objects." 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}) )." 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. 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. 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}) )." (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." 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. Some dEs might still. contain a memory of their former state., Some dEs might still contain a memory of their former state. 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}) )." Moreover. rotationally flattened dEs have been discovered (DeRiekeetal.(20010.Simien&Prugniel (2002))).," Moreover, rotationally flattened dEs have been discovered \cite{dr1,sp}) )." 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}) ). 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}) )." FS373 (Fig. 15) , FS373 (Fig. \ref{ima373}) ) is 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)." FS76 (Fig. 2) , FS76 (Fig. \ref{ima76}) ) is 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." 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.,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. " 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." 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" The 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." 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." 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}." . 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. 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}." . 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}." .. 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." 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." 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." 20 through 30.., \ref{S0_cut} through \ref{AA_cut}. 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 $\ell=200-250\degr$ ." These ranges avoid the degenerate regions that, These ranges avoid the degenerate regions that for three sets of thermal plasma parameters.,for three sets of thermal plasma parameters. 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." 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 $\Theta=0.1$." " 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 $\gamma_{\rm f}=30$ ." 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 $\gamma_{\rm f}=10$ and 100 for $p=3$ (for $p>3$ the influence of the cut-off is much weaker)." 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 $(\gamma_{\rm nth}-1)/\Theta \sim 12$ (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." 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. " 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 $\gamma_{\rm f}$." " 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." 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. 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)." 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, $\approx \ntth$ ), 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." ⋡⋜↧∣⋡↕↓↕↿∙∖⇁⋡↓↿≱∖⋠↓⊔↿⋖⋅⋏∙≟↓⋅⋜⊔⊲↓∪⊔∙∖⋰↓⋖⋅⇂∠⇂⊳∖⇂↓↥∢⊾↿⇂↥⋖⊾↓⋅⊔⋯↓− 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)." " 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." " ""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 $x \la \Theta$, the Comptonization spectrum becomes harder, while for $x \gg \Theta$, above the thermal cut-off, a power-law tail in the spectrum develops." As a result. the overall luminosity produced by Comptonization increases.," As a result, the overall luminosity produced by Comptonization increases." " 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, ${\rm d}\gamma /{\rm d}t$, 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)." 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 $x_{\rm inj}$. 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). 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). 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 $x_{\rm inj}$ up to the" Type IIn SNe is inconsistent with pοςr-?.,Type IIn SNe is inconsistent with $\rho\propto r^{-2}$. 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 $\rho\propto r^{-2}$. 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. " 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." 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. " So far, we just consider a single slope for the dense wind."," So far, we just consider a single slope for the dense wind." 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. " 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." " 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." " (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." " 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." 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. " 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." ". 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." " 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." " 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." " 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." " 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." ". (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." 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. " 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. " 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. 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}) ). The 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}) )). " 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 $t_d$." " 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." " 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." " 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." 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. 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. (Steson1987)).,\citealt{stetson}) ). 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. 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." 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. 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." 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." 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. The spectrum aypears typical of dwar ovae. sliowi strong broad emission lines.," The spectrum appears typical of dwarf novae, showing strong broad emission lines." 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. 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}. . 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. 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. "+) 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}." . Fiewe 3 shows the resu| for he 20(JS Septemyer data., Figure 3 shows the result for the 2005 September data. 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." 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." 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. 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." 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. TheHj velocities co‘roboraed the Ha measurements. but he period ΘΕΟΙecd ambiguous.," The$\beta$ velocities corroborated the $\alpha$ measurements, but the period remained ambiguous." " However. we kuow fj. aie that he Poy, of au SU UMa-type slould be a ew yercent less than Pa."," However, we know $P_{\rm sh}$ , and that the $P_{\rm orb}$ of an SU UMa-type should be a few percent less than $P_{\rm sh}$." 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." 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." " 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 $\epsilon = 0.016(4)$ ." plot log(e) against οσον) for a large number of systems with lycdrogen-rich secoucaries.," \citet{patt03} plot $\epsilon$ ) against $P_{\rm orb}$ ) for a large number of systems with hydrogen-rich secondaries." caustics induced by close or wide binaries.,caustics induced by close or wide binaries. 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. " 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$\theta_{\rm E}$." " 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, $\hat{\theta}_{\rm E}$." The perturbation extends outside the caustic., The perturbation extends outside the caustic. " 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 $A\gtrsim 30$." " 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 $s^{-1}$." " 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}." . type efficiencyhigh-magnification through1.high-magnification , \ref{table:one} of these two classes of object might be ambiguous.,of these two classes of object might be ambiguous. " 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." " 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." " 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 $\delta\kappa\sim 0.01$ ) from GCs would be enough to cause the observed flux-ratio anomaly in B1422+231." This conclusion has been re-examined in this work., This conclusion has been re-examined in this work. 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. " 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 $r_{\rm h}$." " 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." 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. " 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." " 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." " 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." " 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." 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. " However, these low-mass objects are not significant for lensing."," However, these low-mass objects are not significant for lensing." The 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." . 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." 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)." 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. 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} reddening law was used." 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." 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}." 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}. 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." 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" In 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." 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}) ). 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. 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. 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." 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 $i > 19.1$." In all cases. there was no appreciable change in the observed overdensity.," In all cases, there was no appreciable change in the observed overdensity." 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}. 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 $-27.5 \leqslant M_{i} \leqslant -23.2$ $-23.2 < M_{i} \leqslant -22.0$ )." The average magnitude of the brighter (fainter) bin is M;=—23.83 M;=—22.10)., The average magnitude of the brighter (fainter) bin is $\overline{M_{i}} = -23.83$ $\overline{M_{i}} = -22.70$ ). 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." 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." 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." 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. 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." 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. 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 $\approx2\sigma$." 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" We 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." 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." 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. 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). 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." 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." 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. (" 2006) 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. 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." 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." 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). (" ii) 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. 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." 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." 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. 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)." 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. from 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. 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. " 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}." 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. 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. 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}. " As expected, the two diagrams have similar appearances."," As expected, the two diagrams have similar appearances." 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}. Again the observed and semi-synthetic butterfly wings look similar., Again the observed and semi-synthetic butterfly wings look similar. 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. 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 $R_G$. 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. " Figure 15 shows the reconstructed butterfly diagram during 1700-1874 with Rg and Rz, respectively."," Figure \ref{fig:butterly_both} shows the reconstructed butterfly diagram during 1700–1874 with $R_G$ and $R_Z$, respectively." 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}. 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. 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. 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. 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. " 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." The main correlations found are: 1., The main correlations found are: 1. 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. Fie.,Fig. 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. 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. 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." 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. $z = 0.23780 \pm 0.00002$." The peak optical depth is ~ 0.012., The peak optical depth is $\sim$ 0.013. 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}; he resoluion is ~ 10 jin |., the resolution is $\sim$ 10 km $^{-1}$. 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." 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. 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." 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." 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. $z = 0.52476 \pm 0.00005$." " 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." 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. " 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." 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 $^{-1}$." 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. 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." 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. 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." 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." collinear 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 $x(0)= \frac{1}{2}-\mu, y(0)=\pm\frac{\sqrt{3}}{2}$ (for the triangular equilibrium points)." 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 $L_2$." The inuuerical values of (hese points are presented in Table 1.., The numerical values of these points are presented in Table \ref{tab:lpts}. 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." " 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 $L_4$ . 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}. 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}. ." " 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:" The 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)." 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. 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." 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 $|\Delta\mu/\mu| < 3\times10^{-5}$ ." " 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: $\Delta\alpha/\alpha = (\alpha_2 - \alpha_1)/\alpha_1$ . 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 $z \sim 0.4$ ). 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 $|\Delta\alpha/\alpha| < 2\times10^{-8}$." 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)." Current astroplhivsical measurements at higher redshifts are as follows., Current astrophysical measurements at higher redshifts are as follows. 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)." " AMoeasureimenuts of the cosinological p-variatiou exhibit a similar tendency,", Measurements of the cosmological $\mu$ -variation exhibit a similar tendency. 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." 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). 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)." 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)." Thus. t16 nuosf acctrate astronomical estimates," Thus, the most accurate astronomical estimates" are 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}) )." 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}) )." 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}) )." 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. 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. 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. 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. 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. 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." However the mechanism responsible for the illine factor is not explained., However the mechanism responsible for the filling factor is not explained. 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. 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." 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. 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. 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. 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." 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. 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. 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. 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. 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." 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. Whereas he electrons trapped in smaller filaments escape via energization., Whereas the electrons trapped in smaller filaments escape via energization. " 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. 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 $\lambda_c$. " 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 $\lambda>\lambda_c$. 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)." 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. 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. 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. 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." 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." 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. 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. 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." 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. 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. 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. 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). 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. 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." 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." 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. This work has made use of the AJET website., This work has made use of the XJET website. or eroup are then estimated.,or group are then estimated. 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." " 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 $M_{\rm CGM}\lsim 0.6 \times(\frac{0.5}{f_{\rm OVII}})\times(\frac{0.3A_\odot}{A})\times(\frac{R}{500~ {\rm kpc}})^2\times10^{11}M_\odot$ , where $f_{\rm OVII}$ , $A$, and $R$ are the ionization fraction of, metal abundance, and the radius of the hot CGM, respectively." 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}. 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. 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." 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). 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." 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." 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)." 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}." 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. 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." 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. Tuuphrey ct al., Humphrey et al. have mace such mass measurements for four SMDIIS with ddata (2s)..., have made such mass measurements for four SMBHs with data \cite{hum09}. 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. " 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. 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." 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}) )." 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. 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. " 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." " 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}. ." 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}) )." " 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}) ).," 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." 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. 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}) )." 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 a along the iinto the IGM density field.,along the into the IGM density field. " 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." " 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." 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. The adopted procedure has been the following: 1., The adopted procedure has been the following: 1. " 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)." 2., 2. 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. " 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}." " 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." 3., 3. " 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." 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. " 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." 4., 4. " 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." " 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." " 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." 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. 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. " 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." 5., 5. " 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}," " together with the 1, 2 and 3 o confidence levels."," together with the 1, 2 and 3 $\sigma$ confidence levels." 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 $\sim 250$. . 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). Fig., Fig. 8 shows the probabilityexcess considering quadruplets of llines., \ref{fig:PE4} shows the probabilityexcess considering quadruplets of lines. 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 $\sim 250$. ". 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." 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}. " 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." 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. " 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 ." This correlated, This correlated in Section 3.1.,in Section 3.1. " 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." 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. " 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." " '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." 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. " 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." " 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." The, The place 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." 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." " 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 $z_{l1} < z_{s}$." 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 $z_{l2} < z_{l1}$ ." " 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. 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. 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." 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 $\theta > 20''$." " 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., $\gamma^+ (\theta) < \gamma^- (\theta)$ ) on scales $20'' < \theta < 70''$ , and is consistent with no anisotropy on scales $70'' < \theta < 120''$." 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 $\gamma^+ (\theta) = \gamma^- (\theta)$ 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." 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." " 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 $\gamma^+ (\theta) < \gamma^- (\theta)$ 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." 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." 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." 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. 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." 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." 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 $\gamma^+ (\theta) > \gamma^- (\theta)$." 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." 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)." 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." 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." We 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" IL98).. 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." 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. ". 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." 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." 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." 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." 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 $V_r$." 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." 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." . 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." 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." 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." 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 $t=0$ ). 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. 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." 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? 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." 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. 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. " 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 $\propto R^{-1.6}$. A 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 $\simeq 90$. ". 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 $\Phi \propto R^{-2.5}$ ) is $\le 15$." Doubts may be cast on the appropriateness of a spherical model., Doubts may be cast on the appropriateness of a spherical model. 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." 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)." " 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 =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 $ = -38\kms$ and $\sigma_V = 175\kms$." 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 $\simeq 90$. 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 $\Phi(R_{GC}) \propto R_{GC}^{-1.6}$ and with the Gaussian distribution of radial velocities shown in Figure 2." " 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 $\Delta V_r = V_r(obs) - V_r(orb)$ )." 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 $\Delta V_r$." The eucircled xnts are the six clusters highliehted in Figure 1., The encircled points are the six clusters highlighted in Figure 1. 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." 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." 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. 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 ." ". 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." The lower panel of FigureOo 3 is arrangedC» in the same, The lower panel of Figure 3 is arranged in the same These 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}) )." For later use we mention two additional important relations., For later use we mention two additional important relations. 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 $c_{ij}^m=\frac{8\pi}{15}(\mathcal{Y}_{ij}^{2m})^*$." " 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." 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." 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 $t$. 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." 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." ]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. 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." 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." " 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." " 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." 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." This requires pla)= por)., This requires $\rho(\bmath{x})=\rho(r)$ . 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." " ‘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}." . 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. Note that equation (10)) only holds in Forni normal coordinates., Note that equation \ref{eq:stress_ten}) ) only holds in Fermi normal coordinates. 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" "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 $4\times10^6$ $_\odot$." Hence we can estimate the mean density to be (nj)=6x10? cem., Hence we can estimate the mean density to be $\langle n_{H_2}\rangle \gtrsim 6 \times10^3$ $^{-3}$. 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. " 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." Fig., Fig. 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. 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. " 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}. ." " 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}." " 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, $X_{HCN}/X_{CO}=10^{-2}$." " 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." " 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." " 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 $n_{H_2}=10^{6}$ $^{-3}$. 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. Why this occurs can be seen in Fig., Why this occurs can be seen in Fig. 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. 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. " 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." " 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." 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. " 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." " This regime is, however, also associated with very large velocity gradients."," This regime is, however, also associated with very large velocity gradients." " 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." 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. 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. " 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." " 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." 2 here)., \ref{fig:lvg} here). " 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." " 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 $n_{H_2}\sim10^{5.5}$ $^{-3}$." " 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." " 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}. ." " Similarly, in"," Similarly, in" 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." 2001)., 2001). 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. 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." Furthermore. these difficulties merease at aree radi from the eroup ceuter.," Furthermore, these difficulties increase at large radii from the group center." 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. 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." 1998: Fischer et al., 1998; Fischer et al. 2000: Sheldon et al., 2000; Sheldon et al. 2001: Tloekstra et al., 2001; Hoekstra et al. 2001)., 2004). 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. 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. 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." 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. 2001) aud the, 2001) and the the 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. 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." 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. 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)." 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). Using V —19.2 (Thorstensen et al., Using $V$ =19.2 (Thorstensen et al. 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. " 1996). we obtain V, in the range 18.1"," 1996), we obtain $V_{o}$ in the range 18.1--18.9." " 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." " 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)." 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." 1980)., 1980). 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 $\pm$ )." 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." 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." 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). Initially. the X-rays are constant while the source is quiescent.," Initially, the X-rays are constant while the source is quiescent." 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. 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." 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." 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." 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)." 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). At first. the optical [lux rises linearly.," At first, the optical flux rises linearly." 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." 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." 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." 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. 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. 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." 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. 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 $K$. 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." 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." imposed 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 $0.3 < z < 0.9$ in order to remove the tails of the redshift distribution which contain relatively few galaxies." A total of N=56.159 ealaxy redshifts remained.," A total of $N = 56{,}159$ galaxy redshifts remained." 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." 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. 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." 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 $z_{\rm eff} = (0.42, 0.59, 0.78)$." 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." 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 $k_{\rm max} = 0.4 \, h$ $^{-1}$, assuming the value $P_0 = 2500 \, h^{-3}$ $^3$ for the weighting factor in Equation \ref{eqweight}. ." 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." " 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 $n_0 = 5 \times 10^{-5} \, h^3$ $^{-3}$." 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 $\Delta k = 0.01 \, h$ $^{-1}$." 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. Ehe details of this model are. described below in Section. 4.1.., The details of this model are described below in Section \ref{secpkmod}. 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." 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. 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). 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 $(k_{\rm perp}, k_{\rm par})$ 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)." 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. 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." . 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. In order to do this we reconstructed four cillerent selection functions for the 9-hr region. analvzing the full redshift range 0.36 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. 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." 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). 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." 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}." . 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 $\beta = 0.65$." 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. 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." 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." 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." 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." 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}." . 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}. 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." should be different in the two regions of the disk.,should be different in the two regions of the disk. 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." 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. 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." Iu 8&2. governing equations and asstuuptions are preseuted.," In 2, governing equations and assumptions are presented." 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." " 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." A Sununary and discussion is preseuted iu 85., A summary and discussion is presented in 5. 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." The augulu velocity is defined as Q=ήν., The angular velocity is defined as $\Omega = l/r^2 $. 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 $r_g=2GM_{BH}/c^2$." The pseudo-Newtonian potential is widely used to ninüc the Schwarzschild geometry, The pseudo-Newtonian potential is widely used to mimic the Schwarzschild geometry. 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." 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." 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. 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." 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. 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." Iu the geometrical units. the unit of time Is Ty=gfe," In the geometrical units, the unit of time is $\tau_g=r_g/c$." 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. 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." 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." However. without viscosity in such Eulerian," However, without viscosity in such Eulerian" Fin ‘ zou vf to first order in /.,_0(t) = _c - T_c s_c (1+t) to first order in $t$. 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 $T=0$ A 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." However. ealaxy lo galaxy variations are large enough to compronmise this procedure.," However, galaxy to galaxy variations are large enough to compromise this procedure." 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)." 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." 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}." . 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}." .. 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. 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. 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." lxennicutt&IXent.(1983) estimated. on average. | magnitude of extinction in (heir fluxes.," \citet{KK1983} estimated, on average, 1 magnitude of extinction in their fluxes." 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." 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}." . 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." 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. 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." 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. 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." 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." 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 continuum made 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. 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)." 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." 1. and 3.., \ref{allFig} and \ref{2sfig}. 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. " 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." 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." " 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. " 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. 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. 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)." error.,error. 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." We present in Fig., We present in Fig. 2. the resulting image in the K band., \ref{fig:image} the resulting image in the $K$ 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 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)." " 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')." " 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." " 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. 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. 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." 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 $\sim$." 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." Betweer these two main features. the image reveals low or zero emission.," Between these two main features, the image reveals low or zero emission." We interpret the elongated structure as the disk emission., We interpret the elongated structure as the disk emission. 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)." 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." 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)." These features have sizes about or slightly smaller than the maximum angular resolution. and while the separation between the two blobs is resolved at this resolution. the global H-band emission is only marginally resolved by our observations.," These features have sizes about or slightly smaller than the maximum angular resolution, and while the separation between the two blobs is resolved at this resolution, the global $H$ -band emission is only marginally resolved by our observations." In this case. the reconstructed image provides only partial information (2).. such às the orientation of the bulk of the emission. but cannot reproduce the structure of the circumstellar material emitting in the Η band.," In this case, the reconstructed image provides only partial information \citep{lachaume03}, such as the orientation of the bulk of the emission, but cannot reproduce the structure of the circumstellar material emitting in the $H$ band." The large error bars in the H-band data lead to a much smaller dynamical range. probably preventing the ring to appear in the image.," The large error bars in the $H$ -band data lead to a much smaller dynamical range, probably preventing the ring to appear in the image." Finally. the chromaticity of the emission in the H-band has a strong impact on the visibility (with a clear increase with B//. across the spectral channels of an observation: Fig. A2)).," Finally, the chromaticity of the emission in the $H$ -band has a strong impact on the visibility (with a clear increase with $\lambda$, across the spectral channels of an observation; Fig. \ref{fig:V2obs2}) )." " Considering these caveats. the H-band image provides little reliable physical information. and will not be discussed further,"," Considering these caveats, the $H$ -band image provides little reliable physical information, and will not be discussed further." O.lem Considering the incomplete coverage. the limited angular resolution. the large uncertainties. and the scatter in the observations. great caution is required when interpreting the A-band image.," 0.1cm Considering the incomplete coverage, the limited angular resolution, the large uncertainties, and the scatter in the observations, great caution is required when interpreting the $K$ -band image." Interpreting the exhibited details but also the hidden features in these images is not straightforward. as the reconstruction process produces artefacts.," Interpreting the exhibited details but also the hidden features in these images is not straightforward, as the reconstruction process produces artefacts." We performed numerous tests to understand this issue., We performed numerous tests to understand this issue. Our tests show that the images depend on the availability and precision of measurements at high spatial frequency (1.e.. at long baselines). and whether these measurements have a high enough angular resolution to discriminate. e.g.. a ring from a uniform disk.," Our tests show that the images depend on the availability and precision of measurements at high spatial frequency (i.e., at long baselines), and whether these measurements have a high enough angular resolution to discriminate, e.g., a ring from a uniform disk." The ring in the A-band image (~6 mas wide) is resolved at the angular resolution of our measurements. and its appearance is systematic in all the tests we performed with different regularizations.," The ring in the $K$ -band image $\sim$ 6 mas wide) is resolved at the angular resolution of our measurements, and its appearance is systematic in all the tests we performed with different regularizations." On the other hand. the central spot has a size similar to the maximum angular resolutior achieved. with our observations. and is only marginally resolved.," On the other hand, the central spot has a size similar to the maximum angular resolution achieved with our observations, and is only marginally resolved." The exact morphology of this emission can therefore not be determined by the image., The exact morphology of this emission can therefore not be determined by the image. The combination of the different features leads to à complex visibility curve that depends on their morphology but also on their relative flux contributions., The combination of the different features leads to a complex visibility curve that depends on their morphology but also on their relative flux contributions. In addition. possible incorrect calibration of the absolute visibility as well as the chromaticity of the emission (that we consider grey within each band for the image reconstruction) can produce an additional scatter (up to 5-10%)). adding complexity to the visibility curve.," In addition, possible incorrect calibration of the absolute visibility as well as the chromaticity of the emission (that we consider grey within each band for the image reconstruction) can produce an additional scatter (up to ), adding complexity to the visibility curve." However. the ring is encoded in the differential visibilities (corresponding to. different. spatial frequencies) that are not affected by any calibration issue às well as in the closure phases and in the observations at very long baselines that are well-accounted for by MIRA.," However, the ring is encoded in the differential visibilities (corresponding to different spatial frequencies) that are not affected by any calibration issue as well as in the closure phases and in the observations at very long baselines that are well-accounted for by MiRA." Given the large amount of data. the ring 1s systematically retrieved i the reconstructed images.," Given the large amount of data, the ring is systematically retrieved in the reconstructed images." Figs. Ad..," Figs. \ref{fig:V2mira}," A5. show the best-fit to the K-band observations obtained with MIRA Qe=11.2: Vicp= 0.6). and corresponding to the reconstructed image i1 Fig. 2..," \ref{fig:CPmira} show the best-fit to the $K$ -band observations obtained with MiRA $\chi_{r,V^{2}}^{2}=11.2$; $\chi_{r,CP}^{2}=0.6$ ), and corresponding to the reconstructed image in Fig. \ref{fig:image}." One can see that some of the scatter in the observations is Well reproduced indicating a complex structure resulting from a combination of resolved features (such as the ring) anc marginally-resolved features (such as the central spot)., One can see that some of the scatter in the observations is well reproduced indicating a complex structure resulting from a combination of resolved features (such as the ring) and marginally-resolved features (such as the central spot). We nust also consider the sensitivity of the image reconstruction algorithm to a low brightness surface such as the one inside the ring-like feature. a common feature of theses images.," We must also consider the sensitivity of the image reconstruction algorithm to a low brightness surface such as the one inside the ring-like feature, a common feature of theses images." The seatter in the measurements at a given spatial frequency has the consequence of lowering the signal-to-noise ratio (since at a given spatial frequency. different values of the visibilities and CP have to be reproduced for a single image value) and producing a lower dynamical range.," The scatter in the measurements at a given spatial frequency has the consequence of lowering the signal-to-noise ratio (since at a given spatial frequency, different values of the visibilities and CP have to be reproduced for a single image value) and producing a lower dynamical range." In practice. this decreases our capability of detecting low surface brightness emission. and favorssharp transitions m the image.," In practice, this decreases our capability of detecting low surface brightness emission, and favorssharp transitions in the image." On the other hand. if were surrounded by a uniform disk. the reconstructed image would have shown an elongated," On the other hand, if were surrounded by a uniform disk, the reconstructed image would have shown an elongated" of our sample galaxies.,of our sample galaxies. We chose to do so. because (i) Iq. (," We chose to do so, because (i) Eq. (" 2) is a mathematically convenient. function. ancl (ii) the actual profile shapes in the truncation region are erratic due to low S/N ratios and therefore the assumption of any more complicated. functionality than an exponentially. decreasing luminosity density cannot be taken seriously.,"2) is a mathematically convenient function, and (ii) the actual profile shapes in the truncation region are erratic due to low S/N ratios and therefore the assumption of any more complicated functionality than an exponentially decreasing luminosity density cannot be taken seriously." " We will perform. the actual fits to our sky-subtracted images (1.0. in luminosity instead of surface brightness space). to avoid undefined. surface. brightness values due to 7negative"" noise peaks."," We will perform the actual fits to our sky-subtracted images (i.e., in luminosity instead of surface brightness space), to avoid undefined surface brightness values due to “negative” noise peaks." In interpreting the steep [uminositv decline as. truly representative of a decrease in either the light or density distributions of a galactic disc. one has to make sure that the observed. cut-olf is not an artifact duc to inaccurate sky subtraction.," In interpreting the steep luminosity decline as truly representative of a decrease in either the light or density distributions of a galactic disc, one has to make sure that the observed cut-off is not an artifact due to inaccurate sky subtraction." De Vaucouleurs (1948). de Vaucouleurs Capaccioli (1979). and van Dokkum et al. (," De Vaucouleurs (1948), de Vaucouleurs Capaccioli (1979), and van Dokkum et al. (" 1994) have shown that inaccurate sky subtraction (1.6.. oversubtraction) causes a false cut-olf in the luminosity distribution of a galactic disc.,"1994) have shown that inaccurate sky subtraction (i.e., oversubtraction) causes a false cut-off in the luminosity distribution of a galactic disc." This can easily be checked. because the artificial olf would not onv be present in a major axis cut. but also in cuts taken in cXher clireetions.," This can easily be checked, because the artificial cut-off would not only be present in a major axis cut, but also in cuts taken in other directions." 1n all cases. the background. emission in the field. of view of our sanixe galaxies could be well represented. by a plane. of which the slope was determined by the flux in regions sullicientlv far away from the galaxies in order not to be allectecl by residual galactic light.," In all cases, the background emission in the field of view of our sample galaxies could be well represented by a plane, of which the slope was determined by the flux in regions sufficiently far away from the galaxies in order not to be affected by residual galactic light." For most of our observations. these planes could be closely approximated by constant [lux levels across the CCD field.," For most of our observations, these planes could be closely approximated by constant flux levels across the CCD field." The remaining uncertainties in the background. are larecly due to poisson Dolse., The remaining uncertainties in the background are largely due to poisson noise. Fig., Fig. 4 illustrates the quality. of the. background subtraction in. the{ band. where the. background contribution is greater than in our other optical passbands.," \ref{bgcheck.fig} illustrates the quality of the background subtraction in the band, where the background contribution is greater than in our other optical passbands." " The left-hand: panels show the minor-axis (vertical) surface brightness profiles of all sample galaxies (solid lines). racially averaged over ~20"" in order to be able to reach similar or fainter light. levels as for the profiles along the major axes. shown in the right-hand panels."," The left-hand panels show the minor-axis (vertical) surface brightness profiles of all sample galaxies (solid lines), radially averaged over $\sim 20''$ in order to be able to reach similar or fainter light levels as for the profiles along the major axes, shown in the right-hand panels." " We determined the sky noise. e. in the regions used for the background subtraction and created new images by subtracting (background — 20). (background la). (background. | lo). ancl (background | 20). where ""background represents our best estimate of the sky background. in the individual images."," We determined the sky noise, $\sigma$, in the regions used for the background subtraction and created new images by subtracting (background $- 2 \sigma$ ), (background $- 1 \sigma$ ), (background $+ 1 \sigma$ ), and (background $+ 2 \sigma$ ), where “background” represents our best estimate of the sky background in the individual images." Phe under and. oversubtractecd profiles are shown οκο from the solid profiles for reasons of clarity., The under and oversubtracted profiles are shown offset from the solid profiles for reasons of clarity. " The ellects of oversubtraction can clearly be. seen in the minor-axis surface brightness profiles: they show artificial cut-olls and the negative background: values result in undefined surface brightnesses at these heights. above or below z15"" (i.e. the profiles could not be plotted beyond z15"" due to undefined surface brightness values resulting fron oversubtraction of the sky background)."," The effects of oversubtraction can clearly be seen in the minor-axis surface brightness profiles: they show artificial cut-offs and the negative background values result in undefined surface brightnesses at these heights, above or below $\approx 15''$ (i.e. the profiles could not be plotted beyond $\approx 15''$ due to undefined surface brightness values resulting from oversubtraction of the sky background)." Although the effects of oversubtraction on the major-axis profiles. (right-hand panels: vertically averaged between 1.0 and 1.05.) show similar false eut-olfs as for the minor-axis profiles. it appears hat most of the features seen in the light profiles represented » the solid lines are real. since they are also observed. in he undersubtracted light profiles.," Although the effects of oversubtraction on the major-axis profiles (right-hand panels; vertically averaged between $-1.0$ and $1.0 h_z$ ) show similar false cut-offs as for the minor-axis profiles, it appears that most of the features seen in the light profiles represented by the solid lines are real, since they are also observed in the subtracted light profiles." Moreover. a qualitative comparison of both the major and the minor-axis profiles (solid. lines) shows that the apparent truncations in or steepening of the major-axis light profiles do not correspond o similar cut-Us at the same surface brightness levels in the münor-axis profiles in any of our sample galaxies.," Moreover, a qualitative comparison of both the major and the minor-axis profiles (solid lines) shows that the apparent truncations in or steepening of the major-axis light profiles do not correspond to similar cut-offs at the same surface brightness levels in the minor-axis profiles in any of our sample galaxies." We thus conclude that these features are not clue to inaccurate sky subtractions. but represent real deviations from the racial exponential light. profiles.," We thus conclude that these features are not due to inaccurate sky subtractions, but represent real deviations from the radial exponential light profiles." Alternatively. the detection of racially truncated. disces can be artificially enhanced if the disces are strongly warpect.," Alternatively, the detection of radially truncated discs can be artificially enhanced if the discs are strongly warped." In fact. it appears that for a number of our sample galaxies the locus of maximum intensity at large racii may slightly deviate from the main galactic plane direction. (cle Cirijs 1997).," In fact, it appears that for a number of our sample galaxies the locus of maximum intensity at large radii may slightly deviate from the main galactic plane direction (de Grijs 1997)." Llowever. this cllect is negligible for the determination of their radial truncations. because the deviations are.insignificant ancd we average the radial luminosity profiles over a sullicientIy large vertical range to avoid such problems.," However, this effect is negligible for the determination of their radial truncations, because the deviations are and we average the radial luminosity profiles over a sufficiently large vertical range to avoid such problems." In addition. effects due to the galaxies” positions near the CCD edge or to scattered. light [rom foreground. stars are potentially serious.," In addition, effects due to the galaxies' positions near the CCD edge or to scattered light from foreground stars are potentially serious." For our four sample galaxies. the," For our four sample galaxies, the" The two fundamental quantities in explosive phenomena are the kinetic energy. Ex. and the mass of the explosion ejecta. M. or equivalently the expansion velocity. ./=v/c. or Lorentz factor. T=(1—£7.,"The two fundamental quantities in explosive phenomena are the kinetic energy, $E_K$, and the mass of the explosion ejecta, $M_{\rm ej}$, or equivalently the expansion velocity, $\beta\equiv v/c$, or Lorentz factor, $\Gamma= (1-\beta^2)^{-1/2}$." Together. these gross. parameters determine the appearance and evolution. of the resulting explosion.," Together, these gross parameters determine the appearance and evolution of the resulting explosion." Gamma-ray bursts (GRBs) are distinguished by a highly relativistic initial velocity. Do100. as inferred from their nonthermal prompt emission (Goodman=1986;Paezyn-ski 1986).," Gamma-ray bursts (GRBs) are distinguished by a highly relativistic initial velocity, $\Gamma_0\gtrsim 100$, as inferred from their nonthermal prompt emission \citep{goo86,pac86}." ". For the range of 7-ray isotropic-equivalent energies observed in GRBs. E.i,~10?!—107 erg (Bloom.Frail&Sari 2001).. this indicates Μάο~107— M... compared to several .. in supernovae (SNe)."," For the range of $\gamma$ -ray isotropic-equivalent energies observed in GRBs, $E_{\rm\gamma,iso}\sim 10^{51}-10^{54}$ erg \citep{bfs01}, this indicates $M_{\rm ej}\sim 10^{-5}-10^{-3}$ $_\odot$, compared to several $_\odot$ in supernovae (SNe)." The true energy release of GRBs depends sensitively on the geometry of the explosion., The true energy release of GRBs depends sensitively on the geometry of the explosion. " For a collimated outflow (“jet”) with a half-opening angle 0;. itis E=fp£jo. where f,=[1—c0s(0j)] is the beaming fraction: the true ejecta mass is also a factor of ftp lower."," For a collimated outflow (“jet”) with a half-opening angle $\theta_j$, it is $E=f_bE_{\rm iso}$, where $f_b\equiv [1-{\rm cos}(\theta_j)]$ is the beaming fraction; the true ejecta mass is also a factor of $f_b$ lower." Over the past several years there has been growing evidence for such collimated outflows coming mainly from achromatic breaks in the afterglow light curves (e.g.. Kulkarnietal.1999;Staneketal... 1999)).," Over the past several years there has been growing evidence for such collimated outflows coming mainly from achromatic breaks in the afterglow light curves (e.g., \citealt{kdo+99,sgk+99}) )." The epoch at which the break occurs. £j. corresponds to the time at which the ejecta bulk Lorentz factor decreases below p (Rhoads1999;Piran&Halpern 1999).," The epoch at which the break occurs, $t_j$, corresponds to the time at which the ejecta bulk Lorentz factor decreases below $\theta_j^{-1}$ \citep{rho99,sph99}." In this context. several studies have shown that the beaming-corrected energies of most GRBs. in both the prompt -rays and afterglow phase. are of the order of 10?! erg (Frailerαἱ.2001:Bloom.Frail&Kulkarni2003:Yostefαἱ. 2003).," In this context, several studies have shown that the beaming-corrected energies of most GRBs, in both the prompt $\gamma$ -rays and afterglow phase, are of the order of $10^{51}$ erg \citep{fks+01,pk02,bkf03,bfk03,yhs+03}." . The various analyses are sensitive to the energy contained in ejecta with different velocities. [=100 in the 5-rays. PA10 in the early X-rays. and Dzfew in the broad-band afterglow.," The various analyses are sensitive to the energy contained in ejecta with different velocities, $\Gamma\gtrsim 100$ in the $\gamma$ -rays, $\Gamma\gtrsim 10$ in the early X-rays, and $\Gamma\gtrsim {\rm few}$ in the broad-band afterglow." > However. are capable of tracing the existence and energy of ejecta.," However, are capable of tracing the existence and energy of ejecta." " Ενα.Waxman&Kulkarni(2000). overcame this problem in the case of 9970508 by modeling the afterglow radio emission in the non-relativistic phase. thus inferring Ey~ὃν10°"" erg."," \citet{fwk00} overcame this problem in the case of 970508 by modeling the afterglow radio emission in the non-relativistic phase, thus inferring $E_K\approx 5\times 10^{50}$ erg." This analysis has two significant advantages., This analysis has two significant advantages. First and foremost it is independent of jet collimation since the blastwave approaches spherical symmetry on the same timescale that it becomes non-relativistic (Livio&Waxman2000)., First and foremost it is independent of jet collimation since the blastwave approaches spherical symmetry on the same timescale that it becomes non-relativistic \citep{lw00}. . Second. this analysis relies on the simple and well-understood Sedov-Taylor dynamics of spherical blastwaves. as opposed to the hydrodynamics of spreading relativistic jets.," Second, this analysis relies on the simple and well-understood Sedov-Taylor dynamics of spherical blastwaves, as opposed to the hydrodynamics of spreading relativistic jets." In addition. the peak of the synchrotron spectrum on the relevant timescale lies in the radio band where the afterglow is observable for several hundred days.," In addition, the peak of the synchrotron spectrum on the relevant timescale lies in the radio band where the afterglow is observable for several hundred days." Two recent developments make similar analyses crucial., Two recent developments make similar analyses crucial. We now recognize that some GRBs are dominated by mildly relativistic ejecta (Bergerefαἱ.2003b)., We now recognize that some GRBs are dominated by mildly relativistic ejecta \citep{bkp+03}. ". For example. for 0030329 the kinetic energy inferred from the afterglow emission. Εκ~few)=5«10"" erg (Bergererαἱ.2003b).. was an order of magnitude higher than the 7-ray energy release (Priceetαἱ.2003)."," For example, for 030329 the kinetic energy inferred from the afterglow emission, $E_K(\Gamma\sim {\rm few}) \approx 5\times 10^{50}$ erg \citep{bkp+03}, was an order of magnitude higher than the $\gamma$ -ray energy release \citep{pfk+03}." . Similarly. for 9980425 E.=8«1077 erg (Galamaetαἱ.1998:Pianerαἰ.2000) was about 1% of the relativistic kinetic energy of the associated 11998bw. Ex~10°° erg (Kulkarnieraf1998;Li&Chevalier1999).," Similarly, for 980425 $E_\gamma\approx 8\times 10^{47}$ erg \citep{gvp+98,paa+00} was about $1\%$ of the relativistic kinetic energy of the associated 1998bw, $E_K\approx 10^{50}$ erg \citep{kfw+98,lc99}." This begs the question. is there even more energy emerging from the engine. either at the time of the burst or later on. at non-relativistic velocities?," This begs the question, is there even more energy emerging from the engine, either at the time of the burst or later on, at non-relativistic velocities?" " Second. there is a growing interest in ""unification models? for GRBs. X-ray flashes (XRFs) and core-collapse SNe of type Ib/c. relying primarily on energetics arguments."," Second, there is a growing interest in “unification models” for GRBs, X-ray flashes (XRFs) and core-collapse SNe of type Ib/c, relying primarily on energetics arguments." " For example. Lamb.Donaghy&Graziani(2004) argue that GRBs and XRFs share an energy scale of ~107"" erg. and that all type Ib/c SNe give rise to GRBs or XRFs."," For example, \citet{ldg03} argue that GRBs and XRFs share an energy scale of $\sim 10^{49}$ erg, and that all type Ib/c SNe give rise to GRBs or XRFs." Both conclusions result from significantly smaller values of 0; compared to those inferred, Both conclusions result from significantly smaller values of $\theta_j$ compared to those inferred A vivid example of such galaxies that are embedded in a two-dimensional sheet comes from the neighborhood of our Milky Way where nearby spirals are assembled in the Local Super Cluster (deVaucouleursetal.,A vivid example of such galaxies that are embedded in a two-dimensional sheet comes from the neighborhood of our Milky Way where nearby spirals are assembled in the Local Super Cluster \citep{RC3}. 1991).. Although there were some reports of detecting a large-scale coherent orientation of the observed nearby spirals relative to the Local Super Cluster (e.g..Gregoryetal.1981:Helou&Salpeter1982:FlinGocllowskial. 1993).. these previous reports often suffer [rom small sample sizes. hardly being established as compelling evidences.," Although there were some reports of detecting a large-scale coherent orientation of the observed nearby spirals relative to the Local Super Cluster \citep[e.g.,][]{gre-etal81,hel-sal82,fli-god86,gar-etal93}, these previous reports often suffer from small sample sizes, hardly being established as compelling evidences." llowever. very recently. Navarroetal.(2004) used a relatively large sample of nearby ealaxies from the Principal Galaxy Catalog (PGC. Paturel et al.," However, very recently, \citet{nav-etal04} used a relatively large sample of nearby galaxies from the Principal Galaxy Catalog (PGC, Paturel et al." 1997). and. estimated the number distribution of nearby disk galaxies as a function of the supergalatie position angles.," 1997), and estimated the number distribution of nearby disk galaxies as a function of the supergalatic position angles." Thev found that the spin axes of nearby edge-on spirals (c2<1200 kin/s) are stronely inclined relative to the supergalactic plane. and concluded that the observed result is consistent qualitatively with the tidal torque theory.," They found that the spin axes of nearby edge-on spirals $cz < 1200$ km/s) are strongly inclined relative to the supergalactic plane, and concluded that the observed result is consistent qualitatively with the tidal torque theory." Yet. (hey did not make anv (quantitative comparison of the observed result with the predictions of the tidal torque theory.," Yet, they did not make any quantitative comparison of the observed result with the predictions of the tidal torque theory." To make a quanütative comparison. we evaluate (he number distribution of galaxies embedded in sheets with equation (3)).," To make a quantitative comparison, we evaluate the number distribution of galaxies embedded in sheets with equation \ref{eqn:ptheta}) )." Figure 3. plots the results., Figure \ref{fig:obs} plots the results. The (red) dot-dashed line represents our theoretical prediction with the choice of e=0.9 (the best-fit value). while the histogram corresponds to the observational result [roii PGC (seeFig. 2004).," The (red) dot-dashed line represents our theoretical prediction with the choice of $c=0.9$ (the best-fit value), while the histogram corresponds to the observational result from PGC \citep[see Fig. 2 in][]{nav-etal04}." . Obviously. the theoretical curve agrees with the histogram very. well.," Obviously, the theoretical curve agrees with the histogram very well." " determined (he average value of the position angles from (he observed edge-on disk ealaxies to be 0,4,725 in unit of degree. which is in agreement of the theoretical value that we obtained assuming ¢=0.9 in $2."," \citet{nav-etal04} determined the average value of the position angles from the observed edge-on disk galaxies to be $\bar{\theta}_{obs} \approx 25$ in unit of degree, which is in agreement of the theoretical value that we obtained assuming $c=0.9$ in $\S 2$." lt is worth noting that the best-fit value of ¢=0.9 is three times higher than that found in N-body simulation (Lee&Pen2000.2002).," It is worth noting that the best-fit value of $c=0.9$ is three times higher than that found in N-body simulation \citep{lee-pen00,lee-pen02}." . It πια imply that the luminous parts of ealaxies tend (o keep the initial memory of the surrounding matter field better (han (heir dark matter counter parts. consistent with the results from recent gasdynanmical simulations (Chenetal.2003:Navarro2004).," It may imply that the luminous parts of galaxies tend to keep the initial memory of the surrounding matter field better than their dark matter counter parts, consistent with the results from recent gasdynamical simulations \citep{che-etal03,nav-etal04}." . We have predicted. analvGcally a large-scale coherence in the orientation of galaxies embedded in sheets using the tidal torque theory., We have predicted analytically a large-scale coherence in the orientation of galaxies embedded in sheets using the tidal torque theory. Our analvtic model reproduces (he observed inclinations of nearby spiral galaxies in the Local Super Cluster remarkably well. providing a physical quantitative understanding of the observables.," Our analytic model reproduces the observed inclinations of nearby spiral galaxies in the Local Super Cluster remarkably well, providing a physical quantitative understanding of the observables." It should be. however. emphasized," It should be, however, emphasized" parameters (ITarris and Iraxwezvuski. 2002).,"parameters (Harris and Krawczynski, 2002)." With the introduction of the relativistic beaming model of Celotti (Celotti. Cchiscllini. Chiaberge. 2001) and Tavecchio (Tavecchio. et al.," With the introduction of the relativistic beaming model of Celotti (Celotti, Ghisellini, Chiaberge, 2001) and Tavecchio (Tavecchio, et al." 2000). most X-rav cuussion frou jets has been iuterpreted as indicating either svuchrotrou eniüssion or mivorse Compton scattering off the cosmic microwave backeround (CAIB).," 2000), most X-ray emission from jets has been interpreted as indicating either synchrotron emission or inverse Compton scattering off the cosmic microwave background (CMB)." For 3€1129. we show that svuchrotron cluission is the probable process. as has been found for à nuuber of other FRI radio ealaxies (Worrall. Birkinshaw. Tardcastle. 2001: Hardcastle. Birkiushaw. Worral 2001).," For 129, we show that synchrotron emission is the probable process, as has been found for a number of other FRI radio galaxies (Worrall, Birkinshaw, Hardcastle, 2001; Hardcastle, Birkinshaw, Worral 2001)." The iupliceatious of the detected N-ray emission are discussed in sec. ??.., The implications of the detected X-ray emission are discussed in sec. \ref{sec:disc}. " The redshift of the radio galaxy. at the ceuter of the cluster. 1129.1 is z=0.0208 (Spiurad. 1975) aud we take this for our distauce estimate of D; 2126 Mpe with IL, = 50]au + + and q, = 0."," The redshift of the radio galaxy at the center of the cluster, 129.1 is z=0.0208 (Spinrad, 1975) and we take this for our distance estimate of $_L$ =126 Mpc with $_o$ = 50 km $^{-1}$ $^{-1}$ and $_o$ = 0." One aresec then corresponds to 0.60 kpe., One arcsec then corresponds to 0.60 kpc. The Nav observation was obtained with the ACIS-S detector ou the Chandra Observatory (obsid 2218. 2000Dec09).," The X-ray observation was obtained with the ACIS-S detector on the Chandra Observatory (obsid 2218, 2000Dec09)." The exposure time was 31.16 ksec aud the 301129 ealaxy was observed with the back ihuninated S3 chip., The exposure time was 31.46 ksec and the 129 galaxy was observed with the back illuminated `S3' chip. After standard Chandra pipeline xocessuse (RLCUSUPD12.1 ou 2000Dec12) we rejected intervals with excess counting rates (indicative of particle flares) resulting iu a livetinie of 30.105 ksec., After standard Chandra pipeline processing (R4CU5UPD12.1 on 2000Dec12) we rejected intervals with excess counting rates (indicative of particle flares) resulting in a livetime of 30.405 ksec. " Events with euergies less than 0.3keV or greater than & keV were rejected,", Events with energies less than 0.3keV or greater than 8 keV were rejected. " We then binned the data by a factor of l/l to obtain nuages with pixel size 0.123"".", We then binned the data by a factor of 1/4 to obtain images with pixel size $^{\prime\prime}$. Various Gaussian smoothius functions were then convolved with the data aud one example is shown in üeure L. an overlay of the radio nuage with N-rav contours.," Various Gaussian smoothing functions were then convolved with the data and one example is shown in figure \ref{fig:over}, an overlay of the radio image with X-ray contours." " While it is clear that there is excess N-rav cluission coincident with the first visible radio kuot. ""δι, if appears that the X-rav niorphologv is essentially a projection frou the core rather than a completely resolved separate structure."," While it is clear that there is excess X-ray emission coincident with the first visible radio knot, `N2.3', it appears that the X-ray morphology is essentially a projection from the core rather than a completely resolved separate structure." " There is also à 1 to 2 6 excess located at the beeiuuiue of the secoud radio kuot. ""N5.0."," There is also a 1 to 2 $\sigma$ excess located at the beginning of the second radio knot, `N5.0'." All of these features are weak., All of these features are weak. " For a circular aperture of radius 0.9"", we fud only 30 net couuts in the core and an additional 12 net counts defining the jet."," For a circular aperture of radius $^{\prime\prime}$, we find only 30 net counts in the core and an additional 12 net counts defining the jet." N5.0 contains only 1 net counts., N5.0 contains only 4 net counts. " The observation was porkmined with a stage offset Csi z/) of -5.56uuu 19.5"" or 213 pixels oward the readout edge). av offset of -1 to move he target to the center of a node. aud a specified roll augle so as to position the 17 radio tail ou the ACTS-S array."," The observation was performed with a stage offset ('sim z') of -5.86mm $^{\prime\prime}$ or 243 pixels toward the readout edge), a y offset of $^{\prime}$ to move the target to the center of a node, and a specified roll angle so as to position the $^{\circ}$ radio tail on the ACIS-S array." " Since the tare’et position was not he ceuter of the galaxy. this procedure resulted in the core of the 1129 eaaxv being 90"" from he optical axis."," Since the target position was not the center of the galaxy, this procedure resulted in the core of the 129 galaxy being $^{\prime\prime}$ from the optical axis." To check ou the reality of the jet morphology. à l.19keV point spread fiction (PSF) was generated to match the location off-axis and the κα size of 0.1237.," To check on the reality of the jet morphology, a 1.49keV point spread function (PSF) was generated to match the location off-axis and the pixel size of $^{\prime\prime}$." " This PSF nuage was then smoothed with a 1"" Gaussian.", This PSF image was then smoothed with a $^{\prime\prime}$ Gaussian. " The resulting nuage las quasi circular contours with radius of 0.66"" or the inteusitv levels.", The resulting image has quasi circular contours with radius of $^{\prime\prime}$ for the intensity levels. " This value cau be conrpared with 0.8"" for 1129 in directions to he south and south-west (away from the jet) aud 1.2"" for the contour iu the position angle of the jet.", This value can be compared with $^{\prime\prime}$ for 129 in directions to the south and south-west (away from the jet) and $^{\prime\prime}$ for the contour in the position angle of the jet. If he N-vay jet were to be caused by statistical lappenstance. it’s alignment with the radio jet would be coincidental.," If the X-ray jet were to be caused by statistical happenstance, it's alignment with the radio jet would be coincidental." To asses the various eciission iechandsnas or the N-ravs. we need to define areas {aid heir implied cutting volumes) and measure intcusitics.," To asses the various emission mechanisms for the X-rays, we need to define areas (and their implied emitting volumes) and measure intensities." These regious were selected ou the us of the smoothed map (fie. D).," These regions were selected on the basis of the smoothed map (fig. \ref{fig:over}) )," but the neasunrenmients were made on the eveut file., but the measurements were made on the event file. Miudful of the paucity of X-ray photons. we are conteut with order of magnitude estimates.," Mindful of the paucity of X-ray photons, we are content with order of magnitude estimates." " For the core. we have taken a circle of radius 0.95"": for the A-rav jet we use a rotated box of dineusions 2.0351.637: and for the N5.0 feature we use a stnall circle. of radius 0.92”."," For the core, we have taken a circle of radius $^{\prime\prime}$ ; for the X-ray jet we use a rotated box of dimensions $^{\prime\prime}~\times~1.63^{\prime\prime}$; and for the N5.0 feature we use a small circle of radius $^{\prime\prime}$." These regious are shown in fig. 5.., These regions are shown in fig. \ref{fig:regions}. " Usine the PIMIAIS tool and NSPEC/fakeit with a power law spoectruui we fud a conversion value for l οὖν (0.3 to 8S keV) to unabsorbed fiux. £,.(0.5-5keV) of 1.11 (a=0.5): 1.16 (a=L.0): aud 1.27 (a21.5) «10H ere cna*2 ?«L1"," Using the PIMMS tool and XSPEC/fakeit with a power law spectrum, we find a conversion value for 1 c/s (0.3 to 8 keV) to unabsorbed flux, $_x$ (0.5-5keV) of 1.11 $\alpha$ =0.5); 1.16 $\alpha$ =1.0); and 1.27 $\alpha$ =1.5) $\times~10^{-11}$ erg $^{-2}$ $^{-1}$." Thisdoc allows us to determine rough fluxes for the features measured., This allows us to determine rough fluxes for the features measured. The VLA data used in this paper are those described in Tavlor et al. (, The VLA data used in this paper are those described in Taylor et al. ( 2001).Iowever. we mainly used the S CIIz data at thei iuberent resolution of 0.537. FWIOIAL rather thau the,"2001).However, we mainly used the 8 GHz data at their inherent resolution of $^{\prime\prime}$ FWHM rather than the" eas would then fuel star formation there (e.g...Goodman2003).,"gas would then fuel star formation there \citep[e.g.,][]{Goodman03}." . Summarising this. applicability of our model demands that SMDBII. feeding be primary and star. formation secondary in the inner few parsees of ACN.," Summarising this, applicability of our model demands that SMBH feeding be primary and star formation secondary in the inner few parsecs of AGN." Lf this holds. nuclear star clusters grow only when SMDIIS cannot.," If this holds, nuclear star clusters grow only when SMBHs cannot." Finally. our model explicitly. assumes that the nuclear star clusters ancl bulges of chwarl ellipticals form in a quasi-spherical or at least a geometrically thick disc configuration of gas.," Finally, our model explicitly assumes that the nuclear star clusters and bulges of dwarf ellipticals form in a quasi-spherical or at least a geometrically thick disc configuration of gas." Wo instead the gas is in a thin disc configuration before the onset of star formation. the feedback. efficiency would be greatly. reduced. ancl no significant. bulge would be formed.," If instead the gas is in a thin disc configuration before the onset of star formation, the feedback efficiency would be greatly reduced, and no significant bulge would be formed." Therefore our model does not apply to bulgeless spiral galaxies., Therefore our model does not apply to bulgeless spiral galaxies. Hf central. Z5. tens of parsec of these galaxies ave [ed via gaseous disces (e.g.Milosavljevié2004).. then the mass of the NC's need. not saturate at the value given. by equation 5..," If central $\simlt $ tens of parsec of these galaxies are fed via gaseous discs \citep[e.g.,][]{Milosavljevic04a}, then the mass of the NCs need not saturate at the value given by equation \ref{msignc}." The assumption that star formation proceeds on à single dynamical timescale is à lower limit on the time actually required., The assumption that star formation proceeds on a single dynamical timescale is a lower limit on the time actually required. In fact it is more likely that star formation in the bulge takes several dynamical times to complete., In fact it is more likely that star formation in the bulge takes several dynamical times to complete. Indeed. observationally we know that Giant Molecular Clouds in the Milly Way must be contracting much slower than dynamical collapse (Zuckerman&Palmer1974). to explain the low star formation cllicicney in the Galaxy. presumably due to feedback by star formation inside the clouds (MelIxee 1989)..," Indeed, observationally we know that Giant Molecular Clouds in the Milky Way must be contracting much slower than dynamical collapse \citep{ZuckermanPalmer74} to explain the low star formation efficiency in the Galaxy, presumably due to feedback by star formation inside the clouds \citep{McKee89}. ." We would therefore expect a transition. regime. around a~150kms+ where galaxies may contain cither nuclear clusters or black holes.," We would therefore expect a transition regime around $\sigma \sim 150\,\mbox{km\,s}^{-1}$ where galaxies may contain either nuclear clusters or black holes." This boundary region extends over a factor of ~2 in e., This boundary region extends over a factor of $\sim 2$ in $\sigma$. In this region the competition between NCs and. SMDILI depends on the detail of gas deposition in the inner region of the galaxy ancl perhaps the merger history of the galaxy., In this region the competition between NCs and SMBH depends on the detail of gas deposition in the inner region of the galaxy and perhaps the merger history of the galaxy. The picture we have presented. is necessarily very simplified., The picture we have presented is necessarily very simplified. One would like to include effects such as a realistic galaxy bulee potential. density. inhomogencitics. and possible cooling elfects.," One would like to include effects such as a realistic galaxy bulge potential, density inhomogeneities, and possible cooling effects." Further. the changeover between NC anc SALBLEdominated bulges depends on the merger history of the galaxy.," Further, the changeover between NC and SMBH–dominated bulges depends on the merger history of the galaxy." For all these reasons a numerical treatment of this picture is desirable., For all these reasons a numerical treatment of this picture is desirable. The fact that our own Galaxy appears to lic in the regime where the merger history may play an important role should make such studies rewarding., The fact that our own Galaxy appears to lie in the regime where the merger history may play an important role should make such studies rewarding. Theoretical astrophysics rescarch at the University of Leicester is supported by ai STECRolling grant., Theoretical astrophysics research at the University of Leicester is supported by a STFCRolling grant. ALW acknowledges a Roval Society University Rescarch Fellowship., MIW acknowledges a Royal Society University Research Fellowship. for a single pixel as given by equation 4..,for a single pixel as given by equation \ref{e3}. " With the noise (equation 4)) and the signal (equation 3)), it is straight forward to evaluate equation 2 if one assumes a certain PSF shape."," With the noise (equation \ref{e3}) ) and the signal (equation \ref{e2}) ), it is straight forward to evaluate equation \ref{e1} if one assumes a certain PSF shape." " As a simple example, we show the resulting positional uncertainty for a case in which the position is estimated from a Gaussian shaped PSF-core with a FWHM of 6 pixels that contains 3096 of the stellar light."," As a simple example, we show the resulting positional uncertainty for a case in which the position is estimated from a Gaussian shaped PSF-core with a FWHM of 6 pixels that contains $30\%$ of the stellar light." " As above, the light from inside a 4-pixel radius was used."," As above, the light from inside a 4-pixel radius was used." " The error so obtained represents the statistical limit to the positional accuracy for a single, reduced frame."," The error so obtained represents the statistical limit to the positional accuracy for a single, reduced frame." " Usually, astrometry is done on combined objects frames with varying pointing positions (’mosaics’)."," Usually, astrometry is done on combined objects frames with varying pointing positions ('mosaics')." " This improves the statistical precision limit by a factor ,/Npointing compared to equation 4..", This improves the statistical precision limit by a factor $\sqrt{N_\mathrm{pointing}}$ compared to equation \ref{e3}. We briefly describe the method by which we obtain astrometric positions., We briefly describe the method by which we obtain astrometric positions. The lack of any extragalactic background source in the NIR is one of the main obstacles for astrometry in the GC., The lack of any extragalactic background source in the NIR is one of the main obstacles for astrometry in the GC. Therefore all position measurements are relative to other sources in any given image., Therefore all position measurements are relative to other sources in any given image. " The link to the international celestial reference frame ICRF is only possible due to a set of SiO maser stars, which are both NIR and radio sources."," The link to the international celestial reference frame ICRF is only possible due to a set of SiO maser stars, which are both NIR and radio sources." The position vectors relative to Sgr A* of the latter can be measured with high accuracy (??)..," The position vectors relative to Sgr A* of the latter can be measured with high accuracy \citep{Reid:2003p142, Reid:2007p169}." The position and motion of Sgr A* in the ICRF in turn is well known (?7?)..," The position and motion of Sgr A* in the ICRF in turn is well known \citep{Reid:1999p1531,Reid:2004p190}. ." " An additional complication is that with the current 1kx1k NACO detector, a suitable sampling (=Apix/FWHM =13mas/pix, Trippe et al."," An additional complication is that with the current $\times$ 1k NACO detector, a suitable sampling $\approx4\,$ $/$ $\,=13\,$ mas/pix, Trippe et al." " in preparation) is only reached for the central few arcseconds (depending on the dithering scheme), while the SiO maser stars are found out to 20""."," in preparation) is only reached for the central few arcseconds (depending on the dithering scheme), while the SiO maser stars are found out to 20”." Therefore it is more practical to measure the SiO maser positions with a larger pixel scale (27mas/pix for NACO) and relate the finer scale to the coarser sampling by a set of reference stars that can be reliably detected in both scales.," Therefore it is more practical to measure the SiO maser positions with a larger pixel scale $27\,$ mas/pix for NACO) and relate the finer scale to the coarser sampling by a set of reference stars that can be reliably detected in both scales." " That also helps to overcome the large dynamic range needed, given that the brightest SiO maser star used for astrometry has a magnitude of mx8.5 (?7) and that one is interested in the positions of stars as faint as mx&19."," That also helps to overcome the large dynamic range needed, given that the brightest SiO maser star used for astrometry has a magnitude of $m_\mathrm{K}\approx8.5$ \citep{Blum:2003p1118, Reid:2007p169} and that one is interested in the positions of stars as faint as $m_\mathrm{K}\approx19$." " In practical terms, the procedure is as follows: From a set of images, obtained between 2002 and 2009 in the 27 mas/pix scale, we derive astrometric positions and proper motions for a set of e100 reference stars."," In practical terms, the procedure is as follows: From a set of images, obtained between 2002 and 2009 in the $27\,$ mas/pix scale, we derive astrometric positions and proper motions for a set of $\approx 100$ reference stars." " This relies on the work of ?,, which allows us to calculate the astrometric positions of the SiO maser stars for the given NIR epochs."," This relies on the work of \cite{Reid:2007p169}, which allows us to calculate the astrometric positions of the SiO maser stars for the given NIR epochs." " We use mosaics corrected for their geometric distortion (?) and a full, 6-parameter linear transformation to relate pixel and astrometric positions of eight SiO masers."," We use mosaics corrected for their geometric distortion \citep{Trippe:2008p1123} and a full, 6-parameter linear transformation to relate pixel and astrometric positions of eight SiO masers." For any given image in the 13 mas/pix scale we determine the PSF from the image and deconvolve it using the Lucy-Richardson algorithm (?)..," For any given image in the $13\,$ mas/pix scale we determine the PSF from the image and deconvolve it using the Lucy-Richardson algorithm \citep{Lucy:1974p216}." " After beam restoration with a Gaussian beam we determine the stellar pixel positions by Gaussian fits to the positions, both to the reference stars and the sources targeted."," After beam restoration with a Gaussian beam we determine the stellar pixel positions by Gaussian fits to the positions, both to the reference stars and the sources targeted." " The transformation used to link the astrometric reference star positions to their pixel positions is a 20-parameter, third order polynomial transformation, which should also implicitly correct for any large scale (5"") image distortion."," The transformation used to link the astrometric reference star positions to their pixel positions is a 20-parameter, third order polynomial transformation, which should also implicitly correct for any large scale (5”) image distortion." " This is useful since for the smaller pixel scale we were not able to construct a reliable distortion model, indicative that the effect is fairly small (?).."," This is useful since for the smaller pixel scale we were not able to construct a reliable distortion model, indicative that the effect is fairly small \citep{Trippe:2008p1123}." For a more complete description of the procedure see ?.., For a more complete description of the procedure see \cite{Gillessen:2009p1117}. " A multitude of systematic uncertainties are present in the astrometric data, the most important ones being atmospheric turbulence, image distortions, unrecognized source confusion and uncertain PSF halos."," A multitude of systematic uncertainties are present in the astrometric data, the most important ones being atmospheric turbulence, image distortions, unrecognized source confusion and uncertain PSF halos." " The time scales involved are very different; atmospheric effects are present even in a single frame, while confusion of sources happens on time scales of years."," The time scales involved are very different; atmospheric effects are present even in a single frame, while confusion of sources happens on time scales of years." The section discusses the error sources (roughly) by increasing time scale involved., The section discusses the error sources (roughly) by increasing time scale involved. " Time variable refraction in Earth's atmosphere, induced by turbulence cells, blurs ground-based astronomical images, an effect which is called 'seeing'."," Time variable refraction in Earth's atmosphere, induced by turbulence cells, blurs ground-based astronomical images, an effect which is called 'seeing'." " For the observations discussed here, the seeing is partly corrected by the adaptive optics (AO) system."," For the observations discussed here, the seeing is partly corrected by the adaptive optics (AO) system." The resulting PSF is a superposition of a close to diffraction-limited core with a seeing-limited halo., The resulting PSF is a superposition of a close to diffraction-limited core with a seeing-limited halo. Useful parameters to describe the performance of the AO are the Strehl ratio (SR; the ratio of measured central flux compared tothe diffraction-limited central flux) and the FWHM of the PSF., Useful parameters to describe the performance of the AO are the Strehl ratio (SR; the ratio of measured central flux compared tothe diffraction-limited central flux) and the FWHM of the PSF. The AO correction in our data is achieved with a single guide star (single-conjugate AO)., The AO correction in our data is achieved with a single guide star (single-conjugate AO). following argument.,following argument. Usiug the expausious given by equatious (22)) aud (?2)). we find the angular inteeraucl is z(seu(7)) —sgu(? — (91) T|3»1 ancl |r—gQ/Z» L.," Using the expansions given by equations \ref{DVAS}) ) and \ref{DSAS}) ), we find the angular integrand is 2 - - V_2 X_2)^2 + X_1^2 X_2^2 ) - - ]for $|\tilde{\tau}| \gg 1$ and $|\tilde{\tau} - \qe \Omega t| \gg 1$ ." Usine the relation [On+1)=nt). one cau easily show that LX4.(02) ," Using the relation $\Gamma(n+1) = n\Gamma(n)$, one can easily show that X_2 = V_2 = X_1." The integrand therefore simplifies to qp VENTUS (7))— — gQN]?. which is zero unless 0«7gQ! (Lor !> 0).," The integrand therefore simplifies to - V_1^2 ) - - ]^2, which is zero unless $0 < \tilde{\tau} < \qe \Omega t$ (for $t > 0$ )." For large qf. therefore. the augular integral is approximately given byeduQd," For large $\qe \Omega t$, therefore, the angular integral is approximately given by = . )" " ConilDAP oed;(ΗΕ ) P where 1«νάο, "," |, where $1 \ll \nu \ll \qe \Omega t$." For qQI3»p. the above expression cau be approximated by evaluating it al 7=qOIL. giviug πα 1)) 16V NIS OU = 0). . wherewe have used equation15.3.7⋅↽↡⋅−⋅in Abramowitz⋅&Stegun↴(L972)ans to evaluate f(a.ib:e:2xDP ," For $\qe \Omega t \gg \nu$, the above expression can be approximated by evaluating it at $\tilde{\tau} = \qe \Omega t$, giving E_i t 1) 16 V_1^2 X_1^2 E_i(t = 0) , wherewe have used equation15.3.7in \cite{as72} to evaluate $F(a,b;c;1)$ " These are used to fix the values of various scaled quautitics: The best fit curve is shown in Fie.,These are used to fix the values of various scaled quantities: The best fit curve is shown in Fig. 7., 7. The changes iu the spectruini caused by varving central mass AL. accretion rate M. external magnetic feld |By| aud disk’s haltopening angle A are demonstrated in Fies.," The changes in the spectrum caused by varying central mass $M$, accretion rate $\dot{M}$, external magnetic field $\vert B_0\vert$ and disk's half-opening angle $\Delta$ are demonstrated in Figs." " 8. 9. 10 and ll. respectively,"," 8, 9, 10 and 11, respectively." The spectral shapes are very different roni those of the compact-disk case and of the viscous ADAF inodels, The spectral shapes are very different from those of the compact-disk case and of the viscous ADAF models. Syuchrotron oenission has α very wide oeakk and bremsstraliluug is neeligibly αμα]., Synchrotron emission has a very wide peak and bremsstrahlung is negligibly small. The former act is due to a high temperature at the inner edge (see sub-subsection 1.3.2) aud the latter. to lower densities iu he disk.," The former fact is due to a high temperature at the inner edge (see sub-subsection 4.3.2) and the latter, to lower densities in the disk." The emüssiou iu the XN-rav baud is supported w the inverse Compton scattering from the radio baud., The emission in the X-ray band is supported by the inverse Compton scattering from the radio band. The temperature ποσα the outer edge falls even to such a small value that the assumption of complete ionization )econmes invalid., The temperature near the outer edge falls even to such a small value that the assumption of complete ionization becomes invalid. Although the position of outer edge may seein to be relevant from a viewpoiut of spectrum. it is nevertheless iurportaut also in this case as a fitting )mndary of the iuner magnetic field to the external one.," Although the position of outer edge may seem to be irrelevant from a viewpoint of spectrum, it is nevertheless important also in this case as a fitting boundary of the inner magnetic field to the external one." The fitting predicts that the boundary value is comparable o the interstellar field (a few pC)., The fitting predicts that the boundary value is comparable to the interstellar field (a few $\mu$ G). The fitting both to 86 GIIz audROSAT Νταν data »outs is possible also iu this model., The fitting both to 86 GHz and X-ray data points is possible also in this model. However. it is clear hat the fitting curve runs above the observed upper iuits in the IR baud.," However, it is clear that the fitting curve runs above the observed upper limits in the IR band." The fitting in the frequency rauge roni 100 to 1000 CIIz also becomes considerably poor compared with the case of compact disk., The fitting in the frequency range from 100 to 1000 GHz also becomes considerably poor compared with the case of compact disk. For these reasous. we judee that this model cannot reproduce the observed xoadbaud spectrum of Sey A.," For these reasons, we judge that this model cannot reproduce the observed broadband spectrum of Sgr $^*$." This fact sugeests again hat the inner edee of the accretion disk does not coincide with the mareinally stable orbit., This fact suggests again that the inner edge of the accretion disk does not coincide with the marginally stable orbit. The wide range of the disk’s radii which is obtained from this fitting inplies that RORAS)~ον107., The wide range of the disk's radii which is obtained from this fitting implies that $\Re(R_{\rm out}) \sim 6\times 10^3$. Since ROR) ropreseuts the ratio of toroidal to poloidal maenetic fields. most parts of the disk are very likely to be unstable to global MIID instabilities of helical type.," Since $\Re(R)$ represents the ratio of toroidal to poloidal magnetic fields, most parts of the disk are very likely to be unstable to global MHD instabilities of helical type." " For this reason too. we consider that the present case (Le. Ri,= Ry) is quite unrealistic. at least. for Ser A""."," For this reason too, we consider that the present case (i.e., $R_{\rm in} = R_{\rm ms}$ ) is quite unrealistic, at least, for Sgr $^*$." The spectra calculated from ADAF models of both viscous and resistive types commouly have the saturated part at the lower euds of the spectra due to the svuchrotron self-absorption., The spectra calculated from ADAF models of both viscous and resistive types commonly have the saturated part at the lower ends of the spectra due to the synchrotron self-absorption. " It is of great interest to soe that the huninosity jL, of this part is essential to determine the mass of the central black hole. iu both types of models."," It is of great interest to see that the luminosity $\nu L_{\nu}$ of this part is essential to determine the mass of the central black hole, in both types of models." " Especially, in the viscous model. the huninosity of this frequency part is determined almost ouly by the black hole mass."," Especially, in the viscous model, the luminosity of this frequency part is determined almost only by the black hole mass." The reason is as follows., The reason is as follows. The temperature in ADAFs ay be considered essentially as the iou virial temperature aud hence decreases as ~AOL., The temperature in ADAFs may be considered essentially as the ion virial temperature and hence decreases as $\sim R^{-1}$. Apart from a πιοσα] factor due to a reduced I&epleriau rotation. this is exactly true in the resistive mnodel.," Apart from a numerical factor due to a reduced Keplerian rotation, this is exactly true in the resistive model." This is also true in the viscous models for the main part of an accretion flow except im the Inner region Where the electron temperature deviates from the jon temperature aud remains almost coustant (c.e..Naravan Yi 995b).," This is also true in the viscous models for the main part of an accretion flow except in the inner region where the electron temperature deviates from the ion temperature and remains almost constant (e.g.,Narayan Yi 1995b)." Therefore. the coutribution to the spectrum from each aunulus of radius & aud width dW? is equal.," Therefore, the contribution to the spectrum from each annulus of radius $R$ and width $R$ is equal." " Iutegratiug these contributions up to the outer οσο, we obtain LITARIRa-T,(RintR? where Ry is the radius of the disk’s inner edge in the resistive model aud of the outer edge of the two-temperature region in the viscous models."," Integrating these contributions up to the outer edge, we obtain $L^{\rm RJ}_{\nu} \propto T_{e}(R_{\rm in})R_{\rm in}R_{\rm out} =T_e(R_{\rm out})R_{\rm out}^2$, where $R_{\rm in}$ is the radius of the disk's inner edge in the resistive model and of the outer edge of the two-temperature region in the viscous models." We have TRxi0 commonly to both types of ADAF models., We have $T_e R\propto m$ commonly to both types of ADAF models. Further. smee radius scales as the gravitational radius iu the case of viscous ADAFs. we obtain the mass dependence confirming the above statement.," Further, since radius scales as the gravitational radius in the case of viscous ADAFs, we obtain the mass dependence confirming the above statement." " Ou the other haud. iu the case of resistive ADAFs. we have where the dependences on the parameters other thau i have come from the expression of 2,4."," On the other hand, in the case of resistive ADAFs, we have where the dependences on the parameters other than $m$ have come from the expression of $R_{\rm out}$ ." Iu spite of these dependences. themass depeudenuce is essential also im this case.," In spite of these dependences, themass dependence is essential also in this case." This is because the dependence on 5 is rather weak and the value of by is strouely restricted from the position of the svuchrotron peak (see the discussion below)., This is because the dependence on $\dot{m}$ is rather weak and the value of $b_0$ is strongly restricted from the position of the synchrotron peak (see the discussion below). We estimate the svuchrotrou peal frequency following Mahadevan (1997). aud examine its behavior in both viscous and resistive models.," We estimate the synchrotron peak frequency following Mahadevan (1997), and examine its behavior in both viscous and resistive models." For cach aunulus of radius 2 and width da. the svuchrotron photons iu the radio rauge up to a critical frequency m are strongly self-absorbed and result in the Bavleigh-Jewus spectu.," For each annulus of radius $R$ and width $R$, the synchrotron photons in the radio range up to a critical frequency $\nu_{\rm c}$ are strongly self-absorbed and result in the Rayleigh-Jeans spectrum." " Therefore. the critical frequency of the spectrum is determined by equating the contributions to £, from optically thick aud thin sides of the frequency: where wy is defined as (2s=2n(Quy)."," Therefore, the critical frequency of the spectrum is determined by equating the contributions to $L_{\nu}$ from optically thick and thin sides of the frequency: where $x_{\rm c}$ is defined as $x_{\rm c}= 2\nu_{\rm c}/(3\nu_0\theta_e^2)$." Solving this equation. we can determine the value of wee nunuerncallv (Appendix B oof Mahadevan 1997).," Solving this equation, we can determine the value of $x_{\rm c}$ numerically (Appendix B of Mahadevan 1997)." Provided that this value does not depend stronely on RR. A and other parameters. we obtain Itf the disk has uniform temperature aud maeuetic field. then the svuchrotrou peak is rather sharp aud bas a peal frequency at i.," Provided that this value does not depend strongly on $R$, $\Delta$ and other parameters, we obtain If the disk has uniform temperature and magnetic field, then the synchrotron peak is rather sharp and has a well-defined peak frequency at $\nu_{\rm c}$ ." When they vary with the radius R. however. substitution of the dependences of T; aud D iu both viscous aud resistive ADAF models vield," When they vary with the radius $R$, however, substitution of the $r$ -dependences of $T_{\rm e}$ and $B$ in both viscous and resistive ADAF models yield" " 03x525. z22.5: c0 z2. L«10* (te/0.1) AL. £=LrageM, to 2~2. πωης23«103 τω~thaneser10* ra (te~1j). δωνωω, (te~1833). μηνα App. Mi, μυ "," $0\lsim z\lsim 5$ $z\approx 2.5$ $z=0$ $z\approx 2$ $4\times10^7$ $\epsilon$ $\dot M$ $L=L_{\rm Edd}=\epsilon\dot M c^2$ $t_Q$ $z\sim 2$ $n_Q/n_G \sim 3\times 10^{-3}$ $t_Q\sim t_{\rm Hub} n_Q/n_G\sim 10^7$ $t_{\rm Q}\sim10^8$ $M_{\rm bh}/M_{\rm halo}$ $t_{\rm Q}\sim10^6$ $M_{\rm bulge}$ $M_{\rm bh}$ $M_{\rm bh}$ $M_{\rm halo}$ " as wy=1 exactly.,as $w_{0}=1$ exactly. All measurements since 2004 (bar 2) are consistent with this value at the lo level., All measurements since 2004 (bar 2) are consistent with this value at the 1 $\sigma$ level. One of the common themes which has emerged. in the past few vears is that we are now in the era of “precision cosmology”., One of the common themes which has emerged in the past few years is that we are now in the era of “precision cosmology”. IH is instructive to study what the data reveals about how we reached this point and. what precision is currently. achievable for. the dillerent. parameters and using the different techniques., It is instructive to study what the data reveals about how we reached this point and what precision is currently achievable for the different parameters and using the different techniques. We quantify the precision of measurements to be the size of the 1o error bar as a percentage of the ficlucial (WALADPT) value. for each parameter., We quantify the precision of measurements to be the size of the $1\sigma$ error bar as a percentage of the fiducial (WMAP7) value for each parameter. We have also tried using the error bar size as a percentage of the quoted central value of cach measurement. finding5 no significant5 cüllerence in our results (except for," We have also tried using the error bar size as a percentage of the quoted central value of each measurement, finding no significant difference in our results (except for" "Removing the white noise floor bv first subtracting it aud then extrapolating (he noisier portions vields (he lower light spectra in relfig:med.pecbb. Thisisthendividedbytheempiricallydelermined MTF. (03). where f(y=1.04"" as described in the appendix.","Removing the white noise floor by first subtracting it and then extrapolating the noisier portions yields the lower light spectra in \\ref{fig:med_spec}b b. This is then divided by the empirically determined MTF,$M^2(k)=M_d^2(k)/(1+\ell_0^4k^4)$ , where $\ell_0=1.04''$ as described in the appendix." The results are the two upper light CULVES., The results are the two upper light curves. The column density found from these various versions of the median spectra are shown in τοσο με., The column density found from these various versions of the median spectra are shown in \\ref{fig:med_den}. T hesolideurvesofeachshadearetheresullof removingnoiseandcorrectingforthe MTF., The solid curves of each shade are the result of removing noise and correcting for the MTF. Iheb ," The broken curves above these are from the raw spectra, while the dashed curves below are after noise has been removed but no MTF correction performed." 3.0x10.7 ? and 2.9x10* ? respectively., Symbols mark the values of these at $z=1.5$ Mm: $3.0\times10^{-3}$ $^{-2}$ and $2.9\times10^{-3}$ $^{-2}$ respectively. " The median spectra are clearly very close to pure exponentials. S(A)~e 74, "," The median spectra are clearly very close to pure exponentials, $S(k)\sim e^{-2kd}$ ." This [functional form suggests the empirical model for the null column density of one-ininute, This functional form suggests the empirical model for the null column density of one-minute analvsis package (lIligdonetal.2004).. usually with the inproved “optimal extraction procedure in Lebouteilleretal.(2010)Release.,"analysis package \citep{hig04}, usually with the improved ""optimal extraction"" procedure in \citet{leb10}." . The spectral features at rest [rame wavelengths e 8 which we use to make uniform measures of source luminosity can be traced with the IRS continuously with redshift for 0. « , The spectral features at rest frame wavelengths $\sim$ 8 which we use to make uniform measures of source luminosity can be traced with the IRS continuously with redshift for 0 $<$ ol photospheric radius from the measured frequencies (Tripathy Antia 1999).,of photospheric radius from the measured frequencies (Tripathy Antia 1999). If these svslemalic errors are independent of Gime. (then it would be possible to determine the temporal variation in (he solar radius using Emode Ireequencies.," If these systematic errors are independent of time, then it would be possible to determine the temporal variation in the solar radius using f-mode frequencies." The αἱtempts so far (Dziembowski et al., The attempts so far (Dziembowski et al. 1998. 2000. 2001: Antia οἱ al.," 1998, 2000, 2001; Antia et al." 2000. 2001) eive conflicting results.," 2000, 2001) give conflicting results." Using the first few data sets from the Michelson Doppler Imager (MDI). Dziembowski et al. (," Using the first few data sets from the Michelson Doppler Imager (MDI), Dziembowski et al. (" 1998) found that the solar radius is increasing with solar activity.,1998) found that the solar radius is increasing with solar activity. They found an inerease by about 4 km in 6 months just after the solar minimum., They found an increase by about 4 km in 6 months just after the solar minimum. If this variation was indeed correlated to solar activity we would expect a much larger varialion in radius during the solar evcle., If this variation was indeed correlated to solar activity we would expect a much larger variation in radius during the solar cycle. Subsequently. using more data Dziembowski et al. (," Subsequently, using more data Dziembowski et al. (" 2000) found no svstematic variation in the solar radius.,2000) found no systematic variation in the solar radius. This work used all data sets from MDI that were obtained before the contact with SOILO satellite was lost., This work used all data sets from MDI that were obtained before the contact with SOHO satellite was lost. Using a few cata sets Irom (he Global Oscillation network Group (GONG). Antia et al. (," Using a few data sets from the Global Oscillation network Group (GONG), Antia et al. (" 2000) found the solar radius to be decreasing with activitv. but subsecuentlv using more extensive data sets from GONG and MDI Antia et al. (,"2000) found the solar radius to be decreasing with activity, but subsequently using more extensive data sets from GONG and MDI Antia et al. (" 2001) found no evidence for any variation in the solar radius.,2001) found no evidence for any variation in the solar radius. ILowever. using essentially same data seis from MDI. Dziembowski et al. (," However, using essentially same data sets from MDI, Dziembowski et al. (" 2001) (hereinafter DGS) have found a decrease in (he solar radius.,2001) (hereinafter DGS) have found a decrease in the solar radius. Unlortunately. the claimed variation. if any. in all these works is of the order of a few km and even a small chanee in svstemalic errors can give rise to spurious variations of this order.," Unfortunately, the claimed variation, if any, in all these works is of the order of a few km and even a small change in systematic errors can give rise to spurious variations of this order." Clearly. a more careful analvsis of É-mode Irequencies is required before drawing any conclusions about variation of the solar radius.," Clearly, a more careful analysis of f-mode frequencies is required before drawing any conclusions about variation of the solar radius." Antia et al. (, Antia et al. ( 2001) have shown that the variation in mode frequencies is more complex than what is assumed in other studies.,2001) have shown that the variation in f-mode frequencies is more complex than what is assumed in other studies. These variations can be decomposed into at least (wo components., These variations can be decomposed into at least two components. One of these components is oscillatory with a period of 1 vr. while the second component is correlated will solar activity.," One of these components is oscillatory with a period of 1 yr, while the second component is correlated with solar activity." The amplitudes of bot these components increase with frequency and hence are not likely to arise from radius variations., The amplitudes of both these components increase with frequency and hence are not likely to arise from radius variations. Variation in the solar radius will cause frequency. shifts that are proportional to frequency. but the observed variations have much sleeper dependence on frequency.," Variation in the solar radius will cause frequency shifts that are proportional to frequency, but the observed variations have much steeper dependence on frequency." The oscillatory component is most likely to be an artifact introduced by orbital period of the Earth., The oscillatory component is most likely to be an artifact introduced by orbital period of the Earth. Antia et al. (, Antia et al. ( 2001) have also shown that. most of the discrepancy between different results about radius variation using mode [requencies can be explainecl if (hese (wo components are invoked in the temporal variations.,"2001) have also shown that, most of the discrepancy between different results about radius variation using f-mode frequencies can be explained if these two components are invoked in the temporal variations." In particular. Antia et al. (," In particular, Antia et al. (" 2000) failed to detect the oscillatory component as thev used only 5 data sets covering a period of 3 vears.,2000) failed to detect the oscillatory component as they used only 5 data sets covering a period of 3 years. Further. alter accounting Lor these two components in temporal variations there is no evidence for any variation in the solar radius.," Further, after accounting for these two components in temporal variations there is no evidence for any variation in the solar radius." DGS have claimed that the solar radius decreases at à rate of 1.5 km ! during 19962000., DGS have claimed that the solar radius decreases at a rate of 1.5 km $^{-1}$ during 1996–2000. However. thev have not removed (he oscillatory component in [mode Irequency variation and hence their claim needs to be examined carefully.," However, they have not removed the oscillatory component in f-mode frequency variation and hence their claim needs to be examined carefully." js e e (a. e) a (Naef jns!. a7''7. jus! a> 52 53. 64. 53. « e Ad Ae («. e) 0.17. ," $m \, s^{-1}$ $a$ $e$ $a$ $e$ $a$ $\upsilon$ $m \, s^{-1}$ $a^{-1/2}$ $m \, s^{-1}$ $a >$ $\S$ $\S$ $\S$ $\S$ $a$ $e$ $\Delta a$ $\Delta e$ $a$ $e$ $^{\circ}$ " We investigated how the reflected spectrum from the planet would be affected by a tidal lock and planetary rotation. using the following asumptions: The hot Jupiter orbiting 7. Boo rotates In x3.1 days (E1 resonance with the orbital motion). anc the rotation axis is co-aligned with that of the star.,"We investigated how the reflected spectrum from the planet would be affected by a tidal lock and planetary rotation, using the following asumptions: The hot Jupiter orbiting $\tau$ Boo rotates in $\approx3.1$ days (1:1 resonance with the orbital motion), and the rotation axis is co-aligned with that of the star." In addition. the rotation of the planet is assumed to be prograde. and the planetary radius is Ry=1.2Κιμ.," In addition, the rotation of the planet is assumed to be prograde, and the planetary radius is $R_{\rm p} = 1.2~R_{\rm Jup}$." A tidal lock causes that an imaginary observer sitting on the planets always sees the same side of the star; the star appears to be non-rotating., A tidal lock causes that an imaginary observer sitting on the planets always sees the same side of the star; the star appears to be non-rotating. " For this reason. v,,=0kms !."," For this reason, $v_{\rm \star,p}=0~{\rm km~s^{-1}}$ ." " According to Equation. 10.. we find that the reflected absorption lines from the planet are broadened by approximately v,sin? 2kms-."," According to Equation \ref{E2:rot111}, we find that the reflected absorption lines from the planet are broadened by approximately $v_{\rm p}~\sin i=2~{\rm km~s^{-1}}$ ." In order to estimate the resulting full width at half maximum (FWHM) of the reflected stellar absorption lines. we investigate slowly rotating stars of similar spectral type.," In order to estimate the resulting full width at half maximum (FWHM) of the reflected stellar absorption lines, we investigate slowly rotating stars of similar spectral type." " A very good candidate is the star HD 136351] (spectral type: F6 IV). which shows a rotational broadening of v,sini=2.8kms! (Reiners Schmidt 2003)."," A very good candidate is the star HD 136351 (spectral type: F6 IV), which shows a rotational broadening of $v_{\star} \sin i=2.8~{\rm km~s^{-1}}$ (Reiners Schmidt 2003)." The average FWHM of the absorption lines is 12kms., The average FWHM of the absorption lines is $12~{\rm km~s^{-1}}$. Since the rotational velocity of the planet is estimated to be smaller (see above). we estimate the resulting FWHM of the reflected stellar absorption lines to be about 11.8kms7!.," Since the rotational velocity of the planet is estimated to be smaller (see above), we estimate the resulting FWHM of the reflected stellar absorption lines to be about $11.8~{\rm km~s^{-1}}$." We observed τ Boo during two consecutive nights in June 2007 using UVES (Dekker et al., We observed $\tau$ Boo during two consecutive nights in June 2007 using UVES (Dekker et al. 2000) mounted on the VLT/UT2 and collected a total of 406 high-reolution spectra (Table 2))., 2000) mounted on the VLT/UT2 and collected a total of 406 high-reolution spectra (Table \ref{t6:journal}) ). In addition to that. we took spectra of the slowly rotating star HD 136351 and the rapidly rotating B-star HD 116087 Qusini=241kms': Hoffleit Jaschek 1991).," In addition to that, we took spectra of the slowly rotating star HD 136351 and the rapidly rotating B-star HD 116087 $v_\star \sin i=241~{\rm km~s^{-1}}$; Hoffleit Jaschek 1991)." The latter star was observed for the identification of tellurie features in the red part of the visual., The latter star was observed for the identification of telluric features in the red part of the visual. The dates of the observations were selected in such a way that the observations were carried out at orbital phases at which the planetary signal was strongest. Le. close to the position of superior conjunction. which would be the secondary transit in case of/=90°.," The dates of the observations were selected in such a way that the observations were carried out at orbital phases at which the planetary signal was strongest, i.e. close to the position of superior conjunction, which would be the secondary transit in case of $i=90^\circ$." We aimed at taking observations in the phase ranges @=0.30 to 0.45 and 0.55 to 0.70. but avoiding @=0.50 because of intense blending of the planetary and stellar absorption lines.," We aimed at taking observations in the phase ranges $\phi=0.30$ to $0.45$ and $0.55$ to $0.70$, but avoiding $\phi=0.50$ because of intense blending of the planetary and stellar absorption lines." The observations were conducted using the red arm of UVES with a non-standard setting centered at wavelength 2=430nm providing 47 full orders and covering the wavelength range t=425 to 632nm., The observations were conducted using the red arm of UVES with a non-standard setting centered at wavelength $\lambda = 430~\rm{nm}$ providing 47 full orders and covering the wavelength range $\lambda=425$ to $632~\rm{nm}$. We observed through a 0.37 slit and the image slicer [S#33. providing us a spectral resolution of R=A/A4110000.," We observed through a 0.3” slit and the image slicer 3, providing us a spectral resolution of $R=\lambda/\Delta\lambda=110~000$." The integration time for our target was selected to provide the maximum count rate but at the same time avoiding to reach the non-linear regime of neither one of the two CCDs., The integration time for our target was selected to provide the maximum count rate but at the same time avoiding to reach the non-linear regime of neither one of the two CCDs. The exposure times for our bright target ranged between 60 and 400 s (120 s on average) and 30 and 60 s (40 s on average). respectively for the first and the second night.," The exposure times for our bright target ranged between 60 and 400 s (120 s on average) and 30 and 60 s (40 s on average), respectively for the first and the second night." We carried out our observations in the fast-R/O mode: the total dead-time between two exposures was 16 s. Due to clouds and thick cirrus. we only collected half of the expected spectra.," We carried out our observations in the fast-R/O mode; the total dead-time between two exposures was 16 s. Due to clouds and thick cirrus, we only collected half of the expected spectra." In addition to the science frames. we obtained a large number of calibration exposures.," In addition to the science frames, we obtained a large number of calibration exposures." Before the start of the first night. we took 163 flat-field and 104 bias exposures.," Before the start of the first night, we took 163 flat-field and 104 bias exposures." In the afternoon before the second night. we collected 245 flat-field and 65 bias exposures.," In the afternoon before the second night, we collected 245 flat-field and 65 bias exposures." The large number of calibration frames was important to achieve a low photon noise in the finally combined flat-field frame (masterflat)., The large number of calibration frames was important to achieve a low photon noise in the finally combined flat-field frame (masterflat). In order to prevent introducing data reduction artefacts to the data. we aimed at keeping the spectra as raw as possible.," In order to prevent introducing data reduction artefacts to the data, we aimed at keeping the spectra as raw as possible." Consequently. we only adopted the absolutely necessary data reduction steps. as pointed out in the following.," Consequently, we only adopted the absolutely necessary data reduction steps, as pointed out in the following." Effects like errors in the wavelength calibration. trends in the continuum. astrumental profile changes were considered in the model for the star/planet (see Section 5).," Effects like errors in the wavelength calibration, trends in the continuum, instrumental profile changes were considered in the model for the star/planet (see Section 5)." In the first step. we created masterbias frames for each ight. being the median of all bias exposures per night.," In the first step, we created masterbias frames for each night, being the median of all bias exposures per night." These masterbias frames were then subtracted from the science frames as well as from the flat-field frames., These masterbias frames were then subtracted from the science frames as well as from the flat-field frames. The error of the flux 1 the science frames was determined on the basis of Poisson statistics and propagated in the further data analysis steps., The error of the flux in the science frames was determined on the basis of Poisson statistics and propagated in the further data analysis steps. In the following step. for each night the flat-field exposures were scaled with their inverse exposure times and then combined into their median (masterflat) to permit high-quality flat-field correction in order to compensate for sensitivity variations of the pixels.," In the following step, for each night the flat-field exposures were scaled with their inverse exposure times and then combined into their median (masterflat) to permit high-quality flat-field correction in order to compensate for sensitivity variations of the pixels." The science frames were divided by the appropriate masterflat., The science frames were divided by the appropriate masterflat. Since both the flat-field frames as well as the object frames show a similar Blaze function. this function was then mostly removed from the object frame.," Since both the flat-field frames as well as the object frames show a similar Blaze function, this function was then mostly removed from the object frame." Finally. 1-dimensional spectral orders (pixel vs. flux) were extracted from the dimensional frames.," Finally, 1-dimensional spectral orders (pixel vs. flux) were extracted from the 2-dimensional frames." We retrieved 47 orders of 4096 pixels each., We retrieved 47 orders of 4096 pixels each. No order merging was applied., No order merging was applied. The observation of the UVES Thorium-Argon (Th-Ar) lamp enabled us to assign each pixel the appropriate value of the wavelength., The observation of the UVES Thorium-Argon (Th-Ar) lamp enabled us to assign each pixel the appropriate value of the wavelength. For each night. we used the Th-Ar spectrum observed before/after the science exposures and established an 8th order polynomial dispersion solution.," For each night, we used the Th-Ar spectrum observed before/after the science exposures and established an 8th order polynomial dispersion solution." All these data reduction steps were performed with the MIDAS software package., All these data reduction steps were performed with the MIDAS software package. After the data reduction. we identified cosmic-ray hits by way of the following procedure: for each spectrum. we compared the flux in every pixel with the median flux of the same pixel in the three predecessor and the three successor spectra. which had been scaled to the same flux as the spectrum under consideration.," After the data reduction, we identified cosmic-ray hits by way of the following procedure: for each spectrum, we compared the flux in every pixel with the median flux of the same pixel in the three predecessor and the three successor spectra, which had been scaled to the same flux as the spectrum under consideration." We flagged those pixels where the difference exceeded 6c as cosmic-ray hits., We flagged those pixels where the difference exceeded $6 \sigma$ as cosmic-ray hits. These pixels were then excluded from further analysis., These pixels were then excluded from further analysis. We furthermore discarded the most weakly exposed regions of each echelle order (the first 300 pixels as well as the last 240 pixels) since the flux level of the continuum was subjected to strong variations., We furthermore discarded the most weakly exposed regions of each echelle order (the first 400 pixels as well as the last 240 pixels) since the flux level of the continuum was subjected to strong variations. Inaddition. the spectral order around the wavelength of vt=630 nm was," Inaddition, the spectral order around the wavelength of $\lambda=630$ nm was" ANAF HETG is designed to provide high resolution spectroscopy up to E/AE~1000 (for point source) between 0.1 keV and 10 keV. If the DLA systelus contain a sufficient column density of highly ionized metals. the high spectral resolution of the WETC will permit detection of resonance lines.,"AXAF HETG is designed to provide high resolution spectroscopy up to $\Delta$ $\sim1000$ (for point source) between 0.4 keV and 10 keV. If the DLA systems contain a sufficient column density of highly ionized metals, the high spectral resolution of the HETG will permit detection of resonance lines." For specificity. we consider 2223-052. a hieh redshift quasar at z = 1.101 which has a DLA cloud at 2=QSL," For specificity, we consider Q2223-052, a high redshift quasar at z = 1.404 which has a DLA cloud at $z=0.484$." X-ray observations with ΓΗΜο |l] show its flux to be 9.5«LOergsκτομ7 between 0.16-3.5 keV. This implics a count rate of 0.36 counts/sec with ANAF MEG in the first order., X-ray observations with $Einstein$ \cite{wilkes} show its flux to be $9.5\times10^{-12} ergs \ s^{-1}cm^{-2}$ between 0.16-3.5 keV. This implies a count rate of 0.36 counts/sec with AXAF MEG in the first order. Civeu the observation time aud the instrument resolving power we can calculate the muni detectable equivalent width of an absorption feature aud the required ion cohuun denusitv., Given the observation time and the instrument resolving power we can calculate the minimum detectable equivalent width of an absorption feature and the required ion column density. In Table 1 Ny is the required column deusitv., In Table 1 $N_{1}$ is the required column density. Tere 7 is the optical depth at the line ceuter. aud the velocity dispersion b=200Ascc.," Here $\tau$ is the optical depth at the line center, and the velocity dispersion $b=200 km/sec$." All cnereies are in the observer frame., All energies are in the observer frame. We assiuune the spectrum of the quasar has the form of a power law | Calactic absorption | an assumed resonauce line from the DLA system due to Si at 1.26&6V. in the observer frame. then fit it with a model not containing the absorption liuc.," We assume the spectrum of the high-z quasar has the form of a power law + Galactic absorption + an assumed resonance line from the DLA system due to Si at $1.26 keV$ in the observer frame, then fit it with a model not containing the absorption line." In the 47 plot we cau clearly find the hue., In the $\chi^{2}$ plot we can clearly find the line. Gurzadyvan&Mazure.(2001) have recently discovered the existence of (hree subgroups ol galaxies in Coma. one of them associated with the eD galaxy NGC 4874 and the other two with NGC 4889 and NGC 4839.,"\citet{GM01} have recently discovered the existence of three subgroups of galaxies in Coma, one of them associated with the cD galaxy NGC 4874 and the other two with NGC 4889 and NGC 4839." Thev conclude that the non-stationarity of the dvnamical processes at work in the Coma core is due to the merging of small-scale groups of galaxies., They conclude that the non-stationarity of the dynamical processes at work in the Coma core is due to the merging of small-scale groups of galaxies. In (his context. each subgroup formed separately aud (hen the merger between the cifferent eroups took place.," In this context, each subgroup formed separately and then the merger between the different groups took place." If this scenario is valid. is (here any relation between Sy and environment and/or MT inside each subgroup?," If this scenario is valid, is there any relation between $S_N$ and environment and/or $M_V^{\rm TOT}$ inside each subgroup?" In order to analyze (his question. we restricted our figures to galaxies belonging to (απάνοια&Mazure.(2001) subgroup 2 and studied in this paper: NGC 4874. IC 4012. IC 4041. IC: 3976. and IC 3959.," In order to analyze this question, we restricted our figures to galaxies belonging to \citet{GM01} subgroup 2 and studied in this paper: NGC 4874, IC 4012, IC 4041, IC 3976, and IC 3959." In Fig., In Fig. 11. ὧν versus host galaxy. magnitude is plotted. while Fig.," \ref{snmv2} $S_N$ versus host galaxy magnitude is plotted, while Fig." 12. shows Sa versus the distance to the galaxy NGC 4374. which is very close to the center of subgroup 2.," \ref{snr2} shows $S_N$ versus the distance to the galaxy NGC 4874, which is very close to the center of subgroup 2." No relation between Sy and LU is found from Fig 1.., No relation between $S_N$ and $M_V^{\rm TOT}$ is found from Fig \ref{snmv2}. But there is an apparent trend in Fie. 12:, But there is an apparent trend in Fig. \ref{snr2}: Sy is bieger in high density environments., $S_N$ is bigger in high density environments. Is this trend real Or is Hb an artifact of the low number of galaxies considered., Is this trend real or is it an artifact of the low number of galaxies considered?. If this result is confirmed. this will be a strong argument in favor of the IGCs model. so the next step in this work will be to enlarge the number of galaxies of the stud.," If this result is confirmed, this will be a strong argument in favor of the IGCs model, so the next step in this work will be to enlarge the number of galaxies of the study." We are very erateful to. W. E. Iuris for reading a preliminary version of (his paper and to J. J. Fuensalida for his helpful comments., We are very grateful to W. E. Harris for reading a preliminary version of this paper and to J. J. Fuensalida for his helpful comments. This article is based on observations made wilh the 2.5 m Isaac Newton Telescope operated on (he island of La Palma by the ING in (he Spanish Observatorio del Roque de Los Muchachos., This article is based on observations made with the 2.5 m Isaac Newton Telescope operated on the island of La Palma by the ING in the Spanish Observatorio del Roque de Los Muchachos. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated bv the Jet. Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautics and Space Achninis(ration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration." This research has made use of the Digitized Sky Survey. produced at the Space Telescope Science Institute αἱ Baltimore under U.S. erant NAGW-2166.," This research has made use of the Digitized Sky Survey, produced at the Space Telescope Science Institute at Baltimore under U.S. grant NAGW-2166." This research has been supported by the Instituto de sca de Canarias (grant P3/94). the DGESIC of the Kingdom of Spain (grant and the DGUI of the autonomous government of the Canary Islands (grant PIL999/008).," This research has been supported by the Instituto de sica de Canarias (grant P3/94), the DGESIC of the Kingdom of Spain (grant PI97-1438-C02-01), and the DGUI of the autonomous government of the Canary Islands (grant PI1999/008)." The selected classical Algol-tvpe systems are presented in Table 1.,The selected classical Algol-type systems are presented in Table 1. The apparent visual magnitudes anc spectral types were collected from the SIAIBAD data base anc thanogllu ct al. (, The apparent visual magnitudes and spectral types were collected from the SIMBAD data base and Ibanoğllu et al. ( 2006).,2006). Since the EWs of € species are depended: on the ellective temperature of the stars we observed. some standard. stars with the same instrumentation., Since the EWs of C species are depended on the effective temperature of the stars we observed some standard stars with the same instrumentation. The list of the standard. stars and their properties are given in Table 2., The list of the standard stars and their properties are given in Table 2. Since the CLL A 4267 line is produced only for the ellective temperatures higher than 10 000 Ix. the standard stars were selected from the main-sequence stars with the effective temperatures between 10 000 and 30 000 Ix. The stellar. continua of the stars having ellective temperatures higher than LO 000 Ix. are casily defined. in contrary to the cool stars. because of the existence of many spectral regions being relatively line-free. at. the neighbourhood of the € LL A 4267 line.," Since the C II $\lambda$ 4267 line is produced only for the effective temperatures higher than 10 000 K, the standard stars were selected from the main-sequence stars with the effective temperatures between 10 000 and 30 000 K. The stellar continua of the stars having effective temperatures higher than 10 000 K are easily defined, in contrary to the cool stars, because of the existence of many spectral regions being relatively line-free at the neighbourhood of the C II $\lambda$ 4267 line." Therefore the equivalent width of this line can casily be measured in the spectra of the stars earlier than the spectral tvpe of AQ., Therefore the equivalent width of this line can easily be measured in the spectra of the stars earlier than the spectral type of A0. As is presented in Tables 1 and 2 the S/N ratio varies with the apparent magnitudes of the stars., As is presented in Tables 1 and 2 the S/N ratio varies with the apparent magnitudes of the stars. In Fig.l we show a part of the spectra of some Algols and standard stars near the region of CILLA 4267 line., In Fig.1 we show a part of the spectra of some Algols and standard stars near the region of C II $\lambda$ 4267 line. The spectra of the Algols are ordered according to their effective temperatures., The spectra of the Algols are ordered according to their effective temperatures. As the effective temperatures lower the EWs of the CLL A 426 7 line are also decreasing., As the effective temperatures lower the EWs of the C II $\lambda$ 426 7 line are also decreasing. The accuracy of an EW on a typical spectrum is estimated to be about 10 which depends on the S/N ratio., The accuracy of an EW on a typical spectrum is estimated to be about 10 which depends on the S/N ratio. Only one spectrum was taken for AL Dra. RAW Gen and V356 Ser.," Only one spectrum was taken for AI Dra, RW Gem and V356 Sgr." The EWs of the C LEA 4267 line could not be measured for these stars either insullicient exposure-times used: or unsuitable orbital phases., The EWs of the C II $\lambda$ 4267 line could not be measured for these stars either insufficient exposure-times used or unsuitable orbital phases. In. Table 3 we present EWs of the ο LL A 4267 line for the standard: stars measured by us and gathered. from the previous. studies., In Table 3 we present EWs of the C II $\lambda$ 4267 line for the standard stars measured by us and gathered from the previous studies. Since the meaning of any measured. quantity depends. on the associated uncertainty we calculated the errors of the measured EWs using the formula given by Cavrcl (1955) and also by Stetson ancl Pancino (2008)., Since the meaning of any measured quantity depends on the associated uncertainty we calculated the errors of the measured EWs using the formula given by Cayrel (1988) and also by Stetson and Pancino (2008). Thev give an approximate formula for estimating the uncertainty of a measured EW as a function of AX and signal-to-noise-ratio. where AX is the (constant) pixel size.," They give an approximate formula for estimating the uncertainty of a measured EW as a function of $\Delta\lambda$ and signal-to-noise-ratio, where $\Delta\lambda$ is the (constant) pixel size." This value has been taken as 0.086 and 0.036 for the spectra we obtained at Asiago and PUG observatories. respectively.," This value has been taken as 0.086 and 0.036 for the spectra we obtained at Asiago and TUG observatories, respectively." Using the S/N ratios given in the last column of Table 1 the uncertainties are calculated and given. in the fifth. column of Table 4., Using the S/N ratios given in the last column of Table 1 the uncertainties are calculated and given in the fifth column of Table 4. Since the standard stars are very bright and. therefore. have higher S/N ratios their errors are about few milli-Xngstroms (mA)).," Since the standard stars are very bright and, therefore, have higher S/N ratios their errors are about few milli-Angstroms )." Moreover we computed rms in for stars with more than four spectra., Moreover we computed rms in for stars with more than four spectra. The rms dispersion was listed. in the last column of Table 4., The rms dispersion was listed in the last column of Table 4. The ellective temperatures for the primary stars are estimated. in) general. from the wide-band D. and V measurements of a system.," The effective temperatures for the primary stars are estimated, in general, from the wide-band B and V measurements of a system." Then. the/ effective temperatures for the secondary stars are obtained [rom the light. curve analysis.," Then, the effective temperatures for the secondary stars are obtained from the light curve analysis." " In the literature clillerent. Zip, values are given for the same star which are not in agreement with its mass.", In the literature different $T_{eff}$ values are given for the same star which are not in agreement with its mass. " In order to estimate the Zep, values for the primary stars of the semi-detached Algol svstems and the standard stars we decided to use a common temperature indicator as cid Ww Tomkin. Lambert anc Lemke (1993)."," In order to estimate the $T_{eff}$ values for the primary stars of the semi-detached Algol systems and the standard stars we decided to use a common temperature indicator as did by Tomkin, Lambert and Lemke (1993)." Since the strength or EW of the € LL A 4267 line is tightly depended. on he effective temperature of the star we calculated the ει values for the standard stars as well as the Aleols using he intermeciate-band photometric measurements., Since the strength or EW of the C II $\lambda$ 4267 line is tightly depended on the effective temperature of the star we calculated the $T_{eff}$ values for the standard stars as well as the Algols using the intermediate-band photometric measurements. " Phe u-h] color and ο] index are very sensitive to the Ley, of the stars and. therefore. they are elfective temperature indicators for he stars earlier than AO."," The [u-b] color and $ [c_{1}] $ index are very sensitive to the $T_{eff}$ of the stars and, therefore, they are effective temperature indicators for the stars earlier than A0." The calibration between {νε and uch] for a wide temperature interval. from 9500 to 30 00019. is adopted from Napiwotzki et al. (," The calibration between $T_{eff}$ and [u-b] for a wide temperature interval, from 9500 to 30 000K, is adopted from Napiwotzki et al. (" "1993): On the other hand. we derived the following relationship between the 775, and. ο] parameter using the {ει and. ei]- given by Nissen (1974): with a regression coellicient of 0.9991.","1993): On the other hand, we derived the following relationship between the $T_{eff}$ and $ [c_{1}] $ parameter using the $T_{eff}$ and $ [c_{1}] $ -values given by Nissen (1974): with a regression coefficient of 0.9991." " This relationship is valid for the ellective temperatures from. 13 000 to 30 000 Ix. The Z;5,;r-values for the standard stars were computed using the the u-b] and ο) parameters taken from. Hauck ancl Mermilliod (1998. hereafter HENIO9S)and are presented in ‘Table 3."," This relationship is valid for the effective temperatures from 13 000 to 30 000 K. The $T_{eff}$ -values for the standard stars were computed using the the [u-b] and $ [c_{1}] $ parameters taken from Hauck and Mermilliod (1998, hereafter HM98)and are presented in Table 3." Phe EWs of C IL A 4267 line for five standard stars are measured by us which are given in the first five lines of Table 3. the EWs for the others (including these stars) are taken from Larclorp and Scholz (1970). Wane et al. (," The EWs of C II $\lambda$ 4267 line for five standard stars are measured by us which are given in the first five lines of Table 3, the EWs for the others (including these stars) are taken from Hardorp and Scholz (1970), Kane et al. (" 1980). Ixilian οἱ al. (,"1980), Kilian et al. (" 1989) and Tomkin. Lambert and Lemke (1993).,"1989) and Tomkin, Lambert and Lemke (1993)." In Fig.2 we show the measured. EWs/A of the standard stars as a function of the mean elfective temperatures of the stars computed by the Eqs. (, In Fig.2 we show the measured $\lambda$ of the standard stars as a function of the mean effective temperatures of the stars computed by the Eqs. ( 2) and (3).,2) and (3). Phe variation of the EWs as a function of the 7;zr; is represented by a third-order polynomial and shown by a continuous line., The variation of the EWs as a function of the $T_{eff}$ is represented by a third-order polynomial and shown by a continuous line. Phe EWs of À 4267 C IL lines are increased up to 20 000 Ix and. then. decreased. gradually.," The EWs of $\lambda$ 4267 C II lines are increased up to 20 000 K and, then, decreased gradually." The intermeciatce-hand photometry of the Xlgol-tvpe binaries were made by Hilditeh and. Hill (1975. hereafter 1175). Lacv (2002. hereafter CLO2).," The intermediate-band photometry of the Algol-type binaries were made by Hilditch and Hill (1975, hereafter HH75), Lacy (2002, hereafter CL02)." " The (5-45)) colors. mij. c, indices ancl ffs values were also given in the catalog of HEMOS."," The ) colors, $m_{1} $, $ c_{1} $ indices and $ H_{\beta} $ values were also given in the catalog of HM98." Since the orbital phases of the observations are known for the values obtained by LUITS and. CLO2 the parameters given by then are preferred. to calculate. the ellective temperatures of the mass-gaining primary stars of the Aleols., Since the orbital phases of the observations are known for the values obtained by HH75 and CL02 the parameters given by them are preferred to calculate the effective temperatures of the mass-gaining primary stars of the Algols. The observations obtained during the primary eclipse are excluded., The observations obtained during the primary eclipse are excluded. However. it should be noted that the (6-y)) colors obtained by CL02 are svstematically bluer than those obtained by ΕΠΤΟ.," However, it should be noted that the ) colors obtained by CL02 are systematically bluer than those obtained by HH75." Io the stars were not observed. by 1III7T5 and CLO2 we used the parameters given by. LIALOS., If the stars were not observed by HH75 and CL02 we used the parameters given by HM98. The effective temperature computed for the primary of CE Cop is too high with respect to its mass. as given in Table 4.," The effective temperature computed for the primary of GT Cep is too high with respect to its mass, as given in Table 4." For this reason a T;ει value of 19 000 Ix. is adopted from Lohle et al. (, For this reason a $T_{eff}$ value of 19 000 K is adopted from Hohle et al. ( 2010).,2010). The measured EWs are corrected. using the formula eiven below:, The measured EWs are corrected using the formula given below: globular clusters on a star-to-star basis within reach for the firsttime!.,globular clusters on a star-to-star basis within reach for the first. . The simulations performed so far have involved 22000 stars with a primordial binary traction.," The simulations performed so far have involved $22\,000$ stars with a primordial binary fraction." Initial conditions relating to (hie masses. positions and velocities of (he stars. as well as the orbital characteristics of the binaries. are the same as for the V=10000 star simulations described in detail by IIurlevetal.(2001).," Initial conditions relating to the masses, positions and velocities of the stars, as well as the orbital characteristics of the binaries, are the same as for the $N = 10\,000$ star simulations described in detail by \citet{hur01}." . In particular. a realistic initial-mass uncton is used to distribute the stellar masses (INxroupa.Tout&Gilmore1993).. and the cluster is subject to a standard Galactic tidal field.," In particular, a realistic initial-mass function is used to distribute the stellar masses \citep{kro93}, and the cluster is subject to a standard Galactic tidal field." The distribution of orbital separations or the primordial binaries is log-normal with a peak al 30 AU. and spans the range ~6H. io 30000 AU.," The distribution of orbital separations for the primordial binaries is log-normal with a peak at $30\,$ AU, and spans the range $\sim 6 \, R_{\odot}$ to $30\,000\,$ AU." The eccentricitv of each binary orbit is taken from a thermal distribution Ileggie1975)., The eccentricity of each binary orbit is taken from a thermal distribution \citep{heg75}. . Positions and velocities of the stars are assigned according to a Plummer nodel (Aarseth.Πόποι&Wielen1974) in virial equilibrium., Positions and velocities of the stars are assigned according to a Plummer model \citep{aar74} in virial equilibrium. We imclude the outcome of three simulations in the results presented here (see Table 1))., We include the outcome of three simulations in the results presented here (see Table \ref{t:table2}) ). The first had a metallicity of Z=0.004. relevant to 47 Tuc. and included 2000 planets of Jupiter mass.," The first had a metallicity of $Z = 0.004$, relevant to 47 Tuc, and included $2\,000$ planets of Jupiter mass." Each planet was placed in a circular orbit about. a randomly chosen parent star al à separation taken from a uniform distribution between 1 and 50 AU.," Each planet was placed in a circular orbit about a randomly chosen parent star at a separation taken from a uniform distribution between 1 and $50\,$ AU." The second simulation involved 3000 Jupiters with the lower limit of the separation distribution reduced io 0.05 AU and the final simulation differs from this only in the use of Z=0.02.," The second simulation involved $3\,000$ Jupiters with the lower limit of the separation distribution reduced to $0.05\,$ AU and the final simulation differs from this only in the use of $Z = 0.02$." Each sinilation was evolved to an age of 4.5 Gyr when ~25% of the initial cluster mass reniained and the binary fraction was still close to 1056.," Each simulation was evolved to an age of $4.5\,$ Gyr when $\sim 25\%$ of the initial cluster mass remained and the binary fraction was still close to ." . Typically the velocity dispersion of the stars in these model clusters was 2kins+ with a core density of 10* pe*.," Typically the velocity dispersion of the stars in these model clusters was $2\,{\rm km } \,{\rm s}^{-1}$ with a core density of $10^3\,$ $\,{\rm pc}^{-3}$." The density of stars at the hall-mass radius is generally a [actor of 10 less that this., The density of stars at the half-mass radius is generally a factor of 10 less than this. Table 2 shows. as a function of time. the number of planets (hat are liberated from (heir parent stars during (he simulation. the number of planetary svstems (hat escape [rom the cluster. and the number of planets (hat are exchanged [rom their original orbit into orbits about another parent star.," Table \ref{t:table3} shows, as a function of time, the number of planets that are liberated from their parent stars during the simulation, the number of planetary systems that escape from the cluster, and the number of planets that are exchanged from their original orbit into orbits about another parent star." Also shown are the number of planets swallowed by their parent star simply as a result of nuclear driven expansion of the stellar envelope., Also shown are the number of planets swallowed by their parent star simply as a result of nuclear driven expansion of the stellar envelope. These are averaged results from the three simulations., These are averaged results from the three simulations. We find a weak preference lor planets in wide orbits to be liberated from (heir parent star: planetary svstems with a 50 AU separation are 10 times more likely to be than those with 1 AU (see Figure 1)). Hleggie.IIu," We find a weak preference for planets in wide orbits to be liberated from their parent star: planetary systems with a $50\,$ AU separation are 10 times more likely to be broken-up than those with $1\,$ AU (see Figure \ref{f:fig1}) )." t&MeMillan.(1996). showed that, \citet{heg96} showed that though of course. there is no indication of the location in the skv of the event.,"though of course, there is no indication of the location in the sky of the event." Note however that the claim by Rood(1979) that SN events can be detected in this way has been questioned. in subsequent studies (e.g. LerronLOS2.. Rishoetal. 1981)).," Note however that the claim by \citet{rood.et.al79} that SN events can be detected in this way has been questioned in subsequent studies (e.g. \citealt{herron82}, \citealt{risbo.et.al81}) )." HL studies cannot constrain the distance to obecause of the highly confused. nature of this region which is close to the galactic plane (Duncan&Cireen20, H studies cannot constrain the distance to because of the highly confused nature of this region which is close to the galactic plane \citep{duncan&green00}. 00).. Slaneetal.(20011) use the non-thermal spectrum of portions Of wwith a power-law model of the emission to compare derivec 11 column densities with other parts of the Vela SNR., \citet{slane.et.al01a} use the non-thermal spectrum of portions of with a power-law model of the emission to compare derived H column densities with other parts of the Vela SNR. Slaneal.(200110) acknowledge the uncertainties in then scaling the cdillerences in column cdensitv to obtain a distance bu argue that the higher column density of implies that it is located somewhere between the back of the Vela SNI and the Vela molecular ridge at 2Ίνρο., \citet{slane.et.al01a} acknowledge the uncertainties in then scaling the differences in column density to obtain a distance but argue that the higher column density of implies that it is located somewhere between the back of the Vela SNR and the Vela molecular ridge at $1-2~{\rm Kpc}$. The lack of an obvious compact central object within the remnant also seemed at first to indicatethat mmust be located at a large distance (Alereghetti2001)., The lack of an obvious compact central object within the remnant also seemed at first to indicate that must be located at a large distance \citep{mereghetti01}. . Llowever. an X-ray source (but with no associated optical counterpart) has recently been discovered. (Pavlovctal. 2001).," However, an X-ray source (but with no associated optical counterpart) has recently been discovered \citep{pavlov.et.al01}." . It appears that the central object might be rather similar to that of Cas Α - a radio quiet. νους Isolated neutron star., It appears that the central object might be rather similar to that of Cas A - a radio quiet young isolated neutron star. However. it is worth noting that there is a 64 ms pulsar with coordinates within the supernova remnant »oundary.," However, it is worth noting that there is a 64 ms pulsar with coordinates within the supernova remnant boundary." Due to the uncertainties involved in the distance of aan association cannot be ruled out (Reclman Aleaburn. in ep).," Due to the uncertainties involved in the distance of an association cannot be ruled out (Redman Meaburn, in prep)." Phe various distance estimates are not consistent with each other and follow-up work is clearly required to remove he uncertainties inherent in the different techniques., The various distance estimates are not consistent with each other and follow-up work is clearly required to remove the uncertainties inherent in the different techniques. Our optical study. olfers a clear distance constraint if wavas generated within the Vela SNR., Our optical study offers a clear distance constraint if was generated within the Vela SNR. Chaetal.(1999) have used optical absorption lines towards a significant sample of OD stars in the direction of the Vela SNR to constrain the distance as 250r.x30pe with a conservative upper limit of 390+I00pc., \citet{cha.et.al99} have used optical absorption lines towards a significant sample of OB stars in the direction of the Vela SNR to constrain the distance as $250\pm30~{\rm pc}$ with a conservative upper limit of $390\pm 100 {\rm pc}$. Clearly. if indeed iis located within the older Vela SN. then the distance is constrained to be ~250pc.," Clearly, if indeed is located within the older Vela SNR then the distance is constrained to be $\sim 250~{\rm pc}$." We note that if subsequen studies firmly indicate that Ilies well bevond the old. Vela SNR. then our model can be puled out.," We note that if subsequent studies firmly indicate that lies well beyond the old Vela SNR, then our model can be ruled out." New [line profiles of ROW 37 have been presented. that show the kinematics of this nebula for the first time., New line profiles of RCW 37 have been presented that show the kinematics of this nebula for the first time. X partia velocity ellipse is discovered in the py array of line profiles., A partial velocity ellipse is discovered in the pv array of line profiles. The kinematics and morphology could suggest. that. the structure of ROW 37 is that of a thin wavy sheet of optica emission that overlaps itself towards the eastern. edge an is undergoing a svstematic expansion., The kinematics and morphology could suggest that the structure of RCW 37 is that of a thin wavy sheet of optical emission that overlaps itself towards the eastern edge and is undergoing a systematic expansion. The western edge curves towards the line of sight but does not appear to form a complete tube or funnel of emission., The western edge curves towards the line of sight but does not appear to form a complete tube or funnel of emission. We compare this feature. with those found. towards other SNRs., We compared this feature with those found towards other SNRs. The evidence that the ROW 37 optical nebula ancl associate X-rav feature. D/D' are in fact. part of hhas been discussed ancl we conclude that it is likely that this is the case.," The evidence that the RCW 37 optical nebula and associated X-ray feature, D/D' are in fact part of has been discussed and we conclude that it is likely that this is the case." A simple explanation for the origin of the morphology of RCW 37 is that hhas occured. within the older. [larger Vela SNI and that a portion of the supernova ejecta from hhas impacted the pre-existing cold dense wall of the Vela SNR.," A simple explanation for the origin of the morphology of RCW 37 is that has occured within the older, larger Vela SNR and that a portion of the supernova ejecta from has impacted the pre-existing cold dense wall of the Vela SNR." The thin sheet of optical emission then traces out the inside edge of this shocked wall while the X-ray emission marks shock-heated gas., The thin sheet of optical emission then traces out the inside edge of this shocked wall while the X-ray emission marks shock-heated gas. This model predicts that the distance to wwill be similar to that of the main Vela SNR which has been recently measured to lic at 250x30pe.," This model predicts that the distance to will be similar to that of the main Vela SNR which has been recently measured to lie at $250\pm 30~{\rm pc}$." We thank the stall of the Anglo-Australian observatory for their excellent assistance during the observations., We thank the staff of the Anglo-Australian observatory for their excellent assistance during the observations. We have mace use of the Data Archive. Smithsonian Astrophysical Observatory. Cambridge ALA. USA: the UBS'T archive. Roval Observatory Edinburgh. Scotland Ulx: and the0SAT Data Archive of the Max-Plank Institut fürr extraterrestrische Physik at Garching. Germany.," We have made use of the Data Archive, Smithsonian Astrophysical Observatory, Cambridge MA, USA; the UKST archive, Royal Observatory Edinburgh, Scotland UK; and the Data Archive of the Max-Plank Institut fürr extraterrestrische Physik at Garching, Germany." MPH and DILL are supported by. PPARC., MPR and DJH are supported by PPARC. for all points on the optical axis. the gain then decreases slowly (while oscillating) if p increases (oll-oplical line). becoming and going further down to its mean value Go=1 [or pZ9Fry.,"for all points on the optical axis, the gain then decreases slowly (while oscillating) if $\rho$ increases (off-optical line), becoming and going further down to its mean value $G=1$ for $\rho \gg \sqrt{{\cal F} \,r_g}$." Thus. as expected. the evavily lens is very sensitive to a (angential motions (e.q.," Thus, as expected, the gravity lens is very sensitive to a tangential motions (e.q." in the image plane)., in the image plane). Another important feature of the solar gravitv lens is a high angular resolution., Another important feature of the solar gravity lens is a high angular resolution. To describe (he angular resolution we will use the angle. eyy. that corresponds (o the distance from the optical axis to the point where gain decreases by 10 dB: where p4u45 is the distance in the image plane where the gain decreases by 10 dB (the distance is given by piu;=i E ," To describe the angular resolution we will use the angle, $\epsilon_{10}$, that corresponds to the distance from the optical axis to the point where gain decreases by 10 dB: where ${\rho_{10dB}}$ is the distance in the image plane where the gain decreases by 10 dB (the distance is given by $\rho_{10dB}\cong\frac{\lambda}{4\pi}\sqrt{\frac{{\cal F}}{2r_g}}$ )." For wavelength A~ I mim resolution equ is estimated to be ejo4í5(5.1mim)=0.11Ro/bgradνι zvad.," For wavelength $\lambda\sim$ 1 mm resolution $\epsilon_{10}$ is estimated to be $\epsilon_{10dB}(b, 1 ~{\rm mm})=0.11~{\cal R}_\odot/{b} ~\pi {\rm rad} = 0.11~\sqrt{{\cal F}_0/{\cal F}}~\pi$ rad." " Since for the Sun the frequency can have values between LO! Lz (radio waves) and. LO!"" Iz (visible light) or even 1011 Hz (5-ravs). a gravitational lens can enlarge the brightness of a star by the same remarkable factor."," Since for the Sun the frequency can have values between $10^4$ Hz (radio waves) and $10^{10}$ Hz (visible light) or even $10^{14}$ Hz $\gamma$ -rays), a gravitational lens can enlarge the brightness of a star by the same remarkable factor." The plane wave is focused into a narrow beam of extreme intensity: the radius of which is p—AF/z., The plane wave is focused into a narrow beam of extreme intensity; the radius of which is $\rho=\sqrt{\lambda {\cal F}/\pi}$. The components of the Povuting vector and the intensity are oscillating wilh a spatial period Thus for Àe I mm this period is 0p=0.118x6/R.. km.," The components of the Poynting vector and the intensity are oscillating with a spatial period Thus for $\lambda ~\sim$ 1 mm this period is $\delta \rho =0.118\times b/{\cal R}_\odot $ km." It is also useful to discuss (he angular distribution of intensity., It is also useful to discuss the angular distribution of intensity. Thus. if telescope is small. (he observed direction to the source will bv determined by the corresponding deflection angle and the telescope's position.," Thus, if telescope is small, the observed direction to the source will by determined by the corresponding deflection angle and the telescope's position." However. if it is large. it will eive a distributionof intensity Z over (he aperture and the observer would essentially see a sienilicantlv magnilied source al 0= ().," However, if it is large, it will give a distributionof intensity ${\cal I}$ over the aperture and the observer would essentially see a significantly magnified source at $\theta\cong0$ ." the evidence for flaring in our observations of HIIST-1. and use this to constrain the early evolution of this flare.,"the evidence for flaring in our observations of HST-1, and use this to constrain the early evolution of this flare." We summarize our conclusions in section 5., We summarize our conclusions in section 5. The jet of M37 was observed with the WEDPC? detector aboard IST on 2001 February 23., The jet of M87 was observed with the WFPC2 detector aboard HST on 2001 February 23. The galaxy core was centered in (he PC. with the jet oriented along the columns of the detector.," The galaxy core was centered in the PC, with the jet oriented along the columns of the detector." The observations were obtained through the F170W filter. whieh has an effective wavelength of 1666À.," The observations were obtained through the F170W filter, which has an effective wavelength of $1666$." ". Six images were taken in an ""L shaped dither pattern with 0725 shilts between the positions.", Six images were taken in an “L” shaped dither pattern with $0\farcs25$ shifts between the positions. The total integration time of the observations was 7600 seconds., The total integration time of the observations was 7600 seconds. We combined the six observations with the Dither package in ΗΑΕ. using the DRIZZLE algorithm from Fruchter&Hook(2002).," We combined the six observations with the Dither package in IRAF, using the DRIZZLE algorithm from \citet{fruchterandhook}." . This both cleans the final image of cosmic rays ancl CCD [Laws ancl takes advantage of the subpixel spacing between image positions to construct a final image with smaller pixels., This both cleans the final image of cosmic rays and CCD flaws and takes advantage of the subpixel spacing between image positions to construct a final image with smaller pixels. The Dither package also corrects the input images for the geometric distortion of the WEDPC?. which is largest in the ultraviolet.," The Dither package also corrects the input images for the geometric distortion of the WFPC2, which is largest in the ultraviolet." The knots of the jet were photometered based on the apertures defined by in their study of HIST optical images of the jets., The knots of the jet were photometered based on the apertures defined by \citet{Perlman} in their study of HST optical images of the jets. We have chosen to use (he saime apertures (o allow direct comparison of our fluxes wilh those presented., We have chosen to use the same apertures to allow direct comparison of our fluxes with those presented. The boundaries of our aper(ures are defimed by [finding (he closest pixel boundary. (hat matches (he positions listed by Perlman., The boundaries of our apertures are defined by finding the closest pixel boundary that matches the positions listed by Perlman. In order to ensure that the core of the galaxy does not interfere with any ol the knots. we have removed the galaxy profile using the ISOPIIOTE package in IRAE.," In order to ensure that the core of the galaxy does not interfere with any of the knots, we have removed the galaxy profile using the ISOPHOTE package in IRAF." " Onlv knot HS'T-1 has anv possible contribution from (he core. as there is little evidence of the galaxy bevond 0755""nn [rom the core."," Only knot HST-1 has any possible contribution from the core, as there is little evidence of the galaxy beyond $0\farcs55$ from the core." The photometry determined within these apertures was calibrated using the default values for the F170W filter eiven in the WEDPC? Calibration Manual (Daggettοἱal...2002)., The photometry determined within these apertures was calibrated using the default values for the F170W filter given in the WFPC2 Calibration Manual \citep{WFPC2}. . Because our images have low background levels. we need (o account [or possible charge transfer efficiency losses.," Because our images have low background levels, we need to account for possible charge transfer efficiency losses." We caleulated the correction using methods from both (1999) and Dolphin(2000)., We calculated the correction using methods from both \citet{WHC} and \citet{Dolphin}. . As the results were similar. we used the average of the two methods as our final correction. and (he dillerence between (he methods as the uncertainty for this correction.," As the results were similar, we used the average of the two methods as our final correction, and the difference between the methods as the uncertainty for this correction." Since both of these methods are based on the assumption of a point source object. we adopted the suggestion presented in Riess(2000) to half the calculated. correction.," Since both of these methods are based on the assumption of a point source object, we adopted the suggestion presented in \citet{Riess} to half the calculated correction." The tvpical level of this correction was about LOY., The typical level of this correction was about $10\%$. Another possible concern is the effect of contaminants on the ΜΕΡΟΣ is generally worse in the UV than at other wavelengths., Another possible concern is the effect of contaminants on the WFPC2 is generally worse in the UV than at other wavelengths. For this set of observations. (he WFPC2 had been cecontaminatecl less (han a week prior. so the correction we applied is less than 2% of the measured counts.," For this set of observations, the WFPC2 had been decontaminated less than a week prior, so the correction we applied is less than $2\%$ of the measured counts." We, We Consider an extra-solar planet of radius /?p. orbital period 7? and orbital inclination / with fy as the time of mid-transit.,"Consider an extra-solar planet of radius $R_{\mbox{\small p}}$, orbital period $P$ and orbital inclination $i$ with $t_{0}$ as the time of mid-transit." " The planet orbits a star S. of known mass AJ, and radius //,. that has an associated lighteurve."," The planet orbits a star S, of known mass $M_{*}$ and radius $R_{*}$, that has an associated lightcurve." We calculate the predicted transit lighteurves based on a simple planet-star model: we assume a luminous primary. linear limb darkening with η=0.5 and a dark massless companion in a circular orbit.," We calculate the predicted transit lightcurves based on a simple planet-star model: we assume a luminous primary, linear limb darkening with $u = 0.5$ and a dark massless companion in a circular orbit." Adding this signal into the observed lightcurve of the star. we calculate the transit statistic Stra (Eqn. 19) ," Adding this signal into the observed lightcurve of the star, we calculate the transit statistic $S_{\mbox{\small tra}}$ (Eqn. \ref{eqn:trastat}) )" for each transit event. and then evaluate the following detection function: Using the same procedure as above. but without actually adding the predicted transit lightcurve into the observed lightcurve of the star. we evaluate the false alarm function: The function {2 is a trigger function that indicates where the data and detection algorithm are capable of detecting a transit of the specified type. and f° indicates where the data alone suggest that such a transit is actually present.," for each transit event, and then evaluate the following detection function: Using the same procedure as above, but without actually adding the predicted transit lightcurve into the observed lightcurve of the star, we evaluate the false alarm function: The function $D$ is a trigger function that indicates where the data and detection algorithm are capable of detecting a transit of the specified type, and $F$ indicates where the data alone suggest that such a transit is actually present." The BRAOS lightcurve data contains some eclipsing binary stars and possibly transits., The BRA05 lightcurve data contains some eclipsing binary stars and possibly transits. Hence both 2 and # are slightly over estimated., Hence both $D$ and $F$ are slightly over estimated. In the upper panel of Fig., In the upper panel of Fig. 2. we plot a subsection of the lightcurve of star 61377 with an injected 0.02 mag. offset of duration 3 h starting at fy= 2451799.5 d. This 185.20 mag G star has a mass. radius and distance of 0.9637;. 0.96/7; and 3152pe respectively.," \ref{fig:DSFS} we plot a subsection of the lightcurve of star 61377 with an injected 0.02 mag offset of duration 3 h starting at $t_{0} = 2451799.5$ d. This $r^{\prime} \approx 18.20$ mag G star has a mass, radius and distance of $M_{\sun}$, $R_{\sun}$ and 3152pc respectively." In the lower panel of Fig., In the lower panel of Fig. 2 we plot the corresponding periodic functions D(fy) and f°(fy) represented by thick and thin continuous lines respectively., \ref{fig:DSFS} we plot the corresponding periodic functions $D \left(t_{0}\right)$ and $F \left(t_{0}\right)$ represented by thick and thin continuous lines respectively. We adopted ρα=LOL Ninin l.Hp=L2Rp P= τς and ;/=90° for this calculation.," We adopted $S_{\mbox{\small min}}~=~10$, $N_{\mbox{\small min}}~=~1$, $R_{\mbox{\small p}}~=~1.2 R_{\mbox{\small J}}$, $P~=~3.338$ d and $i~=~90\degr$ for this calculation." The function £)(44) attains the value of | where there is data of sufficient precision to detect a transit., The function $D \left(t_{0}\right)$ attains the value of 1 where there is data of sufficient precision to detect a transit. The function £'(/4) attains the value of | where there is data that mimics a transit signature. and it has clearly been triggered by the injected offset in the lightcurve data.," The function $F \left(t_{0}\right)$ attains the value of 1 where there is data that mimics a transit signature, and it has clearly been triggered by the injected offset in the lightcurve data." In Eqn. 2..," In Eqn. \ref{eqn:detfunc}," " we integrate out the “nuisance parameters"" {ο and ? to get: where P(det|S.Sin.«πι.Pp.27) is. the detection probability for star S. and f(fo.7) is the joint probability distribution function (PDF) of /, and ;."," we integrate out the “nuisance parameters” $t_{0}$ and $i$ to get: where $\left(\text{det}\,|\,\text{S},S_{\mbox{\small min}},N_{\mbox{\small min}},R_{\mbox{\small p}},P\right)$ is the detection probability for star S and $f(t_{0},i)$ is the joint probability distribution function (PDF) of $t_0$ and $i$." We assume that the parameters fg and ὁ are independent. fy is uniformly distributed over O in 2005. compared with 5.51].1019 Wm 7? in 2007.," In particular H recombination lines are present in 2005 (as was emerging from eclipse) but were apparently weak in 2007; for example, the flux in $\alpha$ was $1.61[\pm0.05]\times10^{-15}$ W $^{-2}$ in 2005, compared with $5.5[\pm1]\times10^{-16}$ W $^{-2}$ in 2007." " However. both Lhe and HJ are present in an optical spectrum of oobtained on 2007 May δ (within cays of the 2007. LRS spectrum) by one of us (LAID) as are a number of 7Dilfuse Interstellar Bands"" (DIBs). which most likely are of interstellar origin."," However, both $\alpha$ and $\beta$ are present in an optical spectrum of obtained on 2007 May 8 (within days of the 2007 IRS spectrum) by one of us (LAH), as are a number of “Diffuse Interstellar Bands” (DIBs), which most likely are of interstellar origin." Phese data will be presented in a future paper (Llelton et al.," These data will be presented in a future paper (Helton et al.," in preparation)., in preparation). We have extracted a continuum from both spectra to highlight the Ulli. features: the result is shown in Fig. 5.., We have extracted a continuum from both spectra to highlight the UIR features; the result is shown in Fig. \ref{UIR1}. There was little change between 2005 and 2007. except that the aand UULI features were significantly stronger in 2007 (when the Ilt hydrogen emission lines were weak).," There was little change between 2005 and 2007, except that the and UIR features were significantly stronger in 2007 (when the IR hydrogen emission lines were weak)." The central wavelengths of the ULRfeatures in ((o.g. 748dE0.01 iin 2005. 7.79+0.01 iin 2007 for the 7.7 feature) are consistent with excitation bv à source with an elfective temperature in excess of ~10! Kk (e.g.Sloanetal.2007:Xcke2011)... and therefore with excitation by the D star.," The central wavelengths of the UIRfeatures in (e.g. $7.48\pm0.01$ in 2005, $7.79\pm0.01$ in 2007 for the `7.7' feature) are consistent with excitation by a source with an effective temperature in excess of $\sim10^4$ K \citep[e.g.][]{sloan,acke}, and therefore with excitation by the B star." The changes we see in the strengths ancl possibly central wavelengths of the ULR features may be associated with changes in the ionisation of the PALL (c.g.Draine&Li 2001).. possibly as a result of changes in the extinetion in the dust shell around the B star.," The changes we see in the strengths and possibly central wavelengths of the UIR features may be associated with changes in the ionisation of the PAH \citep[e.g.][]{draine}, possibly as a result of changes in the extinction in the dust shell around the B star." Fig., Fig. 4 also shows clear evidence for two broad features hat are present in 2007 but not in 2005., \ref{IRS1} also shows clear evidence for two broad features that are present in 2007 but not in 2005. We have subtracted he continuum to highlight these features. (see Fig. 6))., We have subtracted the continuum to highlight these features (see Fig. \ref{C60}) ). Features at these wavelengths are included in the PALIT xickage (Smithetal.2007). but we consider it unlikely that he two features in anre due to emission by PALL molecules. for the following reasons: (a) their absence in 2005. when other ULT. features were present: (b) the strength of the [feature compared with that of theτμ (c) the {Hux ratio.," Features at these wavelengths are included in the PAHFIT package \citep{pahfit} but we consider it unlikely that the two features in are due to emission by PAH molecules, for the following reasons: (a) their absence in 2005, when other UIR features were present; (b) the strength of the feature compared with that of the; (c) the flux ratio." " The [feature was reported17.43 in 77023 by Werneretal. (2004b).. who assigned. it to ""aromatic hvdrocarbons or nanoparticles of unknown mineralogy”: it has subsequentlybeen attributed to Cou (Sellerenctal. 2010).."," The feature was reported in 7023 by \cite{wernerb}, , who assigned it to “aromatic hydrocarbons or nanoparticles of unknown mineralogy”; it has subsequentlybeen attributed to $_{60}$ \citep{sellgren}. ." Possible identifications for these features are aancl σος which in the gas phase has four active vibrational," Possible identifications for these features are and $_{60}$ , which in the gas phase has four active vibrational" Llere subscript 1 and 2 refer to the inner and outer planet. dis the mean longitude. and ze the longitude of pericenter.," Here subscript 1 and 2 refer to the inner and outer planet, $\lambda$ is the mean longitude, and $\varpi$ the longitude of pericenter." We searched for resonances up to Sth order by monitoring these angles for libration around fixed. values., We searched for resonances up to 8th order by monitoring these angles for libration around fixed values. We find just two double svstems in 3:1 MMIS with libration semi-amplitudes of ~150 and ~SO”., We find just two double systems in 3:1 MMRs with libration semi-amplitudes of $\sim 150$ and $\sim 80^\circ$. The case with the larger libration amplitude did not scatter. until the dise had. been photoevaporated., The case with the larger libration amplitude did not scatter until the disc had been photoevaporated. The low frequeneyv. of 2 planet resonances. and the large libration angles. are symptomatic of random entry into resonance due to purely eravitational cllects2008).. rather than systematic driving into resonance clue to gas disc migration2010).," The low frequency of 2 planet resonances, and the large libration angles, are symptomatic of random entry into resonance due to purely gravitational effects, rather than systematic driving into resonance due to gas disc migration." . We observe a dramatically lower resonant fraction than the ~75 percent seen by(2010)., We observe a dramatically lower resonant fraction than the $\sim 75$ percent seen by. .. Phe dillerence is probably due to the short ifetime of the dises in this study compared to the Myr clispersal timescales assumed by(2010).. which allows less time for post-scattering migration to move jxanets into resonance.," The difference is probably due to the short lifetime of the discs in this study compared to the Myr dispersal timescales assumed by, which allows less time for post-scattering migration to move planets into resonance." As noted in section 3.1.. the disc runs have a higher raction that remain stable for the entire simulation than the only runs.," As noted in section \ref{instabilitytimesection}, the disc runs have a higher fraction that remain stable for the entire simulation than the only runs." Because our initial conditions naturally ace the planets near to several MMIS. there dis. the »ossibilitv that two adjacent. planets may get trapped into resonance. a situation that can enhance the stability of a hree planet system.," Because our initial conditions naturally place the planets near to several MMRs, there is the possibility that two adjacent planets may get trapped into resonance, a situation that can enhance the stability of a three planet system." 2010)... We also search cach adjacent pair of planets in the systems hat never scattered. for NIMIUS., We also search each adjacent pair of planets in the systems that never scattered for MMRs. Out of 27 such cases. we ind three in which the inner two planets are in resonance (two 3:2 and one 2:1). ancl three cases in which the outer wo planets are in a 2:1 resonance.," Out of 27 such cases, we find three in which the inner two planets are in resonance (two 3:2 and one 2:1), and three cases in which the outer two planets are in a 2:1 resonance." These resonant svstems are potentially part of the reason for the large number of unscattered systems., These resonant systems are potentially part of the reason for the large number of unscattered systems. Further investigating the unscattered. runs. we discovered that 12 of the 27 unscattered. runs. are in three body resonance.," Further investigating the unscattered runs, we discovered that 12 of the 27 unscattered runs are in three body resonance." In eight cases the innermicelle ancl middleouter pair move into resonance with librating resonance angles (equation 2)). and in three of these the innerouter pair are likewise in a resonance.," In eight cases the inner–middle and middle–outer pair move into resonance with librating resonance angles (equation \ref{eq:resonanceangles}) ), and in three of these the inner–outer pair are likewise in a resonance." Phe chains we find are 9:6:4 (four Cases) 6:3:2.. 3:2:1. (two cases). and4:22:17.," The chains we find are 9:6:4 (four cases), 6:3:2, 3:2:1 (two cases), and." .. In cach case a Laplace angle of the form is identified.LOSS)... which librates. around a fixed value for small integer values of m and». with subscripts 1.2.3 referring to the inner. middle. ancl outer planets.," In each case a Laplace angle of the form is identified, which librates around a fixed value for small integer values of $m$ and $n$, with subscripts 1,2,3 referring to the inner, middle, and outer planets." The other four of the 12 triple resonances are less deeply in resonance: all three exhibit libration of the m.=1. n=3 Laplace angle but the adjacent. planet. pairs are not in the 2:1 resonances.," The other four of the 12 triple resonances are less deeply in resonance; all three exhibit libration of the $m=1$, $n=3$ Laplace angle but the adjacent planet pairs are not in the 2:1 resonances." In Figure 10. we plot the resonant behavior of three example chains: à representative of the O:6:4 cases (Le. a double 3:2 resonance). the 6:3:2. case. and the Laplace resonance case. the former two of which exhibit asvmimetrical resonance in some of the angles.," In Figure \ref{resonantchains} we plot the resonant behavior of three example chains; a representative of the 9:6:4 cases (i.e. a double 3:2 resonance), the 6:3:2 case, and the Laplace resonance case, the former two of which exhibit asymmetrical resonance in some of the angles." In the 9:6:4 run each adjacent. pair of planets is trapped into a 3:2 resonance at 4000 vr. the same time that the Laplace angle begins librating around 4;=5x.," In the 9:6:4 run each adjacent pair of planets is trapped into a 3:2 resonance at $\sim4000$ yr, the same time that the Laplace angle begins librating around $\varphi_L=\pi$." The innerouter pair move into apsidal alignment. but the resonant angles continue to circulate.," The inner–outer pair move into apsidal alignment, but the resonant angles continue to circulate." The 6:3:2 case moves into triple resonance at 1000 vr. roughly the same time as the innermiddle pair lock into à mJ? resonance. but somewhat before the other two pairings fully enter resonance at ~107 vr.," The 6:3:2 case moves into triple resonance at $\sim1000$ yr, roughly the same time as the inner–middle pair lock into a 3:2 resonance, but somewhat before the other two pairings fully enter resonance at $\sim10^4$ yr." ‘Phe initial innermicelle resonance and the Laplace angle all appear to be settling toward resonant angles of 0 or π. but when middleouter and innerouter resonance begin. most of the angles move into asvnunetrical resonances. including the Laplace angle which shifts to librate around a value (very) slightly. more than π.," The initial inner–middle resonance and the Laplace angle all appear to be settling toward resonant angles of 0 or $\pi$, but when middle–outer and inner–outer resonance begin, most of the angles move into asymmetrical resonances, including the Laplace angle which shifts to librate around a value (very) slightly more than $\pi$." The double 2:1 Laplace resonance shows libration of c; around an angle completely: incommensurate with zx., The double 2:1 Laplace resonance shows libration of $\varphi_L$ around an angle completely incommensurate with $\pi$. In this case the innermiddle 2:1. pair. immediately enters asymmetric resonance. along with the Laplace angle.," In this case the inner–middle 2:1 pair immediately enters asymmetric resonance, along with the Laplace angle." " The middleouter 2:1 pair are in a symmetric. resonance. and the innerouter pair are Dürting with asymmetric resonance. though ó, continues to circulate."," The middle–outer 2:1 pair are in a symmetric resonance, and the inner–outer pair are flirting with asymmetric resonance, though $\phi_1$ continues to circulate." We note that his asvmmetric behavior in the Laplace resonance is a oeferred: outcome of simulations of migration into double resonance2008).. although this particular case did not undergo very much migration.," We note that this asymmetric behavior in the Laplace resonance is a preferred outcome of simulations of migration into double resonance, although this particular case did not undergo very much migration." Lt would appear hat the high incidence of triple resonances. as well as he perhaps enhanced stability due to a single adjacent »ur migrating into resonance. are the underlving reason ind the large number of unscattered: svstems in our ivcirodynamic simulations compared to the runs.," It would appear that the high incidence of triple resonances, as well as the perhaps enhanced stability due to a single adjacent pair migrating into resonance, are the underlying reason behind the large number of unscattered systems in our hydrodynamic simulations compared to the runs." Disc-planet interactions may be able to excite eecentricity to modest values. e~0.1: 0.22006)... but planetary. dynamics are probably necessary to reach higher values.," Disc-planet interactions may be able to excite eccentricity to modest values, $e \sim 0.1$ –0.2, but planetary dynamics are probably necessary to reach higher values." Some of the more interesting features in the disc surface density in our simulations occur when eccentricities are high. during or just after scattering (sce Figures 3 ancl 4).," Some of the more interesting features in the disc surface density in our simulations occur when eccentricities are high, during or just after scattering (see Figures \ref{example1} and \ref{example2}) )." These include non-axisvnunetric features. new gaps being opened. and eccentric gaps.," These include non-axisymmetric features, new gaps being opened, and eccentric gaps." Wo scattering (or at least its signature in the eccentricity of the planets) is reasonably common in transitional disces. then these features may. be observable.," If scattering (or at least its signature in the eccentricity of the planets) is reasonably common in transitional discs, then these features may be observable." We estimate the likelihood that these features might be observed by calculating the amount of time that systems spend with at least one planet's eccentricity above a threshold. value. while also having at least 1 of gas left.," We estimate the likelihood that these features might be observed by calculating the amount of time that systems spend with at least one planet's eccentricity above a threshold value, while also having at least 1 of gas left." " his distribution is shown in Figure 14. for three values of the threshold eccentricity. 0,,;,=0.1. 0.25. and 0.5."," This distribution is shown in Figure \ref{fig:tobs} for three values of the threshold eccentricity, $e_{min} = 0.1$, 0,25, and 0.5." For the higher and more interesting thresholds. mos of the runs do not have eccentric enough. planets for any reasonable amount of time.," For the higher and more interesting thresholds, most of the runs do not have eccentric enough planets for any reasonable amount of time." " Lowe require that. interesting features are present for something like of our tvpica dise lifetime. fan,~35103 vr. a threshold of ον=0.25 means that of the runs will have planets in eccentric enough orbits to be notieceable: thus a few percent. of transition discs might be expected to harbor planets caugh in the act or the aftermath of scattering."," If we require that interesting features are present for something like of our typical disc lifetime, $t_{obs} \sim 3 \times 10^4$ yr, a threshold of $e_{min}=0.25$ means that of the runs will have planets in eccentric enough orbits to be notieceable; thus a few percent of transition discs might be expected to harbor planets caught in the act or the aftermath of scattering." eood agreement between the theoretically computed time delay. and the one obtained from the cross-correlation of photospheric A 10827 aud chromospheric A 10830 velocity maps. filtered around the 6 πι] baud.,"good agreement between the theoretically computed time delay, and the one obtained from the cross-correlation of photospheric $\lambda$ 10827 and chromospheric $\lambda$ 10830 velocity maps, filtered around the 6 mHz band." They showed that the chromospheric 6 mlz signal is a result of lincar wave propagation of the plotospleric perturbations in the 6 ΙΙ range. rather than the consequence of the nonlinear interaction of plotospleric modes asproposed by Camman&Leibacher(198L).," They showed that the chromospheric 6 mHz signal is a result of linear wave propagation of the photospheric perturbations in the 6 mHz range, rather than the consequence of the nonlinear interaction of photospheric modes asproposed by \citet{Gurman+Leibacher1984}." . The works cited above were limited to the study. of oscillations at ouly two heights (one photospheric aud oue chromospheric). separated by several hundreds of kilometers.," The works cited above were limited to the study of oscillations at only two heights (one photospheric and one chromospheric), separated by several hundreds of kilometers." It is thus interesting to perform a more detailed sampling of the sunspot atimosphere. usine more spectral lines formed at several intermediate heights between these two regions.," It is thus interesting to perform a more detailed sampling of the sunspot atmosphere, using more spectral lines formed at several intermediate heights between these two regions." On the one haud. observationally detected spatial wave patterus iu sunspots are rather complex (Bogdan&Judge2006).," On the one hand, observationally detected spatial wave patterns in sunspots are rather complex \citep{Bogdan+Judge2006}." . Ou the other haud. recent numerical simulations of waves πι sunspots also sugeest a complex picture of the fast and slow mmagucto-acoustic waves propagating sinultancouslv in the same lavers but iu different clirections aud with cifferent phase speeds CUshomenuko&Collacos 2009).," On the other hand, recent numerical simulations of waves in sunspots also suggest a complex picture of the fast and slow magneto-acoustic waves propagating simultaneously in the same layers but in different directions and with different phase speeds \citep{Khomenko+Collados2009}." .. This requires a more refined uiltilaver study of sunspot waves., This requires a more refined multi-layer study of sunspot waves. Studies of this kind often represent an observational challenge since several spectral Lucs have to be detected simultancously not oulv iu iuteusitv but also in polarized light., Studies of this kind often represent an observational challenge since several spectral lines have to be detected simultaneously not only in intensity but also in polarized light. In our paper. we report on such multi-line spectropolarimetric observations.," In our paper, we report on such multi-line spectropolarimetric observations." Our alm ds to cover the gap between the photospheric aud chromospheric signals and analyze sunspot oscillations at the formation heights of several spectral lines formed between aandTel., Our aim is to cover the gap between the photospheric and chromospheric signals and analyze sunspot oscillations at the formation heights of several spectral lines formed between and. For that we use simmltaueous observations obtained with two iustymuents. the POlwimetric Llttrow Spectrograph (POLIS.Becketal.2005b) απ the Tenerife Iutrared Polavimeter ΤΠ.Colladosetal. 2007).. attached to the Cerman Vacuuu Tower telescope at the Observatorio del Teide at Tenerife.," For that we use simultaneous observations obtained with two instruments, the POlarimetric LIttrow Spectrograph \citep[POLIS,][]{Beck+etal2005b} and the Tenerife Infrared Polarimeter II \citep[TIP-II,][]{Collados+etal2007}, attached to the German Vacuum Tower telescope at the Observatorio del Teide at Tenerife." Apart from information about waves. our inultidlaver study has also allowed us to estimate the formation heights of the spectral lines in the sunspot atmosphere. iucludiug ]line. several bbleuds in the wing of this line aud the infrared lines of aat A 10827 aad aat À 10830. Α.," Apart from information about waves, our multi-layer study has also allowed us to estimate the formation heights of the spectral lines in the sunspot atmosphere, including line, several blends in the wing of this line and the infrared lines of at $\lambda$ 10827 and at $\lambda$ 10830 ." . The structure of the paper is the following., The structure of the paper is the following. In Sect. 2..," In Sect. \ref{sect:observation}," the observations and data reduction are explained., the observations and data reduction are explained. Section 3 describes the analysis of the velocity oscillations at several heights., Section \ref{sect_ana} describes the analysis of the velocity oscillations at several heights. The results are discussed in Sect. L.," The results are discussed in Sect. \ref{sect_disc}," which also presents our conclusions., which also presents our conclusions. The observatious analyzed in this work were obtained on 2007 August 28 with two different instruments. POLIS and TIP-IL attached to the Cermuan Vacuuu Tower Telescope (VTT) at the Observatorio del Teide.," The observations analyzed in this work were obtained on 2007 August 28 with two different instruments, POLIS and TIP-II, attached to the German Vacuum Tower Telescope (VTT) at the Observatorio del Teide." Simultaneous aud co-spatial scaus of a suuspot located near the center of the Sun (jj= 0.96) were taken with both iustrunients, Simultaneous and co-spatial scans of a sunspot located near the center of the Sun $\mu=0.96$ ) were taken with both instruments. The slit was placed over the center of the sunspot., The slit was placed over the center of the sunspot. The observations were obtained with realtime seeing correction by the Riepeuleucr-Iustitute adaptive optics system (vonderLuchectal.2003)., The observations were obtained with real-time seeing correction by the Kiepenheuer-Institute adaptive optics system \citep{vonderluehe+etal2003}. . The spectra of the blue. channel of POLIS include À 3968 inteusitv profiles and some plotospheric line bleuds iu the wines ofIL. covering a spectral range frou 3061.9 tto 3071.3 wwith a spectral sampling of 20 | and a spatial sampling of 0729 per pixel.," The spectra of the blue channel of POLIS include $\lambda$ 3968 intensity profiles and some photospheric line blends in the wings of, covering a spectral range from 3964.9 to 3971.3 with a spectral sampling of 20 $^{-1}$ and a spatial sampling of $0''29$ per pixel." The Ca spectra were reduced for the flatfield (Beckctal. 20052a.b).. and were also corrected for the transmissjou curve of the order-selecting interterence filter iu frout of the camera.," The Ca spectra were reduced for the flatfield \citep{Beck+etal2005a, Beck+etal2005b}, and were also corrected for the transmission curve of the order-selecting interference filter in front of the camera." For the wavelength calibration. the line-core positions of the iron lines at 3965.15. 3966.07. 3966.63. 3967.12 and 3969.26 ln an average quiet Sun region were determined by a second orderpolvnoudal fit.," For the wavelength calibration, the line-core positions of the iron lines at 3965.45, 3966.07, 3966.63, 3967.42 and 3969.26 in an average quiet Sun region were determined by a second orderpolynomial fit." We then determined the wavelength scale that matched best all the position values., We then determined the wavelength scale that matched best all the position values. TIP-H. viclded the four Stokes paramcters ZQUV ina spectral range from 10822.7 tto LOS33.7 with a spectral sampling of 11 31 and a spatial sampling of 01S per pixel., TIP-II yielded the four Stokes parameters $IQUV$ in a spectral range from 10822.7 to 10833.7 with a spectral sampling of 11 $^{-1}$ and a spatial sampling of $0''18$ per pixel. This spectral region contains information about two differeut heights of the solar atinosphere due to the presence of two spectral lines., This spectral region contains information about two different heights of the solar atmosphere due to the presence of two spectral lines. The line at 10827.09 ls formed at plotospheric heights. whereas the A 10830 triplet. which iucludes a weak blue compoucut at 1052000 aand two blended red components at 1052020. and 10830.31 À.. forms in the chromosphere(Centeuoctal. 2008)..," The line at 10827.09 is formed at photospheric heights, whereas the $\lambda$ 10830 triplet, which includes a weak blue component at 10829.09 and two blended red components at 10830.25 and 10830.34 , forms in the chromosphere\citep{Centeno+etal2008}. ." Iu this case. the wavelength calibration was done using the aan," In this case, the wavelength calibration was done using the and" z <3.,z $\la$ 3. In Figures 3 and 4. we show the results for 571 starbursts and 167 AGN measured wil the IRS.," In Figures 3 and 4, we show the results for 571 starbursts and 167 AGN measured with the IRS." " Results for starbursts are taken [rom (he measurements ancl et in which includes published results froma Drandletal.on)6).. (2007).. Drandetal. (2003b).. Weeclmanetal.(2006a).. Farrahetal.(2008).."" Ποιοetal. (2005)..Weecdnmanetal.(2006b).. Yanetal.(2007).. Popeetal.(2005).. etal.(2007).. lmanishietal.(2007).. and Saresvanetal.OC(2008): additional measurements from Sargsva&Weediman(2009) and Saresvanetal.(2010): ancl additional published results from (2009).. Dasvraetal. (2009).. Haneetal.(2009).. ancl (2009). "," Results for starbursts are taken from the measurements and summary in \citet{wee08} which includes published results from \citet{bra06}, , \citet{hou07}, , \citet{brn08b}, , \citet{wee06a}, \citet{far08}, \citet{hou05}, ,\citet{wee06b}, \citet{yan07}, \citet{pop08}, \citet{far07}, , \citet{ima07}, and \citet{sar08}; additional measurements from \citet{sar09} and \citet{sar10}; and additional published results from \citet{des09}, , \citet{das09}, , \citet{hua09}, , and \citet{men09}. ." Results for AGN are taken from the measurements and summary in Weechnan&LouFK which includes published results from Farrahetal.(2007).. Armusetal.(2007).. ΠαςΕΙetal. (2007).. Saresvanetal. (2008).. Shietal.(2006).. Weedman&Iouck(2009a).. Brandetal. (2008a).. Farrahetal. (2009).. Branclοἱal. (2005Ρ).. Houcketal.( Weedmanetal. (2006a).. Weedimanetal. (2006b).. Pollettaetal. (2008).. Yanetal.(- Sajinaοἱal. (2007).. Martinez-Sansigreοἱal. (2008).. Haoetal. (2005).. Schweitzer (2003).. and Markwick-INemperetal.(2007): and adciGional published results in Caballeroetal. (2009).," Results for AGN are taken from the measurements and summary in \citet{wee09b} which includes published results from \citet{far07}, \citet{arm07}, \citet{ima07}, \citet{sar08}, \citet{shi07}, \citet{wee09a}, \citet{brn08a}, \citet{far09}, \citet{brn08b}, \citet{hou05}, \citet{wee06a}, \citet{wee06b}, \citet{pol08}, \citet{yan07}, \citet{saj08}, \citet{mar08}, \citet{hao05}, \citet{sch07}, and \citet{mk07}; and additional published results in \citet{her09}." . The most important results in Figures 3 and 4 are that the form of luminosity evolutioh is verv similar for both starbursts and AGN. and that no definitive indication is found for the epoch αἱ which Iuminosity evolution reaches a maximum.," The most important results in Figures 3 and 4 are that the form of luminosity evolution is very similar for both starbursts and AGN, and that no definitive indication is found for the epoch at which luminosity evolution reaches a maximum." These results mean that whatever process (riggers (he formation of huninous. dustw galaxies controls the evolution of both starbursts and AGN. but we cannot vet determine whether starbursts or AGN came first.," These results mean that whatever process triggers the formation of luminous, dusty galaxies controls the evolution of both starbursts and AGN, but we cannot yet determine whether starbursts or AGN came first." Tracing the evolution of star formation in (he universe is a fundamental objective ol observational cosmology., Tracing the evolution of star formation in the universe is a fundamental objective of observational cosmology. The star formation rate (SFR) can be estimated with many observational techniques (e.g.Ixennieutt1993:Calzetti2008).," The star formation rate (SFR) can be estimated with many observational techniques \citep[e.g.][]{ken98,cal08}." . Starbursts have been observed to the highest recdshilts (z av> T) using rest frame ultraviolet. humninosities (e.g. 2009).. but. determination of intrinsic source hunünositües and true SEIs requires large corrections lor obscuration by dust.," Starbursts have been observed to the highest redshifts (z $\ga$ 7) using rest frame ultraviolet luminosities \citep[e.g.][]{bou09}, but determination of intrinsic source luminosities and true SFRs requires large corrections for obscuration by dust." The availability of infrared spectra showing the PAII features. suffering much less exiàinction (han optical or ultraviolet features. allows anew lestol obscurationcorrections (Sargsvan& Weedman2009:Sargsvanetal. 2010).," The availability of infrared spectra showing the PAH features, suffering much less extinction than optical or ultraviolet features, allows anew testof obscurationcorrections \citep{sar09,sar10}. ." . Resultsare shown inFigures 5ancl G.Figure 5 illustrates thedramatic contrast in SFRs that would be measured from the PAIL 7.7 feature. compared to SFRs measured fromthe ultraviolet continuum (details in Sargsvan&Weedman (2009))).," Resultsare shown inFigures 5and 6.Figure 5 illustrates thedramatic contrast in SFRs that would be measured from the PAH 7.7 feature, compared to SFRs measured fromthe ultraviolet continuum (details in \citet{sar09}) )." Even [or starbursts selected in the, Even for starbursts selected in the Figure 5. shows the cumulative probability distribution C(m5) for M=500 for three different equations of state.,Figure \ref{fig:disp500} shows the cumulative probability distribution $C(>\sigma_{ij}^2)$ for $W=500$ for three different equations of state. The confidence level at which a single spectrum of he model with equation of state sav (1.5.5/3) (model 1) can be distinguished from the model with equation of state (1.5.1) (model 7) can be directly. read-oll. from this figure.," The confidence level at which a single spectrum of the model with equation of state say (1.5,5/3) (model $j$ ) can be distinguished from the model with equation of state (1.5,1) (model $i$ ) can be directly read-off from this figure." For example. in >95 per cent of cases στι>0.004 for /zj. whereas in only 2 per cent of cases. à model which realA ws the equation of state (1.5.1) will diller from the mean of js mocel to such a large extent.," For example, in $> 95$ per cent of cases $\sigma_{ij}^2 > 0.004$ for $i\ne j$, whereas in only 2 per cent of cases, a model which really has the equation of state (1.5,1) will differ from the mean of this model to such a large extent." A more usual statistic to judge whether a single realisation of a model is drawn from a given probability distribution is the Ixolmogorov-Smirnov. test. based on the maximum absolute cillerence dC=maxCA)CAD] between two cumulative distributions.," A more usual statistic to judge whether a single realisation of a model is drawn from a given probability distribution is the Kolmogorov-Smirnov test, based on the maximum absolute difference $dC={\rm max}|\bar C_i({\cal A}) - C_j({\cal A})|$ between two cumulative distributions." The cumulative distribution of the IxS-statistic is shown in figure6. where we compare it for models (1.5.5/3) and (2.2.1). which resemble cach other most in figure 5..," The cumulative distribution of the KS-statistic is shown in figure, where we compare it for models (1.5,5/3) and (2.2,1), which resemble each other most in figure \ref{fig:disp500}." lor 20 (5) per cent of realisations of mocdel (1.5.5/3) dC!z0.1 (dC!>0.12). and ab this level of contamination. GO (40) per cent of models (2.2.1) have dC larger than that.," For 20 (5) per cent of realisations of model (1.5,5/3), $dC>0.1$ $dC>0.12$ ), and at this level of contamination, 60 (40) per cent of models (2.2,1) have $dC$ larger than that." Finally. figure. 7 illustrates how well the mixcecl-temperature model can be distinguished from either the cold or the hot mocdel with 5?=5/3.," Finally, figure \ref{fig:disp2000_mixed} illustrates how well the mixed-temperature model can be distinguished from either the cold or the hot model with $\gamma=5/3$." This model is most likely mistaken with the colder single temperature counterpart., This model is most likely mistaken with the colder single temperature counterpart. " In το (25) per cent of cases. the mixed model has στ,>0.004 (στι2>0.01)."," In 70 (25) per cent of cases, the mixed model has $\sigma_{ij}^2 > 0.004$ $\sigma_{ij}^2 > 0.01)$." This happens for the cold model in only 10 (5) per cent of realisations., This happens for the cold model in only 10 (5) per cent of realisations. Absorption features are broader in models with a smaller amplitude of the dark matter fluctuations (Pheuns οἱ al., Absorption features are broader in models with a smaller amplitude of the dark matter fluctuations (Theuns et al. 2000). thereby resembling more clustered but hotter mocoels.," 2000), thereby resembling more clustered but hotter models." This may. lead to a degeneracy between {0 and as (Bryan Alachacek 1999: note that Pheuns. Schave Lachnelt (2000) showed that their Voigt profile analysis does not suller from such a degeneracy).," This may lead to a degeneracy between $T_0$ and $\sigma_8$ (Bryan Machacek 1999; note that Theuns, Schaye Haehnelt (2000) showed that their Voigt profile analysis does not suffer from such a degeneracy)." For the statistic presented here. this degeneracy is not very strong. as shown in figure S..," For the statistic presented here, this degeneracy is not very strong, as shown in figure \ref{fig:sigma8}. ." The model with oes=0.775 does not diller much from its more clustered counterpart with e=0.9., The model with $\sigma_8=0.775$ does not differ much from its more clustered counterpart with $\sigma_8=0.9$. Only for very low levels of clustering. ex=0.4. is the effect. important.," Only for very low levels of clustering, $\sigma_8=0.4$, is the effect important." AI models have been scaled to à mean elfective optical depth of 0.26 at a redshift z—3., All models have been scaled to a mean effective optical depth of 0.26 at a redshift $z=3$. Finally we have investigated the influence of the small box size in our numerical simulations. and the result is shown in figure 9..," Finally we have investigated the influence of the small box size in our numerical simulations, and the result is shown in figure \ref{fig:boxsize}." Lack of long wavelength perturbations decreases the observed range in al. as expected. but the clleet of this purely numerical artifact is relatively weak.," Lack of long wavelength perturbations decreases the observed range in ${\cal A}$, as expected, but the effect of this purely numerical artifact is relatively weak." Clues to the thermal history of the Universe are. hidden in the small scale structure of the forest., Clues to the thermal history of the Universe are hidden in the small scale structure of the forest. Phere are two reasons for this., There are two reasons for this. Firstly. the widths of absorption lines arevery sensitive to the temperature of gas. and seconcly.," Firstly, the widths of absorption lines arevery sensitive to the temperature of gas, and secondly," Although. mathematically. the pertu‘bation [rom a poin lass Causes infinite density at he exact locatious of ari boundaries. it is limited to the immediate vicinity of the arm bouudaries. deectable only at extremely high augular “escAdution.,"Although, mathematically, the perturbation from a point mass causes infinite density at the exact locations of arm boundaries, it is limited to the immediate vicinity of the arm boundaries, detectable only at extremely high angular resolution." For aiLex ended object. the very sharp density peaks sinear out cde»eudiug ou the size of he object.jj rs. hitil e peak deusities cliauge siguilicantlv OLy within a distaice of the order of r; from |e bounda“LES (seeFig.6bofIxim2010).," For an extended object, the very sharp density peaks smear out depending on the size of the object, $r_s$, but the peak densities change significantly only within a distance of the order of $r_s$ from the boundaries \citep[see Fig.~6b of][]{kwt10}." ". Iu order to seethe effects o ‘the object size on tle8 0lobal structuο ο“the deusity wake. we colupare he density enhanucemel tain Figures I.. L.. and 5 or the cases of refTp0.0. YL. ancl 0.1. respectively. were the object size r, is defined as the graviational solenue radius of a Pluumer-type object."," In order to see the effects of the object size on the global structure of the density wake, we compare the density enhancement $\alpha$ in Figures \ref{fig:ptm}, \ref{fig:rss}, , and \ref{fig:rsl} for the cases of $r_s/r_p=0$, 0.01, and 0.1, respectively, where the object size $r_s$ is defined as the gravitational softening radius of a Plummer-type object." Freuu Figures laa-b. [aa-b. aud Daa. ole fuds that the sharpuess at )ouncdaries are reduced Wwh the softened egravitational potenial. wlie there are negligible chauges i the global shape alxb morphology of the wake.," From Figures \ref{fig:ptm}a a–b, \ref{fig:rss}a a–b, and \ref{fig:rsl}a a–b, one finds that the sharpness at boundaries are reduced with the softened gravitational potential, while there are negligible changes in the global shape and morphology of the wake." The profiles ο à along the spiral pattern in Figure [cc show the μαioothing of arm boundaries compa‘ed to Figure Lee. chiefly by reducine the peak ceusities.," The profiles of $\alpha$ along the spiral pattern in Figure \ref{fig:rss}c c show the smoothing of arm boundaries compared to Figure \ref{fig:ptm}c c, chiefly by reducing the peak densities." " ""eure DCC indicates. however. that the miainum value of à is also chaiged in the case of the hrther exteuded object with size ry c«ΗλΑαble to or larger than half of tje interarm spacing for ile point mass counterpart. reduciug he conrast between armi auc interarm densities."," Figure \ref{fig:rsl}c c indicates, however, that the minimum value of $\alpha$ is also changed in the case of the further extended object with size $r_s$ comparable to or larger than half of the interarm spacing for the point mass counterpart, reducing the contrast between arm and interarm densities." In Figure 6 zoomiug in ou a high density structure of the wake. the iitially static inecdium Is l'evealed to attain auaproximately spherical velocity [ield.," In Figure \ref{fig:vel} zooming in on a high density structure of the wake, the initially static medium is revealed to attain an approximately spherical velocity field." In order to ulerstaud tlie velocity ealtures o ‘the wakes for circularly orbiting objects. we first inspect the linear Tjectory counterparts ornmulated in Wim&Win 17s (2009) ecquatiols (&19)-(À9QO).," In order to understand the velocity features of the wakes for circularly orbiting objects, we first inspect the linear trajectory counterparts formulated in \citeauthor{kim09}' 's \citeyearpar{kim09} equations (A19)–(A20)." " From their Lcxiuulaenr for the velocity οΟΜΙΡΟΙΟΙs Vy and V pa‘allel and perpencdicilar to tlie object motion. respectively. it is stralghitforward o show that in the linear lach cone (hall-opeune augle of Oa;=δι1M, (1) the pertwbed gas ows towa‘cL the eclge oftle cone perpeucicul:uly. Le.. Ithe |ic augle Is tau1qeMp90*—Ox; in the vicinity of the bouidary. deflected Iro 10° headiug w the objec belind it (see aso Fig.1 ald Fig.8iuNznouul2011 )): €aid (2) the [Iud speed lu ter15 ο. Mac1 uumber approaches the valte of the densiy enhacellel| (M~ a) close to the OUIjes but decreases to M=rg(M,),d! along he liie. of t eoec4 motiou at distance d rom e object (seealsoFig.1iανὡς2009)."," From their formulae for the velocity components $V_\|$ and $V_\bot$ parallel and perpendicular to the object motion, respectively, it is straightforward to show that in the linear Mach cone (half-opening angle of $\Theta_M=\sin^{-1}\mach^{-1}$ ) (1) the perturbed gas flows toward the edge of the cone perpendicularly, i.e., the fluid angle is $\tan^{-1}(|V_\bot/V_\||)\simeq 90\degree-\Theta_M$ in the vicinity of the boundary, deflected from $0\degree$ heading for the object behind it (see also \citealp[Fig.~1 in][]{san99} and \citealp[Fig.~8 in][]{nam11}) ); and (2) the fluid speed in terms of Mach number approaches the value of the density enhancement $\mathcal{M}\sim\alpha$ ) close to the boundaries but decreases to $\mathcal{M}=r_B\,(\mach\,d)^{-1}$ along the line of the object motion at distance $d$ from the object \citep[see also Fig.~1 in][]{kim09}." . Ove‘all. the fluid i na Mach cone has the laNil=ur velocity uear. and towa‘cd. the botxlaries. athotel it delflec 511 angle for considerably slower KHuid parts giving smaller c«utribution Oll average.," Overall, the fluid in a Mach cone has the maximum velocity near, and toward, the boundaries, although it deflects in angle for considerably slower fluid parts giving smaller contribution on average." " I1 the extension of this tenceeucy of tle flow to ageMDregate perpeuxlicularly to theshocked bouncla""vw. it can be uncerstoocl hat the velocity vectors in Figure 6 appear to be spherical especjally arouixd the tiglitly wou spiral- auc circular are-shaped structures."," In the extension of this tendency of the flow to aggregate perpendicularly to theshocked boundary, it can be understood that the velocity vectors in Figure \ref{fig:vel} appear to be spherical especially around the tightly wound spiral- and circular arc-shaped structures." The spiral boundaries, The spiral boundaries straightforward to verity iu the brightest regions of the Stream.,straightforward to verify in the brightest regions of the Stream. The shock models precdict a range of lÓow-iouization cussion lines (e.g. OF. SID. some of which will be detectable even though suppressed by the low gas-phase uctallicity.," The shock models predict a range of low-ionization emission lines (e.g. OI, SII), some of which will be detectable even though suppressed by the low gas-phase metallicity." There are likely to be EUN absorption-ine diagnostics through the shock interfaces revealing nore extreme kinematics (Fig., There are likely to be EUV absorption-line diagnostics through the shock interfaces revealing more extreme kinematics (Fig. 3. inset). but these detections (e.g. OVI) are ouly possible towards fortuitous ckeround sources 22001: Dregnan 2007)," 3, inset), but these detections (e.g. OVI) are only possible towards fortuitous background sources 2001; Bregman 2007)." The predicted EUV/s-rav chussivity from the post-shock regions is much too low o be detected iu emission., The predicted EUV/x-ray emissivity from the post-shock regions is much too low to be detected in emission. The characteristic timescale for large changes ds roughly 200 Myr. aud so the Stream needs to be replenished bv the outer disk of the LMC at a fairly constant rate (e.g. 22005).," The characteristic timescale for large changes is roughly $-$ 200 Myr, and so the Stream needs to be replenished by the outer disk of the LMC at a fairly constant rate (e.g. 2005)." The timescale can be extended with larger η values (see equation (1)). but at the expeuse of substantially diminished ssurface brightness.," The timescale can be extended with larger $\eta$ values (see equation (1)), but at the expense of substantially diminished surface brightness." Tn this respect. we consider j to be fairly well bounded by observation aud theory.," In this respect, we consider $\eta$ to be fairly well bounded by observation and theory." What happens to the eas shedded from the dense clouds?, What happens to the gas shedded from the dense clouds? Much of the diffuse gas will become mixed with the hot halo eas sugeesting a warn accretion towards the inner Galactic halo., Much of the diffuse gas will become mixed with the hot halo gas suggesting a warm accretion towards the inner Galactic halo. " If most of the Stream gas euters the Galaxy via this process. the derived eas accretion rate is ~OIA, Ἡ, "," If most of the Stream gas enters the Galaxy via this process, the derived gas accretion rate is $\sim 0.4$ $^{-1}$." The higher value compared to ((e.g. 22007) is due to the eas already. shredded. mot seen by radio telescopes now.," The higher value compared to (e.g. 2007) is due to the gas already shredded, not seen by radio telescopes now." Iu our model. the VCs observed today are unlikely to lave been dislodged from the Streaun by the process described here.," In our model, the HVCs observed today are unlikely to have been dislodged from the Stream by the process described here." These may have conie from an earlier stage of the LMC-SMC interaction with the outer disk of the Calaxy., These may have come from an earlier stage of the LMC-SMC interaction with the outer disk of the Galaxy. " The ""shock cascade” interpretation for the Stream. clears up a naeeine uucertaimty about the delistauce scale for high-velocity clouds.", The “shock cascade” interpretation for the Stream clears up a nagging uncertainty about the distance scale for high-velocity clouds. Blaud-Tawthorn et al (1998) first showed that distance Iinüits to TWCs cau be determined from their observed sstreneth due to ionization by the Calactic radiation feld. now confined by clouds with reliable. distance brackets from the stellar absorption line technique (Wakker 2001).," Bland-Hawthorn et al (1998) first showed that distance limits to HVCs can be determined from their observed strength due to ionization by the Galactic radiation field, now confirmed by clouds with reliable distance brackets from the stellar absorption line technique (Wakker 2001)." IIVC' have simaller linetie energies compared to the Stream clouds. and their interactious with the halo gas are not expected to produce siguificaut shock-iuduced or mixing layer eenission. thereby supporting the use of aas a crude distance indicator.," HVCs have smaller kinetic energies compared to the Stream clouds, and their interactions with the halo gas are not expected to produce significant shock-induced or mixing layer emission, thereby supporting the use of as a crude distance indicator." Iere. we have not attempted to reproduce the oobservatious of the Stream in detail.," Here, we have not attempted to reproduce the observations of the Stream in detail." This is left to a subsequent paper where we explore a larger parameter space aud include a more detailed comparison with the aand ppower spectrum. iuter alia.," This is left to a subsequent paper where we explore a larger parameter space and include a more detailed comparison with the and power spectrum, inter alia." We introduce additional physics. in particular. the rotation of the hot halo. a range of Stream orbits through the halo eas. the eravitational field of the Galaxy. and so on.," We introduce additional physics, in particular, the rotation of the hot halo, a range of Stream orbits through the halo gas, the gravitational field of the Galaxy, and so on." If we are to arrive at a satisfactory πιοαποιο of the Stream interaction with the halo. future deep ssurvevs will be esseutial.," If we are to arrive at a satisfactory understanding of the Stream interaction with the halo, future deep surveys will be essential." It is plausible that curent oobservations are still missing a substantial amount of eas. iu contrast to the deepest oobservatious.," It is plausible that current observations are still missing a substantial amount of gas, in contrast to the deepest observations." " We cau compare the particle columu density inferred from, ad lnaeing surveys.", We can compare the particle column density inferred from and imaging surveys. The huitius ecol. deusity is about NyzGayyhzm1075 αι? where πμ) is the mean atomic livdrogen density. aud £ is the depth through the slab.," The limiting column density is about $N_H \approx \langle n_H \rangle L \approx 10^{18}$ $^{-2}$ where $\langle n_H \rangle$ is the mean atomic hydrogen density, and $L$ is the depth through the slab." " By comparison. the surface brightuess cau be expressed as an equivalent Cluission measure. £L,cOL~Πρλεν Ποσο η, "," By comparison, the surface brightness can be expressed as an equivalent emission measure, $E_m \approx \langle n_e^2 \rangle L \approx \langle n_e\rangle N_e$." "aud AN, are the local aud column electron density.", Here $n_e$ and $N_e$ are the local and column electron density. " The Iuitiug value of £,, iu inuaeiug is about 1060 mR. aud therefore NV.στ1075(n) cmi "," The limiting value of $E_m$ in imaging is about 100 mR, and therefore $N_e \approx 10^{18}/\langle n_e \rangle$ $^{-2}$." Whether the ionized and neutral gas axe mixed or distinct. we can hide a lot more ionized eas below he imaecine threshold for a fixed £. particularly if the gas is at low density (7.3O1 ?&," Whether the ionized and neutral gas are mixed or distinct, we can hide a lot more ionized gas below the imaging threshold for a fixed $L$, particularly if the gas is at low density $\langle n_e \rangle \ll 0.1$ $^{-3}$ )." A small or variable volume filling factor can complicate this picture mt. in eeneral. the ionized gas still wins out because of ionization of low deusitv yoy the cosmüc UV background (Maloney 1995).," A small or variable volume filling factor can complicate this picture but, in general, the ionized gas still wins out because of ionization of low density by the cosmic UV background (Maloney 1993)." In sunnarv. even within the constrauts of the cosmic microwave background (see Malonev Blaud-Uawthorn 1999). a substantial fraction of the gas can be missed if it occupies a large volume in the form of a low density dlasma.," In summary, even within the constraints of the cosmic microwave background (see Maloney Bland-Hawthorn 1999), a substantial fraction of the gas can be missed if it occupies a large volume in the form of a low density plasma." JBI is indebted to the University of Zurich for organizing the Saas Fee lectures this vear at Miren in he Swiss Alps. a setting that provided the inspiration for he new work.," JBH is indebted to the University of Zurich for organizing the Saas Fee lectures this year at Mürrren in the Swiss Alps, a setting that provided the inspiration for the new work." We wish to thank the referee for insightful and helpful coumnents., We wish to thank the referee for insightful and helpful comments. We are indebted to €. Desla. C. Madsen and T. Pryor for important data in advance of miblication.," We are indebted to G. Besla, G. Madsen and T. Pryor for important data in advance of publication." JDBIT is supported by a Federation Fellowship hrough the Australian Research Council (ARC)., JBH is supported by a Federation Fellowship through the Australian Research Council (ARC). RSS and JBI eratefully acknowledec ARC erant DPOGGL131 hat supports certain aspects of this work., RSS and JBH gratefully acknowledge ARC grant DP0664434 that supports certain aspects of this work. caused by the star formation.,caused by the star formation. The extensive high. velocity features revealed here may. be marking the very base of a superwind localised. around. the 30 Doradus complex., The extensive high velocity features revealed here may be marking the very base of a superwind localised around the 30 Doradus complex. The escape velocity of gas from the LMC in the neighbourhood of 30 Doradus is around 150kms. so that the high specd ionized gas from disrupted shells and giant shells is escaping the gravitational pull of 30 Doradus ancl is being ejected perpendicularly to the plane of the LMC. along the line of sight.," The escape velocity of gas from the LMC in the neighbourhood of 30 Doradus is around $150~{\rm km~s^{-1}}$ so that the high speed ionized gas from disrupted shells and giant shells is escaping the gravitational pull of 30 Doradus and is being ejected perpendicularly to the plane of the LMC, along the line of sight." The ionization boundary. due to the R130 cluster (perpendicular to the plane of the LMC) will depend on the distribution of the gas but an upper limit of a few hundred parsecs can be estimated by caleulating the Strómmeren radius due to an ionizing Lux of ~107s.+ from the ~100 O stars and a mean density of ~1em," The ionization boundary due to the R130 cluster (perpendicular to the plane of the LMC) will depend on the distribution of the gas but an upper limit of a few hundred parsecs can be estimated by calculating the Strömmgren radius due to an ionizing flux of $\sim 10^{51}~{\rm s^{-1}}$ from the $\sim 100$ O stars and a mean gas density of $\sim 1~{\rm cm^{-3}}$." " Assuming an ejection speed. of200s--kms.JL. it will take of the order 2Q0""vr to reach a ofDoradus~500pe from the point of origin ancl thus escape the 30 region."," Assuming an ejection speed of $200~{\rm km~s^{-1}}$, it will take of the order $2\times 10^6~{\rm yr}$ to reach a distance of $\sim 500~{\rm pc}$ from the point of origin and thus escape the 30 Doradus region." The gas will rapidly recombine once Ἡ has passed. the toniziation boundary and will then not be visible on the ppy arrays., The gas will rapidly recombine once it has passed the ioniziation boundary and will then not be visible on the pv arrays. The dynamical timescale of the remaining giant shell walls is much longer since their progress in the direction of the plane of the LMC is slower than the material ejected perpendicular to the plane., The dynamical timescale of the remaining giant shell walls is much longer since their progress in the direction of the plane of the LMC is slower than the material ejected perpendicular to the plane. Ligh velocity LE clouds: will be formed by the escaping material as it recombines and these clouds may be detectable in high resolution and high sensitivity LD kinematical studies., High velocity H clouds will be formed by the escaping material as it recombines and these clouds may be detectable in high resolution and high sensitivity H kinematical studies. Of course. the kinematics ol gas ejected from the LMC rapidly becomes highly complex due to the interaction with the Galaxy (Wakker&vanerden1997)," Of course, the kinematics of gas ejected from the LMC rapidly becomes highly complex due to the interaction with the Galaxy \citep{wakker&woerden97}." In this work the kinematics of sample region of the 30 Doradus nebula have been investigated: using the ALES., In this work the kinematics of sample region of the 30 Doradus nebula have been investigated using the MES. This intensive study has revealed high speed velocity eatures throughout this region., This intensive study has revealed high speed velocity features throughout this region. Although the kinematics are complex. general patterns are discerned at three dilleren spatial scales.," Although the kinematics are complex, general patterns are discerned at three different spatial scales." Small coherent velocity features are presen hroughout the region., Small coherent velocity features are present throughout the region. These knots are often found to form oops and chains in the py arrays and at the largest scales. can form velocity features which vary slowly. between rec and. blue-shifted emission.," These knots are often found to form loops and chains in the pv arrays and at the largest scales, can form velocity features which vary slowly between red and blue-shifted emission." Lt is suggested that all of these eatures are explicable in terms of the current understanding of the 30. Doradus nebula., It is suggested that all of these features are explicable in terms of the current understanding of the 30 Doradus nebula. Shells and giant. shells forme w the winds and supernovae of massive stars form and are hen disrupted in the energetie turbulent ensironment of the alo of 30 Doracdus., Shells and giant shells formed by the winds and supernovae of massive stars form and are then disrupted in the energetic turbulent environment of the halo of 30 Doradus. The fragments of the shells retain the velocity pattern of the original shell and are observed as the small high speed. knots., The fragments of the shells retain the velocity pattern of the original shell and are observed as the small high speed knots. " HE this explanation is correct. then ueh velocity knots are likely to be found across much of the ace of 30 Doradus wherever the size of the giant shells have exceeded the scale-height of the LMC and Ίο to ""blow-out'."," If this explanation is correct, then high velocity knots are likely to be found across much of the face of 30 Doradus wherever the size of the giant shells have exceeded the scale-height of the LMC and led to `blow-out'." The whole 30 Doradus nebula is flattened and. viewed face on., The whole 30 Doradus nebula is flattened and viewed face on. The high speed velocity fragments are likely to form the base of an outllowing superwind that is escaping the galaxy., The high speed velocity fragments are likely to form the base of an outflowing superwind that is escaping the galaxy. This is à microcosm of the processes that are taking place in starburst galaxies such as MS2 in which there are many super star clusters like 30. Doradus and whose combined output lead. to the spectacular optical filaments that mark the MS2 superwind., This is a microcosm of the processes that are taking place in starburst galaxies such as M82 in which there are many super star clusters like 30 Doradus and whose combined output lead to the spectacular optical filaments that mark the M82 superwind. JM ancl ALB would like to thank the stalf at the AAT. who provided their usual exeellent. service during the observing run.," JM and MB would like to thank the staff at the AAT, who provided their usual excellent service during the observing run." AIPR is supported by PPADBC., MPR is supported by PPARC. A Wine Abclulaziz City for Science and Technology ο studentship is acknowledged by ZAA., A King Abdulaziz City for Science and Technology `KACST' studentship is acknowledged by ZAA. We thank the referee for comments which improved the paper., We thank the referee for comments which improved the paper. , The formation anc evolution of galaxies is still hotly debated.,The formation and evolution of galaxies is still hotly debated. The cooling of barvons in dark matter halos should form compact and dense self-supporting. rotating stellar and gaseous disks (o...2?7).," The cooling of baryons in dark matter halos should form compact and dense self-supporting, rotating stellar and gaseous disks \citep[e.g.,][]{Fall80,Navarro00,Governato07}." . Later major mergers between disk galaxies have then been proposed as the main routes to form ellipticalgalaxies (e.g..2)..," Later major mergers between disk galaxies have then been proposed as the main routes to form ellipticalgalaxies \citep[e.g.,][]{Toomre}." Several detailed numerical simulations (c.g..??????) have shown that many dynamical anc photometrical properties of the remnant spheroidal galaxies can be explained. simply. in terms of the merging of progenitors having varving levels of gas-richness.," Several detailed numerical simulations \citep[e.g.,][]{Barnes91,Boylan06,Dekel06,Robertson06,Burkert08,Hop08FP} have shown that many dynamical and photometrical properties of the remnant spheroidal galaxies can be explained simply in terms of the merging of progenitors having varying levels of gas-richness." Galaxies which form from gas-rich. dissipative. mergers result in more compact remnants with larger velocity dispersions.," Galaxies which form from gas-rich, dissipative, mergers result in more compact remnants with larger velocity dispersions." On the other hand. in à pure monolithic model of galaxy formation (c.g.?).. stars are formed in a single burst. of star formation [rom σας falling towards the center. and the evolution is passive thereafter.," On the other hand, in a pure monolithic model of galaxy formation \citep[e.g.,][]{Eggen62}, stars are formed in a single burst of star formation from gas falling towards the center, and the evolution is passive thereafter." Although there is clear evidence for a red and dead population of massive earlv-tvpe ealaxies (see 2? for a review). hierarchical merging could still have plaved some role at late times.," Although there is clear evidence for a red and dead population of massive early-type galaxies (see \citealt{Renzini06} for a review), hierarchical merging could still have played some role at late times." Phe metallicities of vpical carly-type galaxies are well reproduced. in. models with frequent minor mergers at moderate redshifts (e.g.27?) and are not much allectecl by later dry mergers (?)..," The metallicities of typical early-type galaxies are well reproduced in models with frequent minor mergers at moderate redshifts \citep[e.g.,][]{Bournaud07,Naab07} and are not much affected by later dry mergers \citep{Pipino08}." Phe sizes ancl velocity dispersions of BCGs in the ocal Universe are evolving in a manner which suggests requent minor drv mergers as recently as 1 Gyr ago (?).., The sizes and velocity dispersions of BCGs in the local Universe are evolving in a manner which suggests frequent minor dry mergers as recently as 1 Gyr ago \citep{Bernardi09}. The clustering and number density of massive galaxies in he Sloan Digital Sky Survey (SDSS). the 2dE-SDSS LAG and QSO Survey (25LAQ). the NOAO Deep Wide-Field Survey and in DELP? also suggest that some merging events involving massive galaxies must have occurred since recdshift Lo l(eg.?7?7).. but that the majority of the stellar mass had. already been assembled by this time.," The clustering and number density of massive galaxies in the Sloan Digital Sky Survey (SDSS), the 2dF-SDSS LRG and QSO Survey (2SLAQ), the NOAO Deep Wide-Field Survey and in DEEP2 also suggest that some merging events involving massive galaxies must have occurred since redshift $z\sim 1$ \citep[e.g.,][]{Bundy07,White07,Wake08}, but that the majority of the stellar mass had already been assembled by this time." In addition. there is now growing evidence that massive ealaxies at 2~ are much smaller and denser than their local counterparts of the same stellar mass (e.g... 2777).," In addition, there is now growing evidence that massive galaxies at $z\sim 2$ are much smaller and denser than their local counterparts of the same stellar mass \citep[e.g.,][]{Trujillo06,VanDokkum08,Cimatti08,Saracco08}. ." These observations are in line with the idea that, These observations are in line with the idea that ‘To measure the cllective temperatures and surface gravities of 998851 and 1102480. we obtained low-resolution spectroscopic observations with the I04-cm Sampurnanand telescope (£/13) of the State Observatory. Naini Tal on 18 April 2002.,"To measure the effective temperatures and surface gravities of 98851 and 102480, we obtained low-resolution spectroscopic observations with the 104-cm Sampurnanand telescope (f/13) of the State Observatory, Naini Tal on 18 April 2002." We used a LA1 CCD detector and the 320 spectrograph. giving a linear dispersion of ~2.4 per pixel.," We used a $1K \times 1K$ CCD detector and the HR-320 spectrograph, giving a linear dispersion of $\sim 2.4$ per pixel." The spectra were taken using a erating and a 3-mim circular aperture., The spectra were taken using a $^{-1}$ grating and a 3-mm circular aperture. We Covered. a spectral range ofA, We covered a spectral range of. GAS Apart [rom the spectrophotometric standards. we also observed two standard. stars of similar spectral typoe. 111155447 (F2V) and 1140283 (15).," Apart from the spectrophotometric standards we also observed two standard stars of similar spectral type, 5447 (F2V) and 140283 (F5)." The spectroscopic data reductions were performed using the software package (Toely 1993)., The spectroscopic data reductions were performed using the software package (Tody 1993). To estimate the accuracy of the spectral cata we determined. synthetic: Johnson V magnitudes for 998851. and. 1102480., To estimate the accuracy of the spectral data we determined synthetic Johnson $V$ magnitudes for 98851 and 102480. Standard lxurucz (1993) models. with solar metallicity and. micro-turbulent velocity of ss were used to match the observed spectra by normalising the Lux atAA., Standard Kurucz (1993) models with solar metallicity and micro-turbulent velocity of $^{-1}$ were used to match the observed spectra by normalising the flux at. . We considered our spectra to have zero reddening., We considered our spectra to have zero reddening. The best matched. ει and logg parameters for both stars are tabulated in Table 4., The best matched $T_{eff}$ and $\log g$ parameters for both stars are tabulated in Table 4. Phe best matched Ixurucz mocels in both lines and continuum are shown in Fie., The best matched Kurucz models in both lines and continuum are shown in Fig. 5 along with the observed spectra., 5 along with the observed spectra. The logg estimates for both stars indicate that they are giants or sub-giants of Iuminosity class HEZIV., The $\log g$ estimates for both stars indicate that they are giants or sub-giants of luminosity class III/IV. On comparing our spectra with the observed: stars of similar spectral type we estimate that 09885]. and 1102480 are of spectral type FL and F3. respectively.," On comparing our spectra with the observed stars of similar spectral type we estimate that 98851 and 102480 are of spectral type F1 and F3, respectively." In Fig., In Fig. 5 it is notable that the Calll LE and [x lines are weak compared to the Ixurucz mocels. supporting the Am classification of these stars.," 5 it is notable that the II H and K lines are weak compared to the Kurucz models, supporting the Am classification of these stars." We also estimated the equivalent spectral type by using the calibration of Schmicdt-Ixaler (1982) with the absolute colour (D. V) and Popp., We also estimated the equivalent spectral type by using the calibration of Schmidt-Kaler (1982) with the absolute colour $B-V$ ) and $ T_{eff}$. This coniparison 1s consistent with our spectral types of FL and FS for HID98S51 and HD. 102480. respectively. with luminosity class LIL or LY for both stars.," This comparison is consistent with our spectral types of F1 and F3 for HD98851 and HD 102480, respectively, with luminosity class III or IV for both stars." Abt (1984) classified 998851 and 1102480 with a Calll [x line type. Balmer line tvpe. metal lino tvpe as HV/13) and Am(E2/E4/E4). respectively: our spectral type estimates are in good agreement with his.," Abt (1984) classified 98851 and 102480 with a II K line type, Balmer line type, metal line type as IV/F3) and Am(F2/F4/F4), respectively; our spectral type estimates are in good agreement with his." We derived several physical parameters for 998851. and, We derived several physical parameters for 98851 and described.,described. The analysis of the output profiles is developed in Section 4., The analysis of the output profiles is developed in Section 4. A discussion on the implications and relevance of the results is deferred to Section 5. as well as the main conclusions.," A discussion on the implications and relevance of the results is deferred to Section 5, as well as the main conclusions." The interaction between the star and the Inner. disc Boundary eencrates a sheared region fed by turbulent. magnetised material from the accretion disc.," The interaction between the star and the Inner disc Boundary generates a sheared region fed by turbulent, magnetised material from the accretion disc." Shear amplifies the stellar magnetic field. producing a strong toroidal magnetic field component.," Shear amplifies the stellar magnetic field, producing a strong toroidal magnetic field component." Εις toroidal field and the associated magnetic pressure push the stellar poloidal field away from. the stellar/cdisc rotation axis. inflating and opening the poloidal Ποιά lines in a thus producing a current laver between the stellar ancl the disc dominated: regions as clisplaved in Fig.," This toroidal field and the associated magnetic pressure push the stellar poloidal field away from the stellar/disc rotation axis, inflating and opening the poloidal field lines in a thus producing a current layer between the stellar and the disc dominated regions as displayed in Fig." 1., 1. The magnetic link between the star and the disce is broken and. re-establishecl periodically. by magnetic reconnection., The magnetic link between the star and the disc is broken and re-established periodically by magnetic reconnection. The opening angle of the current laver. as well as its extent. depends on the stellar and disc fields. the accretion rate and the ratio between the inner disc radius and the stellar rotation frequency.," The opening angle of the current layer, as well as its extent, depends on the stellar and disc fields, the accretion rate and the ratio between the inner disc radius and the stellar rotation frequency." In the magnetospheric models of ν1204. a slow. hot anc dense outllow driven. mostly by. poloidal magnetic pressure is emanating from stellar regions close to the rotation axis while fast. cooler and less dense magneto-centrifugally accelerated outflows are emanating from lower stellar latitudes and (rom the inner disc.," In the magnetospheric models of vRB04, a slow, hot and dense outflow driven mostly by poloidal magnetic pressure is emanating from stellar regions close to the rotation axis while fast, cooler and less dense magneto-centrifugally accelerated outflows are emanating from lower stellar latitudes and from the inner disc." Phe main dillerence with the magnetospheric models of Goodson et al. (, The main difference with the magnetospheric models of Goodson et al. ( 1997) is that in the Goodson. models the axial (stellar) jet is fast ancl well-collimated - and driven by magneto-centrifugal processes (see also Llirose et al.,1997) is that in the Goodson models the axial (stellar) jet is fast and well-collimated - and driven by magneto-centrifugal processes (see also Hirose et al. LOOT) - and the inner disc wind is divergent. whereas in vl1tDO4 the stellar wind is slow but on the other hand some collimation is clearly seen in the inner (magneto-centrifugally accelerated) disc wind.," 1997) - and the inner disc wind is divergent, whereas in vRB04 the stellar wind is slow but on the other hand some collimation is clearly seen in the inner (magneto-centrifugally accelerated) disc wind." llowever. the stellar wind seen in Romanova et al. (," However, the stellar wind seen in Romanova et al. (" 2002) is also slow. travelling into a rarefied corona.,"2002) is also slow, travelling into a rarefied corona." A very fast (warn and dense) stellar wind is seen in stellar dvnamo mocels of vItDBO6: this wind is mostly driven by toroidal and. poloidal magnetic pressure. as well as gas pressure.," A very fast (warm and dense) stellar wind is seen in stellar dynamo models of vRB06; this wind is mostly driven by toroidal and poloidal magnetic pressure, as well as gas pressure." Though a full description of the numerical simulations can »@ found in vI&DOA4 and vRBOG. we should brielly summarise heir main properties.," Though a full description of the numerical simulations can be found in vRB04 and vRB06, we should briefly summarise their main properties." La both papers. the evolution of the low. magnetic field. density ancl temperature is found. by solving the continuity. the NavierStokes ancl the mean-ield induction. MIEID equations for an axisvmmetric svstenm in cvlindrical polar coordinates. assuming a piecewilse xobvtropic model.," In both papers, the evolution of the flow, magnetic field, density and temperature is found by solving the continuity, the Navier–Stokes and the mean-field induction MHD equations for an axisymmetric system in cylindrical polar coordinates, assuming a piecewise polytropic model." Dynamo action in the disce. (if present) is prescribed by a standard. a7Q2 dynamo (e.g. Ixrause vtaedler 1980). where à is the mean-Lelcl a-ellect and. ο is the angular velocity of the orbiting gas.," Dynamo action in the disc (if present) is prescribed by a standard $\alpha^2 \Omega$ dynamo (e.g. Krause Raedler 1980), where $\alpha$ is the mean-field $\alpha$ -effect and $\Omega$ is the angular velocity of the orbiting gas." a-quenching is included so that the disc dvnamo saturates at a level close to equipartition between magnetic and thermal energies., $\alpha$ -quenching is included so that the disc dynamo saturates at a level close to equipartition between magnetic and thermal energies. The code uses dimensionless variables that have been scaled using as reference values a typical sound speed of the coronal gas (100 ki 1 and a typical surface density at the surface of the disc {1 & em 7)., The code uses dimensionless variables that have been scaled using as reference values a typical sound speed of the coronal gas (100 km $^{-1}$ ) and a typical surface density at the surface of the disc (1 g $^{-2}$ ). Furthermore. the mass of the star has been taken as 1 AL. (solar mass) the mean specific weight as y=0.6 and the polvtropic index as 5=5/3.," Furthermore, the mass of the star has been taken as 1 $_{\odot}$ (solar mass), the mean specific weight as $\mu = 0.6$ and the polytropic index as $\gamma = 5/3$." The computations have been carried out in a domain of extent 0.2 AU in the racial (>) cürection and z0.1 XU above/below the dise mid-plane: mesh sizes are dc=02 0.001AU., The computations have been carried out in a domain of extent 0.2 AU in the radial $\varpi$ ) direction and $\pm 0.1$ AU above/below the disc mid-plane; mesh sizes are $\delta \varpi = \delta z = 0.001$ AU. The inner edge of the disc is at 4 stellar radii (in the mocels with stellar dipolar magnetosphere: “PTable 1) or at 2.4 stellar radii (in the model with stellar dynamo). which in both cases corresponds to 12 solar radii.," The inner edge of the disc is at 4 stellar radii (in the models with stellar dipolar magnetosphere; Table 1) or at 2.4 stellar radii (in the model with stellar dynamo), which in both cases corresponds to 12 solar radii." The dise extends to the outer boundary of the computational domain., The disc extends to the outer boundary of the computational domain. The vRBO4 models represent a step forward over the selí-similar warm disc winds models of Paper Lb., The vRB04 models represent a step forward over the self-similar warm disc winds models of Paper II. Around the inner edge of the disc. the interaction with the stellar magnetosphere and the stellar wind is taken into account.," Around the inner edge of the disc, the interaction with the stellar magnetosphere and the stellar wind is taken into account." Also. the rigiditv of the self-similarity. constraint is lost.," Also, the rigidity of the self-similarity constraint is lost." Furthermore. the Lorentz [force jB ds included. in the Navier-Stokes. equation. as well as the generation. of magnetic fields bv the standard @7Q dynamo in the disc.," Furthermore, the Lorentz force $\vec j \times \vec B$ is included in the Navier-Stokes equation, as well as the generation of magnetic fields by the standard $\alpha ^2 \Omega$ dynamo in the disc." The saturation level of the cise dvnamo is governed. by the equipartition between magnetic and thermal energies in the disc., The saturation level of the disc dynamo is governed by the equipartition between magnetic and thermal energies in the disc. In accordance with observations of protostellar star-disc systems. the model implements a dense. cool disc," In accordance with observations of protostellar star-disc systems, the model implements a dense, cool disc" and the nonrelativistic winds is closely analogous to the hyvdrodynamies of the two nonrelativistic winds collision. which was intensively cliscussed by dillerent authors applied tothe WR|OB binaries since the work of Usov (1976).,"and the nonrelativistic winds is closely analogous to the hydrodynamics of the two nonrelativistic winds collision, which was intensively discussed by different authors applied to the WR+OB binaries since the work of Usov (1976)." The total luminosity of scattered. hard. photons L~ ds equal to the total particle energy losses £7... through the inverse Compton scattering in the course of the particle motion from the pulsar to the inlinitv., The total luminosity of scattered hard photons $L_\gamma $ is equal to the total particle energy losses $L_{loss}$ through the inverse Compton scattering in the course of the particle motion from the pulsar to the infinity. . To estimate L- we note that the rate of the energy losses of a relativistic particle moving in a radiation [field with energv density of soft. photons woopc{νιπαο is about mecdsf/dlτ-in the Thomson limit.," To estimate $L_\gamma $ we note that the rate of the energy losses of a relativistic particle moving in a radiation field with energy density of soft photons $w_{soft}\simeq L_{*}/4\pi a^2c$ is about $mc^2d\gamma /dt\simeq -w_{soft}\sigma _Tc\gamma ^2$in the Thomson limit." Here £L; is a luminosity of the optical star. @ is a binary stars separation and “em? is the Thonison cross-section.," Here $L_{*}$ is a luminosity of the optical star, $a$ is a binary stars separation and $^2$ is the Thomson cross-section." Hence the decrease of the Lorentz factor of a particlesq. isAy~5r(l]|5/54)1] ot.dsamc3fmpL..," Hence the decrease of the Lorentz factor of a particle is $\Delta \gamma \sim \gamma \left[ 1-\left( 1+\gamma /\gamma _{*}\right) ^{-1}\right] ,$ $\gamma _{*}=4\pi amc^3\left/ \sigma _TL_{*}\right. $." " So the rate of all particles total energy. loss is ""Thus in the case +54 the egamma-ray luminosity [rom inary is proportional to the luminosity of the optical star L, and to the luminosity of the wind L,. £.=NL."," So the rate of all particles total energy loss is Thus in the case $\gamma \ll \gamma _{*}$ the gamma-ray luminosity from binary is proportional to the luminosity of the optical star $L_{*}$ and to the luminosity of the wind $L_w$. $L_\gamma =KL_w$," where he transformation parameter A—5/5.., where the transformation parameter $K=\gamma /\gamma _{*}$. " In the close binary system with an optical star with high luminosity 5,25«. In his case practically all energy of the wind transfers to the energy of scattered photons L~was8Lu.", In the close binary system with an optical star with high luminosity $\gamma \gg \gamma _{*}.$ In this case practically all energy of the wind transfers to the energy of scattered photons $L_{\gamma \max }\approx L_w$. In each unit of the volume in the region where he gamma radiation is generated the source function of gamma radiation is highly anisotropic., In each unit of the volume in the region where the gamma radiation is generated the source function of gamma radiation is highly anisotropic. When the pulsar wind is isotropic the gamma luminosity (ο) ( L.={πες(14cos c) has an azimuthal svmimetrey around. the line connected binary companions and. depends heavily on the angle c between the directions to the optical star anc to the observer from the pulsar. see Figure 1.," When the pulsar wind is isotropic the gamma luminosity $L_\gamma (\psi )$ ( $% L_\gamma =\int 2\pi L_\gamma (\psi )d\cos \psi ) has an azimuthal symmetry around the line connected binary companions and depends heavily on the angle $\psi $ between the directions to the optical star and to the observer from the pulsar, see Figure 1." In our case of [ree racial relativistic wind the binary system emits the maximum energv of gamma radiation in the direction of the star (ec=0) and the minimum. οποίον of radiation in the opposite direction (0=x)., In our case of free radial relativistic wind the binary system emits the maximum energy of gamma radiation in the direction of the star $(\psi =0)$ and the minimum energy of radiation in the opposite direction $\psi =\pi )$. The spectrum. of the raciation and the maximal radiated energy also depend on v., The spectrum of the radiation and the maximal radiated energy also depend on $\psi $. During orbital motion c varies periodically giving rise to he periodical change of the intensity of the gamma radiation coming from the binary svstem to the observer., During orbital motion $\psi $ varies periodically giving rise to the periodical change of the intensity of the gamma radiation coming from the binary system to the observer. In section 2 we calculate the spectral shape £2(2.60) of he scattered hard photons in the case of arbitrary value of he parameter PRI &oing bevond the Thomson limit.," In section 2 we calculate the spectral shape $L_\gamma (\varepsilon ,\psi )$ of the scattered hard photons in the case of arbitrary value of the parameter $\frac{\omega \gamma }{mc^2}$, going beyond the Thomson limit." Under he assumption A«1 we receive analvtical formula for the ἐν (οι).," Under the assumption $K\ll 1$ we receive analytical formula for the $% L_\gamma (\varepsilon ,\psi )." " In section 3J) we apply our results to the binary svsten BD1259-63 and find that uncer the assumption of he power law relativistici particles.. spectrum. AL,f[meLy(mimOoμιςΟμ.)J 2A;in the range 10« 500. our model describes the observe photon spectrum rather good but the intensity is less then the observed one by a factor about 30."," In section 3 we apply our results to the binary system B1259-63 and find that under the assumption of the power law relativistic particles spectrum, $\frac{dN_{e^{\pm }}}{d\gamma }=0.4L_w\left/ \left[ mc^2\left( \gamma _{\min }^{-0.4}-\gamma _{\max }^{-0.4}\right) \right] \right. \gamma ^{-2.4}$ in the range $10<\gamma <500$ , our model describes the observe photon spectrum rather good but the intensity is less then the observed one by a factor about 30." " ""This discrepancy ds. clue to the presence of the mass outllow from the De star which disturbed. the free Dow of the pulsar wind.", This discrepancy is due to the presence of the mass outflow from the Be star which disturbed the free flow of the pulsar wind. The centrally ocated shock appears between the pulsar and the star due o the interaction between the two winds., The centrally located shock appears between the pulsar and the star due to the interaction between the two winds. Phe big dillerences tween the values of the velocities of the particles from he dillerent. sides of the tangential discontinuity will lead o the growth of the instabilities and the two winds will »* macroscopically mixed between the shocks., The big differences between the values of the velocities of the particles from the different sides of the tangential discontinuity will lead to the growth of the instabilities and the two winds will be macroscopically mixed between the shocks. ‘Phen the wavy non relativistic wind slows clown the volumes filled w the relativistic electrons and. positrons ancl they acquire essentially non relativistic hyerocvnamic ο velocity ey along the shock while the energy of electrons anc positrons does not changes significantly., Then the heavy non relativistic wind slows down the volumes filled by the relativistic electrons and positrons and they acquire essentially non relativistic hydrodynamic drift velocity $v_d$ along the shock while the energy of electrons and positrons does not changes significantly. With the decrease. of the hyvdrodynamic velocity of the relativistic plasma the time which it spends near the optical star increases in efe; times., With the decrease of the hydrodynamic velocity of the relativistic plasma the time which it spends near the optical star increases in $c/v_d$ times. " The elective transformation parameter A,rr~nA thus can be large enough to overcome the discrepancy. between the simple theory. and observations.", The effective transformation parameter $K_{eff}\sim \frac c{v_d}K$ thus can be large enough to overcome the discrepancy between the simple theory and observations. Lets us consider an interaction between the relativistic oulsar wind and the soft radiation [rom the companion zux ind the spectral ancl angular dependence of the outgoing xard raciation L2(5.0).," Lets us consider an interaction between the relativistic pulsar wind and the soft radiation from the companion and find the spectral and angular dependence of the outgoing hard radiation $L_\gamma (\varepsilon ,\psi )$." We assume that the pulsar wind aux he soft emission from the companion are isotropic and tha here is no mass outflow from the optical star., We assume that the pulsar wind and the soft emission from the companion are isotropic and that there is no mass outflow from the optical star. We treat both he pulsar and the optical star as à point sources., We treat both the pulsar and the optical star as a point sources. In. this case the trajectories of the particles and soft non scatterec οποίας are directed ractially from the pulsar ane from the optical star corresponcdinglv., In this case the trajectories of the particles and soft non scattered photons are directed radially from the pulsar and from the optical star correspondingly. Let 1 denote the location of the small element of volume dV. at à distance r to the pulsar and at an angle 9» to the lino of sight PO (see Figure 1).," Let I denote the location of the small element of volume $dV$ at a distance $% r to the pulsar and at an angle $\theta _2$ to the line of sight $% \overrightarrow{PO (see Figure 1)." In this clement ofvolume optical photons with the energy w scatters by the relativistic particles (electrons or positrons)., In this element ofvolume optical photons with the energy $\omega $ scatters by the relativistic particles (electrons or positrons). " The angle between the directions of the photon and the particle movements before the interaction is denoted by 6,.", The angle between the directions of the photon and the particle movements before the interaction is denoted by $\theta _1$. The photon scattering angle is designated by 8., The photon scattering angle is designated by $\theta $. Lets / signifies the distance from. this volume to the companion 5., Lets $l$ signifies the distance from this volume to the companion $S$. We are interested in the case of a distant observer and lus à vector along the direction to the observer from any point near the system may be considered as parallel to such (vector from the pulsar., We are interested in the case of a distant observer and thus a vector along the direction to the observer from any point near the system may be considered as parallel to such a vector from the pulsar. Only the photons scattered in the irection of the observer within the small solidi angle ο= 5cosx/Dwillreachtheobserver.," Only the photons scattered in the direction of the observer within the small solid angle $% \Omega =S\cos \chi /D^ 2$ will reach the observer." Here S is the area of 106 observer's surface. 2 is a distance from the pulsar to 16 observer and X is an angle between the direction to the observer from. the pulsar ancl from the volume.," Here $S$ is the area of the observer's surface, $D$ is a distance from the pulsar to the observer and $\chi $ is an angle between the direction to the observer from the pulsar and from the volume." As x is of 1e order of afD l. we may neglect the variance of O rom point to point.," As $\chi $ is of the order of $a/D\ll 1$ , we may neglect the variance of $\Omega $ from point to point." As we have already mention relativistic xwticle scatters the photons preferably. along the direction of the particle velocity and thus 65»« 1., As we have already mention relativistic particle scatters the photons preferably along the direction of the particle velocity and thus $\theta _2\ll 1$ . " From this fact it ollows that angles @ and 6, depend only on r and with an accuracy of the order θ~Vwsfe/ are equal.", From this fact it follows that angles $\theta $ and $\theta _1$ depend only on $r$ and with an accuracy of the order $\theta _2\sim \sqrt{\omega /\varepsilon }$ are equal. " ""Therefore. we reckon that the most likely explanatio- to the high IENCO abuudauces in L1157 is dust erai- mautles processing by the shock waves followed by neutral reactions in gas phase."," Therefore, we reckon that the most likely explanation to the high HNCO abundances in L1157 is dust grain mantles processing by the shock waves followed by neutral-neutral reactions in gas phase." We have discussed the line profiles aud the line iuteusities of different species in Sect. 3.1.., We have discussed the line profiles and the line intensities of different species in Sect. \ref{sect:profiles}. The IENCO profiles are very similar to those of SO aud SO»., The HNCO profiles are very similar to those of SO and $_2$. In addition. the lines of most of the molecules show similar intensities iu D1 aud B2 with the exception of CN. which is more intense in Bl. and IINCO. SOs aud OCS. whose lines are more intense chussion ta B2 than in Bl.," In addition, the lines of most of the molecules show similar intensities in B1 and B2 with the exception of CN, which is more intense in B1, and HNCO, $_2$ and OCS, whose lines are more intense emission in B2 than in B1." These similaritics of INCO and the sulfured molecules is somewhat puzzling., These similarities of HNCO and the sulfured molecules is somewhat puzzling. The actual reasou of the chemical differences in Bl aud D2 is not clear., The actual reason of the chemical differences in B1 and B2 is not clear. The preseut eas density in Bl aud B2 is simular (seeFigs.d. and 5727)., The present gas density in B1 and B2 is similar \citep[see Figs. \ref{fig:radex1} and \ref{fig:radex2} . Tn contrast. based ou the line profiles. the shock velocity can be higher iu Bl than in D2.," In contrast, based on the line profiles, the shock velocity can be higher in B1 than in B2." " Taking iuto account the extreme SiO line wines. the difference could reach 10ον, which after the ? models could be significaut."," Taking into account the extreme SiO line wings, the difference could reach 10, which after the \cite{Gusdorf08a} models could be significant." Alternatively. ?— have suggested that the chemical differences between Bl and B2 could be due to differeut shock ages.," Alternatively, \cite{Bachiller97} have suggested that the chemical differences between B1 and B2 could be due to different shock ages." Indeed. in contrast to SO» aud OCS. the TS abuudance is lower in B2 than iu Bl.," Indeed, in contrast to $_2$ and OCS, the $_2$ S abundance is lower in B2 than in B1." This is consisteut since Πο is a parent molecule for other sulfured species., This is consistent since $_2$ S is a parent molecule for other sulfured species. ILS is formed in the grain surfaces and released to the eas phase dy effect of the shock waves., $_2$ S is formed in the grain surfaces and released to the gas phase by effect of the shock waves. " Other sulfta-bearing molecules like SO aud SO» are produced in eas phase very quickly (ew 10° vr) via reactions with Π. ΟΠ and Ου ον, "," Other sulfur-bearing molecules like SO and $_2$ are produced in gas phase very quickly (few $^3$ yr) via reactions with H, OH and $_2$ \citep{Pineau93, Wakelam05}." One possible explanation of the differences in Bl and D2 is that the D2 shock could be older than that in Bl and that ToS las been couverted iuto SO aud SO»., One possible explanation of the differences in B1 and B2 is that the B2 shock could be older than that in B1 and that $_2$ S has been converted into SO and $_2$ . The higher SO2/SO ratio in B2 compared to DJ also points to an older shock iu D2., The higher $_2$ /SO ratio in B2 compared to B1 also points to an older shock in B2. ? have also proposed that the differeut CN abundance in Bl aud B2 can be accounted for m this scenario of au older shock im D2. since after an eubaucemenut of CN in the shock. reactions like οντο » CON could be very efficieut to destroy CN.," \cite{Bachiller97} have also proposed that the different CN abundance in B1 and B2 can be accounted for in this scenario of an older shock in B2, since after an enhancement of CN in the shock, reactions like CN+O $\rightarrow$ CO+N could be very efficient to destroy CN." Our data globally agree with this scenario. nevertheless the clear auticorrelation of the CN aud IENCO intensities aud the simula abundauces of CN and UNCO in LIL57-Bl suggest that al! the CN can tudeed be transformed into IENC'O. once tle shock has increased the temperature and the neutral-neutral reactions foriu NCO from CN and Ου aud IENCO from NCO (see Sect. 2)).," Our data globally agree with this scenario, nevertheless the clear anticorrelation of the CN and HNCO intensities and the similar abundances of CN and HNCO in L1157-B1 suggest that $all$ the CN can indeed be transformed into HNCO once the shock has increased the temperature and the neutral-neutral reactions form NCO from CN and $_2$ and HNCO from NCO (see Sect. \ref{sect:chemistry}) )." Therefore. the chemical differences from Bl aud B2 do support the scenario proposed in Sect.," Therefore, the chemical differences from B1 and B2 do support the scenario proposed in Sect." L2 to explain the IENCO abundauces in the L1157 shocks., \ref{sect:chemistry} to explain the HNCO abundances in the L1157 shocks. Tn addition. the scheme proposed iu Sect.," In addition, the scheme proposed in Sect." L2 also eives insieht on the possible link of TIINC'O and the sulftired 1olecules. in particular with SO aud SO».," \ref{sect:chemistry} also gives insight on the possible link of HNCO and the sulfured molecules, in particular with SO and $_2$." Iu shocks these molecules cau be produced by the reactions SiO»5»SO!O aud SO|OI»SO»OT η.," In shocks these molecules can be produced by the reactions $\mathrm{S+O_2} \rightarrow \mathrm{SO+O}$ and $\mathrm{SO+OH}\rightarrow \mathrm{SO_2+OH}$ \citep{Pineau93, Charnley97, Wakelam05}." Therefore. the coummon link with IINCO would be onaation patlwavs involving O».," Therefore, the common link with HNCO would be formation pathways involving $_2$." Another important shock tracer that could be linked o the Ου chemistry is SiO. Nevertheless. the situation reearding this molecule is more complex.," Another important shock tracer that could be linked to the $_2$ chemistry is SiO. Nevertheless, the situation regarding this molecule is more complex." First. recent nodels can explain the SiO ciuission iu shocks without a significant contribution of Si oxidation iu gas phase. either wW sputtering in gas-erain collisions if there is already SiO in the erain mautles (2) orby dust vaporization iu," First, recent models can explain the SiO emission in shocks without a significant contribution of Si oxidation in gas phase, either by sputtering in gas-grain collisions if there is already SiO in the grain mantles \citep[][]{Gusdorf08b} orby dust vaporization in" stars.,stars. The contribution of these residual field stars to the RDPs is statistically quantified by means of a comparison field., The contribution of these residual field stars to the RDPs is statistically quantified by means of a comparison field. " In practical terms, the use of the CM filters in cluster sequences enhances the contrast of the RDP to the background."," In practical terms, the use of the CM filters in cluster sequences enhances the contrast of the RDP to the background." " The CM filters are shown in Figs. 6,, 7,,"," The CM filters are shown in Figs. \ref{fig:6}, , \ref{fig:7}, ," and 8 as the shaded region superimposed on the decontaminated CMDs., and \ref{fig:8} as the shaded region superimposed on the decontaminated CMDs. " To avoid oversampling near the centre and undersampling for large radii, the RDPs are built by counting stars in concentric rings of increasing width with distance to the centre."," To avoid oversampling near the centre and undersampling for large radii, the RDPs are built by counting stars in concentric rings of increasing width with distance to the centre." The number and width of rings are optimised so that the resulting RDPs have adequate spatial resolution with moderate lo Poisson errors., The number and width of rings are optimised so that the resulting RDPs have adequate spatial resolution with moderate $1\sigma$ Poisson errors. The residual background level of each RDP corresponds to the average number of CM-filtered stars measured in the comparison field., The residual background level of each RDP corresponds to the average number of CM-filtered stars measured in the comparison field. " Usually, the RDPs of star clusters can be described by an analytical profile, like the empirical, single mass, modified isothermal spheres of King(1966) and (1975),, and the power law with a core of Elson,Fall&Freeman (1987)."," Usually, the RDPs of star clusters can be described by an analytical profile, like the empirical, single mass, modified isothermal spheres of \citet{King66} and \citet{Wilson75}, and the power law with a core of \citet{EFF87}." . These functions are characterised by different sets of parameters that are related to the cluster structure., These functions are characterised by different sets of parameters that are related to the cluster structure. " For simplicity and with the RDP error bars (Fig. 11)),"," For simplicity and with the RDP error bars (Fig. \ref{fig:11}) )," " we adopt the two-parameter function c(R)=συᾳ+co/(1-(R/R-)?), where ong is the residual background density, oo the central density of stars, and Reore the core radius."," we adopt the two-parameter function $\sigma(R) = \sigma_{bg} + \sigma_0/(1+(R/R_c)^2)$, where $\sigma_{bg}$ is the residual background density, $\sigma_0$ the central density of stars, and $R_{core}$ the core radius." " Applied to star counts, this function is similar to that used by King(1962) to describe the surface brightness profiles in the central parts of globular clusters."," Applied to star counts, this function is similar to that used by \cite{King1962} to describe the surface brightness profiles in the central parts of globular clusters." " We also estimate the cluster radius (Enpp) by measuring the distance from the cluster centre where the RDP and residual background are statistically indistinguishable (e.g.Bonatto&Bica,200Τα).", We also estimate the cluster radius $R_{RDP}$ ) by measuring the distance from the cluster centre where the RDP and residual background are statistically indistinguishable \citep[e.g.][]{Bonatto07a}. ". The ΠΠΡΡ can be taken as an observational truncation radius, whose value depends both on the radial distribution of member stars and the field density."," The $R_{RDP}$ can be taken as an observational truncation radius, whose value depends both on the radial distribution of member stars and the field density." " The overdensities are classified intothreegroups, according to the photometric and RDP analyses."," The overdensities are classified intothreegroups, according to the photometric and RDP analyses." Usingo the WISB approximation. the square| of o-field wave uuuber Rr) in the spread range reads Thed square] oft o-wave number A(r)P besidesB the spread rangec» cau be read from. the Eq.(10).,"Using the WKB approximation, the square of $\phi$ -field wave number $k^2(r)$ in the spread range reads The square of $\phi$ -wave number $k^2(r)$ besides the spread range can be read from the \ref{kk}) )." By using Savave approximate. the wave nunuber & reduces to be where —(rory)fA aud €=Arg.," By using $S$ -wave approximate, the wave number $k$ reduces to be where $x=(r-r_H)/\Delta$ and $\xi=\Delta /r_H$." Note. the mass of macro black hole we couceru is mach larger than Plauck mass. heuce ©«1.," Note, the mass of macro black hole we concern is much larger than Planck mass, hence $\xi\ll 1$." Now. ingoing aud outgoing wave function of the o with cnerev w are follows Using Eq.(61)). the first iiteeration in r.l.s.," Now, ingoing and outgoing wave function of the $\phi$ with energy $\omega$ are follows Using \ref{sNk}) ), the first integration in r.h.s." of equation can be calculated. Since &«1. we have where the terms of O(£) have been neglected due to £«I. whose effects will be briefly discussed iu the cud of this section.," of equation can be calculated, Since $\xi\ll 1$, we have where the terms of $\mathcal{O}(\xi^2)$ have been neglected due to $\xi\ll 1$, whose effects will be briefly discussed in the end of this section." Takiug the positive sign. we obtain the absolute value," Taking the positive sign, we obtain the absolute value" While brown cbwarfs do not supply the missingin] mass. their properties continue to be of considerable importance. for our understanding of star formation anc stellar evolution.,"While brown dwarfs do not supply the missing mass, their properties continue to be of considerable importance for our understanding of star formation and stellar evolution." the discovery of GI 229D (Nakajima et al. 1995) and of a variety of sub-stellar mass objects in the Pleiades (Rebolo et al. 1995) confirmed. the existence of these objects. but. save for Ixelu 1. (Ruiz ct al. 1997). isolated objects in the Llield remained. elusive.," the discovery of Gl 229B (Nakajima et al, 1995) and of a variety of sub-stellar mass objects in the Pleiades (Rebolo et al, 1995) confirmed the existence of these objects, but, save for Kelu 1 (Ruiz et al, 1997), isolated objects in the field remained elusive." Identifving these intrinsically faint. cool objects requires deep. wide-field imaging at red. or near-infrarecl wavelengths. as emphasised. by the initial results [rom 120m. DENIS (Delfosse et al. 1997) and PALASS (Ixirkpatrick et al. 1998) surveys.," Identifying these intrinsically faint, cool objects requires deep, wide-field imaging at red or near-infrared wavelengths, as emphasised by the initial results from $1-2 \mu m$ DENIS (Delfosse et al, 1997) and 2MASS (Kirkpatrick et al, 1998) surveys." Prior to the availability of large-scale. near-infrared hotometry.. photographic plates ollercd the only viable method of surveying tens or hundreds of square degrees.," Prior to the availability of large-scale near-infrared photometry, photographic plates offered the only viable method of surveying tens or hundreds of square degrees." Such media are limited to wavelengths shortward of Lyn. rut can achieve (single-plate) detection limits of Rew~ 21 ο 21.5 and Lc:~19 to 19.5 magnitudes.," Such media are limited to wavelengths shortward of $\mu m$, but can achieve (single-plate) detection limits of $_C \sim$ 21 to 21.5 and $_C \sim 19$ to 19.5 magnitudes." Moreover. Llawkins las experimented with digital addition of plate scans. and finds that the limiting magnitude can be extended significantIv. (22 magnitudes) if 20-40 plates are available or à given field.," Moreover, Hawkins has experimented with digital addition of plate scans, and finds that the limiting magnitude can be extended significantly $>2$ magnitudes) if 20-40 plates are available for a given field." Although expensive in telescope time. this echnique makes photography competitive with optical or near-infrared CCD imaging for a number of specific projects.," Although expensive in telescope time, this technique makes photography competitive with optical or near-infrared CCD imaging for a number of specific projects." " Llawkins. has concentrated analysis. on a single. field.. ESO/SERC field 287 centred at a=21""28"". 5=45""."," Hawkins has concentrated analysis on a single field, ESO/SERC field 287 centred at $\alpha = 21^h 28^m$, $\delta = -45^o$." Recently. Lawkins ct al (1998) re»orted. on initial results from searching a combination of 65 Ilak and 30 LVN plates for candidate very low mass stars or brown cwarfs.," Recently, Hawkins et al (1998) reported on initial results from searching a combination of 65 IIIaF and 30 IVN plates for candidate very low mass stars or brown dwarfs." Thev announce the discovery of at least three brown clwarks with somewhat unusual properties: the optical and near-infrared colours match those of late-type Al-elwarls. but the absolute magnitudes. calibrated using. οςDe-derived: trigonometric parallaxes. place the objects ~2.5 magnitudes: below the main-sequence.," They announce the discovery of at least three brown dwarfs with somewhat unusual properties: the optical and near-infrared colours match those of late-type M-dwarfs, but the absolute magnitudes, calibrated using CCD-derived trigonometric parallaxes, place the objects $\sim 2.5$ magnitudes below the main-sequence." In. contrast. theoretical evolutionary calculations (c.g. Burrows ct al. 1997) predict that cooling brown dwarfs should. lieabove the stellar main-sequence ab these temperatures.," In contrast, theoretical evolutionary calculations (e.g. Burrows et al, 1997) predict that cooling brown dwarfs should lie the stellar main-sequence at these temperatures." Hawkins ct al suggest. that. their candidates may be either metal-poor or subject to unusual dust formation in the atmosphere., Hawkins et al suggest that their candidates may be either metal-poor or subject to unusual dust formation in the atmosphere. We present here optical spectroscopy of one of the three brown dwarf. candidates. DOL.," We present here optical spectroscopy of one of the three brown dwarf candidates, D04." Phe. following section. cleseribes our observations. while the final section summarises our conclusions.," The following section describes our observations, while the final section summarises our conclusions." Our observations of DO4 were obtained on August 11. 1998 as part of a service allocation with the Low-Iesolution," Our observations of D04 were obtained on August 11, 1998 as part of a service allocation with the Low-Resolution" "where 7, is the back stress created by the concentration of dislocations where Dy is a diffusion coellicient that we take equal to 1 to simplilv the presentation.",where $\tau_b$ is the back stress created by the concentration of dislocations where $D_0$ is a diffusion coefficient that we take equal to $1$ to simplify the presentation. " Introducing the «quantities the full GCZ svstem can be rewritten with y=7,€1-(-1.1) as with boundary conditions on OF: for some constant cy and the initial conditions The non-negativitv5 of the densities 97 at the inital time is equivalent to the following5 condition Aloreover. we will assume the following condition"," Introducing the quantities the full GCZ system can be rewritten with $y=x_1\in I=(-1,1)$ as with boundary conditions on $\partial I$: for some constant $c_0$ and the initial conditions The non-negativity of the densities $\theta^\pm$ at the inital time is equivalent to the following condition Moreover, we will assume the following condition" is hardly relevant as there are no universal criteria for defining a physical companion: the choice of a limit. for the projected linear separation. radial velocity difference. and brightness difference between the primary galaxy and its companion is empirical. hence. arbitrary: moreover. the lack of redshift information has often been substituted by statistical suppositions of the share of projected objects.,"is hardly relevant as there are no universal criteria for defining a physical companion: the choice of a limit for the projected linear separation, radial velocity difference, and brightness difference between the primary galaxy and its companion is empirical, hence, arbitrary; moreover, the lack of redshift information has often been substituted by statistical suppositions of the share of projected objects." In fact. most research has aimed at relative studies of the environment of Sy vs. inactive galaxies.," In fact, most research has aimed at relative studies of the environment of Sy vs. inactive galaxies." No consensus has been reached about the share of Sy galaxies with companions — the results can be grouped into three: those with an excess of Sy galaxies with companions relative to inactive galaxies. those with no difference between Sy and inactive galaxies. and those with an excess of 22 galaxies with companions compared both to 11 and inactive galaxies (Schmitt2004.andreferencestherein )..," No consensus has been reached about the share of Sy galaxies with companions – the results can be grouped into three: those with an excess of Sy galaxies with companions relative to inactive galaxies, those with no difference between Sy and inactive galaxies, and those with an excess of 2 galaxies with companions compared both to 1 and inactive galaxies \citep[][and references therein]{S_04}." Tidal interactions and minor mergers could produce various tidal features and disturbed structures., Tidal interactions and minor mergers could produce various tidal features and disturbed structures. We found. however. no correlation. between asymmetries and. the presence of companions for both samples.," We found, however, no correlation between asymmetries and the presence of companions for both samples." One explanation lies in the delay between the onset of interaction and its optical manifestation in the host galaxy (e.g..Byrdetal.1987).. and bulge prominence can further delay this (Hernquist&Mihos1995).," One explanation lies in the delay between the onset of interaction and its optical manifestation in the host galaxy \citep[e.g.,][]{BSV_87}, and bulge prominence can further delay this \citep{HM_95}." . Second. an ongoing merger would show up as an isolated asymmetric galaxy.," Second, an ongoing merger would show up as an isolated asymmetric galaxy." The fraction of asymmetric galaxies is the same within the errors for the Sy (51+48)% and control (43+8)% sample.," The fraction of asymmetric galaxies is the same within the errors for the Sy $(51\,$$\pm$$\,8)\%$ and control $(43\,$$\pm$$\,8)\%$ sample." Similar results were found by Viranietal.(2000) and Corbin (2000)., Similar results were found by \citet[][]{VRV_00} and \citet[][]{C_00}. . Furthermore. the fraction of asymmetric galaxies without companions is practically equal for both samples (between (20-57)6€ and (26--8). depending on whether candidate companions are excluded from consideration or not).," Furthermore, the fraction of asymmetric galaxies without companions is practically equal for both samples (between $(20\,$$\pm$$\,7)\%$ and $(26\,$$\pm$$\,8)\%$, depending on whether candidate companions are excluded from consideration or not)." Therefore. we could come to the corollary that minor mergers. at least not accompanied by companions. do not occur in the Sy sample more often than in the control one.," Therefore, we could come to the corollary that minor mergers, at least not accompanied by companions, do not occur in the Sy sample more often than in the control one." It turns out that (9145)% of the Sy and (9444)% of the inactive galaxies have bars or/and rings. asymmetries. companions.," It turns out that $(91\,$$\pm$$\,5)\%$ of the Sy and $(94\,$$\pm$$\,4)\%$ of the inactive galaxies have bars or/and rings, asymmetries, companions." Thus. the vast majority of galaxies in. both samples show morphological evidence of non-axisymmetric perturbations of the potential or/and have close companions.," Thus, the vast majority of galaxies in both samples show morphological evidence of non-axisymmetric perturbations of the potential or/and have close companions." The rest of the galaxies all show some signs ofiteraction: they either have à companion within about seven galaxy diameters 3352. JJO1505708-0014040. and 0022). have a candidate companion without redshift information (Mrk509.Borisetal.2002:Rafanelli1993).. or show evidence of a past merger (Mrk304.Lim&Ho 1999).," The rest of the galaxies all show some signs of interaction: they either have a companion within about seven galaxy diameters 352, J01505708+0014040, and 022), have a candidate companion without redshift information \citep[Mrk\,509,][]{BDP_02,RMB_93}, or show evidence of a past merger \citep[Mrk\,304,][]{LH_99}." . Thus. unperturbed galaxies. both Sy and inactive. may turn out to be related to interaction.," Thus, unperturbed galaxies, both Sy and inactive, may turn out to be related to interaction." Instances of fine structures indicative of past mergers in active galaxies that were previously classified as undisturbed have already been adduced (Canalizoetal.2007;Bennert2008).," Instances of fine structures indicative of past mergers in active galaxies that were previously classified as undisturbed have already been adduced \citep[][]{CBJ_07,BCJ_08}." . Even if we consider only the morphological evidence of non-axisymmetric perturbations of the potential. its incidence is equal within the errors in the Sy. (8646)%. and control. (8346)%. sample.," Even if we consider only the morphological evidence of non-axisymmetric perturbations of the potential, its incidence is equal within the errors in the Sy, $(86\,$$\pm$$\,6)\%$, and control, $(83\,$$\pm$$\,6)\%$, sample." Similar results were found by (2000)., Similar results were found by \citet[][]{VRV_00}. All Sy galaxies and about a half of the control ones were imaged with CCDs., All Sy galaxies and about a half of the control ones were imaged with CCDs. HI. and digitized ESO-Uppsala Survey data were used for the rest of the control galaxies.," II, and digitized ESO-Uppsala Survey data were used for the rest of the control galaxies." We examined to what extent the different data sources of the Sy and control galaxies may introduce systematic errors in the results., We examined to what extent the different data sources of the Sy and control galaxies may introduce systematic errors in the results. For all galaxies having CCD data (53 total). we also processed the corresponding DSS data and independently estimated the Hubble type and the presence of structures and asymmetries.," For all galaxies having CCD data (53 total), we also processed the corresponding DSS data and independently estimated the Hubble type and the presence of structures and asymmetries." In the photographie data. we detected the same ncidence of bars and asymmetries as in the CCDdata?.," In the photographic data, we detected the same incidence of bars and asymmetries as in the CCD." . Of the detected rings in the CCD data. we could not trace two inner rings 3376 and 5841) and one outer 5506) in the corresponding photographic data.," Of the detected rings in the CCD data, we could not trace two inner rings 376 and 541) and one outer 506) in the corresponding photographic data." If we use —hese considerations to roughly correct for structures missed because of using photographic data. the expected number of ner rings increases with one. and the number of outer rings remains the same for the photographically imaged galaxies.," If we use these considerations to roughly correct for structures missed because of using photographic data, the expected number of inner rings increases with one, and the number of outer rings remains the same for the photographically imaged galaxies." Thus. regarding the control galaxies. this correction affects only the fraction of inner rings. and 1t gets (43+8)% (vs. (3448)% for the Sy sample).," Thus, regarding the control galaxies, this correction affects only the fraction of inner rings, and it gets $(43\,$$\pm$$\,8)\%$ (vs. $(34\,$$\pm$$\,8)\%$ for the Sy sample)." This translates into a fraction of rings of (57€8)6c for the control sample (vs. (49+8)% for the Sy sample).," This translates into a fraction of rings of $(57\,$$\pm$$\,8)\%$ for the control sample (vs. $(49\,$$\pm$$\,8)\%$ for the Sy sample)." The most that this correction could affect the final results is when the undetected inner ring 1s among the galaxies without morphological evidence of non-axisymmetric perturbations of the potential (and companions)., The most that this correction could affect the final results is when the undetected inner ring is among the galaxies without morphological evidence of non-axisymmetric perturbations of the potential (and companions). Then the fraction of galaxies with bars or/and rings. asymmetries. companions gets (91+5)% vs. (97+3)% for the Sy vs. control sample.," Then the fraction of galaxies with bars or/and rings, asymmetries, companions gets $(91\,$$\pm$$\,5)\%$ vs. $(97\,$$\pm$$\,3)\%$ for the Sy vs. control sample." " Considering just the morphological evidence of non-axisymmetric perturbations of the potential. the two samples show an equal incidence. (86+οσο,"," Considering just the morphological evidence of non-axisymmetric perturbations of the potential, the two samples show an equal incidence, $(86\,$$\pm$$\,6)\%$." As we can see. this correction does not significantly influence the final results. since all features affected by it occur with the same incidence within the errors in both samples.," As we can see, this correction does not significantly influence the final results, since all features affected by it occur with the same incidence within the errors in both samples." The abundances themselves are either equal in both samples or higher in the control one., The abundances themselves are either equal in both samples or higher in the control one. In the context of our study. looking for an eventual excess of features in the Sy sample. this result should mean that the incidence of the features of interest is not lower in the control sample than in the Sy one.," In the context of our study, looking for an eventual excess of features in the Sy sample, this result should mean that the incidence of the features of interest is not lower in the control sample than in the Sy one." io be Gaussian or to have a second-order moment.,to be Gaussian or to have a second-order moment. The notion that the density difference is characterized by a Lévvy. distribution is a constraint on dynamical models for electron density fIuctuations in the ISALA Consecquently the question of how a Lévvy distribution can arise in electron density fIuctuations assumes considerable importance in understauding the ISM., The notion that the density difference is characterized by a Lévvy distribution is a constraint on dynamical models for electron density fluctuations in the ISM.  Consequently the question of how a Lévvy distribution can arise in electron density fluctuations assumes considerable importance in understanding the ISM. Previous work has laid the groundwork for answering this question., Previous work has laid the groundwork for answering this question. " It has been established that electron density. fluctuations associated with interstellar magnetic turbulence undergo a significant change in character near the scale 10p,. where p, is the ion sound evroraclius (Terryetal. 2001)."," It has been established that electron density fluctuations associated with interstellar magnetic turbulence undergo a significant change in character near the scale $10 \rho_s$, where $\rho_s$ is the ion sound gyroradius \citep{ter01}." .. At larger scales. electron density is passively advected by the turbulent flow of an MIID cascade mediated by nonlinear shear Allvénn waves (Goldreich1905].," .  At larger scales, electron density is passively advected by the turbulent flow of an MHD cascade mediated by nonlinear shear Alfvénn waves \citep{goldreich95}." Α At smaller scales the electron density becomes compressive and the turbulent enerev is carried into a cascade mediated by kinetic Alfvénn waves (NAW) 2001)., .  At smaller scales the electron density becomes compressive and the turbulent energy is carried into a cascade mediated by kinetic Alfvénn waves (KAW) \citep{ter01}. .A. The KAW cascade brings electron density into equipartilion with the magnetic field. allowing for a significant increase in amplitude.," .  The KAW cascade brings electron density into equipartition with the magnetic field, allowing for a significant increase in amplitude." A The conversion to a KAW cascade has been observed in numerical solutions of the evrokinetic equations (Llowesetal.2006).. and is consistent with observations from solar wind turbulence (Harmon&Coles2005:Baleetal.2005;Leamion 1998).,"  The conversion to a KAW cascade has been observed in numerical solutions of the gyrokinetic equations \citep{howes06}, and is consistent with observations from solar wind turbulence \citep{harmon05,bale05,leamon98}." ".À nuportantlv. it puts large amplitude electron density fluctuations (and large amplitude density gradients) al the gvroradius scale (~LOS—10!"" cni). a desirable set of conditions for pulsar scintillation (Boldvrey&Ixoniel ?006)."," .  Importantly, it puts large amplitude electron density fluctuations (and large amplitude density gradients) at the gyroradius scale $\sim 10^8-10^{10}$ cm), a desirable set of conditions for pulsar scintillation \citep{boldyrev06}." .A It is therefore appropriate to consider whether large-amplitude non-Gaussian structures can arise in KAW turbulence., .  It is therefore appropriate to consider whether large-amplitude non-Gaussian structures can arise in KAW turbulence. A This question has been parüallv answered in a study of curent filament. formation in decaving KAW turbulence (Terry&Smith2007. 2003).,"  This question has been partially answered in a study of current filament formation in decaying KAW turbulence \citep{terry-smith07,terry-smith08}." .. In munerical solutions to a (wo-Lield model with broadband Gaussian initial conditions large smplitude current filaments spontaneously arose., .  In numerical solutions to a two-field model with broadband Gaussian initial conditions large amplitude current filaments spontaneously arose. A Each filament was associated with a large-anplitude electron density structure. circular in cross-section. (hat persisted in time.,"  Each filament was associated with a large-amplitude electron density structure, circular in cross-section, that persisted in time." A These electron density structures were not as localized as (he corresponding current filaments. but were coherent ancl not mixed by surrounding turbulence.,"  These electron density structures were not as localized as the corresponding current filaments, but were coherent and not mixed by surrounding turbulence." A. The observation of large amplitude current filaments is similar to the Iarge-anplitude vortex filaments found in decaving 2D hwdrodyvnamic turbulence (MleWilliams 1984).,  The observation of large amplitude current filaments is similar to the large-amplitude vortex filaments found in decaying 2D hydrodynamic turbulence \citep{mcw84}. .À Counterparts of such structures in 3D are predicted to be the dominant component lor higher order structure functions (She&Leveque, .  Counterparts of such structures in 3D are predicted to be the dominant component for higher order structure functions \citep{she94}. 1994)..A Terry&Sinith(2007) proposed that a nonlinear refractive magnetic shear mechanism prevents the structures from mixing with turbulence., .  \citet{terry-smith07} proposed that a nonlinear refractive magnetic shear mechanism prevents the structures from mixing with turbulence. A— Radial shear in the azimuthally directed magnetic field associated wilh each Iarge-amplitude current filament decreases the racial correlation length of the turbulent edcdies ancl enhances the decorrelation rate.,  Radial shear in the azimuthally directed magnetic field associated with each large-amplitude current filament decreases the radial correlation length of the turbulent eddies and enhances the decorrelation rate. A 41ος are unable to persist long enough to penetrate the shear boundary laver and disrupt the,  Eddies are unable to persist long enough to penetrate the shear boundary layer and disrupt the lines by demanding that they be tangent to the equipotential contours. which are concentric ellipses.,"lines by demanding that they be tangent to the equipotential contours, which are concentric ellipses." Now. lets turn {ο a general sell-gravitating svstem with some conmpressibilitv.," Now, let's turn to a general self-gravitating system with some compressibility." " II. we adopt a polvtropic equation of state. p=lp!EF"" (pis pressure. his the polvtropic constant and nis the polvtvopic index). Eulers equation for steady-state flows in the rotating frame 15. where II is enthalpy. aud e is the gravitational potential."," If we adopt a polytropic equation of state, $p=k\rho^{1+1/n}$ $p$is pressure, $k$ is the polytropic constant and $n$ is the polytropic index), Euler's equation for steady-state flows in the rotating frame is, where H is enthalpy, and $\Phi$ is the gravitational potential." With the velocity fiekl specified by Eq. (3)).," With the velocity field specified by Eq. \ref{vel}) )," one can show that Eq. (4)), one can show that Eq. \ref{euler}) ) is equivalent to the following equation. llence. within the configuration the following Bernoullis function must be uniform in space: where C' is a constant.," is equivalent to the following equation, Hence, within the configuration the following Bernoulli's function must be uniform in space: where $C_1$ is a constant." It should be mentioned that in this Bernoullis function. w and A are interchangeable.," It should be mentioned that in this Bernoulli's function, $\omega$ and $\lambda$ are interchangeable." This reflects the fact that. for anv direct configuration (w2 A) in which [πα motion is dominated by figure rotation. the adjoint configuration (ω\lambda$ ) in which fluid motion is dominated by figure rotation, the adjoint configuration $\omega<\lambda$ ) in which fluid motion is dominated by internal motions can be obtained by simply interchanging $\omega$ and $\lambda$." " We find it is useful to celine an effective potential Py as: henee. the Bernoullis function ean also be written as: In our later discussion of equi-potential (so-densitv) surfaces. we will often. use the phrase ""equi-potential referring (ο er."," We find it is useful to define an effective potential $\Phi_{\mathrm{eff}}$ as: hence, the Bernoulli's function can also be written as: In our later discussion of equi-potential (iso-density) surfaces, we will often use the phrase “equi-potential” referring to $\Phi_{\mathrm{eff}}$ ." On the other hand. (he steady-state conünuity equation in the rotating frame recquires.," On the other hand, the steady-state continuity equation in the rotating frame requires," Thus. the signature of the marginally stable orbit is most likely to be observed from the most massive neutron stars.,"Thus, the signature of the marginally stable orbit is most likely to be observed from the most massive neutron stars." Alillisecond. x-ray timing is a promising probe of accretion flows m x-ray binarics., Millisecond x-ray timing is a promising probe of accretion flows in x-ray binaries. Robust correlations exist between mullisecoucd tiuiug properties aud spectral properties., Robust correlations exist between millisecond timing properties and spectral properties. Study of these correlation mav help improve our understanding of the plivsies aud ecolctry of accretion flows in neutron star x-ray binaries and. perhaps. also of strong field. eravity.," Study of these correlation may help improve our understanding of the physics and geometry of accretion flows in neutron star x-ray binaries and, perhaps, also of strong field gravity." A set of nine estimated natal spin periods for tsolated. rotation-powered pulsars is given in Table 7 of Faucher-Giguere Kaspi (2006).,"A set of nine estimated natal spin periods for isolated, rotation-powered pulsars is given in Table 7 of Faucher-Giguere Kaspi (2006)." These sources and their natal spin periods are treated in detail in this analysis., These sources and their natal spin periods are treated in detail in this analysis. In the two cases where an initial period is given as a lower limit. we have conservatively adopted the limiting value (this will give higher dimensionless angular momenta).," In the two cases where an initial period is given as a lower limit, we have conservatively adopted the limiting value (this will give higher dimensionless angular momenta)." The measurement of black hole spins is in its infancy. and so we imposed some modest quality metrics in selecting black hole data.," The measurement of black hole spins is in its infancy, and so we imposed some modest quality metrics in selecting black hole data." We required that all spin data must be based on statistical fits wherein a trial spectral model was folded through an instrument response and evaluated against an observed spectrum using a goodness-of-fit statistic., We required that all spin data must be based on statistical fits wherein a trial spectral model was folded through an instrument response and evaluated against an observed spectrum using a goodness-of-fit statistic. Owing to the lack of errorsand goodness-of-fit statistics. then. we have excluded early spin estimates by Zhang. Cut. Chen (1997).," Owing to the lack of errors goodness-of-fit statistics, then, we have excluded early spin estimates by Zhang, Cui, Chen (1997)." Blum et ((2009) report two spin values for GRS 19154105 based on fits to the disk reflection spectrum obtained withSuzaku., Blum et (2009) report two spin values for GRS $+$ 105 based on fits to the disk reflection spectrum obtained with. The higher value of a=0.98£0.01 1s used in this work. as it derives from fits made to a spectrum spanning a much broader energy range.," The higher value of $a = 0.98\pm 0.01$ is used in this work, as it derives from fits made to a spectrum spanning a much broader energy range." A lower value for the spin of GRS 19154105 has also been reported based on fits to the disk continuum (Middelton et 22006)., A lower value for the spin of GRS $+$ 105 has also been reported based on fits to the disk continuum (Middelton et 2006). The high value listed in Table | is likely more robust as it was derived by giving extra weight to observations wherein a standard Novikov-Thorne (1973) accretion disk 1s likely to hold (MeClintock et al., The high value listed in Table 1 is likely more robust as it was derived by giving extra weight to observations wherein a standard Novikov-Thorne (1973) accretion disk is likely to hold (McClintock et al. 2006)., 2006). " A quality cut is automatically imposed on spin measurements made using thermal continuum emission from the aceretion disk. in that the mass and distance to a source must be well-determined if fits are to yield meaningful constraints,"," A quality cut is automatically imposed on spin measurements made using thermal continuum emission from the accretion disk, in that the mass and distance to a source must be well-determined if fits are to yield meaningful constraints." Table | details the black hole dimensionless angular momenta used in this work., Table 1 details the black hole dimensionless angular momenta used in this work. In five of the black hole systems listed (XTE J1652—453. SAX 11711.6—3808. XTE J1752-223. Swift J1753.5-0127. and XTE J19084094). strong dynamical constraints requiring a black hole primary have not yet been obtained through radial velocity techniques.," In five of the black hole systems listed (XTE $-$ 453, SAX $-$ 3808, XTE $-$ 223, Swift $-$ 0127, and XTE $+$ 094), strong dynamical constraints requiring a black hole primary have not yet been obtained through radial velocity techniques." However. myriad phenomena observed from of these sources are consistent with dynamically-constrainted systems. and it is extremely likely that these X-ray binaries harbor black holes (for a review of characteristic properties. see Remillard McClintock 2006).," However, myriad phenomena observed from of these sources are consistent with dynamically-constrainted systems, and it is extremely likely that these X-ray binaries harbor black holes (for a review of characteristic properties, see Remillard McClintock 2006)." Black hole angular momenta are measured using relativistic spectroscopic models: no additional calculations are requied to make use of these data., Black hole angular momenta are measured using relativistic spectroscopic models; no additional calculations are requied to make use of these data. In the case of neutron stars. If ts necessary to calculate the angular momentum of each star using its mass and spin period.," In the case of neutron stars, it is necessary to calculate the angular momentum of each star using its mass and spin period." If the equation of state of ultra-dense matter were known. the moment of inertia could be calculated by integrating the prescription for how mass varies with radius.," If the equation of state of ultra-dense matter were known, the moment of inertia could be calculated by integrating the prescription for how mass varies with radius." At present. the correct equation of state is unknown. and many candidates exist (see Lattimer Prakash 2006).," At present, the correct equation of state is unknown, and many candidates exist (see Lattimer Prakash 2006)." It is worth noting that some soft equations of state have recently been ruled-out with the discovery of an especially massive neutron star (M=1.97+0.04M..; Demorest et 22010)., It is worth noting that some soft equations of state have recently been ruled-out with the discovery of an especially massive neutron star $M = 1.97\pm 0.04~M_{\odot}$; Demorest et 2010). " In order not to bias our analysis in. favor of any particular equation of state. we have simply approximated the moment of inertia as I2(2/MR"" as per a sphere of uniform density."," In order not to bias our analysis in favor of any particular equation of state, we have simply approximated the moment of inertia as ${\rm I} = (2/5){\rm M}{\rm R}^{2}$ as per a sphere of uniform density." Dimensionless angular momenta were calculated using the natal periods given in Faucher-Giguere Kaspi (2006). for different combinations of neutron star mass and radius.," Dimensionless angular momenta were calculated using the natal periods given in Faucher-Giguere Kaspi (2006), for different combinations of neutron star mass and radius." One set of dimensionless angular momenta were calculated assuming canonical parameters: R=10 km and Μνς=1.4M ...," One set of dimensionless angular momenta were calculated assuming canonical parameters: ${\rm R} = 10$ km and ${\rm M}_{\rm NS} = 1.4~{\rm M}_{\odot}$ ." Extreme dimensionless angular momenta result from assuming a larger radius for à given mass., Extreme dimensionless angular momenta result from assuming a larger radius for a given mass. All of the equations of state treated in Lattimer Prakash (2006) predict radii less than or equal to 15 km., All of the equations of state treated in Lattimer Prakash (2006) predict radii less than or equal to 15 km. A set of extreme angular momenta were therefore derived assuming R=15 km and Μις= L4M.., A set of extreme angular momenta were therefore derived assuming ${\rm R} = 15$ km and ${\rm M}_{\rm NS} = 1.4~{\rm M}_{\odot}$ . The mean and median values of the dimensionless angular momentum distributions are given in Table 2. and the distributions are shown in Figure 1.," The mean and median values of the dimensionless angular momentum distributions are given in Table 2, and the distributions are shown in Figure 1." The black hole distributions are consistent with moderately high values: Gea=0.66 for spins derived using disk reflection spectra. and es=0.72 for spins derived using the disk continuum.," The black hole distributions are consistent with moderately high values: $a_{\rm mean} = 0.66$ for spins derived using disk reflection spectra, and $a_{\rm mean} = 0.72$ for spins derived using the disk continuum." These values stand in marked contrast to those derived for the neutron star samples., These values stand in marked contrast to those derived for the neutron star samples. For neutron stars where the natal spin period has been estimated. even extreme stellar parameters only work to yield dyjean=0.029.," For neutron stars where the natal spin period has been estimated, even extreme stellar parameters only work to yield $a_{\rm mean} = 0.029$." The sample of black hole spin parameters derived using disk reflection fits is small (12 measurements). but twice as large as the present sample derived using the disk continuum.," The sample of black hole spin parameters derived using disk reflection fits is small (12 measurements), but twice as large as the present sample derived using the disk continuum." A Gaussian fit to the reflection-derived distribution gives deo=0.71 and o=0.26., A Gaussian fit to the reflection-derived distribution gives $a_{\rm cent} = 0.71$ and $\sigma = 0.26$. A fit to the smaller distribution of continuum-derived spin parameters gives e=0.81 and 7=0.06 (the width should be viewed as a lower limit as the fit was largely insensitive to the lowest spin value)., A fit to the smaller distribution of continuum-derived spin parameters gives $a_{\rm cent} = 0.81$ and $\sigma = 0.06$ (the width should be viewed as a lower limit as the fit was largely insensitive to the lowest spin value). Although likely aided by the small sample sizes currently available. the," Although likely aided by the small sample sizes currently available, the" the source position.,the source position. The background region was defined as an annulus centered on the source with an inner radius of 60 pixels (142”) and an outer radius of 110 pixels (260”)., The background region was defined as an annulus centered on the source with an inner radius of 60 pixels $142^{\prime\prime}$ ) and an outer radius of 110 pixels $260^{\prime\prime}$ ). " In the data analysis, channels below 0.3 keV and above 10 keV were excluded."," In the data analysis, channels below 0.3 keV and above 10 keV were excluded." " The spectrum integrated over the 600 s time-interval was then fitted with the XSPEC package (v. 11.3.1), and the pile-up correction was included."," The spectrum integrated over the 600 s time-interval was then fitted with the XSPEC package (v. 11.3.1), and the pile-up correction was included." " To reduce the Poisson noises, the spectrum data were binned to ensure that each energy bin contains at least 20 counts."," To reduce the Poisson noises, the spectrum data were binned to ensure that each energy bin contains at least 20 counts." " The spectrum is well fitted by an absorbed power- model, with an photon index [=2.297538 and total equivalent Hydrogen column density Ny=6.83*13x1074 ?."," The spectrum is well fitted by an absorbed power-law model, with an photon index $\Gamma = 2.29_{-0.26}^{+0.28}$ and total equivalent Hydrogen column density $N_\hh =6.83_{-1.3}^{+1.5}\times 10^{21}$ $^{-2}$." " The reduced chi-square of the fit is x2=0.64, with 18 degrees of freedom."," The reduced chi-square of the fit is $\chi_\rr^2 = 0.64$, with 18 degrees of freedom." These results are consistent with the analysis by Soderbergetal.(2008)., These results are consistent with the analysis by \citet{sod08}. ". The fit gives rise to an unabsorbed X-ray fluence of 1.36*027x107"" erg cm? in 0.3-10 keV. [A figure of the power-law spectral fit is not shown here since it is very similar to the fig."," The fit gives rise to an unabsorbed X-ray fluence of $1.36_{-0.37}^{+0.51}\times 10^{-7}$ erg $^{-2}$ in $0.3$ –10 keV. [A figure of the power-law spectral fit is not shown here since it is very similar to the fig." 2 of Soderberg et al. (, 2 of Soderberg et al. ( 2008).],2008).] " The fitted Hydrogen column density is much higher than the Galactic Hydrogen column density to the direction of NGC 2770 (2x109 cm-?,2008), but is typical among the Hydrogen column density of GRB host galaxies (Savaglio2006)."," The fitted Hydrogen column density is much higher than the Galactic Hydrogen column density to the direction of NGC 2770 \citep[$2\times 10^{20}$ $^{-2}$, but is typical among the Hydrogen column density of GRB host galaxies \citep{sav06}." ". Given the redshift of the source, z=0.0065, the power-law spectral fit leads to an unabsorbed total energyx104° erg and an unabsorbed average luminosity 241*0221.27*035x1035 erg s! in the XRT's energy range 0.3- 10 keV. The luminosity is 10? times of the Eddington luminosity of a solar mass object."," Given the redshift of the source, $z=0.0065$, the power-law spectral fit leads to an unabsorbed total energy$1.27^{+0.48}_{-0.35}\times 10^{46}$ erg and an unabsorbed average luminosity $2.11^{+0.79}_{-0.58}\times 10^{43}$ erg $^{-1}$ in the XRT's energy range $0.3$ $10$ keV. The luminosity is $10^5$ times of the Eddington luminosity of a solar mass object." " Although the power-law fit is good, the fit of the spectrum is not unique."," Although the power-law fit is good, the fit of the spectrum is not unique." " An interesting result is that, although an absorbed single blackbody does not fit the spectrum of XRF 080109 (x2= 2.2), an absorbed double blackbody model fits the spectrum equally well as the absorbed power-law (Fig. 1))."," An interesting result is that, although an absorbed single blackbody does not fit the spectrum of XRF 080109 $\chi_\rr^2 = 2.2$ ), an absorbed double blackbody model fits the spectrum equally well as the absorbed power-law (Fig. \ref{xrf080109_bb_bb}) )." " The fitted parameters are: Na=4.7778x10? cm the temperature of the first blackbody component Τι?,=0.36*3'9, keV, and the temperature of the second blackbody component keV. The reduced chi-squares of the fit is 0.65, with 16 degrees of freedom."," The fitted parameters are: $N_\hh = 4.7_{-1.8}^{+2.6} \times 10^{21}$ $^{-2}$, the temperature of the first blackbody component $T_1 = 0.36_{-0.094}^{+0.12}$ keV, and the temperature of the second blackbody component $T_2 = 1.24_{-0.24}^{+0.52}$ keV. The reduced chi-squares of the fit is $\chi_\rr^2 = 0.65$ , with $16$ degrees of freedom." " With this double blackbody model, the unabsorbed total bolometric energy radiated by the burst is 7.31773x1045 erg, with 3.49*752x10*° erg in the lower temperature component, and 3.82*029x107 erg in the higher temperature component."," With this double blackbody model, the unabsorbed total bolometric energy radiated by the burst is $7.31_{-1.3}^{+2.4} \times 10^{45}$ erg, with $3.49_{-1.03}^{+2.31} \times 10^{45}$ erg in the lower temperature component, and $3.82_{-0.78}^{+0.80} \times 10^{45}$ erg in the higher temperature component." " I stress that the above result only indicates that a blackbody origin of the X-ray emission cannot be ruled out, and it does not prove that a blackbody component exists in the X-ray emission."," I stress that the above result only indicates that a blackbody origin of the X-ray emission cannot be ruled out, and it does not prove that a blackbody component exists in the X-ray emission." The X-ray spectrum of the 080109 transient can be fitted with a power law (Section 2))., The X-ray spectrum of the 080109 transient can be fitted with a power law (Section \ref{data}) ). No blackbody component is required., No blackbody component is required. A characteristic feature of SN shock breakout is a blackbody-like spectrum (Imshennik&Nadézhin1989; 1999).," A characteristic feature of SN shock breakout is a blackbody-like spectrum \citep{ims89,mat99}." ". Hence, the transient event 080109 is not likely to be a SN shock breakout event."," Hence, the transient event 080109 is not likely to be a SN shock breakout event." " However, as shown in Section 2,, the spectrum can be equally well fitted with a model consisting of two blackbody components (Fig. 1))"," However, as shown in Section \ref{data}, the spectrum can be equally well fitted with a model consisting of two blackbody components (Fig. \ref{xrf080109_bb_bb}) )." Now let us check if one of the two blackbody components might arise from the SN shock breakout event., Now let us check if one of the two blackbody components might arise from the SN shock breakout event. " From the duration of the event and the bolometric total energy of each blackbody, the average bolometric luminosity and hence the average photosphere radius of each component can be derived."," From the duration of the event and the bolometric total energy of each blackbody, the average bolometric luminosity and hence the average photosphere radius of each component can be derived." " For the softer component (Τι=0.36 keV), the radius is [Πρι70.074Ro."," For the softer component $T_1 = 0.36$ keV), the radius is $R_\ph \approx 0.074 R_\odot$." " For the harder component (Το=1.24 keV), the radius is Rpn©0.0062Re."," For the harder component $T_2 = 1.24$ keV), the radius is $R_\ph \approx 0.0062 R_\odot$." Both are much smaller than the solar radius., Both are much smaller than the solar radius. " The underlying SN of the event, SN 2008D, was initially classified as Type Ic and later reclassified as Type Ib (Modjazetal.2008;Valenti2008b)."," The underlying SN of the event, SN 2008D, was initially classified as Type Ic and later reclassified as Type Ib \citep{mod08,val08b}." ". This indicates that the progenitor star should be a Wolf-Rayet star, which usually has a radius of several solar radii."," This indicates that the progenitor star should be a Wolf-Rayet star, which usually has a radius of several solar radii." " SN shock breakout occurs at a radius near the stellar surface (Imshennik&Nadézhin1989;Matzner&McKee1999;Tanetal. 2001),, or the photospheric radius if the star is surrounded by an intense stellar wind (Li2007a)."," SN shock breakout occurs at a radius near the stellar surface \citep{ims89,mat99,tan01}, or the photospheric radius if the star is surrounded by an intense stellar wind \citep{li07}." ". Hence, the above results on the photospheric radius of the blackbody emission indicate that neither of the two blackbody components originates from the shock breakout event."," Hence, the above results on the photospheric radius of the blackbody emission indicate that neither of the two blackbody components originates from the shock breakout event." " From the derived photospheric radii, a limit on the expansion speed of the blackbody photosphere can be estimated."," From the derived photospheric radii, a limit on the expansion speed of the blackbody photosphere can be estimated." Assume that the average photospheric radius corresponds to a time of 100 s after the explosion., Assume that the average photospheric radius corresponds to a time of 100 s after the explosion. " Then, for the softer blackbody component, the photospheric speed UphS0.0017c (where c is the speed of light)."," Then, for the softer blackbody component, the photospheric speed $v_\ph \la 0.0017 c$ (where $c$ is the speed of light)." " For the harder blackbody component, the photospheric speed vpnS 0.00015c."," For the harder blackbody component, the photospheric speed $v_\ph \la 0.00015 c$ ." " These speeds are non-relativistic, contrary to the prediction that shock breakout from a compact Wolf-Rayet star is mildly relativistic (withashockbreakoutvelocityZ;0.3c,Tanetal.2001;Li 2007a).."," These speeds are non-relativistic, contrary to the prediction that shock breakout from a compact Wolf-Rayet star is mildly relativistic \citep[with a shock breakout velocity $\ga 0.3 c$,][]{tan01,li07}. ." " The duration of the X-ray transient 080109 is =600 s, which is also much longer than that predicted for shock breakout in SNe Ibc."," The duration of the X-ray transient 080109 is $\approx 600$ s, which is also much longer than that predicted for shock breakout in SNe Ibc." " Hence, we conclude that the X-ray transient 080109 is not a SN shock breakout event."," Hence, we conclude that the X-ray transient 080109 is not a SN shock breakout event." In Fig.,In Fig. " 10. we present a comparison between our VLA 330 MHz image and new CO ω-ι- data presented by ? on the basis of new observations carried out with the telescope of the Purple Mountain Observatory in China (main beam size of 50""«54"", velocity resolution of 0.37 km s'. and rms noise level of 0.1-0.3 K at a velocity resolution of «0.2 km s! )."," \ref{co-330} we present a comparison between our VLA 330 MHz image and new $^{12}$ CO $J$ =1-0) data presented by \citet{zha09} on the basis of new observations carried out with the telescope of the Purple Mountain Observatory in China (main beam size of $50^{\prime\prime} \times 54^{\prime\prime}$, velocity resolution of 0.37 km $^{-1}$, and rms noise level of 0.1-0.3 K at a velocity resolution of $\sim$ 0.2 km $^{-1}$ )." The contours superposed on the radio emission depict the CO emission integrated in the range between —10 and —1 km s'. which includes the systemic velocity of IC 443.," The contours superposed on the radio emission depict the CO emission integrated in the range between $-10$ and $-1$ km $^{-1}$, which includes the systemic velocity of IC 443." As described before. the molecular material is preferentially located in the center of the remnant extending in the southeast-northwest direction.," As described before, the molecular material is preferentially located in the center of the remnant extending in the southeast-northwest direction." " The spatial distribution of the molecular gas across IC 443 is clearly non-uniform,", The spatial distribution of the molecular gas across IC 443 is clearly non-uniform. Earlier observations have identified the presence of various clumps of molecular gas with broad line widths. as expected from the interaction with the supernova shock front (clumpslabeledfromAtoHinthenomenclatureof?)..," Earlier observations have identified the presence of various clumps of molecular gas with broad line widths, as expected from the interaction with the supernova shock front \citep[clumps labeled from A to H in the nomenclature of][]{dic92}." On the basis of the new image at 330 MHz it is possible to recognize details previously unnoticed in the spatial comparison between the radio emission and the molecular gas., On the basis of the new image at 330 MHz it is possible to recognize details previously unnoticed in the spatial comparison between the radio emission and the molecular gas. In Fig., In Fig. IO. we display the regions where good correlation between radio features and molecular gas distribution is observed., \ref{co-330} we display the regions where good correlation between radio features and molecular gas distribution is observed. Particularly noticeable is Fig., Particularly noticeable is Fig. 1Obb where it is apparent that the indentation of the eastern border i radio occurs near a region where a significant enhancement in the CO emission is detected., \ref{co-330}b b where it is apparent that the indentation of the eastern border in radio occurs near a region where a significant enhancement in the CO emission is detected. The molecular complex is transverse to the radio indentation with the maximum of the CO emission shifted to the southwest in at least 3’ from the border of the SNR (in the region of the molecular clump E)., The molecular complex is transverse to the radio indentation with the maximum of the CO emission shifted to the southwest in at least $3^{\prime}$ from the border of the SNR (in the region of the molecular clump E). It is possible that the singular indentation has formed as the result of the supernova shock front wrapping around a dense clump., It is possible that the singular indentation has formed as the result of the supernova shock front wrapping around a dense clump. Also. Fig.," Also, Fig." " [Occ shows the presence of a concentration in the CO emission around Κ.Α.-06|7""16. dec.2.+22°25'40"" (molecular clump B). that matches a local maximum in the radio emission."," \ref{co-330}c c shows the presence of a concentration in the CO emission around $= 06^{\mathrm{h}}\,17^{\mathrm{m}}\,16^{\mathrm{s}}$, $= +22^{\circ}\,25^{\prime}\,40^{\prime\prime}$ (molecular clump B), that matches a local maximum in the radio emission." " The morphological matehing between the radio synchrotron emission and the molecular gas is especially remarkable at the northern extreme of the southern ridge of IC 443 near R.A.=06""16""45°. dee.=+22°34’00"" (as shown in Fig."," The morphological matching between the radio synchrotron emission and the molecular gas is especially remarkable at the northern extreme of the southern ridge of IC 443 near $= 06^{\mathrm{h}}\,16^{\mathrm{m}}\,45^{\mathrm{s}}$, $= +22^{\circ}\,34^{\prime}\,00^{\prime\prime}$ (as shown in Fig." 1044). where the molecular contours. delineating high density gas in the region of the clump G.are observed enclosing the bright radio emission.," \ref{co-330}d d), where the molecular contours, delineating high density gas in the region of the clump G,are observed enclosing the bright radio emission." We also searched for spectral evidence of shock/cloud interaction., We also searched for spectral evidence of shock/cloud interaction. Figure I] displays an overlay of the 'CO (/=1-0) integrated emission contours with the radio spectral index distribution calculated between 74 and 330 MHz., Figure \ref{co-alpha} displays an overlay of the $^{12}$ CO $J$ =1-0) integrated emission contours with the radio spectral index distribution calculated between 74 and 330 MHz. The CO molecular gas seen in projection onto the plane of the sky. overlaps the only flat spectral region observed in the interior of IC 443.," The CO molecular gas seen in projection onto the plane of the sky, overlaps the only flat spectral region observed in the interior of IC 443." Various small components with a spectrum appreciably flatter than the surrounding synchrotron plasma are observed distributed nearby or in coincidence with local higher density gas as traced by the '*CO contours along the bright southern ridge and towards the northwest. suggesting that these features must be regions where strong shocks encountered denser material ?)..," Various small components with a spectrum appreciably flatter than the surrounding synchrotron plasma are observed distributed nearby or in coincidence with local higher density gas as traced by the $^{12}$ CO contours along the bright southern ridge and towards the northwest, suggesting that these features must be regions where strong shocks encountered denser material \citep[as discussed by][]{and93}. ." In the eastern periphery the situation is different., In the eastern periphery the situation is different. The very flat spectrum component, The very flat spectrum component The left panels of Fig.2 show the DETF FoM for (eg.a.) for a slitless. galaxy redshift survey with flux limit. of 10 Meres tom ta survey area of 20.000 square degrees. and redshift success rates ¢=0.35.0.5.0.7 respectively. as functions of redshift accuracy (for 0.5xz 2.1).,"The left panels of \ref{fig:FoM_w0wa_ENIS_planck_dlnz_zmin} show the DETF FoM for $(w_0,w_a)$ for a slitless galaxy redshift survey with flux limit of $\times 10^{-16}$ $\,$ $^{-1}$ $^{-1}$, a survey area of 20,000 square degrees, and redshift success rates $e=0.35, 0.5, 0.7$ respectively, as functions of redshift accuracy (for $0.5\leq z \leq 2.1$ )." Appendix Al gives the fitting formulae for the dependence of the FoM on the redshift accuracy for the various cases shown in the left panel of Fig.2.., Appendix \ref{sec:fitting_FoM_dlnz} gives the fitting formulae for the dependence of the FoM on the redshift accuracy for the various cases shown in the left panel of \ref{fig:FoM_w0wa_ENIS_planck_dlnz_zmin}. The FoM increases rapidly as σ. decreases fora. 0.001. but the rate of increase slows down beyond this limit (see lef panel of Fig.2}).," The FoM increases rapidly as $\sigma_z$ decreases for $\sigma_z/(1+z)\leq 0.001$ , but the rate of increase slows down beyond this limit (see left panel of \ref{fig:FoM_w0wa_ENIS_planck_dlnz_zmin}) )." There is a minimum redshift accuracy of o./(1|0.001 that is is important to achieve. but that further accuracy is not important if the cost is high.," There is a minimum redshift accuracy of $\sigma_z/(1+z)\simeq0.001$ that is is important to achieve, but that further accuracy is not important if the cost is high." We have assumed that3556...5066... and (corresponding to redshift success rates of ¢=0.35. 0.5. and 0.7) of objects have a correctly recovered redshift (with a redshift uncertainty 0./( 2). and that there is no contaminating fraction.," We have assumed that, and (corresponding to redshift success rates of $e$ =0.35, 0.5, and 0.7) of objects have a correctly recovered redshift (with a redshift uncertainty $\sigma_z/(1+z)$ ), and that there is no contaminating fraction." Performance simulations made for the EUCLID mission show that redshift uncertainties are randomly distributed., Performance simulations made for the EUCLID mission show that redshift uncertainties are randomly distributed. Given the objects” cross-contamination and the high baekground signal present in slitless observation. the redshift measurement is much more difficult with respect to the multi-slit case.," Given the objects' cross-contamination and the high background signal present in slitless observation, the redshift measurement is much more difficult with respect to the multi-slit case." To address this issue. a custom algorithm has been developed by Franzettietal.(2010)... which is strongly linked to the detection of the Ha line within the observational window.," To address this issue, a custom algorithm has been developed by \cite{Franzetti10}, which is strongly linked to the detection of the $\alpha$ line within the observational window." This algorithm selects high quality redshifts and makes line mis-identification very rare. and results in randomly distributed redshift failures (Pranzettietal.2010).," This algorithm selects high quality redshifts and makes line mis-identification very rare, and results in randomly distributed redshift failures \citep{Franzetti10}." As discussed in Section l.. one of the primary advantages of a space-based survey is the ability to measure redshifts out to 2—2.," As discussed in Section \ref{sec:intro}, one of the primary advantages of a space-based survey is the ability to measure redshifts out to $z\simeq2$." We therefore only consider changes to the minimum redshift limit of the sample., We therefore only consider changes to the minimum redshift limit of the sample. Although there will always be a tail to low redshift. we assume here that only redshifts greater than this minimum are used to constrain DE models.," Although there will always be a tail to low redshift, we assume here that only redshifts greater than this minimum are used to constrain DE models." " The right panels in Fig.2 show the FoM for (erg.00,) as a function of the minimum redshift of galaxies within the slitless survey assuming tic.=2.1."," The right panels in \ref{fig:FoM_w0wa_ENIS_planck_dlnz_zmin} show the FoM for $(w_0,w_a)$ as a function of the minimum redshift of galaxies within the slitless survey assuming $z_{max}=2.1$." The dashed and dot-dashed curves are with growth information included and marginalized over respectively., The dashed and dot-dashed curves are with growth information included and marginalized over respectively. " The solid and dotted curves are similar to the dashed and dot-dashed curves. but include BOSS data for 2<=z2,,;5."," The solid and dotted curves are similar to the dashed and dot-dashed curves, but include BOSS data for $z \leq z_{min}$." Appendix A2. gives the fitting formulae for the dependence of the FoM on the minimum redshift for the various cases shown in the right panel of Fig.2..," Appendix \ref{sec:fitting_FoM_zmin} gives the fitting formulae for the dependence of the FoM on the minimum redshift for the various cases shown in the right panel of \ref{fig:FoM_w0wa_ENIS_planck_dlnz_zmin}." The low redshift data have a strong effect on the DETF FoM. and the inclusion of BOSS becomes increasingly important as the minimum redshift of the slitless galaxy redshift survey is increased beyond 2=0.7. the maximum redshift covered by BOSS.," The low redshift data have a strong effect on the DETF FoM, and the inclusion of BOSS becomes increasingly important as the minimum redshift of the slitless galaxy redshift survey is increased beyond $z=0.7$, the maximum redshift covered by BOSS." It is clear that. purely based on the DETF FoM. it would be optimal to observe galaxies at lower redshifts.," It is clear that, purely based on the DETF FoM, it would be optimal to observe galaxies at lower redshifts." The bias of the DETF FoM to low redshifts has been discussed many previous times (e.g. Albrechtetal. 2009)). and ignores the power of a space-based survey. as discussed in Section |..," The bias of the DETF FoM to low redshifts has been discussed many previous times (e.g. \citealt{Albrecht09}) ), and ignores the power of a space-based survey, as discussed in Section \ref{sec:intro}." This is a situation where it is obviously important to consider practical and instrumental issues. aswell as a comparison with what can be achieved from the ground.," This is a situation where it is obviously important to consider practical and instrumental issues, aswell as a comparison with what can be achieved from the ground." The redshift range of the survey of galaxies selected using a given method is usually fixed and derived from instrumentation., The redshift range of the survey of galaxies selected using a given method is usually fixed and derived from instrumentation. For example. for Ha flux selected galaxies observed from space. a wavelength range between | and 2 jm driven by technical considerations. naturally imposes a redshift range 0.52«&z«2.05 in which Ha will be visible (Laureijsetal.2009).," For example, for $\alpha$ flux selected galaxies observed from space, a wavelength range between 1 and 2 $\mu$ m driven by technical considerations, naturally imposes a redshift range $0.521 by choosing f,=2. with very low chance of ο)<1.","Therefore the Universe has tendency to be parity asymmetric $g(l)>1$ by choosing $l'_{\rm min}=2$, with very low chance of $g(l)<1$." However. the WMAP? data show that C(82x)<0 ad 95% CLL. and our Universe belongs to the very rare realizations of the ACDAM cosmological models with given by the WMAP? cosmological parameters.," However, the WMAP7 data show that ${C(\theta=\pi)}<0$ at $95\%$ C.L., and our Universe belongs to the very rare realizations of the $\Lambda$ CDM cosmological models with given by the WMAP7 cosmological parameters." If (he parity violation has the cosmological origin. we should also see the similar parity violation in TE. EE and BB components of the polarized signal.," If the parity violation has the cosmological origin, we should also see the similar parity violation in TE, EE and BB components of the polarized signal." ILowever. in (he curret WAIAP data. the noises of the polarization data. including the TE eross-correlation data are quite large.," However, in the curret WMAP data, the noises of the polarization data, including the TE cross-correlation data are quite large." So we cannot get anv solid results on the parity asvimimetry by using the WAIAP polarization data. when taking into account the large error bars.," So we cannot get any solid results on the parity asymmetry by using the WMAP polarization data, when taking into account the large error bars." Ht 15 expected that the forthcoming Planck data would provide the much better chance to study the parity asvmmnmetire in the polarization data. and be helpful to reveal of the origin of the parity violation.," It is expected that the forthcoming Planck data would provide the much better chance to study the parity asymmetry in the polarization data, and be helpful to reveal of the origin of the parity violation." As shown in the previous section. for the random Gaussian statistically isotropic and homogeneous perturbations of the CMDB. the correlation function C'(Q) is filly determined bv the power spectrum C'(/). which is rotationally invariant.," As shown in the previous section, for the random Gaussian statistically isotropic and homogeneous perturbations of the CMB, the correlation function $C(\Theta)$ is fully determined by the power spectrum $C(l)$, which is rotationally invariant." Statistical invariance means that for any. rotations of the relerence system of coordinate. (he power spectrum ancl the correlation ΠΙΟΙον are invariant.," Statistical invariance means that for any rotations of the reference system of coordinate, the power spectrum and the correlation function are invariant." The idea of the method. proposed in (his section. is {ο replace (he power spectrum C(/) in Eq. (3))," The idea of the method, proposed in this section, is to replace the power spectrum $C(l)$ in Eq. \ref{corf}) )" " by a rotationally variant power spectrum D(/), defined as where""I 9,5"" is the Kroneker svimbol."," by a rotationally variant power spectrum $D(l)$, defined as where $\delta_{mm'}$ is the Kroneker symbol." As it isseen from the definition given bv Eq. (7)).," As it isseen from the definition given by Eq. \ref{dpow}) )," the relative difference between D(/) | DUO TalCU)2jey2imS0σιwehave. AV)uu , the relative difference between $D(l)$ and $C(l)$ is given by $\Delta (l)\equiv \frac{D(l)-C(l)}{C(l)}=-a^2_{l0}/\sum_m|a_{lm}|^2$ . ον↓ O(s;)≀↧↴∐≺∏⋝∣∣⋝↕⊳∖↖↳↴↕∖≼↲∐∣≻⋡∖∆⋖⋝∣∣⋟≓ forcyrandom2 = Gaussian CAIB field., So we have $\Delta(l)\sim O(\frac{1}{2l})$ for random Gaussian CMB field. Thus. the major difference A(/) comes from /=2 and /=3 modes. while for />5 their contributions are smaller than 1054.," Thus, the major difference $\Delta(l)$ comes from $l=2$ and $l=3$ modes, while for $l\ge 5$ their contributions are smaller than $10\%$." Now. we can study. (he power spectvum D(/) in anv coordinate svstem.," Now, we can study the power spectrum $D(l)$ in any coordinate system." . Imagining the Galactic coordinate svstem is rotated bv (the Euler angle (6.8.6). and the coefficients etyQo.8.0) in thisnew coordinate svstem can be ealeulated by," Imagining the Galactic coordinate system is rotated by the Euler angle $(\psi, \theta, \phi)$ , and the coefficients $a_{lm}(\psi,\theta,\phi)$ in thisnew coordinate system can be calculated by" molecules in cold ISAL and because its excitation in astroplivsical conditious is determined by collisious with hydrogen molecules.,molecules in cold ISM and because its excitation in astrophysical conditions is determined by collisions with hydrogen molecules. Using the CO LF derived above. we can for the first time cstimate the total mass density of molecular gas in the local volume.," Using the CO LF derived above, we can for the first time estimate the total mass density of molecular gas in the local volume." Adopting (Hs)πα93100 2? [hv ans. 1|. 1 byYoung&Scoville 1991).. where Seq is total CO flux of a galaxy in Jy kn + aud D is hquuinositv distance in Mpc.," Adopting $N(H_2)/I(CO)=3 \times 10^{20}$ $^{-2}$ [K km $^{-1}$ $^{-1}$ \citep[see review by][]{ysc91}, where $S_{CO}$ is total CO flux of a galaxy in Jy km $^{-1}$ and $D$ is luminosity distance in Mpc." The inoleculu inass density in the local volume contributed by cach huninosity biu is shown im Fieure 7.., The molecular mass density in the local volume contributed by each luminosity bin is shown in Figure \ref{fig:h2mass}. " The donuuaut coutribution to the mass ceusity comes frou, galaxiesaround L as expected.", The dominant contribution to the mass density comes from galaxiesaround $L^*$ as expected. " The sununatio- over the 10 bins gives py,=Ala.τη(2.1x0.7)«10AZ... 7.", The summation over the 10 bins gives $\rho_{H_2}=\sum M_{H_2}/V_m=(2.4 \pm 0.7) \times 10^7 M_{\odot}$ $^{-3}$. " Integration Soof the LF using the Schechter parameters obtained im previous section gives a little bit smaller values: py,=(2.2+L1)«10*A. 7 for the fit trough all 10 bius; aud py,=(2.2+«LOCAL. 7? for fit trough. first 8 bins."," Integration of the LF using the Schechter parameters obtained in previous section gives a little bit smaller values: $\rho_{H_2}=(2.2 \pm 1.1) \times 10^7 M_{\odot}$ $^{-3}$ for the fit trough all 10 bins, and $\rho_{H_2}=(2.2 \pm 0.9) \times 10^7 M_{\odot}$ $^{-3}$ for fit trough first 8 bins." The second fit is more realistic. since itfits mach better bins that dominate coutribution to the total mass. ie. bius around L.," The second fit is more realistic, since itfits much better bins that dominate contribution to the total mass, i.e. bins around $L^*$." The uncertainty stated is clo., The uncertainty stated is $\pm 1\sigma$. " The systematic uncertainty. which includes uncertainties i the flux measurements, distance determinations. and to-IT» couversion. ix probably larger."," The systematic uncertainty, which includes uncertainties in the flux measurements, distance determinations, and $_2$ conversion, is probably larger." " Uuless otherwise is stated. we adopt py,=(2.3d:0.9)«10 ApeP as an average value between values obtained AZ...from the fit and the direct sunuuation."," Unless otherwise is stated, we adopt $\rho_{H_2}=(2.3 \pm 0.9) \times 10^7 M_{\odot}$ $^{-3}$ as an average value between values obtained from the fit and the direct summation." " Since the dependence of the eas nass deusitv onu the IIubble constant (=Ly/100 [kins + Mpe.3]. 3) ds linear. this result ciui be written as Pils=012)ον10ΛΙ, 7."," Since the dependence of the gas mass density on the Hubble constant $h\equiv H_0/{100}$ [km $^{-1}$ $^{-1}$ $^{-1}$ ) is linear, this result can be written as $\rho_{H_2}=(3.1 \pm 1.2)\times 10^7 h M_{\odot}$ $^{-3}$." " The moleculu lyvdrogcu mass deusitv iu the local volume obtained from the B-baud selected saniple is py,= ? using a direct stummation of the contribution of each ealaxy and (3.121.5)«10*5M, ? using thebest fit Schecliter parameters."," The molecular hydrogen mass density in the local volume obtained from the $B$ -band selected sample is $\rho_{H_2}=(3.1\pm 0.9) \times 10^7h M_{\odot}$ $^{-3}$ using a direct summation of the contribution of each galaxy and $(3.1 \pm 1.5) \times 10^7h M_{\odot}$ $^{-3}$ using the best fit Schechter parameters." Values for the local molecular nass deusitv obtaimed from the FIR. selected sample and the B-baud selected sample are in good agreenieunt., Values for the local molecular mass density obtained from the FIR selected sample and the $B$ -band selected sample are in good agreement. Since we lave better statistics for the larger FIR selected sample. we adopt the local molecular gas mass density derived from the FIR selected sample here on.," Since we have better statistics for the larger FIR selected sample, we adopt the local molecular gas mass density derived from the FIR selected sample here on." Using observed Πο ΠΗmass ratio for different morphological types of galaxies aud fraction of cach morphological type Fukugitaetal.(1998). estimated a sinilar value for pg»., Using observed $_2$ /HImass ratio for different morphological types of galaxies and fraction of each morphological type \citet{fuk98} estimated a similar value for $\rho_{H2}$. " Iu comparison. Zwaanctal.(1997). estimated the local atomic gas mass density of pyy=(5.8+1.2)«105A, ? from their Arecibo III strip survey while Rao&Briges(1993) derived pj;=(L8—11)<10HAL.. P? from) a sample ofoptically selected galaxies."," In comparison, \citet{zwa97} estimated the local atomic gas mass density of $\rho_{HI}=(5.8 \pm 1.2)\times 10^7 h M_{\odot}$ $^{-3}$ from their Arecibo HI strip survey while \citet{rab93} derived $\rho_{HI}=(4.8 \pm 1.1) \times 10^7 h M_{\odot}$ $^{-3}$ from a sample ofoptically selected galaxies." Therefore. the molecular eax nass density in the local volume is about of the atomic mass density. ancl molecular eas represents a significant component of the total mass density of the neutral gas.," Therefore, the molecular gas mass density in the local volume is about of the atomic mass density, and molecular gas represents a significant component of the total mass density of the neutral gas." The IIT masses for 176 galaxics iu our sample are known (Youngetal. 1995).. aud we have computed the ITE mass density in the local volume using the same procedure as for the Z75 mass deusitv.," The HI masses for 176 galaxies in our sample are known \citep{yng95}, , and we have computed the HI mass density in the local volume using the same procedure as for the $H_2$ mass density." " A μπαΊο over the ITE mass weightedby V, gives a value consistent with the value obtainby Zwaanetal.(1997).", A summation over the HI mass weighted by $V_m$ gives a value consistent with the value obtain by \citet{zwa97}. ". We exauued our suuple for auv trends in Mp,/Mj ratio vs. Mg, and Afy,.", We examined our sample for any trends in $M_{H_2}/M_{HI}$ ratio vs. $M_{HI}$ and $M_{H_2}$. " For the range of ID πάγκο», NS1). on the other hand. thwarts the growth of instabilities.," Decollimation $\alpha>1$ ), on the other hand, thwarts the growth of instabilities." A conical jet (@=1) constitutes a limiting case where all depends on the combination of parameters 2/(vsin2). which is of order unity.," A conical jet $\alpha = 1$ ) constitutes a limiting case where all depends on the combination of parameters $\varkappa/(\upsilon\, \sin \vartheta')$, which is of order unity." A numerical simulation is necessary to find out whether the instability or expansion prevails., A numerical simulation is necessary to find out whether the instability or expansion prevails. The paper is organized as follows., The paper is organized as follows. In Sect. 2..," In Sect. \ref{sec:model}," we introduce the magnetocentrifugal jet model and aecount for the assumptions made in our simulations., we introduce the magnetocentrifugal jet model and account for the assumptions made in our simulations. A detailed description of the numerical setup. the coordinate system and the scale-free units employed in the analysis is given in Sect. 3..," A detailed description of the numerical setup, the coordinate system and the scale-free units employed in the analysis is given in Sect. \ref{sec:methods}." In Sect., In Sect. 4 we give the parameters of the simulated cases and in Sect., \ref{sec:simulatedcases} we give the parameters of the simulated cases and in Sect. 5 we present the results., \ref{sec:results} we present the results. There. we start by making predictions on the characteristies of instabilities by examining the relevant properties of our simulated jets.," There, we start by making predictions on the characteristics of instabilities by examining the relevant properties of our simulated jets." " We proceed with an analysis of the instabilities that actually appeared and complete with looking for effects on the jets"" dynamics.", We proceed with an analysis of the instabilities that actually appeared and complete with looking for effects on the jets' dynamics. We finish with a discussion and conclusions in Sect. 6.., We finish with a discussion and conclusions in Sect. \ref{sec:discussion}. The model is construed to apply to jets produced by ordered magnetic fields anchored in an accretion disk., The model is construed to apply to jets produced by ordered magnetic fields anchored in an accretion disk. This has become the default interpretation for the jets observed in AGN. microquasars and protostellar objects. though it must be kept in mind that observational evidence of the key ingredient in. this model. the ordered field (??).. is still somewhat indirect.," This has become the default interpretation for the jets observed in AGN, microquasars and protostellar objects, though it must be kept in mind that observational evidence of the key ingredient in this model, the ordered field \citep{1976Bisnovatyi,1982Blandford}, is still somewhat indirect." More uncertain is the shape of this field., More uncertain is the shape of this field. The strength of the field anchored in the disk ts likely to scale in some way with the orbital kinetic energy (or gas pressure) in the disk. hence will decline with distance R from the rotation axis.," The strength of the field anchored in the disk is likely to scale in some way with the orbital kinetic energy (or gas pressure) in the disk, hence will decline with distance $R$ from the rotation axis." In the absence of more detailed information. we consider a simple form for a field of this kind. one in which the vertical (normal to the disk) component at the surface B. varies as BAR)x[1+(R/z0)7|.," In the absence of more detailed information, we consider a simple form for a field of this kind, one in which the vertical (normal to the disk) component at the surface $B_z$ varies as $B_z(R) \propto [1+(R/z_0)^2]^{-\nu}$." Neglecting gas pressure and fluid motions. the field above the disk would be a potential field. its shape defined uniquely by B..," Neglecting gas pressure and fluid motions, the field above the disk would be a potential field, its shape defined uniquely by $B_z$." For v=3/2 it is the field of a monopole with the source at a depth zo below the center of the disk., For $\nu=3/2$ it is the field of a monopole with the source at a depth $z_0$ below the center of the disk. The initial state of the model is a gas distribution in hydrostatic equilibrium in a field of this monopolar shape., The initial state of the model is a gas distribution in hydrostatic equilibrium in a field of this monopolar shape. Rotation is applied at the lower boundary. in a region R< (see Sect.," Rotation is applied at the lower boundary, in a region $R$ 2 s, are typically associated with the core-collapse of rapidly-rotating massive stars (Woosley 1993)." " These events are conunonly acconipauied by multinwavelcneth afterglows and broad-lined Type Ic supernovae (οιο, Calama et 11998. Stanek et 22003. Woosley Bloom 2006)."," These events are commonly accompanied by multi-wavelength afterglows and broad-lined Type Ic supernovae (e.g. Galama et 1998, Stanek et 2003, Woosley Bloom 2006)." Several recent studies lave presented evidence that LORBs may occur preferentially in low-inetallicitv enviroments. a conclusion supported by both inferred (e.g. Fruchter et 11999. 2006: Pxubo et 22003: Le Floch et 22003). aud directly ucasured imoetallicities (0.8. Stanek et 22006. Modjaz ( 22008. IXocevslà et 22009).," Several recent studies have presented evidence that LGRBs may occur preferentially in low-metallicity environments, a conclusion supported by both inferred (e.g. Fruchter et 1999, 2006; Fynbo et 2003; Le Floc'h et 2003), and directly measured metallicities (e.g. Stanek et 2006, Modjaz et 2008, Kocevski et 2009)." Most recently. in Levesque et ((2010a) we published ιο first results from a spectroscopic survey of LORD rost galaxies. calculating ietallicitics and other ISM xoperties for 10 LGRD hosts.," Most recently, in Levesque et (2010a) we published the first results from a spectroscopic survey of LGRB host galaxies, calculating metallicities and other ISM properties for 10 LGRB hosts." A statistical comparison of iis suuple to the ecucral star-forming ealaxy population xeseuts evidence that the ISAL properties of these 10 LORB host galaxies are offset from the seucral »pulatiou. aud have low-inetalliitv. cuviroumenuts out Oo i:~1l.," A statistical comparison of this sample to the general star-forming galaxy population presents evidence that the ISM properties of these 10 LGRB host galaxies are offset from the general population, and have low-metallicity environments out to $z \sim 1$." " This ldlowanetalliitv trend. agrees with xedietiouns of stellar evolutionary theory (assmuine a suele-star progenitor model). which postulate that the rapid rotation required to produce a GRB σας ow line-driven mass loss rates in the progenitor (e.g. Woosley ITeeer 2006). following the amass loss-uctallicity relation of AL,XZ!"" (Vink et 22001)."," This low-metallicity trend agrees with predictions of stellar evolutionary theory (assuming a single-star progenitor model), which postulate that the rapid rotation required to produce a GRB demands low line-driven mass loss rates in the progenitor (e.g. Woosley Heger 2006), following the mass loss-metallicity relation of $\dot M_w \propto Z^{0.7}$ (Vink et 2001)." However. our understaudiug of GRB host cuvirouments and progenitors is still evolving. aud ast strive to accommodate the mereasing nuniber of unusual bursts that are detected and observed. as well as potential selection effects introduced by host galaxy. huninosities and optical afterglows (c.g. Wolf Podsiadlowski 2007. Έντο et 22009).," However, our understanding of GRB host environments and progenitors is still evolving, and must strive to accommodate the increasing number of unusual bursts that are detected and observed, as well as potential selection effects introduced by host galaxy luminosities and optical afterglows (e.g. Wolf Podsiadlowski 2007, Fynbo et 2009)." CRB was originally detected bv the Tiel Encrev Trausieut Explorer (IETE). and found to have the euergetie properties of a typical long burst. with a duration of {ου~20s aud a peak brightucss of 5 crab (IDulev et 22002. Vanderspek et 22002).," GRB was originally detected by the High Energy Transient Explorer (HETE), and found to have the energetic properties of a typical long burst, with a duration of $T_{90} \sim 20$ s and a peak brightness of $\sim$ 5 crab (Hurley et 2002, Vanderspek et 2002)." " However. follow-up observations of the burst detected no optical afterelow to a limiting maenitucde of R=22.2 aud 19 at only 9 hours after the burst: this lack of an optical afterglow detection classifics GRB 020819 as a ""dark πανί (Levan et al."," However, follow-up observations of the burst detected no optical afterglow to a limiting magnitude of $R = 22.2$ and $K' = 19$ at only 9 hours after the burst; this lack of an optical afterglow detection classifies GRB 020819 as a “dark"" burst (Levan et al." 2002. EKKlose et 22003).," 2002, Klose et 2003)." Frail Berger (2002) detected a radio afterglow associated with he burst. and Levan et al. (," Frail Berger (2002) detected a radio afterglow associated with the burst, and Levan et al. (" 2002) find this position to )e coincident with a clearly resolved galaxy at R~19.8.,2002) find this position to be coincident with a clearly resolved galaxy at $R \sim 19.8$. Jakobsson et ((2005) later coufirmed that this galaxy. at a redshift of 2=0.11. was the likely host of CRB POSLO. with a chance superposition probability of.," Jakobsson et (2005) later confirmed that this galaxy, at a redshift of $z = 0.41$, was the likely host of GRB 020819, with a chance superposition probability of." ". The radio afterglow is specifically located on a faint Rx 2[ ""blob of cussion. ~3° from the bright barred spiral host aud assumed to be at the same redshift (Jakobssou et 22005)."," The radio afterglow is specifically located on a faint R $\approx$ 24 “blob"" of emission, $\sim$ 3"" from the bright barred spiral host and assumed to be at the same redshift (Jakobsson et 2005)." lose et ((2003) speculate that the dark nature of GRD 020819 could be due to large amounts of dust extinction in the host., Klose et (2003) speculate that the dark nature of GRB 020819 could be due to large amounts of dust extinction in the host. Uuder this hypothesis. the optical afterglow could have been extineted past the Bits of detection bv a high host Ay.," Under this hypothesis, the optical afterglow could have been extincted past the limits of detection by a high host $A_V$." Jakobssou et ((2005) considered this possibility iu the context of the host redshift., Jakobsson et (2005) considered this possibility in the context of the host redshift. Using fits to the radio elt curve to predict maxima optical fluxes for a variety of afterglow models. they find that a modest amount of extinction - ly~ 0.6-1.5 mae - is required to extinguishi an optical afterglow with a classical bhuuinositv.," Using fits to the radio light curve to predict maximum optical fluxes for a variety of afterglow models, they find that a modest amount of extinction - $A_V \sim$ 0.6-1.5 mag - is required to extinguish an optical afterglow with a classical luminosity." " However. it is also possible that the optical afterglow of GRB 020819 is uudoetected due to intrinsically low hunuiuosity. a scenario proposed for other dark bursts (e.e.. Fever et 11999. De Pasquale et 22003, Jakobsson et 22001. Rol ct 22005)."," However, it is also possible that the optical afterglow of GRB 020819 is undetected due to intrinsically low luminosity, a scenario proposed for other dark bursts (e.g., Fryer et 1999, De Pasquale et 2003, Jakobsson et 2004, Rol et 2005)." Levesque et ((2010a) include the host ealaxy of GRD 051022. another dark burst. i their sample. aud find a metallicity of los(O/II) | 12 = 8.62 according to," Levesque et (2010a) include the host galaxy of GRB 051022, another dark burst, in their sample, and find a metallicity of log(O/H) + 12 = 8.62 according to" "work in the frame of the black hole and the torque on the black hole is is given by where Ay, and Boy are the inner and outer edge of the dise and Cs=(Mt“Moy ds a constant.",work in the frame of the black hole and the torque on the black hole is is given by where $R_{\rm in}$ and $R_{\rm out}$ are the inner and outer edge of the disc and $C_2 = (GM)^{1/2} \Sigma_0 R_{0}^\beta$ is a constant. Acting the Á-component to times the y-component we obtain and. using equation (16)) to substitute for V wefind where the constant £2 is defined by equation (19))., Adding the $x$ -component to $i$ times the $y$ -component we obtain and using equation \ref{W1}) ) to substitute for $W$ wefind where the constant $B$ is defined by equation \ref{B}) ). " We simplify the expression by taking dimensions out of the integral to obtain where so that zi,=20a) and za= zu).", We simplify the expression by taking dimensions out of the integral to obtain where so that $z_{\rm in}=z(R_{\rm in})$ and $z_{\rm out}=z(R_{\rm out})$ . In Appendix 1 we show that Waited)« land (e|d)— 1., In Appendix 1 we show that if $\Re(c-d)<1$ and $\Re(c+d)>-1$. 80 with e=1/((1| and d=(1|λος:2)) this integral is valid for971/2.," So with $c=1/(2(1+\beta))$ and $d=(1+2\beta)/(2(1+\beta))$ this integral is valid for$\beta >-1/2$." We now have In Section 3. we found that We=(fe|ayy)., We now have and using equation \ref{B}) ) to eliminate $B$ we get In Section \ref{sec:inc} we found that $W_\infty=-(j_x+ij_y)$. " We define so that Using equation (2)) we get and equation (11)) for & we ect Then using equations (2)) and (3)) we find We can rewrite equation (49)) as by setting We can then integrate to find where;d is the value of j,|ff, at f=0.", We define so that Using equation \ref{omegap}) ) we get and equation \ref{kappa}) ) for $\kappa$ we get Then using equations \ref{omegap}) ) and \ref{angmom}) ) we find We can rewrite equation \ref{full}) )as by setting We can then integrate to find where$A$ is the value of $j_x+ij_y$ at $t=0$. " In Figure 4 we plot the evolution of j, against ὃν with jd2 1soj,—1 and j,-—0 at / =O.", In Figure \ref{hole} we plot the evolution of $j_y$ against $j_x$ with $A=1$ so $j_x=1$ and $j_y=0$ at $t=0$ . The points along the lines are at times |— 1.2. 3 and 4T.," The points along the lines are at times $t=1$ , $2$ , $3$ and $4 \,\rm T$ ." Thus the timescale for alignment of the black holeis, Thus the timescale for alignment of the black holeis starburst (Alexander οἱ 22005).,starburst (Alexander et 2005). With this study we have increased (he number of submm-selected galaxies with observations from 1 to 3. allhoueh the upper limit on the WON luminosity of one of our sources (J16359) is nol a very sensilive one.," With this study we have increased the number of submm-selected galaxies with $(1-0)$ observations from 1 to 3, although the upper limit on the HCN luminosity of one of our sources (J16359) is not a very sensitive one." The upper limits on the IICN(1—0) line luminosity of these three SMGs are consistent with the Lj—L/HCOCN relation observed in the local Universe (Gao Solomon 2004a.b).," The upper limits on the $(1-0)$ line luminosity of these three SMGs are consistent with the $L_{\mbox{\tiny{FIR}}}-L'_{\mbox{\tiny{HCN}}}$ relation observed in the local Universe (Gao Solomon 2004a,b)." " In order (ο test whether a tvpical SMG with a FIR-Iuminositv of Ly,~LOOL. is inconsistent with the local relation. we need to be sensitive to IICN. huninosities of Lo...HCOCN<10! !ppc?."," In order to test whether a typical SMG with a FIR-luminosity of $L_{\mbox{\tiny{FIR}}}\sim 10^{12.5}\,\Lsolar$ is inconsistent with the local relation, we need to be sensitive to HCN luminosities of $L'_{\mbox{\tiny{HCN}}} \ls 10^{10}\,$ $^{-1}$ $^2$." Thus. we appear to be close (less than a [actor of two) in sensitivity to that needed [rom Figure 2. in order to detect ]1ICN in SAIGs.," Thus, we appear to be close (less than a factor of two) in sensitivity to that needed from Figure \ref{figure:lhcn-lfir} in order to detect HCN in SMGs." We conclude that until deeper observations come along there is no evidence lo suggest5 that SAIGs have higher5 star formation elliciencies per unit dense 5gas mass than local [(U)LIBRGs or indeed Galactic GAICS (Wu et 22005)., We conclude that until deeper observations come along there is no evidence to suggest that SMGs have higher star formation efficiencies per unit dense gas mass than local (U)LIRGs or indeed Galactic GMCs (Wu et 2005). We thank (he referee for useful comments which helped improve the paper substantially., We thank the referee for useful comments which helped improve the paper substantially. We are grateful to NRAO [or financial and scientific support. and in particular to the telescope operators al Green Dank for their expertise.," We are grateful to NRAO for financial and scientific support, and in particular to the telescope operators at Green Bank for their expertise." We thank Ron Maddalena and Toney Alinter for their help in reducing the data aud [ον providing the opacity values used., We thank Ron Maddalena and Toney Minter for their help in reducing the data and for providing the opacity values used. LJII was supported by the GBT graduate student funding program., LJH was supported by the GBT graduate student funding program. AWB acknowledges support from the Alfred SSloan Foundation and the Research Corporation., AWB acknowledges support from the Alfred Sloan Foundation and the Research Corporation. IRS acknowledges support from the Roval Society., IRS acknowledges support from the Royal Society. reduction pipeline procedures at STSclI. The images were combined using the IRAF/STSDAS routine CRREJ whieh removes cosmic ravs in the combined image.,reduction pipeline procedures at STScI. The images were combined using the IRAF/STSDAS routine CRREJ which removes cosmic rays in the combined image. The calculated. errors on the photometric points. including both the photon noise and calibration uncertainity. are 47-10 per cent.," The calculated errors on the photometric points, including both the photon noise and calibration uncertainity, are $\pm$ 7-10 per cent." Four ACS images of PIXS1345--12 are used in this paper., Four ACS images of PKS1345+12 are used in this paper. " The Wide Field Channel (WFC: 0.049 arcseonds 1) was used in combination with FR647M medium band ramp filter to (ake two of the images. one centred on the redshifted Πα emission line wavelength5 (hereafter Ilo image).5C, and the other centred on the nearby continuum (hereafter Πα continuum image)."," The Wide Field Channel (WFC: $0.049$ arcseonds $^{-1}$ ) was used in combination with FR647M medium band ramp filter to take two of the images, one centred on the redshifted $\alpha$ emission line wavelength (hereafter $\alpha$ image), and the other centred on the nearby continuum (hereafter $\alpha$ continuum image)." "SC The Hiehe Resolution Channel (IIRC: 0.027 areseconds pixel1) was used in combination with F550M medium band filler (Ay=5579 Marius,=547 .)) and ERA59M medium band ramp filter to take the other images.", The High Resolution Channel (HRC: $0.027$ arcseconds $^{-1}$ ) was used in combination with F550M medium band filter $\lambda_{0}=5579$ $\Delta\lambda_{FWHM}=547$ ) and FR459M medium band ramp filter to take the other images. In the former. the aim was (o take an image of the galaxy at the wavelength of the n]|A5007. emission line (hereafter image). whereas in the other images the pivot wavelength was chosen (o take an image of the continuum near the ut}]/A5007 line ( hereafter continuum image).," In the former, the aim was to take an image of the galaxy at the wavelength of the $\lambda5007$ emission line (hereafter image), whereas in the other images the pivot wavelength was chosen to take an image of the continuum near the $\lambda5007$ line ( hereafter continuum image)." The FR647M(ÀA.=6615 A)) image is shown in Figure 1., The $\lambda_c=6615$ ) image is shown in Figure 1. The data were reduced following the standard data reduction. pipeline procedures al ST5cl which employ two packages: CALACS package. which performs dark substaction. bias substraction and [Lat field corrections producing calibrated images. aud MULTIDRIZZLE package which corrects for distortion and performs cosmic ravs rejections.," The data were reduced following the standard data reduction pipeline procedures at STScI which employ two packages: CALACS package, which performs dark substaction, bias substraction and flat field corrections producing calibrated images, and MULTIDRIZZLE package which corrects for distortion and performs cosmic rays rejections." Since two of the ACS images were set ttp to measure (the Ila and 11]]A5007. emission lines. they. were not suitable to be used. for modelling the continuum. and only the FR647M (Ay=6615 .)) and FIRA59M images were used for that purpose.," Since two of the ACS images were set up to measure the $\alpha$ and $\lambda5007$ emission lines, they were not suitable to be used for modelling the continuum, and only the FR647M $\lambda_{0}=6615$ ) and FR459M images were used for that purpose." The calculated errors of the photometric points including both the photon noise and calibration uncertanty are £5-7 per cent., The calculated errors of the photometric points including both the photon noise and calibration uncertanty are $\pm$ 5-7 per cent. For the FOC. ΑΕΡΟΣ and ACS data. the routine PHOT in IRAF was used measure skv-sublracted f[Iuxes for the clusters within cireular apertures (vpically 3-10 pixels in radius. correcting Lor aperture losses using a svnthetic PSFs generated wilh the TINYTIM program.," For the FOC, WFPC2 and ACS data, the routine PHOT in IRAF was used measure sky-subtracted fluxes for the clusters within circular apertures typically 3-10 pixels in radius, correcting for aperture losses using a synthetic PSFs generated with the TINYTIM program." The measured fIuxes are summarised in Table 2., The measured fluxes are summarised in Table 2. The observations aud reduction of the NICMOS data aredescribed in ?.., The observations and reduction of the NICMOS data aredescribed in \cite{Scoville00}. The images were (aken using camera 2 of NICMOS. having a spatial resolution of 0.0762 and 0.0755 arcseconds + in x and v respectively (2)..," The images were taken using camera 2 of NICMOS, having a spatial resolution of $0.0762$ and $0.0755$ arcseconds $^{-1}$ in x and y respectively \citep{Thompson98}. ." The FLLOW(1.10 pan. ANApig00.6 jun).," The F110W(1.10 $\mu$ m, $\Delta\lambda_{FWHM} \sim 0.6$ $\mu$ m)," values of 5.,values of $\beta > -1.5$. This mav be useful for those plauuiug further stacking analyses as the CDE-N survey is extended »2\Is.Acknowledgments. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Tustitute of Techuologv. uncer contract with the National Acronautics and Space Aciuinistration.," This may be useful for those planning further stacking analyses as the CDF-N survey is extended to 2 Ms. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration." This work is supported bv the NASA ADP program uuder the erauts NACH5-8279 aud NACH5-600., This work is supported by the NASA ADP program under the grants NAG5-8279 and NAG5-6400. "the Alfred P. Sloan Foundation. then Participating Tustitutions. the National Science Foundation. the US Doepartineut of Enucrev, NASA. the Japanese Alounbukasakusho. the Max Planck Society. iux the Higher Education Fuudiug Council of Euglaud.","the Alfred P. Sloan Foundation, then Participating Institutions, the National Science Foundation, the US Department of Energy, NASA, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council of England." The SDSS is managed by the Astroplysica Research Consortium for the Participating Institutions (sce list at http://www.sdss.oreg/collaboration/credits.litial)., The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions (see list at http://www.sdss.org/collaboration/credits.html). This publication makes use of data from the Two Microu All Sky Survey. which is a joint project of the University of Massachusetts aud the Tutrarce Processing and Analysis Ceuter/California Tistitute of Technology. funded by NASA aud the Nationa Science Foundation.," This publication makes use of data from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by NASA and the National Science Foundation." The NASA Extragalactic Database (NED) is operated by the Jet Propulsion Laboratory. California Tustitute of Techuoloey. uuder contract with the National Aeronautics and Space Acuninistration.," The NASA Extragalactic Database (NED) is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration." backgrouund,und " ~200 1% R.. At~R./2T7e. D =MeV TPo>100 Af 8.~101710""em "," $\sim20\%$ $\sim200$ $0.1 \%$ $\%$ $E_{\rm iso}\simeq5\times10^{51}{\rm erg}$ $R_\gamma$ $\Delta{t}\simeq R_\gamma/2\Gamma^2 c$ $\Gamma$ $\ga{\rm MeV}$ $\Gamma \ga 100$ $\Delta t$ $R_\gamma\sim10^{12}-10^{14}{\rm cm}$ " latitude. i.e.. /(6)=1 instead of Eq.(6)). the general patterns of Fig.2. are hold except that ihe maximum of the toroidal magnetic field is shifted to higher latitude z40°.,"latitude, i.e., $f(\theta)=1$ instead of \ref{conf-alph}) ), the general patterns of \ref{caseI} are hold except that the maximum of the toroidal magnetic field is shifted to higher latitude $\approx 40^{\circ}$." Therefore we can conclude that the aQ- dynamo model with the boundary conditions that allow a small partial penetration of the toroidal field into the outer lavers of the Sun. can robustly reproduce the solar-cvcle butterfly diagram for the near-surface large-scale magnetic field evolution.," Therefore we can conclude that the $\alpha\Omega$ - dynamo model with the boundary conditions that allow a small partial penetration of the toroidal field into the outer layers of the Sun, can robustly reproduce the solar-cycle butterfly diagram for the near-surface large-scale magnetic field evolution." These results demonstrate (he importance of the subsurface rotational shear laver in the solar dvnamo mechanism., These results demonstrate the importance of the subsurface rotational shear layer in the solar dynamo mechanism. This work was supported bv the NASA LWS NNNOOATS5G grant and partially bv the REBR. grant. 10-02-00148-a., This work was supported by the NASA LWS NNX09AJ85G grant and partially by the RFBR grant 10-02-00148-a. HHelou (2002; Eq.,Helou (2002; Eq. " 1) prescription, relating the dust mass to the integrated energy density to which it is exposed in units of the solar neighborhood intensity (2.2x10?Wm; Mathis et 11983)."," 1) prescription, relating the dust mass to the integrated energy density to which it is exposed in units of the solar neighborhood intensity $2.2\times 10^{-5}{\rm W\,m^{-2}}$; Mathis et 1983)." The standard model (model 1) we apply on the strip uses the Galactic ISM dust size distribution and composition of graphite and silicate grains from Zubko et ((2004; BARE-GR-S model) who successfully fit the Galactic ISM dust emission out to submillimeter wavelengths., The standard model (model 1) we apply on the strip uses the Galactic ISM dust size distribution and composition of graphite and silicate grains from Zubko et (2004; BARE-GR-S model) who successfully fit the Galactic ISM dust emission out to submillimeter wavelengths. " The dust emissivity index at the longest wavelengths is 6=2, which is also the assumed emissivity value for the SAGE-LMC ISM study by Bernardetal.(2008)."," The dust emissivity index at the longest wavelengths is $\beta = 2$, which is also the assumed emissivity value for the SAGE-LMC ISM study by \cite{bernard2008}." ". However, as will be shown in Sect."," However, as will be shown in Sect." " 4, the grains of this model do not have enough emissivity in the submillimeter regime to fit the SPIRE fluxes, with a gas-to-dust mass ratio (GDR) consistent with the elemental abundances of the LMC."," 4, the grains of this model do not have enough emissivity in the submillimeter regime to fit the SPIRE fluxes, with a gas-to-dust mass ratio (GDR) consistent with the elemental abundances of the LMC." " As a consequence, we also created another model (model 2) replacing the graphites (of model 1) by amorphous carbons from Rouleau MMartin (1991; ΑΟΙ)."," As a consequence, we also created another model (model 2) replacing the graphites (of model 1) by amorphous carbons from Rouleau Martin (1991; AC1)." This modified model has more emissivity at long wavelengths and therefore gives a realistic GDR., This modified model has more emissivity at long wavelengths and therefore gives a realistic GDR. " For both models, the PAH-to-dust mass fraction, fpay is reported in units of the Galactic PAH fraction of 0.046 (Draine Li 2007); i.e. fpe4g=1 means Galactic PAH abundance."," For both models, the PAH-to-dust mass fraction, $f_{PAH}$ is reported in units of the Galactic PAH fraction of $0.046$ (Draine Li 2007); i.e. $f_{PAH} = 1$ means Galactic PAH abundance." Both dust models provide an adequate fit to the SED of the strip., Both dust models provide an adequate fit to the SED of the strip. " For model 1, the PAH-to-dust mass fraction is slightly lower than the Galactic mass fraction (fpay= 0.85*006), and its mass average stellar light intensity is twice the solar neighborhood intensity ((U)= 2.010)."," For model 1, the PAH-to-dust mass fraction is slightly lower than the Galactic mass fraction $f_{PAH}=0.85_{-0.06}^{+0.06}$ ), and its mass average stellar light intensity is twice the solar neighborhood intensity $\langle U\rangle=2.0_{-0.5}^{+0.4}$ )." " Although regions can show much hotter dust (Hony et 22010), it does not"," Although $\,$ regions can show much hotter dust (Hony et 2010), it does not" , A running median of WIC radii vs. effective temperature. reduced by15%.. is roughly consistent wilh a Yale-Yonsei 5 Gyr solar-metallicity isochrone.,"A running median of KIC radii vs. effective temperature, reduced by, is roughly consistent with a Yale-Yonsei 5 Gyr solar-metallicity isochrone." We therefore performed a second analysis in which star and planet radii were uniformly decreased by (Figure 9dd)., We therefore performed a second analysis in which star and planet radii were uniformly decreased by (Figure \ref{fig.tests}d d). As expected. Chis shifts the locus to both higher a ancl oy.," As expected, this shifts the locus to both higher $\alpha$ and $\sigma_0$." As we discuss below. svslenmatic overestimation of stellar radius and the presence of interloping giant stars may nol necessarily be incompatible.," As we discuss below, systematic overestimation of stellar radius and the presence of interloping giant stars may not necessarily be incompatible." Our combined analvsis ofKepler (transit detections and Doppler radial velocities Lor late IX and early M stars finds that consistency. is possible for a wide but not unlimited range of parameters., Our combined analysis of transit detections and Doppler radial velocities for late K and early M stars finds that consistency is possible for a wide but not unlimited range of parameters. As expected for an analvsis based on RV variance. there is an inverse relationship between acceptable values of planet mass. ie.. (he power-law index a of the planet mass-radius relation. ancl stellar jitter. ie. (he parameter oy (that characterizes its distribution among stars.," As expected for an analysis based on RV variance, there is an inverse relationship between acceptable values of planet mass, i.e., the power-law index $\alpha$ of the planet mass-radius relation, and stellar jitter, i.e. the parameter $\sigma_0$ that characterizes its distribution among stars." However. if the level of radial velocity jitter in. M2IX. stars is as expected. reconciliation ofKepler ancl Doppler observations can only be achieved if à~4. and a~2 is excluded.," However, if the level of radial velocity jitter in M2K stars is as expected, reconciliation of and Doppler observations can only be achieved if $\alpha \sim 4$, and $\alpha \sim 2$ is excluded." " In other words. siall planets around these stars are primarily rockvanetal ""uper-Iurths"" rather than hydrogen gas-dich ""mini-Neptunes."," In other words, small planets around these stars are primarily rocky-metal “super-Earths” rather than hydrogen gas-rich “mini-Neptunes”." We cannot absolutely rule oul higher Πίου (σι>3. corresponding to total svstematic RAIS 245ms 1) that would admit a lower value of a. but there is no evidence to support such a choice.," We cannot absolutely rule out higher jitter $\sigma_0 \ge 3$, corresponding to total systematic RMS $> 4.5$ ) that would admit a lower value of $\alpha$, but there is no evidence to support such a choice." Instead. a)2 |ojds supported by the RMS of our paired Doppler observations. (he predicted stellar jitter based on chromospheric activity ancl the observed levels of iitter among other. similar stars (Appsetal.2010:Isaacson&Fischer2010)..," Instead, $\sigma_0 \sim 2$ is supported by the RMS of our paired Doppler observations, the predicted stellar jitter based on chromospheric activity and the observed levels of jitter among other, similar stars \citep{Apps2010,Isaacson2010a}." Our choice of a=2 to represent gas-rich planets is conservative because theoretical modeling suggests values closer to zero or even negative over the mass range of interest 2011).., Our choice of $\alpha = 2$ to represent gas-rich planets is conservative because theoretical modeling suggests values closer to zero or even negative over the mass range of interest \citep{Rogers2011}. . The two most powerful FR. LE radio sources in the nearby Universe (νο X and ὃς905 are each located at the centre ofa dense. moderately rich cluster of galaxies.,"The two most powerful FR II radio sources in the nearby Universe – Cyg A and 3C295 – are each located at the centre of a dense, moderately rich cluster of galaxies." While such an environment is exceptional for a low-redshilt FR. LL galaxy. it appears to be common around. powerful radio objects at earlier epochs.," While such an environment is exceptional for a low-redshift FR II galaxy, it appears to be common around powerful radio objects at earlier epochs." Above a redshift’ of 0.5. raclio-loucl objects (both the quasars and. radio galaxies) are inferred. to lie in clusters of galaxies of moderate. optical richness.," Above a redshift of 0.5, radio-loud objects (both the quasars and radio galaxies) are inferred to lie in clusters of galaxies of moderate optical richness." The evidence for such an environment includes optical ancl near-IR. galaxy counts (Yoo Green 1987: Yates et al 1989: Lill Lilly 1991: Ellingson et al 1991: Dickinson 1997). high eas pressures within a radius of (Crawford. Fabian 1989: Forbes ct al 1990: Mener οἱ al 1992: Durret et al 1994). cD-tvpe host galaxy profiles (Best οἱ al 1998). à eravitational are (Deltorn ct al 1997). and lensing shear of surrounding field galaxies (Bower Smail 1997).," The evidence for such an environment includes optical and near-IR galaxy counts (Yee Green 1987; Yates et al 1989; Hill Lilly 1991; Ellingson et al 1991; Dickinson 1997), high gas pressures within a radius of (Crawford Fabian 1989; Forbes et al 1990; Bremer et al 1992; Durret et al 1994), cD-type host galaxy profiles (Best et al 1998), a gravitational arc (Deltorn et al 1997), and lensing shear of surrounding field galaxies (Bower Smail 1997)." The properties of the radio source itself. also imply the presence of a confining medium: a large-scale working surface on which the jets form the radio lobes: a steep radio spectrum: and a high. minimum pressure in regions of relaxed. radio structure (Bremer ct al 1992)., The properties of the radio source itself also imply the presence of a confining medium: a large-scale working surface on which the jets form the radio lobes; a steep radio spectrum; and a high minimum pressure in regions of relaxed radio structure (Bremer et al 1992). A Faraday depolarization asvnumetry (Carrington Conway 1991). the distortion and compression of high-redshift racio source morphologies (Llintzen et al 1983: Barthel Miley LOSS) and sources with very high Faraday rotation measures (Carilli et al 1994: οαν et al 1997). all corroborate the inference of a dense. clumpy medium surrounding the racio source.," A Faraday depolarization asymmetry (Garrington Conway 1991), the distortion and compression of high-redshift radio source morphologies (Hintzen et al 1983; Barthel Miley 1988) and sources with very high Faraday rotation measures (Carilli et al 1994; Carilli et al 1997) all corroborate the inference of a dense, clumpy medium surrounding the radio source." Thus it appears that the deepest. potential wells we can readilv pinpoint at 2=1 are those around: powerful radio sources., Thus it appears that the deepest potential wells we can readily pinpoint at $z\ge1$ are those around powerful radio sources. The cluster distribution at high redshift can provide a stringent cosmological test. (see e.g. Donahue ct al 1998). and can also be compared to the N-ray buniinosity function of clusters at low redshift (eg Ebeling et al 1997).," The cluster distribution at high redshift can provide a stringent cosmological test (see e.g. Donahue et al 1998), and can also be compared to the X-ray luminosity function of clusters at low redshift (eg Ebeling et al 1997)." Whilst it may result in a sample of clusters biased to only those that can host an active nucleus. using racio sources to identify the ocation of deep potential wells is a promising way of finding clusters oul to and. ονομα a redshift 2~1 (Crawford 1997).," Whilst it may result in a sample of clusters biased to only those that can host an active nucleus, using radio sources to identify the location of deep potential wells is a promising way of finding clusters out to and beyond a redshift $z\sim1$ (Crawford 1997)." Current X-ray surveys of clusters detected from the LOSAT All-Sky Survey (eg Ebeling et al 1998) do not reach sulliciently faint [ux levels. and studies of deep serencdipitous X-ray pointings (e.g. Rosati et al 1998) cover only a small raction of the sky.," Current X-ray surveys of clusters detected from the ROSAT All-Sky Survey (eg Ebeling et al 1998) do not reach sufficiently faint flux levels, and studies of deep serendipitous X-ray pointings (e.g. Rosati et al 1998) cover only a small fraction of the sky." “Phe first step. however. is simply. to confirm that powerful radio quasars beyond. a redshift of a half really clo lie at the centre of clusters of galaxies.," The first step, however, is simply to confirm that powerful radio quasars beyond a redshift of a half really do lie at the centre of clusters of galaxies." Anv scenario of the stellar halo formation has to impose certain restrictions on the rate of binary and multiple svstems and on their characteristics. i.e. on the distributions of orbital periods. component mass ratios. eccentricities. etc.,"Any scenario of the stellar halo formation has to impose certain restrictions on the rate of binary and multiple systems and on their characteristics, i.e. on the distributions of orbital periods, component mass ratios, eccentricities, etc." Particularly. high percentage of binary and multiple halo field stars indicates that the formation of stellar halo via the destruction of globular clusters is unlikely in our Galaxy. since the relative number of binaries in globular clusters (Sollimaetal.2007) is smaller than (hat of metal-poor field stars.," Particularly, high percentage of binary and multiple halo field stars indicates that the formation of stellar halo via the destruction of globular clusters is unlikely in our Galaxy, since the relative number of binaries in globular clusters \citep{sollima_2007} is smaller than that of metal-poor field stars." It is currently not clear how does the dvnamical evolution of globular clusters influence the binary frequency (Ivanovaetal.2005:ILurlev.Aarseth 2008).. therefore the scenario of the halo field subclwarls formation through a dissociation ol globulars cannot be fully discarded.," It is currently not clear how does the dynamical evolution of globular clusters influence the binary frequency \citep*{ivanova,hurley,sollima_2008}, therefore the scenario of the halo field subdwarfs formation through a dissociation of globulars cannot be fully discarded." The question of the differences between stellar streams in terms of binary aud multiple svslenis requires further accunimlation of observational data., The question of the differences between stellar streams in terms of binary and multiple systems requires further accumulation of observational data. Our material does nol contradict neither an assumption of the parity of binary. and multiple stars frequency in different streams. nor the hypothesis of their dynamical origins (e.g.. Famaevetal. 2008)).," Our material does not contradict neither an assumption of the parity of binary and multiple stars frequency in different streams, nor the hypothesis of their dynamical origins (e.g., \citealt{famaey_2008}) )." some of (he detected speckle interferometric pairs.GT6-21..G63-46.. G28-43.. G217-8.. G130-7.. G102-20.. 1185À.. G&7-47.. with presumably short orbital periods are suitable for monitoring for orbit calculations and mass determination of the metal-poor stars.," Some of the detected speckle interferometric pairs, with presumably short orbital periods are suitable for monitoring for orbit calculations and mass determination of the metal-poor stars." These studies can contribute to a calibration of the mass-luminosity relation and to, These studies can contribute to a calibration of the mass-luminosity relation and to "overall upward or outward bulk motion in the corona account for the ""narrower line found in some Sevtert 1 galaxies?",overall upward or outward bulk motion in the corona account for the `narrower' line found in some Seyfert 1 galaxies? Done.Madoejski&Zvcki(2000) found that IC329A las a relatively narrow line which can be modeled using a disk line having au iuner truncation radius of about SOAL and EW of 21+Lev. NGC1593 was also found to have a relatively narrow line with an iuner truncation radius of 30AL (Lu&Wane2000)., \citet[]{dmz00} found that IC4329A has a relatively narrow line which can be modeled using a disk line having an inner truncation radius of about $50M$ and EW of $210\pm45$ eV. NGC4593 was also found to have a relatively narrow line with an inner truncation radius of $30M$ \citep[]{lw00}. .. Even in NCCh5SLS. the line cussion region was found to be truncated at an inner radius of 1544 (Chiangetal.2000)...," Even in NGC5548, the line emission region was found to be truncated at an inner radius of $15M$ \citep[]{chiang99}." The best-fit line profiles for NCC5518 and IC1329À are also shown (in Fig. D) , The best-fit line profiles for NGC5548 and IC4329A are also shown (in Fig. \ref{fig:offaxisprof}) ) as light solid aud light dotted lines. respectively.," as light solid and light dotted lines, respectively." A significant fraction of the N-rav enission nav come from the region within 15A iu the thin corona regime. which would indicate that the bulk motion in the corona is not the dominant factor makine the line ‘narrower du some objects;," A significant fraction of the X-ray emission may come from the region within $15M$ in the thin $-$ corona regime, which would indicate that the bulk motion in the corona is not the dominant factor making the line `narrower' in some objects." " As shown in Figure L. obviously the observed ""narrower. line profile iu IC1329À cannot be iuterpreted oulv by the corona bulk motion in this case."," As shown in Figure \ref{fig:offaxisprof}, obviously the observed `narrower' line profile in IC4329A cannot be interpreted only by the corona bulk motion in this case." Other parameters (possibly the generally iutroduced inner truucation radius caused by the total ionization or disruption of the disk within this radius) are also still needed. or the corona in IC1329À is more extended and most of the N-ray cussion comes frou an outer region with radius of 5047.," Other parameters (possibly the generally introduced inner truncation radius caused by the total ionization or disruption of the disk within this radius) are also still needed, or the corona in IC4329A is more extended and most of the X-ray emission comes from an outer region with radius of $\sim 50M$." For δις018. a narrow line which may be ciuitted from the broad line regiou or molecular torus. has been detected with the Hielhi-Euncrey. Transmission Crating 01).," For NGC5548, a narrow line which may be emitted from the broad line region or molecular torus, has been detected with the High-Energy Transmission Grating \citep[]{yaq01}." . The corona bulk motion may account for the “narrower line ina NG(C5518- by removing the contribution from distant material., The corona bulk motion may account for the `narrower' line in NGC5548 by removing the contribution from distant material. Here. even the X-ray emission may come mainly the reeion around or within 15M. aud the ionization or disruption of the disk may not be necessary.," Here, even the X-ray emission may come mainly from the region around or within $15M$, and the ionization or disruption of the disk may not be necessary." Detailed models ave bevoud the scope of this paper., Detailed models are beyond the scope of this paper. With the observation of the Calibration and Pavload Verification (Cal-PV) phase ofNewton. a redshifted line at 6.15keV (quasar frame) has been fouud iu the racdio-loud quasar PI&S0537-286 (redshift 2= 23.101) with an EW of 30ceV. which suggests the existence of cold matter near the ceutral black hole (Reevesetal.2001).," With the observation of the Calibration and Payload Verification (Cal-PV) phase of, a redshifted line at 6.15keV (quasar frame) has been found in the radio-loud quasar PKS0537-286 (redshift $z=3.104$ ) with an EW of 30eV, which suggests the existence of cold matter near the central black hole \citep[]{reev01}." . The overall spectral cucrey distribution of this object is dominated by a flat power-law X-ray cluission with a spectral iudex of a~0.27. iudicatiug that the clomiuaut X-ray enission iiechanisui is the inverse Compton emission associated with a face-on relativistic jet 2001).," The overall spectral energy distribution of this object is dominated by a flat power-law X-ray emission with a spectral index of $\alpha\sim 0.27$, indicating that the dominant X-ray emission mechanism is the inverse Compton emission associated with a face-on relativistic jet \citep[]{reev01}." . The reflection fraction was coustraied to be R=0.25 indicating the reflection material subteuds a solid-anele much lower than the 27 expected from au accretion disk., The reflection fraction was constrained to be $R\simeq0.25$ indicating the reflection material subtends a solid-angle much lower than the $2\pi$ expected from an accretion disk. Reevesetal.(2001). explained these catures using two continu eumissiou compoucuts: a “Sevtert-like” steep power-law οuponeut originating roni the region near the accretion disk aud associated with its reflection coutimmun. and a hard bright jet component with au N-aax flat slope.," \citet[]{reev01} explained these features using two continuum emission components: a `Seyfert-like' steep power-law component originating from the region near the accretion disk and associated with its reflection continuum, and a hard bright jet component with an X-ray flat slope." Generally. the radio jet is believed to be launched from the region close o the ceutral black hole. which is possibly related to the ejecting X-ray plasma.," Generally, the radio jet is believed to be launched from the region close to the central black hole, which is possibly related to the ejecting X-ray plasma." These X-ray features in PISSO537-286 max also be explained in a unified model: the N-rays are cuitted frou the upward ejecting asina near the ceutral black hole (with radius of tens AZ) having an effective bulk velocity of ~0.50.7., These X-ray features in PKS0537-286 may also be explained in a unified model: the X-rays are emitted from the upward ejecting plasma near the central black hole (with radius of tens $M$ ) having an effective bulk velocity of $\sim 0.5-0.7$. The dowuward X-ray photous from the plasma are reflected by the accretion disk aud thus produce the lue with a small EW and the sinall reflection fraction due to the beamine effect., The downward X-ray photons from the plasma are reflected by the accretion disk and thus produce the line with a small EW and the small reflection fraction due to the beaming effect. " The redshitting of the ine (from 6.1 keV to 6.15 keV) could also be explained as due to trausverse-Doppler effect aud eravitational redshift if this quasar is secu at a small inclination angle [radio-loud quasars are generally believed to be see- atf a small inclination angle (Urry&Padovani1995).. e.g. 0,Z157. see also the upper pauels of Fig. 1|."," The redshifting of the line (from 6.4 keV to 6.15 keV) could also be explained as due to transverse-Doppler effect and gravitational redshift if this quasar is seen at a small inclination angle [radio-loud quasars are generally believed to be seen at a small inclination angle \citep[]{up95}, e.g. $\theta_{\rm o}\la 15\arcdeg$, see also the upper panels of Fig. \ref{fig:onaxisprof}] ]." This N-rav enmussiou region could be the base of the launching jet., This X-ray emission region could be the base of the launching jet. Therefore. the liue together with its reverberation could be a useful tool to probe the region of jet formation aud to measure the initial velocity of the jet as well as the inclination of the disk in racio-loud quasars.," Therefore, the line together with its reverberation could be a useful tool to probe the region of jet formation and to measure the initial velocity of the jet as well as the inclination of the disk in radio-loud quasars." This may reveal the physical connection between the jet properties aud the cold accretion flow using future X-ray satellites, This may reveal the physical connection between the jet properties and the cold accretion flow using future X-ray satellites However. unlike the optical depth. the rate depends on the mass of the NLACTIOs. and hence this average duration is also a function of mass.,"However, unlike the optical depth, the rate depends on the mass of the MACHOs, = and hence this average duration is also a function of mass." Comparing the calculated: durations to the average observed duration. zz60 cays we finc.," Comparing the calculated durations to the average observed duration, $\approx 60$ days we find, = ]^2." where the rate is calculated. for LAL. NLACTIOs., where the rate is calculated for $1\Msol$ MACHOs. " Contours of this mass estimate for the range of X, and h. are shown in Figure 2.", Contours of this mass estimate for the range of $\Sigma_0$ and $h_z$ are shown in Figure 2. We see that the estimated MACHO mass is ονO.3AL. for the entire allowed region regardless of he ἵνρο of disk., We see that the estimated MACHO mass is $\sim 0.3\Msol$ for the entire allowed region regardless of the type of disk. Fat disks are not a xulacea [or the NLACTIO mass estimate problem., Fat disks are not a panacea for the MACHO mass estimate problem. We calculate the istribution of Einstein crossing times for our models as a Function of MACHO mass and from this we can calculate the probability for a given. ALACTIO mass to produce the observed. distribution of event. crossing times., We calculate the distribution of Einstein crossing times for our models as a function of MACHO mass and from this we can calculate the probability for a given MACHO mass to produce the observed distribution of event crossing times. We show in Figure 3 the probability as a function of mass for a Alestel isk with X=90M.pc «η:2.5kpc.," We show in Figure 3 the probability as a function of mass for a Mestel disk with $\Sigma=90\Msol {\rm pc}^-$, $h_z=2.5\kpc$." Brown cdwarl masses. while not ruled out at the two sigma level. are unlikely.," Brown dwarf masses, while not ruled out at the two sigma level, are unlikely." -— lt is e@enerically true for all of the models we examine that brown clwarl masses are no more likely for than for the standard halo moclels., It is generically true for all of the models we examine that brown dwarf masses are no more likely for than for the standard halo models. This is so because although the average predicted mass is smaller. the clispersion is also slightly smaller and thus the probability for low masses is about the same.," This is so because although the average predicted mass is smaller, the dispersion is also slightly smaller and thus the probability for low masses is about the same." " The analysis of the LMC microlensing events in the context of extended halos vieles a robust estimate of the total mass in MACHOs within 50 kpe of Adiaven.2LOMAL. in order to woduce an LMC optical depth of about 2lo, ", The analysis of the LMC microlensing events in the context of extended halos yields a robust estimate of the total mass in MACHOs within 50 kpc of $M_{\rm baryons} \approx 2 \times 10^{11} \Msol$ in order to produce an LMC optical depth of about $2 \times 10^{-7}$. The production of 210AI. in white cdwarls requires a much greater metal abundance than is seen unless somewhat ad-hoc ellicient galactic winds are invoked to blow the metals out into the intergalactic medium.," The production of $2 \times 10^{11} \Msol$ in white dwarfs requires a much greater metal abundance than is seen unless somewhat ad-hoc efficient galactic winds are invoked to blow the metals out into the intergalactic medium." As discussed in Gates et al., As discussed in Gates et al. 1998. NLACTIIOs in a very tick disk configuration can reduce this mass estimate. but onlv slightly.," 1998, MACHOs in a very thick disk configuration can reduce this mass estimate, but only slightly." Phe total mass tac pieayery thick disk is 6.7101AL. owich results in Hn EN EE τομot about 1.3.Q.," The total mass in a typical very thick disk is $6.7 \times 10^{10} \Msol$, which results in an optical depth of about $1.3 \times 10^{-7}$." ‘This is approximately 1/2 of the tientmass tiapriythat would be recuirec fora halo distribution, This is approximately 1/2 of the mass that would be required for a halo distribution Am(15) are from van den Bergh (1996) and Schaefer (1996a. 19908. 19006).,"$\Delta m(15)$ are from van den Bergh (1996) and Schaefer (1996a, 1996b, 1996c)." lig., Fig. 6 shows the plot of the absolute magnitude at maximum Mg as a function of Am(15)., 6 shows the plot of the absolute magnitude at maximum $_B$ as a function of $\Delta m(15)$. Cireles represent SNe in Spirals. triangles SNe in early type galaxies.," Circles represent SNe in Spirals, triangles SNe in early type galaxies." We have computed the best-fit regression by using a least squares fit. taking into account the errors in both coordinates. and we obtain: Mi=2.4040.33(10).Am(15)22.06E0.4117) Light svmbols in Fig.," We have computed the best-fit regression by using a least squares fit, taking into account the errors in both coordinates, and we obtain: ${\rm M_B}=2.40\pm 0.33(1\sigma) \times \Delta m(15)-22.06\pm0.41(1\sigma)$ Light symbols in Fig." 6 (not used in computing the fit) represent SNe of Tab.6. for which no individual distances to the parent galaxies. obtained via GCOLE or Cepheids. are available.," 6 (not used in computing the fit) represent SNe of \ref{tab.fornax_SNe} for which no individual distances to the parent galaxies, obtained via GCLF or Cepheids, are available." The slope of our fit is similar to that. obtained. by Phillips (1993). though only 4 objects are in common (1990N. 1981D. 1991bg and 1992).," The slope of our fit is similar to that obtained by Phillips (1993), though only 4 objects are in common (1990N, 1981B, 1991bg and 1992A)." The Phillipss intercept is fainter by ~ 0.4 magnitudes. possibly reflecting dilferences in the zero point of the methods used to determine the distances to cach parent galaxy.," The Phillips's intercept is fainter by $\sim $ 0.4 magnitudes, possibly reflecting differences in the zero point of the methods used to determine the distances to each parent galaxy." Le. Surface Brightness Fluctuation and Tullvy-Fisher in Phillips and Cepheids and GCLE in this paper., i.e. Surface Brightness Fluctuation and Tully-Fisher in Phillips and Cepheids and GCLF in this paper. If one restricts the analysis only to the prototypical SNel-a — as defined by Branch. Fisher and Nugent (1993) or Branch and ‘Tammann (1992)] which are the only ones actually usable to determine the clistances. one has to perform the fit after excluding SN 1991bg (dashed. line in Fie.," If one restricts the analysis only to the prototypical SNeI-a [ as defined by Branch, Fisher and Nugent (1993) or Branch and Tammann (1992)] which are the only ones actually usable to determine the distances, one has to perform the fit after excluding SN 1991bg (dashed line in Fig." 6)., 6). In this case we obtain a considerably less steep slope and a fainter intercept My=1.52+0.42(16)5Am(15)21.073: 0.49(10)., In this case we obtain a considerably less steep slope and a fainter intercept ${\rm M_B}=1.52\pm 0.42(1\sigma) \times \Delta m(15)-21.07\pm0.49(1\sigma)$ . Llowever. these data can be more profitably used to improve the zero point of the relationship found by Llamuy ct al. (," However, these data can be more profitably used to improve the zero point of the relationship found by Hamuy et al. (" 1996) whose slope has been determined on 26 SNe whereas the zero point. is based. on 4 SNel-a (1937€. 19721. 1981D. 1990N) which all appeared only in late type galaxies.,"1996) whose slope has been determined on 26 SNe whereas the zero point is based on 4 SNeI-a (1937C, 1972E, 1981B, 1990N) which all appeared only in late type galaxies." " We have fitted our data points by adopting the Llamuy’s slope (0.784) and assuming as zero point the value of the intercept which minimizes the reduced 7"" (1.03).", We have fitted our data points by adopting the Hamuy's slope (0.784) and assuming as zero point the value of the intercept which minimizes the reduced $\chi^2$ (1.03). This fit (solid line in bie., This fit (solid line in Fig. 6) vields: Two other SNel-a have appeared. in the Fornax. cluster: 1980N and 1981D. both in NGC 1316.," 6) yields: Two other SNeI-a have appeared in the Fornax cluster: 1980N and 1981D, both in NGC 1316." Their peak uminoslties were D(mnax)-12.49 and DB(max)-—12.59 (llamuy et al., Their peak luminosities were B(max)=12.49 and B(max)=12.59 (Hamuy et al. 1991. Sandage and Tanmumann 1996).," 1991, Sandage and Tammann 1996)." The only clireet measurement of the distance of their went ealaxvy comes from the Planetary Nebula Luminosity Function (2PNLE: see Tab., The only direct measurement of the distance of their parent galaxy comes from the Planetary Nebula Luminosity Function (=PNLF; see Tab. 7)., 7). By combining the distance modulus. provided Ὃν Ιολία. Ciarcullo απ. Jacoby (1993) and Jacoby (1997) with the respective apparent magnitudes at maximum. we derive Mg=15.69+0.12 and Mg—/—18.5940.12. in good agreement with 18.7930.16 of SN. 19924. This result suggests a number of possible alternative interpretations: In this paper we have determined the distance to NCC 1380. an SO galaxy host of the tvpe Ia SN. 1992. through the use of the TO magnitude of the GCLE.," By combining the distance modulus provided by McMillan, Ciardullo and Jacoby (1993) and Jacoby (1997) with the respective apparent magnitudes at maximum, we derive $_B=-18.69\pm0.12$ and $_B=-18.59\pm0.12$, in good agreement with $_B=-18.79\pm0.16$ of SN 1992A. This result suggests a number of possible alternative interpretations: In this paper we have determined the distance to NGC 1380, an S0 galaxy host of the type Ia SN 1992A, through the use of the TO magnitude of the GCLF." We find a distance modulus of 31.8540.16 corresponding to a distance of 18.61.4. Mpe., We find a distance modulus of $\pm 0.16$ corresponding to a distance of $\pm 1.4$ Mpc. " This is consistent with the distances to other members of the Fornax cluster. utilizing the same method. as well as the Cepheid distance to NGC 1365,"," This is consistent with the distances to other members of the Fornax cluster, utilizing the same method, as well as the Cepheid distance to NGC 1365." By applying this distance to the apparent magnitude of SN 1992A. we findthat at peak brightness SN 1992 reached Mp=18.79+0.16. which is about 0.4 mage fainter than expected for typical SNel-a in carly (wpe galaxies (Branch. ltomanishin and Baron 1996). and about 0.7. magnitucles fainter than SNel-a in spirals. if one accepts as zero point Ale=19.5340.07 CLanmmann et al.," By applying this distance to the apparent magnitude of SN 1992A, we find that at peak brightness SN 1992A reached $M_B= -18.79\pm0.16$, which is about 0.4 mag fainter than expected for typical SNeI-a in early type galaxies (Branch, Romanishin and Baron 1996), and about 0.7 magnitudes fainter than SNeI-a in spirals, if one accepts as zero point $_B=-19.53\pm 0.07$ (Tammann et al." 1996). the absolute magnitude at maximum of SNel-a in Spirals.," 1996), the absolute magnitude at maximum of SNeI-a in Spirals." Lt is worthwhile noting in this respect that recent work by Mazzali et al. (, It is worthwhile noting in this respect that recent work by Mazzali et al. ( in preparation) shows a good correlation between the velocity widths of the nebular lines (at around 300 cays alter the maximum) and the rate of decline (and therefore the absolute magnitude at maximum).,in preparation) shows a good correlation between the velocity widths of the nebular lines (at around 300 days after the maximum) and the rate of decline (and therefore the absolute magnitude at maximum). The, The 4£ V Rea; (1979).. 300 10*. Rea; Dwufuovae Warner(1995).," $\eta$$L$ $V$ $Re_M$ \cite{par79}, $300$ $10^7$ $Re_M$ \cite{war95}." ". Rea, Balbus&Dawley of Balbus&Tawley(1997) Tawlev.Came.Balbus(1996) Rea;=L?Qy=104 ea;=2000 Fea;xLO! Rea, 107 Rea; Cannizzo(L993b) o Shakura&Suuvaev(1973))) Sanak(19812). à "," $Re_M$ \cite{bh91} \cite{bh97} \cite{hgb96} $Re_M \equiv L_z^2 \Omega/\eta = 10^4$ $Re_M = 2000$ $Re_M \lesssim 10^4$ $Re_M$ $10^3$ $Re_M$ \cite{can93b} $\alpha$ \cite{ss73}) \cite{sma84}) $\alpha$ " To comprehend all the phenomenology in particle physics and cosmology one has to construct mathematically consistent and complete theories based on few basic physical principles.,To comprehend all the phenomenology in particle physics and cosmology one has to construct mathematically consistent and complete theories based on few basic physical principles. The theory presented in ref., The theory presented in ref. ? 1s an attempt of solving two main obstacles in the Standard Model (SM) and relativistic quantum field theory: zero-distance singularity and causality-violating SU(2) global anomaly., \citet{Palle1} is an attempt of solving two main obstacles in the Standard Model (SM) and relativistic quantum field theory: zero-distance singularity and causality-violating $SU(2)$ global anomaly. The resulting theory (called BY in ref. 2)), The resulting theory (called BY in ref. \citet{Palle1}) ) is UV finite (not only renormalizable) with heavy and light Majorana neutrinos as cold and hot dark matter (??)..," is UV finite (not only renormalizable) with heavy and light Majorana neutrinos as cold and hot dark matter \citep{Palle2,Palle3}." There ts a perfect balance between bosonic (electroweak gauge bosons) and fermionic (leptons and quarks) particles. owing to exact cancellation of anomalous effective actions and the constraint relation between boson and fermion mixing angles Qj=201.+423034).," There is a perfect balance between bosonic (electroweak gauge bosons) and fermionic (leptons and quarks) particles, owing to exact cancellation of anomalous effective actions and the constraint relation between boson and fermion mixing angles $\theta_{W}=2(\theta_{12}+\theta_{23} +\theta_{31})$." The left-handed chirally-asymmetric weak interactions appear as an inevitable consequence of the assumed dimensionality and noncontractiblity of the physical spacetime., The left-handed chirally-asymmetric weak interactions appear as an inevitable consequence of the assumed dimensionality and noncontractiblity of the physical spacetime. " The absence of Higgs particles is crucial for the cosmological stability of heavy Majorana neutrinos Ta,2»Ty (2)..", The absence of Higgs particles is crucial for the cosmological stability of heavy Majorana neutrinos $\tau_{N_{i}} \gg \tau_{U}$ \citep{Palle2}. . The lepton-number violation. the conservation of B—L. as well as lepton and baryon CP violation. lead to leptogenesis and baryogenesis.," The lepton-number violation, the conservation of $B-L$, as well as lepton and baryon CP violation, lead to leptogenesis and baryogenesis." To summarize. the BY gauge theory is not only mathematically superior to the SM. but also phenomenologically: (1) solar. atmospheric. neutrino and long-baseline neutrino experiments favor massive light neutrinos with mixed flavors. (2) contrary to the SM. the BY theory has heavy Majorana neutrinos as cold dark matter candidates. (3) the SM cannot generate lepto- and baryogenesis while the lepton-number violation in the BY theory together with CP violating phases in the quark and lepton mixing matrices allow cosmological lepto- and baryogenesis. (4) quantum-loop corrections in the electroweak and strong interactions in the SM show some deviations for the forward-backward and left-right asymmetry form factors measured by LEP? and SLC and a difference from the QCD amplitudes at thelargest momenta measured by," To summarize, the BY gauge theory is not only mathematically superior to the SM, but also phenomenologically: (1) solar, atmospheric, neutrino and long-baseline neutrino experiments favor massive light neutrinos with mixed flavors, (2) contrary to the SM, the BY theory has heavy Majorana neutrinos as cold dark matter candidates, (3) the SM cannot generate lepto- and baryogenesis while the lepton-number violation in the BY theory together with CP violating phases in the quark and lepton mixing matrices allow cosmological lepto- and baryogenesis, (4) quantum-loop corrections in the electroweak and strong interactions in the SM show some deviations for the forward-backward and left-right asymmetry form factors measured by LEP2 and SLC and a difference from the QCD amplitudes at thelargest momenta measured by" but with cülferent absorbing hydrogen column densities.,but with different absorbing hydrogen column densities. " The analytical form of the partially covering high energy. cutoll power-law model is where N(E) is the observed intensity. Eds the photon index. Ng, and Nye are the two equivalent hydrogen column densities. σ is the photo-clectric cross-section. Sy and 5» are the respective nornializations of the power law. {ει is the cutolf energy anc £j the οfolding energy."," The analytical form of the partially covering high energy cutoff power-law model is where N(E) is the observed intensity, $\Gamma$ is the photon index, $N_{H1}$ and $N_{\mathrm H2}$ are the two equivalent hydrogen column densities, $\sigma$ is the photo-electric cross-section, $S_{1}$ and $S_{2}$ are the respective normalizations of the power law, $E_{\mathrm c}$ is the cut–off energy and $E_{\mathrm f}$ the e–folding energy." As in previous two cases. the relative instrument normalizations of the three Χίος and PIN. detectors were kept free.," As in previous two cases, the relative instrument normalizations of the three XISs and PIN detectors were kept free." The values obtained are found. to be. 1.00:1.03:0.909:0.99 for NISS:XISO:NISI:PIN with a clear agreement with the previous values., The values obtained are found to be 1.00:1.03:0.99:0.99 for XIS3:XIS0:XIS1:PIN with a clear agreement with the previous values. LO is found that. unlike the previous two continuum models. the blackbody component for soft excess in the pulsar was not required to fit the OS70. keV spectrum.," It is found that, unlike the previous two continuum models, the blackbody component for soft excess in the pulsar was not required to fit the 0.8–70 keV spectrum." The values oft10 equivalent column densities Nay and Nae are found to be ~13 5 107 atoms cem7 and 4.96 1077 atoms E7. res»ectivelv.," The values of the equivalent column densities $_{H1}$ and $_{H2}$ are found to be $\sim$ 1.3 $\times$ $^{22}$ atoms $^{-2}$ and 4.96 $\times$ $^{22}$ atoms $^{-2}$, respectively." " The covering fraction of the more absorbed power-law = Norm» (Norm, | Norme) = 2/05)| S2)] is founc to be 20.36.", The covering fraction of the more absorbed power-law [= $_2$ / $_1$ + $_2$ ) = $S_2 / (S_1 + S_2)$ ] is found to be $\sim$ 0.36. The partial covering model showed improvenxnt in the spectral fitting compared to the previous two coninuum models with reduced 47 of 1.35 (for 1589 dot)., The partial covering model showed improvement in the spectral fitting compared to the previous two continuum models with reduced $\chi^2$ of 1.35 (for 1589 dof). The parameters of the three different continuum models obtained from the simultaneous spectral fitting to the NIS and PIN data of the Suzaki observations of are given in Table 1.., The parameters of the three different continuum models obtained from the simultaneous spectral fitting to the XIS and PIN data of the $Suzaku$ observations of are given in Table \ref{spec_par}. Phe count rate spectra of the pulsar are shown in Figure 4 (for high energy cutoll power-law mocel). Figure 5. (for NPIZN model). anc Figure 6 (for partial covering model) along with the mode components (top panels) and residuals to the best-fit mode (bottom panels).," The count rate spectra of the pulsar are shown in Figure \ref{spec-fg1} (for high energy cutoff power-law model), Figure \ref{spec-fg2} (for NPEX model), and Figure \ref{spec-fg3} (for partial covering model) along with the model components (top panels) and residuals to the best-fit model (bottom panels)." The spectral fitting. of the non-simultancous. OSSE and BATSE observations of the pulsar showed a margina cvclotron resonance feature centered at —SS keV. (Shrader et al., The spectral fitting of the non-simultaneous OSSE and BATSE observations of the pulsar showed a marginal cyclotron resonance feature centered at $\sim$ 88 keV (Shrader et al. 1999)., 1999). Phe corresponding magnetic field of the pulsar is estimated to be 10/7 ο which is at the higher end. of the magnetic field. strengths of the neutron stars in. the accreting X-ray binary. pulsars. suggesting the detection a NN keV could be the second harmonies.," The corresponding magnetic field of the pulsar is estimated to be $\sim$ $^{13}$ G which is at the higher end of the magnetic field strengths of the neutron stars in the accreting X-ray binary pulsars, suggesting the detection at $\sim$ 88 keV could be the second harmonics." However. in our spectral fitting. no such absorption feature was present a 744 keV. Fherefore. we did not add any additional evclotron absorption component to the spectral fitting at 44 keV. The presence of energy dependent dips in the pulse profile of," However, in our spectral fitting, no such absorption feature was present at $\sim$ 44 keV. Therefore, we did not add any additional cyclotron absorption component to the spectral fitting at $\sim$ 44 keV. The presence of energy dependent dips in the pulse profile of" however how well we need to know the HOD and any extra environmentally dependent terms in order to carry out. precision cosmology with an HOD approach to galaxy clustering (e.g. Zheng 2002).,"however how well we need to know the HOD and any extra environmentally dependent terms in order to carry out precision cosmology with an HOD approach to galaxy clustering (e.g., Zheng 2002)." Further work is needed to determine the effect on for example the correlation function of including an environmental term in the HOD., Further work is needed to determine the effect on for example the correlation function of including an environmental term in the HOD. We have also not investigated in this paper the elfect of environment on the distribution of the number of halos at fixed. mass (e.g. Ixravtsov 2004) which may be strongly alfected.," We have also not investigated in this paper the effect of environment on the distribution of the number of halos at fixed mass (e.g., Kravtsov 2004) which may be strongly affected." Lt is also not clear how relevant and. how strong the ellects that we have seen here with dark matter simulations are on the galaxies that form within the subhalos., It is also not clear how relevant and how strong the effects that we have seen here with dark matter simulations are on the galaxies that form within the subhalos. One can clearly enumerate many possible environmental effects that rely on barvonie physies (e.g.. luminosities of backsplash ealaxies. Pimbblet 2011. etc..).," One can clearly enumerate many possible environmental effects that rely on baryonic physics (e.g., luminosities of backsplash galaxies, Pimbblet 2011, etc..)." which will further complicate the elfect of environment on the HOD. and which may even have the opposite sign.," which will further complicate the effect of environment on the HOD, and which may even have the opposite sign." The obvious example where the number of subhalos is used to define a set of objects are optical cluster catalogs., The obvious example where the number of subhalos is used to define a set of objects are optical cluster catalogs. The environmental dependence of halo occupation is likely responsible for a fraction of the scatter in the mass-richness relation noted in optical cluster finders (see c.g. Rozo 2011 for cillerent sources of scatter)., The environmental dependence of halo occupation is likely responsible for a fraction of the scatter in the mass-richness relation noted in optical cluster finders (see e.g. Rozo 2011 for different sources of scatter). The cause of the LOD enviromental effect is a complex issue., The cause of the HOD enviromental effect is a complex issue. Lt has been shown bv many authors that a wide range of variables are allected by halo environment such as concentation (c.g. Wang 2011)., It has been shown by many authors that a wide range of variables are affected by halo environment such as concentation (e.g. Wang 2011). internal halo properties such as substructure ancl shape are nearly all correlated (Jeeson-Daniel 2011. Skibba Alaceio 2011) and the mass function. of subhalos itself. correlates with halo concentration. formation time ete (Cao 2011).," internal halo properties such as substructure and shape are nearly all correlated (Jeeson-Daniel 2011, Skibba Maccio 2011) and the mass function of subhalos itself correlates with halo concentration, formation time etc (Gao 2011)." The relative importance of mergers and smooth accretion in building up the mass of halo (Wang 2011) is likely to plav à role in the enviromental. dependence of the HOD., The relative importance of mergers and smooth accretion in building up the mass of halo (Wang 2011) is likely to play a role in the enviromental dependence of the HOD. Fakhouri and. Ala (2010). have shown that mergers dominate halo growth in overdense regions and dilfuse accretion in voids., Fakhouri and Ma (2010) have shown that mergers dominate halo growth in overdense regions and diffuse accretion in voids. LW they survive the merger and accretion process we therefore expect subhalos to be more numerous in overdense regions (for halos of à given mass). as we have found (see also Wetzel 2007).," If they survive the merger and accretion process we therefore expect subhalos to be more numerous in overdense regions (for halos of a given mass), as we have found (see also Wetzel 2007)." The destruction of subhalos over time by intrahalo merging and stripping will make this relationship even more dilfeult to decipher., The destruction of subhalos over time by intrahalo merging and stripping will make this relationship even more diffcult to decipher. Incorporating environmental dependences into the halo model. making it more complex. but able to deal. with phenomena such as those that have been demonstrated here is one avenue which can be pursued.," Incorporating environmental dependences into the halo model, making it more complex, but able to deal with phenomena such as those that have been demonstrated here is one avenue which can be pursued." Recenthy. Gil-Marin (2011) have presented some first steps in this direction.," Recently, Gil-Marin (2011) have presented some first steps in this direction." Another source. of potential uncertainty in. the xedietions of the halo model is the definition of halo mass., Another source of potential uncertainty in the predictions of the halo model is the definition of halo mass. More (2011) have shown that the mass of a FOE halo ina simulation depends on resolution., More (2011) have shown that the mass of a FOF halo in a simulation depends on resolution. More state that he influence of substructures (which depend on redshift and cosmology) on the FOF halo boundary. will male it düllieult o model this elfect in general.," More state that the influence of substructures (which depend on redshift and cosmology) on the FOF halo boundary, will make it difficult to model this effect in general." In our work. the relationship tween. the number of substructures ancl environment. is ikely also inlluenced by the ellect that substructures have on the mass celinition.," In our work, the relationship between the number of substructures and environment is likely also influenced by the effect that substructures have on the mass definition." Direct computation of the dependence of the correlation unction of halos for cillerent occupations shows more of the complex. relationship between halo properties. and clustering., Direct computation of the dependence of the correlation function of halos for different occupations shows more of the complex relationship between halo properties and clustering. Phe bias of halos of the same mass can vary widely depending on their occupation., The bias of halos of the same mass can vary widely depending on their occupation. For example (from Figure 10)). the lowest 25% of halos by occupation at fixec mass can have a bias which is 25% lower than that for al halos.," For example (from Figure \ref{bias2}) ), the lowest $25\%$ of halos by occupation at fixed mass can have a bias which is $25 \%$ lower than that for all halos." This is similar to the elfect seen by CWO? based on substructure fraction within the FOR group (although no within 72505) and appears to be a stronger trend than tha based on other properties at fixed mass. such as formation redshift (C605). concentration (WOG) or spin (CN07).," This is similar to the effect seen by GW07 based on substructure fraction within the FOF group (although not within $r_{200}$ ) and appears to be a stronger trend than that based on other properties at fixed mass, such as formation redshift (GW05), concentration (W06) or spin (GW07)." In this paper we have [focused on the clustering of halos of galaxy mass. and also only looked at z=1.," In this paper we have focused on the clustering of halos of galaxy mass, and also only looked at $z=1$." Further work is needed to explore the relationship between clustering and halo occupation in cluster size halos and those at lower redshift., Further work is needed to explore the relationship between clustering and halo occupation in cluster size halos and those at lower redshift. H£ the same relationships hold. then this could have interesting consequences for the clustering of galaxy clusters selected in optical surveys.," If the same relationships hold, then this could have interesting consequences for the clustering of galaxy clusters selected in optical surveys." One could make measurements of the dependence of galaxy. cluster bias on mass (measured using velocity dispersion or lensing mass) and richness. equivalent to halo occupation.," One could make measurements of the dependence of galaxy cluster bias on mass (measured using velocity dispersion or lensing mass) and richness, equivalent to halo occupation." Mapping out he bivariate distribution of bias values as in Figure 7 would eive further clues to the nature of galaxy formation in groups and clusters and how much it is allected by the non-barvonic orocesses investigated here., Mapping out the bivariate distribution of bias values as in Figure \ref{biasgrid} would give further clues to the nature of galaxy formation in groups and clusters and how much it is affected by the non-baryonic processes investigated here. Our final perhaps suprising finding is that one can easily select samples of halos (bv picking a fixed occupation) or which there is either no dependence of clustering on mass or even a strong anticorrelation between the two., Our final perhaps suprising finding is that one can easily select samples of halos (by picking a fixed occupation) for which there is either no dependence of clustering on mass or even a strong anticorrelation between the two. This inding is one which could also be tested with observational data on both mass and occupation., This finding is one which could also be tested with observational data on both mass and occupation. It again points to the complexity of halo clustering ancl the dilliculties of using galaxy clustering measurements for precision cosmology., It again points to the complexity of halo clustering and the difficulties of using galaxy clustering measurements for precision cosmology. This work was supported hy NSE Aware OCLO749212 and he Moore Foundation., This work was supported by NSF Award OCI-0749212 and the Moore Foundation. The rescarch was supported by allocation of advanced computing resources provided by the tional Science. Foundation., The research was supported by allocation of advanced computing resources provided by the National Science Foundation. Simulations were performed on WKraken at the National Institute. for Computational Sciences (httpiAwww.nies.tennessee.edu) and. analysis on acilities provided. by the Moore. Foundation. in the AleWilliams Center. for Cosmology at. Carnegie Mellon University., Simulations were performed on Kraken at the National Institute for Computational Sciences (http://www.nics.tennessee.edu) and analysis on facilities provided by the Moore Foundation in the McWilliams Center for Cosmology at Carnegie Mellon University. RACC would like to thank Michael Busha. veal Dalal. Alexie Leauthaud. Jeremy Tinker. David Weinberg and Andrew Zentner for useful discussions.," RACC would like to thank Michael Busha, Neal Dalal, Alexie Leauthaud, Jeremy Tinker, David Weinberg and Andrew Zentner for useful discussions." We also thank Andrew Zenter lor suggesting changes which were incorporated into the manuscript., We also thank Andrew Zenter for suggesting changes which were incorporated into the manuscript. reffig:r.. which includes both -lght and heavy winds (with zl. to be discussed below).,", which includes both “light” and “heavy” winds (with $\mu \gsim 1$, to be discussed below)." In reffig:[S.. we plot the poloidal flow speed oy at a spherical radius of 107AU. for three representative field lines (enclosing respectively 25. 50. and of the total mass fIux) for a niunber of mi.," In \\ref{fig:f8}, we plot the poloidal flow speed $v_\infty$ at a spherical radius of $10^2\AU$ for three representative field lines (enclosing respectively 25, 50, and of the total mass flux) for a number of ${\dot m}_0$." " The data points follow a power law distribution exry"".Ve with o,z1/3."," The data points follow a power law distribution $v_\infty\propto {\dot m}_0^{-\alpha_v}$, with $\alpha_v\approx 1/3$." At the low ting end. there is a slight deviation from power-law: this is most likely due to the fact that the fast surface approaches the outer edee of the simulation box. which leaves little room for the wind to accelerate bevoud the last surface to a terminal speed.," At the low ${\dot m}_0$ end, there is a slight deviation from power-law; this is most likely due to the fact that the fast surface approaches the outer edge of the simulation box, which leaves little room for the wind to accelerate beyond the fast surface to a terminal speed." There is also a deviation present al large values of iiy where the slope of the power appears to become nore shallow., There is also a deviation present at large values of ${\dot m}_0$ where the slope of the power appears to become more shallow. We note that the index of the power law distribution of terminal speed with respect to the mass loading is close to 1/3. as in the simplest case of radial wind geometry (see [2]]).," We note that the index of the power law distribution of terminal speed with respect to the mass loading is close to 1/3, as in the simplest case of radial wind geometry (see ])." The agreement is all the more remarkable considering the fact that the ast point is no longer at infinity because of wind collimation. and that there is substantial increase in [low speed bevond the fast point. bv a factor up to V3 for light winds.," The agreement is all the more remarkable considering the fact that the fast point is no longer at infinity because of wind collimation, and that there is substantial increase in flow speed beyond the fast point, by a factor up to $\sqrt{3}$ for light winds." To be nore quantitative. we note that al large distances from the launching region. the asymptotic speed along anv field line can be written in a form The relation is obtained from the definition of the fast Mach number. the conservation of mass-to-[Iux. ratio [7]]). and the flux freezing condition [3]]).," To be more quantitative, we note that at large distances from the launching region, the asymptotic speed along any field line can be written in a form The relation is obtained from the definition of the fast Mach number, the conservation of mass-to-flux ratio ]), and the flux freezing condition ])." It is a eeneralizalion of ((2)) to an arbitrary. poloidal field geometry., It is a generalization of \ref{terminal}) ) to an arbitrary poloidal field geometry. " In. the radial field limit.−− where λες= Land DB,z? ⋅↽≻−is constant along a field∙ line.⋅ we have ex&L7⋅≀⋡↽qi1 E. recovering (he scaling in ((2)."," In the radial field limit, where $M_{f,\infty}=1$ and $B_p\varpi^2$ is constant along a field line, we have $v_\infty\propto \kappa^{-1/3} \propto \mu^{-1/3}$ , recovering the scaling in (2)." When the flow collimation is taken into account. neither Ap.=l nor constant Bix holds along a field line.," When the flow collimation is taken into account, neither $M_{f,\infty}=1$ nor constant $B_p\varpi^2$ holds along a field line." The fact that the scaling VyCXMy21/3xp4 still. holds approximately. implies. that the combination. (MP4Bz)5.x varies little with mass loading., The fact that the scaling $v_\infty\propto{\dot m}_0^{-1/3}\propto \mu^{-1/3}$ still holds approximately implies that the combination $(M_f^2 B_p\varpi^2)_\infty$ varies little with mass loading. Apparently. the reduction of the (geometric) quantity B27 due to the field collimation is more or less offset bv the continued conversion of magnetic to kinelic energy bevond the fast point. which increases the Mach number Mj.," Apparently, the reduction of the (geometric) quantity $B_p\varpi^2$ due to the field collimation is more or less offset by the continued conversion of magnetic to kinetic energy beyond the fast point, which increases the Mach number $M_f$." Above some mass load. the wind solution remains perpetually unsteady.," Above some mass load, the wind solution remains perpetually unsteady." The inability to reach steady. state beeins around n=300. when ripples of small amplitude start (o propagate along some field lines from near the launching surface to large distances.," The inability to reach steady state begins around ${\dot m}_0=300$, when ripples of small amplitude start to propagate along some field lines from near the launching surface to large distances." As the mass loading increases. (he amplitude ofthe field line oscillation grows.," As the mass loading increases, the amplitude ofthe field line oscillation grows." In the upper panel, In the upper panel One advantage of our approach compared with muuerical simulations or fitting formulas is that it allows us to deconipose the integrated weak-lensing signal over several contributions that are associated with specific properties ofthe underlving 3D deusity field.,One advantage of our approach compared with numerical simulations or fitting formulas is that it allows us to decompose the integrated weak-lensing signal over several contributions that are associated with specific properties of the underlying 3D density field. Thus. we cau distinguish perturbative terms. which can be derived from perturbation theory. from nonperturbative terms that are associated for mstauce with oue-halo contributions. which depend on the density profile aud mass function of virialized halos.," Thus, we can distinguish perturbative terms, which can be derived from perturbation theory, from nonperturbative terms that are associated for instance with one-halo contributions, which depend on the density profile and mass function of virialized halos." This is useful because 1) these ciffereut torus suffer from different theoretical uncertainties aud ii) it allows one to understand which aspects of the matter distribution are probed by weak-leusiug statistics. while aneular scales vary.," This is useful because i) these different terms suffer from different theoretical uncertainties and ii) it allows one to understand which aspects of the matter distribution are probed by weak-lensing statistics, while angular scales vary." Like for the Fourier-space statistics stiucdice Ἡι paper I and the 3D statistics studied in 77.. we found that including one-loop ternis in the perturbative coutributiou Ines a niore siegnificaut daprovement compared with the owest-order perturbation theory for three-point statistics han for two-point statistics.," Like for the Fourier-space statistics studied in paper I and the 3D statistics studied in \citet{Valageas2011d,Valageas2011e}, we found that including one-loop terms in the perturbative contribution brings a more significant improvement compared with the lowest-order perturbation theory for three-point statistics than for two-point statistics." Then. while large scales are described by these perturbative contributions aud small scales by onc-halo coutrbutious. the nouperturbative ialo term that eives an additional contribution to threc-volt statistics is alwavs subdominant.," Then, while large scales are described by these perturbative contributions and small scales by one-halo contributions, the nonperturbative two-halo term that gives an additional contribution to three-point statistics is always subdominant." This is a nice xopertv because this mixed term is more difficult to uodel aud may be less accurate than other coutributious (see also paper I)., This is a nice property because this mixed term is more difficult to model and may be less accurate than other contributions (see also paper I). Consequently. our model provides reliable. predictious or weak-leusing statistics. from simall to large scales. aud or a variety of cosimologics.," Consequently, our model provides reliable predictions for weak-lensing statistics, from small to large scales, and for a variety of cosmologies." It could still be iuproved iu various manners., It could still be improved in various manners. First. the accuracy of the perturbative contribution may be imcreased by includiug higher orders sevoud one-loop or Vv usinge alternative restuuimation schemes.," First, the accuracy of the perturbative contribution may be increased by including higher orders beyond one-loop or by using alternative resummation schemes." Secoud. the nuderlving halo model could be refined to include substructures (?77).. deviations from spherical profiles (?7).. or the effect of barvous (7).," Second, the underlying halo model could be refined to include substructures \citep{Sheth2003a,Giocoli2010}, deviations from spherical profiles \citep{Jing2002,Smith2006}, or the effect of baryons \citep{Guillet2010}." Next. the model could be generalized to non-Gaussian initial coucitious. which vield distiuctive signatures in the bispectrum (?)..," Next, the model could be generalized to non-Gaussian initial conditions, which yield distinctive signatures in the bispectrum \citep{Sefusatti2010}." We would like to thank Takashi Hamana for helpful cliseussions., We would like to thank Takashi Hamana for helpful discussions. ALS. ancl T.N. are supported voa Crant-in-Aid for the Japan Society for Promotion of Science (JSPS) fellows., M.S. and T.N. are supported by a Grant-in-Aid for the Japan Society for Promotion of Science (JSPS) fellows. " “Phis work is supported in part by the French “Programme National de Cosmologic ct Galaxies"" ane the French-Japanese “Programme IHubert. Curien/Sakura. projet 2512TTL. the ISPS Core-to-Core Program |International Research Network for Dark Lnerey”. a Cuant-in-Aic Lor Scientific Research on Priority Areas No."," This work is supported in part by the French “Programme National de Cosmologie et Galaxies” and the French-Japanese “Programme Hubert Curien/Sakura, projet 25727TL”, the JSPS Core-to-Core Program “International Research Network for Dark Energy”, a Grant-in-Aid for Scientific Research on Priority Areas No." 467 “Probing the Dark Energy. through an Extremely Wide.( and Deep Survey with Subaru Telescope”. a Crant-in-Aicl for Nagoya," 467 “Probing the Dark Energy through an Extremely Wide and Deep Survey with Subaru Telescope”, a Grant-in-Aid for Nagoya" and positions reported in the LAU cireulars (Table 1)).,and positions reported in the IAU circulars (Table \ref{96P}) ). Sekanina(19908) notecl a major outburst several weeks after perihelion and suggested that (he comet remained undiscovered in spite of its short period because it is inactive lor much of the time., \citet{S90a} noted a major outburst several weeks after perihelion and suggested that the comet remained undiscovered in spite of its short period because it is inactive for much of the time. Its small perihelion (0.12 AU) leads to a high erosion rate (Sekanina1990b).. so it may have a mostly dormant iceless surface.," Its small perihelion (0.12 AU) leads to a high erosion rate \citep{S90b}, so it may have a mostly dormant iceless surface." Comet 96P was again reported to the LAU on its next apparition in 1991. reported at about 3 AU from the Sun in 1997. and observed by SOIIO on three occasions (Meechetal.1997:Lisse.Fernandez.&Biesecker2002:Grvnko. 2004).," Comet 96P was again reported to the IAU on its next apparition in 1991, reported at about 3 AU from the Sun in 1997, and observed by SOHO on three occasions \citep{M+97,L+02,G+04}." 96P is dvnamically interesting., 96P is dynamically interesting. It 15 the shortest-period Halley family comet. known., It is the shortest-period Halley family comet known. Greenοἱal.(1990). noted that 96P. (then known as comet 1986VIID) travels closer to ihe Sun than all other known comets with orbital periods less (han 150 vears., \citet{G+90} noted that 96P (then known as comet 1986VIII) travels closer to the Sun than all other known comets with orbital periods less than 150 years. It is in a 9/1 resonance with Jupiter. and their orbit evolution calculations show that its perihelion is steaclily decreasing to a minimum of 0.03 AU in about the vear 2450.," It is in a 9/4 resonance with Jupiter, and their orbit evolution calculations show that its perihelion is steadily decreasing to a minimum of 0.03 AU in about the year 2450." 96P has also been suggested as the parent body lor several meteor streams (Sekanina1990a;:McIntosh.1990:Dabadzhanov&Obrubov 1993).," 96P has also been suggested as the parent body for several meteor streams \citep{S90a,M90,BO93}." All other references to 9GP discuss its meteor stream connection (Jenniskensetal.1997:Williams&Collander-Brown1993).. aud (he possibility (hat some sunskirting comets are Iragments of it that were thrust onto their current parabolic orbits after encounters with Jupiter (Ohtsuka.Nakano.&Yoshikawa|Chodas 2005).," All other references to 96P discuss its meteor stream connection \citep{J+97,WC98}, and the possibility that some sunskirting comets are fragments of it that were thrust onto their current parabolic orbits after encounters with Jupiter \citep{OY03,SC05}." . Comet 96P/Machholz was observed post-perihelion on 2007 April 27 UT with the Ixast Spectrometer at the Lick Observatory 2-m Shane telescope., Comet 96P/Machholz was observed post-perihelion on 2007 April 27 UT with the Kast Spectrometer at the Lick Observatory 3-m Shane telescope. The blue side was used with a 1.5x128 aresec slit and a 452/3306 erism giving a dispersion of 2.49 A//pixel., The blue side was used with a $\times$ 128 arcsec slit and a 452/3306 grism giving a dispersion of 2.49 /pixel. A Reticon CCD recorded the 2-D spectra (1199 pixels along (he dispersion direction ancl 164 pixels along the slit al a scale of 0.78 arcsec/pixel)., A Reticon CCD recorded the 2-D spectra (1199 pixels along the dispersion direction and 164 pixels along the slit at a scale of 0.78 arcsec/pixel). The comets orbital parameters ancl observational circumstances are given in Table 1.., The comet's orbital parameters and observational circumstances are given in Table \ref{96P}. The data reduction used standard techniques and custom LDL routines., The data reduction used standard techniques and custom IDL routines. In IRAF. the spectra were trimmed to encompass the length of the slit. flat-field corrected. median liltered (o remove cosmic rays. and wavelength. calibrated using IHellgCd. lamp reference speclra.," In IRAF, the spectra were trimmed to encompass the length of the slit, flat-field corrected, median filtered to remove cosmic rays, and wavelength calibrated using HeHgCd lamp reference spectra." Because 96P rose shortly before morning astronomical twilight. there was time lor one," Because 96P rose shortly before morning astronomical twilight, there was time for one" offers the unique opportunity to study both the PNe and the region populations with the same setup. during the same night. and adopting the same analysis techniques. thus avoiding most biases that commonly affect the comparison of chemical abundances in population of different ages (e.g. Fe/H from old RGB stars is difficult to compare with O/H from the present time regions).,"offers the unique opportunity to study both the PNe and the region populations with the same setup, during the same night, and adopting the same analysis techniques, thus avoiding most biases that commonly affect the comparison of chemical abundances in population of different ages (e.g. Fe/H from old RGB stars is difficult to compare with O/H from the present time regions)." We present here the results from the study of a sample of bright PNe in M81. with the goal of obtaining the metallicity and explore their gradients within the M81 disk.," We present here the results from the study of a sample of bright PNe in M81, with the goal of obtaining the metallicity and explore their gradients within the M81 disk." Their properties as a group are discussed. and compared with those of regions from both our MMT observations and from the literature.," Their properties as a group are discussed, and compared with those of regions from both our MMT observations and from the literature." The combined properties of M81 Pe and regions are also compared with their homologs in other nearby galaxies and in the Milky Way., The combined properties of M81 PNe and regions are also compared with their homologs in other nearby galaxies and in the Milky Way. In $2 we describe the observation and analysis techniques. and give the measured fluxes and calculated abundances.," In $\S$ 2 we describe the observation and analysis techniques, and give the measured fluxes and calculated abundances." $3 includes the analysis of the derived abundances and the determination of the metallicity gradients. $+ presents the discussion of our results. and the conclusions are in ὅδ.," $\S$ 3 includes the analysis of the derived abundances and the determination of the metallicity gradients, $\S$ 4 presents the discussion of our results, and the conclusions are in $\S$ 5." We obtained the spectra of PNe and regions in M81 with the MMT Hectospec fiber-fed spectrograph (Fabricant et al., We obtained the spectra of PNe and regions in M81 with the MMT Hectospec fiber-fed spectrograph (Fabricant et al. 2005)., 2005). The spectrograph was equipped with an Atmospheric Dispersion Corrector and it was used with a single setup: 270 mm.' erating at a dispersion of 1.2 pixel., The spectrograph was equipped with an Atmospheric Dispersion Corrector and it was used with a single setup: 270 $^{-1}$ grating at a dispersion of 1.2 $^{-1}$. The resulting total spectral coverage ranged from approximately 3600 tto 9100A.. thus including the basic emission-lines necessary for the determination of physical and chemical properties.," The resulting total spectral coverage ranged from approximately 3600 to 9100, thus including the basic emission-lines necessary for the determination of physical and chemical properties." The PNe were selected among those observed with the INT through withπη..He.. and Stromgren Y filters (Magrini et al.," The PNe were selected among those observed with the INT through with, and Stromgren Y filters (Magrini et al." 2001). which allowed us to cover the whole field of M81. and to identify a large number of disk PNe at large galactocentric distances.," 2001), which allowed us to cover the whole field of M81, and to identify a large number of disk PNe at large galactocentric distances." An earlier survey by Jacoby et al. (, An earlier survey by Jacoby et al. ( 1989) was limited to the M81 bulge.,1989) was limited to the M81 bulge. It is worth noting that the INT images allow us to have accurate positions (0.5)) and finding charts for the selected PNe and rregions. a crucial information given the crowding of the inner and spiral arm fields of M81.," It is worth noting that the INT images allow us to have accurate positions $<$ ) and finding charts for the selected PNe and regions, a crucial information given the crowding of the inner and spiral arm fields of M81." The first target selection was performed by scaling the PN brightness in with those of M33 PNe. whose medium-resolution spectra have been observed by us using the identical technique (Magrini et al..," The first target selection was performed by scaling the PN brightness in with those of M33 PNe, whose medium-resolution spectra have been observed by us using the identical technique (Magrini et al.," 2009. 2010. hereafter M09. M10).," 2009, 2010, hereafter M09, M10)." We also endeavored to have PN targets at several galactocentric distances. in order to characterize the PN metallicity gradient.," We also endeavored to have PN targets at several galactocentric distances, in order to characterize the PN metallicity gradient." The instrument deploys 300 fibers over a 1 degree diameter field of view and the fiber diameter is~.., The instrument deploys 300 fibers over a 1 degree diameter field of view and the fiber diameter $\sim$. The projected size of M81 on the sky is smaller than the whole field of view of MTT/Hectospec. and we took advantage of this by placing some of the fibers in the outermost periphery of M81. where some regions and few PNe. both belonging to the outer disk and to the intra-group population. have been identified.," The projected size of M81 on the sky is smaller than the whole field of view of MTT/Hectospec, and we took advantage of this by placing some of the fibers in the outermost periphery of M81, where some regions and few PNe, both belonging to the outer disk and to the intra-group population, have been identified." In addition. since the available catalog of regions by Lin et al. (," In addition, since the available catalog of regions by Lin et al. (" 2003) is based on photometry. our INT observations have been useful to select m--bright regions essential for chemical abundance determination.,"2003) is based on photometry, our INT observations have been useful to select -bright regions essential for chemical abundance determination." As stated by Magrini et al. (, As stated by Magrini et al. ( 2001). we expect the misclassification of rregions into PNe and vice-versa to be lower than~3% of the whole sample.,"2001), we expect the misclassification of regions into PNe and vice-versa to be lower $\sim$ $\%$ of the whole sample." The observations were carried out in queue mode in four runs during the months of November and December 2008., The observations were carried out in queue mode in four runs during the months of November and December 2008. Each of the observing runs consisted of 3 to 5 exposures of 1800s each. for a total of 16 exposures (or 8 hours of observation).," Each of the observing runs consisted of 3 to 5 exposures of 1800s each, for a total of 16 exposures (or 8 hours of observation)." We used the same fiber setup during all observing runs. and thus PNe and HII regions were observed within the same conditions. including the same exposure time.," We used the same fiber setup during all observing runs, and thus PNe and HII regions were observed within the same conditions, including the same exposure time." Priority was given to PNe when placing the fibers. since a set of region spectra already exists in the literature (GS87).," Priority was given to PNe when placing the fibers, since a set of region spectra already exists in the literature (GS87)." A large number of fibers were devoted to sky measurements. to ensure that sky spectra were obtained in several positions around each target.," A large number of fibers were devoted to sky measurements, to ensure that sky spectra were obtained in several positions around each target." Cosmic rays were removed with the appropriate routine in the hectospee analysis package., Cosmic rays were removed with the appropriate routine in the hectospec analysis package. Cosmic rays are detected via subtraction of multiple images. flagging the high or low pixels.," Cosmic rays are detected via subtraction of multiple images, flagging the high or low pixels." The flagged pixels are interpolated over. and the resultant images are combined by average.," The flagged pixels are interpolated over, and the resultant images are combined by average." This method avoids problems with clipping that other programs suffer from., This method avoids problems with clipping that other programs suffer from. In order to perform the sky subtraction we first inspected the sky spectra and eliminated those with unusual signals., In order to perform the sky subtraction we first inspected the sky spectra and eliminated those with unusual signals. Then we averaged the six spectra closer (in fiber location) to the targets. scaled the result to match the object spectrum. and subtracted.," Then we averaged the six spectra closer (in fiber location) to the targets, scaled the result to match the object spectrum, and subtracted." The spectral calibration was achieved with the standard star Hilt600 (Massey et al. 1988)).," The spectral calibration was achieved with the standard star Hilt600 (Massey et al. \cite{massey88}) )," observed during the first night., observed during the first night. This star was chosen by its excellent spectral coverage compared to the spectra of the PNe., This star was chosen by its excellent spectral coverage compared to the spectra of the PNe. It is worth noting that our analysis does not hinge on flux calibration. rather spectral calibration and flux ratios. thus this approach ts sufficient to the science goals.," It is worth noting that our analysis does not hinge on flux calibration, rather spectral calibration and flux ratios, thus this approach is sufficient to the science goals." Other stars were observed during the run nights. but the excellent spectral coverage of Hilt600 makes it the ideal choice for this type of calibration.," Other stars were observed during the run nights, but the excellent spectral coverage of Hilt600 makes it the ideal choice for this type of calibration." Variations in sky conditions are taken into account since sky subtractior was performec before flux calibration., Variations in sky conditions are taken into account since sky subtraction was performed before flux calibration. In Table 1 we give the IDs. equatorial coordinates. anc equivalent magnitude of the planetary nebulae and regions observed with MMT medium-resolutior spectroscopy.," In Table 1 we give the IDs, equatorial coordinates, and equivalent magnitude of the planetary nebulae and regions observed with MMT medium-resolution spectroscopy." ΔΗ PN IDs are from Magrini et al. (, All PN IDs are from Magrini et al. ( 2001). except for PN4 and PNS. which are identified PNe with unpublishec positions (Magrini. private communication).,"2001), except for PN4 and PN5, which are identified PNe with unpublished positions (Magrini, private communication)." There are 39 PNe and 20 regions whose spectra have been acquired anc analyzed., There are 39 PNe and 20 regions whose spectra have been acquired and analyzed. With the exception of PN 49m and PN 79m. whose spectral lines are below the detection limit. we detect at least the major spectral lines in each target.," With the exception of PN 49m and PN 79m, whose spectral lines are below the detection limit, we detect at least the major spectral lines in each target." In Table 2. available online in its completeness. we give for each target the ion and wavelength (columns | and 2) of the observed emission line. then the relative observed flux (column 3). its uncertainty (column 4). and the line intensity (column 5) obtained with the extinction correction giver as a header for each target.," In Table 2, available online in its completeness, we give for each target the ion and wavelength (columns 1 and 2) of the observed emission line, then the relative observed flux (column 3), its uncertainty (column 4), and the line intensity (column 5) obtained with the extinction correction given as a header for each target." All fluxes and intensities are normalized for, All fluxes and intensities are normalized for Supersolt sources are a separate class of X-ray objects.,Supersoft sources are a separate class of X-ray objects. The most popular explanation of these sources is à white dwarf sub-giant companion with a high accretion rate. 10000 times greater than in cataclvsmic variables (van den Heuvel et 11992).," The most popular explanation of these sources is a white dwarf sub-giant companion with a high accretion rate, 000 times greater than in cataclysmic variables (van den Heuvel et 1992)." The large accretion rate creates steacv hvdrogen burning on the white cdwarl surface causing X-ray emission., The large accretion rate creates steady hydrogen burning on the white dwarf surface causing X-ray emission. Supersoft sources are dillicult to detect in the Galaxy as the high. column density in the Galactic plane absorbs most of the soft. X-ray radiation., Supersoft sources are difficult to detect in the Galaxy as the high column density in the Galactic plane absorbs most of the soft X-ray radiation. Consequently there have been many more detections at high ealactic latitudes such as in the LAIC. SAIC and M31.," Consequently there have been many more detections at high galactic latitudes such as in the LMC, SMC and M31." As of 1999 (Greiner 2000). here were 57 supersoft sources: 10 in the Galaxy. 4 in the SAIC. 8 in the LMC and 34 in M31. and. 1: in. Νέας 50.," As of 1999 (Greiner 2000), there were 57 supersoft sources: 10 in the Galaxy, 4 in the SMC, 8 in the LMC and 34 in M31 and 1 in NGC 55." Consequently. even though sources in the LMC and SAIC are urther away. they have been studied in greater detail due to heir larger numbers.," Consequently, even though sources in the LMC and SMC are further away, they have been studied in greater detail due to their larger numbers." For example. in LOOT Fender. Southwell Tziowumis (1998) searched. for radio emission fron non-Galactic supersoft sources despite them being prohibitively urther away than their Galactic counterparts.," For example, in 1997 Fender, Southwell Tzioumis (1998) searched for radio emission from non-Galactic supersoft sources despite them being prohibitively further away than their Galactic counterparts." Of the persistent. super-soft: sources. three have been reported to have outHows. detected by emission lines in their optical and. infrared. spectra.," Of the persistent super-soft sources, three have been reported to have outflows, detected by emission lines in their optical and infrared spectra." What is the makeup of these sources. and are they the link between the low velocity jets seen in star-forming systems. ancl the superluminal jets seen in the microquasars?," What is the makeup of these sources, and are they the link between the low velocity jets seen in star-forming systems, and the superluminal jets seen in the microquasars?" n which are intimately MM to low-2 DLAs ond)Rao&Turnshek2000:etal.,", which are intimately related to $z$ DLAs \citep{ChurchillC_00b,RaoS_00a,RaoS_06a}." 2006).. that the host locus GU) and aare anti-correlated., \citet{BoucheN_06c} found that the host halo-mass $M_h$ ) and are anti-correlated. " For virialized clouds. the host mass and the line-of-sight velocity dispersion ought to be correlated. i.e. a AM,— ccorrelationnH icis expected because: iis a measure of the line-of-sight velocity width (Ae) as individual aabsorptions are saturated (Ellison2006).."," For virialized clouds, the host mass and the line-of-sight velocity dispersion ought to be correlated, i.e. a $M_h$ correlation is expected because is a measure of the line-of-sight velocity width $\Delta v$ ) as individual absorptions are saturated \citep{EllisonS_06a}." Thus. the results of Bouchéetal.(2006). imply that cclouds are not virialized in the host halos. and super-novae driven outflows provide a natural mechanism.," Thus, the results of \citet{BoucheN_06c} imply that clouds are not virialized in the host halos, and super-novae driven outflows provide a natural mechanism." While the rresults have been. confirmed by an independent team (Allen. Hewett RRyan-Weber 2008. in prep.).," While the results have been confirmed by an independent team (Allen, Hewett Ryan-Weber 2008, in prep.)," ad-hoe models have been proposed to explain the anti-correlation in a cosmological context (e.g.Tin-ker&Chen20, ad-hoc models have been proposed to explain the anti-correlation in a cosmological context \citep[e.g.][]{TinkerJ_08a}. 08) Since one would expect a mass—metallicity correlation for all galaxies. aanti-correlation. of Bouchéetal.(2006) implies a aanti-correlation. or equivalently a metallicity-velocity width anti-correlation.," Since one would expect a mass–metallicity correlation for all galaxies, the anti-correlation of \citet{BoucheN_06a} implies a anti-correlation, or equivalently a metallicity-velocity width anti-correlation." However. several groups have reported just the opposite: the metallicity in DLAs correlates either w M velocity width Ar (Wolfe&Prochaska1998:Pérouxetal.vire2003:Ledouxetal.2006:Prochaska2008) or with the citepMeiringJu6ea.Aliph yAluta.," However, several groups have reported just the opposite: the metallicity in DLAs correlates either with the velocity width $\Delta v$ \citep{WolfeA_98a,PerouxC_03b,LedouxC_06a,ProchaskaJ_08a} or with the \\citep{MeiringJ_06a,MurphyM_07a}." .dlistemplingloassimet hal Ac is a measure of the line-of-sight velocity dispersion. ie. that it correlates with the mass of the host-galaxy. since when combined with the above results. one would naturally imply a normal mass-metallieity relation.," It is tempting to assume that $\Delta v$ is a measure of the line-of-sight velocity dispersion, i.e. that it correlates with the mass of the host-galaxy, since when combined with the above results, one would naturally imply a normal mass-metallicity relation." " Thus. there appears to be a conflict between the A/),-1 aanti-correlation of Bouchéetal.(2006) and the ccorrelations reported in the literature."," Thus, there appears to be a conflict between the $M_h$ anti-correlation of \citet{BoucheN_06c} and the correlations reported in the literature." In this paper. we show that the conflict is apparent and reflects the various selections at play vvs. ID) using ssystems from the literature.," In this paper, we show that the conflict is apparent and reflects the various selections at play vs. ) using systems from the literature." In section 2. we describe our sample where we collected neutral column density eequivalent widths and metallicities[X/H].," In section 2, we describe our sample where we collected neutral column density, equivalent widths and metallicities." . ΑΗSectionj..3 shows our results., Section3 shows our results. " We combined various samples of aabsorbers and DLAs from the literature. namely we used the MM of Raoetal. Ellison Kulkarni(2005).. n Curranetal."" (2007).. EMurphyet»al.s(2007) Ledouxetal.(200 augmented catalog of Ryinoxetal.(2003).."," We combined various samples of absorbers and DLAs from the literature, namely we used the samples of \citet{RaoS_06a}, \citet{EllisonS_06a}, \citet{KulkarniV_05a}, \citet{CurranS_07a}, \citet{MurphyM_07a} \citet{LedouxC_06a}, augmented by the catalog of \citet{RyabinkovA_03a}." The ccolumn come mostly from the STIS survey of Rao& for the low-redshift absorbers.," The column densities come mostly from the STIS survey of \citet{RaoS_00a,RaoS_06a} for the low-redshift absorbers." The entire catalog contains about 1200. absorbers. of which 377 have both aand mmeasured.," The entire catalog contains about 1200 absorbers, of which 377 have both and measured." ΑΗ We then match the literature samples with published metallicity measurements from Pérouxetal.(2003).. Péroux (20043. Pérouxetal. (2006).. Mólleretal. (2004)...006)... Kulkarnietal.2005)..MeiringLedoux etal.(2006).. 2006).. Prochaskaetal. (2006). etal.(2007)..," We then match the literature samples with published metallicity measurements from \citet{PerouxC_03a}, \citet{PerouxC_04a}, \citet{PerouxC_06a}, \citet{MollerP_04a}. , \citet{KulkarniV_05a}, \citet{LedouxC_06a}, \citet{EllisonS_06a}, \citet{ProchaskaJ_06a}, \citet{MeiringJ_06a}," Meiring2008). and Murphyetal.(2007).., \citet{MeiringJ_08a} and \citet{MurphyM_07a}. The final sample is made of 89 absorbers with knownj..noms and [X/H].," The final sample is made of 89 absorbers with known, and ." . We show the redshift distribution of the sub-samples in Fig. |.., We show the redshift distribution of the sub-samples in Fig. \ref{fig:redshift}. The solid histogram shows the literature sample of 1200 absorbers., The solid histogram shows the literature sample of 1200 absorbers. The thick histogram shows the 377 absorbers with aand j.. and the grey histogram shows the 89 absorbers withWel;Vpp aund [Zn/H].," The thick histogram shows the 377 absorbers with and , and the grey histogram shows the 89 absorbers with, and [Zn/H]." "Ng, In order to have homogeneous metallicity measurements. we impose that all metallicity measurements are from Zn."," In order to have homogeneous metallicity measurements, we impose that all metallicity measurements are from Zn." In order to probe for any redshift evolution. we will split the sample into low-2 (2« L.6) and high-z(> 1.6).," In order to probe for any redshift evolution, we will split the sample into $z$ $z<1.6$ ) and $z$$z>1.6$ )." Fig. 2((, Fig. \ref{fig:intro}( ( a) shows the distribution of absorbers in the pplane as in Raoetal.(2006)..,a) shows the distribution of absorbers in the plane as in \citet{RaoS_06a}. . Note that strong aabsorbers have indeed largerj.. and can be regarded as DLA-dominated. however the opposite is not true.," Note that strong absorbers have indeed larger, and can be regarded as DLA-dominated, however the opposite is not true." A DLA sample covers the entire range ofHi., A DLA sample covers the entire range of. " The large connected squares show the logarithmic mean $. The logarithmic mean is a better statistic to quantify the distribution of the points., The logarithmic mean is a better statistic to quantify the distribution of the points. " Raoetal.(2006) elected to use the meanΔΗ,2» statistics since they were interestedin the mean ccolumn density in order to constrain {2Η1.", \citet{RaoS_06a} elected to use the mean $<\NHI>$ statistics since they were interested in the mean column density in order to constrain $\Omega_{\HI}$. " The solid squares show that «logNHI increases with equivalent width. reflecting an increasing fraction of DLAs as a function of """," The solid squares show that $<\log \NHI>$ increases with equivalent width, reflecting an increasing fraction of DLAs as a function of ." In Fig. 2((, In Fig. \ref{fig:intro}( ( a).asnoted many times (e.g.Raoetal.2006:Ch- 2007).. there are no absorbers to the bottom right of the figure. i.e. with large aand low ccolumn densities.,"a),asnoted many times \citep[e.g.][]{RaoS_06a,CheloucheD_07a}, , there are no absorbers to the bottom right of the figure, i.e. with large and low column densities." The lack of objects in that part of the diagram is not due to selection effects: strong aabsorbers are easy to identify there., The lack of objects in that part of the diagram is not due to selection effects; strong absorbers are easy to identify there. to accumulate a wide data sample. I have retrieved from the ΝΕΤ archive all public spectra taken with the 300V. erism coupled with the order-sorting filter GG435 and a long slit «00 wide. which ts the most frequently used (676 frames).,"to accumulate a wide data sample, I have retrieved from the VLT archive all public spectra taken with the 300V grism coupled with the order-sorting filter GG435 and a long slit 0 wide, which is the most frequently used (676 frames)." The wavelength range was extended down to about in the blue by retrieving also all spectra taken with the same setup but with no order-sorting filter. for a total of 163 frames.," The wavelength range was extended down to about in the blue by retrieving also all spectra taken with the same setup but with no order-sorting filter, for a total of 163 frames." To increase the sample. I have retrieved. also all spectra obtained with the grisms 600B (143 frames) and 600R (207 frames) coupled with the order-sorting filters OG590 and GG435. respectively.," To increase the sample, I have retrieved also all spectra obtained with the grisms 600B (143 frames) and 600R (207 frames) coupled with the order-sorting filters OG590 and GG435, respectively." Also in these two cases the slit was 100 wide., Also in these two cases the slit was 0 wide. The main characteristics of each setup are summarized in Tab. 1.., The main characteristics of each setup are summarized in Tab. \ref{tab:spec}. Exposure times range from a few minutes to one hour., Exposure times range from a few minutes to one hour. 1.5mm All images were processed within the package ofIRAF!., 1.5mm All images were processed within the package of. . Due to the large amount of data and the purpose of this work. the bias subtraction was performed using only a pre-scan correction. while flat-fielding effects were neglected.," Due to the large amount of data and the purpose of this work, the bias subtraction was performed using only a pre-scan correction, while flat-fielding effects were neglected." Wavelength calibration was achieved using a 2D solution derived from a set of reference arc. exposures., Wavelength calibration was achieved using a 2D solution derived from a set of reference arc exposures. Given the procedure adopted for the spectrum extraction. this step is mandatory. since in FORSI the line curvature can reach a peak-to-peak value of about 10 px.," Given the procedure adopted for the spectrum extraction, this step is mandatory, since in FORS1 the line curvature can reach a peak-to-peak value of about 10 px." If not accounted for. this instrumental feature would produce an apparently significant but artificial line broadening when collapsing the 2D spectra perpendicularly to the dispersion direction (see next section).," If not accounted for, this instrumental feature would produce an apparently significant but artificial line broadening when collapsing the 2D spectra perpendicularly to the dispersion direction (see next section)." After applying the appropriate 2D wavelength solution to all frames. the night sky spectrum is extracted.," After applying the appropriate 2D wavelength solution to all frames, the night sky spectrum is extracted." For this purpose I have used a robust algorithm to estimate the mode intensity in each column perpendicular to the dispersion. direction., For this purpose I have used a robust algorithm to estimate the mode intensity in each column perpendicular to the dispersion direction. " This implicitly assumes that most of the pixels are not ""contaminated"" by the contribution of astrophysical objects. which ts reasonable in the majority of the cases. as verified by direct inspection of the whole two-dimensional data sample."," This implicitly assumes that most of the pixels are not “contaminated” by the contribution of astrophysical objects, which is reasonable in the majority of the cases, as verified by direct inspection of the whole two-dimensional data sample." This is both a consequence of the relatively large slit length featured by FORSI (6/88 on 2048 px) and the typical targets observed with this instrument. which are very often faint and star-like sources.," This is both a consequence of the relatively large slit length featured by FORS1 8 on 2048 px) and the typical targets observed with this instrument, which are very often faint and star-like sources." After visual inspection. only a few spectra were removed from the final data set.," After visual inspection, only a few spectra were removed from the final data set." To allow for completely unsupervised line and continuum flux measurements. the accuracy of wavelength calibration is à mandatory requirement.," To allow for completely unsupervised line and continuum flux measurements, the accuracy of wavelength calibration is a mandatory requirement." Possible causes of rigid shifts in the dispersion solution can be identified as instrument interventions. turning into movements of the long slit on the focal plane. and flexures at large zenith distances.," Possible causes of rigid shifts in the dispersion solution can be identified as instrument interventions, turning into movements of the long slit on the focal plane, and flexures at large zenith distances." To correct for these problems. I have produced a reference night sky spectrum for each of the two resolutions I have used. with a typical accuracy (estimated on isolated lines) better than |A.," To correct for these problems, I have produced a reference night sky spectrum for each of the two resolutions I have used, with a typical accuracy (estimated on isolated lines) better than 1." . Then. by means of cross-correlation. the zero point of the wavelength scale of each spectrum is automatically corrected at the end of the extraction procedure.," Then, by means of cross-correlation, the zero point of the wavelength scale of each spectrum is automatically corrected at the end of the extraction procedure." This ensures that. at this stage. all spectra have maximum wavelength errors that do not exceed1A.," This ensures that, at this stage, all spectra have maximum wavelength errors that do not exceed." For the absolute flux calibration I have used à set of spectrophotometric standard stars to derive a reference sensitivity function 56D. which I have applied to all spectra.," For the absolute flux calibration I have used a set of spectrophotometric standard stars to derive a reference sensitivity function $s(\lambda)$, which I have applied to all spectra." Even though this does not take into account the changes in sensitivity which are mainly due to the aging of reflective surfaces (Patat 2003a)). at the wavelengths of interest they are of the order of a few percent. and therefore can be safely neglected in this context.," Even though this does not take into account the changes in sensitivity which are mainly due to the aging of reflective surfaces (Patat \cite{paperI}) ), at the wavelengths of interest they are of the order of a few percent, and therefore can be safely neglected in this context." The flux calibration of the extracted spectrum 0) to physical units is finally computed as:, The flux calibration of the extracted spectrum $f(\lambda)$ to physical units is finally computed as: It is unclear to us why AIT so strongly denigrate our experiment and ils results.,It is unclear to us why MT so strongly denigrate our experiment and its results. Thev appear not to have noticed the limitations and caveats we did cdiseuss. some of which were added to our paper based on discussion with them.," They appear not to have noticed the limitations and caveats we did discuss, some of which were added to our paper based on discussion with them." We do state in our paper that we have proved the AD theory to be wrong., We do state in our paper that we have proved the AD theory to be wrong. " Our conelusion was that the results of our carefully planned experiment were not consistent with the ""idealized AD models. i.e.. those that assume an initially spherical cloud. with a unilorzm magnetic field."," Our conclusion was that the results of our carefully planned experiment were not consistent with the “idealized” AD models, i.e., those that assume an initially spherical cloud with a uniform magnetic field." MIT attack a conclusion that does not exist in our paper., MT attack a conclusion that does not exist in our paper. " All of the ""flaws"" discussed by MT are not flaws. but limitations in testing anv model that does not include all of the complexities of the real world."," All of the “flaws” discussed by MT are not flaws, but limitations in testing any model that does not include all of the complexities of the real world." Based on their discussion. it is unclear to us what observational test of the AD theory could be realistically carried out. that. could provide MT anvthing more than observational “inputs” to the AD theory.," Based on their discussion, it is unclear to us what observational test of the AD theory could be realistically carried out that could provide MT anything more than observational “inputs” to the AD theory." We stand fully behind our experiment and our paper., We stand fully behind our experiment and our paper. As ds evident from Fie. 5.,"As is evident from Fig. \ref{fig5}," the counts are best deteriuued in the 0.3 to 5 mJy fux range., the counts are best determined in the 0.3 to 5 mJy flux range. Tere the areas are laree enough to provide a significant sample., Here the areas are large enough to provide a significant sample. However. the statistical uucertaimties are still large with only 7 sources νο in this range.," However, the statistical uncertainties are still large with only 7 sources lying in this range." At 1l mw we find a cumulative count of 0.913«103 dee2. after correcting for the systematic upward bias. where the upper aud lower bounds are the confidence range.," At 1 mJy we find a cumulative count of $0.9_{0.5}^{1.4}\times 10^4$ $^{-2}$, after correcting for the systematic upward bias, where the upper and lower bounds are the confidence range." This is consistent with the BBlain et ((1999) measurement of (0.79+0.3)«101 deg?., This is consistent with the \markcite{blain99}B Blain et (1999) measurement of $(0.79\pm 0.3)\times 10^4$ $^{-2}$. " At (0,3 mJy the cumulative couuts have risen to 3.393«10! ?. where the upper aud lower bounds are again the confidence range."," At 0.3 mJy the cumulative counts have risen to $3.3_{1.3}^{6.3}\times 10^4$ $^{-2}$, where the upper and lower bounds are again the confidence range." The noise distributions of the uucleaned noise maps (.c.. the maps with the directly detected sources removed) contain additional independent information over the direct counts.," The noise distributions of the uncleaned noise maps (i.e., the maps with the directly detected sources removed) contain additional independent information over the direct counts." In principle. the noise distributions should provide a inore sensitive diagnostic of the counts at πι] Huxes than the direct counts because the useable areas are much larger than the areas over which 36. sources cau o detected.," In principle, the noise distributions should provide a more sensitive diagnostic of the counts at sub-mJy fluxes than the direct counts because the useable areas are much larger than the areas over which $3\sigma$ sources can be detected." Iu Fig., In Fig. 6 we show the distribution fuuctious (combined or all three cluster fields) from both the true noise aud he uucleaned noise maps., \ref{fig6} we show the distribution functions (combined for all three cluster fields) from both the true noise and the uncleaned noise maps. The true noise distribution Muction is well fit bv a smooth Caussian function. which is shown in the figure in place of the actual distribution function.," The true noise distribution function is well fit by a smooth Gaussian function, which is shown in the figure in place of the actual distribution function." " The uucleaned noise distribution ""unctiou (jagged curve) has extensions to the right aud left of the true noise distribution function.", The uncleaned noise distribution function (jagged curve) has extensions to the right and left of the true noise distribution function. The different shapes of these two extensions result from there being twice as any negative positions as positive positions im the beam wattern corresponding to cach source. but at half the fiux (because of the nod and fixed chop observiug procedure used}.," The different shapes of these two extensions result from there being twice as many negative positions as positive positions in the beam pattern corresponding to each source, but at half the flux (because of the nod and fixed chop observing procedure used)." For the present data a IKolinogorov-Suiürnov test (applied. to the absolute values of the distribution to combine the two tails of the distribution functiou) does not reject the hypothesis that the uncleaued noise distribution is drawn from the true noise distribution because there are a relatively small πάσα (approximately 210) of independent points in the fields., For the present data a Kolmogorov-Smirnov test (applied to the absolute values of the distribution to combine the two tails of the distribution function) does not reject the hypothesis that the uncleaned noise distribution is drawn from the true noise distribution because there are a relatively small number (approximately 240) of independent points in the fields. A noise analvsis is therefore primarily useful in placing an upper bound ou the counts., A noise analysis is therefore primarily useful in placing an upper bound on the counts. The differeuce between the observed uncleaned aud the simulated uncleaned distribution fictions can be used to constrain the simulated counts distribution., The difference between the observed uncleaned and the simulated uncleaned distribution functions can be used to constrain the simulated counts distribution. If the iuput function for the counts has too high a normalization or is too steep at the faint ond. then the simulated distribution will be too wide when compared to the observed. distribution.," If the input function for the counts has too high a normalization or is too steep at the faint end, then the simulated distribution will be too wide when compared to the observed distribution." In contrast. if the iuput function has too low a normalization or is too shallow at the fait end. then the simulated distribution will be too narrow when compared to the observed distribution.," In contrast, if the input function has too low a normalization or is too shallow at the faint end, then the simulated distribution will be too narrow when compared to the observed distribution." We performed Monte Carlo simulations using two different paramceterizations to deteriune the ΠΡΟ counts at faint fluxes., We performed Monte Carlo simulations using two different parameterizations to determine the number counts at faint fluxes. " In the first case we used the BBarecr et ((1999a) parameterization with S in mJ. which fit their differential blauk field counts above 2 mJy for a=3.2 aud NV,104 dee7 +t."," In the first case we used the \markcite{bcs99}B Barger et (1999a) parameterization with $S$ in mJy, which fit their differential blank field counts above 2 mJy for $\alpha = 3.2$ and $N_o=3.0\times 10^4$ $^{-2}$ $^{-1}$." Here we varied o., Here we varied $a$. Tu the second case we used a power-law parauneterization of the faint counts normalized to match the Barger ct ccounts and the preseut direct counts at 2 iy., In the second case we used a power-law parameterization of the faint counts normalized to match the Barger et counts and the present direct counts at 2 mJy. Here we varied the power-law iudex., Here we varied the power-law index. Sources were drawn from a population with a count described by the chosen model., Sources were drawn from a population with a count described by the chosen model. For each of the two models, For each of the two models o prescription.,$\alpha$ prescription. It is shown that the growth rate of thermally unstable modes (the upper branch) in the stress evolution scenario is significantly smaller than that in the à stress case., It is shown that the growth rate of thermally unstable modes (the upper branch) in the stress evolution scenario is significantly smaller than that in the $\alpha$ stress case. On the contrary. the growth rates of the viscously unstable modes (the lower branch) of the above two cases are similar.," On the contrary, the growth rates of the viscously unstable modes (the lower branch) of the above two cases are similar." " llere. the thermal timescale £u, is calculated by Figure 1 indicates that. even though the stress evolution process does not change the stability criterion. it may have significant influence on the growth rate of the thermally. unstable moce."," Here, the thermal timescale $t_{\rm th}$ is calculated by Figure 1 indicates that, even though the stress evolution process does not change the stability criterion, it may have significant influence on the growth rate of the thermally unstable mode." For further investigation. we calculate. the solutions under the long-wavelength limit. Le. Adf20.," For further investigation, we calculate the solutions under the long-wavelength limit, i.e., $kH \to 0$." In such case. the non-zero roots of the dispersion equation (22)) are. where ↾∐↥∢⋅⋜↧∣⋡∢≱∖⇁∢⊾∢⊾⊏↥⇂⇂⋜↧↥↕∢⋟↓↥≱∖↓↥∪∖∖⋎⊳∖↿↓↥⋖⋅↓⋅∢⊾↓⋜⊔⊲↓∪⊔⊳∖↓↥⊲↓↓≻∣⋡∢⋅↿∖∖⊽∢⋅⋖⋅⊔↿↓↥∢⊾ ⋏∙≟↓⋅∪∖∖⊽∣⇂⊔⋅⋜⋯⊾∣⇜≮↙⋎⋜⋯∠⇂↿↓↕⋖⋅↿⊲↓⊔↓⋖⊾⊳∖≼⇍⋜↧↓," In such case, the non-zero roots of the dispersion equation \ref{DissipationE}) ) are, where The above equation shows the relationship between the growth rate $\omega$ and the timescale of stress delay $t_{\rm ps}$ ." ∢⊾∪⇂∎⋡∖↿↓⋅⋖⋅⋡∖≱∖∠⇂⋖⋅⇂⋜↧∙∖⇁∣↴≖∖⋡ ↓⊲∖∪↓⋅↥⇂↥∢⊾≼∼⋜↧⊳∖⋖⋅∪⇂⋅∣↻∖∣⋯⋡∶∶∕∶↓⊳∟⊲⊏↥⊳⊔≟∣∩⊲↓⊳," For the case of $t_{\rm ps}/t_{\rm th} \gg 1$, Eq. \ref{GrowthRate}) )" "∖⊳∖⊀↓⊔↓↓≻↓⊲↓∐∢⋅∠⇂⋜↧⊳∖ which means that if £j, is sulliciently larger than ἐν. the growing timescale of thermal instability is around /,,."," is simplified as which means that if $t_{\rm ps}$ is sufficiently larger than $t_{\rm th}$, the growing timescale of thermal instability is around $t_{\rm ps}$." On the contrary. for the case of f/f. Eq. (24))," On the contrary, for the case of $t_{\rm ps}/t_{\rm th}{\ll}1$, Eq. \ref{GrowthRate}) )" is reduced to The above growth rate is exactly the same as that in the à stress case. in which the growing timescale of thermal instability is around Zi.," is reduced to The above growth rate is exactly the same as that in the $\alpha$ stress case, in which the growing timescale of thermal instability is around $t_{\rm th}$." Figure 2 shows the variation of the growth rate of the thermally unstable mode in the long-wavelength limit with hys For 1Ξ0.01. 0.1. and 0.3.," Figure 2 shows the variation of the growth rate of the thermally unstable mode in the long-wavelength limit with $t_{\rm ps}$ for $\beta = 0.01$, 0.1, and 0.3." The figure clearly illustrates that. for the case of |psfine the stress evolution process will have essential elfects on the thermal instability since the erowth rate is significantly cdlecreased.," The figure clearly illustrates that, for the case of $t_{\rm ps} \ga t_{\rm th}$, the stress evolution process will have essential effects on the thermal instability since the growth rate is significantly decreased." 1n this paper. the stress evolution process. which was ignored in previous works. is taken into account in the linear stability analysis of standard. thin accretion. clises.," In this paper, the stress evolution process, which was ignored in previous works, is taken into account in the linear stability analysis of standard thin accretion discs." We show the variation of t10 growth rate of thermally unstable modes with the wavelength of perturbations for two cases: with and without stress delav., We show the variation of the growth rate of thermally unstable modes with the wavelength of perturbations for two cases: with and without stress delay. We find that the growth rate with stress delay can be apparently lower than that without stress delay., We find that the growth rate with stress delay can be apparently lower than that without stress delay. We also make some analytical approximation for the oerowth rate in long-wavelength limit. ancl present the relationship between the s»ecifie growth rate and the timescale of stress delay.," We also make some analytical approximation for the growth rate in long-wavelength limit, and present the relationship between the specific growth rate and the timescale of stress delay." In conclusion. 1the stress evolution process may have essential inlluence on the thermal instability by significantly decreasing the growth rate. in particular for the case in which the timescale of stress delay is comparable to or even larger than the thermal timescale.," In conclusion, the stress evolution process may have essential influence on the thermal instability by significantly decreasing the growth rate, in particular for the case in which the timescale of stress delay is comparable to or even larger than the thermal timescale." In a real system the timescale of stress delay remains unclear., In a real system the timescale of stress delay remains unclear. We would argue that this timescale is possibly comparable to the thermal timescale as. follows., We would argue that this timescale is possibly comparable to the thermal timescale as follows. In simulations with an initially weak toroidal or poloidal magnetic field. the magnetic energy may first experience an exponential growth during the first few orbits due to the linear instability. and then will be followed by the nonlinear evolution.," In simulations with an initially weak toroidal or poloidal magnetic field, the magnetic energy may first experience an exponential growth during the first few orbits due to the linear instability, and then will be followed by the nonlinear evolution." Finally. à saturated quasi-steady state phase may form.," Finally, a saturated quasi-steady state phase may form." TotaIv. it will take 15~20 oralts for the system to enter a fully turbulent state (e.g. Lawleyeal.1996:Fro-mang&Papaloizou2007)).," Totally, it will take $15 \sim 20$ orbits for the system to enter a fully turbulent state (e.g., \citealp{Hawley96,Fromang07}) )." This implies tha the evolution timescale of the magnetoturbulence is around 15~20 times of the dynamical timeseale £444. which can be regarded as a cluration around the thermal timescale £i (e.g. finofavafa ancl a=0.1).," This implies that the evolution timescale of the magnetoturbulence is around $15 \sim 20$ times of the dynamical timescale $t_{\rm dyn}$, which can be regarded as a duration around the thermal timescale $t_{\rm th}$ (e.g., $t_{\rm th} \sim t_{\rm dyn}/\alpha$ and $\alpha = 0.1$ )." As mentioned in the first section. when the theory of he limit evele behaviour between the standard. thin cise and the slim. disc is applied. to the observational quasi-veriodic variability of GRAS 1915. there exists some conlliet tween the theory anc the observation on the duration ratio /nin/lis and the Luminosity ratio Luin’Lis.," As mentioned in the first section, when the theory of the limit cycle behaviour between the standard thin disc and the slim disc is applied to the observational quasi-periodic variability of GRS 1915, there exists some conflict between the theory and the observation on the duration ratio $t_{\rm high}/t_{\rm low}$ and the luminosity ratio $L_{\rm high}/L_{\rm low}$." In our opinion. the stress evolution process maw improve the theory o explain observations due to the following reasons.," In our opinion, the stress evolution process may improve the theory to explain observations due to the following reasons." When he How sullers thermal instability. the growth rate of AZ can x: significantly. decreased. by the stress delay.," When the flow suffers thermal instability, the growth rate of $\dot M$ can be significantly decreased by the stress delay." We therefore can expect a relatively lower Al for the outburst phase. thus a corresponding lower Luisn/ Lis.," We therefore can expect a relatively lower $\dot M$ for the outburst phase, thus a corresponding lower $L_{\rm high}/L_{\rm low}$ ." As à consequence. for a certain fixed mass accretion rate suplv at outer boundary. if AZ at outburst phase drops. the duration of this phase will therefore become longer. thus a moderate value of (isahis should. appear.," As a consequence, for a certain fixed mass accretion rate supply at outer boundary, if $\dot M$ at outburst phase drops, the duration of this phase will therefore become longer, thus a moderate value of $t_{\rm high}/t_{\rm low}$ should appear." In other words. the inlluence of the stress delay on the growth rate may result in moderate ratios of duration. and. luminosity of the outburst phase to the quiescent one. which will be more likely to. explain the observational results than previous caleulations.," In other words, the influence of the stress delay on the growth rate may result in moderate ratios of duration and luminosity of the outburst phase to the quiescent one, which will be more likely to explain the observational results than previous calculations." The further investigation on this issue may require time-dependent numerical calculations including the stress evolution process., The further investigation on this issue may require time-dependent numerical calculations including the stress evolution process. Aloreover. we would point out the possible application of the stress evolution process to another geometricaIx thin ise. namely the Shapiro-Lightman-Eardley cise (t1ο SLE isc. Shapiro et a.," Moreover, we would point out the possible application of the stress evolution process to another geometrically thin disc, namely the Shapiro-Lightman-Eardley disc (the SLE disc, Shapiro et al." 1976). which was originally introduced is the inner region. of a thin dise to provide hare X-ray mission.," 1976), which was originally introduced as the inner region of a thin disc to provide hard X-ray emission." However. it is known that the SLE disc is viscously stable but sullers thermal instability.," However, it is known that the SLE disc is viscously stable but suffers thermal instability." H£ the stress evolution process is taken into consideration in the SLE model. and 10 timescale of stress delay is comparable to the thermal timescale. we can therefore expect the existence of a quasi-stable SLIS disc since the decreased growth rate of thermal instability may not. completely destroy. the dise ancl the viscous stability may help to suppress the thermal instability in the viscous timescale.," If the stress evolution process is taken into consideration in the SLE model, and the timescale of stress delay is comparable to the thermal timescale, we can therefore expect the existence of a quasi-stable SLE disc since the decreased growth rate of thermal instability may not completely destroy the disc and the viscous stability may help to suppress the thermal instability in the viscous timescale." We thank Shoji Ixato and Sheng-Ming Zheng for beneficial discussion., We thank Shoji Kato and Sheng-Ming Zheng for beneficial discussion. This work was supported by the National Basic Research Program ofChina under grant 2000€DS24800. and the National NaturalScience. Foundationof China under erants 10833002 ancl 11073015.," This work was supported by the National Basic Research Program of China under grant 2009CB824800, and the National NaturalScience Foundationof China under grants 10833002 and 11073015." we then synthesised the spectrum using SYNSPEC.,we then synthesised the spectrum using SYNSPEC. The best fit to the observed spectrum was obtained for Teff = 24000 K. log g = 3.0. € = 7 kms.," The best fit to the observed spectrum was obtained for Teff = 24000 K, log g = 3.0, $\xi_{\rm t}$ = 7 $^{-1}$." Since strong lines are usually affected by microturbulence. the use of these lines in determining the atmospheric parameters of the star may contribute to systematic errors.," Since strong lines are usually affected by microturbulence, the use of these lines in determining the atmospheric parameters of the star may contribute to systematic errors." In estimating the atmospheric parameters and abundances. we excluded lines with | > 200.," In estimating the atmospheric parameters and abundances, we excluded lines with $_{\lambda}$ $\ge$ 200." Line blends were also excluded from this analysis., Line blends were also excluded from this analysis. Several absorption and P—Cyent type He I lines were identified in the spectrum of 122023., Several absorption and $-$ Cygni type He I lines were identified in the spectrum of I22023. " The absorption lines are blends with the exception of the strong He (51) (W, = _) line and the He Ι(50) line (W,= ).", The absorption lines are blends with the exception of the strong He I(51) $_{\lambda}$ = ) line and the He I(50) line $_{\lambda}$ = ). For the derived atmospheric parameters of the star. using spectrum synthesis. we estimated the helium abundance from the HeI(50) line.," For the derived atmospheric parameters of the star, using spectrum synthesis, we estimated the helium abundance from the HeI(50) line." We have studied. the asvmptotic magnetic field. evolution promoted by. ambipolar diffusion in a one-dimensional geometry for (wo opposite. limiting regimes.,"We have studied the asymptotic magnetic field evolution promoted by ambipolar diffusion in a one-dimensional geometry for two opposite, limiting regimes." In thelani. in which neutral and charged particles crift easily with respect to each other. the bottleneck for the evolution is the conversion of one species into another. which is required in order to eliminate the charged-particle pressure graclients caused by the magnetic field. whieh impede its evolution.," In the, in which neutral and charged particles drift easily with respect to each other, the bottleneck for the evolution is the conversion of one species into another, which is required in order to eliminate the charged-particle pressure gradients caused by the magnetic field, which impede its evolution." In the[nnd conversions are easy. but the inter-particle collisions are the corresponding bottleneck.," In the, conversions are easy, but the inter-particle collisions are the corresponding bottleneck." In molecular clouds. the second regime appears to be generally relevant (Shu1983:Brandenburg&Zweibel1994).," In molecular clouds, the second regime appears to be generally relevant \citep{Shu-83,BZ-94}." Neutron stars in their hot. early phase will also be in the strong-coupling regime. and evolve to the weak coupling regime as they cool.," Neutron stars in their hot, early phase will also be in the strong-coupling regime, and evolve to the weak coupling regime as they cool." In the(η. the magnetic field evolution is described. by a non-linear. partial integro-cdifferential equation. while in theGani this evolution is described by a non-linear diffusion equation.," In the, the magnetic field evolution is described by a non-linear, partial integro-differential equation, while in the this evolution is described by a non-linear diffusion equation." We mace numerical simulations of the evolution of clillerent initial magnetic field. profiles in cach of these limits and found agreement between our numerical results and some analytic solutions that can be found for these dilferential equations., We made numerical simulations of the evolution of different initial magnetic field profiles in each of these limits and found agreement between our numerical results and some analytic solutions that can be found for these differential equations. From our results. we infer that. in both limits. the ambipolar diffusion process operates in a tendeney to spread out the magnetic Hux. but contrary to the normal Ohmic diffusion this process asymptotically produces. singular points with sharp magnetic field gradients.," From our results, we infer that, in both limits, the ambipolar diffusion process operates in a tendency to spread out the magnetic flux, but contrary to the normal Ohmic diffusion this process asymptotically produces singular points with sharp magnetic field gradients." These. sharp eracients develop around those points where the magnetic Ποια is null. and. separate regions of magnetic fields with opposite signs.," These sharp gradients develop around those points where the magnetic field is null, and separate regions of magnetic fields with opposite signs." We observe some generic properties of this process. as follows: In theUmi. the resulting discontinuities can be modelled as step solutions Eqs. (29)). (24))].," We observe some generic properties of this process, as follows: In the, the resulting discontinuities can be modelled as step solutions [Eqs. \ref{explicit-step}) ), \ref{explicit-step1}) )]." The asvmptotic magnetic field is spatially uniform in cach of he regions separated by these singularities. and its absolute value (and thus the magnetic pressure) is the same in each region.," The asymptotic magnetic field is spatially uniform in each of the regions separated by these singularities, and its absolute value (and thus the magnetic pressure) is the same in each region." Ambipolar cilfusion by itself does not cause magnetic lux transfer (and thus reconnection) across the singularities. rut the associated current sheets will easily. be. dissipated »v Ohmic cülfusion. so reconnection will occur in a realistic system.," Ambipolar diffusion by itself does not cause magnetic flux transfer (and thus reconnection) across the singularities, but the associated current sheets will easily be dissipated by Ohmic diffusion, so reconnection will occur in a realistic system." In thefone. at the singular points he magnetic field. vanishes continuously but with infinite spatial derivative.," In the, at the singular points the magnetic field vanishes continuously but with infinite spatial derivative." Ambipolar diffusion acts in a tencdeney ο spread out the magnetic Πας. but. contrary to the weak coupling limit. the magnetic Εαν is not. preserved. in each one of the regions separated. by the magnetic null. points.," Ambipolar diffusion acts in a tendency to spread out the magnetic flux, but, contrary to the weak coupling limit, the magnetic flux is not preserved in each one of the regions separated by the magnetic null points." 'Pherefore. there is a transfer of magnetic [Lux through these null points. i. e. reconnection without Ohmic resistivity (but see Lleitsch&Zweibel 2003a.b)).," Therefore, there is a transfer of magnetic flux through these null points, i. e. reconnection without Ohmic resistivity (but see \citealp{H-03a,H-03b}) )." The main limitation in applying the present formalism to realistic svstems (either neutron stars or molecular cloud cores) is the very restrictive. one-dimensional geometry.," The main limitation in applying the present formalism to realistic systems (either neutron stars or molecular cloud cores) is the very restrictive, one-dimensional geometry." An extension to more realistic geometries (1. e.. axial svmnmetrv) will be attempted in further work.," An extension to more realistic geometries (i. e., axial symmetry) will be attempted in further work." We are grateful to Alariaa Cristina Depassier ancl Cristóbbal Petrovich for valuable information about the non-linear diffusion equation., We are grateful to Maríaa Cristina Depassier and Cristóbbal Petrovich for valuable information about the non-linear diffusion equation. We also thank the referee for a very helpful report., We also thank the referee for a very helpful report. " This work was financed by the Comini-CONICYT. Fund. project N°? 32070014: FONDECYT regular projects 1060644 ""n 1070854. the FONDADP Center for Astrophysics ""n(15010003). rovecto Basal PED-06/2007 and the joint ""Estudio: Computacional del decaimiento de campos magnétticos en estrellas de neutrones between Universidad. de Alecellinn (Summa Group). Pontificia Universidad. Catollica de Chile and Universidad. de Chile."," This work was financed by the Gemini-CONICYT Fund, project $N^0$ 32070014; FONDECYT regular projects 1060644 and 1070854, the FONDAP Center for Astrophysics (15010003), Proyecto Basal PFB-06/2007 and the joint project “Estudio Computacional del decaimiento de campos magnétticos en estrellas de neutrones” between Universidad de Medellínn (Summa Group), Pontificia Universidad Católlica de Chile and Universidad de Chile." “Phe postdoctoral stay of J.L1L.LI. abo Astrophysikalisches Institut Potsdam was possible due to the financial support| of. Deutscher Xkacemischer Austauschedicnst (DAAL) - Germany anc Comisiónn Nacional ce Investigaciónn Cientifica vv Tecnológgica (CONICYT) - Chile through the postcoctoral fellowship NU A0772255-2007-07-DOCDAAD-25., The postdoctoral stay of J.H.H. at Astrophysikalisches Institut Potsdam was possible due to the financial support of Deutscher Akademischer Austauschdienst (DAAD) - Germany and Comisiónn Nacional de Investigaciónn Cientifica y Tecnológgica (CONICYT) - Chile through the postdoctoral fellowship $N^0$ A0772255-2007-07-DOCDAAD-25. We also thank the FONDECYT International Cooperation Project 7090020., We also thank the FONDECYT International Cooperation Project 7090020. for their simulations but found different relations: 153-0.14[0M;/M;Y—1.25] for early-type galaxies. and 1--0.15[045/MY—1.4] for late-type galaxies.,"for their simulations but found different relations: $r_f/r = 1 + 0.14 [(M_i/M_f)^4-1.25]$ for early-type galaxies, and $r_f/r = 1 + 0.15 [(M_i/M_f)^4-1.4]$ for late-type galaxies." Figure 11. shows the contraction factor for all of our simulations., Figure \ref{fig:rfr} shows the contraction factor for all of our simulations. The effect is clearly more significant than suggested by the above relations., The effect is clearly more significant than suggested by the above relations. " In several cases. the contraction is even stronger at the innermost radi than that predicted by the SAC model. that is rp/r«M;/M,."," In several cases, the contraction is even stronger at the innermost radii than that predicted by the SAC model, that is $r_f/r < M_i/M_f$." It can also be seen in Figure 7.., It can also be seen in Figure \ref{fig:aw2}. Overall. there is no single relation for the contraction factor rp/r.," Overall, there is no single relation for the contraction factor $r_f/r$." The scatter among different systems is intrinsic. similar to the scatter of model parameters A and W.," The scatter among different systems is intrinsic, similar to the scatter of model parameters $A$ and $w$." ? constructed semi-analytical models of galaxy populations using. in addition to the MAC model. an analytic prescription for either halo contraction or expansion of the form ry;/r=(M;/MyY'. with a as a free parameter.," \citet{dutton_etal11} constructed semi-analytical models of galaxy populations using, in addition to the MAC model, an analytic prescription for either halo contraction or expansion of the form $r_f/r = (M_i/M_f)^n$, with $n$ as a free parameter." Their preferred case is halo expansion with n2—0.5., Their preferred case is halo expansion with $n=-0.5$. None of our systems shows evidence for such expansion., None of our systems shows evidence for such expansion. If we were to use this parametrization to envelop the distribution of our simulations. then most of our results would lie within the range 0.63."," In this paper, we report accurate astrometry of two bright SMGs in the COSMOS field whose radio to submm flux ratio indicates that are likely at $z>3$." " We assume standard cosmology with Πο=71 km s! Mpc-!, Qaa—0.73 and Ωνι=0.27."," We assume a standard cosmology with $H_0=71$ km $^{-1}$ $^{-1}$, $\Omega_\Lambda=0.73$ and $\Omega_\mathrm{M}=0.27$." COSMOS is the largest deep survey carried out with thetelescope (HST) covering ~2 deg? in the sky., COSMOS is the largest deep survey carried out with the (HST) covering $\sim2$ $^{2}$ in the sky. Extensive imaging of the COSMOS field has been performed from the X-rays to the radio wavelengths., Extensive imaging of the COSMOS field has been performed from the X-rays to the radio wavelengths. " This includes: complete optical/near-IR coverage in 22 broad and intermediate bands with several ground based observatories including the Subaru telescope, the CFHT, the UKIRT and the KPNO; IR imaging withSpitzer, including new deep 3.6 and 4.5 ym images obtained as part of its warm mission; and radio imaging with the VLA at 20 cm."," This includes: complete optical/near-IR coverage in 22 broad and intermediate bands with several ground based observatories including the Subaru telescope, the CFHT, the UKIRT and the KPNO; IR imaging with, including new deep 3.6 and 4.5 $\mu$ m images obtained as part of its warm mission; and radio imaging with the VLA at 20 cm." For details in the imaging and catalogs of the COSMOS field see optical/IRCapaketal.(2007) and Ilbertetal.(2009)., For details in the optical/IR imaging and catalogs of the COSMOS field see \citet{Capak2007} and \citet{Ilbert2009}. . A complete description of the radio imaging is given in Schinnereretal. (2007).., A complete description of the radio imaging is given in \citet{Schinnerer2007}. . " In the course of the MAMBO 1.2 mm survey of the COSMOS field (Bertoldietal.2007),, fifteen sources were detected with S/N>4, five of which do not have a significant radio counterpart <30 uJy, 30)."," In the course of the MAMBO 1.2 mm survey of the COSMOS field \citep{Bertoldi2007}, fifteen sources were detected with $\mathrm{S/N}> 4$, five of which do not have a significant radio counterpart ( $< 30\ \mu$ Jy, $\sigma$ )." " From these five radio-faint mm sources,( we selected two that were also significantly detected at 1.1 mm with Bolocam: MMJ100016--021549 and MMJ1000474-021018."," From these five radio-faint mm sources, we selected two that were also significantly detected at 1.1 mm with Bolocam: $+$ 021549 and $+$ 021018." " Hereafter, we refer to these sources as MM1 and MM14, respectively, following Bertoldietal. (2007)."," Hereafter, we refer to these sources as MM1 and MM14, respectively, following \citet{Bertoldi2007}." ". The deboosted flux densities for MM1 were Sjomm=6.2+0.9 mJy and Syimm=5.9+1.9 mJy in the MAMBO and Bolocam maps, respectively (Bertoldietal.2007)."," The deboosted flux densities for MM1 were $S_\mathrm{1.2 mm}=6.2\pm0.9$ mJy and $S_\mathrm{1.1 mm}=5.9\pm1.9$ mJy in the MAMBO and Bolocam maps, respectively \citep{Bertoldi2007}." ". This source was recently detected with the Large Bolometer Camera (LABOCA) with =16.4£1.8 mJy (Albrecht et al.,"," This source was recently detected with the Large Bolometer Camera (LABOCA) with $S_{870 \mu \mathrm{m}}=16.4\pm1.8$ mJy (Albrecht et al.," in preparation)., in preparation). " TheSg70um MAMBO and Bolocam deboosted flux densities for MM14 were S132mm=41+1.0 mJy and S14mm=3.6+1.9 mJy, respectively (Bertoldietal.2007),, however no significant emission is seen in the LABOCA image down to 10.5 mJy (3c)."," The MAMBO and Bolocam deboosted flux densities for MM14 were $S_\mathrm{1.2 mm}=4.1\pm1.0$ mJy and $S_\mathrm{1.1 mm}=3.6\pm1.9$ mJy, respectively \citep{Bertoldi2007}, however no significant emission is seen in the LABOCA image down to 10.5 mJy $\sim$ $\sigma$ )." " SMA observations of MM1 and MM14 were carried out in 2009 January 10 and 2009 May 07, respectively, under good weather conditions (TesoGHz<0.1)."," SMA observations of MM1 and MM14 were carried out in 2009 January 10 and 2009 May 07, respectively, under good weather conditions $\tau_{250 \mathrm{GHz}}<0.1$ )." " The receivers have two sidebands, each with 2 GHz bandwidth, which when averaged yield a 4 GHz effective bandwidth centered at 345 GHz (A~890 yum)."," The receivers have two sidebands, each with 2 GHz bandwidth, which when averaged yield a 4 GHz effective bandwidth centered at $345$ GHz $\lambda\sim890\ \mu$ m)." " Seven antennas, arranged in the compact (COM) with the MAMBO source positions as phase tracking centers."," Seven antennas, arranged in the compact (COM) with the MAMBO source positions as phase tracking centers." " The data were calibrated with the MIR package (Scovilleetal.1993) specially adapted for SMA data, using the strong continuum source 3C273 (Ss45anz~4.9 Jy) as passband calibrator and Ceres (S345Guz~4.2 Jy) for primary flux calibration."," The data were calibrated with the MIR package \citep{Scoville1993} specially adapted for SMA data, using the strong continuum source 3C273 $S_{345\mathrm{GHz}}\sim4.9$ Jy) as passband calibrator and Ceres $S_{345\mathrm{GHz}}\sim4.2$ Jy) for primary flux calibration." The flux scale is estimated to be accurate within20%., The flux scale is estimated to be accurate within. . The quasars J0854+201 (~3.1 Jy; ~24.2° away) and J1058+015 (~1.7 Jy; ~14.5° away) were observed every ~25 min for gain calibration., The quasars $+$ 201 $\sim$ 3.1 Jy; $\sim24.2\degr$ away) and $+$ 015 $\sim1.7$ Jy; $\sim14.5\degr$ away) were observed every $\sim25$ min for gain calibration. " Following Youngeretal.(2008,2009,2010),, we also performed hourly scans of a dimmer, but significantly closer test quasar J1008+063 (~0.11 Jy; ~4.5° away) to empirically verify the phase transfer and estimate the positional uncertainty."," Following \citet{Younger2008, Younger2009, Younger2010}, we also performed hourly scans of a dimmer, but significantly closer test quasar $+$ 063 $\sim0.11$ Jy; $\sim4.5\degr$ away) to empirically verify the phase transfer and estimate the positional uncertainty." " The visibility data for MM1 showed good phase stability, however, about half of the data for MM14 had to be flagged due to bad phases."," The visibility data for MM1 showed good phase stability, however, about half of the data for MM14 had to be flagged due to bad phases." The calibrated visibility data were imaged using the AIPS software., The calibrated visibility data were imaged using the AIPS software. " We used the AIPS task IMAGR, which uses the CLEAN algorithm, and natural weighting to deconvolve the images down to lo in a box centered on our targets."," We used the AIPS task IMAGR, which uses the CLEAN algorithm, and natural weighting to deconvolve the images down to $1\sigma$ in a box centered on our targets." " This led to beam sizes of 2.55""x1.86"" and 1.96""x1.86"" and noise levels of 1.5 mJy and 1.95 mJy beam-! for MM1 and MM14, respectively."," This led to beam sizes of $2.55\arcsec\times1.86\arcsec$ and $1.96\arcsec\times1.86\arcsec$ and noise levels of $1.5$ mJy and $1.95$ mJy $^{-1}$ for MM1 and MM14, respectively." " Finally, fluxes were measuredwith Gaussian fits using the JMFIT task, included in the AIPS software."," Finally, fluxes were measuredwith Gaussian fits using the JMFIT task, included in the AIPS software." the photodesorption vield of CO (Obberg et al.,the photodesorption yield of CO (Öbberg et al. 2007)., 2007). For the initial molecular abundances of the coupled evolution between dvnanmies and chemistry. we caleulate the chemical evolution in a constant densitv of 5xLO’ with the same initial atomic abundances as used in Lee et al. (," For the initial molecular abundances of the coupled evolution between dynamics and chemistry, we calculate the chemical evolution in a constant density of $5\times10^3$ $^{-3}$ with the same initial atomic abundances as used in Lee et al. (" 2004) for /=5x10? vears.,2004) for $t=5\times10^5$ years. For the chemical ealeulation. the dense core is asstuned to be surrounded. with material of ly=1.0 mag. where CO is sell-shielded.," For the chemical calculation, the dense core is assumed to be surrounded with material of $A_V =1.0$ mag, where CO is self-shielded." For consistency. adopting the methods used in Lee et al. (," For consistency, adopting the methods used in Lee et al. (" 2004). we also calculate the dust ancl eas Llemperatures with the interstellar radiation field attenuated by Ay=1.0 mae.,"2004), we also calculate the dust and gas temperatures with the interstellar radiation field attenuated by $A_V =1.0$ mag." The time step for data dump of the dvnamical simulation is 4x107 vears. during which the chemistry is calculated based on constant densitv aud temperatures given at a specilic dump (ime. ancl the result of the chemical evolution is used as initial conditions for the next dump time.," The time step for data dump of the dynamical simulation is $4\times10^4$ years, during which the chemistry is calculated based on constant density and temperatures given at a specific dump time, and the result of the chemical evolution is used as initial conditions for the next dump time." We use the Monte-Carlo method (Choi et al., We use the Monte-Carlo method (Choi et al. 1995) to perform the radiative (ransler calculation for the and CO lines., 1995) to perform the radiative transfer calculation for the $^+$ and $^{18}$ O lines. The collision rates for and CO are adopted from Flower (1999) and Flower Launav (1985)., The collision rates for $^+$ and CO are adopted from Flower (1999) and Flower Launay (1985). For the simulation of the line profiles. we assunie the distance to the model core of 250 pe and the beam sizes for the Caltech submillimeter Observatory 10.4 m telescope.," For the simulation of the line profiles, we assume the distance to the model core of 250 pc and the beam sizes for the Caltech Submillimeter Observatory 10.4 m telescope." We also include a constant. microturbulent velocity dispersion of 0.2 km !., We also include a constant microturbulent velocity dispersion of 0.2 km $^{-1}$. We model the 3-2 and 4-3 transitions. which have been used io study infall motion in low mass cores with and without voung stellar objects (Gregersen οἱ al.," We model the $^+$ $-$ 2 and $-$ 3 transitions, which have been used to study infall motion in low mass cores with and without young stellar objects (Gregersen et al." 1997: Gregersen Evans 2000)., 1997; Gregersen Evans 2000). The optically thin CO 3—2 line is also modeled to be compared to the line profiles., The optically thin $^{18}$ O $-$ 2 line is also modeled to be compared to the $^+$ line profiles. We use a one-dimensional (radial) chemical network coupled with a radiative (ransler model to simulate line profiles., We use a one-dimensional (radial) chemical network coupled with a radiative transfer model to simulate line profiles. For this purpose we have to reduce the three-dimensional density and velocity fields into one-dimensional radial distributions using the [following procedures., For this purpose we have to reduce the three-dimensional density and velocity fields into one-dimensional radial distributions using the following procedures. First. we find (he position ol a density peak of the whole computational domain. which is taken as the origin of the radial coordinate.," First, we find the position of a density peak of the whole computational domain, which is taken as the origin of the radial coordinate." " Second. we identify a core as a connected region whose density is larger than my,=10*ni 7."," Second, we identify a core as a connected region whose density is larger than $n_{\rm H_2}=10^3$ $^{-3}$." Third. we subtract a center-of-niass velocity of the core [rom its velocity field.," Third, we subtract a center-of-mass velocity of the core from its velocity field." The three-dimensional center-ol-velocity of the core ranges [rom 0.2 km ο to 2.0 km | Fourth. we take the average of the density and radial velocity al each spherical shell with the width of a computational cell.," The three-dimensional center-of-velocity of the core ranges from 0.2 km $^{-1}$ to 2.0 km $^{-1}$ Fourth, we take the average of the density and radial velocity at each spherical shell with the width of a computational cell." At this point we have to mention the effect of the radial averaging that we have taken in the above., At this point we have to mention the effect of the radial averaging that we have taken in the above. The averaging certainly smoothed out density and velocity variations at an outer laver affected by. for example. a shock.," The averaging certainly smoothed out density and velocity variations at an outer layer affected by, for example, a shock." So the line profiles observed towards a specilic direction may show much stronger variation (han the line profiles that are obtained alter taking (he radial averaging., So the line profiles observed towards a specific direction may show much stronger variation than the line profiles that are obtained after taking the radial averaging. In Figure 1. we plot the density and velocity profiles as a function of the radial distance," In Figure 1, we plot the density and velocity profiles as a function of the radial distance" 8|and [0].. we have prescribed how their horizon area would be quantized.,"\cite{extremekerr} and \cite{carlemos}, we have prescribed how their horizon area would be quantized." This was done by simply assuming they have a uniformly spaced area spectrum eiven by οn. where 0A is the area variation caused by absorption of a quasi-normal mode.," This was done by simply assuming they have a uniformly spaced area spectrum given by $A_n = \delta A \ell^2_P\, n\,$, where $\delta A$ is the area variation caused by absorption of a quasi-normal mode." " This was done in analogy with the Schwarzschild case, where the spacing of its area spectrum was determined by means of the knowledgeof its asymptotic (“large n 7) quasi-normal mode frequencies [5].."," This was done in analogy with the Schwarzschild case, where the spacing of its area spectrum was determined by means of the knowledgeof its asymptotic (“large $n$ “) quasi-normal mode frequencies \cite{hod}." In the cases regarded here. (he results lor the spacing of the area spectrum differ from that for Schwarzschild. as well as for non-extreme Ixerr [0]. black holes. in which cases. the spacing is predicted to be given by 4/7»3.," In the cases regarded here, the results for the spacing of the area spectrum differ from that for Schwarzschild, as well as for non-extreme Kerr \cite{hod2} black holes, in which cases, the spacing is predicted to be given by $4ln\,3$." This factor comes Irom the real part of (he asymptotic quasi-normal mode frequencies of those black holes [5].. |0]..," This factor comes from the real part of the asymptotic quasi-normal mode frequencies of those black holes \cite{hod}, \cite{hod2}." Such a difference may be justified due to the quite different nature of the asymptotic quasi-normal mode spectrum of the near extreme black holes we considered., Such a difference may be justified due to the quite different nature of the asymptotic quasi-normal mode spectrum of the near extreme black holes we considered. Furthermore. it should be nopriori reason for expecting (he same behaviour for the asymptotic quasi-mnormal mode frequencies of near extreme and non-extreme black holes.," Furthermore, it should be no reason for expecting the same behaviour for the asymptotic quasi-normal mode frequencies of near extreme and non-extreme black holes." The authors would like to thank Teenológico) and FAPESP-Drazil Paulo) lor financial support., The authors would like to thank ) and ) for financial support. "distribution of distances obtained using as reference model the WIPASS objects. weighted by their total III line flux $;,; aud subject to different cuts.","distribution of distances obtained using as reference model the HIPASS objects, weighted by their total HI line flux $S_{int}$ and subject to different cuts." " We not only show the distribution expected for data simulated according to the particular HIPASS model considerecL due wh panel anc the isotropic model expectations. but aso show for comparison the distributioi obtained for μπατος data sets following the SWIFT ACN described before (sampling them according to their XN rav fluxes, without imposing the ealacic latitude cut aud vestrictiic thei to those wihin 100 Alpe)."," We not only show the distribution expected for data simulated according to the particular HIPASS model considered in each panel and the isotropic model expectations, but also show for comparison the distributions obtained for simulated data sets following the SWIFT AGN described before (sampling them according to their X ray fluxes, without imposing the galactic latitude cut and restricting them to those within 100 Mpc)." The vertical lines are the correspoudiug distances D for the 27 highest ererey Aue’CY evels., The vertical lines are the corresponding distances $D$ for the 27 highest energy Auger events. Iu the top left panel iu fg., In the top left panel in fig. 2 we have considered extragalactic HE sources 1ji the northern (NIHCAT [9])} aud southern (HICAT |8])) HIPASS catalogs., 2 we have considered extragalactic HI sources in the northern (NHICAT \cite{wo06}) ) and southern (HICAT \cite{me04}) ) HIPASS catalogs. Ii ref., In ref. " [7] northern snrcees were cut a S;z>15JykmsJH and southern oues at 5;,,77.1Jvlans+ to lave the siue compOTOLOoss level. which was in both samples."," \cite {gh08} northern sources were cut at $S_{int}>15\ {\rm Jy\ km\ s^{-1}}$ and southern ones at $S_{int}>7.4\ {\rm Jy\ km\ s^{-1}}$ to have the same completeness level, which was in both samples." We think that keeping objects up to different liuütiug brightuesses introduces j0wever a non-homoesencitv iu the two samples strouger than what is Otained keeping the same fux cut for the two samples. everif they end up having ciffercut Co1upleteuess levels.," We think that keeping objects up to different limiting brightnesses introduces however a non-homogeneity in the two samples stronger than what is obtained keeping the same flux cut for the two samples, even if they end up having different completeness levels." Since the 2DISS test just probes the fractional distributior10 Objects: across the sv. if is muportaut o nüninize the possible distortions introduced in the| selection process aud heuce we will adopt the fux limit ος>7.lJvkins 5i1i both the northern aud southern subsamples.," Since the 2DKS test just probes the fractional distribution of objects across the sky, it is important to minimize the possible distortions introduced in the selection process and hence we will adopt the flux limit $S_{int}>7.4\ {\rm Jy\ km\ s^{-1}} $ in both the northern and southern subsamples." With this selection one is left with 3011 III galaxicsin the field of view of the Auger Observatory., With this selection one is left with 3014 HI galaxies in the field of view of the Auger Observatory. As is secu roni the pot the distances obtained iu the three source models have a senificaut overlap. aud the value οtained with the data set falls just iu the overlap region.," As is seen from the plot the distances obtained in the three source models have a significant overlap, and the value obtained with the data set falls just in the overlap region." Iu particular. beiug consistent with the isotropic values the resuting amisotropy probability is uot large. amounting to," In particular, being consistent with the isotropic values the resulting anisotropy probability is not large, amounting to." The topaight panel in fig., The top-right panel in fig. " 2 is similar but restricted to the HICAT souhern sample with declinatious à.«27? (aud with a cut Sj,9.1Jyans+ as iu vef T[7].. for which the fiux lanited catalog is complete. what leaves 1935 galaxies iu this region of the sky)."," 2 is similar but restricted to the HICAT southern sample with declinations $\delta<2^\circ$ (and with a cut $S_{int}>9.4\ {\rm Jy\ km\ s^{-1}}$ as in ref \cite{gh08}, for which the flux limited catalog is complete, what leaves 1935 galaxies in this region of the sky)." We also restricted the isotropic and ACN based simulations to the southern hemisphere in this pot. and considered oulv the 25 events from the Auger Observatory falling in the same region oftje sky.," We also restricted the isotropic and AGN based simulations to the southern hemisphere in this plot, and considered only the 25 events from the Auger Observatory falling in the same region of the sky." The results are qualitatively similar to those obtained in the previous plot., The results are qualitatively similar to those obtained in the previous plot. The bottou-kft panel is further, The bottom-left panel is further "?, about 2.5 per cent of the observed but unresolved CXB.",", about $2.5$ per cent of the observed but unresolved CXB." " Of course, many of the objects in the calculation of X-ray flux are above the flux limit and should be excluded."," Of course, many of the objects in the calculation of X-ray flux are above the flux limit and should be excluded." The flux from all extended sources the X-ray flux limit is 7.3x10-1”Jm?s!deg?., The flux from all extended sources the X-ray flux limit is $7.3\times 10^{-17}~{\rm J}~{\rm m}^{-2}~{\rm s}^{-1}~{\rm deg}^{-2}$. " Compton ghosts contribute about a tenth of the total X-ray flux: 1.1x10!""Jm?s!deg ?, of which 3.9x105Jm?s!deg comes from sources that are below the X-ray flux limit."," Compton ghosts contribute about a tenth of the total X-ray flux: $1.1\times 10^{-17}~{\rm J}~{\rm m}^{-2}~{\rm s}^{-1}~{\rm deg}^{-2}$ , of which $3.9\times 10^{-18}~{\rm J}~{\rm m}^{-2}~{\rm s}^{-1}~{\rm deg}^{-2}$ comes from sources that are below the X-ray flux limit." The diffuse X-ray background contribution from lobes of powerful double radio sources is found to make up 0.02 of the unresolved CXB., The diffuse X-ray background contribution from lobes of powerful double radio sources is found to make up $0.02$ of the unresolved CXB. IC scattering of the CMB off the nucleus and hotspots of sources as well as X-ray clusters and FR I objects also contribute to the CXB., IC scattering of the CMB off the nucleus and hotspots of sources as well as X-ray clusters and FR I objects also contribute to the CXB. Next the volume filling factor ¢ of all lobes and relic lobes is calculated at each redshift., Next the volume filling factor $\zeta$ of all lobes and relic lobes is calculated at each redshift. " gives the volume filling factor at z for sources with age less than T' (again, the limits of integration altered appropriately determine which objects we care about)."," gives the volume filling factor at $z$ for sources with age less than $T$ (again, the limits of integration altered appropriately determine which objects we care about)." " Τ’ is set to the age of the universe at redshift z if we care about all objects, and is altered appropriately to account for just active lobes or IC ghosts."," $T$ is set to the age of the universe at redshift $z$ if we care about all objects, and is altered appropriately to account for just active lobes or IC ghosts." " We allow for expansion of the volume Vi(t) only until the time the lobe pressure comes into equilibrium with the ambient pressure, calculated from the ambient density profile assuming a temperature of 10°K (temperature of the warm-hot intergalactic medium (?))), at which point the volume remains constant."," We allow for expansion of the volume $V_{\rm l}(t)$ only until the time the lobe pressure comes into equilibrium with the ambient pressure, calculated from the ambient density profile assuming a temperature of $10^5~{\rm K}$ (temperature of the warm-hot intergalactic medium \citep{2006ApJ...650..560C}) ), at which point the volume remains constant." The ratio of the lobe pressure at time £ to the ambient pressure at the distance of the end of the lobe at time ¢ stays well above 1 for times beyond which the lobe has Mpc scale length., The ratio of the lobe pressure at time $t$ to the ambient pressure at the distance of the end of the lobe at time $t$ stays well above $1$ for times beyond which the lobe has Mpc scale length. " The lobe volume and source density will depend on jet power Qj, so in order to find ¢ we bin jet power, calculate ¢ at each and take a weighted average according to the empirically-inferred distribution of jet powers."," The lobe volume and source density will depend on jet power $Q_{\rm j}$, so in order to find $\zeta$ we bin jet power, calculate $\zeta$ at each and take a weighted average according to the empirically-inferred distribution of jet powers." The factor of (1+z)? in the expression for ¢ comes from converting comoving volume to proper volume., The factor of $(1+z)^3$ in the expression for $\zeta$ comes from converting comoving volume to proper volume. " We also consider the relevant volume the lobes are situated in, namely the volume of filamentary structures of the universe."," We also consider the relevant volume the lobes are situated in, namely the volume of filamentary structures of the universe." We divide the volume filling factor by lobes by the volume fraction of the warm-hot intergalacticmedium in figure 1 of ? to account for the relevant volume., We divide the volume filling factor by lobes by the volume fraction of the warm-hot intergalacticmedium in figure 1 of \cite{2006ApJ...650..560C} to account for the relevant volume. Figure 9 shows the volume filling factors as a function of z., Figure \ref{fig:vff} shows the volume filling factors as a function of $z$. " At z—2 and z—3, we predict volume filling factors of all lobes around 0.03 and 0.02 respectively."," At $z=2$ and $z=3$, we predict volume filling factors of all lobes around $0.03$ and $0.02$ respectively." " For a longer jet lifetime, t;=5x10°yr, the predicted volume filling factors at these redshifts are 0.3 and 0.2."," For a longer jet lifetime, $t_{\rm j}=5\times10^8~{\rm yr}$, the predicted volume filling factors at these redshifts are $0.3$ and $0.2$." " While lobes may not significantly fill the entire universe, it is possible that they fill a large fraction of the filaments in which they are located."," While lobes may not significantly fill the entire universe, it is possible that they fill a large fraction of the filaments in which they are located." ? give a simple estimate for the volume filling factor by lobes as well., \cite{2001ApJ...560L.115G} give a simple estimate for the volume filling factor by lobes as well. Their paper estimates ¢=0.01 for t;=10°yr and ¢=0.53 for ἡ=5x10*yr (at z=9)., Their paper estimates $\zeta=0.01$ for $t_{\rm j}=10^8~{\rm yr}$ and $\zeta=0.53$ for $t_{\rm j}=5\times10^8~{\rm yr}$ (at $z=2$ ). " do not use a birth function of radio sources and estimate the number of dead lobes from tge/t;, where tae is the duration of the quasar era."," \cite{2001ApJ...560L.115G} do not use a birth function of radio sources and estimate the number of dead lobes from $t_{\rm qe}/t_{\rm j}$, where $t_{\rm qe}$ is the duration of the quasar era." This estimate gives slightly higher ratios at z—2 than estimated by the birth function due to the simpler age distribution of galaxies., This estimate gives slightly higher ratios at $z=2$ than estimated by the birth function due to the simpler age distribution of galaxies. " Typical lobe volumes are larger in ? than estimated by our model since their paper assumes a constant axial ratio of 2.5 (according to this paper's definition of axial ratio), i.e. assuming more spherical sources."," Typical lobe volumes are larger in \cite{2001ApJ...560L.115G} than estimated by our model since their paper assumes a constant axial ratio of $2.5$ (according to this paper's definition of axial ratio), i.e. assuming more spherical sources." " Thequestion of volume filling factor of lobes is also addressed with more care in the works by ? and ?,, with which the results of our work agree."," Thequestion of volume filling factor of lobes is also addressed with more care in the works by \cite{2007ApJ...658..217B} and \cite{2008ApJ...682L..17B}, with which the results of our work agree." " The former paper investigates the volume filling factor by lobes using the models of ?,, ? and ?,, and also modifications by incorporating a variable hot spot size growing with the source age."," The former paper investigates the volume filling factor by lobes using the models of \cite{1997MNRAS.286..215K}, \cite{1999AJ....117..677B} and \cite{2002A&A...391..127M}, and also modifications by incorporating a variable hot spot size growing with the source age." Table 7 of their paper gives the relevant volume fraction results for the models with a number of parameters varied., Table 7 of their paper gives the relevant volume fraction results for the models with a number of parameters varied. " A wide range of relevant volume filling factors can be produced by modification of the parameters, with the cumulative relevant volume filling factor of radio galaxies over the quasar era around 0.05."," A wide range of relevant volume filling factors can be produced by modification of the parameters, with the cumulative relevant volume filling factor of radio galaxies over the quasar era around $0.05$." " The later paper incorporates radio lobe growth into a numerical cosmological evolution, and finds a volume filling factor of 0.10—0.30."," The later paper incorporates radio lobe growth into a numerical cosmological evolution, and finds a volume filling factor of $0.10$ $0.30$." " The total number of particles placed into the IGM because of the formation of the lobes is N is found to be between 109? to 10"" particles for the different jet energies.", The total number of particles placed into the IGM because of the formation of the lobes is $N$ is found to be between $10^{65}$ to $10^{67}$ particles for the different jet energies. The density of these particles inthe lobes at the time the jet turns off is on the order of 10-77-10?!kgm ?., The density of these particles inthe lobes at the time the jet turns off is on the order of $10^{-32}$ $10^{-31}~{\rm kg}~{\rm m}^{-3}$ . " Therefore, the ratio of the density of particles in the lobes to the critical density of the universe Qyadiolobes is at least 6 orders of magnitude below unity, even for a lobe volume filling factor of 1."," Therefore, the ratio of the density of particles in the lobes to the critical density of the universe $\Omega_{\rm radio~lobes}$ is at least $6$ orders of magnitude below unity, even for a lobe volume filling factor of $1$ ." (e.g.. (he presence of X-ray cooling flows. the nearly isothermal gas. etc.).,"(e.g., the presence of X-ray cooling flows, the nearly isothermal gas, etc.)." We can consider two extreme states: eller only some. non-equilibrium clusters are ganuua-rav bright. or all clusters are close to equilibrium aud we are simply seeing (he lacing emission of an earlier epoch of accretion activity.," We can consider two extreme states: either only some, non-equilibrium clusters are gamma-ray bright, or all clusters are close to equilibrium and we are simply seeing the fading emission of an earlier epoch of accretion activity." In the first case we can exploit the fact that a svstem with an EGRET flux of at least e5x10 phs tem ? (>100MeV) would be directly detectable in the EGRET map., In the first case we can exploit the fact that a system with an EGRET flux of at least $\sim 5 \times 10^{-8}$ ph $^{-1}$ $^{-2}$ $>100$ MeV) would be directly detectable in the EGRET map. Given our mean [lux of ~1.1x10.? (855) and a total of 447 rich clusters. we would obtain an equivalent detection if only ~10 rich clusters had a flux of 5x107 and the rest were ganuna-ray dark.," Given our mean flux of $\sim 1.1\times 10^{-9}$ 5) and a total of 447 rich clusters, we would obtain an equivalent detection if only $\sim 10$ rich clusters had a flux of $5 \times 10^{-8}$ and the rest were gamma-ray dark." This would then provide a lower limit to the number of actively accreting clusters in the local Universe. a fraction by number.," This would then provide a lower limit to the number of actively accreting clusters in the local Universe, a fraction by number." Alternatively. if all clusters are assumed to be close to equilibritun with a mean temperature of kT~ 3keV. a mean gas mass LOMA. and. £.=0.05 then (μον are almost exactly as egamnma-ray luminous as predicted by Equation 2.," Alternatively, if all clusters are assumed to be close to equilibrium with a mean temperature of $kT\simeq 3$ keV, a mean gas mass $\simeq 10^{13}$ $_{\odot}$, and, $\xi_e=0.05$ then they are almost exactly as gamma-ray luminous as predicted by Equation 2." This implies that in fact all clusters V.10uld have been actively accreting recently. certainly within z<0.3—0.4. and possibly at je present Gime (2= 0).," This implies that in fact all clusters should have been actively accreting recently, certainly within $z<0.3-0.4$, and possibly at the present time $z=0$ )." Even in (he low-clensity simulation of Neshetοἱal.(2002) it appears (o be the case that 2=0 clusters can have active gamnma-ray. emission., Even in the low-density simulation of \citet{kes02} it appears to be the case that $z=0$ clusters can have active gamma-ray emission. " Seni-analvtic predictions [or low lensity cosmologies (Q,,T7=0.3. O4=0.7) also suggest that even at z~0. for massive clusters (LOM M, ) several 10P NL. in barvons should accrete per 10 ντ (Lacey&Cole1993)."," Semi-analytic predictions for low density cosmologies $\Omega_m=0.3$, $\Omega_{\Lambda}=0.7$) also suggest that even at $z\sim 0$, for massive clusters $10^{15}$ $_{\odot}$ ) several $10^{13}$ $_{\odot}$ in baryons should accrete per $10^{9}$ yr \citep{lac93}." . The shock regions may form some 5-I0Mpe from the cluster core. creating a gamma-ray ‘rine X emission (Ixeshetetal.2002).," The shock regions may form some 5-10Mpc from the cluster core, creating a gamma-ray `ring' of emission \citep{kes02}." . The suggestion of a rather more extended emission pattern from our cross-correlation (Figure 9) supports this scenario., The suggestion of a rather more extended emission pattern from our cross-correlation (Figure 9) supports this scenario. In (his case our estimated ἐς can be considered a good measure of the typical active non-thermal emission lor rich clusters., In this case our estimated $\bar{L}_{\gamma c}$ can be considered a good measure of the typical active non-thermal emission for rich clusters. This would then imply that the efficiency of transfer of energy [rom (he shocks to relativistic electrons is simular to the value of 5% inferred [rom non-relativistic shocks in the ISM., This would then imply that the efficiency of transfer of energy from the shocks to relativistic electrons is similar to the value of $5$ inferred from non-relativistic shocks in the ISM. The simulations of IXeshetetal.(2002) predict that for £.>0.03. fibre high resolution gamma-ray telescopes with threshold sensitivities >10! [or energies >10 GeV should be able to resolve some ΠΕ halos associated with large scale structures.," The simulations of \citet{kes02} predict that for $\xi_e\geq 0.03$, future high resolution gamma-ray telescopes with threshold sensitivities $>10^{-10}$ for energies $> 10$ GeV should be able to resolve some gamma-ray halos associated with large scale structures." The prospect ol direct. detection of gamma-ray sources with emission attributed to intergalactic shocks wilh GLAST. VERITAS. IIESS. MAGIC. or other atmospheric Cherenkov telescopes is an exciting one.," The prospect of direct detection of gamma-ray sources with emission attributed to intergalactic shocks with GLAST, VERITAS, HESS, MAGIC, or other atmospheric Cherenkov telescopes is an exciting one." Such gamma-ray halos could bea new source class of high energy sources waiting to be discovered., Such gamma-ray halos could be a new source class of high energy sources waiting to be discovered. Their existence would allow an entirely new. aud direct. probe of structure formation processes. leading (o an improved understuxding of inter- and immüra-cluster gas dvnamices. magnetic fields. and energy partitioning.," Their existence would allow an entirely new, and direct, probe of structure formation processes, leading to an improved understanding of inter- and intra-cluster gas dynamics, magnetic fields, and energy partitioning." While extrapolations from EGRET data and simulations for future instruments predict at least a dozen or more detectable sources (Ixeshetοἱal.2002).. direct determination of gamma-ray sources clue (ο shocks can be used as an independent calibration for £..," While extrapolations from EGRET data and simulations for future instruments predict at least a dozen or more detectable sources \citep{kes02}, direct determination of gamma-ray sources due to shocks can be used as an independent calibration for $\xi_e$ ." In fact. if the value of €& were lower than (he inferred," In fact, if the value of $\xi_e$ were lower than the inferred" After Fourier analysis with ~exp(Act|ihΖ) Eqs. (,After Fourier analysis with $\sim \exp{(-i\omega t + ik_z Z)}$ Eqs. ( 9)-(11) lead to the equation where Eq. (,9)-(14) lead to the equation where Eq. ( 15) is the Bessel equation when i?>0. the modified Bessel equation whem i?0$, the modified Bessel equation when $m^2<0$ and Euler equation when $m=0$ \citep{abr}." ere an plavs the role of the radia wave 1iuuber., Here $m$ plays the role of the radial wave number. For mz0 the expression (16) eads to he disversion relation of obliquely propagating hagnetoacoustic waves., For $m{\not=}0$ the expression (16) leads to the dispersion relation of obliquely propagating magnetoacoustic waves. For the paralcl propagation (io. ay= (0) the waves propagate either with sound or with ÁAlfvéóun speeds: for the high ο) plasma (ος29 04) the fast maenetoacoustic waves propagate with the sound speed (e= ce). while the slow magnetoacoustic waves propagate with the Alfvéuu speed (ω=έ ua).," For the parallel propagation (i.e. $m=0$ ), the waves propagate either with sound or with Alfvénn speeds; for the high $\beta$ plasma $c_s \gg v_A$ ) the fast magnetoacoustic waves propagate with the sound speed $\omega=\pm c_s k_z$ ), while the slow magnetoacoustic waves propagate with the Alfvénn speed $\omega=\pm c_A k_z$ )." For m?>(6 the solution to Eq. (, For $m^2>0$ the solution to Eq. ( 15). can be expressed in foxu of the Besse functions (Abramowitz&Steen1961) where eq aud eo» are constants.,"15) can be expressed in form of the Bessel functions \citep{abr} where $c_1$ and $c_2$ are constants." For the parallel propagation (i= 0) the solution to Eq. (, For the parallel propagation $m=0$ ) the solution to Eq. ( 15) cau be expressed as (Abramowitz&Steemn1961) where eq and ο. are constants,"15) can be expressed as \citep{abr} where $c_1$ and $c_2$ are constants." This is the solution to slow maguetoacoustic waves., This is the solution to slow magnetoacoustic waves. For the fast niaguetoacoustic waves Vj=0., For the fast magnetoacoustic waves $V_R=0$. Imposing that the velocity is finite on the axis we obtain This solution is not valid for uubouuded medi as it diverges for lavee AR., Imposing that the velocity is finite on the axis we obtain This solution is not valid for unbounded medium as it diverges for large $R$. Thus in evlindvical coordinates for unubonuuded inedia slow inuagnetoacoustic waves can nof propagate strictly along the magnetic field (wulike to the Cartesian coordinates)., Thus in cylindrical coordinates for unbounded medium slow magnetoacoustic waves can not propagate strictly along the magnetic field (unlike to the Cartesian coordinates). However as far as we are concerned in lower order harmonics of oscillations with the wavelengths comparable to the stellar radius. then it is unjustified to consider uubouuded uediuni in radial direction.," However as far as we are concerned in lower order harmonics of oscillations with the wavelengths comparable to the stellar radius, then it is unjustified to consider unbounded medium in radial direction." Therefore we should eive the boundary couditious at the stellar surface., Therefore we should give the boundary conditions at the stellar surface. Due to the sharp deusitv juup at the surface we nay set up free boundary conditions. for which he expression (19) is valid.," Due to the sharp density jump at the surface we may set up free boundary conditions, for which the expression (19) is valid." Then the velocity has. at the surface. the value Vg=«Ry. where Ry is he radius of the star.," Then the velocity has, at the surface, the value ${\tilde V_R} = c_1R_0$, where $R_0$ is the radius of the star." For suaicity. we conuser the slow maenetoacoustic WAVES pro]eating along a1uiperturbed magnetic field in the medina boundxd along radial direction.," For simplicity, we consider the slow magnetoacoustic waves propagating along anunperturbed magnetic field in the medium bounded along radial direction." The the yee boundary ccuditions at the surface allow the radial componecuts of velocity and uaenetic field Vy.bj to have the linear depeudeuce ou A due to Eqs. (," Then the free boundary conditions at the surface allow the radial components of velocity and magnetic field $V_R,\,b_R$ to have the linear dependence on $R$ due to Eqs. (" 9) aud (19) while by.Vy.py remain independent on 4.,"9) and (19) while $b_Z,\,V_Z,\,\rho_1$ remain independent on $R$." The wave dispersion relation is the same as for the torsional waves., The wave dispersion relation is the same as for the torsional waves. The relation between the different variables in the slow imaeuctoacoustic waves propagating along the magnetic field is as follows: It is casy to show from Eqs. (, The relation between the different variables in the slow magnetoacoustic waves propagating along the magnetic field is as follows: It is easy to show from Eqs. ( 11) and (21). that the total pressure perturbation at the surface vanishes for slow maguetoacoustic waves in the case of hieh § plana (e;>> c4) due to the dispersion relation w=teyh.,"14) and (21), that the total pressure perturbation at the surface vanishes for slow magnetoacoustic waves in the case of high $\beta$ plasma $c_s \gg c_A$ ) due to the dispersion relation $\omega=\pm c_A k_z$." Indeed we have for the total pressure perturbation: therefore the boundary condition is satisfied iu the zero order approximation with respect το)1 , Indeed we have for the total pressure perturbation: therefore the boundary condition is satisfied in the zero order approximation with respect to $\beta^{-1}$ . Thus the slow maguctoacoustic waves lead to the periodical modulation of the Alfvéóuu speed, Thus the slow magnetoacoustic waves lead to the periodical modulation of the Alfvénn speed streneth to the poloidal field threading the πιο parts of the accretiou disk. then the black holes contribution to the electromagnetic output (that is. the output due to the Dlaudford-Zuajek effect) is likely to be iguorable.,"strength to the poloidal field threading the inner parts of the accretion disk, then the black hole's contribution to the electromagnetic output (that is, the output due to the Blandford-Znajek effect) is likely to be ignorable." We lave argued here that it is hard to conceive of a situation in which the magnetic field threading the hole is significantly stronecr than the field threading the imuer disk., We have argued here that it is hard to conceive of a situation in which the magnetic field threading the hole is significantly stronger than the field threading the inner disk. This comes about for two main reasons., This comes about for two main reasons. First. the currents whic[um eenerate the field must. of uecessitv. be in the disk. aud not in the hole: anc secoud. the hole is (n effect) a very poor conductor. compared to the surrounding disk material.," First, the currents which generate the field must, of necessity, be in the disk, and not in the hole; and second, the hole is (in effect) a very poor conductor, compared to the surrounding disk material." We couclude. therefore. that independent of the spin of the black hole. the electromagnetic output of the disk Gu the form of Povutiug flux or maguetically driven wind) dominates that from the hole.," We conclude, therefore, that independent of the spin of the black hole, the electromagnetic output of the disk (in the form of Poynting flux or magnetically driven wind) dominates that from the hole." Iu addition. we have argued that the poloidal field streugths im the centers of standard accretion disks MModerski Sikora 1996b: (αλλον Abramowicz 1997) have heen overestimated in the literature.," In addition, we have argued that the poloidal field strengths in the centers of standard accretion disks Moderski Sikora 1996b; Ghosh Abramowicz 1997) have been overestimated in the literature." We have pointed. however. to some accretion scenarios in which the poloidal field strength could be significantly chhanced with respect to the standard disk picture.," We have pointed, however, to some accretion scenarios in which the poloidal field strength could be significantly enhanced with respect to the standard disk picture." This work was started at the proeranuue on The Dynamics of Astrophysical Discs” held at the Isaac Newton Tustitute for Mathematical Sciences. Cambridge.," This work was started at the programme on `The Dynamics of Astrophysical Discs' held at the Isaac Newton Institute for Mathematical Sciences, Cambridge." We thank Ralph Pudzitz. Pranab Cohosh aud Martiu Rees for useful discussions.," We thank Ralph Pudritz, Pranab Ghosh and Martin Rees for useful discussions." GIO. and JEP thank the Space Telescope Science Institute for EY, GIO and JEP thank the Space Telescope Science Institute for hospitality. ML acknowledges support from NASA Crant NACH5-6857., ML acknowledges support from NASA Grant NAG5-6857. "outburst, are consistent with measurements from previous outbursts.","outburst, are consistent with measurements from previous outbursts." We created X-ray spectra for each observation of GK Per and modelled them in12., We created X-ray spectra for each observation of GK Per and modelled them in. "4. We first used theGRPPHA tool to ensure that there was at least one count per spectral bin, and performed fitting using the C-statistic (this is more reliable than the sstatistic; see."," We first used the tool to ensure that there was at least one count per spectral bin, and performed fitting using the $C$ -statistic (this is more reliable than the statistic; see." HHumphrey 22009)., Humphrey 2009). " The hard X-ray emission in IPs is believed to come from a dense, post-shock plasma cooling via bremsstrahlung emission AAizu 1973; Cropper 11999), which we fitted with the physical model of this developed by Cropper ((1999)."," The hard X-ray emission in IPs is believed to come from a dense, post-shock plasma cooling via bremsstrahlung emission Aizu 1973; Cropper 1999), which we fitted with the physical model of this developed by Cropper (1999)." " A simple photoelectric absorber and two partial covering absorbers were necessary to obtain a good fit to the hard X-ray data, as previously found Ishida 11992)."," A simple photoelectric absorber and two partial covering absorbers were necessary to obtain a good fit to the hard X-ray data, as previously found Ishida 1992)." There were still significant residuals seen at soft energies., There were still significant residuals seen at soft energies. " A number of IPs show evidence for a soft 100 eV) blackbody component in their X-ray spectra dde Martino 22004; Evans HHellier 2007; Anzolin 22008), as did GK Per during the 2002 outburst (Vrielmann 22005; Evans HHellier 2007)."," A number of IPs show evidence for a soft 30--100 eV) blackbody component in their X-ray spectra de Martino 2004; Evans Hellier 2007; Anzolin 2008), as did GK Per during the 2002 outburst (Vrielmann 2005; Evans Hellier 2007)." We thus added a blackbody component., We thus added a blackbody component. " We also added narrow Gaussian lines at 0.423, 0.557 and 0.907 keV to reproduce the lines from the nova shell; the energies, widths and normalisations of these lines were taken from Balman (2005)."," We also added narrow Gaussian lines at 0.423, 0.557 and 0.907 keV to reproduce the lines from the nova shell; the energies, widths and normalisations of these lines were taken from Balman (2005)." " In IPs it is often assumed that most of the accretion luminosity is emitted as hard X-rays Evans HHellier 2007 showed the bolometric luminosity of the soft component to be <00.1 of the bolometric luminosity of the hard component), however since the 0.3-10 keV bandpass of the XRT (and the EPIC instruments on XMM)) covers only the hard tail of the blackbody component, the details of the soft emission are not particularly well constrained."," In IPs it is often assumed that most of the accretion luminosity is emitted as hard X-rays Evans Hellier 2007 showed the bolometric luminosity of the soft component to be 0.1 of the bolometric luminosity of the hard component), however since the 0.3–10 keV bandpass of the XRT (and the EPIC instruments on ) covers only the hard tail of the blackbody component, the details of the soft emission are not particularly well constrained." To remedy this we created a spectral point from the UVOT data for observation 009 (the X-ray brightest observation) using the tool and fitted the combined UVOT and XRT data for this observation., To remedy this we created a spectral point from the UVOT data for observation 009 (the X-ray brightest observation) using the tool and fitted the combined UVOT and XRT data for this observation. The (unabsorbed) bolometric flux from the blackbody component in this fit far exceeded the hard X-ray flux; however at D=470 pc it also exceeded the Eddington luminosity by more than an order of magnitude [assuming a 0.87 wwhite dwarf; Morales-Rueda ((2002)]., The (unabsorbed) bolometric flux from the blackbody component in this fit far exceeded the hard X-ray flux; however at $D=470$ pc it also exceeded the Eddington luminosity by more than an order of magnitude [assuming a 0.87 white dwarf; Morales-Rueda (2002)]. " There thus cannot be a single spectral component, powered by accretion energy, spanning the UV to soft X-ray wavelength range."," There thus cannot be a single spectral component, powered by accretion energy, spanning the UV to soft X-ray wavelength range." A potential contributor to the UV emission is the inner disc., A potential contributor to the UV emission is the inner disc. " Frank, King RRaine (2002) give the temperature ofthe disc at radius R as: Using Mwp-00.87 Mo(Morales-Rueda 22002), the white dwarf relation of Nauenberg (1972), and Mmass-radius>5x 10g s!, we find the disc"," Frank, King Raine (2002) give the temperature ofthe disc at radius $R$ as: Using 0.87 (Morales-Rueda 2002), the white dwarf mass-radius relation of Nauenberg (1972), and $\dot{M} \ge 5\tim{16} $ g $^{-1}$ , we find the disc" "If OB/Oz is positive, the field in the crust will increase over a typical timescale of Traut.","If $\partial B/\partial z$ is positive, the field in the crust will increase over a typical timescale of $\tau_{Hall}$." " We assume henceforth that strong currents exist in the crust at an age of ~10* years, and explore the consequences."," We assume henceforth that strong currents exist in the crust at an age of $\sim 10^4$ years, and explore the consequences." " We model the outer crust as an infinite slab, with $ pointing into the star (see Fig."," We model the outer crust as an infinite slab, with $\bm{\hat x}$ pointing into the star (see Fig." 2)., 2). " The thermal evolution of the neutron star outer crust is described by the energy conservation equation, where p is the density, ου is the specific heat, 1 is the electric current, Q, is the neutrino emissivity, and κ. is the thermal conductivity."," The thermal evolution of the neutron star outer crust is described by the energy conservation equation, where $\rho$ is the density, $c_v$ is the specific heat, $\bm{j}$ is the electric current, $Q_{\nu}$ is the neutrino emissivity, and $\kappa$ is the thermal conductivity." " The magnetic field evolution is described by the induction equation where the magnetic field is related to the current by As justified below, we work in an approximation in which magnetic induction can be ignored, so we need not specify boundary conditions on B."," The magnetic field evolution is described by the induction equation where the magnetic field is related to the current by As justified below, we work in an approximation in which magnetic induction can be ignored, so we need not specify boundary conditions on $\bm{B}$." " The slab consists of of 3 regions - an atmosphere with no magnetic dissipation, an outer crust, and an isothermal inner crust/core."," The slab consists of of 3 regions - an atmosphere with no magnetic dissipation, an outer crust, and an isothermal inner crust/core." " The atmosphere extends from a density of 10gcm-? at the stellar surface to 109gcm?, the outer boundary of the crust."," The atmosphere extends from a density of $10^4 \rm{g} \, \rm{cm}^{-3}$ at the stellar surface to $10^6 \rm{g} \, \rm{cm}^{-3}$, the outer boundary of the crust." " For the atmosphere and outer crust zones, we employ the density model of ?.."," For the atmosphere and outer crust zones, we employ the density model of \cite{friedman}." " The inner crust/core zone is assumed to be an infinite heat reservoir, beginning at a density of p=10!gcm?."," The inner crust/core zone is assumed to be an infinite heat reservoir, beginning at a density of $\rho=10^{11} \rm{g} \, \rm{cm}^{-3}$." " At the stellar surface we choose the unperturbed temperature to be, and require that the heat flux at the boundary equal the blackbody emission rate at temperature Τε, As a simple model of the toroidal component of the neutron star magnetic field, we introduce to the outer crust zone a current sheet of width L: where jo is the amplitude of the current, and zo the location of the peak current."," At the stellar surface we choose the unperturbed temperature to be, and require that the heat flux at the boundary equal the blackbody emission rate at temperature $T_s$, As a simple model of the toroidal component of the neutron star magnetic field, we introduce to the outer crust zone a current sheet of width $L$: where $j_0$ is the amplitude of the current, and $x_0$ the location of the peak current." " This analytic form allows a large, nearly uniform current near the heating peak, falling off sharply for |—xo|>L (Fig. 3))."," This analytic form allows a large, nearly uniform current near the heating peak, falling off sharply for $|x-x_0| > L$ (Fig. \ref{fig:current}) )." " The magnetic field resulting from the current lies in the y-z plane, with variation in the @ direction."," The magnetic field resulting from the current lies in the y-z plane, with variation in the $\bm{\hat x}$ direction." " In our models, the heating region is near the center of the outer crust, with characteristic width much smaller than the crust thickness to ensure negligible heating at the boundaries."," In our models, the heating region is near the center of the outer crust, with characteristic width much smaller than the crust thickness to ensure negligible heating at the boundaries." We note that this current model leads to large pressure gradients in the crust., We note that this current model leads to large pressure gradients in the crust. " To form a stable current model, a complex geometry is required,"," To form a stable current model, a complex geometry is required," of the component multiplied by a factor of 1.8; cf. ?)).,of the component multiplied by a factor of 1.8; cf. \citealt{1999ASPC..180..335P}) ). The flux variability time scale is defined as Aty4;=dt/In(Sι/52)., The flux variability time scale is defined as $\Delta t_\mathrm{var} = dt/\ln(S_\mathrm{1}/S_\mathrm{2})$. " The value of S, is the measured maximum component flux density, while $5 represents the minimum component flux density selected at the time of maximum absolute value of the time derivative of the flux density."," The value of $S_\mathrm{1}$ is the measured maximum component flux density, while $S_\mathrm{2}$ represents the minimum component flux density selected at the time of maximum absolute value of the time derivative of the flux density." " It is then possible to calculate bulk Lorentz factors by combining the derived óy4 With Bapp, Combining the derived values for all components, a mean Lorentz factor of 12.5 and a mean Doppler factor of 14.4 are obtained (see Table 2))."," It is then possible to calculate bulk Lorentz factors by combining the derived $\delta_\mathrm{var}$ with $\beta_\mathrm{app}$, Combining the derived values for all components, a mean Lorentz factor of 12.5 and a mean Doppler factor of 14.4 are obtained (see Table \ref{tab:kinsummary}) )." " An upper limit for the viewing angle © can immediately be determined usingthe average apparent component speed fs, and the relation ógi;=4/1+Beop-", An upper limit for the viewing angle $\Theta$ can immediately be determined usingthe average apparent component speed $\overline{\beta}_\mathrm{app}$ and the relation $\delta_\mathrm{min} = \sqrt{1+\beta_\mathrm{app}^2}$. This combined with the equation yields ©<5.2°., This combined with the equation yields $\Theta \leq 5.2\degr$. " Using the variability time scale argument and the derived values of ὄναι from above, the values ©,,, for each component are obtained, which together have a mean Qu. of 4108, consistent with our upper limit."," Using the variability time scale argument and the derived values of $\delta_\mathrm{var}$ from above, the values $\Theta_\mathrm{var}$ for each component are obtained, which together have a mean $\Theta_\mathrm{var}$ of $^{+0.65}_{-0.51}$, consistent with our upper limit." " ? obtained a similar value of O=5.1°, which was determined by combining the component speeds at GGHz and variability Doppler factors derived from single-dish observations at GGHz."," \citet{2009A&A...507L..33P} obtained a similar value of $\Theta = 5.1\degr$, which was determined by combining the component speeds at GHz and variability Doppler factors derived from single-dish observations at GHz." " Earlier, ? obtained a smaller viewing angle of 2.7°+ uusing VLBI data at GGHz alone."," Earlier, \citet{2005AJ....130.1418J} obtained a smaller viewing angle of $\pm$ using VLBI data at GHz alone." " In the following discussion, we adopt © =5°.."," In the following discussion, we adopt $\Theta$ =." " With the kinematics determined in Section 3.1.1,, it is possible to estimate the time at which a moving jet feature passes the VLBI core at GGHz."," With the kinematics determined in Section \ref{sec:kinematic}, it is possible to estimate the time at which a moving jet feature passes the VLBI core at GHz." These passages are referred to as ejection epochs., These passages are referred to as ejection epochs. The ejection epoch also marks the time at which a new jet feature begins to contribute to the observed radio emission., The ejection epoch also marks the time at which a new jet feature begins to contribute to the observed radio emission. " As a first approach to determine the ejection epochs, we assume that the jet is optically thin all the way to the core and the features already travel at the observed average speed while passing through the VLBI core."," As a first approach to determine the ejection epochs, we assume that the jet is optically thin all the way to the core and the features already travel at the observed average speed while passing through the VLBI core." Under these assumptions the ejection epoch is determined by back tracing the fitted linear trajectories., Under these assumptions the ejection epoch is determined by back tracing the fitted linear trajectories. " The resulting ejection epochs for all features are listed in Table 2,, as well."," The resulting ejection epochs for all features are listed in Table \ref{tab:kinsummary}, as well." " This approach provides reasonable estimates of the ejection epochs for non-accelerating features, while for the apparently accelerating components Q9 and Q10 a different approach is required."," This approach provides reasonable estimates of the ejection epochs for non-accelerating features, while for the apparently accelerating components Q9 and Q10 a different approach is required." " Looking at the radial separations of Q9 and Q10 in Fig. 3,,"," Looking at the radial separations of Q9 and Q10 in Fig. \ref{fig:separation}," the acceleration is most evident for the time before 2009.6., the acceleration is most evident for the time before 2009.6. An upper limit on the ejection epoch can be determined using a linear fit to the data points after 2009.5 for Q9 and 2009.4 for Q10 (Tupper in Table 2))., An upper limit on the ejection epoch can be determined using a linear fit to the data points after 2009.5 for Q9 and 2009.4 for Q10 $\tau_\mathrm{upper}$ in Table \ref{tab:kinsummary}) ). " Similarly, lower limits, Tipwer, on the ejection epochs of Q9 and Q10 are obtained by considering only data points before 2009.5 and 2009.4 respectively."," Similarly, lower limits, $\tau_\mathrm{lower}$, on the ejection epochs of Q9 and Q10 are obtained by considering only data points before 2009.5 and 2009.4 respectively." " In flat spectrum radio quasars (FSRQs), such as 3345, the component flux decay is commonly driven by radiative losses (??),, which was assumed in Section 3.1.1 without further justification."," In flat spectrum radio quasars (FSRQs), such as 345, the component flux decay is commonly driven by radiative losses \citep{1999ApJ...521..509L, 2005AJ....130.1418J}, which was assumed in Section \ref{sec:kinematic} without further justification." " To test this, the maximum component brightness temperature needs to be calculated as a measure for the emissionintensity of each component, using: where Scomp is the component flux density in Jansky, z the redshift of the source, ἆσοπρ the FWHM size of the circular Gaussian in mas and ν the observing frequency in GHz."," To test this, the maximum component brightness temperature needs to be calculated as a measure for the emissionintensity of each component, using: where $S_\mathrm{comp}$ is the component flux density in Jansky, $z$ the redshift of the source, $d_\mathrm{comp}$ the FWHM size of the circular Gaussian in mas and $\nu$ the observing frequency in GHz." In Fig., In Fig. " 4 the brightness temperatures for components Q9, Q10 and Q11 are plotted as a function of the radial separation from the core."," \ref{fig:Tb} the brightness temperatures for components Q9, Q10 and Q11 are plotted as a function of the radial separation from the core." " In the common picture of the shock-in-jet model, a relativistic shock propagates down a conical jet, slowly expanding adiabatically albeit maintaining shock conditions."," In the common picture of the shock-in-jet model, a relativistic shock propagates down a conical jet, slowly expanding adiabatically albeit maintaining shock conditions." " In this scenario the assumption of a power-law electron energy distribution (N(E)dEο.E? dE), a power-law magnetic field evolution (Bος and a constant jet opening angle with the jet transverse size revproportional to the distance along the jet (οιocΠιοSin ©) can be made."," In this scenario the assumption of a power-law electron energy distribution $N(E)\,dE \propto E^{-s}\,dE$ ), a power-law magnetic field evolution $B \propto r_\mathrm{jet}^{-a}$ ) and a constant jet opening angle with the jet transverse size proportional to the distance along the jet $d_\mathrm{jet} \propto r_\mathrm{jet} \sin{\Theta}$ ) can be made." " While the shock continues to travel down the jet, it undergoes three major evolutionary stages dominated by Compton, synchrotron and adiabatic energy losses (?).. "," While the shock continues to travel down the jet, it undergoes three major evolutionary stages dominated by Compton, synchrotron and adiabatic energy losses \citep{1992vob..conf...85M}. ." "From this it follows that the brightness temperature decays as a power-law, Tjcc , where rj« is the distance in the jet at which 7}jet is measured."," From this it follows that the brightness temperature decays as a power-law, $T_\mathrm{b,jet} \propto r_\mathrm{jet}^{-\epsilon}$ , where $r_\mathrm{jet}$ is the distance in the jet at which $T_\mathrm{b,jet}$ is measured." pmThe value of e can be derived, The value of $\epsilon$ can be derived in the C.V. distribution of ddata.,"in the $U,V$ distribution of data." ? even associated close star clusters with some of these streams., \cite{Skuljan99} even associated close star clusters with some of these streams. We refer to ? aud ?. for more on that topic., We refer to \cite{Skuljan99} and \cite{Nord04} for more on that topic. We have calculated the orbits of our stars based on the ealactic potential model of ? (hereafter AS) using an orbit code developed by ?.. and. further adapted for our work (?.. ?)).," We have calculated the orbits of our stars based on the galactic potential model of \cite{AL91} (hereafter AS) using an orbit code developed by \cite{Ode92}, and further adapted for our work \citealt{B97}, \citealt{AB2k4}) )." Orbits are calculated in steps of MMyr over a time span of CiCiyr (since we are not modcling the evolution of the Galaxy. this long span. although physically unrealistic. is allowed for a good sampling of the shape of wide orbits).," Orbits are calculated in steps of Myr over a time span of Gyr (since we are not modeling the evolution of the Galaxy, this long span, although physically unrealistic, is allowed for a good sampling of the shape of wide orbits)." A selected few orbits can be seen in reforbs.., A selected few orbits can be seen in \\ref{orbs}. Most of the orbits are of a regular box shape., Most of the orbits are of a regular box shape. A few are mregularlv shaped. perhaps a result of the close approach of the star to the ealactic center aud thus the interaction with the Bulec potential.," A few are irregularly shaped, perhaps a result of the close approach of the star to the galactic center and thus the interaction with the Bulge potential." By looking at histograms of the orbit ecceutyicitics and normalized z-exteuts refeccnze}). we qualitatively come to the same conuclusious asin ?..," By looking at histograms of the orbit eccentricities and normalized $z$ -extents \\ref{eccnze}) ), we qualitatively come to the same conclusions as in \cite{AB2k4}." In the eee-histograim. a separation between a high and low ccceutricity sample can be made with the help of the IIPS.," In the $ecc$ -histogram, a separation between a high and low eccentricity sample can be made with the help of the HPS." It is roughly at ecc=0.15. above which he halo stars donunate the distribution.," It is roughly at $ecc=0.45$, above which the halo stars dominate the distribution." In the »zc-histograi. the stars at pie>0.3 are clearly of the IIPS.," In the $nze$ -histogram, the stars at $nze > 0.3$ are clearly of the HPS." But IIPS stars also coutribute to th| peak at low normalized z-extents. since our definition of the IIPS does not exclude highly eccentric. coplanar orbits.," But HPS stars also contribute to the peak at low normalized $z$ -extents, since our definition of the HPS does not exclude highly eccentric, coplanar orbits." refekin slows the kinetic energy versus orbital velocity of our star sample., \\ref{ekin} shows the kinetic energy versus orbital velocity of our star sample. Both the measured and medianised values are given., Both the measured and medianised values are given. " Looking at the median values. one can see that most of the disk stars are situated alone a line pointing from the LSR towards lower Ey,«4 aud Oya."," Looking at the median values, one can see that most of the disk stars are situated along a line pointing from the LSR towards lower $E_{\rm kin,med}$ and $\Theta_{\rm med}$." A clear eap can be seen at Θ~1101. below which there are ouly IIPS stars.," A clear gap can be seen at $\Theta\sim110$, below which there are only HPS stars." Usine the information frou rvefToomre we have separated the IPS stars from the disk stars. a separation confined through the kincmatic represcutation of refbott.. 5.. and 6..," Using the information from \\ref{Toomre} we have separated the HPS stars from the disk stars, a separation confirmed through the kinematic representation of \\ref{bott}, \ref{eccnze}, and \ref{ekin}." ILowever. imdividual stars of one group may still be included in the other eroup.," However, individual stars of one group may still be included in the other group." From the stm of the orbits we obtain the :-probability distribution of our sample stars. as introduced in? and further refined im ?..," From the sum of the orbits we obtain the $z$ -probability distribution of our sample stars, as introduced in \cite{B97} and further refined in \cite{AB2k4}." We analysed it for disk aud halo populations with a weiehted \?-fit., We analysed it for disk and halo populations with a weighted $\chi^2$ -fit. The larec range iu Ας) made a weighting scheme necessary that could take iuto account both the disk region and halo region data poiuts., The large range in $N(z)$ made a weighting scheme necessary that could take into account both the disk region and halo region data points. We chose L/N(:) as à weight to accomplish that eoal., We chose $1/N(z)$ as a weight to accomplish that goal. A simple exponential relation of the form [IN(:)=N(O}τέ howas fitted for cach component., A simple exponential relation of the form $N(z)=N(0)\cdot e^{-z/h}$ was fitted for each component. where N() is the star umber density iu the loca ealactic plane aud fis the scale height., where $N(0)$ is the star number density in the local galactic plane and $h$ is the scale height. Both sides of the distribution were used for the calculations., Both sides of the distribution were used for the calculations. Analyses of the orbits showed that the data points with 2o> Sipe are from three stars only., Analyses of the orbits showed that the data points with $z>8$ kpc are from three stars only. They are WD 126778. TD 175305 and ΠΟ 151266.," They are HD 126778, HD 175305 and HD 184266." All the other IIPS stars show stronely elliptic orbits close to the galactic plane., All the other HPS stars show strongly elliptic orbits close to the galactic plane. rofZhist] shows the z-probabilitv distribution. as well as the best fits.," \\ref{Zhist1} shows the $z$ -probability distribution, as well as the best fits." First. a two-component Bt. representing the disk and the halo. was mace.," First, a two-component fit, representing the disk and the halo, was made." But in the range of 2-5 kpc the full :-distribution is uot very well approximated (see left half of refZhistl))., But in the range of 2-5 kpc the full $z$ -distribution is not very well approximated (see left half of \\ref{Zhist1}) ). We therefore also made a three compoucut fit., We therefore also made a three component fit. The results eive a anuch better fit to the data than with only two compoucuts (right half of refZhnistl))., The results give a much better fit to the data than with only two components (right half of \\ref{Zhist1}) ). Assuniug that exponential functions apropriately describe the :-distribution. our data sugecsts the existence of more than two spatially distinct stellar eroups.," Assuming that exponential functions apropriately describe the $z$ -distribution, our data suggests the existence of more than two spatially distinct stellar groups." The results of je fits are eiven in reffits.., The results of the fits are given in \\ref{fits}. We rote that the scale heights of the halo are derived. from ouly τος stellar orbits aud are onlv listed for completeness., We note that the scale heights of the halo are derived from only three stellar orbits and are only listed for completeness. The results obtained are based on what will be called the base-line model., The results obtained are based on what will be called the base-line model. Below we will explore star selections with different parallax accuracies or sclected with different magnitude aud colour limits (as in MDzel))., Below we will explore star selections with different parallax accuracies or selected with different magnitude and colour limits (as in \\ref{CMDsel}) ). We will also explore (in refinodels}) he effects of different. models for the mass distribution iu the Milkv. Way ou our base-line results., We will also explore (in \\ref{models}) ) the effects of different models for the mass distribution in the Milky Way on our base-line results. " Iu we bricfiy gave some details on star samples with different cconstraints,", In \\ref{sample} we briefly gave some details on star samples with different constraints. By analysing the aud, By analysing the and expected for a stellar wind of +0.6 (Simon et al.,expected for a stellar wind of +0.6 (Simon et al. 1983: Wright Barlow 1975) compared to +2 lor optically thick HE II regions., 1983; Wright Barlow 1975) compared to +2 for optically thick H II regions. More conclusively. stellar wind sources have broad (few LOO +). optically thick. near-IR IE I emission lines (Persson οἱ al.," More conclusively, stellar wind sources have broad (few 100 $^{-1}$ ), optically thick, near-IR H I emission lines (Persson et al." 1984: Dunn οἱ al., 1984; Bunn et al. 1995). whilst these lines in UCHILIS are optically thin and a few LOs | broad (e.g. Lumsden IIoare 1996).," 1995), whilst these lines in UCHIIs are optically thin and a few 10s $^{-1}$ broad (e.g. Lumsden Hoare 1996)." Theoretically of course. the origin of the stellar wind material is from the star and/or disc itself. whilst the later UCIT region phase begins when significant surrounding molecular cloud gas has been ionized.," Theoretically of course, the origin of the stellar wind material is from the star and/or disc itself, whilst the later UCHII region phase begins when significant surrounding molecular cloud gas has been ionized." Objects classified as hyper-compact I 1I regions have intermediate properties and may represent a (transition phase (see review by lloare et al., Objects classified as hyper-compact H II regions have intermediate properties and may represent a transition phase (see review by Hoare et al. 2006)., 2006). The ability to resolve the radio emission from the stellar wind sources means (hat insights can be gained into the geometry of the mass-loss., The ability to resolve the radio emission from the stellar wind sources means that insights can be gained into the geometry of the mass-loss. 1t is of particular interest to discover the relationship. if anv. between the ionized wind close to (he star. and the much larger scale bipolar molecular outflows that are invariably associated with massive YSOs.," It is of particular interest to discover the relationship, if any, between the ionized wind close to the star, and the much larger scale bipolar molecular outflows that are invariably associated with massive YSOs." Iu low-mass YSOs. the bipolar molecular outflows are often. accompanied by hiehly collimated stellar jets.," In low-mass YSOs, the bipolar molecular outflows are often accompanied by highly collimated stellar jets." These optical/I jets ends in bow shocks that appear to be responsible for driving the molecular outflows in many cases (Chernin Masson 1995). alühough not necessarily all (Lee et al.," These optical/IR jets ends in bow shocks that appear to be responsible for driving the molecular outflows in many cases (Chernin Masson 1995), although not necessarily all (Lee et al." 2001)., 2001). One max expect highly collimated MIID ciiven jets to be less common in more massive stars since magnetic fields are generally believed to play less of a role compared Lo radiation pressure throughout (heir lives., One may expect highly collimated MHD driven jets to be less common in more massive stars since magnetic fields are generally believed to play less of a role compared to radiation pressure throughout their lives. Indeed. evidence for such. highly collimated jets from high-mass YSOs has been much harder to come by (e.g. Poetzel et al.," Indeed, evidence for such highly collimated jets from high-mass YSOs has been much harder to come by (e.g. Poetzel et al." 1992)., 1992). Searches in the optical will obviously be hindered by the heavy extinction close to the very embedded massive voung stars. although searches for shocked emission further out along the outflows have also shown no signs of bow shock ivpe emission (Alvarez IHoare 2005).," Searches in the optical will obviously be hindered by the heavy extinction close to the very embedded massive young stars, although searches for shocked emission further out along the outflows have also shown no signs of bow shock type emission (Alvarez Hoare 2005)." Similarly. near-IR. observations of shocked molecular hydrogen do not often reveal (he jet and/or cavity structures seen in low-mass YSOs (Davis el al.," Similarly, near-IR observations of shocked molecular hydrogen do not often reveal the jet and/or cavity structures seen in low-mass YSOs (Davis et al." 1998). although see Davis et al. (," 1998), although see Davis et al. (" 2004).,2004). Badio investigations do not suffer [rom extinction ab all and the best example of a jet [rom a massive YSO is the spectacular radio jet from GGD27. the exciting source that crives (he HILSO-81 outflow.," Radio investigations do not suffer from extinction at all and the best example of a jet from a massive YSO is the spectacular radio jet from GGD27, the exciting source that drives the HH80-81 outflow." This parsec-scale precessing radio jel which end in bow shocks was found by Marti et al. (, This parsec-scale precessing radio jet which end in bow shocks was found by Martí et al. ( 1993).,1993). Follow-up multi-epoch studies by Marti et al. (, Follow-up multi-epoch studies by Martí et al. ( "1998) reveal proper motions of clumps in the jet. which correspond to tangential velocities of at least 500 |,","1998) reveal proper motions of clumps in the jet, which correspond to tangential velocities of at least 500 $^{-1}$." Such velocities are similar to the FWZI of emission lines in other massive YSOs. but unfortunately the exciting source of GGD2T cannot be seen directly at near-IR wavelengths and no wind lines have vet been seen (Aspin 1994).," Such velocities are similar to the FWZI of near-IR emission lines in other massive YSOs, but unfortunately the exciting source of GGD27 cannot be seen directly at near-IR wavelengths and no wind lines have yet been seen (Aspin 1994)." Another radio jet is that in Cep À2 (RoclrigenezeD et al., Another radio jet is that in Cep A2 (Rodrígguez et al. 1994) where proper motion studies vield tangential velocities of 600 | (Curiel| eet al., 1994) where proper motion studies yield tangential velocities of 600 $^{-1}$ (Curiel et al. 2006)., 2006). It is perpendicular to a rotating, It is perpendicular to a rotating previous oue isot nüssed to he function: The results for the paraueters are given in reftimefit..,previous one is missed to the function: The results for the parameters are given in \\ref{timefit}. Asstmuing a wait time that is two times lo15fayer (1.6. doubliic the umubers CLIVE( above) οWes a οmxl description of the treud. followed w the bursts forming the second line from the bottom.," Assuming a wait time that is two times longer (i.e., doubling the numbers derived above) gives a good description of the trend followed by the bursts forming the second line from the bottom." This shows again that for these poiuts the previous burst is niüssed., This shows again that for these points the previous burst is missed. Note that formally the fit ix not acceptable (42=5.7. 92 d.o.f.).," Note that formally the fit is not acceptable $\chi^2_\nu=5.7$, 92 d.o.f.)," but the general rend is clearly visible., but the general trend is clearly visible. This meaus that iere are sieuifcan fiuctuatious in the wait time aroun the average relation., This means that there are significant fluctuations in the wait time around the average relation. From theory a linear relation between the burst rate (Giuverse of the wait time) and the persistent flux Is expected. and no bursts are expected anviuore when sow Fyac=0=U OreergCL2.UN El.c. no accretion).," From theory a linear relation between the burst rate (inverse of the wait time) and the persistent flux is expected, and no bursts are expected anymore when $F_{\rm pers}$ =0 $\ergcms$ (i.e. no accretion)." tion). We thereftherefore ried to fit the relation: The resut of the Gt of parameter C is eiven in roftimefit.., We therefore tried to fit the relation: The result of the fit of parameter C is given in \\ref{timefit}. Given the laree nunber of bursts. we lave a investigated the relation betweenthe wait time a oxwisteunt fux for 260 and 0.," Given the large number of bursts, we have also investigated the relation betweenthe wait time and persistent flux for $-$ 260 and $-$ 0." In f widdle panel of refwaiting we show the results for 260. a rotice the strong sueeestionsuge of a linear cepeudenc," In the middle panel of \\ref{waiting} we show the results for $-$ 260, and notice the strong suggestion of a linear dependency." However. this only applies to persistent fux levels helnw LLL 7ss 1.," However, this only applies to persistent flux levels below 0.14 $^{-2}$ $^{-1}$." At higher persistent fux t1ο wait fine between bursts becomes apparently rando11., At higher persistent flux the wait time between bursts becomes apparently random. We fitted t1e relations as eiven above for the bursts with a »orsisteut flux below 0.1 7 | aud where we expect hat the previous burst is not missed., We fitted the relations as given above for the bursts with a persistent flux below 0.14 $^{-2}$ $^{-1}$ and where we expect that the previous burst is not missed. The hest fit parameers are given in reftimefit.., The best fit parameters are given in \\ref{timefit}. Also for 0 there vaguely appears to be a incar relation between the persistent flux aud the weüt ine (wight panel refwaiting)}., Also for $-$ 0 there vaguely appears to be a linear relation between the persistent flux and the wait time (right panel \\ref{waiting}) ). However. the scatter is significantly larger han iu the previous two cases. making a clear distinction )tween the different inuultiples of the wait time very dificult.," However, the scatter is significantly larger than in the previous two cases, making a clear distinction between the different multiples of the wait time very difficult." Therefore. an iterative process was uscd to search or bursts where we expect that the previous one is nof wissecl.," Therefore, an iterative process was used to search for bursts where we expect that the previous one is not missed." We simniultaucouslv fitted a straight line (the single wait fine Lue) plus several lines at multiples of the wait nue., We simultaneously fitted a straight line (the single wait time line) plus several lines at multiples of the wait time. The bursts closes totie single wait finie πιο were attributed to this line axd 1sed for a least-square f to ect a better estimate., The bursts closest to the single wait time line were attributed to this line and used for a least-square fit to get a better estimate. This process was continued unu ila vost fit was found., This process was continued until a best fit was found. The bursts attributed to the siiele wait nue line were also usec o fit the relation: The results are stmmarized in roftiniefit.., The bursts attributed to the single wait time line were also used to fit the relation: The results are summarized in \\ref{timefit}. For the other six sources the number of subsequeut bursts with a wait ine of less than oue day becomes very sunall. and the data does not allow the verification of a linear relation.," For the other six sources the number of subsequent bursts with a wait time of less than one day becomes very small, and the data does not allow the verification of a linear relation." We converted the fit parameters as eiven in from the observed flux to luminosities using the conversion factors aud distances as given in reftop.., We converted the fit parameters as given in \\ref{timefit} from the observed flux to luminosities using the conversion factors and distances as given in \\ref{top}. . " For the parameter C the values are (2.54 1079, (Q8£005)«1079 and (1.9+L1)«1076 eresb for 21. 260 and 0. respectively (taking iuto account au error of in the"," For the parameter C the values are $(2.5\pm1.5)\times10^{36}$ , $(0.8\pm0.5)\times10^{36}$ and $1.9\pm1.1)\times10^{36}$ $\ergs$ for $-$ 24, $-$ 260 and $-$ 0, respectively (taking into account an error of in the" Hs located within or behiud M 3l there navy be an additional contribution from the ealaxy disk.,is located within or behind M 31 there may be an additional contribution from the galaxy disk. " However. the low Nj, values from the N-ray spectral fitting imdicate hat M 31 is uulikelv. to be a niajor contributor to the extinction."," However, the low $_H$ values from the X-ray spectral fitting indicate that M 31 is unlikely to be a major contributor to the extinction." VVo thus conclude that the high flux ratio is not due ο dust reddadenimeg., We thus conclude that the high flux ratio is not due to dust reddening. The lack of a poiike radio counterpart above 1.5 mJy ds net very constrainsie., The lack of a point-like radio counterpart above 1.5 mJy is not very constraining. o For exaniple. using the black hole fundamental plane relatiouship between N-aav hDnunuinosity. racio DIununositv. aud black hole mass. we would uot expect to be able to detect radio emiüssiou Yon al ACN unless it was closer than 1.5 Mpc Cassiuuiug 2006)..," For example, using the black hole fundamental plane relationship between X-ray luminosity, radio luminosity, and black hole mass, we would not expect to be able to detect radio emission from an AGN unless it was closer than 1.5 Mpc \citep[assuming a black hole mass of 10$^6$ M$_\odot$; e.g.][]{koe06}." " At such a distance the galaxy itsel: sliould be casily resolved in the optical/NIR Huaces,", At such a distance the galaxy itself should be easily resolved in the optical/NIR images. " Likewise, radio cussion from the jet of a 20 M. black hole N-rav. binary would not be deectahle unless the svsteni was closer than 20 pe. a clistance at which ciission frou the disk or donor star would surely be detectable in our deep optical Ππασος,"," Likewise, radio emission from the jet of a 20 $_\odot$ black hole X-ray binary would not be detectable unless the system was closer than 20 pc, a distance at which emission from the disk or donor star would surely be detectable in our deep optical images." The EPIC X-rav spectra are consistent with blackbody plus steep power law. double blackbody. disk blackbody plus power law. disk blackbody plus thermal Comptouisation. or thermal bremsstrabhme models (all with the addition of a photoelectric absorption component of low column clensity. consistent with the Cralactic latitude of the source).," The EPIC X-ray spectra are consistent with blackbody plus steep power law, double blackbody, disk blackbody plus power law, disk blackbody plus thermal Comptonisation, or thermal bremsstrahlung models (all with the addition of a photoelectric absorption component of low column density, consistent with the Galactic latitude of the source)." The temperature of the bremsstralhiue model was 0.98 keV. much lower thaw he lowest temperature measured for a CV (KT=1.9keV 2007).," The temperature of the bremsstrahlung model was 0.98 keV, much lower than the lowest temperature measured for a CV \citep[kT = 1.9 keV from thermal plasma fits to \xmm\ spectra of the quiescent dwarf nova GW Lib;][]{hil07}." ". Iu addition. line euids- sion becoux""s luoro sienificant relative to the uu- derlviug countiuuua spectrin for CVs with low temperature spectra."," In addition, line emis- sion becomes more significant relative to the un- derlying continuum spectrum for CVs with low temperature spectra." ence. if NAIA —OBS|LO was a CV ait would be οκροστος that he spectrum would be consistent with a thermal plasma model with nuO11-ZCYO eleiieutal abundances.," Hence, if XMM J0038+40 was a CV it would be expected that the spectrum would be consistent with a thermal plasma model with non-zero elemental abundances." " The spectrum of ls not consistent with such a model. adding further weight to the argument against 1t being a CV,"," The spectrum of is not consistent with such a model, adding further weight to the argument against it being a CV." Spectra of accreting black hole and neutron star N-rav binardes are typically modelled by a power aw (represenπιο verse Compton enmissiou). soluctimes with the addition of a soft thermal conrponeut attributed either to CUSSION TOlu he surface (ii the case of a neutron star) or he accretion disk (e.g.Remillard&AMeClin-ock2006:Orlaudini2006).," Spectra of accreting black hole and neutron star X-ray binaries are typically modelled by a power law (representing inverse Compton emission), sometimes with the addition of a soft thermal component attributed either to emission from the surface (in the case of a neutron star) or the accretion disk \citep[e.g.][]{rem06,orl06}." . Observationallv it can be difficult to cüseriuinate between black role and neutron stars du N-ray binaries unless he compact object undergoes behaviour such as hermouuclear bursts or spin period pulsations hat are definitively ideutified with neutrOl stars., Observationally it can be difficult to discriminate between black hole and neutron stars in X-ray binaries unless the compact object undergoes behaviour such as thermonuclear bursts or spin period pulsations that are definitively identified with neutron stars. However. a clear separation between neutron star aud black hole N-vay binaries has bec4 found enmpincallv in the irduess ratios. particularly evideut in he medium aud hard X-rav bands (Farrell et al.," However, a clear separation between neutron star and black hole X-ray binaries has been found empirically in the hardness ratios, particularly evident in the medium and hard X-ray bands (Farrell et al." 2012. iu preparation).," 2012, in preparation)." This separation was previously voted by Doneetal.(2007) im data anc attributed to the presence of a surface iu neutrou stars anc an event horizon in black holes., This separation was previously noted by \citet{don07} in data and attributed to the presence of a surface in neutron stars and an event horizon in black holes. When compared with a sample of neutron star aud black hole. X-rav binaries drawn from the 2NMM cataoeue the harduess ratios of pplace it in the parameter space populated by black hole N-rayv binaries., When compared with a sample of neutron star and black hole X-ray binaries drawn from the 2XMM catalogue the hardness ratios of place it in the parameter space populated by black hole X-ray binaries. The oulv neuron star systems that have spectra as soft are the rare class of quiescent neutron star N-ray binaries., The only neutron star systems that have spectra as soft are the rare class of quiescent neutron star X-ray binaries. The spectra of these objects are domirated by thermal cussion from the surface or atinosphere of the neutron star (withafaintComptontail:Campana&Stella2001.anclreferences herein). which is inconsistent with the spectral fittine of ((see Table 2)).," The spectra of these objects are dominated by thermal emission from the surface or atmosphere of the neutron star \citep[with a faint Compton tail;][and references therein]{cam04}, which is inconsistent with the spectral fitting of (see Table \ref{specpar}) )." We now consider the possibility. thewt Hs a black hole N-vayv binary., We now consider the possibility that is a black hole X-ray binary. The temperature derived for the disk blackbody componeits when fitting the EPIC spectra with the disk backhocy plus power law 1nodel (see Table 1)) is sis»nificautlv less than that geucrally secu im black hoe binary spectra when the disk is inferred to be af the inner stable circular orbit (ISCO:seethere-etal. 2007).," The temperature derived for the disk blackbody components when fitting the EPIC spectra with the disk blackbody plus power law model (see Table \ref{bhxrb}) ) is significantly less than that generally seen in black hole binary spectra when the disk is inferred to be at the inner stable circular orbit \citep[ISCO; see the reviews of e.g.][]{mcc06,don07}." . Such a low temperature js lost consistent with black hole binaries that are not iu the disk dominated spectral state but are instead transitiouiug to the low/hard state where the disk does not extend to the ISCO., Such a low temperature is most consistent with black hole binaries that are not in the disk dominated spectral state but are instead transitioning to the low/hard state where the disk does not extend to the ISCO. If the disk is truncated at the lowest mass accretion rates, If the disk is truncated at the lowest mass accretion rates from (Cobleetal.1999). and is fully compatible with uo detection (the best fit is negativo aud docs not appear in the plot).,from \cite{pythonV} and is fully compatible with no detection (the best fit is negative and does not appear in the plot). The CODE data points are from (IXogutetal..1996b)., The COBE data points are from \cite{kogut96b}. . The results quoed iu the article were obtained by fitting DIRBE 1Un o the DAIR data., The results quoted in the article were obtained by fitting DIRBE $140\mu\mathrm{m}$ to the DMR data. We therefore corrected them by he average ratio DIRBE 1l0;nu/DIRBE 100710 to have hem in the same uuits as the other data points., We therefore corrected them by the average ratio DIRBE $140\mu\mathrm{m}$ /DIRBE $100\mu\mathrm{m}$ to have them in the same units as the other data points. The FIRS point at 167 GUz was obtained by (Canga.1991).., The FIRS point at 167 GHz was obtained by \cite{kmg_thesis}. . We also overplotted in Fig., We also overplotted in Fig. |. the predicted. spectrum (n terms of ratio to IRAS/DIRDBE 100/40) for vibrational dust iu ercen (ve assunied a spectral index of 2.0) normaised with IRAS/DIRDBE 100/12. aud for spinning dust i1 blue.," \ref{resume_mes} the predicted spectrum (in terms of ratio to IRAS/DIRBE $100\mu\mathrm{m}$ ) for vibrational dust in green (we assumed a spectral index of $2.0$ ) normalised with IRAS/DIRBE $100\mu\mathrm{m}$, and for spinning dust in blue." We also added the spectra. or free-free enidssioi in light blue (arbitrary norializatjon and spectral iudex -2.1)., We also added the spectrum for free-free emission in light blue (arbitrary normalization and spectral index -2.1). For the spinning dust. we follow (DraineauxLazarian.1998a) for the uixiug beween Warm Louise Mediu (WIAD). Warm Nomitral Mediun (AVNAD) aud Cod Neutral Mediu (CNM) models 1sing a respective yactioi of O11. 0.13 anc 0.3.," For the spinning dust, we follow \cite{draine_laz98a} for the mixing between Warm Ionised Medium (WIM), Warm Neutral Medium (WNM) and Cold Neutral Medium (CNM) models using a respective fraction of 0.14, 0.43 and 0.43." The respective normalization of these models was also taken frou (DraineandLazariau.1998a)., The respective normalization of these models was also taken from \cite{draine_laz98a}. . The stun of boti contributions is shown iu Fig., The sum of both contributions is shown in Fig. 1. iu red., \ref{resume_mes} in red. The width othe curves for the spiuniug dust model is due to the ealacic latitude depeudauce of the optical depth of the spinning dust componcuts., The width of the curves for the spinning dust model is due to the galactic latitude dependance of the optical depth of the spinning dust components. We used all the latitudes more than 207 from the Galactic equator., We used all the latitudes more than $20^\circ$ from the Galactic equator. The normalization is that ooOven bv (DraineandLazarian. 19985a)., The normalization is that given by \cite{draine_laz98a}. ". As clearly vields too little cnussion to match the data, we have also done a fit to the poiuts and arbitrarily raised the model curves by this amount."," As clearly yields too little emission to match the data, we have also done a fit to the points and arbitrarily raised the model curves by this amount." This is iudicated by the dotted curve., This is indicated by the dotted curve. The signal to noise for the Q-band detection is only 1.6 (NtA confidence level) so this would not be considered a detection as most CAIB experiments require at least 20., The signal to noise for the Q-band detection is only 1.6 $89\%$ confidence level) so this would not be considered a detection as most CMB experiments require at least $\sigma$. " We would note however that. as opposed to norual CXMB anisotropy analyses. here we are comparing the data to a template aud it is difficult to nuagine that systematic effects or analysis errors that would cause a random correlation with 100442 dust οσοι,"," We would note however that, as opposed to normal CMB anisotropy analyses, here we are comparing the data to a template and it is difficult to imagine that systematic effects or analysis errors that would cause a random correlation with $100\mu\mathrm{m}$ dust emission." The correlation could arise frou random alieuimient between the CAB anisotropics and the dust template., The correlation could arise from random alignment between the CMB anisotropies and the dust template. This. however. should be taken iuto account in our analysis if our covariance matrices for the data and the CAIB are correctly estimated.," This, however, should be taken into account in our analysis if our covariance matrices for the data and the CMB are correctly estimated." If these covariance matrices were underestimated. the error bars we compute on the correlation cocihieient (with Eq. 7))," If these covariance matrices were underestimated, the error bars we compute on the correlation coefficient (with Eq. \ref{err_a}) )" would be too simall and therefore the significance of our result would be overestimated., would be too small and therefore the significance of our result would be overestimated. Iu order to check the validity of our error bars. we correlated the SP91 data with template dust maps obtained by rotating the initial template maps around the Calactic poles aud by inverting North aud South.," In order to check the validity of our error bars, we correlated the SP94 data with template dust maps obtained by rotating the initial template maps around the Galactic poles and by inverting North and South." The Gaaxv was either rotated and/or inverted i36 different wavs (10 degrees each) to make 236 different, The Galaxy was either rotated and/or inverted in36 different ways (10 degrees each) to make 36 different The temperature in this region reaches 1013 Ik. for which inverse Compton processes ust be taken iuto account.,"The temperature in this region reaches $\sim 10^{11}$ K, for which inverse Compton processes must be taken into account." The sclfComptonization of the sub-nun radiation is calculated according to the prescription in Melia et al. (, The self-Comptonization of the sub-mm radiation is calculated according to the prescription in Melia et al. ( 2001). based on the algorithm described iu Melia Fatuzzo (1989).,"2001), based on the algorithm described in Melia Fatuzzo (1989)." The best-fit iiodel for the polarized nua auc sub-nua emission from Ser A* (Aitken et al., The best-fit model for the polarized mm and sub-mm emission from Sgr A* (Aitken et al. 2000) is shown in Figures 1 (the inset) and (the solid curve of} 2., 2000) is shown in Figures 1 (the inset) and (the solid curve of) 2. The peak frequency of the dux density is 2.1«1011 Iz. aud the flip frequency (at which the position anele clhauges by 90°) is 2.8.101. Πο.," The peak frequency of the flux density is $2.4\times 10^{11}$ Hz, and the flip frequency (at which the position angle changes by $90^o$ ) is $2.8\times 10^{11}$ Hz." Below this frequency. the first component is smaller than the second. and the corresponding percentage polarization is therefore (bv definition) negative.," Below this frequency, the first component is smaller than the second, and the corresponding percentage polarization is therefore (by definition) negative." Above the flip frequency. the first comiponent is larger.," Above the flip frequency, the first component is larger." Although the fit is not optimized. both the spectrum aud the percentage polarization appear to be consistent with the data.," Although the fit is not optimized, both the spectrum and the percentage polarization appear to be consistent with the data." It is to be noted that the peak frequency is actually{ο than the flip frequency. which is distinct frou other models that may also produce a rotation of the position anele (sec Aitken et al.," It is to be noted that the peak frequency is actually than the flip frequency, which is distinct from other models that may also produce a rotation of the position angle (see Aitken et al." 2000)., 2000). It is rather straightforward to understaud the polarization characteristics in this model., It is rather straightforward to understand the polarization characteristics in this model. " In the optically thick region (below about 1.6«10"" Iz). the specitic intensity of the Extraordinary and Ordinary waves is almost isotropic in the co-moving frame because the optical depth 7 is very huge."," In the optically thick region (below about $1.6\times 10^{11}$ Hz), the specific intensity of the Extraordinary and Ordinary waves is almost isotropic in the co-moving frame because the optical depth $\tau$ is very large." Even with the inclusion of the Doppler effect. the euissivitv of the source is relatively independent of position angle.," Even with the inclusion of the Doppler effect, the emissivity of the source is relatively independent of position angle." But the optical depths are different for the two waves. as indicated by Equation (7)). aud the specific intensity of the Extraordinary wave is slightly lavecr than that of the Ordinary wave.," But the optical depths are different for the two waves, as indicated by Equation \ref{depth}) ), and the specific intensity of the Extraordinary wave is slightly larger than that of the Ordinary wave." " From Equations (11)) and (12)). we see that the second component is lareer than the first. aud the percentage polarization is therefore negative according to the definition of D,,."," From Equations \ref{com1}) ) and \ref{com2}) ), we see that the second component is larger than the first, and the percentage polarization is therefore negative according to the definition of $P_{\nu_0}$." With an increase in frequency. the Extraordinary amplitude becomes even larger (relative to that of the Ordinary wave) aud so the percentage polarization increases.," With an increase in frequency, the Extraordinary amplitude becomes even larger (relative to that of the Ordinary wave) and so the percentage polarization increases." However. iu the optically thin region. the specific intensity is elven by Equation (8)).," However, in the optically thin region, the specific intensity is given by Equation \ref{Intensity2}) )." The svuchrotrou endüssivitv is very sensitive to the angle between the line of sight aud the maguctic field vectorB: svuchrotron radiation is beamed iuto a plane perpendicular to in the co-moving frame., The synchrotron emissivity is very sensitive to the angle between the line of sight and the magnetic field vector; synchrotron radiation is beamed into a plane perpendicular to in the co-moving frame. With the inclusion of the Doppler effect. the radiation is beamed iuto a cone. and the dominant contribution comes from the blue shifted region which has an azimuth of about zero.," With the inclusion of the Doppler effect, the radiation is beamed into a cone, and the dominant contribution comes from the blue shifted region which has an azimuth of about zero." Therefore. since the Extraordinary wave is more inteuse than the Ordinary wave aud the integrals (11)) aud (12)) are dominated by radiation from the ciitting clement with an azimuth of about zero. the first component is larger than the second.," Therefore, since the Extraordinary wave is more intense than the Ordinary wave and the integrals \ref{com1}) ) and \ref{com2}) ) are dominated by radiation from the emitting element with an azimuth of about zero, the first component is larger than the second." Iu this case. the fractional polarization becomes positive.," In this case, the fractional polarization becomes positive." in the first epoch data).,in the first epoch data). In SGP. we adopted a floor of1.," In SGP, we adopted a floor of." 2%.. Here we adopt a more conservalive value of consistent with the use of much smaller apertures on average for bright sources in the current study than in SGP., Here we adopt a more conservative value of consistent with the use of much smaller apertures on average for bright sources in the current study than in SGP. As should be apparent. this is a reasonable limit for photometric precision (o adopt. but in detail remains somewhat arbitrary.," As should be apparent, this is a reasonable limit for photometric precision to adopt, but in detail remains somewhat arbitrary." Figure ta is the absolute value. CTE-corrected. magnitude differences [or sources. in the IDF.," Figure 4a is the absolute value, CTE-corrected magnitude differences for sources in the HDF." The solid line represents the 3o. limit lor variability significance (2x the RAIS indicated by the solid line in Figure 3b)., The solid line represents the $\sigma$ limit for variability significance $\times$ the RMS indicated by the solid line in Figure 3b). Objects above this limit are selected as significant variables and are indicated with open hexagons., Objects above this limit are selected as significant variables and are indicated with open hexagons. Figure 4b is (he result of normalizing the magnitude difference bv this solid line., Figure 4b is the result of normalizing the magnitude difference by this solid line. Ilere the Y-axis indicates the level of significance of each source in units of o., Here the Y-axis indicates the level of significance of each source in units of $\sigma$. " The X-axis extends at the faint end to V,,.""729.0. which is the estimated photometric completeness magnitude limit for galaxy nuclei in (his survey."," The X-axis extends at the faint end to $_{nuc}$$=$ 29.0, which is the estimated photometric completeness magnitude limit for galaxy nuclei in this survey." Devond (his limit. the number counts for galaxies in (he ΠΣΕ begin to decrease.," Beyond this limit, the number counts for galaxies in the HDF begin to decrease." We find sixteen galaxies whose nuclei have undergone al least à 30 variation over the 5 vear (ime interval., We find sixteen galaxies whose nuclei have undergone at least a $\sigma$ variation over the 5 year time interval. " These sources are listed in Table 1 with columns as follows: (1) Williams (1996) ID. (2) (3) RA DEC (J2000). (4) Redshift from the literature. (5) Spectral type based on photometry [rom Fernánndez-Soto. Lanzetta and Yahil (1999. hereafter: FLY). (6) V, internal to 1=3 pixel aperture. (7) Magnitude difference between 1995 and 2000: positive implies brighter in 1995. (8) Signilicance of change obtained when normalized by the expected error as a function of magnitude. (8) Dulge-to-Total (B/T) 2-dimensional model fits for the I(ES14W) images from Marleau Simard (1998)."," These sources are listed in Table 1 with columns as follows: (1) Williams (1996) ID, (2) (3) RA DEC (J2000), (4) Redshift from the literature, (5) Spectral type based on photometry from Fernánndez-Soto, Lanzetta and Yahil (1999, hereafter: FLY), (6) $_{nuc}$ internal to r=3 pixel aperture, (7) Magnitude difference between 1995 and 2000; positive implies brighter in 1995, (8) Significance of change obtained when normalized by the expected error as a function of magnitude, (8) Bulge-to-Total (B/T) 2-dimensional model fits for the I(F814W) images from Marleau Simard (1998)." The last several columns relate to the source detection at other wavelengths discussed in Section 5., The last several columns relate to the source detection at other wavelengths discussed in Section 5. There are (wo distinct. completeness issues (hat effect our survey., There are two distinct completeness issues that effect our survey. The first is related to the incomplete time-saampling of the variable sources we wish to detect., The first is related to the incomplete time-sampling of the variable sources we wish to detect. Most variability survevs emplov a method where (he survey Ποιά is imaged several (mes over many vears (e.g. Trevese 1994: LLawkins 2002)., Most variability surveys employ a method where the survey field is imaged several times over many years (e.g. Trevese 1994; Hawkins 2002). Depending on the quality of the data. these surveys have shown that virtually all known AGN will be found to vary if observed periodically over several vears.," Depending on the quality of the data, these surveys have shown that virtually all known AGN will be found to vary if observed periodically over several years." Our study is limited by the fact that we have only two epochs with which to determine variabili: and therefore sample just two points on the Lehtcwurve of a varving source., Our study is limited by the fact that we have only two epochs with which to determine variability and therefore sample just two points on the lightcurve of a varying source. Because of this. we will be incomplete in our census of AGN since some varving sources could lie at magnitudes close to their original magnitude measured 5 vears earlier and would thus go undetected in our survey.," Because of this, we will be incomplete in our census of AGN since some varying sources could lie at magnitudes close to their original magnitude measured 5 years earlier and would thus go undetected in our survey." We estimate our incompleteness due to undersampling of the lighteurve by using variability, We estimate our incompleteness due to undersampling of the lightcurve by using variability "Applving the same argument as in Step 1. of the proof of Theorem t.4.. lor the convergence of A(u*)οOu. we see that Therefore. using the weaklyconvergence in L?((0./)xE). we gel Remark also that for i=O0,u'. we have where in the first line we have used. (3.19)). in the second line we have used. (4.27)). in the third line we have used the weaklv-* convergence of 477 towards iw in L*((0.D):LlogL(R)) and in the fourth line. we have used (4.30)).","Applying the same argument as in Step 1, of the proof of Theorem \ref{Passage}, for the convergence of $\l(u^\e )\diamond \partial_x u^\e $, we see that Therefore, using the weaklyconvergence in $L^{2}((0,t)\times\R)$, we get Remark also that for $w^i =\partial_x u^{i} $, we have where in the first line we have used \ref{estimationLlogL}) ), in the second line we have used \ref{L1estimate_x}) ), in the third line we have used the $\star$ convergence of $w^{\e,i}$ towards $w^i$ in $L^{\infty}((0,T); L\log L(\R))$ and in the fourth line, we have used \ref{estimation_ux}) )." Putting this result together with (4.31)). we get (1.5)) μονόκό”.," Putting this result together with \ref{estimate_passe}) ), we get \ref{EM:entropy}) ) with $C_1=C+C'$." In this section. we present a model describing the dynamics of dislocation densities.," $\hfill\Box$ In this section, we present a model describing the dynamics of dislocation densities." We refer to Hirth et al., We refer to Hirth et al. |?| for a physical presentation of dislocations which are (moving) defects in crystals., \cite{HL92} for a physical presentation of dislocations which are (moving) defects in crystals. Even if the problem is naturally a thiree-dimensional problem. we will first assume that the geometry of the problem is invariant by translations in (he -ry-," Even if the problem is naturally a three-dimensional problem, we will first assume that the geometry of the problem is invariant by translations in the $x_3$ -direction." This reduces the problem to the study of dislocations densities delined on the plane Cr4..79) and moving in a given direction 5 belonging to the plane (σι.ο) (which is called the “Burger's In Subsection ??.. we present the 2D-model with multi-slip directions.," This reduces the problem to the study of dislocations densities defined on the plane $(x_1,x_2)$ and moving in a given direction ${b}$ belonging to the plane $(x_1,x_2)$ (which is called the “Burger's In Subsection \ref{mod_2D}, , we present the 2D-model with multi-slip directions." Ii the particular eeomelry where (he dislocations densiües only depend on the variable +=ry ute.," In the particular geometry where the dislocations densities only depend on the variable $x=x_1+x_2$ ," "5.5. while the ""MO. simulation converges to higher resolution results onlv at. seone0.",", while the `M0' simulation converges to higher resolution results only at $z_{conv} \sim 0$." The lower panel of Fig., The lower panel of Fig. 1 shows a similar comparison for the cluster simulations., \ref{fig01} shows a similar comparison for the cluster simulations. In comparison to the field region. convergence is reached. at earlier times.," In comparison to the field region, convergence is reached at earlier times." This is due to the fact that structure growth is accelerated. in the proto-cluster region so that its star formation becomes dominated by relatively massive galaxies much earlier than in the field., This is due to the fact that structure growth is accelerated in the proto-cluster region so that its star formation becomes dominated by relatively massive galaxies much earlier than in the field. " Thus. the “S2° and ""SI simulations converge to 783 already at ngos79 and nossec9NS respectively."," Thus, the `S2' and `S1' simulations converge to `S3' already at $z_{conv} \sim 9$ and $z_{conv}\sim 8$, respectively." " Comparing the 783. and the 7S4. simulations we conclude that the 783. which has a mass resolution of Al,=2.41075. +ALL somewhat lower than M3. already accounts for all significant star formation."," Comparing the `S3' and the `S4' simulations we conclude that the `S3', which has a mass resolution of $M_p=2.4 \times 10^8 h^{-1}$ $_\odot$, somewhat lower than `M3', already accounts for all significant star formation." A simulation of the field region with mass resolution comparable to 7S4. is not available., A simulation of the field region with mass resolution comparable to `S4' is not available. " We therefore estimate the redshift after which the ""M3 run accounts for all star formation by deriving the contribution to the total star formation from objects with masses in dillerent ranges.", We therefore estimate the redshift after which the `M3' run accounts for all star formation by deriving the contribution to the total star formation from objects with masses in different ranges. In Fig., In Fig. " 2 we plot Ad, as a function of the halo mass. Al at different redshift."," \ref{fig02} we plot $\dot{M}_\star$ as a function of the halo mass, $M$ at different redshift." The bins are 0.5 wide. in. units of log Al and they have been chosen so that the lower limit is equivalent to our mass resolution.," The bins are 0.5 wide, in units of log $M$ and they have been chosen so that the lower limit is equivalent to our mass resolution." Before. redshift ~10 the main contribution comes from the smallest. mass objects. but larger and larger objects become important as the redshift decreases.," Before redshift $\sim 10$ the main contribution comes from the smallest mass objects, but larger and larger objects become important as the redshift decreases." This can be seen more clearly in Fig., This can be seen more clearly in Fig. 8 where the redshift evolution of the total star formation rate is plotted. (solid line) together with the contribution from haloes with masses in different ranges., \ref{fig03} where the redshift evolution of the total star formation rate is plotted (solid line) together with the contribution from haloes with masses in different ranges. As expected. at the higher redshifts the major contribution comes from objects with mass of few 10 M...," As expected, at the higher redshifts the major contribution comes from objects with mass of few $10^9$ $_\odot$." AU z~LE their contribution drops below half of the total., At $z\sim 11$ their contribution drops below half of the total. " We have plotted the contribution of haloes with. mass up to Loe""N M. as more massive. objects are important only at z«5. and thus are not relevant for our study."," We have plotted the contribution of haloes with mass up to $\sim 10^{11}$ $_\odot$, as more massive objects are important only at $z<5$, and thus are not relevant for our study." " From this analysis we can conclude that the ""MS simulation accounts for most star formation at οαν1", From this analysis we can conclude that the `M3' simulation accounts for most star formation at $z \simlt 11$. ‘Lo follow the propagation of ionizing radiation. produced by the sources through the given IGM density distribution. we use the Monte. Carlo (AIC) radiative transfer code Llydrodynamecs) described in CEMIL.," To follow the propagation of ionizing radiation produced by the sources through the given IGM density distribution, we use the Monte Carlo (MC) radiative transfer code ) described in CFMR." Le should. be noted hat in the present study a wider range of densities is encountered. reaching values of the optical depth of a few iundreds in the highest density regions.," It should be noted that in the present study a wider range of densities is encountered, reaching values of the optical depth of a few hundreds in the highest density regions." For this reason. aciditional tests. that we do not report here. have been run to check its reliability. finding that it reaches the same accuracy ovidine a right number of photon packets is emitted. (see xedow).," For this reason, additional tests, that we do not report here, have been run to check its reliability, finding that it reaches the same accuracy providing a right number of photon packets is emitted (see below)." For clarity. we briellv summarize the main features of the numerical scheme relevant to the present study.," For clarity, we briefly summarize the main features of the numerical scheme relevant to the present study." demonstrates that for the redshift range we consider here we are analysing AGN that populate the break in the hard X-rav luminosity function.,demonstrates that for the redshift range we consider here we are analysing AGN that populate the break in the hard X-ray luminosity function. This is important because the wreak in anv Luminosity function. with a shallow faint end slope (a« 1) constitutes the peak in. luminosity-density., This is important because the break in any luminosity function with a shallow faint end slope $\alpha<1$ ) constitutes the peak in luminosity-density. ''herefore. sources near the break cllectively contribute more ο the luminosity-censity ofthe population than either lower or higher luminosity sources.," Therefore, sources near the break effectively contribute more to the luminosity-density of the population than either lower or higher luminosity sources." " In a sense. they represent. the ""average sources in a population."," In a sense, they represent the `average' sources in a population." Combine this with the act that the numboer-density of GN. also peaks near to he redshift range we are considering (2~ 0.7). and we ave Clearly studying an important epoch for aceretion onto SBLIs.," Combine this with the fact that the number-density of AGN also peaks near to the redshift range we are considering $z\sim0.7$ ), and we are clearly studying an important epoch for accretion onto SBHs." All but one of the 31 sources in this sample lie above the Jog(fxων)=1 line in ligure 8 of paper 2 (source 14.144 ies just below). confirming that they are highly likely to be AGN rather than starburst galaxies.," All but one of the 31 sources in this sample lie above the $log(f_{X}/f_{opt}) = -1$ line in figure 3 of paper 2 (source 14.144 lies just below), confirming that they are highly likely to be AGN rather than starburst galaxies." Starbursts also typically have upper limits on their hard X-ray Iuminosities of ~10M erg 1. safely below the lower linit for ourAGN sample.," Starbursts also typically have upper limits on their hard X-ray luminosities of $\sim10^{41}$ erg $^{-1}$, safely below the lower limit for ourAGN sample." Figure 3 shows thumbnail £ band images centred on cach AGN in the sample. labelled as in table 1..," Figure \ref{thumbnails} shows thumbnail $I$ band images centred on each AGN in the sample, labelled as in table \ref{AGN_clustering}." The circles that are also clisplaved all have a physical. raclius of 50 προ while the thumbnail images themselves are all 40 square.," The circles that are also displayed all have a physical radius of 50 kpc, while the thumbnail images themselves are all $\sim 40\arcsec$ square." None of the ΔΟΝ. in this sample has a stellar light. profile. so all are unambiguousv extended. as measured by the stellarity parameter in he SExtractor output catalogue.," None of the AGN in this sample has a stellar light profile, so all are unambiguously extended, as measured by the stellarity parameter in the SExtractor output catalogue." Therefore. we can be fairly confident that the photometric redshifts for this sample are reliable.," Therefore, we can be fairly confident that the photometric redshifts for this sample are reliable." [t is also clear from this figure that none of he AGN show obvious signs of interactions or major distortions arising [rom recent mergers., It is also clear from this figure that none of the AGN show obvious signs of interactions or major distortions arising from recent mergers. The clustering amplitude of galaxies. around a point of interest gives a £ood indication as to the environmental density at that point., The clustering amplitude of galaxies around a point of interest gives a good indication as to the environmental density at that point. " The quantity D, is one of the more common measures of the clustering amplitude and has been used in many of the previous studies into the environments of quasars (e.g.222)..."," The quantity $B_{gq}$ is one of the more common measures of the clustering amplitude and has been used in many of the previous studies into the environments of quasars \citep[e.g.][]{2000MNRAS.316..267W,2001MNRAS.321..515M, 2003MNRAS.346..229B}." We follow the same procedure here. although with one addition that improves the reliability of the measurements — through the use of photometric recdshift estmates.," We follow the same procedure here, although with one addition that improves the reliability of the measurements – through the use of photometric redshift estimates." To summarise: the number of galaxies within 0.5 Alpe and dz0.1 (found to be the optimum dz for enhancing he contrast of over-densities against the background »pulation) of each AGN are counted (discounting the AGN itself) and compared to the number expected for the xikeround. as calculated fron he total number of galaxies in the same redshift range for he whole CEDE catalogue (increasing the value of dz sothat the whole inpu catalogue is searched has a negligible elfect on the results in section 5 - save for massively increasing the size of the error bars due o the higher background count - showing that the analysis is robust).," To summarise: the number of galaxies within 0.5 Mpc and $dz\leq 0.1$ (found to be the optimum $dz$ for enhancing the contrast of over-densities against the background population) of each AGN are counted (discounting the AGN itself) and compared to the number expected for the background, as calculated from the total number of galaxies in the same redshift range for the whole CFDF catalogue (increasing the value of $dz$ so that the whole input catalogue is searched has a negligible effect on the results in section \ref{results} - save for massively increasing the size of the error bars due to the higher background count - showing that the analysis is robust)." What we aim to measure with this is the 2-point angular correlation function of the galaxies in the vicinity of he AGN., What we aim to measure with this is the 2-point angular correlation function of the galaxies in the vicinity of the AGN. We assume that it takes the form: and that 4=L7. the canonical value for the field. galaxy population (?)..," We assume that it takes the form: and that $\gamma=1.77$ , the canonical value for the field galaxy population \citep{1977ApJ...217..385G}." " By integrating WW(8) out to a radius 6 the following expression is obtained: where Αν is the total number of galaxies within the circle of racius @ and Ny, is the number of background: galaxies expected. to be found within the same circle.", By integrating $W(\theta)$ out to a radius $\theta$ the following expression is obtained: where $N_{tot}$ is the total number of galaxies within the circle of radius $\theta$ and $N_{b}$ is the number of background galaxies expected to be found within the same circle. At dilferent redshilts the value of 8 is dilferent so as to keep the same physical 0.5 \lpe counting racius for all the AGN., At different redshifts the value of $\theta$ is different so as to keep the same physical 0.5 Mpc counting radius for all the AGN. " The value Lt, is the angular clustering amplitucle between the AGN and the surrounding galaxies (equivalent to 8,.. ~) but what we are really afterM is the clustering. amplitude D, (= rj). which gives the strength of the true 3-dimensional 2-point correlation function: We convert from zl, to By, in the sume way as 7. by using the following relation: where Ny is the mean surface density of galaxies. por steraciian. do is the angular diameter distance to the AGN and {-—3T8 is an integration constant."," The value $A_{gq}$ is the angular clustering amplitude between the AGN and the surrounding galaxies (equivalent to $\theta_{0}^{\gamma-1}$ ) but what we are really after is the clustering amplitude $B_{gq}$ $=r_{0}^{\gamma}$ ), which gives the strength of the true 3-dimensional 2-point correlation function: We convert from $A_{gq}$ to $B_{gq}$ in the same way as \citet{2000MNRAS.316..267W} by using the following relation: where $N_{g}$ is the mean surface density of galaxies per steradian, $d_{\theta}$ is the angular diameter distance to the AGN and $I_{\gamma}=3.78$ is an integration constant." " The final quantity. Pla,2) is the integrated. luminosity function (LE) of galaxies at the redshift of the AGN. down to some limiting maenituce."," The final quantity, $\Phi(m_{lim},z)$ is the integrated luminosity function (LF) of galaxies at the redshift of the AGN, down to some limiting magnitude." Vhe detailed. derivation of the conversion from οἱey to Dey can be found in ?.., The detailed derivation of the conversion from $A_{gq}$ to $B_{gq}$ can be found in \citet{1979MNRAS.189..433L}. The error in the clustering amplitude is given by: (?).. the L.37 factor coming from deviations of thefield galaxy population from a true Poisson distribution.," The error in the clustering amplitude is given by: \citep{1999AJ....117.1985Y}, , the $1.3^{2}$ factor coming from deviations of thefield galaxy population from a true Poisson distribution." Only galaxies with Zig«23 are counted in this study., Only galaxies with $I_{AB}<23$ are counted in this study. The reason for this (aside from. ensuring the most, The reason for this (aside from ensuring the most «10N cre 2.,$\times10^{-8}$ erg $^{-2}$. Within-: the large uncertainties.. the fluence distribution is consisteut with the power law slope found bv Cógüs et al (," Within the large uncertainties, the fluence distribution is consistent with the power law slope found by Göğüş et al. (" 2000).,2000). Many. of these bursts are αλλος the faintest ever detected frou SCRs at these enereles., Many of these bursts are among the faintest ever detected from SGRs at these energies. For the bursts with more than 500 not counts we could perform a detailed spectral analysis., For the bursts with more than 500 net counts we could perform a detailed spectral analysis. The 15-200 keV spectra. integrated over the whole duration of cach burst. were well fitted by an Optically Thin Thermal Breusstrahling (OTTB) model. viclding teiiperatures iu the range from 32 to 12 keV. We tried other models. like a power law or a black body. but they were clearly ruled out.," The 15-200 keV spectra, integrated over the whole duration of each burst, were well fitted by an Optically Thin Thermal Bremsstrahlung (OTTB) model, yielding temperatures in the range from 32 to 42 keV. We tried other models, like a power law or a black body, but they were clearly ruled out." Adopting a temperature AT=38 keV (consistent with the average spectra of the brightest bursts) we derived a conversion factor of L count | = 1.5410. 1 ere ? + (15-100 keV). which we adopted for all the bursts.," Adopting a temperature $kT$ =38 keV (consistent with the average spectra of the brightest bursts) we derived a conversion factor of 1 count $^{-1}$ = $\times$ $^{-10}$ erg $^{-2}$ $^{-1}$ (15-100 keV), which we adopted for all the bursts." To investigate the time evolution of the burst spectra we computed harcuess ratios. defined as 1=(JTSVMF| S8). based ou the backeround subtracted counts in the ranees [0-100 keV 01) and 15-10 keV (9).," To investigate the time evolution of the burst spectra we computed hardness ratios, defined as $HR=(H-S)/(H+S)$ , based on the background subtracted counts in the ranges 40-100 keV $H$ ) and 15-40 keV $S$ )." The time resolved [PR values were compute for al the bursts with more than 200 net counts (1.0. for 12 bursts of our sample)., The time resolved $HR$ values were computed for all the bursts with more than 200 net counts (i.e. for 12 bursts of our sample). The duration of the tucividual time bius were chosen iu order to have at least δ net counts in the total C/7| 5S) baud., The duration of the individual time bins were chosen in order to have at least 80 net counts in the total $H+S$ ) band. " Some bursts show a significant spectral evolution. while others. particularly those with a “flat topped"" profile. do not."," Some bursts show a significant spectral evolution, while others, particularly those with a “flat topped” profile, do not." Some examples are given in Fig. 2.., Some examples are given in Fig. \ref{trehr}. While several bursts slow a soft-to-hard evolution (0.9. number 6). others show a amorecomplex evolution (eg.," While several bursts show a soft-to-hard evolution (e.g. number 6), others show a morecomplex evolution (eg." e. απνο 19)., number 19). We investigated the variation of the hardnuess ratio versus intensity (2)., We investigated the variation of the hardness ratio versus intensity $I$ ). Considering all the time bius of all he bursts (see Fig. 3)).," Considering all the time bins of all the bursts (see Fig. \ref{hi}) )," we find a larducss-iuteusity auti-correlation., we find a hardness-intensity anti-correlation. The linear correlation coefficieut of the data rlotted in Fig., The linear correlation coefficient of the data plotted in Fig. 3 has a chance probability P smaller thui LO? of being due to uncorrelated data.," \ref{hi} has a chance probability $P$ smaller than $^{-3}$ of being due to uncorrelated data." According to an est. the data are siguificautly (~5.2 0) better described by a linear fit ZR—0.150.22«7og( £)) than by a coustaut value.," According to an F-test, the data are significantly $\sim$ 5.2 $\sigma$ ) better described by a linear fit $HR = 0.45 - 0.22\times log(I)$ ) than by a constant value." The exclusion ofthe three “flat topped” bursts frou ie fif does no affect he statistical sieuificance of the uti-correlation., The exclusion of the three “flat topped” bursts from the fit does not affect the statistical significance of the anti-correlation. " We also fix au harduess-flueuce auti-correlation over ie entire fluence range of our bursts, although with a stualler statistical siguificauce (P = 5410 7). which is cousisteut with our hirduess-iunteusitv auti-correlation aud also with the results obtained with data at lower energies (Cssetal. 20013)."," We also find an hardness-fluence anti-correlation over the entire fluence range of our bursts, although with a smaller statistical significance $P$ = $\times$ $^{-3}$ ), which is consistent with our hardness-intensity anti-correlation and also with the results obtained with data at lower energies \cite{gogus}) )." Previous studies imedicated weak or no spectral evolution for SCR bursts (c.g. Fenimoreetal.199 1.. Ixouveliotouetal. 1987)).," Previous studies indicated weak or no spectral evolution for SGR bursts (e.g. \cite{fenimore}, , \cite{kouveliotou}) )." Up to now iudicatioun for a ατατοπο evolution has been reported only for a single burst from (Strolumaver&Ενατα 1998)), Up to now indication for a hard-to-soft evolution has been reported only for a single burst from \cite{strohmayer}) ) sunspot area. shown in the bottom panel.,"sunspot area, shown in the bottom panel." We observe that the umbral area is of the total observed sunspot area and the ratio stays within this range throughout the cycle., We observe that the umbral area is of the total observed sunspot area and the ratio stays within this range throughout the cycle. Even though a large variety of sunspot shapes and configurations are seen. the fractional area of associated umbra does not show high amplitude fluctuations unlike the naximum sunspot area observed - the dominant characteristic is a relatively smooth variation.," Even though a large variety of sunspot shapes and configurations are seen, the fractional area of associated umbra does not show high amplitude fluctuations unlike the maximum sunspot area observed - the dominant characteristic is a relatively smooth variation." Note that this does not hold for individual sunspots due to the variety of configurations seen. only to the large scale distribution of sunspots over time.," Note that this does not hold for individual sunspots due to the variety of configurations seen, only to the large scale distribution of sunspots over time." TIhere are also interesting features present. most of all the dip 1 the year 1999.," There are also interesting features present, most of all the dip in the year 1999." At this time. the sunspot area Is increasine mewe quickly thai the area of the associated umbrae.," At this time, the sunspot area is increasing more quickly than the area of the associated umbrae." This soon changes and the umbral areas start to occupy more of the sunspot again. rising by a few percent by 2004 before starting to drop off again.," This soon changes and the umbral areas start to occupy more of the sunspot again, rising by a few percent by 2004 before starting to drop off again." During the first peak in solar activity in 2000 we see that the umbra is occupying a lower fraction of the sunspot and from Fig., During the first peak in solar activity in 2000 we see that the umbra is occupying a lower fraction of the sunspot and from Fig. | this is when the International Sunspot Number was higher than the STARA sunspot count., \ref{fig:emergences} this is when the International Sunspot Number was higher than the STARA sunspot count. This could indicate that there are sunspot groups with lower than ten sunspots present 1 them., This could indicate that there are sunspot groups with lower than ten sunspots present in them. This suggests that there is more space in these groups for the sunspot penumbrae to grow., This suggests that there is more space in these groups for the sunspot penumbrae to grow. In comparison to this. i the second peak of activity in 2002 we see that the fractio of sunspot area occupied by umbrae has grown and that the STARA count rate is above the International Sunspot Number.," In comparison to this, in the second peak of activity in 2002 we see that the fraction of sunspot area occupied by umbrae has grown and that the STARA count rate is above the International Sunspot Number." This suggests that we are seeing sunspot groups with more tha ten spots in them., This suggests that we are seeing sunspot groups with more than ten spots in them. These would be very complex groups anc so it may be the case that the sunspots have multiple umbrae present within them which would likely increase the fractional umbral area., These would be very complex groups and so it may be the case that the sunspots have multiple umbrae present within them which would likely increase the fractional umbral area. In Fig., In Fig. 5 and Fig., \ref{fig:areas} and Fig. 4 we show the error in the areas measured as a shaded band surrounding the line representing the data points., \ref{fig:ratio_areas} we show the error in the areas measured as a shaded band surrounding the line representing the data points. Estimating the errors involved is done by examining the output of the STARA algorithm., Estimating the errors involved is done by examining the output of the STARA algorithm. When detecting sunspots and sunspot umbrae. the centroid of the region is determined with good accuracy.," When detecting sunspots and sunspot umbrae, the centroid of the region is determined with good accuracy." However. when defining the perimeter of the region. we believe that there is an error of | pixel both towards and away from the centre of the region.," However, when defining the perimeter of the region, we believe that there is an error of 1 pixel both towards and away from the centre of the region." This means that large sunspots will have a smaller fractional error than small spots. even though the absolute value of the error will be greater for large spots.," This means that large sunspots will have a smaller fractional error than small spots, even though the absolute value of the error will be greater for large spots." We also show the percentage of the projected solar disk covered by sunspots from the viewpoint of the SOHO spacecraft in Fig. 5.., We also show the percentage of the projected solar disk covered by sunspots from the viewpoint of the SOHO spacecraft in Fig. \ref{fig:deproj_areas}. The trend is very similar to that of the absolute total area of sunspots looked at previously., The trend is very similar to that of the absolute total area of sunspots looked at previously. We see the fraction of the solar disk covered by sunspots rise to about at the peak of activity in cycle 23 which is equivalent to 3500 MSH (millionths of a solar hemisphere)., We see the fraction of the solar disk covered by sunspots rise to about at the peak of activity in cycle 23 which is equivalent to 3500 MSH (millionths of a solar hemisphere). This. is comparable to some of the largest sunspots ever detected., This is comparable to some of the largest sunspots ever detected. There are significant short-term fluctuations in this series. in addition to the overall solar cycle variation.," There are significant short-term fluctuations in this series, in addition to the overall solar cycle variation." "instabilities) and the induced activity is synchronous, there should be observable correlations between them, unless additional factors regulate such trends.","instabilities) and the induced activity is synchronous, there should be observable correlations between them, unless additional factors regulate such trends." " Indeed, ? remarked on what is now called the “Holmberg effect”, whereby the colors of galaxies in pairs are correlated (e.g.,2???) which suggests the presence of tidally induced star formation in both of the interacting galaxies."," Indeed, \citet{holmberg58} remarked on what is now called the “Holmberg effect”, whereby the colors of galaxies in pairs are correlated \citep[e.g., ][]{madore86,kennicutt87,laurikainen89} which suggests the presence of tidally induced star formation in both of the interacting galaxies." " We have selected a sample of 1286 pairs of AGNs with projected separations r,<100 kkpc and line-of-sight velocity offsets Av«600 km s! from the Seventh Data Release (DR7;?) of the Sloan Digital Sky Survey (SDSS;?) and examined their frequency among the parent sample of optically selected AGNs (?,PaperI)..", We have selected a sample of 1286 pairs of AGNs with projected separations $r_p <100$ kpc and line-of-sight velocity offsets $\Delta v <600$ km $^{-1}$ from the Seventh Data Release \citep[DR7;][]{SDSSDR7} of the Sloan Digital Sky Survey \citep[SDSS;][]{york00} and examined their frequency among the parent sample of optically selected AGNs \citep[][Paper I]{liu11a}. " The sample is defined in detail in Paper I. In the present paper, we their BH-accretion and recent star-formation properties in studythe host galaxies to constrain the effects of galaxy tidal interactions."," The sample is defined in detail in Paper I. In the present paper, we study their BH-accretion and recent star-formation properties in the host galaxies to constrain the effects of galaxy tidal interactions." " AGN pairs characterize a special population of galaxy pairs, in which the central SMBHs of both galaxies are actively accreting at the same time."," AGN pairs characterize a special population of galaxy pairs, in which the central SMBHs of both galaxies are actively accreting at the same time." " A statistical sample of AGN pairs enables us to examine whether there is a correlation in the accretion power of the central SMBHs between the components, akin to what has been Observed for star interactingformation in galaxy pairs."," A statistical sample of AGN pairs enables us to examine whether there is a correlation in the accretion power of the central SMBHs between the interacting components, akin to what has been observed for star formation in galaxy pairs." In §?? we describe the construction of our AGN pair sample and the control sample of single AGNs., In \ref{sec:data} we describe the construction of our AGN pair sample and the control sample of single AGNs. " In ?? we the recent star formation and BH accretion properties of presentAGN pairs, and we examine their dependence on the projected pair separation and recessional velocity offset in §?2,, the dependence on host-galaxy properties in §??,, the correlation between the two components in each AGN pair in ??,, and the correlation between recent star formation and AGN activity in $2?.."," In \ref{sec:result} we present the recent star formation and BH accretion properties of AGN pairs, and we examine their dependence on the projected pair separation and recessional velocity offset in \ref{subsec:prop}, the dependence on host-galaxy properties in \ref{subsec:progenitor}, the correlation between the two components in each AGN pair in \ref{subsec:correlation}, and the correlation between recent star formation and AGN activity in \ref{subsec:sfagn}." We discuss the implications of our results in $2? and conclude in §??..," We discuss the implications of our results in \ref{sec:discuss} and conclude in \ref{sec:sum}." " Throughout we assume a cosmology with Q,,=0.3, Q420.7, and Hp270 hyo km s! Mpc."," Throughout we assume a cosmology with $\Omega_m = 0.3$, $\Omega_{\Lambda} = 0.7$, and $H_{0} = 70$ $h_{70}$ km $^{-1}$ $^{-1}$." We describe the basic and physical measurementsbriefly of our AGN pairs., We briefly describe the basic properties and physical measurements of our AGN pairs. " Details propertiesof our sample selection are presented in Paper I. We have selected AGN pairs with rj<100 kkpc and Av<600 km s! from a parent sample of 138,070 AGNSs spectroscopically identified based on their optical diagnostic emission-line and/or widths."," Details of our sample selection are presented in Paper I. We have selected AGN pairs with $r_p <100$ kpc and $\Delta v <600$ km $^{-1}$ from a parent sample of 138,070 AGNs spectroscopically identified based on their optical diagnostic emission-line and/or widths." " of the sample is contained in the SDSS main galaxy catalog (?),, and for the present analysis we have excluded broad-line objects (?) to avoid AGN continuum contamination on host-galaxy measurements."," of the sample is contained in the SDSS main galaxy catalog \citep{strauss02}, and for the present analysis we have excluded broad-line objects \citep{hao05a} to avoid AGN continuum contamination on host-galaxy measurements." We refer to this sample as the “pair” sample., We refer to this sample as the “pair” sample. " As discussed in Paper I, 256 of the 1286 AGN pairs show unambiguous morphological tidal features tails in the SDSS images, such as bridges, and/or rings, indicative of strong tidal interactions, and we refer to this subset as the ""tidal"" sample."," As discussed in Paper I, 256 of the 1286 AGN pairs show unambiguous morphological tidal features tails in the SDSS images, such as bridges, and/or rings, indicative of strong tidal interactions, and we refer to this subset as the “tidal” sample." " We consider the tidal sample to be ""cleaner"" than the pair sample for studies of interactions, as the pair sample may include closely separated AGN pairs that are not yet tidally interacting."," We consider the tidal sample to be “cleaner” than the pair sample for studies of interactions, as the pair sample may include closely separated AGN pairs that are not yet tidally interacting." " On the other hand, as discussed in Paper I, the tidal sample is incomplete and subject to biases due to the surface-brightness and image-resolution limits in our ability to recognize tidal features."," On the other hand, as discussed in Paper I, the tidal sample is incomplete and subject to biases due to the surface-brightness and image-resolution limits in our ability to recognize tidal features." We thus analyze both samples and compare results to quantify the range of possible values., We thus analyze both samples and compare results to quantify the range of possible values. " As discussed in Paper I, due to the finite size of the SDSS fibers, galaxy pairs with separations smaller than wwill not both be observed unless they fall in the overlap regions on adjacent plates (??)."," As discussed in Paper I, due to the finite size of the SDSS fibers, galaxy pairs with separations smaller than will not both be observed unless they fall in the overlap regions on adjacent plates \citep{strauss02,blanton03}." " We correct for this spectroscopic incompleteness by supplementing the observed sample of AGN pairs with (C— repeated systems randomly drawn from the AGN pairs ΗΝ),with smaller than55"", where is the observed numberseparations of pairs and Cz3.3 is the correctionN, factor (see Paper I for details)."," We correct for this spectroscopic incompleteness by supplementing the observed sample of AGN pairs with $(C-1)N_{p}$ repeated systems randomly drawn from the AGN pairs with separations smaller than, where $N_{p}$ is the observed number of pairs and $C\approx 3.3$ is the correction factor (see Paper I for details)." The small separation AGN pairs fall in the overlap regions on adjacent plates so that they both got spectroscopic observations., The small separation AGN pairs fall in the overlap regions on adjacent plates so that they both got spectroscopic observations. There should be no biases introduced here because the spectroscopically observed small separation pairs are randomly distributed on the sky and are therefore representative of the parent small separation population., There should be no biases introduced here because the spectroscopically observed small separation pairs are randomly distributed on the sky and are therefore representative of the parent small separation population. " We adopt redshifts z and stellar velocity dispersions σ. of each galaxy from the (?;; ?;; see also discussion in ?)) and excluded extreme pipelinevalues of c, (c,«30 or >500 km s!) and those with large uncertainties (S/N« 3) or negative errors from bad fits.", We adopt redshifts $z$ and stellar velocity dispersions $\sigma_{\ast}$ of each galaxy from the pipeline \citealt{SDSSDR6}; \citealt{SDSSDR8}; see also discussion in \citealt{blanton05}) ) and excluded extreme values of $\sigma_{\ast}$ $\sigma_{\ast} <30$ or $>500$ km $^{-1}$ ) and those with large uncertainties $<3$ ) or negative errors from bad fits. " Additional spectral and photometric properties such as emission-line fluxes,continuum spectral indices, stellar masses, and half-light radii are taken from the MPA-JHU data"," Additional spectral and photometric properties such as emission-line fluxes,continuum spectral indices, stellar masses, and half-light radii are taken from the MPA-JHU data" stars shown in Figure 2 have been obtained by. assuming a Reimers mass loss rate with 1—4.,stars shown in Figure 2 have been obtained by assuming a Reimers mass loss rate with $\eta=4$. This is considered. a reasonable average mass loss rate for Population I intermediate mass AGB stars (see van den Hoeck Gronewegen 1997)., This is considered a reasonable average mass loss rate for Population I intermediate mass AGB stars (see van den Hoeck Gronewegen 1997). We emphasize that the !!N production from IMS is quite different from the value adopted here if a different value of η is asstuned., We emphasize that the $^{14}$ N production from IMS is quite different from the value adopted here if a different value of $\eta$ is assumed. For example. asstuning 7z1. the !N vield decreases by a [actor ~3.," For example, assuming $\eta\approx 1$ the $^{14}$ N yield decreases by a factor $\sim 3$." On the other hand. Chieffi et al. (," On the other hand, Chieffi et al. (" "2001) also show that in the most massive models (11224 AL. ). ""Li can also be svnthesized via hot bottom burning by the Cameron&Fowler.(1971) mechanism in the same way as occurs in higher metallicity models 1992)..","2001) also show that in the most massive models $m> 4$ $_\odot$ ), $^7$ Li can also be synthesized via hot bottom burning by the \citet{cam71} mechanism in the same way as occurs in higher metallicity models \citep{sac92}. ." " The Li mass fraction in the envelope can reach peak values ~10.7. although the final Li vield would be lower than this value because of the progressive ""Ie consumption and Li depletion at the base of the envelope during the AGB phase."," The Li mass fraction in the envelope can reach peak values $\sim 10^{-8}$, although the final Li yield would be lower than this value because of the progressive $^3$ He consumption and Li depletion at the base of the envelope during the AGB phase." Concerning the lowest mass range among IMS (1.5mM.S 3). Fujimoto.Iben(2000) have shown that these stars develop TP ancl also become C aud N-rich.," Concerning the lowest mass range among IMS $1.5\la m/M_\odot\la 3$ ), \citet{fuj00} have shown that these stars develop TP and also become C and N-rich." Unfortunately. (hese authors did not compute vields from (his mass range.," Unfortunately, these authors did not compute yields from this mass range." However. we believe thev can be omitted from our analysis. lor the following reasons: 1) Most studies of the fragmentation of primordial gas agree (hat objects with mass m<2 M. are very difficult to form.," However, we believe they can be omitted from our analysis, for the following reasons: i) Most studies of the fragmentation of primordial gas agree that objects with mass $m< 2$ $_\odot$ are very difficult to form." ii) We are mainly interested in the verv early chemical enrichment of the IGAL, ii) We are mainly interested in the very early chemical enrichment of the IGM. Stars with m«3 M. have a long lifetime and. if they formed. would only contribute ab very late times in the chemical evolution of the ICM.," Stars with $m< 3$ $_\odot$ have a long lifetime and, if they formed, would only contribute at very late times in the chemical evolution of the IGM." The adopted stellar vields for the mass range LOτν2/M.<40 are taken from Limongi.Chieffi. (2000).., The adopted stellar yields for the mass range $10\la m/M_\odot\la 40$ are taken from \citet{lim00}. . These vields are based on presupernova evolutions computed with the FRANEC code plus a simulated explosion based on the radiation dominated shock approximation (Weaver&Woosley1980)., These yields are based on presupernova evolutions computed with the FRANEC code plus a simulated explosion based on the radiation dominated shock approximation \citep{wos80}. . The location of the mass cut has been chosen by requiring that ~0.05 M. of Ni are ejected by each stellar model., The location of the mass cut has been chosen by requiring that $\sim 0.05$ $_\odot$ of $^{56}$ Ni are ejected by each stellar model. This amount ofNi is very similar to that used to explain the observational propertiesof the SN 1937À. Let us, This amount ofNi is very similar to that used to explain the observational propertiesof the SN 1987A. Let us since the emission from such sources must be partially absorbed by gas in the galactic disk of NGC LOGS.,since the emission from such sources must be partially absorbed by gas in the galactic disk of NGC 1068. The expected nunber of background sources can also be estimated from the deusity of sources detected iu the deep imaging[n] sky surveys with (see e.g. Cowie et al.," The expected number of background sources can also be estimated from the density of sources detected in the deep imaging sky surveys with (see e.g., Cowie et al." 2002 aud relereuces thereit., 2002 and references therein). In order to determine the limiting flux level during our. observation. we need to compute the correlation of the Mexican Hat Dunction with a two-dimeusional Gaussian (represeitine the point spread function) using the procedure described in Appendix A of Freemanοἱal.(2002).," In order to determine the limiting flux level during our observation, we need to compute the correlation of the Mexican Hat function with a two-dimensional Gaussian (representing the point spread function) using the procedure described in Appendix A of \citet{fre02}." . The result of this correlation is then compared with the value expected [or a given siguificauce and background level (see Appendix B of Freeman et al., The result of this correlation is then compared with the value expected for a given significance and background level (see Appendix B of Freeman et al. 2002)., 2002). For sources bevoud the 25.0 (arc 7 isophote of the galactic clisk. the point spread Duuction is large. aud we adopt a Gaussian of width σ=3.0 pixels. which is appropriate for a source 5’ off-axis and an energy of 1.5 keV. We find the detection threshold to be ~13.5 couuts for our significance aud background ⋅ ↥≺↵∖," For sources beyond the $25.0$ B-magnitude (arc $^{-2}$ isophote of the galactic disk, the point spread function is large, and we adopt a Gaussian of width $\sigma = 3.0$ pixels, which is appropriate for a source $5^{\prime}$ off-axis and an energy of $4.5$ keV. We find the detection threshold to be $\sim 13.5$ counts for our significance and background level." ⊽≺↵↥⋅⊺↥∐⊳∖∐⋃∐∣⋈↵↕⋅∩↥⋯⋯∐⊳∖∢∙∩↕⋅⋅≺↵⊳∖↥↽≻∩⊓⇂⊳∖∩⋜↕⋃∐⋜↕∣≻⊳∖∩↥⋅∣⋈↵≺⇂∐⇂∟∖∩↥↥⋅↖∖≍∐≻↓↗≺↵↕⋅∑≟∢∙⋯−⊳∖↓⊔↕∐≺↵ ⋅ ⋅↽⋝ ↽5 > ⋅ Q.1-5 keV ban or2.1x€)7E10.P5 erg 27s + in: the i2-8] keV; band. assuming. a power-law of. photon index DP—1.2 and the Galactic column density towards NGC 1068 of Nyy(Gal)=3.53x10? 2 (Dickey&Lockmanu1990).," This number of counts corresponds to a unabsorbed flux of $1.8 \times 10^{-15}$ erg $^{-2}$ $^{-1}$ in the 0.4–5 keV band or $2.1 \times 10^{-15}$ erg $^{-2}$ $^{-1}$ in the 2–8 keV band, assuming a power-law of photon index $\Gamma = 1.2$ and the Galactic column density towards NGC 1068 of $N_{\rm H} (\rm Gal) = 3.53 \times 10^{20}$ $^{-2}$ \citep{dl90}." . At this [lus level. we would expect a surface density of 0.38 sources / LE ↸↜⋜⋃⋅∢∙∐⊔↥∏−∐⋅∩∐⊔∐↩↕⋅≺↵⊳∖⋃∐⊳∖∩↥∊∣∣↙∣∣∣↙∣∣⋅↙∣∣≻⋜↕∐↕⊆∐≺↵↥≺⇂∩∣≻⊳∖≺↵↥⋅∖⇁⋜↕⊔∩∐⊳∖∐⊔∐≺↲−∟↖∖↕⊊≺," At this flux level, we would expect a surface density of $0.38$ sources (arc $^{-2}$ from the results of blank field observations in the 2–8 keV band \citep{cow02}." "↲∖∣≻⋜↕∐≺⊔⊂∩∖∖↽∐↵≺↵↕⋜↕↥⋅ ""opt ⋅ ⋅ ⋅ οo E ⊇∪∪⊇⋝⋅⋅∖∏↕∐↩↕∏⊳∖∐⊔∐∣≻↩↕⋅↕⊳∖⊳∖∐∐∐⋜⋃⋅↕∩↕∐↩⊳∖⇂⊔⋅↥∎⋜↕∢∙≺↵≼⇂≺↵∐⊳∖∐⊽∖⊽∩↥∎⊳∖⋯⊔⋅∢∙≺↵⊳∖⋯↕⊳∖↥≺⇂≺↵↕∐≺↵⊇⋅↴⋅∪⊟−⋯⋜↕∑∸∐∎⊓∐⇂↩ 2. ↸↜⋜⋯∙⊳∖≺↵∢∙⋝−↥⊳∖∩↥↽≻∐∩↕≺↵⋯↕∐≺↵↓∖∁↽∶⊂∐≻↻↖∖∩∣≻⊳∖≺↵↓⋅∖⇁⋜↕⋃∩∐⋅↕∐≺↲∢∙∩⋯↥↽≻⋜↕↓⋅↥⊳∖∩∐⊳∖↥⋯∐≺⇂∣⋈↲∢∙∩∐⊳∖∐⇂≺↵↓⋅≺↵≺⇂⋜↕⊳∖∩∐↥⊽∖⊽⋅ - ""atO ⋅ ⋅ ⋅ ⋜↕↥↽≻↥↽∐⋅∩⊸∖∐∐⋜↕↕↩⋅⊳∖∎∐∢∙↩∐≺↵↩∐≺↵↕⋅∑∸⊽∖⊽∣≻⋜↕∐≺⇂⋖∫⊇↰∖⋝↥⊆≺↵∖⊽⋝⋃⊳∖≺↵≺⇂∣≻⊽∖⇁⊂⊲∩∖∖↽↥≺↲≺↵↕⋜↕↥⋅↸⋮⊇∪∩⊇⋟↥⊳∖≺∐∐⇀≺↵↕⋅≺↵∐↕∐⋅∩∐⊔∐≺↵ ∩∐≺↵⋃"," While this number is similar to the surface density of sources outside the $25.0$ B-magnitude (arc $^{-2}$ isophote in the NGC 1068 observation, the comparison should be considered as only approximate, since the energy band (2–8 keV) used by \citet{cow02} is different from the one used in our analysis (0.4–5 keV)." ⊳∖↩≺⇂↥∐⋯⊔⋅⋜↕∐⋜↕⊽∖⇁⊳∖↥⊳∖↸⋮∪⋅⊢⋅↴↥⊆≺↵∖⊽⋝⋅ The source spectra were initially moclelec in the 0.178 keV baud with two alternative descriptions olf the continuum: (1) a multi-color disk (MCD) blackbody which represents the emission expected from au optically thick accretion disk (Mitsudaetal.198£:Makishima1986). auc (ii) a power-law spectrum (plioton spectral iudex D).," The source spectra were initially modeled in the $0.4$ $8$ keV band with two alternative descriptions of the continuum: (i) a multi-color disk (MCD) blackbody which represents the emission expected from an optically thick accretion disk \citep{mit84,mak86} and (ii) a power-law spectrum (photon spectral index $\Gamma$ )." We have included in tle mocel absorption by both the Galactic columndensity towards NGC 1068 of Ny(Gal)=3.5310? em7 and a column density Nyy lutriusic to the source: the atomic eross-sectious aud abuudauces for the absorption columns were taken from Morrison&MeCatnimon(1983) aud Ancers&Grevesse(L089). respectively.," We have included in the model absorption by both the Galactic column density towards NGC 1068 of $N_{\rm H} (\rm Gal) = 3.53 \times 10^{20}$ $^{-2}$ and a column density $N_{\rm H}$ intrinsic to the source; the atomic cross-sections and abundances for the absorption columns were taken from \citet{mm83} and \citet{ag89}, respectively." The results are given in Table 2.., The results are given in Table \ref{tbl-2}. The MCD aud power-law models both provide a reasonable description of the data for each of the sources. with neither mocel being rejected at >99% confidence using a X7> test.," The MCD and power-law models both provide a reasonable description of the data for each of the sources, with neither model being rejected at $\geq 99\%$ confidence using a $\chi^{2}$ test." Most ofJ the source spectra have color temperatures aud immer. disk. radii niu the rauge, Most of the source spectra have color temperatures and inner disk radii in the range lensing effect they produce ou backgrouud stars (Paczyisski 1997. Roulet aud Mollerach 1997).,"lensing effect they produce on background stars (Paczyńsski 1997, Roulet and Mollerach 1997)." It is expected that Space Literferometry Mission (SIM). planned to be launched in 2005. will allow a determination of the mass. the distance. aud the proper motion of virtually auy MACHO capable of inclucing a microleusing event (Mirakla-Escudé 1996. Paczyisski 1005).," It is expected that Space Interferometry Mission (SIM), planned to be launched in 2005, will allow a determination of the mass, the distance, and the proper motion of virtually any MACHO capable of inducing a microlensing event (Miralda-Escudé 1996, Paczyńsski 1998)." For putative microlensiug event cue to Nemesis the angular Eiustein ring radius would be (Paczyiisski 1995) where AM is the Nemesis mass aud D the distauce to it., For putative microlensing event due to Nemesis the angular Einstein ring radius would be (Paczyńsski 1998) where $M_N$ is the Nemesis mass and $D_N$ the distance to it. Thus it will be resolved by SIM which is expected to have angular resolution of about LO mas., Thus it will be resolved by SIM which is expected to have angular resolution of about 10 mas. Therelore if such a microlensiug event is really detected. it will give a very detailed information about Nemesis.," Therefore if such a microlensing event is really detected, it will give a very detailed information about Nemesis." The only. problem is that jecause the present position of the Nemesis is unknown we are forced to relay merely ou a chance o discover the event or perform a full sky cleclicatecl search for it., The only problem is that because the present position of the Nemesis is unknown we are forced to relay merely on a chance to discover the event or perform a full sky dedicated search for it. Whether or not mirror matter exists will become clearer as time goes by., Whether or not mirror matter exists will become clearer as time goes by. Iu the mean time. itis fun to think about the implicatious of [ascinating possibilities such as mirror planets in our solar system.," In the mean time, it is fun to think about the implications of fascinating possibilities such as mirror planets in our solar system." In addition to the (acdinittedly very speculative) evidence lor faint solar companions »ovided by observations discussed above. it is also possible that some other much closer aud sinaller uirror planet cau also exist.," In addition to the (admittedly very speculative) evidence for faint solar companions provided by observations discussed above, it is also possible that some other much closer and smaller mirror planet can also exist." " Over time. if its orbit is eccentric enough. such planet cau approach to various ""normal"" solar planets aud cause observed oddities in the solar system. like Pluto's orbi"," Over time, if its orbit is eccentric enough, such planet can approach to various “normal” solar planets and cause observed oddities in the solar system, like Pluto's orbit." We can also speculate that the formation of the Moon was a result of tidal fission of the Earth caused by a close encounter with a mirror planet., We can also speculate that the formation of the Moon was a result of tidal fission of the Earth caused by a close encounter with a mirror planet. But speculations apart. the livpothesis that there are some mirror objects in the solar system is in principle testable hypothesis. because these mirror objects can lead to observable effects due to their gravitational iuteractious and they may also observably radiate if they coutain enough ordinary matter.," But speculations apart, the hypothesis that there are some mirror objects in the solar system is in principle testable hypothesis, because these mirror objects can lead to observable effects due to their gravitational interactions and they may also observably radiate if they contain enough ordinary matter." Q.lem Q.lem Π.Ε. is an Australian Research Fellow., 0.4cm 0.4cm R.F. is an Australian Research Fellow. We also thank J.B. Murray aud J. Matese for correspondence., We also thank J. B. Murray and J. Matese for correspondence. ealaxies. several redshift estimators have been developed sed on the πα aud radio data ον.,"galaxies, several redshift estimators have been developed based on the submm and radio data only." Carilli&Yun(1999) proposed to use the radio-o-subuun spectral mdex as a redshift estimator. which is based on the local radio-to-£u-iufrared correlation.," \citet{car99} proposed to use the radio-to-submm spectral index as a redshift estimator, which is based on the local radio-to-far-infrared correlation." Table 3. lists the redshif estimates calculated usine he Carli∙∙&Yun⇁(2000)⊀ oT⋅≻⇁↣∶⇁ models., Table \ref{zestimates} lists the redshift estimates calculated using the \citet{car00} $\alpha_{\rm 1.4 GHz}^{\rm 250 GHz}$ models. The↴ quoted uncertainties include both the leo measurement uncertainties iu our photometry and the lo scatter iu he ieodels., The quoted uncertainties include both the $\sigma$ measurement uncertainties in our photometry and the $\sigma$ scatter in the models. The estimate redshifts are clearly lower hau the :—L.1 of the radio galaxy. hough := 1.1 is still within the Lo uncertainties for nost sources (excep ILO).," The estimated redshifts are clearly lower than the $z$ =4.1 of the radio galaxy, though $z$ =4.1 is still within the $\sigma$ uncertainties for most sources (except M10)." Ilowever. a conrparisou with spectroscopic redshifts of SACs indicates tha the spectral-index redshifts teud to ο svstolatically underestimated for t.pe6e2 objects (ey.Clementsctal.2001).," However, a comparison with spectroscopic redshifts of SMGs indicates that the spectral-index redshifts tend to be systematically underestimated for $z_{\rm spec}>2$ objects \citep[\eg][]{cle04}." . Tu fact. the Carilli&Yun(2000) models predict a spectral iudex oT 1.00 or i—l1l. so for the average ΣΣ ΓΡ iun our haps. we expect to find a radio source with a fiux deusitv 53Ίο —184)Jy. well below the detection limit of our VLA map.," In fact, the \citet{car00} models predict a spectral index $\alpha_{\rm 1.4 GHz}^{\rm 250 GHz}$ =1.00 for $z$ =4.1, so for the average $S_{1200}$ =3.3 mJy in our maps, we expect to find a radio source with a flux density $S_{\rm 1.4 GHz}$ $\mu$ Jy, well below the detection limit of our VLA map." However. Petricetal.(2003). report 1.1 GIIz detections of τομ in two 2>5 radio quiet quasars With Syooy flux densities of 0.9 and 5.5.Γ ταν.," However, \citet{pet03} report 1.4 GHz detections of $\sim$ $\mu$ Jy in two $z>5$ radio quiet quasars with $S_{1200}$ flux densities of 0.9 and 5.5 mJy." A possible explanation for this higher than expected CGIIz cunission is that an optically uucletected AGN contributes to the radio ciission., A possible explanation for this higher than expected 1.4 GHz emission is that an optically undetected AGN contributes to the radio emission. Note that ACNs lave been spectroscopically confirmed in two proto-clusters surrounding IIZRCs (LeFevreetal.1996:Peuter-iccietal. 2002). while ον].etal.(2003b)— report the discovery of N-ray sources. coiucideu with subi sources surrounding three HzRCs. suggesting the ALAMDBO sources surrounding TN 1912 if they are part of the protocluster may well contain ACNs.," Note that AGNs have been spectroscopically confirmed in two proto-clusters surrounding HzRGs \citep{lef96,pen02}, while \citet{sma03b} report the discovery of X-ray sources coincident with submm sources surrounding three HzRGs, suggesting the MAMBO sources surrounding TN $-$ 1942 – if they are part of the protocluster – may well contain AGNs." lleuce. a velatively dwight radio detection of a MAMDBO source does not exclude it as a potential iieniber of the 2=[Ll protocluster.," Hence, a relatively bright radio detection of a MAMBO source does not exclude it as a potential member of the $z=4.1$ protocluster." Ealesetal.(2003) have also predicted the redshitt evolution of the Sssojau/S1200jan ratio. bv fitfiug a fwo-temperature imodol to a sample of LOL ealaxies from the IRAS bright galaxy survev (Dunne&Eales.2001).," \citet{eal03} have also predicted the redshift evolution of the $S_{\rm 850\mu m}$ $S_{\rm 1200\mu m}$ ratio, by fitting a two-temperature model to a sample of 104 galaxies from the IRAS bright galaxy survey \citep{dun01}." . We lave used their median predicted. value (Fie.1intheEalesetal.2003.paper) to obtain an additional redshift estimate., We have used their median predicted value \citep[Fig.~4 in the ][paper]{eal03} to obtain an additional redshift estimate. " Table 3 lists these estimates: the quoted uncertainties include the lo measurement uncertainties in the 5s39,5n/ 120044 ratios aud the full spread in the nodel predictions.", Table \ref{zestimates} lists these estimates; the quoted uncertainties include the $\sigma$ measurement uncertainties in the $S_{\rm 850\mu m}$ $S_{\rm 1200\mu m}$ ratios and the full spread in the model predictions. We fud that. except for a.>2.2 int for MOL anne AIO2. this ratio docs uot provide a useful constraint on the redshifts due to (1) the small difference in wavelength between the nuu aud πια points aud (11) he relatively low S/N of our detections.," We find that, except for a $z>2.2$ limit for M01 and M02, this ratio does not provide a useful constraint on the redshifts due to (i) the small difference in wavelength between the mm and submm points and (ii) the relatively low S/N of our detections." lu sumunuuux. while the radio. nuu and subi photometry are ecnerally cousisteut with «Ξ1.1. the uncertainties from these redshift estimate techniques are ar too laree to provide proof that the sources are at he redshift of the radio galaxy.," In summary, while the radio, mm and submm photometry are generally consistent with $z$ =4.1, the uncertainties from these redshift estimate techniques are far too large to provide proof that the sources are at the redshift of the radio galaxy." Better sampled SEDs. especially in the subiuu would be needed to coustrain the redshifts with photometry ouly.," Better sampled SEDs, especially in the submm would be needed to constrain the redshifts with photometry only." None of the Ll spectroscopically coufixiied. eenütters within the c<1.2 mJv region (excludiug the radio galaxy) is detected at 220 in our 1.2 nuu map., None of the 14 spectroscopically confirmed emitters within the $\sigma<1.2$ mJy region (excluding the radio galaxy) is detected at $>2\sigma$ in our 1.2 mm map. To test if there is a statistical signal in our nou- we have stacked the cussion from these 11 positions. aud find 653on) =0.2540.2 | uJy.," To test if there is a statistical signal in our non-detections, we have stacked the emission from these 14 positions, and find $\langle S_{\rm 1.2mm}\rangle$ $\pm$ 0.24 mJy." " Usine this 3o upper μπιτ, and assuning dust parameters 7,4233 Is and 3=2.0 used for LBGs (Bakereal..2001).. we derive (Leip)XLIl0PL... mupbeiug a mean star formation rate (ΕΕ Ρις;ον LIO [ων + Gey.Omoutetal.2001)."," Using this $\sigma$ upper limit, and assuming dust parameters $T_{\rm d}$ =33 K and $\beta$ =2.0 used for LBGs \citep{bak01}, we derive $\langle L_{\rm FIR}\rangle \simlt 4.4 \times 10^{12}{\rm L_{\odot}}$, implying a mean star formation rate $\langle$ $_{\rm FIR}\rangle \simlt$ 440 $_{\odot}$ $^{-1}$ \citep[\eg][]{omo01}." ". Similarly. roni our VLA ap. we πια O5,em) 25.9 py."," Similarly, from our VLA map, we find $\langle S_{\rm 1.4GHz}\rangle$ $-$ $\pm$ 2.9 $\mu$ Jy." Using the relation between the radio emission aud star formation rate (C'ondou.1992).. we cau use this 30 upper Bait of 8.7 jiJy on the 1.1 Gz chussion to caleulate an upper Limit to the star formation rate (SFR) from the cemitters.," Using the relation between the radio emission and star formation rate \citep{con92}, we can use this $\sigma$ upper limit of 8.7 $\mu$ Jy on the 1.4 GHz emission to calculate an upper limit to the star formation rate (SFR) from the emitters." " Asstunine a radio spectral iudex eqq, (ha. we derive (SER? <265 Myr l"," Assuming a radio spectral index $\alpha_{\rm radio}$ $-$ 0.8, we derive $\langle$ $_{\rm radio}\rangle < $ 265 $_{\odot}$ $^{-1}$." The values should be compared with the SER derived frou he mean Ihuuunositv of the same |1 cinitters (exchiding the radio ealaxy) (Lye )=2.77\10 Pore 1, The values should be compared with the SFR derived from the mean luminosity of the same 14 emitters (excluding the radio galaxy) $\langle L_{\rm Ly\alpha} \rangle$ $\times$ $^{42}$ erg $^{-1}$. " Asundug a case D ratio 2110. anc using the Ikeunicutt.Taiiblvu.&Conedon(01991). relation between SER aud Lyp,. we find (SERL,,;22.2 M.vr 1"," Assuming a case B ratio 10, and using the \citet{ken94} relation between SFR and $L_{\rm H\alpha}$, we find $\langle$ $_{\rm Ly\alpha}\rangle$ =2.2 $_{\odot}$ $^{-1}$." " Note that this value is likely to be an underestimate, as ls often quenched by dust enüsson. as illustrated by Iketal.(2001).. who report ivafios siguificautly lower than the case D value for a sample of aad eenuütters surrounding the :—2.16 radio e@alaxyv PISS 262."," Note that this value is likely to be an underestimate, as is often quenched by dust emission, as illustrated by \citet{kurk04}, who report ratios significantly lower than the case B value for a sample of and emitters surrounding the $z$ =2.16 radio galaxy PKS $-$ 262." However. it is obvious that the deep limagine probes much lower SFR than the MAMDBO and VLA aps.," However, it is obvious that the deep imaging probes much lower SFR than the MAMBO and VLA maps." Although we could not put strong constraints on he redshifts of the 9 MANDO: sources suouncdiue TN 1912 using photometric redshift cstimetors or very deep VLT/FORSL spectroscopy of two of tho. he analysis of the source censity and the photometric redshift estimates suggests half of the 9 ALAMIBO sources. and in particular the brightest oues. may wel belong o the :=L1 xoto-cluster.," Although we could not put strong constraints on the redshifts of the 9 MAMBO sources surrounding TN $-$ 1942 using photometric redshift estimators or very deep VLT/FORS1 spectroscopy of two of them, the analysis of the source density and the photometric redshift estimates suggests half of the 9 MAMBO sources, and in particular the brightest ones, may well belong to the $z$ =4.1 proto-cluster." To confu (or refute) this requires alternative redshift determünatious such as (1) deep near-IR spectroscopy. 1) mid-IR spectroscopy with Spitzer using the PAT features. andl (ii) mun spectroscopy using molecular CO lines.," To confirm (or refute) this requires alternative redshift determinations such as (i) deep near-IR spectroscopy, (ii) mid-IR spectroscopy with using the PAH features, and (iii) mm spectroscopy using molecular CO lines." this riso iu the dow temperatures. bubbles heated with the same P rise to higher temperatures.,"this rise in the flow temperatures, bubbles heated with the same $h$ rise to higher temperatures." In addition. when eg=0.7 the density eracicut develops an unstable positive density gradieut withiu about 2 kpc.," In addition, when $e_d = 0.7$ the density gradient develops an unstable positive density gradient within about 2 kpc." From these aud other circulation flowswith nonzero e; we conclude that the appareut NM has no undesirable radial eradieuts as long as scertaiuegὃς0.5: this is a reasonable constraiut in view of the nature of the bubble-flow heating process., From these and other circulation flowswith nonzero $e_d$ we conclude that the apparent temperature has no undesirable radial gradients as long as $e_d \lta 0.5$; this is a reasonable constraint in view of the uncertain nature of the bubble-flow heating process. Figure{ shows three flows assumed to be heated only bvbubble expausion with efficiencies ej4;=0.1 0.5 and 0.7 (and ο= 0), Figure 4 shows three flows assumed to be heated only by bubble expansion with efficiencies $e_{pdv} = 0.1$ 0.5 and 0.7 (and $e_d = 0$ ). As before. the apparent enissiou-weighted teniperature profiles (dotted lines in Fie.," As before, the apparent emission-weighted temperature profiles (dotted lines in Fig." 1b) become strouglv negative muless ej4*X0.5., 4b) become strongly negative unless $e_{pdv} \lta 0.5$. Our primay objective iu coustructing these models is to explore the possibility that cooling How eas cau of heated at some small radius m such a mauner that (1) no gas cools to very low teniperatures and (2) the apparent temperature eradient of the cooling flow docs tot become ucgative iu the ceutral regious., Our primary objective in constructing these models is to explore the possibility that cooling flow gas can be heated at some small radius in such a manner that (1) no gas cools to very low temperatures and (2) the apparent temperature gradient of the cooling flow does not become negative in the central regions. We have ENcluoustrated that flows satisfving these two criteria are rdeed possible., We have demonstrated that flows satisfying these two criteria are indeed possible. With appropriately chosen parameters. movant bubbles cau carry the cooling flow iiass AT wav frou he core with velocities sufficieutlv laree that i6 apparent (cluuission-weighted) temperature eracicut aT)fdr ds virtually unaffectedby the hot gas inside ie bubbles.," With appropriately chosen parameters, buoyant bubbles can carry the cooling flow mass ${\dot M}$ away from the core with velocities sufficiently large that the apparent (emission-weighted) temperature gradient $d\langle T \rangle/dr$ is virtually unaffected by the hot gas inside the bubbles." Iu addition. the local iuterbubble eas can heated the bubbles with up to 25 50 percent cficiency without adversely disturbing the temperature οeradieut.," In addition, the local interbubble gas can be heated by the bubbles with up to 25 – 50 percent efficiency without adversely disturbing the temperature gradient." This positive assessiueut of idealized circulation Hows contrasts wii the less satisfactory results of our Muuerical simulations iu which all cooling flows that were sufficieutlv heated to noticeably reduce the ceutral cooling AT also resulted in sronglv negative appareut temperature eradicuts 1 Mathews 2002: 2003)., This positive assessment of idealized circulation flows contrasts with the less satisfactory results of our numerical simulations in which all cooling flows that were sufficiently heated to noticeably reduce the central cooling ${\dot M}$ also resulted in strongly negative apparent temperature gradients (Brighenti Mathews 2002; 2003). However. (μμthebubble returü model clearly fails if the bubbles are too sinall.," However, the bubble return model clearly fails if the bubbles are too small." " As ry, decreases.oa the large umber ofbubbles required to transport AT (particularly near the central heating source atf rj) coustuues all the available volue. eutirelv. displaciug the cooling inflow (Condition 21)."," As $m_b$ decreases, the large number of bubbles required to transport ${\dot M}$ (particularly near the central heating source at $r_h$ ) consumes all the available volume, entirely displacing the cooling inflow (Condition 21)." Iu these circumstances the heated ceutral region would erow iu size and would almost certainly result in an extended hot thermal core aud dit)fdr< which is rot generally observed in N-ravs.," In these circumstances the heated central region would grow in size and would almost certainly result in an extended hot thermal core and $d\langle T \rangle/dr < 0$, which is not generally observed in X-rays." The circulation flows we consider do not specify the plysical nature of the heating xocess interior to the heating radius νι, The circulation flows we consider do not specify the physical nature of the heating process interior to the heating radius $r_h$. " Consequently. if he bubbles are heated too slowly. there is some conceru hat cinission from r rr. coustaut nass loss youn stars. bubble fraeimieutation. cosniüc rav oressure in thebubbles. ax:1ος of heating factors P for the »xibbles.bubble-flow ther:dization. aud a distribution of »ibble masses iy, ni each flosv."," The idealized circulation flows we describe here could be extended to include cooling inflow from $r > r_c$ , constant mass loss from stars, bubble fragmentation, cosmic ray pressure in the bubbles, a range of heating factors $h$ for the bubbles, bubble-flow thermalization, and a distribution of bubble masses $m_b$ in each flow." It seems Likely however that, It seems likely however that "our fit to the cumulative age distribution. showing the ""uncertainties frou our Moute Carlo tests. which iuclude he effects of pushing star formation between adjacent nue bius.","our fit to the cumulative age distribution, showing the uncertainties from our Monte Carlo tests, which include the effects of pushing star formation between adjacent time bins." Ou the other hand. within a given time bin. the uncertaintv on the measured mean SER is related to he sensitivity of the CMD to stars in that age bin.," On the other hand, within a given time bin, the uncertainty on the measured mean SFR is related to the sensitivity of the CMD to stars in that age bin." As he size of the bin increases. more locations of the CMD will be affected by the biu.," As the size of the bin increases, more locations of the CMD will be affected by the bin." Thus. increasing tle biu size lnereases the sensitivity of the CAID fit to that time yn. thereby reduciug the uncertainty ou the mean rate within that time bin.," Thus, increasing the bin size increases the sensitivity of the CMD fit to that time bin, thereby reducing the uncertainty on the mean rate within that time bin." It is therefore possible to reduce he uncertainties ou the measured SER by increasing the cheth of the time bius., It is therefore possible to reduce the uncertainties on the measured SFR by increasing the length of the time bins. To determine optimal time bius for our differential SEIL. we apply the uncertainties in our eunuulative aee distribution. as determined from our Monte Carlo tests.," To determine optimal time bins for our differential SFH, we apply the uncertainties in our cumulative age distribution, as determined from our Monte Carlo tests." Specifically. we define bins for which the cunulative action of stars increased with statistical significance.," Specifically, we define bins for which the cumulative fraction of stars increased with statistical significance." Specifically. the bins are defined so that at cach biu ndary. the lo wpper-linut of the cunulative fraction of stars formed in the older bin wast be less than the 1o ower-uit of the vouuger biu.," Specifically, the bins are defined so that at each bin boundary, the $\sigma$ upper-limit of the cumulative fraction of stars formed in the older bin must be less than the $\sigma$ lower-limit of the younger bin." Thus. each bin coutains enough signal iu the CMD that if the bin were removed. he fit to the data would be significantly degraded.," Thus, each bin contains enough signal in the CMD that if the bin were removed, the fit to the data would be significantly degraded." We rote that for the optical and UV fits. we adopted the ine bins measured from the IR fits because the optical and UV data were not seusitive chough to the old stellar »»pulatious to provide cumulative distributions.," We note that for the optical and UV fits, we adopted the time bins measured from the IR fits because the optical and UV data were not sensitive enough to the old stellar populations to provide cumulative distributions." The resultiug SFIS for our CAD fits to the | reeious are shown in Figure 5.., The resulting SFHs for our CMD fits to the 4 regions are shown in Figure \ref{sfhs}. The UVIS data did not provide sufficient depth to probe ages greater than 2.200 Myr. aud thus no poiuts are plotted for older ages.," The UVIS data did not provide sufficient depth to probe ages greater than $\sim$ 200 Myr, and thus no points are plotted for older ages." Ciunulative plots of the stellar mass formed are shown iu Figure 6.. and the results for all regions are overplotted in Figure 7..," Cumulative plots of the stellar mass formed are shown in Figure \ref{cum}, and the results for all regions are overplotted in Figure \ref{allcum}." Since the UVIS data were not sensitive to old populations. we could not generate cumulative ΕΠΣ roni the UVIS data.," Since the UVIS data were not sensitive to old populations, we could not generate cumulative SFHs from the UVIS data." The SFUs show that in all of the areas observed. he majority of the stellar population is old.," The SFHs show that in all of the areas observed, the majority of the stellar population is old." Iu the central portion of the ealaxy. the relatively shallow data are oulv able to constrain the population oulv weakly. o»ittine a lower limit of 2805 of the stellar mass having ages 21 Cyr.," In the central portion of the galaxy, the relatively shallow data are only able to constrain the population only weakly, putting a lower limit of $>$ of the stellar mass having ages $>$ 4 Gyr." In the outermost (and deepest) field. the constraint is tighter. with 71 of the stellar mass ving ages SS Coy.," In the outermost (and deepest) field, the constraint is tighter, with $>$ of the stellar mass having ages $>$ 8 Gyr." Takiug uncertainties into account. all of our data are consistent with this coustraimt from he deepest photoietry.," Taking uncertainties into account, all of our data are consistent with this constraint from the deepest photometry." The cousistency of all of our data. from the optical to he IR. from the ceuter to the outskirts of the disk. with nore than three quarters of the stellar mass beiug very old is surprising.," The consistency of all of our data, from the optical to the IR, from the center to the outskirts of the disk, with more than three quarters of the stellar mass being very old is surprising." This ealaxy is welldsaown for beiug a voung starburst galaxy. being kuown as a “Wolt-Ravet™ ealaxy1991).," This galaxy is well-known for being a young starburst galaxy, being known as a “Wolf-Rayet” galaxy." . While the current star burst is already known to be responsible for only a few percent of the stellar inass1983). it is still surprising that such a small percentage of the population is vouug (< in the past 50 Myr. 10 MeV. photons could result in significant amounts of V. Ti. Cr and Mu.,"region where the red wing is observed, but Skibo (1997) has suggested that spallation of iron nuclei by $> 10$ MeV photons could result in significant amounts of V, Ti, Cr and Mn." There are numerous difficulties with such a model., There are numerous difficulties with such a model. For example. the observed profile changes (sce above) argue forcefully against such a suggestion. as all the fluorescence Lines should vary together.," For example, the observed profile changes (see above) argue forcefully against such a suggestion, as all the fluorescence lines should vary together." None of these alternatives is as conipelliug as the standard disk. but some open questions remain.," None of these alternatives is as compelling as the standard disk, but some open questions remain." The broad lines have been confirmed by DeppoSax (Caouünazzi et al, The broad lines have been confirmed by BeppoSax (Guainazzi et al. 1999). but we await further confirmation and definition of the profiles.," 1999), but we await further confirmation and definition of the profiles." Iu particular. it is miportant to quantifv and decouvolve the disk line contribution from narrower componcuts from the BLR aud obscuring torus.," In particular, it is important to quantify and deconvolve the disk line contribution from narrower components from the BLR and obscuring torus." ASCA observatious have shown some differences comparing objects. but the hieh signal-to-noise profiles all show common features. and in particular the derived iuclinations are often very simular.," ASCA observations have shown some differences comparing objects, but the high signal-to-noise profiles all show common features, and in particular the derived inclinations are often very similar." This. aud possible disagreements with other inclination indicators (Suleutic et al.," This, and possible disagreements with other inclination indicators (Sulentic et al." 1998b) are not vet significant problems. but it will be important in the future o relate the properties derived from iron Kea with other ACN observables.," 1998b) are not yet significant problems, but it will be important in the future to relate the properties derived from iron $\alpha$ with other AGN observables." With aree collecting area. it iav be possible to discover the weak aud very broad. lines expected from edge-on accretion disks. which have so far cluded us.," With large collecting area, it may be possible to discover the weak and very broad lines expected from edge-on accretion disks, which have so far eluded us." Decouvolution roni a (poteutiall-coimplex) continua is the kev here., Deconvolution from a (potentially-complex) continuum is the key here. The Ίνα observations so far have been of great importance. but have shown unexpected complicatious.," The $\alpha$ observations so far have been of great importance, but have shown unexpected complications." The interpretation of future observatious is therefore ikelv to be challenging., The interpretation of future observations is therefore likely to be challenging. Two particular issues are the cuuissivity aud ionization of he disk as a fuuctioun of radius., Two particular issues are the emissivity and ionization of the disk as a function of radius. These are both arbitrary from an observational standpoint. and difficult to predict theoretically.," These are both arbitrary from an observational standpoint, and difficult to predict theoretically." Detailed interpretation of. e.g... variability data - including reverberation mapping (e.g. Revuolds et al.," Detailed interpretation of, e.g., variability data - including reverberation mapping (e.g. Reynolds et al." 1999) will require an understanding of these effects., 1999) - will require an understanding of these effects. Tron Ίνα observers can therefore look forward to developing the kind of complex pliysical models aud advanced data analysis techuiques that niauv other astronomers have been cujoving for may vears., Iron $\alpha$ observers can therefore look forward to developing the kind of complex physical models and advanced data analysis techniques that many other astronomers have been enjoying for many years. We hope and expect the rewards to be substantial., We hope and expect the rewards to be substantial. aneular velocity be a function of the cexliudiical radius alone. 1.06... Q=Qtrsind) (Tassoul2000).,"angular velocity be a function of the cylindrical radius alone, i.e., $\Omega=\Omega(r\sin\theta)$ \citep{Tassoul:2000}." . In this article. we asstune a differcut rotation law for cach laver. which means that the augular velocity is not a function of the evliudrical radius alone even if the rotation law is evlindrical in each laver.," In this article, we assume a different rotation law for each layer, which means that the angular velocity is not a function of the cylindrical radius alone even if the rotation law is cylindrical in each layer." As a result. the EOS cannot be a sinele continuous barotropic oue.," As a result, the EOS cannot be a single continuous barotropic one." In fact. the augular velocity is discontinuous across the laver boundary. which leads in eeueral to the discontinuity in density as shown later.," In fact, the angular velocity is discontinuous across the layer boundary, which leads in general to the discontinuity in density as shown later." Ou the other haud. the pressure is continuous at the laver boundary. which can be understood as follows: Multiplied by the deusitv. Eq. (1))," On the other hand, the pressure is continuous at the layer boundary, which can be understood as follows: Multiplied by the density, Eq. \ref{eq:hydro2}) )" is written at the laver boundary as The right haud side (RIS) of this eqation contains step fuuctious. that is. the deusity and augular velocity.," is written at the layer boundary as The right hand side (RHS) of this equation contains step functions, that is, the density and angular velocity." No that the eravitational potential. which is obtained by the integration of the density. is contiuuous.," Note that the gravitational potential, which is obtained by the integration of the density, is continuous." Then the pressure also continuous because otherwise the let haud side of Eq. (10)), Then the pressure is also continuous because otherwise the left hand side of Eq. \ref{eq:hydro3}) ) would eive a delta function., would give a delta function. This iu turn leads to the conchision that a single continuous baretropic EOS cannot be applied across the laver boundary. since tle pressure could not be continuous for the discoutimous density for such an EOS.," This in turn leads to the conclusion that a single continuous barotropic EOS cannot be applied across the layer boundary, since the pressure could not be continuous for the discontinuous density for such an EOS." Therefore. EOSs that are barotropic in cach laver but differeut from laver to laver are required.," Therefore, EOS's that are barotropic in each layer but different from layer to layer are required." As the simplest example. we eiuploy in this article polvtropic EOS's with a differcut polvtropic coustant aud/or mdex in cach laver.," As the simplest example, we employ in this article polytropic EOS's with a different polytropic constant and/or index in each layer." The esseutial poiuts of our formmla are sunmuuiauized as follows: (1) the rotational equilibrium is locally eusured by the Bernoulli equation i cach laver aud (2) the laver boundary is the location where the lavers are joined so that the pressure should become continuous., The essential points of our formula are summarized as follows: (1) the rotational equilibrium is locally ensured by the Bernoulli equation in each layer and (2) the layer boundary is the location where the layers are joined so that the pressure should become continuous. The problem is now reduced to the solution of Eqs. (62) , The problem is now reduced to the solution of Eqs. \ref{eq:Ber}) ) aud (2)) aud the search of the location where the pressures of the different lavers coincide., and \ref{eq:gravity}) ) and the search of the location where the pressures of the different layers coincide. Before discussing multi configurations. we biefiv review the Hachisu Field (IISCE) scheme (IHachisu1956).. which dlaveredis known to be a very robust algorithin to solve iteratively Eqs. (6))," Before discussing multi-layered configurations, we briefly review the Hachisu Self-Consistent Field (HSCF) scheme \citep{Hachisu:1986}, which is known to be a very robust algorithm to solve iteratively Eqs. \ref{eq:Ber}) )" and (2)) for sinele-lavered configurations in rotational equilibrium aud on which our formmla is based., and \ref{eq:gravity}) ) for single-layered configurations in rotational equilibrium and on which our formula is based. Iu this scheme. we first introduce the following non-dimensional variables: where fux Pmax sud € are the maxiumun density. pressure and speed of light. respectively. aud the subscript / is dropped in Jg. A. e and E.," In this scheme, we first introduce the following non-dimensional variables: where $\rho_{\rm max}$, $p_{\rm max}$ and $c$ are the maximum density, pressure and speed of light, respectively, and the subscript $i$ is dropped in $h_0$ , $A$, $c$ and $H$." The radius is normalized by the equatorial radius of the equilibrium coufieuration. οι which is unknown a priori aud is expressed as r2= by the introduction of anew variable 3.," The radius is normalized by the equatorial radius of the equilibrium configuration, $r_e$ , which is unknown a priori and is expressed as $r_{e}=\displaystyle{\sqrt{\frac{1}{\beta} \frac{p_{\rm max}}{4\pi {\rm G}\rho_{\rm max}^2}}}$ by the introduction of anew variable $\beta$." Then Eqs. (6)), Then Eqs. \ref{eq:Ber}) ) and (2)) are reducedto Iu Eqs. (18)), and \ref{eq:gravity}) ) are reducedto In Eqs. \ref{eq:Ber2}) ) and (19)). we have two uuknown fuictions Ορ.0) aud ptr.0) aud three constants 3. fig. aud € once the EOS aud rotation law (7-—-9)) ave specified.," and \ref{eq:pois2}) ), we have two unknown functions $\hat{\phi}_g(\hat{r},\theta)$ and $\hat{\rho}(\hat{r},\theta)$ and three constants $\beta$, $\hat{h}_0$, and $\hat{c}$ once the EOS and rotation law \ref{eq:rot0}- \ref{eq:rot2}) ) are specified." It is noted that the specific cuthalpy 1 is a function of the density alone because of the barotropic codition., It is noted that the specific enthalpy $H$ is a function of the density alone because of the barotropic condition. " In the IISCE iiethod. we give pias the equatorial radius 7 aud polar radius +, instead of 3. fy. and © to specifv the model aud tje latter three are treated as unknown variables to be solved."," In the HSCF method, we give $\rho_{\rm max}$ , the equatorial radius $\hat{r}_e$ and polar radius $\hat{r}_p$ instead of $\beta$, $\hat{h}_0,$ and $\hat{c}$ to specify the model and the latter three are treated as unknown variables to be solved." " Note that r, dis unitv by the definiion of 3 (see Eq. (12) ).", Note that $\hat{r}_e$ is unity by the definition of $\beta$ (see Eq. \ref{eq:defofbeta}) )). This choice of variables is esseutial for the SCF scheme., This choice of variables is essential for the HSCF scheme. Iudeed other choices such as fias aid fy (and ες= 1) fai to obtain convergence in the iteration(see below) more often than hot., Indeed other choices such as $\rho_{\rm max}$ and $\hat{h}_0$ (and $\hat{r}_e=1$ ) fail to obtain convergence in the iteration(see below) more often than not. The two unknown fuuctiois our0) aud ptr.0) aud three unknown coustauts 2. fy. aud e are obtained iteratively in the IISCFE inethod as folows.," The two unknown functions $\hat{\phi}_g(\hat{r},\theta)$ and $\hat{\rho}(\hat{r},\theta)$ and three unknown constants $\beta$, $\hat{h}_0$, and $\hat{c}$ are obtained iteratively in the HSCF method as follows." First we eive a rial deusity distribution p aud solve Eq. (19)), First we give a trial density distribution $\hat{\rho}$ and solve Eq. \ref{eq:pois2}) ) toobtain oy., toobtain $\hat{\phi}_g$ . As a second step. Eq. (E8))," As a second step, Eq. \ref{eq:Ber2}) )" is evauated at the following points:the stellay surfaces ou the equator aud ou the rotation axis and the point of the maxiuuπι deusitv. which aredenoted as E. P aud C. respectively (sce Fig. 1)).," is evaluated at the following points:the stellar surfaces on the equator and on the rotation axis and the point of the maximum density, which aredenoted as $E$ , $P$ and $C$ , respectively (see Fig. \ref{fig:multi}) )." The results obtained here are consistent with the idea that the different racio structures ol FRI and FRII sources are due to differences in their gaseous environments (e.g. Burns οἱ al.,The results obtained here are consistent with the idea that the different radio structures of FRI and FRII sources are due to differences in their gaseous environments (e.g. Burns et al. 1994: Bicknell 1995). and suggests that the gaseous environments of these sources has evolved significantlv.," 1994; Bicknell 1995), and suggests that the gaseous environments of these sources has evolved significantly." The evolution of the gaseous environment could be due in part to the large-scale outflows (e.g. Silk Rees 1995; Eilek Owen 2002)., The evolution of the gaseous environment could be due in part to the large-scale outflows (e.g. Silk Rees 1998; Eilek Owen 2002). It is remarkable (hat so few sources have values of j close to the theoretical limit οἱ univ: that is. almost. all sources have values of r much less than the theoretical limit of 0.29.," It is remarkable that so few sources have values of $j$ close to the theoretical limit of unity; that is, almost all sources have values of $r$ much less than the theoretical limit of 0.29." All of the FRIIb sources have r~10.7., All of the FRIIb sources have $r \sim 10^{-3}$. This suggests that each svstem is in a similar physical state at the Gime the outflow is generated. and may. indicate that the outflow. is triggered when a particular threshold is reached.," This suggests that each system is in a similar physical state at the time the outflow is generated, and may indicate that the outflow is triggered when a particular threshold is reached." If the sources have intrinsic values of j that start oul close to one. each outflow event is tapping a verv small fraction of (he available spin energv. and each source may have multiple outflow events.," If the sources have intrinsic values of $j$ that start out close to one, each outflow event is tapping a very small fraction of the available spin energy, and each source may have multiple outflow events." The spin values obtained here could be compared with independent measures of the black hole spin., The spin values obtained here could be compared with independent measures of the black hole spin. This may provicle a diagnostic of whether it is (he black hole spin or (he accretion disk that is powering large-scale outflows [rom these sources., This may provide a diagnostic of whether it is the black hole spin or the accretion disk that is powering large-scale outflows from these sources. In addition. the method of using outflow energies and black hole masses to estimate black hole spins presented here mav be applicable to other svstenis.," In addition, the method of using outflow energies and black hole masses to estimate black hole spins presented here may be applicable to other systems." It is a pleasure to thank George Djorgovski. Brian \leNamara. David Meier. ancl the releree of this paper for very helpful comments and suggestions on (his work.," It is a pleasure to thank George Djorgovski, Brian McNamara, David Meier, and the referee of this paper for very helpful comments and suggestions on this work." lt is also a pleasure to thank Ross MeLure for providing stellar masses for the fourteen highest recshift sources listed in Table 1., It is also a pleasure to thank Ross McLure for providing stellar masses for the fourteen highest redshift sources listed in Table 1. This work was supported in part by U.S. National Science Foundation grants AST-0507465., This work was supported in part by U. S. National Science Foundation grants AST-0507465. discuss a few alternative possibilities for the host galaxy. of this GRB.,discuss a few alternative possibilities for the host galaxy of this GRB. While none of these possibilities can be strongly ruled out. we nevertheless consider (hem less likely as potential hosts than C. for various stated reasons.," While none of these possibilities can be strongly ruled out, we nevertheless consider them less likely as potential hosts than $G*$, for various stated reasons." The original ART error circle contains two other optical sources. designated Gl and $2.," The original XRT error circle contains two other optical sources, designated 'G1' and 'S2'." Our refined NRT error circle. while generally consistent. with the original NRT error circle. excludes both of these sources to confidence.," Our refined XRT error circle, while generally consistent with the original XRT error circle, excludes both of these sources to confidence." Nevertheless. as this does nol completely eliminate the possibility of association (especially considering the possibility of election). we can ask whether or not the proximity of these sources to the AT position suggests. on probabilistic grounds. that one of these objects is physically. associated. with ihe GRB.," Nevertheless, as this does not completely eliminate the possibility of association (especially considering the possibility of ejection), we can ask whether or not the proximity of these sources to the XRT position suggests, on probabilistic grounds, that one of these objects is physically associated with the GRB." The extended object G1 (the brightest source ancl therefore the least likely to be coincident with the error circle bv random chance) has a magnitude of H222 24: the inlegrated skv density [or galaxies of equal or greater brightness is about 20 per arcmii., The extended object G1 (the brightest source and therefore the least likely to be coincident with the error circle by random chance) has a magnitude of $R \approx$ 24; the integrated sky density for galaxies of equal or greater brightness is about 20 per $^2$. The probability of a chance association wilh such an object at (his distance or less is 2 0.5 that is. a randomly placed ART error circle of this size will be as close or closer to such a ealaxy about hall (he time.," The probability of a chance association with such an object at this distance or less is $\approx$ 0.5 – that is, a randomly placed XRT error circle of this size will be as close or closer to such a galaxy about half the time." The probabilities will be comparable or higher for 52 and several additional. fainter sources we identify in our imaging ($3. S4. and G2).," The probabilities will be comparable or higher for S2 and several additional, fainter sources we identify in our imaging (S3, S4, and G2)." So while association ol the GRB with one of these faint sources cannot be ruled out. the large size of the NRT error circle simply does not allow Chis possibility to be strongly. teste.," So while association of the GRB with one of these faint sources cannot be ruled out, the large size of the XRT error circle simply does not allow this possibility to be strongly tested." Visible on our LRIS imaging is a nearly edge-on spiral at a distance of nnorthwest of the center of the NRT error circle., Visible on our LRIS imaging is a nearly edge-on spiral at a distance of northwest of the center of the XRT error circle. Unfortunately this galaxy is strongly blended with a bright Galactie star. so an accurate magnitude measurement is difficult. though the blended source has a combined magnitude of 15.56 in the 2MASS catalog. slightly fainter than G*.," Unfortunately this galaxy is strongly blended with a bright Galactic star, so an accurate magnitude measurement is difficult, though the blended source has a combined magnitude of 15.56 in the 2MASS catalog, slightly fainter than $G^*$." " Even making (he conservative assumption that Ap,7Ac. however. the probability of random association with an object of this magnitude at this distance is about a [actor of 4 larger (han for the association with C."," Even making the conservative assumption that $K_{D*} \approx K_{G*}$, however, the probability of random association with an object of this magnitude at this distance is about a factor of 4 larger than for the association with $G^*$." So on probabilistic grounds. if we are to associate GRB 060502D with anv object in Figure 1. C is by far the strongest candidate.," So on probabilistic grounds, if we are to associate GRB 060502B with any object in Figure 1, $G*$ is by far the strongest candidate." There are (wo additional objects visible at much greater angular distances from the GRB that suggest themselves as possible hosts on account of their unusual brightness., There are two additional objects visible at much greater angular distances from the GRB that suggest themselves as possible hosts on account of their unusual brightness. At a distance of nnorth of the NRT position is a bright spiral galaxy. visible in 2MÀSS with a magnitude of Kk=12.5.," At a distance of north of the XRT position is a bright spiral galaxy, visible in 2MASS with a magnitude of $K = 12.5$." Despite this large distance. (he probability of random! association in (hiis case is x0.043. about twice that of association with Gs.," Despite this large distance, the probability of 'random' association in this case is $\approx 0.043$, about twice that of association with $G*$." Even more suggestivelv. at a distance of iis (he bright galaxy UGC 11292. and with a magnitude of A — 10.05 (IXochaneketal.2001).. the probability. of such a close random association is only 0.005) (less than our probability for Gx).," Even more suggestively, at a distance of is the bright galaxy UGC 11292, and with a magnitude of $K$ = 10.05 \citep{kpf+01}, the probability of such a close random association is only 0.005 (less than our probability for $G*$ )." Süll. we tend to disfavor (his hypothesis on theoretical grounds: at the measured," Still, we tend to disfavor this hypothesis on theoretical grounds: at the measured" "In the soft state, the inner disk radius can be estimated from the model as: where Ny is the normalization, D is the distance, 9 is the angle of the disk. ζω is the fractional change of the color temperature and 7j is the correction factor for the inner torque-tree boundary condition (Zhang et al.","In the soft state, the inner disk radius can be estimated from the model as: where $N_{\rm disk}$ is the normalization, $D$ is the distance, $\theta$ is the angle of the disk, $f_{\rm col}$ is the fractional change of the color temperature and $\eta$ is the correction factor for the inner torque-free boundary condition (Zhang et al." 1997: Gierlinsski Done 2002)., 1997; Gierlińsski Done 2002). " For X-ray Binaries. we cannot restrict the inclination very well in most cases, unless the companion’s light curve modulation is observed."," For X-ray Binaries, we cannot restrict the inclination very well in most cases, unless the companion's light curve modulation is observed." " Since neither eclipses nor absorption dips have been observed (Lin07), we assume a reasonable inclination angle ~ 70°, however, do not exclude the possibility of smaller ones."," Since neither eclipses nor absorption dips have been observed (Lin07), we assume a reasonable inclination angle $\sim$ $70\degr$, however, do not exclude the possibility of smaller ones." D=3.6 kpc. η = 0.7. and fi=1.7 are adopted in this work.," $D = 3.6$ kpc, $\eta$ $=$ 0.7, and $f_{\rm col}= 1.7$ are adopted in this work." Our main interest here is the trend of accretion disk evolution that does not strongly depend on the precise values of the inclination angle and these correction factors., Our main interest here is the trend of accretion disk evolution that does not strongly depend on the precise values of the inclination angle and these correction factors. " With the inner disk radius and its temperature, the bolometric luminosity of the disk can also be derived as: Ly,disk=4zRcospsT."," With the inner disk radius and its temperature, the bolometric luminosity of the disk can also be derived as: $L_{\rm disk}=4\pi R^2\sigma_{\rm SB} T^4$." The Eddington luminosity is Lew=1.3x107xM/M. erg s! with M being the mass of central compact object.," The Eddington luminosity is $L_{\mathrm{Edd}}=1.3 \times 10^{38} \times M/M_{\odot}$ erg $^{-1}$ with $M$ being the mass of central compact object." " Assuming that the mass of NS is 1.4 solar mass, then its Eddington luminosity is 1.82x10? erg s!."," Assuming that the mass of NS is 1.4 solar mass, then its Eddington luminosity is $1.82 \times 10^{38}$ erg $^{-1}$." In Figure 3 we plot the radius of the inner accretion disk versus the bolometric luminosity of the disk in units of Legy., In Figure \ref{fig3} we plot the radius of the inner accretion disk versus the bolometric luminosity of the disk in units of $L_{\mathrm{Edd}}$. " Above ~ 0.1 Legg. the inner disk radius remains constant (~~ 13 km). that is, the innermost stable circular orbit (SCO) of NS."," Above $\sim$ 0.1 $L_{\mathrm{Edd}}$, the inner disk radius remains constant ( $\sim$ 13 km), that is, the innermost stable circular orbit (ISCO) of NS." The dashed line in the right panel of Figure 3 represents Luis=AxRcssT with R=13 km.," The dashed line in the right panel of Figure 3 represents $L_{\rm disk}=4\pi R^2\sigma_{\rm SB} T^4$ with $R = 13$ km." These results are in agreement with Lin07 (Figure 7 in their paper)., These results are in agreement with Lin07 (Figure 7 in their paper). There are two XRT observations below 0.1 Legy that deviate from the constant radius and [μιxT., There are two XRT observations below 0.1 $L_{\mathrm{Edd}}$ that deviate from the constant radius and $L_{\rm disk} \propto T^4$. " Since these two observations cover the lower luminosity (IMS) just before the source returns to LHS, we need to check the spectral model carefully."," Since these two observations cover the lower luminosity (IMS) just before the source returns to LHS, we need to check the spectral model carefully." " Fitting the data with MCD+BB and BB+PL shows that the MCD+BB model is favored; adding a PL component to MCD+BB, the photon index pegs at the hard limit of 10.0."," Fitting the data with MCD+BB and BB+PL shows that the MCD+BB model is favored; adding a PL component to MCD+BB, the photon index pegs at the hard limit of 10.0." " However, there is a caveat when we use the simple PL model to depict the Compton component in fitting the spectra of X-ray binaries: it rises without limit at low energies, which evidently disagrees with Comptonization."," However, there is a caveat when we use the simple PL model to depict the Compton component in fitting the spectra of X-ray binaries: it rises without limit at low energies, which evidently disagrees with Comptonization." " To eliminate this divergence, we further fit the data with a more appropriate Compton model (SIMPL, in XSPEC), which is developed by Steiner et al. ("," To eliminate this divergence, we further fit the data with a more appropriate Compton model (SIMPL, in XSPEC), which is developed by Steiner et al. (" 2009).,2009). " With only two tree parameters, SIMPL incorporates the basic features of Compton scattering of soft photons by energetic coronal electrons."," With only two free parameters, SIMPL incorporates the basic features of Compton scattering of soft photons by energetic coronal electrons." " Since the seed photons for the Comptonized component can be from MCD and/or BB, we combine the SIMPL, DISKBB, and BB in a variety of ways to fit the spectra (1...stapl(diskbb+bb),(simpl*diskbb+bb), and *bb))."," Since the seed photons for the Comptonized component can be from MCD and/or BB, we combine the SIMPL, DISKBB, and BB in a variety of ways to fit the spectra (i.e., and )." " Though all these models cannot constrain the parameters owing to limited photons, the fitting results all indicate that the inner disk radius really moves out."," Though all these models cannot constrain the parameters owing to limited photons, the fitting results all indicate that the inner disk radius really moves out." Figure 4. shows the ratio between the BB and MCD luminosity versus the inner disk radius., Figure \ref{fig4} shows the ratio between the BB and MCD luminosity versus the inner disk radius. " Assuming that the accretion matter falls freely from the inner disk to the surface of NS, the"," Assuming that the accretion matter falls freely from the inner disk to the surface of NS, the" "The X-ray energy [ιν al 5 KeV (Fe,5SiveV)) can be estimated as follows.",The X-ray energy flux at 5 KeV $F(\epsilon_{\gamma}=5KeV)$ ) can be estimated as follows. " Since IC energy flux is. given. by Fle.).2e2(e,)↜~ei1/2 because n\~[ο-τι we can estimate the enerev [lux at 5 Ιον F(e;=54AveV) from its peak energy Πας."," Since IC energy flux is given by $F(\epsilon_{\gamma})\approx \epsilon_{\gamma}^2\Phi(\epsilon_{\gamma})\sim \epsilon_{\gamma}^{1/2}$ because $\frac{dN}{dE_e}\sim E_e^{-2}$, we can estimate the energy flux at 5 KeV $F(\epsilon_{\gamma}=5KeV)$ from its peak energy flux." " We have argued that the relic photons should be (he most important photons to generate the N-ravs through IC process. therefore F(e,=5ANeV) produced by IC of relie photons is given by where Fiz; is (he peak energy flix of the inverse Compton scattering relic photons and the characteristic upward scattering energy of relic photons is ~8352.MeV."," We have argued that the relic photons should be the most important photons to generate the X-rays through IC process, therefore $F(\epsilon_{\gamma}=5KeV)$ produced by IC of relic photons is given by where $F_{relic}$ is the peak energy flux of the inverse Compton scattering relic photons and the characteristic upward scattering energy of relic photons is $\sim 8\gamma_{w5}^2MeV$." " We can estimate the peak energy [lux of the scattered relie photons by Freie—το)opiMy, where F°?* is the observed gamma-ray energy flux in the GeV energy range. 0,45 21d 16,57; are (he energy density of the relie photons aud the soft photons. which upward scatter to produce gamnma-ravs."," We can estimate the peak energy flux of the scattered relic photons by $F_{relic}=(w_{relic}/w_{soft})F_{\gamma}^{obs}$, where $F_{\gamma}^{obs}$ is the observed gamma-ray energy flux in the GeV energy range, $w_{relic}$ and $w_{soft}$ are the energy density of the relic photons and the soft photons, which upward scatter to produce gamma-rays." The strength5 of magnetic field 5 near the clusters is not known exactly. it is estimated to be of order of 10. C (Deck et al.," The strength of magnetic field $B$ near the clusters is not known exactly, it is estimated to be of order of $10^{-6}$ G (Beck et al." 2003)., 2003). The energy. loss ratio between svnchrotron radiation and inverse Compton scattering is given by where B; is the magnetic field in units of 10. °C. We can see that the svnchrotron loss is not negligible., The energy loss ratio between synchrotron radiation and inverse Compton scattering is given by where $B_{-6}$ is the magnetic field in units of $10^{-6}$ G. We can see that the synchrotron loss is not negligible. The characteristic svuchrotvon Irequency is given by which is in the radio band., The characteristic synchrotron frequency is given by which is in the radio band. We can estimate the enerey flux al 1GIIz, We can estimate the energy flux at 1GHz wih strongly differential rotations.,with strongly differential rotations. This may be important iu dealing with the progenitors of GRD 2006).., This may be important in dealing with the progenitors of GRB \citep{Woosley:2005gy}. Bearing in mind the applicatiou to the study of rotational massive stars in their late evolutionary phase. in this paper we have proposed a new formula to construct multi-Iavered configurations in rotational equilibrium.," Bearing in mind the application to the study of rotational massive stars in their late evolutionary phase, in this paper we have proposed a new formula to construct multi-layered configurations in rotational equilibrium." This is au exteusion of the Iachisu selt-cousisteut field scheme that is based ou the Bernoulli equation aud meant originally for sinele-lavered coufiguratious that are rotating cvlindvically with a barotropic EOS., This is an extension of the Hachisu self-consistent field scheme that is based on the Bernoulli equation and meant originally for single-layered configurations that are rotating cylindrically with a barotropic EOS. Iu our method. on the other haud. each laver is assumed to rotate still evlindvically with a barotropic EOS but the rotation laws and EOS's are differeut from laver to laver.," In our method, on the other hand, each layer is assumed to rotate still cylindrically with a barotropic EOS but the rotation laws and EOS's are different from layer to layer." We have shown that the pressure should be continuous at the laver boundary whereas the deusity is in eeneral discontinuous across thie boundary. which is an alternative demonstration that the EOS cannot be identical for the adjacent lavers.," We have shown that the pressure should be continuous at the layer boundary whereas the density is in general discontinuous across the boundary, which is an alternative demonstration that the EOS cannot be identical for the adjacent layers." We have icleutified the variables that are appropriate to make the iteration scheme convergent., We have identified the variables that are appropriate to make the iteration scheme convergent. This is indeed a crucial iugredieut in our forma., This is indeed a crucial ingredient in our formula. For demoustration. we have ac‘tually constructed several coufieuratious with two lavers for three represcutative rotation laws. which we have referred to as the -coustaut. j-coustaut and c-constaut laws in this paper.," For demonstration, we have actually constructed several configurations with two layers for three representative rotation laws, which we have referred to as the $\Omega$ -constant, $j$ -constant and $v$ -constant laws in this paper." We have found that the virial equation is satisfied with a typical eror of 10.7D irrespective of the rotation laws if we deploy 1000«200 mesh points aud we je also demonstrated that the eror is reduced as the nuuber of mesh poiuts is increased., We have found that the virial equation is satisfied with a typical error of $10^{-5}$ irrespective of the rotation laws if we deploy $1000 \times 200$ mesh points and we have also demonstrated that the error is reduced as the number of mesh points is increased. IDuucideutalbv. it has lec ‘confirmed that à non-rotational configuration is also reproduced by the prescut scheme.," Incidentally, it has been confirmed that a non-rotational configuration is also reproduced by the present scheme." From these results it is obvious that our method works well aud is robust indeed., From these results it is obvious that our method works well and is robust indeed. The application of the xeseut formula to more realistic xoblems will be published elsesvhliere CNagakuraetal.2010)., The application of the present formula to more realistic problems will be published elsewhere \citep{Nagakura:2010}. As commented in Sec. ??..," As commented in Sec. \ref{sec:basic}," if 1s straightforward to exteud our scheme to the configurations with more than two avers though the procedure becoues a bit more involved., it is straightforward to extend our scheme to the configurations with more than two layers though the procedure becomes a bit more involved. Although we have combined the rotation laws of the same zuuilv but with differeut paraitcrs for siuuplicity in this paper. two rotation laws of differcut familics can be treated in the same wav.," Although we have combined the rotation laws of the same family but with different parameters for simplicity in this paper, two rotation laws of different families can be treated in the same way." The implementation of more realistic EOSs will pose no problemi iu principle as long as they are xwotropic., The implementation of more realistic EOSs will pose no problem in principle as long as they are barotropic. We may employ the icea by Jacksonetal.(2005):MacCaegor(2007). that the pressure. density. aud eniperature are assumed to be functions of the effective potential alone.," We may employ the idea by \citet{Jackson:2005,MacGregor:2007zy} that the pressure, density, and temperature are assumed to be functions of the effective potential alone." Moreover. the preseut formula will be able to reat configurations with a topology of torus by relaxing the assuuption that the surface exteuds itself to the svuuuctry axis and by choosing appropriate poiuts ou the equator to inpose the conditions corresponding to Eqs. (25)). (26))," Moreover, the present formula will be able to treat configurations with a topology of torus by relaxing the assumption that the surface extends itself to the symmetry axis and by choosing appropriate points on the equator to impose the conditions corresponding to Eqs. \ref{eq:cond4}) ), \ref{eq:cond3}) )" aud (28)) although we do not ku»v how realistic such configurations are., and \ref{eq:cond6}) ) although we do not know how realistic such configurations are. Iu our formula. the laver boundary is determined frou the condition that the pressure be contiuuous there.," In our formula, the layer boundary is determined from the condition that the pressure be continuous there." Iu reality. however. the lavers in the stellar interior correspond to the regions of different cliemical compositions aud their boundaries are determined by the thermodvuamical couditious for nuclear burnings.," In reality, however, the layers in the stellar interior correspond to the regions of different chemical compositions and their boundaries are determined by the thermodynamical conditions for nuclear burnings." This difference originates from the fact that we lave imposed piece-wise cevliudrical rotation laws., This difference originates from the fact that we have imposed piece-wise cylindrical rotation laws. " Iu the actual stellar iuterior. cach laver obeys a boroclinic EOS and. as a result. rotates nou-cvlindrically,"," In the actual stellar interior, each layer obeys a boroclinic EOS and, as a result, rotates non-cylindrically." " Moreover. the eas motions in the meridian section such as convections and meridional circulations are likely to exist eeuically,"," Moreover, the gas motions in the meridian section such as convections and meridional circulations are likely to exist generically." Then the original partial differcutial equations should be solved somehow. which is a formidable task aud will need an eutirelv new approach.," Then the original partial differential equations should be solved somehow, which is a formidable task and will need an entirely new approach." Our formmla. therefore. is adiuittedly a rather crude approximation to the reality but. hopefully. not so bad one if one chooses an appropriate rotation law for each laver.," Our formula, therefore, is admittedly a rather crude approximation to the reality but, hopefully, not so bad one if one chooses an appropriate rotation law for each layer." Iu fact. dt will be uch better than anv approximate configurations with oulv a sinele-laver.," In fact, it will be much better than any approximate configurations with only a single-layer." The real challenge will be to somehow implement chemical evolutions to the sequence of rotational configurations., The real challenge will be to somehow implement chemical evolutions to the sequence of rotational configurations. Oue possibility may be an extension of the idea emploved i- nost of the current one climensional evolution models of rotational massive stars (ποσαetal.20002:ITirschi20014:xLiniongi2000)..," One possibility may be an extension of the idea employed in most of the current one dimensional evolution models of rotational massive stars \citep{Heger:2000ud,Hirschi:2004ks,Limongi:2000km}." Under the assumption that the thermodynamical conditions as well as the elieniical abuudances are uniform on cach surface of constant effective, Under the assumption that the thermodynamical conditions as well as the chemical abundances are uniform on each surface of constant effective with WFC aud. ASM.,with WFC and ASM. In Sect. 3.," In Sect. \ref{secspec}," we discuss the broacl- spectrmu of the persistent enuission as well as a burst detected with the NEL, we discuss the broad-band spectrum of the persistent emission as well as a burst detected with the NFI. The PCA observation is discussed in Sect. L.," The PCA observation is discussed in Sect. \ref{secvar}," it focuses on the short-term variability of the source., it focuses on the short-term variability of the source. We review the results aud their duplications iu Sect. 5.., We review the results and their implications in Sect. \ref{secdis}. The WFC (Jager et al., The WFC (Jager et al. 1997) on the satellite (BocHa ct al., 1997) on the satellite (Boella et al. " L997a) Is carving out a program of uonitorius observatious of the 10""«[07 field. around he Galactic center.", 1997a) is carrying out a program of monitoring observations of the $^{\rm o}\times40^{\rm o}$ field around the Galactic center. The purpose i8 to detect X-rav transient activity. particularly from Qw-nass N-ray inanes (LAINBs) whose Calactic population exhibits a stroug concentratiou dn thus field. and to monitor he behavior of persistently bright X-ray sources.," The purpose is to detect X-ray transient activity, particularly from low-mass X-ray binaries (LMXBs) whose Galactic population exhibits a strong concentration in this field, and to monitor the behavior of persistently bright X-ray sources." Some xevious results have been published im Iu t Zand et al. (, Some previous results have been published in In 't Zand et al. ( 1998b). Heise (1998). Cocchi et al. (,"1998b), Heise (1998), Cocchi et al. (" 1998).,1998). The program consists of campaigus durug the spring and fall of each year., The program consists of campaigns during the spring and fall of each year. Each campaign lasts about two mouths and typically comprises weekly observations., Each campaign lasts about two months and typically comprises weekly observations. Up to the spring 1998 campaign. a total net exposure time of 2 wullion seconds was accumulated duinue { campaigus.," Up to the spring 1998 campaign, a total net exposure time of 2 million seconds was accumulated during 4 campaigns." The fall 1998 campaign consists of five observations of ~50 ks cach hetween August 22 and October 7. 1998.," The fall 1998 campaign consists of five observations of $\sim50$ ks each between August 22 and October 7, 1998." During he first observation. on August. 22.10-23.1L. 1998. a transicut was detected at a position consistent," During the first observation, on August 22.40-23.14, 1998, a transient was detected at a position consistent" the probability of there being a companion to based on a rough fit to the mass-dependent companion fraction reported by ?..,the probability of there being a companion to based on a rough fit to the mass-dependent companion fraction reported by \citet{Lada-2006}. " If a companion exists, we also select its mass from the IMF, rejecting and redrawing if the mass exceeds the primary's mass."," If a companion exists, we also select its mass from the IMF, rejecting and redrawing if the mass exceeds the primary's mass." " Finally, we select the orbital period of the binary by drawing from the distribution observed for field G star binaries (?) where 7 is the period in days, 155 —2.3, and log7= 4.8."," Finally, we select the orbital period of the binary by drawing from the distribution observed for field G star binaries \citep{DuquennoyMayor-1991} where $\tau$ is the period in days, $\sigma_{\log\tau}$ =2.3, and $\overline{\log\tau}=4.8$ ." " We determine the impact parameter of the encounter, b, randomly with probability proportional to b, with a maximum, 5,444, of 2000 AU."," We determine the impact parameter of the encounter, $b$, randomly with probability proportional to $b$, with a maximum, $b_{max}$, of 2000 AU." " We randomize the relative orientations of the incoming star, the Solar ecliptic, and the binary orbital plane."," We randomize the relative orientations of the incoming star, the Solar ecliptic, and the binary orbital plane." " Finally, for each incoming system, we run the simulation for a series of relative velocities between the system and the Sun."," Finally, for each incoming system, we run the simulation for a series of relative velocities between the system and the Sun." We use velocities of v—0.1-2.5 at intervals of 0.1 km/s and v—3.0-20.0 km/s at km/sintervals of 0.5km/s. Over 2.1 million runs were preformed in total., We use velocities of $v$ =0.1-2.5 km/s at intervals of 0.1 km/s and $v$ =3.0-20.0 km/s at intervals of 0.5km/s. Over 2.1 million runs were preformed in total. " In Sections 3.1 — 3.3,, we first examine the effects of encounters on the Jovian planets, on the Kuiper Belt, and on Tyche in the more likely scenario where the Sun was born in a cluster with a lifetime tite=teross."," In Sections \ref{sec:jovian} – \ref{sec:tyche}, we first examine the effects of encounters on the Jovian planets, on the Kuiper Belt, and on Tyche in the more likely scenario where the Sun was born in a cluster with a lifetime $t_{\rm life} = t_{\rm cross}$." " In Section 3.4 we examine how these results change in the scenario where the Sun's parent cluster was one of the ~1096 that reach ages of tj,=30 Myr.", In Section \ref{sec:longlife} we examine how these results change in the scenario where the Sun's parent cluster was one of the $\sim 10\%$ that reach ages of $t_{\rm life} = 30$ Myr. alew (ens degrees ahead of (he MP. whereas the transverse scattering forms the IP. which lags ihe MP by more than 1307.,"a few tens degrees ahead of the MP, whereas the transverse scattering forms the IP, which lags the MP by more than $180^\circ$." The numerical estimates show that at the conditions relevant to pulsar magnetospheres the intensity transfer [rom the radio beam (o the background can indeed be efficient., The numerical estimates show that at the conditions relevant to pulsar magnetospheres the intensity transfer from the radio beam to the background can indeed be efficient. Stronger scattering is favored by. shorter pulse periods. larger radio luminosities and lower frequencies aud is expected to be especially efficient in the millisecond pulsars.," Stronger scattering is favored by shorter pulse periods, larger radio luminosities and lower frequencies and is expected to be especially efficient in the millisecond pulsars." All this is in line with the trends known for the observed IP emission., All this is in line with the trends known for the observed IP emission. Note that the IP component is led by the MP radiation of much higher frequencies. νιzzvd?/4.," Note that the IP component is fed by the MP radiation of much higher frequencies, $\nu_1\approx\nu\theta^2/4$." With the decreasing spectrum of the original MP. this implies that the IP cannot be as large as the MP at the same frequency unless the latter is substantially suppressed by (he scattering to still lower frequencies.," With the decreasing spectrum of the original MP, this implies that the IP cannot be as large as the MP at the same frequency unless the latter is substantially suppressed by the scattering to still lower frequencies." Our model can account for the peculiar properties of the IP emission., Our model can account for the peculiar properties of the IP emission. As the region ol efficient. transverse scattering lies [ar from the emission region. at clistances of order of the evelotron resonance radius. and the characteristic scattering altitude is an extremely weak function of Irequencey. the MP-IP separation should remain almost (he same over (he observed radio frequency range.," As the region of efficient transverse scattering lies far from the emission region, at distances of order of the cyclotron resonance radius, and the characteristic scattering altitude is an extremely weak function of frequency, the MP-IP separation should remain almost the same over the observed radio frequency range." Note that the scattering al somewhat lower altitudes max also be noticeable. giving rise to the emission bridge between the AIP and the ID.," Note that the scattering at somewhat lower altitudes may also be noticeable, giving rise to the emission bridge between the MP and the IP." The position angle of linear polarization of the scattered radiation is determined bv the orientation of the kyx b-plane in the scattering region and generally differs from the position angle of the incident radiation.," The position angle of linear polarization of the scattered radiation is determined by the orientation of the ${\bf k_1}\times{\bf b}$ -plane in the scattering region and generally differs from the position angle of the incident radiation." Furthermore. the magnetic field is believed to be almost uniform throughout the scattering region. so (hat the position angle swing in the IP should be shallow.," Furthermore, the magnetic field is believed to be almost uniform throughout the scattering region, so that the position angle swing in the IP should be shallow." Although both orthogonal polarization modes can grow as a result of the transverse scattering. the efficiencies of intensity (transfer may differ markedly. making expect high percentage of linear polarization in (he resultant. IP emission.," Although both orthogonal polarization modes can grow as a result of the transverse scattering, the efficiencies of intensity transfer may differ markedly, making expect high percentage of linear polarization in the resultant IP emission." The IP formation as a result of the MP scattering implies a physical connection between these components. which is believed to manilest itself in their intensity fluctuations al different. timescales.," The IP formation as a result of the MP scattering implies a physical connection between these components, which is believed to manifest itself in their intensity fluctuations at different timescales." Our model is strongly. supported by the recent observations of PSR 1102-19 (Weltevredeetal.2007).. which have revealed (hat (he subpulse patterns in the MP and (he IP ave intrinsically in phase.," Our model is strongly supported by the recent observations of PSR B1702-19 \citep{welt07}, which have revealed that the subpulse patterns in the MP and the IP are intrinsically in phase." Furthermore. the peculiar temporal ancl frequency structure of the eiant. pulses in the IP of the Crab pulsar (Eilek&Hankins2007) may well be interpreted as a modification of the giant. MP structure in the scattering process.," Furthermore, the peculiar temporal and frequency structure of the giant pulses in the IP of the Crab pulsar \citep{eh07} may well be interpreted as a modification of the giant MP structure in the scattering process." The peculiar moding behavior of PSR D1822-09 is suggested to result from the fIuctuations of the physical conditions in the scattering region. which affect the relative efficiency. of the longitudinal ancl transverse scatterings aud lead (to the observed interplay between the resultant precursor and IP components.," The peculiar moding behavior of PSR B1822-09 is suggested to result from the fluctuations of the physical conditions in the scattering region, which affect the relative efficiency of the longitudinal and transverse scatterings and lead to the observed interplay between the resultant precursor and IP components." The pulse-to-pulse fluctuations of the plasma number densitv and the original MP intensiv. which affect the scattering efficiency. are believed to result in the peculiar intensity," The pulse-to-pulse fluctuations of the plasma number density and the original MP intensity, which affect the scattering efficiency, are believed to result in the peculiar intensity" of the RECs does not varv significauth with redshift.,of the REGs does not vary significantly with redshift. Because the BEGs have very simular morphological propertics to the RECs (elliptical shape ac RYO surface brightuess profile) aud because there is 10 conspicuous discontinuity between the RECs and the BECs (as shown iu Fig., Because the BEGs have very similar morphological properties to the REGs (elliptical shape and $R^{1/4}$ surface brightness profile) and because there is no conspicuous discontinuity between the REGs and the BEGs (as shown in Fig. 2 and Fig., 2 and Fig. 3). it may be concluded that the DECs will evolve into RECs.," 3), it may be concluded that the BEGs will evolve into REGs." Evidence of recent star-formation mn nearby earπρο galaxies also supports this idea (Ferrareseetal.2006:Ikavirajal. 2006).," Evidence of recent star-formation in nearby early-type galaxies also supports this idea \citep{fer06,kav06}." . On that assumpti m.thesize redslüft relation of BECs seems to indicate that the mass ofthe BEC-REC migration dOCreases as tinie goes. supporting the “quenching mass decreasing with time” sugeested by Faberetal.(2006).," On that assumption, the size – redshift relation of BEGs seems to indicate that the mass of the BEG-REG migration decreases as time goes, supporting the `quenching mass decreasing with time' suggested by \citet{fab06}." .. According to this scenario. BECs may be the imtermeciate objects roni blue galaxies (late-type galaxies) to red galaxies (earlv-tyvpe galaxies).," According to this scenario, BEGs may be the intermediate objects from blue galaxies (late-type galaxies) to red galaxies (early-type galaxies)." For small blue E/S0 ealaxies. however. a new explanation was suggested.," For small blue E/S0 galaxies, however, a new explanation was suggested." Ferrerasetal.(2005) regarde the faint blue E/S0 ealaxies as a different »pulation from the bright blue E/S0 ealaxics. ou the basis of the low surface brightness of the aut blue E/SO0 galaxies.," \citet{fer05} regarded the faint blue E/S0 galaxies as a different population from the bright blue E/S0 galaxies, on the basis of the low surface brightness of the faint blue E/S0 galaxies." Ferrerasetal.(2005) concluded that the faint blue E/S0 galaxies may ο spirals with strong starbursts. whereas the xieht blue E/SO ealaxies will probably evolve iuto rormal red ESO galaxics.," \citet{fer05} concluded that the faint blue E/S0 galaxies may be spirals with strong starbursts, whereas the bright blue E/S0 galaxies will probably evolve into normal red E/S0 galaxies." IIowever. if the small BEGs are really late-tvpe galaxies with very faint disks and spiral arias. the visible parts of them are xobablv ealactic bulges. whose color is typically red due to old stellay populations (Zoccalictal.2003) unlike the color of the small BECs.," However, if the small BEGs are really late-type galaxies with very faint disks and spiral arms, the visible parts of them are probably galactic bulges, whose color is typically red due to old stellar populations \citep{zoc03} unlike the color of the small BEGs." Another possible explanation is that they may he he ‘progenitors’ of late-typc| galaxies;, Another possible explanation is that they may be the `progenitors' of late-type galaxies. " According o the spiral rebuiklius scchario sugeested by Παππάςetal.(2005).. normal spiral galaxies nay evolve aud grow through the phases of ""uxuereer — Ceonipact galaxw disk growth. from Dm tocmOL "," According to the spiral rebuilding' scenario suggested by \citet{ham05}, normal spiral galaxies may evolve and grow through the phases of `merger' – `compact galaxy' – `disk growth', from $z\approx 1$ to $z\approx 0.4$." The small DECs are possibly natched with objects iu the ‘compact ealaxv yhase., The small BEGs are possibly matched with objects in the `compact galaxy' phase. However. this explanation also has two weak points.," However, this explanation also has two weak points." First. may sinall BEGs are found a even 2«0. Lin our sample.," First, many small BEGs are found at even $z<0.4$ in our sample." T1 addition. the “spiral rebuilding’ scenario docs not explain the size of the spiral bulges decreasing with time. which is the opposite of the predictio1 of that scenario.," In addition, the `spiral rebuilding' scenario does not explain the size of the spiral bulges decreasing with time, which is the opposite of the prediction of that scenario." A good possibility for the destiny of the siual BEGs is that they ay evolve iuto dwarf elliptica ealaxies., A good possibility for the destiny of the small BEGs is that they may evolve into dwarf elliptical galaxies. " Ibertetal.(2006) also predicted that ""blue nlee-galaxies iav evolve iuto local chwart spheroidal galaxies.", \citet{ilb06} also predicted that `blue bulge-galaxies' may evolve into local dwarf spheroidal galaxies. LIuterestiusbhv. this iuference is consistent with the scheme in the formation of carly-type galaxies.," Interestingly, this inference is consistent with the scheme in the formation of early-type galaxies." By analyzing the luuünosifv vs. πιrface brightuess relation of bright aud dwarfe liptical 8galaxies. Calais&Cuzuui(2003) showed that there is no iutrinsic Sap between briehtOo elliptical. Oogalaxies and chvart elliptical eaAXlOS. AL that they may be one continuous population just with different masses. unlike the traditional belief that there is a dichotoniv between tje two galaxy populations (INormendy1977.1955}," By analyzing the luminosity vs. surface brightness relation of bright and dwarf elliptical galaxies, \citet{gra03} showed that there is no intrinsic gap between bright elliptical galaxies and dwarf elliptical galaxies, and that they may be one continuous population just with different masses, unlike the traditional belief that there is a dichotomy between the two galaxy populations \citep{kor77,kor85}." (Iu addition. Ferrareseetal.(2006) showed that here is no clear biiiodalitv between dwirf aud regulu οiptical ealaxies in the surface brightuess profile aud isophotal parameters. in their analysis of 1060 carly-tvpe ealaxies in the Vireo cluster usiιο ST/ACS.," In addition, \citet{fer06} showed that there is no clear bimodality between dwarf and regular elliptical galaxies in the surface brightness profile and isophotal parameters, in their analysis of 100 early-type galaxies in the Virgo cluster using HST/ACS." " Iu this viewpoint. BECs are probably the progenitors of norma and dwarf elliptical galaxies. mostly orienmate from imerecrs/interacting-ealaxics or ΔΝ»,"," In this viewpoint, BEGs are probably the progenitors of normal and dwarf elliptical galaxies, mostly originated from mergers/interacting-galaxies or AGNs." Tn this paper. we preseut a study of t properties of BEGs in the GOODS IIST/ÀC fields.," In this paper, we present a study of the properties of BEGs in the GOODS HST/ACS fields." We selected 171 carly-type galaxies visua in the GOODS IIST/ACS archival data wi spectroscopic redshift., We selected 171 early-type galaxies visually in the GOODS HST/ACS archival data with spectroscopic redshift. We divided the carly-ty ealaxies iuto S58 BECs aud 112 REGs using thei (7D)jags color distribution at eiven redshif, We divided the early-type galaxies into 58 BEGs and 112 REGs using their $(i-z)_{AB}$ color distribution at given redshift. The BEGs have well-defined elliptical shapes a RO surface profiles similar to the REGs. wi just a few exceptions.," The BEGs have well-defined elliptical shapes and $R^{1/4}$ surface profiles similar to the REGs, with just a few exceptions." Iowever. the analysis internal color distribuion. N-rav Dhnuuinositw. aIn spectral line. features show that anost a half of heιο BEGsBECs 1have evidencel off ticaltidal events audl a cast a quarter of the DECs probably contain an ACN in their centers.," However, the analysis of internal color distribution, X-ray luminosity, and spectral line features show that almost a half of the BEGs have evidence of tidal events and at least a quarter of the BEGs probably contain an AGN in their centers." From the analysis of he size and magnitude of the BECs aud the REGs. we rave fouud the evidence that the sizes of DECGs are decreasing as redshitt decreases. which is consistent with the scenario with hierarchical mereiug.," From the analysis of the size and magnitude of the BEGs and the REGs, we have found the evidence that the sizes of BEGs are decreasing as redshift decreases, which is consistent with the scenario with hierarchical merging." We conclude that the BECs may be primarily descendants of past merger/iuteracting-ealaxies and secondarily the ACN-host carly-type galaxies. aud that BECs may evolve iuto normal or dwart elliptical galaxies.," We conclude that the BEGs may be primarily descendants of past merger/interacting-galaxies and secondarily the AGN-host early-type galaxies, and that BEGs may evolve into normal or dwarf elliptical galaxies." However. there are still several," However, there are still several" optimized statistics. while ignoring the possibility of subtle temporal variations of Jovs law (for which there seems to be no evidence).,"optimized statistics, while ignoring the possibility of subtle temporal variations of Joy's law (for which there seems to be no evidence)." To establish a well-defined reference relation for Joys law with optimized statistics. we use all bipolar regions for both hemispheres and all phases of (he solar evcle together.," To establish a well-defined reference relation for Joy's law with optimized statistics, we use all bipolar regions for both hemispheres and all phases of the solar cycle together." Since for approximately half (he regions the positive polaritv is (he preceding polarity. while for the other half it is the following polarity. we get a bimodal angular distribution. with two peaks separated by 1807.," Since for approximately half the regions the positive polarity is the preceding polarity, while for the other half it is the following polarity, we get a bimodal angular distribution, with two peaks separated by $180^\circ$." Since these peaks are identical except lor their 1807 separation. we bring them on top of each other by subtracüng 1807 from tilt angles Chat fall within quadrants 3 and 4 (90°—270°. to make all aneles fall within quadrants 1 ancl 2.," Since these peaks are identical except for their $180^\circ$ separation, we bring them on top of each other by subtracting $180^\circ$ from tilt angles that fall within quadrants 3 and 4 $90^\circ -270^\circ$, to make all angles fall within quadrants 1 and 2." This gives us a single peak for (he angular distribution. which we can fit with a Gaussian to determine ils position and spread.," This gives us a single peak for the angular distribution, which we can fit with a Gaussian to determine its position and spread." The analvsis has been made for a set of 9 latitude bins. spanning the range 0°—45° with a bin width of 5°.," The analysis has been made for a set of 9 latitude bins, spanning the range $0^\circ -45^\circ$ with a bin width of $5^\circ$." The corresponding latitude range for the $ hemisphere has been mapped on top of these positive latitude bins. since there is no evidence for anv difference in the behavior of Jov's law between the two hemispheres except for the sign change of the tilt.," The corresponding latitude range for the S hemisphere has been mapped on top of these positive latitude bins, since there is no evidence for any difference in the behavior of Joy's law between the two hemispheres except for the sign change of the tilt." We recall that the (lt angles that we have determined for the N hemisphere are defined to be positive if the (lt is clockwise. while (hose in (he 5 hemisphere are positive if the tilt is counter-clockwise.," We recall that the tilt angles that we have determined for the N hemisphere are defined to be positive if the tilt is clockwise, while those in the S hemisphere are positive if the tilt is counter-clockwise." The result for the mean tilt angles in each Iatitude bin. as derived from a Gaussian-lvpe fit to the angular distributions. is shown in Fig.," The result for the mean tilt angles in each latitude bin, as derived from a Gaussian-type fit to the angular distributions, is shown in Fig." 2. as the solid circles with (their respective 1-σ error bars., \ref{fig:globaltilt} as the solid circles with their respective $\sigma$ error bars. Through this set of points we have fitted the analvtical hunction, Through this set of points we have fitted the analytical function ionize the K-shell of tron are solely located close to the hole. near the marginally stable orbit.,"ionize the K-shell of iron are solely located close to the hole, near the marginally stable orbit." This provides a natural explanation for concentrating energy release in the form of X-rays near the central object., This provides a natural explanation for concentrating energy release in the form of X-rays near the central object. If the Fe Ka line emission disk via turbulent Comptonization. then the ionization and thermal structure of the disk must be carefully modeled in order to determine whether or not this effect reproduces the observed equivalent widths.," If the Fe $\alpha$ line emission disk via turbulent Comptonization, then the ionization and thermal structure of the disk must be carefully modeled in order to determine whether or not this effect reproduces the observed equivalent widths." Cyg X-1 is the most highly studied galactic black hole (GBH) source., Cyg X-1 is the most highly studied galactic black hole (GBH) source. Like other GBH. it is observed in both the hard (low) and soft (high) spectral states (Done 2002) while mostly spending its time in the low state.," Like other GBH, it is observed in both the hard (low) and soft (high) spectral states (Done 2002) while mostly spending its time in the low state." For GBH in general. the soft spectral state is dominated by a cool optically thick black body while a steep Comptonized power law extends deep into the hard ray/soft 7-ray region of the spectrum.," For GBH in general, the soft spectral state is dominated by a cool optically thick black body while a steep Comptonized power law extends deep into the hard X-ray/soft $\gamma$ -ray region of the spectrum." In the hard state. the photon output is dominated by a somewhat flat hard Comptonized power law with a moderate thermal contribution from the cool optically thick disk.," In the hard state, the photon output is dominated by a somewhat flat hard Comptonized power law with a moderate thermal contribution from the cool optically thick disk." The measured luminosities of GBH in the hard state are typically lower than the soft state. implying a smaller 77 and/or smaller radiative efficiency compared to sources in the soft state.," The measured luminosities of GBH in the hard state are typically lower than the soft state, implying a smaller ${\dot m}$ and/or smaller radiative efficiency compared to sources in the soft state." Gierlinsski et al. (, Gierlińsski et al. ( 1997. hereafter G97) found that in the low state. the SED of Cyg X-1 could not be modeled with a standard disk-corona geometry.,"1997, hereafter G97) found that in the low state, the SED of Cyg X-1 could not be modeled with a standard disk-corona geometry." In order to fit the observed spectra. they required a hot 50 keV optically thick (7~ 6) Wien-like spectral component in addition to cool thermal disk emission and a hard relatively optically thin (7~ 1—2) 100 keV power law. presumably from thermal Comptonization.," In order to fit the observed spectra, they required a hot 50 keV optically thick $\tau\sim 6$ ) Wien-like spectral component in addition to cool thermal disk emission and a hard relatively optically thin $\tau\sim 1-2$ ) 100 keV power law, presumably from thermal Comptonization." They concluded that the observed photon-starved spectrum may be explained by à geometry similar to the one proposed by Shapiro. Lightman. Eardley (1976) Le.. a geometrically thick hot central corona surrounded by a cool optically thick disk.," They concluded that the observed photon-starved spectrum may be explained by a geometry similar to the one proposed by Shapiro, Lightman, Eardley (1976) i.e., a geometrically thick hot central corona surrounded by a cool optically thick disk." In a later study. Gierlinsski et al. (," In a later study, Gierlińsski et al. (" "1999, hereafter G99) modeled Cyg X-I in the soft state during a hard to soft state transition (Zhang et al.","1999, hereafter G99) modeled Cyg X-1 in the soft state during a hard to soft state transition (Zhang et al." 1997)., 1997). The hard power law extended to —600 keV with a spectral index D—2.5 implying a very optically thin plasma with 7~10., The hard power law extended to $\sim 600$ keV with a spectral index $\Gamma\sim 2.5$ implying a very optically thin plasma with $\tau\sim 10^{-2}$. If thermal Comptonization were responsible for the hard continuum. bumps would appear in the X-ray spectrum due to the distinct scattering orders.," If thermal Comptonization were responsible for the hard continuum, bumps would appear in the X-ray spectrum due to the distinct scattering orders." However. these features are not present.," However, these features are not present." As a solution. G99 proposed that the Comptonizing corona was composed of a hybrid thermal/non thermal plasma whose distribution function. was roughly the sum of a relatively cool ~50 keV Maxwellian and a power law.," As a solution, G99 proposed that the Comptonizing corona was composed of a hybrid thermal/non thermal plasma whose distribution function was roughly the sum of a relatively cool $\sim 50$ keV Maxwellian and a power law." Zhang et al. (, Zhang et al. ( 1997) noted that during the state transition. the bolometric luminosity of Cyg X-1 changed very little.,"1997) noted that during the state transition, the bolometric luminosity of Cyg X-1 changed very little." From this fact. Poutanen. Krolik. and Ryde (1997) PKR97 put forth the proposition that the observed state transition of Cyg X-1 corresponded to a change in the mechanical state of the disk characterized by the inner edge moving inward as the spectral state changed from hard to soft.," From this fact, Poutanen, Krolik, and Ryde (1997) PKR97 put forth the proposition that the observed state transition of Cyg X-1 corresponded to a change in the mechanical state of the disk characterized by the inner edge moving inward as the spectral state changed from hard to soft." This claim was supported by the fact that the temperature of the thermal disk component increased as Cyg Χ-{ evolved into the soft state., This claim was supported by the fact that the temperature of the thermal disk component increased as Cyg X-1 evolved into the soft state. The increase in the number of soft photons then has the ability to cool the corona. thus steepening the hard continuum.," The increase in the number of soft photons then has the ability to cool the corona, thus steepening the hard continuum." Adopting this general picture. further details regarding the aceretion flow of Cyg X-1 can be inferred if the ~ SOkeV spectral component fitted by G97 and G99 is assumed to result from turbulent ," Adopting this general picture, further details regarding the accretion flow of Cyg X-1 can be inferred if the $\sim 50\,$ keV spectral component fitted by G97 and G99 is assumed to result from turbulent Comptonization." If we approximate that the bolometric luminosity L=eMc? and Comptonization.Τι are constants during the state transition. then νι. is the relevant parameter which is allowed to change.," If we approximate that the bolometric luminosity $L=\epsilon {\dot M}c^2$ and $T_w$ are constants during the state transition, then $y_w$ is the relevant parameter which is allowed to change." In the hard state. the 50 keV component was fit with a Wien-law. implying saturated Comptonization while in the soft state. the 50 keV component was fit with a steep power law. typical of unsaturated Comptonization.," In the hard state, the 50 keV component was fit with a Wien-law, implying saturated Comptonization while in the soft state, the 50 keV component was fit with a steep power law, typical of unsaturated Comptonization." " Thus. during the transition from the hard to soft spectral state. v,, decreased."," Thus, during the transition from the hard to soft spectral state, $y_w$ decreased." " As previously discussed. the outer scale of the turbulence AQ may approach the photon mean free path A, near the inner edge of the disk. where the spectral contribution from turbulent Comptonization is greatest."," As previously discussed, the outer scale of the turbulence $\lambda_0$ may approach the photon mean free path $\lambda_p$ near the inner edge of the disk, where the spectral contribution from turbulent Comptonization is greatest." With this. eq. (72))," With this, eq. \ref{youter}) )" shows us that v.xa7!. Thus.tran, shows us that $y_w\propto\alpha^{-1}$. sition.," Thus,." This ts consistent with the constant luminosity and wave temperature condition by noting the dependencies of the wave temperature on the outer scale given by eq. (40))., This is consistent with the constant luminosity and wave temperature condition by noting the dependencies of the wave temperature on the outer scale given by eq. \ref{kerrwavetemp}) ). That is. the quantity imer must decrease during the transition.," That is, the quantity ${\dot m}^2/\epsilon^2 r^{3}$ must decrease during the transition." A constant luminosity requires mx€! which constrains |/e*r? to decrease., A constant luminosity requires ${\dot m}\propto\epsilon^{-1}$ which constrains $1/\epsilon^4r^3$ to decrease. But. ex17! yielding the result that 7 must have decreased. which is consistent with the hypothesis of PKR97.," But, $\epsilon\propto r^{-1}$ yielding the result that $r$ must have decreased, which is consistent with the hypothesis of PKR97." To summarize. by making the assumption that the 50 keV component in both the hard and soft spectral state of Cyg X- is due to turbulent Comptonization we may then determine further details of the accretion flow.," To summarize, by making the assumption that the 50 keV component in both the hard and soft spectral state of Cyg X-1 is due to turbulent Comptonization we may then determine further details of the accretion flow." If the proposition of PKR97 is utilized to explain the spectral evolution of Cyg X-1. the basic model dependencies of turbulent Comptonization necessarily require that o increased while #7 decreased during the spectral transition.," If the proposition of PKR97 is utilized to explain the spectral evolution of Cyg X-1, the basic model dependencies of turbulent Comptonization necessarily require that $\alpha$ increased while ${\dot m}$ decreased during the spectral transition." Turbulent Comptonization may prove to be an important mediator of gravitational energy release in accretion disks., Turbulent Comptonization may prove to be an important mediator of gravitational energy release in accretion disks. If so. simultaneously modeling both the mechanics and radiative processes of the flow not only becomes possible. but in order to accurately fit the data.," If so, simultaneously modeling both the mechanics and radiative processes of the flow not only becomes possible, but in order to accurately fit the data." We have shown that the amplitude and shape of the spectral feature resulting from turbulent Comptonization coincides with observed components in both AGN and X-ray binaries., We have shown that the amplitude and shape of the spectral feature resulting from turbulent Comptonization coincides with observed components in both AGN and X-ray binaries. " If turbulent Comptonization does not manifest itself spectrally. then its absence in the SED of accretion flows constrains values of fundamental disk parameters such as ο.ή,ande."," If turbulent Comptonization does not manifest itself spectrally, then its absence in the SED of accretion flows constrains values of fundamental disk parameters such as $\alpha, {\dot m},\, {\rm and}\,\epsilon$." We emphasize that throughout this paper. we have assumed that turbulent accretion stresses may greatly exceed the gas pressure.," We emphasize that throughout this paper, we have assumed that turbulent accretion stresses may greatly exceed the gas pressure." It is this fact that allows turbulent Comptonization to operate as an important process., It is this fact that allows turbulent Comptonization to operate as an important process. It has been argued that in radiation pressure supported disks. buoyancy limits the turbulent magnetic pressure to values below that of the gas (Sakimoto Coroniti 198]. 1989: Stella Rosner 1984).," It has been argued that in radiation pressure supported disks, buoyancy limits the turbulent magnetic pressure to values below that of the gas (Sakimoto Coroniti 1981, 1989; Stella Rosner 1984)." Further. we assumed that large turbulent stresses exist down to the scale of the photon mean free path.," Further, we assumed that large turbulent stresses exist down to the scale of the photon mean free path." However. there may be other dissipation mechanisms acting on scales larger than A).," However, there may be other dissipation mechanisms acting on scales larger than $\lambda_p$." One such example is Silk damping ofcompressive motions in the turbulence (Agol Krolik 1998)., One such example is Silk damping of compressive motions in the turbulence (Agol Krolik 1998). Recent numerical simulations of un-stratified radiation pressure supported disks show that Silk damping may be responsible for a significant (but not dominant) fraction of energy release (Turner et al., Recent numerical simulations of un-stratified radiation pressure supported disks show that Silk damping may be responsible for a significant (but not dominant) fraction of energy release (Turner et al. 2003)., 2003). Such simulations performed in a vertically stratified medium will address both Silk damping and buoyancy effects simultaneously., Such simulations performed in a vertically stratified medium will address both Silk damping and buoyancy effects simultaneously. Another uncertainty in determining the relative importance of turbulent Comptonization ts the vertical structure of the disk., Another uncertainty in determining the relative importance of turbulent Comptonization is the vertical structure of the disk. The presence of turbulent Comptonization provides a means of turning turbulent mechanical energy into photon power without requiring a cascade down to a microscopte dissipation scale., The presence of turbulent Comptonization provides a means of turning turbulent mechanical energy into photon power without requiring a cascade down to a microscopic dissipation scale. How this affects the structure and dynamies of the flow in a time-averaged fashion is difficult to predict., How this affects the structure and dynamics of the flow in a time-averaged fashion is difficult to predict. In terms of, In terms of thick H Ly 2S signal EUVS detected. will be discussed. in a secoud publication.,thick H Ly $\beta$ signal EUVS detected will be discussed in a second publication. Regarding the latter. here we simply note that the Lyman 2» feature is bleucdecd with a coutributiou (rom au OL [XU D4ο 2:72p/ Popo] triplet at 1025.7. 1027.L. aud 1028.7A... which. owing to radiative pumping by Ly 29. is difficult to precisely 1uodel. but which to first order contributes 12 B: the telluric backgrouud Ly? brightuess is estimated to coutribute some 20 R above the background.," Regarding the latter, here we simply note that the Lyman $\beta$ feature is blended with a contribution from an OI $^3$ $_{1,2,0}$ $>$ $^2$ $^4$ $^3$ $_{2,1,0}$ ] triplet at 1025.7, 1027.4, and 1028.7, which, owing to radiative pumping by Ly $\beta$, is difficult to precisely model, but which to first order contributes $\sim$ 15 R; the telluric background $\beta$ brightness is estimated to contribute some 20 R above the background." Sky background spectra obtained while EUVS was maneuvering toward Hale-Bopp contain only a weak instrumental background aud HI Ly 9% emission generated by a combination of geocoroual aud interplanetary medium hydrogeu., Sky background spectra obtained while EUVS was maneuvering toward Hale-Bopp contain only a weak instrumental background and H I Ly $\beta$ emission generated by a combination of geocoronal and interplanetary medium hydrogen. The fact that no other features are present in EUVS sky ockgrouud spectra. combined with the observing altitude aud geometry discussecl above. virtually Müuninates the possibility of the features seen at Hale-Bopp as being due to telluric contamination.," The fact that no other features are present in EUVS sky background spectra, combined with the observing altitude and geometry discussed above, virtually eliminates the possibility of the features seen at Hale-Bopp as being due to telluric contamination." Returning now to the main subject of this paper. additional evidence for the Ar identification comes in three forms.," Returning now to the main subject of this paper, additional evidence for the Ar identification comes in three forms." First. the width of the MRES feature extending from 1015-1070 iis consistent with a pair of blended lines 19 aapart (such as the two Ar lines).," First, the width of the MRES feature extending from 1045–1070 is consistent with a pair of blended lines 19 apart (such as the two Ar lines)." Second. the seuse of the asymmetry seen in the 1015-1070 eelission is consistent with the fact that the 1015 lline's resonance [orescence efficiency in sunlight. (Le.. its e-factor) is 2.1 times higher than the 1066 lline’s.," Second, the sense of the asymmetry seen in the 1045–1070 emission is consistent with the fact that the 1048 line's resonance fluorescence efficiency in sunlight (i.e., its g-factor) is 2.4 times higher than the 1066 line's." Third. as shown in the righthaud panel of Figure 1. there is also both clear evidence [or a 1018 Ar [eature (present some 3.2 0 above the local background) and an bint of the 1066 [leature in the bigher-resolution ΠΙΕΙΣ data. thereby all but elininating pathological detection cases (e.g.. due to flat field effects or count statistics variations) of the Ar features in the main slit.," Third, as shown in the righthand panel of Figure 1, there is also both clear evidence for a 1048 Ar feature (present some 3.2 $\sigma$ above the local background) and an hint of the 1066 feature in the higher-resolution HRES data, thereby all but eliminating pathological detection cases (e.g., due to flat field effects or count statistics variations) of the Ar features in the main slit." Since the MRES data has cousiderably better count levels than the HRES data. we used our liue detection software to retrieve individual. backgrouucd-subtracted gaussians (witli widtlis established [rom calibration liue sources) for the two suspected MRES dataset argon features.," Since the MRES data has considerably better count levels than the HRES data, we used our line detection software to retrieve individual, background-subtracted gaussians (with widths established from calibration line sources) for the two suspected MRES dataset argon features." This software. which obtains best fit waveleneths and integrated brightuesses gaussiaus for features cletected above a specified background. retrieved brightnesses and statistical error bars of 218 R centered at 1019A.. and 1255 Rat 1066 (1 R=L0° ph 7s + emitted into Dx sr).," This software, which obtains best fit wavelengths and integrated brightnesses gaussians for features detected above a specified background, retrieved brightnesses and statistical error bars of $\pm$ 8 R centered at 1049, and $\pm5$ R at 1066 (1 $^6$ ph $^{-2}$ $^{-1}$ emitted into $\pi$ sr)." " Π is worth pointing out that the 2.0-£0.6 ratio of these two retrieved brightuesses correspouds well (within our statistics) to the 2.1 value predicted by their"" e-factors.+ auc line. formation+. theory lor+ optically. thin"," It is worth pointing out that the $\pm$ 0.6 ratio of these two retrieved brightnesses corresponds well (within our statistics) to the 2.4:1 value predicted by their g-factors, and line formation theory for optically thin" " Π is worth pointing out that the 2.0-£0.6 ratio of these two retrieved brightuesses correspouds well (within our statistics) to the 2.1 value predicted by their"" e-factors.+ auc line. formation+. theory lor+ optically. thin."," It is worth pointing out that the $\pm$ 0.6 ratio of these two retrieved brightnesses corresponds well (within our statistics) to the 2.4:1 value predicted by their g-factors, and line formation theory for optically thin" "One o the few tools available for studying the ""Dark. Ages"" following the era of cecoupling is the Cosmic Iufralted Backeround (CIRB) radiation.",One of the few tools available for studying the “Dark Ages” following the era of matter-radiation decoupling is the Cosmic InfraRed Background (CIRB) radiation. The CIRB is tle result oL the cuuilative. short wavelenetl euissions from pregalactie. protogalactjc. auc galactic syselus which throwh dust. reprocessing aud cosmological recdshiftiug are now a rared wavelengths.," The CIRB is the result of the cumulative, short wavelength emissions from pregalactic, protogalactic, and galactic systems which through dust reprocessing and cosmological redshifting are now at infrared wavelengths." Although tie importance of looking for au extragalactic infrared backero has been discussedscl for some tiine (PartridgeandPeebles1967:LowTucker1965:Peeb]xaufinan 1976).. relatively little theoretical attention had been paid to i e to the cificulties inherent in rying to observe aid verify theoretical predictions.," Although the importance of looking for an extragalactic infrared background has been discussed for some time \citep{PP67,LT68,Pe69,Ha70,Ka76}, relatively little theoretical attention had been paid to it due to the difficulties inherent in trying to observe and verify theoretical predictions." But advances in infrared techinology have stiinulated an increasiug amouut of interest in trying to determiue tec laracteristies of the CIRB (Bondefal.1986:MeDowell1956:Fabbri1957:19858:Boundαἰ.1001:Lonsdale1995:Makau&Stecker1998:Peiefal. 1999).," But advances in infrared technology have stimulated an increasing amount of interest in trying to determine the characteristics of the CIRB \citep{BCH86,McD86,Fab87,Fab88,BCH91,Lo95, MS98, Pei99}." . The theoretical work indicates that neasur]ug the spect‘al inteusity aud the anisotropy of the CIRB will have iiiportant implications 'egalcliig the amouit οἱ matter uudergoiug luminous episodes iu the pregalactic Universe. the lature aud evolution oL those luminosity sources. tle nature aud distribution of cosnic dist. and he clesity and luminosity evolution of i[rarecd-bright galaxies (for review see Hauser(1)96))).," The theoretical work indicates that measuring the spectral intensity and the anisotropy of the CIRB will have important implications regarding the amount of matter undergoing luminous episodes in the pregalactic Universe, the nature and evolution of those luminosity sources, the nature and distribution of cosmic dust, and the density and luminosity evolution of infrared-bright galaxies (for review see \citet{Ha96}) )." AhoughOm technologyOe is no longerOm a hixdrance in observing the CIRB. there are other difficulties in trv& to see this cosmic relic.," Although technology is no longer a hindrance in observing the CIRB, there are other difficulties in trying to see this cosmic relic." The bright foreground from the atuosphere of the earth. he dust in the solar svsten. aid the stellar ancl iuerstellar emissious of our own galaxy combine to make detecting the CIRB a formidable task.," The bright foreground from the atmosphere of the earth, the dust in the solar system, and the stellar and interstellar emissions of our own galaxy combine to make detecting the CIRB a formidable task." Several experiuieibs have been carried out to try to determine the CIRB from within the atinosphere., Several experiments have been carried out to try to determine the CIRB from within the atmosphere. l]atsuimotoeLal.(1988) and Nodaefaf(1992) used rocket Orne cameras to try to escape tlie coitanmdnatloln rom the atinosphere aud observe the CIRB., \citet{Ma88} and \citet{No92} used rocket borne cameras to try to escape the contamination from the atmosphere and observe the CIRB. They acl only limited success aud could se upper limis on the CIRB without any detectious., They had only limited success and could set upper limits on the CIRB without any detections. Lower limits were determined [rom deep galaxy couils conducted in the near-IR., Lower limits were determined from deep galaxy counts conducted in the near-IR. These two limits beean setting the first tight COLslrails o1 galaxy evoution mocdlels., These two limits began setting the first tight constraints on galaxy evolution models. Tie logic‘al next step in trying to detect the CIRB was to go into space to try anc eliminate the more |ocal [ο'eground: tliis. the Cosiule Background Explorer (COBE) satellite carried with it au experiment syecilically desigued to detect the CIRB (Bogeessefaf.1992).," The logical next step in trying to detect the CIRB was to go into space to try and eliminate the more local foreground; thus, the Cosmic Background Explorer (COBE) satellite carried with it an experiment specifically designed to detect the CIRB \citep{Bo92}." . The Diffuse InfraRed Backeοιud Experimer| (DIRBE was crvogeulcally cooled. thus allowing it to observe multiple infrared. waveeugtlis wittout much instrumental background.," The Diffuse InfraRed Background Experiment (DIRBE) was cryogenically cooled, thus allowing it to observe multiple infrared wavelengths without much instrumental background." Having eliminated the effect of the earths a11105yhere aix ile instrmental background. only the zodiacal dust in the solar system and the stellar ald iuterstell:w emissions of the Galaxy remained.," Having eliminated the effect of the earth's atmosphere and the instrumental background, only the zodiacal dust in the solar system and the stellar and interstellar emissions of the Galaxy remained." " Eve wil] the colullallo ol the atiuosphere removed. the DIRBE data dic not. reaclily reveal au Isotopic baeXBC0""'OU"," Even with the contamination of the atmosphere removed, the DIRBE data did not readily reveal an isotropic background." Lxl Reloving the remaining foregrounds turued out to be a difficult task witl the zodiacal cdist proving to be especially difficult as none of the mocels were able to complete velininate it [Icim the data. especially iu the near aud mid-iufrared where the dust emits and scatters t μοιjost.," Removing the remaining foregrounds turned out to be a difficult task with the zodiacal dust proving to be especially difficult as none of the models were able to completely eliminate it from the data, especially in the near and mid-infrared where the dust emits and scatters the most." The eiMissions from interstellar dust were more readily modelect and removed, The emissions from interstellar dust were more readily modeled and removed "measure of line width than IxSIx. called. 2,42. ii) we use the improved. reddening corrections of Schlegel. Finkbeiner Davis (1998). and iv) we use the Ca LE Ix absorption line EW as an additional classification filter.","measure of line width than KSK, called $D_{0.15}$, iii) we use the improved reddening corrections of Schlegel, Finkbeiner Davis (1998), and iv) we use the Ca II K absorption line EW as an additional classification filter." In the rest of this paper we refer to this method as theColour method., In the rest of this paper we refer to this method as the method. In the course of this work we discovered. that the dependence of the profile (i.e. the detailed shape) of the jalmer lines on both temperature ancl surface gravity is measurable., In the course of this work we discovered that the dependence of the profile (i.e. the detailed shape) of the Balmer lines on both temperature and surface gravity is measurable. This led to what we have called. the classification method., This led to what we have called the classification method. These two classification methods are the subject of the remainder of the paper., These two classification methods are the subject of the remainder of the paper. Note that the two methods are not. entirely independent since they both use parameters derived from a fit to the line shape., Note that the two methods are not entirely independent since they both use parameters derived from a fit to the line shape. In 855 we consider the circumstances under which one or other is more useful., In 5 we consider the circumstances under which one or other is more useful. In this section we summarise details of the INSIx.sample of spectra used in developing the classification methocds., In this section we summarise details of the KSK–sample of spectra used in developing the classification methods. We then describe the procedure for measuring the profiles of the Balmer lines. and its application to the two methods of classification.," We then describe the procedure for measuring the profiles of the Balmer lines, and its application to the two methods of classification." Lastly we explain the procedure for measuring the Ca LE Ix line EW. and the uses of this measure.," Lastly we explain the procedure for measuring the Ca II K line EW, and the uses of this measure." The high S/N spectra of stars analysed bv KSI were kinclv made available in electronic form by Dr Nick SuntzelT., The high S/N spectra of stars analysed by KSK were kindly made available in electronic form by Dr Nick Suntzeff. The total sample includes 214 stars ranging in spectral type from D to E. The majority of the sample are Itype stars. including BLIB stars. mainsequence A stars. and blue stragelers.," The total sample includes 214 stars ranging in spectral type from B to F. The majority of the sample are A–type stars, including BHB stars, main–sequence A stars, and blue stragglers." The methods of classification we apply are effective in the temperature range where the Balmer lines are strong aud do not work blueward of (2Voy=0., The methods of classification we apply are effective in the temperature range where the Balmer lines are strong and do not work blueward of $(B-V)_0=0$. Beeause the method does not use colours. but both methocks Use spectroscopy. we need a spectroscopic criterion. rather than a colour criterion. for defining the type of star to which the classification methods apply.," Because the method does not use colours, but both methods use spectroscopy, we need a spectroscopic criterion, rather than a colour criterion, for defining the type of star to which the classification methods apply." We select all stars with LEW >IBA...," We select all stars with EW $\gamma> 13\,$." This sample contains 131 stars., This sample contains 131 stars. " We refer to this as the ""INSIN total sample’.", We refer to this as the `KSK total sample'. “Phe EW limit corresponcls approximately to the colour range 0«(D.1o<0.2., The EW limit corresponds approximately to the colour range $0<(B-V)_0<0.2$. The EW limit was chosen by trial and error to produce the largest clean samples of BILB stars., The EW limit was chosen by trial and error to produce the largest clean samples of BHB stars. With a lower limiting EW we include stars with (D.Vy«O0 and (D.Vy>0.2 where discrimination is more cdillieult., With a lower limiting EW we include stars with $(B-V)_0<0$ and $(B-V)_0>0.2$ where discrimination is more difficult. With a higher limiting LEW we remove DIID stars from the sample but retain most of the blue stragelers., With a higher limiting EW we remove BHB stars from the sample but retain most of the blue stragglers. The main-sequence stars in this sample are typically of solar metallicity., The main-sequence stars in this sample are typically of solar metallicity. Since we are interested in classilving lowermetallicity halo stars we focus in particular on a subsample ol fainter highCalaetic Latitude stars. consisting of 66 stars. of magnitudes 13.0—Vx16.5 in two Ποιά». SA57 at the Northern Polar Cap. and RR in the direction of the Galactic anticentre.," Since we are interested in classifying lower--metallicity halo stars we focus in particular on a subsample of fainter high–Galactic latitude stars, consisting of 66 stars, of magnitudes $13.0 \leq V \leq 16.5$ in two fields, SA57 at the Northern Polar Cap, and RR7 in the direction of the Galactic anticentre." Phese stars have S/N in the range 23 to SOA. lo.with a mean of ⋅⋅⋅66 A7.," These stars have S/N in the range 23 to 80 ${\mathrm\AA}^{-1}$, with a mean of 66 ${\mathrm\AA}^{-1}$." ⊥⇁We refer⋅ to this. subsample as the INSIX halo sample’., We refer to this subsample as the `KSK halo sample'. Phe ον total sample is useful for garowing the broad trends in the classification parameters. cause with the larger sample the sequences of the two »opulations are better defined (e.g. Fig. 5)).," The KSK total sample is useful for showing the broad trends in the classification parameters, because with the larger sample the sequences of the two populations are better defined (e.g. Fig. \ref{colour_width}) )," but because of 16 Issue of metallicity we use the ο halo sample only in clining the classification boundaries in plots of the relevant αςΠΙΟΤΟΥ»., but because of the issue of metallicity we use the KSK halo sample only in defining the classification boundaries in plots of the relevant parameters. In comparing line widths measured for the same star in 16 IXSIN spectra observed in different runs. we discovered a small svstematic dilference between the spectra in the two valves of the dataset.," In comparing line widths measured for the same star in the KSK spectra observed in different runs, we discovered a small systematic difference between the spectra in the two halves of the dataset." Phe origin of the dillerence was traced. with the assistance of Dr Suntzell to the details of the luxcalibration proceclures emploved for cilferent observing runs.," The origin of the difference was traced, with the assistance of Dr Suntzeff, to the details of the flux–calibration procedures employed for different observing runs." We were able to correct the half of the data in error » comparing the WSK spectra of the Bux standard. Dux calibrated by itsell. to the original Massey. ct al. (," We were able to correct the half of the data in error by comparing the KSK spectra of the flux standard, flux calibrated by itself, to the original Massey et al. (" 1988) spectrum.,1988) spectrum. The results of a functional fit to the Balmer lines are used. in both classification methods., The results of a functional fit to the Balmer lines are used in both classification methods. Phe width Dis is determined from the fit. while the parameters of the Lit themselves are used in the method.," The width $D_{0.15}$ is determined from the fit, while the parameters of the fit themselves are used in the method." Before fitting the Balmer lines each spectrum is normalised o the continuum by fitting a polynomial of degree three o regions of continuum well away from the wines of the ines., Before fitting the Balmer lines each spectrum is normalised to the continuum by fitting a polynomial of degree three to regions of continuum well away from the wings of the lines. Decause the Balmer lines are so broad care must be aken in fitting the continuum. and we spent some time experimenting with the degree of the polynomial ancl with cillerent wavelength ranges for fitting.," Because the Balmer lines are so broad care must be taken in fitting the continuum, and we spent some time experimenting with the degree of the polynomial and with different wavelength ranges for fitting." The intervals chosen or the fit were 38633868. 39023925. 40204048. 41464275. 43884494A.," The intervals chosen for the fit were 3863–3868, 3902–3925, 4020–4048, 4146--4275, 4388–4494." While the final choice of procedure is inevitably subjective this is not à concern. provided. other observers who follow the same procedure obtain the same results. within the errors.," While the final choice of procedure is inevitably subjective this is not a concern provided other observers who follow the same procedure obtain the same results, within the errors." This will be the case provided there is no systematic trend. of the measured. parameters with S/N. To test for systematics we created artificial spectra by adding noise to high quality spectra of four stars., This will be the case provided there is no systematic trend of the measured parameters with S/N. To test for systematics we created artificial spectra by adding noise to high quality spectra of four stars. For each star we created: 1000 spectra of a specified S/N. for several values of S/N in the range 7 to 30.," For each star we created 1000 spectra of a specified S/N, for several values of S/N in the range 7 to 30." t à given. S/N we nmieasured the lines in cach artificial spectrum. ancl then calculated the mean and the error on the mean for cach measured. parameter.," At a given S/N we measured the lines in each artificial spectrum, and then calculated the mean and the error on the mean for each measured parameter." For no parameter. at any S/N. was the mean value of the parameter inconsistent with the value nieasured for the original high S/N spectrum.," For no parameter, at any S/N, was the mean value of the parameter inconsistent with the value measured for the original high S/N spectrum." In other words we found no significant svstematic errors associated with the continuum Lit., In other words we found no significant systematic errors associated with the continuum fit. In the long exposure regime. additional colour scintillation due to atmospheric dispersion will depend on the angle ϐ between the direction of the wind vector and the azimuth of the star.,"In the long exposure regime, additional colour scintillation due to atmospheric dispersion will depend on the angle $\theta$ between the direction of the wind vector and the azimuth of the star." Indeed. during long exposure the wavelront is averaged along the wind direction over an area of about iT.," Indeed, during long exposure the wavefront is averaged along the wind direction over an area of about $w\tau D$." When the displacement «c is transverse to the wind. the non-overlapping area is z2rer. much larger than 2.D for the case when wr is parallel to the wind.," When the displacement $x$ is transverse to the wind, the non-overlapping area is $\approx 2xw\tau$ , much larger than $\approx 2xD$ for the case when $x$ is parallel to the wind." 'herefore. during the transition from. two-dimensional integration over spatial frequeney to the integration over its modulus. we must average over the angle ó the product of the two filters. the one for aperture displacement. and another for the wind shear.," Therefore, during the transition from two-dimensional integration over spatial frequency to the integration over its modulus, we must average over the angle $\phi$ the product of the two filters, the one for aperture displacement and another for the wind shear." " In the equation (17)) the factor of 2.2Jy(2zrf) is the result of the averaging overthe angle of the asymmetric filter of the aperture displacement 2.2cos(2;rfcosoó)=Asin""(arfcosó)."," In the equation \ref{eq:ddz}) ) the factor of $2-2\,J_0(2 \pi xf)$ is the result of the averaging overthe angle of the asymmetric filter of the aperture displacement $2-2\cos(2\pi xf\cos\phi) = 4\sin^2(\pi xf\cos\phi)$." We include the filter of the wind shear in the formi of sinc?(izfcosO) by rotating the coordinate x-axis by the angle 8 in the direction ( ‘the wind., We include the filter of the wind shear in the form of $\sinc^2(w\tau f\cos\phi)$ by rotating the coordinate x-axis by the angle $\theta$ in the direction of the wind. The product is averaged over ©: The asymptote of the integral Z at wrx depends on the angle 8., The product is averaged over $\phi$: The asymptote of the integral $\mathcal L$ at $w\tau \to \infty $ depends on the angle $\theta$. Since cf=gq1. the linear approximation sin(arfcosió0))zm;fcos(ó|8) may be used.," Since $xf = yq \la 1$, the linear approximation $\sin^2(\pi xf\cos(\phi-\theta)) \approx \pi^2x^2f^2\cos^2(\phi-\theta)$ may be used." For 6—0 (same wind and source azimuth). this gives: I ϐ=π (wind direction perpendicular to. the atmospheric dispersion). the averaging results in: where 7Zi(werzf) is the wind filter (2). which equals Lirerf in the long-exposure regime.," For $\theta = 0$ (same wind and source azimuth), this gives: If $\theta = \pi/2$ (wind direction perpendicular to the atmospheric dispersion), the averaging results in: where ${\mathcal T}_1(w\tau f)$ is the wind filter \citep{wind2010} which equals $1/\pi w\tau f$ in the long-exposure regime." Comparison of the relations for ον and shows that both components are approximately equal at. Zvery low frequencies foléswr., Comparison of the relations for $\mathcal L_{\perp}$ and $\mathcal L_{\parallel}$ shows that both components are approximately equal at very low frequencies $f \la 1/\pi w\tau$. s At larger frequencies. £47Ly.," At larger frequencies, $\mathcal L_{\perp} \gg \mathcal L_{\parallel}$." ‘Taking into account that the maximum of the scintillation is at. f=0.555/rp~5r10 (maximum of the product qVsi (rq) and that L/£zwr« 0.1. it can be argued that the investigated cllect is mainly determined. by the perpendicular component of wind.," Taking into account that the maximum of the scintillation is at $f = 0.555/r_F \sim 5-10$ (maximum of the product $q^{-8/3}\,\sin^2(\pi q^2)$ ) and that $1/\pi w\tau \ll 0.1$ , it can be argued that the investigated effect is mainly determined by the perpendicular component of wind." Corresponding WE CA(2) can be obtained by replacing the [actor 22Ju(2xyq) with the expression for £ in the formula (17)) or in formula (19)) in the case of two monochromatic bands and a circular aperture.," Corresponding WF $U^{\prime}_{\Delta}(z)$ can be obtained by replacing the factor $2-2\,J_0(2\pi yq)$ with the expression for $\mathcal L$ in the formula \ref{eq:ddz}) ) or in formula \ref{eq:wddz}) ) in the case of two monochromatic bands and a circular aperture." To ect a formula like (24)). we have to isolate the factor Lf.," To get a formula like \ref{eq:assimp_w}) ), we have to isolate the factor $1/w\tau$." Exeept for the factor 1Ju(A4zierf) which almost everywhere is equal to unity. the component ο does not depend on the frequency and can be taken out of the integral.," Except for the factor $1-J_0(4\pi w\tau f) $ which almost everywhere is equal to unity, the component $\mathcal L_{\parallel}$ does not depend on the frequency and can be taken out of the integral." In this case where Γιος) is the cross-index WE (3)) having the usual asymptote.," In this case where $R_{1,2}(z)$ is the cross-index WF \ref{eq:r12}) ) having the usual asymptote." In calculating the component Z4. one can neglect the term £j.," In calculating the component $\mathcal L_{\perp}$, one can neglect the term $\mathcal L_{\parallel}$." After replacing f£ with the dimensionless frequency q. replacing the aperture filter with its approximation (11)). separation of l/wr and easy. transformations we obtain: The approximation of the integrand near zero frequency is poor because the power of the ¢H7 torn is close to the limit for integrability.," After replacing $f$ with the dimensionless frequency $q$, replacing the aperture filter with its approximation \ref{eq:j1_approx}) ), separation of $1/w\tau$ and easy transformations we obtain: The approximation of the integrand near zero frequency is poor because the power of the $q^{-14/3}$ term is close to the limit for integrability." Numerical integration of the original formula shows that the error of the asvmptotic expression (30)) is on the order 20 percent for D.=2.4m and 2o8d km., Numerical integration of the original formula shows that the error of the asymptotic expression \ref{eq:uddz_per}) ) is on the order 20 percent for $D = 2-4\mbox{ m}$ and $z \approx 4\mbox{ km}$ . In this equation. the integral can be calculated analytically and it equals to: The formulae (29)) anc (30)) allow usto calculate. the relative increase of the colour scintillation caused. by the turbulence wind drift.," In this equation, the integral can be calculated analytically and it equals to: The formulae \ref{eq:uddz_par}) ) and \ref{eq:uddz_per}) ) allow usto calculate the relative increase of the colour scintillation caused by the turbulence wind drift." To do this. we can use the methodof," To do this, we can use the methodof" (2:7). ~ ?:: ?:: 2)) νε ~0.05 ?)). 2:7:?:ey). 2)). (7:?:7:es 2)). (7:7)). (?)). ?:: ?:: ?)). 2)) (C73) (2)). ?:7:7)),"\newcommand{\shortcite}{\cite*} \cite{Cole2000,Granato00}) $\sim$ \shortcite{GPB}; \shortcite{BdJ_ML}; \cite{Cole2000}) $K_s$ $\sim0.05$ \cite{Silva}) \cite{SAPMI,EEP,marzke_cfa,L+96,Zucca,Ratcliffe}) \shortcite{Sloan_lf}) \cite{MSE,GPMC,Gardner,SSCM,Loveday-klf,Kochanek-KLF}; \shortcite{Cole-2mass}) \cite{WDEF,NBW}) \cite{RO}) \shortcite{Larson74}; \shortcite{Cole91}; \shortcite{baryons}) \cite{LC93}) \cite{BBKS,NBW}) \cite{harass}) \cite{DTS,B+97,B+98,P+99,MW00})" (2:7). ~ ?:: ?:: 2)) νε ~0.05 ?)). 2:7:?:ey). 2)). (7:?:7:es 2)). (7:7)). (?)). ?:: ?:: ?)). 2)) (C73) (2)). ?:7:7)).,"\newcommand{\shortcite}{\cite*} \cite{Cole2000,Granato00}) $\sim$ \shortcite{GPB}; \shortcite{BdJ_ML}; \cite{Cole2000}) $K_s$ $\sim0.05$ \cite{Silva}) \cite{SAPMI,EEP,marzke_cfa,L+96,Zucca,Ratcliffe}) \shortcite{Sloan_lf}) \cite{MSE,GPMC,Gardner,SSCM,Loveday-klf,Kochanek-KLF}; \shortcite{Cole-2mass}) \cite{WDEF,NBW}) \cite{RO}) \shortcite{Larson74}; \shortcite{Cole91}; \shortcite{baryons}) \cite{LC93}) \cite{BBKS,NBW}) \cite{harass}) \cite{DTS,B+97,B+98,P+99,MW00})" "Observatory (LÀO). Hanle. India. on 16"" March 2005.","Observatory (IAO), Hanle, India, on $^{th}$ March 2005." The Hanle Faint Object Spectrograph Camera (LIFOSC). which is equipped with a SITe 2K. x Ην pixel CCD. was used.," The Hanle Faint Object Spectrograph Camera (HFOSC), which is equipped with a SITe 2K $\times$ 4K $^2$ CCD, was used." " With a pixel scale of 0.296"". the FOV of ΠΕΟΣ where only the central 2 x 21 region is used [or imaging. is ~ 10 x 10 arcmin?."," With a pixel scale of $\arcsec$, the FOV of HFOSC, where only the central 2K $\times$ 2K region is used for imaging, is $\sim$ 10 $\times$ 10 $^2$." Further details on the telescope and the instrument can be found athttp://www., Further details on the telescope and the instrument can be found at. liap.res.in/1ao/hfosc.htinl.. Observations were carried out. under good photometric sky conditions., Observations were carried out under good photometric sky conditions. The tvpical seeing [full width at half-imaximum (FWIIM)| during the period of observations was ~ 1.8”., The typical seeing [full width at half-maximum (FWHM)] during the period of observations was $\sim$ $\arcsec$. Dias and flat frames were obtained at the beginning and αἱ the end of the observing night., Bias and flat frames were obtained at the beginning and at the end of the observing night. Photometric standard stars around the SA 111-775 region (Landolt1992) were observed to obtain the transformation coefficients., Photometric standard stars around the SA 111-775 region \citep{lan92} were observed to obtain the transformation coefficients. The data reduction was again carried ont using IRAF tasks., The data reduction was again carried out using IRAF tasks. Object frames were flat- using mecdian-combined normalized flat frames., Object frames were flat-fielded using median-combined normalized flat frames. Identification and photometry of point sources were performed using the DAOFIND and DAOPIIOT tasks. respectively.," Identification and photometry of point sources were performed using the DAOFIND and DAOPHOT tasks, respectively." Photometry was obtained using the PSF algorithm ALLSTAR in the DAOPIIOT package (Stetson1987)., Photometry was obtained using the PSF algorithm ALLSTAR in the DAOPHOT package \citep{stet87}. . The residuals to the photometric solution were «0.05 mag., The residuals to the photometric solution were $\le$ 0.05 mag. The 5pizer-GLIMDPSE survey IRAC and MIPS images and IRAC photometry of (his target were analysed using the IRSA-IPAC image cutouts and. GATOR facilities., The -GLIMPSE survey IRAC and MIPS images and IRAC photometry of this target were analysed using the IRSA-IPAC image cutouts and GATOR facilities. MIDPS 24 jam photometry was extracted using the APEX single frame pipeline on the Post-Basie-Calibrated Data., MIPS 24 $\mu$ m photometry was extracted using the APEX single frame pipeline on the Post-Basic-Calibrated Data. The photometric data in theSpilzer bands (3.6 - 24.0 jm) were combined with 2\TASS NIR photometry and IRAS clata to construct SEDs for the four brightest sources in the region (he massive voung star candidates., The photometric data in the bands (3.6 - 24.0 $\mu$ m) were combined with 2MASS NIR photometry and IRAS data to construct SEDs for the four brightest sources in the region – the massive young star candidates. The online SED fitting tool developed by was used to fit the resulting SEDs in the 1 - 24 jm bands., The online SED fitting tool developed by \citet{rob07} was used to fit the resulting SEDs in the 1 - 24 $\mu$ m bands. The SED fitting tool is based on matching the observed SEDs with a Lurge grid of precomputed radiative transfer models., The SED fitting tool is based on matching the observed SEDs with a large grid of precomputed radiative transfer models. The models assume an accretion scenario wilh a star. disk. envelope and bipolar cavity. all under radiative equilibrium.," The models assume an accretion scenario with a star, disk, envelope and bipolar cavity, all under radiative equilibrium." While (he mass and age of the star are unilormlv sampled within the erid limits. the radius and temperature are interpolated using evolutionary models.," While the mass and age of the star are uniformly sampled within the grid limits, the radius and temperature are interpolated using evolutionary models." The optical and NIR data points constrain the stellar parameters. the mid-infrared fluxes constrain the disk parameters and (he far-intrarecl points are sensitive {ο envelope emission (see Robitailleetal.2006. for more details).," The optical and NIR data points constrain the stellar parameters, the mid-infrared fluxes constrain the disk parameters and the far-infrared points are sensitive to envelope emission (see \citealt*[]{rob06} for more details)." The SED fitting tool has been successfully tested on low mass stars and shown to produce reliable estimates of physical parameters by comparing against values obtained bw other independent measurements., The SED fitting tool has been successfully tested on low mass stars and shown to produce reliable estimates of physical parameters by comparing against values obtained by other independent measurements. 128h-!Mpc of the simulation cube.,Mpc of the simulation cube. The slice includes the center of the quarter cube., The slice includes the center of the quarter cube. The top panel shows the shear ellipticity field E/cg in the slice calculated from all dark halos in the simulation., The top panel shows the shear ellipticity field $E/\sigma_E$ in the slice calculated from all dark halos in the simulation. We show only the bottom left corner of the slice where a comparison with the half cube result is possible., We show only the bottom left corner of the slice where a comparison with the half cube result is possible. " The contour levels correspond to lo high (red contours), mean, 1.50 low, and 2.50 low (black) shear ellipticity."," The contour levels correspond to $1\sigma$ high (red contours), mean, $1.5\sigma$ low, and $2.5\sigma$ low (black) shear ellipticity." In the middle panel the shear ellipticity field calculated from the dark halos in the half cube is shown., In the middle panel the shear ellipticity field calculated from the dark halos in the half cube is shown. The contour levels are the same., The contour levels are the same. It is clear that the shear field of the half cube is extraordinarily similar with that of the full cube., It is clear that the shear field of the half cube is extraordinarily similar with that of the full cube. " This is particularly true near the center of the half cube, namely at the position (256, 256)."," This is particularly true near the center of the half cube, namely at the position (256, 256)." " However, large differences are also observed near the boundaries."," However, large differences are also observed near the boundaries." The bottom panel shows the shear field of the quarter cube., The bottom panel shows the shear field of the quarter cube. " It again shows that the shear ellipticity of the quarter cube agree quite well with those of the other ones, particularly near the center of the quarter cube."," It again shows that the shear ellipticity of the quarter cube agree quite well with those of the other ones, particularly near the center of the quarter cube." It can be seen that there is a weak shear field extending beyond the sample boundary., It can be seen that there is a weak shear field extending beyond the sample boundary. The shear field of the half cube also has such leakage outside the boundaries (truncated in the middle panel)., The shear field of the half cube also has such leakage outside the boundaries (truncated in the middle panel). To quantitatively estimate the accuracy of the potential and its derivatives obtained from subcubes we calculate the RMS differences of the fields within a cubical shell centered on the center of the subcubes., To quantitatively estimate the accuracy of the potential and its derivatives obtained from subcubes we calculate the RMS differences of the fields within a cubical shell centered on the center of the subcubes. " The solid lines in the top panel of Figure 2 are the difference between the potential from the full cube and that of the half cube within 2 h~'Mpc-thick cubical shell centered at (x,y,z)=(256h-!Mpc,2561256h~!Mpc)."," The solid lines in the top panel of Figure 2 are the difference between the potential from the full cube and that of the half cube within 2 $h^{-1}$ Mpc-thick cubical shell centered at $(x, y, z)=(256 h^{-1}{\rm Mpc}, 256 h^{-1}{\rm Mpc}, 256 h^{-1}{\rm Mpc})$." " Size of a cubical shell is 2(257h~+Mpc1Μρς,— d), where is the distance of the shell from the surface of the subcube."," Size of a cubical shell is $257h^{-1}{\rm Mpc}-d$ ), where $d$ is the distance of the shell from the surface of the subcube." "d For example, d= 1h-!Mpc corresponds the outermost"," For example, $d=1h^{-1}$ Mpc corresponds the outermost" [or the neutral gas. the induction equation for the topology of the magnetic field Amperre’s Law (where. as customary. we have neglected.— the displacement current) and the solenoidal condition on the magnetic field (V-2— 0).,"for the neutral gas, the induction equation for the topology of the magnetic field Ampèrre's Law (where, as customary, we have neglected the displacement current), and the solenoidal condition on the magnetic field $\nabla \cdot \bmath{B} = 0$ )." In the above expressions. 7? is the eas pressure ancl & is the gravitational potential of the central object. where € is the gravitational constant and M is the mass of the protostar.," In the above expressions, $P$ is the gas pressure and $\Phi$ is the gravitational potential of the central object, where $G$ is the gravitational constant and $M$ is the mass of the protostar." In ideal-MIID flows. the magnetic field aud velocity vectors are parallel in a frame that moves with the angular velocity £255 of the magnetic Dux surfaces. where &/4x is the of the wind (the ratio of the constant mass Lux to the constant magnetic flux)," In ideal-MHD flows, the magnetic field and velocity vectors are parallel in a frame that moves with the angular velocity $\bmath{\Omega}_{\rm B}$ of the magnetic flux surfaces, where $k/4\pi$ is the of the wind (the ratio of the constant mass flux to the constant magnetic flux)." In the poloidal (+ 2) plane (subscript p). this equation reduces to The variables 5 anc & satisty (B-V)Os—(B-NV) 0. and thus are constant along the magnetic field lines (or. ecquivalently. the wind Dowlines).," In the poloidal $r-z$ ) plane (subscript `p'), this equation reduces to The variables $\Omega_{\rm B}$ and $k$ satisfy $(\bmath{B} \cdot \nabla) \Omega_{\rm B} = (\bmath{B} \cdot \nabla) k = 0$ , and thus are constant along the magnetic field lines (or, equivalently, the wind flowlines)." Additional quantities that remain constant along the flow are the specific energv where P is the enthalpy per unit mass. and the specific angular momentum. which incorporates the contributions of both the matter (the first term on the right-hand side) and the magnetic field (the second term).," Additional quantities that remain constant along the flow are the specific energy where $h$ is the enthalpy per unit mass, and the specific angular momentum which incorporates the contributions of both the matter (the first term on the right-hand side) and the magnetic field (the second term)." " The quantities &. e and / can be expressed in cimensionless forni as and where the subscript ""b denotes the location of the base of the wind."," The quantities $k$, $e$ and $l$ can be expressed in dimensionless form as and where the subscript `b' denotes the location of the base of the wind." " We now introduce the self-similarity scalings using the notation of DIPS2: In these expressions. €=tangD,/D, is the inclination of the field lines with respect to the rotation axis of the star and cise."," We now introduce the self-similarity scalings using the notation of BP82: In these expressions, $\xi' \equiv \tan \varphi = B_r/B_z$ is the inclination of the field lines with respect to the rotation axis of the star and disc." " At the base of the wind. we take ví0. £i=1. gi=Land fi,=0. so the Luicl velocity at the launching point of the outflow is exactly Ixeplerian."," At the base of the wind, we take $\chi_{\rm b} = 0$, $\xi_{\rm b} = 1$, $g_{\rm b} = 1$ and $f_{\rm b} = 0$, so the fluid velocity at the launching point of the outflow is exactly Keplerian." We now sketch the procedure followed. by DPS2 to obtain the set of ODEs in X that describe the self-similar wind solution., We now sketch the procedure followed by BP82 to obtain the set of ODEs in $\chi$ that describe the self-similar wind solution. First. from the scalings. (39)) (41)). we deduce where with the prime indicating à derivative with respect. to v.," First, from the scalings \ref{eq:scalingvr}) \ref{eq:scalingvz}) ), we deduce where with the prime indicating a derivative with respect to $\chi$." " Similarly. the gravitational potential can be expressed as where the quantity S is defined by Furthermore. since we restrict. our analysis to ""cold? solutions. the enthalpy termi in equation (32)) can be neglected in comparison with the other terms."," Similarly, the gravitational potential can be expressed as where the quantity $S$ is defined by Furthermore, since we restrict our analysis to `cold' solutions, the enthalpy term in equation \ref{eq:energy}) ) can be neglected in comparison with the other terms." Substituting equations (32)). (33)). (42)) ancl (44)) into equations (35)) ancl (36)) vields where we used Qi=(GAL)7.," Substituting equations \ref{eq:energy}) ), \ref{eq:wind9}) ), \ref{eq:vsquared}) ) and \ref{eq:gravpot}) ) into equations \ref{eq:energy2}) ) and \ref{eq:l2}) ) yields where we used $\Omega_{\rm B} = (GM/r_{\rm b}^3)^{1/2}$." Lhe numerical value on the right-hand. side of equation. (46)) is obtained. by evaluating this expression at the disk surface: it remains constant along the Low., The numerical value on the right-hand side of equation \ref{eq:energy1}) ) is obtained by evaluating this expression at the disk surface; it remains constant along the flow. To make further progress. one can use equation 30)) to write which. together with equation (33)). gives Then. substituting equation (48)) into quation (47)). one obtains where m is the square of the Alfvénn Mach number (the ratio of the poloidal speed to the poloidal Alfvénn speed)," To make further progress, one can use equation \ref{eq:vB}) ) to write which, together with equation \ref{eq:wind9}) ), gives Then, substituting equation \ref{eq:bphi}) ) into quation \ref{eq:vphi}) ), one obtains where $m$ is the square of the Alfvénn Mach number (the ratio of the poloidal speed to the poloidal Alfvénn speed)." "the strong deviation of the phase in many CO lines from that in the continuum, this linear fit does not go through all the continuum points.","the strong deviation of the phase in many CO lines from that in the continuum, this linear fit does not go through all the continuum points." " Therefore, the non-zero DPs in the continuum spectral channels lead to a systematic error in the phase restored in the continuum, which affects the subsequent image reconstruction."," Therefore, the non-zero DPs in the continuum spectral channels lead to a systematic error in the phase restored in the continuum, which affects the subsequent image reconstruction." " We found out that the continuum one-dimensional projection image reconstructed using the restored phase shows a systematic wavelength dependence from the shortest to the longest wavelength of the observed spectral range, which is not seen in the continuum images reconstructed from the visibilities and CPs alone."," We found out that the continuum one-dimensional projection image reconstructed using the restored phase shows a systematic wavelength dependence from the shortest to the longest wavelength of the observed spectral range, which is not seen in the continuum images reconstructed from the visibilities and CPs alone." It is necessary to use the same spectral channels in the linear fit to the phase for the derivation of DP and for the derivation of the phase offset and gradient., It is necessary to use the same spectral channels in the linear fit to the phase for the derivation of DP and for the derivation of the phase offset and gradient. " Therefore, we refitted the DP from amdlib with a linear function (with respect to wavenumber) at the same continuum points as used for the derivation of the phase offset and gradient (dashed lines in Figs."," Therefore, we refitted the DP from amdlib with a linear function (with respect to wavenumber) at the same continuum points as used for the derivation of the phase offset and gradient (dashed lines in Figs." Claa and 6150) and subtracted the fitted linear function from the observed DP., \ref{refitDP}a a and \ref{refitDP}b b) and subtracted the fitted linear function from the observed DP. This procedure enforces the DP in the, This procedure enforces the DP in the "Towards condensation 1, a high luminosity, high mass source is found that has a high accretion rate.","Towards condensation 1, a high luminosity, high mass source is found that has a high accretion rate." " The values given in Table 1 are for the entire condensation 1, including YSO#11 and YSO#33."," The values given in Table 1 are for the entire condensation 1, including 1 and 3." The 704m emission is dominated by YSO#33., The $\mu$ m emission is dominated by 3. " This is an extended green object and is associated with a methanol maser (Cyganowski et al. 2008,, 2009)),"," This is an extended green object and is associated with a methanol maser (Cyganowski et al. \cite{cyg08}, \cite{cyg09}) )," which implies a massive YSO with an age younger than 3.5x10* years (Breen et al. 2010))., which implies a massive YSO with an age younger than $\times$ $^{4}$ years (Breen et al. \cite{bre10}) ). " However, no emission is seen in its direction at 20 cm on the MAGPIS image."," However, no emission is seen in its direction at 20 cm on the MAGPIS image." The high accretion rate derived for condensation 1 (see Table 1) may prevent the development of the ionized region (Churchwell 2002))., The high accretion rate derived for condensation 1 (see Table 1) may prevent the development of the ionized region (Churchwell \cite{chu02}) ). The emission may also be optically thick at 20 cm., The emission may also be optically thick at 20 cm. The results of the fit for condensation | are shown in Fig. 2.., The results of the fit for condensation 1 are shown in Fig. \ref{fit}. The sources observed towards condensations 2 and 3 are also massive objects with high accretion rates., The sources observed towards condensations 2 and 3 are also massive objects with high accretion rates. The emission that is barely detected at jum towards condensation 4 cannot be fit using the Robitaille et al., The emission that is barely detected at $\mu$ m towards condensation 4 cannot be fit using the Robitaille et al. SED fitting tool because no data at shorter wavelengths exist to constrain the fit., SED fitting tool because no data at shorter wavelengths exist to constrain the fit. This object is probably a cold core with no internal source of heating., This object is probably a cold core with no internal source of heating. " However, it is interesting to detect this emission farther away from the ionization front as it may represent an"," However, it is interesting to detect this emission farther away from the ionization front as it may represent an" of B wrt A (1.e. B being ejected). and A and B as an exactly co-moving pair: 1.e.. both objects having the same motion in w and 9. so that the separation in both « and 6 remain constant.,"of B wrt A (i.e. B being ejected), and A and B as an exactly co-moving pair; i.e., both objects having the same motion in $\alpha$ and $\delta$, so that the separation in both $\alpha$ and $\delta$ remain constant." Assuming that a priori those five models are equally probable and provide à complete set of hypotheses. we calculated global likelihoods (Bayesian model comparison. see Gregory 2005).," Assuming that a priori those five models are equally probable and provide a complete set of hypotheses, we calculated global likelihoods (Bayesian model comparison, see Gregory 2005)." According to these calculations. an elliptic orbit is most likely. with a probability for this hypothesis being 0.63. which is not yet very significant. but 2 to 3 times larger than the probabilities for the two other likely hypotheses (constant change and hyperbola). and even many times larger than for circular orbit and exactly co-moving.," According to these calculations, an elliptic orbit is most likely, with a probability for this hypothesis being 0.63, which is not yet very significant, but 2 to 3 times larger than the probabilities for the two other likely hypotheses (constant change and hyperbola), and even many times larger than for circular orbit and exactly co-moving." The best fit ellipse has a position angle of 106° and an eccentricity of -0.45., The best fit ellipse has a position angle of $106^{\circ}$ and an eccentricity of $e \simeq 0.45$. Hence. we have weak evidence that an elliptic orbit i5 more probable than any other model. hence evidence for curvature in the orbital motion of B around A. If this can be confirmed. TWA 5 A+B would be the first substellar companion outside the solar system. where such evidence is reported from direct imaging observations.," Hence, we have weak evidence that an elliptic orbit is more probable than any other model, hence evidence for curvature in the orbital motion of B around A. If this can be confirmed, TWA 5 A+B would be the first substellar companion outside the solar system, where such evidence is reported from direct imaging observations." Then. we can also try to investigate whether we can detect a small periodic wobble in the separation of B from A. which would stem from the expected photocenter shift of the close pair Aa+b.," Then, we can also try to investigate whether we can detect a small periodic wobble in the separation of B from A, which would stem from the expected photocenter shift of the close pair Aa+b." This wobble should be seen in periodic residuals to the best fit (ellipse of B around A) in the wncorrected data from Table 1., This wobble should be seen in periodic residuals to the best fit (ellipse of B around A) in the corrected data from Table 1. The period would then give the orbital period of Aatb. and the amplitude would yield the total mass of Aa-b.," The period would then give the orbital period of Aa+b, and the amplitude would yield the total mass of Aa+b." For the uncorrected (1.9. directly observed) data in Table 1. we also obtain an ellipse as the best geometric fit to the data by Bayesian statistics.," For the uncorrected (i.e. directly observed) data in Table 1, we also obtain an ellipse as the best geometric fit to the data by Bayesian statistics." As can be seen in Fig., As can be seen in Fig. 4. the residuals to that best fit do show a small-amplitude (periodic) sinusoid.," 4, the residuals to that best fit do show a small-amplitude (periodic) sinusoid." We searched for the periodicity only in a small window of 3-8 years (around the known orbital period of 5.94 yr) and detected a best-fit period of ~5.72+1.14 yr., We searched for the periodicity only in a small window of 3-8 years (around the known orbital period of 5.94 yr) and detected a best-fit period of $\sim 5.72 \pm 1.14$ yr. The (half-)amplitude of the sinusoidal wobble is 18+9 mas., The (half-)amplitude of the sinusoidal wobble is $18 \pm 9$ mas. Both values are close to the values from the orbital fit of Aa+b in KO7. where they give 5.94+0.09 yr period.," Both values are close to the values from the orbital fit of Aa+b in K07, where they give $5.94 \pm 0.09$ yr period." Given the semi-major axis. eccentricity. and inclination. the maximum photocenter shift on the sky (for equal brightness of Aa and Ab) is ~28 mas (their Fig.," Given the semi-major axis, eccentricity, and inclination, the maximum photocenter shift on the sky (for equal brightness of Aa and Ab) is $\sim 28$ mas (their Fig." 3 and Table 2)., 3 and Table 2). Our residuals are close to zero (minimum of residuals) at epoch ~1998. roughly six years before the epoch of closest approach given in ΚΟ7.," Our residuals are close to zero (minimum of residuals) at epoch $\sim 1998$, roughly six years before the epoch of closest approach given in K07." Periastron and closest separation on sky are very close together (ΚΟ., Periastron and closest separation on sky are very close together (K07). " As a result. our data are consistent with the orbit found in KO7,"," As a result, our data are consistent with the orbit found in K07." Even though our data have lower angular resolution (8m VLT) compared to KO7 using the 10m Keck. so that the inner TWA 5 Aa+b pair is unresolved in our NACO data. we can detect and measure the photocenter wobble of TWA 5 Aa+b in the separation changes between A and B. In principle. we could also measure the total mass of the TWA 5 Aa+b pair: however. we refrain from doing so. because our images do no resolve for," Even though our data have lower angular resolution (8m VLT) compared to K07 using the 10m Keck, so that the inner TWA 5 Aa+b pair is unresolved in our NACO data, we can detect and measure the photocenter wobble of TWA 5 Aa+b in the separation changes between A and B. In principle, we could also measure the total mass of the TWA 5 Aa+b pair; however, we refrain from doing so, because our images do no resolve for" Field lines wrapping around a eap as in refsketch aso have a fluting-uustable curvature.,Field lines wrapping around a gap as in \\ref{sketch} also have a fluting-unstable curvature. As suggested in Payver II (sectio17) the ubiquitous striation seen in poenuniDu filaments is thus plausibly due to fiutiug., As suggested in Paper II (section 7) the ubiquitous striation seen in penumbral filaments is thus plausibly due to fluting. If Cncditins for fiuting iustabilitv are onlv mareinallv saisfiect. external orcing by “Moise” in the form of irreeularitics 1u the flow inside tl16 gap would contribute as well.," If conditions for fluting instability are only marginally satisfied, external forcing by `noise' in the form of irregularities in the flow inside the gap would contribute as well." The presence of the strialon Is an argument agaist he existence of: vloielucinal (filament-aliguce) maenetic fell iu the gap (such as proposed by Zakharov ct al., The presence of the striation is an argument against the existence of a longitudinal (filament-aligned) magnetic field in the gap (such as proposed by Zakharov et al. 2008)., 2008). The displaceuxnts of the eap boundary due to Πιο would bend sch a feld., The displacements of the gap boundary due to fluting would bend such a field. The restoring teusiou forces resulting from this bending «»pose fiutiug., The restoring tension forces resulting from this bending oppose fluting. " This is exploited in t16 design of coutrolled fusion devices by judiciously shearing tjio field. Line| directions across the naguctic surfaccκ, Which would otherwise be unstable to Πο,"," This is exploited in the design of controlled fusion devices by judiciously shearing the field line directions across the magnetic surfaces, which would otherwise be unstable to fluting." This stailiziug effect is strongest at the shortest wavelengths., This stabilizing effect is strongest at the shortest wavelengths. The τον narrow widhs observed in the stration (at tle| resolution luit) tWs argue against a ongitudinal fiek of significant sticΙστ] iu the gap., The very narrow widths observed in the striation (at the resolution limit) thus argue against a longitudinal field of significant strength in the gap. Tow does such a corrugated surface cause the brightucss contrast observed as striation?, How does such a corrugated surface cause the brightness contrast observed as striation? The corrugation develops slowly compared with the relevant sound (fast node) crossing times. hence it must take place approxiuatolv imequilibriimn:: P|Bossa= cst..," The corrugation develops slowly compared with the relevant sound (fast mode) crossing times, hence it must take place approximately in: $P+B^2/8\pi=$ cst.," both in time anc across the boundary., both in time and across the boundary. Gap fluid. with low fie dstreneth and Ligh plasima density. forms ridecs protrudiie into the maenetic field where the deusitv axl optical clepth is low.," Gap fluid, with low field strength and high plasma density, forms ridges protruding into the magnetic field where the density and optical depth is low." Badiative losses from such a ridex (are dareer hau du its surroundings., Radiative losses from such a ridge are larger than in its surroundings. TI10 resulting steepeing of the eniperature eradicut causes he ridge to appear dark., The resulting steepening of the temperature gradient causes the ridge to appear dark. The physical conditions eiving rise to the ¢Ontrast secu as stration of o»uunmbral fihuueifs are thus the same as in the dark cores over poemxal filameits. dn light bricdecs (see Noxlud aud Schariicy 20090) a idin the dark striaflon dà sia] uuaguetic cleueuts seen in refoslo..," The physical conditions giving rise to the contrast seen as striation of penumbral filaments are thus the same as in the dark cores over penumbral filaments, in light bridges (see Nordlund and Scharmer 2009) and in the dark striation in small magnetic elements seen in \\ref{oslo}." Since the feld. lines wrapping around the gap coutiuue iuto the dark ccore over a filament. this interpretation of striation conrast also acccounts for the observed close enuection of stration with the dark cores overving flameits.," Since the field lines wrapping around the gap continue into the dark core over a filament, this interpretation of striation contrast also accounts for the observed close connection of striation with the dark cores overlying filaments." It is also consistent wit1i the analysis by Carlsson ct al. (, It is also consistent with the analysis by Carlsson et al. ( 2001) of the striafion seen in their sinmulations of all magnetic structures.,2004) of the striation seen in their simulations of small magnetic structures. " For a field «ποιοι of 1500 €; (anid-peuunbra) the magnetic- pressure 7DSamLO? ποσα, ", For a field strength of 1500 G (mid-penumbra) the magnetic pressure $B^2/8\pi\approx 10^5$ $^3$. This matches the photospheric pressure fairly closely., This matches the photospheric pressure fairly closely. The boundary between field ancl gap will thus occur close to a (continui) optical depth unity., The boundary between field and gap will thus occur close to a (continuum) optical depth unity. It is conceivable that most of the line formation takes place in the magnetic volue. with littlCO itribution from the eapinterior.," It is conceivable that most of the line formation takes place in the magnetic volume, with little contribution from the gap." . Iu this case it would be iupossible to detect the magnetic boundary through its effect on the polarized line profile., In this case it would be impossible to detect the magnetic boundary through its effect on the polarized line profile. Ou he other haud. if the deusitv above the boundary is low enough. the optical depth to the boundary Is low. SO tie line profile will be forme: i part the botnnlary. resultiie 1ja weaker polarization signal.," On the other hand, if the density above the boundary is low enough, the optical depth to the boundary is low, so the line profile will be formed in part the boundary, resulting in a weaker polarization signal." Observatiorally. his NOIId have an effect simular te) a “stray ight⋅ coitribution. and a lower apparent field strenet[u," Observationally, this would have an effect similar to a `stray light' contribution, and a lower apparent field strength." m The elevatioi of bright filbuueds over heir surroundCs.me Q the order 300 X1i (as seen in the miuerical siuulatlons. and consisteiut with the cinge aspect of observec filaments with vicsaving anele) is :Xout WO pressure scae heights at the observed teuperature of he filamens.," The elevation of bright filaments over their surroundings, of the order 300 km (as seen in the numerical simulations, and consistent with the changing aspect of observed filaments with viewing angle) is about two pressure scale heights at the observed temperature of the filaments." The time scales for claiges du he fianuents (10-30 1mites) are longer than the sound ravel nne over such a height (about Los}., The time scales for changes in the filaments (10-30 minutes) are longer than the sound travel time over such a height (about 40s). T10 gas pressure O1 he field lines unding the eap must thereore decrcase with height approxinatelv accorcling to wdrosatic equilibriuu., The gas pressure on the field lines bounding the gap must therefore decrease with height approximately according to hydrostatic equilibrium. Near the top of the ieap ε10 pressire on these ποια lines woud then be a factor 10 lower than at the optical depth 1uty level between the gaps (cf. rofsketch)).," Near the top of the gap the pressure on these field lines would then be a factor 10 lower than at the optical depth unity level between the gaps (cf. \\ref{sketch}) )," and the optical depth to the maetic )oundaryv woud be correspoudingly lower., and the optical depth to the magnetic boundary would be correspondingly lower. One would expect this difference to be reflected in the polarization signals: it woud reduce the interred field streugth in the dark cores (already low because of the cusped nature of the field configuration)., One would expect this difference to be reflected in the polarization signals: it would reduce the inferred field strength in the dark cores (already low because of the cusped nature of the field configuration). The magneticOo signalsOo to be expected «cepend critically on he thickuess of tιο boundary betwcen the eap aud he field surrounding it., The magnetic signals to be expected depend critically on the thickness of the boundary between the gap and the field surrounding it. If oulv. Olunic «ifusion plavs a xje. he transition may beas thin as a few kan. which would iot wave nmcelh consecποιος for spectral line formation.," If only Ohmic diffusion plays a role, the transition may be as thin as a few km, which would not have much consequence for spectral line formation." The depth iuto the σα]) where optical «js >2 are reaclred is only ~20 kin. jowever. so only : nuld increase of he scnetration of the maenetic field iitO he eap couk have sjenificaut effects c nt16 expected poarization signals.," The depth into the gap where optical depths $>2$ are reached is only $\sim 20$ km, however, so only a mild increase of the penetration of the magnetic field into the gap could have significant effects on the expected polarization signals." For coniparison. this is of the order o| the grid resoutiou in current uuinierkal snulatious of snuspots.," For comparison, this is of the order of the grid resolution in current numerical simulations of sunspots." Simmlatic11 sufficient for realistic ine formatio1 calculations wil Lecxl significantly hieher resolution., Simulations sufficient for realistic line formation calculations will need significantly higher resolution. " A complication in this context is he possiülit that the trausitiou between the magnetic fek aud the couvecting flow nu the eap lav be broenc bv the consequences of fiuπιο,", A complication in this context is the possibility that the transition between the magnetic field and the convecting flow in the gap may be broadened by the consequences of fluting. The stnallest dkqe scale perpencdictlar to the fied lines is linüted. oilv by unicroscopic diffusion. aud the erowth rate of instability is independent of he| leneth scale as lo19 osas it exceeds this liuit.," The smallest length scale perpendicular to the field lines is limited only by microscopic diffusion, and the growth rate of the instability is independent of the length scale as long as it exceeds this limit." If the ayudable time (the flaw ti along the bouneav) is suthicjeut for the instabili+ erow siguificautly. siadll leneth scales are thus likely develop.," If the available time (the flow time along the boundary) is sufficient for the instability to grow significantly, small length scales are thus likely to develop." If this happens the transition may be significa, If this happens the transition may be significantly "In this section we summarize the available in the literature kinematical data for the SPRC objects, as far as we present the results of original observations of six previously uninvestigated galaxies.","In this section we summarize the available in the literature kinematical data for the SPRC objects, as far as we present the results of original observations of six previously uninvestigated galaxies." T'he results of observations clearly demonstrate that morphological selection is an effective tool for recognizing the true PRGs — 5 of 6 objects were confirmed to be classical PRGs., The results of observations clearly demonstrate that morphological selection is an effective tool for recognizing the true PRGs — 5 of 6 objects were confirmed to be classical PRGs. SPRC-7.. The kinematics of its gaseous and stellar subsystems was studied by Broschetal.(2010)., The kinematics of its gaseous and stellar subsystems was studied by \citet{Brosch2010}. . It is demonstrated that the central object is an early-type galaxy., It is demonstrated that the central object is an early-type galaxy. " 'The outer ring, characterised by its blue colour, consists of a younger stellar population and emits lines of ionized gas."," The outer ring, characterised by its blue colour, consists of a younger stellar population and emits lines of ionized gas." The analysis of the velocity field in the H8 line has shown that this giant ring (with a diameter of 48 kpc) rotates at a noticeable angle to the plane of the central galaxy., The analysis of the velocity field in the $\beta$ line has shown that this giant ring (with a diameter of 48 kpc) rotates at a noticeable angle to the plane of the central galaxy. " According to various estimates, the angle between them amounts to Ai=58+10? or 73117.4262)."," According to various estimates, the angle between them amounts to $\Delta i=58\pm10\degr$ or $73\pm11\degr$." ". In a recent paper by Bettonietal.(2010) it was shown that both the ionized gas in the inner region and the neutral hydrogen at large distances from the centre, rotate in the plane, that is strongly inclined to the stellar disc of this galaxy with a central bar."," In a recent paper by \citet{Bettoni2010} it was shown that both the ionized gas in the inner region and the neutral hydrogen at large distances from the centre, rotate in the plane, that is strongly inclined to the stellar disc of this galaxy with a central bar." " In addition, the UV images demonstrate the presence of a young stellar population in the ring of neutral hydrogen, having the outer diameter of about 18—20 kpc."," In addition, the UV images demonstrate the presence of a young stellar population in the ring of neutral hydrogen, having the outer diameter of about $18-20$ kpc." " Bettonietal.(2010) chose to speak of an inclined ring, but a formal calculationof the mutual inclination angle (seeformula(1)inMoiseev2008) yields two solutions: Ai=39° and 90°.The latter corresponds to the polar ring, as noted in their subsequent work (Busonetal.2011)."," \citet{Bettoni2010} chose to speak of an inclined ring, but a formal calculationof the mutual inclination angle \citep[see formula (1) in][]{Moiseev2008} yields two solutions: $\Delta i=39\degr$ and $90\degr$.The latter corresponds to the polar ring, as noted in their subsequent work \citep{Buson2011}." ". On the background of a bright lenticular body of the galaxy a small blue ring is visible with a diameter of approximately 45 arcsec (~3.9 kpc), strongly inclined to the plane of the galaxy, elongated along PAz45°."," On the background of a bright lenticular body of the galaxy a small blue ring is visible with a diameter of approximately 45 arcsec $\sim3.9$ kpc), strongly inclined to the plane of the galaxy, elongated along $PA\approx45\degr$." " According to the radio observations of Noordermeeretal.(2005) with the WSRT, the HI rotation occurs in the disc, the kinematic axis of which coincides with this blue ring, and its diameter reaches about 15 kpc."," According to the radio observations of \citet{Noordermeer2005} with the WSRT, the HI rotation occurs in the disc, the kinematic axis of which coincides with this blue ring, and its diameter reaches about 15 kpc." " The HI distribution also reveals a tidal tail, extending over at least 20 kpc."," The HI distribution also reveals a tidal tail, extending over at least 20 kpc." " It is noted that the galaxy belongs to a group, rich in HI clouds, the accretion of which (or a capture of a companion) has formed a polar structure."," It is noted that the galaxy belongs to a group, rich in HI clouds, the accretion of which (or a capture of a companion) has formed a polar structure." 060020).. The kinematics and photometry of this galaxy were studied at the 6-m telescope by Karataevaetal.(2011)., The kinematics and photometry of this galaxy were studied at the 6-m telescope by \citet{Karataeva2011}. ". It was found that the outer ring rotates at a large angle to the plane of the disc of the central galaxy, therefore the polar ring is kinematically confirmed."," It was found that the outer ring rotates at a large angle to the plane of the disc of the central galaxy, therefore the polar ring is kinematically confirmed." A well-known interacting galaxy., A well-known interacting galaxy. According to Young(2002) the molecular gas here is rotating in a warped inclined disc with a diameter of at least 8—9 kpc., According to \citet{Young2002} the molecular gas here is rotating in a warped inclined disc with a diameter of at least $8-9$ kpc. " Furthermore, Balcells&Stanford(1990) have discovered at the distance of r<1 kpc a kinematically decoupled core, rotating perpendicular to the disc of the galaxy."," Furthermore, \citet{Balcells1990} have discovered at the distance of $r<1$ kpc a kinematically decoupled core, rotating perpendicular to the disc of the galaxy." Spectral observations were carried out at the prime focus of the SAO RAS 6-m telescope., Spectral observations were carried out at the prime focus of the SAO RAS 6-m telescope. In August 2010 we used the SCORPIO focal reducer (Afanasiev&Moiseev2005) with a EEV CCD42-40 CCD chip sized 2048x pixels as a detector., In August 2010 we used the SCORPIO focal reducer \citep{AfanasievMoiseev2005} with a EEV CCD42-40 CCD chip sized $2048\times2048$ pixels as a detector. " The further observations were carried out with a new experimental instrument SCORPIO-2 (Afanasiev&Moiseev 2011),, where a E2V CCD42-90 CCD chip, sized 2048x4600 was implemented, providing a two times larger spectral range."," The further observations were carried out with a new experimental instrument SCORPIO-2 \citep{AfanasievMoiseev2011}, where a E2V CCD42-90 CCD chip, sized $2048\times4600$ was implemented, providing a two times larger spectral range." " The other characteristics of both devices were similar — the slit width of 1 arcsec, its height — 6 arcmin, the scale along the slit amounted to 0.35 arcsec/pix, and the spectral resolution FWHM= 5A.."," The other characteristics of both devices were similar – the slit width of 1 arcsec, its height – 6 arcmin, the scale along the slit amounted to 0.35 arcsec/pix, and the spectral resolution $FWHM=5$ ." The log of observations is presented in Table 1.., The log of observations is presented in Table \ref{tab_obs}. " The spectral range included both the absorption lines of the stellar population, and emission"," The spectral range included both the absorption lines of the stellar population, and emission" INSs moving through a high density medium (the only ones with high enough luminosities to be xotentiallv detected) and with strong magnetic ields can become accretors alter S few. Gye.,INSs moving through a high density medium (the only ones with high enough luminosities to be potentially detected) and with strong magnetic fields can become accretors after $\la $ few Gyr. Ht was shown above that INSs like the MY. which rave magnetic fields higher that those typical of racio pulsars. and at the same time have not very arge spatial velocities. are the most favored. as Accretors predecessors.," It was shown above that INSs like the M7, which have magnetic fields higher that those typical of radio pulsars, and at the same time have not very large spatial velocities, are the most favored as Accretors predecessors." Although the number of ALNSs might o! even larger than that originally estimated in. Paper 1. the conclusion that at low luxes Aceretors outnumber cooling isolated NS (Coolers) is based. on the assumption that the umiinosity corresponds to the Bondi: accretion rate.," Although the number of AINSs might be even larger than that originally estimated in Paper I, the conclusion that at low fluxes Accretors outnumber cooling isolated NS (Coolers) is based on the assumption that the luminosity corresponds to the Bondi accretion rate." This is a quite controversial issue., This is a quite controversial issue. " nave shown that. for typical ΕΛ densities (nzmlem "") aceretion rate does not exceed ~ Low 10°οκ loeven if the star. velocity. drops. below ~(G0kms+."," have shown that for typical ISM densities $n\approx 1\ {\rm cm^{-3}}$ ) accretion rate does not exceed $\sim$ few $10^9\ {\rm g\, s^{-1}}$, even if the star velocity drops below $\sim 60\ {\rm km\, s^{-1}}$." This is due to the ionization of the ISM. surrounding the star by the X-ray radiation which. in turn. produces an increase in the sound. speed. freezing the accretion rate.," This is due to the ionization of the ISM surrounding the star by the X-ray radiation which, in turn, produces an increase in the sound speed freezing the accretion rate." Llowever. in Paper Lit was shown that the velocity distribution of Aceretors peaks at 50kms and for these velocities the effect is small.," However, in Paper I it was shown that the velocity distribution of Accretors peaks at $\sim 50\ {\rm km\, s^{-1}}$, and for these velocities the effect is small." So. or most Accretors. heating of the ISM can be neglected. especially if they appear in regions of high. ISAT density.," So, for most Accretors, heating of the ISM can be neglected, especially if they appear in regions of high ISM density." A further issue is the role jXaved by the star magnetic field in the accretion low cdvnanmies outside the Propeller stage., A further issue is the role played by the star magnetic field in the accretion flow dynamics outside the Propeller stage. On the osls Of 2D. MILD calculations. concluded that only a fraction of the initial (Bondi) Dow reaches he star surface. and this fraction decreases with erowing magnetic [field of a NS.," On the basis of 2D MHD calculations, concluded that only a fraction of the initial (Bondi) flow reaches the star surface, and this fraction decreases with growing magnetic field of a NS." Whether 3D instabilities may counteract this elfect is still an open question., Whether 3D instabilities may counteract this effect is still an open question. Anyway. if several weak sources without measured proper motions and interpreted as INS candidates can be identified in IROSAXTE. Chandra or/and XMM-Newton. archives (see and references therein). or discovered. by. «⊰↻∺⊔≵∖⊳ then it is not trivial to clistineuish Coolers [rom Accretors.," Anyway, if several weak sources without measured proper motions and interpreted as INS candidates can be identified in ROSAT, Chandra or/and XMM-Newton archives (see and references therein), or discovered by eROSITA, then it is not trivial to distinguish Coolers from Accretors." Ian INS comes to the Accretor stage only after à long subsonic Propeller episode. its spin period. is Z0! s. Such long periods are not unexpected even if the subsonic Propeller stage is neelectecd.," If an INS comes to the Accretor stage only after a long subsonic Propeller episode, its spin period is $\ga 10^4$ s. Such long periods are not unexpected even if the subsonic Propeller stage is neglected." " When a NS starts to acerete it continues to spin down. until it reaches a (quasi-equilibrium period. 2,%10"" s for n=1 cm(??).."," When a NS starts to accrete it continues to spin down, until it reaches a quasi-equilibrium period, $P_\mr{{eq}}\approx 10^6$ s for $n=1$ $^{-3}$." The ultra-Iong spin periods of Accretors could be the best diseriminator between this tvpe of sources ancl Coolers. which are expected. to have spin periods [ew seconds (like the M7 and cooling PSRs).," The ultra-long spin periods of Accretors could be the best discriminator between this type of sources and Coolers, which are expected to have spin periods $\la$ few seconds (like the M7 and cooling PSRs)." However. at low fluxes it would be extremely difficult to. discover. pulsations in Coolers. so the non-detection of a periodicity is not à strong argument in favour of an ALNS.," However, at low fluxes it would be extremely difficult to discover pulsations in Coolers, so the non-detection of a periodicity is not a strong argument in favour of an AINS." Opposite to Coolers. AXceretors are expected to. show both spin-up and. spin-down as their periods Uuetuate around. the. quasi-equilibrium value.," Opposite to Coolers, Accretors are expected to show both – spin-up and spin-down -- as their periods fluctuate around the quasi-equilibrium value." However. 2 measurements can be impossible for faint sources with very long periods.," However, $\dot P$ measurements can be impossible for faint sources with very long periods." The period of accreting LINSs can be significantly shorter than =10 s in the case of magnetic fields decaying down to small values (~10° G). although some kind of line tuning is necessary.," The period of accreting INSs can be significantly shorter than $\approx 10^6$ s in the case of magnetic fields decaying down to small values $\sim 10^9$ G), although some kind of fine tuning is necessary." As discussed above. to reach accretion in a time shorter than the Hubble time an INS should have at least a magnetic field e1077 C. So. clecay should. not be significant during the first ~ 1 Gye of the evolution. otherwise a NS spends all its life as an Ejector or a Propeller(??7).," As discussed above, to reach accretion in a time shorter than the Hubble time an INS should have at least a magnetic field $\approx 10^{12}$ G. So, decay should not be significant during the first $\sim$ 1 Gyr of the evolution, otherwise a NS spends all its life as an Ejector or a Propeller." . I the field decays during the Aceretor (or even subsonie Propeller) phase. an INS can attain a period ~10. 107 s. since £A is smaller for smaller fields.," If the field decays during the Accretor (or even subsonic Propeller) phase, an INS can attain a period $\sim10^3$ $10^4$ s, since $P_\mr{{eq}}$ is smaller for smaller fields." Accretors. at. variance with coolers. are not expected to be steady sources because of changes in the accretion rate. due to inhomogencities of the ISM. on a time-scale Note that this time scale is shorter for fainter ποιος.," Accretors, at variance with coolers, are not expected to be steady sources because of changes in the accretion rate, due to inhomogeneities of the ISM, on a time-scale Note that this time scale is shorter for fainter sources." Spatial distribution of Aceretors ancl new weaker Coolers are expected. {ο be. slightly diflerent. as the first. represent much older population. and for the first higher ISM density is favorable for detection in contrast with the second.," Spatial distribution of Accretors and new weaker Coolers are expected to be slightly different, as the first represent much older population, and for the first higher ISM density is favorable for detection in contrast with the second." New (Le. undiscovered. vet) Coolers according to απο expected. to be found: at distances 1 kpe.," New (i.e., undiscovered, yet) Coolers according to are expected to be found at distances $\sim 1 $ kpc." So. they should. be relatively right. ~1075 erg +.," So, they should be relatively bright, $\sim 10^{31}$ erg $^{-1}$." Accretors cannot be that sight. and so they are expected to be found closer.," Accretors cannot be that bright, and so they are expected to be found closer." Young Coolers should trace starforming regions., Young Coolers should trace starforming regions. Acerctors. which already experienced ong evolution in the Galactic potential. should be clistributed more smoothly.," Accretors, which already experienced long evolution in the Galactic potential, should be distributed more smoothly." However. for them to »( detectable it is important to be inside regions of relatively high LSAT density.," However, for them to be detectable it is important to be inside regions of relatively high ISM density." The X-ray spectrum of a NS acercting at ow rate from the ISM is very similar to those of cooling INSs. at least in the case when the," The X-ray spectrum of a NS accreting at low rate from the ISM is very similar to those of cooling INSs, at least in the case when the" AU Mon (11D 50846. LLP 33237) is an eclipsing. double-ined spectroscopic binary.,"AU Mon (HD 50846, HIP 33237) is an eclipsing, double-lined spectroscopic binary." “Lhe svstem consists of a De-vpe primary (which will be referred. to as the gainer in he rest of the text) and an evolved. C-type secondary (which we will refer to as the donor) that has likely illed its Roche lobe and is losing mass to its companion.," The system consists of a Be-type primary (which will be referred to as the gainer in the rest of the text), and an evolved G-type secondary (which we will refer to as the donor), that has likely filled its Roche lobe and is losing mass to its companion." Spectroscopic evidence indicates the presence of several avers of circumstellar matter in the svstem. and allows for he existence of a permanent accretion disk (Sahade&Ferrer 1982).," Spectroscopic evidence indicates the presence of several layers of circumstellar matter in the system, and allows for the existence of a permanent accretion disk \citep{sahade82}." . According to these characteristics. AU Mon belongs o the class of hot. massive Algols.," According to these characteristics, AU Mon belongs to the class of hot, massive Algols." Vhe orbit of the system is circular. with an orbital »eriod of about 11 davs.," The orbit of the system is circular, with an orbital period of about 11 days." Phere is an additional periodicity in he total light of the system. with a period of about 417 days and an amplitude of about 0.25 mag.," There is an additional periodicity in the total light of the system, with a period of about 417 days and an amplitude of about 0.25 mag." This variability was discovered. by Lorenzi(19808). ancl interpreted. by Peters(1991.1994) as resulting from periodic Duetuations in the mass transfer rate. which may be caused by oscillations of he donor star about its critical Itoche surface.," This variability was discovered by \citet{lorenzi80a} and interpreted by \citet{peters91, peters94} as resulting from periodic fluctuations in the mass transfer rate, which may be caused by oscillations of the donor star about its critical Roche surface." A thorough overview of previous. knowledge about he svstem can be found in the recent paper by Desmetetal. (2010). who performed a very. detailed: analysis of the system based on Colo photometry (the same data this study. is based on). a collection of previously published groune-basecl photometry. and on high-resolution spectroscopy.," A thorough overview of previous knowledge about the system can be found in the recent paper by \citet{des10}, who performed a very detailed analysis of the system based on CoRoT photometry (the same data this study is based on), a collection of previously published ground-based photometry, and on high-resolution spectroscopy." Based on the analysis of erounc-based data. they concluded that the long-term variation originates from. changes in the transparency of cireumbinary material.," Based on the analysis of ground-based data, they concluded that the long-term variation originates from changes in the transparency of circumbinary material." They have also found periodicities shorter than the orbital period in ColtoT data., They have also found periodicities shorter than the orbital period in CoRoT data. " ""Two reliable frequencies of 10.4 and 8.34 ! were tentatively assigned to the pulsation of the gainer. and the power excess in low-frequency region to the solar-like oscillations of the donor."," Two reliable frequencies of 10.4 and 8.3 $d^{-1}$ were tentatively assigned to the pulsation of the gainer, and the power excess in low-frequency region to the solar-like oscillations of the donor." Llowever. the attempt by Desmetctal.(2010) is) model XU Alon as a semicletached svstem wasn't entirely successful.," However, the attempt by \citet{des10} to model AU Mon as a semidetached system wasn't entirely successful." Most notably. the semidetached model could not reproduce the Itossiter-MeLbaughlin effect. (Rossiter1924:AMeLaughlin 1924)). and required an unusually large gravity darkening exponent to fit the lieht-curves.," Most notably, the semidetached model could not reproduce the Rossiter-McLaughlin effect \citealt{rossiter24,mc24}) ), and required an unusually large gravity darkening exponent to fit the light-curves." The authors therefore. suggested: that the svstem. should. be analyzed using a model which includes the gas stream ancl the accretion disk around the primary componont., The authors therefore suggested that the system should be analyzed using a model which includes the gas stream and the accretion disk around the primary component. There are several spectroscopic indications [for the existence. of an acerction disk in AU Alon. discussed. in detail by Desmetet.al. (2010)..," There are several spectroscopic indications for the existence of an accretion disk in AU Mon, discussed in detail by \citet{des10}. ." " The couble-peaked 14, emission line. and the variation of Lf, and. df. line profiles with the orbital phase (Atwood-Stoneetal.2010).. can be successfully explained. with a model of the system with an accretion disc around the gainer."," The double-peaked $H_{\alpha}$ emission line, and the variation of $H_{\alpha}$ and $H_{\beta}$ line profiles with the orbital phase \citep{atwood10}, can be successfully explained with a model of the system with an accretion disc around the gainer." Peters&Polidan(1998) have found evidence of disk absorption in the Fejj (UVI) resonance lines., \citet{pp98} have found evidence of disk absorption in the $\rm{Fe_{\ III}}$ (UV1) resonance lines. Moreover. according to the criterion of Lubow&Shu.(1975).. AU Mon should have a permanent accretion disk (Richares&Albright|1999).," Moreover, according to the criterion of \citet{LubowShu}, AU Mon should have a permanent accretion disk \citep{richards99}." . These spectroscopic indicators and the cdilliculties in reconciling the semidetached model with the observations. prompted us to repeat the light curve analvsis of Colo photometry using a binary system modcl with an accretion disk.," These spectroscopic indicators and the difficulties in reconciling the semidetached model with the observations, prompted us to repeat the light curve analysis of CoRoT photometry using a binary system model with an accretion disk." The model includes active regionson the disk. edge. accounting for the gas stream and the spiral arms in the," The model includes active regionson the disk edge, accounting for the gas stream and the spiral arms in the" ol the mass of the galaxy. bulge (Magorrian οἱ al.,of the mass of the galaxy bulge (Magorrian et al. 1993: Harring Rix 2004). and there is an even tighter correlation between the DII mass and the velocity dispersion of the bulge (Ferrarese Merritt 2000: Tremaine et al.," 1998; Härring Rix 2004), and there is an even tighter correlation between the BH mass and the velocity dispersion of the bulge (Ferrarese Merritt 2000; Tremaine et al." 2002): the latter quantity is. of course. a measure of the galaxy mass via (he virial theorem.," 2002); the latter quantity is, of course, a measure of the galaxy mass via the virial theorem." These correlations suggest that there is an intimate connection between (he supermassive DII and the galaxy. even though the DII constitutes only a small fraction of the galaxy in terms of mass.," These correlations suggest that there is an intimate connection between the supermassive BH and the galaxy, even though the BH constitutes only a small fraction of the galaxy in terms of mass." A munber of explanations have been offered [or the correlations (e.g.. Rees Silk 19983: Murray. Quataert Thompson 2005). but there is no real understaiuding of the correlation at present.," A number of explanations have been offered for the correlations (e.g., Rees Silk 1998; Murray, Quataert Thompson 2005), but there is no real understanding of the correlation at present." " Aye the two kinds of BIIs discussed above the only ones in the universe or are (here other kinds. e.g.. intermediate mass DIIs with masses of sav. 10*—105,?"," Are the two kinds of BHs discussed above the only ones in the universe or are there other kinds, e.g., intermediate mass BHs with masses of say $10^3-10^4M_\odot$?" This question has attracted recent attention., This question has attracted recent attention. In several nearby galaxies there is a class of ultra-Duminous X-ray sources (FEabbiano 1989: Colbert Mushotzky. 1999) which seem to be too bright to be ordinary LOA. Bis: some of these sources have luminosities of 1011eres+ or more. whereas the nominal maximum steady. Iuminositv of a gravitating object is the Edcington limit. Lyaq=1.3κLOMCAL/LOAL.)eres|.," In several nearby galaxies there is a class of ultra-luminous X-ray sources (Fabbiano 1989; Colbert Mushotzky 1999) which seem to be too bright to be ordinary $10M_\odot$ BHs; some of these sources have luminosities of $10^{41} ~{\rm erg\,s^{-1}}$ or more, whereas the nominal maximum steady luminosity of a gravitating object is the Eddington limit, $L_{\rm Edd} =1.3\times 10^{39}(M/10M_\odot) ~{\rm erg\,s^{-1}}$." The Eddington limit is the luminosity at which the outward acceleration of gas by radiation pressure is just equal to the inward acceleration bv eravitv., The Eddington limit is the luminosity at which the outward acceleration of gas by radiation pressure is just equal to the inward acceleration by gravity. For Iuminosities greater (han Lygq. the radiation lorce is expected to overwheln eravily and to cause the accretion rate to reduce such that the hiuminosity falls below Laa (see Shapiro Teukolsky 1983 for additional diseussion).," For luminosities greater than $L_{\rm Edd}$, the radiation force is expected to overwhelm gravity and to cause the accretion rate to reduce such that the luminosity falls below $L_{\rm Edd}$ (see Shapiro Teukolsky 1983 for additional discussion)." Although there are wavs awound the Exdington limit. (hese require special conditions: so there is à good. chance that at least some of the ultraluminous X-ray sources are much more massive (han LOAL..," Although there are ways around the Eddington limit, these require special conditions; so there is a good chance that at least some of the ultraluminous X-ray sources are much more massive than $10M_\odot$." On the other hand. the sources are not likely to be (underluminous) 109. DIIS because they are generally located away from the nuclei of their host galaxies.," On the other hand, the sources are not likely to be (underluminous) $10^6M_\odot$ BHs because they are generally located away from the nuclei of their host galaxies." Also. in some galaxies. several ultra-Iuminous sources have been found whereas only one supermassive BIL is (wpically found in a galaxy.," Also, in some galaxies, several ultra-luminous sources have been found whereas only one supermassive BH is typically found in a galaxy." It is unclear al present what exactly (he ultra-Iumninous X-ray sources are and whether thev are even a single homogeneous population (see Miller Colbert 2004 lor a review)., It is unclear at present what exactly the ultra-luminous X-ray sources are and whether they are even a single homogeneous population (see Miller Colbert 2004 for a review). Dynamical mass measurements would obviously settle Che issue., Dynamical mass measurements would obviously settle the issue. Unfortunately. none of the sources has a confirmed binary companion. so there is no prospect of making a robust mass measurement anv time soon.," Unfortunately, none of the sources has a confirmed binary companion, so there is no prospect of making a robust mass measurement any time soon." If uliraluminous X-ray. sources are ultimately confirmed to be intermediate mass BIIs. an interesting question would then need to be settled: are {ον a distinct new population or are they. just an extended (ail of the mass distribution of either stellar-mass DIIs or supermassive DIIS?," If ultraluminous X-ray sources are ultimately confirmed to be intermediate mass BHs, an interesting question would then need to be settled: are they a distinct new population or are they just an extended tail of the mass distribution of either stellar-mass BHs or supermassive BHs?" (7~1 Quangetal.(2010) dee?," $\tau\sim1$ $d=140$ \citet{qua10} \cite[SDSS;][]{yor00,fin04}." Quiuzctal.(2010) (CLuluuau, $^{2}$ \citet{qua10} \citep{luh09tau}. etal.2009).. (Werneretal.2001). 275 which were designated as SSTB213 J011757.75|271105.5 A and B (henceforth JO11757 A and D)., \citet{bar09} \citep{wer04} $2\farcs5$ which were designated as SSTB213 J041757.75+274105.5 A and B (henceforth J041757 A and B). Although spectroscopy Was un:wailable for these objects. Barracdoetal.(2009). conclued that the proper motion of the A coniponenut supports its membership in Taurus aud that the colors of the B component are inconsistent with a ealaxy. which is the primary source of contamination m a survey for protostellar brown clwarts.," Although spectroscopy was unavailable for these objects, \citet{bar09} concluded that the proper motion of the A component supports its membership in Taurus and that the colors of the B component are inconsistent with a galaxy, which is the primary source of contamination in a survey for protostellar brown dwarfs." We have performed IR spectroscopy on CAITA Tan 1 and JOLL757 A to determine whether they are voung brown dwarfs., We have performed IR spectroscopy on CAHA Tau 1 and J041757 A to determine whether they are young brown dwarfs. We also have used the available colors aud proper motion measurcments for these two objects aud the remaining candidates from Quauzctal.(2010) aud Barracdoetal.(2009). to determine if they are likely to be substellar1iemibers of Taurus., We also have used the available colors and proper motion measurements for these two objects and the remaining candidates from \citet{qua10} and \citet{bar09} to determine if they are likely to be substellarmembers of Taurus. We obtained low-resolution near-IR spectra of CATIA Tau 1 and JO11757 A with SpeXN (Ravuerctal.2003) at the NASA Infrared Telescope Facility (RTF)., We obtained low-resolution near-IR spectra of CAHA Tau 1 and J041757 A with SpeX \citep{ray03} at the NASA Infrared Telescope Facility (IRTF). We used the prism mode of SpeX with a 078 slit. which xovided a waveleugth coverage of 0.8-2.5 aand a resolution of R—150.," We used the prism mode of SpeX with a $0\farcs8$ slit, which provided a wavelength coverage of 0.8-2.5 and a resolution of $R\sim150$." We collected 12 and 16 exposures of CAITÀ Tau 1 on the nights of 2010 January 3 and L. respectively. and 20 exposures of J011757 A ou he night of 2010 January 16.," We collected 12 and 16 exposures of CAHA Tau 1 on the nights of 2010 January 3 and 4, respectively, and 20 exposures of J041757 A on the night of 2010 January 16." The images had exposure iues of 90 5 aud were taken durius dither sequences οποσα two positious along the slit., The images had exposure times of 90 s and were taken during dither sequences between two positions along the slit. The observatious of CATIA Tau 1 were performed with the slit rotated to the xwallactie angle., The observations of CAHA Tau 1 were performed with the slit rotated to the parallactic angle. For J011757. A. we aligued the slit so hat it enconrpassed the A aud B sources sinmultaueously.," For J041757 A, we aligned the slit so that it encompassed the A and B sources simultaneously." Spectra that are not obtained at the parallactic angele are susceptible to waveleneth-dependent slit losses. but such losses should be neglieible for the observations of J011757 since they were performed at a ταν low aninass (< 1.03).," Spectra that are not obtained at the parallactic angle are susceptible to wavelength-dependent slit losses, but such losses should be negligible for the observations of J041757 since they were performed at a very low airmass $\leq1.03$ )." These data were reduced with the Spextool package (Cushingetctal.22001) ancll correctted for Spextooltelluric packageabsorption (Vaccactal.2003)., These data were reduced with the Spextool package \citep{cus04} and corrected for telluric absorption \citep{vac03}. . The average sigual-to-noise ratios were ~230 and 12 per pixel for CATIA Tau 1 and JOLLT5S7 A. respectively.," The average signal-to-noise ratios were $\sim30$ and 12 per pixel for CAHA Tau 1 and J041757 A, respectively." We scotled the reduced spectra to a slightlylower resolution (R~ 135) to nuprove these ratios., We smoothed the reduced spectra to a slightlylower resolution $R\sim135$ ) to improve these ratios. The resulting spectra for (‘ATTA Tau 1 and JOLIT57 A are presented in Figure[m] 1..., The resulting spectra for CAHA Tau 1 and J041757 A are presented in Figure \ref{fig:spec}. . A, A with We follow the evolution of the electron and positron spectra to Lorentz factors of 3. below which the bremsstrahlung emissivity is not caleulated and the annihilation spectrum is derived in the non-relativistic limit.,"with We follow the evolution of the electron and positron spectra to Lorentz factors of 3, below which the bremsstrahlung emissivity is not calculated and the annihilation spectrum is derived in the non-relativistic limit." Synchrotron emission can be expected in the optical to X- frequency range., Synchrotron emission can be expected in the optical to X-ray frequency range. For head-on jets synchotron emission may be observable at X-ray energies., For head-on jets synchotron emission may be observable at X-ray energies. " The peak of the observed synchrotron spectra inv Ε,, representation scales roughly as with D denoting the Doppler factor. but free-free absorption and the Razin-Tsytovich effect. in addition to synchrotron self-abssorpttion. would inhibit strong synchrotron emission in the near infrared and at lower frequencies."," The peak of the observed synchrotron spectra in $\nu F_\nu$ representation scales roughly as with $D$ denoting the Doppler factor, but free-free absorption and the Razin-Tsytovich effect, in addition to synchrotron tion, would inhibit strong synchrotron emission in the near infrared and at lower frequencies." Radio emission may become observable at later phases. when the blast wave has decelerated and the Doppler factor is reduced. or when the blast wave medium its diluted. e.g. as a result of imperfect collimation.," Radio emission may become observable at later phases, when the blast wave has decelerated and the Doppler factor is reduced, or when the blast wave medium is diluted, e.g. as a result of imperfect collimation." " The peak of the observed z""-decay spectrum in. ΡΕ, representation scales as Comparing Eqs.(10199 and (102)) we see that hard X- synchrotron emission as apparently observed from the BL Lacertae object Mkn 501 (Pian et al. 1998))", The peak of the observed $\pi^0$ -decay spectrum in $\nu F_\nu$ representation scales as Comparing \ref{symax}9 9 and \ref{pimax}) ) we see that hard X-ray synchrotron emission as apparently observed from the BL Lacertae object Mkn 501 (Pian et al. \cite{pia98}) ) " implies that the vF,, peak of the high energy emission is located far in the TeV range of the spectrum.", implies that the $\nu F_\nu$ peak of the high energy emission is located far in the TeV range of the spectrum. At this point we like to issue a warning to the reader. that one has to be careful when comparing the model spectra to actual data.," At this point we like to issue a warning to the reader, that one has to be careful when comparing the model spectra to actual data." The TeV spectra of real sources. even the closeby ones. are modulated during the passage through the intergalactic medium. for the photons undergo pair production in collision with infrared background photons.," The TeV spectra of real sources, even the closeby ones, are modulated during the passage through the intergalactic medium, for the photons undergo pair production in collision with infrared background photons." Unfortunately the intergalactic infrared background spectra. and thus the magnitude and the energy dependence of the optical depth. are not well known.," Unfortunately the intergalactic infrared background spectra, and thus the magnitude and the energy dependence of the optical depth, are not well known." The current limits are compatible with severe absorption at all energies above | TeV even for Mkn 421 and Mkn 501., The current limits are compatible with severe absorption at all energies above 1 TeV even for Mkn 421 and Mkn 501. " Therefore. model spectra which display av F;,, peak at 10 TeV are not incompatible with the observed peak energies in the range of ~ 0.5 TeV for Mkn 421 and Mkn 501."," Therefore, model spectra which display a $\nu F_\nu$ peak at 10 TeV are not incompatible with the observed peak energies in the range of $\sim$ 0.5 TeV for Mkn 421 and Mkn 501." In Fig., In Fig. 4. we show the spectral evolution of high energy emission from a collimated blast wave for a homogeneous external medium., \ref{speca} we show the spectral evolution of high energy emission from a collimated blast wave for a homogeneous external medium. Even for very moderate ambient gas densities the high energy emission will be very intense., Even for very moderate ambient gas densities the high energy emission will be very intense. Some general characteristics of our model are visible in this figure., Some general characteristics of our model are visible in this figure. " The z""- component dominates the bolometric luminosity.", The $\pi^0$ -decay component dominates the bolometric luminosity. This is a direct consequence of the hadronic origin of emission. as the source power available to the leptonic emission processes Is always less than the pion source power. for the neutrinos carry away part of the energy.," This is a direct consequence of the hadronic origin of emission, as the source power available to the leptonic emission processes is always less than the pion source power, for the neutrinos carry away part of the energy." " The energy loss time scale of the high energy electrons is always smaller than that of the protons. and therefore the X-ray synchrotron intensity will follow dlosely variations in the TeV z""-decay emission."," The energy loss time scale of the high energy electrons is always smaller than that of the protons, and therefore the X-ray synchrotron intensity will follow dlosely variations in the TeV $\pi^0$ -decay emission." Thus there shoulc be a general, Thus there should be a general the classification. procedure based on (X. eriteria defined. by Schuster et al. (,the classification procedure based on $X$ criteria defined by Schuster et al. ( (1993).,1993). The only expection might be IID. 16623: its afe is low by a factor of 1.5 relative to the seven other thick- stars in Fable 3., The only expection might be HD 16623; its $\alpha/Fe$ is low by a factor of 1.5 relative to the seven other thick-disk stars in Table 3. Phe kinematics and photometric (anc μα»ectroscopic) MILI] abundance of LED. 16623 indicate tha this star is a a member of the thick disk., The kinematics and photometric (and spectroscopic) [M/H] abundance of HD 16623 indicate that this star is a a member of the thick disk. Phe mean aFe] of —ID 16623 is low due to its Ca/Fe] and Ti/Fe] abundances. which are more similar to that of the thin disk. whereas its Mg/Fe] abundance is higher and more similar to tha of the thick disk.," The mean $[\alpha/Fe]$ of HD 16623 is low due to its [Ca/Fe] and [Ti/Fe] abundances, which are more similar to that of the thin disk, whereas its [Mg/Fe] abundance is higher and more similar to that of the thick disk." This star is perhaps transitional between the thick and thin clisks. with a more mixed chemical anc dynamical history.," This star is perhaps transitional between the thick and thin disks, with a more mixed chemical and dynamical history." Another star which stands out in Table 3. and also in Vig.," Another star which stands out in Table 3, and also in Fig." 6. is HD 104556.," 6, is HD 104556." " Its NY. MZHos. and W (= 115 km +. from ""Table 2) values would all indicate a (thick) clisk star while its μα value (174 km 1) is more indicative of the halo."," Its $X$, $[M/H]_{phot}$, and W' (= +15 km $^{-1}$, from Table 2) values would all indicate a (thick) disk star while its $V_{\rm rot}$ value (+74 km $^{-1}$ ) is more indicative of the halo." For example. from Table 5 of Schuster et. al. (," For example, from Table 5 of Schuster et al. (" 1993) the V4. value of LID 104556 is 2.16. removed from the mean value of the thick disk. but only 0.5o. [rom tha of the halo.,"1993) the $V_{\rm rot}$ value of HD 104556 is $2.1\sigma$ removed from the mean value of the thick disk, but only $0.5\sigma$ from that of the halo." Other studies have also given compositions for LD 104556 whieh are more thick-disk-like than halo-Llike. such as Frick (1987). who gives efit]=0.64 dex. anc Eeeen (1997). who gives Fef1]=0.55 dex.," Other studies have also given compositions for HD 104556 which are more thick-disk-like than halo-like, such as Friel (1987), who gives $[Fe/H] = -0.64$ dex, and Eggen (1997), who gives $[Fe/H]=-0.55$ dex." Fhese stars point out the risks in using only a sinele parameter. such as X. FeflH]. or a/Fe]. to derive the population type of an individual star. and also show that some stars do no fit cleanly into any one population tvpe. according to al criteria.," These stars point out the risks in using only a single parameter, such as $X$, [Fe/H], or $[\alpha/Fe]$, to derive the population type of an individual star, and also show that some stars do not fit cleanly into any one population type, according to all criteria." lig., Fig. S shows the position of all the thin-disk stars in our sample. with a mean metal abundance of dex for the metallicity range 043=-0.04$ dex for the metallicity range $-0.43\leq [M/H] \leq +0.35$ dex, as compared with the isochrones of VandenBerg (2003) as transformed to the $uvby$ photometry by Clem et al. (" 2004).,2004). Lt is seen that the majority of the stars are clistributecl inside the isochrones., It is seen that the majority of the stars are distributed inside the isochrones. Possible systematic shifts between the isochrones ancl the positions of the redder main-sequence stars have been examined. and no need. for systematic corrections was found.," Possible systematic shifts between the isochrones and the positions of the redder main-sequence stars have been examined, and no need for systematic corrections was found." Lt is also conspicuous that a [ew stars with the values of (6ye20.44 and Aly24.5 fie off the isochrone grid. Le. ages 216 Cr.," It is also conspicuous that a few stars with the values of $(b-y)_{o}\ga 0.44$ and $M_{\rm V}\ga 4.5$ lie off the isochrone grid, i.e. ages $\ga 16$ Gyr." These may be unidentified binary stars., These may be unidentified binary stars. ]|sochrone ages are determined. by placing the stars in observational Εν cüagrams (such as Fig., Isochrone ages are determined by placing the stars in observational HR diagrams (such as Fig. S) using the observed. Ay. (bHU). values for cach star. and then reading olf the age of the star by interpolating between the theoretically computed. isochrones.," 8) using the observed $M_{\rm V}$, $(b-y)_{o}$ values for each star, and then reading off the age of the star by interpolating between the theoretically computed isochrones." “Lhe isochrones of VandenBere (2003) as transformed to the weby system by the colour-tempoerature relations of Clem et al. (, The isochrones of VandenBerg (2003) as transformed to the $uvby$ system by the colour-temperature relations of Clem et al. ( 2004) have been chosen for the age determination of the thin-disk stars.,2004) have been chosen for the age determination of the thin-disk stars. These icby isochrones cover the range 0.60[0.50 dex and ages from 1 to 20 ον in 1 Car steps., These $uvby$ isochrones cover the range $-0.60<[M/H]<+0.50$ dex and ages from 1 to 20 Gyr in 1 Gyr steps. Whereas. for the age determination of the thick-disk and halo stars. which are separated according to the .X criterion. the set of isochrones [rom Berebusch VaneenBere (2001). as transformed. by the same colour-temperature relations. have been used.," Whereas, for the age determination of the thick-disk and halo stars, which are separated according to the $X$ criterion, the set of isochrones from Bergbusch VandenBerg (2001), as transformed by the same colour-temperature relations, have been used." This latter set of isochrones cover 2.31< dex and ages from 620 Civr in 1 Gyr steps., This latter set of isochrones cover $-2.31<[M/H]<-0.30$ dex and ages from 6–20 Gyr in 1 Gyr steps. The ages of the 22 thick-disk stars have been interpolated, The ages of the 22 thick-disk stars have been interpolated Likkpe and ry= Q.SI5kkpe at kkpce.,kpc and $r_{1}=0.815$ kpc at kpc. Phe shear laver initially expancs slowly. then goes through a phase of faster expansion before recollimating at the ened of the flaring region.," The shear layer initially expands slowly, then goes through a phase of faster expansion before recollimating at the end of the flaring region." In the outer region. the shear laver expands conically with an intrinsic hall-anele of 13.17.," In the outer region, the shear layer expands conically with an intrinsic half-angle of $13.1^{\circ}$." At the beginning of he Yering region. we assume that there is no shear laver. so we use the on-axis bulk velocity inferred. by LBO2a to characterize the jet. e;=0.776.," At the beginning of the flaring region, we assume that there is no shear layer, so we use the on-axis bulk velocity inferred by LB02a to characterize the jet, $v_{j}=0.77c$." We suppose that the shear aver makes up essentially all of the flow at the end of the ling region., We suppose that the shear layer makes up essentially all of the flow at the end of the flaring region. LDO2a infer a variation of velocity across he Low from 0.376. 0.55ce at this distance so we take a representative value of ος=0.45c., LB02a infer a variation of velocity across the flow from $0.37c$ – $0.55c$ at this distance so we take a representative value of $v_{s}=0.45c$. 7. have estimated the external density and pressure ooliles for 331 from X-ray observations., \citet{hardcastle02} have estimated the external density and pressure profiles for 31 from X-ray observations. " The density oofile is given by: where my, is the mass of a proton. ya=0.74 is the abundance of hydrogen by mass and nire) is the proton number density of the environment given by: The numerical values of the parameters are: mm ny=19.105 7. o3.=0.73. 3,= O38. we= L2kkpe.ry,=52 kkpe."," The density profile is given by: where $m_{p}$ is the mass of a proton, $\chi_{H}=0.74$ is the abundance of hydrogen by mass and $n_{e}(x)$ is the proton number density of the environment given by: The numerical values of the parameters are: $^{-3}$, $n_{g}=1.9\times10^{3}$ $^{-3}$ , $\beta_{c}=0.73$, $\beta_{g}=0.38$ , $x_{c}=1.2$ kpc, $x_{g}=52$ kpc." " Phe temperatures estimated by ? range [rom 4.9.10"" WK to 1.7107 IXIx. corresponding to ο t0 1.5.107."," The temperatures estimated by \citet{hardcastle02} range from $4.9 \times 10^6$ K to $1.7 \times 10^7$ K, corresponding to $\mathscr{R}_{e} = 5 \times 10^5$ to $1.5 \times 10^5$." Phus the approximation 1|167.%1 (Section 3.1.3) is valid to high accuracy., Thus the approximation $1+1/\mathscr{R}_{e}\approx1$ (Section 3.1.3) is valid to high accuracy. “Phe pressure is eiven by 7: where po=0.6 is the mass per particle., The pressure is given by \citet{BW93}: where $\mu=0.6$ is the mass per particle. For simplicity. weapproximate the pressure and density distributions using power-law forms: where vy is the position of the brightening point.," For simplicity, weapproximate the pressure and density distributions using power-law forms: where $x_{0}$ is the position of the brightening point." poo=216.107 and py=1.9310 ρα are the density ancl pressure at ary. respectively.," $\rho_{e,0}=2.16\times10^{-22}$ $^{-3}$ and $p_{0}=1.93\times10^{-11}$ Pa are the density and pressure at $x_{0}$, respectively." " Phe values o,=L5 and as=1.1 give good. approximations to the profiles. and we adopt them in the following calculation."," The values $\alpha_{1}=1.5$ and $\alpha_{2}=1.1$ give good approximations to the profiles, and we adopt them in the following calculation." The corresponding density ancl the pressure profiles. are compared. withthose from? in Figure 2.., The corresponding density and the pressure profiles are compared withthose from\citet{hardcastle02} in Figure \ref{density}. . Although we use an isothermal approximation in the development of our, Although we use an isothermal approximation in the development of our Physical. processes allecting satellite galaxy evolution. in their host haloes are an important component of galaxy formation in the cold dark matter (CDM) cosmogony as galaxies are built up from the assembly of small structures.,Physical processes affecting satellite galaxy evolution in their host haloes are an important component of galaxy formation in the cold dark matter (CDM) cosmogony as galaxies are built up from the assembly of small structures. This assembly includes the process of satellite: galaxies merging with their host galaxies., This assembly includes the process of satellite galaxies merging with their host galaxies. Moreover. recent CDM cosmological simulations predict the existence. of a large number of (Chignaetal.1998:WKhypinet. 1999).," Moreover, recent CDM cosmological simulations predict the existence of a large number of \citep{Ghigna98, Klypin99}." . Consequently. understanding the detailed: physical processes alfecting satellite evolution are kev ingredients to understanding galaxy formation in the C'DAL cosmogonv.," Consequently, understanding the detailed physical processes affecting satellite evolution are key ingredients to understanding galaxy formation in the CDM cosmogony." Several basic questions about satellite halo evolution remain., Several basic questions about satellite halo evolution remain. First. how is the satellite stripped?," First, how is the satellite stripped?" In other words. what parts of the initial mass distribution might persist to the present day?," In other words, what parts of the initial mass distribution might persist to the present day?" Second. what is the rate of satellite halo disruption?," Second, what is the rate of satellite halo disruption?" " ""Fhird. how does a satellite's internal structure evolve?"," Third, how does a satellite's internal structure evolve?" In a satellite-galaxy merger. the stars and gas of the satellite galaxy can be stripped and become halo stars and halo gas (e.g.Quilisetal.2000:Bullock2001).," In a satellite-galaxy merger, the stars and gas of the satellite galaxy can be stripped and become halo stars and halo gas \citep[e.g.][]{QBB00,BKW01}." . The interaction between the satellite galaxy and its host. during the course of the merger results in evolution of the satellite galaxy (e.g.Mooreetal.1996)., The interaction between the satellite galaxy and its host during the course of the merger results in evolution of the satellite galaxy \citep[e.g.][]{MKL96}. . The remaining components of the satellite galaxy merge with the host galaxy. and this merging causes the host galaxw to gain mass (e.g.Muralietal. 2002)., The remaining components of the satellite galaxy merge with the host galaxy and this merging causes the host galaxy to gain mass \citep[e.g.][]{Murali02}. . Current cosmological simulations can only provide statistical properties of subhaloes since even in the highest resolution cosmological simulations (Chignaetal.2000:etal.2008). the detailed. physical processes of individual subhalo evolution have not been accurately studied. owing to limited resolution.," Current cosmological simulations can only provide statistical properties of subhaloes since even in the highest resolution cosmological simulations \citep{Ghigna00, DLucia04, Diemand04, Gao04, OL04, Diemand.etal:07, Springel.etal:08} the detailed physical processes of individual subhalo evolution have not been accurately studied, owing to limited resolution." To investigate the physical processes in detail. we perform high resolution idealised simulations with cosmologically motivated initial conditions instead of using cosmological simulations.," To investigate the physical processes in detail, we perform high resolution idealised simulations with cosmologically motivated initial conditions instead of using cosmological simulations." In these idealised simulations. a live satellite orbits in a static host halo.," In these idealised simulations, a live satellite orbits in a static host halo." Although too simplified: to reproduce a satellites evolution in realistic detail. several authors have used. similar non-cosmological simulations to study satellite disruption. with alternative simulation methods (e.g.Llavashietal.2003:Ixazantzicis 2008)..," Although too simplified to reproduce a satellite's evolution in realistic detail, several authors have used similar non-cosmological simulations to study satellite disruption with alternative simulation methods \citep[e.g.][]{Hayashi.etal:03,Kazantzidis.etal:04,Read.etal:06, Boylan-Kolchin.Ma:07,Penarrubia.Navarro.McConnachie:08}. ." These studies have demonstrated, These studies have demonstrated (pressure) of the photosphere or the magnetic energy density in a sunspot. being the energy density of a 40 MG magnetic field!,"(pressure) of the photosphere or the magnetic energy density in a sunspot, being the energy density of a 40 MG magnetic field!" Even when the kinetic energy is converted by ablation and ram pressure to heat and kinetic energy of explosion. it is mitially spread over only a few scale heights.," Even when the kinetic energy is converted by ablation and ram pressure to heat and kinetic energy of explosion, it is initially spread over only a few scale heights." Hence the explosive airburst energy density of a comet like a Shoemaker- 9 (10% &) is about 10° erg/em* equivalent to that of a 5 kG field and still more than the thermal energy density of the photosphere., Hence the explosive airburst energy density of a comet like a Shoemaker-Levy 9 $10^{15}$ g) is about $10^6$ $^3$ equivalent to that of a 5 kG field and still more than the thermal energy density of the photosphere. Thus. while the total energy of most impacting sun-grazers Is small compared to that of large flares and CMEs their energy density ts so high that local disruption of magnetic fields and triggering of larger scale events are not impossible.," Thus, while the total energy of most impacting sun-grazers is small compared to that of large flares and CMEs their energy density is so high that local disruption of magnetic fields and triggering of larger scale events are not impossible." Our simple analytic treatment of comet nucleus sublimation gives results for mass loss in reasonable agreement with previous numerical simulations., Our simple analytic treatment of comet nucleus sublimation gives results for mass loss in reasonable agreement with previous numerical simulations. We have proved that nuclet reaching p=αλ.\propto v^{-x}$ at non-relativistic velocities." ∙∙ Whileannt it is conunon to assunie ο=0. anv new particle⋅ candidates. with. «=:1 have )oen proposed (e.g. Tisano. et al.," While it is common to assume $x=0$, many new particle candidates with $x=1$ have been proposed (e.g. Hisano et al." .2001: Profumo. 2005: Lattanzi Silk 2008)., 2004; Profumo 2005; Lattanzi Silk 2008). " Tere weshall assume that 6 cau ake anv value in the plhivsicallv. plausible rauge pour<2,", Here weshall assume that $x$ can take any value in the physically plausible range $0\leq x<2$. After decoupling from radiation matter density drops to a point when the annihilation time-scale. fanny=Gre(annt))1> becomes longer than the Hubble time. so that the comoving density is frozen.," After decoupling from radiation matter density drops to a point when the annihilation time-scale, $t_{ann}=(n_x \left<\sigma_{ann} v\right>)^{-1}$, becomes longer than the Hubble time, so that the comoving density is frozen." " As long as the density feld remains nearlyο... homogeueousCOTO EEwith theB densitywyeity= aud velocitsτονtye dispersion falling respectively asa and «a with the increasing scale factor. a. tanaΗμ], coutinues to rise."," As long as the density field remains nearly homogeneous with the density and velocity dispersion falling respectively as $a^{-3}$ and $a^{-2}$ with the increasing scale factor, $a$, $t_{ann}/t_{Hubble}$ continues to rise." However. this treud is reversed after matter collapses iuto halos.," However, this trend is reversed after matter collapses into halos." " Iuside an isolated eravitationally bound halos both the local density and velocity dispersionco remain roughly constant. freezing.M,HOx theH growthOy,7 of: fj,, untilH ifH becomesmEIT comparable wih Fase."," Inside an isolated gravitationally bound halos both the local density and velocity dispersion remain roughly constant, freezing the growth of $t_{ann}$ until it becomes comparable with $t_{Hubble}$." At this point à halo would start losing ass at a significant rate via particle annihilation., At this point a halo would start losing mass at a significant rate via particle annihilation. The subsequent halo evolution of cau be described as following., The subsequent halo evolution of can be described as following. The mass loss from particle annihilation and the resulting decrease of binding energv would cause the halo to expand. so that the annihilation time-scale tracks the age of the halo.," The mass loss from particle annihilation and the resulting decrease of binding energy would cause the halo to expand, so that the annihilation time-scale tracks the age of the halo." Because the dvuaudüe time is much shorter than fine the halo always remains close to dynamical equilibriunu.," Because the dynamic time is much shorter than $t_{Hubble}$, the halo always remains close to dynamical equilibrium." " Since the gravitational binding cucerey is- proportional. to E,«xDM/Ti where M aud R are the total mass and the radius of the halo. chaugiugSm1 the] assWM and radius⋅⊀⋅↴ by- dA aud; dA2 respectively, changes Ly 15 The change of halo kinetic energv. £j. iu the aunihilatiou process depends ou the velocity dependence of Fann aud. the particle velocity distribution."," Since the gravitational binding energy is proportional to $E_g\propto M^2/R$, where $M$ and $R$ are the total mass and the radius of the halo, changing the mass and radius by $dM$ and $dR$ respectively, changes $E_g$ by The change of halo kinetic energy, $E_k$ , in the annihilation process depends on the velocity dependence of $\sigma_{ann}$ and the particle velocity distribution." Asstuning Maxwell-Boltziium distribution.," Assuming Maxwell-Boltzmann distribution," therefore be easy to detect. but this was not the case.,"therefore be easy to detect, but this was not the case." In the second. or distant-slab model. one expects very little change of surface brightness with time. since the echo light is essentially forward seattering at all times. however this is not observed.," In the second, or distant-slab model, one expects very little change of surface brightness with time, since the echo light is essentially forward scattering at all times, however this is not observed." Given the slab models” Inconsistencies with distance to the star and dust scattering properties. we consider that the slab does not appear to be a good approximation to the 3-dimensional dust structure and we will focus on the spherical or quasi spherical dust shell.," Given the slab models' inconsistencies with distance to the star and dust scattering properties, we consider that the slab does not appear to be a good approximation to the 3-dimensional dust structure and we will focus on the spherical or quasi spherical dust shell." A plot showing the angular radit measured and the best fits is presented in Fig., A plot showing the angular radii measured and the best fits is presented in Fig. 4 An Issue that might require some discussion is the fact that some echoes are fainter than others of similar age.," \ref{fig4} An issue that might require some discussion is the fact that some echoes are fainter than others of similar age." This can be explained by the different intensity of the outbursts that give rise to the echoes., This can be explained by the different intensity of the outbursts that give rise to the echoes. In fact. the farthest (and oldest) echoes from the star were only visible from the largest outburst (the one that took place around 10th of August 2007).," In fact, the farthest (and oldest) echoes from the star were only visible from the largest outburst (the one that took place around 10th of August 2007)." Echoes as old as 40 days could only be seen from the August IOth outburst because it was extraordinarily bright (as is demonstrated in the light curve of 3)) compared to the others., Echoes as old as 40 days could only be seen from the August 10th outburst because it was extraordinarily bright (as is demonstrated in the light curve of \ref{fig3}) ) compared to the others. Echoes as old as these were not seen in our data from the other outbursts because a much more sensitive instrument would have been needed., Echoes as old as these were not seen in our data from the other outbursts because a much more sensitive instrument would have been needed. Although the echoes appear to have an overall circular or ring aspect. the flux is generally restricted to the northern half of the image. with a notable lack of echo flux toward the southeast.," Although the echoes appear to have an overall circular or ring aspect, the flux is generally restricted to the northern half of the image, with a notable lack of echo flux toward the southeast." This could imply a lack of significant circumstellar dust to the south of S CrA. or perhaps interstellar dust could be selectively blocking the light from the echoes toward the south east direction.," This could imply a lack of significant circumstellar dust to the south of S CrA, or perhaps interstellar dust could be selectively blocking the light from the echoes toward the south east direction." The existence of an outflow in exactly that direction was shown by Wangetal.(2004) and thus. it is possible that such outflow is sweeping any dust.," The existence of an outflow in exactly that direction was shown by \cite{Wang2004} and thus, it is possible that such outflow is sweeping any dust." Therefore it must be stressed that the spherical shell that We propose as the best first order approximation cannot be a complete sphere because we do not see complete rings but ares., Therefore it must be stressed that the spherical shell that we propose as the best first order approximation cannot be a complete sphere because we do not see complete rings but arcs. What is the origin of the dust?., What is the origin of the dust?. The most straightforward interpretation is that such dust is the remains of the stellar envelope. which would still be dense enough for a star as young as ο CrA. Even though Carmonaetal.(2007) quote an age for S CrA of around 2 Myear and for that age the envelope and protoplanetary disk should have dissipated already. in their paper Carmonaetal.(2007) implicitly admit that the resolution of their spectra is too low to detect the photospheric spectrum of this object.," The most straightforward interpretation is that such dust is the remains of the stellar envelope, which would still be dense enough for a star as young as S CrA. Even though \cite{Carmona2007} quote an age for S CrA of around 2 Myear and for that age the envelope and protoplanetary disk should have dissipated already, in their paper \cite{Carmona2007} implicitly admit that the resolution of their spectra is too low to detect the photospheric spectrum of this object." High resolution echelle spectra which show the photospheric spectrum (Appenzelleretal.1986).. give a lower photospheric temperature. which results in à lower age than estimated by Carmonaetal.(2007).," High resolution echelle spectra which show the photospheric spectrum \citep{Appen1986}, give a lower photospheric temperature, which results in a lower age than estimated by \cite{Carmona2007}." . Jost estimates result in ~ 0.5 Myear or lower., Most estimates result in $\sim$ 0.5 Myear or lower. A young age is also indicated by the strong mm and sub-mm dust emission (Reipurthetal.1993:Chinietal.2003:Nutter2005:Juvela 2009).. the presence of an HH flow (HH 82) and the high and variable mass aceretion rate (e.g.Walter&Miner2005).," A young age is also indicated by the strong mm and sub-mm dust emission \citep{Rei1993,Chini2003,Nutter2005,Juvela2009}, the presence of an HH flow (HH 82) and the high and variable mass accretion rate \cite[e.g.][]{Walter2005}." . Nevertheless. the concentration of dust at 10* AU from the star is somewhat," Nevertheless, the concentration of dust at $10^4$ AU from the star is somewhat" "where J, is the specific intensity. ancl j, is the fluid-Iraame emissivity. given by: Integrating over all 4j, to lind the bolometric huninosity is equivalent to setting Land v=1/z: the latter procedure is done in practice.","where $I_\nu$ is the specific intensity and $j_\nu$ is the fluid-frame emissivity, given by: Integrating over all $\nu_\mathrm{cam}$ to find the bolometric luminosity is equivalent to setting $\nu_\mathrm{cam}=1$ and $\nu = 1/z$; the latter procedure is done in practice." " To set the units of the observed luminosity, we note that the units of power density are the units of energy. density (pe) divided by the unit of time (CM /e*)."," To set the units of the observed luminosity, we note that the units of power density are the units of energy density $\rho c^2$ ) divided by the unit of time $GM/c^3$ )." The end result is llowever. these units are also unnecessary. because all our results for variability will be shown in fractional terms. relative to the mean luminosity.," The end result is However, these units are also unnecessary because all our results for variability will be shown in fractional terms, relative to the mean luminosity." We are therefore left with three parameters to explore: i. 0 and 4.," We are therefore left with three parameters to explore: $\dot{m}$, $\vartheta$ and $\varphi$." We vary mr [rom a value low enough that the entire flow is optically thin up to the Edclington limit: The simulation should not be biased toward any particular pole. so we sample J only over one hemisphere. uniformly in sinv: sinilulv. (he physics of our accretion disk has no special azimuthal orientation. so any observed dependence of the light curves on y must be only statistical fInctuations.," We vary $\dot{m}$ from a value low enough that the entire flow is optically thin up to the Eddington limit: The simulation should not be biased toward any particular pole, so we sample $\vartheta$ only over one hemisphere, uniformly in $\sin\vartheta$: Similarly, the physics of our accretion disk has no special azimuthal orientation, so any observed dependence of the light curves on $\varphi$ must be only statistical fluctuations." However. our simulation domain spans only (he first quadrant in azimuthi. from 0 to 7/2.," However, our simulation domain spans only the first quadrant in azimuth, from $0$ to $\pi/2$." To cope with this limitation. we remap the densitv and velocity. data into the other quadrants. but not the emissivity.," To cope with this limitation, we remap the density and velocity data into the other quadrants, but not the emissivity." By doing so. we can compute the portion of the lieht reaching infinity [rom (his quadrant alone with a proper allowance for optical depth effects in all directions.," By doing so, we can compute the portion of the light reaching infinity from this quadrant alone with a proper allowance for optical depth effects in all directions." In principle. there are four different ways we mieht have placed the radiating quadrant with respect to the quadrants having only opacity.," In principle, there are four different ways we might have placed the radiating quadrant with respect to the quadrants having only opacity." From the expectation of azimuthal svinmetry. it then follows that a full description of (he statistical character of the light curve can be obtained from viewing (is «quadrant from only four azimuthal directions. which we choose as," From the expectation of azimuthal symmetry, it then follows that a full description of the statistical character of the light curve can be obtained from viewing this quadrant from only four azimuthal directions, which we choose as" determines the overall scaling. aud lence Iunuinositv aud QUI).,"determines the overall scaling, and hence luminosity and $Q(\mathrm{H})$." Please note that AZ; does not represent the mass of the resulting nebula. which may either be higher or lower than A4. depending on QUT) and the gas paralcters (7(1D). fa. fé; and to simaller extent Za.).," Please note that $M_\mathrm{tot}$ does not represent the mass of the resulting nebula, which may either be higher or lower than $M_\mathrm{tot}$ , depending on $Q(\mathrm{H})$ and the gas parameters $n(\mathrm{H})$, $f_\mathrm{fill}$, $f_\mathrm{cov}$ and to smaller extent $Z_\mathrm{gas}$ )." As in the Zackrissonetal.(2001) imodel. the inner radius of the ionizing cloud is set to: where £ represeuts the bolometric bDpuuinositv of the model galaxy.," As in the \citet{Zackrisson et al. a} model, the inner radius of the ionizing cloud is set to: where $L$ represents the bolometric luminosity of the model galaxy." This gives au effective. mean ionization paralucter in the same range as observed iu local IIT reeious (Ixewley&Dopita2002).. if fay=0.01 aud BE)=100 7.," This gives an effective mean ionization parameter in the same range as observed in local HII regions \citep{Kewley & Dopita}, if $f_\mathrm{fill}=0.01$ and $n(\mathrm{H})=100$ $^{-3}$." Throughout this paper. we adopt Mag=10°AL... to reflect the likely stellar population masses of the faintest ealaxies detectable with IWST (see Sect. D).," Throughout this paper, we adopt $M_\mathrm{tot}=10^6\ M_\odot$, to reflect the likely stellar population masses of the faintest galaxies detectable with JWST (see Sect. \ref{masslimits}) )." " Ποπονο, we have verified that the resulting JIWST colours remain practically unchanged for objects that are a up to a factor of ~107 more massive."," However, we have verified that the resulting JWST colours remain practically unchanged for objects that are a up to a factor of $\sim 10^3$ more massive." While dust extinction is not expected to be preseut during the very fist star formation episode of pop HI ealaxies. if niav well become portant after à few My. when pair-instability supernovac from 260AL. stars or type II supernovae with AL«50AZ. GassLineal.2002). release them uucleosvuthesis vields iuto the suroundiues.," While dust extinction is not expected to be present during the very first star formation episode of pop III galaxies, it may well become important after a few Myr, when pair-instability supernovae from $260 \ M_\odot$ stars or type II supernovae with $M<50 \ M_\odot$ \citep[mass limits valid in the absence of stellar rotation;][]{Heger et al.} release their nucleosynthesis yields into the surroundings." In pop IL/I galaxies. extinction is likely to be relevant at all ages.," In pop II/I galaxies, extinction is likely to be relevant at all ages." To allow for the treatineut of dust extinction. Yeedrasib allows a choice of four different dust-correction recipes: the AG. Was. LMC. SAIC (Pei1992) and Calzetti(1997) attenuation models.," To allow for the treatment of dust extinction, Yggdrasil allows a choice of four different dust-correction recipes: the Milky Way, LMC, SMC \citep{Pei} and \citet{Calzetti} attenuation models." Iu the latter case. corrections are applied separately to the nebular aud stellar contributions to the SED. so that the nebular eudssion experiences a higher extinction.," In the latter case, corrections are applied separately to the nebular and stellar contributions to the SED, so that the nebular emission experiences a higher extinction." All dust extinction corrections are applied after the nebular SED has been generated., All dust extinction corrections are applied after the nebular SED has been generated. This is equivalent to assuimiug that the dust is located outside the WIT region. aud hence does not affect the Lxiuau continuum flux prior to eas absorption.," This is equivalent to assuming that the dust is located outside the HII region, and hence does not affect the Lyman continuum flux prior to gas absorption." This is reasonable assumption. at least for voung pop IIT ealaxics experiencing a brief star formation episode. since no current models precict dust formation in the iunnediate vieciuities of pop III stars.," This is reasonable assumption, at least for young pop III galaxies experiencing a brief star formation episode, since no current models predict dust formation in the immediate vicinities of pop III stars." Nebular cussion typically has a strong oenupact on the SEDs of vouug or star-forming galaxies. and the relative coutributiou from nebulu eas is expected to become stronecr if the metallicity becomes very low or if the IAIF turus more top-heavy (Schacrer2002.2003: 2010b)..," Nebular emission typically has a strong impact on the SEDs of young or star-forming galaxies, and the relative contribution from nebular gas is expected to become stronger if the metallicity becomes very low or if the IMF turns more top-heavy \citep{Schaerer a,Schaerer b,Raiter et al. b}. ." This is demonstrated in Fie. 1..," This is demonstrated in Fig. \ref{spectra}," where we compare the rest-frame SEDs of 1 Myr old SSP amodels for à pop I galaxy (Z=0.020. Kroupa2001 IMFE) and a pop IILI galaxy.," where we compare the rest-frame SEDs of 1 Myr old SSP models for a pop I galaxy $Z=0.020$, \citealt{Kroupa} IMF) and a pop III.1 galaxy." In both cases. the blue line represeuts the purely stellar SEDs whereas the red line describes the total SED. ic. the SED including both stellar and uebulu contributions.," In both cases, the blue line represents the purely stellar SEDs whereas the red line describes the total SED, i.e. the SED including both stellar and nebular contributions." The nebular conrponeut completely transforms the appearance of the SED for both tvpes of galaxies. but the rolative contribution of nebular emission becomes much stronger for the zeroauetallicitv. top-heavy IAIF object (pop IIL1).," The nebular component completely transforms the appearance of the SED for both types of galaxies, but the relative contribution of nebular emission becomes much stronger for the zero-metallicity, top-heavy IMF object (pop III.1)." As we have argued in several previous papers (e.g.Za-ckrissonuetal.2008:Schacrer&deBarros2009.2010).. the flux boost due to plhotoiouized eas cau also have a notable inpact ou the broadbaud fluxes of high-redshift ealaxies.," As we have argued in several previous papers \citep[e.g.][]{Zackrisson et al. b,Schaerer & de Barros a,Schaerer & de Barros b}, the flux boost due to photoionized gas can also have a notable impact on the broadband fluxes of high-redshift galaxies." In Fig., In Fig. 2aa. we clemoustrate this bv plotting the ratio of nebula to stellar fux. fuafaa da the JIWST/NTRCan ΕΤΩΝ filter (at Ltt jan) as function of vedshitt (withiu the rauge :=0 20) for newboru (age 1 Myr). galaxies with SEDs representative of pop I(Z =0020). pop II (Z=0.0001). pop III with lroupa(2001) IME. pop IIL2 aud pop IIL1 SEDs. assuming au iustantauecous burst.," \ref{fneb}a a, we demonstrate this by plotting the ratio of nebular to stellar flux, $f_\mathrm{neb}/f_\mathrm{stars}$, in the JWST/NIRCam F444W filter (at 4.44 $\mu$ m) as function of redshift (within the range $z=0$ –20) for newborn (age 1 Myr), galaxies with SEDs representative of pop I $Z=0.020$ ), pop II $Z=0.0004$ ), pop III with \citet{Kroupa} IMF, pop III.2 and pop III.1 SEDs, assuming an instantaneous burst." Nebular ciissiow is seen to dominate the flix iu this filter at all redshifts considered for the pop III models., Nebular emission is seen to dominate the flux in this filter at all redshifts considered for the pop III models. As expected. the liehest ινἕως are produced by the pop ILI IME (cvan line). followed by the pop IIL.2 IAIF (blue line) and pop HT witha I&roupa(2001) TAIF (green liuc).," As expected, the highest $f_\mathrm{neb}/f_\mathrm{stars}$ are produced by the pop III.1 IMF (cyan line), followed by the pop III.2 IMF (blue line) and pop III with a \citet{Kroupa} IMF (green line)." The pop II (red liue) and pop I inodels (black line) produce sienificautly lower iouiziug fluxes per wait mass., The pop II (red line) and pop I models (black line) produce significantly lower ionizing fluxes per unit mass. The bumps aud wieegles aloug the lines in Fie., The bumps and wiggles along the lines in Fig. 2aa are produced when various cluission lines aud continu features redshift in and out of the filter., \ref{fneb}a a are produced when various emission lines and continuum features redshift in and out of the filter. The παρ at DocDOT is due to the Πα line at 6563À.. and the exteusion of this bump to :z9 in the case of the pop Il galaxy is primarily duc to the [OTH line at 5007A.. which is strong at low to intermediate moetallicities. weak in hiel-inetallicity objects and completely issue frou pop III spectra due to lack of moetals iu these objects. as further discussed in Sect. 5..," The bump at $z\approx 5$ –7 is due to the $\alpha$ line at 6563, and the extension of this bump to $z\approx 9$ in the case of the pop II galaxy is primarily due to the [OIII] line at 5007, which is strong at low to intermediate metallicities, weak in high-metallicity objects and completely missing from pop III spectra due to lack of metals in these objects, as further discussed in Sect. \ref{typeA}." " The overall merease in fuafora, towards verv low redshifts is due to the very cifferent spectral slopes of the stellar aud. nebular contimuun at rest-frame wavelengths above 101 (seo Fig. 1)).", The overall increase in $f_\mathrm{neb}/f_\mathrm{stars}$ towards very low redshifts is due to the very different spectral slopes of the stellar and nebular continuum at rest-frame wavelengths above $10^4$ (see Fig. \ref{spectra}) ). Iu Fig., In Fig. 2bb. we plot the fua;faas. ratio at +=10 as a function of age for the same instantancous-burst models as in Fie.," \ref{fneb}b b, we plot the $f_\mathrm{neb}/f_\mathrm{stars}$ ratio at $z=10$ as a function of age for the same instantaneous-burst models as in Fig." 2aa. At an age of 1 Myr. going from a Iroupa(2001) IMFE pop I (black lino) to a pop II (red line) iereases the Έριςfas ratio by a factor of zz2.5. and going froma pop II to a pop III galaxy. (ereen lino) boosts fuiffaa by au additionalfactor of zL.," \ref{fneb}a a. At an age of 1 Myr, going from a \citet{Kroupa} IMF pop I (black line) to a pop II (red line) increases the $f_\mathrm{neb}/f_\mathrm{stars}$ ratio by a factor of $\approx 2.5$, and going from a pop II to a pop III galaxy (green line) boosts $f_\mathrm{neb}/f_\mathrm{stars}$ by an additionalfactor of $\approx 4$." Shifting to more top-heavy IMEs (blue for pop IIL2 aud evan for pop IILI) raises fuo/faa even further., Shifting to more top-heavy IMFs (blue for pop III.2 and cyan for pop III.1) raises $f_\mathrm{neb}/f_\mathrm{stars}$ even further. These overall ratios between the models are approximately stable as a function of age. except for the pop IILI model. which evolves inch faster than the others due to the lack of stars with masses below 50AL... fading from sight after just 3 Alyy.," These overall ratios between the models are approximately stable as a function of age, except for the pop III.1 model, which evolves much faster than the others due to the lack of stars with masses below $50\ M_\odot$, fading from sight after just 3 Myr." In the case of the pop IIL2 and pop III. Iroupa(2001) IME models. it takes z12 16 My before direct star ght starts to dominate over uebular emission (thin horizoutal dashed line). and ~*~LO 50 Myr. πα nebular cussion gives a neelieible contribution.. as dudicated by the thick horizoutal dashed line) to the flux.," In the case of the pop III.2 and pop III, \citet{Kroupa} IMF models, it takes $\approx 12$ –16 Myr before direct star light starts to dominate over nebular emission (thin horizontal dashed line), and $\approx 40$ –50 Myr until nebular emission gives a negligible contribution, as indicated by the thick horizontal dashed line) to the flux." Even though Lsanan coutimmun leakage from lieh-redshiff ealaxics iuav well reduce the relative contribution from nebular emission (as further discussed below). it is clear from Fig.," Even though Lyman continuum leakage from high-redshift galaxies may well reduce the relative contribution from nebular emission (as further discussed below), it is clear from Fig." 2. that it would takea very large amount of leakage to break the dominance of nebular light in the SEDs of young pop III galaxies., \ref{fneb} that it would takea very large amount of leakage to break the dominance of nebular light in the SEDs of young pop III galaxies. For a 1l Any pop IIL1l galaxy. ωνfanc20 at 2= LO. whereas the corresponding values for pop IITL2 and pop III galaxies with a Wroupa(2001) ΤΙ are ωνaus815 and zLO respectively.," For a 1 Myr pop III.1 galaxy, $f_\mathrm{neb}/f_\mathrm{stars}\approx 20$ at $z=10$ , whereas the corresponding values for pop III.2 and pop III galaxies with a \citet{Kroupa} IMF are $f_\mathrm{neb}/f_\mathrm{stars}\approx 15$ and $\approx 10$ respectively." After LO My. pop HI galaxies with a pop IIL2or a IK&roupa(2001) ," After 10 Myr, pop III galaxies with a pop III.2or a \citet{Kroupa} " Using c=1. the electromagnetic contribution then las the same form as in Masawell’s theory the difference πιο in the connection between the vector potential aud the field given im E«q.t1)).,"Using $c=1$, the electromagnetic contribution then has the same form as in Maxwell's theory the difference lying in the connection between the vector potential and the field given in \ref{equ:Fmn-A}) )." The enerey-inoimentiuim teusor of the scalar field € is lu what follows. we use the redefined field As we consider local phenomena. we can work in a locally iuertial coordinate system.," The energy-momentum tensor of the scalar field $\epsilon$ is In what follows, we use the redefined field As we consider local phenomena, we can work in a locally inertial coordinate system." " We deuote the ""feld part of the enerey-momentium tensor"" as the scalar plus clectromaguctic energy moneutuni tensor Iu terms of c and replacing gi” with yf"". we obtain The equatious| of motion Eqs.(9)) are which can be used in Eq.(22)) obtaining Thnis expression can be simplified usinec» the homogeneous[m] Maxwell equations| which cancels out the first bracket."," We denote the “field part of the energy-momentum tensor” as the scalar plus electromagnetic energy momentum tensor In terms of $\psi$ and replacing $g^{\mu\nu}$ with $\eta^{\mu\nu}$ , we obtain The divergence of $T_{\rm f}$ is The equations of motion \ref{ecs:MovBeck}) ) are which can be used in \ref{equ:div:Tf}) ) obtaining This expression can be simplified using the homogeneous Maxwell equations which cancels out the first bracket." The first aud last terim in the second bracket also cancel out. thus we obtain for Eq.(21)) the expression We add to both sides of the equation the divergence of the eucrgy 1nonienutuni tensor of matter TAY iu order to find the enerev transter (according to the hvpothesis Sin Sect. 2..," The first and last term in the second bracket also cancel out, thus we obtain for \ref{equ:div:Tf:Subs}) ) the expression We add to both sides of the equation the divergence of the energy momentum tensor of matter ${T^{\mu\nu}_{\rm m}}_{,\nu}$ in order to find the energy transfer (according to the hypothesis 8 in Sect. \ref{sec:alfadot}," we asstume that Eimsteiuns equations hold ποαπο for the eravitatioual field aud hence that the total euergv momentum tensor is conserved) This equation explicitly shows the enerey trausfer from. the field € to matter which is the source of any observable effect., we assume that Einstein's equations hold unmodified for the gravitational field and hence that the total energy momentum tensor is conserved) This equation explicitly shows the energy transfer from the field $\epsilon$ to matter which is the source of any observable effect. " From. we find that the “machian” coutribution to cucrey transfer is given by Using Dekenstein's uotation. that is. if the time-space components of e""F"" are ideutified with E while space- components are identified with B. the coutribution then takes the formu where 8=ae "," From we find that the “machian” contribution to energy transfer is given by Using Bekenstein's notation, that is, if the time-space components of $e^{\psi}F^{\mu\nu}$ are identified with $\mathbf E$ while space-space components are identified with $\mathbf B$, the contribution then takes the form where $\mathbf S=\frac{\mathbf E \times \mathbf B}{4\pi}$." Then. the component 0 of Eq.(28)) reads Animplicit assumption of our previous analysis aud algebra is the generalized Povuting theorem.," Then, the component $0$ of \ref{div:Tm}) ) reads Animplicit assumption of our previous analysis and algebra is the generalized Poynting theorem." Iu its, In its considered.,considered. Woitke Ilelling (2004) and Ielline. Woitke Thi (2008) applied this model to the formation of stationary clouds in atmospheres including gravitational settling. element depletion. and convective element replenishment.," Woitke Helling (2004) and Helling, Woitke Thi (2008) applied this model to the formation of stationary clouds in atmospheres including gravitational settling, element depletion, and convective element replenishment." The atmosphere model (Dehn 2007. IIlelling et al.," The atmosphere model (Dehn 2007, Helling et al." 2008a.b: Witte. Helling IHauschildt 2009) couples this detailed kinetic model of dust cloud formation wilh a radiative transfer code (IIauschildi Baron 1999. Baron et al.," 2008a,b; Witte, Helling Hauschildt 2009) couples this detailed kinetic model of dust cloud formation with a radiative transfer code (Hauschildt Baron 1999, Baron et al." 2003)., 2003). We use the output of the atmosphere simulations in this paper., We use the output of the atmosphere simulations in this paper. In the number of solids growing the mantle is restricted to seven (που). AlaOs[s]. Fels]. SiOs[s]. MeOs}. MgSiOs[s]. MgoSiO;[s]) and to 32 surface reactions.," In the number of solids growing the mantle is restricted to seven $_2$ [s], $_2$ $_3$ [s], Fe[s], $_2$ [s], MgO[s], $_3$ [s], $_2$ $_4$ [s]) and to 32 surface reactions." provides the local gas temperature T [Kk]. the gas pressure paa. 7]. the maximum convective velocity vCONlux +}. and dust quantities such as the number density of dust particles n4 7] of mean grain size (a) fem] at each laver of ihe atmosphere.," provides the local gas temperature T [K], the gas pressure $p_{\rm gas}$ $^{-2}$ ], the maximum convective velocity $\rm v_{\rm conv}^{\rm max}$ $^{-1}$ ], and dust quantities such as the number density of dust particles $n_{\rm d}$ $^{-3}$ ] of mean grain size $\langle a \rangle$ [cm] at each layer of the atmosphere." Because of the definition of the dust moments. peipL;=JyyVIdy (V grain volume. Vy volume of smallest possible grain). the dust moments L; ()=1....4) that result [rom a simulations are used to derive a representative grain size distribution function (for details see Appendix A in IIelling. Woitke Thi 2003).," Because of the definition of the dust moments, $\rho L_{\rm j} = \int_{\rm V_l}^{\infty} V^{\rm j/3} f(V) dV$ $V$ – grain volume, $V_{\rm l}$ – volume of smallest possible grain), the dust moments $_{\rm j}$ $j=1, \ldots 4$ ) that result from a simulations are used to derive a representative grain size distribution function (for details see Appendix A in Helling, Woitke Thi 2008)." We consider in (his paper a double-peaked grain size distribution f(«). to calculate the relative dust velocities (Sect ??.. ??)) between grains of clifferent sizes d in each laver of the atmospheric cloud (Fig. 10)).," We consider in this paper a double-peaked grain size distribution $f(a)$, to calculate the relative dust velocities (Sect \ref{ss:dd_sed}, \ref{ss:dd_turb}) ) between grains of different sizes $a$ in each layer of the atmospheric cloud (Fig. \ref{fig:grain_size}) )." Parameters Ny. No. ay and do are determined such that the resulting dust moments reproduce the solution of the dust," Parameters $N_1$, $N_2$, $a_1$ and $a_2$ are determined such that the resulting dust moments reproduce the solution of the dust" DgvarPy]. is where B(b) is fixed by our normalization convention and absorbs all factors that co not. depend. on n. and this maximization the subdominant olf-diagonal covariances so that neglectsvarPy]=2p. (,"$P_{\rm F}^2/{\rm var}[\widehat{P}_{\rm F}]$, is where $\mathcal{B}(k_{\parallel})$ is fixed by our normalization convention and absorbs all factors that do not depend on $n$, and this maximization neglects the subdominant off-diagonal covariances so that ${\rm var}[\widehat{P}_{\rm F}] = 2 \, P_{\rm tot}^2$. (" We show in Section 24 that a simple generalization. of these weights can be casily applied to real data.),We show in Section \ref{ss:realspace} that a simple generalization of these weights can be easily applied to real data.) This choice of weights results in {πω becoming where ‘Thus. a single number. nr. characterizes the sensitivity of a Lye forest survey to Jy. and ο is a measure of the importance of cach quasar on a scale of 0 to 1.," This choice of weights results in ${P}_{\rm tot}$ becoming where Thus, a single number, $\bar{n}_{\rm eff}$, characterizes the sensitivity of a $\alpha$ forest survey to $P_{\rm F}$, and $\nu_n$ is a measure of the importance of each quasar on a scale of $0$ to $1$." While na depends on Aj. in practice this dependence is likely to be weak because Z4) has roughly a white noise power spectrum at relevant wavevectors and nar also. depends relatively weakly on {ρα ," While $\bar{n}_{\rm eff}$ depends on $k_\parallel$, in practice this dependence is likely to be weak because $P_{\rm los}(k_{\parallel})$ has roughly a white noise power spectrum at relevant wavevectors and $\bar{n}_{\rm eff}$ also depends relatively weakly on $P_{\rm los}(k_{\parallel})$ ." "Phe constaney of 3, at kox0.5 is quantified in Table 2.. which tabulates measurements of Z1. from 2? at several Ay ancl redshifts."," The constancy of $P_{\rm los}$ at $k \leq 0.5~$ $^{-1}$ is quantified in Table \ref{table:Plos}, which tabulates measurements of $P_{\rm los}$ from \citet{mcdonald05b} at several $k_{\parallel}$ and redshifts." Constancy should be an even better approximation at smaller &j than is tabulated., Constancy should be an even better approximation at smaller $k_{\parallel}$ than is tabulated. Por a DOSS-like Lye forest survey ab zo—2.5. a factor of 2 smaller 2..0h)) from its small-A) asvniptote results in only a factor of 1.4 decrease in mar.," For a BOSS-like $\alpha$ forest survey at $z=2.5$, a factor of $2$ smaller $P_{\rm los}(k_{\parallel})$ from its $k_{\parallel}$ asymptote results in only a factor of $1.4$ decrease in $\bar{n}_{\rm eff}$." The decrease is even smaller for a deeper survey., The decrease is even smaller for a deeper survey. " The gains in sensitivity to fp are meager [rom improving the S/N on a quasar once £x,

3 and z/Jx1 would successful isolate our high-redshift LBG candidates from low-redshift EROs. it also illustrates the potential or contamination by M dwarf stars (as discussed in Section 3.2.1).," Although Fig 4 suggests that traditional colour-colour selection based on $R-z^{\prime}\geq3$ and $z^{\prime}-J\leq1$ would successful isolate our high-redshift LBG candidates from low-redshift EROs, it also illustrates the potential for contamination by M dwarf stars (as discussed in Section 3.2.1)." However. once again. the location of the stacked LBG photometry on the 7?L versus τ΄J plane strongly suggests that the tinal LBG candidate list is not significantly contaminated by low-redshift interlopers.," However, once again, the location of the stacked LBG photometry on the $R-z^{\prime}$ versus $z^{\prime}-J$ plane strongly suggests that the final LBG candidate list is not significantly contaminated by low-redshift interlopers." For the purposes of obtaining a robust sample of high-redshift LBG candidates. Fig 4 further emphasises the importance of modelling the full BVR7ης)A SEDs. using both galaxy and stellar templates. rather than relying on simple colour selection.," For the purposes of obtaining a robust sample of high-redshift LBG candidates, Fig 4 further emphasises the importance of modelling the full $BVRi^{\prime}z^{\prime}JK$ SEDs, using both galaxy and stellar templates, rather than relying on simple colour-colour selection." In Table 2 we list the best-fitting galaxy template parameters resulting from the optical+near-intrared SED fits to each of the final nine high-redshift LBG candidates (as illustrated in Fig |)., In Table 2 we list the best-fitting galaxy template parameters resulting from the optical+near-infrared SED fits to each of the final nine high-redshift LBG candidates (as illustrated in Fig 1). All of the candidates have best-titting photometric redshifts in the range 5.1)ϱz«5.9. validating our original selection criteria.," All of the candidates have best-fitting photometric redshifts in the range $5.125.," By concentrating exclusively on the brightest $z^{\prime}\leq25$ ) candidates, this study was designed to investigate the most massive LBGs at $z\geq5$." The success of this policy can be seen from Table 2. which shows that six of the nine final candidates have estimated stellar masses ο«LOMXL... and five have estimated masses z10H8ML...," The success of this policy can be seen from Table 2, which shows that six of the nine final candidates have estimated stellar masses $\gtsim\, 5\times 10^{10}\Msolar$, and five have estimated masses $\gtsim\, 10^{11}\Msolar$." Tf these stellar mass estimates ure accurate. then he LBG candidates are among the most massive galaxies vet discovered at these redshifts (see discussion in Section 5). and are comparable to the highest stellar masses found for LBGs at z&3 by Shapleyet al. (," If these stellar mass estimates are accurate, then the LBG candidates are among the most massive galaxies yet discovered at these redshifts (see discussion in Section 5), and are comparable to the highest stellar masses found for LBGs at $z\simeq3$ by Shapleyet al. (" 2001). who also adopted a Salpeter IMF.,"2001), who also adopted a Salpeter IMF." " In fact. hese stellar mass estimates suggest that several of the >=5 LBG candidates have already built-up a stellar mass comparable with T4, today (71044AL.: Cole et al."," In fact, these stellar mass estimates suggest that several of the $z\geq5$ LBG candidates have already built-up a stellar mass comparable with $_{\rm{stars}}^{\star}$ today $\simeq10^{11}\Msolar$; Cole et al." 2001)., 2001). However. given the current depth of the near-infrared data rom the UDS EDR. and the fact that the SWIRE data covering he UDS field is not deep enough to individually detect the LBG candidates. it is clear that on an object-by-object basis the stellar mass estimates must be regarded with some caution.," However, given the current depth of the near-infrared data from the UDS EDR, and the fact that the SWIRE data covering the UDS field is not deep enough to individually detect the LBG candidates, it is clear that on an object-by-object basis the stellar mass estimates must be regarded with some caution." The first issue o consider is the range of stellar masses which are allowable within he SED templates we have adopted to fit the optical+near-infrared shotometry., The first issue to consider is the range of stellar masses which are allowable within the SED templates we have adopted to fit the optical+near-infrared photometry. By identifying the SED templates with the lowest and lighest masses which still provide a statistically acceptable fit to he observed photometry (conservatively A\>10. marginalised over all other free parameters}. we have calculated the allowable stellar mass range for each of the LBG candidates (Table. 2).," By identifying the SED templates with the lowest and highest masses which still provide a statistically acceptable fit to the observed photometry (conservatively $\Delta \chi^{2}\leq10$, marginalised over all other free parameters), we have calculated the allowable stellar mass range for each of the LBG candidates (Table 2)." This ealeulation reveals that the photometry of most of the LBG candidates can be acceptably reproduced (although with a worse v by SED templates with a factor of ~3 less stellar mass., This calculation reveals that the photometry of most of the LBG candidates can be acceptably reproduced (although with a worse $\chi^{2}$ ) by SED templates with a factor of $\simeq 3$ less stellar mass. In addition. there is also the added uncertainty introduced by the choice of a specitic IMF.," In addition, there is also the added uncertainty introduced by the choice of a specific IMF." For the SED tits presented in this paper we have made the standard choice of adopting a Salpeter IMF. for ease of comparison with previous results in the literature.," For the SED fits presented in this paper we have made the standard choice of adopting a Salpeter IMF, for ease of comparison with previous results in the literature." However. it is widely recognised that the Salpeter IMF results in higher stellar mass estimates than other popular choices.," However, it is widely recognised that the Salpeter IMF results in higher stellar mass estimates than other popular choices." For example. re-fitting the LBG optical+near-infrared photometry with a Kennicutt or Chabrier IMF would produce stellar mass estimates a factor of c1.5 lower.," For example, re-fitting the LBG optical+near-infrared photometry with a Kennicutt or Chabrier IMF would produce stellar mass estimates a factor of $\simeq1.5$ lower." In conclusion. it is clear that the individual stellar mass estimates for the LBG candidates are very likely uncertain to within a factor of & 5.," In conclusion, it is clear that the individual stellar mass estimates for the LBG candidates are very likely uncertain to within a factor of $\simeq5$ ." In order to obtain a more robust estimate of the typical mass, In order to obtain a more robust estimate of the typical mass following Swartz et al. (,following Swartz et al. ( 1991).,1991). " Where Lis the total Iuminositv and 75,4, Is the photospheric radius.", Where $L$ is the total luminosity and $R_{photo}$ is the photospheric radius. Finally the velocity at the photosphere. ρου is the velocity of the material at the the photosphere.," Finally the velocity at the photosphere, $_{photo}$ is the velocity of the material at the the photosphere." The models A-I] (Table I) were constructed in order to easily compare the behavior of one parameter while holding the other parameters constant., The models A-H (Table I) were constructed in order to easily compare the behavior of one parameter while holding the other parameters constant. The standard model is model D(M-16 M.. R = 430 R.) with E = 1x10°! eves. My; = 0.07 M... and Ni mixing throughout the 6 AL. core.," The standard model is model B (M = 16 $_\odot$ , R = 430 $_\odot$ ) with E = $1\times10^{51}$ ergs, $_{Ni}$ = 0.07 $_\odot$, and Ni mixing throughout the 6 $_\odot$ core." These are similar to the values of SN 1987À except with a larger radius. taking into consideration that SN 1987À might have had a nonstandard radius.," These are similar to the values of SN 1987A except with a larger radius, taking into consideration that SN 1987A might have had a nonstandard radius." Thus ] take (he standard model as having the most average values around which the parameters are varied., Thus I take the standard model as having the most average values around which the parameters are varied. " The 5 parameters are the progenitor radius. envelope mass. explosion energy. mass of Ni. and ""Ni mixing."," The 5 parameters are the progenitor radius, envelope mass, explosion energy, mass of $^{56}$ Ni, and $^{56}$ Ni mixing." All LC eraphs are plots of absolute magnitude versus time in days and all caleulations proceed to 400 days and include the observed LC of SN 19875 for comparison (Catchpoleanclothers1987)., All LC graphs are plots of absolute magnitude versus time in days and all calculations proceed to 400 days and include the observed LC of SN 1987A for comparison \citep{c87}. . Figs., Figs. 1-3 show the affects of progenitor radius. Figs.," 1-3 show the affects of progenitor radius, Figs." +6 show the affects of ejected mass. Figs.," 4-6 show the affects of ejected mass, Figs." 7-9 show the affects of explosion energy. Figs.," 7-9 show the affects of explosion energy, Figs." 10-12 show the affects of Ni mass. Figs.," 10-12 show the affects of Ni mass, Figs." 13-15 show the affects of Ni mixing., 13-15 show the affects of Ni mixing. Figs., Figs. " 1. 4. 7. 10. and 13 show bolometric and visual light curves. aud photospheric temperature aud. velocity for each of the ""affects of” series."," 1, 4, 7, 10, and 13 show bolometric and visual light curves, and photospheric temperature and velocity for each of the “affects of” series." Figs., Figs. " 2. 5. 8. 11. ancl 14. show the density aud temperature profiles for each of the ""affects of” series at times 0. 36 hours. ancl 47 days."," 2, 5, 8, 11, and 14, show the density and temperature profiles for each of the “affects of” series at times 0, 36 hours, and 47 days." Also shown is (he final velocity profile ancl the luminosity versus mass at times 94. 159. and 379 days.," Also shown is the final velocity profile and the luminosity versus mass at times 94, 189, and 379 days." Figs., Figs. " 3. 6. 9. 12. and 15. show the affects on the LC at different values of the parameters that are held constant for each of the ""affects of” series and for reference compare them to the instantaneous energy released from (he Ni-Co decay."," 3, 6, 9, 12, and 15, show the affects on the LC at different values of the parameters that are held constant for each of the “affects of” series and for reference compare them to the instantaneous energy released from the Ni-Co decay." In this way I am exploring the parameter space in (he most svstemalic wav For example. the affects of radius graphs show models with the radius ranging from 43 R. to 4300 R.while holding the envelope mass at 16 M... explosion energv αἱ {κ107! eres. nass of Ni at 0.07. AL. and the Ni mixing to 6 M...," In this way I am exploring the parameter space in the most systematic way For example, the affects of radius graphs show models with the radius ranging from 43 $_\odot$ to 4300 $_\odot$while holding the envelope mass at 16 $M_\odot$, explosion energy at $1\times10^{51}$ ergs, mass of $^{56}$ Ni at 0.07 $M{_\odot}$ and the $^{56}$ Ni mixing to 6 $M{_\odot}$." Figs., Figs. la. Lb. le. and 1d show the affects of radius on the bolometric LC. visual LC. Tyagi. and photospheric velocity respectively.," 1a, 1b, 1c, and 1d show the affects of radius on the bolometric LC, visual LC, $_{photo}$, and photospheric velocity respectively." Figs., Figs. 2a. 2c show the affects of radius on the density. temperature versus mass al ( = 0. 36 hours. and 47 davs alter explosion.," 2a, 2c show the affects of radius on the density, temperature versus mass at t = 0, 36 hours, and 47 days after explosion." Figure 2b shows the final velocity versus mass and Figure 2d shows the Iumninosi(w versus mass al ( = 94. 189. 319 days alter explosion.," Figure 2b shows the final velocity versus mass and Figure 2d shows the luminosity versus mass at t = 94, 189, 379 days after explosion." Figs., Figs. 3a. 3b. 3c.D 3d each show the affects of varying the progenitor radius when changingthe value of one parameter: ejected mass to 8 M... the explosion energy to 2x10°! eres. the," 3a, 3b, 3c, 3d each show the affects of varying the progenitor radius when changingthe value of one parameter; ejected mass to 8 $M_{\odot}$ , the explosion energy to $2\times10^{51}$ ergs, the" 3o.LAL...,"$3\times 10^{11} M_\odot$." These parameters are chosen to put the initial ealaxy on the Fundamental Plane (Djorgovski&Davis1987:Dresslerctal. 1987).. the FaberJacksou (1976) relation. aud the Magorrianetal.(1998). relation.," These parameters are chosen to put the initial galaxy on the Fundamental Plane \citep{djorgovski:87, dressler:87}, , the Faber–Jackson \citeyearpar{faber:76} relation, and the \citet{magorrian:98} relation." All of the relevant dynamical properties of the ealaxy models are given in Ciottietal.(2009a).., All of the relevant dynamical properties of the galaxy models are given in \citet{ciotti:09-dynamics}. The gas density is initially set to a very low value so that the eas in the simulation comes alinost exclusively frou explicit source ternis arising from stellar evolution., The gas density is initially set to a very low value so that the gas in the simulation comes almost exclusively from explicit source terms arising from stellar evolution. We assune reflecting boundary conditions on the Ó boundaries occuring at either pole., We assume reflecting boundary conditions on the $\theta$ boundaries occurring at either pole. On the outer radial boundary we assume that all finid quantities are constant., On the outer radial boundary we assume that all fluid quantities are constant. This allows both outflow aud inflow depenudiug ou the state of eas just inside the outer boundary., This allows both outflow and inflow depending on the state of gas just inside the outer boundary. Ou the inner radial boundary we assume reflecting boundary conditions if the iunermost radial velocity is positive., On the inner radial boundary we assume reflecting boundary conditions if the innermost radial velocity is positive. Plivsical processes that inject mass (such as the BAL wind) are handled as explicit source terms acting in the first set of radial cells., Physical processes that inject mass (such as the BAL wind) are handled as explicit source terms acting in the first set of radial cells. This allows us to casily handle the cases of very strong. very weal. and intermediate flows of energv. mass. aud momentum onto the computational exid with a sinele source terii.," This allows us to easily handle the cases of very strong, very weak, and intermediate flows of energy, mass, and momentum onto the computational grid with a single source term." If the iunerinost radial velocity is negative. we use an outflow (off of the computational exid toward the ceuter of the simulation) boundary coudition where all fluid variables are constant across the boundary.," If the innermost radial velocity is negative, we use an outflow (off of the computational grid toward the center of the simulation) boundary condition where all fluid variables are constant across the boundary." The one exception iu this case is the radial velocity itself., The one exception in this case is the radial velocity itself. Tf the cellis aside the locally estimated Boudi radius (that is. the Boudi radius has been resolved). then no nuit is imposed upou the inflow velocity.," If the cell is inside the locally estimated Bondi radius (that is, the Bondi radius has been resolved), then no limit is imposed upon the inflow velocity." However. if the cell is outside the locally estimated Bondi radius (the Bondi radius is unresolved). then the radial velocity is hnüted to the velocity that would result i mass transport consistent with the Boucdi accretion rate.," However, if the cell is outside the locally estimated Bondi radius (the Bondi radius is unresolved), then the radial velocity is limited to the velocity that would result in mass transport consistent with the Bondi accretion rate." That is As discussed above. we are careful to resolve the Doudi radius even for gas heated to the maxima expected temperature for Παπιο gas. the Compton temperature.," That is As discussed above, we are careful to resolve the Bondi radius even for gas heated to the maximum expected temperature for infalling gas, the Compton temperature." However. the BAL wind has an even higher specific cuerev.," However, the BAL wind has an even higher specific energy." Typically. the BAL wind is flowing strouelv outward and the Boudi radius is always resolved.," Typically, the BAL wind is flowing strongly outward and the Bondi radius is always resolved." " However, it is possible for the wind to fill the tuner region of the galaxy with gas heated above the Compton teiiperature."," However, it is possible for the wind to fill the inner region of the galaxy with gas heated above the Compton temperature." In this case. Equation (22)) cusures that the SMDIT accretion rate is reduced accordingly.," In this case, Equation \ref{eq:bondi-boundary-condition}) ) ensures that the SMBH accretion rate is reduced accordingly." Tt is unfortunately not possible to cleanly separate the SMDITI scales from the galactic ones;, It is unfortunately not possible to cleanly separate the SMBH scales from the galactic ones. Physically. this is because the source of eas in the galaxw is the stars. evolving on galactic timescales.," Physically, this is because the source of gas in the galaxy is the stars, evolving on galactic timescales." \[eauwhile. the SMDBIT is casily able to affect eas ou kiloparsec scales.," Meanwhile, the SMBH is easily able to affect gas on kiloparsec scales." This ties the scales together in a feedback loop that cannot be easily separated into two separate simulations. or a simulation plus a sub-erid model.," This ties the scales together in a feedback loop that cannot be easily separated into two separate simulations, or a simulation plus a sub-grid model." Furthermore. the classic Bouci solution is for the simple case of a point mass.," Furthermore, the classic Bondi solution is for the simple case of a point mass." If the mass enclosed by the Boudi radius is dominated by the ealaxy rather than the central DIT. then the classic Boudi solution is modified. particularly if the galactic mass is not spherically sviuimetric.," If the mass enclosed by the Bondi radius is dominated by the galaxy rather than the central BH, then the classic Bondi solution is modified, particularly if the galactic mass is not spherically symmetric." The character of the SMBIT accretion changes dramatically in goie from one to two dimensions., The character of the SMBH accretion changes dramatically in going from one to two dimensions. Iu oue dimension. accretion events happen when a cold shell of eas forms at & 100 pc.," In one dimension, accretion events happen when a cold shell of gas forms at $\simeq$ 100 pc." The shell falls iuto the SMDII as a nuit and. after a series of sub-bursts in which direct ar reflected shock waves interact and carry new materia or accretion on the SMDIT. triggers a dramatic release of enerev from the SMDIL," The shell falls into the SMBH as a unit and, after a series of sub-bursts in which direct and reflected shock waves interact and carry new material for accretion on the SMBH, triggers a dramatic release of energy from the SMBH." This leaves a sphere of hot gas at he ceuter of the simulated galaxy., This leaves a sphere of hot gas at the center of the simulated galaxy. Subsequent cold shells can oulv reach the ceuter when the eas beneath them either cools or is conrpressed inside the iuuernmiost eric xut., Subsequent cold shells can only reach the center when the gas beneath them either cools or is compressed inside the innermost grid point. The hot eas generated by radiative aud mechanica ACN feedback is able to prevent SAIBIT accretiou muti it cools., The hot gas generated by radiative and mechanical AGN feedback is able to prevent SMBH accretion until it cools. These processes lead to dramatic bursts followec w loug. extremely quiet periods. spaced by the cooling inue of the central eas.," These processes lead to dramatic bursts followed by long, extremely quiet periods, spaced by the cooling time of the central gas." As the collapsing cold shell sits ou top of hot aud low density gas. it was already clear roni the previous one-dimensional simulations that the shells ave RT unstable.," As the collapsing cold shell sits on top of hot and low density gas, it was already clear from the previous one-dimensional simulations that the shells are RT unstable." Tn two dimensions. cold sas forms again at & 100 oc.," In two dimensions, cold gas forms again at $\simeq$ 100 pc." Tlowever. cold gas takes the form of rings rather han shells due to the classical RT instability.," However, cold gas takes the form of rings rather than shells due to the classical RT instability." Shells sometimes form. but they fragment quickly.," Shells sometimes form, but they fragment quickly." If there is hot eas beneath the cold ring. both the RT aud couvective instabilities operate to allow the cold gas to fall to the center of the simulation. uuinipeded.," If there is hot gas beneath the cold ring, both the RT and convective instabilities operate to allow the cold gas to fall to the center of the simulation unimpeded." These instabilities cannot operate m one dimension., These instabilities cannot operate in one dimension. In two dineusious. they allow both higher aud more chaotic SMIBID accretion rates.," In two dimensions, they allow both higher and more chaotic SMBH accretion rates." Figure Lo shows the simulation during a relatively quiet period., Figure \ref{fig:snap-quiescent} shows the simulation during a relatively quiet period. Fieure 2. shows the start of an accretion event., Figure \ref{fig:snap-before} shows the start of an accretion event. A cold blob of eas is freely falling to the ceuter of a two-dimensional simulation., A cold blob of gas is freely falling to the center of a two-dimensional simulation. Figure 3. shows a simulation snapshot just after an accretion event with the bipolar BAL wind flowing away from the center of the simulation., Figure \ref{fig:snap-during} shows a simulation snapshot just after an accretion event with the bipolar BAL wind flowing away from the center of the simulation. Cas is able to continue to fall iuto the SAIBIT via the simulation midplane., Gas is able to continue to fall into the SMBH via the simulation midplane. Finally. Figure { shows a simulation suapshot significantly after an accretion event (but not so long that the ealaxy is able to return to a quiesceut state).," Finally, Figure \ref{fig:snap-after} shows a simulation snapshot significantly after an accretion event (but not so long that the galaxy is able to return to a quiescent state)." Dense overlying gas has caused the BAL wind to become nearly isotropic. making additional accretion via the midplane inpossible.," Dense overlying gas has caused the BAL wind to become nearly isotropic, making additional accretion via the midplane impossible." Figure 5- shows SMDII amass versus mechanical feedback efficiency for one- and two-dimensional A models as well as ouc-dimenusioual D 1nodels., Figure \ref{fig:bh-vs-eff} shows SMBH mass versus mechanical feedback efficiency for one- and two-dimensional A models as well as one-dimensional B models. The SMDITs nudereo iore erowth in two diuensious atf a fixed feedback efficicucy owing to RT instabilities. makine it easier for cold eas to fall in.," The SMBHs undergo more growth in two dimensions at a fixed feedback efficiency owing to RT instabilities, making it easier for cold gas to fall in." The character of the time depeudence of SMDII accretion is much different iu two dimiensious than in the one-dimensional case., The character of the time dependence of SMBH accretion is much different in two dimensions than in the one-dimensional case. Iu one dimension. SAIBIT accretion occurs du a few bursts well separated in time.," In one dimension, SMBH accretion occurs in a few bursts well separated in time." Occasionally a given burst will have a complex character. beige composed of πας sib-bursts.," Occasionally a given burst will have a complex character, being composed of many sub-bursts." Iu two dimensions. there are still occasionally eveuts that can be characterized as bursts followed by quiescent periods.," In two dimensions, there are still occasionally events that can be characterized as bursts followed by quiescent periods." Uowever. the quiesceunt periods are shorter and the SMIDIT is more active during them compared to the ouc- case.," However, the quiescent periods are shorter and the SMBH is more active during them compared to the one-dimensional case." Furthermore. during times far from a,"Furthermore, during times far from a" classical transport method since the remainder is lower or equal to 0.5 in absolute value Gt has to be x:1 in order for the standard transport method to be possible). with the additional simplicity that the correspondiug velocity fiek is uniforii (Gvhich is actually why shift aud transport happen ο. colucide in this special case. since there is no compression in the corresponding flow).,"classical transport method since the remainder is lower or equal to $0.5$ in absolute value (it has to be $\leq 1$ in order for the standard transport method to be possible), with the additional simplicity that the corresponding velocity field is uniform (which is actually why shift and transport happen to coincide in this special case, since there is no compression in the corresponding flow)." The second substep just corresponds to an integer ΠΟ of cells shift. which is done in our exauiple simply by copying the content of cell j iuto cell;|5. for anv j.," The second substep just corresponds to an integer number of cells shift, which is done in our example simply by copying the content of cell $j$ into cell $j+5$, for any $j$." A μονο formal aud detailed description of the FARGO algoritlin is elven in the uext section., A more formal and detailed description of the FARGO algorithm is given in the next section. Iu the modified algoritluu. the azimuthal transport substep is split in several parts.," In the modified algorithm, the azimuthal transport substep is split in several parts." We asstme that the timestep Af has already be chosen. aud defer discussion of the timestep constraints until section 32h.," We assume that the timestep $\Delta t$ has already be chosen, and defer discussion of the timestep constraints until section \ref{subsec:ts}." " Wo first compute the average azimuthal velocity at cach radius: We then introduce: the residual: velocity:: σύ, and the ---""shift πανο. at each radius. : where E|X] denotes the ucarest integer to the real X."," We first compute the average azimuthal velocity at each radius: We then introduce the residual velocity: $v_{ij}^{\theta {\rm res}} =v_{ij}^{\theta a}-\overline{v}_i^\theta$ , and the “shift number” at each radius : where $E[X]$ denotes the nearest integer to the real $X$." We define the coustaut residual velocity to be: the total velocity can be expressed as: wa SILAu ⋅⋅↴↴ ↖↖↕∐∖∐∖↑↕∐∖↴∖↕∐⇈↖↸∖↕∪↸⊳↕↑⋅↖∠↴∣⇁ ↑∪⋜↧⋯∐↕≯∪↥⋅⋯↴∖↴↕∐↕≯↑∪↕≯∣∣∣⇁↸⊳↸∖∐↴∖↴∪↖↽↸∖↥⋅∪∐↸∖↑↕⋯↸∖↴∖↴↑↸∖↻∙ ," We define the constant residual velocity to be: Hence the total velocity can be expressed as: where the “shift velocity” $v_i^{\theta {\rm SH}}= n_i\frac{\Delta y_i}{\Delta t}$ corresponds to a uniform shift of $n_i$ cells over one timestep." We first transport the IID quantities according to the flow Jos of:then to the uniform- flow 0?) We split the trausport iuto two parts Hes } : ⋅⋡ ⋖∠↴↙∣↕↖⋜⋯≼↧∠↴⊔↕⋟↕∐↴∖↴↑↸∖⋜↧≼↧∪↕∏↴∖↴↕∐∶↴∙⋜↧↴∖↴↕∐∶↴∙↕↸∖⊓⋅⋜⋯↴∖↴⋯↥⋅↑↴∖↴↑↸∖↻ with the velocity οMeshespoY erosy order to ensure (as can be checked below eiveu the timestep constraiuts) that in each of these transport substeps the material sweeps at most half a cellapply.," We first transport the HD quantities according to the flow $v^{\theta {\rm res}}$ :then to the uniform flow $v^{\theta {\rm cr}}$: We split the transport into two parts $v^{\theta {\rm res}}$ and $v^{\theta {\rm cr}}$ ) instead of using a single transport step with the velocity $v^{\theta {\rm res}}+v^{\theta {\rm cr}}$, in order to ensure (as can be checked below given the timestep constraints) that in each of these transport substeps the material sweeps at most half a cell." . Finally. the quantities are transported along the 075!in auiformτρ flow: Ouly the first two parts of this transport step introduce sole nunerical diffusion.," Finally, the quantities are transported along the $v^{\theta {\rm SH}}$ uniform flow: Only the first two parts of this transport step introduce some numerical diffusion." The last oue.(12). which in many cases corresponds to the largest part of the motion. does not introduce any uiuuierical error. since it just corresponds to a circular penuutation of the exid cells. Tu the transport method. he timestep Iuitatio- avises from the combination of four different constraints (sce e.c. Stone Norman 1992). namely the fact that a flow advectec test particle in cell [fj] should not sweep a distance longer han Ay; in azimuth nor longer tha- HiiR; in radius over one timestep Ovhich introduces he limit timestep ófo and df; in Stone Normas oper) an hat he wavefront of amy wave present iu he system shouk not travel across a whole coll over one nuestep (Richtiuver Morton. 1957). which corresponds o the limit timestep δι iu Stone Norma's paper.," The last one, which in many cases corresponds to the largest part of the motion, does not introduce any numerical error, since it just corresponds to a circular permutation of the grid cells, In the transport method, the timestep limitation arises from the combination of four different constraints (see e.g. Stone Norman 1992), namely the fact that a flow advected test particle in cell $[i,j]$ should not sweep a distance longer than $\Delta y_i$ in azimuth nor longer than $R_{i+1}-R_i$ in radius over one timestep (which introduces the limit timestep $\delta t_2$ and $\delta t_3$ in Stone Norman's paper), and that the wavefront of any wave present in the system should not travel across a whole cell over one timestep (Richtmyer Morton, 1957), which corresponds to the limit timestep $\delta t_1$ in Stone Norman's paper." The last constraint comes from a stability lait arising roni the viscosity. (numerical or plysical)., The last constraint comes from a stability limit arising from the viscosity (numerical or physical). With the uodified aziuuthal transport aleorithiu. the coustraiut ou the aziuutha motion ji fo be modified slieltly.," With the modified azimuthal transport algorithm, the constraint on the azimuthal motion has to be modified slightly." " Following Stoue Noruumu's notation. instead of writing at?=Ay;H eO, we write: which means that the timestep linitation comes now from the perturbed azinmthal velocity. which results in a nmchhigher absolute value of óf4."," Following Stone Norman's notation, instead of writing $\delta t_3^{ij}=\Delta y_i/v^{\theta a}_{ij}$ , we write: which means that the timestep limitation comes now from the perturbed azimuthal velocity, which results in a muchhigher absolute value of $\delta t_3$." Another limitation arises from the shear., Another limitation arises from the shear. Indeed we do notwant the shear, Indeed we do notwant the shear When the PWN has more or less relaxed to a steady subsonic expansion the PWN has gaiued energy as a result of the interaction with the reverse shock.,When the PWN has more or less relaxed to a steady subsonic expansion the PWN has gained energy as a result of the interaction with the reverse shock. Consequently. the radius of the PWN is roughly larecr than the value predicted by the semi-analytical solution obtained from Equ. (18))," Consequently, the radius of the PWN is roughly larger than the value predicted by the semi-analytical solution obtained from Eqn. \ref{ThermD}) )" iu Section 3.2., in Section 3.2. In figure 9 we show the ratio between the (miostlv thermal) cnerey of the pulsar wind bubble. tthe part of the PWN that cousists of shocked pulsar wind material. and the total mechanical enerev deposited by the pulsar.," In figure 9 we show the ratio between the (mostly thermal) energy of the pulsar wind bubble, the part of the PWN that consists of shocked pulsar wind material, and the total mechanical energy deposited by the pulsar." One can clearly sec tle increase m the cnerey coutent of the pulsar wind bubble., One can clearly see the increase in the energy content of the pulsar wind bubble. A laree fraction of the energy deposited by the pulsar wind in the stage when the expansion is supersonic is contained in the kinetic energy of the shocked stellar ejecta in the PWN shell., A large fraction of the energy deposited by the pulsar wind in the stage when the expansion is supersonic is contained in the kinetic energy of the shocked stellar ejecta in the PWN shell. When the reverse SNR shock is interacting with the PWN bubble. cnerey is apparently transterred frou this thin shell to the interior of the bubble through the dissipation of he waves trausuütted iuto he bubble.," When the reverse SNR shock is interacting with the PWN bubble, energy is apparently transferred from this thin shell to the interior of the bubble through the dissipation of the waves transmitted into the bubble." are more common for planets of unknown eccentricities. very low density ratios will also occur. albeit rarely.,"are more common for planets of unknown eccentricities, very low density ratios will also occur, albeit rarely." These will exhibit very distinctive light curves that display very long. flat-bottomed t(ransits.," These will exhibit very distinctive light curves that display very long, flat-bottomed transits." A density ration of 0.01 would result in an increase in the duration by a [actor of /1/0.1=4.6 over that expected [or à circular orbit with the same period., A density ration of 0.01 would result in an increase in the duration by a factor of $\sqrt[3]{1/0.1} = 4.6$ over that expected for a circular orbit with the same period. Given (hat planets in circular orbits wilh periods of a vear would have transit durations over 12 hours. such planets could have transit cdurations up to several davs. but would stand oul among [alse positives wilh similar densitv ratios.," Given that planets in circular orbits with periods of a year would have transit durations over 12 hours, such planets could have transit durations up to several days, but would stand out among false positives with similar density ratios." To the best of our knowledge. only eclipses of giant stars could produce similar events ancl these can be quickly identilied with spectra due to their low surface gravity.," To the best of our knowledge, only eclipses of giant stars could produce similar events and these can be quickly identified with spectra due to their low surface gravity." For the interpretation of transit candidates. (his means (hat cases with low p;/pjy (or pi/pau. M available) should first be studied to see if the prospective parent star is a giant.," For the interpretation of transit candidates, this means that cases with low $\rho_{t}/\rho_{JK}$ (or $\rho_{t}/\rho_{a}$, if available) should first be studied to see if the prospective parent star is a giant." If not. the probability that the candidate is a planet remains very low (see Fig. 8))," If not, the probability that the candidate is a planet remains very low (see Fig. \ref{ltprob_e}) )" and should thus be assigned a very low priority., and should thus be assigned a very low priority. To apply this method. we recommend selecting a lower limit for the density ratio as a function of the period: only planets with periods =1004 are currently known to have a chance to have very extreme eccentricities: in fact. the maximim possible eccentricity dereases with period: e<0.35log(T/1d)+0.24 (based on figure 4 from Deegetal. (2010))).," To apply this method, we recommend selecting a lower limit for the density ratio as a function of the period: only planets with periods $\gtrsim 100d$ are currently known to have a chance to have very extreme eccentricities; in fact, the maximim possible eccentricity dereases with period: $e \lesssim 0.35 \log (T/1d) + 0.24$ (based on figure 4 from \citet{corot9b}) )." Accordingly. no known ‘hot’ planets (77< 5d) have an eccentricitv higher than 0.265.," Accordingly, no known 'hot' planets $T < 5d$ ) have an eccentricity higher than 0.265." With (his in mid. we can therefore conclude. per Fig. 5..," With this in mind, we can therefore conclude, per Fig. \ref{ltprob_e}," that all candidates with density ratios lower than 0.45 can be stronely de-prioritized., that all candidates with density ratios lower than 0.45 can be strongly de-prioritized. Similar secure cut-olfs could be established for candidates with longer periods. which could potentially possess larger eccentricities.," Similar 'secure' cut-offs could be established for candidates with longer periods, which could potentially possess larger eccentricities." Additionally. semi-secure! eut-offs could be implemented. which would have small residual probabilities of falsely de-prioritizing very eccentric planets.," Additionally, 'semi-secure' cut-offs could be implemented, which would have small residual probabilities of falsely de-prioritizing very eccentric planets." However. should ος be used to create the density ratio. it is perhaps better to be more circumspect given (his density measures difficulties with evolved stars.," However, should $\rho_{JK}$ be used to create the density ratio, it is perhaps better to be more circumspect given this density measure's difficulties with evolved stars." "eccentricities have been reported for several planets on extremely close orbits (below 3 days), including WASP-12b (?), WASP-14b (?),, WASP-18b (?),, WASP-19b and GJ 436b (?) — see top panel of Fig. 1..","eccentricities have been reported for several planets on extremely close orbits (below 3 days), including WASP-12b \citep{heb09}, WASP-14b \citep{jos09},, WASP-18b \citep{hel09}, , WASP-19b \citep{heb10} and GJ 436b \citep{but04} — see top panel of Fig. \ref{exoe}." " Specific scenarios have been invoked to explain these apparently anomalous cases, such as the presence of a perturbing companion (??), or widely different coefficients in the intrinsic response of planets to tides (?).."," Specific scenarios have been invoked to explain these apparently anomalous cases, such as the presence of a perturbing companion \citep{rib08,mar08}, or widely different coefficients in the intrinsic response of planets to tides \citep{mats09}." " Another relevant recent development is the detection of several systems with strong spin-orbit misalignment (?,andreferencestherein),, which is presently interpreted as an indication that the disc-migration scenario is in need of significant updates, and that dynamical evolution after the dissipation of the disc is probably more important than previously thought, and even possibly dominant in determining the orbital properties of close-in planets."," Another relevant recent development is the detection of several systems with strong spin-orbit misalignment \citep[][and references therein]{win10}, which is presently interpreted as an indication that the disc-migration scenario is in need of significant updates, and that dynamical evolution after the dissipation of the disc is probably more important than previously thought, and even possibly dominant in determining the orbital properties of close-in planets." " We have been performing a series of observational programmes to gather more radial-velocity (RV) data on known transiting planets, in order to study these issues."," We have been performing a series of observational programmes to gather more radial-velocity (RV) data on known transiting planets, in order to study these issues." " In this paper, we revisit the data on orbital eccentricity for transiting planets, based on new data and a re-analysis of extant data, and examine the implications in terms of the ensemble properties of close-in planets regarding the orbital circularisation and the stopping mechanism."," In this paper, we revisit the data on orbital eccentricity for transiting planets, based on new data and a re-analysis of extant data, and examine the implications in terms of the ensemble properties of close-in planets regarding the orbital circularisation and the stopping mechanism." Our sample consists of all known transiting planets fulfilling the following selection criteria: (i) objects with precisely determined parameters (i.e. planetary radius and planetary mass measured to better than accuracy) (ii) host stars brighter than V=15 mag (iii) objects known from reviewed publication by 1st July 2010., Our sample consists of all known transiting planets fulfilling the following selection criteria: (i) objects with precisely determined parameters (i.e. planetary radius and planetary mass measured to better than accuracy) (ii) host stars brighter than $V$ =15 mag (iii) objects known from peer-reviewed publication by 1st July 2010. " We use published radial velocity data as well as new HARPS data from our observation programme for WASP-2, WASP-4, WASP-5 and WASP-7T."," We use published radial velocity data as well as new HARPS data from our observation programme for WASP-2, WASP-4, WASP-5 and WASP-7." " The radial velocity data for these objects is presented and discussed in more details in ?,, and is available as an electronic table."," The radial velocity data for these objects is presented and discussed in more details in \citet{hus11}, and is available as an electronic table." The brightest known transiting planets were identified by Doppler planet surveys first and only subsequently found to be transiting., The brightest known transiting planets were identified by Doppler planet surveys first and only subsequently found to be transiting. " Their orbital eccentricity is therefore usually well determined, because a sizeable number of individual radial velocity measurements is required to find the period of a planetary orbit."," Their orbital eccentricity is therefore usually well determined, because a sizeable number of individual radial velocity measurements is required to find the period of a planetary orbit." " Most of our sample, however, consists of objects discovered by photometric searches for transits."," Most of our sample, however, consists of objects discovered by photometric searches for transits." " In that case, the number of radial velocity measurement is lower, since the RV data are only required to detect the presence of an orbital signal at the period and phase of the transits."," In that case, the number of radial velocity measurement is lower, since the RV data are only required to detect the presence of an orbital signal at the period and phase of the transits." " Transiting planets from photometric searches are on average much fainter than the targets of Doppler searches, so that in general the RV data is also less precise."," Transiting planets from photometric searches are on average much fainter than the targets of Doppler searches, so that in general the RV data is also less precise." " In these case, there are three options to calculate the orbital parameters: - the eccentricity is set to zero, under the assumption that it is small and undetectable, and the data is solved for the other parameters of the system (e.g. the planets from the OGLE, HAT and TrES surveys) - the RV data clearly indicate an eccentric orbit, and the eccentricity e is solved together with the other parameters (e.g. HAT-P-2). -"," In these case, there are three options to calculate the orbital parameters: - the eccentricity is set to zero, under the assumption that it is small and undetectable, and the data is solved for the other parameters of the system (e.g. the planets from the OGLE, HAT and TrES surveys) - the RV data clearly indicate an eccentric orbit, and the eccentricity $e$ is solved together with the other parameters (e.g. HAT-P-2). -" " a Monte-Carlo Markov Chain (MCMC) integration is run on all data, with the eccentricity as a free parameters (e.g. planets from the WASP survey)."," a Monte-Carlo Markov Chain (MCMC) integration is run on all data, with the eccentricity as a free parameters (e.g. planets from the WASP survey)." " The problem with the third method is that there is an intrinsic bias in the determination of eccentricity from radial-velocity data, because measurement errors on RV data for a circular orbit will always give rise to a finite best-fit eccentricity."," The problem with the third method is that there is an intrinsic bias in the determination of eccentricity from radial-velocity data, because measurement errors on RV data for a circular orbit will always give rise to a finite best-fit eccentricity." This effect was studied in the context of stellar binaries by ? and more recently by ?.., This effect was studied in the context of stellar binaries by \citet{luc71} and more recently by \citet{Shen2008}. " As a result, even when the measurement uncertainties are correctly estimated, the centre of the posterior distribution from a MCMC for a circular orbit will tend to be 1-3 sigma away from zero."," As a result, even when the measurement uncertainties are correctly estimated, the centre of the posterior distribution from a MCMC for a circular orbit will tend to be 1-3 sigma away from zero." An additional issue is the presence of other sources of signal in the radial velocity data., An additional issue is the presence of other sources of signal in the radial velocity data. " The most common causes are stellar activity, instrumental drifts, and additional companions in the system."," The most common causes are stellar activity, instrumental drifts, and additional companions in the system." " When these sources are not included in the orbital analysis, they may induce spurious eccentricity detections (??) because any radial-velocity offset from a circular orbit will make it appear more eccentric."," When these sources are not included in the orbital analysis, they may induce spurious eccentricity detections \citep{Rodigas2009,hus10} because any radial-velocity offset from a circular orbit will make it appear more eccentric." A large fraction of published eccentricities for transiting planets are significantly different from zero at the few-sigma level only., A large fraction of published eccentricities for transiting planets are significantly different from zero at the few-sigma level only. " Particular attention to this issue is justified to avoid spurious detections, which would be especially confusing in the context of studying tidal evolution, since they would tag some circularised objects as having low but significant eccentricity, thus being good candidates for rapid on-going tidal evolution."," Particular attention to this issue is justified to avoid spurious detections, which would be especially confusing in the context of studying tidal evolution, since they would tag some circularised objects as having low but significant eccentricity, thus being good candidates for rapid on-going tidal evolution." " The recent case of WASP-12, discussed in ????,, shows how false positives can arise in non-circular orbit detections."," The recent case of WASP-12, discussed in \citet{heb09,Morales2009,Cam10,hus10}, shows how false positives can arise in non-circular orbit detections." " The orbital eccentricity of WASP-12b, initially thought to be significant at the 3-sigma level, was subsequently found to be spurious by furtherRV measurements and the detection of the secondary eclipse by the Spitzer satellite."," The orbital eccentricity of WASP-12b, initially thought to be significant at the 3-sigma level, was subsequently found to be spurious by furtherRV measurements and the detection of the secondary eclipse by the Spitzer satellite." " Another example is WASP-10, recently re-analysed by ?."," Another example is WASP-10, recently re-analysed by \citet{mac10}." .These, .These the cross-section for a binary to undergo an exchange interaction. which also serves as a likelihood-of-disruption inclicator. scales linearly with the orbital separation.,"the cross-section for a binary to undergo an exchange interaction, which also serves as a likelihood-of-disruption indicator, scales linearly with the orbital separation." This has been confirmed by Davies&Sigurdsson(2001) in the case of planetary systems., This has been confirmed by \citet{dav01} in the case of planetary systems. The fact that we do not observe (his relation is primarily a result of the large fraction of escaping svstenis which cleprives the cluster of orbits to break-up., The fact that we do not observe this relation is primarily a result of the large fraction of escaping systems which deprives the cluster of orbits to break-up. Another factor is the relatively weak binding enerev of (he planetary svstems compared to that of (he binaries., Another factor is the relatively weak binding energy of the planetary systems compared to that of the binaries. It is evident from Figure that we are limited at Chis stage to a fairly low number of svstems per orbital separation bin and not until we can saturate the distribution with a large number of svstems. all sitnatec in the core of the cluster. will we be able to fully test the statistical results mentioned above.," It is evident from Figure \ref{f:fig1} that we are limited at this stage to a fairly low number of systems per orbital separation bin and not until we can saturate the distribution with a large number of systems, all situated in the core of the cluster, will we be able to fully test the statistical results mentioned above." Planetary svstems primarily escape from a cluster owing to stripping of stars in the outer cluster regions by the Galactic tidal field., Planetary systems primarily escape from a cluster owing to stripping of stars in the outer cluster regions by the Galactic tidal field. As à natural consequence of mass-segregation there is a preference lor svstems will low parent star mass (o escape., As a natural consequence of mass-segregation there is a preference for systems with low parent star mass to escape. " Planetary svstems οἱ all orbital separations are equally likely to escape (as planets just “lag along lor (he ride"". see Figure 1))."," Planetary systems of all orbital separations are equally likely to escape (as planets just “tag along for the ride”, see Figure \ref{f:fig1}) )." It is also possible for stus to be ejected from the cluster due to close encounters with other stars or binaries but in the case of planetary svstems (he encounter more likely results in liberation of the planet., It is also possible for stars to be ejected from the cluster due to close encounters with other stars or binaries but in the case of planetary systems the encounter more likely results in liberation of the planet. The (vpical erossing-time for these simulations is 2—10 Myr.," The typical crossing-time for these simulations is $2-10\,$ Myr." Figure 2. shows (he distribution of time spent in the cluster by the free-floating planets., Figure \ref{f:fig2} shows the distribution of time spent in the cluster by the free-floating planets. The planets are preferentially liberated in the cluster core aud. are liberated with a velocily less than the cluster escape velocity (see Figure 3))., The planets are preferentially liberated in the cluster core and are liberated with a velocity less than the cluster escape velocity (see Figure \ref{f:fig3}) ). The velocity dispersion of the Iree-[loating planets is approximately (vice that of the cluster stars., The velocity dispersion of the free-floating planets is approximately twice that of the cluster stars. We expect this to have only a minimal effect on the determination of the lensing mass in M22 (Sahuοἱal.2001)., We expect this to have only a minimal effect on the determination of the lensing mass in M22 \citep{sah01}. . 50 the planets generally begin their free-Iloating existence deep within (he potential well ol the cluster and will then journey towards the outer regions of the cluster driven by the elect of two-hocly relaxation., So the planets generally begin their free-floating existence deep within the potential well of the cluster and will then journey towards the outer regions of the cluster driven by the effect of two-body relaxation. Chernoff&Weinberg(1990) derive the timescale for segregation to be directly related to the relaxation timescale of the cluster but with an inverse dependence on stellar mass., \citet{che90} derive the timescale for mass-segregation to be directly related to the relaxation timescale of the cluster but with an inverse dependence on stellar mass. Therefore we would expect the planets to take much longer to reach the tidal boundary of the cluster than low-mass stars., Therefore we would expect the planets to take much longer to reach the tidal boundary of the cluster than low-mass stars. This is not what we see in Figure 4. which illustrates (he average position within the cluster over time for various mass groups., This is not what we see in Figure \ref{f:fig4} which illustrates the average position within the cluster over time for various mass groups. As expected the 0.5—1.03. group. which always contains the average stellar mass. shows little movement.," As expected the $0.5-1.0 M_{\odot}$ group, which always contains the average stellar mass, shows little movement." For the remaining stellar. mass eroups Chere is a strong correlation between deviation from the average stellar mass and the rate of mass-segregation. whether it be invards lor high-mass or outwards for low-mass.," For the remaining stellar mass groups there is a strong correlation between deviation from the average stellar mass and the rate of mass-segregation, whether it be inwards for high-mass or outwards for low-mass." This Clearly demonstrates that equipartition of energy is dominating the dynamical evolution., This clearly demonstrates that equipartition of energy is dominating the dynamical evolution. The picture is complicated for the planets because. in (his case. (he core population is replenished," The picture is complicated for the planets because, in this case, the core population is replenished" oue has the desired advection-dilfusion equatiou: Au interesting feature of the above result is that if the diffusion coellicient D(J) varies with J. then it influences the uileration rate.,"one has the desired advection-diffusion equation: An interesting feature of the above result is that if the diffusion coefficient $D(J)$ varies with $J$, then it influences the migration rate." That is to say. oue cau rewrite the [lux in Eq. (5))," That is to say, one can rewrite the flux in Eq. \ref{diffusion}) )" " as Fy, = un ⋅⋅ ↜∖∩↕∐⋜↕↕⇥⋅⊽∣∐↙∕∕∣≺↙∣⋮∣∢∙∩∐⋃⋅∐∥⊔≺↵⊳∖↕∩↕∐≺↵⋜↕≺⇂∖⊽≺↵∢∙∏∩∐↕≺↵↥⋅⋯⋅ "," as F_J = )f - , so that $-\partial D/\partial J$ contributes to the advection term." We have tried to abstract a value aud scaling for DCJ) from the MHD situlatious of N2005: the results of were cillicult to trauslate into our framework., We have tried to abstract a value and scaling for $D(J)$ from the MHD simulations of N2005; the results of were difficult to translate into our framework. Nelson reports that the typical timescale of fluctuations in 9D is of order half an orbital period., Nelson reports that the typical timescale of fluctuations in $\delta\Gamma$ is of order half an orbital period. Hence we take A direct estimate of the correlation function of the data suggests. however. that correlations ay persist to much longer than au orbital period. aud it is conceivable that the integral (1)) lor DJ) does not even exist (Nelson 2005. private comumuuication).," Hence we take A direct estimate of the correlation function of the data suggests, however, that correlations may persist to much longer than an orbital period, and it is conceivable that the integral \ref{Ddef}) ) for $D(J)$ does not even exist (Nelson 2005, private communication)." If tlie correlation time does uot exist. then the methods of this paper are inapplicable to migration.," If the correlation time does not exist, then the methods of this paper are inapplicable to migration." Such long-term correlations iuply a “memory” in the turbuleuce. presumably involving persistent structures in addition to he planet of interest: for example. lone-livecl vortices2005).. or of course other planets.," Such long-term correlations imply a “memory” in the turbulence, presumably involving persistent structures in addition to the planet of interest: for example, long-lived vortices, or of course other planets." Peucdineg further numerical evideuce. we adopt as a working pothesis that το exist but with uncertain maguitude.," Pending further numerical evidence, we adopt as a working hypothesis that $\tau_{\rm c}$ exist but with uncertain magnitude." To complete the diffusion coelficieut. we require a parametrization of the variauce of the luctuating torque in terms of time-averaged disk properties.," To complete the diffusion coefficient, we require a parametrization of the variance of the fluctuating torque in terms of time-averaged disk properties." This entails some guesswork. as the simulatious of N2005 aud have explored ouly a limited rauge of disk nodels and planetary radii.," This entails some guesswork, as the simulations of N2005 and have explored only a limited range of disk models and planetary radii." A natural scale for the gravitational force exerted on the planet by he local gas is 22CXMy. where X is the surface deusity ofthe disk.," A natural scale for the gravitational force exerted on the planet by the local gas is $2\pi G\Sigma M_p$, where $\Sigma$ is the surface density ofthe disk." This is the force that the, This is the force that the with that of CO.,with that of $\rm C^{18}O$. As indicated in Table 1.. only a coarse upper limit to the detection of f=21 was obtained.," As indicated in Table \ref{tab:gaussfit}, only a coarse upper limit to the detection of $^+\,J=2-1$ was obtained." The HCO J=1—0 emission was observed in (he same window as SiO 2—1 and HCO 1—0 and appears slightly blended to the latter.," The HCO $J=1-0$ emission was observed in the same window as SiO $2-1$ and $^{13}$ $^+\,1-0$ and appears slightly blended to the latter." With a significantly improved signal-Lo-noise ratio. we confirm (he previous tentative detection of this IICO transition reported bv Sage&Ziurvs(1995) with the NRAO 12mm telescope.," With a significantly improved signal-to-noise ratio, we confirm the previous tentative detection of this HCO transition reported by \citet{Sage95} with the NRAO m telescope." " Moreover. using the main beam brightness temperature from Sage&Ziurvs(1995). of ~Lmmlx with at 72"" beam and our observed ~ 4iumly with a 28” beam we can make an estimate of the emitting source extent of >20""."," Moreover, using the main beam brightness temperature from \citet{Sage95} of $\sim1$ mK with at $72''$ beam and our observed $\sim4$ mK with a $28''$ beam we can make an estimate of the emitting source extent of $>20''$." The double Gaussian proliles fitted to each species were constrained to have similar linewidths., The double Gaussian profiles fitted to each species were constrained to have similar linewidths. The resulting fitted line positions agree within (he errors to those expected from the rest frequencies of each line., The resulting fitted line positions agree within the errors to those expected from the rest frequencies of each line. Fig., Fig. 2. shows the results of the fit superimposed on the observations as well as the position of the hvperfine structure lines of 1ICO., \ref{fig:HCO} shows the results of the fit superimposed on the observations as well as the position of the hyperfine structure lines of HCO. Only the brightest of the eroup CF=2— 1) has been taken into account for the fit., Only the brightest of the group $F=2-1$ ) has been taken into account for the fit. Assuming optically thin emission. the F=1—0 and F—1 transitions (at 86.708 and GGIIZ) are expected (to show an intensity half of the main transition but thev are completely blended to the IICO emission.," Assuming optically thin emission, the $F=1-0$ and $F=1-1$ transitions (at 86.708 and GHz) are expected to show an intensity half of the main transition but they are completely blended to the $^{13}$ $^+$ emission." The F=0—1 transition at GCLIz is expected to be even fainter by a factor of 5. well below our detection limit.," The $F=0-1$ transition at GHz is expected to be even fainter by a factor of 5, well below our detection limit." Fig., Fig. 2. shows in dotted line a synthetic spectrum of ΠΟ assuming one velocity. component centered al with a linewidth of (as derived if only one component is fitted to the spectrum from the other lines) and a peak intensity of the ICO Fo=2—1 line of 3.6mmlk. This shows that the fainter ICO hvperline transitions may account for up to a 10—20% of the IICO — integrated intensity., \ref{fig:HCO} shows in dotted line a synthetic spectrum of HCO assuming one velocity component centered at with a linewidth of (as derived if only one component is fitted to the spectrum from the other lines) and a peak intensity of the HCO $F=2-1$ line of mK. This shows that the fainter HCO hyperfine transitions may account for up to a $10-20\%$ of the $^{13}$ $^+$ integrated intensity. "Within 2 kpc, 70—90% of stars have been found to form in the clusters (Lada&Lada2003).","Within 2 kpc, $70-90$ of stars have been found to form in the clusters \citep{lada03}." ". These newly formed stars, however, are embedded deeply in dense molecular cloud and there exists various difficulties in identifying sources and deriving physical parameters."," These newly formed stars, however, are embedded deeply in dense molecular cloud and there exists various difficulties in identifying sources and deriving physical parameters." " Several statistical tools, such as the K-band luminosity function (KLF), the color-color or color-magnitude diagrams, etc.,"," Several statistical tools, such as the K-band luminosity function (KLF), the color-color or color-magnitude diagrams, etc.," " have been successfully used to constrain the characteristics of deeply embedded stellar clusters (e.g.,Lada&2003)."," have been successfully used to constrain the characteristics of deeply embedded stellar clusters \citep[e.g.,][]{lada03}." ". Development of new sensitive equipments, such as, large mosaic IR array, enables us to observe embedded stellar cluster in greater detail than previous effort."," Development of new sensitive equipments, such as, large mosaic IR array, enables us to observe embedded stellar cluster in greater detail than previous effort." " The Sh 2-233IR region is a well studied star-forming region in our Galaxy (e.g.,Porrasetal.2000) and it provides an ideal laboratory for understanding properties of embedded clusters."," The Sh 2-233IR region is a well studied star-forming region in our Galaxy \citep[e.g.,][]{porras00} and it provides an ideal laboratory for understanding properties of embedded clusters." " Therefore, we revisit this region with higher sensitivity near-infrared data taken toward a wider region to better constrain the properties of the embedded stellar cluster than previous studies."," Therefore, we revisit this region with higher sensitivity near-infrared data taken toward a wider region to better constrain the properties of the embedded stellar cluster than previous studies." " Toward the direction of the Galactic Anticenter, Sh 2-233IR (hereafter S233IR), as a part of the Sh 2-235 GMC complex (Reipurth&Yan2008),, is located at a distance of about 1.8 kpc 2000),, in association with four extended HII regions, Sh 2-231, 232, 233, and 235 1996)."," Toward the direction of the Galactic Anticenter, Sh 2-233IR (hereafter S233IR), as a part of the Sh 2-235 GMC complex \citep{ry08}, is located at a distance of about 1.8 kpc \citep{porras00}, in association with four extended HII regions, Sh 2-231, 232, 233, and 235 \citep{heyer96}." ". Its position coincides with an IRAS source, IRAS 05358+3543 (a9oo=0539""'10* 02900= 4-35?45/19"")."," Its position coincides with an IRAS source, IRAS 05358+3543 $\alpha_{2000}=05^h39^m10^s$ $\delta_{2000}=+35^{\circ}45^\prime19^{\prime\prime}$ )." " S233IR is classified as a massive star formation region (Sridharanetal. 2002),, showing CO outflows (Snelletal.1990) and various maser emissions associated with this region (Henningetal.1992;Tofani1995;Beuther2002b;Menten1991;Minier2005)."," S233IR is classified as a massive star formation region \citep{sri02}, , showing CO outflows \citep{snell90} and various maser emissions associated with this region \citep{henning92,tofani95,beuther02b,menten91,minier05}." . The K' band image of this region shows many bright stellar sources and also extended nebulous features associated with dust emission (Hodapp1994)., The $K^\prime$ band image of this region shows many bright stellar sources and also extended nebulous features associated with dust emission \citep{hodapp94}. ". The two embedded young clusters, Sh SW (hereafter SW, located in the south-west direction from the center) and Sh 2-233IR NE (hereafter NE, in the north-east direction), are notable in this region, with remarkable Hz bow shocks associated with the NE cluster (Porrasetal.2000)."," The two embedded young clusters, Sh 2-233IR SW (hereafter SW, located in the south-west direction from the center) and Sh 2-233IR NE (hereafter NE, in the north-east direction), are notable in this region, with remarkable $_2$ bow shocks associated with the NE cluster \citep{porras00}." ". In addition, numerous studies have been reported, especially for the NE cluster, including polarimetric observations (Jiangetal.2001;Yaoetal. 2000),, molecular outflows (Beutheretal.2007;Mao&Zeng2004;Beuther2002a;Cesaronietal.1999;Larionov 1999),, and mid-infrared sources (Longmoreetal.2006)."," In addition, numerous studies have been reported, especially for the NE cluster, including polarimetric observations \citep{jiang01,yao00}, molecular outflows \citep{beuther07,mz04,beuther02a,cesaroni99,lari99}, and mid-infrared sources \citep{longmore06}." ". In thispaper, we revisit this S233IR region with wider field of view, higher resolution, and better sensitivity data in near-infrared and radio wavelengths."," In this, we revisit this S233IR region with wider field of view, higher resolution, and better sensitivity data in near-infrared and radio wavelengths." " Our goal is to understand star formation history in terms of age, star formation efficiency and initial mass function."," Our goal is to understand star formation history in terms of age, star formation efficiency and initial mass function." " We summarize our observations at radio and near-infrared in ??,, and the observed results in ??.."," We summarize our observations at radio and near-infrared in \ref{obs}, and the observed results in \ref{results}." " Discussion is given in ??,, and the summary in ??.."," Discussion is given in \ref{discuss}, and the summary in \ref{summary}." This is the first paper in the series of our work for the S233IR. and associatedregion., This is the first paper in the series of our work for the S233IR and associatedregion. Here we focus on properties of the embedded stellar clusters in the, Here we focus on properties of the embedded stellar clusters in the "where 2=(r/R) ll. iQ,lp=150 describes the location of the peak at r/R.=1.0067 and A:=30 eives the width of the bump (Ar~ 0.0015R.).","where $z=1/\{(r/R_*)-1\}$ , $z_p=150$ describes the location of the peak at $r/R_*=1.0067$ and $\Delta z=30$ gives the width of the bump $\Delta r \simeq 0.0015 R_*$ )." The line acceleration with the extra bumps is shown in Fie. 1.., The line acceleration with the extra bumps is shown in Fig. \ref{f_testbumps}. The solution of the momentum equation. with the condition that it passes smoothly through the sonic point. eives the velocity at the lower boundary and hence the niass-loss vate.," The solution of the momentum equation, with the condition that it passes smoothly through the sonic point, gives the velocity at the lower boundary and hence the mass-loss rate." The upper paucl of Fig., The upper panel of Fig. 2. shows the resulting mass-loss rates as a function of the peak value of the mn iu the line acceleration iu the subsonic region., \ref{fig:models} shows the resulting mass-loss rates as a function of the peak value of the bump in the line acceleration in the subsonic region. " We soe that as the line acceleration iu the subsonic region nucreases, lncreases."," We see that as the line acceleration in the subsonic region increases, increases." Ouce iis fixed by the processes iu the subsonic region. the radiative acceleration iu the Supersonic region then determines the termunal velocity tthat the wind will reach.," Once is fixed by the processes in the subsonic region, the radiative acceleration in the supersonic region then determines the terminal velocity that the wind will reach." This can easily be seeu iu the following wav., This can easily be seen in the following way. Iuteerating the momentum equation (Eq. 1)), Integrating the momentum equation (Eq. \ref{eq:motion}) ) " iu the supersonic region from the critical point r, to infinity. aud ieuoriug the influence of the gas pressure. elves sO Iere we have used the observed property that ος29« and that rn.rgKRe. so rezmRu"," in the supersonic region from the critical point $r_c$ to infinity, and ignoring the influence of the gas pressure, gives so Here we have used the observed property that $\vinf \gg a$ and that $r_c - r_0 \ll R_*$, so $r_c \simeq R_*$." Eq., Eq. 7 says that Hs determined by the integral of ο1) in thesupersonic reelonu., \ref{eq:vinfty} says that is determined by the integral of $g_{\rm L}(r)$ in the region. The radiative acceleration iu the part of the wind willdecrease as Ds forced to increase by an in the raciative acceleration in thesubsonic part of the wind., The radiative acceleration in the part of the wind will as is forced to increase by an in the radiative acceleration in the part of the wind. This is because the optical depth of the optically thick driving lues. which is proportional to the deusitv iu the wiud. will increase.," This is because the optical depth of the optically thick driving lines, which is proportional to the density in the wind, will increase." Thus an increase in ivesults im an increase of the line optical depth., Thus an increase in results in an increase of the line optical depth. This results in a decrease of gp in the Supersonic region. which eives a lower terminal velocity.," This results in a decrease of $g_{\rm L}$ in the supersonic region, which gives a lower terminal velocity." . We will estimate this effect below., We will estimate this effect below. Asune that the radiative acceleration by lues depends ou the optical depth in the wind. as eiven bx CAT theory (Castor et al.," Assume that the radiative acceleration by lines depends on the optical depth in the wind, as given by CAK theory (Castor et al." 1975)., 1975). where & and © are coustauts and gy. is a reference value describing the acceleration due to electron scattering., where $k$ and $\alpha$ are constants and $g_{\rm e}$ is a reference value describing the acceleration due to electron scattering. It is given by qo=Li., It is given by $g_{\rm e}=\frac{\sigma_e L_*}{4 \pi r^2 c}$. " The optical depth parameter is where eg, is the mean thermal velocity of the protons.", The optical depth parameter is where $v_{th}$ is the mean thermal velocity of the protons. Lot us define qi(re) as the radiative acceleration iu the part of the initial wind model. ic. without the increased mass-loss rate due to the bump im the subsonic region. aud gi(rr) as the radiative acceleration of the model with the increased.," Let us define $g_{\rm L}^{\rm init}(r)$ as the radiative acceleration in the part of the initial wind model, i.e. without the increased mass-loss rate due to the bump in the subsonic region, and $g_{\rm L}(r)$ as the radiative acceleration of the model with the increased." M. From Eqs., From Eqs. δ and 9 with Eq., \ref{eq:CAK} and \ref{eq:tCAK} with Eq. 2 we find that where the superscript “iit” refers to the initial model.," \ref{eq:continuity} we find that where the superscript “init” refers to the initial model." Let us now compare the terminal velocities of the initial model without the bump. to that with the increased niass-loss rate due to the bump. in a simple but crude wav. by solving the moment equation im the supersonic part of the wind.," Let us now compare the terminal velocities of the initial model without the bump, to that with the increased mass-loss rate due to the bump, in a simple but crude way, by solving the momentum equation in the supersonic part of the wind." If we neelect the terms due to the gas pressure aud due to the exavitv. the momentum equation in the supersonic partof the wind reduces to Solving the equation for the initial model aud the model with the increased results in the following expression," If we neglect the terms due to the gas pressure and due to the gravity, the momentum equation in the supersonic partof the wind reduces to Solving the equation for the initial model and the model with the increased results in the following expression" images at 1.4 anc GGHz.,images at 1.4 and GHz. " The confusion flux density at à given frequetcy Is given by the sum where v is the frequency in MHz. Sjs ts the flux density measured in the VLA image at 1425 MHz. o; is the spectral index of the confusing source measured from the VLA images at 1.4 and GGHz. and N, is the number of sources that fall within the beam of the catalog at frequency v."," The confusion flux density at a given frequency is given by the sum where $\nu$ is the frequency in MHz, $S_{1425}$ is the flux density measured in the VLA image at 1425 MHz, $\alpha_{i}$ is the spectral index of the confusing source measured from the VLA images at 1.4 and GHz, and $N_{\nu}$ is the number of sources that fall within the beam of the catalog at frequency $\nu$." Finally. we calculated the source flux density at a given frequency as this is the quantity listed in 77 of 55.," Finally, we calculated the source flux density at a given frequency as this is the quantity listed in 7 of 5." The total spectra of the five dying radio sources are show 1 bottom panel of Figs.11 to 5., The total spectra of the five dying radio sources are show in bottom panel of 1 to 5. For four of them. namely WNBI73446407.. WNB18314-5707. B2. 0120433. and B2 1610229. the integrated spectrum presents a strong exponential cutoff in the observed frequency range.," For four of them, namely WNB1734+6407, WNB1851+5707, B2 0120+33, and B2 1610+29, the integrated spectrum presents a strong exponential cutoff in the observed frequency range." However. WNBI829-691] shows an evident flattening of the integrated spectrun at high frequency.," However, WNB 1829+6911 shows an evident flattening of the integrated spectrum at high frequency." This flattening is due to the presencee of the core-jet component that dominates the spectrun at the highest frequencies., This flattening is due to the presence of the core-jet component that dominates the spectrum at the highest frequencies. We modeled the integrated spectra assuming the radiative energy losses to be dominant with respect to other processes (e.g. adiabatic losses)., We modeled the integrated spectra assuming the radiative energy losses to be dominant with respect to other processes (e.g. adiabatic losses). The pitch angles of the radiating electrons are assumed to be continually isotropized in a time that is shorter than the radiative time scale., The pitch angles of the radiating electrons are assumed to be continually isotropized in a time that is shorter than the radiative time scale. According to this assumption the synchrotron energy losses are statistically the same for all electrons., According to this assumption the synchrotron energy losses are statistically the same for all electrons. After its birth the source is supposed to be fuelled at a constant rate (1.e. phase) by the nuclear activity. for a duration fe).," After its birth the source is supposed to be fuelled at a constant rate (i.e. ) by the nuclear activity, for a duration $t_{\rm CI}$." " The injected particles are assumed to have a power law energy spectrum N(«e)xo€"", which will result in a power law radiation spectrum with spectral index «jj=(inj—13/2."," The injected particles are assumed to have a power law energy spectrum $N(\epsilon) \propto \epsilon^{-\delta_{\rm inj}}$, which will result in a power law radiation spectrum with spectral index $\alpha_{\rm inj} = (\delta_{\rm inj} - 1)/2$." " In this phase the source radio spectrum changes às a function of time in a way described by the shift of break frequency v, to ever lower values as the time. ἐς, increases: where B and Bc3.2501+zK are the source magnetic field and the inverse Compton equivalent magnetic. field. respectively."," In this phase the source radio spectrum changes as a function of time in a way described by the shift of break frequency $\nu_{\rm b}$ to ever lower values as the time, $t_s$, increases: where $B$ and $B_{IC}=3.25(1+z)^2$ are the source magnetic field and the inverse Compton equivalent magnetic field, respectively." Below and above ήν the spectral indices are respectively ayy) and a4 0.5., Below and above $\nu_{\rm b}$ the spectral indices are respectively $\alpha_{\rm inj}$ and $\alpha_{\rm inj}$ +0.5. " At the time fe, the power supply from the nucleus is switched-off.", At the time $t_{\rm CI}$ the power supply from the nucleus is switched-off. After that a new phase of duration. toy: begins (e. the phase)., After that a new phase of duration $t_{\rm OFF}$ begins (i.e. the ). A new break frequency vij; then appears. beyond which the radiation spectrum drops exponentially.," A new break frequency $\nu_{b\,high}$ then appears, beyond which the radiation spectrum drops exponentially." " This second high frequency break is related to the first by: where f,=fci+foie is the total source age (see e.g. Komissarov Gubanov 1994. Slee et al."," This second high frequency break is related to the first by: where $t_{\rm s}=t_{\rm CI}+t_{\rm OFF}$ is the total source age (see e.g. Komissarov Gubanov 1994, Slee et al." 2001. Parma et al.," 2001, Parma et al." 2007)., 2007). Thus. the above synchrotron model (hereafter Cloj4:) ts described by four parameters: In the CIoj4: model the magnetic field strength ts assumed to be uniform within the source.," Thus, the above synchrotron model (hereafter $_{\rm OFF}$ ) is described by four parameters: In the $_{\rm OFF}$ model the magnetic field strength is assumed to be uniform within the source." The fit of the Cloj4: is shown as as line in bottom panels of 11 to 5 while the best fit parameters are listed in 66., The fit of the $_{\rm OFF}$ is shown as as line in bottom panels of 1 to 5 while the best fit parameters are listed in 6. The fits are very good for all the five dying sources., The fits are very good for all the five dying sources. "weak flat priors (Mme ντ) on O,h? and η. instead of fixing them to the besttit values from CMB data.",weak flat priors $\pm 7\sigma_{WMAP7}$ ) on $\Omega_b h^2$ and $n_s$ instead of fixing them to the bestfit values from CMB data. In this section. we apply the method with two sealing parameters described in sec 3.42 to measure // and Oy.," In this section, we apply the method with two scaling parameters described in sec \ref{sec:two_rescaling} to measure $H$ and $D_A$." The main parameter space that we explore is LOAEOh.noedi(zopr).Datzorp).hl) and. the prior ranges are (οιορ2.0.3). (0.01859.0.02657). (0.865.— 1.059). (41.123). (723.1343). (0.00.0.13)1. respectively.," The main parameter space that we explore is $\{\Omega_mh^2, \Omega_bh^2, n_s, H(z_{eff}), D_A(z_{eff}), k_\star \}$ and the prior ranges are $\{(0.025,0.3)$, $(0.01859,0.02657)$, $(0.865,1.059)$ , $(41,123)$ , $(723,1343)$, $(0.09,0.13)\}$ respectively." " We obtainthe model independent measurements. //(0.35)=83n km ‘Mpc Land 24(0.35)=1089κ Mpc. from the LRG data alone (see reftable:mean,da))."," We obtainthe model independent measurements, $H(0.35)=83^{+13}_{-15}$ km $^{-1}$ $^{-1}$ and $D_A(0.35)=1089^{+93}_{-87}$ Mpc, from the LRG data alone (see \\ref{table:mean_hda}) )." " able reflable:cover, alrieydashowsthenormalizedeovariancemealtricof (HO.435) OQ,hb. LE(0.35)xraa). rsCa£D(C35), 100.35)\ and reffig:hdaSparams shows the 2D marginalized contours of this parameter set."," \\ref{table:covar_matrix_hda} shows the normalized covariance matrix of $\{H(0.35)$ , $D_A(0.35)$, $\Omega_mh^2$, $H(0.35)*r_s(z_d)$, $r_s(z_d)/D_A(0.35)$ $A(0.35)\}$, and \\ref{fig:hda5params} shows the 2D marginalized contours of this parameter set." Although using two rescaling parameters on the spherically-averaged correlation function cannot give better constraints on the cosmological parameters. it gives the model independent measurements of // and 24 which cannot be derived directly from the measurement of D.," Although using two rescaling parameters on the spherically-averaged correlation function cannot give better constraints on the cosmological parameters, it gives the model independent measurements of $H$ and $D_A$ which cannot be derived directly from the measurement of $D_V$." These can be compared to our result. for the two-dimensional two-point correlation function (Chuang&Wang 2011). //(0.35).=82.1rykms‘Alpe| and D'4(0.35)=1048.77 Mpe.," These can be compared to our result for the two-dimensional two-point correlation function \citep{Chuang:2011fy}, , $H(0.35)=82.1_{-4.9}^{+4.8}\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$ and $D_A(0.35)=1048_{-58}^{+60}$ Mpc." Not surprisingly. information is lost in the spherical averaging of data.," Not surprisingly, information is lost in the spherical averaging of data." To explore theredshtit dependency ofthe measurements., To explore theredshfit dependency ofthe measurements. We apply the method of one rescaling parameteron twosubsamples have +=and z=0.28 OAL., We apply the method of one rescaling parameter on twosubsamples have $z=0.16-0.36$and $z=0.28-0.44$ . The average weighted redshiftsof, The average weighted redshifts of Since the pioneering work of 7..77. and ?the presence of ÀA2196.2803 absorbers in ‘haloes’ extending to distances of ~50 l100h kpe about luminous galaxies has been well established.,"Since the pioneering work of \citet{1986A&A...155L...8B}, ,\citet{1990ApJ...357..321L, 1992ApJ...391...48L} and \citet{1994ApJ...437L..75S} the presence of $\lambda\lambda$ 2796,2803 absorbers in `haloes' extending to distances of $\sim$ $h^{-1}$ kpc about luminous galaxies has been well established." The more recent recognition of the importance of outllow. infall anc feedback processes in general for our knowledge of galaxy evolution has reinvigorated attempts to. understand. the processes responsible for the existence of extended: gaseous. haloes associated with luminous galaxies.," The more recent recognition of the importance of outflow, infall and feedback processes in general for our knowledge of galaxy evolution has reinvigorated attempts to understand the processes responsible for the existence of extended gaseous haloes associated with luminous galaxies." Strong. aabsorbers. A2796. rest-equivalent width (EW) 20.5AA. seen in the spectra of background: quasars reveal the presence. of relatively cool 277—103. ionised gas with neutral hydrogen. column. densitiess of⋅ 107.⊥↴ 22 2," Strong absorbers, $\lambda$ 2796 rest-equivalent width (EW) $\ga$, seen in the spectra of background quasars reveal the presence of relatively cool, $T$$\sim$ $^4$ , ionised gas with neutral hydrogen column densities of $\simeq$ $^{18}$ $^{22}$ $^{-2}$." llowever. we note that the selection effects are included in the results of Evans et al.(2009) and Campana et al.(2010).,"However, we note that the selection effects are included in the results of Evans et al.(2009) and Campana et al.(2010)." As pointed ont by Campana et al. (, As pointed out by Campana et al. ( 2010). at high redshift larger (han 4. (he intrinsic X-ray. emissions suffer lower absorption: thus. (he X-ray alterglows with low X-rav column densities are hard to be identified by Swift-NRT.,"2010), at high redshift larger than 4, the intrinsic X-ray emissions suffer lower absorption; thus, the X-ray afterglows with low X-ray column densities are hard to be identified by Swift-XRT." On the other hand. as we use the data [rom Scehady et al. (," On the other hand, as we use the data from Schady et al. (" "2010). alühough it was claimed that generally the selection effects on the distribution of host column densities are not significant. in our paper. in order to investigate the possible selection ellects on our results. first. we check the possible Ny,—z relation and the v1,—z relation respectively from the data of Schacly et al. (","2010), although it was claimed that generally the selection effects on the distribution of host column densities are not significant, in our paper, in order to investigate the possible selection effects on our results, first, we check the possible $N_{H,x}-z$ relation and the $A_v-z$ relation respectively from the data of Schady et al. (" 2010).,2010). " We see that the correlation between /Nq,, aud redshift has the efficient r=0.67 with null hvpotheses 0.0006. Chis relation could be due to the selection ellect. mentioned above. but we do not lind anv possible relation between <1, and redshift."," We see that the correlation between $N_{H,x}$ and redshift has the efficient $r=0.67$ with null hypotheses 0.0006, this relation could be due to the selection effect mentioned above, but we do not find any possible relation between $A_v$ and redshift." " As Ny), increases with redshift. /Nj,,/:.1. also increases wilh redshift."," As $N_{H,x}$ increases with redshift, $N_{H,x}/A_v$ also increases with redshift." " Second. aiming (to avoicl this selection effect. we use the average value <μιιν>=3.3xLO""?em? given by Schady οἱ al. ("," Second, aiming to avoid this selection effect, we use the average value $=3.3\times 10^{22} cm^{-2}$ given by Schady et al. (" "2010) to (οσίου v1, (o Nyy, again.","2010) to transfer $A_v$ to $N_{H,x}$ again." We plot the results in Fig., We plot the results in Fig. 8. panel (b)., \ref{f5} panel (b). By using the mean value of /NyyAly. the selection effect can be effectively depressed.," By using the mean value of $N_{H,x}/A_v$, the selection effect can be effectively depressed." After the depression of selection elleet. our model results still show a slight. trend of X-ray absorption evolution.," After the depression of selection effect, our model results still show a slight trend of X-ray absorption evolution." This evolution trend may be intrinsic., This evolution trend may be intrinsic. From our model. we see that the A-ray absorption is originally from (he SFR.," From our model, we see that the X-ray absorption is originally from the SFR." SFR has the redshift evolution as SER~(14 :)*!. , SFR has the redshift evolution as $SFR\sim (1+z)^{2.71}$ . "Under the assumption of solar metallicity. we have the intrinsic X-ray attenuation Vip,c(1+2)'°?."," Under the assumption of solar metallicity, we have the intrinsic X-ray attenuation $N_{H,x}\sim (1+z)^{1.22}$." Therefore. we conclude that the SFR redshilt evolution is ihe dominant reason for the X-ray attenuation evolution shown in Fig.," Therefore, we conclude that the SFR redshift evolution is the dominant reason for the X-ray attenuation evolution shown in Fig." 8. (b)., \ref{f5} (b). " If. we use the linear relation between N,,,./24,HNt and redshift. meaning the possible selection effects are included. we have the final results shown in Fig & (a)."," If we use the linear relation between $N_{H,x}/A_v$ and redshift, meaning the possible selection effects are included, we have the final results shown in Fig \ref{f5} (a)." We see that the intrinsic evolution plus the selection effects can fit (he observational data of Evans et al. (, We see that the intrinsic evolution plus the selection effects can fit the observational data of Evans et al. ( 2009) ancl Campana et al. (,2009) and Campana et al. ( 2010) well.,2010) well. " ""Through the analysis above we clearly see. (hat the final results of GRB N-ray absorption are the calculations of intrinsic SFR. redshift evolution. modified bv (he variation between Nyyfd and redshift."," Through the analysis above we clearly see, that the final results of GRB X-ray absorption are the calculations of intrinsic SFR redshift evolution, modified by the variation between $N_{H,x}/A_v$ and redshift." The later could be due to the selection effect., The later could be due to the selection effect. From Fig. 8..," From Fig. \ref{f5}," we see that the observational data have large scatter., we see that the observational data have large scatter. On the other hand. our model provides the different. values under the different dark halo masses and evolutionary (ime.," On the other hand, our model provides the different values under the different dark halo masses and evolutionary time." Therefore. we also conclude that the large absorption is due to the longer galactic evolution (me within the massive dark halo. while the small attenuation is due to the shorter galactic evolution lime within the smaller dark halo.," Therefore, we also conclude that the large absorption is due to the longer galactic evolution time within the massive dark halo, while the small attenuation is due to the shorter galactic evolution time within the smaller dark halo." From the theoretical point of view. we confirm that the absorption is [rom (he local environment of GRD. assuggested by Campana et al. (," From the theoretical point of view, we confirm that the absorption is from the local environment of GRB, assuggested by Campana et al. (" 2010).,"2010)," photometry (c.g. Wurtzetal. 2011).,photometry (e.g. \citealt{Kurtz11}) ). We obtained 34 UVES spectra to test the star for rapid racial velocity. variations., We obtained 34 UVES spectra to test the star for rapid radial velocity variations. The analysis of these spectra will be presented in a separate paper., The analysis of these spectra will be presented in a separate paper. ‘This star is among the faintest (V= 10.15) and. hottest (ο=LOOOO WI) stars we observed with FEROS.," This star is among the faintest $V = 10.15$ ) and hottest $T_{\rm eff} = 10\,000$ K) stars we observed with FEROS." Lines ofextscii..exiscii.. and some other rare earth. elements are present in he spectrum at moderate strength. for an Ap star.," Lines of, and some other rare earth elements are present in the spectrum at moderate strength for an Ap star." Some rotational broadening is present corresponding to sins=r0L5kkmss +., Some rotational broadening is present corresponding to $v \sin i = 7.0 \pm 1.5$ $^{-1}$. The magnetic field is strong and many ines show Zeeman splitting., The magnetic field is strong and many lines show Zeeman splitting. Components of the line are clearly. resolved as seen in refsv61513.., Components of the line are clearly resolved as seen in \\ref{sy61513}. Direct measurements of the magnetic field rom. his line and by fitting with synthetic spectrum calculated with οἶνο similar results. kkCi. This is another hot star (Zi= 98001xXIlx) in our target list.," Direct measurements of the magnetic field from this line and by fitting with synthetic spectrum calculated with give similar results, kG. This is another hot star $T_{\rm eff} = 9800$ K) in our target list." The spectrum is peculiar with rare earth element lines present. including andtextsci.. but many lines are rather shallow.," The spectrum is peculiar with rare earth element lines present, including and, but many lines are rather shallow." ‘The star shows a very strong magnetic field of kkC. which was not easv to recognize because of significant rotational broadening. resin?=17.0+L5kkmss +.," The star shows a very strong magnetic field of kG, which was not easy to recognize because of significant rotational broadening, $v \sin i = 17.0 \pm 1.5$ $^{-1}$." The rotational period should be no longer than several days., The rotational period should be no longer than several days. A comparison of the observed and synthetic profiles allowed us to distinguish blending and Zeeman splitting in the Iline and determine a significant magnetic field in this star., A comparison of the observed and synthetic profiles allowed us to distinguish blending and Zeeman splitting in the line and determine a significant magnetic field in this star. Zeeman splitting in the line is presented in relsv70702.., Zeeman splitting in the line is presented in \\ref{sy70702}. The split components show a complex doublet structure., The split components show a complex doublet structure. This may be explained. by high noise level or ending., This may be explained by high noise level or blending. A nonuniform distribution of iron in the line ormation region combined with different field: strengths also may be responsible for the asymmetry of the Zeeman oatterns., A nonuniform distribution of iron in the line formation region combined with different field strengths also may be responsible for the asymmetry of the Zeeman patterns. Some other spectral lines also show Zeeman structure. as is confirmed. by synthetic calculations for magnetic field streneths in the range 14.I6 kkCGi.. Zeeman splitting is visible. for example. inAA.. in aand inAA.," Some other spectral lines also show Zeeman structure, as is confirmed by synthetic calculations for magnetic field strengths in the range $14 - 16$ kG. Zeeman splitting is visible, for example, in, in and in." Most other. lines demonstrate. just magnetic xroacdening., Most other lines demonstrate just magnetic broadening. With such a strong magnetic Lickel this star is an important target for further observations and magnetic field analysis., With such a strong magnetic field this star is an important target for further observations and magnetic field analysis. This star has a peculiar spectrum with narrow lines., This star has a peculiar spectrum with narrow lines. Fhose of are very strong while rare earth clement lines. including andtextscii.. have moderate intensities.," Those of are very strong while rare earth element lines, including and, have moderate intensities." Phe doublet line of iis also present in the spectrum., The doublet line of is also present in the spectrum. The magnetic field is strong enough for partial splitting of the, The magnetic field is strong enough for partial splitting of the with increasing mass-loss rate. thus decreasing the prominence of the SiC feature in comparison to the AmC continuum.,"with increasing mass-loss rate, thus decreasing the prominence of the SiC feature in comparison to the AmC continuum." This decrease in SiC/AmC ratio with increasing. mass loss was verified by Chan&Kwok(1990) and explained as being due to carbon star evolution., This decrease in SiC/AmC ratio with increasing mass loss was verified by \citet{ChanKwok1990} and explained as being due to carbon star evolution. Similar trends were also reported by Lorenz-Martins&Lefévre(1993.1994) and by Groenewegen (1995)... Groenewegen (1995," Similar trends were also reported by \citet{Lorenz-MartinsLefevre1993,Lorenz-MartinsLefevre1994} and by \citet{Groenewegen1995}. \citet{Groenewegen1995}," ).. Specketal.(1997) and Blancoetal.(1998) compared the results of models using «- and B-SiC. finding that the dust containing e- was able to reproduce the spectra of most of their sources.," \citet{Specketal1997} and \citet{Blancoetal1998} compared the results of models using $\alpha$ - and $\beta$ -SiC, finding that the dust containing $\alpha$ -SiCwas able to reproduce the spectra of most of their sources." Bressanetal.(1998) included a treatment of AGB dust shells in their stellar population models. and they generated isochrones for comparison with IRAS data for Miras and OH/IR stars.," \citet{Bressanetal1998} included a treatment of AGB dust shells in their stellar population models, and they generated isochrones for comparison with IRAS data for Miras and OH/IR stars." vanLoonetal.(1999) performed RT modeling on the spectroscopy of LMC AGB stars to identify the chemistry of the circumstellar dust and calculated their mass-loss rates and luminosities., \citet{vanLoonetal1999} performed RT modeling on the spectroscopy of LMC AGB stars to identify the chemistry of the circumstellar dust and calculated their mass-loss rates and luminosities. Suh(2000) obtained empirical opacity functions for amorphous carbor dust based on their RT modeling of IR spectra as well as laboratory-measured optical data., \citet{Suh2000} obtained empirical opacity functions for amorphous carbon dust based on their RT modeling of IR spectra as well as laboratory-measured optical data. Groenewegen(2006) presented synthetic. photometry for O-rich and C-rich AGB. stars from the results of RT models that spanned the relevant range of stellar and dust shell parameters seen in Galactic AGB stars., \citet{Groenewegen2006} presented synthetic photometry for O–rich and C–rich AGB stars from the results of RT models that spanned the relevant range of stellar and dust shell parameters seen in Galactic AGB stars. In particular. they considered two kinds of dust species for carbon star dust shells: AmC and a mixture of AmC and a-SiC by mass.," In particular, they considered two kinds of dust species for carbon star dust shells: AmC and a mixture of AmC and $\alpha$ -SiC by mass." The theoretical work of Mattssonetal.(2008) and Wachteretal.(2008) showed that the mass-loss rates of carbon stars may not be sensitive to metallicity., The theoretical work of \citet{Mattssonetal2008} and \citet{Wachteretal2008} showed that the mass-loss rates of carbon stars may not be sensitive to metallicity. Numerous recent studies using spectra of AGB stars in low-metallicity Local Group galaxies (e.g... seem to support this claim.," Numerous recent studies using spectra of AGB stars in low-metallicity Local Group galaxies \citep[{\it e.g.}, seem to support this claim." Similar results were obtained by Groenewegenetal.(2007).. who found in their modeling of the IRS spectra of 60 carbon stars in the Magellanic Clouds that the trend of mass-loss rates with period of luminosity was comparable to that of Galactic sources.," Similar results were obtained by \citet{Groenewegenetal2007}, who found in their modeling of the IRS spectra of 60 carbon stars in the Magellanic Clouds that the trend of mass-loss rates with period of luminosity was comparable to that of Galactic sources." Groenewegenetal.(2009) extended this study to a larger sample. including 110 carbon stars. and compared their mass-loss rates and luminosities with those predicted by evolutionary models as well as dynamical wind models.," \citet{Groenewegenetal2009} extended this study to a larger sample, including 110 carbon stars, and compared their mass-loss rates and luminosities with those predicted by evolutionary models as well as dynamical wind models." Our aim is to develop a grid of RT models for dust shells around carbon stars so that we may fit the SAGE photometry of carbon star candidates and derive their mass-loss rates., Our aim is to develop a grid of RT models for dust shells around carbon stars so that we may fit the SAGE photometry of carbon star candidates and derive their mass-loss rates. These mass-loss rates will enable the calculation of the total carbon-star mass-loss return to the LMC., These mass-loss rates will enable the calculation of the total carbon-star mass-loss return to the LMC. As a first step. in this paper. we determine a representative set of dust properties for LMC C-rich AGB stars to be used as input to the modeling.," As a first step, in this paper, we determine a representative set of dust properties for LMC C–rich AGB stars to be used as input to the modeling." We present a rradiative transfer model for the circumstellar shell around the variable carbon star OGLE LMC LPV 28579 (SAGE J051306.40-690946.3) with the primary goal of deriving the dust properties with a physically realistic model of the source. as constrained by available data.," We present a radiative transfer model for the circumstellar shell around the variable carbon star OGLE LMC LPV 28579 (SAGE J051306.40-690946.3) with the primary goal of deriving the dust properties with a physically realistic model of the source, as constrained by available data." We have also used this approach in Sargent et al., We have also used this approach in Sargent et al. 2010 (in press) for the O-rich AGB stars and red supergiants., 2010 (in press) for the O–rich AGB stars and red supergiants. This paper ts organized as follows., This paper is organized as follows. We describe the observational data for OGLE LMC LPV 28579 (hereafter LPV 28579) from various studies in Sect. 2.., We describe the observational data for OGLE LMC LPV 28579 (hereafter LPV 28579) from various studies in Sect. \ref{sec:cagbmodel:obs}. In Sect. 3..," In Sect. \ref{sec:cagbmodel:analysis}," we provide details of our radiative transfer model for the circumstellar dust. as well as a simple model for the molecular features observed in the spectrum.," we provide details of our radiative transfer model for the circumstellar dust, as well as a simple model for the molecular features observed in the spectrum." We discuss the results of the models in Sect. 4.., We discuss the results of the models in Sect. \ref{sec:cagbmodel:discuss}. The choice of LPV 28579 for this study was motivated by the availability of both SAGE photometry and SAGE-Spec spectroscopic data., The choice of LPV 28579 for this study was motivated by the availability of both SAGE photometry and SAGE-Spec spectroscopic data. The SAGE-Spee program selected a bright subsample of the SAGE AGB candidates for good quality spectra., The SAGE-Spec program selected a bright subsample of the SAGE AGB candidates for good quality spectra. This requirement means that the spectroscopic sample is biased towards redder colors. and that LPV 28579 is redder than most carbon stars in the LMC.," This requirement means that the spectroscopic sample is biased towards redder colors, and that LPV 28579 is redder than most carbon stars in the LMC." Nevertheless. it is only moderately optically thick. and exhibits features found in typical carbon stars.," Nevertheless, it is only moderately optically thick, and exhibits features found in typical carbon stars." Its spectrum (see Sect., Its spectrum (see Sect. 2.3 for details) shows the overall continuum emission from carbon dust as well as a significant 11.3 gem feature due to SiC. which makes it a good testbed for the dust properties around LMC carbon stars.," \ref{subsec:cagbmodel:obs:sagespec} for details) shows the overall continuum emission from carbon dust as well as a significant 11.3 $\mu$ m feature due to SiC, which makes it a good testbed for the dust properties around LMC carbon stars." " Groenewegen(2004) classified the star as an obscured AGB candidate. while in Paper I we labelled it an ""extreme"" AGB star based on the Blumetal.(2006). selection criterion (J-[3.6]>3.1] mag)."," \citet{Groenewegen2004} classified the star as an obscured AGB candidate, while in Paper I we labelled it an “extreme"" AGB star based on the \citet{Blumetal2006} selection criterion $J-[3.6]>3.1$ mag)." Examination of the SAGE-Spec spectrum (Section 2.3)) shows the 11.3 jm ssilicon carbide feature to be in emission., Examination of the SAGE-Spec spectrum (Section \ref{subsec:cagbmodel:obs:sagespec}) ) shows the 11.3 $\mu$ silicon carbide feature to be in emission. Moreover. results from the present modeling work (Section 3.1.5)) suggest at best a moderate 11.3 jm ooptical depth.," Moreover, results from the present modeling work (Section \ref{subsubsec:cagbmodel:parvar}) ) suggest at best a moderate 11.3 $\mu$ optical depth." Based on this information. LPV 28579 would not be considered an extreme carbon star (Specketal.2009).," Based on this information, LPV 28579 would not be considered an extreme carbon star \citep{Specketal2009}." . Photometry for LPV 28579 is available from many recent LMC surveys (e.g...2007). enabling us to constrain its spectral energy distribution (SED).," Photometry for LPV 28579 is available from many recent LMC surveys \citep[{\it e.g.}, enabling us to constrain its spectral energy distribution (SED)." We have combined the SAGE data with photometry from the optical Magellanic Clouds Photometric Survey (MCPS:Zantskyetal.1997) as well as the 2 micron All Sky Survey (2MASS.Skrutskieetal.2006).," We have combined the SAGE data with photometry from the optical Magellanic Clouds Photometric Survey \citep[MCPS;][]{Zaritskyetal1997} as well as the 2 micron All Sky Survey \citep[2MASS,][]{Skrutskieetal2006}." .. We discuss the optical and NIR variability observations in Sect. 2.1..," We discuss the optical and NIR variability observations in Sect. \ref{subsec:cagbmodel:obs:variability}," the SAGE photometry in Sect., the SAGE photometry in Sect. 2.2. and the SAGE-Spec data in Sect. 2.3.., \ref{subsec:cagbmodel:obs:sagephot} and the SAGE-Spec data in Sect. \ref{subsec:cagbmodel:obs:sagespec}. In Fig. 5...," In Fig. \ref{fig:cagbmodel:variability}," we show the full range of photometry and spectroscopy values measured to illustrate the source variability., we show the full range of photometry and spectroscopy values measured to illustrate the source variability. In this paper. we only model the SAGE Epoch | photometry. using the optical and NIR data along with the IRS spectrum to constram the shape of the resulting SED.," In this paper, we only model the SAGE Epoch 1 photometry, using the optical and NIR data along with the IRS spectrum to constrain the shape of the resulting SED." LPV 28579 was observed as part of the Optical Gravitational Lensing Experiment (OGLE-II:Zebrunetal.2001) survey of the Magellanic Clouds., LPV 28579 was observed as part of the Optical Gravitational Lensing Experiment \citep[OGLE-II;][]{Zebrunetal2001} survey of the Magellanic Clouds. The bband light curve ts available as part of the OGLE-II variable star catalog (Szymanski2005) as well as the OGLE-III list of long-period variables (LPVs) as described in Soszynskietal.(2009).. Based on its light curve. LPV 28579 was classified as a Mira-type LPV.," The band light curve is available as part of the OGLE-II variable star catalog \citep{Szymanski2005} as well as the OGLE-III list of long-period variables (LPVs) as described in \citet{Soszynskietal2009}.. Based on its light curve, LPV 28579 was classified as a Mira-type LPV." Itaet and Groenewegen(2004) crossmatched the OGLE- data with the IRSF LMC Survey (Katoetal. 2007).. DENIS (Epchteinetal.1999) and 2MASS All-Sky Release," \citet{Itaetal2004} and \citet{Groenewegen2004} crossmatched the OGLE-II data with the IRSF LMC Survey \citep{Katoetal2007}, , DENIS \citep{Epchteinetal1999} and 2MASS All-Sky Release" only the deviation /=f—f* from anarbilrary.. but judiciously chosen. underlying equilibrium distribution f.,"only the deviation $f^d \equiv f - f^e$ from an, but judiciously chosen, underlying equilibrium distribution $f^e$." la other words. computational particles represent the deviation from equilibrium and. as a result. they may be positive or negative. depending on (the sign of the deviation [rom equilibrium at the location in phase space where they reside.," In other words, computational particles represent the deviation from equilibrium and, as a result, they may be positive or negative, depending on the sign of the deviation from equilibrium at the location in phase space where they reside." As in other particle schemes |10].. in (he interest of computational efficiency. eachcomputational devialional particle represents annumber Noy of physical deviational particles.," As in other particle schemes \cite{bird}, in the interest of computational efficiency, each deviational particle represents an $N_\textrm{eff}$ of physical deviational particles." " A dilute gas in equilibrium is described by a Maxwell-Doltzmann distribution. leading to a local equilibrium distribution that is parametrized by the local number densitv Àj,=Πορτ.) Che local flow velocity uu.= unmd(r./). and the most probable speed cj=/2/hT1,./mr based on local temperature TioeDyG.)."," A dilute gas in equilibrium is described by a Maxwell-Boltzmann distribution, leading to a local equilibrium distribution that is parametrized by the local number density $n_{loc}=n_{loc}({\bf r},t)$ the local flow velocity ${\bf u}_{loc}={\bf u}_{loc}({\bf r},t)$ , and the most probable speed $c_{loc}=\sqrt{2k_bT_{loc}/m} $ based on local temperature $T_{loc}=T_{loc}({\bf r},t)$." " Here. fy, is Doltzmann's constant and m is the molecular mass."," Here, $k_b$ is Boltzmann's constant and $m$ is the molecular mass." " In the work that follows. the underlying equilibrium distribution (/*) will be identified wilh absolute equilibrium where. ny is-- a reference.., (equilibrium)+15[ναλ number-. densityM7 and eg.=—/2,T4/m‘+ isio the mostH probable molecular speed based on (he reference temperature Z5."," In the work that follows, the underlying equilibrium distribution $f^e$ ) will be identified with absolute equilibrium where $n_0$ is a reference (equilibrium) number density and $c_0=\sqrt{2k_bT_0/m}$ is the most probable molecular speed based on the reference temperature $T_0$." This choice provides a reasonable balance between generalitv. computational elliciency ancl simplicity.," This choice provides a reasonable balance between generality, computational efficiency and simplicity." Other choices are of course possible aud. depending on (he problem.perhapsmore efficient.," Other choices are of course possible and, depending on the problem,perhapsmore efficient." However. care needs to be taken," However, care needs to be taken" W7V star.,K7V star. RY analysis supports the single nature of FR Che., RV analysis supports the single nature of FR Cnc. Anticorrelation between BIS and RY also indicates that the RV variations are due to stellar activity variations and not due to à secondary companion., Anticorrelation between BIS and RV also indicates that the RV variations are due to stellar activity variations and not due to a secondary companion. " The kinematies study. based on obtained galactic space- components (C.V. M) of FR οπο, shows that this star clearly lies in the voung disc population velocity space and might also belong to LC 2391 moving group. although the Eeeen kinematic criteria shows that PR €nc may not be a member of anv ALG in the voung disc area."," The kinematics study, based on obtained galactic space-velocity components $U,~V,~W$ ) of FR Cnc, shows that this star clearly lies in the young disc population velocity space and might also belong to IC 2391 moving group, although the Eggen kinematic criteria shows that FR Cnc may not be a member of any MG in the young disc area." Phe Lil A6707.8 averaged: M measured is 34niX.. eiving the spectral tvpe of FR Che. it is in agreement. with being a voung object tween LO120 Myr.," The Li $\lambda$ 6707.8 averaged $EW$ measured is 34, giving the spectral type of FR Cnc, it is in agreement with being a young object between 10–120 Myr." The Ho line was always observed above the continuum in all the obtained spectra., The $\alpha$ line was always observed above the continuum in all the obtained spectra. Measuring. the £M of this ine. we found that the Ho emission. £M average in every season is quite dilferent.," Measuring the $EW$ of this line, we found that the $\alpha$ emission $EW$ average in every season is quite different." In. 2004. as with the photometry. spectroscopic indicators of chromospheric activity show a ueh level of activity which decreased. in 2005.," In 2004, as with the photometry, spectroscopic indicators of chromospheric activity show a high level of activity which decreased in 2005." The Ca (ICE) is included in our echelle spectra., The Ca (IRT) is included in our echelle spectra. Erom the ratio of excess emission {ΕΕ we found that in PR Che. Ca emission comes from plage-like regions.," From the ratio of excess emission $EW$ we found that in FR Cnc, Ca emission comes from plage-like regions." We noticed that PR οπο can show an activity evele of 4-5 vears. although further follow up will confirm this perioclicity.," We noticed that FR Cnc can show an activity cycle of 4-5 years, although further follow up will confirm this periodicity." " Since FR Cne is a rapid rotator. we generated an indirect starspot map using the DopplerTomography of Stars imagine, code."," Since FR Cnc is a rapid rotator, we generated an indirect starspot map using the DopplerTomography of Stars imaging code." From it we derive e sin ¢ = 46.2+0.8 1 . ∣∖ ⋅ latest ↳⊔↓⊳∖⋜⋯∠⇂∣∶⋅↱≻⋅↱≻∶," From it we derive $v$ sin $i$ = $46.2 \pm 0.8$ km $^{-1}$ and $i = 55 \pm 5^{\circ}$." ∶⋅↱≻⊳↓⊲∐≺⊔≼⇍∣⋊⋅⇂∪⊔⋏∙≟≱∖↥∪∪⊔⋖⋅∪⇂↥⇂↥∢⋅ spectral types to have been imaged with the Doppler ‘Tomography., FR Cnc belongs to one of the latest spectral types to have been imaged with the Doppler Tomography. " We independently estimated a rotational velocity. of L""It €ne during our observations using Queloz method (Sect.", We independently estimated a rotational velocity of FR Cnc during our observations using Queloz method (Sect. 53B) and by the DL fits (Sect., 5.3) and by the D.I. fits (Sect. 7)., 7). Although they are dillerences in the results of the two methods. they are consistent.," Although they are differences in the results of the two methods, they are consistent." In Table 7 we have put as the rotational velocity of FR οπο. the value obtained in the D.L as it is likely more accurate.," In Table \ref{tab:par} we have put as the rotational velocity of FR Cnc, the value obtained in the D.I. as it is likely more accurate." Despite the short rotation period and its late spectral ἵνρο FR Cne shows very. few [lare events.," Despite the short rotation period and its late spectral type, FR Cnc shows very few flare events." Lt shows high level of activity as it is à voung star. but an unusually short variability clue to the redistribution of activity features on the stellar surface.," It shows high level of activity as it is a young star, but an unusually short variability due to the redistribution of activity features on the stellar surface." While this variability is. rellected in the changes of the amplitude of brightness. the mean xiehtness permanently is nearly constant. indicating that he percentage of stellar surface. covered. by spots is also constant.," While this variability is reflected in the changes of the amplitude of brightness, the mean brightness permanently is nearly constant, indicating that the percentage of stellar surface covered by spots is also constant." The spots location is also unusual. not showing a volar spot like other EIx stars do but a distribution more resembling those seen in AILM2 cbwarfs.," The spots location is also unusual, not showing a polar spot like other F–K stars do but a distribution more resembling those seen in M1–M2 dwarfs." Although this may » indicative of a distributed dvnamo. the mid-high Latitude spot locations are more suggestive of an interface ονπαπιο under the action of rapid rotation.," Although this may be indicative of a distributed dynamo, the mid-high latitude spot locations are more suggestive of an interface dynamo under the action of rapid rotation." We can only speculate as o whether FR Cne is representative of a regime in which a convective-shell-tvpe dvnamo gives way to a Lully convective dvnamo., We can only speculate as to whether FR Cnc is representative of a regime in which a convective-shell-type dynamo gives way to a fully convective dynamo. Polarimetric observations of the magnetic field by Donatietal. (2008)) ancl Morinetal. (2008)) for example sugeest that this occurs at a later spectral tvpe of MA. whereas other chromospheric indicators show no obvious changes until later M spectral types (e.g. Alohanty&Basri 2003)).," Polarimetric observations of the magnetic field by \citeauthor{donati08mdwarfs} \citeyear{donati08mdwarfs}) ) and \citeauthor{morin08mdwarfs} \citeyear{morin08mdwarfs}) ) for example suggest that this occurs at a later spectral type of M4, whereas other chromospheric indicators show no obvious changes until later M spectral types (e.g. \citeauthor{mohanty03activity} \citeyear{mohanty03activity}) )." Further spectroscopy with a higher cadence would enable more detailed maps to be derived. with multiple epochs enabling the evolution of starspots to be investigated.," Further spectroscopy with a higher cadence would enable more detailed maps to be derived, with multiple epochs enabling the evolution of starspots to be investigated." " A. Golovin is thankful to Dr. Anju Alukaclam ancl Dr. Paula Szkody for useful discussions concerning Fisher tandomiüzation “Test in. periodogram analysis. to Dr. Ancdráss Holl (IXonkolv. Observatory. Budapest. Hungary) or valuable comments on VOTable format and help with converting photometric sequence to it in order to align on DSS image inALADIN. to Nick Malvgin ancl Dr. Lucila ""akulialkk for useful cliscussions ancl proof-reading of the nianuscript."," A. Golovin is thankful to Dr. Anju Mukadam and Dr. Paula Szkody for useful discussions concerning Fisher Randomization Test in periodogram analysis, to Dr. Andráss Holl (Konkoly Observatory, Budapest, Hungary) for valuable comments on VOTable format and help with converting photometric sequence to it in order to align on DSS image in, to Nick Malygin and Dr. Ludmila Pakuliak for useful discussions and proof-reading of the manuscript." ALCGállvez-Ortiz acknowledges the financial support rom the European Conimission in the form of Marie Curie. Intra. European Fellowship ΣΕο and the partial support by the Spanish MICINN. under he C'onsolider-Ingenio 2010 Program grant CSD2006-00070: First Science with the GPC (http://wwwdac.es/consolicler-ingenio-gtc)., M.C.Gállvez-Ortiz acknowledges the financial support from the European Commission in the form of Marie Curie Intra European Fellowship (PIEF-GA-2008-220679) and the partial support by the Spanish MICINN under the Consolider-Ingenio 2010 Program grant CSD2006-00070: First Science with the GTC (http://www.iac.es/consolider-ingenio-gtc). ALC. Gállvez-Ortiz and J. Barnes also has received support from RoPACS during this research. a Marie Curie. Initial Training Network funded. by the European Commission's Seventh Framework Programme.," M.C. Gállvez-Ortiz and J. Barnes also has received support from RoPACS during this research, a Marie Curie Initial Training Network funded by the European Commission's Seventh Framework Programme." This work was partly supported by the Spanish Ministerio de Ciencia ο Innovacion (CMICINN). Programa Nacional ce AXstronomia y Astrofisica under grant AYA2008-00695. ancl under erant AYA2008-06423-C'03-03.. and the Comunidad: cle Madrid uncer PRICIT project 82009/LESP-1496 CXstroMacrid).," This work was partly supported by the Spanish Ministerio de Ciencia e Innovacion (MICINN), Programa Nacional de Astronomia y Astrofisica under grant AYA2008-00695, and under grant AYA2008-06423-C03-03, and the Comunidad de Madrid under PRICIT project S2009/ESP-1496 (AstroMadrid)." X. Golovin is thankful to Universidad Complutense de Madrid for hospitality and for all the efforts and the help during his visit to Spain in 2008 July and. 2009 February., A. Golovin is thankful to Universidad Complutense de Madrid for hospitality and for all the efforts and the help during his visit to Spain in 2008 July and 2009 February. This publication mace use of the interactive sky atlas. operated at CDS. Strasbourg. France (Bonnarel 20002) and of NASA's Astrophysics Data System.,"This publication made use of the interactive sky atlas, operated at CDS, Strasbourg, France \citeauthor{aladin} \citeyear{aladin}) ) and of NASA's Astrophysics Data System." 1021. Ginx=2000 and (ag=1021. with a preferred direction pointing towards (0.0)=(577.517) and ananisotropy alplitude of g.= 0.1. using the best-fit vear WAIAP ACDAL power spectrum Usomatsuetal. 2009).,", $\ell_{\textrm{max}}=2000$ and $\ell_{\textrm{cutoff}}=1024$, with a preferred direction pointing towards $(\theta, \phi) = (57^{\circ}, 57^{\circ})$ and ananisotropy amplitude of $g_* = 0.1$ , using the best-fit 5-year WMAP $\Lambda$ CDM power spectrum \citep{komatsu:2009}." . The map is convolved with a Caussian beam corresponding to the 113 GITz Planck channel. and white. uniforiiu noise is finally added.," The map is convolved with a Gaussian beam corresponding to the $143$ GHz Planck channel, and white, uniform noise is finally added." " The beam FEWIIM for this frequeney chamucl is 7.1"". aud the temperature noise RAIS per Naa=1021 pixel is στ=12.248."," The beam FWHM for this frequency channel is $7.1'$, and the temperature noise RMS per $N_{\textrm{side}}=1024$ pixel is $\sigma_T = 12.2\mu\textrm{K}$." The polarization noise RAIS is 0p=23.34 (ThePlauckCollaboration 2006).., The polarization noise RMS is $\sigma_P = 23.3\mu\textrm{K}$ \citep{planck}. We perform three analyses of the simulated Planck sky map., We perform three analyses of the simulated Planck sky map. The first is au analysis on low-f ouo= 100) temperature data. the second high-( (LU= 500) temperature data while the third is alow-f analysis of TT|TE)EE polarization data.," The first is an analysis on $\ell$ $l_{\textrm{max}}^{\textrm{cutoff}}=400$ ) temperature data, the second $\ell$ $l_{\textrm{max}}^{\textrm{cutoff}}=800$ ) temperature data while the third is a$\ell$ analysis of TT+TE+EE polarization data." The results are showu in Table 2.. where we reproduced the input parameters with typically ος=0.11£0.025.," The results are shown in Table \ref{tab:PLANCK}, where we reproduced the input parameters with typically $g_* = 0.11 \pm 0.025$." Note how the standard deviation of the posterior is lower than for the WALAP case., Note how the standard deviation of the posterior is lower than for the WMAP case. This is to be expected. as ligher imultipoles ( contribute more to the anisotropic effect. but not sienificautlv.," This is to be expected, as higher multipoles $\ell$ contribute more to the anisotropic effect, but not significantly." This is due to the fact that the off-diagonal correlation terms iu the covariance matrix have a lower values ou smaller scales., This is due to the fact that the off-diagonal correlation terms in the covariance matrix have a lower values on smaller scales. We determine the standard deviation of the yg posterior as a function of multipoles ( bv simulating a. uuconvolved. noiseless isotropic imap Including polarization data using the best-fit ACDMD power spectrum.," We determine the standard deviation of the $g_*$ posterior as a function of multipoles $\ell$ by simulating a unconvolved, noiseless isotropic map including polarization data using the best-fit $\Lambda$ CDM power spectrum." We then analyze this map for various f. obtaining the posterior distribution for cach run.," We then analyze this map for various $\ell$, obtaining the posterior distribution for each run." The results are seen in Figure 6.., The results are seen in Figure \ref{fig:planck_sigma}. Tere. we see that σέ} is very close to a power law in f. in good agreement witli the arguments given by Pullen&Kamioulkowski(2007) and (ουςου&Eriksen (2009)..," Here, we see that $\sigma(\ell_*)$ is very close to a power law in $\ell$ , in good agreement with the arguments given by \citet{pullen:2007} and \cite{groeneboom:2008b}. ." The best-fit power law function is and this cau be used toproduce rough forecasts for the, The best-fit power law function is and this can be used toproduce rough forecasts for the Acknowledgments.,Acknowledgments. This work has been funded by the following WBN grants: 2P03D01616.— 2PO3DO00911 2pP03D00415 and 2P03D01113. and also made use of the NASA Astrophysics Data System.," This work has been funded by the following KBN grants: 2P03D01616 2P03D00911, 2P03D00415 and 2P03D01113, and also made use of the NASA Astrophysics Data System." TD is grateful for the hospitality. of Ecole. Polvtechnique where this work was finishect., TB is grateful for the hospitality of Ecole Polytechnique where this work was finished. ETG samples constructed using this kind of color pre-selection.,ETG samples constructed using this kind of color pre-selection. This is the reason why. in Fig.," This is the reason why, in Fig." " | at masses /Vf,>3xΙΟ Mi. a range populated only by galaxies belonging to the NICMOS sample (see Fig."," 1 at masses $\mathcal{M}_*>3\times 10^{11}$ $_\odot$, a range populated only by galaxies belonging to the NICMOS sample (see Fig." 3) there are only compact ETGs., 3) there are only compact ETGs. In spite of this. Fig.," In spite of this, Fig." " | (lower panel) shows that the compactness of a galaxy. defined as the ratio between its effective radius R, and the effective radius R,--9 of an equal mass galaxy at z=0 derived from the local SM relation. does not show any trend with mass."," 1 (lower panel) shows that the compactness of a galaxy, defined as the ratio between its effective radius $_e$ and the effective radius $_{e,z=0}$ of an equal mass galaxy at $z=0$ derived from the local SM relation, does not show any trend with mass." This evidence conflicts with the hypothesis of a mass-dependent size evolution of ETGs. hypothesis suggested by many authors.," This evidence conflicts with the hypothesis of a mass-dependent size evolution of ETGs, hypothesis suggested by many authors." For instance.it has been suggested that only high-mass ETGs undergo size evolution (e.g. Newman et al.," For instance, it has been suggested that only high-mass ETGs undergo size evolution (e.g. Newman et al." 2010) or that they undergo the most rapid evolution (e.g. Ryan et al., 2010) or that they undergo the most rapid evolution (e.g. Ryan et al. 2010) being them on average smaller than their local counterparts., 2010) being them on average smaller than their local counterparts. At the same time. other authors have suggested at odd with this that only low-mass ETGs undergo size evolution to match the apparent lack of compact low-mass ETGs in the local Universe (e.g. van der Wel et al.," At the same time, other authors have suggested at odd with this that only low-mass ETGs undergo size evolution to match the apparent lack of compact low-mass ETGs in the local Universe (e.g. van der Wel et al." 2009)., 2009). " Actually. we find that normal and compact ETGs co-exist for large intervals of effective radius (0.4 kpe 1$ ). Furthermore. carbon-bearing molecules have different spectral appearances from the oxygen-bearing ones and thus cause Ap to have a different funetional behaviour.," Furthermore, carbon-bearing molecules have different spectral appearances from the oxygen-bearing ones and thus cause $\kappa_\mathrm{R}$ to have a different functional behaviour." Hellingetal.(2000) provided examples of monochromatic absorption coefficients for carbon-bearing molecules., \citet{2000A&A...358..651H} provided examples of monochromatic absorption coefficients for carbon-bearing molecules. The only two molecules that contribute significantly for either chemistry are CO and CN., The only two molecules that contribute significantly for either chemistry are CO and CN. As emphasised earlier. the presented data are primarily relevant to the envelopes of evolved low mass stars.," As emphasised earlier, the presented data are primarily relevant to the envelopes of evolved low mass stars." Chemical composition variations due to the TDU acting in AGB stars concern mostly the enrichment in carbon., Chemical composition variations due to the TDU acting in AGB stars concern mostly the enrichment in carbon. However. the dredged-up carbon in the envelope can be inputted back into the CN eyele. which partly converts to (see Introduction).," However, the dredged-up carbon in the envelope can be inputted back into the CN cycle, which partly converts to (see Introduction)." " By varying the abundance of nitrogen (more precisely '""N)). we add a further dimension to our data tables."," By varying the abundance of nitrogen (more precisely ), we add a further dimension to our data tables." These alterations have more direct consequences on the behaviour of the Rosseland mean in the sense that an increase in nitrogen always causes an increase in the opacity, These alterations have more direct consequences on the behaviour of the Rosseland mean in the sense that an increase in nitrogen always causes an increase in the opacity ihe OMCHI outflow.,the OMC1 outflow. The strongest fields are likely to be generated by shear dvnamos in the innermost parts of circumstellar disks surrounding individual massive stars., The strongest fields are likely to be generated by shear dynamos in the innermost parts of circumstellar disks surrounding individual massive stars. Future Zeeman measurements of clamps containing sub-clusters of massive protostars using the 24 to 26 jm iron lines with SOFIA may determine if energetically signilicant. eauss-strength fields can be generated in such environments (Il. Crutcher - private communication).," Future Zeeman measurements of clumps containing sub-clusters of massive protostars using the 24 to 26 $\mu$ m iron lines with SOFIA may determine if energetically significant, gauss-strength fields can be generated in such environments (R. Crutcher - private communication)." The DN/IXL outflow is velocity. segregated with relatively slow eas confined to a few tens of arc-seconds from radio source I and (he fastest ejecta. located near the tips of the (Fell) and Hs fingers about nnorlhwest aud southeast of (he core region.," The BN/KL outflow is velocity segregated with relatively slow gas confined to a few tens of arc-seconds from radio source I and the fastest ejecta, located near the tips of the [FeII] and $_2$ fingers about northwest and southeast of the core region." Proper motion measurements of visual-waveleneth ILL objects (such as IHE 205 through 210). near-infrared emission from shock-excited [Fell] and Ils (Figures 1 and 2). and the interferometric CO J=21 study of Zapata et al. (," Proper motion measurements of visual-wavelength HH objects (such as HH 205 through 210), near-infrared emission from shock-excited [FeII] and $_2$ (Figures 1 and 2), and the interferometric CO J=2–1 study of Zapata et al. (" 2010) inclicate that the DN/IXL outflow was generated by an explosive event about. 500 vears ago.,2010) indicate that the BN/KL outflow was generated by an explosive event about 500 years ago. This age coincides with the dvnamical re-arrangement of the massive stars in OAC curing whieh radio sources I. n. and BN were ejected (Gomez οἱ al.," This age coincides with the dynamical re-arrangement of the massive stars in OMC1 during which radio sources I, n, and BN were ejected (Gomez et al." 2005: 2008)., 2005; 2008). The slowest star. radio source I. i$ probably a compact binary consisting of roughly 160 AL. stars with a separation less than about 2 AU.," The slowest star, radio source I, is probably a compact binary consisting of roughly 10 $_{\odot}$ stars with a separation less than about 2 AU." Future long-baseline radio interferometry. or precision radial velocity measurements in the infrared may determine if this conjecture is true.," Future long-baseline radio interferometry, or precision radial velocity measurements in the infrared may determine if this conjecture is true." It. is proposed that the formation of this binary and the consequent release of 2 to 6xLOM eres of gravitational potential enerev powered both the motion of the stars and the supersonic expulsion of gas in the DN/IXL outflow., It is proposed that the formation of this binary and the consequent release of $2$ to $6 \times 10^{47}$ ergs of gravitational potential energy powered both the motion of the stars and the supersonic expulsion of gas in the BN/KL outflow. The slowest ejecta may have been produced al laree radii as the pre-ejection orbits of clumps in the envelope became unbound [following stellar ejection., The slowest ejecta may have been produced at large radii as the pre-ejection orbits of clumps in the envelope became unbound following stellar ejection. The fastest ejecta max. have originated [rom near the center of the potential well vacated bv the stars., The fastest ejecta may have originated from near the center of the potential well vacated by the stars. This situation is similar to that postulated by MeCauglirean and. Mac Low (1997) and Stone et al. (, This situation is similar to that postulated by McCaughrean and Mac Low (1997) and Stone et al. ( 1995). where the II; fingers are generated by the interaction between a slow. outer wind and a last. later ejected flow.,"1995), where the $_2$ fingers are generated by the interaction between a slow, outer wind and a fast, later ejected flow." The estimates based on simple models of envelopes and circumstellar disks with power-law density distributions indicate that (he gravitational energy. stored in orbital motion prior (o ejection can explain the energelies of the outflow following stellar ejection., The estimates based on simple models of envelopes and circumstellar disks with power-law density distributions indicate that the gravitational energy stored in orbital motion prior to ejection can explain the energetics of the outflow following stellar ejection. However. numerical modeling of realistic configurations is need to determine of this hypothesis is valid.," However, numerical modeling of realistic configurations is need to determine of this hypothesis is valid." The explosive OMCI. outflow: consists of multiple fingers and wakes of II» emission produced by the fastest ejecta plowing through the OAC core., The explosive OMC1 outflow consists of multiple fingers and wakes of $_2$ emission produced by the fastest ejecta plowing through the OMC1 core. The volume filling factor of the cavities created by (his ejecta is likely to be lower than the enclosed volume. especially towarcds tlie southeast.," The volume filling factor of the cavities created by this ejecta is likely to be lower than the enclosed volume, especially towards the southeast." Observations show that à reservoir of dense gas is located in the ‘hot, Observations show that a reservoir of dense gas is located in the `hot We investigate the relationship between the mass function and the magnification pattern using (wo light-curve statistics.,We investigate the relationship between the mass function and the magnification pattern using two light-curve statistics. The first is the structure function (Nj). delined by: where gy is the source position (or equivalently an," The first is the structure function $S(\Delta y)$, defined by: where $y$ is the source position (or equivalently an" "figure the emissions at Ho, FUV,micron,, and SPIRE bands in a set of Ha-shells located in the north part of the galaxy.","figure the emissions at $\alpha$, FUV, and SPIRE bands in a set of $\alpha$ -shells located in the north part of the galaxy." The location of these shells within the galaxy (white rectangle in Fig. 1)), The location of these shells within the galaxy (white rectangle in Fig. \ref{fig:spire250cat}) ) " is in a region where no significant oor eemission has been detected, but where diffuse emission is observed in the SPIRE bands."," is in a region where no significant or emission has been detected, but where diffuse emission is observed in the SPIRE bands." " The PACS bands aand micron)) were also examined, and we found some diffuse emission in the bbut no significant emission in the bband."," The PACS bands and ) were also examined, and we found some diffuse emission in the but no significant emission in the band." " As shown in Fig. 3,,"," As shown in Fig. \ref{fig:shell}," the shells have strong FUV emission in their centres., the shells have strong FUV emission in their centres. " The northern shell seems to have a knot where the emissions at FUV and Ha coincide, but the FUV is very nicely located in the centre for the bigger middle shell, suggesting that the shell could have been created by the stellar winds (SW) or supernova (SN) explosions coming from the stars in the cluster emitting at FUV."," The northern shell seems to have a knot where the emissions at FUV and $\alpha$ coincide, but the FUV is very nicely located in the centre for the bigger middle shell, suggesting that the shell could have been created by the stellar winds (SW) or supernova (SN) explosions coming from the stars in the cluster emitting at FUV." " Using the Ha image, the radius of the central Ha shell is estimated to be —150ppc."," Using the $\alpha$ image, the radius of the central $\alpha$ shell is estimated to be $\sim$pc." " Assuming an expansion velocity of ~50kkmss~! for the Ha shell consistent with previous observations of Ha expanding shells in rregions (?),, we derive a kinematical age for the central shell of ~3MMyr."," Assuming an expansion velocity of $\sim$ $^{-1}$ for the $\alpha$ shell consistent with previous observations of $\alpha$ expanding shells in regions \citep{2005A&A...430..911R}, we derive a kinematical age for the central shell of $\sim$ Myr." Dynamical ages of a few Myr are consistent with ages estimated for shells in dwarf galaxies (?).., Dynamical ages of a few Myr are consistent with ages estimated for shells in dwarf galaxies \citep{1998ApJ...506..222M}. " It is remarkable that no emission at iis seen in the central and southern shells, but there is emission from cool dust in the three SPIRE bands."," It is remarkable that no emission at is seen in the central and southern shells, but there is emission from cool dust in the three SPIRE bands." " We suggest that, during the time the shell is forming, the dust is mixed with ionised gas inside the rregion, a dust fraction is heated by the ionising radiation and emits atmicron,, while the rest is cool and emits in the SPIRE bands."," We suggest that, during the time the shell is forming, the dust is mixed with ionised gas inside the region, a dust fraction is heated by the ionising radiation and emits at, while the rest is cool and emits in the SPIRE bands." This could be the case for the northern shell in the process of formation., This could be the case for the northern shell in the process of formation. " Later, when the shell is created by the SW and SNe, we observe FUV emission in the centre, Ha emission from the shell, and cool dust outlining the Ha structure (see the central shell where the eemission clearly delineates the Ha shell)."," Later, when the shell is created by the SW and SNe, we observe FUV emission in the centre, $\alpha$ emission from the shell, and cool dust outlining the $\alpha$ structure (see the central shell where the emission clearly delineates the $\alpha$ shell)." This would be the first evidence that the dust participates in the kinematics of the gas inside the rregions and that the impact of the SW and SNe into the ISM also affects the interstellar dust., This would be the first evidence that the dust participates in the kinematics of the gas inside the regions and that the impact of the SW and SNe into the ISM also affects the interstellar dust. The behaviour shown in Fig., The behaviour shown in Fig. " 3 is also seen in a significant number of shells in the outer parts of the galaxy, and it would be very interesting to relate it with the existence of bbubbles observed in other galaxies (?)."," \ref{fig:shell} is also seen in a significant number of shells in the outer parts of the galaxy, and it would be very interesting to relate it with the existence of bubbles observed in other galaxies \citep{2009ApJ...704.1538W}." A multi-wavelength comparison in a larger sample of shells would be needed to study this issue further., A multi-wavelength comparison in a larger sample of shells would be needed to study this issue further. " For the Local Group spiral galaxy 333, using the unprecedented resolution and sensitivity of the Herschel SPIRE photometric data, we focus on the compact emission and conclude the following."," For the Local Group spiral galaxy 33, using the unprecedented resolution and sensitivity of the SPIRE photometric data, we focus on the compact emission and conclude the following." ) and {ἐν=0.03.,10 and $H/r=0.03$. The outer magnetic resonance is also represented., The outer magnetic resonance is also represented. To each of these outer turning points ancl resonance eeponi an inner turning point or resonance located at the same distance from corotation to first order in £f/r or 17m., To each of these outer turning points and resonance corresponds an inner turning point or resonance located at the same distance from corotation to first order in $H/r$ or $1/m$. Similar plots are obtained for other values of 17r., Similar plots are obtained for other values of $H/r$. Artvmowicz (1993) has calculated that. in a nonmagnetized disc. the location of the turning points is given by. (his eq. ," Artymowicz (1993) has calculated that, in a nonmagnetized disc, the location of the turning points is given by (his eq. [" "39)): so that. for mτο, the distance to corotation is 2/4points.","39]): so that, for $m \rightarrow \infty$, the distance to corotation is $2H/3$." In a magnetized. we identify up to three turning that we label Ra. 12 and is: In figureD 1.. the shaded areas indicate where the waves are evanescent (Le. A<0).," In a magnetized, we identify up to three turning points, that we label R1, R2 and R3: In figure \ref{fig1}, the shaded areas indicate where the waves are evanescent (i.e. ${\cal K}<0$ )." In contrast to the nonmagnetic5 case. there is a region inside the outermost turning points where waves propagate.," In contrast to the nonmagnetic case, there is a region inside the outermost turning points where waves propagate." This region moves toward the corotation radius and. decreases in size as 2 increases., This region moves toward the corotation radius and decreases in size as $\beta$ increases. Lt disappears altogether for infinite 2., It disappears altogether for infinite $\beta$. Note that the magnetic resonances are contained within this region. so that the singular slow modes excited at the magnetic resonances can propagate.," Note that the magnetic resonances are contained within this region, so that the singular slow modes excited at the magnetic resonances can propagate." Since waves do not propagate around corotation for m2»mo. we expect a torque eutollat large m like in the nonmagnetic Case.," Since waves do not propagate around corotation for $m>m_{\rm crit}$, we expect a torque cutoff at large $m$ like in the nonmagnetic case." We can check whether waves propagate or not around corotation bv taking the limit Nos0 (Le. rsrj) in the expression (55)) above., We can check whether waves propagate or not around corotation by taking the limit $X \rightarrow 0$ (i.e. $r \rightarrow r_p$ ) in the expression \ref{Kcoef}) ) above. In the nonmagnetic case (7.7 oc): Since this is negative. the waves are evanescent around corotation in that case.," In the nonmagnetic case $\beta \rightarrow \infty$ ): Since this is negative, the waves are evanescent around corotation in that case." When 2 is finite: This is positive when m«moa with moi=3V/3/(h). so that waves propagate around corotation for these values of nm.," When $\beta$ is finite: This is positive when $mT1, at r> 35R.."," In the numerical solution presented in Section \ref{sec:solution}, , $T_{\parallel \rm p} > T_{\perp \rm p}$ at $r > 35 R_{\sun}$ ." " Incontrast.in Helios measurements of fast- streams with U>700 Knys. Tj, typically exceeds Tj, between r=GOR. and r=1308. (2)."," Incontrast,in Helios measurements of fast-wind streams with $U>700$ km/s, $T_{\perp \rm p}$ typically exceeds $T_{\parallel \rm p}$ between $r=60 R_{\sun}$ and $r= 130 R_{\sun}$ \citep{marsch82b}. ." Part of this, Part of this The smetallie-lined™ or Ani stars are A-type stars which have strong absorption lines of some metals such as Zn. Sr. Zr and. Ba ancl weaker lines of other metals such as Ca and/or Se relative to their spectral type as determined by the strength of the hydrogen lines (PrestonLOT4).,"The “metallic-lined” or Am stars are A-type stars which have strong absorption lines of some metals such as Zn, Sr, Zr and Ba and weaker lines of other metals such as Ca and/or Sc relative to their spectral type as determined by the strength of the hydrogen lines \citep{preston74}." . The strong metallic lines are more tvpical of an E star rather than an A star., The strong metallic lines are more typical of an F star rather than an A star. The work of Michaud:(1970) established radiative diffusion in a strong magnetic field as the likely cause of the chemical peculiarities in Ap stars., The work of \citet{michaud70} established radiative diffusion in a strong magnetic field as the likely cause of the chemical peculiarities in Ap stars. When the magnetic field is absent. diffusion leads to the Αναι stars (Watson1971).," When the magnetic field is absent, diffusion leads to the Am/Fm stars \citep{watson71}." . The presence of magnetic fields in Ani stars has been investigated. but with negative results. (c.g. Fossatictal. (200723).," The presence of magnetic fields in Am stars has been investigated, but with negative results, (e.g. \citet{fossati07}) )." A peculiarity of Am stars is that their mojectecd rotational velocities are generally much. smaller han normal A stars and they are nearly always members of close binary systems., A peculiarity of Am stars is that their projected rotational velocities are generally much smaller than normal A stars and they are nearly always members of close binary systems. Rotational braking by tical friction in a binary system is regarded as a possible explanation for the ow rotational velocities in nmi stars., Rotational braking by tidal friction in a binary system is regarded as a possible explanation for the low rotational velocities in Am stars. Slow rotation further assists the segregation of elements by dillusion., Slow rotation further assists the segregation of elements by diffusion. The abundance anomalies predicted: by the cilfusion hypothesis are usually much larger than observed., The abundance anomalies predicted by the diffusion hypothesis are usually much larger than observed. " Richer.Alichaud&""Turcotte.(2000) developed detailed models of the structure anc evolution of Am/Enm stars using OPAL opacities. taking into account atomic cliffusion ancl the elect of radiative: acceleration."," \citet{richer00} developed detailed models of the structure and evolution of Am/Fm stars using OPAL opacities, taking into account atomic diffusion and the effect of radiative acceleration." “Phese models develop a convective zone due to ionization of iron-group elements at a temperature of approximately 200.000 Ix. In. addition to his convective zone. these stars also have a thin superficial convective zone in which IE ancl are partially ionizect.," These models develop a convective zone due to ionization of iron-group elements at a temperature of approximately 200,000 K. In addition to this convective zone, these stars also have a thin superficial convective zone in which H and are partially ionized." Dv assuming sullicicnt overshoot due to turbulence. these separate convective zones become one large convective zone.," By assuming sufficient overshoot due to turbulence, these separate convective zones become one large convective zone." ‘The resulting mixing cilutes the large abundance anomalies wedieted by previous mocdel. leading to abuncances which closely resemble those observed in πιη stars.," The resulting mixing dilutes the large abundance anomalies predicted by previous model, leading to abundances which closely resemble those observed in Am/Fm stars." " A detailed abundance analysis of οσα Am stars xloneing to the Praesepe cluster (Fossatietal.2007). show good agreement with the predictions of Richer.Michaud&‘Tureotte(2000). for almost all the common elements except or Na ancl possibly S. The models of Richer.Michaud.&""Turcotte.(2000) assume a certain acd-hoe parametrization of turbulent transport cocllicicnts which are adjusted o reproduce observations.", A detailed abundance analysis of eight Am stars belonging to the Praesepe cluster \citep{fossati07} show good agreement with the predictions of \citet{richer00} for almost all the common elements except for Na and possibly S. The models of \citet{richer00} assume a certain ad-hoc parametrization of turbulent transport coefficients which are adjusted to reproduce observations. Other parameterizations of, Other parameterizations of shock acceleration.,shock acceleration. If dark matter in galaxy clusters consisted of neutralinos. their annihilation would produce high-energy charged particles as well.," If dark matter in galaxy clusters consisted of neutralinos, their annihilation would produce high-energy charged particles as well." For a review. see e.g.. Colafrancesco 2010 and references therein.," For a review, see e.g., Colafrancesco \cite{Cola10} and references therein." The inverse-Compton spectrum of this component is very different from that of the thermal component. because the energy of CMB photons is boosted to frequencies much higher than the submm frequencies observable with CMB instruments (see Colafrancesco 2008 for details).," The inverse-Compton spectrum of this component is very different from that of the thermal component, because the energy of CMB photons is boosted to frequencies much higher than the submm frequencies observable with CMB instruments (see Colafrancesco \cite{Cola08} for details)." " This component is normally sub-dominant with respect to the thermal component: its optical depth 7,, is at least 50 times less than r,.", This component is normally sub-dominant with respect to the thermal component: its optical depth $\tau_{nt}$ is at least 50 times less than $\tau_t$. The parameters characterizing the spectrum. in addition to the optical depth. are the spectral index of the power-law spectrum of the energy of the electrons c (typically around -2.7). and their minimum momentum pj. typically of the order of a few MeV/c.," The parameters characterizing the spectrum, in addition to the optical depth, are the spectral index of the power-law spectrum of the energy of the electrons $\alpha$ (typically around -2.7), and their minimum momentum $p_1$, typically of the order of a few $MeV/c$." Additional sources of signal along the same line of sight are d) the intrinsic anisotropy of the CMB (see point b) above) Since components b) and d) have exactly the same spectrum. we will describe them in the following with the parameter AZcijg=Adcypi+AL. (or the equivalent AT (37g). which ts the sum of the intrinsic anisotropy of the CMB and of the kinetic SZ effect along the line of sight.," Additional sources of signal along the same line of sight are d) the intrinsic anisotropy of the CMB (see point b) above) Since components b) and d) have exactly the same spectrum, we will describe them in the following with the parameter $\Delta I_{CMB} = \Delta I_{CMBi} + \Delta I_{\rm{v}}$ (or the equivalent $\Delta T_{CMB}$ ), which is the sum of the intrinsic anisotropy of the CMB and of the kinetic SZ effect along the line of sight." e) The emission of dust A/; in our Galaxy and in the galaxies of the cluster., e) The emission of dust $\Delta I_d$ in our Galaxy and in the galaxies of the cluster. " This is modelled as a thermal spectrum with temperature 7,~20K and a spectral index of emissivity --1.5. ora superposition of several components with different Ty."," This is modelled as a thermal spectrum with temperature $T_d \sim 20K$ and a spectral index of emissivity $\sim -1.5$, or a superposition of several components with different $T_d$." It is important as a contaminant at frequencies where the thermal SZ is positive., It is important as a contaminant at frequencies where the thermal SZ is positive. " f) The free-free and synchrotron emission (A/;;. A/,,) from the diffuse medium in our Galaxy and from the galaxies in the cluster: this component can be important at low frequencies. where the SZ is negative."," f) The free-free and synchrotron emission $\Delta I_{ff}$, $\Delta I_{sy}$ ) from the diffuse medium in our Galaxy and from the galaxies in the cluster: this component can be important at low frequencies, where the SZ is negative." According to these considerations it follows that SZ measurements promise to estimate several physical parameters of the cluster on the line of sight. provided there are more observation bands than parameters to be determined. or some of the contributions are known to be negligible.," According to these considerations it follows that SZ measurements promise to estimate several physical parameters of the cluster on the line of sight, provided there are more observation bands than parameters to be determined, or some of the contributions are known to be negligible." Multi-frequency measurements are therefore mandatory to separate the contributions of the different physical components. taking advantage of the characteristic spectrum of the SZ effect. which significantly departs from the spectra of the foreground and background components (see fig. 1)).," Multi-frequency measurements are therefore mandatory to separate the contributions of the different physical components, taking advantage of the characteristic spectrum of the SZ effect, which significantly departs from the spectra of the foreground and background components (see fig. \ref{fig1}) )." The wider and more detailed the frequency coverage of the observations. the more effective the separation of the different components.," The wider and more detailed the frequency coverage of the observations, the more effective the separation of the different components." The recent results of Planck (Planck collaboration 2011b)). for example. have been obtained by exploiting the excellent frequency coverage of the mission and sophisticated component separation techniques (see Leach et al. 2008)).," The recent results of Planck (Planck collaboration \cite{Plan11b}) ), for example, have been obtained by exploiting the excellent frequency coverage of the mission and sophisticated component separation techniques (see Leach et al. \cite{Leac08}) )." " In. this paper we study how effective the various experimental configurations are in separating all the different physical components and in providing unbiased estimates of the cluster parameters (like v. v. Tp. τι, T4. pj ...) and of the other parameters that describe the signals along the same line of sight (Ty. ty. HF Eo. Aloappil ss)."," In this paper we study how effective the various experimental configurations are in separating all the different physical components and in providing unbiased estimates of the cluster parameters (like $y$, $\rm{v}$ , $T_e$ , $\tau_t$ , $\tau_{nt}$, $p_1$ ...) and of the other parameters that describe the signals along the same line of sight $T_d$ , $\tau_d$, $I_s$, $I_{ff}$, $\Delta I_{CMBi}$, ...)." Evidently. ground-based few-band photometers cannot provide enough information. to. separate. all physical components.," Evidently, ground-based few-band photometers cannot provide enough information to separate all physical components." Observations are hampered at high frequencies ες 200GHz) by atmospheric noise (see fig.1): this significantly limits the coverage of the positive part. of the thermal SZ spectrum. and makes the removal of parameter degeneracies much more difficult.," Observations are hampered at high frequencies $\simgt 200 GHz$ ) by atmospheric noise (see \ref{fig1}) ): this significantly limits the coverage of the positive part of the thermal SZ spectrum, and makes the removal of parameter degeneracies much more difficult." These instruments need external information (optical. X-ray. far-IR. ete.)," These instruments need external information (optical, X-ray, far-IR, etc.)" " to produce mainly measurements of r,.", to produce mainly measurements of $\tau_t$. With the addition of external data. these experiments provide invaluable informatior in the current exploration phase: a large database ofclusters is being built. and new cluster candidates have been discovered (see e.g. Hincks et al. 2010:," With the addition of external data, these experiments provide invaluable information in the current exploration phase: a large database ofclusters is being built, and new cluster candidates have been discovered (see e.g. Hincks et al. \cite{Hinc10};" Marriage et al. 2010:, Marriage et al. \cite{Marr10}; Brodwin et al. 2011::, Brodwin et al. \cite{Brod10}; Hand et al. 2011:, Hand et al. \cite{Hand11}; Sehgal et al. 2011::, Sehgal et al. \cite{Sehg11}; Foley et al. 2011::, Foley et al. \cite{Fole11}; Story et al. 2011::, Story et al. \cite{Stor11}; Williamson et al. 2011))., Williamson et al. \cite{Will11}) ). In principle. future space-based spectrometers can cover the full range of interesting frequencies and offer much more information: with these machines it should be possible to measure the parameters of a cluster. and use external information. when available. as a cross-check.," In principle, future space-based spectrometers can cover the full range of interesting frequencies and offer much more information: with these machines it should be possible to measure the parameters of a cluster, and use external information, when available, as a cross-check." Also. other important scientific targets of these instruments are. the measurement of the C and CO lines in theredshift desertand beyondfora large number of galaxies (see e.g. de Bernardis et al. 2010:: ," Also, other important scientific targets of these instruments are the measurement of the $C^+$ and CO lines in theredshift desertand beyondfora large number of galaxies (see e.g. de Bernardis et al. \cite{debe10}; ;" Gong et al. 2011))., Gong et al. \cite{Gong11}) ). , experieence drastic orbital changes on a timescale of107 years., ence drastic orbital changes on a timescale of$10^4$ years. and we used these data to investigate the period behaviour of CCyg.,and we used these data to investigate the period behaviour of Cyg. " TheKepler light curve of V2279CCyg seems stable, without any noticeable light curve changes (part of the Q2 light curve is plotted in refkepphot))."," The light curve of Cyg seems stable, without any noticeable light curve changes (part of the Q2 light curve is plotted in \\ref{kepphot}) )." " We only see long term variations similar in amplitude to what we noted for V1154 Cyg refv1154lc)), which in this case might also just be instrumental effects."," We only see long term variations similar in amplitude to what we noted for V1154 Cyg ), which in this case might also just be instrumental effects." " What makes CCyg particularly suspicious is the presence of many flares, one of them is clearly seen at 0030.0 in refkepphot.."," What makes Cyg particularly suspicious is the presence of many flares, one of them is clearly seen at 030.0 in \\ref{kepphot}." The (almost) strictly periodic variations and the value of the period is consistent with a rotational modulation., The (almost) strictly periodic variations and the value of the period is consistent with a rotational modulation. Table 4. shows that the average shell radius and expansion velocity of the Magellanic Bridge shell population are smaller than for the SAIC population. while the average kinematic age is slightly larger.,"Table \ref{tab:Comptab} shows that the average shell radius and expansion velocity of the Magellanic Bridge shell population are smaller than for the SMC population, while the average kinematic age is slightly larger." The cispersions of shell radius and expansion velocity of the Bridge population are also slightly lower than the SALC population. while the dispersion for kinematic age. which is a dependent of both the shell radius and expansion velocity. is slightly larger for the Bridge population.," The dispersions of shell radius and expansion velocity of the Bridge population are also slightly lower than the SMC population, while the dispersion for kinematic age, which is a dependent of both the shell radius and expansion velocity, is slightly larger for the Bridge population." We also see that the mean energy of the shell population is considerably lower in the Magellanie, We also see that the mean energy of the shell population is considerably lower in the Magellanic known planets. 14 of them are in wide binary stellar svstenmis.,"known planets, 14 of them are in wide binary stellar systems." In. addition. given the hieh frequeney of binary stellar svstems among svstenis older (han 1 Gyr. Duquennoy&AMavor(1991))). it is clear (hat anv comprehensive planetary census mist address the question of how frequently planets occur in such svstems.," In addition, given the high frequency of binary stellar systems among systems older than 1 Gyr, \cite{Duq:91}) ), it is clear that any comprehensive planetary census must address the question of how frequently planets occur in such systems." This is all the more relevant given that several (heoretical investigations have indicated that there exist regions in binary parameter space where planets can form and exist in stable orbits over long periods of time. though this does remain controversial (Whitmireetal.1998:BossMarzari&Scholl 2002)..," This is all the more relevant given that several theoretical investigations have indicated that there exist regions in binary parameter space where planets can form and exist in stable orbits over long periods of time, though this does remain controversial \citep{Whi:98::,Bos:98::,Mar:00::,Nel:00::,Bar:02::}." An instrument such as PTI. capable of 10 jras verv-narrow-angle astrometry. could be used to search many of the brightest speckle binary svstems for planets.," An instrument such as PTI, capable of 10 $\mu$ as very-narrow-angle astrometry, could be used to search many of the brightest speckle binary systems for planets." We have compiled a list of approximately 50 suitable systems. will m;<4.5. separations less than 1 arcsecond. and within the field of regard of PTI.," We have compiled a list of approximately 50 suitable systems, with $m_K < 4.5$, separations less than 1 arcsecond, and within the field of regard of PTI." The median orbital separation between the binary components in these svstenms is 19 AU. and hence there should be regions where planets can remain stable for long periods.," The median orbital separation between the binary components in these systems is 19 AU, and hence there should be regions where planets can remain stable for long periods." In parüceular. adopting the result from we calculate the largest stable orbit in each svstem.," In particular, adopting the result from \cite{holman99} we calculate the largest stable orbit in each system." We find that the median detectable planetary mass in such an orbit is 0.5 Jupiter masses (assuming 30 confidence detections)., We find that the median detectable planetary mass in such an orbit is 0.5 Jupiter masses (assuming $3 \sigma$ confidence detections). The corresponding median orbital period is 2.2 vears., The corresponding median orbital period is 2.2 years. A limited survey. could quickly begin to provide useful constraints on the [frequency of planets in binary stellar svstems., A limited survey could quickly begin to provide useful constraints on the frequency of planets in binary stellar systems. As a new generation of long-baseline optical interferometers become operational in the next lew vears. (his (wpe of survey could be easily extended to sample sizes of several hundred stus. hence proviling strong constraints on planetary formation in the binary environment.," As a new generation of long-baseline optical interferometers become operational in the next few years, this type of survey could be easily extended to sample sizes of several hundred stars, hence providing strong constraints on planetary formation in the binary environment." We would like to thank IE. Dertschinger. A. Doden. D. F. Burke. M. Colavita. M. ]xonacki. 5. BR. Kulkarni N. Salizadeh [or their contributions to (his effort.," We would like to thank E. Bertschinger, A. Boden, B. F. Burke, M. Colavita, M. Konacki, S. R. Kulkarni N. Safizadeh for their contributions to this effort." We also particularly acknowledge the extraordinary efforts of Ix. Rykoski. whose work in operating and maintaining PTI is invaluable ancl goes far bevond the call of duty.," We also particularly acknowledge the extraordinary efforts of K. Rykoski, whose work in operating and maintaining PTI is invaluable and goes far beyond the call of duty." Observations with PTI are made possible through the efforts of the PTI Collaboration. which we acknowledge.," Observations with PTI are made possible through the efforts of the PTI Collaboration, which we acknowledge." Part of the work described in (his paper was performed at the Jet Propulsion Laboratory under contract with the National Aeronautics and Space Administration., Part of the work described in this paper was performed at the Jet Propulsion Laboratory under contract with the National Aeronautics and Space Administration. Interferometer cata was obtained at the Palomar Observatory using the NASA Palomar Testbecl Interferometer. supported by NASA contracts to the Jet Propulsion Laboratory.," Interferometer data was obtained at the Palomar Observatory using the NASA Palomar Testbed Interferometer, supported by NASA contracts to the Jet Propulsion Laboratory." This research has made use of (he Simbad database. operated al CDS. Strasbourg. France.," This research has made use of the Simbad database, operated at CDS, Strasbourg, France." MWM acknowledges the support of the Michelson Graduate Fellowship program., MWM acknowledges the support of the Michelson Graduate Fellowship program. DEL acknowledges support from a Pappalardo Fellowship in Physics., BFL acknowledges support from a Pappalardo Fellowship in Physics. "These difficulties led us to explore two additional ""non-staudard models for NGC 1172: flows (1) with extreme mass dropout inside 300 pc or (2) with additional non-thermal pressure in this same reelon.",These difficulties led us to explore two additional “non-standard” models for NGC 4472: flows (1) with extreme mass dropout inside 300 pc or (2) with additional non-thermal pressure in this same region. It is often claimed that mass dropout reduces the N-rav- surface. brightuess. iu. the central regions. of. cooling. flows. but this ⋅⋅is not true iu. general.," It is often claimed that mass dropout reduces the X-ray surface brightness in the central regions of cooling flows, but this is not true in general." For flows iu which most of the gas in the central region advected iuward from⋅ large⋅⋅ τας. cooling⋅ .Hows dropout at large radiον can reduce the amount of. eas ancl associated⋅ emission. ⋅⋅⊽≽⋅1) in the ceutral ⋯↥⋅↸∖," For flows in which most of the gas in the central region has advected inward from large radii, cooling dropout at large radii can reduce the amount of gas and associated emission $\Sigma_x(R)$ in the central core." ⋅∐∪↖↖⇁↸∖↖↽↸∖↥⋅∙↑↕∐↴∖↴≼↧∪↸∖↴∖↴∐∪⋜∏∏≻↕⋅↖⇁↑∪∶↴∙⋜↧↕⋜↧↸⊳∐⊳ . .⋅ cooling flows in which much of the gas in the ceutral How originates from stars within or near this region.," However, this does not apply to galactic cooling flows in which much of the gas in the central flow originates from stars within or near this region." Tn addition. the N-vav cinissivity and SAR) ave locally enhanced. at (deuser) cooling. sites⋅ where mass dropout occurs.," In addition, the X-ray emissivity and $\Sigma_x(R)$ are locally enhanced at (denser) cooling sites where mass dropout occurs." " To ↴⋅illustrate the futility. of lowering the coutral X,(CR) in NGC 1172 with increased local cooling. we show iu Figure 3 deusitv aud temperature profiles for the standard flow (at f, aud with SMDII) but with a cooling dropout that truucatesthe backeround flaw density: gar)=c""! with s,,=0.006 αμ7."," To illustrate the futility of lowering the central $\Sigma_x(R)$ in NGC 4472 with increased local cooling, we show in Figure 3 density and temperature profiles for the standard flow (at $t_n$ and with SMBH) but with a cooling dropout that truncatesthe background flow density: $q(r) = e^{n(r)/n_m}$ with $n_m = 0.006 $ $^{-3}$." " The thermal spike around the SMDIT is still present in this solution. but the apparent itr) (and X,CR)) within several 100 pe is ouly slightly reduced."," The thermal spike around the SMBH is still present in this solution, but the apparent $n(r)$ (and $\Sigma_x(R)$ ) within several 100 pc is only slightly reduced." The mean projected temperature within 100 pe is TCR«100)=1.910* K. Finally. we consider cooling flow models in which wir) and YX.CR) in the imner flow are lowered by an additional non-thermal pressure due to relativistic particles or maeuectic fields. as suggested by radio emission observed iu lost elliptical cores.," The mean projected temperature within 100 pc is $T(R < 100) = 1.9 \times 10^7$ K. Finally, we consider cooling flow models in which $n(r)$ and $\Sigma_x(R)$ in the inner flow are lowered by an additional non-thermal pressure due to relativistic particles or magnetic fields, as suggested by radio emission observed in most elliptical cores." " To explore this possibility we slow ini FigureSodan 23 the vut.standardqr flow -d.(at f,=13 CigGyrs SMDII)ES in:) which; andue additional. pressure.M is ∙elliptical im the galactic core: Pie =PCL|lonecr42d ⋅ ⋅↱⊐↙∣−↕∖↧⋉⋝∙↖↖↽↕∐∖↥⋅↸∖∫≽↕↴∖↴↑∐↸∖↑∐↸∖↥⋅⋯⋜↧↕∶↴∙⊾⋜↧↴∖↴↻↥⋅↸∖↴∖∷"," To explore this possibility we show in Figure 3 the standard flow (at $t_n = 13$ Gyrs with SMBH) in which an additional pressure is introduced in the galactic core: $P_{tot} = P(1 + 5 e^{-r/2~{\rm kpc}})$ , where $P$ is the thermal gas pressure." ∖↴↿∐⋅↸∖∙ ⊺↕∐∖≼∐∖∐↴∖↴↕↑↖⇁⋖⋜⋯≼↧∑⊽↗⋅⋟↕∐↑↕∐∖↸⊳∪∪∐∐∶↴∙⊾∏∪↖↖⇁↖↖↽↕↑↕∐∐ DOO> pe are ∙∙reduced by aye.this additional∙∙ pressure⋅↴↴⋅ and parameters⋅ for otnPole). could be adjusted⊳↴ iu⋅ focto achieve⋅ a more4 perfect fiton ∙a ∙ ⊱⋀∖↕≧∐↕↴∖↴↸⊳∪∐↴∖↴, The density (and $\Sigma_x$ ) in the cooling flow within $\sim 300$ pc are reduced by this additional pressure and parameters for $P_{tot}(r)$ could be adjusted in an fashion to achieve a more perfect fit with the observations. ↕≼∐∖↥⋅⋜∏⋝↕↖⇁↥⋅↸∖≺↧⋯⊳↸∖≼↧⋯≺∏∐⋅⋯∪≼∐∖↕↴∖↴∙ ↖↖↕↑∐↑∐∖∪↴⋝↴∖↸∖↥↖⋜↕⊓∪∐↴∖∙∐∪↖↖↸∖↖↸∖↥∙↑∐↸∖⋜∏∏≻⋜⋯∖∐↑ ⋅ thetemperature eas is dramatically (1) As long as flow is now supported assunptious hold. we expec," However, the apparent temperature of the thermal gas is dramatically lowered since the external flow is now supported mostly by non-thermal pressure." t The projected rie steadily toward the = LOO pe isoulyas op x or K.assumingthisgas is notc» heated [m]that such a eas by collective interactions with the relativistic gas.," The projected apparent temperature within $R = 100$ pc is only $T = 0.40 \times 10^7$ K, assuming this gas is not heated by collective interactions with the relativistic gas." The disceruibilitv of the thermal spike near the SMDIT is now ereatlv reduced., The discernibility of the thermal spike near the SMBH is now greatly reduced. Iu this. study we have examined. ceutral cooling. Hows in. a Παπ⋅⋅οτι elliptical⋅⋅ similar⋅⋅ to NGC⇁⊲⊲↼ 1172., In this study we have examined central cooling flows in a luminous elliptical similar to NGC 4472. have. emphasized. the.⋅ evolution of⋅ quiesceutWe that arise naturally frou gas ...and cucrey has supplied. by galactic⋅ stars aud by secondary iufall in. the outer regions., We have emphasized the evolution of quiescent flows that arise naturally from gas and energy supplied by galactic stars and by secondary infall in the outer regions. . We- have not explored possible⋅⋅ ↥⋅⋜⋯↴∖↴↕↸∖∐↑↕∐↑↸∖↥⋅⋜↧↸⊳↑↕∪∐↴∖↴↴⋝↸∖↑↖↖↽↸∖↸∖∐↑∐∖↸⊳∪∪∐∐∶↴⋁∏∪↖↖↽ and an iutermittently⋅ active⋅ ealactic. core (e.g. Ciotti Ostriker 1997)., We have not explored possible transient interactions between the cooling flow and an intermittently active galactic core (e.g. Ciotti Ostriker 1997). Our objective here has con to anticipate some of the iuterpretive issues hata mayWu ‘arise when observations‘ become available., Our objective here has been to anticipate some of the interpretive issues that may arise when observations become available. Our main conclusions are as follows: (1) Some dark amatter currently attributed o the central supermassive black hole (SMDIT) nav be due fo a population of non-luminous stars created frou cooled interstellar eas having a bottom-leavy IMF., Our main conclusions are as follows: (1) Some dark matter currently attributed to the central supermassive black hole (SMBH) may be due to a population of non-luminous stars created from cooled interstellar gas having a bottom-heavy IMF. " In the standard cooling Bow for NGC 1172 with SMDIL neutral clouds ecole eravitatiouallv unstable (aud tziucate the TMF) at masses i,=0.2. 0.3 aud (.8 AL. at r=50. 100 and 300 pe respectively (Mathlieses Brigheuti 1999)."," In the standard cooling flow for NGC 4472 with SMBH, neutral clouds become gravitationally unstable (and truncate the IMF) at masses $m_u = 0.2$, 0.3 and 0.8 $M_{\odot}$ at $r = 50$, 100 and 300 pc respectively (Mathews Brighenti 1999)." Such dark stars. possibly haviug approximately radial orbits. can also produce a radial variation iu the elobal barvonic M. (," Such dark stars, possibly having approximately radial orbits, can also produce a radial variation in the global baryonic $M/L$. (" 2) A successful observation ofa high teiuperature peak Ἡ rX50 pe byChandra in a nearby bright elliptical would provide additional strong evideuce for the. existence of SMBIIS,2) A successful observation of a high temperature peak in $r \lta 50$ pc by in a nearby bright elliptical would provide additional strong evidence for the existence of SMBHs. However. ifn additionale non-thermal pressure is. present iu. cores∙⊲ the SMDIE thermalwith peak may io introduced bee discernible :. ⋖," However, if additional non-thermal pressure is present in elliptical cores the SMBH thermal peak may no longer be discernible. (" ∶≩⋝↻↿∐⋅↸⊳↸∖∐⊓⋅⋜↕↕∏∪↖↖↰∖↴≺∣⋮⋎∿∖∶≩∩∩↻↸⊳⋟≼∐↕−↥∎↸∖↥⋅ . ≱⋅ ↕↥⋅∪⊔↑∐↸∖↕≻∪∐≺∐≓↑↖↽↻↸∖⊓⋅⋜⋯↴∖↴∪↕∐↸⊳∏∪↖↖↽≼∐∖↴∖↴↸⊳↥⋅↕↴⋝↸∖≼↧⋝↖↽⋅ ⋅ :M ⇁⋅ ∩∏⋜↧↑⋜∥∖↥⋅↑∙∖↽⋀∖⋜∐⋅⋜∏⇁⋜⋯⋖↓≝↭≝⊔↴∖↴∐∐⊳↸∖↖↖↽↸∖≺↧∪∐∪↑↕∐↴∖↴↕↴∖↴↑↽ ∙ ⋅∙⋅ sonic transition.,3) Our central flows $r \lta 300$ pc) differ from the Bondi-type transonic flow described by Quataert Narayan (1999) since we do not insist on a sonic transition. The mass flow rate into the aun ad . , The mass flow rate into the SMBH is considerably reduced in our models. ( E of ⋅ our standard cooling flow lowered since the external the gas deusitv to mostly by uou-thermal pressure. SMDIT. approximately apparent tempcrature within R,"4) As long as our standard cooling flow assumptions hold, we expect the gas density to rise steadily toward the SMBH approximately as $n \propto r^{-5/4}$ ." " 71, Butcurrentobservations suggest T —0.140 « 10* density peal is [m]not present.", But current observations suggest that such a gas density peak is not present. About half of the gas within 300 pe in NGC, About half of the gas within 300 pc in NGC "missing, while the high column density tail shows a sort of correlation between the CIV Doppler parameters and Norv.","missing, while the high column density tail shows a sort of correlation between the CIV Doppler parameters and $N_{\rm CIV}$." We interpret this latter as a 7'—p relation: lines with higher column densities (i.e. associated to denser regions) have higher Doppler parameters (i.e. temperature)., We interpret this latter as a $T-\rho$ relation: lines with higher column densities (i.e. associated to denser regions) have higher Doppler parameters (i.e. temperature). " The fact that this relation appears only at high column densities is not a surprise: for high values of Nerv, absorption lines are very strong and well resolved, so they are good tracers of the physical state of the intergalactic gas and also they are better fit byVPFIT."," The fact that this relation appears only at high column densities is not a surprise: for high values of $N_{\rm CIV}$, absorption lines are very strong and well resolved, so they are good tracers of the physical state of the intergalactic gas and also they are better fit by." " The case of run kr37agn is different: in fact theT'—p relation for large Norv values is missing, while a clump of systems with a large spread in bcrv values at low column density is clearly visible."," The case of run kr37agn is different: in fact the$T-\rho$ relation for large $N_{\rm CIV}$ values is missing, while a clump of systems with a large spread in $b_{\rm CIV}$ values at low column density is clearly visible." " This distribution results because, at redshift z—3, in the kr37agn run the gas resides inside the high density high temperature cores of the haloes where it is reprocessed by the stars, and the amount of diffused CIV is rather low (see the right panel of Figure 12))."," This distribution results because, at redshift $z=3$, in the kr37agn run the gas resides inside the high density high temperature cores of the haloes where it is reprocessed by the stars, and the amount of diffused CIV is rather low (see the right panel of Figure )." " Therefore, since the CIV absorption lines are weak and not well defined, the quality of the fit made byVPFIT is rather poor."," Therefore, since the CIV absorption lines are weak and not well defined, the quality of the fit made by is rather poor." " As we reported in Section5.2,, in such a caseVPFIT tends to add broad components in order to minimize the x? statistics and this results in the feature of spurious systems at low column density shown in the lower right panel of Figure16."," As we reported in Section, in such a case tends to add broad components in order to minimize the $\chi^{2}$ statistics and this results in the feature of spurious systems at low column density shown in the lower right panel of Figure." ". While the effect is less evident (but present) for the other runs or in the case of the bg—Nut relation, it is now much more prominent."," While the effect is less evident (but present) for the other runs or in the case of the $b_{\rm HI}-N_{\rm HI}$ relation, it is now much more prominent." " Of course, observational data do not present such a feature, because in the “by eye"" procedure of fitting these spurious lines are removed."," Of course, observational data do not present such a feature, because in the “by eye” procedure of fitting these spurious lines are removed." At redshift z—2.25 (Figure 17)) and z—1.5 (Figure 18)) the kr37agn run approaches the other two simulations., At redshift $z=2.25$ (Figure ) and $z=1.5$ (Figure ) the kr37agn run approaches the other two simulations. The bcrv—Nery correlation at high column densities is now present for all the runs but the simulated distributions are still different from the observed one., The $b_{\rm CIV}-N_{\rm CIV}$ correlation at high column densities is now present for all the runs but the simulated distributions are still different from the observed one. " The clump of low density systems disappears almost completely at z=2.25, but is visible also for the runs kr37edw500 and kr37mdw at redshift z—1.5."," The clump of low density systems disappears almost completely at $z=2.25$, but is visible also for the runs kr37edw500 and kr37mdw at redshift $z=1.5$." " There is a simple reason for this: at low redshift the amount of CIV, traced by random line-of- along the box, decreases (right panel of Figure 12)), while the number of low column density systems significantly increases (Figure 11)) and typically these lines have a large spread in their Doppler parameter value."," There is a simple reason for this: at low redshift the amount of CIV, traced by random line-of-sight along the box, decreases (right panel of Figure ), while the number of low column density systems significantly increases (Figure ) and typically these lines have a large spread in their Doppler parameter value." " The difference between simulated and observed distributions could also be due to the fact that simulated haloes, and in particular their outskirts, can have different properties from that of the observed ones: for example this is also seen from the Sill statistics in DLA systems that appear to be not in agreement with observations."," The difference between simulated and observed distributions could also be due to the fact that simulated haloes, and in particular their outskirts, can have different properties from that of the observed ones: for example this is also seen from the SiII statistics in DLA systems that appear to be not in agreement with observations." " Although in the present paper we explore the effect of feedback, there might be other physical effects that can contribute as well in shaping the properties of the bcry—Nerv distribution."," Although in the present paper we explore the effect of feedback, there might be other physical effects that can contribute as well in shaping the properties of the $b_{\rm CIV}-N_{\rm CIV}$ distribution." The last part of this work is dedicated to the HI-CIV correlated absorption., The last part of this work is dedicated to the HI-CIV correlated absorption. " We define as correlated absorption HI-CIV systems in which CIV and HI are physically dependent or, in other words, related to the same absorptive structure."," We define as correlated absorption HI-CIV systems in which CIV and HI are physically dependent or, in other words, related to the same absorptive structure." " In real spectra, however, two absorbers each containing CIV could be very close in redshift space but far in real space due to the bulk motions and the peculiar velocity."," In real spectra, however, two absorbers each containing CIV could be very close in redshift space but far in real space due to the bulk motions and the peculiar velocity." For this reason there are often serious problem on how to associate each CIV components to physically corresponding HI components., For this reason there are often serious problem on how to associate each CIV components to physically corresponding HI components. " In this Section, besides the data of ?,, we compare with the fitting formulae obtained from the ? data."," In this Section, besides the data of \citet{vale10}, , we compare with the fitting formulae obtained from the \citet{kimsub} data." In oder to do, In oder to do where ρε=15M./(8nR3) is the density at the centre.,where $\rho_c=15\mstar/(8\pi\rstar^3)$ is the density at the centre. " The gravitational acceleration (i.e., the gradient of the gravitational potential V4) corresponding to this steady state is | where M. and R. denote the mass and radius of the star, respectively and G is Newton’s gravitational constant."," The gravitational acceleration (i.e., the gradient of the gravitational potential $\nabla\Phi$ ) corresponding to this steady state is = where $\mstar$ and $\rstar$ denote the mass and radius of the star, respectively and $G$ is Newton's gravitational constant." " From the gravitational acceleration, we obtain the pressure profile ο where p.=15G.M?/(167R?) is the pressure at the centre."," From the gravitational acceleration, we obtain the pressure profile p=p_c where $p_c=15G\mstar^2/(16\pi\rstar^4)$ is the pressure at the centre." " We emphasize that this is a particular, simple choice of density profile, chosen to render the following calculations tractable; it is not motivated directly by physical arguments or observations."," We emphasize that this is a particular, simple choice of density profile, chosen to render the following calculations tractable; it is not motivated directly by physical arguments or observations." " For this steady state, Eq. ("," For this steady state, Eq. (" 13) gives where Besurface is the surface magnetic field strength at the equator; we have Bsurface=NpBo in our formulation.,13) gives where $B_{\mathrm{surface}}$ is the surface magnetic field strength at the equator; we have $B_{\mathrm{surface}}=\eta_p B_0$ in our formulation. " For comparison, we also consider the n=1 polytropic star, whose zeroth-order density and pressure configurations are given by (Akgiin&Wasserman2008;Dall’Ossoetal.2009)sin(ar)rr, kp” The gradient of the gravitational potential is For this steady state, Eq. ("," For comparison, we also consider the $n=1$ polytropic star, whose zeroth-order density and pressure configurations are given by \citep{aw08,detal09} , ^2, The gradient of the gravitational potential is = For this steady state, Eq. (" 13) gives,13) gives In order to derive an ephemeris for the system and initial parameters for the individual eclipsing binary components. we first generated a single recitified light curve from the discovery data by removing the out-of-eclipse variability on each night and combining all 3 seasons of SuperWASP photometry.,"In order to derive an ephemeris for the system and initial parameters for the individual eclipsing binary components, we first generated a single recitified light curve from the discovery data by removing the out-of-eclipse variability on each night and combining all 3 seasons of SuperWASP photometry." We fit a second order polynomial to the out-of-eclipse photometry on each night and applied the polynomial fit to all the data obtained that night., We fit a second order polynomial to the out-of-eclipse photometry on each night and applied the polynomial fit to all the data obtained that night. We excluded from the rectified light curve any data taken on nights in which there was no out-of-eclipse photometry., We excluded from the rectified light curve any data taken on nights in which there was no out-of-eclipse photometry. The fitting functions are not physical. and we made no attempt to model the starspot variability because the existing data are only in a single band and therefore any physical model would be too full of degeneracies to provide a useful result.," The fitting functions are not physical, and we made no attempt to model the starspot variability because the existing data are only in a single band and therefore any physical model would be too full of degeneracies to provide a useful result." The data include 17 near complete primary or secondary eclipses which show the eclipse minimum and out-of-eclipse photometry before and/or after the eclipse., The data include 17 near complete primary or secondary eclipses which show the eclipse minimum and out-of-eclipse photometry before and/or after the eclipse. The final rectified light curve contains 11808 photometric measurements., The final rectified light curve contains 11808 photometric measurements. We fit the rectified light curve using the JKT Eclipsing Binary Orbit Program (EBOP) (Popper&Etzel.1981:South-worth. 2007).," We fit the rectified light curve using the JKT Eclipsing Binary Orbit Program (EBOP) \citep{popperetzel,southworth}." . The program determines the optimal model light curve that matches the observed photometry and reports the binary parameters for the model., The program determines the optimal model light curve that matches the observed photometry and reports the binary parameters for the model. The algorithm on which it is based is only valid when analysing well-detached eclipsing binaries in which the tidal distortion is small (re. nearly spherical stars with oblateness < 0.04)., The algorithm on which it is based is only valid when analysing well-detached eclipsing binaries in which the tidal distortion is small (i.e. nearly spherical stars with oblateness $< 0.04$ ). This is the case for MML 53., This is the case for MML 53. " The derived light curve parameters include the period. P. time of minimum light. 75. surface brightness ratio in the SuperWASP filter. ονκ. relative sum of the radii. (R,+Ria. inclination angle. i. eccentricity. e. and angle of periastron. co."," The derived light curve parameters include the period, $P$, time of minimum light, $T_0$, surface brightness ratio in the SuperWASP filter, $J_{V+R}$ , relative sum of the radii, $(R_1+R_2)/a$, inclination angle, $i$, eccentricity, $e$, and angle of periastron, $\omega$." The routine takes into account the effects of limb darkening. gravity brightening. and reflection effects and can account for the presence of light from a third component.," The routine takes into account the effects of limb darkening, gravity brightening, and reflection effects and can account for the presence of light from a third component." We adopted the quadratic limb darkening coefficients from Claret(2000) using the temperatures for the eclipsing components that are defined below in Sect. 3.3..," We adopted the quadratic limb darkening coefficients from \citet{claret} using the temperatures for the eclipsing components that are defined below in Sect. \ref{sec:modelspec}," Tay.)= 4886K and Zr»=4309 K. We initially ran the fitting program allowing the eccentricity to be a free parameter. however the resulting value was within 3c of zero. and there is no further evidence in the light curve for a non-circular orbit.," $T_{\rm eff,1}=4886$ K and $T_{\rm eff,2}=4309$ K. We initially ran the fitting program allowing the eccentricity to be a free parameter, however the resulting value was within $\sigma$ of zero, and there is no further evidence in the light curve for a non-circular orbit." Thus. in the final run of the light curve modelling program. we fixed the eccentricity and angle of periastron to zero.," Thus, in the final run of the light curve modelling program, we fixed the eccentricity and angle of periastron to zero." The result is shown in Fig., The result is shown in Fig. + with the best fitting model overplotted on the final rectified light curve., \ref{fig:lcrect} with the best fitting model overplotted on the final rectified light curve. The fit provides à precise system ephemeris of: As an additional check. we determined the ephemeris from each individual season of data. and found the periods agree to within 5x107° days.," The fit provides a precise system ephemeris of: As an additional check, we determined the ephemeris from each individual season of data, and found the periods agree to within $5\times10^{-6}$ days." However. the epoch of mininum light varies by ~0.001 in phase (~3 min) between the 2006 and 2007-08 seasons.," However, the epoch of mininum light varies by $\sim 0.001$ in phase $\sim 3$ min) between the 2006 and 2007-08 seasons." This offset could be caused by effects from the third component (e.g. direct. gravitational influence. light travel time variations). if ultimately confirmed with current epoch eclipse data.," This offset could be caused by effects from the third component (e.g. direct gravitational influence, light travel time variations), if ultimately confirmed with current epoch eclipse data." Based on the variations from season to season.we adopt an uncertainty on the time of minimum light of 0.002 days and an uncertainty on the period of 0.000005 days.," Based on the variations from season to season,we adopt an uncertainty on the time of minimum light of $0.002$ days and an uncertainty on the period of $0.000005$ days." The model fit also gives a measurement for the relative sum of the radii. (R)+R»)/a=0.260. the inclination angle. 7= 83.1°. and the surface brightness ratio in the SuperWASP filter. Jy-g=0.461.," The model fit also gives a measurement for the relative sum of the radii, $(R_1+R_2)/a = 0.260$, the inclination angle, $i = 83.1^{\circ}$ , and the surface brightness ratio in the SuperWASP filter, $J_{V+R} = 0.461$." These values depend on the flux contribution of the third component which we estimate to be of the total luminosity based on our self consistent analysis of the light curve and the FEROS spectrum described in Sect. 3.3.., These values depend on the flux contribution of the third component which we estimate to be of the total luminosity based on our self consistent analysis of the light curve and the FEROS spectrum described in Sect. \ref{sec:modelspec}. However. we stress that the fitted parameters will change when definitive temperatures for all three components and accurate lummosity ratios can be derived through spectral disentangling of multiple high resolution. high signal-to-noise spectra of MML 53.," However, we stress that the fitted parameters will change when definitive temperatures for all three components and accurate luminosity ratios can be derived through spectral disentangling of multiple high resolution, high signal-to-noise spectra of MML 53." Furthermore. star spots which we know are present are likely to have an affect on these parameters. and multi-band photometry is necessary to derive a comprehensive solution that models both the spots and the eclipses.," Furthermore, star spots which we know are present are likely to have an affect on these parameters, and multi-band photometry is necessary to derive a comprehensive solution that models both the spots and the eclipses." Using the radial velocity measurements of the primary and secondary star from the single archive spectrum. the precise ephemeris and inclination angle estimate from the photometry. and the systemtie radial velocity from the literature. we derive approximate masses for the individual eclipsing components of MML 53.," Using the radial velocity measurements of the primary and secondary star from the single archive spectrum, the precise ephemeris and inclination angle estimate from the photometry, and the systemtic radial velocity from the literature, we derive approximate masses for the individual eclipsing components of MML 53." The FEROS observation was obtained very near to quadrature at an orbital phase of 0.287., The FEROS observation was obtained very near to quadrature at an orbital phase of $0.287$. With the phase of the observation fixed. the radial velocity measurements for the primary and secondary (-85.8. +111.1 constrain the amplitudes of the sinusoidal (circular orbit)radial velocity curves for the two components. Ay and A>.," With the phase of the observation fixed, the radial velocity measurements for the primary and secondary (-85.8, +111.1 ) constrain the amplitudes of the sinusoidal (circular orbit)radial velocity curves for the two components, $K_1$ and $K_2$ ." Adopting 2.0 s'(Torresetal..2006) for the systemic RV. we find Ky=90 and Ky=112 (assuming no uncertainty in," Adopting 2.0 \citep{Torres} for the systemic RV, we find $K_1 = 90$ and $K_2=112$ (assuming no uncertainty in" would be able to detect in the first and the second case.,would be able to detect in the first and the second case. The other important question. close to the previous one. is that how much (and what?)," The other important question, close to the previous one, is that how much (and what?)" it is possible to distinguish a fine structure of solar radio bursts in both cases., it is possible to distinguish a fine structure of solar radio bursts in both cases. Next. we have compared the ordinary. simultaneous observations. carried out bv the array of 720 dipoles (a part of the radiotelescope UWPR-2) and the Waves WIND instruments.," Next, we have compared the ordinary simultaneous observations, carried out by the array of 720 dipoles (a part of the radiotelescope UTR-2) and the Waves WIND instruments." This allows us to establish a real elfectiveness of space radiotelescopes in the study of weak solar events., This allows us to establish a real effectiveness of space radiotelescopes in the study of weak solar events. Usually the observations of solar radio emission. in. the framework of the telescope UTIU-2 are carried out. by four banks of the antenna arm “North” or “South” (see the details about the instrument in Braude et al., Usually the observations of solar radio emission in the framework of the telescope UTR-2 are carried out by four banks of the antenna arm “North” or “South” (see the details about the instrument in Braude et al. 1978)., 1978). In this case the antenna directional pattern covers all the size of the solar upper corona from which the cecameter radio bursts. are eenerated., In this case the antenna directional pattern covers all the size of the solar upper corona from which the decameter radio bursts are generated. These four banks are groupecl into an antenna array of 720 dipoles (4. = 900 52 m). permitting one to receive a signal in the continuous frequcney hand from. 9 to 31. Mllz.," These four banks are grouped into an antenna array of 720 dipoles $A_{e}$ = 900 $\times$ 52 $^2$ ), permitting one to receive a signal in the continuous frequency band from 9 to 31 MHz." As a recording back-end. we use a two-channel discrete spectrum analyzer (DSP).," As a recording back-end, we use a two-channel discrete spectrum analyzer (DSP)." Its features are described in the paper of MelUnik et al. (, Its features are described in the paper of Mel'nik et al. ( 2004).,2004). We recorded Lgimultanceously solar signals from the two antennas., We recorded simultaneously solar signals from the two antennas. The first antenna had four banks of the antenna arm “South”. and re second. contained. only one dipole of the antenna arn orth’.," The first antenna had four banks of the antenna arm “South”, and the second contained only one dipole of the antenna arm “North”." The observations were obtained. between 15 and 27 August 2007 during three hours forenoon and afternoon., The observations were obtained between 15 and 27 August 2007 during three hours forenoon and afternoon. The solar activity was weak enough., The solar activity was weak enough. Nevertheless. we have observed some weak solar events.," Nevertheless, we have observed some weak solar events." The tracking of the solar motion in the skv by the antenna directional pattern of WPR-2 is performed electronically by switehing the phase-shift network of the telescope antenna., The tracking of the solar motion in the sky by the antenna directional pattern of UTR-2 is performed electronically by switching the phase-shift network of the telescope antenna. Antenna steering and data acquisition are computer controlled., Antenna steering and data acquisition are computer controlled. The observation range was between 18.5 and 30.5 Mllz., The observation range was between 18.5 and 30.5 MHz. The calibration was carried out by the noise generator with the well-known spectral density for both antenna channels simultaneously., The calibration was carried out by the noise generator with the well-known spectral density for both antenna channels simultaneously. " Since the back end in the solar observations was the same for both antennas. it is convenient to choose à measure of their sensitivity in the following form: where Z4 is the equivalent antenna temperature. 4, he fux density in sfu (1 sfu = 1077 Wom7 3). Fk he Boltzmann's constant."," Since the back end in the solar observations was the same for both antennas, it is convenient to choose a measure of their sensitivity in the following form: where $T_{\rm A}$ is the equivalent antenna temperature, $S_o$ the flux density in sfu (1 sfu = $^{-22}$ W $^{-2}$ $^{-1}$ ), $k$ the Boltzmann's constant." Four banks of the antenna arm “South gives a sensitivity of z 170.000 Ix/sfu. and a single dipole (receiving over a perfect conducting ground plane) ias only z 228 Ix/sfu at 18.5 MllIz. falling to = S4 Ix/sfu at 30.5 Mllz.," Four banks of the antenna arm “South” gives a sensitivity of $\approx$ 170,000 K/sfu, and a single dipole (receiving over a perfect conducting ground plane) has only $\approx$ 228 K/sfu at 18.5 MHz, falling to $\approx$ 84 K/sfu at 30.5 MHz." One of these records is represented in Fig. 1.., One of these records is represented in Fig. \ref{fig1}. The op panel shows the spectrogram. received. by the array of 720 dipoles. and the bottom panel. demonstrates. a dynamical spectrum of emission received by only one dipole.," The top panel shows the spectrogram, received by the array of 720 dipoles, and the bottom panel demonstrates a dynamical spectrum of emission received by only one dipole." About 10:34:35. UT in 2007 August 21 we have detected a single type LLL solar burst with a weak Εαν., About 10:34:35 UT in 2007 August 21 we have detected a single type III solar burst with a weak flux. Prom these pictures it is clearly seen that the detection of such solar bursts is hardly possible for one dipole., From these pictures it is clearly seen that the detection of such solar bursts is hardly possible for one dipole. The Wind spectrum records do not show any burst at this time too (see rrad2/rad2pdf)., The Wind spectrum records do not show any burst at this time too (see rad2/rad2pdf/). Probably. the burst [ux density was less than the minimum detectable value of the instrument.," Probably, the burst flux density was less than the minimum detectable value of the instrument." The other restriction. leaving traces on the observations by one dipole. is that its performance does not. permit one to study a fine structure of the decameter bursts in detail.," The other restriction, leaving traces on the observations by one dipole, is that its performance does not permit one to study a fine structure of the decameter bursts in detail." As a significant example. let us consider Fig. 2..," As a significant example, let us consider Fig. \ref{fig2}." It presents a spectroeram of a set of solar bursts with dilferent features in intensity. that were observed in 2007 August 17 at abou 9:50 UE.," It presents a spectrogram of a set of solar bursts with different features in intensity, that were observed in 2007 August 17 at about 9:50 UT." The spectrogram. obtained by one dipole. shows only one strongest burst. and it just plain didn't look like the set of bursts that represented in the top panels.," The spectrogram, obtained by one dipole, shows only one strongest burst, and it just plain didn't look like the set of bursts that represented in the top panels." In contras to the burst. represented in Fig. 1..," In contrast to the burst, represented in Fig. \ref{fig1}," for which the intensity and the duration. increased uniformly with the ἄοσαν of [requeney. the peculiarity of the given set of bursts is tha their intensity and duration were irregular in frequency.," for which the intensity and the duration increased uniformly with the decay of frequency, the peculiarity of the given set of bursts is that their intensity and duration were irregular in frequency." llowever. this can be tracked: more or less successfully in the top panels of Fig. 2..," However, this can be tracked more or less successfully in the top panels of Fig. \ref{fig2}," which give a sullicient resolution of this event in intensity owing to the considerable dominance of the array in cllective area., which give a sufficient resolution of this event in intensity owing to the considerable dominance of the array in effective area. Phe Wind. spectrum. also cannot resolve any fine structure of this event. although the strongest burst is noticeable.," The Wind spectrum also cannot resolve any fine structure of this event, although the strongest burst is noticeable." To resume as a preliminary. we should tell that the antenna array of 720 dipoles has a considerable advantage for the study of weak solar bursts as well as for the analysis of a fine structure of strong ones.," To resume as a preliminary, we should tell that the antenna array of 720 dipoles has a considerable advantage for the study of weak solar bursts as well as for the analysis of a fine structure of strong ones." One more interesting problem is that. as is known. the solar type LLL bursts observed at. metric wavelengths often disappear in decametric range. whereas other bursts appear at decametric wavelengths and may or may not continue to the low-frequency limit of most. ground-based spectrographs at frequencies less than 20-30 MIz.," One more interesting problem is that, as is known, the solar type III bursts observed at metric wavelengths often disappear in decametric range, whereas other bursts appear at decametric wavelengths and may or may not continue to the low-frequency limit of most ground-based spectrographs at frequencies less than 20-30 MHz." Applying the large decameter racioastronomy for this study. it would be useful also.," Applying the large decameter radioastronomy for this study, it would be useful also." The spacecraft. WIND is located in the Lagrangian point L1 between the Earth and the Sun. where the gravitational attraction ofthis spacecraft to the Earth becomes balanced with the eravitation attraction of the spacecraft to the Sun.," The spacecraft WIND is located in the Lagrangian point L1 between the Earth and the Sun, where the gravitational attraction of this spacecraft to the Earth becomes balanced with the gravitation attraction of the spacecraft to the Sun." This point is situated about 1.5 million km from the Earth., This point is situated about 1.5 million km from the Earth. Llowever. the distance from the spacecraft to the Sun is more in 99 times.," However, the distance from the spacecraft to the Sun is more in 99 times." To recall one of formulae from Ixraus (1967). the [Dux density of radio emission observed at the distance ris inversely as the square of the distance.," To recall one of formulae from Kraus (1967), the flux density of radio emission observed at the distance $r$ is inversely as the square of the distance." Therefore. the antenna of the spacecraft WIND receives a signal only. in 2% greater than the same antenna from the Earth. if we do not account for scattering. absorption and rejection of radio emission in the terrestrial ionosphere and the near-Earth space.," Therefore, the antenna of the spacecraft WIND receives a signal only in $\%$ greater than the same antenna from the Earth, if we do not account for scattering, absorption and rejection of radio emission in the terrestrial ionosphere and the near-Earth space." However. the increase of the antenna cllective area for any spacecraft is problematic enough because of the causes discussed. above in Introduction. whereas for any &rouncd-based antenna this is quite real (by building an antenna array).," However, the increase of the antenna effective area for any spacecraft is problematic enough because of the causes discussed above in Introduction, whereas for any ground-based antenna this is quite real (by building an antenna array)." What does this give?, What does this give? The spectral power. received bv antenna. is directly proportional to its effective. area.," The spectral power, received by antenna, is directly proportional to its effective area." This means that the array of 720 dipoles increase a spectral density of received. signals proportionally so many times as its ellective area is more in comparison with one dipole., This means that the array of 720 dipoles increase a spectral density of received signals proportionally so many times as its effective area is more in comparison with one dipole. In aclelition to that it should be added an appreciable advance of interference protection in many times., In addition to that it should be added an appreciable advance of interference protection in many times. This problem quite relates to the one-dipole antenna of the spacecraft, This problem quite relates to the one-dipole antenna of the spacecraft "The correspondingm Euler equations1 are: llere. τονD is the (co-moving)5 electron-proton1 collision time scale: 7,=L/(narea) is the photon-clectron Thompson scattering time scale.","The corresponding Euler equations are: Here, $\tau_{ep}$ is the (co-moving) electron-proton collision time scale; $\tau_{\gamma e} = 1/(n_e \sigma_{\scriptscriptstyle T}a )$ is the photon-electron Thompson scattering time scale." E.B. are the physical electric and magnetic fields. A!—dp./3p.. and £2.) are the pressures which. for aciabatic fluids. can be written as 2=P(p).," ${\mathbf{E,B}}$ are the physical electric and magnetic fields, $ R\equiv 4\rho_{\gamma}/3\rho_{e}$, and $P_{e,p}$ are the pressures which, for adiabatic fluids, can be written as $P\equiv P(\rho)$." By taking curl of the Euler equations and using Maxwell's equations. we can got the evolution equation for the vorticities (δν νι) of the Duids as: To arrive at the equation governing the evolution of magnetic field. we use the Euler equations for the charged. Duids and Alaxwell’s equations CXppendix D).," By taking curl of the Euler equations and using Maxwell's equations, we can get the evolution equation for the vorticities ${\mathbf{\Omega}}_{e,p}\equiv\nabla\times {\mathbf{v}}_{e,p}$ ) of the fluids as: To arrive at the equation governing the evolution of magnetic field, we use the Euler equations for the charged fluids and Maxwell's equations (Appendix B)." Subtracting I5q. (6)), Subtracting Eq. \ref{euler_p}) ) from Eq. (7)), from Eq. \ref{euler_e}) ) ancl using Maxwell'sequations we first obtain the evolution of the current J: In the above equation we have neglected forces on the proton IHuid due to pressure gradient and electric field since they are smaller than that for the electron fluid by the factor mfmy., and using Maxwell'sequations we first obtain the evolution of the current $\mathbf{J}$: In the above equation we have neglected forces on the proton fluid due to pressure gradient and electric field since they are smaller than that for the electron fluid by the factor $m_{e}/m_{p}$. Taking curl of equation (9) and using Maxwell's equations. we get the equation for the generation of magnetic fields: For studying the generation. of magnetic fields in the carly universe most of the terms in the above equation can be ropped.," Taking curl of equation (9) and using Maxwell's equations, we get the equation for the generation of magnetic fields: For studying the generation of magnetic fields in the early universe most of the terms in the above equation can be dropped." Ehe first term on the right hand side can be shown to be negligible as compared to the term on the Left hand side see c.g. Widrow 2002)., The first term on the right hand side can be shown to be negligible as compared to the term on the left hand side (see e.g. Widrow 2002). Similarly all the terms proportional to B can be neglected if one wishes to study the generation of magnetic fields from zero magnetic field initial conditions., Similarly all the terms proportional to ${\bf B}$ can be neglected if one wishes to study the generation of magnetic fields from zero magnetic field initial conditions. Phese terms can back-react once the magnetic field is eenerated., These terms can back-react once the magnetic field is generated. We garow later that the back-reaction terms are negligible for the magnitude of the generated magnetic field., We show later that the back-reaction terms are negligible for the magnitude of the generated magnetic field. These considerations simplify the above equation to: with We now cliscuss the nature of these source terms of magnetic field. generation in first ancl second order in. perturbation theory., These considerations simplify the above equation to: with We now discuss the nature of these source terms of magnetic field generation in first and second order in perturbation theory. The source term for any Fourier mode SCk.5) can be simplified for the linear case.," The source term for any Fourier mode ${\mathbf{S}}({\mathbf{k}},\eta)$ can be simplified for the linear case." In this case. /?=4p./(38p.). and σ). are unperturbed quantities and hence don't carry any spatial dependence.," In this case, $R=4\bar\rho_{\gamma}/ (3\bar\rho_{e})$, and $\tau_{\gamma e}=1/(\bar n_e \sigma_ {\rss T})$ , are unperturbed quantities and hence don't carry any spatial dependence." Ehe first term of the right hand side of Ίσα. (12)), The first term of the right hand side of Eq. \ref{source_b}) ) identically vanishes in this case., identically vanishes in this case. The source term can then be written as: Thus. we see that the source for the magnetic field in the plasma is the dilferential vorticity between electrons and photons.," The source term can then be written as: Thus, we see that the source for the magnetic field in the plasma is the differential vorticity between electrons and photons." The vorticity equation for photons is essentially the Boltzmann moment equation for /—Lom=1 (Iq. CX8))).," The vorticity equation for photons is essentially the Boltzmann moment equation for $l=1,m=1$ (Eq. \ref{boltz_eq}) ))." " We note that the source of photon vorticity is de,./7.,x O,.", We note that the source of photon vorticity is $4v_{\ell1}/\tau_{\gamma e}\propto \Omega_{e}$ . This implies that the only source which can excite any /momoent for m=1 , This implies that the only source which can excite any $l$ -moment for $m=1$ We have improved the accuracy of the rotational period of the most rapidly rotating CP star tto P=045214410(4) and determined its rate of period change to be P/P=2.48)x109yr!.,"We have improved the accuracy of the rotational period of the most rapidly rotating CP star to $P=0\fd5214410(4)$ and determined its rate of period change to be $\dot{P}/P=2.4(8)\times 10^{-6}\,\mathrm {yr}^{-1}$." We propose that the period variations could be eyclic on a timescale of a few decades., We propose that the period variations could be cyclic on a timescale of a few decades. Observed light vartations may be caused by the unever surface distribution of overabundant helium., Observed light variations may be caused by the uneven surface distribution of overabundant helium. rremains a very appealing target for continued photometric and spectroscopic observations. as well as for the modelling of its unusual behaviour.," remains a very appealing target for continued photometric and spectroscopic observations, as well as for the modelling of its unusual behaviour." extreme conditions iu the neutro jisfar vicinity.,extreme conditions in the neutron star vicinity. \ajor gains in the understanding of these phenomena lave becu uade since the launch of the Rossi X-ray Timing Explorer (RATE) in late 1995., Major gains in the understanding of these phenomena have been made since the launch of the Rossi X-ray Timing Explorer (RXTE) in late 1995. Ilieh frequency quasiperiodic oscillatious (QPOs) and short strings of «ολο! p]satious duris musts have been used to argue convincingly that effects associaed with mner disk οσος aud the inneriost stable orbits predicted by Ceneral Relativity are being seen (van der Elis 1998)., High frequency quasiperiodic oscillations (QPOs) and short strings of coherent pulsations during bursts have been used to argue convincingly that effects associated with inner disk edges and the innermost stable orbits predicted by General Relativity are being seen (van der Klis 1998). Another milestone is the establishment of he spiuup evoluion of neutro istais througi the discovery of the first accretion powered millisecond pulsar (SAN JI1808.1-3655)., Another milestone is the establishment of the spinup evolution of neutron stars through the discovery of the first accretion powered millisecond pulsar (SAX J1808.4-3658). USA will make further coutrinitions to the stiv of LAINBs with the application of its unique streneths., USA will make further contributions to the study of LMXBs with the application of its unique strengths. Iu some cases this will mean exploiine the abiliv to dedicate large blocks of time to a key source. o.g.. to refine uiuerstandius of SAN Ηδ0δ.3658 or to observe transitions between modes or states.," In some cases this will mean exploiting the ability to dedicate large blocks of time to a key source, e.g., to refine understanding of SAX J1808.4-3658 or to observe transitions between modes or states." üificant tine Is being devoted to searches for cohereut periods. both ou aud off birsts.," Significant time is being devoted to searches for coherent periods, both on and off bursts." ο rst work is carried out using coherence recovery searclies for periods., Off burst work is carried out using coherence recovery searches for periods. Observations cau also be carried out i various wavs to detect or refine orbital veriods in LAINBs., Observations can also be carried out in various ways to detect or refine orbital periods in LMXBs. Overall. LAINBs are sources that stand to bring major rewards including advances in understanding the role of General Relativity iu the dviuamuics of ier disk regions. but past experience has also shown that these rewards are achieved ouly through major iuvestiuenuts of observiug time and analvsis. chiefly because of the elusiveuess and short timescale of tle spin ]x3locds.," Overall, LMXBs are sources that stand to bring major rewards including advances in understanding the role of General Relativity in the dynamics of inner disk regions, but past experience has also shown that these rewards are achieved only through major investments of observing time and analysis, chiefly because of the elusiveness and short timescale of the spin periods." "on the knee of the [a/Fe] ratios, in the sense that a flatter IMF predicts a knee of [a/Fe] ratio at larger [Fe/H] values.","on the knee of the $\alpha$ /Fe] ratios, in the sense that a flatter IMF predicts a knee of $\alpha$ /Fe] ratio at larger [Fe/H] values." " Therefore, the length of the plateau can in principle be used to impose constraints on the IMF."," Therefore, the length of the plateau can in principle be used to impose constraints on the IMF." " However, for the bulge the knees occur always at [Fe/H]> 0 since the strong assumed SFR always induces a very fast increase of the [Fe/H], thus having the SNe Ia occurring when the ISM has already reached a solar Fe abundance."," However, for the bulge the knees occur always at $>$ 0 since the strong assumed SFR always induces a very fast increase of the [Fe/H], thus having the SNe Ia occurring when the ISM has already reached a solar Fe abundance." " It is worth noting that the effect of varying the IMF is different for different elements, being more evident for O and almost negligible for S. This of course depends on the specific progenitors of each elements and in particular on whether two elements are produced by the same stars or in different mass ranges: the largest difference is, in fact, seen in the O plot, since O is mainly produced in massive stars whereas Fe is mainly produced in low and intermediate mass stars (SNe Ia)."," It is worth noting that the effect of varying the IMF is different for different elements, being more evident for O and almost negligible for S. This of course depends on the specific progenitors of each elements and in particular on whether two elements are produced by the same stars or in different mass ranges: the largest difference is, in fact, seen in the O plot, since O is mainly produced in massive stars whereas Fe is mainly produced in low and intermediate mass stars (SNe Ia)." " In the case of S and Si instead, SNe Ia contribute in a non-negligible way to these two elements."," In the case of S and Si instead, SNe Ia contribute in a non-negligible way to these two elements." " From a look at Figure 1 we can conclude that the Scalo IMF predicts too low [a/Fe] ratios, whereas the Salpeter and BMORO7 IMFs produce results more in agreement with observations."," From a look at Figure 1 we can conclude that the Scalo IMF predicts too low $\alpha$ /Fe] ratios, whereas the Salpeter and BMOR07 IMFs produce results more in agreement with observations." " In Figure 2 we show the predicted and observed [el/Fe] vs. [Fe/H] for el=Ba, Cr, Ti and Ca."," In Figure 2 we show the predicted and observed [el/Fe] vs. [Fe/H] for el=Ba, Cr, Ti and Ca." " This is the first time that predictions for Ba, Cr and Ti for the bulge are presented."," This is the first time that predictions for Ba, Cr and Ti for the bulge are presented." " Also in this case the general agreement with the data is good and the best one is for the BMORO7 and Salpeter IMF, thus reinforcing the conclusion that the IMF in the bulge should be flatter than in the disk, as claimed by many papers before (e.g. Matteucci Brocato, 1990; Matteucci et al."," Also in this case the general agreement with the data is good and the best one is for the BMOR07 and Salpeter IMF, thus reinforcing the conclusion that the IMF in the bulge should be flatter than in the disk, as claimed by many papers before (e.g. Matteucci Brocato, 1990; Matteucci et al." 1999; BMORO?7)., 1999; BMOR07). This result has important implications for the [o/Fe] ratios and their behaviour with [Fe/H] in bulge and thick disk stars (Chiappini et al., This result has important implications for the $\alpha$ /Fe] ratios and their behaviour with [Fe/H] in bulge and thick disk stars (Chiappini et al. in preparation)., in preparation). " In fact, there are some indications (e.g. Alves-Brito al."," In fact, there are some indications (e.g. Alves-Brito al." 2010; Melénndez al., 2010; Melénndez al. 2008) that some ratios are the same for bulge and thick disk stars., 2008) that some ratios are the same for bulge and thick disk stars. " However, the most convincing evidence for an IMF flatter in the bulge is provided by Figure 3 where the predicted and observed stellar metallicity distribution function (MDF) for bulge stars is plotted."," However, the most convincing evidence for an IMF flatter in the bulge is provided by Figure 3 where the predicted and observed stellar metallicity distribution function (MDF) for bulge stars is plotted." " As one can see, the position of the peak in the bulge MDF is extremely sensitive to the assumed IMF."," As one can see, the position of the peak in the bulge MDF is extremely sensitive to the assumed IMF." " A Scalo IMF, which is good for reproducing the solar neighbourhood properties, it fails completely for the bulge."," A Scalo IMF, which is good for reproducing the solar neighbourhood properties, it fails completely for the bulge." The results obtained by Zoccali et al. (, The results obtained by Zoccali et al. ( "2008) are also consistent with the presence of a gradient in the bulge, as the ones by Minniti (1996).","2008) are also consistent with the presence of a gradient in the bulge, as the ones by Minniti (1996)." " So, their findings support our scenario in which both infall and outflow are important and in which the bulge formed very fast by dissipative collapse of gas shed by the halo, rather than the scenario in which the bulge would result solely from the vertical heating of the bar."," So, their findings support our scenario in which both infall and outflow are important and in which the bulge formed very fast by dissipative collapse of gas shed by the halo, rather than the scenario in which the bulge would result solely from the vertical heating of the bar." " On the other hand, the presence of a radial metallicity gradient warns us about the limitations of our model which predicts only a global MDF for the bulge."," On the other hand, the presence of a radial metallicity gradient warns us about the limitations of our model which predicts only a global MDF for the bulge." A very important result is the change in slope observed for bulge stars in the ratio [O/Mg] for [Mg/H]»0., A very important result is the change in slope observed for bulge stars in the ratio [O/Mg] for $>0$. McWilliam et al. (, McWilliam et al. ( 2008) and Cescutti et al. (,2008) and Cescutti et al. ( 2009) interpreted this effect as due to the mass loss in massive stars.,2009) interpreted this effect as due to the mass loss in massive stars. " In fact, the mass loss becomes important only for metallicities larger than solar and induces the effect of producing more C and He, which are the elements preferentially lost through mass loss by stellar winds, at expenses of O which is produced in a lower amount due to the loss of its progenitor elements, C and He."," In fact, the mass loss becomes important only for metallicities larger than solar and induces the effect of producing more C and He, which are the elements preferentially lost through mass loss by stellar winds, at expenses of O which is produced in a lower amount due to the loss of its progenitor elements, C and He." This, This VV being the accessible co-moving volume of the i! AGN.,$V_a^i$ being the accessible co-moving volume of the $i^{\rm th}$ AGN. " The estimate of Vi, was based on suas derived from the AGN’s X-ray Hux and EMSS [lux limits. assuming an X-ray spectral index ax=dE: fpxvUN."," The estimate of $V_a$ was based on $z_{\rm max}$ derived from the AGN's X-ray flux and EMSS flux limits, assuming an X-ray spectral index $\alpha_{\rm X}=1$; $f_{\nu} \propto \nu^{-\alpha_{\rm X}}$." " To construct an optical OLE. we binned the 1/V, estimates according to their optical nuclear Ale magnitudes."," To construct an optical OLF, we binned the $1/V_a$ estimates according to their optical nuclear $M_{B}$ magnitudes." We. computed Poisson errors on the binned estimates of the OLE using ο. Not all 127 AGN with z<0.15 in the EXISS were observed by SBL and so a straightforward normalising factor of 0.6 (76/127) was applied to the area coverage function when computing the accessible volume.," We computed Poisson errors on the binned estimates of the OLF using $\sigma = \left(\sum \frac{1}{(V_a^i)^2} \right) ^{0.5}$ Not all 127 AGN with $z < 0.15$ in the EMSS were observed by SBL and so a straightforward normalising factor of 0.6 (76/127) was applied to the area coverage function when computing the accessible volume." INS tests confirmed that the redshift and lux distribution for the SBL sample is consistent with the sample being drawn at random from the z0.15 IE2MSS parent sample., KS tests confirmed that the redshift and flux distribution for the SBL sample is consistent with the sample being drawn at random from the $z < 0.15$ EMSS parent sample. The OLE was calculated at. 1-maeg intervals for the full redshift range z<0.15., The OLF was calculated at 1-mag intervals for the full redshift range $z \leq 0.15$. We mace no correction for evolution across the redshift bin., We made no correction for evolution across the redshift bin. We also constructed separate OLES for AGN in elliptical and spiral hosts to investigate any host- trends., We also constructed separate OLFs for AGN in elliptical and spiral hosts to investigate any host-related trends. " The dillerential OLE calculated. for an. Einstein-de Sitter universe in which {10=50f-4 km ο, ονAL=1. Q4=0. is presented in Table 1 and plotted in Fig."," The differential OLF calculated for an Einstein-de Sitter universe in which $H_0 = 50 h_{50}$ km $^{-1}$ $^{-1}$, $\Omega_{\rm M}=1$, $\Omega_\Lambda=0$, is presented in Table 1 and plotted in Fig." 33. over plotted with data from WOT (their Table 5).," 3, over plotted with data from K97 (their Table 5)." As a comparison values using total ewlaxy luminosity (host | nucleus) are shown in Table 2 and plotted in Figure 5., As a comparison values using total galaxy luminosity (host + nucleus) are shown in Table 2 and plotted in Figure 5. The WOT data comprises 27 objects extending out to a redshift of 0.3., The K97 data comprises 27 objects extending out to a redshift of 0.3. Of these. eight were at redshifts greater than the z=0.15 cut-olf adopted in the SBL sample. all of which have Mg<24. Le. brighter than the most luminous AGN in the SBL sample.," Of these, eight were at redshifts greater than the $z = 0.15$ cut-off adopted in the SBL sample, all of which have $M_B < -24$, i.e. brighter than the most luminous AGN in the SBL sample." In 33 we have also plotted two predictions of the ><0.15 OLE based on the luminosity evolution moclels of Bovle et ((2000)., In 3 we have also plotted two predictions of the $z<0.15$ OLF based on the luminosity evolution models of Boyle et (2000). These authors fit a varietv of evolutionary models to a cata set. comprising over 6000 QSOs with Alp<23 and 0.35«c2.3 selected: from he 2dEl QSO redshift survey (Bovle et 11999). and the Large. Bright QSO survey (LBQS. Llewett et 11995).," These authors fit a variety of evolutionary models to a data set comprising over 6000 QSOs with $M_B<-23$ and $0.350.35$. We obtained a reduced 47=1.0 for the exponential model fit to the SBL data at Alp< 19. but were able to reject the extrapolation of the polvnoniual model at the 99 per cent confidence level.," We obtained a reduced $\chi^2=1.0$ for the exponential model fit to the SBL data at $M_B <-19$ , but were able to reject the extrapolation of the polynomial model at the 99 per cent confidence level." After completing steyw 2- 13 above. an iteration of the Cabs sunpler is Complete.,"After completing steps \ref{i-ycens}- \ref{i-wsqr0} above, an iteration of the Gibbs sampler is complete." One thems ses the new simulated values of £.4.0.¢ and the prior parameters. and repeats steps 2- 13..," One then uses the new simulated values of $\xi,\eta,\theta,\psi,$ and the prior parameters, and repeats steps \ref{i-ycens}- \ref{i-wsqr0}." The aleorithiu 1s repeated until convergence. aud tje values of ϐ and © at cach iteration are saved.," The algorithm is repeated until convergence, and the values of $\theta$ and $\psi$ at each iteration are saved." " U)01l reaching colverechice, one discards the values of 7 aud c from the beeimuing of the simulation. aud the relmaiing values of a.d.07.µ. and 7? (or T) may be tr""ated as a random draw from the posterior distribuion. polegy)."," Upon reaching convergence, one discards the values of $\theta$ and $\psi$ from the beginning of the simulation, and the remaining values of $\alpha, \beta, \sigma^2, \mu,$ and $\tau^2$ (or $T$ ) may be treated as a random draw from the posterior distribution, $p(\theta,\psi|x,y)$." Ore can then use these values to caleuate estimates of the parameters. and their correspoiding variances ας coufideuce intervals.," One can then use these values to calculate estimates of the parameters, and their corresponding variances and confidence intervals." " The posterior ¢listribution of the parameters can also be estimate| from these values of 0 and c using histogram techliniqies,", The posterior distribution of the parameters can also be estimated from these values of $\theta$ and $\psi$ using histogram techniques. Techniques for mouitering convergence of the Aarkov Chaius can o found iu Cehnanetal.(2001)., Techniques for monitering convergence of the Markov Chains can be found in \citet{gelman04}. . The output from the Cibbs sampler may be used to perform Bayesian 1erence on other cnautities of interest., The output from the Gibbs sampler may be used to perform Bayesian inference on other quantities of interest. In particular. the Pearson linear correlation coefficieut. p. is often used in assessing the sreneth of a relationship between the c aud y.," In particular, the Pearson linear correlation coefficient, $\rho$, is often used in assessing the strength of a relationship between the $x$ and $y$." A random draw from the posterior distribution for the correlation between jj aud €;. denoted as p;. cau be calculated from Equation (5)) for cach draw frou the Cübbs sanypler.," A random draw from the posterior distribution for the correlation between $\eta$ and $\xi_j$, denoted as $\rho_j$, can be calculated from Equation \ref{eq-rho}) ) for each draw from the Gibbs sampler." For the Catssian mixture iiodel. the variance Var() and covariance matrix Ne=Ver(£) are," For the Gaussian mixture model, the variance $Var(\eta)$ and covariance matrix $\Sigma_{\xi} \equiv Var(\xi)$ are" scattering in (he previous subsection (except that the integral can not be expressed in ternis ol elementary funetions) and can be found in any textbooks on general relativilv. Weinberg. Chap.,"scattering in the previous subsection (except that the integral can not be expressed in terms of elementary functions) and can be found in any textbooks on general relativity Weinberg, Chap." 8)., 8). Ir the linear regine r>>GM. we obtain the Einstein deflection angle =|. where ry is the distance of the periastron of the photon trajectory.," In the linear regime $r >> GM$, we obtain the Einstein deflection angle =, where $r_0$ is the distance of the periastron of the photon trajectory." " Ho is worth noting that gj=—D and g,=A+ equally contribute to the Einstein deflection angle. and the Newtonian deflection augle amounts to the contribution from g,,."," It is worth noting that $g_{tt} = -B$ and $g_{rr} = A^{-1}$ equally contribute to the Einstein deflection angle, and the Newtonian deflection angle amounts to the contribution from $g_{tt}$." The factor 2 discrepancy between the Newtonian and Einstein deflection angles are the well-known general relativistic [actor 2. which was tested in 1919 during the eclipse notably by Eddington and his crew ancl numerously since.," The factor 2 discrepancy between the Newtonian and Einstein deflection angles are the well-known general relativistic factor 2, which was tested in 1919 during the eclipse notably by Eddington and his crew and numerously since." " It should be useful to note that the variation of the action 5 in ((2.2)) leads to the “standard” geodesic equation. Q= + where D, is (he affine connection."," It should be useful to note that the variation of the action $S$ in \ref{eqAction}) ) leads to the “standard"" geodesic equation, 0 = +, where $\Gamma^\lambda_{\mu\nu}$ is the affine connection." Hence the path parameter p is a so-called affine parameter which is a linear [function of the proper time., Hence the path parameter $p$ is a so-called affine parameter which is a linear function of the proper time. If we choose an arbitrary. parameter. the equation develops extra terms as one can check easily.," If we choose an arbitrary parameter, the equation develops extra terms as one can check easily." The source star and the observer are [ar away [rom the lensing mass Af. and there the metric is effectively flat.," The source star and the observer are far away from the lensing mass $M$, and there the metric is effectively flat." The coordinates have been chosen such that D.4—1 as r—ox. hence the observer should feel relaxed. to use the familiar flat space coordinate svstenis io make local measurements or to chart the skv knowing that the coordinate svstems are valid all the wav from the observer's neighborhood to the neighborhood of the source star except inside the star.," The coordinates have been chosen such that $B, \, A \rightarrow 1$ as $r\rightarrow \infty$, hence the observer should feel relaxed to use the familiar flat space coordinate systems to make local measurements or to chart the sky knowing that the coordinate systems are valid all the way from the observer's neighborhood to the neighborhood of the source star except inside the star." In the asvimptotically flat coordinate system. the photon arriving al (he observer's detector aller a long flight. along a null geodesic would seem to come from a position in the sky that differs from the position of the source star where the latter is determined bx hvpothetically turning; off the gravity by selling the Newton's constant G=0.," In the asymptotically flat coordinate system, the photon arriving at the observer's detector after a long flight along a null geodesic would seem to come from a position in the sky that differs from the position of the source star where the latter is determined by hypothetically turning off the gravity by setting the Newton's constant $G=0$." The relation between a source position and its images in the observers skv is (he lens ecuation., The relation between a source position and its images in the observer's sky is the lens equation. studies has been systematically biased towards emission-line stars.,studies has been systematically biased towards emission-line stars. Therefore. these studies could not conclude whether this departure rom the main flux-flux relationships was restricted to late-type stars with clear emission line characteristics or was common to a arger group of late K- and M-type stars.," Therefore, these studies could not conclude whether this departure from the main flux–flux relationships was restricted to late-type stars with clear emission line characteristics or was common to a larger group of late K- and M-type stars." The main objective of his work is to check which type of stars depart from the main flux-fiux relationships when two chromospheric indicators are compared., The main objective of this work is to check which type of stars depart from the main flux–flux relationships when two chromospheric indicators are compared. In addition. we aim to properly quantify this departure using chromospheric fluxes that are appropriately corrected from he atmospheric basal contribution.," In addition, we aim to properly quantify this departure using chromospheric fluxes that are appropriately corrected from the atmospheric basal contribution." By so doing we will provide unique information on the validity of the use of such relationships when trying to convert between fluxes in different lines., By so doing we will provide unique information on the validity of the use of such relationships when trying to convert between fluxes in different lines. For this research. we used high resolution optical echelle spectra.," For this research, we used high resolution optical echelle spectra." A noteworthy advantage of echelle spectra is that they cover a large fraction of the optical spectrum simultaneously., A noteworthy advantage of echelle spectra is that they cover a large fraction of the optical spectrum simultaneously. Therefore. they allow a simultaneous observation of all the activity indicator lines present in this spectral range. avoiding the spread in the relations caused by temporal variability of activity levels.," Therefore, they allow a simultaneous observation of all the activity indicator lines present in this spectral range, avoiding the spread in the relations caused by temporal variability of activity levels." This fact implies a significant improvement of the flux-flux relationships with respect to those previously obtained. because most of the latter were built by using activity diagnostics that were not measured simultaneously.," This fact implies a significant improvement of the flux–flux relationships with respect to those previously obtained, because most of the latter were built by using activity diagnostics that were not measured simultaneously." In addition. the chromospheric fluxes obtained from this method are corrected for the basal chromospheric emission.," In addition, the chromospheric fluxes obtained from this method are corrected for the basal chromospheric emission." Details on the technical information of the observations and data reduction are given in Section 2., Details on the technical information of the observations and data reduction are given in Section 2. Section 32 describes the analysis of the observations and the obtained excess emission equivalent widths. excess surface fluxes and X-ray luminosities and fluxes.," Section 3 describes the analysis of the observations and the obtained excess emission equivalent widths, excess surface fluxes and X-ray luminosities and fluxes." Finally. Sections + and 5 are devoted. respectively. to the discussion of the results and conclusions of this work.," Finally, Sections 4 and 5 are devoted, respectively, to the discussion of the results and conclusions of this work." The present study is based on high resolution echelle spectra., The present study is based on high resolution echelle spectra. The total sample comprises 298 main-sequence. late-type (spectral types F to M). single. active stars.," The total sample comprises 298 main-sequence, late-type (spectral types F to M), single, active stars." We used data from ?. (hereafter LS!0) for [44 stars and data from ο (hereafter MAIO) for73'., We used data from \citet{2010A&A...514A..97L} (hereafter LS10) for 144 stars and data from \citet{2010A&A...520A..79M} (hereafter MA10) for. . The former sample is mainly formed by main-sequence stars but also includes some stars members of young associations and kinematic groups., The former sample is mainly formed by main-sequence stars but also includes some stars members of young associations and kinematic groups. The 16 binaries of that sample have not been included in our study., The 16 binaries of that sample have not been included in our study. The MAIO sample is formed only by main-sequence single stars., The MA10 sample is formed only by main-sequence single stars. Thus. all the active stars in this sample have been included in our study.," Thus, all the active stars in this sample have been included in our study." We refer the reader to the mentioned works for a detailed explanation on the observing runs. telescopes and instruments they used as well as the characteristics of their spectra.," We refer the reader to the mentioned works for a detailed explanation on the observing runs, telescopes and instruments they used as well as the characteristics of their spectra." We also note that there are 22 common stars between LSIO and MAIO., We also note that there are 22 common stars between LS10 and MA10. After eliminating all binaries in LS10 and cross-correlating this sample with MALO. we obtained a total of 279 late-type stars.," After eliminating all binaries in LS10 and cross-correlating this sample with MA10, we obtained a total of 279 late-type stars." We note that MAIO and LSIO samples are complementary in terms of emission levels: while the former includes mainly low activity stars. the latter is principally formed by young active stars.," We note that MA10 and LS10 samples are complementary in terms of emission levels: while the former includes mainly low activity stars, the latter is principally formed by young active stars." This fact is important bearing in mind that we aim to obtain precise flux-flux relationships and determine whether they hold for all spectral types and activity levels., This fact is important bearing in mind that we aim to obtain precise flux–flux relationships and determine whether they hold for all spectral types and activity levels. Given that previous studies showed a peculiar behaviour for some late-K and M stars (2).. and that MAIO and LS10 samples only include a small number of these types of stars. we considered it necessary to increase the number of these types of stars in the otal sample.," Given that previous studies showed a peculiar behaviour for some late-K and M stars \citep{2005ESASP.560..775L}, and that MA10 and LS10 samples only include a small number of these types of stars, we considered it necessary to increase the number of these types of stars in the total sample." To complete the sample and increase the ratio of ate-K and M stars. we obtained high resolution echelle spectra of 21 late-K and M stars. some of them well-known members of young associations and moving groups.," To complete the sample and increase the ratio of late-K and M stars, we obtained high resolution echelle spectra of 21 late-K and M stars, some of them well-known members of young associations and moving groups." Bearing in mind that orevious studies suggested that those stars deviating from the main flux-flux relationships were only those with emission features. the stars chosen to increase the sample are late-K and M type with and without such features.," Bearing in mind that previous studies suggested that those stars deviating from the main flux–flux relationships were only those with emission features, the stars chosen to increase the sample are late-K and M type with and without such features." The chosen stars were also selected on he grounds of their known activity levels and youth., The chosen stars were also selected on the grounds of their known activity levels and youth. Only those Palars with no signatures of accretion that could. eventually. attect chromospheric emission have been used (see Section 4.1)).," Only those stars with no signatures of accretion that could, eventually, affect chromospheric emission have been used (see Section \ref{sec_flux--flux}) )." The observations of this new sample of late-K and M stars were carried out at the European Southern Observatory. ESO (La Silla. Chile) in February 2005 with FEROS (Fiber-fed Extended Range Optical Spectrograph) linked to the Cassegrain focus of the 2.2 m telescope. with the CCD 2048 x 4096 (0.15 sem/pixel).," The observations of this new sample of late-K and M stars were carried out at the European Southern Observatory, ESO (La Silla, Chile) in February 2005 with FEROS (Fiber-fed Extended Range Optical Spectrograph) linked to the Cassegrain focus of the 2.2 m telescope, with the CCD 2048 x 4096 (0.15 $\mu$ m/pixel)." This configuration provides observations within the spectral range 3500-9200 with a resolution of 48000 (reciprocal dispersion ranging from 0.03 to 0.09 A//pixel from the red to the blue region of the spectrum) in a total of 39 orders., This configuration provides observations within the spectral range 3500–9200 with a resolution of 48000 (reciprocal dispersion ranging from 0.03 to 0.09 /pixel from the red to the blue region of the spectrum) in a total of 39 orders. This campaign will be referred as the FEROSOS observing run hereafter., This campaign will be referred as the FEROS05 observing run hereafter. Preliminary results for some of the stars observed in this observing run are found in (22)..," Preliminary results for some of the stars observed in this observing run are found in \citep{2007seadmg,2008cooldmg}." We note that there is one star in common with LS1O and one in common with MAIO., We note that there is one star in common with LS10 and one in common with MA10. We used the reduction procedures in the packages and the standard method: bias and dark subtraction. flat-field division. cosmic rays correction. scattered light subtraction. and optimal extraction of the spectra.," We used the reduction procedures in the packages and the standard method: bias and dark subtraction, flat-field division, cosmic rays correction, scattered light subtraction, and optimal extraction of the spectra." Th-Ar lamps were used to perform the wavelength calibration., Th-Ar lamps were used to perform the wavelength calibration. Finally. all the spectra were normalized by using a cubic spline polynomial fit to the observed continuum.," Finally, all the spectra were normalized by using a cubic spline polynomial fit to the observed continuum." We note that both the reduction process and data analysis for the stars in FEROSOS observing run were completely analogous to those used by LS10 and MAIO in their respective works., We note that both the reduction process and data analysis for the stars in FEROS05 observing run were completely analogous to those used by LS10 and MA10 in their respective works. This. together with the fact that the technique used to obtain chromospheric fluxes (see Section 3.1) was the same. ensures the compatibility of all the data used in this study.," This, together with the fact that the technique used to obtain chromospheric fluxes (see Section \ref{sub:spectralsubtraction}) ) was the same, ensures the compatibility of all the data used in this study." The complete stellar sample contains 298 stars., The complete stellar sample contains 298 stars. The spectral type distribution of the whole sample is: 17 F type stars. 60 G type stars. 182. K type stars and. 39 M type stars.," The spectral type distribution of the whole sample is: 17 F type stars, 60 G type stars, 182 K type stars and, 39 M type stars." Fig., Fig. |. shows the spectral type distribution for L$10. MAIO and the FEROSOS observing run.," \ref{fig:histograma} shows the spectral type distribution for LS10, MA10 and the FEROS05 observing run." As we mentioned in Section |.. (power law) flua—flux relationships between chromospheric features are found only when basal chromospheric activity is subtracted.," As we mentioned in Section \ref{intro}, (power law) flux–flux relationships between chromospheric features are found only when basal chromospheric activity is subtracted." This basal flux is common to active and non-active stars., This basal flux is common to active and non-active stars. Therefore. it is subtracted from the active star when using a non-active star as reference for the spectral subtraction instead of theoretical synthetic photospheric spectra (see MAIO and LSIO for details).," Therefore, it is subtracted from the active star when using a non-active star as reference for the spectral subtraction instead of theoretical synthetic photospheric spectra (see MA10 and LS10 for details)." We used the same technique to reveal and measure equivalent widths of chromospheric lines in the FEROSOS stars., We used the same technique to reveal and measure equivalent widths of chromospheric lines in the FEROS05 stars. Then. we converted equivalent widths to fluxes using empirical calibrations.," Then, we converted equivalent widths to fluxes using empirical calibrations." In the following sections we give the details of the analvsis process., In the following sections we give the details of the analysis process. ranging between Aa~0.75 and Aa~1.25 correspond. to the range of parameters ay and oj which lead to models for the near-zone relation that are in good agreement with the cata.,ranging between $\Delta \alpha\sim0.75$ and $\Delta \alpha\sim1.25$ correspond to the range of parameters $\alpha_0$ and $\alpha_1$ which lead to models for the near-zone relation that are in good agreement with the data. Our simulations of quasar near-zones assume a semi-analvtic model for the ionizing background (see2).., Our simulations of quasar near-zones assume a semi-analytic model for the ionizing background \citep[see ][]{wyithe2008}. Ht is therefore important to ask whether the results in this paper pertaining to the dependence of near-zone size on luminosity (ic. the constraints on D). and the resulting conclusions regarding the quasar spectral index à are sensitive to this model.," It is therefore important to ask whether the results in this paper pertaining to the dependence of near-zone size on luminosity (i.e. the constraints on $B$ ), and the resulting conclusions regarding the quasar spectral index $\alpha$ are sensitive to this model." To address this issue we have repeated our modelling of quasar near-zones assuming an ionizing background that is independent. of redshift., To address this issue we have repeated our modelling of quasar near-zones assuming an ionizing background that is independent of redshift. We first take the +=6 value from our fiducial model: Figure 6 shows contours describing the resulting constraints (στον curves)., We first take the $z=6$ value from our fiducial model; Figure \ref{fig6} shows contours describing the resulting constraints (grey curves). The results are very similar to the fiducial case. with the exception of οἱ. which shows that the redshift evolution of near-zone size in the constant. background. model is smaller than observed.," The results are very similar to the fiducial case, with the exception of $ A$, which shows that the redshift evolution of near-zone size in the constant background model is smaller than observed." This is consistent with the previous inference that the trend. of near-zone size with redshift is being driven by the rising intensity of the ionizing background (2). at z~6., This is consistent with the previous inference that the trend of near-zone size with redshift is being driven by the rising intensity of the ionizing background \citep{wyithe2008} at $z\sim 6$. We have also tested sensitivity to the ionizing background amplitude bv repeating our analvsis for 16 dilferent values ranging between 1/100 and VIO times the fiducial model., We have also tested sensitivity to the ionizing background amplitude by repeating our analysis for 16 different values ranging between 1/100 and $\sqrt{10}$ times the fiducial model. In. the left panel of Figure 7 we show the resulting range for ay às à function of the background. photoionization rate Γιο—Lu/10£s+.," In the left panel of Figure \ref{fig7} we show the resulting range for $\alpha_0$ as a function of the background photoionization rate $\Gamma_{12}=\Gamma_{\rm HI}/10^{-12}\rm\,s^{-1}$." This ligure illustrates that results for a depend on the assumed. value of E15., This figure illustrates that results for $\alpha$ depend on the assumed value of $\Gamma_{12}$. As a result. we next constrain Di» following the work of ?..," As a result, we next constrain $\Gamma_{12}$ following the work of \citet{bolton2007b}. ." 7 present eight. values of transmission 7. (with uncertainty OT) measured. in redshift. intervals of As=0.1 centred on redshifts in the range 5.920/2, that would be inferred from the centrally peaked CO fundamental emission profiles of most T. Tauri stars (Najita et 22003).","radius $\sim 6 \Rin$, significantly less than the $>20 \Rin $ that would be inferred from the centrally peaked CO fundamental emission profiles of most T Tauri stars (Najita et 2003)." Thus. 1e outer radius of the V836 Tau CO emission is in the range 0.3—0.5 AAU.," Thus, the outer radius of the V836 Tau CO emission is in the range $0.3-0.5$ AU." We can provide constraints on (he mean conditions in the emitting eas by modeling the CO spectrum with a radially constant excitation temperature and column density., We can provide constraints on the mean conditions in the emitting gas by modeling the CO spectrum with a radially constant excitation temperature and column density. The V.imilar shape ancl strength of the e—1 0 emission lines over a wide range in J reveals that the emission lines are optically thick. ie. that the gas column density is >0.001gem7 if turbulent line broadening is negligible.," The similar shape and strength of the $v$ =1–0 emission lines over a wide range in $J$ reveals that the emission lines are optically thick, i.e., that the gas column density is $> 0.001\gpersqcm$ if turbulent line broadening is negligible." In addition. the absence of detectable ο 0 CO enmission lines limits the column density to <0.03gcm7 for a CO abundance of 3x10.! relative to hydrogen and an interstellar 0Ο 00 ratio of 90.," In addition, the absence of detectable $v$ =1–0 $^{13}$ CO emission lines limits the column density to $< 0.03\gpersqcm$ for a CO abundance of $3\times 10^{-4}$ relative to hydrogen and an interstellar $^{13}$ $^{12}$ CO ratio of 90." The weakness of (he r=21 and e—32 lines in (he spectrum requires either a low average excitation temperature or that the vibrational levels above e—1 depart significantly from thermal equilibrium., The weakness of the $v$ =2–1 and $v$ =3–2 lines in the spectrum requires either a low average excitation temperature or that the vibrational levels above $v$ =1 depart significantly from thermal equilibrium. For LTE level populations. the relative strengths of the c=1 0 lines aud (he limit on the strength of the e=21 transitions constrain (he mean excitation temperature to the range IxIx. Smaller excitation temperatures require larger emitting areas (o produce the required Ine fIux. as well as larger inclinations in order to produce the emission over the required range of velocities.," For LTE level populations, the relative strengths of the $v$ =1–0 lines and the limit on the strength of the $v$ =2–1 transitions constrain the mean excitation temperature to the range K. Smaller excitation temperatures require larger emitting areas to produce the required line flux, as well as larger inclinations in order to produce the emission over the required range of velocities." As a result. at temperatures STOO IWIN. the requirement on the line flux drives the emitting radii to values large enough that the required velocities cannot be obtained at any inclination.," As a result, at temperatures $\lesssim 700$ K, the requirement on the line flux drives the emitting radii to values large enough that the required velocities cannot be obtained at any inclination." For a radially constant excitation temperature IXIx. the e=2-1 lines are too strong relative to the e=10 lines.," For a radially constant excitation temperature $\gtrsim 1200$ K, the $v$ =2-1 lines are too strong relative to the $v$ =1–0 lines." In addition. given the constraints on the radial range (and therefore the emitting area) of the emission. the strength of the r=10 lines are overpredicted al such high temperatures.," In addition, given the constraints on the radial range (and therefore the emitting area) of the emission, the strength of the $v$ =1–0 lines are overpredicted at such high temperatures." We can obtain a better fit to the average line profiles bv allowing the temperature {ο vary as a [funetion of radius., We can obtain a better fit to the average line profiles by allowing the temperature to vary as a function of radius. " Consistent with the above considerations. a gas teniperature that varies slowly with radius (7=1200IX(7/H;,) OO"") and a line-ol-sieht disk column density of X=0.003@¢m7 that is racially constant between 2,,=132. and Rog=54. eives a reasonable fit to the spectra assuming LTE level populations (Fie."," Consistent with the above considerations, a gas temperature that varies slowly with radius $T = 1200\,{\rm K} (r/\Rin)^{-0.30}$ ) and a line-of-sight disk column density of $\Sigma = 0.003\gpersqcm$ that is radially constant between $\Rin= 13 \Rsun$ and $\Rout = 5 \Rin$, gives a reasonable fit to the spectra assuming LTE level populations (Fig." 6)., 6). In addition to providing a reasonable fit to the relative line strengths of the e—10 lines. the model also reasonably fits (he average line profiles of the c=10 lines (Figs.," In addition to providing a reasonable fit to the relative line strengths of the $v$ =1–0 lines, the model also reasonably fits the average line profiles of the $v$ =1–0 lines (Figs." 4 and 5: heavy dashed line}., 4 and 5; heavy dashed line). We can also fit (he spectra wilh a model that uses a steep temperature gradient rather (han a specified outer radius to limit the radial extent of (he emission., We can also fit the spectra with a model that uses a steep temperature gradient rather than a specified outer radius to limit the radial extent of the emission. " Wilh a temperature profile T=1400IK(r/HRj,)"""" and a radiallv-constant. line-ol-sight column density X=0.0037gem7 and Ry,=16.2/2.. the 10 emission decreases sharply bevond 7—Sly because the Planck function contributes little at 4.7pm at the low temperatures achieved at these radii (5400 NIN)."," With a temperature profile $T=1400\,{\rm K}(r/\Rin)^{-0.6}$ and a radially-constant line-of-sight column density $\Sigma=0.0037 \gpersqcm$ and $\Rin=16.2\Rsun$, the 1–0 emission decreases sharply beyond $7-8\Rin$ because the Planck function contributes little at $4.7\micron$ at the low temperatures achieved at these radii $\lesssim 400$ K)." The high-J P-branch lines ave also optically thin at these radii., The $J$ P-branch lines are also optically thin at these radii. The model provides a reasonable fit to the relative strengths of the e=10 lines., The model provides a reasonable fit to the relative strengths of the $v$ =1–0 lines. The, The "In the context of BBH systems, the last two categories shown in Table 10 are the most interesting, as we expect the SMBH at the centers of the merging systems to be close enough for the gravitational pull to bind them together.","In the context of BBH systems, the last two categories shown in Table \ref{tab:evolution_candidates} are the most interesting, as we expect the SMBH at the centers of the merging systems to be close enough for the gravitational pull to bind them together." " For the merger phase, we select sources that have disturbed morphologies and also show signs of ongoing starburst activity (similar to Mrk 231)."," For the merger phase, we select sources that have disturbed morphologies and also show signs of ongoing starburst activity (similar to Mrk 231)." For the final category we select sources that appear extremely variable across their spectrum (variable in at least 3 different wavelength regimes) in an almost periodic manner., For the final category we select sources that appear extremely variable across their spectrum (variable in at least 3 different wavelength regimes) in an almost periodic manner. " These sources do not show signs of ongoing interaction, merging (apart from 1418+546, see Sources)), or starburst activity."," These sources do not show signs of ongoing interaction, merging (apart from 1418+546, see ), or starburst activity." These are probably BBH systems., These are probably BBH systems. " In the context of the above categorization, we can identify these sources as possible post-merger systems."," In the context of the above categorization, we can identify these sources as possible post-merger systems." " At least three of the sources in Table 10 (0954+658, 0108+388, and 0248+430) cannot be unambiguously categorized as one evolutionary phase, as they exhibit properties common to more than one stages of evolution."," At least three of the sources in Table \ref{tab:evolution_candidates} (0954+658, 0108+388, and 0248+430) cannot be unambiguously categorized as one evolutionary phase, as they exhibit properties common to more than one stages of evolution." Sources selected in the last two categories (merger and post-merger) are the most likely BBH candidates in the CJF sample., Sources selected in the last two categories (merger and post-merger) are the most likely BBH candidates in the CJF sample. We plot their NIR colors in Fig. 3.., We plot their NIR colors in Fig. \ref{fig:color_diagram_candidates}. " As expected, most candidate sources are found to be above the power-law line, while most post-merger classified sources (selected solely by their variability properties) are found just above the power-law line, in the transitory area of the color-color diagram."," As expected, most candidate sources are found to be above the power-law line, while most post-merger classified sources (selected solely by their variability properties) are found just above the power-law line, in the transitory area of the color-color diagram." This provides us with an additional selection tool for transitory systems (see Sect. Appendix A:))., This provides us with an additional selection tool for transitory systems (see Sect. \ref{sec:individual}) ). " In previous sections, we have presented the accumulated literature information available for the CJF sources and a sample of CJF sources that trace AGN evolution, indicating the most likely BBH candidates among them."," In previous sections, we have presented the accumulated literature information available for the CJF sources and a sample of CJF sources that trace AGN evolution, indicating the most likely BBH candidates among them." We now investigate the criteria used to identify candidates as BBH systems., We now investigate the criteria used to identify candidates as BBH systems. It is interesting to discuss which subset of these criteria can provide us with a robust enough argument for the existence of a BBH., It is interesting to discuss which subset of these criteria can provide us with a robust enough argument for the existence of a BBH. " Before we proceed with the discussion, we are interested in assessing the completeness of the information for the CJF sample presented here, as these were collected from the available literature and are not the result of a uniform observational campaign."," Before we proceed with the discussion, we are interested in assessing the completeness of the information for the CJF sample presented here, as these were collected from the available literature and are not the result of a uniform observational campaign." " To achieve this goal, we create two subsamples of CJF sources."," To achieve this goal, we create two subsamples of CJF sources." " For the first one, we selected sources with available near-infrared information, as this information was primarily presented and analyzed in this paper."," For the first one, we selected sources with available near-infrared information, as this information was primarily presented and analyzed in this paper." " In addition, we excluded sources without redshift information."," In addition, we excluded sources without redshift information." " We identified 74 of these sources, the number of sources being explicitly controlled by the availability of infrared information (see Table 4))."," We identified 74 of these sources, the number of sources being explicitly controlled by the availability of infrared information (see Table \ref{tab:infrared}) )." " For the second subsample, we selected those CJF sources that have been observed and have available information across the whole spectrum (radio to y-rays)."," For the second subsample, we selected those CJF sources that have been observed and have available information across the whole spectrum (radio to $\gamma$ -rays)." " We found only 10 of these sources, the number of sources mainly being regulated by availability of y-ray information (see Table 11)."," We found only 10 of these sources, the number of sources mainly being regulated by availability of $\gamma$ -ray information (see Table \ref{tab:cjfsubsample}) )." " This subsample, having been selected on the basis of detection in the near-IR, is expected to be more sensitive to infrared bright sources and consequently have a higher probability of containing sources associated with merger events."," This subsample, having been selected on the basis of detection in the near-IR, is expected to be more sensitive to infrared bright sources and consequently have a higher probability of containing sources associated with merger events." This bias should be accounted for., This bias should be accounted for. We begin by investigating whether this subsample is differs fundamentally from the CJF sample from which it was selected., We begin by investigating whether this subsample is differs fundamentally from the CJF sample from which it was selected. " The subsample has an average redshift of z;,,,,""= 0.864, effectively probing more nearby sources than the CJF (z;,4c;r= 1.254)."," The subsample has an average redshift of $z_{avg,sub}=0.864$ , effectively probing more nearby sources than the CJF $z_{avg, CJF}=1.254$ )." " We also check the radio spectral index ato, a measure of the compactness of the sources."," We also check the radio spectral index $\alpha^{4800}_{1400}$, a measure of the compactness of the sources." The subsample has lower average and median values of the index than the whole sample., The subsample has lower average and median values of the index than the whole sample. This indicates that this subsample contains less compact objects., This indicates that this subsample contains less compact objects. " Finally we check the range of luminosities for which almost complete information for the CJF is available (in radio, optical, and X-ray) for both the subsample and the CJF as a whole."," Finally we check the range of luminosities for which almost complete information for the CJF is available (in radio, optical, and X-ray) for both the subsample and the CJF as a whole." " In both samples, we find that the ranges are the same for all three different wavelengths."," In both samples, we find that the ranges are the same for all three different wavelengths." We conclude that this subsample probably contains sources that are closer and more extended but is otherwise quite similar to the CJF., We conclude that this subsample probably contains sources that are closer and more extended but is otherwise quite similar to the CJF. " In the context of merger-driven evolution, we find that of the sources in this subsample, exhibit morphological distortions and starburst activity."," In the context of merger-driven evolution, we find that of the sources in this subsample, exhibit morphological distortions and starburst activity." Eleven sources (14.9%)) are found to have companions., Eleven sources ) are found to have companions. " Compared to the CJF sample in total of sources exhibit distortions; have companions), merger effects appear to be more prominent in this subsample, as expected."," Compared to the CJF sample in total of sources exhibit distortions; have companions), merger effects appear to be more prominent in this subsample, as expected." " However, the more than three times higher percentage of distorted sources and sources with companions than theCJF as a whole indicates that the"," However, the more than three times higher percentage of distorted sources and sources with companions than theCJF as a whole indicates that the" ?? with the n(m)-estimated o5; values.,\ref{discussion} with the $n(m)$ -estimated $\sigma_{\rm BG}^2$ values. In (his section. a couple of consistency tests have been performed in order to check the of⋅⋅⋅ our⋅↽≽ SBF-measured ope; results.reliability," In this section, a couple of consistency tests have been performed in order to check the reliability of our SBF-measured $\sigma_{\rm BG}^2$ results." " Together with the PSE-convolved variance. £5. SBFs provide the value of /?,. the variance."," Together with the PSF-convolved variance, $P_0$, SBFs provide the value of $P_1$, the non-PSF-convolved variance." This can be compared wilh ils expected value. directly. obtained from the read-out noise. the dark current. and the skv brightness analvsis of each image.," This can be compared with its expected value, directly obtained from the read-out noise, the dark current, and the sky brightness analysis of each image." For IIDF Version 2. each of the weighted5 and cosmic-ray cleaned images is the result of combining several exposures with the same dither position.," For HDF Version 2, each of the weighted and cosmic-ray cleaned images is the result of combining several exposures with the same dither position." The different exposures are combined with weights5 proportional to the inverse variance (1/7)ο... at the mean background5 level., The different exposures are combined with weights proportional to the inverse variance $1/P_1$ ) at the mean background level. The variance /4. in electrons. is computed rom the following noise model 1996): where / is the exposure time. 5 is (he skv background rate. d is the dark current. and r is (he read-out noise.," The variance $P_1$ , in electrons, is computed from the following noise model \citep{W96}: where $t$ is the exposure time, $b$ is the sky background rate, $d$ is the dark current, and $r$ is the read-out noise." The inverse variances. 1/2). of each exposure are provided in the header ol the resulting weighted and cosmic-ray cleaned image.," The inverse variances, $1/P_1$, of each exposure are provided in the header of the resulting weighted and cosmic-ray cleaned image." From this information. the value of corresponding to the latter can be computed.," From this information, the value of $P_1$ corresponding to the latter can be computed." As an example. these values are listed in Table 8 (column 2) for the WF2 images and 2y59.," As an example, these values are listed in Table \ref{t-p1} (column 2) for the WF2 images and $B_{450}$." " The P4 values obtained directly [rom the SBF analvsis of the images. using m,=28.8. are listed in column 3."," The $P_1$ values obtained directly from the SBF analysis of the images, using $m_{\rm c}=28.8$, are listed in column 3." " Both computed and observed values of P, are equivalent in all cases.", Both computed and observed values of $P_1$ are equivalent in all cases. Only. a slight excess in the observed. 2) is noticeable., Only a slight excess in the observed $P_1$ is noticeable. " This excess is produced by cosmic rays. which also contribute to the measured I, values. as we have shown."," This excess is produced by cosmic rays, which also contribute to the measured $P_0$ values, as we have shown." This test shows that. with this technique. the white noise (74) is determined with high precision. (hereby reinforcing (he correctness of /4)measurements.," This test shows that, with this technique, the white noise $P_1$ ) is determined with high precision, thereby reinforcing the correctness of $P_0$measurements." As argued in Section 4.2.. our sample is complete down to L2A/..,"As argued in Section \ref{comp}, our sample is complete down to $M_\odot$." In Table 5. we list ihe number of vellow supergiants we observed between various mass tracks relative to the number of stars we found between the 12 and 15M. tracks., In Table \ref{tab:numbers} we list the number of yellow supergiants we observed between various mass tracks relative to the number of stars we found between the 12 and $M_\odot$ tracks. Further. we compare this ratio to that predicted by the evolutionary models.," Further, we compare this ratio to that predicted by the evolutionary models." Recall that the number of stars expected between masses m4 and me will be where I is the slope of the initial mass function. taken here to be -1.35 (Salpeter 1955). and 7 is (he average duration of the evolutionary phase lor masses mg and mo. shown in Table 4..," Recall that the number of stars expected between masses $m_1$ and $m_2$ will be where $\Gamma$ is the slope of the initial mass function, taken here to be -1.35 (Salpeter 1955), and $\bar \tau$ is the average duration of the evolutionary phase for masses $m_1$ and $m_2$, shown in Table \ref{tab:ages}." This equation assumes that the star formation rate has been relatively constant over the relevant time frame. which in this case is about 20 Mir. or the lifetime of a 12M. star.," This equation assumes that the star formation rate has been relatively constant over the relevant time frame, which in this case is about 20 Myr, or the lifetime of a $M_\odot$ star." Table 5 shows that both the models with no initial rotation (SO) and an initial rotation of 300 kam 1 (83) did a fairly good job predicting the number of 15 25M. stars relative {ο ihe nunber of 1 15.U. stars., Table \ref{tab:numbers} shows that both the models with no initial rotation (S0) and an initial rotation of 300 km $^{-1}$ (S3) did a fairly good job predicting the number of 15 – $M_\odot$ stars relative to the number of 12 – $M_\odot$ stars. We observe a ratio of 1.6 to 2.0 and the 53 models predict a ratio of 1.6 while the SO models predict 1.0., We observe a ratio of 1.6 to 2.0 and the S3 models predict a ratio of 1.6 while the S0 models predict 1.0. This is significantly better than what Drout οἱ ((2009) found in M31. where the number of 15 25M. stars were a [actor of 11 greater (han predicted by (the models. relative to the number of 12. 19481. stars.," This is significantly better than what Drout et (2009) found in M31, where the number of 15 – $M_\odot$ stars were a factor of 11 greater than predicted by the models, relative to the number of 12 – $M_\odot$ stars." Bul. we observe no stars will masses above 25A/. rather than the 3 to 6 predicted by the S0 or $3 moclels.," But, we observe no stars with masses above $M_\odot$ rather than the 3 to 6 predicted by the S0 or S3 models." This is similar {ο the case for M21 where (he models predicted 110 150 stars with masses above 253... and none were observed.," This is similar to the case for M31 where the models predicted 110 – 150 stars with masses above $M_\odot$, and none were observed." Now that weve compared (he (racks in relative terms. we can compare the lifetimes in an absolute sense.," Now that we've compared the tracks in relative terms, we can compare the lifetimes in an absolute sense." Because we know the number of unevolved (OD-t(vpe) massive stars in the SAIC and we now know the number of vellow supergiants. we can compute the expected lifetimes.," Because we know the number of unevolved (OB-type) massive stars in the SMC and we now know the number of yellow supergiants, we can compute the expected lifetimes." According to a Sehmidt survey. of the bluest stars (Massey. 2003). the niunber ol unevolved SAIC stars with masses greater than 20... is around 2600 (Massey 2009).," According to a Schmidt survey of the bluest stars (Massey 2003), the number of unevolved SMC stars with masses greater than $20M_\odot$ is around 2600 (Massey 2009)." The IAIF-weighted H-burning lifetime is around 5 Myr. and if we assume a constant star formation rate. we would expect 5x10| Inassive stars lo be born per vear.," The IMF-weighted H-burning lifetime is around 5 Myr, and if we assume a constant star formation rate, we would expect $5 \times 10^{-4}$ massive stars to be born per year." We can now make a comparison between the number of vellow supergiants greater (han 20.4. observed (just one) tthe number predicted by the Schmidt survey (2600)., We can now make a comparison between the number of yellow supergiants greater than $20M_\odot$ observed (just one) the number predicted by the Schmidt survey (2600). Recall that we were onlv able to observe of the G77 stars we selected., Recall that we were only able to observe of the 677 stars we selected. Bul. the Schmidt survey covered an area of the sky smaller than our surveved area.," But, the Schmidt survey covered an area of the sky smaller than our surveyed area." So. these two percentages essentially cancel out.," So, these two percentages essentially cancel out." Therefore. we can estimate (he actual ages of the vellow supergiant stage as 1/2600 x5 Myr.," Therefore, we can estimate the actual ages of the yellow supergiant stage as 1/2600 $\times\ 5$ Myr." This works out to be around 1900 vears. more than an order of magnitude lower than predicted by the evolutionary tracks (of order 0.1 Myr).," This works out to be around 1900 years, more than an order of magnitude lower than predicted by the evolutionary tracks (of order 0.1 Myr)." We also tried this test with stars above 15M..., We also tried this test with stars above $15M_\odot$. In this mass range there are around. 4000 unevolved SAIC stars and the duration is around & Mvr., In this mass range there are around 4000 unevolved SMC stars and the duration is around 8 Myr. Since we found eight stars greater than 15M... the age should be around 5/4000 x8 Myr. or 0.02 Myr.," Since we found eight stars greater than $15M_\odot$, the age should be around 8/4000 $\times\ 8$ Myr, or 0.02 Myr." This corresponds (to an order of magnitude lower than (hat predicted by the $3 models for (he average duration of this stage., This corresponds to an order of magnitude lower than that predicted by the S3 models for the average duration of this stage. While the, While the For each observation (ObsID). the source detection is performed with the CIAO aleorithim.,"For each observation (ObsID), the source detection is performed with the CIAO algorithm." Au exposure map is created using the task prior to the source detection., An exposure map is created using the task prior to the source detection. The exposure threshold is sot to 0.1 and the wavelet detection scales are set to8., The exposure threshold is set to 0.1 and the wavelet detection scales are set to. 07.. Thirty-five sources are detected (σ> 3) on the ObsID 2668. 37 sources on ObsID 2669. 66 sources on ObsID 7160. 18 ou ObsID TIGL. aud 37 on the ACIS-I observation ObsID 79.," Thirty-five sources are detected $\sigma>3$ ) on the ObsID 2668, 37 sources on ObsID 2669, 66 sources on ObsID 7460, 48 on ObsID 7461, and 37 on the ACIS-I observation ObsID 79." This paper is solely focused on radius measurement and fiume analysis on the qLAINB τοι., This paper is solely focused on radius measurement and timing analysis on the qLMXB U24. While the source detection is performed over the whole ACTS chip. the following analysis pertains ouly to the source U21.," While the source detection is performed over the whole ACIS chip, the following analysis pertains only to the source U24." Counts are extracted with the CLAO script around the source position in a circular region of radius37. which ensures that of the enclosed enerev fraction at Bs mehuded.," Counts are extracted with the CIAO script around the source position in a circular region of radius, which ensures that of the enclosed energy fraction at is included." |... The closest detected. source. located at ddistaunce from U21. has 21.6 counts (background subtracted) within1.," The closest detected source, located at distance from U24, has 21.6 counts (background subtracted) within." "5"". It contributes to <001 contanunation counts within the extraction radius of U21 (on the longest observation).", It contributes to $\ll0.04$ contamination counts within the extraction radius of U24 (on the longest observation). " The background is extracted. from an annulus centered at the qLMXD position with inner radius5"".. and outer radius30""."," The background is extracted from an annulus centered at the qLMXB position with inner radius, and outer radius." . Other detected sources within the backeround aunulus are excluded with a rradius region. Which eliminate of source counts in the background region.," Other detected sources within the background annulus are excluded with a radius region, which eliminate of source counts in the background region." For the deepest observation (ObsID 7160). 15 counts from other sources are within the extracted background @vhich contains 6187 counts).," For the deepest observation (ObsID 7460), 15 counts from other sources are within the extracted background (which contains 6187 counts)." Iu other words. these coustraiuts eusure that ~0.25% of the background counts are due to other sources.," In other words, these constraints ensure that $\sim 0.25\%$ of the background counts are due to other sources." Finally. the extraction radius (containing of the ECF) docs uot require to apply a correction to the flux.," Finally, the extraction radius (containing of the ECF) does not require to apply a correction to the flux." Following the CIAO Science Thread the response imatrices files (RAIFs) are recalculated prior to the spectral analysis since the RMES obtained from are not suited for ACTS observations with focal plane temperature of 120°C (the uxual conmnand docs not use the latest calibration available in the case of 120°C ACTS imagine data).," Following the CIAO Science Thread, the response matrices files (RMFs) are recalculated prior to the spectral analysis since the RMFs obtained from are not suited for ACIS observations with focal plane temperature of C (the usual command does not use the latest calibration available in the case of C ACIS imaging data)." In addition. the ancillary response files (CARES) are also recalculated using the ασιαον erid of the newly obtained RAIFs.," In addition, the ancillary response files (ARFs) are also recalculated using the energy grid of the newly obtained RMFs." Overall. the extracted spectra. together with the RMFs and ARFs. are used for the spectral analysis.," Overall, the extracted spectra, together with the RMFs and ARFs, are used for the spectral analysis." In those spectra. the effect of backeromnel counts can be ignored.," In those spectra, the effect of background counts can be ignored." Indeed. in the worst case (for ObsID 7160). the umber of expected background events accounts for of the total number of counts in the extracted region (78.0 backerouud counts out of a total of 3188 counts). so that the background is ueelected for the spectral analysis.," Indeed, in the worst case (for ObsID 7460), the number of expected background events accounts for of the total number of counts in the extracted region (78.0 background counts out of a total of 3188 counts), so that the background is neglected for the spectral analysis." For each of the five observations. two spectral files are created. one with uubiuued eveuts (for fitting with the Caslistatisties. 2)) aud one with binuine (for fitting with the \?--statistics).," For each of the five observations, two spectral files are created, one with unbinned events (for fitting with the Cash-statistics, \citealt{cash79}) ) and one with binning (for fitting with the -statistics)." For the latter. the bin width iu the eenerev range matches the energy resolution of the ACTS-S3 chip. ie. 0.15keV.," For the latter, the bin width in the energy range matches the energy resolution of the ACIS-S3 chip, i.e., $\sim$." .. AbovekeV. four wider biuskeV...keV... and two wwide spectral bius) are created.," Above, four wider bins, and two wide spectral bins) are created." Iu some cases of low count statistics. the last 2 or 3 bins are grouped together to maintain a minima of 20 counts per bin.," In some cases of low count statistics, the last 2 or 3 bins are grouped together to maintain a minimum of 20 counts per bin." The main criterion for the creation of the spectral bius is the energy resolution of the detector. but the 20 counts ΙΙΙ is imposed to ensure approximate Cassia uncertainty in each bin.," The main criterion for the creation of the spectral bins is the energy resolution of the detector, but the 20 counts minimum is imposed to ensure approximate Gaussian uncertainty in each bin." Such a binning avoids au artificially smallreduced-\7.. aud couserves the validity of \?--statistics.," Such a binning avoids an artificially small, and conserves the validity of -statistics." Spectral fitting is performed with the software v12.5.1 (7)| uxiug the publicly available model of NS TL-atinosphere (??)..," Spectral fitting is performed with the software v12.5.1 \citep{arnaud96} using the publicly available model of NS H-atmosphere \citep{mcclintock04, heinke06}." The model assimes non-magnetic NSs and has been computed for a rauge of surface gravity ο=(0.110)1οσαν?., The model assumes non-magnetic NSs and has been computed for a range of surface gravity $g=(0.1-10)\tee{14} \cgsaccel$. For the normalization paranieter. uses the cmitting fraction of the NS surface.," For the normalization parameter, uses the emitting fraction of the NS surface." It is kept fixed to πατν in this work: in other words. the whole NS surface cuits.," It is kept fixed to unity in this work; in other words, the whole NS surface emits." The distance parameter is held fixed as well at the value of NGC 6397. d=25kpe (C??)..," The distance parameter is held fixed as well at the value of NGC 6397, $d=2.5\kpc$ \citep{hansen07,strickler09}." The NS mass is assumed to be LIAL..., The NS mass is assumed to be $1.4\msun$. Finally. the ealactic absorption is taken iuto account using the multiplicative model. withNy. the hwdrosen coluun deusitv parameter. set to Nip=0d.," Finally, the galactic absorption is taken into account using the multiplicative model, with, the hydrogen column density parameter, set to $\nhtt = 0.14$." The errors ou the best-fit parameters(Rx. g)) ave calculated using the comnmiaud in with confidence or using the commandsteppar.," The errors on the best-fit parameters, ) are calculated using the command in with confidence or using the command." Confidence contours in massradius space are obtained with the connnaud with both the mass and the radius as free parameters., Confidence contours in mass–radius space are obtained with the command with both the mass and the radius as free parameters. The results of the spectral analysis are preseuted in Section 3.2.., The results of the spectral analysis are presented in Section \ref{sec:spec_res}. For each of the five observations. we porforii two analyses to search for source variability on timescales," For each of the five observations, we perform two analyses to search for source variability on timescales" in both tiue auc space: aud because he weather was cooyerative. with relaively little temporal να]lou in sky background uw10 ninipiun to imaxlunmii any night and filter. ancl 1isually ess) αμα subarcsecoud seeing (allowiug stnall photometry apertires).,"in both time and space; and because the weather was cooperative, with relatively little temporal variation in sky background $<10\%$ minimum to maximum in any night and filter, and usually less) and subarcsecond seeing (allowing small photometry apertures)." Further yossible error sources iuclude ceitroikdiug of the afterglow aid reference star (expected to be systetjalic-error limiLec at he 0.1 pixel level) and residual [latfieling difficulties., Further possible error sources include centroiding of the afterglow and reference star (expected to be systematic-error limited at the $0.1$ pixel level) and residual flatfielding difficulties. Neither will be large corupared to our |photou counting oise., Neither will be large compared to our photon counting noise. To be couservative. we estimate that sky subraction and Latliecling errors combinedil uay allect all of our photometry at uj» to the L% level.," To be conservative, we estimate that sky subtraction and flatfielding errors combined may affect all of our photometry at up to the $4\%$ level." Table 1 lists both pure photon couing errors aud error bars includiug this systematic error added in q1aclrature., Table \ref{obslog} lists both pure photon counting errors and error bars including this systematic error added in quadrature. In addition to the IRTF data. we iuclide in our analysis data from other observatories presented in the literature (both the CRB Coordinate Network Circula* and preprints by Masetti et al 2000 aud Jensen et al 2000).," In addition to the IRTF data, we include in our analysis data from other observatories presented in the literature (both the GRB Coordinate Network Circulars and preprints by Masetti et al 2000 and Jensen et al 2000)." These cata are suumainarized in table 2.., These data are summarized in table \ref{litlog}. For data poiuts reported uuultiple times. we use the most recently 'eported value.," For data points reported multiple times, we use the most recently reported value." La particular. for the Uttar Pradesh State Observatory data we take values [rom Masetti et al (2000) rather tLan Sagar et al (2000).," In particular, for the Uttar Pradesh State Observatory data we take values from Masetti et al (2000) rather than Sagar et al (2000)." Two early time Wo data points come lOu Calar Alto data o“Ste ckluu et al (2000) and Subaru data of Ixobayashi et al (2000a.b).," Two early time K' data points come from Calar Alto data of Stecklum et al (2000) and Subaru data of Kobayashi et al (2000a,b)." Flux valies [roin both were 1leaswed relative to the Carnavich et al (2000a) star A. The use of a uniform reerence star allows the da rour multiple observatories to be compared with reasonable coulideuce., Flux values from both were measured relative to the Garnavich et al (2000a) star A. The use of a uniform reference star allows the data from multiple observatories to be compared with reasonable confidence. Residual dillereuces inco ‘terns should be small since all three observatories used the same plotorjetric baucdpass., Residual differences in color terms should be small since all three observatories used the same photometric bandpass. To allow x color terms. we have used o=(0.03mae as the ellective error on the Stbaru data. rather t1all t shotometric error 0.01mae reported by Ixobayashi et al (2000a.)).," To allow for color terms, we have used $\sigma = 0.03 \mag$ as the effective error on the Subaru data, rather than the photometric error $0.01 \mag$ reported by Kobayashi et al (2000a,b)." Sinilarlv. the optical data reported in the literature aud 1sed in this paper has all been calibrated to either stars A-D of Garnavielh et al (2000a) (for some R baud data) or to the photometry of Heiden et al (2000) (for other optical fillers au the ‘est of the R band data).," Similarly, the optical data reported in the literature and used in this paper has all been calibrated to either stars A-D of Garnavich et al (2000a) (for some R band data) or to the photometry of Henden et al (2000) (for other optical filters and the rest of the R band data)." The R baud fluxes ueasured by Heiden et al for stars A-D agree with those from Carnavich et al within the uncertaiules. which are ~5(.," The R band fluxes measured by Henden et al for stars A-D agree with those from Garnavich et al within the uncertainties, which are $\sim 5\%$." The mean aud inediatr nagutucle clilferences between the two calibrations are 0.050 aid 0.036 maeutucde respectively. in the sense that Carnavich et al report brighter jagnitudes than do Heude1 et al.," The mean and median magnitude differences between the two calibrations are $0.050$ and $0.036$ magnitude respectively, in the sense that Garnavich et al report brighter magnitudes than do Henden et al." The possibility [9] “inconsistent photometri zero poiuts in clillerent cata sets herefore amoiits to about 0.05 iuagnitide between authors using calibratious from te two alternative sources. 20 ss!) sometimes offset from the source velocity (ursn—-7.2-7.7 ss!); a medium-broad emission component (FWHM-5-10 kmss!); and a deep, narrow absorption component (FWHM~2 ss!) seen at the source velocity."," The $_2$ Olines exhibit multiple components: a broad emission component $>$$20$ $^{-1}$ ) sometimes offset from the source velocity $\varv_{\rm LSR}$ $+$ 7.2–7.7 $^{-1}$ ); a medium-broad emission component $\sim$ 5–10 $^{-1}$ ); and a deep, narrow absorption component $\sim$ 2 $^{-1}$ ) seen at the source velocity." The individual components are all reproduced well by Gaussian functions., The individual components are all reproduced well by Gaussian functions. " The absorption is only seen in the H5O 11,-0oo line and is saturated in IRAS2A and IRASAA. In IRAS4B, the absorption extends below the continuum level, but is not saturated."," The absorption is only seen in the $_2$ O $_{11}$ $_{00}$ line and is saturated in IRAS2A and IRAS4A. In IRAS4B, the absorption extends below the continuum level, but is not saturated." " Furthermore, the IRAS4A spectrum of the 29-1;; line exhibits an inverse P Cygni profile."," Furthermore, the IRAS4A spectrum of the $_{02}$ $_{11}$ line exhibits an inverse P Cygni profile." The shape of the lines is the same within a source; only the relative contribution between the broad and medium components changes., The shape of the lines is the same within a source; only the relative contribution between the broad and medium components changes. " For example, in IRAS2A the ratio of the peak intensities is ~2, independent of the line, whereas in IRASAA it ranges from 1 to 2."," For example, in IRAS2A the ratio of the peak intensities is $\sim$ 2, independent of the line, whereas in IRAS4A it ranges from 1 to 2." " The Η:5Ο line profiles compare well to the broad component seen in H5O, ie., similar FWHM>20 kmss~! and velocity offset."," The $_2^{18}$ O line profiles compare well to the broad component seen in $_2$ O, i.e., similar $>$ 20 $^{-1}$ and velocity offset." " The width is much larger than isotopologue emission of, e.g., C'*O (~I- 2 kmss'!) and is centred on the source velocity (?)."," The width is much larger than isotopologue emission of, e.g., $^{18}$ O $\sim$ 1--2 $^{-1}$ ) and is centred on the source velocity ." . The medium and narrow components are not seen in the H;80 1j0- 1ρι spectra down to an rms of 2-3 mK in 0.5 ss! bins., The medium and narrow components are not seen in the $_2^{18}$ O $_{10}$ $_{01}$ spectra down to an rms of 2–3 mK in 0.5 $^{-1}$ bins. The possibility that an appreciable fraction of the atomic hwdroseen (IL1)) found iu the spiral arms of disk galaxies is dissociated molecular gas was first suggested about a decade ago from a comparison of the relative placement of the dust lanes. ireeious (a). and rridges in parts of M53 (Allen. Atherton. Tilauus 1985. 1986) aud ADSL (CIilanus Allen 1987).,"The possibility that an appreciable fraction of the atomic hydrogen ) found in the spiral arms of disk galaxies is dissociated molecular gas was first suggested about a decade ago from a comparison of the relative placement of the dust lanes, regions $\alpha$ ), and ridges in parts of M83 (Allen, Atherton, Tilanus 1985, 1986) and M51 (Tilanus Allen 1987)." This interpretation of the observations is based ou the deusitv-wave inodel for spiral structure. im which the temporal sequence of massive star formation is spread out iu space across a spiral aria by the action of a density wave driving the interstellar eas.," This interpretation of the observations is based on the density-wave model for spiral structure, in which the temporal sequence of massive star formation is spread out in space across a spiral arm by the action of a density wave driving the interstellar gas." More detailed worl: has subsequently been done. iuchiding colmparisous with other spiral tracers. such as the nonthermal radio continuum and the CO enission. for M83 (Tilauus Allen 1993). for M51 (Vogel. Kulkarni. Scoville 1988: Tilanus Allen 1989. 1990. 1991: Rand. Iulkaurnui. Rice 1992: Kuapenu et al.," More detailed work has subsequently been done, including comparisons with other spiral tracers, such as the nonthermal radio continuum and the CO emission, for M83 (Tilanus Allen 1993), for M51 (Vogel, Kulkarni, Scoville 1988; Tilanus Allen 1989, 1990, 1991; Rand, Kulkarni, Rice 1992; Knapen et al." 1992). and more receutlv for MIOQO (INKnapen Beekman 1991. 1996).," 1992), and more recently for M100 (Knapen Beckman 1994, 1996)." Shava Federman (1987) provided the first theoretical discussion of the UV photodissociation process as au explanation for the eeuerall-fHat racial distribution of ln galaxies., Shaya Federman (1987) provided the first theoretical discussion of the UV photodissociation process as an explanation for the generally-flat radial distribution of in galaxies. More receutlv. from observatious of the eenmission from ealaxies aud quantitative modelling of he results. Stacey et (01991) have coufirmed that xiotodissociation regions (PDRs: HIIollenbach Ticlens 1995) ave the sites of substantial production iu galaxy disks.," More recently, from observations of the emission from galaxies and quantitative modelling of the results, Stacey et (1991) have confirmed that photodissociation regions (PDRs; Hollenbach Tielens 1995) are the sites of substantial production in galaxy disks." Madden et (019923) lave even sugeested that. m the preferred model. virtually all of the in the disk of NGC 6916 could be produced in PDRs.," Madden et (1993) have even suggested that, in their preferred model, virtually all of the in the disk of NGC 6946 could be produced in PDRs." Unfortunately. the angular resolution available with current instrumentation iu the Ine at 158g: is inadequate for the study of individual PDRs in nearby ealaxies.," Unfortunately, the angular resolution available with current instrumentation in the line at $158 \mu$ is inadequate for the study of individual PDRs in nearby galaxies." The morphologicalOo details of tracers im spiral avis represent new evidence for the production of bby the exteusive dissociation of in PDRs., The morphological details of tracers in spiral arms represent new evidence for the production of by the extensive dissociation of in PDRs. There are two new elements in the prescut study., There are two new elements in the present study. First. ASL (NGC23031) is a galaxy which is not bright in CO cinission BBrouillet et 1991).," First, M81 (NGC3031) is a galaxy which is not bright in CO emission Brouillet et 1991)." " The conventional interpretation using CO as a tracer for lis that this ealaxy contains relatively little molecular eas, contrary to the situation for the previouslystudied galaxies M83. M51. aud MI00."," The conventional interpretation using CO as a tracer for is that this galaxy contains relatively little molecular gas, contrary to the situation for the previously-studied galaxies M83, M51, and M100." Second. the availability of UV imaee data for M81 from the Ultraviolet Imaging Telescope (CIT) permits a comparison of the nunorpholoey to the distribution of UV. photons at Azc150 um (z8.5 eV). in the iuxddle of the range of photon energies which are iuportaut for the dissociation of ((Stecher Williams1967).," Second, the availability of UV image data for M81 from the Ultraviolet Imaging Telescope (UIT) permits a comparison of the morphology to the distribution of UV photons at $\lambda \approx 150$ nm $\approx 8.3$ eV), in the middle of the range of photon energies which are important for the dissociation of (Stecher Williams." .. To interpret the UV data. any effects of patchy obscuration by dust mist be understood o properly compare the UV. aud uimorphologies.," To interpret the UV data, any effects of patchy obscuration by dust must be understood to properly compare the UV and morphologies." Ho images of M81 aid iu our investigation of this effect., $\alpha$ images of M81 aid in our investigation of this effect. In our Galaxy. the fu-UV extinction (iu πας») at Àz150 nia ds greater than the extinction at Πα (Az650 um) by a factor of more than 3.," In our Galaxy, the far-UV extinction (in mags) at $\lambda \approx 150$ nm is greater than the extinction at $\alpha$ $\lambda \approx 650$ nm) by a factor of more than 3." Therefore. auv effect of varving obscuration on the norpholoey of the Πα im M81 is greatly magnified iu he far UV.," Therefore, any effect of varying obscuration on the morphology of the $\alpha$ in M81 is greatly magnified in the far UV." The 610 sec far-UV exposure of M81 (FUV(0556: Till et 1995) is from the UTIT/ASTRO-1 archive. and is centered at A=152 um with bandwidth 35.1 um (Stecher et 1992).," The 640 sec far-UV exposure of M81 (FUV0556; Hill et 1995) is from the UIT/ASTRO-1 archive, and is centered at $\lambda = 152$ nm with bandwidth 35.4 nm (Stecher et 1992)." The VLA ddata were taken by Wine RRots. aud are provided byWWestpfall?.," The VLA data were taken by Hine Rots, and are provided by." . We used the ddata cube to caleulate a imap of ccoluin density NOTI))., We used the data cube to calculate a map of column density ). Ouly those pixels with absolute values in excess of 2.5 times the rius noise in the channel maps are used in the moment calculation. with the additional restriction that such values iust occur in at least two adjacent velocity chanucls Gvlich are separated by 10 Ny," Only those pixels with absolute values in excess of 2.5 times the rms noise in the channel maps are used in the moment calculation, with the additional restriction that such values must occur in at least two adjacent velocity channels (which are separated by 10 )." y KKaufuin and DDevereus provided Ta images of MS1., Kaufman and Devereux provided $\alpha$ images of M81. Although we, Although we Executive Council (ADEC) and the AAS journals issued guidelines aimed at improving the situation (Eichhorn2004)..,Executive Council (ADEC) and the AAS journals issued guidelines aimed at improving the situation \citep{2004AAS...204.7502E}. This new effort was aimed at addressing four separate issues in {he management of these links: (heir curation. naming. resolution ancl persistence.," This new effort was aimed at addressing four separate issues in the management of these links: their curation, naming, resolution and persistence." The creation of links to data products has been a time-consuming activity usually carried out by a librarian or archivist., The creation of links to data products has been a time-consuming activity usually carried out by a librarian or archivist. Rotsetal.(2004). describe the effort required to perform this activity. which (vpically consists of scanning the literature to identily which papers mention one or more data products from a particular archive. and then link those papers with the relevant datasets.," \cite{2004ASPC..314..605R} describe the effort required to perform this activity, which typically consists of scanning the literature to identify which papers mention one or more data products from a particular archive, and then link those papers with the relevant datasets." In 2004. in order to facilitate this activity. and in coordination with the ADEC proposal. the Astrophysical Journal introduced the capability for authors to properly tag the datasets analvzed in the paper.," In 2004, in order to facilitate this activity, and in coordination with the ADEC proposal, the Astrophysical Journal introduced the capability for authors to properly tag the datasets analyzed in the paper." This introduced a mechanism to formally 7cite data in a way similar to how scientists cite other papers., This introduced a mechanism to formally “cite” data in a way similar to how scientists cite other papers. According to this plan. citations to data products would be vetted by both editors and referees during (he manuscript editorial process. and links would be created to the corresponding data products as part of the process which generates the online IITML version of the paper.," According to this plan, citations to data products would be vetted by both editors and referees during the manuscript editorial process, and links would be created to the corresponding data products as part of the process which generates the online HTML version of the paper." The correlation between a paper and (he datasets referenced therein would then be propagated back to the ADS and the participating data centers via metadata exchange., The correlation between a paper and the datasets referenced therein would then be propagated back to the ADS and the participating data centers via metadata exchange. The implementation of this linking proposal would not only benefit end-users. but would potentially provide significant savings in the curation efforts of archivists aud librarians. who could now harvest these linkages directly from ADS. thus reducing the need for the manual scanning of the literature.," The implementation of this linking proposal would not only benefit end-users, but would potentially provide significant savings in the curation efforts of archivists and librarians, who could now harvest these linkages directly from ADS, thus reducing the need for the manual scanning of the literature." In order to properly cite the datasets in the literature. the ADEC and AAS adopted astandard wav to uniquely identify data resources based on the IVOA Identifier standard (Plante.etal.2006).," In order to properly cite the datasets in the literature, the ADEC and AAS adopted a standard way to uniquely identify data resources based on the IVOA Identifier standard \citep{IVOAIDS}." . The proposed svstem of nomenclature (Accomazzietal.2007) provided a stander for dataset identiliers which featured some important properties., The proposed system of nomenclature \citep{2007ASPC..376..467A} provided a standard for dataset identifiers which featured some important properties. Among them: uniqueness (one resource corresponds (o a single identifier). aud. persistence (iclentifiers cdo nol change even when data products are migrated to a different archive).," Among them: uniqueness (one resource corresponds to a single identifier), and persistence (identifiers do not change even when data products are migrated to a different archive)." " The identiliers were designed to support the naming of resources with a broad range of granularity ancl included a “public” prefix identilvine the archive or mission that generated the dataset as well as a ""private"" kev identilvine the data item within a specific collection.", The identifiers were designed to support the naming of resources with a broad range of granularity and included a “public” prefix identifying the archive or mission that generated the dataset as well as a “private” key identifying the data item within a specific collection. In order to ensure the proper use and persistence of links to datasets. the ADEC charged the ADS with the task of setting up a verification and resolution service for dataset identifiers.," In order to ensure the proper use and persistence of links to datasets, the ADEC charged the ADS with the task of setting up a verification and resolution service for dataset identifiers." In this role. the ADS would act as the registration authority on behalf of the community. creating the infrastructure necessary (ο enable the dataset linking.," In this role, the ADS would act as the registration authority on behalf of the community, creating the infrastructure necessary to enable the dataset linking." During of a paper. the editors would use an automated tool provided by ADS to verily that," During copy-editing of a paper, the editors would use an automated tool provided by ADS to verify that" About 15% of all observed lines at this redshift have Doppler parameters of 40 to 60 kms+ which would correspond to teniperatures of 110 2«107IX if the broadening were purely thermal.,About 15 of all observed lines at this redshift have Doppler parameters of 40 to 60 $\kms$ which would correspond to temperatures of $1$ to $2 \times 10^5\K$ if the broadening were purely thermal. Εις is well above what can plausibly be reached bv photoionization., This is well above what can plausibly be reached by photoionization. This may indicate either. (1) that our simulations significantly underestimate the fraction of the IGM in a hot collisionally ionized. phase because they do not include any feedback ellects due to star formation or (ii) that there is à turbulent component to the broadening on scales below the resolution limit of the simulations which is more important at lower redshift.," This may indicate either, (i) that our simulations significantly underestimate the fraction of the IGM in a hot collisionally ionized phase because they do not include any feedback effects due to star formation or (ii) that there is a turbulent component to the broadening on scales below the resolution limit of the simulations which is more important at lower redshift." Our results suggest that a larger. ancl homogenous sample of lines. extending over a wider redshift range. will be an excellent tool to further constrain the reionization history.," Our results suggest that a larger and homogenous sample of lines, extending over a wider redshift range, will be an excellent tool to further constrain the reionization history." We thank Simon White for a careful. reading. of the manuscript and are erateful to Romecl Davé for providing the line-fitting software ΑΙΤΟΝΟ, We thank Simon White for a careful reading of the manuscript and are grateful to Romeel Davé for providing the line-fitting software AUTOVP. Support. by NATO erant CRC 950752 and the Sonderforschungsbercich 315-95 [ürr Astro-Toilehenphysik der Deutschen Forschunesecmeinschalt” is also gratefully acknowledged., Support by NATO grant CRG 950752 and the “Sonderforschungsbereich 375-95 fürr Astro-Teilchenphysik der Deutschen Forschungsgemeinschaft” is also gratefully acknowledged. where r is (he closest approach of the lisht.,where $r$ is the closest approach of the light. " In the weak-field limit (7—2x). the deflection angle becomes The angle between the lens (wormhole) and the source 2 can then be written as where D,. Ds. Djs. and 5 are the distances lrom the observer to the lens. from the observer to the source. ancl [rom the lens (o the source. and the impact parameter of the light. respectively."," In the weak-field limit $r \rightarrow \infty$ ), the deflection angle becomes The angle between the lens (wormhole) and the source $\beta$ can then be written as where $D_L$ , $D_S$, $D_{LS}$, and $b$ are the distances from the observer to the lens, from the observer to the source, and from the lens to the source, and the impact parameter of the light, respectively." In (he asvimptotic limit. Schwarzschild lensing aud massive JanisNewmanWinnicour (JNW) wormhole lensing (Dev&Sen2003). have the same leading term of o(1/1).," In the asymptotic limit, Schwarzschild lensing and massive Janis--Newman--Winnicour (JNW) wormhole lensing \citep{dey08} have the same leading term of $o\left(1/r\right)$." Therefore. the lensing property of the JNW wornnhbole is approximately the same as that of Schwarzschild lensing ancl is difficult to distinguish.," Therefore, the lensing property of the JNW wormhole is approximately the same as that of Schwarzschild lensing and is difficult to distinguish." As shown in Equation (3)). the deflection anele of the Ellis wormhole does not have the term of o(1/r) and starts from o(1/r7).," As shown in Equation \ref{eqn:defl}) ), the deflection angle of the Ellis wormhole does not have the term of $o\left(1/r\right)$ and starts from $o\left(1/r^2\right)$." This is due to the massless nature of the Ellis wormhole and indicates the possibility of observational discrimination from the ordinary. gravitational lensing effect., This is due to the massless nature of the Ellis wormhole and indicates the possibility of observational discrimination from the ordinary gravitational lensing effect. In the weak-field limit. b is approximately equal to the closest approach r.," In the weak-field limit, $b$ is approximately equal to the closest approach $r$." For the Ellis wormhole. b=yr?+4?—r(roc).," For the Ellis wormhole, $b = \sqrt{r^2 + a^2} \rightarrow r (r \rightarrow \infty)$." We thus obtain The light passing through the other side of the lens mary also form images., We thus obtain The light passing through the other side of the lens may also form images. However. Equation (5)) represents dellection in the wrong direction at r<0.," However, Equation \ref{eqn:proj}) ) represents deflection in the wrong direction at $r < 0$." Thus. we must change the sien of the deflection angle: It would beuseful to note that a single equation is suitable both for r>0 and r«0 ," Thus, we must change the sign of the deflection angle: It would beuseful to note that a single equation is suitable both for $r > 0$ and $r < 0$ " 128 objects were classified as “merger” by the galaxy zoo team (fraction of votes > 0.5).,128 objects were classified as “merger” by the galaxy zoo team (fraction of votes $>0.5$ ). We show in Fig., We show in Fig. " 4 some typical examples of pairs we classified as M and T, while galaxy zoo assigned an extremely low fraction of votes for a “merger” in these objects."," \ref{zoo} some typical examples of pairs we classified as $M$ and $T$, while galaxy zoo assigned an extremely low fraction of votes for a “merger” in these objects." It is expected that the effects of an interacting companion on a given object will strongly depend on their relative luminosity (mass proxy) ratio., It is expected that the effects of an interacting companion on a given object will strongly depend on their relative luminosity (mass proxy) ratio. " For this reason, in this section we explore the dependence on the luminosity ratio of the interaction-induced star formation activity and colors."," For this reason, in this section we explore the dependence on the luminosity ratio of the interaction-induced star formation activity and colors." This analysis may help to deepen our understanding of this issue which has been explored by different authors under diverse approaches., This analysis may help to deepen our understanding of this issue which has been explored by different authors under diverse approaches. Observational evidence (e.g. Donzelli Pastoriza 1997) shows that the faint members of an interacting pair are more strongly affected by the companion., Observational evidence (e.g. Donzelli Pastoriza 1997) shows that the faint members of an interacting pair are more strongly affected by the companion. " Nevertheless, in a previous work (Lambas et al."," Nevertheless, in a previous work (Lambas et al." " 2003), using a detailed statistical analysis on 2dF Galaxy Redshift Survey (2dFGRS, Colles et al."," 2003), using a detailed statistical analysis on 2dF Galaxy Redshift Survey (2dFGRS, Colles et al." " 2001) data, showed that the brightest component of a pair has the most enhanced star formation activity when compared to isolated galaxies of similar luminosity, suggesting that interactions may effectively trigger star formation on the brighter member pairs."," 2001) data, showed that the brightest component of a pair has the most enhanced star formation activity when compared to isolated galaxies of similar luminosity, suggesting that interactions may effectively trigger star formation on the brighter member pairs." Ellison et al. (, Ellison et al. ( "2008) found an enhancement of the SFR of galaxy pairs at projected separations «30—40kpch!, an effect that is stronger in major mergers.","2008) found an enhancement of the SFR of galaxy pairs at projected separations $< 30-40 \rm \,kpc \,h^{-1}$, an effect that is stronger in major mergers." " More recently, Ellison et."," More recently, Ellison et." " al (2010) also found that both, the median mass ratio of pairs and the fraction of major-to-minor pairs, are independent of local environment."," al (2010) also found that both, the median mass ratio of pairs and the fraction of major-to-minor pairs, are independent of local environment." " In a similar way, Alonso et al. ("," In a similar way, Alonso et al. (" "2010), showed that galaxies with high stellar mass, low metallicity content and disturbed morphologies (characteristics of merger remnants) have bluer colors and younger stellar populations.","2010), showed that galaxies with high stellar mass, low metallicity content and disturbed morphologies (characteristics of merger remnants) have bluer colors and younger stellar populations." " These results would indicate that a close minor companion can induce significant inflows of external gas onto the central region which would lower the metallicity and trigger star formation in the most massive, morphologically disturbed galaxies."," These results would indicate that a close minor companion can induce significant inflows of external gas onto the central region which would lower the metallicity and trigger star formation in the most massive, morphologically disturbed galaxies." " For the present analysis we have divided our sample in major and minor interaction pairs according to the luminosity ratio of the galaxy members, the usually adopted criterium for the classification into major or minor interaction."," For the present analysis we have divided our sample in major and minor interaction pairs according to the luminosity ratio of the galaxy members, the usually adopted criterium for the classification into major or minor interaction." In Fig., In Fig. " 5 (a) we show the distribution of the {2/11 ratio, and the adopted threshold L5/L,=0.33 which gives 877 minor and 1082 major interactions."," \ref{HLum} $a$ ) we show the distribution of the $L_2/L_1$ ratio, and the adopted threshold $L_2/L_1 =0.33$ which gives 877 minor and 1082 major interactions." The luminosity distributions of the galaxy members of these subsamples of pairs are shown in Fig., The luminosity distributions of the galaxy members of these subsamples of pairs are shown in Fig. 5 (b and c) and in Fig., \ref{HLum} $b$ and $c$ ) and in Fig. 6 we show some examples of major and minor galaxy encounters., \ref{mm} we show some examples of major and minor galaxy encounters. " Table 3 shows the percentages of pairs classified as M, T and N in minor and major interactions where it can be seen their similarity regardless the relative luminosity ratio."," Table 3 shows the percentages of pairs classified as $M$, $T$ and $N$ in minor and major interactions where it can be seen their similarity regardless the relative luminosity ratio." " Following section 2.1.1, we performed the same analysis of the dependence of pair classification on projected distances, rp, and relative velocities, AV, for the subsamples of major and minor pairs."," Following section 2.1.1, we performed the same analysis of the dependence of pair classification on projected distances, $r_p$, and relative velocities, $\Delta V$, for the subsamples of major and minor pairs." We show in Fig., We show in Fig. " 7 density contours in the rp-AV plane for galaxies of the different interaction classes, M, T and N, in major and minor interactions (left and right panels, respectively)."," \ref{rpVMTN1} density contours in the $r_p$ $\Delta V$ plane for galaxies of the different interaction classes, $M$, $T$ and $N$, in major and minor interactions (left and right panels, respectively)." The gray scale correspond to different percentages of pairs enclosed in a given contour., The gray scale correspond to different percentages of pairs enclosed in a given contour. It can be, It can be The energy dissipated through obliquity tides comes at the expeuse of the orbital euergy.,The energy dissipated through obliquity tides comes at the expense of the orbital energy. We uimst examine whether it is possible for the dissipation rate to be large enough to inflate the planet. vet slow enough to allow the orbit to survive for 5x10? vr. the approximate main-sequence age of the star (Cody Sasselov 2002).," We must examine whether it is possible for the dissipation rate to be large enough to inflate the planet, yet slow enough to allow the orbit to survive for $5\times 10^9$ yr, the approximate main-sequence age of the star (Cody Sasselov 2002)." To iullate the planet. Bodeulieiner. Laughlin. Lin (2003) found the requiredH power to be [x4107*MI erg + ifequ the planet lias a dense core. aud an order ofH magnitudeH smaller if the planet is coreless.," To inflate the planet, Bodenheimer, Laughlin, Lin (2003) found the required power to be $4\times 10^{27}$ erg $^{-1}$ if the planet has a dense core, and an order of magnitude smaller if the planet is coreless." With reference to Eq. (1)).," With reference to Eq. \ref{eq:heat}) )," this correspouds to au upper limit ou Q/h of 10° for a cored planet and 10* for a coreless planet., this corresponds to an upper limit on $Q/h$ of $10^6$ for a cored planet and $10^7$ for a coreless planet. Thecondition yields a lower limit on Q/h of 5x10°., Thecondition yields a lower limit on $Q/h$ of $5\times 10^6$. In reality. Eq. (6))," In reality, Eq. \ref{eq:timescale}) )" is probably too restrictive by a [actor of a few: the clissipatiou rate was smaller in the past. when the planet πας a smaller raclius. a larger orbital distauce. and possibly a larger mass (Vidal-Madjar et 22003).," is probably too restrictive by a factor of a few; the dissipation rate was smaller in the past, when the planet had a smaller radius, a larger orbital distance, and possibly a larger mass (Vidal-Madjar et 2003)." Thus. Q// should be «105 if the planet has a core aud 109—10* if it does not.," Thus, $Q/h$ should be $\sim$ $^6$ if the planet has a core and $10^6$ $10^7$ if it does not." " In comparison. for Jupiter it is thought that Q is between LO? and LO"" (Goldreich Soter 1966) aud /iZ0.6 (Cavrilov Zharkov 1977)."," In comparison, for Jupiter it is thought that $Q$ is between $10^5$ and $10^6$ (Goldreich Soter 1966) and $h\gsim 0.6$ (Gavrilov Zharkov 1977)." The required Q/f for HD 209158b is comparable to. or somewhat larger that. the nominal Joviau value.," The required $Q/h$ for HD 209458b is comparable to, or somewhat larger than, the nominal Jovian value." The last chapter of the story is that the planet remains in Cassini state 2 for billious of vears., The last chapter of the story is that the planet remains in Cassini state 2 for billions of years. Here the difficulty is that as € decreases. the width of the resonance also decreases. reduciug the robustuess of state 2 to perturbations.," Here the difficulty is that as $\epsilon$ decreases, the width of the resonance also decreases, reducing the robustness of state 2 to perturbations." For e210.7. the angle between the separatrix angles (see Fie.," For $\epsilon=10^{-5}$, the angle between the separatrix angles (see Fig." 2: i2) is: only cu(022., 2) is only $0\fdg2$. For2 e=E107. it is LEEiucreased to -7°.," For $\epsilon=10^{-2}$, it is increased to $7\arcdeg$." The impact: of. a body of. mass 11 at escape velocity would produce a maximum obliquity shift of where the maximum is achieved for eraziug incidence at the pole., The impact of a body of mass $m$ at escape velocity would produce a maximum obliquity shift of where the maximum is achieved for grazing incidence at the pole. Hence we must also suppose HD 209[58b sullered no major collisions after tlie disappearauce of the protoplanetary clisk., Hence we must also suppose HD 209458b suffered no major collisions after the disappearance of the protoplanetary disk. Hot Jupiters should be in Cassini states., Hot Jupiters should be in Cassini states. Since the obliquity of a Cassini state is uot necessarily sinall. obliquity tides are a potentially important internal heat source.," Since the obliquity of a Cassini state is not necessarily small, obliquity tides are a potentially important internal heat source." Whether a giveu planet cau ualutaln a significant obliquity clepeuds upou its initial obliquity as well as its precessional aud collisional histories., Whether a given planet can maintain a significant obliquity depends upon its initial obliquity as well as its precessional and collisional histories. " Obliquity tides could be the ""missiug heat source that bloats the transitiug dlanet HD 20915sb.", Obliquity tides could be the “missing” heat source that bloats the transiting planet HD 209458b. " The implications of this hypothesis are that the plauet’s obliquity is nearly907.. its tidal dissipation [actor Q aud displacement Love inunber // obey 100.9 since their position angles will be meaningless.," We remove from our final catalogue those clusters whose BCGs are round, which we define as $b/a>0.9$ since their position angles will be meaningless." This eliminates an additional 1050 clusters., This eliminates an additional $1050$ clusters. The final cluster catalogues are sumnmarised in second part of Table 1.., The final cluster catalogues are summarised in second part of Table \ref{tab:cutsummary}. Phroughout the subsequent analysis we use the cluster sample labelled as b/egesc;«0.9 in Table l asthe Total sample and split this into the Centre and Ollset samples., Throughout the subsequent analysis we use the cluster sample labelled as $b/a_{BCG}<0.9$ in Table \ref{tab:cutsummary} as the Total sample and split this into the Centre and Offset samples. With our measurements of the position angles of clusters in hand. we investigated a number of alignment signals between BGs and their host clusters.," With our measurements of the position angles of clusters in hand, we investigated a number of alignment signals between BCGs and their host clusters." We define the alignment of the BCC with the cluster as and we sav that the BCC and cluster are aligned [or Aox 30°. following ?..," We define the alignment of the BCG with the cluster as and we say that the BCG and cluster are aligned for $\Delta\phi\leq30^{\circ}$ , following \citet{Binggeli:1982p376}." We quantify the strength. of the alignment signal bv calculating the ratio Ro of the number of clusters with Ao<307 to the number with Ao30., We quantify the strength of the alignment signal by calculating the ratio $\mathcal{R}$ of the number of clusters with $\Delta\phi \le 30^{\circ}$ to the number with $\Delta\phi > 30^{\circ}$. This definition of the alignment signal gives an indication of the steepness of the distribution. as well as the relative number of aligned. ancl non-alignecl cluster-BCG pairs., This definition of the alignment signal gives an indication of the steepness of the distribution as well as the relative number of aligned and non-aligned cluster-BCG pairs. " Phe errors are determined assuming that the counts are Poisson processes with uncertainty m,=να where e is the count. and that the uncertainties in the two counts are independent."," The errors are determined assuming that the counts are Poisson processes with uncertainty $\sigma_a=\sqrt{a}$ where $a$ is the count, and that the uncertainties in the two counts are independent." A random distribution would. vield R= 0.5., A random distribution would yield $\mathcal{R}$$=0.5$ . We show the distribution of alignments in Figure 5 and. tabulate 7. in Table 2.., We show the distribution of alignments in Figure \ref{fig:histocuty} and tabulate $\mathcal{R}$ in Table \ref{tab:lambdasumgen}. There is a clear anc unambiguous alignment signal. (the Bingeeli effect)., There is a clear and unambiguous alignment signal (the Binggeli effect). In the Centre sample the alignment signal (R= 0.865) is approximately 5.50. stronger than in the OUsct sample (R= 0.659) where the significanceis defined as the cillerencebetween ον and Roprser weighted by the uncertainties summed in quacdrature., In the Centre sample the alignment signal $\mathcal{R}$$=0.865$ ) is approximately $5.5\sigma$ stronger than in the Offset sample $\mathcal{R}$$=0.659$ ) where the significanceis defined as the differencebetween $\mathcal{R}_{Centre}$ and $\mathcal{R}_{Offset}$ weighted by the uncertainties summed in quadrature. We find only a, We find only a models i which the outer disc radius is kept coustaut (see e.g. Ihuneurv at al. 1995)).,"models in which the outer disc radius is kept constant (see e.g. Hameury at al. \cite{hmdlh98}) )," which mav lappen when the outer disc radius reaches the tidal truucation radius., which may happen when the outer disc radius reaches the tidal truncation radius. However. oue does not normally obtain extremely long outbursts: the 1985 outburst of U Cem was il fact so long that. more mass was accreted duiug this outburst than what was coutained in the pre-outhurst disc.," However, one does not normally obtain extremely long outbursts; the 1985 outburst of U Gem was in fact so long that, more mass was accreted during this outburst than what was contained in the pre-outburst disc." The asim mass Aqagas of a quiescent disc during quiescence is the integral of the iiaxinmun surface density Mayas ou the cool brauch: using the fits even by Tameury et al. (1998)).," The maximum mass $M_{\rm d,max}$ of a quiescent disc during quiescence is the integral of the maximum surface density $\Sigma_{\rm max}$ on the cool branch; using the fits given by Hameury et al. \cite{hmdlh98}) )," one ects where a. is the Shakura-Sunvaey viscosity parameter ou the cool brauch. M4 is the primary mass in solar wits. aud four is the outer disc radius.," one gets where $\alpha_{\rm c}$ is the Shakura-Sunyaev viscosity parameter on the cool branch, $M_1$ is the primary mass in solar units, and $r_{\rm out}$ is the outer disc radius." Ou the other haud. during a long outburst. the whole disc is eutirely on the lot brauch. aud the local mass transfer rate in the outer regions of a disc must be large enough to prevent a cooling wave formation: using again the analytical fits of Tameury al al. (1998)).," On the other hand, during a long outburst, the whole disc is entirely on the hot branch, and the local mass transfer rate in the outer regions of a disc must be large enough to prevent a cooling wave formation; using again the analytical fits of Hameury al al. \cite{hmdlh98}) )," this gives Tere. M is the local mass transfer rate in the outer parts of the disc. which is close to the mass accretion rate outo the white dwarf if the whole disc sits for a lone time ou the hot brauch.," this gives Here, $\dot{M}_{\rm out}$ is the local mass transfer rate in the outer parts of the disc, which is close to the mass accretion rate onto the white dwarf if the whole disc sits for a long time on the hot branch." The maxinuun curation of such au outburst is thus finax=MaauaxAL.," The maximum duration of such an outburst is thus $t_{\rm max} = M_{\rm d,max}/\dot{M}$." " For the paralucters appropriate for U Cem. one vets As a. is laveer than 0.01 for this prototypical dwarf rova (Livio Spruit 1991. for example fud that a, must vc equal to 0.011 to account for the timing properties of U Gom). fija cab never be as high as {0 davs."," For the parameters appropriate for U Gem, one gets As $\alpha_{\rm c}$ is larger than 0.01 for this prototypical dwarf nova (Livio Spruit \cite{ls91} for example find that $\alpha_{\rm c}$ must be equal to 0.044 to account for the timing properties of U Gem), $t_{rm \max}$ can never be as high as 45 days." This neaus that the total amount of mass accreted during lis long outburst is lareer than the mass of the disc in quiescence: this is possible only if the mass transfer rate from the secondary has increased to a value close o the mass accretion rate onto the white dwarf. be. is close to the critical rate for stable accretion.," This means that the total amount of mass accreted during this long outburst is larger than the mass of the disc in quiescence; this is possible only if the mass transfer rate from the secondary has increased to a value close to the mass accretion rate onto the white dwarf, i.e. is close to the critical rate for stable accretion." Such au iucrease of the mass transfer rate is very likely caused w the illuniuuation of the secondary., Such an increase of the mass transfer rate is very likely caused by the illumination of the secondary. This reinforces tle conclusion of Sms (1999a)) tha long outbursts result roni large masstransfer enlancemoenuts., This reinforces the conclusion of Smak \cite{s99a}) ) that long outbursts result from large mass–transfer enhancements. We use here the umuuerical code described in Ibuueurv et al (1998))., We use here the numerical code described in Hameury et al. \cite{hmdlh98}) ). This code solves the usual mass. aneular moment and enerev conservation equations on al adaptive erd. with a fully inplicit scheme.," This code solves the usual mass, angular momentum and energy conservation equations on an adaptive grid, with a fully implicit scheme." This allows to resolve narrow structures in the accretion dise (Menon et al. 19993).," This allows to resolve narrow structures in the accretion disc (Menou et al. \cite{mhs99}) )," aud avoids the Courant coucition which woul severely limit the time step., and avoids the Courant condition which would severely limit the time step. To describe disc irracliation we use a version of the code described iu Dubus et al. (1999)) (, To describe disc irradiation we use a version of the code described in Dubus et al. \cite{dlhc99}) ) ( see also Huueury et al. 1999)).,see also Hameury et al. \cite{hld99}) ). A erid of vertica structures is usec to determine the cooliug rate of the disc as a functiou of the vertical eravity. the integrate RNisc surface density X. the ceutra temperature T; aud the μαχο temperature Ty. defined as Ty=Guo)! where Fi is the ilhuninating fiux.," A grid of vertical structures is used to determine the cooling rate of the disc as a function of the vertical gravity, the integrated disc surface density $\Sigma$, the central temperature $T_{\rm c}$ and the illumination temperature $T_{\rm ill}$, defined as $T_{\rm ill} = (F_{\rm ill}/\sigma)^{1/4}$ where $F_{\rm ill}$ is the illuminating flux." In what follows. we USC guae=0.2 and aeoig=0.01. except where otherwise PAtated.," In what follows, we use $\alpha_{\rm hot} = 0.2$ and $\alpha_{\rm cold} = 0.04$, except where otherwise stated." We also neglect the albedo ο) of the disc: taking i oeito account introduces a multiplicative factor (1.4)j1 or the white chwarf tempcratiures., We also neglect the albedo $\beta$ of the disc; taking it into account introduces a multiplicative factor $(1-\beta)^{-1/4}$ for the white dwarf temperatures. It iust also be stressed that the white dwarf surface cluperature cannot be too large: this is because the intrinsic (quiescent) white chart luninesitv mast be sjenificautly less than the accretion Iuninositv in outburst: or M4 = 0.6 AL... the quiescent white dwarf temperature as to be smaller than 33.000 Ts if the outburst auiplitude is to be larger than 2 maguitudes.," It must also be stressed that the white dwarf surface temperature cannot be too large; this is because the intrinsic (quiescent) white dwarf luminosity must be significantly less than the accretion luminosity in outburst; for $M_1$ = 0.6 $_\odot$, the quiescent white dwarf temperature has to be smaller than 33,000 K if the outburst amplitude is to be larger than 2 magnitudes." We are interested here in the effect of illumination of the secondary ou its mass transfer rate on short time scales (days). and we do not consider auv loug term effects that uav lead to evcles accounting for the observed dispersion of the average mass transfer rate for à eiven orbital period (MeConuick Fraux 1998)).," We are interested here in the effect of illumination of the secondary on its mass transfer rate on short time scales (days), and we do not consider any long term effects that may lead to cycles accounting for the observed dispersion of the average mass transfer rate for a given orbital period (McCormick Frank \cite{mf98}) )." Even on short time scales. he respouse of the secondary. to illumination is complex (seo e.g. IEbuneurv et al. 1988):," Even on short time scales, the response of the secondary to illumination is complex (see e.g. Hameury et al. \cite{hlk88}) );" we prefer to use here a siupler approach iu which we assume a linear relation jetween the mass transfer rate from the secoudarv Mj and the mass acerction rate outo the white dwarf M. Le. where Afy is he imass trausfer rate in the absence of illumination.," we prefer to use here a simpler approach in which we assume a linear relation between the mass transfer rate from the secondary $\dot{M}_{\rm tr}$ and the mass accretion rate onto the white dwarf $\dot{M}_{\rm acc}$, i.e. where $\dot{M}_0$ is the mass transfer rate in the absence of illumination." This is similar to the formula used wv Απο oet al. (1993)), This is similar to the formula used by Augusteijn et al. \cite{aks93}) ) in the context of soft Noaav transicuts., in the context of soft X-ray transients. Although if is an extremely crude approximation. it has. nevertheless. the advantage of ving onlv one ree paranueter +.," Although it is an extremely crude approximation, it has, nevertheless, the advantage of having only one free parameter $\gamma$." Its value must © iu he range |Q1 or stability reasons., Its value must be in the range $[0-1]$ for stability reasons. Such an approach obviously requires the illumination Oo Lave a noticeable effects on the secondaryvs surface lavers., Such an approach obviously requires the illumination to have a noticeable effects on the secondary's surface layers. As incutioned earlier. strongly mradiated colupanion stars are observed du several systems.," As mentioned earlier, strongly irradiated companion stars are observed in several systems." To describe the effects of radiation of a Roche-lobe filling star we shall follow the approach of Osaki (1985)) and Παιν et al. (1986))., To describe the effects of irradiation of a Roche-lobe filling star we shall follow the approach of Osaki \cite{o85}) ) and Hameury et al. \cite{hkl86}) ). The nass transfer rate from the secoudary cau he written as (Lubow Shu 1975)):, The mass transfer rate from the secondary can be written as (Lubow Shu \cite{ls75}) ): Despite the observational and theoretical efforts of the last decades. the evolutionary status of early-tvpe galaxies is still an unsolved problem.,"Despite the observational and theoretical efforts of the last decades, the evolutionary status of early-type galaxies is still an unsolved problem." The stellar populations of nearby elliplicals preserve a record of their formation and evolution., The stellar populations of nearby ellipticals preserve a record of their formation and evolution. hr particular. the study of their element abundance ratios should be a powerful discriminant between different. star formation histories (e.g. Worthev. 1998)).," In particular, the study of their element abundance ratios should be a powerful discriminant between different star formation histories (e.g. \citealt{W98}) )." ILowever. this last approach is still at its infancy.," However, this last approach is still at its infancy." The pioneering works of late 1970s already revealed (hat abundance ratios in earlv-tvpe ealaxies are often non-solar (OConnell1976: Peterson1976))., The pioneering works of late 1970s already revealed that abundance ratios in early-type galaxies are often non-solar \citealt{Ocon76}; \citealt{Pet76}) ). Since then. several studies have provided compelling evidence of Mg/Fe overabundances in massive ellipticals as compared with the solar ratio (Worthev.Faber.&González1992: Peletier1939: 1997)). which have been interpreted in the Leht of several possible scenarios based on the understanding that Mg is mainiv produced in (wpe LD supernovae (Faber.Worthey.González 1992:: Worthev.Faber.&González 1005: Alatteucei1994)).," Since then, several studies have provided compelling evidence of Mg/Fe overabundances in massive ellipticals as compared with the solar ratio \citealt{b42}; \citealt{b41}; \citealt{b60}) ), which have been interpreted in the light of several possible scenarios based on the understanding that Mg is mainly produced in type II supernovae \citealt{Fab92}; \citealt{b42}; \citealt{Mat94}) )." However. and in contrast wilh the above findings. another a/pha element. namely Ca. seems to be underabuncdant in ellipticals (OConnell 1976: Sagliaetal.2002: Cenarroetal. 2003:: Thomas.Maraston.&Bender 20033). challenging current chemical evolution models Matteueci1994: GarciaVargas2000) ).," However, and in contrast with the above findings, another $alpha$ element, namely Ca, seems to be underabundant in ellipticals \citealt{Ocon76}; ; \citealt{Sag02}; \citealt{Cen03}; \citealt{Tho03}) ), challenging current chemical evolution models \citealt{Mat94}; \citealt{Moll00}) )." several authors (Worthev1998: Vazdekisetal. 2001)) have also noted a strengthening in other absorption line-streneths. in particular in the IDS/Lick C4668 and CN» indices. when compared with stellar population models predictions.," Several authors \citealt{W98}; \citealt{b37}) ) have also noted a strengthening in other absorption line-strengths, in particular in the IDS/Lick C4668 and $_{2}$ indices, when compared with stellar population models predictions." The variations of these two indices are mainly driven by C and N (in the case of CN) abundances. 1995)). which could suggest a possible enhancement of these two elements relative to Fe when compared with the solar values.," The variations of these two indices are mainly driven by C and N (in the case of CN) abundances \citealt{Tri95}) ), which could suggest a possible enhancement of these two elements relative to Fe when compared with the solar values." In contrast with Mg. C and N are mainly produced in low- and intermecdiate-mass stars (Renzini&Voli1931: Chiappini. 2003.. although there are recent suggestions that most of the C should come from massive stars).," In contrast with Mg, C and N are mainly produced in low- and intermediate-mass stars \citealt{Ren81}; \citealt{Chia03}, although there are recent suggestions that most of the C should come from massive stars)." " During the AGB phase. these stars eject into the ISM significant amounts of ο, Po PC and UN, enriching the medium from which new stars will be formed."," During the AGB phase, these stars eject into the ISM significant amounts of $^{4}$ He, $^{12}$ C, $^{13}$ C and $^{14}$ N, enriching the medium from which new stars will be formed." Therefore. il seems clifficult to simultaneously. reproduce the abtndances of all these elements with a simple chemical evolution scenario.," Therefore, it seems difficult to simultaneously reproduce the abundances of all these elements with a simple chemical evolution scenario." The problem of C and N abundances has been more thoroughly studied in the field of elobulw clusters., The problem of C and N abundances has been more thoroughly studied in the field of globular clusters. An interesting puzzling problem is the existence of a CN clichotomy in Galactic ancl M31 elobular clusters (Bursteinοἱal. 1984))., An interesting puzzling problem is the existence of a CN dichotomy in Galactic and M31 globular clusters \citealt{b15}) ). " Although this is a controversial issue. recent works (IIarbeck.Smith.&Grebel 2003)) tend to favor the scenarios of different abundances in (he parental clouds against (hie ones that predict abundance changes produced internally by the evolution of the stars (see Cannonetal.1993.[or a review),"," Although this is a controversial issue, recent works \citealt{Har03}) ) tend to favor the scenarios of different abundances in the parental clouds against the ones that predict abundance changes produced internally by the evolution of the stars (see \citealt{Can98} for a review)." Given the expected sensilivilies οἱ relative abundances to the star formation history of, Given the expected sensitivities of relative abundances to the star formation history of A high resolution long-slit spectrum of 11-2 was obtained with at the Nordic Optical Telescope (NOT) on ltoque de los Muchachos Observatory (La Palma) on 2004 June.,A high resolution long-slit spectrum of 1-2 was obtained with at the Nordic Optical Telescope (NOT) on Roque de los Muchachos Observatory (La Palma) on 2004 June. We used à Lk Thompson CCD and a narrowband filter to isolate the La and AA6548.6583 emission lines.," We used a $\times$ 1k Thompson CCD and a narrow–band filter to isolate the $\alpha$ and $\lambda$$\lambda$ 6548,6583 emission lines." The slit (0765. wide) was oriented. at position angle (PA) 320. the orientation of the knots of 11-2 (see below).," The slit $\farcs$ 65 wide) was oriented at position angle (PA) $^{\circ}$, the orientation of the knots of 1-2 (see below)." The orientation of the slit is also shown in H1., The orientation of the slit is also shown in 1. " Exposure time was 9005s. The spectral resolution (EWILM) is 8S kiss and the seeing was 2 1"".", Exposure time was s. The spectral resolution (FWHM) is 8 $^{-1}$ and the seeing was $\simeq$ $''$. Phe spectrum was reduced. using standard: procedures for long-slit’ spectroscopy within the IRAP package., The spectrum was reduced using standard procedures for long-slit spectroscopy within the IRAF package. Figure22 presents a position-velocity map of the u]]A6583 emission line obtained from this spectrum., 2 presents a position-velocity map of the $\lambda$ 6583 emission line obtained from this spectrum. The imageὃν in Fie.ll shows lLlull-2 consistingὃν of an ∢⊾↓↓↓≻↿↓⋯∣⋡↓↓≻∪⇂⋜⊔⋅⊔↓⋜⊔⊔⊳∖↓↥∢⊾∐∪⇂≥↓≟−≽≟↓⊔⊳∖↓∠⋖⊾⋜⋯∠--. . ∕∕⋅∕∕⋠⋠ oriented at. PX 2 3207. and reveals several outer structures around the polar regions of the main shell (see Miranda e al.," The image in 1 shows 1-2 consisting of an elliptical/bipolar main shell of $\simeq$ $''$$\times$ $''$ in size and oriented at PA $\simeq$ $^{\circ}$, and reveals several outer structures around the polar regions of the main shell (see Miranda et al." 2011 for a description of the morphological components in 11-2)., 2011 for a description of the morphological components in 1-2). The northwestern knot hinted by Manchadoeal.(1996). is clearly detected. in the 2008.67 image., The northwestern knot hinted by \citet{b4} is clearly detected in the 2008.67 image. The southeastern counterpart is identified in this image for the first time owing its subaresecond spatial resolution tha permits to separate the knot from a very close field star., The southeastern counterpart is identified in this image for the first time owing its subarcsecond spatial resolution that permits to separate the knot from a very close field star. We will refer to them as the NW and SE knots., We will refer to them as the NW and SE knots. They presen bow-shock-like morphology with a central emission peak an extended wings. are located at 2775 from the central star of 11-2 (Heap et al.," They present bow-shock-like morphology with a central emission peak and extended wings, are located at $\farcs$ 5 from the central star of 1-2 (Heap et al." 1990: Miranda et al., 1990: Miranda et al. 2011). and oriente at PA 320° iab coincides with the orientation of the main nebular axis.," 2011), and oriented at PA $^{\circ}$ that coincides with the orientation of the main nebular axis." Phe SE knot is brighter than the NW one., The SE knot is brighter than the NW one. Emission features from the bipolar knots are detectec in the long-slit spectrum 22) with radial velocities of + + (NW. knot blueshifted. SE knot redshifted).," Emission features from the bipolar knots are detected in the long-slit spectrum 2) with radial velocities of $\pm$ $^{-1}$ (NW knot blueshifted, SE knot redshifted)." The inclination angle of the knots is unknown., The inclination angle of the knots is unknown. From an analvsis of high-resolution. long-slit Lla spectra at. severa PAs. Miranda et al. (," From an analysis of high-resolution, long-slit $\alpha$ spectra at several PAs, Miranda et al. (" 2011) obtained an upper limit of 107 with respect to the plane of the sky for the inclination of the main nebular axis of 11-2 (see also Miranda et al.,2011) obtained an upper limit of $^{\circ}$ with respect to the plane of the sky for the inclination of the main nebular axis of 1-2 (see also Miranda et al. 2012 in preparation)., 2012 in preparation). Lf the knots moved along the main nebular axis. as suggested by the coincidence of the orientations. heir expansion velocity would be > +.," If the knots moved along the main nebular axis, as suggested by the coincidence of the orientations, their expansion velocity would be $>$ $^{-1}$." Ht should »' noted that a more accurate value for the expansion velocity cannot be obtained mainly because of the very small inclination angle of the object (see below)., It should be noted that a more accurate value for the expansion velocity cannot be obtained mainly because of the very small inclination angle of the object (see below). In any case. hese results conclusively demonstrate that the NW and SE knots constitute a high velocity. collimated bipolar outflow.," In any case, these results conclusively demonstrate that the NW and SE knots constitute a high velocity, collimated bipolar outflow." Moreover. the morphological and kinematical properties »»int out that the NW ancl SE knots represent the working surfaces of high-velocity bullets.," Moreover, the morphological and kinematical properties point out that the NW and SE knots represent the working surfaces of high-velocity bullets." We also note that the, We also note that the accounts for the dependence of the bulk of matter ou the scalar field. which is mainly given by the electromagnetic contribution to the nuclear mass.,"accounts for the dependence of the bulk of matter on the scalar field, which is mainly given by the electromagnetic contribution to the nuclear mass." " Equation (32)) then will finally reac Since the scalar field is space imdependent. and eiven that the clectromaguctic cnerey of matter is mainly accounted for the nuclear content. we assuue that the following condition £77""aae30 as) fulfilled."," Equation \ref{div:Tm0}) ) then will finally read Since the scalar field is space independent, and given that the electromagnetic energy of matter is mainly accounted for the nuclear content, we assume that the following condition $\frac{\partial \sigma}{\partial\psi}-\frac{\partial\sigma_{\mu}}{\partial\psi}\approx 0$ is fulfilled." We consequcutly obtain This equation becomes clearer if we make a trivial change to produce which clearly shows that besides the staudard cooling mechanism of the body. there is a contribution from the partial release of the maguetic enerev injected by the scalar field.," We consequently obtain This equation becomes clearer if we make a trivial change to produce which clearly shows that besides the standard cooling mechanism of the body, there is a contribution from the partial release of the magnetic energy injected by the scalar field." We define to be equal to twice the cuerey production per mass unit of anv material substance ¢ (usine the approximation. E24»] when ce<< 1).," We define to be equal to twice the energy production per mass unit of any material substance $a$ (using the approximation, $e^{-2\psi}\to 1$ when $\psi<<1$ )." We row consider our nain physical assumption:field., We now consider our main physical assumption:. The reasons for this assmuption are fold: 1) as we have just shown. the electrostatic enerev “injected” bv the scalar field remains within the bulk matter (the cancellation ofternis occurriues as seen in Eq.Cls))). aud 2) the thermal evolution should not change given the high thermal conductivity of the Earth aud white dwarfs considered iu this work.," The reasons for this assumption are fold: 1) as we have just shown, the electrostatic energy “injected” by the scalar field remains within the bulk matter (the cancellation ofterms occurring as seen in \ref{cooling}) )), and 2) the thermal evolution should not change given the high thermal conductivity of the Earth and white dwarfs considered in this work." Thus. we expect the magnetic energy excess to be radiated away. increasingthe heat flux J as shown in Eq.(19)).," Thus, we expect the magnetic energy excess to be radiated away, increasingthe heat flux $\mathbf J$ as shown in \ref{cooling2}) )." As we mnentioned in the Sect. 3.," As we mentioned in the Sect. \ref{sec:Edot}," " the ouly ""iuput is that derived from the magnetic field.", the only “input” is that derived from the magnetic field. Stationary electric currents eencerated by charged particles aud their static magnetic moments. and quautu fluctuations of the umuber density are responsible for the gcucratiou of magnetic fields in quautunumechanics.," Stationary electric currents generated by charged particles and their static magnetic moments, and quantum fluctuations of the number density are responsible for the generation of magnetic fields in quantummechanics." These contributions have been studied aud calculated by? and ? from a nininial nuclear shell model using the following analysis (for more details see ?))., These contributions have been studied and calculated by \citet{Haugan:1977px} and \citet{WillTh} from a minimal nuclear shell model using the following analysis (for more details see \citet{KV1-09}) ). The total maguetic energv of the nucleus can be written as where 6 runs over a complete set of cigcustates of the nuclear Wauultoniaun 77., The total magnetic energy of the nucleus can be written as where $\alpha$ runs over a complete set of eigenstates of the nuclear Hamiltonian $H$. " Neelecting the moment dependence of the nuclear potential and assunüug a coustant density within the nucleus; we obtain the result where dy, is the dipole density. Vy=ZR5 is the nuclear volume. aud 0 is the angle between a aud a’."," Neglecting the momentum dependence of the nuclear potential and assuming a constant density within the nucleus, we obtain the result where $\bm{d}_{0\alpha}$ is the dipole density, $V_N = \frac{4\pi}{3} R_N^3 $ is the nuclear volume, and $\theta$ is the angle between $\hat{\bm{x}}$ and $\hat{\bm{x}}'$." ence. Tn the last equation. Ui is equal to RD and the first term can be computedR3 from the connection between the streueth function aud the photoabsorption CTOSS-SCCTION Frou this. we casily fiud that where FE-—25MeV is the mean absorption euergw. which is roughly independent of A (ο of nucleons).," Hence, In the last equation, $\frac{\int d\bm{x}d\bm{x}' \frac{\cos\theta}{\vert \bm{x}-\bm{x}' \vert}}{V_N^2}$ is equal to $\frac{3}{5R_N}$, and the first term can be computed from the connection between the strength function and the photoabsorption cross-section From this, we easily find that where $\bar{E} \sim \unit[25]{MeV}$ is the mean absorption energy, which is roughly independent of $A$ (number of nucleons)." The cross-section satisfies the Thomas-BRoeiche-I&uliu stn rule where.90.2 takes iuto account exchange aud velociv dependence of unclear interactions., The cross-section satisfies the Thomas-Reiche-Kuhn sum rule where $x \sim 0.2$ takes into account exchange and velociy dependence of nuclear interactions. Combining Eqs.(53).. (55).. and (56).. we obtain," Combining , , and , we obtain" MBO). and considering a pure hydrogen plasma with a depth along the line of sight equal to the size in the plane of the sky. electron density estimates and are obtained for and MBO. respectively.,"MBO), and considering a pure hydrogen plasma with a depth along the line of sight equal to the size in the plane of the sky, electron density estimates and are obtained for and MBO, respectively." As a different approach to3503.. the rms electron density and 10nized mass can be obtained using the spherical model of ? and the flux density at 4800 MHz.," As a different approach to, the rms electron density and ionized mass can be obtained using the spherical model of \citet{mh67} and the flux density at 4800 MHz." Assuming a constant electron density. and à radiouspe.. we obtain andM«.," Assuming a constant electron density, and a radious, we obtain and." . Thus. the electron density of 35031s about a factor of 5 lower than the density of Component I. which clearly indicates that the nebula has expanded.," Thus, the electron density of is about a factor of 5 lower than the density of Component 1, which clearly indicates that the nebula has expanded." An estimate of the filling factor can be obtained by taking into account the maximum electron. density derived from optical. linescm-:?)., An estimate of the filling factor can be obtained by taking into account the maximum electron density derived from optical lines. We obtain f = 0.5 - 0.8., We obtain $f$ = 0.5 - 0.8. Then. the ionized 154733mass for f = 0.5 - 0.8 is in the range 8 - 10ML.," Then, the ionized mass for $f$ = 0.5 - 0.8 is in the range 8 - 10." .. Regarding MBO. rms electron densities and masses estimated from the image at 843 MHz are and⋅⋅ respectively.," Regarding MBO, rms electron densities and masses estimated from the image at 843 MHz are and, respectively." The emission distribution at 8.13. pm (MSX-A band) superposed to the image at 24 ym (MIPSGAL) is shown in the left panel of Fig. 8.., The emission distribution at 8.13 $\mu$ m (MSX-A band) superposed to the image at 24 $\mu$ m (MIPSGAL) is shown in the left panel of Fig. \ref{fig:msx-halfa}. The Band includes the strong emission features at 7.7 and 8.6 um attributed to molecules. which are considered tracers of UV-irradiated (PDR) (?)..," The Band includes the strong emission features at 7.7 and 8.6 $\mu$ m attributed to molecules, which are considered tracers of -irradiated (PDR) \citep{ht97}." This image displays a small and strong feature. from hereonwards dubbed theKnot. or for short (indicated. with a white rectangle). which is coincident with the location of3503... and a weaker and more extended emission region detected in the north-western area of the image.," This image displays a small and strong feature, from hereonwards dubbed the, or for short (indicated with a white rectangle), which is coincident with the location of, and a weaker and more extended emission region detected in the north-western area of the image." The last feature will be referred to as theEmission. or for short.," The last feature will be referred to as the, or for short." IR emission at 8.3 and 24 jm appears mixed along the whole feature., IR emission at 8.3 and 24 $\mu$ m appears mixed along the whole feature. A region of low IR emission is seen between the IRK and, A region of low IR emission is seen between the IRK and seen in numerous mean-field calculations during the nonlinear stage of NEMPI (Brandenburgetal.2010;Kapyla 2011).,"seen in numerous mean-field calculations during the nonlinear stage of NEMPI \citep{BKR10,KBKMR11}." ". Using the technique described in BKKR, we have found that for Rey;Z1.1 and Pray=0.5. the effective has a minimum. As magneticexpected"," Using the technique described in BKKR, we have found that for $\Rm\ga1.1$ and $\Pm=0.5$, the effective magnetic pressure has a negative minimum." " pressurefrom theory negativeand mean-field calculations, NEMPI is excited in a certain of field strengths."," As expected from theory and mean-field calculations, NEMPI is only excited in a certain range of field strengths." " In particular, only for between range0.02 and 0.2 do we see large-scale magnetic Bo/structures."," In particular, only for $B_0/\Beqz$ between 0.02 and 0.2 do we see large-scale magnetic structures." "Beqo This is shown in3,, where we see B,, again averaged over y and a time Figureinterval At£z80075, in which the field is statistically steady."," This is shown in, where we see $B_y$, again averaged over $y$ and a time interval $\Delta t\approx800\tauto$, in which the field is statistically steady." The clearest flux structure formations are seen for Bo/Beqo9” 0.05., The clearest flux structure formations are seen for $B_0/\Beqz\approx0.05$ . " However, even for this case the flux concentrations are barely visible in a single snapshot."," However, even for this case the flux concentrations are barely visible in a single snapshot." This has been one of the reasons why NEMPI has not been noticed before in DNS., This has been one of the reasons why NEMPI has not been noticed before in DNS. " An additional handicap was that the simulations of BKKR used smaller scale separation ratio of only 5, which is neverthelessa still sufficient for the governing mean-field coefficients and allows one to determiningreach larger values of Rey."," An additional handicap was that the simulations of BKKR used a smaller scale separation ratio of only 5, which is nevertheless still sufficient for determining the governing mean-field coefficients and allows one to reach larger values of $\Rm$." " In we plot as a function of Bo/Beo, a at B1/B.q70.05."," In we plot $B_1/\Beq$ as a function of $B_0/\Beqz$, showing a peak at $B_0/\Beqz\approx0.05$." " We recall that Beq applies showinghere to peakthe location Bo/Beqo2€kiz<3 where D, has been evaluated, and there we have Beg/Bego7:0.3."," We recall that $\Beq$ applies here to the location $2\leq k_1z\leq3$ where $B_1$ has been evaluated, and there we have $\Beq/\Beqz\approx0.3$." " The fact that large-scale flux concentrations develop only for a certain of field supports our interpretation that rangethey are imposedcaused by NEMPI strengthsand not, for example, by some unknown mechanism."," The fact that large-scale flux concentrations develop only for a certain range of imposed field strengths supports our interpretation that they are caused by NEMPI and not, for example, by some yet unknown dynamo mechanism." " In all these cases, B—Bo yetgrows rapidly and dynamoreaches a saturation field strength that is independent of Bo, Rej;>35."," In all these cases, $\BB-\BB_0$ grows rapidly and reaches a saturation field strength that is independent of $\BB_0$, provided $\Rm\ge35$." This suggests that this field is produced by providedsmall-scale dynamo action and not just byfield line tangling., This suggests that this field is produced by small-scale dynamo action and not just byfield line tangling. " Another piece of evidence of the physical reality of NEMPI is shown in5,, where we see that B, does indeed increase exponentiallyFigure for the first 2000 turnover times, corresponding to about 37,4."," Another piece of evidence of the physical reality of NEMPI is shown in, where we see that $B_1$ does indeed increase exponentially for the first 2000 turnover times, corresponding to about $3\tautd$." " The growth rate is zz which is much less than 7,;!, but entirely compatible with 0.470k?,mean-field calculations (BKKR;ΚἄργΙᾶal. 2011)."," The growth rate is $\approx0.4\etatz k_1^2$, which is much less than $\tauto^{-1}$, but entirely compatible with mean-field calculations \citep[BKKR;][]{KBKMR11}." ". Finally, to investigate the effects of the domain aspect ratio on the instability, we perform a calculation with 0.05, Rey;=36, and change L,, to 167/k ."," Finally, to investigate the effects of the domain aspect ratio on the instability, we perform a calculation with $B_0/\Beqz=0.05$ , $\Rm=36$, and change $L_x$ to $16\pi/k_1$ ." We findBo/Bego that the most unstable mode has a wavelength approximately equal to L;£z , We find that the most unstable mode has a wavelength approximately equal to $L_z \approx6H_\rho$. "This result is also in agreement with field models 6H,.(e.g.,Fig.14ofKápylàetal.2011)."," This result is also in agreement with mean-field models \citep[e.g., Fig.~14 of][]{KBKMR11}." ". The large-scale flux concentrations have an amplitude of only z:0.1 and are therefore not seen in single snapshots, where B4the field reaches peak strengths comparable to "," The large-scale flux concentrations have an amplitude of only $\approx0.1\Beq$ and are therefore not seen in single snapshots, where the field reaches peak strengths comparable to $\Beq$." "Furthermore, as for any linear instability, the flux concentrationsB4. form a repetitive pattern, but this might be an artifact of idealized conditions."," Furthermore, as for any linear instability, the flux concentrations form a repetitive pattern, but this might be an artifact of idealized conditions." " The simulations have, for the first time, demonstrated presentconclusively that NEMPI can operate in turbulence under proper conditions, namely, strong hydromagneticstratification, sufficient scale separation (here kp/k,= 15), and a mean field in an optimal range (here ~ see 4))."," The present simulations have, for the first time, demonstrated conclusively that NEMPI can operate in hydromagnetic turbulence under proper conditions, namely, strong stratification, sufficient scale separation (here $\kf/k_1=15$ ), and a mean field in an optimal range (here $\approx0.15\Beq$ ; see )." This instability has so far been 0.15Beq;seen in mean-field simulations., This instability has so far onlybeen seen in mean-field simulations. " By contrast, the onlypresent simulations are completely free of any mean-field"," By contrast, the present simulations are completely free of any mean-field" A-ray enilssion may emerge al twosages in the evolion of a supernova: uear the time of the shock breakout aud via circuustellar interaction at a later date.,X-ray emission may emerge at two stages in the evolution of a supernova: near the time of the shock breakout and via circumstellar interaction at a later date. Three different processes generae X-rays: [rom the prompt therual burst: via Comptou-seatered 5-rays from the synthesized matter’W. radioactive decay (lrom whic1 X-rays are emitted while tie debris is optically thick to 2-rays): a [rom the interaction of the slock with circtunstellar iate‘ial in the vicinity of the progenitor., Three different processes generate X-rays: from the prompt thermal burst; via Compton-scattered ${\gamma}$ -rays from the synthesized matter's radioactive decay (from which X-rays are emitted while the debris is optically thick to ${\gamma}$ -rays); and from the interaction of the shock with circumstellar material in the vicinity of the progenitor. Oul SNLOSTA has been seen to euit. X-rays definitely attribued to Compton-scattered 5-rays (Dota et al., Only SN1987A has been seen to emit X-rays definitely attributed to Compton-scattered ${\gamma}$ -rays (Dotani et al. 1987. Nature. 330. 230J.," 1987, Nature, 330, 230)." Two mechanisins exist or the circuimstellar production of N-rays: X-rays from the outgoi[n]€ shock or from the reverse shock (Franssouetal.1996)., Two mechanisms exist for the circumstellar production of X-rays: X-rays from the outgoing shock or from the reverse shock \citep{Fran96}. . Below 10 keV. the reverse shock should be the dominant emitter because the deusity behind the shock is higher. by a [actor of L. than tlT," Below 10 keV, the reverse shock should be the dominant emitter because the density behind the shock is higher, by a factor of $\sim$ 4, than the" have blueshifts (?3..,have blueshifts \citep{Bertram:2007p10319}. There is an offset of z 140 laus! between the two bulge componeuts (80952315 lau + for Ack data739E and 89534515 kin ! for AG 739W)., There is an offset of $\approx$ 40 km $^{-1}$ between the two bulge components $\pm$ 15 km $^{-1}$ for Mrk 739E and $\pm$ 15 km $^{-1}$ for Mrk 739W). The CO also show evidence of two components wit1 the peak brightuess tures similar to the radia1 volocities in the Na Dfepe absorption lines (Figure 5)., The CO data also show evidence of two components with the peak brightness temperatures similar to the radial velocities in the Na D absorption lines (Figure 5). Whe1 fit with gaussiuis. the peaks cousistent with Hiec «aL ) radial velocities (8921422 and SOSOGIG kins in CO 2 αμα 8956412 and 80034022 kms +).," When fit with gaussians, the peaks consistent with the Na D radial velocities $\pm$ 22 and $\pm$ 16 km $^{-1}$ in CO 2–1 and $\pm$ 12 and $\pm$ 22 km $^{-1}$ )." Ilieh resolution (17) iuterferoiietric CO imagine of this svsteii. would xovide evidence to confirin this picture., High resolution $\arcsec$ ) interferometric CO imaging of this system would provide evidence to confirm this picture. — There is als« evidence of outflows in the narrow line region of ας 739E. There is a 192+22 kins 1 blueshift iu the [O ΠΠ ine and a 153425 kins + iu the lower ionization 10 I| A 6300 line compared to the Na D absorption., There is also evidence of outflows in the narrow line region of Mrk 739E. There is a $\pm22$ km $^{-1}$ blueshift in the [O III] line and a $\pm$ 25 km $^{-1}$ in the lower ionization [O I] $\lambda$ 6300 line compared to the Na D absorption. This dueshift is consistent with other nearby QSOs which rave an average [O ΠΠ blueshift of -171 kins + (7)., This blueshift is consistent with other nearby QSOs which have an average [O III] blueshift of -174 km $^{-1}$ \citep{Bertram:2007p10319}. Tu Mykliic739W. there is no evidence of outflows in the JRITOWO region.," In Mrk 739W, there is no evidence of outflows in the narrow line region." Using Chandra and UV photometry aud following T. the bolometric buuinositv is «107 erg s| in Abk 0739E (Figure 5).," Using $\C$ and UV photometry and following \citet{Vasudevan:2009p7223}, the bolometric luminosity is $\times$ $^{45}$ erg $^{-1}$ in Mrk 0739E (Figure 5)." The extinction corrected 2500 A dDuuinositv is logL.us13.7dE0.3., The extinction corrected 2500 $\AA$ luminosity is $\log L_{\mathrm{2500\AA}}=43.7\pm0.3$. Usine ID? aud contimmiunenusson (7). the black hole mass is log My 1.0440.1. ceiving an Eddinetou ratio of Agqq420.71. he highest amones all the Sa/ft BAT selected AGN (?7)..," Using $\beta$ and continuumemission \citep{Vestergaard:2006p11438}, , the black hole mass is log $M_{\mathrm{BH}}$ $\pm$ 0.4, giving an Eddington ratio of $\lambda_{\mathrm{Edd}}$ =0.71, the highest amongs all the $Swift$ BAT selected AGN \citep{Vasudevan:2010p5970}." Our estimates are consistent with ? who fiud Agdq=0.78 using only optical spectra and the same uecthod to determine black hole mass., Our estimates are consistent with \citet{Ho:2008p11625} who find $\lambda_{\mathrm{Edd}}$ =0.78 using only optical spectra and the same method to determine black hole mass. Vucertaitics iu intrinsic dust reddening. as well as the inclination angle and spectral hardening parameter in the accretion disk nodel can lower the Eddinetou ratio at most to Araqa 0.230.," Uncertainties in intrinsic dust reddening, as well as the inclination angle and spectral hardening parameter in the accretion disk model can lower the Eddington ratio at most to $\lambda_{\mathrm{Edd}}$ =0.30." Iu Mrk 739W. the bolometric huninositv is 2410/7 eres usine only the hard N-rav datawitli a xlomietric correction1 factor of 22 frou ?..," In Mrk 739W, the bolometric luminosity is $\times$ $^{43}$ erg $^{-1}$ using only the hard X-ray datawith a bolometric correction factor of 22 from \citet{Vasudevan:2009p7223}. ." (seealso???)..," \citep[see also][]{Koss:2010p7366,Goulding:2009p6170,Veilleux:2009p9544}." erowing wavelength scales as the radius #2 or the isothermal scale height /7 of the evlincler. depending on the ratio 2/H.,"growing wavelength scales as the radius $R$ or the isothermal scale height $H$ of the cylinder, depending on the ratio $R/H$." In the conditions thought to be appropriate to Nessie. the spacing between clumps is predicted to be 4 to 6 pe. in good agreement with the observed spacing of 4.5 pe.," In the conditions thought to be appropriate to Nessie, the spacing between clumps is predicted to be 4 to 6 pc, in good agreement with the observed spacing of 4.5 pc." Because of the ubiquity of the association between Lilamentary molecular clouds: aud hieh-mass star forming regions. il is temptüng (ο suggest that the physics of molecular filaments has a profound influence on cluster formation.," Because of the ubiquity of the association between filamentary molecular clouds and high-mass star forming regions, it is tempting to suggest that the physics of molecular filaments has a profound influence on cluster formation." Indeed. such filaments may be a necessary initial condition to form dense cluster-Iorming cores wilh the observed properties.," Indeed, such filaments may be a necessary initial condition to form dense cluster-forming cores with the observed properties." " We speculate that the ""sausage"" instability may be the dominant physical mechanism {ο produce cores [rom filamentary IRDCs.", We speculate that the “sausage” instability may be the dominant physical mechanism to produce cores from filamentary IRDCs. We suggest an evolutionary sequence in which filamentary IDCs [ragment into cores. which in turn spawn star clusters ancl high-mass stars.," We suggest an evolutionary sequence in which filamentary IRDCs fragment into cores, which in turn spawn star clusters and high-mass stars." " Thus. familiar high-mass star-forming clouds such as Orion may have begun their lives as filamentary IRDCs,"," Thus, familiar high-mass star-forming clouds such as Orion may have begun their lives as filamentary IRDCs." The authors gratefully acknowledge the funding support through NASA grant. NAGS5-10808 and NSF grants AST-0093562. AST-0507657. and AST-0808001.," The authors gratefully acknowledge the funding support through NASA grant NAG5-10808 and NSF grants AST-0098562, AST-0507657, and AST-0808001." The authors are erateful to Prof. Mark Johnson of Northwestern University lor suggesting the idea of varicose instabilities. to Julia. Duval-Roman for her assistance. and (o an anonvmous referee. [or mnuportant suggestions.," The authors are grateful to Prof. Mark Johnson of Northwestern University for suggesting the idea of varicose instabilities, to Julia Duval-Roman for her assistance, and to an anonymous referee for important suggestions." observed to coincide with the phase of photometric light minimum (i.e. phase 0.0 of the photometric ephemeris of DBSS10).,observed to coincide with the phase of photometric light minimum (i.e. phase 0.0 of the photometric ephemeris of DBSS10). " The activity indicators measured from Ca H K, the Ca IR triplet and Ha are shown to vary with small amplitude and in phase with |B;|."," The activity indicators measured from Ca H K, the Ca IR triplet and $\alpha$ are shown to vary with small amplitude and in phase with $|B_{\ell}|$." " However some strong deviations are observed, which may suggest episodes of flares."," However some strong deviations are observed, which may suggest episodes of flares." " The radial velocity also varies in a reasonably coherent way according to the photometric ephemeris, but with a phase delay of about 0.1 cycles."," The radial velocity also varies in a reasonably coherent way according to the photometric ephemeris, but with a phase delay of about 0.1 cycles." " For our Zeeman Doppler imaging (ZDI) investigation we used the 308.8 d photometric period (DBSS10) which is similar to our best rotational period, based on of-fit of the ZDI maps, of about 311 d. For all the described models we find that the large scale magnetic field of EK Eri is poloidal (more than 98 % of the magnetic energy is contained in this component)."," For our Zeeman Doppler imaging (ZDI) investigation we used the 308.8 d photometric period (DBSS10) which is similar to our best rotational period, based on quality-of-fit of the ZDI maps, of about 311 d. For all the described models we find that the large scale magnetic field of EK Eri is poloidal (more than 98 $\%$ of the magnetic energy is contained in this component)." " In addition, the surface magnetic field variations of EK Eri appear to be dominated by a strong magnetic spot (of negative polarity) which is phased with the darker, redder (and therefore presumably cool) photometric spot."," In addition, the surface magnetic field variations of EK Eri appear to be dominated by a strong magnetic spot (of negative polarity) which is phased with the darker, redder (and therefore presumably cool) photometric spot." The ratio between dipolar and quadrupolar components of the magnetic field increases with decreasing value of the rotational axis inclination 4., The ratio between dipolar and quadrupolar components of the magnetic field increases with decreasing value of the rotational axis inclination $i$. " Whereas the quadrupolar component dominates for i greater than 80?, for i — 60?, we obtain a model that is almost purely dipolar."," Whereas the quadrupolar component dominates for $i$ greater than $^\circ$, for $i$ = $^\circ$, we obtain a model that is almost purely dipolar." " In the dipolar model, the photometric spot at phase 0 corresponds to the pole of negative polarity of the dipole, which could be the remnant of that of the Ap star progenitor of EK Eri."," In the dipolar model, the photometric spot at phase 0 corresponds to the pole of negative polarity of the dipole, which could be the remnant of that of the Ap star progenitor of EK Eri." The evolution of a magnetic (2 Μο) Ap star from the main sequence to the red giant branch is characterized by a surface magnetic field which is expected to weaken (as 1/R? if conservation of magnetic flux is assumed) while the convective envelope deepens., The evolution of a magnetic (2 $M_{\odot}$ ) Ap star from the main sequence to the red giant branch is characterized by a surface magnetic field which is expected to weaken (as $1/R^{2}$ if conservation of magnetic flux is assumed) while the convective envelope deepens. The rotational period of the surface also lengthens as the star expands., The rotational period of the surface also lengthens as the star expands. " For an Ap star progenitor of EK Eri, one can infer a magnetic field of several thousand gauss and a very thin convective envelope on the main sequence (Stepieá 1993, Aurierre et al."," For an Ap star progenitor of EK Eri, one can infer a magnetic field of several thousand gauss and a very thin convective envelope on the main sequence (Stepień 1993, Aurièrre et al." 2008)., 2008). " At the main sequence evolutionary stage, the magnetic field would be sufficient to suppress convection (e.g. discussion by Théaado et al."," At the main sequence evolutionary stage, the magnetic field would be sufficient to suppress convection (e.g. discussion by Théaado et al." 2005)., 2005). " At the present evolutionary stage of EK Eri we measure a large scale surface magnetic field dominated (for i= 60°) by a dipole of about 200 G strength, when the convective envelope of our 2 Mo model contains ~0.37 Mo of the star’s mass (Auriérre et al."," At the present evolutionary stage of EK Eri we measure a large scale surface magnetic field dominated (for $i=60^\circ$ ) by a dipole of about 200 G strength, when the convective envelope of our 2 $M_{\odot}$ model contains $\sim 0.37$ $M_{\odot}$ of the star's mass (Aurièrre et al." 2008)., 2008). The outstanding magnetic activity properties of EK Eri are therefore the result of the interplay of the remaining magnetic field from one Ap star and deep convection., The outstanding magnetic activity properties of EK Eri are therefore the result of the interplay of the remaining magnetic field from one Ap star and deep convection. Such an interaction between a pre- magnetic field and thermal convection has been studied through numerical simulations mostly in the solar, Such an interaction between a pre-existing magnetic field and thermal convection has been studied through numerical simulations mostly in the solar In chemical physics literature HCOOH hydrogenation on catalytic surfaces has been shown to lead to decomposition of HCOOH rather than methanediol formation (Benitezetal.. 1993).,In chemical physics literature HCOOH hydrogenation on catalytic surfaces has been shown to lead to decomposition of HCOOH rather than methanediol formation \citep{benitez1993}. . HCOOH adsorbs onto such a surface as HCOO™ and H which can be further hydrogenated., HCOOH adsorbs onto such a surface as $^-$ and $^+$ which can be further hydrogenated. The catalytic surface. however. clearly affects the end products and overcomes a reaction barrier that prohibits spontaneous decomposition.," The catalytic surface, however, clearly affects the end products and overcomes a reaction barrier that prohibits spontaneous decomposition." If hydrogen atom addition and dissociation occur simultaneously. C-O bond cleavage is more energetically favorable (as shown in Fig. 6)).," If hydrogen atom addition and dissociation occur simultaneously, C–O bond cleavage is more energetically favorable (as shown in Fig. \ref{energy-hcooh}) )." However. it is clear from the results in 5.1. that no H:O and H2CO formation occurs.," However, it is clear from the results in \ref{hcooh_res} that no $_2$ O and $_2$ CO formation occurs." Thus a high barrier for H-addition to HCOOH must exist for both mechanisms and HCOOH + H reactions in the ice are inefficient., Thus a high barrier for H-addition to HCOOH must exist for both mechanisms and HCOOH $+$ H reactions in the ice are inefficient. The infrared spectroscopic features detected for pure CH;CHO ice match with those detected by Bennettetal.(2005)and Moore&Hudson(1998.2003).," The infrared spectroscopic features detected for pure $_3$ CHO ice match with those detected by \citet{bennett2005a} and \citet{moore1998,moore2003}." . The strongest CH;CHO band is the C=O stretching mode. vs(C=O). at 1728 em! (5.79 pm).," The strongest $_3$ CHO band is the C=O stretching mode, $\nu_{\rm S}$ (C=O), at 1728 $^{-1}$ (5.79 $\mu$ m)." During H-atom bombardment the intensity decreases. but a small positive wing is observed at 1710 em! (see Fig. 7)).," During H-atom bombardment the intensity decreases, but a small positive wing is observed at 1710 $^{-1}$ (see Fig. \ref{ch3chobomb}) )." This band ts assigned to the C=O stretching mode of HCO., This band is assigned to the C=O stretching mode of $_2$ CO. " Other CH3CHO features (e.g.. the umbrella deformation mode. vp. at 1345 em!) also decrease and new bands appear at 1030 and 1300 em! that are attributed to the C-O stretching mode of CH;OH and the deformation mode of CH,. respectively."," Other $_3$ CHO features (e.g., the umbrella deformation mode, $\nu_{\rm D}$, at 1345 $^{-1}$ ) also decrease and new bands appear at 1030 and 1300 $^{-1}$ that are attributed to the C–O stretching mode of $_3$ OH and the deformation mode of $_4$, respectively." No clear absorption is observed at 1050 em!. where the strongest C4H3OH band. the C—O stretching mode. is expected.," No clear absorption is observed at 1050 $^{-1}$, where the strongest $_2$ $_5$ OH band, the C–O stretching mode, is expected." " Since this frequency region is particularly problematic in our detector. the detection upper limit on N(C+HsOH) amounts to only 3x10"" molecules em. i.e.. 3 ML."," Since this frequency region is particularly problematic in our detector, the detection upper limit on $N$ $_2$ $_5$ OH) amounts to only $\times$ $^{15}$ molecules $^{-2}$, i.e., 3 ML." Another strong band of C:HsOH is expected at 3.5 gm. Unfortunately. this feature overlaps with a number of CH;OH modes.," Another strong band of $_2$ $_5$ OH is expected at 3.5 $\mu$ m. Unfortunately, this feature overlaps with a number of $_3$ OH modes." Broad weak features are indeed detected in this range. but due to the complexity of both C4H&OH and CH;OH absorptions and the relatively weak signal this cannot be used to determine whether C3Hs;OH its present.," Broad weak features are indeed detected in this range, but due to the complexity of both $_2$ $_5$ OH and $_3$ OH absorptions and the relatively weak signal this cannot be used to determine whether $_2$ $_5$ OH is present." Additionally. it is important to note that no strong features are observed around 2140 em7!. where both CO and CH>CO have infrared features.," Additionally, it is important to note that no strong features are observed around 2140 $^{-1}$, where both CO and $_2$ CO have infrared features." This is perhaps not surprising. because the formation of CO would involve not only the breaking of a C-C bond. but also hydrogen-abstraction. which 15 not very likely in this hydrogen-rich environment.," This is perhaps not surprising, because the formation of CO would involve not only the breaking of a C–C bond, but also hydrogen-abstraction, which is not very likely in this hydrogen-rich environment." The formation of ketene. CH;CO. is even less likely because its formation is strongly endothermic.," The formation of ketene, $_2$ CO, is even less likely because its formation is strongly endothermic." The formation of CH;. H:CO and CH3iOH its corroborated by the TPD spectra. where 16. 30 and 31 amu mass peaks at 45 K. 100 K and I40 K are found. respectively (see Fig.," The formation of $_4$ , $_2$ CO and $_3$ OH is corroborated by the TPD spectra, where 16, 30 and 31 amu mass peaks at 45 K, 100 K and 140 K are found, respectively (see Fig." " 8 for CH, and CH;OH).", \ref{tpd} for $_4$ and $_3$ OH). The peaks for 16 amu at, The peaks for 16 amu at this instance).,this instance). This. along with the observation that our characteristic radius r;—reafe exceeds the larger of the softening lengths by an order of magnitude. leads us to rule out excessive softening as the cause for our value of e.," This, along with the observation that our characteristic radius $r_s \equiv r_{200}/c$ exceeds the larger of the softening lengths by an order of magnitude, leads us to rule out excessive softening as the cause for our lower-than-expected value of $c$." There should. be no need. to add. power down to the xuticle Nyquist wavenumber., There should be no need to add power down to the particle Nyquist wavenumber. The short-wavelength cutoll or our original 128 grid in à 45.+ Alpe box corresponds o à characteristic mass of about 1.70AZ.. less than “the virial mass of our haloes.," The short-wavelength cutoff for our original $128^3$ grid in a $4 h^{-1}$ Mpc box corresponds to a characteristic mass of about $1.7\times 10^7\Msun$, less than of the virial mass of our haloes." Iteproducing the NEW wolile is expected. to require resolving the collapse of a wogenitor with of the final virial mass: our limiting wavelength: is just small enough to achieve this., Reproducing the NFW profile is expected to require resolving the collapse of a progenitor with of the final virial mass; our limiting wavelength is just small enough to achieve this. Adding power on even smaller scales would force us to start the simulations at a higher redshift. which in turn would require smaller particle softenings and a larger number of particles o counter collisional relaxation.," Adding power on even smaller scales would force us to start the simulations at a higher redshift, which in turn would require smaller particle softenings and a larger number of particles to counter collisional relaxation." Although our changes to the time step selection criterion lead to a more efficient. distribution of individual xuwticle time steps. we used a value of the overall tolerance xwameter at the high. end. of the permissible range.," Although our changes to the time step selection criterion lead to a more efficient distribution of individual particle time steps, we used a value of the overall tolerance parameter at the high end of the permissible range." " We herefore. repeated: once of our runs with a much smaller olerance. resulting in a sixteen-fold. decrease in time step (rom +10"" to 2.510 vears)."," We therefore repeated one of our runs with a much smaller tolerance, resulting in a sixteen-fold decrease in time step (from $4\times 10^6$ to $2.5\times 10^5$ years)." For the first. Gyr. no dilference was observed in the density. profiles with respect o the run with larger time steps: but starting at a redshift 2o4 the results began to diverge.," For the first Gyr, no difference was observed in the density profiles with respect to the run with larger time steps; but starting at a redshift $z\sim 4$ the results began to diverge." The less accurate run evolved: towards the shallow. pxr cusp of the NEW oofile while the new run maintained a central logarithmic slope much closer to 2.," The less accurate run evolved towards the shallow, $\rho \propto r^{-1}$ cusp of the NFW profile while the new run maintained a central logarithmic slope much closer to $-2$." X run with an intermediate choice of time step gave results in agreement with the smaller-olerance run. suggesting that results may have converged (or else that they are now limited. by a parameter other han the time >granularity of the simulation).," A run with an intermediate choice of time step gave results in agreement with the smaller-tolerance run, suggesting that results may have converged (or else that they are now limited by a parameter other than the time granularity of the simulation)." This seems to confirm the results of Pukushige Makino (1997).. and clearly deserves further investigation.," This seems to confirm the results of Fukushige Makino \shortcite{FM97}, and clearly deserves further investigation." We plan to address this issue in. more detail in a forthcoming paper., We plan to address this issue in more detail in a forthcoming paper. A second run with initial conditions from one of our other haloes. however. vielded a profile more similar to that of NEW with a concentration c7ὃν (," A second run with initial conditions from one of our other haloes, however, yielded a profile more similar to that of NFW with a concentration $c\sim 8$. (" This halo still displavs a mass excess at small radii however.,"This halo still displays a mass excess at small radii, however." Figure ο shows the clensitw profiles. for these two runs.), Figure \ref{f:rho3h} shows the density profiles for these two runs.) H0 appears therefore that at. least. some haloes are reasonably (but not outstandinglv) well fitted by NEW profiles. and that for such haloes the concentration increases only moderately if smaller time steps are used.," It appears therefore that at least some haloes are reasonably (but not outstandingly) well fitted by NFW profiles, and that for such haloes the concentration increases only moderately if smaller time steps are used." Aloreover. we have no particular reason for favouring f=3.0 Gyr as the time at which the disk began to form: we could equally have picked an earlier time. when the concentration parameter e was smaller (but not smaller. as that turns out to require unreasonably high initial redshifts).," Moreover, we have no particular reason for favouring $t=3.0$ Gyr as the time at which the disk began to form: we could equally have picked an earlier time, when the concentration parameter $c$ was smaller (but not smaller, as that turns out to require unreasonably high initial redshifts)." Or the true cosmological model could be one in which haloes in this range of masses collapse later. and therefore have smaller e values. than in standard CD.," Or the true cosmological model could be one in which haloes in this range of masses collapse later, and therefore have smaller $c$ values, than in standard CDM." This is the case in particular for the more favoured A-CDAL models. in which O«1 and the cosmological constant iX is of the right magnitude to make the model Hat.," This is the case in particular for the more favoured $\Lambda$ -CDM models, in which $\Omega<1$ and the cosmological constant $\Lambda$ is of the right magnitude to make the model flat." Open CDM models may also be suitable in this perspective., Open CDM models may also be suitable in this perspective. We therefore. proceed. with the analysis of our main series of runs. having no serious grounds for rejecting €~4 haloes as a valid starting point for disk growth.," We therefore proceed with the analysis of our main series of runs, having no serious grounds for rejecting $c\sim 4$ haloes as a valid starting point for disk growth." For completeness we also. performed. a lew experiments. with the more concentrated. haloes from. the shorter time step integrations., For completeness we also performed a few experiments with the more concentrated haloes from the shorter time step integrations. Dhese experiments are computationally much more expensive than our previous ones. ancl we could only perform a small number of them.," These experiments are computationally much more expensive than our previous ones, and we could only perform a small number of them." We shall briefly. discuss the main dillerences in the results., We shall briefly discuss the main differences in the results. We compare the rotation curves from our simulation runs with the observations of Carignan Beaulicu (1989).. as updated by Carignan Purton (1997.asreported.in 38)..," We compare the rotation curves from our simulation runs with the observations of Carignan Beaulieu \shortcite{CB89}, as updated by Carignan Purton \shortcite[as reported in BS]{CP97}." For the purpose of estimating the mass and. the characteristic length scale we place at a distance of 4 Alpe. consistent with photometric data (Carignan&Beaulicu1989:Hopp&Schultce-Lacdbeck 1995).," For the purpose of estimating the mass and the characteristic length scale we place at a distance of 4 Mpc, consistent with photometric data \cite{CB89,HS95}." The published rotation curve data are accompanied by error estimates: we use these in computing a formal 4? sum for each of our simulated rotation curves., The published rotation curve data are accompanied by error estimates; we use these in computing a formal $\chi^2$ sum for each of our simulated rotation curves. We caution. however. against taking these X7E values too Literally.," We caution, however, against taking these $\chi^2$ values too literally." The measure relies on the published uncertainties in the rotation curve. and. is therefore dominated by the nominally better data from the inner regions.," The measure relies on the published uncertainties in the rotation curve, and is therefore dominated by the nominally better data from the inner regions." Lt also assumes a Ciaussian distribution of errors. which may. be unrealistic.," It also assumes a Gaussian distribution of errors, which may be unrealistic." Finally. it does not take into account the scatter in the numerical models. which is expected to be larger in the inner regions," Finally, it does not take into account the scatter in the numerical models, which is expected to be larger in the inner regions" density of Lx10I e ? during the flare (Allvecl et al.,density of $1 \times 10^{-10}$ g $^{-3}$ during the flare (Allred et al. 2006) and a Mg II emitting region ol height 300 km (see Figures LO and 11 below) along with a flare area of of the visible stellar surface. the kinetic energy. implied by chromospheric material moving al such large velocities [ar exceeds the energy radiated by the flare. by several orders of magnitude.," 2006) and a Mg II emitting region of height 300 km (see Figures 10 and 11 below) along with a flare area of of the visible stellar surface, the kinetic energy implied by chromospheric material moving at such large velocities far exceeds the energy radiated by the flare, by several orders of magnitude." Wood et al. (, Wood et al. ( 1996) found that the Mg II h and k lines in IL. 1099. an active RS CVn binary svstem. showed a broad component during quiescence that looked similar to the broad components observed in the C IV. transition region resonance lines. with FWIIM ~ 170 km Ll.,"1996) found that the Mg II h and k lines in HR 1099, an active RS CVn binary system, showed a broad component during quiescence that looked similar to the broad components observed in the C IV transition region resonance lines, with FWHM $\sim$ 170 km $^{-1}$." They were skeptical. as we are. that the dense. optically thick chromosphere could respond to explosive microflaring events to drive mass motions al (hese velocities. and carried out. detailed modelling that led them (o suggest that opacity effects in the line wings mieht account for the observed broadening.," They were skeptical, as we are, that the dense, optically thick chromosphere could respond to explosive microflaring events to drive mass motions at these velocities, and carried out detailed modelling that led them to suggest that opacity effects in the line wings might account for the observed broadening." Again however. these elfects were associated with the star in quiescence. not in the midst of an obvious strong Llare.," Again however, these effects were associated with the star in quiescence, not in the midst of an obvious strong flare." Recently. Allred οἱ al. (," Recently, Allred et al. (" 2005. 2006) produced models of solar ancl stellar [Lares aimed at understanding the chromospheric and transition region emission.,"2005, 2006) produced models of solar and stellar flares aimed at understanding the chromospheric and transition region emission." The models use solutions to the 1-D equations of radiative hvdrodynamics. including non-LTE radiative transfer in LL. He and Ca IL with flare heating provided by an electron beam.," The models use solutions to the 1-D equations of radiative hydrodynamics, including non-LTE radiative transfer in H, He and Ca II, with flare heating provided by an electron beam." The results include predictions of atmospheric structure (temperature. density. profiles). velocity and line profiles at many lime steps during an episode of flare heating.," The results include predictions of atmospheric structure (temperature, density profiles), velocity and line profiles at many time steps during an episode of flare heating." We used the results of their preflare and E10 models (o investigate the Mg II Kk emission curing the YZ CAL flares., We used the results of their preflare and F10 models to investigate the Mg II k emission during the YZ CMi flares. The F10 model used here represents an average mid-flave atmosphere near a time step of 85 sec: see Allred et al. (, The F10 model used here represents an average mid-flare atmosphere near a time step of $\sim$ 85 sec; see Allred et al. ( 2006).,2006). Note that the FLO model refers to electron beam heating of LOM eres ! 7 during the model flare ancl is not to be confused with our observed FLO flare presented in Section 2 above., Note that the F10 model refers to electron beam heating of $^{10}$ ergs $^{-1}$ $^{-2}$ during the model flare and is not to be confused with our observed F10 flare presented in Section 2 above. Since the Allred et al., Since the Allred et al. models do not predict Meg LII emission line profiles. the preflare and F10 models were futher analvzed with the “RIP non-LTE radiative transler code described in Uitenbroek (2001).," models do not predict Mg II emission line profiles, the preflare and F10 models were further analyzed with the `RH' non-LTE radiative transfer code described in Uitenbroek (2001)." The RII code is based on the Multi-level Accelerated Lambda (NALLI) formalism of Bybicki ποτ (1991. 1992). which allows both bound-bound aud radiative (ransilions to overlap in wavelength.," The RH code is based on the Multi-level Accelerated Lambda (MALI) formalism of Rybicki Hummer (1991, 1992), which allows both bound-bound and bound-free radiative transitions to overlap in wavelength." It also includes the effects of partial redistribution for strong bound-bound transitions such as Mg II h and k. Figure 10 shows the temperature and densitwv (electron. hvdrogen) structure of the preflare atinosphere. together with the resulüing Ale II k line profile and (he contribution function.," It also includes the effects of partial redistribution for strong bound-bound transitions such as Mg II h and k. Figure 10 shows the temperature and density (electron, hydrogen) structure of the preflare atmosphere, together with the resulting Mg II k line profile and the contribution function." Figure 11 is a similar plot for the model E10 flaring atmosphere., Figure 11 is a similar plot for the model F10 flaring atmosphere. The contribution, The contribution inconsistent with the continuous star formation rate model.,inconsistent with the continuous star formation rate model. Applying the relation between aand tine since truncation. 1.0. Figure 6 solid curve. we conclude that star formation ceased at least LOO Ny ago at R25 kpce.," Applying the relation between and time since truncation, i.e. Figure \ref{fig:agemeasures} solid curve, we conclude that star formation ceased at least 100 Myr ago at $R > 5$ kpc." The 778 equivalent width varies iiucli like in Fieure 6 owing to its simular origin., The $H\delta$ equivalent width varies much like in Figure \ref{fig:agemeasures} owing to its similar origin. The eeracdicnt continues towards the center of IRAS 233653601.| and we interpret this as evidence that the nue since tfruncation decreases towards the center.," The gradient continues towards the center of IRAS 23365+3604, and we interpret this as evidence that the time since truncation decreases towards the center." Iu other words. star formation is apparently being shutdown roni the outside msvairds.," In other words, star formation is apparently being shutdown from the outside inwards." Another popular diaenostic ofstellar age is the spectral xeak known as DLOOV, Another popular diagnostic of stellar age is the spectral break known as D4000. " Our spectral bandpass does not completely cover this απο, but we can use the stellar x»pulation models along with our observed treud iu Bahuer equivalent widh to predict the radial variation im Dlo00."," Our spectral bandpass does not completely cover this feature, but we can use the stellar population models along with our observed trend in Balmer equivalent width to predict the radial variation in D4000." " The DLOO0 παςex grows as the stellar population ages,", The D4000 index grows as the stellar population ages. Measurements o: DIOOD break the age degeucracy o either side of the maxima in aat LOO Ny., Measurements of D4000 break the age degeneracy to either side of the maximum in at 400 Myr. Hence. we expect D1000 would show a steady increase with 1wcreasing radius in ULIRGs.," Hence, we expect D4000 would show a steady increase with increasing radius in ULIRGs." Our simple stellar populations represent the most extreme limiting cases., Our simple stellar populations represent the most extreme limiting cases. A declining star formation rate produces a rising ssituilar to our models with complete cessation., A declining star formation rate produces a rising similar to our models with complete cessation. The stronger the rate of change in the star formation rate. the closer the ccolnes to that of the truncated. model.," The stronger the rate of change in the star formation rate, the closer the comes to that of the truncated model." We can distinguish these two star formation historics by the absence/prescnce of Balmer ciission in our ULIRG spectra., We can distinguish these two star formation histories by the absence/presence of Balmer emission in our ULIRG spectra. The presence of nebular emission indicates the level of ongoing star formation., The presence of nebular emission indicates the level of ongoing star formation. Complete truncatiou of star formation activity reduces the ionization rate. and Balmer cinission ceases.," Complete truncation of star formation activity reduces the ionization rate, and Balmer emission ceases." We examine the radial depedence of the implied star formation rate ealaxy by ealaxy., We examine the radial depedence of the implied star formation rate galaxy by galaxy. Iu Section 3. we identified 10 galaxies having extracted spectra in a least four apertures with SNR = 5.," In Section 3, we identified 10 galaxies having extracted spectra in a least four apertures with SNR $\geq$ 5." Pre-uerecr and merger svstenis dominate this spatially resolved subsample., Pre-merger and merger systems dominate this spatially resolved subsample. We discuss the recent star formation ustory in each individually here., We discuss the recent star formation history in each individually here. For reference. Table 2. lists the measured star formation rate and stellar »pulatiou ages for different apertures in each object.," For reference, Table \ref{tab:posdep} lists the measured star formation rate and stellar population ages for different apertures in each object." The star formation rates near the center should be reated cautiously due to two nuportaut svsteniatic errors., The star formation rates near the center should be treated cautiously due to two important systematic errors. First. au active galactic nucleus may contribute o the ionizing photon lLunuinositw. thereby boxvceriug he inferred star formation rate.," First, an active galactic nucleus may contribute to the ionizing photon luminosity, thereby lowering the inferred star formation rate." Second. the reddening neasuredl by the Bahuer decrement im the central aperature reflects onlv the least obsured reeious: the extinction may be too high in some regious for Balucr photons to escape causing us to underestinate the central star formation rate.," Second, the reddening measured by the Balmer decrement in the central aperature reflects only the least obsured regions; the extinction may be too high in some regions for Balmer photons to escape causing us to underestimate the central star formation rate." These factors have little inpact on our analysis of spectra extracted outside ofthe central kiloparsec aud our discussion of radial eraclicuts., These factors have little impact on our analysis of spectra extracted outside of the central kiloparsec and our discussion of radial gradients. Our results sugeest the following star formation histories., Our results suggest the following star formation histories. This ULIRG has two EK baud uuclei separatedi by z Uspc., This ULIRG has two K band nuclei separated by $\approx$ 4kpc. " These two nuclei host star formation of L83E(0.05 and G822.1 ffor the brighter south-east nucleus and diuuaer uorth west uucleus respectively,", These two nuclei host star formation of $4.83 \pm 0.05$ and $6.8 \pm 2.1$ for the brighter south-east nucleus and dimmer north west nucleus respectively. The relative diuness in the visible baud of the southeast nucleus is due to high levels of extinction by dust., The relative dimness in the visible band of the southeast nucleus is due to high levels of extinction by dust. The brighter nucleus in the iuteraction has 5.0x0.1 wwhich indicates that star formation lias been going ou for 0.22£0.02 Cyr., The brighter nucleus in the interaction has $5.0 \pm 0.1$ which indicates that star formation has been going on for $0.22 \pm 0.02$ Gyr. At 7 kpc. however. there is little to no star formation occuring eureutlv.," At 7 kpc, however, there is little to no star formation occurring currently." indicates that 0.200.1 Car has passed since tzuncation., indicates that $0.2 \pm 0.1$ Gyr has passed since truncation. From detailed analyses of galactic relative welocities and tidal tail characteristics. it is deternuned that 16-0623 has gone through pericenter in the ITRAS200last few times 105 vears (7).," From detailed analyses of galactic relative velocities and tidal tail characteristics, it is determined that IRAS20046-0623 has gone through pericenter in the last few times $10^{7}$ years \citep{murphy01}." The separated nuclei are masked within the extended ceutral bulge that appears in 6hi I& baud aud R baud imagine., The separated nuclei are masked within the extended central bulge that appears in both K band and R band imaging. The morphology of the exteuded tails are represcutative of two nearly orthogonal disks in the process of mcreie., The morphology of the extended tails are representative of two nearly orthogonal disks in the process of merging. Peaks in star formation (3.95+0.05 and 8.2+7 23) occur in the uuelei indicated in 7.., Peaks in star formation $3.95 \pm 0.05$ and $8.3 \pm 0.7$ ) occur in the nuclei indicated in \cite{murphy01}. As shown iu figure 2., As shown in figure \ref{fig:ew_im}. .c. these nuclear regions have that indicate star formation has continued for 0.158 403 Carr and 0.36 4 0.07 Cr.," .c, these nuclear regions have that indicate star formation has continued for 0.18 $\pm$ 0.03 Gyr and 0.36 $\pm$ 0.07 Gyr." In the outer regions ~ 2 kpc bevoud both nuclei. star formation is weaker. aud hei iis bevoud that attainable bv CSF.," In the outer regions $\sim$ 2 kpc beyond both nuclei, star formation is weaker, and their is beyond that attainable by CSF." The truucation time scale indicated by these measurements for these bius are Toni NO to LOO Myr., The truncation time scale indicated by these measurements for these bins are from 80 to 100 Myr. Galactic dust contributes ~ 0.16 naguitudes of extinction at the redshifted wavelength ofIIo., Galactic dust contributes $\sim$ 0.16 magnitudes of extinction at the redshifted wavelength of. .. Tho amorpholoev of the K-band nuage shows a single nucleus. implying that the two ealaxies have fully inerged.," The morphology of the K-band image shows a single nucleus, implying that the two galaxies have fully merged." Simularly we see one ceutrally located position on the slit with continuing star ormatiou., Similarly we see one centrally located position on the slit with continuing star formation. The SNR for this object males ddifücult to measure. but the nuclear micasurement im his object does appear slightly lower than the extended reeions.," The SNR for this object makes difficult to measure, but the nuclear measurement in this object does appear slightly lower than the extended regions." This difference is uot significaut chough to neasure a gradient in the population age. so we estimate an overall age of LOO Myr since star formation stopped across the disk.," This difference is not significant enough to measure a gradient in the population age, so we estimate an overall age of 100 Myr since star formation stopped across the disk." Galactic dust contributes ~ 0.31 naguitudes of extinction at the redshifted wavelength ofIIa., Galactic dust contributes $\sim$ 0.31 magnitudes of extinction at the redshifted wavelength of. This galaxy has a sinele EK baud micleus withπα diffuse disturbed regions around it in the R baud., This galaxy has a single K band nucleus withmany diffuse disturbed regions around it in the R band. The aperture with peak star formation (0.GI20.03. 7)) is adjacent to the region with the ΠΙΟ... CL7£0.2 A) which corresponds to 170430 Myr. of continuous star formation (Figure 2., The aperture with peak star formation $0.64 \pm 0.03$ ) is adjacent to the region with the smallest $4.7 \pm 0.2$ ) which corresponds to $170 \pm 30$ Myr of continuous star formation (Figure \ref{fig:ew_im}. 0)., .e). Next to the Ix baud ceutroid at the mas of the R baud coutiuummna == οσο aand the star formation is diminished to 0.016—0.00372, Next to the K band centroid at the max of the R band continuum = $6.6 \pm 0.3$ and the star formation is diminished to $0.016 \pm 0.003$. This aperture shows an underbug population| with a truuncation time scale of 57+10 Myr.," This aperture shows an underlying population with a truncation time scale of $ 57 \pm 10 $ Myr." The furthest aperture with a center 1.25 kpe from the uucleus has a slightly larger aand very little star formation. making the time since truneation of this population slightlv lareer at 100 + 35 Myr.," The furthest aperture with a center 4.25 kpc from the nucleus has a slightly larger and very little star formation, making the time since truncation of this population slightly larger at 100 $\pm$ 35 Myr." Galactic dust contributes 0.67 magnitudes of extinction at the redshifted wavelength of Π, Galactic dust contributes $\sim$ 0.67 magnitudes of extinction at the redshifted wavelength of . α... Το ἵνα morphology. is a suele nucleus with the R baud revealing a faint tidal, The K-band morphology is a single nucleus with the R band revealing a faint tidal 10 km objects and another 35 Myr to produce 100 km objects.,10 km objects and another 3–5 Myr to produce 100 km objects. Continued stirring reduces eravitational focusing [actors., Continued stirring reduces gravitational focusing factors. Collisions between the leftover planetesimals produce debris instead of mergers., Collisions between the leftover planetesimals produce debris instead of mergers. Runaway growth ends and the collisional cascade begins., Runaway growth ends and the collisional cascade begins. During the collisional cascade. the mass in 110 km and smaller objects declines precipitously.," During the collisional cascade, the mass in 1–10 km and smaller objects declines precipitously." Because gravitational locusing factors are small. collisions between. (wo planetesimals are more likely (han collisions between a planetesimal and a LOO1000 km protoplanet.," Because gravitational focusing factors are small, collisions between two planetesimals are more likely than collisions between a planetesimal and a 100–1000 km protoplanet." Thus. disruptive collisions grind leftover planetesimals into small dust grains. which are removed by raciation pressure and Povutine-Robertson drag (e.g..Burns.Lamy.&Artvinowiez 2001).," Thus, disruptive collisions grind leftover planetesimals into small dust grains, which are removed by radiation pressure and Poynting-Robertson drag \citep[e.g.,][]{bur79,tak01}." . At 4050 AU. the surface density falls bv a factor of two in LOO200 Myr. a factor of 45 in 1 Gyr. and more than an order of magnitude in 34 Gyr 2004).," At 40–50 AU, the surface density falls by a factor of two in 100–200 Myr, a factor of 4–5 in 1 Gyr, and more than an order of magnitude in 3–4 Gyr \citep[see also][]{kb04}." . After 4.5 Gyr. the tvpical amount of solid material remaining al 4050 AU is to of the initial mass (see below).," After 4.5 Gyr, the typical amount of solid material remaining at 40–50 AU is to of the initial mass (see below)." As collisions and radiation remove material from the svstem. the largest objects continue {ο grow slowly.," As collisions and radiation remove material from the system, the largest objects continue to grow slowly." In most calculations. it takes 1050 Myr to produce the first 1000 km object.," In most calculations, it takes 10–50 Myr to produce the first 1000 km object." The largest objects then double their mass everv LOO Myr to 1 Gyr., The largest objects then double their mass every 100 Myr to 1 Gyr. " After 4.5 Gvr. the largest objects have radii ranging from ~ LOO km (Qi0."," As shown below, we find evidence for $M_{cut} > 0$." " Half of haloswith mass ων host central LRGs. and σα quantifies the width of the transition from N4,CM)=0 to νι)=1."," Half of haloswith mass $M_{min}$ host central LRGs, and $\sigma_{log M}$ quantifies the width of the transition from $N_{cen}(M) = 0$ to $N_{cen}(M) = 1$." " AL, sets (he mass scale at which satellite ealaxies become probable. aud. M4; sels a cut-off below which halos do not host satellites."," $M_1$ sets the mass scale at which satellite galaxies become probable, and $M_{cut}$ sets a cut-off below which halos do not host satellites." " In the case M5AL, and M4>ALi, we expect a=1. or (he number of satellite galaxies to be proportional to the halo 1»(ANMXLRGsalN(ÀM)) is assumed to be Poisson distributed: (his assumption is supported by the distribution of subhalo counts in simulations (2). as well as observations (??).."," In the case $M \gg M_{cut}$ and $M_1 \gg M_{min}$, we expect $\alpha = 1$, or the number of satellite galaxies to be proportional to the halo $P(N_{LRG,sat}|N(M))$ is assumed to be Poisson distributed; this assumption is supported by the distribution of subhalo counts in simulations \citep{kravtsov/etal:2004} as well as observations \citep{lin/mohr/stanford:2004,ho/etal:2007}." " Often statistics are used to fit the HOD: they depend only on the first ancl second moments of PUN,pe;AL).", Often two-point statistics are used to fit the HOD; they depend only on the first and second moments of $P(N_{LRG}|M)$. The technique we present here to constrain the LOD. Counts-Imn-Cvlinders. makes use of higher-order statistics in the galaxy distribution.," The technique we present here to constrain the HOD, Counts-In-Cylinders, makes use of higher-order statistics in the galaxy distribution." This technique has excellent constraining power [for (he parameters of Ny. but is dependent upon the accuracy. of the Poisson assumption for deriving accurate LOD parameters.," This technique has excellent constraining power for the parameters of $N_{sat}$, but is dependent upon the accuracy of the Poisson assumption for deriving accurate HOD parameters." Using the Poisson assumption. the expected number of halos with IN;=1 satellites is given bv Equ.," Using the Poisson assumption, the expected number of halos with $N_{sat} = n$ satellites is given by Eqn." 10 is central to our maximum likelihood analysis described in 2.6.., \ref{satexp} is central to our maximum likelihood analysis described in \ref{maximumL}. " The CiCmethod constrains only the HOD parameters in ;|NG,,LM).", The CiCmethod constrains only the HOD parameters in $N_{sat}(M)$ . " In this work we fix the \.,,, parameters {ων and σι bv matching the observed 57 and amplitude of the projected correlation function in the 2-halo", In this work we fix the $N_{cen}$ parameters $M_{min}$ and $\sigma_{log M}$ by matching the observed $\bar{n}$ and amplitude of the projected correlation function in the 2-halo CR intensity and the estimated enerevof the primary particle.,CR intensity and the estimated energy of the primary particle. The intensity correction factor for the measured CR flux due to a rapidly falling cuerey spectra and iustrmucutal errors was derived m Moscow niuiv vears ago., The intensity correction factor for the measured CR flux due to a rapidly falling energy spectrum and instrumental errors was derived in Moscow many years ago. EAS imodeliug uncertainty in the primacy cherev estimation is due to unknown nucleus interaction characteristics at energies far bevoud those studied in accelerator experiments., EAS modeling uncertainty in the primary energy estimation is due to unknown nucleus–nucleus interaction characteristics at energies far beyond those studied in accelerator experiments. Tn particulary. there may be a difference between energies estimated in the superposition and fracimentation models of uucleus-uucleus— interactions.," In particular, there may be a difference between energies estimated in the superposition and fragmentation models of nucleus-nucleus interactions." — It is shown that. iudeed. using the superposition model to analyze the surface array data. e.g. 9699. we obtain E. which has to be corrected due to the fragmentation rate overestimated.," It is shown that, indeed, using the superposition model to analyze the surface array data, e.g. $S_{600}$, we obtain $\hat{E}$, which has to be corrected due to the fragmentation rate overestimated." Applving the essential correction factors. if is shown that UIIECR. cucrey spectra imeasured with EAS arrays are coneruous within experimental errors arising from iustruneutal auc model unucertaimties.," Applying the essential correction factors, it is shown that UHECR energy spectra measured with EAS arrays are congruous within experimental errors arising from instrumental and model uncertainties." Residual ifercuces in the energy scales of giat arrays are used to estimate UITECTR cucrey determination error inherent oe1 EAS detection techniques., Residual differences in the energy scales of giant arrays are used to estimate UHECR energy determination error inherent in EAS detection techniques. Model calculations in dip and ankle scenarios of the transition from € to EG. components of CRs are In aercement with observed ankle aud CZIN features of the cuerey spectrum., Model calculations in dip and ankle scenarios of the transition from G to EG components of CRs are in agreement with observed ankle and GZK features of the energy spectrum. However. the experiueutal ucertaintics are too large to be able to distinguish between the scenarios.," However, the experimental uncertainties are too large to be able to distinguish between the scenarios." More data are needed from future arravs CAÁuger-North. satellite projects. etc.)," More data are needed from future arrays (Auger-North, satellite projects, etc.)" to elucidate the details of the spectrum measured., to elucidate the details of the spectrum measured. The author is grateful to the Yakutsk array staff for he data analysis and valuable discussions., The author is grateful to the Yakutsk array staff for the data analysis and valuable discussions. This work is supported in part by RFBR eraut uo., This work is supported in part by RFBR grant no. 09-02-12028 aud by he Russian Federal Program Scieutiic aud Educational yersonmel (contract uo., 09-02-12028 and by the Russian Federal Program `Scientific and Educational personnel' (contract no. 02.710.11.02I8)., 02.740.11.0248). to the instruments operation at the WIP by the ING stall. in particular P. Moore and CLR. Benn.,"to the instrument's operation at the WHT by the ING staff, in particular P. Moore and C.R. Benn." component.,component. " A second problem arises, for this solution, with the spectral shape."," A second problem arises, for this solution, with the spectral shape." " The observed low energy spectral index (in the X-ray band) is typically close to zero, while this solution requires a steeply rising flux from v5; to vr."," The observed low energy spectral index (in the X-ray band) is typically close to zero, while this solution requires a steeply rising flux from $\nuopt$ to $\nu_L$." Note that in Fig., Note that in Fig. " 2 we show conservatively curves for a=0,0.5,1 even though the ""canonical"" value is 0."," \ref{fig:Y} we show conservatively curves for $\alpha=0, 0.5, 1$ even though the ""canonical"" value is 0." " Moreover, unless there is a pair loading (that is if there is one electron per proton), then the low γε required for the UV solution implies that the protons carry significantly more energy than the electrons by at least a factor of m,/y.m.."," Moreover, unless there is a pair loading (that is if there is one electron per proton), then the low $\gamma_e$ required for the UV solution implies that the protons carry significantly more energy than the electrons by at least a factor of $m_p/\gamma_e m_e$." Thus this solution is a very inefficient., Thus this solution is a very inefficient. " The analysis above is based on the optical limits but for the modest values of γε needed for the UV solution, vr, the peak flux frequency of the seed photons becomes large (Eq. 1))"," The analysis above is based on the optical limits but for the modest values of $\g_e$ needed for the UV solution, $\nu_L$, the peak flux frequency of the seed photons becomes large (Eq. \ref{gamma}) )" and PF; is now limited by prompt soft X-ray observations in additional to the optical limits., and $F_L$ is now limited by prompt soft X-ray observations in additional to the optical limits. " For the discussion below, we use o4 and o» as the low energy and high energy spectral indices, respectively."," For the discussion below, we use $\alpha_1$ and $\alpha_2$ as the low energy and high energy spectral indices, respectively." " As stated before, the canonical values are αι=0 and ag=—1.25 (Bandetal.1993)"," As stated before, the canonical values are $\alpha_1=0$ and $\alpha_2=-1.25$ \citep{b93}" the previous code. but we have overcome it bv cluploving a new method.,"the previous code, but we have overcome it by employing a new method." Iu addition. we enmplov a wide variety of EOSs: piecewise polvtropie EOSs (Readetal.20092.b).. tabulated realistic EOSs derived. from nuclear physics. and fitted EOSs to the tabulated realistic EOSs.," In addition, we employ a wide variety of EOSs; piecewise polytropic EOSs \citep{rea09a,rea09b}, tabulated realistic EOSs derived from nuclear physics, and fitted EOSs to the tabulated realistic EOSs." Some of the first aud second EOSs were. respectively. used in Urvuetal.(2009) and in Bejgeretal.(2005).. but we adopt a wider set of EOSs in this paper.," Some of the first and second EOSs were, respectively, used in \citet{ury09} and in \citet{bej05}, but we adopt a wider set of EOSs in this paper." Furthermore. we systematically study the unequaliuass binaries. whereas Bejecretal.(2005). and Urvuet(2009) focused only ou the equalauass case.," Furthermore, we systematically study the unequal-mass binaries, whereas \citet{bej05} and \citet{ury09} focused only on the equal-mass case." This paper is orgauized as follows., This paper is organized as follows. We briefly review the basic equations aud explain the imiprovement of the nuuuerieal code in Section 2., We briefly review the basic equations and explain the improvement of the numerical code in Section 2. In Section 3. the results for the code test are shown.," In Section 3, the results for the code test are shown." In Section l|. we show numerical results and discuss the effects of EOS ou cach sequence.," In Section 4, we show numerical results and discuss the effects of EOS on each sequence." Section 5 is devoted to a summus., Section 5 is devoted to a summary. Throughout this paper we adopt eeconmoetrized units with G=e1. where G denotes the gravitational constant aud e the speed of light.," Throughout this paper we adopt geometrized units with $G=c=1$, where $G$ denotes the gravitational constant and $c$ the speed of light." Latin and Creek indices denote purely spatial and spacetime components. respectively.," Latin and Greek indices denote purely spatial and spacetime components, respectively." Tn this section. we briefiv describe the basic equations to be solved aud the method to calculate a quasi-equilibimu configuration in circular orbits.," In this section, we briefly describe the basic equations to be solved and the method to calculate a quasi-equilibrium configuration in circular orbits." For more details. we would like to recomuuend readers to refor to Cook(2000).. Dawngarte&Shapiro (2003).. and Coureoulhon(2007)— for the part of eravitational feld equations. and Coursoullhouetal.(2001). for that of hyvdrostatic equations.," For more details, we would like to recommend readers to refer to \citet{coo00}, \citet{bau03}, and \citet{gou07} for the part of gravitational field equations, and \citet{gou01} for that of hydrostatic equations." The line clement ii 3|1 form is written as where gu? is the spacetime metris o is the lapse function. 3 is the shift vector. aud 56 Is the spatial metric imuduced ou a spatial hypersurface My.," The line element in 3+1 form is written as where $g_{\mu \nu}$ is the spacetime metric, $\alpha$ is the lapse function, $\beta^i$ is the shift vector, and $\gamma_{ij}$ is the spatial metric induced on a spatial hypersurface $\Sigma_t$." Note here that the direction of the shift vector is the normally used one which bas a sign opposite to that used in Gourgoulliouetal.(2001) and Tauiguchi&Coureoulhon(20025.2003).," Note here that the direction of the shift vector $\beta^i$ is the normally used one which has a sign opposite to that used in \citet{gou01} and \citet{tan02b,tan03}." ". The spatial metric 5;; is further decomposed iuto the conformal factor c and a backeround ποο 5;j. and is written as The extrinsic curvature is defined by where £, is the Lie derivative along the wit normal to the hwpersmface Sy."," The spatial metric $\gamma_{ij}$ is further decomposed into the conformal factor $\psi$ and a background metric $\tilde{\gamma}_{ij}$, and is written as The extrinsic curvature is defined by where ${\cal L}_n$ is the Lie derivative along the unit normal to the hypersurface $\Sigma_t$ ." We split it iuto the trace A and the traceless part ely) as We further rewrite the traceless part as where Aj; μι.," We split it into the trace $K$ and the traceless part $A_{ij}$ as We further rewrite the traceless part as where $\tilde A_{ij} =\tilde{\gamma}_{ik} \tilde{\gamma}_{jl} \tilde{A}^{kl}$ ." The Ibkuuitouau constraint. then. takes the form where V? denotes UNSS V; the coviriant derivative with respect to σεν aud R the scalar curvature with respect to ie," The Hamiltonian constraint, then, takes the form where $\tilde{\nabla}^2$ denotes $\tilde{\gamma}^{ij} \tilde{\nabla}_i \tilde{\nabla}_j$, $\tilde{\nabla}_i$ the covariant derivative with respect to $\tilde{\gamma}_{ij}$, and $\tilde{R}$ the scalar curvature with respect to $\tilde{\gamma}_{ij}$." The matter term. pu. inv Equation (6)) is caleulatec bv takine a projection. of the stress-energv CUSsOr. (," The matter term, $\rho_H$, in Equation \ref{eq:ham_constr}) ) is calculated by taking a projection of the stress-energy tensor. (" See Equation (11)) below.)Equatious (3)). CE). aud (5b)) vield Using Equation (7)) for the traceless part of the extrimsic curvature. the momentum constraiut js written as,"See Equation \ref{eq:rhoh}) ) below.)Equations \ref{eq:extr_curv}) ), \ref{eq:extr_decomp}) ), and \ref{eq:extr_traceless})) yield Using Equation \ref{eq:traceless_extr}) ) for the traceless part of the extrinsic curvature, the momentum constraint is written as" Though we have focused on z=0.55. Fig.,"Though we have focused on $z=0.55$, Fig." |] shows that he scale-dependent Gaussian streaming model works extremely well for massive halos both at z=| and z=0., \ref{fig:redshiftdep} shows that the scale-dependent Gaussian streaming model works extremely well for massive halos both at $z=1$ and $z=0$. " In the upper j»unel. we compare samples containing all halos above LOPS?A! Mc. for which the best fit bias values are ερ,=3.83.2.79 and 1.88 tin order of decreasing redshift)."," In the upper panel, we compare samples containing all halos above $M_{\rm min} = 10^{13.387} \; h^{-1} M_{\sun}$ , for which the best fit bias values are $b_{LPT} = 3.83, 2.79$ and 1.88 (in order of decreasing redshift)." " In the lower xinel. we vary Minin=10/77,1075957,LORSfeMos. so that the bias of the samples is fixed at bpp,=2.8."," In the lower panel, we vary $M_{\rm min} = 10^{12.9}, 10^{13.387}, 10^{13.95} \; h^{-1} M_{\sun}$, so that the bias of the samples is fixed at $b_{LPT}\simeq 2.8$." " The redshift dependence of £&/£j, on small scales is opposite in the two panels. which can be understood simply in terms of the absolute real space clustering amplitude that enters the convolution in Eq. 25.."," The redshift dependence of $\xi_2/\xi_{2,{\rm lin}}$ on small scales is opposite in the two panels, which can be understood simply in terms of the absolute real space clustering amplitude that enters the convolution in Eq. \ref{streamingeqn}." At the fixed value of M we have chosen. &«btcyors(z) decreases as structure grows. whereas at fixed bias. £&' increases with time as σκίς).," At the fixed value of $M$ we have chosen, $\xi^r \propto b(z) \sigma_8(z)$ decreases as structure grows, whereas at fixed bias, $\xi^r$ increases with time as $\sigma_8(z)$." We use this example to emphasise that the non-linear corrections are no necessarily smaller at higher redshift. since more highly biased objects are often being selected.," We use this example to emphasise that the non-linear corrections are not necessarily smaller at higher redshift, since more highly biased objects are often being selected." We have checked the behaviour of the perturbation theory predictions at z=O and z=| for the rea space statistics examined in Section 5.1.. and find good agreemen with naive expectations.," We have checked the behaviour of the perturbation theory predictions at $z=0$ and $z=1$ for the real space statistics examined in Section \ref{sec:PT}, , and find good agreement with naive expectations." At fixed 6=2.8. the sudden upturn in the LPT prediction for £&' occurs at increasingly large r as structure evolves (22. 26. and 314! Mpe at 21. 0.5. 0. respectively).," At fixed $b=2.8$, the sudden upturn in the LPT prediction for $\xi^r$ occurs at increasingly large $r$ as structure evolves (22, 26, and $31\,h^{-1}$ Mpc at z=1, 0.5, 0, respectively)." A fixed z. the upturn increases with 5. as can be seen in Fig. 7..," At fixed $z$, the upturn increases with $b$, as can be seen in Fig. \ref{fig:xirealPTfit}." We find similar results when comparing pairwise halo velocity statistics: in general. the perturbation theory predictions are better at higher redshift and lower bias.," We find similar results when comparing pairwise halo velocity statistics; in general, the perturbation theory predictions are better at higher redshift and lower bias." " However. the ""sweet spot"" in the perturbation theory prediction at b=1.9 in Fig."," However, the “sweet spot” in the perturbation theory prediction at $b=1.9$ in Fig." 9. persists at z=0 as well. though the halo mass range at fixed 5 depends on ς.," \ref{fig:vstats} persists at $z=0$ as well, though the halo mass range at fixed $b$ depends on $z$." As we have emphasised. there are two relatively large corrections to the Kaiser prediction for &>.," As we have emphasised, there are two relatively large corrections to the Kaiser prediction for $\xi_2$." In this section we illustrate explicitly how they depend on bias., In this section we illustrate explicitly how they depend on bias. The suppression of the halo velocity statistics relative to linear theory lowers the amplitude of &>. while the non-linear mappingrye between real and redshift space increases the amplitude of €) in the bias range we have studied (see Fig. 49).," The suppression of the halo velocity statistics relative to linear theory lowers the amplitude of $\xi_2$, while the non-linear mapping between real and redshift space increases the amplitude of $\xi_2$ in the bias range we have studied (see Fig. \ref{fig:streaminglin}) )." To illustrate the effect of the former. we use the Kaiser limit mapping between real space clustering and velocity statistics (Equations 16. through 18)). but input the real space AN- simulation results for these quantities rather than the linear theory expectations.," To illustrate the effect of the former, we use the Kaiser limit mapping between real space clustering and velocity statistics (Equations \ref{fisherlinearxi} through \ref{vdispexpand}) ), but input the real space $N$ -body simulation results for these quantities rather than the linear theory expectations." The results for the halo subsamples in Table are the lower three curves in Fig. 12.., The results for the halo subsamples in Table \ref{table:halos} are the lower three curves in Fig. \ref{fig:biasdep}. The weak dependence of the non-linear corrections on the velocity statistics (Fig. 9)), The weak dependence of the non-linear corrections on the velocity statistics (Fig. \ref{fig:vstats}) ) translates into a relatively weak dependence on halo bias on £»., translates into a relatively weak dependence on halo bias on $\xi_2$. In contrast. the effect of the non-linear mapping depends strongly on halo bias.," In contrast, the effect of the non-linear mapping depends strongly on halo bias." " To see this explicitly, one can expand Eq."," To see this explicitly, one can expand Eq." 25. by assuming that the pairwise velocity PDF Έτ) is a smooth and slowly varying function of r: this procedure will be more accurate at small ji. where a smaller range of real space separations contribute pairs at à given redshift space separation.," \ref{streamingeqn} by assuming that the pairwise velocity PDF $\mathcal{P}(v_z ; {\bf r})$ is a smooth and slowly varying function of ${\bf r}$; this procedure will be more accurate at small $\mu$, where a smaller range of real space separations contribute pairs at a given redshift space separation." Eq., Eq. 53 of does this in the case of the exact Gaussian result. and the same terms (along with many others) appear when the expansion is performed on our Eq. 25..," 53 of does this in the case of the exact Gaussian result, and the same terms (along with many others) appear when the expansion is performed on our Eq. \ref{streamingeqn}." We have verified that the dominant non-linear correction term for £j» in our bias range comes from the term —d/dv[£vi»]: The upper curves in Fig.," We have verified that the dominant non-linear correction term for $\xi_{0,2}$ in our bias range comes from the term $-d/dy [\xi v_{12}]$: The upper curves in Fig." 12. are the same as the lower ones. but with this extra term included to approximate the non-linear mapping step: these predictions are in reasonable agreement with Eq. 25..," \ref{fig:biasdep} are the same as the lower ones, but with this extra term included to approximate the non-linear mapping step; these predictions are in reasonable agreement with Eq. \ref{streamingeqn}," but performing the full integral is a noticeably better fit to the simulation results., but performing the full integral is a noticeably better fit to the simulation results. What we wish to emphasise is that the non-linear mapping produces a term (Eq. 343) , What we wish to emphasise is that the non-linear mapping produces a term (Eq. \ref{b3term}) ) that contributes to £o and £» and scales like *., that contributes to $\xi_0$ and $\xi_2$ and scales like $b^3$. This is in disagreement with the recent results of(2011). who use a non-linear correction term equivalent to the (δινιi) contribution in our Eq. 27..," This is in disagreement with the recent results of, who use a non-linear correction term equivalent to the $\left < \delta_i \delta_j {\bf v}_{4-i-j}\right >$ contribution in our Eq. \ref{vinfallPT}." We can see why that term (the dotted curve in Figure 8) provides a reasonable fit to their simulation results at one value of h: its shape roughly mimics our non-linear mapping term that dominates on small scales., We can see why that term (the dotted curve in Figure \ref{fig:PTtot}) ) provides a reasonable fit to their simulation results at one value of $b$: its shape roughly mimics our non-linear mapping term that dominates on small scales. However. our more detailed analysis demonstrates that many other terms are of comparable size to the one considered in(2011).," However, our more detailed analysis demonstrates that many other terms are of comparable size to the one considered in." find that the value of £ recovered from massive halos 5>1.5 is relatively close to the expected linear value. but lower mass halos recover a smaller value compared with linear theory.," find that the value of $\beta$ recovered from massive halos $b \gtrsim 1.5$ is relatively close to the expected linear value, but lower mass halos recover a smaller value compared with linear theory." Fig., Fig. 12. illustrates why: for our central galaxy sample (dotted curves). the non-linear effects of velocity suppression and real-to-redshift space mapping approximately cancel for s> 'Mpe: at low halo bias. we expect the non-linear mapping corrections to be small. and the measured & should be closer to the lower curves.," \ref{fig:biasdep} illustrates why: for our central galaxy sample (dotted curves), the non-linear effects of velocity suppression and real-to-redshift space mapping approximately cancel for $s > 30\,h^{-1}$ Mpc; at low halo bias, we expect the non-linear mapping corrections to be small, and the measured $\xi_2$ should be closer to the lower curves." Of course. the bias where this near-cancellation occurs will depend on redshift. and because of the 5? correction term. it will only be true in a limitedrange of bias values.," Of course, the bias where this near-cancellation occurs will depend on redshift, and because of the $b^3$ correction term, it will only be true in a limitedrange of bias values." " To be more quantitative. for the halo bias range we have studied (5=|.4— 2.8). fitting the Kaiser formula to & and & to derive constraints on b and f on scales r~3077 'Mpe will bias the constraints on / by +2. -6. and -10 per cent for bj,= 2.67. 1.84. 1.81. respectively. under the assumption that the smallest scales"," To be more quantitative, for the halo bias range we have studied $b=1.4-2.8$ ), fitting the Kaiser formula to $\xi_0$ and $\xi_2$ to derive constraints on $b$ and $f$ on scales $r \sim 30\,h^{-1}$ Mpc will bias the constraints on $f$ by +2, -6, and -10 per cent for $b_{lin} =$ 2.67, 1.84, 1.41, respectively, under the assumption that the smallest scales" The program is composed of the following steps: 1.,The program is composed of the following steps: 1. The image is trimmed to make the field square and to include only areas of the skv that were well-observed by ROTSE-I. This step ensures that each area of the sky is only covered once., The image is trimmed to make the field square and to include only areas of the sky that were well-observed by ROTSE-I. This step ensures that each area of the sky is only covered once. Also. individual observations with magnitudes outside the calibrated range. 9.0 to 15.5 magnitude. are cdiscardec.," Also, individual observations with magnitudes outside the calibrated range, 9.0 to 15.5 magnitude, are discarded." 2., 2. Objects for which there are fewer than 10 observations are discarded because these light curves are too poorly sampled to determine whether or not thev are supernovae., Objects for which there are fewer than 10 observations are discarded because these light curves are too poorly sampled to determine whether or not they are supernovae. 3., 3. We remove outliers [rom the light curves bv comparing the light curves to actual SNe la light curves given in Branch(1993)., We remove outliers from the light curves by comparing the light curves to actual SNe Ia light curves given in \citet{bra98}. . This step eliminates data points that are most likely due to incorrect. calibration., This step eliminates data points that are most likely due to incorrect calibration. 4., 4. Subsequently stricter criteria are applied to the objects. light. curves: we discarcl observations (hat are >0.3 magnitude dimmer (han (he previous observation if (he observations are before the maximum and observations that are >0.3 magnitude brighter than the previous observation if the observations are alter maxinuun (i.e. we eliminate observations that drop too much when the lieht curve is increasing and rise too much when the light curve is decreasing).," Subsequently stricter criteria are applied to the objects' light curves: we discard observations that are $> 0.3$ magnitude dimmer than the previous observation if the observations are before the maximum and observations that are $> 0.3$ magnitude brighter than the previous observation if the observations are after maximum (i.e., we eliminate observations that drop too much when the light curve is increasing and rise too much when the light curve is decreasing)." AcdiGonally. the maximum and minimum must occur at least five cays apart.," Additionally, the maximum and minimum must occur at least five days apart." These steps further refine the light curves by removing points that differ from the SN la light curve template., These steps further refine the light curves by removing points that differ from the SN Ia light curve template. 5., 5. Points that differ from the entire light curves mean by more than 36. are removed., Points that differ from the entire light curve's mean by more than $\sigma$ are removed. This step should not affect SNe la lisht curves because (hese curves have relatively large a., This step should not affect SNe Ia light curves because these curves have relatively large $\sigma$. 6., 6. If the modified light curve has less than 10 observations. the object is discarded.," If the modified light curve has less than 10 observations, the object is discarded." 7., 7. À series of fillers is applied to the modified light curve., A series of filters is applied to the modified light curve. These fillers require the curve to vary with (ime in a manner consistent wilh tvpical SNe Ia light curves. taken from (1993).," These filters require the curve to vary with time in a manner consistent with typical SNe Ia light curves, taken from \citet{bra98}." ". Specifically, there must be at least one magnitude variation over (he entire curve."," Specifically, there must be at least one magnitude variation over the entire curve." We require all objects with light curves that peak below 12th magnitude to be visible for less than 150 days., We require all objects with light curves that peak below 12th magnitude to be visible for less than 150 days. All objects that peak between 12th and 9th magnitude must show at least 2 magnitudes variation., All objects that peak between 12th and 9th magnitude must show at least 2 magnitudes variation. These filters eliminate most long-term variable stars., These filters eliminate most long-term variable stars. The filters described above vielded a set of possible SNe Ia for each field. which were subsequently examined by eve.," The filters described above yielded a set of possible SNe Ia for each field, which were subsequently examined by eye." The number of possible SNe Ia per field ranged from zero to hundreds. varving directly with Galaetie latitude and inversely with the time coverage of," The number of possible SNe Ia per field ranged from zero to hundreds, varying directly with Galactic latitude and inversely with the time coverage of" that. deteriuned from fitting a model to ouly the SZ effect data.,"that, determined from fitting a model to only the SZ effect data." Current SZ effect data alone. however. eaunot 0.1iu tightly coustrain these quantities.," Current SZ effect data alone, however, cannot 0.1in tightly constrain these quantities." In §l. we show that the high quality data to be produced by the upcoming and the (soon to be) uperaded array will make it possible to accurately measure these quantities for massive clusters at virtually auy redshift aud without Lavine to use auv N-ray results.," In 4, we show that the high quality data to be produced by the upcoming and the (soon to be) upgraded array will make it possible to accurately measure these quantities for massive clusters at virtually any redshift and without having to use any X-ray results." The next set of scaling relations we exiuuine are the SZ ctfect - cluster mass relations., The next set of scaling relations we examine are the SZ effect - cluster mass relations. Theoretical arguiuceuts Sugeest that these relations should be very sensitive to the presence of entropy floor. at least when the SZ effect Is measured near the cluster center (e... 0).," Theoretical arguments suggest that these relations should be very sensitive to the presence of entropy floor, at least when the SZ effect is measured near the cluster center (e.g., $y_0$ )." luterestinglv. these trends too can also potentially be measured indepeudent of N-rav results.," Interestingly, these trends too can also potentially be measured independent of X-ray results." " Future SZ effect observations will allow oue to estimate yy and Shape!f, accurately purely through SZ effect surface briehtuess profiles (see 81). while both strong and weal: Ieusine are increasinely Deine used to measure the mass profiles of clusters out to radi comparable in size to that of που (ee. Clowe Schneider 2001)."," Future SZ effect observations will allow one to estimate $y_0$ and $S_{\nu,arc}/f_{\nu}$ accurately purely through SZ effect surface brightness profiles (see 4), while both strong and weak lensing are increasingly being used to measure the mass profiles of clusters out to radii comparable in size to that of $r_{500}$ (e.g., Clowe Schneider 2001)." At prescut. however. only a few of the clusters iu our sample have Όσοι weighed using leusing.," At present, however, only a few of the clusters in our sample have been weighed using lensing." Iu Figure 2. we plot the observed yyM(rgo) relation.," In Figure 2, we plot the observed $y_0-M(r_{500})$ relation." This is superimposedon the predicted 2=0.2 yoM(rsoo) relations for the selfsimuilar model (dotted line) aud the Ay = 100 (short-dashed). 300 (loug-dashed). 500. (dot-dashed). and 700 keV cni? (solid) eutropv floor models.," This is superimposed on the predicted $z = 0.2$ $y_0-M(r_{500})$ relations for the self-similar model (dotted line) and the $K_0$ = 100 (short-dashed), 300 (long-dashed), 500 (dot-dashed), and 700 keV $^2$ (solid) entropy floor models." " Because the majority of the clusters with published masses in Tables 1 and 2 le in a narrow redshift range arouud Doce44.2. dt ds possible to courpare the theoretical models to the data ""by eve” before using the quantitative method outlined in 83.1."," Because the majority of the clusters with published masses in Tables 1 and 2 lie in a narrow redshift range around $z \sim 0.2$, it is possible to compare the theoretical models to the data “by eye” before using the quantitative method outlined in 3.1." " A simple. eat. and fair qualitative comparison was not possible for the previous relation μμfoYo). as the data spanned 0.1iu a wide range of redshifts aud because that relation is especially seusitive to 2 (S, scales as 1D?)"," A simple, neat, and fair qualitative comparison was not possible for the previous relation $S_{\nu,arc}/f_{\nu}-y_0$ ), as the data spanned 0.1in a wide range of redshifts and because that relation is especially sensitive to $z$ $S_{\nu}$ scales as $1/D_a^{2}$ )." By visual mspectiou. of Figure 2. it is obvious that ouly the high eutropy floor models (AyZ300 keV cui) provide a reasonable ft to the observational data.," By visual inspection of Figure 2, it is obvious that only the high entropy floor models $K_0 \gtrsim 300$ keV $^2$ ) provide a reasonable fit to the observational data." Iu addition. the observed correlation does uot seem to depeud ou the cooling flow status or redshift of the clusters. although the sample is far too small to make anv robust conclusious to this effect.," In addition, the observed correlation does not seem to depend on the cooling flow status or redshift of the clusters, although the sample is far too small to make any robust conclusions to this effect." Fitting all niue clusters with the method outlined in 82.1. our best-fit eutropy floor level is Ry=500/02 keV cu? with AZ = 8.02/8 = 1.00.," Fitting all nine clusters with the method outlined in 3.1, our best-fit entropy floor level is $K_0 = 500^{+65}_{-65}$ keV $^2$ with $\chi^2_{\nu}$ = 8.02/8 = 1.00." This is consistent with the results derived in 83.2 and with N-ray observations of nearby massive clusters., This is consistent with the results derived in 3.2 and with X-ray observations of nearby massive clusters. A plot of the residuals between the data aud the Ay=500 keV em? inodel is shown in the left-hand pauel of Figure 3., A plot of the residuals between the data and the $K_0 = 500$ keV $^2$ model is shown in the left-hand panel of Figure 3. Also shown (viglt-hand paucl) are the residuals of a comparison between the data aud the selfsimilar model (AZ = 316.05/9 = I1.80)., Also shown (right-hand panel) are the residuals of a comparison between the data and the self-similar model $\chi^2_{\nu}$ = 376.05/9 = 41.80). The residuals for the A=500 τον cu? inodel display a tight scatter about the zero ine. while the residuals for the sclfsimular model indicate hat yo is observed to be uch lower [for a fixed value of AfCrsyy)} than predicted by this model.," The residuals for the $K_0 = 500$ keV $^2$ model display a tight scatter about the zero line, while the residuals for the self-similar model indicate that $y_0$ is observed to be much lower [for a fixed value of $M(r_{500})$ ] than predicted by this model." The entropy floor uodels with Ay~500 keV cm? ave able to provide a good natch to the data because the addition of au eutropy floor reduces the eas pressure near the centers of clusters (see AIBIIDO23 for a detailed discussion)., The entropy floor models with $K_0 \sim 500$ keV $^2$ are able to provide a good match to the data because the addition of an entropy floor reduces the gas pressure near the centers of clusters (see MBHB03 for a detailed discussion). This. iu turn. reduces he maenitude of yo.," This, in turn, reduces the magnitude of $y_0$." The mass within rsyy. however. is unaffected by the modification of the gas eutropy.," The mass within $r_{500}$, however, is unaffected by the modification of the gas entropy." Although the available gyAf(rsyy) data exhibit ouly a verv siuall amount of scatter about the Ay~500 keV cm? relation (aud the 42 indicates a very eood ft) the estimated error bars on our best-fit value of Ay from this relation are almost certainly too stall.," Although the available $y_0-M(r_{500})$ data exhibit only a very small amount of scatter about the $K_0 \sim 500$ keV $^2$ relation (and the $\chi^2_{\nu}$ indicates a very good fit), the estimated error bars on our best-fit value of $K_0$ from this relation are almost certainly too small." We sav this because (1) we were unable to calculate anv uncertaimty for ALrsoy) as there were no published error bars for the best-ft NEW parameters for the clusters in Figures 2 aud 23. and (2) the sample is too small to eet anv kind of a handle on the," We say this because (1) we were unable to calculate any uncertainty for $M(r_{500})$ as there were no published error bars for the best-fit NFW parameters for the clusters in Figures 2 and 3, and (2) the sample is too small to get any kind of a handle on the" the objects identilied as extended in Table 2 of Walter(2001) are indeed extended: all other objects are consistent will point sources.,the objects identified as extended in Table 2 of \cite{Wal01} are indeed extended; all other objects are consistent with point sources. We did not include the extended objects 104. 105. or 109 in this analvsis.," We did not include the extended objects 104, 108, or 109 in this analysis." We analvzed (he measured positions by three independent methods., We analyzed the measured positions by three independent methods. The derived proper motions and parallaxes are presented in Table 2.., The derived proper motions and parallaxes are presented in Table \ref{tbl-2}. First. we performed full 47 minimizations for the proper motions and parallaxes of the objects in the field. including image offsets. residual rotations from the nominal roll angles. and scale factor changes from the nominal plate scale (45.5 mas |).," First, we performed full $\chi^2$ minimizations for the proper motions and parallaxes of the objects in the field, including image offsets, residual rotations from the nominal roll angles, and scale factor changes from the nominal plate scale (45.5 mas $^{-1}$ )." This procedure was performed twice. both excluding aud including the neutron star in the optimization.," This procedure was performed twice, both excluding and including the neutron star in the optimization." In the former case. (he proper motion and parallax of the neutron star were obtained using the image offsets. residual rotations and scale [actor changes from the other objects.," In the former case, the proper motion and parallax of the neutron star were obtained using the image offsets, residual rotations and scale factor changes from the other objects." This distinction was made since the expected proper motion and parallax of the neutron star are much greater than for those expected from the field objects., This distinction was made since the expected proper motion and parallax of the neutron star are much greater than for those expected from the field objects. As anticipated. we found the parallax and proper motion of the neutron star are sliehtly smaller in the second. analysis.," As anticipated, we found the parallax and proper motion of the neutron star are slightly smaller in the second analysis." The results «quoted in Table 2. are [rom the first analysis., The results quoted in Table \ref{tbl-2} are from the first analysis. secondly. we determined the proper motion and parallax of the neutron star independently in the N-S and E-W directions.," Secondly, we determined the proper motion and parallax of the neutron star independently in the N-S and E-W directions." We registered the images with the assumption that the mean proper motions and parallaxes of the field stars are negligible., We registered the images with the assumption that the mean proper motions and parallaxes of the field stars are negligible. We rotated the measured positions to an equatorial coordinate frame using the nominal roll angles., We rotated the measured positions to an equatorial coordinate frame using the nominal roll angles. We registered the images bv shifting bv the median offset in each coordinate., We registered the images by shifting by the median offset in each coordinate. We iterated (he registration. excluding stars whose residual differences are significant al 2236. significance.," We iterated the registration, excluding stars whose residual differences are significant at $>$ $\sigma$ significance." Registration using a weiehted mean shift produced insignificant differences., Registration using a weighted mean shift produced insignificant differences. We then determined the deviations from the nominal roll angle and plate scale by minimizing the cillences between ihe positions at each epoch and those of the first epoch., We then determined the deviations from the nominal roll angle and plate scale by minimizing the diffences between the positions at each epoch and those of the first epoch. After resetting the roll angles and the plate scales. we re-registered the images.," After resetting the roll angles and the plate scales, we re-registered the images." Uncertainties in the image registrations are, Uncertainties in the image registrations are enussion lines despite (he high inclination. aud hieh excitation spectral features including Ie II (4686) emission and strong Balmer emission on a blue continuum. high velocity emission S-waves with maximum blueshift near phase ~ 0.5. delay of emission line radial velocities relative to the motion of the WD. and cental absorption dips in the emission lines around phase ~ 0.4 - 0.7 hRodriguez-Giletal.(2007);Hoard(2002).,"emission lines despite the high inclination, and high excitation spectral features including He II (4686) emission and strong Balmer emission on a blue continuum, high velocity emission S-waves with maximum blueshift near phase $\sim$ 0.5, delay of emission line radial velocities relative to the motion of the WD, and cental absorption dips in the emission lines around phase $\sim$ 0.4 - 0.7 \citet{Rodriguez-Gil2007,Hoard2003}." . The white clwarls in many. if not all. of these systems are suspected of being magnetic mi," The white dwarfs in many, if not all, of these systems are suspected of being magnetic \citep{Rodriguez-Gil2007}." nce (hese objects are found near the upper boundary of the period gap and references therein). their study is of eritical importance1 to understanding& CV evolution as thev enter the period gap.," Since these objects are found near the upper boundary of the period gap \citet{Warner1995} and references therein), their study is of critical importance to understanding CV evolution as they enter the period gap." Shalier(1983) determined. a spectroscopic period for W380 Oph Irom observations wilh very moderate spectral resolution., \citet{Shafter1983} determined a spectroscopic period for V380 Oph from observations with very moderate spectral resolution. Roclriguez-Giletal.(2007) improved its orbital period and measured I-alpha emission radial velocity variations with an amplitude of 400 km/sec., \citet{Rodriguez-Gil2007} improved its orbital period and measured H-alpha emission radial velocity variations with an amplitude of 400 km/sec. Photometric observations have revealed orbital variability wilh possible negative superhunps., Photometric observations have revealed orbital variability with possible negative superhumps. The reddening of the svstems was taken from available estimates in the literature., The reddening of the systems was taken from available estimates in the literature. The (τος principal sources of reddening for cataclysmic variables are the compilations of VerbuntDous(1991):Bruch&Engel. (1994).," The three principal sources of reddening for cataclysmic variables are the compilations of \citet{Verbunt1987,LaDous1991,Bruch1994}." . For V751 Cveni. Greineretal.(1999) eave — E(5V) = 0.2540.05 which is the value we adopted for V751 Cveni.," For V751 Cygni, \citet{Greiner1999} gave $\bv$ ) = $\pm$ 0.05 which is the value we adopted for V751 Cygni." For V380 Oph. we (reated the reddening as a [ree parameter in the model fitting.," For V380 Oph, we treated the reddening as a free parameter in the model fitting." The FUV spectra of V751 Cyeni objects were de-reddened using the IUERDAF IDL routine UNRED., The FUV spectra of V751 Cygni objects were de-reddened using the IUERDAF IDL routine UNRED. The spectrum ol BIX Lyn was not clerecldened as the galactic reddeniug in the direction of DIx Lyn is very sinall CZ(D.—V)~0.01., The spectrum of BK Lyn was not dereddened as the galactic reddening in the direction of BK Lyn is very small $(E(B-V) \sim 0.01$. The observed. properties of all three svstems are summarized in Table 1., The observed properties of all three systems are summarized in Table 1. We have computed strict lower limit distances to BIX Lyn. V751 Cveni and V380 Oph using a method by IXnigge.(2006) which uses 2ÀSS JILIN photometry.," We have computed strict lower limit distances to BK Lyn, V751 Cygni and V380 Oph using a method by \citet{Knigge2006} which uses 2MASS JHK photometry." For each svstem. we obtained the JILIN apparent magnitudes [rom 2MASS.," For each system, we obtained the J,H,K apparent magnitudes from 2MASS." For a given orbital period. provides absolute J. IL and Io magnitudes based upon his semi-empirical donor sequence for CVs.," For a given orbital period, \citet{Knigge2006} provides absolute J, H and K magnitudes based upon his semi-empirical donor sequence for CVs." Hit is assumed that the donor provides of the light in J. IE and Ix. then the distance is a strict lower limit.," If it is assumed that the donor provides of the light in J, H and K, then the distance is a strict lower limit." If the donor emits of the light (the remainder being aceretion light). then a very approximate upper limit is obtained.," If the donor emits of the light (the remainder being accretion light), then a very approximate upper limit is obtained." At the Kk-bancl. the latter limit is a [actor of 1.75 (mes the lower limit clistance.," At the K-band, the latter limit is a factor of 1.75 times the lower limit distance." The lower limit distances are used as constraints in the svuthetic spectral fitting procedures described below., The lower limit distances are used as constraints in the synthetic spectral fitting procedures described below. For BIX Lvn. this leads (o a lower limit distance of 116 pc. for V380 Oph. this method vields a range of," For BK Lyn, this leads to a lower limit distance of 116 pc, for V380 Oph, this method yields a range of" " P/2P=17.500 £=3.1«107 1 range2.13.2 x-ray 5-ray 5-rav 5T#£12% zz27"". 918.5 "," $P/2\dot P = 17,500$ $\dot{E} = 3.4 \times 10^{36}$ $^{-1}$ $2.4-3.2$ $\gamma$ $-$ $\gamma$ $\gamma$ $-$ $-$ $57 \pm 12$ $\approx 27^{\prime\prime}$ $-$ $9-18.5$ " "their associated eigenvalues στιΑΣ(λ/)=vi,where v; is the eigenvalue of the i'th component), so the dominant components exhibit larger excursions from zero.","their associated eigenvalues $\sum_{j=1}^{7}A_{i}^{2}(\lambda_{j})=v_{i}$,where $v_{i}$ is the eigenvalue of the $i$ 'th component), so the dominant components exhibit larger excursions from zero." The eigenprojections (C;(t) from Equation 1)) are shown in Figures 8 9.., The eigenprojections $C_{i}(t)$ from Equation \ref{pca}) ) are shown in Figures \ref{polar1_eigenprojections} \ref{polar2_eigenprojections}. The standard deviation of an eigenprojection corresponds to the variance or eigenvalue of that component., The standard deviation of an eigenprojection corresponds to the variance or eigenvalue of that component. " By definition, the low-order eigenprojections have the largest deviations from 0."," By definition, the low-order eigenprojections have the largest deviations from 0." " Note that in Cowanetal.(2009) we instead plotted the normalized eigenprojections σε)= 1), which made it easier to compare (22.the shapes of the eigenprojections but masked their relative importance."," Note that in \cite{Cowan_2009} we instead plotted the normalized eigenprojections $\sum_{k=1}^{25}C_{i}(t_{k})^{2}=1$ ), which made it easier to compare the shapes of the eigenprojections but masked their relative importance." The North polar observations are dominated by two eigencolors., The North polar observations are dominated by two eigencolors. " At first glance, the two eigencolors are identical, only offset in the vertical direction, but they are construction) orthogonal."," At first glance, the two eigencolors are identical, only offset in the vertical direction, but they are (by construction) orthogonal." " The more important of the (bytwo is blue, in that it is most non-zero at short wavelengths and nearly independent of what is going on at long wavelengths; the second eigencolor is red: it is most non-zero at long wavelengths and is largely insensitive to variability in blue wavebands."," The more important of the two is blue, in that it is most non-zero at short wavelengths and nearly independent of what is going on at long wavelengths; the second eigencolor is red: it is most non-zero at long wavelengths and is largely insensitive to variability in blue wavebands." " Based on the findings presented in 3.1,, we may infer that clouds and continents are rotating in and out of view as seen from this vantage point."," Based on the findings presented in \ref{numerical_experiment}, we may infer that clouds and continents are rotating in and out of view as seen from this vantage point." " Furthermore, cloud-related variability appears to be more important here than it was for the equatorial observations, which had a dominant red eigenvector followed by a blue, rather than vice-versa."," Furthermore, cloud-related variability appears to be more important here than it was for the equatorial observations, which had a dominant red eigenvector followed by a blue, rather than vice-versa." " The South polar observations are dominated by a single, gray eigencolor."," The South polar observations are dominated by a single, gray eigencolor." " Snow and clouds both have gray optical albedo spectra, so either may be contributing to the photometric variability."," Snow and clouds both have gray optical albedo spectra, so either may be contributing to the photometric variability." The absence of an important red eigencolor is due to the relative dearth of continents in the southern hemisphere., The absence of an important red eigencolor is due to the relative dearth of continents in the southern hemisphere. " The second eigencolor is two orders of magnitude down in variance, or one order of magnitude in variability."," The second eigencolor is two orders of magnitude down in variance, or one order of magnitude in variability." " It indicates that red and blue surfaces are trading places as the world turns is positive at short wavelengths, negative at long (Ao(A)wavelengths, and zero in between), but the forced orthogonality of the eigencolors makes this interpretation ambiguous."," It indicates that red and blue surfaces are trading places as the world turns $A_{2}(\lambda)$ is positive at short wavelengths, negative at long wavelengths, and zero in between), but the forced orthogonality of the eigencolors makes this interpretation ambiguous." In this section we address how to infer the longitudinal color inhomogeneities of the unresolved planet based on time-resolved photometry., In this section we address how to infer the longitudinal color inhomogeneities of the unresolved planet based on time-resolved photometry. Note that this is in principle an independent question from that of identifying surface types on the planet 3)., Note that this is in principle an independent question from that of identifying surface types on the planet 3). One could try to infer the surface types on a planet without knowing or caring about their spatial distribution; or one could simply produce longitudinal color maps while remaining agnostic about what these tell us about surfaces (where “surface” here includes clouds)., One could try to infer the surface types on a planet without knowing or caring about their spatial distribution; or one could simply produce longitudinal color maps while remaining agnostic about what these tell us about surfaces (where “surface” here includes clouds). " In practice, however, the two are intimately tied: a planet only exhibits rotational variability if it has a variegated surface substantial spatial inhomogeneities in the distribution of these surfaces."," In practice, however, the two are intimately tied: a planet only exhibits rotational variability if it has a variegated surface substantial spatial inhomogeneities in the distribution of these surfaces." " As in Cowanetal. (2009),, we wish to estimate disk- cloud variability, as this imposes a limit on"," As in \cite{Cowan_2009}, we wish to estimate disk-integrated cloud variability, as this imposes a limit on" "where mp is the proton mass, rr=2.33 to factor in the abundance of He relative to H2 and mcisg=30.","where $m_\mathrm{p}$ is the proton mass, $\bar{m}=2.33$ to factor in the abundance of He relative to $_2$ and $m_\mathrm{C^{18}O}=30$." " This yields for a shallow power law clump, n=1.5, consistent with the shapes found by fal](2008) We expect objects in equipartition to have Myir~Mgso whilst those that are self-gravitating should have Myi;S2Mgso."," This yields for a shallow power law clump, $n=1.5$, consistent with the shapes found by \citet{enoch08} We expect objects in equipartition to have $M_\mathrm{vir}\sim M_{850}$ whilst those that are self-gravitating should have $M_\mathrm{vir}\la 2M_{850}$." We take data on the clumps’ dust properties from Richer] (2010).., We take data on the clumps' dust properties from \citet{scubapaper}. " Each clump's mmass (Mgso) assumes the dust is optically thin, has an opacity, κ= 0.012ccm? ος| and is at a single temperature, T."," Each clump's mass $M_{850}$ ) assumes the dust is optically thin, has an opacity, $\kappa = 0.012$ $^{2}$ $^{-1}$ and is at a single temperature, $T_\mathrm{D}$." " Again these temperatures are taken as the kkinetic temperatures (Rosolowskyet where available, or KK (for starless cores) and KK (for al][2008),,protostars) where not."," Again these temperatures are taken as the kinetic temperatures \citep{rosolowsky08}, , where available, or K (for starless cores) and K (for protostars) where not." " The core radius, Rgec, is the geometric mean of the two core semi- and -minor axis ‘sizes’ each deconvolved with the beam size."," The core radius, $R_\mathrm{dec}$, is the geometric mean of the two core semi-major and -minor axis `sizes' each deconvolved with the beam size." " These ‘sizes’ are the standard deviation of the pixel coordinates about the core centroid, weighted by the pixel values."," These `sizes' are the standard deviation of the pixel coordinates about the core centroid, weighted by the pixel values." There are considerable uncertainties in any dust and virial mass estimates., There are considerable uncertainties in any dust and virial mass estimates. The errors are very difficult to quantify for individual clumps without detailed modelling., The errors are very difficult to quantify for individual clumps without detailed modelling. " Thus, we follow complementary studies citealtbuckle10,enoch08)) and do not attempt to account for the uncertainties in our analysis, except for a discussion of their magnitude, which follows."," Thus, we follow complementary studies \\citealt{buckle10,enoch08}) ) and do not attempt to account for the uncertainties in our analysis, except for a discussion of their magnitude, which follows." The dust masses depend on the assumed distance to Perseus and the dust properties (temperature and opacity)., The dust masses depend on the assumed distance to Perseus and the dust properties (temperature and opacity). " We try to minimize the effects of dust temperature by using the kkinetic temperature as an estimate of 7p, which should be an accurate measurement at high volume densities (>10cmthree,, citealt*galli02)), where the gas and dust are thermally coupled."," We try to minimize the effects of dust temperature by using the kinetic temperature as an estimate of $T_\mathrm{D}$, which should be an accurate measurement at high volume densities $\gtrsim 10^4$, \\citealt*{galli02}) ), where the gas and dust are thermally coupled." Nevertheless our dust temperature estimates still do not account for variations in the dust temperature across a clump., Nevertheless our dust temperature estimates still do not account for variations in the dust temperature across a clump. A range of distances have been used in the literature for Perseus (220 to ppc see citetaliaspaper1)) and indeed it may not be a contiguous cloud at a single distance., A range of distances have been used in the literature for Perseus (220 to pc see \\citetalias{paper1}) ) and indeed it may not be a contiguous cloud at a single distance. These result in an uncertainty of a factor of ~5 in the dust mass estimates., These result in an uncertainty of a factor of $\sim 5$ in the dust mass estimates. " The virial masses depend on the assumed clump profile, with steeper profiles producing smaller masses, however it only varies by a factor of 1.7 between a constant density and 1/r? profile."," The virial masses depend on the assumed clump profile, with steeper profiles producing smaller masses, however it only varies by a factor of 1.7 between a constant density and $1/r^2$ profile." This combined with the uncertainties in the distance and linewidth produce again around a factor of —5 in uncertainty.," This combined with the uncertainties in the distance and linewidth produce again around a factor of $\sim 5$ in uncertainty." " As we previously noted (§3-])), it is likely that the lline only traces the envelope of a clump, which could lead to an over-estimate of the non-thermal llinewidth (compared to estimates from say oor N5H)) and correspondingly the virial mass."," As we previously noted \ref{sec:linewidths}) ), it is likely that the line only traces the envelope of a clump, which could lead to an over-estimate of the non-thermal linewidth (compared to estimates from say or ) and correspondingly the virial mass." " Even if our estimates of the dust and virial masses were infallible, assuming that a clump with Μγι>>Mgso is unbound may be misleading; external pressure and/or magnetic fields may contain such a clump."," Even if our estimates of the dust and virial masses were infallible, assuming that a clump with $M_\mathrm{vir}\gg M_{850}$ is unbound may be misleading; external pressure and/or magnetic fields may contain such a clump." " For instance [KJTO7| calculate that cores with external pressures consistent with their previous Bonnor-Ebert sphere modelling (Kirk,Johnstone&DiFrancesco|2006),, should be considered in not merely self-gravitating if Myi,~2Mgso."," For instance \citetalias{hkirk07} calculate that cores with external pressures consistent with their previous Bonnor-Ebert sphere modelling \citep*{kirk06}, should be considered in not merely self-gravitating if $M_\mathrm{vir}\sim 2 M_{850}$." " The vvirial masses, which we plot in reffig:virial against the mmass, lie in the range 0.8 to MM. for the ssources and 0.4 to MM, for the ssources, reflecting their smaller radii."," The virial masses, which we plot in \\ref{fig:virial} against the mass, lie in the range 0.8 to $_\odot$ for the sources and 0.4 to $_\odot$ for the sources, reflecting their smaller radii." " Most of the clumps lie scattered near the ‘equipartition’ line, My;,—Mgso."," Most of the clumps lie scattered near the `equipartition' line, $M_\mathrm{vir} =M_{850}$." " The results are similar for the different algorithms, regions and evolutionary types (see Tables B| and for summaries of the population statistics)."," The results are similar for the different algorithms, regions and evolutionary types (see Tables \ref{tab:mvir_clfind} and \ref{tab:mvir_gclumps} for summaries of the population statistics)." Least-squares straight-lineH] fitting results in poorly-constrained power law exponents of 0.8—0.9 for almost all thecorrelations., Least-squares straight-line fitting results in poorly-constrained power law exponents of 0.8–0.9 for almost all thecorrelations. " Given the uncertainties in both the virial and dust mass estimates, it is not possible to draw unequivocal conclusions about the stability of individiual clumps."," Given the uncertainties in both the virial and dust mass estimates, it is not possible to draw unequivocal conclusions about the stability of individiual clumps." " However, we will compare"," However, we will compare" For anw sel(-gravitating object. the definition οἱ “compactness” may be given in terms of the surface eravitational recshift(Weinberg 1972): where By=2CMfcο is the Schwarzschild radius of the object having a gravitational mass AZ and radius A.,"For any self-gravitating object, the definition of “compactness” may be given in terms of the surface gravitational redshift(Weinberg 1972): where $R_s = 2 G M/c^2$ is the Schwarzschild radius of the object having a gravitational mass $M$ and radius $R$." Here. G is the Newtonian gravitational constant and. e is the speed of light.," Here, $G$ is the Newtonian gravitational constant and $c$ is the speed of light." " For the Sun. one has z2«10"" while for a typical neutron star z~0.15."," For the Sun, one has $z \approx 2 \times 10^{-6}$ while for a typical neutron star $z \sim 0.15$." " Anotherimportant parameter [or a self-gravitating object is ar= ενω. where p, is the pure radiation pressure and p, is the kinetic pressure (Mitra 2009a.b)."," Anotherimportant parameter for a self-gravitating object is $x= p_r/p_g$ , where $p_r$ is the pure radiation pressure and $p_g$ is the kinetic pressure (Mitra 2009a,b)." While the central region of Sun has ο20.006. obviously. à.cold object at temperature Z7=0 has c=0.," While the central region of Sun has $x \approx 0.006$, obviously, a object at temperature $T=0$ has $x=0$." lt ijs known that strictly static anccold stars have an upper mass limit both in Newtonian and Einstein gravity., It is known that strictly static and stars have an upper mass limit both in Newtonian and Einstein gravity. " In the Newtonian case. this is obtained by the marriage of Newtonian gravity and Special Relativity. and is known as ""Chandrasekhar \lass”. Ad,"," In the Newtonian case, this is obtained by the marriage of Newtonian gravity and Special Relativity, and is known as “Chandrasekhar Mass”, $M_{ch}$." " On the other hand. in Einstein eravity. such an upper mass limit is known as ""Oppenheimer ΝΟκο Mass"" (Weinberg 1972)."," On the other hand, in Einstein gravity, such an upper mass limit is known as “Oppenheimer -Volkoff Mass” (Weinberg 1972)." Phe precise values of such limits depend. on the equation. of state (EOS) ancl other details., The precise values of such limits depend on the equation of state (EOS) and other details. " However. for a purecold. Helium: dwarf. AL, L4Al.. where M. is the solar mass."," However, for a pure, Helium dwarf, $M_{ch} \sim 1.4 M_\odot$ , where $M_\odot$ is the solar mass." " On the other hand. for a pure free neutron Fermi-Dirac Εις, AZ,OAL.."," On the other hand, for a pure free neutron Fermi-Dirac fluid, $M_{ov} \sim 0.8 M_\odot$." But if such. upper limits were the full story. we would not have had stars of masses as large as LOOAL..," But if such upper limits were the full story, we would not have had stars of masses as large as $\sim 100 M_\odot$." Further. there are interstellar eas clouds of mass probably as large as ~10AL...," Further, there are interstellar gas clouds of mass probably as large as $\sim 10^6 M_\odot$." Phe reason behind the existence of non-singular cosmic objects with such higher masses is that they are not supported bycold quantum. pressure alone., The reason behind the existence of non-singular cosmic objects with such higher masses is that they are not supported by quantum pressure alone. " On the other hand. they aresupported not only by p, but partly by p, too (Mitra 2009a.b)."," On the other hand, they aresupported not only by $p_g$ but partly by $p_r$ too (Mitra 2009a,b)." Even when one would work at a purely Newtonian level (2« 1l) the probable increase in the value of ue would support the higher self-gravity of a star M.LAM...," Even when one would work at a purely Newtonian level $z \ll 1$ ), the probable increase in the value of $x$ would support the higher self-gravity of a star $M \gg 1 M_\odot$." And this was probably first realized by Llovle Fowler (1963)ancl Fowler (1966) who conceivec of the Racliation Pressure Supported Stars (RPSS) having +91., And this was probably first realized by Hoyle Fowler (1963)and Fowler (1966) who conceived of the Radiation Pressure Supported Stars (RPSS) having $x\gg 1$. IH turns out that. given the self-imposed restriction. z< 7200 M_\odot$ in order to have $x >1$ (Weinberg 1972)." With the increase ofr and attendant self-egravity. the star tends to be more compact. i.e... 2 would increase Mitra(2009a.b).," With the increase of $x$ and attendant self-gravity, the star tends to be more compact, i.e., $z$ would increase Mitra(2009a,b)." " For instance even though “supermassive stars” are Newtonian (Le. 2« 1). they possess 2 much larger than the solar value of 2.zz2.10 ""."," For instance even though “supermassive stars” are Newtonian (i.e., $z \ll 1$ ), they possess $z$ much larger than the solar value of $z_\odot \approx 2 \times 10^{-6}$ ." Accordingly. itis possible to conceive of a Newtonian RPSS with z~ 0.1. Le. one which is almost as compact as a neutron star.," Accordingly, itis possible to conceive of a Newtonian RPSS with $z \sim 0.1$ , i.e., one which is almost as compact as a neutron star." A related important, A related important A revised statistical analvsis of the properties of the low-redshift PG QSOs has been performed. with updated measurements.,"A revised statistical analysis of the properties of the low-redshift PG QSOs has been performed, with updated measurements." Two principal components have been identified. corresponding. as in DG92. to the Fe IL[O II] anticorrelation and to the luminosity.," Two principal components have been identified, corresponding, as in BG92, to the Fe II–[O III] anticorrelation and to the luminosity." Black hole masses for this sample have been estimated using the formula derived by Laor(2000)., Black hole masses for this sample have been estimated using the formula derived by \citet{Laor00}. ". These indicate that the (vo principal components correspond closely to the Eddington ratio and the accretion rate. respectively,"," These indicate that the two principal components correspond closely to the Eddington ratio and the accretion rate, respectively." Two additional radio-loud samples have been added to the analvsis. by using the principal component definitions derived [rom the PG sample.," Two additional radio-loud samples have been added to the analysis, by using the principal component definitions derived from the PG sample." Inspection of the PCI-PCY diagram for this enlarged sample shows (hat: ] wish to thank Richard Green ancl Michael Brotherton for helpful discussions. and Ari Laor lor the use of his database.," Inspection of the PC1-PC2 diagram for this enlarged sample shows that: I wish to thank Richard Green and Michael Brotherton for helpful discussions, and Ari Laor for the use of his database." This research has made tse ofthe NASA/IPAC Extragalactic Database (NED) which is operated bv the Jet Propulsion Laboratory. California Institute ol Technology. under contract with the National Aeronautics ancl Space Adminsitration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Adminsitration." of ®|V is the same as in GR. which is true for DOP (Ixovama2006) and f) for fio<1 (Ovaizuetal.2008)..,"of $\Phi + \Psi$ is the same as in GR, which is true for DGP \citep{Koyama:2006ef} and $f(R)$ for $f_{R0} \ll 1$ \citep{Oyaizu:2008tb}." Figures S(a) and S(b) demonstrate the dependence of the parameters on one another when fitting weak lensing predictions for varving 5. 24. ay and às to a ACDAL fiducial model when ο and ay are fixed at the central. values fitting WAIAP|BAOSNe.," Figures \ref{fig:lcdm des central} and \ref{fig:lcdm euclid central} demonstrate the dependence of the parameters on one another when fitting weak lensing predictions for varying $\gamma$, $A$ , $\alpha_1$ and $\alpha_2$ to a $\Lambda$ CDM fiducial model when $\Omega_m$ and $\sigma_8$ are fixed at the central values fitting WMAP+BAO+SNe." The slight. widening in the > constraint as el. ay and à» increase is due to being able to recover XCDAI at non-linear scales by increasing οἱ and o4 as varies.," The slight widening in the $\gamma$ constraint as $A$ , $\alpha_1$ and $\alpha_2$ increase is due to being able to recover $\Lambda$ CDM at non-linear scales by increasing $A$ and $\alpha_1$ as $\gamma$ varies." This means that the constraint on . degrades slightly by including the parameters in the Llu and Sawicki fitting formula (2k. ay and a»).," This means that the constraint on $\gamma$ degrades slightly by including the parameters in the Hu and Sawicki fitting formula $A$, $\alpha_1$ and $\alpha_2$ )." The constraint obtained by mareginalising over all ο and os shown in Figures O(a) and 9(b) shows that the constraint for . for a ACDAL fiducial model is very good. as shown in Table 5.. measuring ~ within ofits value for the &round-based: survey and within for Euclid. while the other parameters are cdillieult to constrain.," The constraint obtained by marginalising over all $\Omega_m$ and $\sigma_8$ shown in Figures \ref{fig:lcdm des param} and \ref{fig:lcdm euclid param} shows that the constraint for $\gamma$ for a $\Lambda$ CDM fiducial model is very good, as shown in Table \ref{sigma1 sigma2 lcdm}, measuring $\gamma$ within ofits value for the ground-based survey and within for Euclid, while the other parameters are difficult to constrain." A better constraint on the parameters can be found for a growth history that is not . CDM. such as DGD. as shown in Figures 9(c). and 9(d)..," A better constraint on the parameters can be found for a growth history that is not $\Lambda$ CDM, such as DGP, as shown in Figures \ref{fig:dgp des param} and \ref{fig:dgp euclid param}." Ες provides a better constraint on ch ay and a». but the constraint on * is not as tight. as shown in Table οι. measuring within of its value for the ground-based survey and within for Euclid.," This provides a better constraint on $A$, $\alpha_1$ and $\alpha_2$, but the constraint on $\gamma$ is not as tight, as shown in Table \ref{sigma1 sigma2 dgp}, , measuring $\gamma$ within of its value for the ground-based survey and within for Euclid." This is due to the degeneracy between 5 and the other parameters in this instance., This is due to the degeneracy between $\gamma$ and the other parameters in this instance. " These degeneracies can be seen moreclearly before the results are marginalisedover ,, and ox as shown in Figures S(c) and S(d)..", These degeneracies can be seen moreclearly before the results are marginalisedover $\Omega_m$ and $\sigma_8$ as shown in Figures \ref{fig:dgp des central} and \ref{fig:dgp euclid central}. . Phe large dependence on the other fitting parametersdemonstrates that care should be taken when predicting ~ constraints using this parameterisation., The large dependence on the other fitting parametersdemonstrates that care should be taken when predicting $\gamma$ constraints using this parameterisation. coniet. however. πηρα aneular momentum in one direction of one componcut ouly. depending ou the angle between rand ον.,"comet, however, impart angular momentum in one direction of one component only, depending on the angle between $\hat r_b$ and $\hat v_p$." Not coincidentally. the mean torque found in the sinooth distribution linüt. Equation 1.. is attributed to the disk of stars passing between the Sun aud the comet.," Not coincidentally, the mean torque found in the smooth distribution limit, Equation \ref{eqGalTorque}, is attributed to the disk of stars passing between the Sun and the comet." We quantify the effect of this asvuunetry by calculating the marginal probability density of cach component of the aneulay momentum vector due to single interactions., We quantify the effect of this asymmetry by calculating the marginal probability density of each component of the angular momentum vector due to single interactions. " Since we have lost the svuumetiv that aciuitted the simple aualytic solutions. we eniploy a Monte-Carlo procedure,"," Since we have lost the symmetry that admitted the simple analytic solutions, we employ a Monte-Carlo procedure." " The position of the comot. which we hold fixed in this example. ix,=y|τι so the Sueconmet distance ix ry=V2."," The position of the comet, which we hold fixed in this example, is $\vec r_b = \hat y + \hat z$, so the Sun-comet distance is $r_b = \sqrt{2}$." The perturber velocities are set to the : direction: =2., The perturber velocities are set to the $\hat z$ direction: $\hat v_p = -\hat z$. The possible impact parameters of the perturbers are then restricted to the...y plane., The possible impact parameters of the perturbers are then restricted to the $x-y$ plane. We raudonmly chooseον impact piriuueters such that they are uniformly distributed over the plane aud calculate the AJ delivered to the comet., We randomly choose impact parameters such that they are uniformly distributed over the plane and calculate the $\Delta \vec J$ delivered to the comet. " We assunie the other parameters of the svstem are held coustaut aud aud to reduce the notation. we use mits where 26,/0,=1."," We assume the other parameters of the system are held constant $v_p$ and $m_p$ ), and to reduce the notation, we use units where $2 G m_p/v_p \equiv 1$." " The angular ποιο is coufined to the (6,plane perpeudicular,). to rj. which iu these coordinates is defined by the basis vectors er aud (9:)/ V2."," The angular momentum is confined to the plane perpendicular to $\vec r_b$, which in these coordinates is defined by the basis vectors $\hat x$ and $(\hat y - \hat z)/\sqrt{2}$ ." For sinplicitv we diseuss the c aud y componeuts of the perturbation. AJ:=JL and AJ:y=J.," For simplicity we discuss the $x$ and $y$ components of the perturbation, $\Delta \vec J \cdot \hat x = J'_x$ and $\Delta \vec J \cdot \hat y = J'_y$." Iu the z-direction. AJ+2 is exactly the same as J.," In the $z$ -direction, $\Delta \vec J \cdot \hat z$ is exactly the same as $J'_y$." The positive and negative values for Ji aud. J7 are binned separately: the resulting four histograms then describe the niarginal PDF for cach coniponent., The positive and negative values for $J'_x$ and $J'_y$ are binned separately; the resulting four histograms then describe the marginal PDF for each component. Figure 1l illustrates the caleulation of the sinele interaction PDF., Figure \ref{figContours} illustrates the calculation of the single interaction PDF. " Pauels a audb ""mshow logarithmically spaced contours of constant 7 and Ji respectively in the plane of possible impact parame with the other parameters of the interaction fixed (rj.vy. i4)."," Panels a and b show logarithmically spaced contours of constant $J'_x$ and $J'_y$ respectively in the plane of possible impact parameters, with the other parameters of the interaction fixed $\vec r_b, \vec v_p, m_b$ )." The iupaet parzuueter plotted is scaledby rj::—rs.=1d., The impact parameter plotted is scaled by $\vec r_b \cdot \hat z = r_z = 1$. The solid coutours correspoud to positive perturbatious aud the dashed lines to negative oues., The solid contours correspond to positive perturbations and the dashed lines to negative ones. Iu pauclb). the coutours for £47 exhibit an axisvinunetrie pattern: for each unit of area that contributes perturbations of a given magnitude ereater than zero. there is au equivalent area where perturbations have the opposite sign.," In panel b), the contours for $\pm J'_y$ exhibit an axisymmetric pattern; for each unit of area that contributes perturbations of a given magnitude greater than zero, there is an equivalent area where perturbations have the opposite sign." Thus the single interaction mareinal PDF of perturbations in the y directious are identical aud unchanged from the isotropic case: 1η for the distant perturbatious. JiD»org). ancl Ji? for the close euconuters. Jixrp).," Thus the single interaction marginal PDF of perturbations in the $\hat y$ directions are identical and unchanged from the isotropic case: ${J'_y}^{-1}$ for the distant perturbations, $J'_y(b \gg r_b)$, and ${J'_y}^{-2}$ for the close encounters, $J'_y(b \ll r_b)$." There is no coherent accumulation of augular momentum in the y direction., There is no coherent accumulation of angular momentum in the $\hat y$ direction. The contours of panel a). while svuumetric at larger b. are not svuumetric iu the center. where the perturbations ouly add angular ποιοται in the negative.e direction.," The contours of panel a), while symmetric at larger $\vec b$ , are not symmetric in the center, where the perturbations only add angular momentum in the negative $\hat x$ direction." There is no equivalent area that delivers aneular moment with the oppositesign., There is no equivalent area that delivers angular momentum with the opposite sign. We plot the mareial PDF of 'TlThe in panel ο) of FigureordinateL.. where the solid line is for perturbations where J7>0 and the dashed licis for theJf.," We plot the marginal PDF of $J'_x$, $|J'_x| {\cal R}(J'_x)$, in panel c) of Figure \ref{figContours}, where the solid line is for perturbations where $J'_x>0$ and the dashed line is for $J'_x<0$." J 6G).values along the represent the probability of perturbations with strength of order 77.of relative to lowest value plotted., The values along the ordinate represent the probability of perturbations with strength of order $J'_x$ relative to the lowest value plotted. Iu the tidal aud close encounter regimes. the two functious are identical.," In the tidal and close encounter regimes, the two functions are identical." For J.a order unitv.the contribution of the ceutral region iu paucl a) is obvious.," For $J'_x$ of order unity,the contribution of the central region in panel a) is obvious." It is these interactions that eive riseto the torque associated with the Galactic tides., It is these interactions that give riseto the torque associated with the Galactic tides. velocity widths for a given EW than DLAs (parameterized by the D-index).,velocity widths for a given EW than DLAs (parameterized by the $D$ -index). Since we have already shown that Av is correlated with metallicity in sub-DLAs (Fig. 2).," Since we have already shown that $\Delta {\rm v}$ is correlated with metallicity in sub-DLAs (Fig. \ref{velocity-metallicity}) )," we then expect that sub-DLAs selected on their high EWs will have higher metallicities., we then expect that sub-DLAs selected on their high EWs will have higher metallicities. We conclude that the selection bias is a viable explanation for the systematically higher metallicities in redshift sub-DLAs2007)., We conclude that the selection bias is a viable explanation for the systematically higher metallicities in low-redshift sub-DLAs. . The ultimate test of this explanation would be to conduct a blind sub-DLA survey at z«1.7., The ultimate test of this explanation would be to conduct a blind sub-DLA survey at $z<1.7$. In summary. we conclude that in general sub-DLAs are not uniquely synonymous with massive galaxies and that their high metallicities observed at z<1.7 that drives an apparently steep evolution may be due to selection eftects.," In summary, we conclude that in general sub-DLAs are not uniquely synonymous with massive galaxies and that their high metallicities observed at $z<1.7$ that drives an apparently steep evolution may be due to selection effects." We are grateful to Nikola Milutinovie for supplying results from his Cloudy models. and we thank Max Pettini and Jason X. Prochaska for very helpful exchanges.," We are grateful to Nikola Milutinovic for supplying results from his Cloudy models, and we thank Max Pettini and Jason X. Prochaska for very helpful exchanges." MD-Z is supported by the Swiss National Funds and SLE by an NSERC Discovery grant., MD-Z is supported by the Swiss National Funds and SLE by an NSERC Discovery grant. MTM thanks the Australian Research Council fora QEII Research Fellowship (DP0877998)., MTM thanks the Australian Research Council for a QEII Research Fellowship (DP0877998). Observational evidences of απ intracluster stellar population (hereafter ISP) are mainly based on the detection of planetary nebulae auc red giaut brauch stars freely floating in the intergalactic space.,Observational evidences of an intracluster stellar population (hereafter ISP) are mainly based on the detection of planetary nebulae and red giant branch stars freely floating in the intergalactic space. For example. Theuns Warren (1996) identified 10. interealactic planetary nebulae in the Fornax cluster. while Ménudez et al (," For example, Theuns Warren (1996) identified 10 intergalactic planetary nebulae in the Fornax cluster, while Ménndez et al. (" 1997) detected 11 interealactic objects im the Virgo cluster whose cumulative huiinositv functions is in good agreement with plauetarv nebula. dDunüinositv function.,1997) detected 11 intergalactic objects in the Virgo cluster whose cumulative luminosity functions is in good agreement with planetary nebula luminosity function. Iu addition. Ferguson et al. (," In addition, Ferguson et al. (" 1998) identified an interealactic red giant branch stars population iu the Vireo cluster. while Fekünueier et al. (,"1998) identified an intergalactic red giant branch stars population in the Virgo cluster, while Feldmeier et al. (" 1998) (with observations of three blank fields iu the Vireo cluster). confine lat a significant fraction of Virgo's starlight is due to the ISP.,"1998) (with observations of three blank fields in the Virgo cluster), confirmed that a significant fraction of Virgo's starlight is due to the ISP." More recently Okamura οἳ al. (, More recently Okamura et al. ( 2002) have identified 238 candidates of intracluster planetary nebulac iu the core of the Virgo cluster.,2002) have identified 38 candidates of intracluster planetary nebulae in the core of the Virgo cluster. Overall. the data sugeest that approximately (or even more) of the stellar inass of the cluster is im intergalactic stars (6.9. see Ferguson et al.," Overall, the data suggest that approximately (or even more) of the stellar mass of the cluster is in intergalactic stars (e.g., see Ferguson et al." 1998. Aruaboldi et al.," 1998, Arnaboldi et al." 2002. Duel et al.," 2002, Durrel et al." 2002. Απο et al.," 2002, Arnaboldi et al." 2003. Totani 2003. see also Arnaboldi. Gerhard Frecimau 2003. and references therein).," 2003, Totani 2003, see also Arnaboldi, Gerhard Freeman 2003, and references therein)." " The usual scenario assumed to explain the finding above is that the idal interactions between galaxies (for exanuple diving a fast encounter. e.g. see Merritt 1982. 1981. 19585). aud of ealaxies with the cluster eravitational field. lead to a substantial stripping of stars from galaxies to the parent cluster (the so-called vealaxy harassicut™ sCOLhaYlO. SOC. ονο, Moore et al."," The usual scenario assumed to explain the finding above is that the tidal interactions between galaxies (for example during a fast encounter, e.g., see Merritt 1983, 1984, 1985), and of galaxies with the cluster gravitational field, lead to a substantial stripping of stars from galaxies to the parent cluster (the so-called “galaxy harassment” scenario, see, e.g., Moore et al." 1996: Napolitano ct al., 1996; Napolitano et al. 2003)., 2003). In this paper we explore an additional “stripping” mechanisni namely we quantitatively discuss the effect of resonant interaction between stellar orbits inside the ealaxies and the cluster tidal field (hereafter. CTF).," In this paper we explore an additional “stripping” mechanism, namely we quantitatively discuss the effect of resonant interaction between stellar orbits inside the galaxies and the cluster tidal field (hereafter, CTF)." The present study is supported by the fact that the characteristic oscillation times of a galaxw near its equilibrimm position in the CTF and the mean stellar orbital times in the ealaxy external regions are of the same order of maguitude. as already recognized by Ciotti Ciuupieri (1998. hereafter CO9s).," The present study is supported by the fact that the characteristic oscillation times of a galaxy near its equilibrium position in the CTF and the mean stellar orbital times in the galaxy external regions are of the same order of magnitude, as already recognized by Ciotti Giampieri (1998, hereafter CG98)." Iu fact. Haley Peebles (1975) reported a possible indication (confirmed by Thompson L976). that the ealaxies are preferentially aligned along the radius vector to the ceuter of the cluster for the Coma cluster: they also suggested the CTF as the possible cause of the aliguinent.," In fact, Hawley Peebles (1975) reported a possible indication (confirmed by Thompson 1976), that the galaxies are preferentially aligned along the radius vector to the center of the cluster for the Coma cluster; they also suggested the CTF as the possible cause of the alignment." The best evidence for alienneut is for brightest cluster galaxies: Adams. Strom Strom (1980) found. in 7 very clongated clusters. a general trend for clipticals to be aligned with the cluster major axis. aud also Trevese. Ciuucle Flin (1992) fouud a strong aligument of the brightest ealaxy uajor with the long axis of the pareut cluster.," The best evidence for alignment is for brightest cluster galaxies: Adams, Strom Strom (1980) found, in 7 very elongated clusters, a general trend for ellipticals to be aligned with the cluster major axis, and also Trevese, Cirmele Flin (1992) found a strong alignment of the brightest galaxy major with the long axis of the parent cluster." Numerical N-body simulations (Ciotti Dutta 1991. hereafter CD91) iideed confined ie hwpothesis that the CTF could be at the origin of the observed aliguinent and. i particular. revealed vat their model clliptical galaxies (Es) behaved with eood approximation as rigid bodies.," Numerical N-body simulations (Ciotti Dutta 1994, hereafter CD94) indeed confirmed the hypothesis that the CTF could be at the origin of the observed alignment and, in particular, revealed that their model elliptical galaxies (Es) behaved with good approximation as rigid bodies." In a complementary ualvtical exploration of this xoblem C698 determined ie equilibrium positions of triaxial cllipsoids iu the CTF for various cases. and showed that the oscillatious σος. of the galaxies. when slightly displaced from 1011 equilibrium confgurations. are of the same order of magnitude of the stellar orbital periods iu the galaxy outskirts.," In a complementary analytical exploration of this problem CG98 determined the equilibrium positions of triaxial ellipsoids in the CTF for various cases, and showed that the oscillations period of the galaxies, when slightly displaced from their equilibrium configurations, are of the same order of magnitude of the stellar orbital periods in the galaxy outskirts." This curious finding naturally leads to ask what could be the effect of possible “resonances” between stellar orbital periods iu cluster Ex aud their oscillation periods., This curious finding naturally leads to ask what could be the effect of possible “resonances” between stellar orbital periods in cluster Es and their oscillation periods. Untortunately. the N-body sinulatious of CD9 ποσο characterized by a limited ummber of particles (1.6... /Nτς 3105) and by he usual softening. so that evaporations rates could not be properly iuvestigated.," Unfortunately, the $N$ -body simulations of CD94 were characterized by a limited number of particles (i.e., $N\simeq 3\times 10^4$ ) and by the usual softening, so that evaporations rates could not be properly investigated." Iu order to investigate the scenario described above. Afuccioue Chotti (2003a.b. hereafter AIC03a.)) performed a few prelhiüuarv ALloute-Carlo suulatious οἳ orbital exploration of oscillating galaxies. aud the results were," In order to investigate the scenario described above, Muccione Ciotti (2003a,b, hereafter MC03a,b) performed a few preliminary Monte-Carlo simulations of orbital exploration of oscillating galaxies, and the results were" ejecta but of indicativea hot central source. vet accompanied by strong Balmer lines extending to high series components and by Tell emission lines. with only moderate LL and 4650A Bowen lluorescence Lines.,"ejecta but indicative of a hot central source, yet accompanied by strong Balmer lines extending to high series components and by I emission lines, with only moderate II and 4650 Bowen fluorescence lines." These are more characteristic of dwarf novae spectra. than of old. novae., These are more characteristic of dwarf novae spectra than of old novae. Schmidtobreick et al. (, Schmidtobreick et al. ( 2005) find that the much older nova NX Tau (Nova Tauri 1927. /4=42 d) has a similar unusual emission line spectrum and suggest that both of these novae could be currently in states of low rates of mass transfer (M).,"2005) find that the much older nova XX Tau (Nova Tauri 1927, $t_3 = 42$ d) has a similar unusual emission line spectrum and suggest that both of these novae could be currently in states of low rates of mass transfer $\dot{M}$ )." Finally. previous high speed. photometry of VS42 Cen. carried out in 2000 (Woudt Warner 2003: hereafter WWO3). showed extreme activity with [Lares up to 0.25 mag on time scales 5 min but no evident orbital or short period coherent. brightness mocdulations. though there were quasi-periodic oscillations (QPOs) on time scales —1000. s. A parallel was drawn with the light curve of PP Ari. which isa hieh AL nova-like cataclvsmic variable (CV).," Finally, previous high speed photometry of V842 Cen, carried out in 2000 (Woudt Warner 2003: hereafter WW03), showed extreme activity with flares up to 0.25 mag on time scales $\sim 5$ min but no evident orbital or short period coherent brightness modulations, though there were quasi-periodic oscillations (QPOs) on time scales $\sim 1000$ s. A parallel was drawn with the light curve of TT Ari, which is a high $\dot{M}$ nova-like cataclysmic variable (CV)." With a view to checking whether V842 Cen had changed its light curve character in the S vears since it was last observed we mace an initial exploration in February 2008. and the surprising result. led us to concentrate on it. [or the remainder of that and the following observing run.," With a view to checking whether V842 Cen had changed its light curve character in the 8 years since it was last observed we made an initial exploration in February 2008, and the surprising result led us to concentrate on it for the remainder of that and the following observing run." The optical observations are described and analysed in Section 2. X-Ray observations in Section 3. and a discussion is given in Section 4.," The optical observations are described and analysed in Section 2, X-Ray observations in Section 3, and a discussion is given in Section 4." Our observations were mace with the University of Cape ‘Town's frame transfer CCD photometer (ODonoghue 1995) attached to the 74-in Badelille telescope at the Sutherland site of the South African. Astronomical Observatory., Our observations were made with the University of Cape Town's frame transfer CCD photometer (O'Donoghue 1995) attached to the 74-in Radcliffe telescope at the Sutherland site of the South African Astronomical Observatory. All yhotometry was unlilterecl (io. in white light). with 6 s integrations. and a white dwarf stanclard star was used to oovide an approximate V magnitude scale.," All photometry was unfiltered (i.e. in white light), with 6 s integrations, and a white dwarf standard star was used to provide an approximate V magnitude scale." Lhe observing runs are listed in Table 1.., The observing runs are listed in Table \ref{v842centab1}. Fig., Fig. 1 shows the light curves for February 2008 (note hat V842 Cen was only. accessible at the end of the night or à maximum of about 4 hours) and Fig., \ref{v842cenfig1} shows the light curves for February 2008 (note that V842 Cen was only accessible at the end of the night for a maximum of about 4 hours) and Fig. 2. shows the Alarch 2008 light. curves., \ref{v842cenfig2} shows the March 2008 light curves. In the latter we have phased the ight curves on a period of 3.780 h. for reasons explained rclow.," In the latter we have phased the light curves on a period of 3.780 h, for reasons explained below." Comparison with the 2000 light curves (NVO3) shows one immediately obvious change — there are now recurrent »eaks of amplitude ~0.3 mag on a time scale 4 h. A more subtle addition appears when comparing the high frequency xuwts of the Fourier traüsforms. (LPs) of individual runs in June 2000. February 2008 and March. 2008.," Comparison with the 2000 light curves (WW03) shows one immediately obvious change – there are now recurrent peaks of amplitude $\sim 0.3$ mag on a time scale $\sim 4$ h. A more subtle addition appears when comparing the high frequency parts of the Fourier transforms (FTs) of individual runs in June 2000, February 2008 and March 2008." As seen in Fie. 3..," As seen in Fig. \ref{v842cenfig3}," a modulation at ~57 s has appeared in the interval., a modulation at $\sim 57$ s has appeared in the interval. There is no sign of this in à short run made in March. 2002 (NNOA)., There is no sign of this in a short run made in March 2002 (WW03). BL Lacertae objects (BL Lacs) are active galactic nuclet (AGN) characterized by a featureless nonthermal continuum. high optical and radio polarization. and variability across the entire electromagnetic spectrum.,"BL Lacertae objects (BL Lacs) are active galactic nuclei (AGN) characterized by a featureless nonthermal continuum, high optical and radio polarization, and variability across the entire electromagnetic spectrum." These properties arise from a relativistic jet pointed almost towards the observer (?)., These properties arise from a relativistic jet pointed almost towards the observer . . The strong continuum emission from the jet in the optical sometimes presents a problem when attempting to properly characterize the underlying host galaxy or measure its redshift. especially since by definition the emission lines are very weak in BL Laes.," The strong continuum emission from the jet in the optical sometimes presents a problem when attempting to properly characterize the underlying host galaxy or measure its redshift, especially since by definition the emission lines are very weak in BL Lacs." Hence. it is unsurprising that even after very deep searches many BL Laces remain without a spectroscopically determined redshift.," Hence, it is unsurprising that even after very deep searches many BL Lacs remain without a spectroscopically determined redshift." The redshift i5 a fundamental property of any extragalactic object. without which e.g. the luminosity or intrinsic variability properties of the target cannot be determined.," The redshift is a fundamental property of any extragalactic object, without which e.g. the luminosity or intrinsic variability properties of the target cannot be determined." Furthermore. many BL Laes have been recently detected at TeV gamma-rays using ground-based Cherenkov telescopes MAGIC. HESS. and VERITAS ?).," Furthermore, many BL Lacs have been recently detected at TeV gamma-rays using ground-based Cherenkov telescopes MAGIC, HESS, and VERITAS ." . Since VHE gamma-rays ean be absorbed by the interaction with low energy photons of the EBL via pair production. this opens the possibility of measuring the amount of extragalactic background light in the optical through to the far infrared. which provides important information about the galaxy and star formation history.," Since VHE gamma-rays can be absorbed by the interaction with low energy photons of the EBL via pair production, this opens the possibility of measuring the amount of extragalactic background light in the optical through to the far infrared, which provides important information about the galaxy and star formation history." The absorption depends strongly on the distance of the source and the energy of the gamma-rays., The absorption depends strongly on the distance of the source and the energy of the gamma-rays. If the redshift of the source is known. the VHE gamma-ray spectrum can be used to derive limits on the EBL ??).," If the redshift of the source is known, the VHE gamma-ray spectrum can be used to derive limits on the EBL ." . On the other hand. if the redshift is unknown. the VHE gamma-ray spectra can be used to set an upper limit to the redshift of the source ?).," On the other hand, if the redshift is unknown, the VHE gamma-ray spectra can be used to set an upper limit to the redshift of the source ." ". After its discovery as a bright (Sse, > 1 Jy) flat-spectrum (vy€-0.5. S.x v"") radio source. the BL Lae object has been studied intensively at all frequency bands."," After its discovery as a bright $_{\rm 5 Ghz}$ $>$ 1 Jy) flat-spectrum $\alpha \leq -0.5$, $_{\nu} \propto \nu^{\alpha}$ ) radio source, the BL Lac object has been studied intensively at all frequency bands." The object is highly variable with rapid variations observed from radio to X-ray bands(??).., The object is highly variable with rapid variations observed from radio to X-ray bands. The nucleus of is typically bright in the optical?).. thus previous attempts to either characterize its host galaxy or to determine its redshift spectroscopically have not been successful.," The nucleus of is typically bright in the optical, thus previous attempts to either characterize its host galaxy or to determine its redshift spectroscopically have not been successful." Thus. in spite of numerous variability studies of0716+714.. it has never been possible to determine reliably e.g. the linear dimensions and luminosities of the varying components.," Thus, in spite of numerous variability studies of, it has never been possible to determine reliably e.g. the linear dimensions and luminosities of the varying components." has also been detected in TeV gamma-rays(?)., has also been detected in TeV gamma-rays. . Given that previous estimates place at z > 0.3. this would make the target one of the most distant TeV sources detected so far.," Given that previous estimates place at z $>$ 0.3, this would make the target one of the most distant TeV sources detected so far." Given the obvious importance of to EBL studies. it is be important to secure an accurate spectroscopic redshift for or at least constrain the redshift by some other means.," Given the obvious importance of to EBL studies, it is be important to secure an accurate spectroscopic redshift for or at least constrain the redshift by some other means." is regularly monitored at Tuorla Observatory as part of the blazar monitoringprogram!., is regularly monitored at Tuorla Observatory as part of the blazar monitoring. . On December 17. 2007 we observed to go into a fairly deep optical minimum (R ~ 14.8) and initiated prompt i-band imaging at the Nordic Optical Telescope (NOT) to detect its host galaxy.," On December 17, 2007 we observed to go into a fairly deep optical minimum (R $\sim$ 14.8) and initiated prompt i-band imaging at the Nordic Optical Telescope (NOT) to detect its host galaxy." The imaging was performed five days after the minimum and the results are reported in this Letter., The imaging was performed five days after the minimum and the results are reported in this Letter. Throughout this Letter. we use the cosmology Hy=70 km s! Mpe7!. Q4; = 0.3 and Q4 = 0.7.," Throughout this Letter, we use the cosmology $H_0 = 70$ km $^{-1}$ $^{-1}$, $\Omega_{M}$ = 0.3 and $\Omega_{\Lambda}$ = 0.7." was observed at the Nordic Optical Telescope (NOT). La Palma on Dec 22. 2007.," was observed at the Nordic Optical Telescope (NOT), La Palma on Dec 22, 2007." We used the ALFOSC instrument in imaging mode with a 2k E2V CCD chip of a gain 0.726 e ADU and readout noise 3.2 electrons., We used the ALFOSC instrument in imaging mode with a 2k E2V CCD chip of a gain 0.726 $^-$ $^{-1}$ and readout noise 3.2 electrons. Twenty-eight exposures of 45 s were acquired using an i-band interference filter of almost uniform transmission between 725 and 875 nm. which provided a total exposure time of 1260 s. The 1-band filter was chosen because it detects light above the 4000 bbreak of the host galaxy even at z = 0.5. which maximizes the amount of light from the host galaxy.," Twenty-eight exposures of 45 s were acquired using an i-band interference filter of almost uniform transmission between 725 and 875 nm, which provided a total exposure time of 1260 s. The i-band filter was chosen because it detects light above the 4000 break of the host galaxy even at z = 0.5, which maximizes the amount of light from the host galaxy." " The individual images were bias-subtracted and flat-fielded with twilight flats in the usual way usingIRAF"".", The individual images were bias-subtracted and flat-fielded with twilight flats in the usual way using. . A fringe pattern with an amplitude of ~ of the sky background was visible in the reduced images., A fringe pattern with an amplitude of $\sim$ of the sky background was visible in the reduced images. A fringe correction image was produced by median combining all 28 images and applying simultaneously a sigma clipping cut to the pixel intensity, A fringe correction image was produced by median combining all 28 images and applying simultaneously a sigma clipping cut to the pixel intensity its faintness.,its faintness. Also. spectra of stars that are located closer than tto a bright neighbouring star im dispersion direction were left out. since if is possible that their spectral contributions overlap.," Also, spectra of stars that are located closer than to a bright neighbouring star in dispersion direction were left out, since it is possible that their spectral contributions overlap." Second. we rejected all but the exposure with the highest S/N of those stars that had »een observed multiple times through different slit masks.," Second, we rejected all but the exposure with the highest S/N of those stars that had been observed multiple times through different slit masks." Tn total. 508 stars (of originally 662 individual spectra) passed these quality checks.," In total, 508 stars (of originally 662 individual spectra) passed these quality checks." We went ou to sclect the stars based on their observed radial velocity., We went on to select the stars based on their observed radial velocity. These were determined using the IRAF asks RVIDLINES and EXCOR., These were determined using the IRAF tasks RVIDLINES and FXCOR. Since thas a heliocentric velocity. of 232.3kins5| (~~|. Oreground stars could easily. be ideutifiec by their 1ο] ower radial velocities.," Since has a heliocentric velocity of $232.3\unit{km\;s^{-1}}$ \citep{H:96}, foreground stars could easily be identified by their much lower radial velocities." We selected all those stars with observed radial velocities iu the range 150 to 350kins|., We selected all those stars with observed radial velocities in the range 150 to $350\unit{km\: s^{-1}}$. This wide range was chosen to account for possible systematic effects in the velocity determination hat lave uot been corrected for (e$. slight nüsmnatcehes of the arc-lamp aud science exposures curing day auc night observations}., This wide range was chosen to account for possible systematic effects in the velocity determination that have not been corrected for (e.g. slight mismatches of the arc-lamp and science exposures during day and night observations). The radial velocity selection resulted in a salple of £82 1ienüber stars with good quality., The radial velocity selection resulted in a sample of 483 member stars with good quality. The final step was to select only SCIB/MSTO-region stars from the member sample., The final step was to select only SGB/MSTO-region stars from the member sample. We included only those stars with magnitudes of 16.820 ms., We define a DRP as an isolated pulsar in the Galactic disk with $B<3 \times 10^{10}$ G and $P>20$ ms. The latter criterion ensures that no isolated millisecond pulsars. which are thought to have had a different evolutionary history. ave included in our sample.," The latter criterion ensures that no isolated millisecond pulsars, which are thought to have had a different evolutionary history, are included in our sample." Phe actual value of the limiting spin period was chosen such that reevelecl pulsars in. the known DNS sample would have been selectec had: their rosting binaries been disrupted., The actual value of the limiting spin period was chosen such that recycled pulsars in the known DNS sample would have been selected had their hosting binaries been disrupted. Phe isolated. millisecond )ulsars with 2«35107 € and Pox20 ms (about 28 known) are believed to accreted [rom a low mass companion (c.g.. a white dwarl) over long period of time (LO” vr) and then the companion was evaporated (e.g.. Lorimer et al.," The isolated millisecond pulsars with $B<3 \times 10^{10}$ G and $P<20$ ms (about 28 known) are believed to accreted from a low mass companion (e.g., a white dwarf) over long period of time $\sim 10^8$ yr) and then the companion was evaporated (e.g., Lorimer et al." 2004 and references therein)., 2004 and references therein). " The population of isolated oulsars with small magnetic field (D«310 €) but arger spin periods (2?720 ms) is believed to acereted from. a high mass companion over relatively short. period. of time (~10""' vr) and then the companion was ejected [rom a παν while undergoing supernova explosion.", The population of isolated pulsars with small magnetic field $B<3 \times 10^{10}$ G) but larger spin periods $P>20$ ms) is believed to accreted from a high mass companion over relatively short period of time $\sim 10^{6-7}$ yr) and then the companion was ejected from a binary while undergoing supernova explosion. There are a dozen such objects., There are a dozen such objects. We now discuss possible selection blases esent in these samples. and draw some simpleconclusions xised on the available data.," We now discuss possible selection biases present in these samples, and draw some simpleconclusions based on the available data." " In Table 1.. we subdivide the DNS sample into ""compact systems with orbital periods less than one day which will merge due to gravitational wave emission within a Llubble time and. ""wide systems? with longer orbital periods hat will cllectively never merge on relevant timescales."," In Table \ref{tab:dnsdrp}, we subdivide the DNS sample into “compact systems” with orbital periods less than one day which will merge due to gravitational wave emission within a Hubble time and “wide systems” with longer orbital periods that will effectively never merge on relevant timescales." Despite the small-number statistics. it is apparent. both rom ‘Table 1 and Fig.," Despite the small-number statistics, it is apparent, both from Table 1 and Fig." E that the compact systems appear o be vounger than the wide systenis., 1 that the compact systems appear to be younger than the wide systems. As noted by severa oevious authors (Phinney1992:Arzoumanianetal.1999:Chaurasia&Bailes 2005).. this is a selection effect: causcc » the shorter coalescence time compared. to. the radio ifetimes of these systems.," As noted by several previous authors \citep{phi92,acw99,cb05}, this is a selection effect caused by the shorter coalescence time compared to the radio lifetimes of these systems." " The. wide DNS binaries anc DIS effectively. spin-down until they reach the so-calle ""death linc” at which radio emission is thought to become incllective ancl cease for all radio pulsars Chen&luceerman (1993).", The wide DNS binaries and DRPs effectively spin-down until they reach the so-called “death line” at which radio emission is thought to become ineffective and cease for all radio pulsars \cite{cr93}. . ln our simulations of the uncerlving anc observed DNS sample described below. we will account for this important selection elfect. by carefully. modeling both the orbital evolution (Section 3) and Doppler smearing (Section 4) of such systems.," In our simulations of the underlying and observed DNS sample described below, we will account for this important selection effect by carefully modeling both the orbital evolution (Section 3) and Doppler smearing (Section 4) of such systems." " Our choice. of a maximum. magneticH field⋅ of ⋅⋅3«10!""I C4 to select DRPs is determined by the maximum magnetic fielel observed for a reeveled pulsar in a DNS: 2.3«1077 C for B1913|16 (Llulse&Taylor1975)..", Our choice of a maximum magnetic field of $3 \times 10^{10}$ G to select DRPs is determined by the maximum magnetic field observed for a recycled pulsar in a DNS: $2.3 \times 10^{10}$ G for B1913+16 \citep{ht75a}. This cut-olf is valid. provided that higher magnetic field objects do not. evolve into either sample during their observational lifetimes.," This cut-off is valid, provided that higher magnetic field objects do not evolve into either sample during their observational lifetimes." Given the lack of observational evidence for magnetic field. decay in reevelecl pulsars (Eaucher-Ciguére&Ixaspi2006). there is no reason to suspect that this cutoll. will impose any significant bias into the numbers of pulsars in each sample.," Given the lack of observational evidence for magnetic field decay in recycled pulsars \citep{fk06}, there is no reason to suspect that this cutoff will impose any significant bias into the numbers of pulsars in each sample." " An important selection ellect for ΕΝ. however. is the ""contamination"" in the sample from the isolated population of non-reevcled pulsars (Ixalogera.&Lorimer2000)."," An important selection effect for DRPs, however, is the “contamination” in the sample from the isolated population of non-recycled pulsars \citep{kl00}." ".. To quantify this effect. we have used the results of recent studies of the normal pulsars (Faucher-Ciguére&Ixaspi2006:Iti-cley&Lorimer2010) whieh predict the fraction. of non-recveled pulsars in the observed sample with B«3.107"" € to be about4."," To quantify this effect, we have used the results of recent studies of the normal pulsars \citep{fk06,rl10} which predict the fraction of non-recycled pulsars in the observed sample with $B<3 \times 10^{10}$ G to be about." .. Given the present sample of ~1500 non-recycled. objects. we therefore expect 4:5 of these to have no binary origin.," Given the present sample of $\sim 1500$ non-recycled objects, we therefore expect 4–5 of these to have no binary origin." We conclude that the best estimate for the observational ratio of the DRP to DNS systems is therefore currently ron.~1., We conclude that the best estimate for the observational ratio of the DRP to DNS systems is therefore currently $r_{\rm obs} \sim 1$. Our population svnthesis of the DNS and. DI. samples discussed. below requires some estimate of the likely racio lifetime of the mildly recycled: pulsars produced. in. these systems., Our population synthesis of the DNS and DRP samples discussed below requires some estimate of the likely radio lifetime of the mildly recycled pulsars produced in these systems. With their relatively weak: magnetic fields. DNS and DRPs are expected. to have longer radio lifetimes by comparison to normal pulsars which are thought to be a [ow 10s of Myr (e.g. Lyne. Manchester Vavlor 1985).," With their relatively weak magnetic fields, DNS and DRPs are expected to have longer radio lifetimes by comparison to normal pulsars which are thought to be a few 10s of Myr (e.g. Lyne, Manchester Taylor 1985)." LFor all 20 objects Listed in Table 1. the characteristic ages range between 100 Myr and 50 Cwr with mean and median values of 54 and 3.0 νε respectively.," For all 20 objects listed in Table 1, the characteristic ages range between 100 Myr and 50 Gyr with mean and median values of 5.4 and 3.0 Gyr respectively." As recently discussed. by. IWiziltan “Phorsett (2009)., As recently discussed by Kiziltan Thorsett (2009). Phe characteristic ages of reeveleck pulsars are. likely to both significantly underestimate and overestimate the true ages., The characteristic ages of recycled pulsars are likely to both significantly underestimate and overestimate the true ages. Phe underestimate is caused. by secular accelerations which contribute to the observed. P. while overestimates arise due to sub-Eddington accretion in the progenitor phase (Ixiziltan TFhorsett 2009) which result in a birth period that is close to the current value.," The underestimate is caused by secular accelerations which contribute to the observed $\dot{P}$, while overestimates arise due to sub-Eddington accretion in the progenitor phase (Kiziltan Thorsett 2009) which result in a birth period that is close to the current value." Taken as a whole. the characteristic ages suggest atypical lifetime for the population that is close to 10 Gar. anc we adopt this number in our evolutionary simulations cescribed in Section 3.3.," Taken as a whole, the characteristic ages suggest a typical lifetime for the population that is close to 10 Gyr, and we adopt this number in our evolutionary simulations described in Section 3.3." Despite the small-number statistics present in Fable. 1.. it is immediately. apparent that the height above/bclow the Galactic plane z is. on average. significantly larger for ας han for DNS binaries.," Despite the small-number statistics present in Table \ref{tab:dnsdrp}, it is immediately apparent that the height above/below the Galactic plane $z$ is, on average, significantly larger for DRPs than for DNS binaries." Taking the z values from. Table we find |z|=200 pe for the DNS svstems compared. to ;|=480 pe for the DRPs.," Taking the $z$ values from Table \ref{tab:dnsdrp}, we find $|z|= 200$ pc for the DNS systems compared to $|z|= 480$ pc for the DRPs." This dillerence between th wo populations could be explained by a Lager velocity dispersion for DRPs and/or longer radio lifetimes., This difference between the two populations could be explained by a larger velocity dispersion for DRPs and/or longer radio lifetimes. We have already remarked that the radio lifetimes of DADs are likely-— o be longer than the DNSs., We have already remarked that the radio lifetimes of DRPs are likely to be longer than the DNSs. In the following section. we will also show on evolutionary. grounds that the expected velocity. distributions of the two populations are indeed ‘undamentally cillerent.," In the following section, we will also show on evolutionary grounds that the expected velocity distributions of the two populations are indeed fundamentally different." The population synthesis code we use.StarTrack. was initially developed to studs double compact object mergers in the context of gamma-ray burst progenitors (Belezvnski. Bulik Rudak 2002b) anc gravitational-wave inspiral sources (Delezenski. Ixalogera. Bulik 2002a).," The population synthesis code we use, was initially developed to study double compact object mergers in the context of gamma-ray burst progenitors (Belczynski, Bulik Rudak 2002b) and gravitational-wave inspiral sources (Belczynski, Kalogera, Bulik 2002a)." In recent vears StarTrack has undergone major updates and revisions in the physical treatment of various binary evolution phases.," In recent years has undergone major updates and revisions in the physical treatment of various binary evolution phases," "ealaxies are intrinsically aligned: this is the ""IE term Mackeyetal.(2002)..",galaxies are intrinsically aligned; this is the `II' term \citet{2002MNRAS.332..788M}. The third term can arise when a foreground. gravitational potential tically clistorts a neighbouring galaxy. while also lensing a background galaxy: this is the “GL term Llirata&Seljak(2004)..," The third term can arise when a foreground gravitational potential tidally distorts a neighbouring galaxy, while also lensing a background galaxy; this is the `GI' term \citet{2004PhRvD..70f3526H}." Phe final term involves only systematic shear., The final term involves only systematic shear. In general. this can be larec and requires a good understanding of the experiment and sophisticated techniques to remove any spurious signal.," In general, this can be large and requires a good understanding of the experiment and sophisticated techniques to remove any spurious signal." The disentangling of the pure £55? term from the above equation is therefore very challenging., The disentangling of the pure $\langle\gamma\gamma\rangle$ term from the above equation is therefore very challenging. " Llowever. let us now suppose we have a joint radio and optical survey. containing a set of galaxies cach of which has a radio or optical shear estimator (2, and Z, respectively). or frequently. both."," However, let us now suppose we have a joint radio and optical survey, containing a set of galaxies each of which has a radio or optical shear estimator $\tilde\gamma_r$ and $\tilde\gamma_o$ respectively), or frequently both." In this case. a cross correlation function can be measured: ↾↓∖↓↥↕≻↓∢⊾⋜↧∠⇂≻∣∪⊳∖∢⊾∖⇁⋖⋅↓⋅⋜↧↓⋯⇂∖," In this case, a cross correlation function can be measured: This leads to several advantages." ⇁⋜⋯↿⋜↧⋏∙≟⋖⊾⊳∖⊳↓⊲∖⊲↓↓⋅⊳∖↿↓∙∖⇁⊳↕⇂⊳∖↓↕∪⊔↓∠⇂ be noted that if the covariance between shapes in optical and radio is negligible. the error upon the first. term is substantially reduced. due to an elfective increase in ealaxy number censity. as shown bv (Jarvis&Jain 2008): we can elfectively consider the optical and racio sources as independent galaxies.," Firstly, it should be noted that if the covariance between shapes in optical and radio is negligible, the error upon the first term is substantially reduced due to an effective increase in galaxy number density, as shown by \citep{2008JCAP...01..003J}; we can effectively consider the optical and radio sources as independent galaxies." This is an advantage over Cross-correlating two optical bands. where a strong shape correlation is found. ancl little increase in effective number density results (Jarvis&Jain2008)..," This is an advantage over cross-correlating two optical bands, where a strong shape correlation is found and little increase in effective number density results \citep{2008JCAP...01..003J}." We see that besides the cosmic shear signal. we now have two GL terms. one from the optical and. one from the racio data: these will still need to be measured. marginalised over or nulled (Joachimi&Schneider2008)...," We see that besides the cosmic shear signal, we now have two GI terms, one from the optical and one from the radio data; these will still need to be measured, marginalised over or nulled \citep{2008A&A...488..829J}." However. the other terms are reduced. in. amplitude by. the correlation: in refcrossobs we have shown that £555 is small: there is little correlation between optical and radio shapes.," However, the other terms are reduced in amplitude by the cross-correlation: in \\ref{crossobs} we have shown that $\langle\gamma_{o}^{i}\gamma_{r}^{i}\rangle$ is small; there is little correlation between optical and radio shapes." In addition. the last term will be small: the svstematics associated with a given optical and radio telescope and ensuing data reduction are so distinct that they could hardly be correlated.," In addition, the last term will be small; the systematics associated with a given optical and radio telescope and ensuing data reduction are so distinct that they could hardly be correlated." " ""his is related to the approach of (Jarvis&Jain2004) who advocate cross-correlating shear measurements in cilferent exposures: however. this might still leave chronic svstematies uncorrected. which would be removed by a radio-optical correlation."," This is related to the approach of \citep{2004astro.ph.12234J} who advocate cross-correlating shear measurements in different exposures; however, this might still leave chronic systematics uncorrected, which would be removed by a radio-optical correlation." We conclude then that cross-correlating future large radio and optical datasets could be a powerful method for lensing studies. substantially reducing the issues associated with intrinsic alignments and svstematies.," We conclude then that cross-correlating future large radio and optical datasets could be a powerful method for lensing studies, substantially reducing the issues associated with intrinsic alignments and systematics." Our results in refcosmic already give some evidence of this but better radio data will be required. for the eross-correlation to be fully studied and. utilised., Our results in \\ref{cosmic} already give some evidence of this but better radio data will be required for the cross-correlation to be fully studied and utilised. Recently Battye&Browne(2009) stucliec the orientation of racio and optical galaxies in the FIRST and SDS SULVONVS., Recently \citet{2009arXiv0902.1631B} studied the orientation of radio and optical galaxies in the FIRST and SDSS surveys. They found a clear excess of galaxies in which the major axes of the radio ancl optical emission. were aligned., They found a clear excess of galaxies in which the major axes of the radio and optical emission were aligned. “Phis may appear to be in tension with what we have shown in ligure 12.. but the comparison is not direct: since this figure shows shear estimates. it mixes orientation and llattening information.," This may appear to be in tension with what we have shown in Figure \ref{fig:grgo}, but the comparison is not direct; since this figure shows shear estimates, it mixes orientation and flattening information." In order to compare more directly with Dattve&Browne (2009).. we calculate for all matched objects (solid histogram) the angle between radio and optical major axes: our results are shown in Figure 14..," In order to compare more directly with \citet{2009arXiv0902.1631B}, we calculate for all matched objects (solid histogram) the angle between radio and optical major axes; our results are shown in Figure \ref{fig:orient}." We also plot in Figure 14 the corresponding histogram for the third of the matched objects with the highest signal-to-noise (dashed histogram)., We also plot in Figure \ref{fig:orient} the corresponding histogram for the third of the matched objects with the highest signal-to-noise (dashed histogram). We see that there is only a la excess of the total objects with a small angle between radio and optical major axes., We see that there is only a $1\sigma$ excess of the total objects with a small angle between radio and optical major axes. We also see that the histogram for the high signal-to-noise objects does not show any evidence of such an alignment., We also see that the histogram for the high signal-to-noise objects does not show any evidence of such an alignment. ‘Thus there is some level of disparity between our work and Battve&Browne(2009).., Thus there is some level of disparity between our work and \citet{2009arXiv0902.1631B}. We note that our sample is much smaller in number than that of Battye&Browne(2009). and as such. we are not able to usefully bin our sample more finely than shown in Figure 14..," We note that our sample is much smaller in number than that of \cite{2009arXiv0902.1631B}, and as such, we are not able to usefully bin our sample more finely than shown in Figure \ref{fig:orient}. ." Equally it is important to note that this study involves highly resolved imaging using sub-arcsecond angular resolution radio and optical data., Equally it is important to note that this study involves highly resolved imaging using sub-arcsecond angular resolution radio and optical data. La comparison. he studv by Dattye&Browne(2009) uses much. lower resolution data: they use VLA FIRST radio data with an angular resolution of aarcsec correlated with SDSS which ms tvpical seeing in the range 1 to aarcsec.," In comparison, the study by \citet{2009arXiv0902.1631B} uses much lower resolution data; they use VLA FIRST radio data with an angular resolution of arcsec correlated with SDSS which has typical seeing in the range 1 to arcsec." At these resolutions both the radio and optical data tvpically. trace he extended smooth emission from the galaxy and hence its shape on scales of a few tens of kpe at the typical redshifts of these sources., At these resolutions both the radio and optical data typically trace the extended smooth emission from the galaxy and hence its shape on scales of a few tens of kpc at the typical redshifts of these sources. As such the correlations seen by Battve&Browne(2009) are not surprising., As such the correlations seen by \cite{2009arXiv0902.1631B} are not surprising. “Phe objects studied here in the LIDE-N are much fainter. and at the 0744 angular resolution of this study we are typically resolving structure with linear sizes of just a few kpe.," The objects studied here in the HDF-N are much fainter, and at the 4 angular resolution of this study we are typically resolving structure with linear sizes of just a few kpc." Additionally the types of galaxies involved in cach of these two studies diller considerably. with the sources. in the HLDE-N sample being predominantly moderate to high redshift svstems with intense voung star-formation and large levels of optical extinction. and the Dattye&Browne(2009) sources beinglower redshift. more quiescent ealaxies.," Additionally the types of galaxies involved in each of these two studies differ considerably, with the sources in the HDF-N sample being predominantly moderate to high redshift systems with intense young star-formation and large levels of optical extinction, and the \cite{2009arXiv0902.1631B} sources beinglower redshift, more quiescent galaxies." Thus there are clear reasons why there may be, Thus there are clear reasons why there may be The discovery of afterelows from gamma-ray bursts (GRBs) has opened up a new era in the field.,The discovery of afterglows from gamma-ray bursts (GRBs) has opened up a new era in the field. ‘Till the end. of August 1999. X-ray. optical. and radio afterglows have been observed from about 16. 11. and5 GRBs respectively (Costa et al.," Till the end of August 1999, X-ray, optical, and radio afterglows have been observed from about 16, 11, and 5 GRBs respectively (Costa et al." 1997: Bloomet al., 1997; Bloom et al. 1998: Groot et al., 1998; Groot et al. 1998> Γκκατη et al., 1998; Kulkarni et al. 1998. 1999: Llarrison ct al.," 1998, 1999; Harrison et al." 1999: Stanek et al., 1999; Stanek et al. 1999: Fruchter et al., 1999; Fruchter et al. 1999: Galama et al., 1999; Galama et al. 19992)., 1999a). The so called fireball model (Goodman 1986: Paczyüsski 198€x Mésszárros Rees 1992: Rees Mésszárros 1992. 1994: Ixatz. 1994: Sari. Naravan Piran 1996) is strongly [avored. which is Found: successful at explaining the major features of GIUS (Mésszárros Rees 19907: Vietri 1997 slavani. 1997: alterglowsWaxman 19972: Wijers. Rees Mésszárros 1997: Sari 1997a: Sari. Piran Naravan 1998: Huang ct al.," The so called fireball model (Goodman 1986; Paczyńsski 1986; Mésszárros Rees 1992; Rees Mésszárros 1992, 1994; Katz 1994; Sari, Narayan Piran 1996) is strongly favored, which is found successful at explaining the major features of GRB afterglows (Mésszárros Rees 1997; Vietri 1997; Tavani 1997; Waxman 1997a; Wijers, Rees Mésszárros 1997; Sari 1997a; Sari, Piran Narayan 1998; Huang et al." 1998a. b. 99a. b: Dai Lu 1998a. b. c: Mésszárros. lees Wijers 1998: Wijers Galama 1999).," 1998a, b, 1999a, b; Dai Lu 1998a, b, c; Mésszárros, Rees Wijers 1998; Wijers Galama 1999)." " Llowever. we are still far [rom resolving the puzzle of GRBs. because their ""inner engines? are well hidden from direct afterglow observations."," However, we are still far from resolving the puzzle of GRBs, because their “inner engines” are well hidden from direct afterglow observations." Alost GRBs localized. by BeppoSAX. have. indicated isotropic energies of 1013 1077 eres. well within the energy output. from. solar-mass compact stellar objects.," Most GRBs localized by BeppoSAX have indicated isotropic energies of $10^{51}$ — $10^{52}$ ergs, well within the energy output from solar-mass compact stellar objects." However. GRB 971214. 980703. 990123. and 990510 have implied isotropic gamma-ray releases of 3.0«10. eres (0.17 AL.ο Wulkarni. et al.," However, GRB 971214, 980703, 990123, and 990510 have implied isotropic gamma-ray releases of $3.0 \times 10^{53}$ ergs (0.17 $M_{\odot} c^2$, Kulkarni et al." 1998). LO.1077:5 eres (0.06 AL.c7. Bloom et al," 1998), $1.0 \times 10^{53}$ ergs (0.06 $M_{\odot} c^2$, Bloom et al." 1998). 34.1075 eres (1.0 Aloο. Kulkarni ct al.," 1998), $3.4 \times 10^{54}$ ergs (1.9 $M_{\odot} c^2$, Kulkarni et al." 1909: Andersen et al., 1999; Andersen et al. 1999). and 2.9107 eres (0.16 Al.ο. Harrison et al.," 1999), and $2.9 \times 10^{53}$ ergs (0.16 $M_{\odot} c^2$, Harrison et al." 1999) respectively., 1999) respectively. Moreover. if really located. at a redshift of 25 as suggested by Iteichart. et al. (," Moreover, if really located at a redshift of $z \geq 5$ as suggested by Reichart et al. (" 1998). GRB 980329. would POMan eamnma-rav energv of 5«1075 ergs (2.79 neeM.(7). ded,"1998), GRB 980329 would imply an isotropic gamma-ray energy of $5 \times 10^{54}$ ergs (2.79 $M_{\odot} c^2$ )." uSuch epeenormous energeties has forced: some lo that CRB radiation must be highly collimated in these cases. with . ↓↥⋜↧∐∪↓≻∢⊾⊔↓⊔⋏∙≟⋜⋯⋏∙≟↓⋖⋅↙⇥≦∪⋅⇉⊳⊳∖∪↿↓⋯↿↿↓↕⋖⋅↓⊔↿↓⋅↓⊔⊳∖⊔∼⋏∙≟⋜⋯↓⊔↓⋜⊢↓⋅⋜↧∙∖⇁ ⊀⊀∢ ∢⋅⊔∢⋅↓⋅⋏↳≱∙∖⇁≼∙⋯⇂↓∠⇂∣⋡∢⊾↓⋅∢⊾∠⇂⋯⇍⋖⊾∠⇂∣⋡∙∖⇁⋜↧⇂∎⋯∙⋯↓⋅∪⇂∎↓∪⇉ 10. and could still come from compact stellar objects (Pugliese. Falcke Aermann 1999).," Such enormous energetics has forced some theorists to deduce that GRB radiation must be highly collimated in these cases, with half opening angle $\theta \leq 0.2$, so that the intrinsic gamma-ray energy could be reduced by a factor of $10^2$ — $10^3$, and could still come from compact stellar objects (Pugliese, Falcke Biermann 1999)." Obviously. whether GRBs are beamed or not is of fundamental importance to our understanding of their nature.," Obviously, whether GRBs are beamed or not is of fundamental importance to our understanding of their nature." For theorists. the degree of beaming can place severe constraints on CRB models.," For theorists, the degree of beaming can place severe constraints on GRB models." Llow can we tell a jet from an isotropic fireball?, How can we tell a jet from an isotropic fireball? Direct clues may come from afterglow light curves., Direct clues may come from afterglow light curves. As argued by Panaitescu Alésszarros (1999) and Wulkarni et al. (, As argued by Panaitescu Mésszárros (1999) and Kulkarni et al. ( 1999).,"1999)," the associated isotropisation length A we consider the extreme case that the wave spectrum is constant and equals the wave intensity spectrum after the isotropisation.,the associated isotropisation length $\lambda $ we consider the extreme case that the wave spectrum is constant and equals the wave intensity spectrum after the isotropisation. " By this method an approximation of the pitch angle Fokker-Planck coefficient Dj, is possible so that one gets a strict lower limit to the isotropisation length A.", By this method an approximation of the pitch angle Fokker-Planck coefficient $D_{\rm \mu\mu }$ is possible so that one gets a strict lower limit to the isotropisation length $\lambda $. By demonstrating that this length i5 much smaller than the thickness ¢ of the blast wave region we will establish that the inflowing proton-electron-beam is effectively isottroppised in the blast wave plasma., By demonstrating that this length is much smaller than the thickness $d$ of the blast wave region we will establish that the inflowing proton-electron-beam is effectively pised in the blast wave plasma. Inserting Eqs. (??)),Inserting Eqs. \ref{35}) ) and (41)) we find with Fu.t-üu)- that Eq. (39))," and \ref{36}) ) we find with ,t=0)] and ,t=0)] that Eq. \ref{34}) )" becomes The general solution of Eqs. (30)), becomes The general solution of Eqs. \ref{27a}) ) and (31)) at time t=T; Is where Ij(Qu If the initial turbulence is much weaker than the self-generated turbulence Z(&.0)<<|Z(K)| and has a vanishing cross-helliceitty 7;(4.0)=I(0)Πο0) we obtain for Eqs. (45..46..47))," and \ref{27b}) ) at time $t=T_i$ is where I_+(0)I_-(0) If the initial turbulence is much weaker than the self-generated turbulence $I(k,0)<<|Z(k)|$ and has a vanishing ty $I_+(k,0)=I_-(k,0)=I(k,0)$ we obtain for Eqs. \ref{39a}, \ref{39b}, \ref{39c}) )" approximately According to Eq. (44)), approximately According to Eq. \ref{38}) ) Z(&) is negative so that Eq. (??)), $Z(k)$ is negative so that Eq. \ref{40}) ) reduces to and |Z(h)| (orie.dt theEye beam mainlyTi) generates backward moving↼↴∕ Alfvénn waves in the blast wave plasma., reduces to and |Z(k)| i.e. the beam mainly generates backward moving Alfvénn waves in the blast wave plasma. BThe total enhancement in magnetic field fluctuation power due to proton and electron isotropisation is obtained by integrating Eq. (31)), The total enhancement in magnetic field fluctuation power due to proton and electron isotropisation is obtained by integrating Eq. \ref{27b}) ) using Eq. (44) , using Eq. \ref{38}) ) so that the change in the magnetic field fluctuation energy density is .-iani Alfvénn waves possess equipartition of wave energy density between magnetic and plasma velocity fluctuations. so that the total change in fluctuation energy density due to pitch angle isotropisation is | =Ἐν For consistency we show that this increase in the energy density of the fluctuations is balanced by a corresponding decrease in the energy density of the beam protons and electrons during their isotropization.," so that the change in the magnetic field fluctuation energy density is = Alfvénn waves possess equipartition of wave energy density between magnetic and plasma velocity fluctuations, so that the total change in fluctuation energy density due to pitch angle isotropisation is + = For consistency we show that this increase in the energy density of the fluctuations is balanced by a corresponding decrease in the energy density of the beam protons and electrons during their isotropization." . We follow here the argument of Bogdan et al. (1991)).," We follow here the argument of Bogdan et al. \cite{bls91}) )," made originally for up ions in the solar wind. and generalise it to relativistic beam Véldeities.," made originally for pick-up ions in the solar wind, and generalise it to relativistic beam velocities." As the beam particles scatter away from their initial pitch angle κι=zx and speed V. at each intermediate µ=p/p they are confined to scatter approximately on a sphere centered on," As the beam particles scatter away from their initial pitch angle $\alpha =\pi $ and speed $V$ , at each intermediate $\mu =p_{\parallel}/p$ they are confined to scatter approximately on a sphere centered on" CPR2002) prescuted a low resolution Z7- and Av-band spectroscopic survey of 2\LASS identified sources towards Cre OB2.,CPR2002) presented a low resolution $H$ - and $K$ -band spectroscopic survey of 2MASS identified sources towards Cyg OB2. While these spectra were not of the quality required for near-infrared spectral classification (sce Hanson. Towarth aud Conti 1997). they were sufficient to quickly coufiiui which stars already showing “blue” near-infrared colors lacked discernible molecular bands. cousisteut with them being carly-type stars.," While these spectra were not of the quality required for near-infrared spectral classification (see Hanson, Howarth and Conti 1997), they were sufficient to quickly confirm which stars already showing “blue” near-infrared colors lacked discernible molecular bands, consistent with them being early-type stars." Thev identified 77 carly-type caucidates., They identified 77 early-type candidates. Less than half. just 31 stars. had been previously classified with optical spectra to have been OB stars. leaving 16 new candidate OB stars towards (νο OD2.," Less than half, just 31 stars, had been previously classified with optical spectra to have been OB stars, leaving 46 new candidate OB stars towards Cyg OB2." Iu this study. we have obtained classification-quality blue spectra for Ll of the 16 OD star cauclidates identified by CPR2002 to determine their ME classifications.," In this study, we have obtained classification-quality blue spectra for 14 of the 46 OB star candidates identified by CPR2002 to determine their MK classifications." A 15th star from the CPR2003 list was observed. but it turned out to have been previously studied spectroscopicallv.," A 15th star from the CPR2003 list was observed, but it turned out to have been previously studied spectroscopically." The primary goal of this study is to determine ifthe OB candidates ideutified using 2\TASS colors aud low-resolution near-infrared survey spectra are indeed OB stars., The primary goal of this study is to determine if the OB candidates identified using 2MASS colors and low-resolution near-infrared survey spectra are indeed OB stars. In this way. the observations preseuted here serve as a useful test of this newly explored. but clearly important. near-infrared iiethod of identifving OB star populations through out our galaxy aud behind large line-ofsight extinction.," In this way, the observations presented here serve as a useful test of this newly explored, but clearly important, near-infrared method of identifying OB star populations through out our galaxy and behind large line-of-sight extinction." Observations are preseuted in 82. aud the new spectra are presented iu 83.," Observations are presented in 2, and the new spectra are presented in 3." A second goal of this paper. which is more difficult than its first. is to determine if the newly found OD stars are associated with the optically studied Cre OB2 cluster of NT91.," A second goal of this paper, which is more difficult than its first, is to determine if the newly found OB stars are associated with the optically studied Cyg OB2 cluster of MT91." This will require a thorough evaluation of the clusters characteristics to determiue the likelihood of membership for auy newly found OB stars in the region., This will require a thorough evaluation of the cluster's characteristics to determine the likelihood of membership for any newly found OB stars in the region. A review of the (νο OB2 cluster characteristics and the characteristics of the newly found OB stars is given in $l., A review of the Cyg OB2 cluster characteristics and the characteristics of the newly found OB stars is given in 4. A final discussion of the search for possible super star clusters within our Galaxy is presented in 85., A final discussion of the search for possible super star clusters within our Galaxy is presented in 5. " Concludiug remarks are found in 56,", Concluding remarks are found in 6. Observations were made the niehts of 6. 7. 8 July. 2002 on the University of Arizona’s 2.312 Bok Telescope. located ou Witt Peak. outside of Tucson. AZ.," Observations were made the nights of 6, 7, 8 July, 2002 on the University of Arizona's 2.3m Bok Telescope, located on Kitt Peak, outside of Tucson, AZ." The Boller and Chivens (BCC) spectrograph was eniploved. and operated with an 832 ομαι erating aud a Schott 8612 order separating filter., The Boller and Chivens C) spectrograph was employed and operated with an 832 g/mm grating and a Schott 8612 order separating filter. A fullawidth. half-iaxinmia resolution of FWIIM = 2.0 ((about 2.8 pixels) was achieved for a resolution of R ~ 2200 over the spectral range from 3960 to £800.," A full-width, half-maximum resolution of FWHM $\approx$ 2.0 (about 2.8 pixels) was achieved for a resolution of R $\approx$ 2200 over the spectral range from 3960 to 4800." Α.. The BECC spectrograph uses a long slit C1)., The C spectrograph uses a long slit $'$ ). " All observations were made using a slit width of 2.5"".", All observations were made using a slit width of $''$. " An average bias as well as sky. cussion lines were removed by subtracting a median averaged image of several ""uique slit positions.", An average bias as well as sky emission lines were removed by subtracting a median averaged image of several unique slit positions. Pixcl-to-pixel gain variations ou the CCD detector were removed using observations of an ilhuninated reflective spot inside the dome., Pixel-to-pixel gain variations on the CCD detector were removed using observations of an illuminated reflective spot inside the dome. Observations of a Welimu-Areon lamp taken periodically through the nieht provided the wavelength calibrations., Observations of a Helium-Argon lamp taken periodically through the night provided the wavelength calibrations. Integration times ranged from 16 minutes (Cve OB2 Α16) to as long as an hour (νο OB2 A20)., Integration times ranged from 16 minutes (Cyg OB2 A46) to as long as an hour (Cyg OB2 A20). The signal-to-noise ratio in the line free coutimmun exceeds 50 for nearly all spectra., The signal-to-noise ratio in the line free continuum exceeds 50 for nearly all spectra. A few spectra drop just below this value at the shortest wavelengths where the CCD response Is Wanile., A few spectra drop just below this value at the shortest wavelengths where the CCD response is waning. A list of the stars observed and their positions is given in Table 1., A list of the stars observed and their positions is given in Table 1. Stars were selected from the list of candidate carly-type iienboers eiven in CPR2002., Stars were selected from the list of candidate early-type members given in CPR2002. Tuterstellar extinction towards this sample is exceedingly hieh in the bluc-optical. ranging from Ap = 6 to more than 10 maenitudes.," Interstellar extinction towards this sample is exceedingly high in the blue-optical, ranging from $_B$ = 6 to more than 10 magnitudes." Estimated B magnitudes, Estimated $B$ magnitudes We use the stellar population models described in rofsfr to compare the stellar composition of pair and unpaired field galaxies.,"We use the stellar population models described in \\ref{sfr} to compare the stellar composition of pair and unpaired field galaxies." The stellar population uodels ft the spectra with a discrete set of starbursts of age 0.005. 0.025. 0.1. 0.3. 0.6. 0.9. 1.1. 2.5. 5 and 10 Cir.," The stellar population models fit the spectra with a discrete set of starbursts of age 0.005, 0.025, 0.1, 0.3, 0.6, 0.9, 1.4, 2.5, 5 and 10 Gyr." From the models we extract he contribution of cach starburst population to he flux at 5500 A., From the models we extract the contribution of each starburst population to the flux at 5500 . . Figure 15. shows the ratio (pair/ficld) of the 11011 fraction of flux at 5500 attributed to cach discrete starburst as a function «f starburst age or the starburst populations iucluded iu the uodel., Figure \ref{fluxratio} shows the ratio (pair/field) of the mean fraction of flux at 5500 attributed to each discrete starburst as a function of starburst age for the starburst populations included in the model. The pair galaxies clearly contain a larger raction of voung stellar populations up to burst agesaes ~300OO Mx., The pair galaxies clearly contain a larger fraction of young stellar populations up to burst ages $\sim 300-400$ Myr. The ταio of the mean raction of flux from cach starburst population dips slightly below one for burst ages Z500 Aly. vecatise the vounger stellar populations coutain a ereater fraction of the flux in the pair galaxies.," The ratio of the mean fraction of flux from each starburst population dips slightly below one for burst ages $\gtrsim 500$ Myr, because the younger stellar populations contain a greater fraction of the flux in the pair galaxies." Our iieasurement agrees well with the results of Bartonetal. (2000).. who apply spectral svuthesis nodels (Leithereretal.1999:Druzual&Char-ot1996) to their data from the CfA2 Redshift Survey (Falcoctal.1999).," Our measurement agrees well with the results of \citet{bgk}, , who apply spectral synthesis models \citep{l99,bruzual+ch96} to their data from the CfA2 Redshift Survey \citep{cfa2}." . They determine that he Πα cutissionaud the ealaxy colors arebest, They determine that the $\alpha$ emissionand the galaxy colors arebest their abundance is low (sav similar {ο solar composition). in most cases (his does not affect the computed atmospheric structure.,"their abundance is low (say similar to solar composition), in most cases this does not affect the computed atmospheric structure." For high temperatures we use the NLTE option., For high temperatures we use the NLTE option. For (he disk rings the input is the local mass accretion rate. mass of the accreting star. radius of the star. and radius of the ring and solar composition.," For the disk rings the input is the local mass accretion rate, mass of the accreting star, radius of the star, and radius of the ring and solar composition." Alternatively. one can input for each rine (he effective temperature. effective vertical eravily and the column mass al midplane.," Alternatively, one can input for each ring the effective temperature, effective vertical gravity and the column mass at midplane." second. the code SYNSPEC is used to derive the detailed radiation aud flux distribution of continuum and lines (Ilabeny&Lanz1995).," Second, the code SYNSPEC is used to derive the detailed radiation and flux distribution of continuum and lines \citep{hub95}." SYNSPEC generates the output spectrum of the stellar atinosphere structure and disk vertical structure computed by TLUSTY., SYNSPEC generates the output spectrum of the stellar atmosphere structure and disk vertical structure computed by TLUSTY. The input for SYNSPEC is the same as lor TLUSTY and it uses the structure computed by TLUSTY as an input., The input for SYNSPEC is the same as for TLUSTY and it uses the structure computed by TLUSTY as an input. Composition is specilied here with an additional input file. and can include species up to iron or even zinc.," Composition is specified here with an additional input file, and can include species up to iron or even zinc." In the present modeling we ineluclecl only IH. He. C. N. O. $1. P. and S. In the next step the code ROTIN is used to account for rotational ancl instrumental broadening of the lines for the stellar synthetic spectrum. while the code DISIKSYN is used to combine the disk rings together (where we substitute the inner rines wilh hot DL rings if a BL is computed) aud account for rotational broadening due to Keplerian motion.," In the present modeling we included only H, He, C, N, O, Si, P, and S. In the next step the code ROTIN is used to account for rotational and instrumental broadening of the lines for the stellar synthetic spectrum, while the code DISKSYN \citep{wad98} is used to combine the disk rings together (where we substitute the inner rings with hot BL rings if a BL is computed) and account for rotational broadening due to Keplerian motion." Limb darkening is also included in the codes DISINRSYN ROTIN., Limb darkening is also included in the codes DISKSYN ROTIN. Boundary laver synthetic spectra are generated by computing inner disk rings with an elevated temperature matching the DL temperature obtained from theoretical estimates., Boundary layer synthetic spectra are generated by computing inner disk rings with an elevated temperature matching the BL temperature obtained from theoretical estimates. The rings of the BL are then substituted to the inner disk rings., The rings of the BL are then substituted to the inner disk rings. We then use a reduced 47 fitting technique to find the best fit to the observed spectrum., We then use a reduced $\chi^2_{\nu}$ fitting technique to find the best fit to the observed spectrum. During the V7 fitting process ol theFUSE spectrum taken in the high state the mass of the WD. the inclination of the svslem. and the composition are kept constant because (μον have been firmly. established from previous observations.," During the $\chi^2_{\nu}$ fitting process of the spectrum taken in the high state the mass of the WD, the inclination of the system, and the composition are kept constant because they have been firmly established from previous observations." The remaining parameters. ie. the temperature of (he WD. the mass accretion rate. the number of BL rings included. and the temperature of the DL rings are allowed (o vary as they are unknown.," The remaining parameters, i.e. the temperature of the WD, the mass accretion rate, the number of BL rings included, and the temperature of the BL rings are allowed to vary as they are unknown." The distance to the svstem is obtainedposteriori from the spectral fitting as an output parameter: resulting models with a distance that does not agreed with the assumed distance are rejected (see next section)., The distance to the system is obtained from the spectral fitting as an output parameter; resulting models with a distance that does not agreed with the assumed distance are rejected (see next section). In the present work we use the following versions of the software: TLUSTY202. SYNSPECAS. ROTINA for WD photospheric spectra runing on a Linux platform (Cvewin-X) with a GNU FORTRAN 77 compiler: TLDISK195 (a previous variant of TLUSTY). SYNSPECI3. ROTINS and DISKSYN?7 for disk aud BL spectra runing on a Unix machine also using a GNU FORTRAN 77 compiler (the GNU FORTRAN 77 compiler runs slightly cdilferentlv under Unix and Linux operating svstems).," In the present work we use the following versions of the software: TLUSTY202, SYNSPEC48, ROTIN4 for WD photospheric spectra runing on a Linux platform (Cygwin-X) with a GNU FORTRAN 77 compiler; TLDISK195 (a previous variant of TLUSTY), SYNSPEC43, ROTIN3 and DISKSYN7 for disk and BL spectra runing on a Unix machine also using a GNU FORTRAN 77 compiler (the GNU FORTRAN 77 compiler runs slightly differently under Unix and Linux operating systems)." The software packages and users guiles are available online (ree download) at http://nova.astro.umcd.edu/ ., The software packages and user's guides are available online (free download) at http://nova.astro.umd.edu/ . The mass of Saturn is slightly below1/3 that of Jupiter ancl as a consequence. onlv of its mass lies al P>1 Mbar. compared to for Jupiter.,"The mass of Saturn is slightly below$1/3$ that of Jupiter and as a consequence, only of its mass lies at $P>1\,$ Mbar, compared to for Jupiter." Saturn is therefore less sensitive to the larger EOS uncertainties (han Jupiter., Saturn is therefore less sensitive to the larger EOS uncertainties than Jupiter. Saturns response (o rotation is also qualitatively different. as can be seen from its Inear response coefficient: As2ο where q=aREΛΙ is (he ratio of the centrifugal to the gravitational potentials.," Saturn's response to rotation is also qualitatively different, as can be seen from its linear response coefficient: $\Lambda_2\approx J_2/q$ where $q=\omega^2R_{\rm eq}^3/GM$ is the ratio of the centrifugal to the gravitational potentials." The value of A» is 0.108 for Saturn compared to 0.166 for Jupiter. implving that Saturn's interior is more concentrated. ie. il is expected to have a proportionally larger core (han Jupiter 1989)..," The value of $\Lambda_2$ is $0.108$ for Saturn compared to $0.166$ for Jupiter, implying that Saturn's interior is more concentrated, i.e. it is expected to have a proportionally larger core than Jupiter \citep{hubbard89}. ." Finally. the error bars on the gravitational moments Js and J; of Saturn are much larger (han for Jupiter.," Finally, the error bars on the gravitational moments $J_2$ and $J_4$ of Saturn are much larger than for Jupiter." We anticipate (hat the results will be qualitatively different., We anticipate that the results will be qualitatively different. The solutions lor Saturn are summarized in Fig. 11.., The solutions for Saturn are summarized in Fig. \ref{fig:boites-sat}. We present only the case where the perturbation on the EOS (Eq., We present only the case where the perturbation on the EOS (Eq. 7) has been included as this has only a slight effect on Saturn models., 7) has been included as this has only a slight effect on Saturn models. We find that there is much more overlap between the solutions for the different EOS than is the case for Jupiter and that we can usefully constrain the core mass and the mass of heavy elements in the envelope to 9SUuS224AL and 1SMz;x5S.V for a total mass of heavy elements between 13 and M...," We find that there is much more overlap between the solutions for the different EOS than is the case for Jupiter and that we can usefully constrain the core mass and the mass of heavy elements in the envelope to $9 \wig< M_{\rm core} \wig< 22\,M_\oplus$ and $1 \wig< M_{\sss Z} \wig< 8\,M_\oplus$ for a total mass of heavy elements between 13 and $\,M_\oplus$." The EOS is an important source of uncertainty in modeling Saturn's interior but it is not as dominant as in Jupiter., The EOS is an important source of uncertainty in modeling Saturn's interior but it is not as dominant as in Jupiter. We also find that the LM-D. EOS and the original SESAME EOS (not shown) give acceptable models of Saturn., We also find that the LM-B EOS and the original SESAME EOS (not shown) give acceptable models of Saturn. The amount of heavy elements in the envelope is rather modest but the total amount of heavy. elements in Saturni represents a 6- to IH-fold. enrichment compared to the solar value., The amount of heavy elements in the envelope is rather modest but the total amount of heavy elements in Saturn represents a 6- to 14-fold enrichment compared to the solar value. Saturn may contain more heavy elements than Jupiter., Saturn may contain more heavy elements than Jupiter. The choice of LOS has no discernible effect on Ac. however. and the uncertainty on the helium EOS barely affects the ensemble of solutions for Saturn.," The choice of EOS has no discernible effect on $M_{\rm core}$, however, and the uncertainty on the helium EOS barely affects the ensemble of solutions for Saturn." The distribution and the amount of heavy elements in Saturn is in verv good agreement with the core accretion formation model., The distribution and the amount of heavy elements in Saturn is in very good agreement with the core accretion formation model. While the (27p) relation along the aciabat determines the internal structure of the planet. the (7.T) relation influences its cooling age by selling its internal heat content.," While the $(P,\rho)$ relation along the adiabat determines the internal structure of the planet, the $(P,T)$ relation influences its cooling age by setting its internal heat content." The cooling rate itself is determined by the rate al which heat can escape al the surface. which is controlled by the atmosphere of the planet. (treated as à surface boundary condition in the cooling caleulation.," The cooling rate itself is determined by the rate at which heat can escape at the surface, which is controlled by the atmosphere of the planet, treated as a surface boundary condition in the cooling calculation." In section. 4. we showed how rather modest variations in density along the adiabat (Fig. 1))," In section 4, we showed how rather modest variations in density along the adiabat (Fig. \ref{fig:adiab_Prho}) )" are responsible for astroplivsicallv significant changes in internal structure., are responsible for astrophysically significant changes in internal structure. The variations in adiabat temperatures between the EOS can be as large as 6054., The variations in adiabat temperatures between the EOS can be as large as . .. The largest variations occur al pressures above Mbar ancl involve most of (he mass of Jupiter and Saturn.," The largest variations occur at pressures above$\,$ Mbar and involve most of the mass of Jupiter and Saturn." charged IHuids undergo less wind-up than in the ideal ALD case.,charged fluids undergo less wind-up than in the ideal MHD case. This is demonstrated by the plots of the transverse kinetic energv of these Uuids (figure 6.. second and. third panels). and the lower maxima reached.," This is demonstrated by the plots of the transverse kinetic energy of these fluids (figure \ref{nonideal_KEx4}, second and third panels), and the lower maxima reached." Finally. the plot representing the dust. erain [Iuid. (figure 6.. bottom. panel) shows similar behaviour to that observed in the bulk Duid.," Finally, the plot representing the dust grain fluid (figure \ref{nonideal_KEx4}, bottom panel) shows similar behaviour to that observed in the bulk fluid." This confirms that the dust grains remain well-coupled to the neutral Uuicd. and are less alfected by the magnetic field than the other charged. fluids.," This confirms that the dust grains remain well-coupled to the neutral fluid, and are less affected by the magnetic field than the other charged fluids." The results detailed. above can be attributed to the introduction of ambipolar clilfusion into the svstem., The results detailed above can be attributed to the introduction of ambipolar diffusion into the system. Llowever. there is a significant. amount of Hall. resistivity included. in the set-up as well.," However, there is a significant amount of Hall resistivity included in the set-up as well." While the system: remains ambipolar-cdominated. results from. Paper LE indicate. that there should. be observable consequences of including this moderate amount of Πα resistivity.," While the system remains ambipolar-dominated, results from Paper I indicate that there should be observable consequences of including this moderate amount of Hall resistivity." Alost notably. a," Most notably, a" very low accretion rates (such that the observed N-ray πιοτν is primarily from deep crustal heating as in DDR9s8) the upper lavers of the atmosphere should be essentially pure hydrogen (Romani 1987).,very low accretion rates (such that the observed X-ray luminosity is primarily from deep crustal heating as in BBR98) the upper layers of the atmosphere should be essentially pure hydrogen (Romani 1987). Therefore we focus on hydrogen atmosphere models for X5., Therefore we focus on hydrogen atmosphere models for X5. The possible xeriod of 5.5 hours for X7 also suggests a mai-sequence secondary. and a hydrogen atmosphere.," The possible period of 5.5 hours for X7 also suggests a main-sequence secondary, and a hydrogen atmosphere." We note that NOs eclipsing and dipping (with iucreased Nyy coli) vchavior is very simular to that of the quiescent neutron stars [U 2129]LF. as reported by Nowak ct al. (," We note that X5's eclipsing and dipping (with increased $N_H$ column) behavior is very similar to that of the quiescent neutron stars 4U 2129+47, as reported by Nowak et al. (" 2002). and MXD 1659-29 (Wijnands et al..,"2002), and MXB 1659-29 (Wijnands et al.," 2002). although X5'« dipping behavior secus to be less regular.," 2002), although X5's dipping behavior seems to be less regular." To ft the spectra of X5 aud. NXT in detail. we prepared the event files without removing cosmic ray afterglows. as this tends to remove valid events in the cores of bright sources AACTS team advice?)).," To fit the spectra of X5 and X7 in detail, we prepared the event files without removing cosmic ray afterglows, as this tends to remove valid events in the cores of bright sources ACIS team )." This change mereased the total flux bv 5$ ). No Bavinoud-Smüth thermal plasiua model with abunudanuces above solar ft the data acceptably., No Raymond-Smith thermal plasma model with abundances above solar fit the data acceptably. Sinele-componcut power-law inodels require a spectral photon mdex >5. which would be highly uuusual (pulsars with power-law N-rav spectra generally display indices ~1-3).," Single-component power-law models require a spectral photon index $>5$, which would be highly unusual (pulsars with power-law X-ray spectra generally display indices $\sim$ 1-3)." Thermal bremsstrahbhme models require kT below 600 eV. which is muuch softer than du cataclysmic variables (CVs) that display high X-ray bhuuiuositv (Eracleous ct 11991). and the Fy/Fy ratios are higher than those of kuowu CVs.," Thermal bremsstrahlung models require kT below 600 eV, which is much softer than in cataclysmic variables (CVs) that display high X-ray luminosity (Eracleous et 1991), and the $F_X/F_V$ ratios are higher than those of known CVs." Although we cannot formally exclude the blackbody models. we note difficulties with this model: the derived radii are rather small (while the lack of ταν pulsations in other qLMXDs sueecsts that the emission 1s isotropic. Chandler Rutledge 2000). and recent accretion is expected to leave an atmosphere of II or We on the NS.," Although we cannot formally exclude the blackbody models, we note difficulties with this model: the derived radii are rather small (while the lack of X-ray pulsations in other qLMXBs suggests that the emission is isotropic, Chandler Rutledge 2000), and recent accretion is expected to leave an atmosphere of H or He on the NS." We include parameters for blackbodyv fits in Table 1 for conrparisou with previous studies., We include parameters for blackbody fits in Table 1 for comparison with previous studies. Ποπ atuospleres are ruled out for X5 due to the main sequence nature of the companion (Edinonds ct al., Helium atmospheres are ruled out for X5 due to the main sequence nature of the companion (Edmonds et al. 2001)., 2001). We note that, We note that the specific radiative mechanism.,the specific radiative mechanism. " Assuming that this functional dependence is known. this equation vields the desired algebraic equation for 36.8 erg sec!: these are large HII regions with an AGB star from a previous generation-star or close by in projection.," We retain as YSCs the few sources associated to MIR selected AGBs which have a non-negligible number of ionizing photons, log $\alpha > 36.8$ erg $^{-1}$: these are large HII regions with an AGB star from a previous generation-star or close by in projection." The YSCs selected at 24 im have a wide range in size and luminosity and they are found in a variety of environments: from fully isolated. mainly in the galaxy outskirts. to crowded groups. especially inthe inner spiral arms.," The YSCs selected at $24\,\mu$ m have a wide range in size and luminosity and they are found in a variety of environments: from fully isolated, mainly in the galaxy outskirts, to crowded groups, especially inthe inner spiral arms." Sources in Table 2 are mostly in the outer regions and isolated., Sources in Table \ref{T400} are mostly in the outer regions and isolated. In order to clearly assess the presence of UV and Πα counterparts and the reliability of the extraction process. we made up and inspectec an atlas where. for each source. we assembled the images of the surrounding field in Ho. FUV. 8 and 24 jm. This allowec us to select also a sample of 24 4m sources with insignificant FUV and H« brightness as candidate embedded star forming regions which will be examined in a forthcoming paper.," In order to clearly assess the presence of UV and $\alpha$ counterparts and the reliability of the extraction process, we made up and inspected an atlas where, for each source, we assembled the images of the surrounding field in $\alpha$, FUV, 8 and $24\,\mu$ m. This allowed us to select also a sample of $24\,\mu$ m sources with insignificant FUV and $\alpha$ brightness as candidate embedded star forming regions which will be examined in a forthcoming paper." Ai insight on their nature could come from a possible associatior with a molecular cloud or clump (?) but we have to wait for deep enough CO maps with sufficiently high spatial resolutior to help in this regard., An insight on their nature could come from a possible association with a molecular cloud or clump \citep{2011A&A...528A.116C} but we have to wait for deep enough CO maps with sufficiently high spatial resolution to help in this regard. Throughout the paper we assume a distance D to M33 of 840 kpe (2). to convert fluxes into luminosities or to compute galactocentric distances., Throughout the paper we assume a distance $D$ to M33 of 840 kpc \citep{1991ApJ...372..455F} to convert fluxes into luminosities or to compute galactocentric distances. Assuming that the sources lie in the disk and adopting the geometry and warp model of ?.. described in detail in ?.. we derive the distance Ae; from the center of our sample objects.," Assuming that the sources lie in the disk and adopting the geometry and warp model of \citet{1997ApJ...479..244C}, described in detail in \citet{2000MNRAS.311..441C}, we derive the distance $R_G$ from the center of our sample objects." The radial distribution of the 24um sources and the selected YSCs are plotted in the top right panel of Fig. 2..," The radial distribution of the $24\,\mu$ m sources and the selected YSCs are plotted in the top right panel of Fig. \ref{map}." We can see that the MIR sources are found up to the largest distances. while YSCs are distributed over the whole area of overlap of the various maps.," We can see that the MIR sources are found up to the largest distances, while YSCs are distributed over the whole area of overlap of the various maps." In Fig 2. the bottom panels display the radial density distribution in linear and log scale. respectively.," In Fig \ref{map} the bottom panels display the radial density distribution in linear and log scale, respectively." The densities of the 24um sources and of the YSCs behave similarly with an overall exponential decay with radius.," The densities of the $24\,\mu$ m sources and of the YSCs behave similarly with an overall exponential decay with radius." In particular. we note 1) a shallow slope in the inner disk. 0-4.5 kpe: 11) a steep decrease between 4.5 and 8.5 kpe: and i) a flattening in the outer disk.," In particular, we note i) a shallow slope in the inner disk, 0-4.5 kpc; ii) a steep decrease between 4.5 and 8.5 kpc; and iii) a flattening in the outer disk." Past studies have found evidence for systematic. radial variations m the star formation history of the M33 disk., Past studies have found evidence for systematic radial variations in the star formation history of the M33 disk. ? showed that the number of young stellar groups drops suddenly at radii > 4 kpe and attributed this result to a change in the properties of the star forming sites., \citet{2007MNRAS.379.1302B} showed that the number of young stellar groups drops suddenly at radii $>$ 4 kpc and attributed this result to a change in the properties of the star forming sites. " To study the inner and outer region clusters separately. we divide the 24jm sources in ""inner clusters? with Rc;<4kpe and ""outer clusters” at larger distances."," To study the inner and outer region clusters separately, we divide the $24\,\mu$ m sources in `inner clusters' with $R_G<4\,$ kpc and `outer clusters' at larger distances." In this way. the size of the two groups is about the same.," In this way, the size of the two groups is about the same." " The bolometric luminosity of YSCs can be computed as the sum of the FUV and NUV luminosities uncorrected for absorption. the Ha luminosity corrected for extinction. Ly, and the total infrared luminosity Lyjj: where the terms Ha account for the ionizing radiation (?) and Ly; for the UV radiation absorbed by grains and re-emitted in the IR."," The bolometric luminosity of YSCs can be computed as the sum of the FUV and NUV luminosities uncorrected for absorption, the $\alpha$ luminosity corrected for extinction, $L^0_{H\alpha}$, and the total infrared luminosity $L_{TIR}$: where the terms $\alpha$ account for the ionizing radiation \citep{1999ApJS..123....3L} and $L_{TIR}$ for the UV radiation absorbed by grains and re-emitted in the IR." We have not considered the radiation longward of 2800 A which becomes important only for young clusters with luminosities lower than 10° erg s7!., We have not considered the radiation longward of 2800 A which becomes important only for young clusters with luminosities lower than $10^{38}$ erg $^{-1}$. The lummosity in the FUV and NUV has been derived from with D the distance to M33. v=1.95x10 Hz for the FUV and v=1.310 Hz for the NUV. and AB indicates the corresponding magnitude in the FUV or NUV band.," The luminosity in the FUV and NUV has been derived from with $D$ the distance to M33, $\nu = 1.95\times10^{15}$ Hz for the FUV and $\nu = 1.3\times10^{15}$ Hz for the NUV, and AB indicates the corresponding magnitude in the FUV or NUV band." " The total IR flux (Fy;4) and Ly;g are computed from the expressions: where Fyjp is in Wm? and F, in Jy (2).. ", The total IR flux $(F_{TIR})$ and $L_{TIR}$ are computed from the expressions: where $F_{TIR}$ is in $^{-2}$ and $F_\nu$ in Jy \citep{2002ApJ...576..159D}. . The size of a large fraction of sources in our YSC sample is below the Spitzer telescope resolution limit at 70 and 160 jm. Hence. we cannot use the above expression to compute Ly; except for a limited sample of extended resolved sources.," The size of a large fraction of sources in our YSC sample is below the Spitzer telescope resolution limit at 70 and 160 $\mu$ m. Hence, we cannot use the above expression to compute $_{TIR}$ except for a limited sample of extended resolved sources." We can estimate, We can estimate We can estimate, We can estimate$ We can estimate, We can estimate$_ We can estimate, We can estimate$_{ We can estimate, We can estimate$_{T We can estimate, We can estimate$_{TI We can estimate, We can estimate$_{TIR We can estimateL, We can estimate$_{TIR} We can estimateLy, We can estimate$_{TIR}$ aud therefore we start with a comparison of the plasiua-ouly part. tthe Euler equation solvers used. by these eroups for their plasma part uuder the assmuption that here are no source terms on the right-haud-sides of the Hid equations (uo neutrals in the svsten).,"and therefore we start with a comparison of the plasma-only part, the Euler equation solvers used by these groups for their plasma part under the assumption that there are no source terms on the right-hand-sides of the fluid equations (no neutrals in the system)." All groups ran their plasina code with the solar wiid and interstellar voundary conditious listed in Table 1., All groups ran their plasma code with the solar wind and interstellar boundary conditions listed in Table 1. I Was μπα. hat the plasma consists of equal (comswi12) densities of rotons aud electrons. iu other words. fic hermal plasma oressure equals twice the thermal proon pressure.," It was assumed that the plasma consists of equal (comoving) densities of protons and electrons, in other words, the thermal plasma pressure equals twice the thermal proton pressure." The uaenetic field. as well as the solar exaviY. were ueelected.," The magnetic field, as well as the solar gravity, were neglected." As can be expected. the resuls from he four eroups are very close to each other (the plasma parts of the Ίος aud the Flo models are identical. aud not listed separately).," As can be expected, the results from the four groups are very close to each other (the plasma parts of the Hee and the Flo models are identical, and not listed separately)." Figure l shows his with the ΙΟ density profiles of all four models. in three representative directions im f16 conmauonlv useL heliocentric reference frame.," Figure \ref{figsnoverv} shows this with the number density profiles of all four models, in three representative directions in the commonly used heliocentric reference frame." In all three directions. all tιο densities ⋅⋅⋟follow ar⋅≻7 power law in the supersouic solar wind before encountering the terminatioi shock.," In all three directions, all the densities follow a $r^{-2}$ power law in the supersonic solar wind before encountering the termination shock." The upwind termination shock (CTS) distances are VOYV €lose to each other. whereas downwind there is more variability.," The upwind termination shock (TS) distances are very close to each other, whereas downwind there is more variability." The shock streneths (ratio of downsrea to upstream density) are more or less he same., The shock strengths (ratio of downstream to upstream density) are more or less the same. Also the density contrast across the heliopause (IP) is similar across the four models., Also the density contrast across the heliopause (HP) is similar across the four models. Aso obvious 1s hat the DM iiodel uses capturing methods to identify aud euforce discoutinuities. whereas the other three models do rot eniplov such techniques. aud trausitiols are spread over a few erid pons (see the bow shock of the Mue nodel for an example. refiiesnovervb)|.," Also obvious is that the BM model uses capturing methods to identify and enforce discontinuities, whereas the other three models do not employ such techniques, and transitions are spread over a few grid points (see the bow shock of the Mue model for an example, \\ref{figsnoverv}b b)." Table 2 lists soue sey results for fιο shock aud reliopause locations., Table \ref{resplas} lists some key results for the shock and heliopause locations. The simulavities iu the results are evideut., The similarities in the results are evident. The last colum1i colmprises a simple average across the four modes for each result. aud the standard deviation hiuts at the raise that the resiIts span.," The last column comprises a simple average across the four models for each result, and the standard deviation hints at the range that the results span." The different models basically aeree on the upwind TS and TIP locations. aud are a litle bit more spread for he DS. and vet more for the downvind TS results.," The different models basically agree on the upwind TS and HP locations, and are a little bit more spread for the BS, and yet more for the downwind TS results." Besides the treatment of shocks aud discoutijuities. there are obviously iuaiv other reasons why fjio. four models varv from each other.," Besides the treatment of shocks and discontinuities, there are obviously many other reasons why the four models vary from each other." Each of the four models nuüakkes different choices rclated to the exid. coufietration. resolution. aud the exten of the simulation domed1.," Each of the four models makes different choices related to the grid configuration, resolution, and the extent of the simulation domain." Also. there are four different choices of the ummerical trausport aud diffusion schemes to solve. the Euler equations.," Also, there are four different choices of the numerical transport and diffusion schemes to solve the Euler equations." BAL use a Godunov-tvpe numerical scheme with moving adaptive exid while capturing three discoutiuuities the wchopause as contact discontinuity. aud the termination aud bow shocks.," BM use a Godunov-type numerical scheme with moving adaptive grid while capturing three discontinuities — the heliopause as contact discontinuity, and the termination and bow shocks." " The accuracy of the uminerical scheme resolution is 1nproved by usmeg a ""1duuod lnüter.", The accuracy of the numerical scheme resolution is improved by using a “minmod” limiter. T1C asma part «of the αποΊσα] algorithu of the Flo iuli-flick model uses the total variation «liaminishinge (TVD) finite volume scheme based on the Cotraut-Isaacsou-Rees approxiuate Rican solver., The plasma part of the numerical algorithm of the Flo multi-fluid model uses the total variation diminishing (TVD) finite volume scheme based on the Courant-Isaacson-Rees approximate Riemann solver. Conservation laws for 1C jeutral components (section 3) are solved using the more diffusive TVD Lax-Fuedrichs imethoc., Conservation laws for the neutral components (section 3) are solved using the more diffusive TVD Lax-Friedrichs method. The Hee plasμα wart is ideutical to that of Flo., The Hee plasma part is identical to that of Flo. " The ZEUS-3D aleoritm nuderling tlie Ahe model is based on the metlocl of finite cBffereuces oji a stagecred mesh. meorporating a van Leer monotonic advection scheme. aud x""on Neunmimu-Iüchtiiver artificial viscosity at shock frouts."," The ZEUS-3D algorithm underlying the Mue model is based on the method of finite differences on a staggered mesh, incorporating a van Leer monotonic advection scheme, and von Neumann-Richtmyer artificial viscosity at shock fronts." For all fluids in the Schi ποσο] tje Euler equatious are ornmulated for uantitfies conserviis the flux of mass. nknuuentun. and energy. and are subjected to secoud order Rieniuiu solvers sing the Lax-Friccvichs method with an οitropy. fix.," For all fluids in the Sch model the Euler equations are formulated for quantities conserving the flux of mass, momentum, and energy, and are subjected to second order Riemann solvers using the Lax-Friedrichs method with an entropy fix." For large pressurc| eradicuts a Tarten-Lax-vau Leer solver is nuplemenuted., For large pressure gradients a Harten-Lax-van Leer solver is implemented. τσ The ligh-Alach ΠΙΟ reginae of the sipersonic solar wind is an instructive example of the modeling technique differences. axd their consequence for heliosoierie studies.," The high-Mach number regime of the supersonic solar wind is an instructive example of the modeling technique differences, and their consequence for heliospheric studies." While cach echuique is optimized to coserve crucial quantities (fo rooxiunple. mass flux fi1u erid cell to exid cell). the calculations of density. veocity and pressure eviate frou nodel to model.," While each technique is optimized to conserve crucial quantities (for example, mass flux from grid cell to grid cell), the calculations of density, velocity and pressure deviate from model to model." " S1ual üX eruow are evident in Fieure 2 showiis the conserved total particle flux Dmere, where he ideal value (2.625&105 AU? om2s 4) 1s approxiniaed we] by the DM uodel."," Small flux errors are evident in Figure \ref{figsninner} showing the conserved total particle flux $n v r^2$, where the ideal value $2.625\times 10^8$ $^2$ $^{-2}$ $^{-1}$ ) is approximated well by the BM model." The Flo model also conserves this quantity. albeit a maler value was iutroduced. a the )oundarv.," The Flo model also conserves this quantity, albeit a smaller value was introduced at the boundary." " Tnunecdiately upstream of the TS. the inodeled densities ra1ος from 6.75 to 7.35 ""£r.5 alc| the veocitics (idealv 375 Kkwos 1 range frou, 316 to 383 lau st."," Immediately upstream of the TS, the modeled densities range from 6.75 to 7.35 $^{-3}/r^2$, and the velocities (ideally 375 km $^{-1}$ ) range from 376 to 383 km $^{-1}$." As the location of the TS is determiued by the ran pressure a the TS valancing the ISAL pressure. the sutle variatious dn ram pressure are a natural explanation of the TS differences in Table 2..," As the location of the TS is determined by the ram pressure at the TS balancing the ISM pressure, the subtle variations in ram pressure are a natural explanation of the TS differences in Table \ref{resplas}." Siuuilar effects explain the other discrepancies., Similar effects explain the other discrepancies. The BS distances basically folow the trend of the WP distances. as the BS shock compression ratios are quite simular between all four modeIs (2.22.3:," The BS distances basically follow the trend of the HP distances, as the BS shock compression ratios are quite similar between all four models (2.2–2.3;" of dust destruction and photoionization during the GRB event in close proximity to the bursts.,of dust destruction and photoionization during the GRB event in close proximity to the bursts. Properties of the GRB itself such as amount and spectrum of the energy output influence the alteration of the environment., Properties of the GRB itself such as amount and spectrum of the energy output influence the alteration of the environment. " Therefore, differences in the final gas-to-dust ratio is clouded by understandingthese factors which are difficult to disentangle between properties of the environment and the GRB itself."," Therefore, understanding differences in the final gas-to-dust ratio is clouded by these factors which are difficult to disentangle between properties of the environment and the GRB itself." " This measurement is also model dependent, and can be biased by assumptions about the spectral model."," This measurement is also model dependent, and can be biased by assumptions about the spectral model." " Regardless, the LAT bursts appear to have little to no dust along the line-of-sight compared to the GBM and BAT bursts."," Regardless, the LAT bursts appear to have little to no dust along the line-of-sight compared to the GBM and BAT bursts." " At this time, there are insufficient statistics on gas and dust content of the LAT bursts to draw any strong conclusions from this sample."," At this time, there are insufficient statistics on gas and dust content of the LAT bursts to draw any strong conclusions from this sample." Further study with more objects and broader band data are needed to distinguish any strong environmental differences between these populations., Further study with more objects and broader band data are needed to distinguish any strong environmental differences between these populations. " The luminosity light curves in Figures 1 and 2 reveal several interesting observational and possibly intrinsic differences between the BAT, GBM, and LAT populations."," The luminosity light curves in Figures \ref{fig:xlc} and \ref{fig:olc} reveal several interesting observational and possibly intrinsic differences between the BAT, GBM, and LAT populations." The GBM and to a higher extent LAT X-ray afterglows are clustered much more than the BAT afterglows., The GBM and to a higher extent LAT X-ray afterglows are clustered much more than the BAT afterglows. " From an instrumental perspective, BAT is more sensitive to detecting faint GRBs than GBM, therefore having a wider and fainter distribution of X-ray afterglows (that correlates with prompt fluence, ?)) is reasonable."," From an instrumental perspective, BAT is more sensitive to detecting faint GRBs than GBM, therefore having a wider and fainter distribution of X-ray afterglows (that correlates with prompt fluence, \citealt{gehrels08}) ) is reasonable." " However, due to the correlation between γ- fluence and X-ray flux, with the LAT GRBs having comparatively extreme fluences we would have expected the LAT GRBs to be at the (????),,bright end of the X-ray afterglow distribution."," However, due to the correlation between $\gamma$ -ray fluence and X-ray flux, with the LAT GRBs having comparatively extreme fluences \citep{swenson10,cenko10,mcbreen10,ghisellini10}, we would have expected the LAT GRBs to be at the bright end of the X-ray afterglow distribution." " This distribution is present in all permutations of these light curves (count rate, flux, flux so it is not an effect of one of our count rate density,to flux, flux luminosity),density, or luminosity correction factors."," This distribution is present in all permutations of these light curves (count rate, flux, flux density, luminosity), so it is not an effect of one of our count rate to flux, flux density, or luminosity correction factors." " This unexpected distribution is shown more clearly in the histograms of Figure 7,, demonstrating a cross-section of the luminosity at 11 hours and 1 day in the rest frame of each GRB."," This unexpected distribution is shown more clearly in the histograms of Figure \ref{fig:lumhist}, demonstrating a cross-section of the luminosity at 11 hours and 1 day in the rest frame of each GRB." " With this large sample of X-ray and optical afterglows, redshifts, and simple assumptions about the environment and physical parameters, we can estimate the total isotropic equivalent y-ray energy output in a systematic way over the same energy range for all of the GRBs in our samples."," With this large sample of X-ray and optical afterglows, redshifts, and simple assumptions about the environment and physical parameters, we can estimate the total isotropic equivalent $\gamma$ -ray energy output in a systematic way over the same energy range for all of the GRBs in our samples." " Despite the fact that we do not have accurate measurements of Eyeax for most of the BAT bursts, we can estimate both Epeak the power law index correlation from ?)), and either (usingestimate the Band function or cutoff power law parameters, use typical values, or use measurements from other instruments with larger energy coverage (e.g. Konus-Wind, Fermi-GBM, Suzaku-WAM) especially if they have constrained "," Despite the fact that we do not have accurate measurements of $E_{peak}$ for most of the BAT bursts, we can estimate both $E_{peak}$ (using the power law index correlation from \citealt{sakamoto09}) ), and either estimate the Band function or cutoff power law parameters, use typical values, or use measurements from other instruments with larger energy coverage (e.g. Konus-Wind, }-GBM, Suzaku-WAM) especially if they have constrained $E_{peak}$." "Using the assumed spectrum for each GRB and the Eneak.measured redshift, we integrate over a common rest frame energy range (?) of 10 keV to 10 MeV, as: The functional forms and assumptions are described in more detail in the appendix of ?.."," Using the assumed spectrum for each GRB and the measured redshift, we integrate over a common rest frame energy range \citep{amati02} of 10 keV to 10 MeV, as: The functional forms and assumptions are described in more detail in the appendix of \cite{racusin09}." " Using this method, we infer a reasonable value of Eyis, for each GRB in a systematic way."," Using this method, we infer a reasonable value of $E_{\gamma,iso}$ for each GRB in a systematic way." ? and? established that LAT GRBs include some of the most energetic GRBs ever detected., \cite{ghisellini10} and \cite{swenson10} established that LAT GRBs include some of the most energetic GRBs ever detected. " On average, the LAT GRBs have isotropic equivalent y-ray energy"," On average, the LAT GRBs have isotropic equivalent $\gamma$ -ray energy" The current understanding of galaxy formation ancl evolution has improved. considerably. in recent times owing {ο new. controversial results such as the downsizing scenario (Cimattietal.2006).. and the detailed chemical composition of possible galactie building blocks (ναπια.&Char-lot.1998:Geisleretal.,"The current understanding of galaxy formation and evolution has improved considerably in recent times owing to new, controversial results such as the downsizing scenario \citep{cim}, and the detailed chemical composition of possible galactic building blocks \citep{kau,geis}." 2007).. The former has promoted the inclusion of important. processes into models for galaxy evolution that. had. either. been ignored or treated in a simplified wav. such as the presence of active galactic nuclei in the centres of galaxies (Bowerctal.2006:Crotonet2006:Lagos.Cora&Padilla 2008).," The former has promoted the inclusion of important processes into models for galaxy evolution that had either been ignored or treated in a simplified way, such as the presence of active galactic nuclei in the centres of galaxies \citep{bow,cro,lagos}." . Phe latter controversy has fostered studies of satellites and central galaxies. of similar masses. to discover that the search lor the building blocks of present-dav. galaxies is a problematic endeavour. since the formation times plav an important role in the characteristics of galaxies (e.g. Robertson et al..," The latter controversy has fostered studies of satellites and central galaxies of similar masses, to discover that the search for the building blocks of present-day galaxies is a problematic endeavour, since the formation times play an important role in the characteristics of galaxies (e.g. Robertson et al.," 2005. Lagos. Padilla Cora. 2009).," 2005, Lagos, Padilla Cora, 2009)." Hints to these results have become available only recently. [rom studies of the importance of assembly on the clustering of dark-matter (DM) haloes (e.g. Croton et al.," Hints to these results have become available only recently, from studies of the importance of assembly on the clustering of dark-matter (DM) haloes (e.g. Croton et al.," 2007: Gao White. 2006) anc on shaping the population of galaxies in haloes or groups (Zapatactal. 2009).," 2007; Gao White, 2006) and on shaping the population of galaxies in haloes or groups \citep{zap}." .. lt is currently thought that the star formation activity in galaxies is a complicated: process where several factors are interlaced. such as the inter-stellar medium (18M). the cooling of hot gas. the chemical compositions of the dillerent eas phases. feedback processes which return energy ancl metals into the ISM. ancl dynamical effects such as mergers. winds. tidal interactions (see for instance Cole et al..," It is currently thought that the star formation activity in galaxies is a complicated process where several factors are interlaced, such as the inter-stellar medium (ISM), the cooling of hot gas, the chemical compositions of the different gas phases, feedback processes which return energy and metals into the ISM, and dynamical effects such as mergers, winds, tidal interactions (see for instance Cole et al.," 2000: Baugh. 2007).," 2000; Baugh, 2007)." Furthermore. a successful model of galaxy formation also needs to deal with the problematic formation of the first stars which form in a metal free medium (Ciao 2007)..," Furthermore, a successful model of galaxy formation also needs to deal with the problematic formation of the first stars which form in a metal free medium \citep{gao3}. ." Semi-analvtic models assume that the first, Semi-analytic models assume that the first Fleming Stone (2002) conducted numerical simmulatious of vertically-stratified disk models in which the upper lavers were MhlL-active while the ceutral regions were quiescent.,Fleming Stone (2002) conducted numerical simulations of vertically-stratified disk models in which the upper layers were MRI-active while the central regions were quiescent. They found that. although the MRI did not operate in the maguetically dead zone. the turbulence in tlie upper lavers could generate a significaut. Reynolds stress in the midplaue. which would allow the cdeacl laver to accrete albeit with a lower effective viscosity.," They found that, although the MRI did not operate in the magnetically dead zone, the turbulence in the upper layers could generate a significant Reynolds stress in the midplane, which would allow the dead layer to accrete albeit with a lower effective viscosity." Fleming Stone found that the BRevuolds stress in the midplaue uever dropped below about of the Maxwell stress in the active layers. and that there was significant mass mixiug between active and dead layers.," Fleming Stone found that the Reynolds stress in the midplane never dropped below about of the Maxwell stress in the active layers, and that there was significant mass mixing between active and dead layers." HE this were generally the case for protostellar disks. it would simply mean hat the effective a parameter for the evolution of the total surface cleusity would simply be at nost an order of magnitude lower in regions of dead zones.," If this were generally the case for protostellar disks, it would simply mean that the effective $\alpha$ parameter for the evolution of the total surface density would simply be at most an order of magnitude lower in regions of dead zones." This would result in au increase in the uass surface density. which will be inversely proportional to a in steady state (e.g.. Reves-Ruiz Stepiuski 1995): it would. vield a different depeudeuce of inass accretion rate on disk. parameters han in the orieiuale lavered model. at largee times beineOm dependent on the mass supply [rom the outer disk as iu tlie moclels of Hartiuaun (1998): aud it would limit the buildup of mass iu he dead zone with tine in the layered model. eventually evolving to a steady state.," This would result in an increase in the mass surface density, which will be inversely proportional to $\alpha$ in steady state (e.g., Reyes-Ruiz Stepinski 1995); it would yield a different dependence of mass accretion rate on disk parameters than in the original layered model, at large times being dependent on the mass supply from the outer disk as in the models of Hartmann (1998); and it would limit the buildup of mass in the dead zone with time in the layered model, eventually evolving to a steady state." However. for numerical reasous Flemine Stoue were able ouly to consider models in which he surface density of the active laver was of order of the surface density of the dead layer or arger.," However, for numerical reasons Fleming Stone were able only to consider models in which the surface density of the active layer was of order of the surface density of the dead layer or larger." An activen laver ofHJ ~E100&cin>7 could be or less ofn the total surfacen densityn at 0.1.H Al- in a disk like that of the staudard minunum mass solar nebula model.," An active layer of $\sim 100 {\rm g \, cm^{-2}}$ could be or less of the total surface density at 0.1 AU in a disk like that of the standard minimum mass solar nebula model." It seems iutuitively unlikely hat the turbulence generated in such au active layer could penetrate so effectively through such a 'elatively massive dead zone., It seems intuitively unlikely that the turbulence generated in such an active layer could penetrate so effectively through such a relatively massive dead zone. The mass accretion rate depends upon the vertical integral of δι if he viscosity tn the dead zoue drops by au order of inaguitude. the Revuolds stresses will have to ;»enetrate {ο a surface density larger by an order of maguitude or more iu order to have any ellect ou AZ.," The mass accretion rate depends upon the vertical integral of $\nu \Sigma$; if the viscosity in the dead zone drops by an order of magnitude, the Reynolds stresses will have to penetrate to a surface density larger by an order of magnitude or more in order to have any effect on $\mdot$." Ifthe Reynolds stresses do not penetrate to very much deeper layers. they will uot chauge he overall picture of layered accretio[u," If the Reynolds stresses do not penetrate to very much deeper layers, they will not change the overall picture of layered accretion." n The layered disk. model is affected by many aspects of non-thermal iouization (e.g.. grain erowth aud settling. N-ray Πανός. presence or absence of cosmic rays) whose effects could rauge from allowing a full MRI to operate to shutting it olf completely at some radii except for very thin surlace layers.," The layered disk model is affected by many aspects of non-thermal ionization (e.g., grain growth and settling, X-ray fluxes, presence or absence of cosmic rays) whose effects could range from allowing a full MRI to operate to shutting it off completely at some radii except for very thin surface layers." The ubiquity of disk accretion among voung stars (when immer disks are present) exhibiting a substantial but finite rauge of accretion rates at a given mass (Hartmann 1905) suggests that some process might be operating which minimizes the possible variatious in MRI activity., The ubiquity of disk accretion among young stars (when inner disks are present) exhibiting a substantial but finite range of accretion rates at a given mass (Hartmann 1998) suggests that some process might be operating which minimizes the possible variations in MRI activity. One process ofangular moienutum trausler that plausibly operates duriug at least the protostellar, One process of angular momentum transfer that plausibly operates during at least the protostellar "where the absolute brightnesses My and M; come from theoretical calibrations in Catelanetal.(2004) with the following conversion between Z and [Fe/H]: The conversion is based on a solar metallicity of Zo=0.01716, as required to match the metal-to-hydrogen ratio Z/X of Grevesse&Noels(1993)..","where the absolute brightnesses $M_V$ and $M_I$ come from theoretical calibrations in \cite{2004ApJS..154..633C} with the following conversion between $Z$ and $\feh$: The conversion is based on a solar metallicity of $Z_{\odot}=0.01716$ , as required to match the metal-to-hydrogen ratio $Z/X$ of \cite{1993oee..conf...15G}." Intrinsic colors of RRc stars are between 0.32 and 0.42 mag (based on models in Feuchtinger1999))., Intrinsic colors of RRc stars are between 0.32 and 0.42 mag (based on models in \citealt{1999A&A...351..103F}) ). " Since the metallicites of this type of RR Lyr variables are not determined, we use the mean value of (V—I)o=0.37 mag for each RRc star."," Since the metallicites of this type of RR Lyr variables are not determined, we use the mean value of $(V-I)_0=0.37$ mag for each RRc star." " In the above calculation, we adopt an uncertainty of the mean J-band brightness at a level of c;=0.02 mag etal.2008))."," In the above calculation, we adopt an uncertainty of the mean $I$ -band brightness at a level of $\sigma_I=0.02$ mag \citealt{2008AcA....58...69U}) )." The OGLE-III V-band light curves are(Udalski less well sampled and the adopted accuracy of the mean V-band brightness is oy=0.05 mag., The OGLE-III $V$ -band light curves are less well sampled and the adopted accuracy of the mean $V$ -band brightness is $\sigma_V=0.05$ mag. " The errors propagate to a range of στο=0.07-0.20 mag for the sample of 10,259 RRab stars with a median value of 0.09 mag."," The errors propagate to a range of $\sigma_{I0}=0.07$ –0.20 mag for the sample of 10,259 RRab stars with a median value of 0.09 mag." We estimate theposition of the Galactic center by measuring the mean distance to the bulge RR Lyr variables., We estimate theposition of the Galactic center by measuring the mean distance to the bulge RR Lyr variables. The distances R to individual bulge RRab star are estimated using the relation: To obtain the real distance to the center of the population we have to apply the following two geometric corrections., The distances $R$ to individual bulge RRab star are estimated using the relation: To obtain the real distance to the center of the population we have to apply the following two geometric corrections. " First, we have to project all the individual distances onto the Galactic plane by taking the cosine of the Galactic latitude, yielding Rcosb."," First, we have to project all the individual distances onto the Galactic plane by taking the cosine of the Galactic latitude, yielding $R{\rm cos}b$." " Second, we have to take into account the “cone-effect” — our subfields subtend solid angles on the sky with more volume further away — by scaling their distance distribution by R-?."," Second, we have to take into account the “cone-effect” — our subfields subtend solid angles on the sky with more volume further away — by scaling their distance distribution by $R^{-2}$." " A corrected and normalized distance distribution for the 10,259 RRab stars is presented in Figure 11.."," A corrected and normalized distance distribution for the 10,259 RRab stars is presented in Figure \ref{fig:histdist}." The symmetry of this distribution further confirms the high completeness of the RR Lyr catalog of Soszyfiskietal. (2011).., The symmetry of this distribution further confirms the high completeness of the RR Lyr catalog of \cite{2011AcA....61....1S}. The slightly flat peak in the distribution between 8.2 and 8.8 kpc is consistent with the presence of an elongated inner structure (see Section 5))., The slightly flat peak in the distribution between 8.2 and 8.8 kpc is consistent with the presence of an elongated inner structure (see Section \ref{sec:structure}) ). The distance distribution is very well represented by a Lorentzian with a maximum value at 8.540+0.013 kpc., The distance distribution is very well represented by a Lorentzian with a maximum value at $8.540\pm0.013$ kpc. A resulting distance to the Milky Way center of Ry=8.54+0.42 kpc is obtained by quadratically adding the median uncertainty in the distance to the individual stars of 0.418 kpc., A resulting distance to the Milky Way center of $R_0=8.54\pm0.42$ kpc is obtained by quadratically adding the median uncertainty in the distance to the individual stars of 0.418 kpc. This result is in good agreement with the weighted average of 8.15+0.140.35 kpc determined from eleven different measuring methods by (2010)., This result is in good agreement with the weighted average of $8.15\pm0.14\pm0.35$ kpc determined from eleven different measuring methods by \cite{2010RvMP...82.3121G}. . " In this section, we study the structure of the bulge RR Lyr population using their mean dereddened magnitudes"," In this section, we study the structure of the bulge RR Lyr population using their mean dereddened magnitudes" Las Campanas Swope telescope (lin) aud the Great Circle Camera (Zaritskycetal. (1996))) with a 2I CCD. we obtained diift-scean images for both Magellanic Clouds iu Johnson C.B.V. aud Cuma 7.,"Las Campanas Swope telescope (1m) and the Great Circle Camera \cite{zsb96}) ) with a 2K CCD, we obtained drift-scan images for both Magellanic Clouds in Johnson $U, B, V, $ and Gunn $I$." " The effective exposure time is between [ and 5 miu for SAIC scans aud the pixel scale is Ο.Τ aresec pixelο, ", The effective exposure time is between 4 and 5 min for SMC scans and the pixel scale is 0.7 arcsec $^{-1}$ . Typical seeing is —1.5 aresee and seans with ποσο worse than ~ 2.5 arcsec are not accepted., Typical seeing is $\sim$ 1.5 arcsec and scans with seeing worse than $\sim$ 2.5 arcsec are not accepted. AMaenitudes are placed on the Johuson-IE&ron-Cousins photometric system (Landolt 1983: 1992)., Magnitudes are placed on the Johnson-Kron-Cousins photometric system (Landolt 1983; 1992). Data from) observing ruus from November 1996 to December 1999 are included iu this catalog., Data from observing runs from November 1996 to December 1999 are included in this catalog. The data are reduced using a pipelie that utilizes DAOPIIOT II. (Stetson (1987))) audIRAF!., The data are reduced using a pipeline that utilizes DAOPHOT II \cite{stet97}) ) and. . Ouly stars with both B aud V detections are included in the final catalog., Only stars with both $B$ and $V$ detections are included in the final catalog. The pipeline for reducing individual scaus is a fairly standard application of DAOPIIOT., The pipeline for reducing individual scans is a fairly standard application of DAOPHOT. Each of the 21 scans (x LE for the four filters). which are either 9500 or 11000 pixels long (depending ou whether they are on the caster or western side of the SAIC survey region) and 2011 pixels wide. is divided iuto 9 bv 2 or LL by 2 subscaus that are roughly 1100 by 1100 pixels. with an overlap of about LOO xxel« between the subscaus that enables us to compare he results from the indepeudeut photometric reductions.," Each of the 24 scans $\times$ 4 for the four filters), which are either 9500 or 11000 pixels long (depending on whether they are on the eastern or western side of the SMC survey region) and 2011 pixels wide, is divided into 9 by 2 or 11 by 2 subscans that are roughly 1100 by 1100 pixels, with an overlap of about 100 pixels between the subscans that enables us to compare the results from the independent photometric reductions." There are two sources of discrepancy in the plotometiv roni subscaus: clifferiue ancl incousistent PSF iuodels and aperture corrections. aud nonplotometric conditions.," There are two sources of discrepancy in the photometry from subscans; differing and inconsistent PSF models and aperture corrections, and nonphotometric conditions." The latter is dificult to evaluate on a subscean basis jecause each subscean is smaller than the ον CCD used or the observations. aud so adjacent subscans are nof independeut of atimospheric variations.," The latter is difficult to evaluate on a subscan basis because each subscan is smaller than the 2K CCD used for the observations, and so adjacent subscans are not independent of atmospheric variations." Comparing the rotometry from adjacent seins. rather than subscaus. enables us to check the observing conditions. which were judeed by eve during the observing to be photometric aluost cutively over the Lt vers.," Comparing the photometry from adjacent scans, rather than subscans, enables us to check the observing conditions, which were judged by eye during the observing to be photometric almost entirely over the 4 years." These two classes of overlaps. subsean and scan. provide complementary internal checks.," These two classes of overlaps, subscan and scan, provide complementary internal checks." The result of the reduction pipeline is a catalog of instrumental photometry for cach detected star iu cach filter aud its right ascension and declination., The result of the reduction pipeline is a catalog of instrumental photometry for each detected star in each filter and its right ascension and declination. The astrometric solution is derived from a comparison to stars in the Magellanic Catalogue of Stars (NLACS: Tucholkeetal. (1996))). whose coordinates are ou the FICS system.," The astrometric solution is derived from a comparison to stars in the Magellanic Catalogue of Stars (MACS; \cite{tu96}) ), whose coordinates are on the FK5 system." Solutions are reviewed aud iterated if either the number of stars in the solution is less than 20 over the ~ 12 arcmin «12 arcnin subscan. or the riis positional scatter of the matched stars is larger than 0.5 arcsec.," Solutions are reviewed and iterated if either the number of stars in the solution is less than 20 over the $\sim$ 12 arcmin $\times 12$ arcmin subscan, or the rms positional scatter of the matched stars is larger than 0.5 arcsec." There are ouly teu subscaus for which we were unable- to reduce the positional scatter below 0.5 aresec (aud these have riis x 0.6 aresec). while the median ruis is 0.3 arcsec.," There are only ten subscans for which we were unable to reduce the positional scatter below 0.5 arcsec (and these have rms $<$ 0.6 arcsec), while the median rms is 0.3 arcsec." The iustiineutal maenitudes of stars in different filters are matched using a positional match that associates the nearest star on the sky within an aperture that is 3 times either the positional ruis of that subscau or 1.2 arcsec. whichever is lager.," The instrumental magnitudes of stars in different filters are matched using a positional match that associates the nearest star on the sky within an aperture that is 3 times either the positional rms of that subscan or 1.2 arcsec, whichever is larger." The V frame is used as the reference aud oulv stars that have a match in the B frame are retained for the final catalog., The $V$ frame is used as the reference and only stars that have a match in the $B$ frame are retained for the final catalog. Iu crowded areas it is possible that the “nearest” star in one filter is not the correct match to the V. reference because of the uncertainties in the astrometric solution., In crowded areas it is possible that the “nearest” star in one filter is not the correct match to the $V$ reference because of the uncertainties in the astrometric solution. We see some evidence of this problem when comparing to other data and wheu fitting atimospheric models (stars with hiehlv anomalous colors). but except near the faint uit of the catalog or in extremely crowded regious this issue appears to be a 1iuor problem.," We see some evidence of this problem when comparing to other data and when fitting atmospheric models (stars with highly anomalous colors), but except near the faint limit of the catalog or in extremely crowded regions this issue appears to be a minor problem." It is evident that one could invest more effort iu attempting to make “correct” matches. but the quality of the photometry iu regions where multiple stars are within Laresec of cach other in nuages with typical 1.5 arcsec sccing is strongly compromised in any case.," It is evident that one could invest more effort in attempting to make “correct” matches, but the quality of the photometry in regions where multiple stars are within $\sim$ 1 arcsec of each other in images with typical 1.5 arcsec seeing is strongly compromised in any case." Tu all cases we accept the closest match., In all cases we accept the closest match. Unlike errors in the photometric calibration. these errors can be estimated reliable using artificial star simulations.," Unlike errors in the photometric calibration, these errors can be estimated reliably using artificial star simulations." To place cach subscan on a seltcousisteut photometric system. we use the overlap region (these typically coutain several hundred stars in common in 2. V. aud F and several tens in C] to measure photometric differences.," To place each subscan on a self-consistent photometric system, we use the overlap region (these typically contain several hundred stars in common in $B$, $V$, and $I$ and several tens in $U$ ) to measure photometric differences." Each subscan has either two (f at the frout or back οσο of a scan) or three ucighborime subscaus within its scan and one more in the adjaceut scan. unless the subscean is at the edge of the survey region.," Each subscan has either two (if at the front or back edge of a scan) or three neighboring subscans within its scan and one more in the adjacent scan, unless the subscan is at the edge of the survey region." We calculate 1e niedian photometric shift of cach subscau relative to ns neighbors aud we find the subsean with the largest f&set., We calculate the median photometric shift of each subscan relative to its neighbors and we find the subscan with the largest offset. The photometry of that subsceau is adjusted by 1e offset and the process is repeated until all subscaus with a inedian offset that is greater than 0.02 maguitudes re corrected., The photometry of that subscan is adjusted by the offset and the process is repeated until all subscans with a median offset that is greater than 0.02 magnitudes are corrected. This process converges quickly because of 10 use of medias rather than means., This process converges quickly because of the use of medians rather than means. The subscaus are ien combined to produce a photometric catalog for cach scan., The subscans are then combined to produce a photometric catalog for each scan. A stellar density map. constructed from the resulting catalog. is visually inspected for areas that correspoud to scan or subscan regions that are of anomalously high or low density relative to their nciglibors.," A stellar density map, constructed from the resulting catalog, is visually inspected for areas that correspond to scan or subscan regions that are of anomalously high or low density relative to their neighbors." The photometry is adjusted interactively in these cases to correct the haudful of clearly anomalous subscaus or scaus., The photometry is adjusted interactively in these cases to correct the handful of clearly anomalous subscans or scans. This method ouly addresses anomalies that are 2 0.05 mae., This method only addresses anomalies that are $>$ 0.05 mag. Although we are concerned that this procedure could lead to systematic diiff4 from the correct zeropoiuts. our photometry is extensively tested by comparison to external data sets (see 833.2).," Although we are concerned that this procedure could lead to systematic drifts from the correct zeropoints, our photometry is extensively tested by comparison to external data sets (see 3.2)." The iustrmucutal maeuitucdes are placed ou the Jolusou-EIrou-Cousius Landolt svstem (1983: 1992)., The instrumental magnitudes are placed on the Johnson-Kron-Cousins Landolt system (1983; 1992). Residuals for the standard stars frou our photometric sohition are shown in Figure P. over the four vear period of the observing prograin., Residuals for the standard stars from our photometric solution are shown in Figure \ref{stands} over the four year period of the observing program. The photometric solutions involve a zeropoiut terni. an airmass term. and one linear color term (using BV for D aud V aud V.I for J) or two linear color terms (C. Band B.V separately for U).," The photometric solutions involve a zeropoint term, an airmass term, and one linear color term (using $B-V$ for $B$ and $V$ and $V-I$ for $I$ ) or two linear color terms $U-B$ and $B-V$ separately for $U$ )." Over the color range covered by the standards (see Figure 1)) there is little evidence for additional color terius., Over the color range covered by the standards (see Figure \ref{stands}) ) there is little evidence for additional color terms. The statistical zeropoiut uncertainty is typically 0.02 mag per run. sliehtlv higher iu the C baud (0.03 to 0.01 mae) with oulv oue run having a C band uncertainty as high as 0.0L7 mae.," The statistical zeropoint uncertainty is typically 0.02 mag per run, slightly higher in the $U$ band (0.03 to 0.04 mag) with only one run having a $U$ band uncertainty as high as 0.047 mag." The catalog of astrometry aud photometry for 5.156.057 stars ispresented as an ASCTI table (see Table 1 for a sunuple).," The catalog of astrometry and photometry for 5,156,057 stars ispresented as an ASCII table (see Table 1 for a sample)." Columns 1 and 2 contain the right ascension and declination (J2000.0) for cach star., Columns 1 and 2 contain the right ascension and declination (J2000.0) for each star. Cohuuus 3-10 contain the pairings of magnitudes aud uncertainties for U. D. V. aud £ imaguitudes.," Columns 3-10 contain the pairings of magnitudes and uncertainties for $U$, $B$, $V$, and $I$ magnitudes." The subsequentcolunums are described iu 855., The subsequentcolumns are described in 5. V baud stellar density aud hunuinositv maps of the SAIC are constructed from the catalog using stars with V20 and shown in Figure 2.., $V$ band stellar density and luminosity maps of the SMC are constructed from the catalog using stars with $V < 20$ and shown in Figure \ref{smcimage}. . The digital catalogs allow one to make analogous images for a variety, The digital catalogs allow one to make analogous images for a variety w. Whose strength. and shape satisfy equation so that Ov.../O/=0.,$\tilde{\omega}_z$ whose strength and shape satisfy equation so that $\partial\mathbf{\tilde{v}_{\bot}}/\partial t = 0$. The ellipses at different heights do not necessarily have to have the same size. shape. or strength: in the folowing subsections. we will describe (wo different wavs of “stacking” 2D elliptical vortices to create a 3D vortex.," The ellipses at different heights do not necessarily have to have the same size, shape, or strength; in the following subsections, we will describe two different ways of “stacking” 2D elliptical vortices to create a 3D vortex." The anticvclonie core of the vortex is surrounded bv a larger elliptical “halo” of weak cvclonic vorticity so that the net circulation in each horizontal plane equals zero: [=--—(., The anticyclonic core of the vortex is surrounded by a larger elliptical “halo” of weak cyclonic vorticity so that the net circulation in each horizontal plane equals zero: $\Gamma\equiv\int_A\tilde{\omega}_z dxdy = 0$. We define a 2D streamfunction c such that: V.=xe£ and ω.Ξ-NV?as, We define a 2D streamfunction $\tilde{\psi}$ such that: $\mathbf{\tilde{v}_{\bot}}\equiv\mathbf{\nabla_{\bot}}\times\tilde{\psi}\mathbf{\hat{z}}$ and $\tilde{\omega}_z = -\nabla^2_{\bot}\tilde{\psi}$. Thus. once z. is initialized al each height. we invert a 2D Poisson operator to obtain the streamlunetion. whieh in turn generates the horizontal velocity field.," Thus, once $\tilde{\omega}_z$ is initialized at each height, we invert a 2D Poisson operator to obtain the streamfunction, which in turn generates the horizontal velocity field." The 2D pressure field can be found by taking the horizontal divergence of the horizontal momentum equation and inverling another 2D Poisson operator., The 2D pressure field can be found by taking the horizontal divergence of the horizontal momentum equation and inverting another 2D Poisson operator. The pressure will likely have a nonzero vertical eradient. which if left unbalanced. will lead to large vertical accelerations.," The pressure will likely have a nonzero vertical gradient, which if left unbalanced, will lead to large vertical accelerations." We still have one more degree of freedom: we initialize the temperature Ποιά so that the buovancy force exactly balances the vertical pressure force: Thus. all three components of the momentum equation are exactly balanced. and the accelerations are all initially zero: QvΟἱ=0.," We still have one more degree of freedom: we initialize the temperature field so that the buoyancy force exactly balances the vertical pressure force: Thus, all three components of the momentum equation are exactly balanced and the accelerations are all initially zero: $\partial\mathbf{\tilde{v}}/\partial t = 0$." Of course. only under very special circumstances would this procedure just so happen to also exactly balance the temperature equation.," Of course, only under very special circumstances would this procedure just so happen to also exactly balance the temperature equation." In general. OT(Olz() initiallv. leading to an immediate evolution of the temperature field.," In general, $\partial\tilde{T}/\partial t\ne 0$ initially, leading to an immediate evolution of the temperature field." Vertical motions will then be generated by the temperature changes through the buovancey force. and these vertical velocities will (hen couple the horizontal motions at different heights.," Vertical motions will then be generated by the temperature changes through the buoyancy force, and these vertical velocities will then couple the horizontal motions at different heights." " For our first iniGal condition. we constructed (he simplest 3D analog of a 2D vortex: an ""infinite"" column created by stacking identical 2D elliptical vortices at every heieht."," For our first initial condition, we constructed the simplest 3D analog of a 2D vortex: an “infinite” column created by stacking identical 2D elliptical vortices at every height." The vertical vorticity à. horizontal velocity ν΄ and enthalpy p/p were all independent of height. and the temperature perturbation was set identically to zero inside and outside the vortex.," The vertical vorticity $\tilde{\omega}_z$, horizontal velocity $\mathbf{\tilde{v}_{\bot}}$ and enthalpy $\tilde{p}/\bar{\rho}$ were all independent of height, and the temperature perturbation was set identically to zero inside and outside the vortex." This initial condition was an exact equilibrium solution of the momentum and temperature equations: Qv/OI=OT/Ol0., This initial condition was an exact equilibrium solution of the momentum and temperature equations: $\partial\mathbf{\tilde{v}}/\partial t = \partial\tilde{T}/\partial t = 0$. However. it turned out that this quasi-2D vortex is unstable to small perturbations in 3D. Figure 3. shows the evolution of a perturbed columnar vortex.," However, it turned out that this quasi-2D vortex is unstable to small perturbations in 3D. Figure \ref{F:tall_column} shows the evolution of a perturbed columnar vortex." " The domain dimensions [or the simulation were (L,.L,.L.)=(2.8.8). and the numbers of grid points/spectral coelficients along each direction were CV,.V,..V.)=(64.256.256).The vertical velocity was forced to vanish on the top aud bottom boundaries of the domain: ¢.(2=+4) 0. The"," The domain dimensions for the simulation were $(L_x,L_y,L_z)=(2,8,8)$, and the numbers of grid points/spectral coefficients along each direction were $(N_x,N_y,N_z) = (64,256,256)$.The vertical velocity was forced to vanish on the top and bottom boundaries of the domain: $\tilde{v}_z(z\!=\!\pm 4) = 0$ The" be very helpful to pin down the real fractions of binary. triple and quadruple systems. and thus constrain dillerent models of star formation.,"be very helpful to pin down the real fractions of binary, triple and quadruple systems, and thus constrain different models of star formation." In Section 3.1 we pointed out that. in our 0.5 Myr models. very low mass objects (often brown dwarfs) are. very COMMON as companions to more massive stars. but at large separations.," In Section 3.1 we pointed out that, in our 0.5 Myr models, very low mass objects (often brown dwarfs) are very common as companions to more massive stars, but at large separations." Furthermore. most of these outliers are bound not to single stars but to close binaries. triples or binary quacruples.," Furthermore, most of these outliers are bound not to single stars but to close binaries, triples or binary quadruples." At an age of 10.5 Myr. the fraction of multiple systems exhibiting. brown cdwarls at. large separations is much lower: 3 out of 18. in contrast with the result of 10 out of 13 found at 0.5 Myr.," At an age of 10.5 Myr, the fraction of multiple systems exhibiting brown dwarfs at large separations is much lower: 3 out of 18, in contrast with the result of 10 out of 13 found at 0.5 Myr." Nevertheless. 3 out of the + brown cdwarfs that remain bound do so orbiting binaries or higher-order multiples at large separations.," Nevertheless, 3 out of the 4 brown dwarfs that remain bound do so orbiting binaries or higher-order multiples at large separations." The exception is the brown cdwarf. secondary. found. in. simulation. asc. which is only 10 AU away from the primary.," The exception is the brown dwarf secondary found in simulation $\alpha3$ C, which is only 10 AU away from the primary." Therefore. it appears that many bound. brown dwarfs ( 3/4). and most bound brown chwarls in wide orbits ( 3/3). should be orbiting binary. triple or quadruple systems.," Therefore, it appears that many bound brown dwarfs $\sim 3/4$ ), and most bound brown dwarfs in wide orbits $\sim 3/3$ ), should be orbiting binary, triple or quadruple systems." Currently. 12 brown cdwarl/very low mass companions at wide separations are known (Ixirkpatrick et al.," Currently, 12 brown dwarf/very low mass companions at wide separations are known (Kirkpatrick et al." 2001a.b: Wilson et al.," 2001a,b; Wilson et al." 2001). proving that the does not extend to large separations (CGizis et al.," 2001), proving that the does not extend to large separations (Gizis et al." 2001)., 2001). Two of these brown chvarls (GI337€ ancl GI584€) are orbiting visual binaries. at z 900 ancl 3600 AU respectively. and a third (CL5TOD) is bound to a triple system. (at a distance of 1500 AU).," Two of these brown dwarfs (Gl337C and Gl584C) are orbiting visual binaries, at $\approx$ 900 and 3600 AU respectively, and a third (Gl570D) is bound to a triple system (at a distance of 1500 AU)." That is. 3 out of the 11 brown dwarfs orbiting stars at large separations are known to orbit a binary or triple system.," That is, 3 out of the 11 brown dwarfs orbiting stars at large separations are known to orbit a binary or triple system." A clear prediction. of our. simulations can be applied. to he other S systems in which a brown cwarf is apparently orbiting a single star., A clear prediction of our simulations can be applied to the other 8 systems in which a brown dwarf is apparently orbiting a single star. A Large fraction of these singles should urn out. after closer exanination. to be Α2 multiples i.e. à spectroscopic binary. triple. etc).," A large fraction of these singles should turn out, after closer examination, to be $N \geq 2$ multiples (i.e. a spectroscopic binary, triple, etc.)." This could be tested very simply. since a significant fraction of all spectroscopic unaries are known to beAes Le. have nearly equal-amass components (Halbwachs et al.," This could be tested very simply, since a significant fraction of all spectroscopic binaries are known to be – i.e. have nearly equal-mass components (Halbwachs et al." 2003)... as is also the case in our models. and twins are easier to detect spectroscopically han low mass ratio binaries.," 2003) –, as is also the case in our models, and twins are easier to detect spectroscopically than low mass ratio binaries." An observational case in ine with our predictions has been described by Brandeker. Javawardhana Najita (2003) who have recently shown hat the brown cdwarf TWA 5 D is bound at z120 AU o TWA 5 X. which in turn is resolved into à very. tight. 3 AU separation. binary (or possibly afriple: Mohbanty. Javawardhana Barraclo v Navascuéss 2003).," An observational case in line with our predictions has been described by Brandeker, Jayawardhana Najita (2003) who have recently shown that the brown dwarf TWA 5 B is bound at $\approx 120$ AU to TWA 5 A, which in turn is resolved into a very tight, 3 AU separation, binary (or possibly a; Mohanty, Jayawardhana Barrado y Navascuéss 2003)." We have uncertaken the first hyerodyvnamical. | IN-body simulations of multiple star formation that have produced a statistically significant number of stablehierarchical systems. with component separations in the range 1.1000 AU.," We have undertaken the first hydrodynamical $+$ $N$ -body simulations of multiple star formation that have produced a statistically significant number of stablehierarchical systems, with component separations in the range $\sim 1-1000$ AU." These simulations have demonstrated that multiple star formation is a major channel for star formation in turbulent flows., These simulations have demonstrated that multiple star formation is a major channel for star formation in turbulent flows. The hyvdrodyvnamical simulations are followed. for z0.5 Myr: subsequently. the remaining gas is removed. and the stellar svstems followed. as N-body ensembles for an additional 10 Myr.," The hydrodynamical simulations are followed for $\approx 0.5$ Myr; subsequently, the remaining gas is removed and the stellar systems followed as $N$ -body ensembles for an additional 10 Myr." At this point. all but one of the surviving multiple svstems are stable. according to the criteria. of Eeelcton Ixiseleva. (1995).," At this point, all but one of the surviving multiple systems are stable, according to the criteria of Eggleton Kiseleva (1995)." We find that the properties of the resulting multiple systems are not significantly sensitive to the large scale geometry of the cloucl — determined vogue turbulence δα rather to the dynamical ancl competitive accretion processes taking place within the mini-clusters [ormed out of the collapse and fragmentation of the cloud., We find that the properties of the resulting multiple systems are not significantly sensitive to the large scale geometry of the cloud – determined by the turbulence – but rather to the dynamical and competitive accretion processes taking place within the mini-clusters formed out of the collapse and fragmentation of the cloud. At an age of 0.5 Myr. we find that about 60% of stars and brown cwarls are in multiple svstems. with about a third. of these being low mass. weakly bound outliers.," At an age of $0.5$ Myr, we find that about $60 \%$ of stars and brown dwarfs are in multiple systems, with about a third of these being low mass, weakly bound outliers." Exclucling these outliers ancl unbound objects. πετά of the remaining objects are in pure binaries (2 svstenis) 144 are in quadruples (2 svstems). 35% are in. quintuples (4 systems). 32% are in sextuples (3 svstemis) and 12% are in multiples with seven components (1 system)," Excluding these outliers and unbound objects, $7 \%$ of the remaining objects are in pure binaries $2$ systems), $14 \%$ are in quadruples $2$ systems), $35 \%$ are in quintuples $4$ systems), $32 \%$ are in sextuples $3$ systems) and $12 \%$ are in multiples with seven components $1$ system)." The companion frequency is therefore very high. z1.," The companion frequency is therefore very high, $\approx 1$." We find hat our multiples consist. of hierarchies of binarics and riples and that (in which companions are not members of binarv/triple svstems other than the multiple itself) are comparatively rare (occurring 25% of he time)., We find that our multiples consist of hierarchies of binaries and triples and that (in which companions are not members of binary/triple systems other than the multiple itself) are comparatively rare (occurring $\sim 25 \%$ of the time). There is a distinctive pattern of mass distribution within these multiples. with the mass ratio within binaries. and the mass ratios between binaries. rarely deviating far rom unity (values of 0.51 are tvpical).," There is a distinctive pattern of mass distribution within these multiples, with the mass ratio within binaries, and the mass ratios between binaries, rarely deviating far from unity (values of $0.5-1$ are typical)." On the other yan. such systems are typically orbited by several low mass outliers (twpically at separations of ~10 AU) on eccentric orbits.," On the other hand, such systems are typically orbited by several low mass outliers (typically at separations of $\sim 10^4$ AU) on eccentric orbits." About of these objects are unstable in timescales ola few LO? vr (Lea few their typical orbital timescale)., About of these objects are unstable in timescales of a few $\times 10^6$ yr (i.e. a few $\times$ their typical orbital timescale). We find that the 40% of objects that are unbound are overwhelmingly. of low mass (median mass z0.02 M. )., We find that the $40 \%$ of objects that are unbound are overwhelmingly of low mass (median mass $\approx 0.02$ $_\odot$ ). ‘Thus our results imply that in the stellar regime. most stars are in multiples (2: SO) and that this multiplicity fraction Ji is an increasing function of mass.," Thus our results imply that in the stellar regime, most stars are in multiples $\approx 80\%$ ) and that this multiplicity fraction $f_{\rm m}$ is an increasing function of mass." In this latter respect. these results are qualitatively consistent with a large body of previous works on the decay. of small svstems. both with and without eas (van Albada LOGS: MeDonald Clarke 1903. 1995: Sterzik Durisen 1998. 2003: DCD03).," In this latter respect, these results are qualitatively consistent with a large body of previous works on the decay of $N$ systems, both with and without gas (van Albada 1968; McDonald Clarke 1993, 1995; Sterzik Durisen 1998, 2003; DCB03)." " The high fi, values for GN stars are consistent with adaptive optics measurements of nearby. voung associations such as MDSM 12 anc TW Lvclrac ος. Brandeker. Javawardhana Najita 2003). where multiplicity fractions as high 0.64 are found. and radial velocity surveys of visual binaries (ος. Tokovinin Smekhov 2002) which raise the percentage of spectroscopic sub-systems to at least404."," The high $f_{\rm m}$ values for GK stars are consistent with adaptive optics measurements of nearby young associations such as MBM 12 and TW Hydrae (e.g. Brandeker, Jayawardhana Najita 2003), where multiplicity fractions as high 0.64 are found, and radial velocity surveys of visual binaries (e.g. Tokovinin Smekhov 2002) which raise the percentage of spectroscopic sub-systems to at least." .. Low-mass SER. such as ‘Taurus or p Ophiuchus also show companion frequencies in the range 0.80.5. comparable το those predicted by our models at later times.," Low-mass SFR such as Taurus or $\rho$ Ophiuchus also show companion frequencies in the range $0.3-0.5$, comparable to those predicted by our models at later times." " It must be pointed out that the values of the multiplicity fraction fy, for each mass range do not change significantly. during the N-body evolution of the svstems.", It must be pointed out that the values of the multiplicity fraction $f_{\rm m}$ for each mass range do not change significantly during the $N$ -body evolution of the systems. At an age of 10.5 Mr. the fraction of bound. and unbound objects has reversed: remain in multiples and are singles., At an age of 10.5 Myr the fraction of bound and unbound objects has reversed: remain in multiples and are singles. The companion frequency has dropped to =0.3 due to the ejection of bound outliers to the field., The companion frequency has dropped to $\approx 0.3$ due to the ejection of bound outliers to the field. This transference of objects from bound to unbound orbits results in an increase of the number of free floating brown clwarls by & 60%., This transference of objects from bound to unbound orbits results in an increase of the number of free floating brown dwarfs by $\approx 60 \%$ . In this 10 Myr time-span. many multiple svstenis also experience internal decav: excluding the remaining 3 outliers. of the remaining bound. objects are in. pure binaries (11 svstemis). are in triples (2 systems). are," In this 10 Myr time-span, many multiple systems also experience internal decay: excluding the remaining 3 outliers, of the remaining bound objects are in pure binaries (11 systems), are in triples (2 systems), are" The decrhuination of Ooealactic Ooelobular cluster (CC) agesOo has recentlv come into a state of flux. first due ο updated stellar physics aud lately due to the WIPPARCOS results.,"The determination of galactic globular cluster (GC) ages has recently come into a state of flux, first due to updated stellar physics and lately due to the HIPPARCOS results." " Theoretical iSochliroikss were challenecd by. BiOnanuo ot ((199s. hereafter BCP). who have preseued a selt-consistent method for the deerniuatiou of relative cluster ages, Which as much a8 possille makes use of observational oxoperties aud tries f» nininize theiuput from theoretical isochroucs."," Theoretical isochrones were challenged by Buonanno et (1998, hereafter BCP), who have presented a self-consistent method for the determination of relative cluster ages, which as much as possible makes use of observational properties and tries to minimize the input from theoretical isochrones." They aree that hee tested sets of isochroucs al to reproduce the enipiriceal relation between ACBΕΟΝ (the (BV) «ifferenὉ between the TO aud the vase of the RGB) iux [Fe/T1 at a given age., They argue that three tested sets of isochrones fail to reproduce the empirical relation between $\triangle (B-V)_{\rm TO}^{\rm RGB}$ (the (B-V) difference between the TO and the base of the RGB) and [Fe/H] at a given age. Furthermore. relative ages based οι1i brightuess or colour differences are inconsistent in all cases.," Furthermore, relative ages based on brightness or colour differences are inconsistent in all cases." In thisLetter we will coufrout he isochroues by Saavis Weiss (1997. 1998: hereafter SW9; SW9s) with the observational results and show hat this set passes t1ο fest fo a great extent.," In this we will confront the isochrones by Salaris Weiss (1997, 1998; hereafter SW97 SW98) with the observational results and show that this set passes the test to a great extent." SWOT have determined GC ages by imeaus of the traditional theoretical approach of comparing theoretical isocchrones with an observed CAID., SW97 have determined GC ages by means of the traditional theoretical approach of comparing theoretical chrones with an observed CMD. The differences with respect to related. works are (1) that thev use the very lates (canonical) iuput plysics. (1) that also a- clement eiaucenient in the GC composition is tasen into accolut nn the opacity tables) aud (mi) tlat ev determined ages onlv for thevery few μίας wrere both CMD norxhologv aud avülable data arantee an accurate dalug.," The differences with respect to related works are (i) that they use the very latest (canonical) input physics, (ii) that also $\alpha$ -element enhancement in the GC composition is taken into account in the opacity tables) and (iii) that they determined ages only for the very few clusters where both CMD morphology and available data guarantee an accurate dating." The brightuess «iffereice between Turn-Off (TO) arid Zero-Aee IHorizouta] Braich (ZAMB). AVE. Was OHSCCL as he asolute age 1xdicaOr.," The brightness difference between Turn-Off (TO) and Zero-Age Horizontal Branch (ZAHB), $\triangle V^{\rm HB}_{\rm TO}$, was used as the absolute age indicator." Tje danposed constraints resul in a rather small sample of 7 clusters of all metalicities Guecluding dis5 GC in SW9s) suitable for the «eternaion of absoute ages (sce SWOT iud SW9s for detail)., The imposed constraints result in a rather small sample of 7 clusters of all metallicities (including disk GC in SW98) suitable for the determination of absolute ages (see SW97 and SW98 for details). All other ages in their xuuple of 31 GC have been determined diffiYentiallv with respect to these template clusters by using the (theoretical) dependence of A(Bpy on age., All other ages in their sample of 31 GC have been determined differentially with respect to these template clusters by using the (theoretical) dependence of $\triangle (B-V)_{\rm TO}^{\rm RGB}$ on age. o For ΠΠ he errors arising from uncertainties in the adopted colour transformations aud the uixiug leneth calibration. SW97 aud SW98 evaluated tlic Bulative ages ouly witlin uctallicity eroups.," For minimizing the errors arising from uncertainties in the adopted colour transformations and the mixing length calibration, SW97 and SW98 evaluated the relative ages only within metallicity groups." " Whether the relative ages would also be valid across metallicity eroi )oundaries. SWOT checked in only one case,"," Whether the relative ages would also be valid across metallicity group boundaries, SW97 checked in only one case." This an her checks aavailaημίν of two clusters with iu solute age determination iu the same netallicity eroup. comparison of the template clusters distances obtaie: from the theoretical ZATIB 1uodels with iain-sequeuce fitting distances using HIPPARCOS subcdwarts) restIted iu the confirmation of the internal consisenev of the SWOT and SW98 ages and of the reliabilits* of their theoretical isochrones.," This and other checks availability of two clusters with an absolute age determination in the same metallicity group, comparison of the template clusters distances obtained from the theoretical ZAHB models with main-sequence fitting distances using HIPPARCOS subdwarfs) resulted in the confirmation of the internal consistency of the SW97 and SW98 ages and of the reliability of their theoretical isochrones." We now recall briefly the BCP iehocl for determiinue homogencous relative ages for GC., We now recall briefly the BCP method for determining homogeneous relative ages for GC. The first step is to define a sample of coeval clusters in a wide range of metallicities., The first step is to define a sample of coeval clusters in a wide range of metallicities. " This requies age deermumnatious. which at least iuust be able to define correctlv what is ""coeval."," This requires age determinations, which at least must be able to define correctly what is “coeval”." To this scope. BCP used a variant of the vertical method used by SWOT. emplovius a point on," To this scope, BCP used a variant of the vertical method used by SW97, employing a point on" angle ancl in enerev. transforms into complex angular and energy dependencies.,"angle and in energy, transforms into complex angular and energy dependencies." " subrelativistic protons lose their enerey mainly by Coulomb collisions. i.e. EiL,=—imeInX. where vj is the proton velocity. and InX is the Coulomb↽↽∙ logarithm."," Subrelativistic protons lose their energy mainly by Coulomb collisions, i.e. $\frac{dE_p}{dt}=-\frac{4\pi ne^4}{m_e \mathrm{v}_{\rm{p}}}\ln\Lambda$, where $\mathrm{v}_{\rm{p}}$ is the proton velocity, and $\ln\Lambda$ is the Coulomb logarithm." In this wav the protons (iransfer almost all their energy. to the background. plasma and heat it., In this way the protons transfer almost all their energy to the background plasma and heat it. This process was analvsed in Dogieletal.(2009c.d)..," This process was analysed in \citet{dog_pasj,dog_aa}." For the GC parameters the average (me of Coulomb losses lor several tens MeV. protons is several million vears., For the GC parameters the average time of Coulomb losses for several tens MeV protons is several million years. The racius of plasma heated by (he protons is estimated [rom the diffusion equation describing propagation and energy losses ofprotons in the GC (Doeieletal.2009b).., The radius of plasma heated by the protons is estimated from the diffusion equation describing propagation and energy losses ofprotons in the GC \citep[][]{dog_pasj2}. This radius is about. LOO pc., This radius is about 100 pc. The temperature of heated plasma is determined by (he energv which these protons transfer to the backeround gas., The temperature of heated plasma is determined by the energy which these protons transfer to the background gas. For Wo10ης [OHergs ! the plasma temperature is about. 10 keV Cxovamaetal.2007). just as observed by Suzaku lor the GC., For $\dot{W}\sim 10^{40}-10^{41}$ erg $^{-1}$ the plasma temperature is about 10 keV \citep{koyama07} just as observed by Suzaku for the GC. The plasma with such a high temperature cannot be confined at the GC and therefore il expands into the surrounding medium., The plasma with such a high temperature cannot be confined at the GC and therefore it expands into the surrounding medium. Iverodyvnaimics of gas expansion was described in many monographs and reviews Disnovatvi-IXogan&Silich 1995)., Hydrodynamics of gas expansion was described in many monographs and reviews \citep[see e.g.][]{kogan}. . As the time of star capture may be smaller than the time of proton enerev losses. we have almost stationary energv release in (he central region with a power VW3x107 erg 4.," As the time of star capture may be smaller than the time of proton energy losses, we have almost stationary energy release in the central region with a power $\dot{W}\sim 3\times 10^{40}$ erg $^{-1}$." This situation is verv similar to that described bv Weaveretal.(1977). for a stellar wind expanding into a uniform density medium., This situation is very similar to that described by \citet{weav77} for a stellar wind expanding into a uniform density medium. " The model describes à star al lime (—0begins to blow a spherically svnunetric wind with a velocily. ofB stellar wind. - V. mass-loss rate dA,αἲ= M, and a luminosity. L,,=MMT)tee/2i "," The model describes a star at time t=0begins to blow a spherically symmetric wind with a velocity of stellar wind $V_w$ , mass-loss rate $dM_w/dt=\dot{M_w}$ , and a luminosity $L_w=\dot{M_w}V_w^2/2$ " The detection rate then begins to rise again towards higher redshifts as the number of radio-Ioud sources increases.,The detection rate then begins to rise again towards higher redshifts as the number of radio-loud sources increases. In contrast to our X-ray. selected. sample. high redshift optical quasar samples. even at the brightest magnitudes. ind that only ~9025 percent of the objects are radio loud (c.g. 7)).," In contrast to our X-ray selected sample, high redshift optical quasar samples, even at the brightest magnitudes, find that only $\sim20-25$ percent of the objects are radio loud (e.g. \citet{2007ApJ...656..680J}) )." his may go some wav to explaining the Latter sight end slope of the QSO luminosity function derived rom the X-ray (c.g. ?)). as compared. to the optical (?:: ?)).," This may go some way to explaining the flatter bright end slope of the QSO luminosity function derived from the X-ray (e.g. \citet{2005A&A...441..417H}) ), as compared to the optical \citet{2006AJ....131.2766R}; \citet{croom09}) )." The number of bright X-ray quasars is boosted by a population which is dominated by X-ray emission from the jet. prestunably beamed at some level.," The number of bright X-ray quasars is boosted by a population which is dominated by X-ray emission from the jet, presumably beamed at some level." Phis is also consistent with both ? and ? who find a flatter slope in the racio aminosity function for a sample of radio-Ioud QSOs., This is also consistent with both \citet{1998MNRAS.300..625W} and \citet{2005MNRAS.357.1267C} who find a flatter slope in the radio luminosity function for a sample of radio-loud QSOs. Since the RASS64 catalogue was selected to be he brightest X-ray sources over a large area of sky we would only expect to see this elfect in a sample such as this one., Since the RASS–6dFGS catalogue was selected to be the brightest X-ray sources over a large area of sky we would only expect to see this effect in a sample such as this one. Deeper X-ray. surveys would. not observe this due to the small area of sky. covered and the rarity of these extremely uminous sources., Deeper X-ray surveys would not observe this due to the small area of sky covered and the rarity of these extremely luminous sources. As such. the bright end of the luminosity. ‘unetion is not constrained by these surveys.," As such, the bright end of the luminosity function is not constrained by these surveys." Ix-8 tests comparing the redshift and optical magnitucle distributions of the full sample and the radio sample show hat they are different populations at a significance level of 994., K-S tests comparing the redshift and optical magnitude distributions of the full sample and the radio sample show that they are different populations at a significance level of $\%$. This highlights the need to study the full RASSGARGS sample as opposed. to just the sources with radio Counterparts., This highlights the need to study the full RASS--6dFGS sample as opposed to just the sources with radio counterparts. The Gelb Galaxy Survey takes its targets from a number of different samples., The 6dF Galaxy Survey takes its targets from a number of different samples. These were all given a number referrec o as the programme ID (proglD) and then listed in order of priority. (2).., These were all given a number referred to as the programme ID (progID) and then listed in order of priority \citep{6df}. Sources selected [rom theROSAL ALL Sky Survey were designated a proglD of 113., Sources selected from the All Sky Survey were designated a progID of 113. However. many of he targets were also Listed in other 04105 target samples.," However, many of the targets were also listed in other 6dFGS target samples." Due to this the progelD of each spectrum refers to the targe sample of the highest. priority. where the higher priorities carried ereater importance in the allocation of fields: i.e. ifà arect is also listed in the primary sample then it is assignec a proglD number of 1 since that target List had the highes priority.," Due to this the progID of each spectrum refers to the target sample of the highest priority, where the higher priorities carried greater importance in the allocation of fields; i.e. if a target is also listed in the primary sample then it is assigned a progID number of 1 since that target list had the highest priority." Table 5. shows the different proglD numbers listed in the RASSασ catalogue., Table \ref{progidtab} shows the different progID numbers listed in the RASS–6dFGS catalogue. Ehe majority first appear in the RASS targetsample.. with 15.4% of RASS targets also appearing in the primary saniple. selected from the 2\LASS eXtended Source Catalogue (2\LASS NSC).," The majority first appear in the RASS target, with $\%$ of RASS targets also appearing in the primary sample, selected from the 2MASS eXtended Source Catalogue (2MASS XSC)." In order to compare our RASS6dEGS catalogue with the RBSCNVSS sample (2).. à subset of objects were selected from each in the overlapping region of sky.," In order to compare our RASS–6dFGS catalogue with the RBSC–NVSS sample \citep{bauer}, a subset of objects were selected from each in the overlapping region of sky." Ehis involved selecting only the sources in the declination range 40°«Ó« OFF |b)>15° and counts/sz0.1.," This involved selecting only the sources in the declination range $-40^{\circ}<\delta<0^{\circ}$ , $|b|>15^{\circ}$ and $>0.1$." This leaves 609 sources in the RBSCNVSS comparison catalogue ancl 956 in the RASS6dEGS comparison catalogue., This leaves 609 sources in the RBSC–NVSS comparison catalogue and 956 in the RASS–6dFGS comparison catalogue. Llowever. only," However, only" eood measurement requires too many transitions or too many lines of sight.,good measurement requires too many transitions or too many lines of sight. Thus we wish to perform some mock. experiments using the above distributions of calibration shifts to see what the effect ou 2e would be., Thus we wish to perform some mock experiments using the above distributions of calibration shifts to see what the effect on $\delalpha$ would be. " Iu an actual experiuent. a value of 2e js estimated by doing a large joint ft of the Voigt line profiles. the system redshifts. and the possible velocity offset due to A,"," In an actual experiment, a value of $\delalpha$ is estimated by doing a large joint fit of the Voigt line profiles, the system redshifts, and the possible velocity offset due to $\delalpha$." Iu our Monte Carlo mock experiments we try to caleulate a value of 2e using the UVES VLT data. bu without measming anv actual absorption lines.," In our Monte Carlo mock experiments we try to calculate a value of $\delalpha$ using the UVES VLT data, but without measuring any actual absorption lines." Iustead of using the fitted system redshitts to find velocity offsets. we use the wavelength calibration offsets eiven bv the fine-biuned (blue aud red) lines in Figures 1. and 2.. aux add these to the lab values of Ay in Equation (3)).," Instead of using the fitted system redshifts to find velocity offsets, we use the wavelength calibration offsets given by the fine-binned (blue and red) lines in Figures \ref{fig:vshiftallu} and \ref{fig:vshiftalll}, and add these to the lab values of $\lambda_0$ in Equation \ref{eqn:eqvj}) )." The basic method is as follows., The basic method is as follows. We first choose a raudom redshift iu the ranec :0.2 to 2=3.7. ane calculate the wavelengths of the 23 atomic trausitious that were studied im Murphy et al. (," We first choose a random redshift in the range $z=0.2$ to $z=3.7$, and calculate the wavelengths of the 23 atomic transitions that were studied in Murphy et al. (" 2003).,2003). We define Mean the nunber of these 23 trausitious that fal at waveleneths for which we have iodine wavelength calibration.," We define $\Ntran$, the number of these 23 transitions that fall at wavelengths for which we have iodine wavelength calibration." " We require at least Nj, estou alu show our results as a function of thisNay, (a tvpica value ds Xu=[o and we do not find anv cases with Neva,c 9)."," We require at least $\Nmin$ transitions, and show our results as a function of this $\Nmin$ (a typical value is $\Nmin=4$, and we do not find any cases with $\Ntran>9$ )." For each such transition we shift its wavelengthby au amount eiveu by the fine-binued (blue or red) line from oue of the exposures in Figures 1. iux 2.., For each such transition we shift its wavelength by an amount given by the fine-binned (blue or red) line from one of the exposures in Figures \ref{fig:vshiftallu} and \ref{fig:vshiftalll}. We then perform a fit of Equation (3)) for 2e alu its error., We then perform a fit of Equation \ref{eqn:eqvj}) ) for $\delalpha$ and its error. This couuts as one absorption svstem. and we repeat this procedure NS times. averaging the values of obtained.," This counts as one absorption system, and we repeat this procedure $\Nsys$ times, averaging the values of $\delalpha$ obtained." We consider values of Ni. ranging from Nowae=l1. the ummber of svstems used in Murpliy ο al. (," We consider values of $\Nsys$ ranging from $\Nsys=143$, the number of systems used in Murphy et al. (" 2001). to Now=1. the value when nls One svsteuni in one QSO is being analvzed.,"2004), to $\Nsys=1$, the value when only one system in one QSO is being analyzed." Theutabove procedure constitutes one Monte Carlo experime, The above procedure constitutes one Monte Carlo experiment. Wo repeat the experiment many times to fud au average value of ae and its standard deviation (uecasured by the variance of Aa for the many experiments)., We repeat the experiment many times to find an average value of $\delalpha$ and its standard deviation (measured by the variance of $\delalpha$ for the many experiments). “We resent resulting average values of24- along with their standard deviations as a function of NS aud Nus iu Table 3. for 200.000 mock experiments.," We present resulting average values of $\delalpha$ along with their standard deviations as a function of $\Nsys$ and $\Nmin$ in Table \ref{tab:monteresults} for 200,000 mock experiments." " Thetable shows results for AL.113 aud AN,1].", The table shows results for $\Nsys=143$ and $\Nsys=1$. Note one expects the standard deviation in 22 to simply scale as .12 ⋅⋅ ⊀∖∖∖↽∖∙↖↖↽∐↕↸⊳∐↕↴∖↴↸⊳↕∪↴∖↴↸∖↑∪↖↖⇁∐⋜↧↑↖↖↽↸∖∏∐≼⊔∐⊺⋜∏⋝↕↸∖⋅≩∙∙↽∕∏⋯↴∖↴∙ ⋅∙↴," Note one expects the standard deviation in $\delalpha$ to simply scale as $\Nsys^{-1/2}$, which is close to what we find in Table \ref{tab:monteresults}." ∙ ↴ we will use this scaling from now on aud only report Moute Carlo experiments for Nu.=1.," Thus, we will use this scaling from now on and only report Monte Carlo experiments for $\Nsys=1$." Besides using the actual wavelength calibration errors above. we also rau several Monte Carlo simulations sine two simple models of the calibration offsets.," Besides using the actual wavelength calibration errors above, we also ran several Monte Carlo simulations using two simple models of the calibration offsets." The results of these simple models are also reported in Table offset, The results of these simple models are also reported in Table \ref{tab:monteresults}. For the first model we used a Caussian raudon velocity 3.. with a standard deviation equal to 91 ms, For the first model we used a Gaussian random velocity offset with a standard deviation equal to 91 $\ms$. For the second. we modeled the velocity offsets as a sine function with amplitude equal to 7/2 times the standard deviation of the velocity offsets for one ofthe exposures above. aud with a waveleneth of about one echelle order.," For the second, we modeled the velocity offsets as a sine function with amplitude equal to $\pi/2$ times the standard deviation of the velocity offsets for one of the exposures above, and with a wavelength of about one echelle order." For this case. we found the results did not depend strouglv ou the sine wavelength.," For this case, we found the results did not depend strongly on the sine wavelength." As seen in Table 3) the results for σί are quite simular for all three exposures and for the as)Gaussian and sine function models., As seen in Table \ref{tab:monteresults} the results for $\sigma(\delalpha)$ are quite similar for all three exposures and for the Gaussian and sine function models. Table 3. shows several interesting things., Table \ref{tab:monteresults} shows several interesting things. " First in all cases when μὴν=2. both the mean calibration offset aud staudard deviation iu aw are substantially larger than expected from a simple 1/4254, scaling."," First in all cases when $\Nmin=2$, both the mean calibration offset and standard deviation in $\delalpha$ are substantially larger than expected from a simple $1/\sqrt{\Ntran}$ scaling." We think this is due to occasional cases where there are very few trausitious found. but these Be close together uoc; ——2eq;A;.," We think this is due to occasional cases where there are very few transitions found, but these lie close together in $x_j= -2cq_j \lambda_j$." Since ds basically the slope in Equation 3)). a πα Ar offset eau result iu à very large slope aud therefore a large error in 22.," Since $\delalpha$ is basically the slope in Equation \ref{eqn:eqvj}) ), a small $\Delta x$ offset can result in a very large slope and therefore a large error in $\delalpha$." It takesdex just a few such cases to ereatlv increase the standard jation., It takes just a few such cases to greatly increase the standard deviation. A lesson here may be not to use svsteiis m which very few transitions cau be compared., A lesson here may be not to use systems in which very few transitions can be compared. For example. in the alkali doublet method (e.g.. Dalicall ct al.," For example, in the alkali doublet method (e.g., Bahcall et al." 1967. Varshalovicl et al.," 1967, Varshalovich et al." 2000. etc.)," 2000, etc.)" two transitions that are close together in waveleneth are compared. so this method would be sensitive to intra-order distortions.," two transitions that are close together in wavelength are compared, so this method would be sensitive to intra-order distortions." More generally. eveu for Minin=d and Mig=6. we find the errors droppiug more quickly with N than L1/y/N.," More generally, even for $\Nmin=4$ and $\Nmin=6$, we find the errors dropping more quickly with $N$ than $1/\sqrt{N}$." " Next. we note that the results for all three exposures and for the Gaussian and sine fiction error nodels aro quite consistent. especially when one takes iuto account that the standard deviation of velocity offsets for exposure Lois slightlv smaller than for the other exposures,"," Next, we note that the results for all three exposures and for the Gaussian and sine function error models are quite consistent, especially when one takes into account that the standard deviation of velocity offsets for exposure 1 is slightly smaller than for the other exposures." Also as expected. the lavee overall velocity shift for exposure 3 had no effect.," Also as expected, the large overall velocity shift for exposure 3 had no effect." If we restrict ourselves to the Min6G coluun. and consider Now=113. we see that the systematic error introduced to a many multiplet. measurement of ae is around 0.2810©. sieuificautly smaller than the statistical crror of 1.16«10.© stated in Murphy. et al. (," If we restrict ourselves to the $\Nmin=6$ column, and consider $\Nsys=143$, we see that the systematic error introduced to a many multiplet measurement of $\delalpha$ is around $0.28 \ten{-6}$, significantly smaller than the statistical error of $1.16 \ten{-6}$ stated in Murphy et al. (" 2003. 2001).,"2003, 2004)." We do note that Murphy et al. (, We do note that Murphy et al. ( 2003. 2001) used the Ieck IIIRES spectrograph and not the. VLT-UVES instruneut.,"2003, 2004) used the Keck HIRES spectrograph and not the VLT-UVES instrument." An important problem with the above results is that the value of ae and its standard deviation depends strouglv on Miran. the umuber of transitions compared in cach system. aud that no cases were found with Mean>9.," An important problem with the above results is that the value of $\delalpha$ and its standard deviation depends strongly on $\Ntran$, the number of transitions compared in each system, and that no cases were found with $\Ntran>9$." This latter fact is because the results above oulv included lines that overlapped with our iodine cell coverage., This latter fact is because the results above only included lines that overlapped with our iodine cell coverage. " Thus. Nira, found iu our Monte Carlo experinuents are artificially lower than in au actual experiauenut. which typically has more spectral coverage."," Thus, $\Ntran$ found in our Monte Carlo experiments are artificially lower than in an actual experiment, which typically has more spectral coverage." Since the value of σί drops quickly with au increase Miran We also expect au as)actual experiment to fud sinaller deviations than the ones we report.," Since the value of $\sigma(\delalpha)$ drops quickly with an increase $\Ntran$, we also expect an actual experiment to find smaller deviations than the ones we report." " We find this low value of N44, to be especially true for certain values of 2. where very few interesting lines fall within our iodine cell coverage."," We find this low value of $\Ntran$ to be especially true for certain values of $z$, where very few interesting lines fall within our iodine cell coverage." Our attempt to ect around this by setting a nuniunni number of transitions. AQ. Was partially successful. but Table 3. shows strong dependence ou Muine," Our attempt to get around this by setting a minimum number of transitions, $\Nmin$, was partially successful, but Table \ref{tab:monteresults} shows strong dependence on $\Nmin$." " Even more cleary. we see this in Table where he values of signa of24 depend on Miran substantially nore stronely than 1/4""Nuap"," Even more clearly, we see this in Table \ref{tab:ntran} where the values of sigma of $\delalpha$ depend on $\Ntran$ substantially more strongly than $1/\sqrt{\Ntran}$." " We wore that when Nu, is specified in thetable. exactly specifiedN44, transitions are compared. while when PN is all cases that wave Nonas2Ninin are used."," We note that when $\Ntran$ is specified in the table, exactly $\Ntran$ transitions are compared, while when $\Nmin$ is specified all cases that have $\Ntran\geq\Nmin$ are used." To remedy this situation. we need to somehow estimate he calibration offsets in regions of the spectra where we do not have iodine cell coverage.," To remedy this situation, we need to somehow estimate the calibration offsets in regions of the spectra where we do not have iodine cell coverage." We attempt to do lis by replicating the calibration offsets from the regious where we measure them to all the other spectral regious where interesting transitions occur: bo. we assume that he distributions of shifts illustrated iu Figures 1 and 2 apply to all wavelengths.," We attempt to do this by replicating the calibration offsets from the regions where we measure them to all the other spectral regions where interesting transitions occur; i.e., we assume that the distributions of shifts illustrated in Figures \ref{fig:vshiftallu} and \ref{fig:vshiftalll} apply to all wavelengths." We then repeat the Monte Carlo experiments above., We then repeat the Monte Carlo experiments above. Results of these simulatious are shown in Figure 5 ," Results of these simulations are shown in Figure \ref{fig:sigvsnmin} " So the ratio between the terminal velocities of the models with aud without the increased miass-loss rate 1s where we adopted a=0.60 (Pauldrach et al.,So the ratio between the terminal velocities of the models with and without the increased mass-loss rate is where we adopted $\alpha = 0.60$ (Pauldrach et al. 1986) for the last expression., 1986) for the last expression. We see that wwill⋅ decrease roughly as ALMI when the mass-loss rate increases., We see that will decrease roughly as $\Mdot^{-3/4}$ when the mass-loss rate increases. Tje result is shown iu the lower panel of Fie. 2, The result is shown in the lower panel of Fig. \ref{fig:models}. We realize that this nunerical test is ao drastic sinplificatio1 of the real situation: (a) we have asstuuect zu isothermal wind: (b) we have taken the lower boundary at a fixed clesity: (0) we have ignored possible changes iu the ionizatio1 of the wind due to changes in aid (dj we have ignored the role of the gas pressure aud of eravity in estimating the chanee in., We realize that this numerical test is a drastic simplification of the real situation: (a) we have assumed an isothermal wind; (b) we have taken the lower boundary at a fixed density; (c) we have ignored possible changes in the ionization of the wind due to changes in and (d) we have ignored the role of the gas pressure and of gravity in estimating the change in. . However. this siuple test serves the purpose of explaining that the mass-loss rate depends ou the radiative acceleration in tle subsonic part of the wind only. aud that an increase im the mass-loss rate due to au increase of gp iu the subsouic region will also be accompanied by a decrease icx," However, this simple test serves the purpose of explaining that the mass-loss rate depends on the radiative acceleration in the subsonic part of the wind only, and that an increase in the mass-loss rate due to an increase of $g_{\rm L}$ in the subsonic region will also be accompanied by a decrease in." In the rest of the paper. we will calculate radiative accelerations aud miass-loss rates with aancthod which will be described in Sect. 3..," In the rest of the paper, we will calculate radiative accelerations and mass-loss rates with a method which will be described in Sect. \ref{sec:method}." Thus. an in the radiative acceleration in the region of the wind results in an of aan adecrease dàiCa," Thus, an in the radiative acceleration in the region of the wind results in an of and a in." So. in order to uuderstaud the origin of the bistability jump of radiation driven winds. and to predict its effect ou aandex... we should pay close attention to the calculated radiative acceleration iu the part of the wind.," So, in order to understand the origin of the bi-stability jump of radiation driven winds, and to predict its effect on and, we should pay close attention to the calculated radiative acceleration in the part of the wind." " Tn order to uuderstand the nature of the bistability jump. we calculate a series of radiation driven wind models for «ipergiauts in the ranee of T;44, 12 500 to 10 000 k. Tre caleulatiou of the radiative acceleration of the winds requires the couputation of he coutributious of avery large nuuber of spectral lues."," In order to understand the nature of the bi-stability jump, we calculate a series of radiation driven wind models for supergiants in the range of = 12 500 to 40 000 K. The calculation of the radiative acceleration of the winds requires the computation of the contributions of a very large number of spectral lines." To this eud. we first calculate the thermal. clensity iud iouzation structure of a wind model computed with the non-LTE expanding atmosphere code (de Ioter et al.," To this end, we first calculate the thermal, density and ionization structure of a wind model computed with the non-LTE expanding atmosphere code (de Koter et al." 1993)(for cletails. see Sect. 1)).," 1993)(for details, see Sect. \ref{sec:isa}) )." We then calculate the radiative acceleration by following the fate of avery larec uuuber of photons that are recased from below the plotosphere iuto the wind. bv moais of a Monte Carlo echuique.," We then calculate the radiative acceleration by following the fate of a very large number of photons that are released from below the photosphere into the wind, by means of a Monte Carlo technique." Iu this section. we describe the basic plivsical properties of the adopted Monte Carlo (MC) technique which was first applied to the study of winds of early-type stars by Abbott Lucy (1985).," In this section, we describe the basic physical properties of the adopted Monte Carlo (MC) technique which was first applied to the study of winds of early-type stars by Abbott Lucy (1985)." Then. we describe the caleulation of the radiative acceleration by lines with t16 MC method. aud finally the method for caleulatiug theoretical niass-loss rates.," Then, we describe the calculation of the radiative acceleration by lines with the MC method, and finally the method for calculating theoretical mass-loss rates." The lunes iu the MC method are described iu the Sobolev approximation., The lines in the MC method are described in the Sobolev approximation. This approximation for the line acceleration is valid if the plysical conditious over a Sobolev leugth do not change siguificautly. ic. wherefois anv physically relevant variable for the line daiving. e.g. density. temperature or ionization fraction.," This approximation for the line acceleration is valid if the physical conditions over a Sobolev length do not change significantly, i.e. where is any physically relevant variable for the line driving, e.g. density, temperature or ionization fraction." ος να combination of thermal anc turbulent velocities., $v_{\rm t}$ is a combination of thermal and turbulent velocities. Eq., Eq. 11 shows that the validity range of the Sobolev approxination is n practice somewhat arbirary. since it depends ou the value of tje turbueut velocity which is »orlv known.," \ref{eq:sob} shows that the validity range of the Sobolev approximation is in practice somewhat arbitrary, since it depends on the value of the turbulent velocity which is poorly known." Nevertheless. tιο Sobolev approximation is often used (e.g. Abbott Lucy 1985) aud we will also adopt it in calculating he ine acceleration aud nass loss. mainly because of couputational limitations.," Nevertheless, the Sobolev approximation is often used (e.g. Abbott Lucy 1985) and we will also adopt it in calculating the line acceleration and mass loss, mainly because of computational limitations." We cannot exclude that due to the use of the Sobolev approximation we may predict cuantitativelv Inaccurate ine accelerations below the sonic poit., We cannot exclude that due to the use of the Sobolev approximation we may predict quantitatively inaccurate line accelerations below the sonic point. However.if au exact treatment would be followed. then this is expected o have a systematic effect on the line acceleration for models.," However, an exact treatment would be followed, then this is expected to have a systematic effect on the line acceleration for models." Therefore. we do not expect our conclusions reearding the origin of the bi-stabilitv Jump to be affected.," Therefore, we do not expect our conclusions regarding the origin of the bi-stability jump to be affected." The Sobolev approxiuation iuplies tha for scatterings iu the frame co-moving with the ious iu the wind (co-moving franc. CMF). he incident and emiereiue frequencies are both equal to he rest frequency of the line transition my iu the CAIF.," The Sobolev approximation implies that for scatterings in the frame co-moving with the ions in the wind (co-moving frame, CMF), the incident and emerging frequencies are both equal to the rest frequency of the line transition $\nu_{0}$ in the CMF." " where np and v4), are the incident and oenmiergiug frequencies in the CALF.", where $\nu_{\rm in}^{\prime}$ and $\nu_{\rm out}^{\prime}$ are the incident and emerging frequencies in the CMF. " In terms of quantities seen by an outside observer. these two CALF frequencies are eiveu by: and where My, aud Moy, are the incident and cuierecut frequencies for an outside observer: jg, and fone are the direction cosines with respect to the radial flow velocity of the xiotous at the scattering poiut aud e is the radial flow velocity of the scatering jon for au outside observer."," In terms of quantities seen by an outside observer, these two CMF frequencies are given by: and where $\nu_{\rm in}$ and $\nu_{\rm out}$ are the incident and emergent frequencies for an outside observer; $\mu_{\rm in}$ and $\mu_{\rm out}$ are the direction cosines with respect to the radial flow velocity of the photons at the scattering point and $v$ is the radial flow velocity of the scattering ion for an outside observer." Thermal imofious of the scattering 1ος are assunied to be negligible compared to the motion of the outward flow., Thermal motions of the scattering ions are assumed to be negligible compared to the motion of the outward flow. Note that we adopted the same velocity ο for the ion before and after the photon iueraction (Eqs., Note that we adopted the same velocity $v$ for the ion before and after the photon interaction (Eqs. 16 aud 17))., \ref{e_nuin} and \ref{e_nuout}) ). This is justified since the chauge in velocity due to the trauster of ποιοτα frou a photon to au jon is very small. ic. about 103 curs | per scattering. Therefore. the elige iu," This is justified since the change in velocity due to the transfer of momentum from a photon to an ion is very small, i.e. about $10^1$ cm $^{-1}$ per scattering.. Therefore, the change in" Many voung stars are sturounded by gasdust disks (Boclenheimer Lin 2002).,Many young stars are surrounded by gas–dust disks (Bodenheimer Lin 2002). Planetary formation is thought to start with inelastically collicing gaseous and clust particles se(tling to the central plane of a disk to form a thin aud relatively dense laver around the plane., Planetary formation is thought to start with inelastically colliding gaseous and dust particles settling to the central plane of a disk to form a thin and relatively dense layer around the plane. During the early evolution of this disk it is believed that the dust particles coagulate into kilometer-sized rocky asteroids~planetesimals” (~10! such bodies) owing to the gravitational instability (Goldreich Ward 1973) ancl/or to the collisional sticking (Beckwith et al.," During the early evolution of this disk it is believed that the dust particles coagulate into kilometer-sized rocky asteroids–“planetesimals"" $\sim 10^{10}$ such bodies) owing to the gravitational instability (Goldreich Ward 1973) and/or to the collisional sticking (Beckwith et al." 1990)., 1990). OF these processes. dust particle settling can now be observable.," Of these processes, dust particle settling can now be observable." We suggest thataff planets of the solar svstemi were created by disk instability., We suggest that planets of the solar system were created by disk instability. That is. as a result of local gravitational instability. on attaining a certain critical thickness (and density. respectively). small in comparison with the outer radius of the svslem A. the οποίαν gasdust disk disintegrated into a large number of separate protoplanets.," That is, as a result of local gravitational instability, on attaining a certain critical thickness (and density, respectively), small in comparison with the outer radius of the system $R$, the circumsolar gas–dust disk disintegrated into a large number of separate protoplanets." Following Boss (2003). this hypothesis envisions coagulation and settling of dust erains within the protoplanets to form rock and ice cores.," Following Boss (2003), this hypothesis envisions coagulation and settling of dust grains within the protoplanets to form rock and ice cores." A protoplanet accreted a, A protoplanet accreted a "may correspond to a ""saturation"" of the infilling evident in models 2 and 3 once the o field has become homogenised, in accordance with previous studies of LCSs in turbulent convection(?).","may correspond to a “saturation” of the infilling evident in models 2 and 3 once the $\sigma$ field has become homogenised, in accordance with previous studies of LCSs in turbulent convection." ". At this stage, magnetic field lines in the whole region will have become mixed/braided in a manner likely to promote reconnection and subsequently heating of the coronal plasma."," At this stage, magnetic field lines in the whole region will have become mixed/braided in a manner likely to promote reconnection and subsequently heating of the coronal plasma." " A saturation is also seen in the maximum value of C, and this occurs after a shorter time for higher flow speed."," A saturation is also seen in the maximum value of $\sigma$, and this occurs after a shorter time for higher flow speed." " This may be due to the LCS widths falling below the tracing grid scale, but it is unclear what other effects might cause such saturation; this bears further investigation."," This may be due to the LCS widths falling below the tracing grid scale, but it is unclear what other effects might cause such saturation; this bears further investigation." " Note that certain consequences of a faster plume velocity, namely (i) sharper LCS with higher peaks of c, and (ii) a faster rate of increase in flog;oQdxdy, would also result if one left the plume velocities unchanged but increased their coherence time."," Note that certain consequences of a faster plume velocity, namely (i) sharper LCS with higher peaks of $\sigma$, and (ii) a faster rate of increase in $\int\log_{10}Q\,dxdy$, would also result if one left the plume velocities unchanged but increased their coherence time." " This is demonstrated in Fig. 10,,"," This is demonstrated in Fig. \ref{fig:long}," " which shows model results after six hours with a single velocity pattern, rather than changing the pattern every 15 minutes."," which shows model results after six hours with a single velocity pattern, rather than changing the pattern every 15 minutes." The peak o (c.f., The peak $\sigma$ (c.f. Fig. 7)), Fig. \ref{fig:model}) ) and slope of the fΊοσιρQdxdy curve (not shown) become comparable to the run with (Vi)=0.3kmsl.," and slope of the $\int\log_{10}Q\,dxdy$ curve (not shown) become comparable to the run with $\langle V_i\rangle=0.3\,\textrm{km}\,\textrm{s}^{-1}$." " Yet there are fewer LCS, filling less of the area."," Yet there are fewer LCS, filling less of the area." " This illustrates how the pattern of σ depends on the time history of the flow, not just on its pattern at any given instant."," This illustrates how the pattern of $\sigma$ depends on the time history of the flow, not just on its pattern at any given instant." " For simplicity, the models here are limited to convective cells with a single spatial scale, flow speed and lifetime."," For simplicity, the models here are limited to convective cells with a single spatial scale, flow speed and lifetime." " On the real Sun, convection seems to operate simultaneously on a range of scales."," On the real Sun, convection seems to operate simultaneously on a range of scales." " Experiments with superimposing a ""supergranular"" flow in the model (cells 10 times larger, with slower speeds and longer lifetimes) indicate that the LCS pattern and increase of flogoQdxdy are determined primarily by the original, faster flow component."," Experiments with superimposing a “supergranular” flow in the model (cells 10 times larger, with slower speeds and longer lifetimes) indicate that the LCS pattern and increase of $\int\log_{10}Q\,dxdy$ are determined primarily by the original, faster flow component." The supergranular flow can generate localised magnetic gradients only over a longer timescale of many hours., The supergranular flow can generate localised magnetic gradients only over a longer timescale of many hours. We have proposed a practical method for inferring the topology of the 3D coronal magnetic field not by extrapolation (as is typically used) but rather by integrating trajectories of an observed sequence of horizontal flows in the photosphere., We have proposed a practical method for inferring the topology of the 3D coronal magnetic field not by extrapolation (as is typically used) but rather by integrating trajectories of an observed sequence of horizontal flows in the photosphere. " Assuming an ideal evolution in the corona, this enables us to infer the resulting magnetic field line mapping between photospheric footpoints, and therefore the squashing factor"," Assuming an ideal evolution in the corona, this enables us to infer the resulting magnetic field line mapping between photospheric footpoints, and therefore the squashing factor" For the case when ERC emission dominates. we have investigated the multilrequency light curves and determined Chat ERC fares at lower frequencies can incur an extra time delay due to the minimum Lorentz [actor eut-off in the injected distribution of electrons.,"For the case when ERC emission dominates, we have investigated the multifrequency light curves and determined that ERC flares at lower frequencies can incur an extra time delay due to the minimum Lorentz factor cut-off in the injected distribution of electrons." The simulations indicate that the spectral index of the ERC emission must be positive lor at least half of the duration of the flare for such a delay to occur. which distinguishes it [rom a time delay of the SSC emission. which is characterized bv a negative spectral index al all times.," The simulations indicate that the spectral index of the ERC emission must be positive for at least half of the duration of the flare for such a delay to occur, which distinguishes it from a time delay of the SSC emission, which is characterized by a negative spectral index at all times." We have also found that if the energy losses of electrons are dominated by ERC emission. the dependence of the observed flux (synchrotron. SSC. and ERC) on the bulk speed of the emitting plasma is different from that expected in homogeneous models.," We have also found that if the energy losses of electrons are dominated by ERC emission, the dependence of the observed flux (synchrotron, SSC, and ERC) on the bulk speed of the emitting plasma is different from that expected in homogeneous models." In particular. there is no double boosting of the ERC emission. while the SSC flix might even decrease at higher values of the bulk Lorentz factor of (he emitting plasma.," In particular, there is no double boosting of the ERC emission, while the SSC flux might even decrease at higher values of the bulk Lorentz factor of the emitting plasma." When the blazar is observed along the jet axis. flat tops are expected in lieht curves observed at [frequencies sufficiently above the break frequency.," When the blazar is observed along the jet axis, flat tops are expected in light curves observed at frequencies sufficiently above the break frequency." Lf the flares are symmetric. 1 is possible lor both SSC and ERC emission (o peak in the soft X-ray band. alter the maximum of the svnchrotron light curve.," If the flares are symmetric, it is possible for both SSC and ERC emission to peak in the soft X-ray band after the maximum of the synchrotron light curve." The value of the X-ray. spectral index during the flare distinguishes between (he SSC and ERC emission mechanism., The value of the X-ray spectral index during the flare distinguishes between the SSC and ERC emission mechanism. The latter is characterized bv more shallow or even positive spectral index., The latter is characterized by more shallow or even positive spectral index. The delaved ERC! emission indicates (hat (he minimum Lorentz lactor of the injected electrons is high enough so that the Irequency of observation is al or below the turn-over Irequencey of tbe ERC spectrum., The delayed ERC emission indicates that the minimum Lorentz factor of the injected electrons is high enough so that the frequency of observation is at or below the turn-over frequency of the ERC spectrum. Otherwise. ERC enussion should peak at the same time as the svnchrotron flare.," Otherwise, ERC emission should peak at the same time as the synchrotron flare." When superhuninal apparent motion is observed in VLBI images. (he viewing angle cannot be zero.," When superluminal apparent motion is observed in VLBI images, the viewing angle cannot be zero." " In this case the behavior of the light curves is different: it is closer to that found for &,,,=907.", In this case the behavior of the light curves is different; it is closer to that found for $\theta_{obs}=90^{\circ}$. " Svnchrotron flares that peak at LR or optical Ireeuencies precede the S5C and ERC flares in soft X-rays by Al~1/,,/2aec owing to lrequency stratification.", Synchrotron flares that peak at IR or optical frequencies precede the SSC and ERC flares in soft X-rays by $\Delta{t}\sim t_{ac}/2$ owing to frequency stratification. This material is based on work supported by NASA grants NAG5-13074 and NNGO4GOS5G. as well as National Science Foundation grant AST-0406865.," This material is based on work supported by NASA grants NAG5-13074 and NNG04GO85G, as well as National Science Foundation grant AST-0406865." We use the expansion times of the jets ancl tori as estimates for the time since they were ejected [rom the central star svstems.,We use the expansion times of the jets and tori as estimates for the time since they were ejected from the central star systems. The large masses and low expansion velocities of the dense molecular tori mean that (heir expansion times (/;) provide excellent estimates for (heir travel times., The large masses and low expansion velocities of the dense molecular tori mean that their expansion times $t_t$ ) provide excellent estimates for their travel times. For the jets. there is a good deal of observational evidence [rom detailed studies of individual objects for approximately Hubble-tvpe outflows Chat also suggest. constant velocity. ballistie motions (e.g..Aleoleaοἱal.2001:Corradi2004:Ueta2006).," For the jets, there is a good deal of observational evidence from detailed studies of individual objects for approximately Hubble-type outflows that also suggest constant velocity, ballistic motions \citep[e.g.,][]{alc01,cor04,uet06}." . We assume (hat this applies to the jet heads considered here., We assume that this applies to the jet heads considered here. We discuss this assumption further in 833.2., We discuss this assumption further in 3.2. Fie., Fig. l compares the expansion (mes of the jets with the expansion times of the tori., 1 compares the expansion times of the jets with the expansion times of the tori. The squares denote cases where (he torus is resolved. aud (he diamonds denote cases where it is not well resolved.," The squares denote cases where the torus is resolved, and the diamonds denote cases where it is not well resolved." The solid line shows the relation /;=/;., The solid line shows the relation $t_j = t_t$. One major uncertainty that affects the location of the data points in Fig., One major uncertainty that affects the location of the data points in Fig. lis caused bv uncertain distances to the nebulae., 1 is caused by uncertain distances to the nebulae. " Apart from the exceptions noted below. this affects both /; and /, in the same way: it moves the plotted points parallel to the line /;= in the ligure and does not appreciably affect our discussion."," Apart from the exceptions noted below, this affects both $t_j$ and $t_t$ in the same way: it moves the plotted points parallel to the line $t_j=t_t$ in the figure and does not appreciably affect our discussion." A second important effect. that affects the location of the data points in Fig., A second important effect that affects the location of the data points in Fig. 1 is uncertainty in (he inclination angles of the jets and tori., 1 is uncertainty in the inclination angles of the jets and tori. The adopted values and estimates of the uncertainties are given in the appendix., The adopted values and estimates of the uncertainties are given in the appendix. In most cases the values of /; and /; vary with inclination as sin# and cot9. respectively. and (he error bars shown in Fig.," In most cases the values of $t_t$ and $t_j$ vary with inclination as $\sin \theta$ and $\cot \theta$, respectively, and the error bars shown in Fig." 1 represent the uncertainty due to the inclination angle., 1 represent the uncertainty due to the inclination angle. For the three objects whose jet expansion (mes are determined [rom proper motions. /; is independent of the inclination and the distance. and the error bars in the figure reflect the formal errors from the proper motions.," For the three objects whose jet expansion times are determined from proper motions, $t_j$ is independent of the inclination and the distance, and the error bars in the figure reflect the formal errors from the proper motions." For these objects. the distance does contribute to the uncertaintv in ἐν. but in all cases il is well determined (to within ~z15.. see relerences in Table 1). and for simplicity this additional contribution is omitted in the figure.," For these objects, the distance does contribute to the uncertainty in $t_t$, but in all cases it is well determined (to within $\sim \pm15$, see references in Table 1), and for simplicity this additional contribution is omitted in the figure." A third effect. which is important for Ile 3-1475 ancl AGFL 618. arises because their equatorial regions are only mareinally resolved by the observations so the dimensions of the lori are not. well determined.," A third effect, which is important for He 3-1475 and AGFL 618, arises because their equatorial regions are only marginally resolved by the observations so the dimensions of the tori are not well determined." In both cases the values for the torus parameters are taken from models of the CO enission (see appendix)., In both cases the values for the torus parameters are taken from models of the CO emission (see appendix). The errors are difficult to quantify but are probably within a nominal overall [actor of two in /;. and these are shown as gray error bars in the figure.," The errors are difficult to quantify but are probably within a nominal overall factor of two in $t_t$, and these are shown as gray error bars in the figure." The expansion times of the jets and tori shown in Fig., The expansion times of the jets and tori shown in Fig. 1 span a laree range. [from," 1 span a large range, from" results shown in Table 4 of Ross et al. (,results shown in Table 4 of Ross et al. ( 2007) CAXOmega: ro=9.03£0.93 and 5=1.τὸ 0.05. 28LAO ry=1.4540.35 and 5=1.72X 0.06).,"2007) (AAOmega: $r_0=9.03\pm0.93$ and $\gamma=1.73\pm0.08$ , 2SLAQ: $r_0=7.45\pm0.35$ and $\gamma=1.72\pm0.06$ )." " We find. bj,440,=2.35x0.20 and Όροςτων=L9040.08."," We find, $b_{L(AA\Omega)}=2.35\pm0.20$ and $b_{L(2SLAQ)}=1.90\pm0.08$." The latter is in reasonable agreement with the value found by Ross ct al. (, The latter is in reasonable agreement with the value found by Ross et al. ( "2007). from redshift-space distortions. ενοςa,=1.66+0.35.","2007), from redshift-space distortions, $b_{L(2SLAQ)}=1.66\pm0.35$." The derived QSO bias values for cach case are shown in Table (as well as the corresponding : values) and in Figures and 23., The derived QSO bias values for each case are shown in Table \ref{table:biases_qso} (as well as the corresponding $\beta _Q$ values) and in Figures \ref{fig:biases_qso_1} and \ref{fig:biases_qso_2}. . Comparing the values for the QSO biases [rom the different samples. we note that the QSO biases using 25LAQ LRG samples show indications for luminosity. dependent QSO bias. in the sense that bo reduces for higher luminosity samples. at least in the case of spectroscopic 25LAQ LRGs.," Comparing the values for the QSO biases from the different samples, we note that the QSO biases using 2SLAQ LRG samples show indications for luminosity dependent QSO bias, in the sense that $b_Q$ reduces for higher luminosity samples, at least in the case of spectroscopic 2SLAQ LRGs." The same pattern is repeated when using AXOmesa LRG samples., The same pattern is repeated when using AAOmega LRG samples. The spectroscopic samples. vicld lower bo values than the photometric samples., The spectroscopic samples yield lower $b_Q$ values than the photometric samples. This is due to the fact that he amplitude of the £(r). measurements of the photometric samples is higher. than the amplitude of the wo) measurements of the spectroscopic samples (sce Lig. 10))., This is due to the fact that the amplitude of the $\xi (r)$ measurements of the photometric samples is higher than the amplitude of the $w_p(\sigma)$ measurements of the spectroscopic samples (see Fig. \ref{fig:projected1}) ). " Combining the 25LAQ (photometric and spectroscopic) samples with the photometric AAOniega samples we find 5,=1.900.10. bo=LS5+0.23 and bo=145cx0.11. for 25LAQ. 2QZ and SDSS QSOs. respectively."," Combining the 2SLAQ (photometric and spectroscopic) samples with the photometric AAOmega samples we find $b_Q=1.90\pm0.16$, $b_Q=1.85\pm0.23$ and $b_Q=1.45\pm0.11$, for 2SLAQ, 2QZ and SDSS QSOs, respectively." Comparing now the values for the QSO bias from the spectroscopic 25LAQ LAG samples with those obtained in Section 7.8. we note that the amplitude results. slve an average of bo=1.540.1 which is in very good agreement with the average of b=1.43:0.2 obtained from he redshift-space distortion results.," Comparing now the values for the QSO bias from the spectroscopic 2SLAQ LRG samples with those obtained in Section 7.3, we note that the amplitude results, give an average of $b_Q=1.5\pm0.1$ which is in very good agreement with the average of $b_Q=1.4\pm0.2$ obtained from the redshift-space distortion results." " Our measurements give an overall QSO bias of bo21.5 at z20.55 and My,z23.", Our measurements give an overall QSO bias of $b_Q\approx1.5$ at $z=0.55$ and $M_{b_J}\approx-23$. In Figures 22. and 23. we have also plotted two points (stars). that are at low redshifts. taken from Fig.," In Figures \ref{fig:biases_qso_1} and \ref{fig:biases_qso_2} we have also plotted two points (stars), that are at low redshifts, taken from Fig." 13 of da Angela et al. (, 13 of da $\hat{A}$ ngela et al. ( 2008).,2008). The one with ον=24.0 at zcKT is in statistical agreement with our bo values from the AAOmega LRG samples. at the same mean redshift and rightness.," The one with $M_{b_J}\simeq-24.0$ at $z\simeq0.7$ is in statistical agreement with our $b_Q$ values from the AAOmega LRG samples, at the same mean redshift and brightness." " Phe second one with Ade,&22.9 at ς50.6 is lower than our bo values from 25LAQ LAG samples. at >= 0.55. but statistically not rejected by them (at. least not bv those from the spectroscopic samples)."," The second one with $M_{b_J}\simeq-22.9$ at $z\simeq0.6$ is lower than our $b_Q$ values from 2SLAQ LRG samples, at $z=0.55$ , but statistically not rejected by them (at least not by those from the spectroscopic samples)." Phe overall inipression is that our biz1.5 at z=0.55 is in agreement with the values found. by da. ctagela et al. (, The overall impression is that our $b_Q\approx1.5$ at $z=0.55$ is in agreement with the values found by da $\hat{A}$ ngela et al. ( "2008). bo=1540.2 a2.=L4 and slightly higher than 5,=1.13:0.2 found at z=0.6.","2008), $b_Q=1.5\pm0.2$ at $z=1.4$ and slightly higher than $b_Q=1.1\pm0.2$ found at $z\simeq0.6$." Since the bias of Dark Matter Llalos is correlated to their mass (Mo White 1996). we shall attempt to measure this mass (para).," Since the bias of Dark Matter Halos is correlated to their mass (Mo White 1996), we shall attempt to measure this mass $M_{DMH}$ )." In our analysis we shall follow da -ingela et al., In our analysis we shall follow da $\hat{A}$ ngela et al. and. Croom et al., and Croom et al. ancl assume an ellipsoidal collapse moclel. described by Sheth et al. (," and assume an ellipsoidal collapse model, described by Sheth et al. (" 2001).,2001). The bias and the Alpara are related via where à=0.707. 6=0.5 and e=0.6.," The bias and the $M_{DMH}$ are related via where $\alpha=0.707$, $b=0.5$ and $c=0.6$." " & is delined as vos)folAlpvy.2). with 6, to be the critical density for collapse. given by. 5,=0.15(122)5]0,(2)OOS (Navarro- ct al."," $\nu$ is defined as $\nu=\delta _c(z)/\sigma(M_{DMH},z)$, with $\delta _c$ to be the critical density for collapse, given by, $\delta _c=0.15(12\pi)^{\frac{2}{3}}\Omega_m(z)^{0.0055}$ (Navarro et al." 1991). c(AMpuns.2)=TAlparaJs).," 1997). $\sigma(M_{DMH},z)=\sigma(M_{DMH})G(z)$," where e(AMpua) is the rms fluctuation of the density [field on the mass scale with value Mpg and G2) is the linear. growth [actor (Pechlos 1984)., where $\sigma(M_{DMH})$ is the rms fluctuation of the density field on the mass scale with value $M_{DMH}$ and $G(z)$ is the linear growth factor (Peebles 1984). " The etMparg) can then calculated as with P(k) to be the power spectrum. of density perturbations anc w(Ar) is the Fourier. transform. of a spherical top hat. which is given by (Peebles 1980): where the radius and mass are related through where py is the present mean density of the Universe. given by po=O7pi,2781010B2AL;Mpe7."," The $\sigma (M_{DMH})$ can then calculated as with P(k) to be the power spectrum of density perturbations and $w(kr)$ is the Fourier transform of a spherical top hat, which is given by (Peebles 1980): where the radius and mass are related through where $\rho _0$ is the present mean density of the Universe, given by $\rho _0=\Omega_m^0\rho_{crit}^0=2.78\times10^{11}\Omega _m^0h^2M_{\sun} Mpc^{-3}$." " The power spectrum. used. in our analvsis has the linear. form. PU)2DUGOKk"". with £5 to bea normalisation parameter which depends on ax and T(k) is the transfer function (Barcleen ct al."," The power spectrum used in our analysis has the linear form, $P(k)=P_0T(k)^2k^n$, with $P_0$ to be a normalisation parameter which depends on $\sigma_8$ and T(k) is the transfer function (Bardeen et al." 1986)., 1986). The results are shown in Figures 24. and 25., The results are shown in Figures \ref{fig:halo_qso_1} and \ref{fig:halo_qso_2}. . Once again. although for the ANOmeea LRG samples the derived OQSO halo masses show indications of increasing as we move to fainter QSO samples. in the case of 28LAC) (photometric and spectroscopic) LRG samples halo masses stay statistically constant.," Once again, although for the AAOmega LRG samples the derived QSO halo masses show indications of increasing as we move to fainter QSO samples, in the case of 2SLAQ (photometric and spectroscopic) LRG samples halo masses stay statistically constant." The average value is Albay= 134.., The average value is $M_{DMH}=10^{13}h^{-1}M_{\sun}$ . Comparing now this result. with those from other authors (Croom et al., Comparing now this result with those from other authors (Croom et al. 2005. cla Angela et al.," 2005, da $\hat{A}$ ngela et al." 2008). we note that their ο estimates are generally lower than ours (~3.10775.TALS ) although at higher redshifts (2= L4).," 2008), we note that their $M_{DMH}$ estimates are generally lower than ours $\sim3\times10^{12}h^{-1}M_{\sun}$ ) although at higher redshifts $z=1.4$ )." They also find that the hosts of QSOs have the same mass at all redshifts. thus rejecting cosmologically long-lived QSO models.," They also find that the hosts of QSOs have the same mass at all redshifts, thus rejecting cosmologically long-lived QSO models." Our higher masses at 2=0.55 may be more consistent with the long-lived predictions of 6.LohΑς ats—0 and 10%Τίς at zc0.5., Our higher masses at $z=0.55$ may be more consistent with the long-lived predictions of $6\times10^{14}h^{-1}M_{\sun}$ at $z=0$ and $10^{13}h^{-1}M_{\sun}$ at $z\simeq0.5$. Lhe caveat is that for our measurements we need to use a value for by in order to derive be., The caveat is that for our measurements we need to use a value for $b_L$ in order to derive $b_Q$. In this paper we have performed an analysis of the clustering of QSOs with LRGs., In this paper we have performed an analysis of the clustering of QSOs with LRGs. For this purpose. we first. used the 2-point angular cross-correlation function. (A). and measured the cross-correlation between 25LAQ and AANOmega LRGs ancl cifferent luminosity QSOs.," For this purpose, we first used the 2-point angular cross-correlation function, $w(\theta)$, and measured the cross-correlation between 2SLAQ and AAOmega LRGs and different luminosity QSOs." Phe results show that there is little cross-correlation dependence on QSO Luminosity., The results show that there is little cross-correlation dependence on QSO luminosity. - Next. we measured the redshift-space cross-correlation function.," Next, we measured the redshift-space cross-correlation function." We again see no QSO-LRG clusteringdependence on QSO luminosity. as all the QSO-spectroscopie LRG samples gave similar results.," We again see no QSO-LRG clusteringdependence on QSO luminosity, as all the QSO-spectroscopic LRG samples gave similar results." We used. Limber's formula to fit ry to 2-D results., We used Limber's formula to fit $r_0$ to 2-D results. The fits for ry [rom3-D £(s) are in very good agreement with the fits to the 2-D w(8) results., The fits for $r_0$ from3-D $\xi (s)$ are in very good agreement with the fits to the 2-D $w(\theta)$ results. Then. we compared our QSO-LItG. clustering with 28LAC LRO-LRG (Ross et al.," Then, we compared our QSO-LRG clustering with 2SLAQ LRG-LRG (Ross et al." 2007) and 2QZ|25LAQQSO-LBCG (cla Angela et al., 2007) and 2QZ+2SLAQQSO-LRG (da $\hat{A}$ ngela et al. 2008) clustering results., 2008) clustering results. On small scales. the QSO-QSO and QSO-LAG results appear Latter than the LRO-LAG results.," On small scales, the QSO-QSO and QSO-LRG results appear flatter than the LRG-LRG results." " As confirmed later by the w,(a)/o ", As confirmed later by the $w_p(\sigma )/\sigma$ "For photons of frequencyw’ emitted at μ΄=0. re.. normal to & in this frame. one finds (Schwingeretal.1998) ο) |- where K, is a modified Bessel function of the second kind.","For photons of frequency$\omega'$ emitted at $\mu'=0$, i.e., normal to $\hat{\bm{x}}$ in this frame, one finds \citep{schwinger98} ) ]^2, where $K_1$ is a modified Bessel function of the second kind." This approximate solution involves extending the limits of the integration over the trajectory to 7=ze. and Is accurate provided the endpoints in the new (primed) frame of reference are far from the point at which the particle ts at rest O«roτι.," This approximate solution involves extending the limits of the integration over the trajectory to $\tau=\pm\infty$, and is accurate provided the endpoints in the new (primed) frame of reference are far from the point at which the particle is at rest: $0\ll\tau_0\ll\tau_L$." Returning to the frame in which the stellar surface is at rest. (50)) describes the radiation emitted at uj=BXy?-I/y.," Returning to the frame in which the stellar surface is at rest, \ref{mcdonald}) ) describes the radiation emitted at $\mu = \beta=\sqrt{\gamma^2-1}/\gamma$." " Therefore. exploiting the transformations w’=Dw. dU’=Od. dQ=1077dO"" where D=yl-uf)=XI—4€ is the Doppler factor. = jode(518) whence fraeac)]-(53) where #=cos”!yt."," Therefore, exploiting the transformations $\omega'=\Doppler\omega$, $\diff U'=\Doppler\diff U$, $\diff\Omega=\Doppler^{-2}\diff\Omega'$ where $\Doppler=\gamma(1-\mu\beta) =\sqrt{1-\mu^2}$ is the Doppler factor, = ^2, whence ) ]^2 where $\theta=\cos^{-1}\mu$." The result ean be checked by integrating over all frequencies. using the identity CAT to find in agreement with the expression given by Schwingeretal. (1998).," The result can be checked by integrating over all frequencies, using the identity x^2 to find, in agreement with the expression given by \citet{schwinger98}." . For small argument. Κιν)=1/x. so that the low frequency spectrum ts flat: d," For small argument, $K_1(x)\approx1/x$, so that the low frequency spectrum is flat: ." "odo-NET Using the asymptotic form of K, for large argument. one finds the high frequency spectrum: which has a cut-off at the frequency."," Using the asymptotic form of $K_1$ for large argument, one finds the high frequency spectrum:, which has a cut-off at the frequency." .(60) As expected.xyVine for relativistic particles. most of the energy 1s radiated close to the forward direction.," As expected, for relativistic particles, most of the energy is radiated close to the forward direction." The method applies only to radiation inside a small forwardly directed cone of opening angle 41-072«1. because otherwise xo is too close to the stellar surface.," The method applies only to radiation inside a small forwardly directed cone of opening angle $\sqrt{1-\mu^2}\ll1$, because otherwise $x_0$ is too close to the stellar surface." However. the region outside of this cone is not expected to contain significant power.," However, the region outside of this cone is not expected to contain significant power." The approximation also fails within a very small. forwardly directed cone. because the appropriate value of ro approaches or exceeds τι.," The approximation also fails within a very small, forwardly directed cone, because the appropriate value of $\tau_0$ approaches or exceeds $\tau_L$." This is potentially a more serious shortcoming. since it prevents one computing the emissivity on the beaming cone of a particle when it reaches its maximum Lorentz factor Vina=(Le)/a? at the pair production front.," This is potentially a more serious shortcoming, since it prevents one computing the emissivity on the beaming cone of a particle when it reaches its maximum Lorentz factor $\gamma_{\rm max}=\left(L+\accel\right)/\accel$ at the pair production front." " In fact. an explicit expression for the emission at ji=ο be written down by evaluating the integral over the orbit between the limits τς—co and r=7: fracaLe). )- Le) where /, 1s the modified Bessel function of the first kind and L, is the modified Struve function (Abramowitz&Stegun 1972)."," In fact, an explicit expression for the emission at $\mu=\sqrt{\gamma_{\rm max}^2-1}/\gamma_{\rm max}$ can be written down by evaluating the integral over the orbit between the limits $\tau=-\infty$ and $\tau=\tau_L$: ) )- ) where $I_1$ is the modified Bessel function of the first kind and $L_{1}$ is the modified Struve function \citep{AbramowitzStegun}." . The spectrum at different angles. using this formula and equation (52)) is shown in figure 1..," The spectrum at different angles, using this formula and equation \ref{HyperAllmu}) ) is shown in figure \ref{spectrumK}." At high frequencies ω>Leja7 one finds from (619) the asymptotic expression(60) In contrast with the emission at larger angle. this spectrum does not exhibit an exponential cut-off. but is a power law xw7.," At high frequencies $\omega\gg Lc/\accel^2$ one finds from \ref{Struve}) ) the asymptotic expression, In contrast with the emission at larger angle, this spectrum does not exhibit an exponential cut-off, but is a power law $\propto\omega^{-2}$." This behavior is clearly related to the discontinuity in the electric field at x=L., This behavior is clearly related to the discontinuity in the electric field at $x=L$. In reality. the pair production front is not a sharp boundary. but rather a region of finite width over which the field drops continuously to zero.," In reality, the pair production front is not a sharp boundary, but rather a region of finite width over which the field drops continuously to zero." The width of this region is determined by the distance over which the electric field can induce a substantial charge separation in the newly created pairs., The width of this region is determined by the distance over which the electric field can induce a substantial charge separation in the newly created pairs. " Assuming these are born with Lorentz factor yy,=p/L. where p is the radius of curvature of the trajectory imposed by the strong magnetic field (see section 5)). the width of the front can be estimated to be roughly Av=γιάαρ.>> a’."," Assuming these are born with Lorentz factor $\gamma_{\rm pair}\approx \rho/L$, where $\rho$ is the radius of curvature of the trajectory imposed by the strong magnetic field (see section \ref{pulsars}) ), the width of the front can be estimated to be roughly $\Delta x\approx\gamma_{\rm pair}\accel\approx\accel\rho/L\gg\accel$ ." Thus. the emission produced at small beaming angles @~a’/L is unlikely to differ qualitatively from emission at larger ones. and the entire pattern can be approximated as a hollow cone. with a cut-off frequency that increases towards the inner edge," Thus, the emission produced at small beaming angles $\theta\sim\accel/L$ is unlikely to differ qualitatively from emission at larger ones, and the entire pattern can be approximated as a hollow cone, with a cut-off frequency that increases towards the inner edge" Thus. the emission produced at small beaming angles @~a’/L is unlikely to differ qualitatively from emission at larger ones. and the entire pattern can be approximated as a hollow cone. with a cut-off frequency that increases towards the inner edge ," Thus, the emission produced at small beaming angles $\theta\sim\accel/L$ is unlikely to differ qualitatively from emission at larger ones, and the entire pattern can be approximated as a hollow cone, with a cut-off frequency that increases towards the inner edge" Thus. the emission produced at small beaming angles @~a’/L is unlikely to differ qualitatively from emission at larger ones. and the entire pattern can be approximated as a hollow cone. with a cut-off frequency that increases towards the inner edge d," Thus, the emission produced at small beaming angles $\theta\sim\accel/L$ is unlikely to differ qualitatively from emission at larger ones, and the entire pattern can be approximated as a hollow cone, with a cut-off frequency that increases towards the inner edge" Thus. the emission produced at small beaming angles @~a’/L is unlikely to differ qualitatively from emission at larger ones. and the entire pattern can be approximated as a hollow cone. with a cut-off frequency that increases towards the inner edge do," Thus, the emission produced at small beaming angles $\theta\sim\accel/L$ is unlikely to differ qualitatively from emission at larger ones, and the entire pattern can be approximated as a hollow cone, with a cut-off frequency that increases towards the inner edge" Thus. the emission produced at small beaming angles @~a’/L is unlikely to differ qualitatively from emission at larger ones. and the entire pattern can be approximated as a hollow cone. with a cut-off frequency that increases towards the inner edge dod," Thus, the emission produced at small beaming angles $\theta\sim\accel/L$ is unlikely to differ qualitatively from emission at larger ones, and the entire pattern can be approximated as a hollow cone, with a cut-off frequency that increases towards the inner edge" Thus. the emission produced at small beaming angles @~a’/L is unlikely to differ qualitatively from emission at larger ones. and the entire pattern can be approximated as a hollow cone. with a cut-off frequency that increases towards the inner edge dodo," Thus, the emission produced at small beaming angles $\theta\sim\accel/L$ is unlikely to differ qualitatively from emission at larger ones, and the entire pattern can be approximated as a hollow cone, with a cut-off frequency that increases towards the inner edge" Thus. the emission produced at small beaming angles @~a’/L is unlikely to differ qualitatively from emission at larger ones. and the entire pattern can be approximated as a hollow cone. with a cut-off frequency that increases towards the inner edge dodo-," Thus, the emission produced at small beaming angles $\theta\sim\accel/L$ is unlikely to differ qualitatively from emission at larger ones, and the entire pattern can be approximated as a hollow cone, with a cut-off frequency that increases towards the inner edge" "For an observation of length 7,4, witha GW detector. the contribution from background sources binaries in this work) depends on the number of sources within the frequency resolution. Af=L1/T4,.","For an observation of length $T_{\rm obs}$ with a GW detector, the contribution from background sources binaries in this work) depends on the number of sources within the frequency resolution, $\Delta f = 1/T_{\rm obs}$ ." Following Schneideretal.(2001).. we define an elfective GW amplitude hf)=felDONDE> where Auf) is a characteristic strain amplitude.," Following \citet{s01}, we define an effective GW amplitude $h_{\rm rms}(f) \equiv h_{\rm c}(f) {({\Delta f}/ f)}^{1/2}$, where $h_{\rm c}(f)$ is a characteristic strain amplitude." showed a simple analvtic formula (ο calculate h.(f) lor a population of inspiraling cireular-orbil binaries with a given number density in (he nearby Universe., showed a simple analytic formula to calculate $h_{\rm c}(f)$ for a population of inspiraling circular-orbit binaries with a given number density in the nearby Universe. " We use ((16) in his paper to calculate Pf).. and find where is the ""chirp mass” of a binary defined by and ἂν is the comoving number density ofNS-WD.. ie. (he number of sources per Mpec?. We calculate the GW amplitude of binaries in a frequency range fuae "," We use (16) in his paper to calculate $h_{\rm c}(f)$, and find where is the “chirp mass” of a binary defined by and $N_{\rm o}$ is the comoving number density of, i.e. the number of sources per $^{3}$ We calculate the GW amplitude of binaries in a frequency range $f_{\rm min} < f < f_{\rm max}$ ." Estimated GW frequencies of three binaries based on their current separations are all less than 0.1 mllz., Estimated GW frequencies of three binaries based on their current separations are all less than $\sim 0.1$ mHz. In our calculation. however. we set (he minimum frequency finn (o be 1 mllz taking into account (he fact that the confusion. noise level is mainly dominated by Galactic WD binaries at lower lrequency range /STZ and Suv> St], and 2: [Sir SUV]."," Using this method, both samples can be considered together: the combined sample is split into two `domains', defined by $1: [S_{IR} > S^{lim}_{IR}$ and $S_{UV} > S^{lim}_{UV}$ ], and 2: $S_{IR} < S^{lim}_{IR}$ and $S_{UV} > S^{lim}_{UV}$ ]." " Any duplicates must be dealt with, as each galaxy is clearly just a single probe of the population."," Any duplicates must be dealt with, as each galaxy is clearly just a single probe of the population." " The duplicate is removed, and the remaining galaxy is assigned whichever value of Vmax (i.e. based on either the IR or UV limit) is - this is because for the object to be included, it is sufficient that it satisfies the weaker selection criteria."," The duplicate is removed, and the remaining galaxy is assigned whichever value of $_{\mathrm{max}}$ (i.e. based on either the IR or UV limit) is - this is because for the object to be included, it is sufficient that it satisfies the weaker selection criteria." Objects in the first domain then have Vmax values calculated as normal., Objects in the first domain then have $_{\mathrm{max}}$ values calculated as normal. " Objects in the second domain, being constrained by having an IR flux below the limit of the IR-selected sample (and thus only appearing in the UV selected sample), have a reduced region of parameter space to exist in, and have their values of Vmax defined by (Vmax,rg - Vmax,uv)-"," Objects in the second domain, being constrained by having an IR flux below the limit of the IR-selected sample (and thus only appearing in the UV selected sample), have a reduced region of parameter space to exist in, and have their values of $_{\mathrm{max}}$ defined by $_{\mathrm{max, IR}}$ - $_{\mathrm{max, UV}}$ )." " We cannot apply the same technique to combine with the Local Volume data, as the LVL sample is designed to be volume limited and therefore has a less cleanly-defined selection function; where the samples overlap with LVL, we simply weight the two datasets inversely by their bootstrap-derived errors."," We cannot apply the same technique to combine with the Local Volume data, as the LVL sample is designed to be volume limited and therefore has a less cleanly-defined selection function; where the samples overlap with LVL, we simply weight the two datasets inversely by their bootstrap-derived errors." " The final, combined sample consists of 10,704 galaxies (257 from the LVL, 562 from the UV, and 10,141 from the IR, where duplicate galaxies have been removed as explained above)."," The final, combined sample consists of 10,704 galaxies (257 from the LVL, 562 from the UV, and 10,141 from the IR, where duplicate galaxies have been removed as explained above)." 'The star formation rate function is shown in 4.., The star formation rate function is shown in \ref{fig:sfr_tot}. The purple data points are Vmax-derived points for the combined sample as described above., The purple data points are $_{\mathrm{max}}$ -derived points for the combined sample as described above. " We use least squares fitting to fit a standard Schechter function to the points: the best fitting parameters are found to be (®*=0.00015+0.0003Mpc?,*=9.00.3Mcyr!,a —1.48+40.07)."," We use least squares fitting to fit a standard Schechter function to the points: the best fitting parameters are found to be $\Phi^* = 0.00015\pm0.0003\; \mathrm{Mpc}^{-3},\; \psi^*=9.0\pm0.3\;\mathrm{M}_{\sun} \; \mathrm{yr}^{-1}, \;\alpha=-1.48\pm0.07$ )." This Schechter function is shown in Fig., This Schechter function is shown in Fig. 4 as a black line., \ref{fig:sfr_tot} as a black line. " We also used the maximum likelihood method described above to find the best-fitting Schechter function to the combined sample; the best fitting parameters (are found to be (Φ""=0.00016+0.0004Mpc?,ϕ""92-c0.3Meyr,a=—1.51+0.08), and this is plotted on Fig."," We also used the maximum likelihood method described above to find the best-fitting Schechter function to the combined sample; the best fitting parameters (are found to be $\Phi^* = 0.00016\pm0.0004\; \mathrm{Mpc}^{-3},\; \psi^*=9.2\pm0.3\;\mathrm{M}_{\sun} \; \mathrm{yr}^{-1}, \;\alpha=-1.51\pm0.08$ ), and this is plotted on Fig." 4 as a blue line., \ref{fig:sfr_tot} as a blue line. " The two methods of calculating the star formation rate function match closely, suggesting that the Vmax points are not overly biased by the presence of clustering."," The two methods of calculating the star formation rate function match closely, suggesting that the $_{\mathrm{max}}$ points are not overly biased by the presence of clustering." " Hereafter, we adopt the parameters of the maximum likelihood-derived function."," Hereafter, we adopt the parameters of the maximum likelihood-derived function." " 'The faint end slope of -1.51 continues monotonically almost to the limits of the data, until the low galaxy numbers available at SFRs «107?Moyr! lead to the degradation of the relation due to noise."," The faint end slope of -1.51 continues monotonically almost to the limits of the data, until the low galaxy numbers available at SFRs $<10^{-3}\; \mathrm{M}_{\sun} \; \mathrm{yr}^{-1}$ lead to the degradation of the relation due to noise." " This is in contrast to previous extrapolations (e.g. ?)) which predicted a lognormal form for the star formation rate distribution function, with a maximum value of Φ(4) at $~107Mgyr and a gradual decline thereafter."," This is in contrast to previous extrapolations (e.g. \citealt{2005ApJ...619L..59M}) ) which predicted a lognormal form for the star formation rate distribution function, with a maximum value of $\Phi(\psi)$ at $\psi \sim 10^{-2} \;\mathrm{M}_{\sun} \; \mathrm{yr}^{-1}$ and a gradual decline thereafter." This result is particularly interesting in the light of theoretical predictions of structure formation., This result is particularly interesting in the light of theoretical predictions of structure formation. " There has been a long-running conflict between the small-scale predictions for Dark Matter haloes, and the observational results of the galaxies that dwell inside them (?).."," There has been a long-running conflict between the small-scale predictions for Dark Matter haloes, and the observational results of the galaxies that dwell inside them \citep{1999ApJ...522...82K}." " Galaxy formation models predict a scale-invariant form for Dark Matter, which clusters hierarchically even on the smallest scales; this manifests as a steep faint end slope to the mass function, of a~—1.8."," Galaxy formation models predict a scale-invariant form for Dark Matter, which clusters hierarchically even on the smallest scales; this manifests as a steep faint end slope to the mass function, of $\alpha \sim -1.8$." " Observations of galaxy luminosity functions, however, have found a dearth of small scale objects at the bottom of the luminosity function, indicating a much shallower faint end slope."," Observations of galaxy luminosity functions, however, have found a dearth of small scale objects at the bottom of the luminosity function, indicating a much shallower faint end slope." " Either the predictions for the Dark Matter mass function are incorrect, or the complex non-linear processes involved in galaxy formation conspire to suppress the formation of baryonic structures on the smallest scales."," Either the predictions for the Dark Matter mass function are incorrect, or the complex non-linear processes involved in galaxy formation conspire to suppress the formation of baryonic structures on the smallest scales." " One suggestion has been that the lack of satellite-scale galaxies results from star formation being systematically suppressed on the smallest scales (ie. ?;; ?)); the form of our SFR distribution function, however, is consistent with the idea that this is not the case: a monotonically increasing faint-end slope to the SFR distribution function suggests that any process suppressing star formation must be operating in a scale-free manner with respect to halo mass."," One suggestion has been that the lack of satellite-scale galaxies results from star formation being systematically suppressed on the smallest scales (i.e. \citealt{2000ApJ...539..517B}; \citealt{2005ApJ...632..872R}) ); the form of our SFR distribution function, however, is consistent with the idea that this is not the case: a monotonically increasing faint-end slope to the SFR distribution function suggests that any process suppressing star formation must be operating in a scale-free manner with respect to halo mass." " Using the distribution of star formation rate, it is possible to calculate the distribution of star formation ratedensity."," Using the distribution of star formation rate, it is possible to calculate the distribution of star formation rate." . We define the distribution function of star formation rate density: Fig., We define the distribution function of star formation rate density: Fig. " 5 shows the distribution of star formation rate volume density, for the ‘combined’ sample shown in Fig. 4,,"," \ref{fig:sfr_den} shows the distribution of star formation rate volume density, for the `combined' sample shown in Fig. \ref{fig:sfr_tot}," along with the convolved Schechter fit for the parameters given above., along with the convolved Schechter fit for the parameters given above. " We can therefore integrate Φ(Ψ) to give the total star formation rate volume density in the local Universe, which for the parameters of the Schechter fit to our"," We can therefore integrate $\psi \,\Phi(\psi) $ to give the total star formation rate volume density in the local Universe, which for the parameters of the Schechter fit to our" components of the TD model are: a power law with an exponential eut-olf fixed αἱ 200 keV (Gilli et al.,components of the TD model are: a power law with an exponential cut-off fixed at 200 keV (Gilli et al. 2007) lor the primary spectrum plus intrinsic absorption. a reflection component from neutral eas(pexrav: Maegdziarz Zelziarski 1995) and iron Ix emission (both Ίνα and Ix. whenever required by (he spectral fits).," 2007) for the primary spectrum plus intrinsic absorption, a reflection component from neutral gas; Magdziarz Zdziarski 1995) and iron K emission (both $\alpha$ and $\beta$, whenever required by the spectral fits)." The photon index of the reflection component is linked to that of the primary continuum aid no absorption on the rellected spectrum is considered., The photon index of the reflection component is linked to that of the primary continuum and no absorption on the reflected spectrum is considered. The RD model includes the same spectral components except for the absorbed primary power law., The RD model includes the same spectral components except for the absorbed primary power law. The photon index of the RD model is left free to vary., The photon index of the RD model is left free to vary. The intensity of the reflection component /2 in TD model is delined as the ratio between the normalization of the reflected and primary (e. power law) spectrum., The intensity of the reflection component $R$ in TD model is defined as the ratio between the normalization of the reflected and primary (i.e. power law) spectrum. The inclination angle of the reflection component is fixed to cos/=0.9. which is equivalent to assume a rather laceon geometry for the reflecting material. likely to be associated with the inner walls of the obscuring torus.," The inclination angle of the reflection component is fixed to $cosi$ =0.9, which is equivalent to assume a rather face–on geometry for the reflecting material, likely to be associated with the inner walls of the obscuring torus." soft Xrav emission in excess of the extrapolation of the absorbed nuclear continuum al low energv is observed in all the sources of our sample., Soft X–ray emission in excess of the extrapolation of the absorbed nuclear continuum at low energy is observed in all the sources of our sample. This emission may be due to hot eas associated (o the host galaxy ancl is modeled with an updated: version of the original Havmond Smith (1977) code for thermal plasmas in Xspec). and to AGN primary continuum scattered on the lime of sight or leaking through the nuclear absorber. represented bv a partial covering XSPEC). in the TD model. and with a power law in (he RD model.," This emission may be due to hot gas associated to the host galaxy and is modeled with an updated version of the original Raymond Smith (1977) code for thermal plasmas in ), and to AGN primary continuum scattered on the line of sight or leaking through the nuclear absorber, represented by a partial covering ), in the TD model, and with a power law in the RD model." In both models the power law slope is assumed to be the same of the intrinsic hard X.rav continuum. with the exception of one object (see § 4.4).," In both models the power law slope is assumed to be the same of the intrinsic hard X–ray continuum, with the exception of one object (see $\S$ 4.4)." The scattering Iraction f can be defined only for the TD model. because the level of the intrinsic continuum in RD lits is unknown.," The scattering fraction $f$ can be defined only for the TD model, because the level of the intrinsic continuum in RD fits is unknown." In order to compare (he intensity of the soft Xrav power law in TD and RD models. we report the monochoromatic flux densities al 1 keV in Table 2.," In order to compare the intensity of the soft X–ray power law in TD and RD models, we report the monochoromatic flux densities at 1 keV in Table 2." We have also considered an alternative possibility lor the origin of soft X.ταν emission in obseured AGN in terms of emission [rom a photoionized plasma modeled in as lor TD sources and as for RD AGN (Table 3)., We have also considered an alternative possibility for the origin of soft X–ray emission in obscured AGN in terms of emission from a photoionized plasma modeled in as for TD sources and as for RD AGN (Table 3). Nis the number of fitted lines in the soft XN.ταν band which varies form source to source (Table 4)., $N$ is the number of fitted lines in the soft X–ray band which varies form source to source (Table 4). The additional component accounts for Ίνα and Wo lines., The additional component accounts for $\alpha$ and $\beta$ lines. Given that the energy resolution is not appropriate to fit à photoionization code model (Dxwasawa et al., Given that the energy resolution is not appropriate to fit a photoionization code model (Iwasawa et al. 2003). the expected soft Xrav specirum of a photoionized plasma is modeled with a power law with photon index [ree to vary (Table 3).M plus intrinsically narrow (setting σ-θ in the model) Gaussian lines al the energv expected (Table 4) for the strongest leatures observed in hieh resolution spectra of obscured. AGN (see Guainazzi Bianchi 2007).," 2003), the expected soft X–ray spectrum of a photoionized plasma is modeled with a power law with photon index free to vary (Table 3), plus intrinsically narrow (setting $\sigma$ =0 in the model) Gaussian lines at the energy expected (Table 4) for the strongest features observed in high resolution spectra of obscured AGN (see Guainazzi Bianchi 2007)." The presence of (he line is evaluated on the basis of a visual inspection of the residuals obtained by fitting a single power law., The presence of the line is evaluated on the basis of a visual inspection of the residuals obtained by fitting a single power law. The best fit energies. fInxes and associated La errors of the various lines for each source arereported in Table 4.," The best fit energies, fluxes and associated $\sigma$ errors of the various lines for each source arereported in Table 4." 50.512.9.2. since it is identical to simulation 50.512.9.,"$50\_512\_9\_2$, since it is identical to simulation $50\_512\_9$." As in the results of Pawliketal. (2009). we [ind that photoheating from the ionizing background results in a decrease in the chunping factor.," As in the results of Pawlik (2009), we find that photoheating from the ionizing background results in a decrease in the clumping factor." The clumping [actors fall alone (wo tracks: a higher track at recdshilts above the turn-on of the UV background. and a lower one after turn-on.," The clumping factors fall along two tracks: a higher track at redshifts above the turn-on of the UV background, and a lower one after turn-on." By 2=5. we find nearly identical clumping factors for both backerounds.," By $z = 5$, we find nearly identical clumping factors for both backgrounds." After a substantial recovery time. the redshift when the background is turned on is not important.," After a substantial recovery time, the redshift when the background is turned on is not important." Before this recovery. the clumpineg [actor of the earlier background is lower by a [actor of ~2. resulüng in earlier relonizalion.," Before this recovery, the clumping factor of the earlier background is lower by a factor of $\sim$ 2, resulting in earlier reionization." " One can compare the strengths of feedback to reionization. where ""positive feedback lowers the ehunping factor and “negative feedback suppresses star formation."," One can compare the strengths of feedback to reionization, where “positive feedback"" lowers the clumping factor and “negative feedback"" suppresses star formation." At z=5 the total stellar mass (SFR. densitv) of simulation 50.512.7 is 1.19 (1.13) times lower Chan that of simulation 50.512.0. while the clumping factor is 1.64 limes lower.," At $z=5$ the total stellar mass (SFR density) of simulation $50\_512\_7$ is 1.19 (1.13) times lower than that of simulation $50\_512\_0$, while the clumping factor is 1.64 times lower." For simulation 50.512.9. the total stellar mass (SER density) and clamping factor are 1.52 (1.49) and 1.66. respectively. times lower (han those of simulation 50.512.0.," For simulation $50\_512\_9$, the total stellar mass (SFR density) and clumping factor are 1.52 (1.49) and 1.66, respectively, times lower than those of simulation $50\_512\_0$." This suggests that (he positive feedback introduced by the background is greater than the negative feedback., This suggests that the positive feedback introduced by the background is greater than the negative feedback. However. the stellar mass (SFR. densitv) does not recover in the same manner as the clumping factor.," However, the stellar mass (SFR density) does not recover in the same manner as the clumping factor." Once photoheating suppresses the formation of small-anass halos. the Hubble flow takes over and prevents (hem from collapsing and forming stars.," Once photoheating suppresses the formation of small-mass halos, the Hubble flow takes over and prevents them from collapsing and forming stars." Therefore. the redshift at which the backeround is (urned on determines whether the positive or negative feedback. dominates and whether the ionizing background will cause reionization to be accelerated or delaved.," Therefore, the redshift at which the background is turned on determines whether the positive or negative feedback dominates and whether the ionizing background will cause reionization to be accelerated or delayed." In connection with (his project. we have developed a user interface for calculating the critical SFR densitv (544) needed to maintain the ICM ionization al a given redshilt.," In connection with this project, we have developed a user interface for calculating the critical SFR density $\left(\dot{\rho}_{\rm crit}\right)$ needed to maintain the IGM ionization at a given redshift." The software computes the effects of variations in the stellar IME (slope. mass-range) and model abmospheres. and the redshift evolution of metallicity and eas thermodynamics (density. temperature. coupling to the CMD).," The software computes the effects of variations in the stellar IMF (slope, mass-range) and model atmospheres, and the redshift evolution of metallicity and gas thermodynamics (density, temperature, coupling to the CMB)." The clumping factor and LyC escape fraction are [ree parameters in (he caleulator., The clumping factor and LyC escape fraction are free parameters in the calculator. " Our simulations lind ranges of Cy,zz1—10 depending on recshift. overdensityv. ancl thermal phase of the (photoionized or shock-heated) IGM."," Our simulations find ranges of $C_H \approx 1 - 10$ depending on redshift, overdensity, and thermal phase of the (photoionized or shock-heated) IGM." " For the new 1536"" simuation. the global mean clumping factor is (C)23. with a power-law fit Cle)=(0.9)4+2)/6]FH! for redshifts between 5LO within roc402s., $\lambda_{crit} / \Delta x > 10 $ within $r < 40 R_S$. " The accretion at the peak is dominated by the aceretion Crom torus. (AL,Aly reaches 0.06) ancl typically stavs at this level for less than 5.1 fava."," The accretion at the peak is dominated by the accretion from torus, $\dot{M}_{\rm a} /\MDOT_{\rm B}$ reaches 0.06) and typically stays at this level for less than $\sim 5.1$ $t_{\rm dyn}$." 51 appears in he mass accretion rate curve many times (ie. all spikes correspond to the torus accretjon)., S1 appears in the mass accretion rate curve many times (i.e. all spikes correspond to the torus accretion). The aceretion from torus is subsequently accompanied w the polar funnel inflow Cleaking) of the matter that was eft in the polar regions after the outflow., The accretion from torus is subsequently accompanied by the polar funnel inflow (`leaking') of the matter that was left in the polar regions after the outflow. The density in he polar funnel is relatively low in comparison to the torus density (or in comparison to thelow-Z matter removed fron he polar funnel by the outflow)., The density in the polar funnel is relatively low in comparison to the torus density (or in comparison to the matter removed from the polar funnel by the outflow). " Is value is artificially set w the assumed py, parameter (see Sect. 2.2)).", Its value is artificially set by the assumed $\rho_{\rm min}$ parameter (see Sect. \ref{sec:init_mhd}) ). Phe matter rom the polar funnel contributes to the mass accretion rate and sets its mean level around 0.02 (Fig. 10))., The matter from the polar funnel contributes to the mass accretion rate and sets its mean level around 0.02 (Fig. \ref{fig:accretion_evolution_mini}) ). " During state 52 in run 1. AL,Aly is very low and it corresponds to a state when the torus is truncated. from the 1211."," During state S2 in run 1, $\MDOT_{\rm a}/\MDOT_{\rm B}$ is very low and it corresponds to a state when the torus is truncated from the BH." The truncation is due to magnetic elfects πο.," The truncation is due to magnetic effects (ie.," " a ""magnetic barrier) as in Ὁ state described in PBO3b (see also Proga&Zhang2006 and fig.", a `magnetic barrier') as in `C' state described in PB03b (see also \citealt{proga:2006} and fig. 1 there)., 1 there). We find that the poloidal magnetic field is larger than the toroidal component for r«LORS during this state., We find that the poloidal magnetic field is larger than the toroidal component for $r < 10 R_{\rm S}$ during this state. Phe magnetic field lines are stretched for r«LORS., The magnetic field lines are stretched for $r < 10 R_{\rm S}$. The MIRI does not operate in the inner 2077s., The MRI does not operate in the inner $20 R_{\rm S}$. The matter from the polar funnel also Lows outward during state S2., The matter from the polar funnel also flows outward during state S2. Pherefore. AL/My drops much below the mean value of z 0.02.," Therefore, $\dot{M}_{\rm a} / \dot{M}_{\rm B}$ drops much below the mean value of $\approx$ 0.02." " The duration of S2 state is comparable to the duration of S1 and all moments with Al,Aly«0.02 correspond to the same 82 state.", The duration of S2 state is comparable to the duration of S1 and all moments with $\dot{M}_{\rm a} / \dot{M}_{\rm B} < 0.02$ correspond to the same S2 state. " In our run 1l. we do not see an accretion state corresponding to the ""D state found in ΕΣ"," In our run 1, we do not see an accretion state corresponding to the `D' state found in PB03b." " In the 7D state. Al,Aly should. increase above 0.1 level. because of the slowly rotating matter previously pushed away by the coronal outflow. reentering the DII vicinity."," In the `D' state, $\MDOT_{\rm a}/\MDOT_{\rm B}$ should increase above 0.1 level, because of the slowly rotating matter previously pushed away by the coronal outflow, reentering the BH vicinity." We attribute lack of the D state in run 1 to a relatively short duration of our simulations., We attribute lack of the 'D' state in run 1 to a relatively short duration of our simulations. We performed our simulation for much shorter time (Table 1)) in comparison to PBO3b (2.5 £444)., We performed our simulation for much shorter time (Table \ref{tab:mhd_sum}) ) in comparison to PB03b (2.5 $t_{\rm dyn}$ ). 1n our simulations. the[ow-Z matter is far away (r72 500425) from the center at the end of the simulation.," In our simulations, the matter is far away $r > 500 R_{\rm S}$ ) from the center at the end of the simulation." " Por + —4/3. S1 state corresponds to the episode of torus accretion. but has a much. lower amplitude than narrow peaks found lor 5225/3 ( SI is representative of all narrow peaks with amplitude of AL,/As~0.01 in Fig. 10.."," For $\gamma$ =4/3, S1 state corresponds to the episode of torus accretion, but has a much lower amplitude than narrow peaks found for $\gamma$ =5/3 ( S1 is representative of all narrow peaks with amplitude of $\dot{M}_{\rm a} / \dot{M}_{\rm B} \sim 0.01$ in Fig. \ref{fig:accretion_evolution_mini}," panel for 5—4/3)., panel for $\gamma$ =4/3). We find that MIL causes the torus accretion. but our grid resolution was not adequate to capture the fastest erowing mode of MI. AgaNe<15 within kr«40725.," We find that MRI causes the torus accretion, but our grid resolution was not adequate to capture the fastest growing mode of MRI, $\lambda_{crit} / \Delta x < 1.5 $ within $r < 40 R_S$." ‘Thus. the mass accretion rate [from the torus is lower than it would be if the fastest mode of MIR were resolved.," Thus, the mass accretion rate from the torus is lower than it would be if the fastest mode of MRI were resolved." 1n Sl state. the torus accretion is accompanied by accretion of the matter with density of piis from the polar region.," In S1 state, the torus accretion is accompanied by accretion of the matter with density of $\rho_{\rm min}$ from the polar region." This polar funnel accretion sets the mean accretion rate at the level of 0.01. similar to the mean accretion rate obtained for .”..," This polar funnel accretion sets the mean accretion rate at the level of 0.01, similar to the mean accretion rate obtained for $\gamma$ =5/3." During S2 state (Fig. 10..," During S2 state (Fig. \ref{fig:accretion_evolution_mini}," panel for ? —4/3). the torus is pushed. away from the DII by the magnetic barrier (as in S2 state [or 2 —5/3 case).," panel for $\gamma$ =4/3), the torus is pushed away from the BH by the magnetic barrier (as in S2 state for $\gamma$ =5/3 case)." The mentioned D state appears in run 2 despite of a short curation of the simulation., The mentioned `D' state appears in run 2 despite of a short duration of the simulation. 83 state (Fig. 10..," S3 state (Fig. \ref{fig:accretion_evolution_mini}," panel or —4/23) is characterized by the the sudden increase of XL/Mg up to the level of ~0.2 and much longer duration 300/444 compared to state marked as S1.," panel for $\gamma$ =4/3) is characterized by the the sudden increase of $\MDOT_{\rm a}/\MDOT_{\rm B}$ up to the level of $\sim 0.2$ and much longer duration $\sim 300 t_{\rm dyn}$ compared to state marked as S1." In Fig. 10..," In Fig. \ref{fig:accretion_evolution_mini}," panel or *5—4/3. one can see only one state 83. but in Viel one can find two broad features corresponding to state 83.," panel for $\gamma$ =4/3, one can see only one state S3, but in \ref{fig:accretion_evolution} one can find two broad features corresponding to state S3." During state 83. thelow-Z matter accretes on to the DII near he equator.," During state S3, the matter accretes on to the BH near the equator." This matter has been pushed: away from the Bll bv the expanding magnetic corona during the bipolar outllow formation but not as far as in run 1., This matter has been pushed away from the BH by the expanding magnetic corona during the bipolar outflow formation but not as far as in run 1. Pherefore the weakly rotating matter may reenter the region close to the DII in a much shorter time-scale., Therefore the weakly rotating matter may reenter the region close to the BH in a much shorter time-scale. In the intermediate case of 5—1.2 (run 3). the mass accretion rate remains relatively high during the whole simulation (Lig. LO.," In the intermediate case of $\gamma$ =1.2 (run 3), the mass accretion rate remains relatively high during the whole simulation (Fig. \ref{fig:accretion_evolution_mini}," panel for 51.2) due to almost »ersistent.Iow-£ polar racial inflow., panel for $\gamma$ =1.2) due to almost persistent polar radial inflow. Therefore. contrary to run 1 and 2. it is dillicult to distinguish anv characteristic xuterns in the mass accretion rate curve.," Therefore, contrary to run 1 and 2, it is difficult to distinguish any characteristic patterns in the mass accretion rate curve." " S4 marks AL,Aly »aking at 0.2. when the torus accretes along with thef matter."," S4 marks $\MDOT_{\rm a}/\MDOT_{\rm B}$ peaking at 0.2, when the torus accretes along with the matter." However. in this case the grid. does not. resolve he Lastest growing mode of the MIU for kr«2072.," However, in this case the grid does not resolve the fastest growing mode of the MRI for $r < 20 R_{\rm S}$." The orus accretion is dominated by the slower MIR moces., The torus accretion is dominated by the slower MRI modes. " The main contribution to AL, comes from a polar inflow of thelow-f matter.", The main contribution to $\dot{M}_{\rm a}$ comes from a polar inflow of the matter. The mass accretion rate is slightly üeher than average because the matter from. polar regions simultaneously accretes from both. N aad ο sides (84).," The mass accretion rate is slightly higher than average because the matter from polar regions simultaneously accretes from both, N and S sides (S4)." State S4 appears only a few times during run 3., State S4 appears only a few times during run 3. For most of the ime. the matter in the polar regions aceretes [rom one side only.," For most of the time, the matter in the polar regions accretes from one side only." S4 is similar to the $3 in run 2. but during 83 Í matter approaches the BLL in the equatorial plane rather han from the poles. like in S4.," S4 is similar to the S3 in run 2, but during S3 matter approaches the BH in the equatorial plane rather than from the poles, like in S4." In 85 state. the mass accretion rate is dominated mainly » the torus. because almost all matter is removed from the »xolar funnel due to the episodic coronal outburst. described in 35.," In S5 state, the mass accretion rate is dominated mainly by the torus, because almost all matter is removed from the polar funnel due to the episodic coronal outburst described in \ref{sec:outburst}." " At that time Al,Aly becomes lower than 0.01."," At that time $\dot{M}_{\rm a}/\dot{M}_{\rm B}$ becomes lower than 0.01." In run 3. thehigh-£ torus never undergoes the truncation cause the poloidal magnetic fick is very weak ancl does not form a barrier for accretion.," In run 3, the torus never undergoes the truncation because the poloidal magnetic field is very weak and does not form a barrier for accretion." For 5=1.2 85 appears wo times at the end of the simulation., For $\gamma=1.2$ S5 appears two times at the end of the simulation. Note that S5 is similar to state 81 in run 1 and 2. but here the torus accretes inelliciently. therefore 55 appears as a dip (not as a spike like in c.g. run 1) above the mean level of accretion.," Note that S5 is similar to state S1 in run 1 and 2, but here the torus accretes inefficiently, therefore S5 appears as a dip (not as a spike like in e.g. run 1) above the mean level of accretion." " Lor *=1.01 (run 4). AL,Aly remains relatively hieh (Pig. 1O.."," For $\gamma$ =1.01 (run 4), $\dot{M}_{\rm a}/\dot{M}_{\rm B}$ remains relatively high (Fig. \ref{fig:accretion_evolution_mini}," panel for ? =1.01) for most of the duration of the simulation., panel for $\gamma$ =1.01) for most of the duration of the simulation. Thelow-f matter accretes quite persistently (as in run 3) along the torus surface (S4). on its N or ο sides. or both.," The matter accretes quite persistently (as in run 3) along the torus surface (S4), on its N or S sides, or both." Although MIU operates in the torus. again the accretion fastest mode is not resolved. with the simulation.," Although MRI operates in the torus, again the accretion fastest mode is not resolved with the simulation." ‘Thus. the torus aceretion rate is underestimated.," Thus, the torus accretion rate is underestimated." In run 4. the torus never experiences a truncation.," In run 4, the torus never experiences a truncation." “PheIow-£ matter inflow is only occasionally stopped by the turbulent corona but such episodes are short since the outflow is weak (85)., The matter inflow is only occasionally stopped by the turbulent corona but such episodes are short since the outflow is weak (S5). In this article we present results from the axisvmmetric 2-D AMLBLD simulations of a low angular momentum accretion Low on to the DII., In this article we present results from the axisymmetric 2-D MHD simulations of a low angular momentum accretion flow on to the BH. Our work is an extension of MIPOS. which in turn was initiated by PDO03a and PBOSb (see also Progaetal. 2003)).," Our work is an extension of MP08, which in turn was initiated by PB03a and PB03b (see also \citealt{proga:2003}) )." Llere. we concentrate on investigation of cllects of eas pressure on the flow structure and evolution.," Here, we concentrate on investigation of effects of gas pressure on the flow structure and evolution." In particular. we study how the Dow properties change asa function of the," In particular, we study how the flow properties change asa function of the" photous keV.tem 7s +.,photons $^{-1}$ $^{-2}$ $^{-1}$. The model results iu a goodness-of-fit of 4?=38.37 with LO d.o.f., The model results in a goodness-of-fit of $\chi^{2}=38.37$ with 40 d.o.f. The interred column density frou fitting the jet spectrum dis cousistent with that iuferred from the ulsur spectra., The inferred column density from fitting the jet spectrum is consistent with that inferred from the pulsar spectrum. Ou the other haud. in examining whether a thermal scenario is capable to describe 1c observed data. we attempted to ft a thermal wenasstralhlung model to the spectrum of the jet.," On the other hand, in examining whether a thermal scenario is capable to describe the observed data, we attempted to fit a thermal bremsstrahlung model to the spectrum of the jet." ILowever. we found that it results in au unplysically lieh temperature of AL—180 keV. Therefore. our investigation further supports a ron-therimal origin of the X-rays frou the jet.," However, we found that it results in an unphysically high temperature of $kT\sim180$ keV. Therefore, our investigation further supports a non-thermal origin of the X-rays from the jet." Tn order to constrain the spectral properties of lis system more tightly. we follow the method adopted by Johnson Wane (2010) to jointly fit individual power-law models for the X-ray spectra of the pulsar aud the jet with the column deusity iu the individual model tied together.," In order to constrain the spectral properties of this system more tightly, we follow the method adopted by Johnson Wang (2010) to jointly fit individual power-law models for the X-ray spectra of the pulsar and the jet with the column density in the individual model tied together." The results are sununarized in Table L1., The results are summarized in Table \ref{spec_par}. The joint analysis vields a colunm density. of: ny=(2.5!-n.ςapdtort 97., The joint analysis yields a column density of $n_{H}=(2.5^{+1.0}_{-0.7})\times10^{21}$ $^{-2}$. " The photon index aud the normalization at 1 keV or the pulsar are found to be Ty=2.2!"" aud (S3""Aτς)2.«↽10© photous -! ⋅ respectively,", The photon index and the normalization at 1 keV for the pulsar are found to be $\Gamma_{X}=2.2^{+0.2}_{-0.3}$ and $(8.3^{+2.1}_{-1.6})\times10^{-6}$ photons $^{-1}$ $^{-2}$ $^{-1}$ respectively. The corresponding best-fit spectral xuanieters for the jet are Dy=12401 and (8.77)«LO9 photons keV.1 2s t respectively., The corresponding best-fit spectral parameters for the jet are $\Gamma_{X}=1.2\pm0.1$ and $(8.7^{+1.0}_{-1.5})\times10^{-6}$ photons $^{-1}$ $^{-2}$ $^{-1}$ respectively. Iu the energv baud of 0.510 keV. he observed fux aud absorptiou-correct fluxes for anre found. to be (2.κ1!Sso)410il Cres 2os 1 and (3.1!.ο)»+10Tl oyes cinDὃς |1 respectively.," In the energy band of $0.5-10$ keV, the observed flux and absorption-correct fluxes for are found to be $(2.4^{+1.8}_{-1.0})\times10^{-14}$ ergs $^{-2}$ $^{-1}$ and $(3.4^{+1.7}_{-1.0})\times10^{-14}$ ergs $^{-2}$ $^{-1}$ respectively." ": And the observed flux. and absorption-corrected flux for its jet im the same euergv band are (9.1ans32)«:10.th eres 52s | and ,10iH eres )? s+ respectively.", And the observed flux and absorption-corrected flux for its jet in the same energy band are $(9.1^{+3.2}_{-2.8})\times10^{-14}$ ergs $^{-2}$ $^{-1}$ and $(10.0^{+3.1}_{-2.7})\times10^{-14}$ ergs $^{-2}$ $^{-1}$ respectively. . X-ray ondsson of the jet can possibly be owvered bv the euergv loss of the svuchrotrou uitfine leptons curing thei rides from the oulsar., X-ray emission of the jet can possibly be powered by the energy loss of the synchrotron emitting leptons during their rides from the pulsar. If the svuchrotrou cooling time is less iui the timescale for the flow of leptous across ie feature. steepenius of the photon iudex for 1ο svuchrotrou radiation is expected along the jet.," If the synchrotron cooling time is less than the timescale for the flow of leptons across the feature, steepening of the photon index for the synchrotron radiation is expected along the jet." Iu order to investieate this possible spectral variation along the jet. we divide the extraction region for the whole jet equally iuto two parts along its orieutation.," In order to investigate this possible spectral variation along the jet, we divide the extraction region for the whole jet equally into two parts along its orientation." Iu the following. we refer the seeieut closer to the pulsar as region 1l aud the further one as region 2.," In the following, we refer the segment closer to the pulsar as region 1 and the further one as region 2." The total photou y.atistics collected by three EPIC cameras for region 1 and region 2 are 379+28 cts and 376X26 cts respectively., The total photon statistics collected by three EPIC cameras for region 1 and region 2 are $379\pm28$ cts and $376\pm26$ cts respectively. For modeling the spectra of these seeleuts. we also consider the power-law model.," For modeling the spectra of these segments, we also consider the power-law model." For a amore coustrainiug analysis. we again joiutlv fit the spectra of regious 1 and 2 as well as the whole jet with the column density in the individual model tied together.," For a more constraining analysis, we again jointly fit the spectra of regions 1 and 2 as well as the whole jet with the column density in the individual model tied together." The results are stumarized in Table 1.., The results are summarized in Table \ref{spec_par}. Iu this joint analysis. tle N-rav spectra iu both regions can be well-modeled with a power-law with a slope Py~1.3 and heuce no variation of photon index have been found.," In this joint analysis, the X-ray spectra in both regions can be well-modeled with a power-law with a slope $\Gamma_{X}\sim1.3$ and hence no variation of photon index have been found." Since a knot-like N-vayv feature along the jet is identified aud ai possible optical source is found within its positional uucertaimty. this leads us to speculate whether this is a field object just happens to locate in the error circle bv chance instead of intrinsically related to the jet.," Since a knot-like X-ray feature along the jet is identified and a possible optical source is found within its positional uncertainty, this leads us to speculate whether this is a field object just happens to locate in the error circle by chance instead of intrinsically related to the jet." Therefore. we also attempt to examine the X-rav spectrum of this kuot-like feature.," Therefore, we also attempt to examine the X-ray spectrum of this knot-like feature." " Within a circular region with a radius of 15"" centered at its nominal position (see 833.1). there are 100+15r cts collected by all three EPIC cameras after vackeround subtraction."," Within a circular region with a radius of $15''$ centered at its nominal position (see 3.1), there are $100\pm15$ cts collected by all three EPIC cameras after background subtraction." We have examined its spectrum by fitting with various single component uodels which include a power-law. a therma xenisstraliluug as well as a collisional ionization equilibrimiu plasima model.," We have examined its spectrum by fitting with various single component models which include a power-law, a thermal bremsstrahlung as well as a collisional ionization equilibrium plasma model." In view of the linitec photon statistic of this feature. we simply assuiie he colui absorption is at the level coustraine in the aforementioned joint analysis (ie. ο=2s.10%! 72).," In view of the limited photon statistic of this feature, we simply assume the column absorption is at the level constrained in the aforementioned joint analysis (i.e. $n_{H}=2.8\times10^{21}$ $^{-2}$ )." We found that all three testec nodels result in a similar eooduess-of-fit (4?=15.1 with 23 d.o.£), We found that all three tested models result in a similar goodness-of-fit $\chi^{2}=18.1$ with 23 d.o.f.) and heuce we are not able ο. discrinimate these competing scenarios., and hence we are not able to discriminate these competing scenarios. We rotice that all the models vield an observed fiux at the level of fy—1.5«10+! eres ? 1 (0.5.10 keV)., We notice that all the models yield an observed flux at the level of $f_{X}\sim1.5\times10^{-14}$ ergs $^{-2}$ $^{-1}$ $0.5-10$ keV). In the UST nunage. the possible optical counterpart of this feature has a magnitude of R-—22.31.," In the HST image, the possible optical counterpart of this feature has a magnitude of $R\sim22.31$." This gives rise to au X-ray-to-optical flux ratio of fy/fie~0.77., This gives rise to an X-ray-to-optical flux ratio of $f_{X}/f_{R}\sim0.77$. This value is higher than that expected for a field star which typically has a ratio of fy/fopr<0.3 (Maccacaro ct al., This value is higher than that expected for a field star which typically has a ratio of $f_{X}/f_{\rm opt}<0.3$ (Maccacaro et al. 1988) but conforms with the expected range of au AGN which typically las a ratio of fy/for<50 (Stocke et al., 1988) but conforms with the expected range of an AGN which typically has a ratio of $f_{X}/f_{\rm opt}<50$ (Stocke et al. 1991)., 1991). Since the nature of the kuot-like feature cannot be confirmed. we have also reexamined the spectral behavior of the jet with the knot removed as if it were a background source.," Since the nature of the knot-like feature cannot be confirmed, we have also reexamined the spectral behavior of the jet with the knot removed as if it were a background source." Iu particular. as the kuot is located in region 1. we would Like to investigate whether its removal has an effect iu," In particular, as the knot is located in region 1, we would like to investigate whether its removal has an effect in" for the GSC? detection are somewhat more conservative). or with counterparts at other wavelengths (RAS Faint Sources Catalog. Moshir et al. 1990)).,"for the GSC2 detection are somewhat more conservative), or with counterparts at other wavelengths (IRAS Faint Sources Catalog, Moshir et al. \cite{moshir1990}) )." We prefer not to be too severe at this stage. deferring strict cuts after the boresight correction.," We prefer not to be too severe at this stage, deferring strict cuts after the boresight correction." 72 sources survived this phase., 72 sources survived this phase. We put aside from the primary sample sources which have not been detected in a longer HRI or ROSAT PSPC pointing (the PSPC had the same passband but a substantially larger effective area than the HRI)., We put aside from the primary sample sources which have not been detected in a longer HRI or ROSAT PSPC pointing (the PSPC had the same passband but a substantially larger effective area than the HRI). These could be variable sources detected at peak flux. but they are also candidates for false detections.," These could be variable sources detected at peak flux, but they are also candidates for false detections." No source has been inserted in this subclass on à non-detection basis with other instruments. because of the different passband. 1.8.. given the absence of spectral information on our sources. the non-detection could be ought to a peculiar spectral shape.," No source has been inserted in this subclass on a non-detection basis with other instruments, because of the different passband, i.e., given the absence of spectral information on our sources, the non-detection could be ought to a peculiar spectral shape." For some sources the suspicion of a false detection is strengthened by the number of non-detections or by the respective length of the pointings., For some sources the suspicion of a false detection is strengthened by the number of non-detections or by the respective length of the pointings. However. there are cases for which source parameters like detection probability and number of counts seem to indicate a real source.," However, there are cases for which source parameters like detection probability and number of counts seem to indicate a real source." Furthermore. as discussed in Section 3.4. we expected only ~2 spurious detection in 201 sources.," Furthermore, as discussed in Section 3.4, we expected only $\sim 2$ spurious detection in 201 sources." Of the 72 sources. 16 were placed i1 this transient candidate sub-sample. while for the other 56 there was no evidence of a transient nature.," Of the 72 sources, 16 were placed in this transient candidate sub-sample, while for the other 56 there was no evidence of a transient nature." We performed some astrometry on the remaining fields (including those of transient candidates). in order to get rid of the 10 fiducial boresight uncertainty and therefore to fully exploit the HRI angular resolution capability.," We performed some astrometry on the remaining fields (including those of transient candidates), in order to get rid of the $10''$ fiducial boresight uncertainty and therefore to fully exploit the HRI angular resolution capability." Furthermore. the error given by the detection algorithm (see Section 2.1). while not being entirely statistical. can be às a first approximation treated as random. so that the usual Gaussian relations can be used.," Furthermore, the error given by the detection algorithm (see Section 2.1), while not being entirely statistical, can be as a first approximation treated as random, so that the usual Gaussian relations can be used." " In contrast. the offset given by the boresight uncertainty varies in a random way in the ensemble of all the pointings. but is systematic in nature for all the sources in the single pointing. weakening the rejection of distant optical associations to BFS,"," In contrast, the offset given by the boresight uncertainty varies in a random way in the ensemble of all the pointings, but is systematic in nature for all the sources in the single pointing, weakening the rejection of distant optical associations to BFS." " For each pointing. we matched X-ray sources to optical counterparts (optical positions of known X-ray emitters). 1f any. or to optical catalog sources distant less than 10""."," For each pointing, we matched X-ray sources to optical counterparts (optical positions of known X-ray emitters), if any, or to optical catalog sources distant less than $10''$." " We excluded X-ray extended sources and sources with no optical catalog entry in 10"".", We excluded X-ray extended sources and sources with no optical catalog entry in $10''$. Ambiguous cases. Le. with two or more optical sources present. were treated individually using the distance and the optical luminosity as eriteria for the identification and then checked a posteriori.," Ambiguous cases, i.e. with two or more optical sources present, were treated individually using the distance and the optical luminosity as criteria for the identification and then checked a posteriori." Even if. only another X-ray source was present. the shift for this source has been applied to the pointing. although obviously in these cases the corrected positions and uncertainties have to be takensalis.," Even if only another X-ray source was present, the shift for this source has been applied to the pointing, although obviously in these cases the corrected positions and uncertainties have to be taken." ". Generally. the new error is less than 10”: even if it remains around 10"". the new position should be free from systematic boresight uncertainty."," Generally, the new error is less than $10''$; even if it remains around $10''$, the new position should be free from systematic boresight uncertainty." Note that performing the boresight correction only after the selection of Section 3.1 can bring to the loss of BFS., Note that performing the boresight correction only after the selection of Section 3.1 can bring to the loss of BFS. However. this allows us to deal with a limited number of sources and boresight corrections.," However, this allows us to deal with a limited number of sources and boresight corrections." The elimination of sources with an off-band counterpart in à 4o radius from the boresight corrected position left us with our final sample of four sources (three of them transient candidates)., The elimination of sources with an off-band counterpart in a $4\sigma$ radius from the boresight corrected position left us with our final sample of four sources (three of them transient candidates). This 4c limit assures us that starting with 1340 sources (Le. sources outside the inner 3’ in the BMW-HRI catalog and obeying to the cuts above unless th lack of counterparts). only 0.08 of them would lie outside the error region by chance.," This $4\sigma$ limit assures us that starting with 1340 sources (i.e. sources outside the inner $3'$ in the BMW-HRI catalog and obeying to the cuts above unless th lack of counterparts), only 0.08 of them would lie outside the error region by chance." In summary. our final BMW-HRI Blank Fields Sources are: After this selection we end up with one persistent BFS plus three transient BFS.," In summary, our final BMW-HRI Blank Fields Sources are: After this selection we end up with one persistent BFS plus three transient BFS." We report the new positions and error radii (as obtained from the boresight correction procedure). the flux. the detection probability (1e. the probability to detect a background fluctuation as a source). the total number of counts. the Galactic coordinates. the integrated Galactic column density. the distance from the nearest off-band association (in terms of error radij). the lower limit on the fy/fg; and the upper limit on the radio emission (see Table 2)).," We report the new positions and error radii (as obtained from the boresight correction procedure), the flux, the detection probability (i.e. the probability to detect a background fluctuation as a source), the total number of counts, the Galactic coordinates, the integrated Galactic column density, the distance from the nearest off-band association (in terms of error radii), the lower limit on the $\rm f_{X}/f_{BJ}$ and the upper limit on the radio emission (see Table \ref{finalbmw}) )." Note that. though with different depth. all but one (1IBMW200739.8-484819) of the sources have a radio flux upper limit.," Note that, though with different depth, all but one (1BMW200739.8-484819) of the sources have a radio flux upper limit." " The final error radius estimate for our sources is quite different from case to case. ranging from ~3” to 7""; the latter large error is due to the large off-axis angle and to the low number of counts (see Fig. 1))."," The final error radius estimate for our sources is quite different from case to case, ranging from $\sim 3''$ to $\sim 7''$; the latter large error is due to the large off-axis angle and to the low number of counts (see Fig. \ref{offaxis}) )." In fact. all our sources are quite offset from the center of the pointing (> 15).," In fact, all our sources are quite offset from the center of the pointing $>15'$ )." This depends from the used selection procedure and needs some comments., This depends from the used selection procedure and needs some comments. First. we concentrate on the consequences of the requirement of absence of offband counterparts in à 10 radius.," First, we concentrate on the consequences of the requirement of absence of offband counterparts in a $10''$ radius." This affects strongly the overall distribution in detector coordinates., This affects strongly the overall distribution in detector coordinates. In fact. the fiducial 10 radius for the initial correlation. chosen to match the worst case boresight error. is huge in comparison to the statistical positional error for the innermost sources. but it corresponds to the intrinsic error for the outermost sources (see Fig. 1)).," In fact, the fiducial $10''$ radius for the initial correlation, chosen to match the worst case boresight error, is huge in comparison to the statistical positional error for the innermost sources, but it corresponds to the intrinsic error for the outermost sources (see Fig. \ref{offaxis}) )." Sources in the innermost part are preferentially associated with optical counterparts which may not be the true ones. since they have been searched for over a region much larger than their error boxes.," Sources in the innermost part are preferentially associated with optical counterparts which may not be the true ones, since they have been searched for over a region much larger than their error boxes." The overall effect is to deplete the distribution from inner sources. enhancing the proportion of outer sources.," The overall effect is to deplete the distribution from inner sources, enhancing the proportion of outer sources." This bias is present independently of the real size of the boresight correction error., This bias is present independently of the real size of the boresight correction error. Second. there is a," Second, there is a" Fig.,Fig. 1. shows the EPIC MOS count rate images of the FilD region in the 0.3—0.5 keV. 0.5—] keV. and 0.3—2 keV energy bands.," \ref{fig:XMM} shows the EPIC MOS count rate images of the FilD region in the $0.3-0.5$ keV, $0.5-1$ keV, and $0.3-2$ keV energy bands." "The bin size is 10.4"" and the images are adaptively smoothed to a signal-to-noise ratio of 10 and vignetting-corrected as in 2)..",The bin size is $10.4''$ and the images are adaptively smoothed to a signal-to-noise ratio of 10 and vignetting-corrected as in \citet{mdb06}. The images show that shape and size of the ΕΠΟ X-ray knot are similar in the three energy bands., The images show that shape and size of the FilD X-ray knot are similar in the three energy bands. In Paper I we found that the extension of the X-ray emitting knot is ~(2x1x1)105 em., In Paper I we found that the extension of the X-ray emitting knot is $\sim (2\times 1\times 1)\times 10^{18}$ cm. The Vela FilD emits both in the X-ray and optical bands., The Vela FilD emits both in the X-ray and optical bands. Fig., Fig. 2 shows an Ha image of the FilD region. including the X-ray contour levels.," \ref{fig:X-Halpha} shows an $\alpha$ image of the FilD region, including the X-ray contour levels." A bright optical filament spans between the FilD regions with the highest X-ray surface brightness., A bright optical filament spans between the FilD regions with the highest X-ray surface brightness. The filament 15 almost aligned along the South-North direction and. therefore. it is perpendicular to the plane of the incident shock front.," The filament is almost aligned along the South-North direction and, therefore, it is perpendicular to the plane of the incident shock front." Optical filaments in SNRs are usually associated to the plasma behind the transmitted shock which travels through dense interstellar clouds. because they are typically aligned with the transmitted shock front planes: the peculiar orientation of the FilD optical filament is difficult to explain according to this scenario.," Optical filaments in SNRs are usually associated to the plasma behind the transmitted shock which travels through dense interstellar clouds, because they are typically aligned with the transmitted shock front planes; the peculiar orientation of the FilD optical filament is difficult to explain according to this scenario." As discussed in Paper 1. the spectral analysis of the EPIC data shows that the X-ray emission in. the FilD region is described well by two thermal components in collisional ionization equilibrium (CIE) at ~Dx109 K and ~3x10° K. respectively.," As discussed in Paper I, the spectral analysis of the EPIC data shows that the X-ray emission in the FilD region is described well by two thermal components in collisional ionization equilibrium (CIE) at $\sim 1\times 10^{6}$ K and $\sim 3\times 10^{6}$ K, respectively." The emission measure (EM) of the cooler component is about an order of magnitude larger than that of the hotter component (Paper 1. Fig.8).," The emission measure $EM$ ) of the cooler component is about an order of magnitude larger than that of the hotter component (Paper I, Fig.8)." We associated these components with two different phases of the clouds: the cloud core (which corresponds to the cooler component). surrounded by a hotter and less dense corona.," We associated these components with two different phases of the clouds: the cloud core (which corresponds to the cooler component), surrounded by a hotter and less dense corona." The core post-shock density is n;=1.5—5 em and the corona post-shock density 1s about three times lower., The core post-shock density is $n_{core}=1.5-5$ $^{-3}$ and the corona post-shock density is about three times lower. " Moreover. we calculated the distance of the FilD cloud from the center of the Vela shell and. by using the Sedov model (?)). we estimated that the shock velocity in the intercloud medium is 5.7—7.8x107 em/s. Therefore. following ?).. the shock temperature is Ty,=4.6—8.6x10° K. We also derived the mean abundances of O (O/O,,s? 1.0). Fe (Fe/Fes=0.39+ 0.05). and Ne (Ne/Ne;=1.7£ 0.2)."," Moreover, we calculated the distance of the FilD cloud from the center of the Vela shell and, by using the Sedov model \citealt{sed59}) ), we estimated that the shock velocity in the intercloud medium is $5.7-7.8\times10^{7}$ $/$ s. Therefore, following \citet{mh80}, , the shock temperature is $T_{sh}=4.6-8.6\times10^{6}$ K. We also derived the mean abundances of O $\overline{O}/O_\odot\approx 1.0$ ), Fe $\overline{Fe}/Fe_\odot =0.39\pm 0.05$ ), and Ne $\overline{Ne}/Ne_\odot=1.7\pm 0.2$ )." We found that the inhomogeneity of the surface brightness in the FilD region is determined by different volume distributions along the line of sight of the two components., We found that the inhomogeneity of the surface brightness in the FilD region is determined by different volume distributions along the line of sight of the two components. In particular. the surface brightness increases with the EM per unit area of the soft component.," In particular, the surface brightness increases with the $EM$ per unit area of the soft component." Finally. we estimated that FilD was shocked ~1300--4500 yr ago.," Finally, we estimated that FilD was shocked $\sim 1300-4500$ yr ago." We will use these results as constraints for our modeling., We will use these results as constraints for our modeling. We model the impact of a plane-parallel SNR shock on an isolated uniform. cloud in pressure equilibrium. with the ambient (intercloud) isothermal medium (Fig.3))., We model the impact of a plane-parallel SNR shock on an isolated uniform cloud in pressure equilibrium with the ambient (intercloud) isothermal medium \ref{fig:initial}) ). The plane-parallel approach ts justified because the FilD cloud ts small (<| pe) with respect to the curvature radius of the Vela shell (~15 pe)., The plane-parallel approach is justified because the FilD cloud is small $<1$ pc) with respect to the curvature radius of the Vela shell $\sim15$ pc). The shock-cloud interaction is described by means of a two-dimensional hydrodynamic model., The shock-cloud interaction is described by means of a two-dimensional hydrodynamic model. The model solves the time-dependent compressible fluid equations of mass. Momentum. and energy conservation. including radiative losses from an optically thin thermal plasma and. thermal conduction (considering also the effects of heat flux saturation).," The model solves the time-dependent compressible fluid equations of mass, momentum, and energy conservation, including radiative losses from an optically thin thermal plasma and thermal conduction (considering also the effects of heat flux saturation)." " The model equations are: with where is the bulk velocity of the gas. ¢ is the time. P the pressure. 7 the temperature. 2, and 7 are the electron and hydrogen number density. respectively (we assume n,=nj). P=μμ is the mass density (jp=1.26. assuming cosmic abundances). A(T) is the radiative losses function. per unit emission measure (?.. 2)). and q is the conductive flux. defined following ?) as g=(l/quu+I/qeq)!. where q«,; and Gesu, are the classical (?)) and saturated (2)) conductive flux. respectively with 7)=5.6x10ΤΟ erg s! K em! à=0.3 (in agreement with the values suggested by ? and ? for a fully ionized cosmic gas). and where c, is the isothermal sound speed."," The model equations are: with where is the bulk velocity of the gas, $t$ is the time, $P$ the pressure, $T$ the temperature, $n_e$ and $n_H$ are the electron and hydrogen number density, respectively (we assume $n_{e}=n_{H}$ ), $\rho=\mu m_{H}n_{H}$ is the mass density $\mu=1.26$ , assuming cosmic abundances), $\Lambda(T)$ is the radiative losses function per unit emission measure \citealt{rs77}, \citealt{mgv85}) ), and $q$ is the conductive flux, defined following \citet{db93} as $q=(1/q_{spi}+1/q_{sat})^{-1}$, where $q_{spi}$ and $q_{sat}$ are the classical \citealt{spi62}) ) and saturated \citealt{db93}) ) conductive flux, respectively with $\kappa(T)=5.6\times10^{-7}T^{5/2}$ erg $^{-1}$ $^{-1}$ $^{-1}$, $\phi=0.3$ (in agreement with the values suggested by \citealt{giu84} and \citealt{bsm89} for a fully ionized cosmic gas), and where $c_{s}$ is the isothermal sound speed." We solved the set of equations by using the FLASH code (?). upgraded to include thermal conduction and radiative losses from an optically thin thermal plasma (see ?)).," We solved the set of equations by using the FLASH code \citealt{for00}) ), upgraded to include thermal conduction and radiative losses from an optically thin thermal plasma (see \citealt{opr05}) )." The FLASH code is based on a directionally split PPM Riemann solver (?)). and uses adaptive mesh refinement (PARAMESH. ?). particularly appropriate to describe the moving steep gradients at the boundaries of the shock front.," The FLASH code is based on a directionally split PPM Riemann solver \citealt{wc84}) ), and uses adaptive mesh refinement (PARAMESH, \citealt{mom00}) ), particularly appropriate to describe the moving steep gradients at the boundaries of the shock front." Our simulations have been performed on an IBM pSeries p4 machine and on a Linux cluster of AMD opteron processors. for a total of ~9000 CPU hours.," Our simulations have been performed on an IBM pSeries p4 machine and on a Linux cluster of AMD opteron processors, for a total of $\sim 9000$ CPU hours." We show results of four simulations with different model setups., We show results of four simulations with different model setups. The setup of the physical parameters is dictated by the results of our analysis of the X-ray data., The setup of the physical parameters is dictated by the results of our analysis of the X-ray data. The relevant parameters are: the cloud/intercloud density contrast. the shock temperature. and the cloud dimension.," The relevant parameters are: the $/$ intercloud density contrast, the shock temperature, and the cloud dimension." Table | shows the initial physical parameters of our four setups., Table \ref{tab:setups} shows the initial physical parameters of our four setups. " In all the setups the intercloud pre-shock temperature is 10 K and the intercloud pre-shock density is 0.05 cm. In setup Sphl and Sph2 the cloud is spherical. whereas in setupEll] and Ell? we consider an ellipsoidal cloud. with the semimajor axis 6,, aligned with the incident shock velocity."," In all the setups the intercloud pre-shock temperature is $10^{4}$ K and the intercloud pre-shock density is $0.05$ $^{-3}$ In setup Sph1 and Sph2 the cloud is spherical, whereas in setupEll1 and Ell2 we consider an ellipsoidal cloud, with the semimajor axis $b_{cl}$ aligned with the incident shock velocity." The Machnumber At (1. e. the shock speed in units of the intercloud isothermal sound speed) and the density contrast y (1. e. the ratio cloud/intercloud density) of our setups are Afs;e)= SO. ysier=20 (for," The Machnumber $\mathcal{M}$ (i. e. the shock speed in units of the intercloud isothermal sound speed) and the density contrast $\chi$ (i. e. the ratio $/$ intercloud density) of our setups are $\mathcal{M}_{S1E1}=50$ , $\chi_{S1E1}=20$ (for" Table | lists these fitted parameters for six baryonic Hernquist masses over a large mass range.,Table \ref{surfdens} lists these fitted parameters for six baryonic Hernquist masses over a large mass range. The combinations of the masses and effective radit in Table 1. follow equation (5) of GOI (n accordance with the fundamental plane). where we transformed their luminosities into massesby using M/L5z8 for all galaxy baryonic masses.," The combinations of the masses and effective radii in Table \ref{surfdens} follow equation (5) of G01 (in accordance with the fundamental plane), where we transformed their luminosities into massesby using $M/L_B$ =8 for all galaxy baryonic masses." Fig.] shows the values of the fitted dark halo parameters derived from applying MOND to the baryonic Hernquist-profiles. together with the observational scaling relations given by GOL (dotted lines) and TO9 (dashed lines).," \ref{fig:gerhard} shows the values of the fitted dark halo parameters derived from applying MOND to the baryonic Hernquist-profiles, together with the observational scaling relations given by G01 (dotted lines) and T09 (dashed lines)." The upper panel shows the characteristic phase space density. the middle panel the central volume density. and the lower panel the characteristic surface density.," The upper panel shows the characteristic phase space density, the middle panel the central volume density, and the lower panel the characteristic surface density." Let us note that the plotted relations are indicative only. since the data (Fig.18 of GO] and Figs.," Let us note that the plotted relations are indicative only, since the data (Fig.18 of G01 and Figs." | and 4 of T09) show a very large scatter even when logarithmically displayed., 1 and 4 of T09) show a very large scatter even when logarithmically displayed. However. within this observational uncertainty. it is remarkable that some features are perfectly reproduced. particularly the slopes of the phase space density and of the central volume density as a function of baryonte mass (given the observational scatter. the almost. perfect reproduction of the central volume density of GOL might of course be coincidental).," However, within this observational uncertainty, it is remarkable that some features are perfectly reproduced, particularly the slopes of the phase space density and of the central volume density as a function of baryonic mass (given the observational scatter, the almost perfect reproduction of the central volume density of G01 might of course be coincidental)." As first emphasized by GOL. the phase-space density values are at a given mass higher than in spirals. which means that under the A Cold Dark Matter paradigm. dark halos of ellipticals cannot be the result of collisionless mergers of present-day spirals. but must have been assembled at a very early time. when the cosmological density was higher.," As first emphasized by G01, the phase-space density values are at a given mass higher than in spirals, which means that under the $\Lambda$ Cold Dark Matter paradigm, dark halos of ellipticals cannot be the result of collisionless mergers of present-day spirals, but must have been assembled at a very early time, when the cosmological density was higher." In MOND this is of course not necessarily the case. as the argument does not apply to phantom halos.," In MOND this is of course not necessarily the case, as the phase-space argument does not apply to phantom halos." One also notes a remarkable exception to the sealing relations: the fitted characteristic dark matter surface density S is fully independent from the Hernquist parameters. and it is systematically lower than in GOT and TO9.," One also notes a remarkable exception to the scaling relations: the fitted characteristic dark matter surface density $S$ is fully independent from the Hernquist parameters, and it is systematically lower than in G01 and T09." We emphasize that this constancy is not related to the special relation of mass and effective radius., We emphasize that this constancy is not related to the special relation of mass and effective radius. " Varying R;,; by a factor of two at a given mass does not change the constant surface density significantly.", Varying $R_{eff}$ by a factor of two at a given mass does not change the constant surface density significantly. This prediction of MOND thus brings the value closer to the (also constant) value of S observed in spiral galaxies. logS=2.1 (?)..," This prediction of MOND thus brings the value closer to the (also constant) value of $S$ observed in spiral galaxies, ${\rm log}S=2.1$ \citep{donato09}." Letus note that MOND also predicts the observed constant value of S in spirals. which ts somewhat lower because (1) spirals are a bit deeper into the MOND regime (?)) and (11) their flattened baryonic profiles lead to a somewhat higher Newtonian gravity at a given mass. and in turn a somewhat lower MOND contribution to the phantom halo.," Let us note that MOND also predicts the observed constant value of $S$ in spirals, which is somewhat lower because (i) spirals are a bit deeper into the MOND regime \citealt{milgrom09}) ) and (ii) their flattened baryonic profiles lead to a somewhat higher Newtonian gravity at a given mass, and in turn a somewhat lower MOND contribution to the phantom halo." On the first glance one might interpret this constarcy and the other scaling relations as a clear signature of MOND in ellipticals: however. CDM may also predict that the surface density within the scale radius of NFW halos weakly depends on dark matter total mass (?X.," On the first glance one might interpret this constancy and the other scaling relations as a clear signature of MOND in ellipticals: however, CDM may also predict that the surface density within the scale radius of NFW halos weakly depends on dark matter total mass \citep{boyarsky10}." For spiral galaxies. this ts of little interest as it is known that cuspy profiles often do not fit rotation curves (???).. the mystery then bei5 how to erase the cusp by the feedback from the baryons while keeping the product poro constant.," For spiral galaxies, this is of little interest as it is known that cuspy profiles often do not fit rotation curves \citep{fb05, deblok10, gentile05}, the mystery then being how to erase the cusp by the feedback from the baryons while keeping the product $ \rho_0 r_0$ constant." In elliptical galaxies. the situation is less clear as NEW profiles often do fit the data equally well as cored profiles (2)..," In elliptical galaxies, the situation is less clear as NFW profiles often do fit the data equally well as cored profiles \citep{schuberth10}." We thus fitted. NFW profiles to the same MONDian phantom halos and found a perfect agreement., We thus fitted NFW profiles to the same MONDian phantom halos and found a perfect agreement. The question remains whether these NFW-halos are “cosmological” or in other words. fulfill the relation between virial mass and concentration predicted by cosmological simulations.," The question remains whether these NFW-halos are ”cosmological” or in other words, fulfill the relation between virial mass and concentration predicted by cosmological simulations." " Fig.2 displays for our Hernquist masses the resulting concentrations of the NFW-halos (open circles) corresponding to the MONDuian phantom halos. while the triangles show the concentration values expected from the equation (9) of ?.. using 200 times the critical density as the mean density within the virial radius (standard cosmology: hz0.7. O,,=0.3. O4= 0.7)."," \ref{fig:M_C} displays for our Hernquist masses the resulting concentrations of the NFW-halos (open circles) corresponding to the MONDian phantom halos, while the triangles show the concentration values expected from the equation (9) of \citet{maccio08}, using 200 times the critical density as the mean density within the virial radius (standard cosmology: h=0.7, $\Omega_m = 0.3$, $\Omega_\Lambda=0.7$ )." One concludes that for high masses the MONDian phantom halos are not distinguishable from cosmological NFW halos. given also that the simulations predict considerable scatter.," One concludes that for high masses the MONDian phantom halos are not distinguishable from cosmological NFW halos, given also that the simulations predict considerable scatter." For smaller masses the difference between MONDian phantom halos and NEW. cosmological halos is larger., For smaller masses the difference between MONDian phantom halos and NFW cosmological halos is larger. Due to the non-linearity of MOND and its associated breaking of the Strong Equivalence Principle. à MONDian stellar system embedded in an external gravitational field (EF) stronger than its own internal field behaves in a quasi-Newtonian way. with an effectively higher gravitational constant (22)..," Due to the non-linearity of MOND and its associated breaking of the Strong Equivalence Principle, a MONDian stellar system embedded in an external gravitational field (EF) stronger than its own internal field behaves in a quasi-Newtonian way, with an effectively higher gravitational constant \citep{milgrom83,famaey07}. ." Most of the sample galaxies are located m clusters or groups where the EF might have an influence., Most of the sample galaxies are located in clusters or groups where the EF might have an influence. ? for instance showed how the EF, \citet{wu10} for instance showed how the EF These models need to invose special sviuuetries to insure unusualv long lifetimes for SIRs aud that a sufficieutly small percentage decays today xoduciug κ As in the toplogical defects case. the decay of these reIcs also eoncrates jets of hadrous.,"These models need to invoke special symmetries to insure unusually long lifetimes for SHRs and that a sufficiently small percentage decays today producing \cite{BKV97,CKR99KT99} As in the topological defects case, the decay of these relics also generates jets of hadrons." These outicles behave like cold dark nater and could constitute a fair fraction of the halo of οιr Galaxy., These particles behave like cold dark matter and could constitute a fair fraction of the halo of our Galaxy. Therefore. tlijr halo decay products would not be lumied by the €Zl cutoff allowing for a large flux at UITEs (see Figure 10 andSIRs in Table 2).," Therefore, their halo decay products would not be limited by the GZK cutoff allowing for a large flux at UHEs (see Figure 10 and in Table 2)." Similar signatures cauoccur if topological defects are microscopic. such as monopolouia aud vortous. and decay in the Talo of our Galaxy in Table 2).," Similar signatures can occur if topological defects are microscopic, such as monopolonia and vortons, and decay in the Halo of our Galaxy in Table 2)." Iu both cases(19/15 and TD) the composition of the primary would be a good discriminant since the decay products are usually dominated by photons., In both cases and ) the composition of the primary would be a good discriminant since the decay products are usually dominated by photons. Future experiments should be able to probe these hypotheses., Future experiments should be able to probe these hypotheses. For iustaucoe. in the case of SUR aud iionopolouiua decays. the arrival direction distribution should be close to isotropic but show an asviuinetry due to the position of the Earth iu he Caactic ILido'* aud the clusteqiue due to simall scale dark matter ES Studyiug plausible hedo models for their expected asynunetry and imhouogeneitis will help coustrai1 halo distributions especially when larger ¢ata ses are available in the futire.," For instance, in the case of SHR and monopolonium decays, the arrival direction distribution should be close to isotropic but show an asymmetry due to the position of the Earth in the Galactic \cite{BBV98} and the clustering due to small scale dark matter \cite{BlSe00} Studying plausible halo models for their expected asymmetry and inhomogeneitis will help constrain halo distributions especially when larger data sets are available in the future." Tigh euergv gama rav experiments such as GLAST will also help οςstrain SUR models via the electromagnetic decay «ου Next generation experiments such as the Wiel Resolution Flvs Eve which recently started operating. the Pierre Auger Project which is now uuder coustinction. the proxosed Telescope Array. and the EUSO aud OWL satellites will significatly oeUprove| the data at the extremel-hieh cud of the cosmic ray spectrum! With tτοσο observatories a clear determination of the spectrum aud spatia πιtion of UTIECR sources is within reach.," High energy gamma ray experiments such as GLAST will also help constrain SHR models via the electromagnetic decay \cite{B99} Next generation experiments such as the High Resolution Fly's Eye which recently started operating, the Pierre Auger Project which is now under construction, the proposed Telescope Array, and the EUSO and OWL satellites will significantly improve the data at the extremely-high end of the cosmic ray \cite{revdata} With these observatories a clear determination of the spectrum and spatial distribution of UHECR sources is within reach." The! lack of a GZIK cutoff should become clear with WiRes and Auger iux most extragalactic Zevatrous may be ruled out., The lack of a GZK cutoff should become clear with HiRes and Auger and most extragalactic Zevatrons may be ruled out. The observed spectrum wil istinetish Zevatrous from new pliyvsics models by testing the harcducss of the, The observed spectrum will distinguish Zevatrons from new physics models by testing the hardness of the auc augular momentuui along the photon trajectory.,and angular momentum along the photon trajectory. " Here. gi, is the jrr—eleient of the metric. and A is an affine parameter."," Here, $g_{\mu\nu}$ is the $\mu\nu-$ element of the metric, and $\lambda$ is an affine parameter." Usiug these two conserved quantities. we now write two first-order differential equations for the evolution of the /— and ó— components of the photon position as aud where we have defined the normalized affine parameter A’=EA and the impact parameter for the photon trajectory b=L/E.," Using these two conserved quantities, we now write two first-order differential equations for the evolution of the $t-$ and $\phi-$ components of the photon position as and where we have defined the normalized affine parameter $\lambda^\prime\equiv E\lambda$ and the impact parameter for the photon trajectory $b\equiv L/E$." For the r— and 0— components of the photon position we use the secoud-orcder geodesic equations. whieh for a general axisyinnetric metric take the form and Here. P5. are the various Christolfel svyinbols for the metric (1)).," For the $r-$ and $\theta-$ components of the photon position we use the second-order geodesic equations, which for a general axisymmetric metric take the form and Here, $\Gamma^\alpha_{\beta\gamma}$ are the various Christoffel symbols for the metric \ref{eq:GB}) )." A final integral of motion arises from the requirement that the norm of the photon [-1inomentuim has to vanish. Le.. This integral of motion is not useful for replaciug either the geodesic equation (11)) or (12)) because it contains the squares of the derivatives of the r— and 0— coordinates with respect to the alline parameter.," A final integral of motion arises from the requirement that the norm of the photon 4-momentum has to vanish, i.e., This integral of motion is not useful for replacing either the geodesic equation \ref{eq:r}) ) or \ref{eq:theta}) ) because it contains the squares of the derivatives of the $r-$ and $\theta-$ coordinates with respect to the affine parameter." Weeping track of the appropriate sien for the two derivatives. especially near the inflection points of the geodesies. would more than offset the benefit of using a first-order integral of motion as opposed to a second-order geoclesic equatiou.," Keeping track of the appropriate sign for the two derivatives, especially near the inflection points of the geodesics, would more than offset the benefit of using a first-order integral of motion as opposed to a second-order geodesic equation." Therefore. followiug Cadeau et ((2007). we use this integral of motion only iu order to monitor the accuracy of the calculation.," Therefore, following Cadeau et (2007), we use this integral of motion only in order to monitor the accuracy of the calculation." To this enc. we clefine the parameter," To this end, we define the parameter" is calculated for each. individual output as the average over all halos N; available at that time step.,is calculated for each individual output as the average over all halos $N_i$ available at that time step. A large dispersion 634773; now indicates a violent formation history whereas low values correspond το quiescent formation histories., A large dispersion $\sigma_{\Delta M/M}$ now indicates a violent formation history whereas low values correspond to quiescent formation histories. As we can see in1.. our qualitative classification scheme is confirmed by the maria values.," As we can see in, our qualitative classification scheme is confirmed by the $\sigma_{\Delta M/M}$ values." ‘To eain further insight into the hierarchical build-up of the host and the evolution of its satellite population we plot the fraction of its mass locked. up in the satellite distribution in1., To gain further insight into the hierarchical build-up of the host and the evolution of its satellite population we plot the fraction of its mass locked up in the satellite distribution in. . We show the total mass of all the satellites (identilied by the mmethod outlined in GAGI)) living within the virial racius cliviclect by the mass of the host halo as a function of recshilt., We show the total mass of all the satellites (identified by the method outlined in ) living within the virial radius divided by the mass of the host halo as a function of redshift. Ato=ϐ the average mass of all substructure is approximately of the host halo's virial mass with the scatter allowing or as much as and as little as3%., At $z=0$ the average mass of all substructure is approximately of the host halo's virial mass with the scatter allowing for as much as and as little as. . We do not observe any pronounced trend. for this fraction to depend on the age of the dark matter halo. which is consistent. with the ucrarchical model of satellite accretion: both small and large objects continuously. fall in.," We do not observe any pronounced trend for this fraction to depend on the age of the dark matter halo, which is consistent with the hierarchical model of satellite accretion: both small and large objects continuously fall in." Ehe history is clearly reflected in1.. where the infall of large satellites gives rise o the spiky nature of the curves.," The history is clearly reflected in, where the infall of large satellites gives rise to the spiky nature of the curves." These large variations are. however. a combination of massive halos merging via dynamical [rietion ancl “transitory structures.," These large variations are, however, a combination of massive halos merging via dynamical friction and “transitory structures”." ‘Transitory structures are small subsets of satellites that interact with a halo. but are not bound to it.," Transitory structures are small subsets of satellites that interact with a halo, but are not bound to it." An example is given in where we show one of these transitory events for halo #77., An example is given in where we show one of these transitory events for halo 7. The peak near redshift z=0.2 for this halo in is caused by an object of roughly of the mass of the host orbiting in the outskirts (but still within Z2444)) of the host halo at a relative speed of approximately, The peak near redshift $z=0.2$ for this halo in is caused by an object of roughly of the mass of the host orbiting in the outskirts (but still within ) of the host halo at a relative speed of approximately. captures this event showing the host and its virial radius at redshift z=0 with the path of the satellite indicated by a line., captures this event showing the host and its virial radius at redshift $z=0$ with the path of the satellite indicated by a line. Phe perturber itself is represented by its particles., The perturber itself is represented by its particles. lis tidal disruption while passing near the host can also be appreciated in2., Its tidal disruption while passing near the host can also be appreciated in. ". We particularly highlight this ealactic encounter not onlv to explain the rise in but also to raise the readers attention o the potential of already ""harassed galaxies falling into he host halo.", We particularly highlight this galactic encounter not only to explain the rise in but also to raise the readers attention to the potential of already ”harassed” galaxies falling into the host halo. The largoὃν peak for halo #88 in is due to an interaction with one of the other two large objects in the svstem., The large peak for halo 8 in is due to an interaction with one of the other two large objects in the system. The violent history of halos £55 and 466 can also be seen inL., The violent history of halos 5 and 6 can also be seen in. . The more quiescent halos also stand out in this figure. with less variation in the substructure evolution except. for halo #22 with a mass merger at 2=nu0.53.," The more quiescent halos also stand out in this figure, with less variation in the substructure evolution except for halo 2 with a mass merger at $z=0.53$." In summary. we have selected a sample of halos displaying widely different formation histories. which should aid in gaining insight into the environmental elfects of halo formation.," In summary, we have selected a sample of halos displaying widely different formation histories, which should aid in gaining insight into the environmental effects of halo formation." We now investigate the temporal evolution of. satellite accretion and tidal disruption as a function of host halo environment and richness., We now investigate the temporal evolution of satellite accretion and tidal disruption as a function of host halo environment and richness. In we displav the normalised. number of satellites within the respective host halo as a function of time after the initial formation epoch., In we display the normalised number of satellites within the respective host halo as a function of time after the initial formation epoch. As we intend. to, As we intend to temperatures. only simall amounts (less than in total) of TO. COs. aud/or O» are allowed iu the ices.,"temperatures, only small amounts (less than in total) of $_2$ O, $_2$ , and/or $_2$ are allowed in the ices." Larger concentrations would violate the observed narrow width., Larger concentrations would violate the observed narrow width. A laboratory CO spectra with CO» content at a laboratory temperature of 77 —10 lk can already be excluded. for example (Fig.," A laboratory CO spectrum with $_2$ content at a laboratory temperature of $T=$ 10 K can already be excluded, for example (Fig." tbh). ⊀≚↑↕∐∶↴∙⊾∐↸∖↥⋅, \ref{f:labfit2}b b). ↕⋜∏⋝∪↥⋅⋜↧↑∪↥⋅∙↖⇁↑↸∖∐∏⋉∖↥⋅⋜↧⊓∐⋅↸∖↴∖↴∙≼⊲≼≓≽⊐∐∐⊼⊓∐⋅↸∖↴∖↹∖↴↑↕∐ poorly match the observations.," At higher laboratory temperatures, $_2$ mixtures still poorly match the observations." In Oo mixtures. the band narrows sufficicutly at higher teupcratures (~30 EK) to eive reasonable fits even at huge Ov concentrations 50: Fie.," In $_2$ mixtures, the band narrows sufficiently at higher temperatures $\sim$ 30 K) to give reasonable fits even at large $_2$ concentrations $>50$ ; Fig." ldd aud f)., \ref{f:labfit2}d d and f). Finally. the mixture No:CO=1:1 gives a somewhat poorer fit to the observed bbaud because of à 70.5 sshift to shorter wavelengths (Fig.," Finally, the mixture $_2$ :CO=1:1 gives a somewhat poorer fit to the observed band because of a $\sim$ 0.5 shift to shorter wavelengths (Fig." hh)., \ref{f:labfit2}h h). However. we considerthis mixture still reasonable because of the good fit to the bbuud 3.1.2).," However, we considerthis mixture still reasonable because of the good fit to the band 3.1.2)." This is the largest Fornax galaxy. at the center of the cluster.,"This is the largest Fornax galaxy, at the center of the cluster." Its dominant status is confirmed by its large velocity dispersion (notice however that the peak value of σ is underestimated by our data because of the relatively poor seeing. see Sect.," Its dominant status is confirmed by its large velocity dispersion (notice however that the peak value of $\sigma$ is underestimated by our data because of the relatively poor seeing, see Sect." 4)., 4). The VDP quickly declines to 250 km + by a radius of 10”. to remain approximately flat to the outer data points.," The VDP quickly declines to 250 km $^{-1}$ by a radius of $\arcsec$, to remain approximately flat to the outer data points." " The RC presents strong evidence for a kinematically distinct inner component. with an inflexion point evident over the central 4""."," The RC presents strong evidence for a kinematically distinct inner component, with an inflexion point evident over the central $\arcsec$." " The W side of the RC reaches a maximum value of 30 kms. + at 15"", where it then steadily falls to zero by 55."," The W side of the RC reaches a maximum value of 30 km $^{-1}$ at $\arcsec$, where it then steadily falls to zero by $\arcsec$." " It then changes sign. increases to 10 km 1 at 60"" and then decreases again."," It then changes sign, increases to 10 km $^{-1}$ at $\arcsec$ and then decreases again." " The wiggles of the RC in the range 40-70"" are associated to wiggles in the VDP in the same range and with the same amplitude.", The wiggles of the RC in the range $\arcsec$ are associated to wiggles in the VDP in the same range and with the same amplitude. The Eoof the RC appears identical to the W uuntil reaching 30” where it increases to 50 km + to then stagger back down to a rotational speed of 20 km + at the outer data point., The Eof the RC appears identical to the W until reaching $\arcsec$ where it increases to 50 km $^{-1}$ to then stagger back down to a rotational speed of 20 km $^{-1}$ at the outer data point. " The E oof the VDP resembles the W uuntil at 55"" where it decreases by 40 km +1 over the following 5” and then starts climbing. still inereasing at the outer data point."," The E of the VDP resembles the W until at $\arcsec$ where it decreases by 40 km $^{-1}$ over the following $\arcsec$ and then starts climbing, still increasing at the outer data point." " The RC has a steep gradient of 200 km + ! inside 10 "". with the exception of the two inner arcseconds. where the RC remarkably flattens."," The RC has a steep gradient of 200 km $^{-1}$ $^{-1}$ inside 10 $''$, with the exception of the two inner arcseconds, where the RC remarkably flattens." At r~10” and r~22” there are two local maxima around V—100 km +. which are symmetric with respect to the center.," At $r$$\sim$$10$$''$ and $r$$\sim$$22$$''$ there are two local maxima around $V$$\sim$$100$ km $^{-1}$, which are symmetric with respect to the center." " The rotation velocity starts increasing again beyond 730"". reaching 110 kms. ? at the last observed point: the RC seems actually to be increasing even beyond 3 effective radii."," The rotation velocity starts increasing again beyond $r$ $30$$''$, reaching $\sim$$140$ km $^{-1}$ at the last observed point: the RC seems actually to be increasing even beyond 3 effective radii." In the central region the VDP dips by 15 km + from the two local maxima situated at +2 from the center., In the central region the VDP dips by 15 km $^{-1}$ from the two local maxima situated at $\pm 2''$ from the center. " The velocity dispersion then decreases at à nearly constant rate in the inner 20"". until reaching a plateau around 200 km +."," The velocity dispersion then decreases at a nearly constant rate in the inner $''$, until reaching a plateau around 200 km $^{-1}$." " In the range from 40” to 50"" the VDP decreases before increasing to à local maximum of 180 km 1 around | aremin from the center.", In the range from $''$ to $''$ the VDP decreases before increasing to a local maximum of 180 km $^{-1}$ around 1 arcmin from the center. This galaxy has a very similar RC to NGC 1336. with —-15 kms 1 wiggles observed out to 2 FR...," This galaxy has a very similar RC to NGC 1336, with $\sim$ 15 km $^{-1}$ wiggles observed out to 2 $R_e$." " The VDP is largely flat (at 120 km +) over the inner 9""(172,.). then it steadily decreases to —70 kms ! reaching the outer radius limit of the data."," The VDP is largely flat (at $\sim$ 120 km $^{-1}$ ) over the inner $\arcsec$ $R_e$ ), then it steadily decreases to $\sim$ 70 km $^{-1}$ reaching the outer radius limit of the data." Like NGC 1336. this galaxy also has à very strong isophotal twist (~ 100°) over the inner region. where the RC is observed to remain flat.," Like NGC 1336, this galaxy also has a very strong isophotal twist $\sim$ $^{\circ}$ ) over the inner region, where the RC is observed to remain flat." Also in this case we thus find evidence for a possible bar-like structure., Also in this case we thus find evidence for a possible bar-like structure. This galaxy has a wiggly VDP which peaks around 180 km ! and falls to 140 km Lat the data boundary., This galaxy has a wiggly VDP which peaks around 180 km $^{-1}$ and falls to 140 km $^{-1}$ at the data boundary. The CVD is ~13 kms. ! below the peak value which occurs 4 W from the center., The CVD is $\sim$ 13 km $^{-1}$ below the peak value which occurs $\arcsec$ W from the center. The RC. after reaching a first maximum of 25 kms. ! at 5”. shows a series of secondary maxima on both sides. that are anti-correlated to the wiggles in the VDP.," The RC, after reaching a first maximum of $\sim$ 25 km $^{-1}$ at $\arcsec$ , shows a series of secondary maxima on both sides, that are anti-correlated to the wiggles in the VDP." There is also marginal evidence for an inflexion in the center which. if real. and if related to the dip in the VDP could," There is also marginal evidence for an inflexion in the center which, if real, and if related to the dip in the VDP could" metal-poor dwarfs under LTE calculations would give log g values too low by 0.8 dex (Sy = 0) or 0.5 dex (Sy = 1).,metal-poor dwarfs under LTE calculations would give log $g$ values too low by 0.8 dex $\rm S_{H}$ = 0) or 0.5 dex $\rm S_{H}$ = 1). LTE calculations for HD140283 have occasionally yielded gravities lower than the gravity by ~ 0.3 (e.g.2). and for a selection of 13 halo main sequance turnoff stars with parallaxes Ryan et al. (," LTE calculations for HD140283 have occasionally yielded gravities lower than the gravity by $\sim$ 0.3 \citep[e.g.][]{Ryanetal1996b}, and for a selection of 13 halo main sequance turnoff stars with parallaxes Ryan et al. (" 2009 - in preperation) determine a mean difference of 0.2 in log e compared to LTE ionization balance.,2009 - in preperation) determine a mean difference of 0.2 in log $g$ compared to LTE ionization balance. These differences are less than what we compute for Sy = I. and suggest that for the model atom we are using. the choice of Sy = | may underestimate the role of collisions with neutral hydrogen in diminishing the departures from LTE for Fe. 1.8. that Sy>I.," These differences are less than what we compute for $\rm S_{H}$ = 1, and suggest that for the model atom we are using, the choice of $\rm S_{H}$ = 1 may underestimate the role of collisions with neutral hydrogen in diminishing the departures from LTE for Fe, i.e. that $\rm S_{H} > 1$." Whilst we have not attempted a detailed derivation of Sy by this method. ? has. arriving at a value of Sy = 3 based on the analysis of four halo stars and two others.," Whilst we have not attempted a detailed derivation of $\rm S_{H}$ by this method, \citet{Kornetal2003} has, arriving at a value of $\rm S_{H}$ = 3 based on the analysis of four halo stars and two others." Our results are broadly consistent with their conclusion., Our results are broadly consistent with their conclusion. We have discussed the processes of NLTE line formation of Fe lines., We have discussed the processes of NLTE line formation of Fe lines. Here. we have shown the challenges posed by such calculations and the uncertainties that still arise. in particular due to the unknown magnitude of collisions.," Here, we have shown the challenges posed by such calculations and the uncertainties that still arise, in particular due to the unknown magnitude of collisions." As there is at present no better theoretical or experimental description of the role ofH collisions. one obvious next step would be to tie down the value of Sy for metal-poor stars. for example by forcing the equality of gravities and those determined by ionization equilibrium by changing Sy (?)..," As there is at present no better theoretical or experimental description of the role of H collisions, one obvious next step would be to tie down the value of $\rm S_{H}$ for metal-poor stars, for example by forcing the equality of gravities and those determined by ionization equilibrium by changing $\rm S_{H}$ \citep{Kornetal2003}." For this reason we have discussed the effectof NLTE corrections on the tonization equilibrium and the magnitude of the effect on log g., For this reason we have discussed the effectof NLTE corrections on the ionization equilibrium and the magnitude of the effect on log $g$. Six of the original program stars from Paper I have been analysed to calculate the effects of NLTE on the 7. scale aserived from lines via excitation equilibrium., Six of the original program stars from Paper I have been analysed to calculate the effects of NLTE on the $T_{\rm eff}$ scale derived from lines via excitation equilibrium. We have ound that the effect of the correction is to cause an increase 1 Tay ranging from 2 K to 150 K for Sy =O and 41 K to 122K ateor Sy = I., We have found that the effect of the correction is to cause an increase in $T_{\rm eff}$ ranging from 2 K to 150 K for $\rm S_{H}$ = 0 and 41 K to 122 K for $\rm S_{H}$ = 1. There is one exception; the star CD-—33°1173 has a esoegative correction (—93 K) for the Sy = 0 case., There is one exception; the star $-$ $^{\circ}$ 1173 has a negative correction $-93$ K) for the $\rm S_{H}$ = 0 case. " This may be ue to the limited number of Fe lines available for this star. but also emphasises the intricacies of NLTE work which make it ""Sifficult to make reliable generalisations."," This may be due to the limited number of Fe lines available for this star, but also emphasises the intricacies of NLTE work which make it difficult to make reliable generalisations." Our new temperatures have been compared to the photometric temperatures of ?.. the IRFM of ?.. and the Balmer line wing method of ?..," Our new temperatures have been compared to the photometric temperatures of \citet{Ryanetal1999}, the IRFM of \citet{MelendezRamirez2004}, and the Balmer line wing method of \citet{Asplundetal2006}." We find that the NLTE temperatures are hotter than ? by an average of 132 K for Sy 2 O and 162 K for Sy = I., We find that the NLTE temperatures are hotter than \citet{Ryanetal1999} by an average of 132 K for $\rm S_{H}$ = 0 and 162 K for $\rm S_{H}$ = 1. Similar results are found when comparing against ? with average differences of 76 K and 110 K for Sy = 0 and | respectively., Similar results are found when comparing against \citet{Asplundetal2006} with average differences of 76 K and 110 K for $\rm S_{H}$ = 0 and 1 respectively. The difference between our temperatures and the ? temperatures may be removed if the Balmerline wing method suffers from NLTE effects (?).. or the effects of granulation are properly described.," The difference between our temperatures and the \citet{Asplundetal2006} temperatures may be removed if the Balmerline wing method suffers from NLTE effects \citep{Barklem2007}, , or the effects of granulation are properly described." We find that even with NLTE corrections we are unable to match the high Των ?.., We find that even with NLTE corrections we are unable to match the high $T_{\rm eff}$ \citet{MelendezRamirez2004}. ? (?)., \citet{Hosfordetal2009} \citep{Cyburt2008}. . ," \nocite{*} " 10 line. the distribution is flat up to. probably. 10.,"10 line, the distribution is flat up to, probably, 10." "A,.. We plot the five objects above the line for completeness.", We plot the five objects above the line for completeness. The (wo vertical lines represent the minimum and maximum orbital periods found in the sample., The two vertical lines represent the minimum and maximum orbital periods found in the sample. The ascending line at the bottom of the figure corresponds (o a constant radial-velocity amplitude. A. ofwis.," The ascending line at the bottom of the figure corresponds to a constant radial-velocity amplitude, $K$, of." .. The detection rate of the present planet-search projects below this line is low., The detection rate of the present planet-search projects below this line is low. This is easily seen in the ligure. which includes only five planets below this border line.," This is easily seen in the figure, which includes only five planets below this border line." Again. we plotted these live planets only lor (he sake of completeness.," Again, we plotted these five planets only for the sake of completeness." We assume that planets detected above (hat line have all been reported., We assume that planets detected above that line have all been reported. We now proceed to analyze the 66 planets inside the trapezoid. assuming a constant detection rate over ils area.," We now proceed to analyze the 66 planets inside the trapezoid, assuming a constant detection rate over its area." A close examination of Figure |. reveals a paucity of planets at the corner of the trapezoid., A close examination of Figure \ref{fig1} reveals a paucity of planets at the high-mass--short-period corner of the trapezoid. Onlv three planets appear at that corner., Only three planets appear at that corner. This is certainly nol a selection effect. because planets al that part of the diagram have the largest racial-velocity amplitudes. ancl (therefore are the easiest to detect.," This is certainly not a selection effect, because planets at that part of the diagram have the largest radial-velocity amplitudes, and therefore are the easiest to detect." It is not clear vet what is (he shape of the area in which we find low Irequencey of planets., It is not clear yet what is the shape of the area in which we find low frequency of planets. Tt might have. for example. a rectangular shape bordered by logP=1.6 ancl 0.3. or could have a wedge shape. bordered by the line [rom (logP7.log(M»sin7))=(0.46.0.2) to (1.5.1).," It might have, for example, a rectangular shape bordered by $\log P = 1.6$ and $\log(M_2\sin i)=0.3$ , or could have a wedge shape, bordered by the line from $\left( \log P,\log(M_2\sin i ) \right) = (0.46,0.2)$ to $(1.5,1)$." In any case. it seems (hat there are enough planets in the trapezoid to render this paucitv significant.," In any case, it seems that there are enough planets in the trapezoid to render this paucity significant." To estimate quantitatively (he statistical significance of the high-massshort-period paucity seen in the figure we first consider (he mass-period correlation coefficient. of the sample of planets in the trapezoid., To estimate quantitatively the statistical significance of the high-mass–short-period paucity seen in the figure we first consider the mass-period correlation coefficient of the sample of planets in the trapezoid. The resulting value was 0.661., The resulting value was 0.661. We claim that (is hieh value means (here is a real correlation in the planets population hieher than the one induced by the selection effect., We claim that this high value means there is a real correlation in the planets population — higher than the one induced by the selection effect. In terms of statistical hypotheses testing. we have to reject the null hypothesis that there is no mass-period correlation in (he planets population. and the correlation we find in the sample comes solely from the wedege-shape of the area removed by the selection elfect.," In terms of statistical hypotheses testing, we have to reject the null hypothesis that there is no mass-period correlation in the planets population, and the correlation we find in the sample comes solely from the wedge-shape of the area removed by the selection effect." " To assess (he statistical significance of the null hvpothesis rejection we used simulations in which we created an artificial saunple. randomly drawn out of a two- uniform distribution in loe-mass aud log-period. between the period limits of the trapezoid. ancl between 0.175 and 10M,."," To assess the statistical significance of the null hypothesis rejection we used Monte-Carlo simulations in which we created an artificial sample, randomly drawn out of a two-dimensional uniform distribution in log-mass and log-period, between the period limits of the trapezoid, and between 0.175 and 10." . To simulate the selection effect we have discarded every. planet whose implied radial velocity was (oo small and drawn another one instead. until we had in hand 66 planets.," To simulate the selection effect we have discarded every planet whose implied radial velocity was too small and drawn another one instead, until we had in hand 66 planets." The process was repeated 105 times. calculating the correlation for each simulated sample.," The process was repeated $10^6$ times, calculating the correlation for each simulated sample." Figure 2. shows the histogram of the simulated, Figure \ref{fig2} shows the histogram of the simulated "actual redshift and its photometric redshift, we refer at times to the former quantity as itsredshift.","actual redshift and its photometric redshift, we refer at times to the former quantity as its." . All magnitudes are on the AB system., All magnitudes are on the AB system. " Here we illustrate how it is possible to estimate the distribution of photometric redshift errors in a completely empirical way, even in the absence of spectroscopic redshifts."," Here we illustrate how it is possible to estimate the distribution of photometric redshift errors in a completely empirical way, even in the absence of spectroscopic redshifts." " The underlying principle is that galaxies in an ordinary astronomical image will show significant angular clustering (ie. an excess number of near neighbors over what would be expected from a purely random distribution), which simply reflects the real-space clustering projected on the sky."," The underlying principle is that galaxies in an ordinary astronomical image will show significant angular clustering (i.e. an excess number of near neighbors over what would be expected from a purely random distribution), which simply reflects the real-space clustering projected on the sky." " But the angular clustering arises only from galaxies that are physically associated with each other, and thus lie at (nearly) the same redshift."," But the angular clustering arises only from galaxies that are physically associated with each other, and thus lie at (nearly) the same redshift." " In other words, a sample of all close pairs of objects in an astronomical image will have a random contribution from projected pairs, and an excess contribution from pairs in which both objects lie at the same To demonstrate this principle, we use mock observations generated from the Millennium Simulation (Springeletal."," In other words, a sample of all close pairs of objects in an astronomical image will have a random contribution from projected pairs, and an excess contribution from pairs in which both objects lie at the same To demonstrate this principle, we use mock observations generated from the Millennium Simulation \citep{springel05}." The method used to create these “lightcones” is 2005).described by Kitzbichler&White (2007)., The method used to create these “lightcones” is described by \citet{kitzbichler07}. . We obtained the positions and redshifts of all simulated galaxies down to K=23.9 in a single ~2deg? lightcone from the Millennium database 4., We obtained the positions and redshifts of all simulated galaxies down to $K = 23.9$ in a single $\sim 2 \rm{deg}^2$ lightcone from the Millennium database . ". We select objects with 0.9«z1.0 in the lightcone, and determine the redshift distribution of all objects lying within a small angular separation of the selected objects."," We select objects with $0.9=3.6617 in the spectrum of this quasar., There is a LLS absorber at $z=3.6617$ in the spectrum of this quasar. There are two relatively bright candidates in this field., There are two relatively bright candidates in this field. With FORS on the ΝΕΤ we have obtained a spectrum of the brightest source N-15-2C. which lies at an angular separation of1.," With FORS on the VLT we have obtained a spectrum of the brightest source N-15-2C, which lies at an angular separation of." "53”.. ""Phis spectrum shows that the candidate source is a quasar al the same redshift as 1626 {rw spectrum will be presented in a future paper describing spectroscopy of our NICALOS and STIS candidates).", This spectrum shows that the candidate source is a quasar at the same redshift as $-$ 1626 (the spectrum will be presented in a future paper describing spectroscopy of our NICMOS and STIS candidates). While the hypothesis requires. further investigation al present we consider it unlikely that this is a gravitational lens svstem. as we see no sign of a lensing galaxy in our NICMOS image.," While the hypothesis requires further investigation at present we consider it unlikely that this is a gravitational lens system, as we see no sign of a lensing galaxy in our NICMOS image." Phe faint dilfuse source N-16- with ILig=25.05 is the counterpart of the LLS at 2= 3.1501., The faint diffuse source N-16-1D with ${\mathrm H_{AB}=25.05}$ is the counterpart of the LLS at $z=3.1501$ . " This object was first. detected. ancl proposed as the couterpart. by Steidel. Pettini. and. Hamilton. (1995r) who measured. an olfset. from. the quasar of 2.97. in agreement with our value of 2.78""."," This object was first detected, and proposed as the couterpart, by Steidel, Pettini, and Hamilton (1995), who measured an offset from the quasar of $2.9\arcsec$, in agreement with our value of $2.78\arcsec$." " ""Phe object was discoverce independently by Djorgovski ct al (1996). who confirmed the identification through the spectroscopic detection of emission."," The object was discovered independently by Djorgovski et al (1996), who confirmed the identification through the spectroscopic detection of emission." They. quote a smaller. ollset of 2.37., They quote a smaller offset of $2.3\arcsec$. Εμ» object has also been detected. in our STIS image (Moller et al. in preparation).," This object has also been detected in our STIS image ller et al, in preparation)." As with the quasar 1005 13 after psf subtraction there is residual emission close to the quasar. inside our detection radius limit. which we do not believe is associated with the absorber.," As with the quasar $\#$ 13 after psf subtraction there is residual emission close to the quasar, inside our detection radius limit, which we do not believe is associated with the absorber." Ixullkarni et al. (, Kulkarni et al. ( "2000) observed the quasar LBOS 1210|1731 with the NIC2 camera and FIGOW filter for a single orbit (2560 sec integration time). and detected a candidate DLA absorber counterpart at an impact parameter of 0.25"". at dle significance.","2000) observed the quasar LBQS 1210+1731 with the NIC2 camera and F160W filter for a single orbit (2560 sec integration time), and detected a candidate DLA absorber counterpart at an impact parameter of $0.25\arcsec$, at $4.1\sigma$ significance." The object is compact ancl would lave an aperture magnitude of ILig=21.57.," The object is compact and would have an aperture magnitude of ${\mathrm H_{AB}=21.87}$." This object is rather bright., This object is rather bright. Placing it in Fig., Placing it in Fig. 4 it can be seen hat it is more than three magnitudes brighter than the hree spectroscopcially confirmed DLA galaxy counterparts (1Lig=25.05.25.11. 25.54). indicated. by triangles.," 4 it can be seen that it is more than three magnitudes brighter than the three spectroscopcially confirmed DLA galaxy counterparts ${\mathrm H_{AB}=25.05, 25.11, 25.54}$ ), indicated by triangles." As seen in Fie., As seen in Fig. ὃν 4. our averageo detection limit becomes rapidly brighter at Lgsmall impact. parameters.," 4, our average detection limit becomes rapidly brighter at small impact parameters." Nevertheless heir object lies well above our 60. detection limits., Nevertheless their object lies well above our $6\sigma$ detection limits. Our average limit for compact objects at 0.37 is Lhye=23:87. with range 22.49 to 25.33 (able 3). so we would easily nave detected. a similar object in any of our frames.," Our average limit for compact objects at $0.3 \arcsec$ is ${\mathrm H_{AB}=23.87}$, with range 22.49 to 25.33 (Table 3), so we would easily have detected a similar object in any of our frames." Indeed we do find a few bright candidates at small impact xwameters., Indeed we do find a few bright candidates at small impact parameters. " However we have chosen. conservatively. not to ist candidates inside 0.56"" Lor the reasons set out in section 2.4."," However we have chosen, conservatively, not to list candidates inside $0.56\arcsec$ for the reasons set out in section 2.4." The accuracy of psf subtraction of the two methods appears to be comparable., The accuracy of psf subtraction of the two methods appears to be comparable. We compute an equivalent detection. limit for thew data of τν=99.193. by scaling their measured noise at 0.37 (O.28yely por pixel) to our longer integration time.," We compute an equivalent detection limit for their data of ${\mathrm H_{AB}=22.12}$, by scaling their measured noise at $0.3\arcsec$ $0.28\mu$ Jy per pixel) to our longer integration time." " ""Their quasar has dlig—16.950.05. (total. P Lewett. private communication). similar in brightness to our two brightest targets. quasars 13 and. 14."," Their quasar has ${\mathrm H_{AB}=16.95\pm0.05}$ (total, P Hewett, private communication), similar in brightness to our two brightest targets, quasars 13 and 14." Our detection limits for these (quasars are ον | 22.49., Our detection limits for these quasars are 22.72 and 22.49. In this paper we have described a search. for the galaxy counterparts of 23 high-redshift’ high-column clensity Lye absorbers seen in the spectra of 16 quasars. using the LIST NICMOS instrument.," In this paper we have described a search for the galaxy counterparts of 23 high-redshift high-column density $\alpha$ absorbers seen in the spectra of 16 quasars, using the HST NICMOS instrument." " Within a box of side 7.5"" centred on each quasar. over all the fields we have found a total of 41 candidates. of which 3 have already. been confirmed spectroscopically as the counterparts."," Within a box of side $7.5\arcsec$ centred on each quasar, over all the fields we have found a total of 41 candidates, of which 3 have already been confirmed spectroscopically as the counterparts." We provide detection imits as a function of impact parameter for cach field. and the use of aperture magnitudes makes it very. simple o compute whether a hypothetical galaxy of. specified uminositv profile ancl impact parameter would have been detected. in our survey.," We provide detection limits as a function of impact parameter for each field, and the use of aperture magnitudes makes it very simple to compute whether a hypothetical galaxy of specified luminosity profile and impact parameter would have been detected in our survey." " Our aperturc-magnitucde detection imits το~25. the small minimum. impact parameter 156"". and the sample size make this the most. sensitive search vet made for the galaxies producing high-redshift DLA absorption lines."," Our aperture-magnitude detection limits ${\mathrm H_{AB}\sim 25}$, the small minimum impact parameter $0.56\arcsec$, and the sample size make this the most sensitive search yet made for the galaxies producing high-redshift DLA absorption lines." At the same time we are obtaining verv-deep optical images using STIS. which will provide an additional list of candidates (Moller et al..," At the same time we are obtaining very-deep optical images using STIS, which will provide an additional list of candidates ller et al.," in preparation)., in preparation). Except for unusually red. galaxies the STIS. images wil reach substantially deeper than the NICMOS images. ane vwerelore can be used to check the reliability of the cancliclate list. provided. in Table 4.," Except for unusually red galaxies the STIS images will reach substantially deeper than the NICMOS images, and therefore can be used to check the reliability of the candidate list provided in Table 4." X. discussion. of the conclusions iu may be drawn from the imaging data. and the lLimitec spectroscopic follow-up so far completed. is deferred to the ulTIS paper.," A discussion of the conclusions that may be drawn from the imaging data, and the limited spectroscopic follow-up so far completed, is deferred to the STIS paper." The next stage of this programme is a campaign of spectroscopy to measure the redshifts of the candidates. o identify which are counterparts of the absorbers.," The next stage of this programme is a campaign of spectroscopy to measure the redshifts of the candidates, to identify which are counterparts of the absorbers." Since re galaxies are mostly faint. and close to the quasar. redshift’ determination will be cifficult.," Since the galaxies are mostly faint, and close to the quasar, redshift determination will be difficult." The best hope will x» to detect Lye emission., The best hope will be to detect $\alpha$ emission. Although this line is reaclilv extinguished by dust. ancl therefore may be weak. it is likely o be the easiest to detect because at this wavelength the ight from the quasar is removed by the absorber itself.," Although this line is readily extinguished by dust, and therefore may be weak, it is likely to be the easiest to detect because at this wavelength the light from the quasar is removed by the absorber itself." We are grateful to Beth Perriello (our STSel Program Coordinator) and Al Schultz (our STSel Contact Scientist) for help during the design and execution of the programme. and to Mark Dickinson for detailed guidance on how best to reduce the data.," We are grateful to Beth Perriello (our STScI Program Coordinator) and Al Schultz (our STScI Contact Scientist) for help during the design and execution of the programme, and to Mark Dickinson for detailed guidance on how best to reduce the data." formation and stellar feedback are modeled with subgrid recipes as described in Stinsonetal.(2006).,formation and stellar feedback are modeled with subgrid recipes as described in \citet{Stinson2006}. ". Importantly, the stellar feedback prescriptions include SN II, SN Ia and AGB metal production, as well as injection of supernova energy which impacts the thermodynamic properties of the disk interstellar medium (ISM)."," Importantly, the stellar feedback prescriptions include SN II, SN Ia and AGB metal production, as well as injection of supernova energy which impacts the thermodynamic properties of the disk interstellar medium (ISM)." Metal diffusion is calculated from a subgrid model of eddy turbulence based on the local smoothing length and velocity gradients (Smagorinsky1963;Wadsleyetal. 2008).," Metal diffusion is calculated from a subgrid model of eddy turbulence based on the local smoothing length and velocity gradients \citep{Smagorinsky1963, Wadsley2008}." ". The simulation we utilize is nearly identical to R08ab RO8ab for further details), but with the addition of (seemetal diffusion (Shenetal.2009)."," The simulation we utilize is nearly identical to R08ab (see R08ab for further details), but with the addition of metal diffusion \citep{Shen2009}." . No assumptions about the disk’s structure are made — its growth and the subsequent evolution of its stellar populations are completely spontaneous and governed only by hydrodynamics/stellar feedback and gravity., No assumptions about the disk's structure are made — its growth and the subsequent evolution of its stellar populations are completely spontaneous and governed only by hydrodynamics/stellar feedback and gravity. " Although we do not account for the full cosmological context, merging in the ACDM paradigm is a higher order effect at the epochs in question (Brooketal.2005)."," Although we do not account for the full cosmological context, merging in the $\Lambda$ CDM paradigm is a higher order effect at the epochs in question \citep{Brook2005}." ". Thus, our model galaxy lacks some structural components such as a stellar halo, which in ACDM is built up primarily during the merging process (e.g.Bullock&Johnston2005;Zolotovetal.2009)."," Thus, our model galaxy lacks some structural components such as a stellar halo, which in $\Lambda$ CDM is built up primarily during the merging process \citep[\eg][]{Bullock2005, Zolotov2009}." ". Our focus here, however, is disk evolution; by simplifying our assumptions, we are able to use much higher resolution and more easily study the impact of key dynamical effects on observational properties of stellar populations within the disk."," Our focus here, however, is disk evolution; by simplifying our assumptions, we are able to use much higher resolution and more easily study the impact of key dynamical effects on observational properties of stellar populations within the disk." " Based on such simulations, RO8ab presented the implications of stellar radial migration resulting from the interactions of stars with transient spiral arms (Sellwood&Binney on the observable properties of disk stellar populations."," Based on such simulations, R08ab presented the implications of stellar radial migration resulting from the interactions of stars with transient spiral arms \citep{Sellwood2002} on the observable properties of disk stellar populations." "2002) Radial migration efficiently mixes stars throughout the disk into the solar neighborhood, resulting in a flattened age-metallicity relation (R08ab)."," Radial migration efficiently mixes stars throughout the disk into the solar neighborhood, resulting in a flattened age-metallicity relation (R08ab)." " Figures 1,, 2,, 3 illustrate the basic premise of this paper — stars migrate radially and in the process rise out of the plane over time, so many stars are presently not near their birth place."," Figures \ref{f:rform}, \ref{f:rform_cont}, \ref{f:rform_cont_comp} illustrate the basic premise of this paper — stars migrate radially and in the process rise out of the plane over time, so many stars are presently not near their birth place." Previous studies have shown (Loebmanetal.2008;Sales2009;CaruanaSchónrich&Binney2009) that the vertical evolution that results from radial migration can influence the characterization of the thick disk.," Previous studies have shown \citep{Loebman2008, Sales2009, Caruana2009, Schoenrich2009} that the vertical evolution that results from radial migration can influence the characterization of the thick disk." " In order to further illustrate the importance of radial migration within our adopted Milky Way (MW) simulation, we have repeated much of our analysis on a control case."," In order to further illustrate the importance of radial migration within our adopted Milky Way (MW) simulation, we have repeated much of our analysis on a control case." The control simulation is a system with the same initial conditions as the MW simulation except for having a higher angular momentum content with a dimensionless spin parameter A=0.1 (Bullocketal., The control simulation is a system with the same initial conditions as the MW simulation except for having a higher angular momentum content with a dimensionless spin parameter $\lambda = 0.1$ \citep{Bullock2001}. " This results in a more extended disk (final disk scale-length2001).. =5.04 kpc, versus 3.23 kpc for the MW simulation), possibly similar to a low surface brightness galaxy; we therefore refer to this simulation as the LSB simulation."," This results in a more extended disk (final disk scale-length $= 5.04$ $\kpc$, versus $3.23$ $\kpc$ for the MW simulation), possibly similar to a low surface brightness galaxy; we therefore refer to this simulation as the LSB simulation." " Due to its lower surface density, the disk forms weaker spirals and as a result the stellar populations at all radii are less affected by radial mixing."," Due to its lower surface density, the disk forms weaker spirals and as a result the stellar populations at all radii are less affected by radial mixing." " When we compare migration as a function of scale-lengths, we find that there is significantly less migration in the LSB galaxy than inthe MW galaxy."," When we compare migration as a function of scale-lengths, we find that there is significantly less migration in the LSB galaxy than inthe MW galaxy." " The distribution of stellar mass away from the midplane is strongly affected by radial migration; this can be seen in Figure 4,, which contrasts the MW simulation against the LSB case."," The distribution of stellar mass away from the midplane is strongly affected by radial migration; this can be seen in Figure \ref{f:density_comp}, , which contrasts the MW simulation against the LSB case." Here the normalized mass density, Here the normalized mass density a resolution of Pspwg=4/3.,"a resolution of $b_{\rm{SD,FWHM}}=4\farcm3$." In this case we cannot directly compare the visibilities in the plane. since the data is multiplied by the Fourier transform of the convolving beam. Psp.," In this case we cannot directly compare the visibilities in the plane, since the data is multiplied by the Fourier transform of the convolving beam, $b_{\rm{SD}}$." In the map plane. however. we can recover usable datasets for comparison when the MEM method of deconvolution is applied.," In the map plane, however, we can recover usable datasets for comparison when the MEM method of deconvolution is applied." In brief. when deconvolving interferometric data using the algorithm a recovered sky will have the form: where /(/.m) is the true sky distribution. B(/.77) is the primary beam response and fo(/.r) is the clean beam.," In brief, when deconvolving interferometric data using the algorithm a recovered sky will have the form: where $I(l,m)$ is the true sky distribution, $B(l,m)$ is the primary beam response and $b_0(l,m)$ is the clean beam." In the case where we sample single dish data our input intensity distribution is no longer the true sky but instead a model sky. which is the convolution of the true sky with the single dish beam. /'(J.m)—Hm)xbsp.," In the case where we sample single dish data our input intensity distribution is no longer the true sky but instead a model sky, which is the convolution of the true sky with the single dish beam, $I'(l,m) = I(l,m)\ast b_{\rm{SD}}$." Since this convolution is non-associative with the multiplication by the primary beam response. the two maps cannot be quantitatively compared.," Since this convolution is non-associative with the multiplication by the primary beam response, the two maps cannot be quantitatively compared." However. if instead we choose to deconvolve using an MEM method. such as the AIPS task VTESS. the primary beam response is accounted for in the fitting.," However, if instead we choose to deconvolve using an MEM method, such as the AIPS task VTESS, the primary beam response is accounted for in the fitting." MEM lets us recover: Since convolution is associative with itself we can then convolve our own AMI data to match our sampled data., MEM lets us recover: Since convolution is associative with itself we can then convolve our own AMI data to match our sampled data. We do this by deconvolving the AMT data using WTESS to recover IH.m)sbo(l.m) and convolving this recovered map with the single dish beam sp.," We do this by deconvolving the AMI data using VTESS to recover $I(l,m)\ast b_0(l,m)$ and convolving this recovered map with the single dish beam $b_{\rm{SD}}$." This will result in our comparison maps. both the sampled data and the convolved AMI data. having a clean beam of b(l.m)=xbotl.m)—bsp.m).," This will result in our comparison maps, both the sampled data and the convolved AMI data, having a clean beam of $b(l,m) = \sqrt{b_0(l,m)^2 + b_{\rm{SD}}(l,m)^2}$." We note that this process will degrade the original AMI data. however it results in maps which have identical resolution and contain the same angular scales.," We note that this process will degrade the original AMI data, however it results in maps which have identical resolution and contain the same angular scales." The morphology of the sources in these observations is often not well described by a Gaussian fit., The morphology of the sources in these observations is often not well described by a Gaussian fit. We therefore estimate their flux densities by removing a tilted plane fitted to the local background and integrating the remaining flux. see for example Green (2007).," We therefore estimate their flux densities by removing a tilted plane fitted to the local background and integrating the remaining flux, see for example Green (2007)." We do this by drawing a polygon around each source and fitting a ilted plane to the pixels around the edge of the polygon., We do this by drawing a polygon around each source and fitting a tilted plane to the pixels around the edge of the polygon. Where an edge of the polygon crosses a region confused by another source the background is subjective and we omit this edge from the fitting., Where an edge of the polygon crosses a region confused by another source the background is subjective and we omit this edge from the fitting. Example polygons are shown in e.g. Fig., Example polygons are shown in e.g. Fig. 2. with omitted edges shown as dashed lines., \ref{fig:l675both} with omitted edges shown as dashed lines. Where we believe there may be some confusion as to the aperture selected in what follows we qyave depicted an example aperture in the same way. see the figure captions for details.," Where we believe there may be some confusion as to the aperture selected in what follows we have depicted an example aperture in the same way, see the figure captions for details." Since this method is dependent to some degree on the aperture selected around the source we perform five fits or each object changing the aperture slightly each time. and take he flux density as the average of these fits.," Since this method is dependent to some degree on the aperture selected around the source we perform five fits for each object changing the aperture slightly each time, and take the flux density as the average of these fits." The vertices of these apertures are listed in Appendix A2., The vertices of these apertures are listed in Appendix A2. We denote the variance of hese fits as on and include it in the final error on the calculated flux density as: Here we represent the r.m.s., We denote the variance of these fits as $\sigma_{\rm{fit}}^2$ and include it in the final error on the calculated flux density as: Here we represent the r.m.s. " fluctuations outside the primary beam measured from the map as oj, and the flux density of the source as S.", fluctuations outside the primary beam measured from the map as $ \sigma_{\rm{rms}}$ and the flux density of the source as $S$. This calculation assumes a conservative 5 percent error on the flux calibration., This calculation assumes a conservative 5 percent error on the flux calibration. We note that images made using CLEAN are often systematically different to. those made using MEM through VTESS., We note that images made using CLEAN are often systematically different to those made using MEM through VTESS. The major. although not only. difference arises due to the positive definite nature of the model assumed in VTESS.," The major, although not only, difference arises due to the positive definite nature of the model assumed in VTESS." This has the effect of raising the background level in images reconstructed by VTESS relative to those made using CLEAN., This has the effect of raising the background level in images reconstructed by VTESS relative to those made using CLEAN. Consequently it is nof recommended to use these MEM reconstructions for comparison with images restored with CLEAN., Consequently it is not recommended to use these MEM reconstructions for comparison with images restored with CLEAN. Our method of flux extraction acts to mitigate this effect through subtracting a tilted plane., Our method of flux extraction acts to mitigate this effect through subtracting a tilted plane. However. we note that we have not used MEM images for quantitative comparison except in the case of L675 where we have compared like with like.," However, we note that we have not used MEM images for quantitative comparison except in the case of L675 where we have compared like with like." In later sections we have sometimes included a flux density recovered using an MEM map to enhance a flux spectrum. but this is purely for illustrative purposes and will be explicitly commented upon in the text.," In later sections we have sometimes included a flux density recovered using an MEM map to enhance a flux spectrum, but this is purely for illustrative purposes and will be explicitly commented upon in the text." " We reiterate: Case (1) employs CLEAN deconvolution, Case (2) employs MEM deconvolution."," We reiterate: Case (1) employs CLEAN deconvolution, Case (2) employs MEM deconvolution." The SCUBA data of Visser et al. (, The SCUBA data of Visser et al. ( 2001:2002) in conjunction with IRAS data available from the literature allows us to place constraints on the thermal dust spectrum of these objects and their dust temperature. 77.,"2001;2002) in conjunction with IRAS data available from the literature allows us to place constraints on the thermal dust spectrum of these objects and their dust temperature, $T_d$." Following Andre. Ward-Thompson Barsony (1993) we use a modified greybody spectrum of the form to fit these data. where By(7) is the Planck spectrum for a temperature 77; at a frequency v.," Following Andre, Ward-Thompson Barsony (1993) we use a modified greybody spectrum of the form to fit these data, where $B_{\nu}(T_d)$ is the Planck spectrum for a temperature $T_d$ at a frequency $\nu$." " τν is the optical depth of the cloud. generally assumed to be proportional to v!2. and Ως, is the extent of the source at a given frequency."," $\tau_{\nu}$ is the optical depth of the cloud, generally assumed to be proportional to $\nu^{1.5}$, and $\Omega_{S,\nu}$ is the extent of the source at a given frequency." " The inclusion of Ως, allows us to account for the different source sizes seen by IRAS and SCUBA."," The inclusion of $\Omega_{S,\nu}$ allows us to account for the different source sizes seen by IRAS and SCUBA." In this section we describe the radio emission seen towards the Lynds dark nebulae listed in Table | between 14.2 and GGHz., In this section we describe the radio emission seen towards the Lynds dark nebulae listed in Table \ref{tab:lclouds} between 14.2 and GHz. Sources are listed in Table 2.., Sources are listed in Table \ref{tab:list}. In what follows we identify potential excess microwave emission from the SCUBA clouds as any source which falls within a 2aaremin radius of the SCUBA position and which shows an excess of emission relative to lower frequency radio data., In what follows we identify potential excess microwave emission from the SCUBA clouds as any source which falls within a arcmin radius of the SCUBA position and which shows an excess of emission relative to lower frequency radio data. In addition. any source which satisties these two criteria but has a falling spectrum across the AMI band will be rejected as a spinning dust candidate.," In addition, any source which satisfies these two criteria but has a falling spectrum across the AMI band will be rejected as a spinning dust candidate." This allows us to distinguish those sources which may be optically thick at lower radio frequencies. but have spectra which turn over before the AMI band.," This allows us to distinguish those sources which may be optically thick at lower radio frequencies, but have spectra which turn over before the AMI band." All errors are quoted tolo., All errors are quoted to $\sigma$. L675 shows a large radio counterpart at GGHz., L675 shows a large radio counterpart at GHz. This region lies outside the the limits of the CGPS data. however it is covered by NVSS at GGHz. Effelsberg at GGHz and the," This region lies outside the the limits of the CGPS data, however it is covered by NVSS at GHz, Effelsberg at GHz and the" accreting black hole svstem (Gaskell 1988). or biconical outflows (Zheng et al.,"accreting black hole system (Gaskell 1988), or biconical outflows (Zheng et al." 1991)., 1991). ETIIO3 and S03 argued (hat the observed properties of double-peaked line emitters favor the disk line model (see also Halpern Filippenko 1983)., EH03 and S03 argued that the observed properties of double-peaked line emitters favor the disk line model (see also Halpern Filippenko 1988). " By applving relativistic disk models to the double-peaked line profiles. thev suggested that inner disk radii are around 200—800r, /c) and outer radii larger than 2.000r,. and that significant deviation from circular. relativistic IXeperian clisk is required in about 40-60% of the objects (803: ELIO3)."," By applying relativistic disk models to the double-peaked line profiles, they suggested that inner disk radii are around $-$ $r_g$ $r_g\equiv GM/c^2$ ) and outer radii larger than $r_g$, and that significant deviation from circular, relativistic Keperian disk is required in about $-$ of the objects (S03; EH03)." Relativistic disk lines have also been detected in A-ray band (e.g.. Fe Ίνα line: Fabian οἱ al.," Relativistic disk lines have also been detected in X-ray band (e.g., Fe $\alpha$ line; Fabian et al." 2000)., 2000). " These lines are produced at much smaller racii(<10r,).", These lines are produced at much smaller $\le 10r_g$ ). X-ray eniission lines from the disk at larger radii might also have been detected. but cannot be confirmed up to now due to the limitation of the spectral resolution and sensitivity of current X-ray missions (e.g.. Lu Wang 2000).," X-ray emission lines from the disk at larger radii might also have been detected, but cannot be confirmed up to now due to the limitation of the spectral resolution and sensitivity of current X-ray missions (e.g., Lu Wang 2000)." In this paper. we report the discovery of two extreme clouble- lime emitters SDSS JO94215.1+090015 (SDSS J0942--0900: z=0.21262) and SDSS J141742.952-614152 (SDSS J14172-6141: z=0.119) in the Sloan Digital Skv Survey (SDSS: York et al.," In this paper, we report the discovery of two extreme double-peaked line emitters SDSS J094215.1+090015 (SDSS J0942+0900; z=0.21262) and SDSS J141742.95+614152 (SDSS J1417+6141; z=0.119) in the Sloan Digital Sky Survey (SDSS: York et al." 2000) data release 3 (DR3: Abazajian et al., 2000) data release 3 (DR3: Abazajian et al. 2005)., 2005). It was noticed for its anomalous emission lines during our svstematic modelling of the continuum and emission lines of SDSS spectra classilied as QSO or galaxies bv the SDSS pipeline., It was noticed for its anomalous emission lines during our systematic modelling of the continuum and emission lines of SDSS spectra classified as QSO or galaxies by the SDSS pipeline. The PSF magnitudes (AB) are 17.921. 17.387. 16.946. 16.688. 16.552. in u. gor. ? and z. respectively.," The PSF magnitudes (AB) are 17.921, 17.387, 16.946, 16.688, 16.552, in $u$, $g$, $r$, $i$ and $z$, respectively." It was detected in the 2 Micron. All Sky Survev. (241A55) with total magnitudes of 15.482:0.06.. 14.98+0.09 ancl 14.3040.06 in J. ID and Ix; bands. respectively. aud in the FIRST strvev (White οἱ al.," It was detected in the 2 Micron All Sky Survey (2MASS) with total magnitudes of $\pm$ 0.06, $\pm$ 0.09 and $\pm$ 0.06 in J, H and $_s$ bands, respectively, and in the FIRST survey (White et al." 1997) with a radio flux of 1.9340.15 mJv al 20 cm and a compact radio morphology., 1997) with a radio flux of $\pm$ 0.15 mJy at 20 cm and a compact radio morphology. " Following Ivezié et al (2002). we find the ratio of radio-to-optical [lux density R;=log(fsu4,//;)0.58. where f; ancl foun, are the flux densities at Z-band and 20 cm. respectively."," Following Ivezić et al (2002), we find the ratio of radio-to-optical flux density $R_i \equiv \log (f_{20cm}/f_i)=0.58$, where $f_i$ and $f_{20cm}$ are the flux densities at -band and 20 cm, respectively." Thus this quasar is radio quiet., Thus this quasar is radio quiet. " The spectral energy distribution (SED: »/,) peaks at the near-infrared. which is also typical for double-peaked line objects (E403)."," The spectral energy distribution (SED; $\nu f_\nu$ ) peaks at the near-infrared, which is also typical for double-peaked line objects (EH03)." The optical spectrum of SDSS J0942--0900 in the source rest frame. after correction for Galactic reddening of E(B-V)=0.031 mag (Schlegel et al.," The optical spectrum of SDSS J0942+0900 in the source rest frame, after correction for Galactic reddening of $-$ V)=0.031 mag (Schlegel et al." 1993). is presented in Figure 1.," 1998), is presented in Figure 1." The most surprising characteristic is (he presence of very broad. double-peaked Balmer lines.," The most surprising characteristic is the presence of very broad, double-peaked Balmer lines." The line profile of broad Ha extends over a wavelength range of about in the source rest fraane., The line profile of broad $\alpha$ extends over a wavelength range of about in the source rest frame. . The Ilo line displavs a similar profile. but its blue peak is blended with the expected red peak of the H5 line.," The $\beta$ line displays a similar profile, but its blue peak is blended with the expected red peak of the $\gamma$ line." Similar profiles may also be present in higher order Balmer lines. but it is diffieult to identify them due to their weakness and the effect of line-blencdiug.," Similar profiles may also be present in higher order Balmer lines, but it is difficult to identify them due to their weakness and the effect of line-blending." "on the dynamics of the disk, beyond setting the time-scale on which the Kozai effect operates, provided that itis large enough that condition (7)) is satisfied.","on the dynamics of the disk, beyond setting the time-scale on which the Kozai effect operates, provided that it is large enough that condition \ref{condition}) ) is satisfied." " In this section, we shall assume that the nodal reference plane of the disk precesses rigidly, and the disk remains un-warped."," In this section, we shall assume that the nodal reference plane of the disk precesses rigidly, and the disk remains un-warped." " In other words, we assume that no mutual inclination is excited between neighboring disk annuli."," In other words, we assume that no mutual inclination is excited between neighboring disk annuli." " This feature is implicitly essential to our argument, and we will justify this assumption quantitatively in the next section."," This feature is implicitly essential to our argument, and we will justify this assumption quantitatively in the next section." " In accord with the reasoning outlined above, we solely retain the Kozai term in the disturbing potential of the stellar companion."," In accord with the reasoning outlined above, we solely retain the Kozai term in the disturbing potential of the stellar companion." " Consequently, the planetesimal's Hamiltonian now reads (KinoshitaandNakai,1999) "," Consequently, the planetesimal's Hamiltonian now reads \citep{1999CeMDA..75..125K} " This can be understood intuitively in the following way.,This can be understood intuitively in the following way. " The conservation of the Poincaré integral invariant. with (he sum taken over coordinate dimensions. along any trajectory implies sviupleclicily (recall (hat shows that conservation of the Qvo-form O40,off(.a.d⋅⋅⋅⋅⋅4d)daydqo on state space implies conservation of Z on phase space)."," The conservation of the Poincaré integral invariant, with the sum taken over coordinate dimensions, along any trajectory implies symplecticity (recall that shows that conservation of the two-form $\partial_1 \partial_{n+2} H\left( h, q_1, q'_1, \ldots, q_1^{(n)}, q_2 \right) dq_1 \wedge dq_2$ on state space implies conservation of $\mathcal{I}$ on phase space)." Note that dq! ancl dp; are exterior derivatives and that Z is a (wo-form., Note that $dq^i$ and $dp_i$ are exterior derivatives and that $\mathcal{I}$ is a two-form. The Poincaré integral invariant measures the stun of the areas of a tube of trajectories infinitesimally near a reference trajectory. projected onto the sub-phase-spaces (d.pj).," The Poincaré integral invariant measures the sum of the areas of a tube of trajectories infinitesimally near a reference trajectory projected onto the sub-phase-spaces $\left(q^i, p_i\right)$." But an integrator with an adaptive timestep does not advance all trajectories in the tube with the same ., But an integrator with an adaptive timestep does not advance all trajectories in the tube with the same $h$. Even if we had an adaptive timestep integrator which implemented the exact. continuous evolution of the svstem it still would not conserve A over a single stepstopping the evolution of the different. trajectories in (he tube at different (mes spoils the svanplecticity of the continuous evolution.," Even if we had an adaptive timestep integrator which implemented the exact, continuous evolution of the system it still would not conserve $\mathcal{I}$ over a single step—stopping the evolution of the different trajectories in the tube at different times spoils the symplecticity of the continuous evolution." For an adaptive timestep integrator sviplecticitv after a fixed number of stepsconsider., For an adaptive timestep integrator symplecticity after a fixed number of steps. Rather. we should ask whether the integrator conserves (he svinplectic form over a fixed total time of evolution.," Rather, we should ask whether the integrator conserves the symplectic form over a fixed total time of evolution." In general. any integrator (including a variational integrator with general adaptive stepsizes) which has trajectory. error of order h conserves (he svinplectic form at least to order in (his sense.," In general, any integrator (including a variational integrator with general adaptive stepsizes) which has trajectory error of order $h^r$ conserves the symplectic form at least to order $h^r$ in this sense." For variational integrators which choose timesteps using the popular block-power-of-two scheme we can do better: these integrators conserve the sviiplectic form almost evervwhere in phase space., For variational integrators which choose timesteps using the popular block-power-of-two scheme we can do better: these integrators conserve the symplectic form almost everywhere in phase space. " In the block-power-ol-lwo scheme. a function μιας(a.qiquU.) limits (he maxinunm timestep: the actual timestep taken is rounded down from P544; to the nearest number of the form 7/2"". with nv an integer. ancl 7 some total evolution interval."," In the block-power-of-two scheme, a function $h_{\rm{max}}\left( q_1, q'_1, \ldots, q_1^{(n)}, q_2 \right)$ limits the maximum timestep; the actual timestep taken is rounded down from $h_{\rm{max}}$ to the nearest number of the form $T/2^n$, with $n$ an integer, and $T$ some total evolution interval." II the [Iunction P444 is continuous. about every point in state space for which for some n there is an open neighborhood of points which round down to the same timestep.," If the function $h_{\rm{max}}$ is continuous, about every point in state space for which $h_{\rm{max}}\left( q_1, q'_1, \ldots, q_1^{(n)}, q_2 \right) \neq T/2^n$ for some $n$ there is an open neighborhood of points which round down to the same timestep." Thus. the actual timestep function 7(n.qei) js piecewise-constant on state space. and the derivatives in equation vanish almost evervwhere on state space for each step.," Thus, the actual timestep function $h\left(q_1, q'_1, \ldots, q_1^{(n)}, q_2 \right)$ is piecewise-constant on state space, and the derivatives in equation vanish almost everywhere on state space for each step." " A variational integrator with adaptive block-power-ol-two timesteps is therefore svinplectic almost. evervwhere on state space because il is a composition of svmplectic steps. (""", A variational integrator with adaptive block-power-of-two timesteps is therefore symplectic almost everywhere on state space because it is a composition of symplectic steps. (“ "Almost everywhere” should be taken in the mathematical sense of ""except on a",Almost everywhere” should be taken in the mathematical sense of “except on a " Collisional ring galaxies. of which he Cartwheel is the “prototypical” candidate. are believed. to forma when an “intruder” ealaxv passes through the ceuter of a rotating disk of a larecr ""target ealaxy (Lyvuds Toommre 1976: Thevs Spiegel 1976: Appletou Struck-Marcell 1996 απ references therein)."," Collisional ring galaxies, of which the Cartwheel is the “prototypical” candidate, are believed to form when an “intruder” galaxy passes through the center of a rotating disk of a larger “target” galaxy (Lynds Toomre \cite{lt}; Theys Spiegel \cite{ts}; ; Appleton Struck-Marcell \cite{rings} and references therein)." The perturbation trigecrs a radially expanding rine-like deusitv wave ou the disk. causing massive star formation iu the rine (sec Appleton Marston 1997)).," The perturbation triggers a radially expanding ring-like density wave on the disk, causing massive star formation in the ring (see Appleton Marston \cite{ring97}) )." The svuuuetry and well defined dynamical history of rime galaxies has made them. ideal candidates for studies of the phase transition of the interstellar medium due to collisionally iuduced. star formation., The symmetry and well defined dynamical history of ring galaxies has made them ideal candidates for studies of the phase transition of the interstellar medium due to collisionally induced star formation. " The Cartwheel galaxy owas discovered bx Zwickv (1911)) at oa distance of 121 Alpe (IL,— I iy ", The Cartwheel galaxy was discovered by Zwicky \cite{zwicky}) ) at a distance of 121 Mpc $_{o}$ $^{-1}$ $^{-1}$ ). Tt das a bright outer rue and au inner rime which is connected to the outer one with a series of spokes (see Iiedou 1996 Fie., It has a bright outer ring and an inner ring which is connected to the outer one with a series of spokes (see Higdon \cite{jim_hi} Fig. 1)., 1). Three «ια. companion galaxies locate north aud uorth-cast of the ring complete the eroup., Three small companion galaxies located north and north-east of the ring complete the group. It is still unclear which of the companions is the culprit for the creation of the Cartwheel rine (Davies Morton 1982: Struck-Marcel Iliedou. 1993)). but it is likely that each of them contaius sufficient ass to trigger the generation of the star forming rine (see discussion bv Appleton Struck-Miucell 1996)).," It is still unclear which of the companions is the culprit for the creation of the Cartwheel ring (Davies Morton \cite{dm}; Struck-Marcel Higdon \cite{curt_jim}) ), but it is likely that each of them contains sufficient mass to trigger the generation of the star forming ring (see discussion by Appleton Struck-Marcell \cite{rings}) )." Ou-eoing efforts to simulate the οπαήος o the system have been focused on the nearby colupanion G2 (Dosmia priv., On-going efforts to simulate the dynamics of the system have been focused on the nearby companion G2 (Bosma priv. commun.), comm.) aud on the most distant one. C3. (Struck L997:: EHorelou priv.," and on the most distant one, G3, (Struck \cite{curt}; Horellou priv." cou.), comm.) which seenas to be connected to the Cartwheel with a πιο of eas (Iiedou 1996))., which seems to be connected to the Cartwheel with a plume of gas (Higdon \cite{jim_hi}) ). Due to its unique morphology. the Cartwheel has been he subject of early optical studies (Thevs Spicecl 1976: Fosburv Hawarden 1977)) as well as αναισα] nodchug (Struck-Marcel. Iiedou 1993: Ileruquist Weil 1993)).," Due to its unique morphology, the Cartwheel has been the subject of early optical studies (Theys Spiegel \cite{ts}; Fosbury Hawarden \cite{fh}) ) as well as dynamical modeling (Struck-Marcel Higdon \cite{curt_jim}; Hernquist Weil \cite{hw}) )." " The outer rine of the Cartwheel (~ 70"" in diameter) is expanding. has blue colours aud is populated Nonnassive star-forming regions (Iliedon 1995. Amram ot al. 1998))."," The outer ring of the Cartwheel $\sim$ $\arcsec$ in diameter) is expanding, has blue colours and is populated by massive star-forming regions (Higdon \cite{jim_ha}, Amram et al. \cite{amram}) )." Most of the star formation though. appears ο occur im a localized. area of a few complexes in he southern sector of the ring.," Most of the star formation though, appears to occur in a localized area of a few complexes in the southern sector of the ring." The Πα emissiou. as well as the 20cm aud. Gem radio σοι enission vary as a function of the azimuth along the riug aud peak iu the siue region of the southern sector (Higedon 1996)).," The ${\alpha}$ emission, as well as the 20cm and 6cm radio continuum emission vary as a function of the azimuth along the ring and peak in the same region of the southern sector (Higdon \cite{jim_hi}) )." Optical and near-IR imaging show strong radial colour gradieuts in the disk behiud the outer ring. which may trace the evolution ofthe stellar population in the wake of the density wave (Marcum et al.," Optical and near-IR imaging show strong radial colour gradients in the disk behind the outer ring, which may trace the evolution ofthe stellar population in the wake of the density wave (Marcum et al." 1992)., \cite{marcum} ). Broad baud inages, Broad band images structures in active and inactive earlv-0tvpe galaxies.,structures in active and inactive early-type galaxies. We have also identified ancl analyzed a pair-matched sample of 31 active and 31 inactive Iate-tvpe galaxies., We have also identified and analyzed a pair-matched sample of 31 active and 31 inactive late-type galaxies. This paper is organized as lollows: In Section 2. we present the sample selection ancl (he pair-matching; technique: in section 3 we present data reduction and analysis procedures: in Sections + and 5Hr we present our results and discussion. respectively. and finally in Section G we present our conclusions.," This paper is organized as follows: In Section \ref{sec-sample} we present the sample selection and the pair-matching technique; in Section \ref{sec-data} we present data reduction and analysis procedures; in Sections \ref{sec-results} and \ref{sec-discussion} we present our results and discussion, respectively, and finally in Section \ref{sec-conclusions} we present our conclusions." A kev issue in the comparison of active and inactive galaxies is the selection of a control sample known (o be inactive., A key issue in the comparison of active and inactive galaxies is the selection of a well-defined control sample known to be inactive. This is difficult. because identification of a low-Iuminosity AGN often requires less sensitive observations than confirmation that a AGN is not present., This is difficult because identification of a low-luminosity AGN often requires less sensitive observations than confirmation that a low-luminosity AGN is not present. In order (ο avoid this problem. we have drawn our sample from the large. uniform. and sensitive Palomar Survey. of Iloetal.(1995).," In order to avoid this problem, we have drawn our sample from the large, uniform, and sensitive Palomar Survey of \citet{ho95}." . The Palomar Survey contains spectra of (he closest 486 brieht galaxies in a set region of the sky. and all of the nuclear spectra are classified as: absorption-line nuclei. HII. LINERs. transition objects. and Sevfert galaxies (Iloetal.1997a).," The Palomar Survey contains spectra of the closest 486 bright galaxies in a set region of the sky and all of the nuclear spectra are classified as: absorption-line nuclei, HII, LINERs, transition objects, and Seyfert galaxies \citep{ho97a}." . The Palomar Survey is considered to be the most complete and homogeneous representation of (he nearby universe., The Palomar Survey is considered to be the most complete and homogeneous representation of the nearby universe. Our first selection of the active galaxy. sample comprised all Palomar Sevfert and LINEN ealaxies with available broad-band WWEPC? images in the optical spectral region. excluding (ransiüon objects and (hose with uncertain classification.," Our first selection of the active galaxy sample comprised all Palomar Seyfert and LINER galaxies with available broad-band WFPC2 images in the optical spectral region, excluding transition objects and those with uncertain classification." The sample of inactive galaxies comprised all Palomar galaxies Classified as absorplion-line and HIE unelei with available broad-band WEDPC? images in the optical spectral region., The sample of inactive galaxies comprised all Palomar galaxies classified as absorption-line and HII nuclei with available broad-band WFPC2 images in the optical spectral region. We then carefully selected a well-imatched control sample from (his sample of inactive ealaxies (rough use of a pairmatching algoritlim., We then carefully selected a well-matched control sample from this sample of inactive galaxies through use of a pair-matching algorithm. This approach is similar to Chat adopted by Martinietal.(2003).. who argue that the best way to match control samples is to identilv a control galaxy pair for each active galaxy with similar values of all properties (hat may allect (he identification of dust structure (e.g.. morphology. distance. Iuminositv. inclination).," This approach is similar to that adopted by \citet{martini03}, who argue that the best way to match control samples is to identify a control galaxy pair for each active galaxy with similar values of all properties that may affect the identification of dust structure (e.g., morphology, distance, luminosity, inclination)." More traditional and commonly. emploved techniques. in contrast. just match the mean or median value of each property between the target and control samples. or the distribution of each property individually. and may be susceptible to different correlations between. various properties in (he two samples.," More traditional and commonly employed techniques, in contrast, just match the mean or median value of each property between the target and control samples, or the distribution of each property individually, and may be susceptible to different correlations between various properties in the two samples." In order to make a robust comparison between active and inactive galaxies we have identified] an inactive pair for each active galaxv with the following criteria: maximum difference between absolute magnitudes of παρ maximum difference between morphological T types of 1: maximunm difference between galaxy. inclinations of 15°: maximum clillerence, In order to make a robust comparison between active and inactive galaxies we have identified an inactive pair for each active galaxy with the following criteria: maximum difference between absolute magnitudes of mag; maximum difference between morphological $T$ types of 1; maximum difference between galaxy inclinations of $\arcdeg$ ; maximum difference We shall now show what novel features arise iu the dynamical evolution prescribed bv (12) due to the inclusion of the pressurelike term: iu contrast to the evolution prescribed by (2.5).,"We shall now show what novel features arise in the dynamical evolution prescribed by (12) due to the inclusion of the pressure–like term in contrast to the evolution prescribed by (2,5)." Iu order to compare our model with the commonly studied. approxiuation schemes for hugescale structure we shall perform a change of variables., In order to compare our model with the commonly studied approximation schemes for large–scale structure we shall perform a change of variables. " We consider the homogeucousisotropic solutions of the basic equations tre backgrounds) characterized by the expansion factor a(t) (aud IHubbles function fF= afa). ox define ""comioviue coordinates’ q. au peculiarvelocity fell u aud a (menn field) eravitational peculiaracceleration w as follows: where oy(tf) is the homogeneous backeround density (satistving ὁμ|3Iog= 0). which coincides with the spatially averaged density. if we impose periodic boundary conditions on ü aud w: in this case the ITubble.flow exists and is uuiquely defined (see Buchert Ellers1997)?."," We consider the homogeneous–isotropic solutions of the basic equations tre backgrounds) characterized by the expansion factor $a(t)$ (and Hubble's function $H=\dot{a} / a$ ), and define `comoving coordinates' ${\bf q}$, an peculiar–velocity field ${\bf \bar u}$ and a (mean field) gravitational peculiar--acceleration ${\bf w}$ as follows: where $\varrho_H(t)$ is the homogeneous background density (satisfying $\dot{\varrho}_H + 3 H \varrho_H =0$ ), which coincides with the spatially averaged density, if we impose periodic boundary conditions on ${\bf \bar u}$ and ${\bf w}$; in this case the Hubble–flow exists and is uniquely defined (see Buchert Ehlers." . Iu terms of these variables. Eqs. (," In terms of these variables, Eqs. (" "12) become (spatial derivatives refer now to q aud time derivatives are taken at constant q: hereafter. we drop the bar above u for notational simplicity): Combining (11b)) aud (110)) we find the following equation. using the Lagrangian derivative operator ©:=Or.|Gil,=OlyOil, Gvritten in vector fori): with the cocffücient ¢=SEE.15x(L which depends on deusity aud explicitly on tine.","12) become (spatial derivatives refer now to ${\bf q}$ and time derivatives are taken at constant ${\bf q}$ ; hereafter, we drop the bar above ${\bf u}$ for notational simplicity): Combining \ref{momentcomovingb}) ) and \ref{momentcomovingc}) ) we find the following equation, using the Lagrangian derivative operator $\; \dot{ } := \partial_{t}\vert_x + {\bar v}_{i} \partial_{i}\vert_x = \partial_{t}\vert_q + {u_i\over a} \partial_{i}\vert_q$ (written in vector form): with the coefficient $\zeta = {5\over 3}{\kappa\over 4\pi G a^2}\varrho^{-1/3} > 0$, which depends on density and explicitly on time." The dciffereuce between Eq. (15)), The difference between Eq. \ref{mastereq1}) ) and the one generally. used to model largescale structure formation (which is found by setting ο= 0) is the Aw term., and the one generally used to model large–scale structure formation (which is found by setting $\zeta=0$ ) is the $\Delta {\bf w}$ term. Recal first the case of “dust” (Le. no velocity dispcrsio- ο= O)," Recall first the case of “dust” (i.e., no velocity dispersion, $\zeta = 0$ )." In the weakly nonlinear regime Zeldovichs approximation (Zeldovich 1970. 1973) is ἃ successful model until shellcrossing sineularitics develop.," In the weakly nonlinear regime Zel'dovich's approximation (Zel'dovich 1970, 1973) is a successful model until shell–crossing singularities develop." " The trajectories in that approximation obey the parallelixiu of peculiar.gravitational acceleration aid peculiarvelocity (see. e.g. Bildhaucer Buchert 1991. Ἱνοβμα 1991. Buchert 1992). where b(f) is the erowine mode solution of the linear theory of eravitational iustability for ""dust G.ec.. if solves the equation b.|27fbIxGogb=0)."," The trajectories in that approximation obey the parallelism of peculiar–gravitational acceleration and peculiar–velocity (see, e.g. Bildhauer Buchert 1991, Kofman 1991, Buchert 1992), where $b(t)$ is the growing mode solution of the linear theory of gravitational instability for “dust” (i.e., it solves the equation $\ddot{b} + 2 H \dot{b} - 4 \pi G \varrho_{H} b = 0$ )." Since Eqs. (, Since Eqs. ( 14). were obtained uuder the condition of sinall velocity dispersion. we cau try to extrapolate Zeldovich’s approximation (16)) iuto this regiae (vhich is equivaleut to solving Eq. (15)),"14) were obtained under the condition of small velocity dispersion, we can try to extrapolate Zel'dovich's approximation \ref{parallelity}) ) into this regime (which is equivalent to solving Eq. \ref{mastereq1}) )" by iteration) aud thus find from Eq. (15)):, by iteration) and thus find from Eq. \ref{mastereq1}) ): Iu order to construct the model we have to derive from the solution of Eq. (17)), In order to construct the model we have to derive from the solution of Eq. \ref{mastereq2}) ) the trajectory field of the flow q=F(X.f) by quadrature: u=«EF.," the trajectory field of the ${\bf q} = {\bf F}({\bf X},t)$ by quadrature: ${\bf u}=a {\dot{\bf F}}$ ." Changing the temporal variable from f to b (this is possible since b(f) is a monotonically iucreasing function of time) aud define a rescaled. velocity field à=u/ab. Eq. (12))," Changing the temporal variable from $t$ to $b$ (this is possible since $b(t)$ is a monotonically increasing function of time) and defining a rescaled velocity field $\tilde{\bf u} = {\bf u} / a \dot{b}$, Eq. \ref{mastereq2}) )" becomes where gs—Εν> 0., becomes where $\mu = \zeta F(t) / {\dot b} > 0$ . YE Bowere independent of density. this equation would become 3D Burgers equation. whose solution is analytically known.," If $\mu$ were independent of density, this equation would become 3D Burgers equation, whose solution is analytically known." The fact that gi depends on density preseuts an obstacle for Ποπιο an analytical solution., The fact that $\mu$ depends on density presents an obstacle for finding an analytical solution. The principal advantage of Eq. (18)), The principal advantage of Eq. \ref{mastereq3}) ) OVor he same equation with jj=0 is that it does not lead to caustic formation. since velocity dispersion sinoothes out the singuluitv (Zeldovichi Shancarin 1982. Shandarin Zeldovich 1989: see Cünaumneschi 1998 and ref.," over the same equation with $\mu = 0$ is that it does not lead to caustic formation, since velocity dispersion smoothes out the singularity (Zel'dovich Shandarin 1982, Shandarin Zel'dovich 1989; see Ginanneschi 1998 and ref." therein for a thorough analysis)., therein for a thorough analysis). " Therefore. this equation could be used as it stands to follow the dynamical evolution bevoud the time when sueguluities in the ""dust? οσοπα. would arise."," Therefore, this equation could be used as it stands to follow the dynamical evolution beyond the time when singularities in the “dust” continuum would arise." To be iore precise. “shellcrossing” wouk still happen. but this doesu't παπα[ο itself as a sineularity in the average flow. rather as a (1nooth) peak iu the density field.," To be more precise, “shell–crossing” would still happen, but this doesn't manifest itself as a singularity in the average flow, rather as a (smooth) peak in the density field." " Morphlologicallv distinct patterus. classified by the Lagraugesinguluitv theory iu the case of ""dust? (Seo Arnold et al."," Morphologically distinct patterns, classified by the Lagrange–singularity theory in the case of “dust” (see Arnol'd et al." " 1982). wi also cimeree iu the seuse of sinoothedout inuiages of critical sets ou the Lagrangian manifold of the ""dust medium."," 1982), will also emerge in the sense of smoothed–out images of critical sets on the Lagrangian manifold of the “dust” medium." This picture mieht not be true for large velocity dispersion., This picture might not be true for large velocity dispersion. As time Oogoes by aud the system becomes more aud more virialized. Eqs. (," As time goes by and the system becomes more and more virialized, Eqs. (" 11) ceaseto be a good description of the dynamical evolution. because velocity dispersion eenerically both erows aud. becomes anisotropic.,"14) ceaseto be a good description of the dynamical evolution, because velocity dispersion generically both grows and becomes anisotropic." Eq. (18)), Eq. \ref{mastereq3}) ) isformally equivaleut to the keyequation of the “adhesion model inwhichthe coefficient pois positive, isformally equivalent to the keyequation of the “adhesion model” inwhichthe coefficient $\mu$ is positive where formula (27)) is good to better than0.,where formula \ref{eq:sigma8norm}) ) is good to better than. "596. Note that at the WAIAP best-fi values of n=0.99 and τις=0.17. this formula gives the WALAP best-fit value of a,=0.9."," Note that at the WMAP best-fit values of $n=0.99$ and $\tau_{\rm es}=0.17$, this formula gives the WMAP best-fit value of $\sigma_8=0.9$." " We assume the following heuristic form [or the time-dependence of the UV-efficiency: where /, is the [raction of barvons in stars.", We assume the following heuristic form for the time-dependence of the UV-efficiency: where $f_\ast$ is the fraction of baryons in stars. Thus. the Iuminositv of each ionizing source is given by The new parameters A and fyi define the time-dependence of the efficiency.," Thus, the luminosity of each ionizing source is given by The new parameters $A$ and $f_{\ast, \rm crit}$ define the time-dependence of the efficiency." " The essential features are Chat at very. high redshift. the total efficiency. is (1+A) times greater than at lower redshift. with the transition occuring al f,ye."," The essential features are that at very high redshift, the total efficiency is $(1+A)$ times greater than at lower redshift, with the transition occuring at $f_\ast \sim f_{\ast,\rm crit}$." Chis form is motivated by ihe notion that the first stars. being metal-free. should have had a higher effective efficiency. but that as metals were produced by this generation of stars ancl reinjected back into the IGA. the efficiency. would decrease.," This form is motivated by the notion that the first stars, being metal-free, should have had a higher effective efficiency, but that as metals were produced by this generation of stars and reinjected back into the IGM, the efficiency would decrease." However. we emphasize (hat (this model was simply selected heuristically. and was not based on any detailed model of star formation feedback on the UV-elliciency.," However, we emphasize that this model was simply selected heuristically, and was not based on any detailed model of star formation feedback on the UV-efficiency." " For instance. it should be noted that the ""enhancement factor may be a combination of changes in the intrinsic elliciency ei and the resolution factor e, related to the fraction of cooling gas (hat. [orms stars."," For instance, it should be noted that the “enhancement” factor may be a combination of changes in the intrinsic efficiency $\epsilon_{\rm UV}$ and the resolution factor $\epsilon_\ast$ related to the fraction of cooling gas that forms stars." " To give a sense of the meaning of fyori. Table 4. presents the (ransilion redshifts zya,, where f.2(In2)fa 80 Chaat ένο 2)."," To give a sense of the meaning of $f_{\ast,\rm crit}$, Table \ref{tab:ztrans} presents the transition redshifts $z_{\rm trans}$ where $f_\ast \approx (\ln 2) f_{\ast,\rm crit}$ so that $\epsilon_{\rm UV}(z_{\rm trans}) \approx \epsilon_{\rm UV,0} (1+A/2)$ ." We fix the value of [νι=LO+ (we discuss the sensitivity to this parameter below).," We fix the value of $f_{\ast,\rm crit} = 10^{-4}$ (we discuss the sensitivity to this parameter below)." " Thus. for each point in the n—7, plane. our procedure searching parameter space is as follows: (1) Pick value of A: (2) Adjust eio so that Zadar (CCaleulated by model) is consistent with Tent (3) Stop LA? is minimized. otherwise go back tostep (1)."," Thus, for each point in the $n-\tau_{\rm es}$ plane, our procedure searching parameter space is as follows: (1) Pick value of $A$; (2) Adjust $\epsilon_{\rm UV,0}$ so that $\tau_{\rm es,model}$ (calculated by model) is consistent with $\tau_{\rm es}$; (3) Stop if $\chi^2$ is minimized, otherwise go back tostep (1)." " For each point in the nm—7, plane. we have a value of a best fit απο7)."," For each point in the $n-\tau_{\rm es}$ plane, we have a value of a best fit $\tilde{\chi}^2(n,\tau_{\rm es})$." We treat. V7 as approximately the —21n£. where £07.T4fia) is the likelihood Iunction. and integrate (wilh unilorm priors) to find lind the confidence regions (the results are insensitive to the priors).," We treat $\tilde{\chi}^2$ as approximately the $-2\ln {\cal L}$, where ${\cal L}(n,\tau_{\rm es}|f_{\ast,\rm crit})$ is the likelihood function, and integrate (with uniform priors) to find find the confidence regions (the results are insensitive to the priors)." The effective optical depth for several models is shown in Figure 3.., The effective optical depth for several models is shown in Figure \ref{fig:taueffplot}. " The three illustrative ""eood-fitting models are in the region. and the ""badlv-fitting model is outside the region."," The three illustrative “good-fitting” models are in the region, and the “badly-fitting” model is outside the region." Clearly. high values of à and 7. are ruled out by the data.," Clearly, high values of $n$ and $\tau_{\rm es}$ are ruled out by the data." Considering all (he constraints together. (he results are shown in Figure 4..," Considering all the constraints together, the results are shown in Figure \ref{fig:ntauresults}. ." Our analvsis stronely favors a narrow range errors):, Our analysis strongly favors a narrow range errors): coverage of the frequency range 85 to 105 GllIz. with a possible extension to 115 GllIz.,"coverage of the frequency range 85 to 105 GHz, with a possible extension to 115 GHz." All calibration and imaging was performed with the \URIAD software., All calibration and imaging was performed with the MIRIAD software. Complex gains were derived [rom frequent observations of nearby quasars., Complex gains were derived from frequent observations of nearby quasars. Because (he narrow band provided low signal-to-noise ratios on (he quasars. a phase offset between the wide band and narrow band was determined rom short observations of a strong source on each day. either. or J0533-440.," Because the narrow band provided low signal-to-noise ratios on the quasars, a phase offset between the wide band and narrow band was determined from short observations of a strong source on each day, either J0423-012 or J0538-440." These short observations of strong sources were also used to determine the bandpass response., These short observations of strong sources were also used to determine the bandpass response. For TW Ilva. additional weaker quasars located close to the star were included in the observing sequence to provide an empirical check on (he atmospheric seeing and effectiveness of the phase calibration.," For TW Hya, additional weaker quasars located close to the star were included in the observing sequence to provide an empirical check on the atmospheric seeing and effectiveness of the phase calibration." Typical svstem temperatures were 300 to 400 Ix (SSB). with higher values at low elevations.," Typical system temperatures were 300 to 400 K (SSB), with higher values at low elevations." The flux densities were set with reference to the planet Mars: (he scatter in derived fluxes on consecutive days suggests uncertainties of approximately2054., The flux densities were set with reference to the planet Mars; the scatter in derived fluxes on consecutive days suggests uncertainties of approximately. .. ]nmnages were made of (he sum of the two linear polarizations using natural weighting to obtain best sensitivity., Images were made of the sum of the two linear polarizations using natural weighting to obtain best sensitivity. All images were cleaned to a cutoff of twice (he r.m.s., All images were cleaned to a cutoff of twice the r.m.s. noise level., noise level. Because Doppler tracking was not applied during the observations. (ae correspondence between individual lrequency. channels auc velocity changes with time during the course of the observations.," Because Doppler tracking was not applied during the observations, the correspondence between individual frequency channels and velocity changes with time during the course of the observations." Therefore. (he spectral cata were imaged in resampled velocity bins of 0.5 km 1 width. coarse compared to (these chanees. rather than individual frequency channels.," Therefore, the spectral data were imaged in resampled velocity bins of 0.5 km $^{-1}$ width, coarse compared to these changes, rather than individual frequency channels." Figure 1. shows (he 89 GlIIz continuum emission detected from TW IIva., Figure \ref{fig:tw_cont} shows the 89 GHz continuum emission detected from TW Hya. The position is coincident with the optical star and radio detections at longer wavelengths., The position is coincident with the optical star and radio detections at longer wavelengths. A Gaussian fit to (he visibililies gives a flux of 41d4 mJv (random error only) ancl an apparent size consistent wilh an unresolved source slightly broadened by the phase noise on the longer baselines., A Gaussian fit to the visibilities gives a flux of $41\pm4$ mJy (random error only) and an apparent size consistent with an unresolved source slightly broadened by the phase noise on the longer baselines. This Gaussian fit is also compatible with the extended disk seen in scattered light. since the dust enussion from the cireumstellar disk is strongly centrally peaked by the combination of low opacily and increasing column density ancl temperature towards (he star (see Mundy et al.," This Gaussian fit is also compatible with the extended disk seen in scattered light, since the dust emission from the circumstellar disk is strongly centrally peaked by the combination of low opacity and increasing column density and temperature towards the star (see Mundy et al." 1996: Wilner et al., 1996; Wilner et al. 2000)., 2000). The TW Ilva 89 GlIIz continuum flux measurement agrees well with expectations from previously reported measurements al bot higher (350 Gllz) and lower (43 Gllz) radio frequencies (Weintraub. Sandell Duncan 1989. Wilner et al.," The TW Hya 89 GHz continuum flux measurement agrees well with expectations from previously reported measurements at both higher (350 GHz) and lower (43 GHz) radio frequencies (Weintraub, Sandell Duncan 1989, Wilner et al." 2000. Wilner 2001).," 2000, Wilner 2001)." In addition. il is consistent wilh predictions of various disk models based on the radio observations (hat," In addition, it is consistent with predictions of various disk models based on the radio observations that" that the influence of metallicity on the theoretical initial-final mass relationship seems to be almost negligible below 2Mo.,"that the influence of metallicity on the theoretical initial-final mass relationship seems to be almost negligible below $2\, \rm M_{\sun}$." Other factors. such as magnetic fields or rotation (Domínguez et al.," Other factors, such as magnetic fields or rotation nguez et al." 1996) should be studied in detail in order to discern their effect on this relation., 1996) should be studied in detail in order to discern their effect on this relation. The ages of star clusters are usually calculated to a higher accuracy than in the case of the individual low-mass. stars considered in this work. which should allow to obtain the initial masses with better accuracy.," The ages of star clusters are usually calculated to a higher accuracy than in the case of the individual low-mass stars considered in this work, which should allow to obtain the initial masses with better accuracy." However. from Fig.," However, from Fig." 5 it can be noted that white dwarfs mn clusters display a large dispersion. especially between 3 and 4Mo.," \ref{fig:mif} it can be noted that white dwarfs in clusters display a large dispersion, especially between $3$ and $4\, \rm M_{\sun}$." Thus. this scatter in the observational data seems to be a real effect. rather than a consequence of the uncertainties in the mass estimates.," Thus, this scatter in the observational data seems to be a real effect, rather than a consequence of the uncertainties in the mass estimates." Hence. there is no apparent reason for which the mitial-final mass relationship should be considered a single-valued function.," Hence, there is no apparent reason for which the initial-final mass relationship should be considered a single-valued function." A thorough complete comparison of our results based in common proper motion pairs with cluster data will be discussed in a forthcoming paper (Catalann et al., A thorough complete comparison of our results based in common proper motion pairs with cluster data will be discussed in a forthcoming paper (Catalánn et al. 2008)., 2008). One of the most important contributions of our work is the study of the range of initial masses corresponding to 1.5722Mo. which was not covered by the research based on open cluster data (Ferrario et al.," One of the most important contributions of our work is the study of the range of initial masses corresponding to $1.5-2\, \rm M_{\sun}$, which was not covered by the research based on open cluster data (Ferrario et al." 2005. Dobbie et al.," 2005, Dobbie et al." 2006)., 2006). The recent study of Kaliratetal.(2007) using old open clusters has also provided some new data in the low-mass domain., The recent study of \cite{kal07} using old open clusters has also provided some new data in the low-mass domain. It 15 worth to mention that 5 of the 6 white dwarfs of our final sample have masses near the typical values derived by. e.g.. Kepler et al. (," It is worth to mention that 5 of the 6 white dwarfs of our final sample have masses near the typical values derived by, e.g., Kepler et al. (" 2007). M»0.6Me. which represent of the white dwarfs found in the SDSS.,"2007), $M\sim0.6\,\rm M_{\sun}$, which represent of the white dwarfs found in the SDSS." This stems from the fact that the progenitors of white dwarfs in open clusters were usually more massive (M>2 Ma) since clusters are relatively young and the low-mass stars. which would produce the typical white dwarfs. are still on the main sequence.," This stems from the fact that the progenitors of white dwarfs in open clusters were usually more massive $M>2\,\rm M_{\sun}$ ) since clusters are relatively young and the low-mass stars, which would produce the typical white dwarfs, are still on the main sequence." Since some of the pairs that we have studied have larger ages than the typical values for open clusters. the white dwarfs that belong to these pairs can be less massive.," Since some of the pairs that we have studied have larger ages than the typical values for open clusters, the white dwarfs that belong to these pairs can be less massive." Thus. we consider that white dwarfs in common proper motion pairs are more representative of the Galactic white dwarf field population than white dwarfs in open clusters.," Thus, we consider that white dwarfs in common proper motion pairs are more representative of the Galactic white dwarf field population than white dwarfs in open clusters." We have studied à sample of common proper motion pairs comprised of a white dwarf and a FGK star., We have studied a sample of common proper motion pairs comprised of a white dwarf and a FGK star. We have performed high signal-to-noise low resolution spectroscopy of the white dwarf members. which led us to carry out a full analysis of their spectra and to make a re-classification when necessary.," We have performed high signal-to-noise low resolution spectroscopy of the white dwarf members, which led us to carry out a full analysis of their spectra and to make a re-classification when necessary." From the fit of their spectra to white dwarf models we have derived their atmospheric parameters., From the fit of their spectra to white dwarf models we have derived their atmospheric parameters. Then. using different cooling sequences — namely those of Salarisetal.(2000) and Fontaineetal.(2001) — their masses and cooling times were obtained.," Then, using different cooling sequences — namely those of \cite{sal00} and \cite{fon01} — their masses and cooling times were obtained." Simultaneously. we have performed independent high resolution spectroscopic observations of their companions.," Simultaneously, we have performed independent high resolution spectroscopic observations of their companions." Using the available photometry we have obtained their effective temperatures., Using the available photometry we have obtained their effective temperatures. Then. from a detailed analysis of their spectra and using either isochrones or X-ray lummosities. we have derived their metallicities and ages (1.e.. the metallicities of the progenitors of the white dwarfs and their total ages).," Then, from a detailed analysis of their spectra and using either isochrones or X-ray luminosities, we have derived their metallicities and ages (i.e., the metallicities of the progenitors of the white dwarfs and their total ages)." These observations allowed us to obtain the initial and final masses of six white dwarfs in common proper motion pars. four of them corresponding to initial masses below 2Me. a range which has not been previously covered by the open cluster data.," These observations allowed us to obtain the initial and final masses of six white dwarfs in common proper motion pairs, four of them corresponding to initial masses below $2\,\rm M_{\sun}$, a range which has not been previously covered by the open cluster data." Our semi-empirical relation shows significant scatter. compatible with the results obtained by Ferrarioetal.(2005) and... Dobbieetal.(2006)... which are mainly based on open cluster data.," Our semi-empirical relation shows significant scatter, compatible with the results obtained by \cite{fer05} and \cite{dob06}, which are mainly based on open cluster data." However. the dispersion of the results is higher than the error bars. which leaves some open questions that should be studied in detail (e.g.. rotation or magnetic fields).," However, the dispersion of the results is higher than the error bars, which leaves some open questions that should be studied in detail (e.g., rotation or magnetic fields)." We have shown that common proper motion pairs containing white dwarfs can be useful to improve the initial-final mass relationship. since they cover a wide range of ages. masses and metallicities. and they are also representative of the disk white dwarf population.," We have shown that common proper motion pairs containing white dwarfs can be useful to improve the initial-final mass relationship, since they cover a wide range of ages, masses and metallicities, and they are also representative of the disk white dwarf population." We have seen that the accuracy in the total ages depends almost exclusively on the evolutionary state of the low-mass companions., We have seen that the accuracy in the total ages depends almost exclusively on the evolutionary state of the low-mass companions. Such relative accuracy becomes poor when the star is close to the ZAMS., Such relative accuracy becomes poor when the star is close to the ZAMS. However. this limitation may not be critical to many common proper motion pairs.," However, this limitation may not be critical to many common proper motion pairs." Planned deep surveys like GAIA. LSST or the Alhambra Survey will discover thousands of new white dwarfs. some of them belonging to wide binaries.," Planned deep surveys like GAIA, LSST or the Alhambra Survey will discover thousands of new white dwarfs, some of them belonging to wide binaries." In the meantime. our most immediate priority is to further extend the sample of wide binaries valid for this study.," In the meantime, our most immediate priority is to further extend the sample of wide binaries valid for this study." We are working in the search for more wide binaries of our interest in the NLTT catalog (Gould Chanamé 2004) and also in the LSPM-north catalog (Léppine Bongiorno 2007)., We are working in the search for more wide binaries of our interest in the NLTT catalog (Gould Chanamé 2004) and also in the LSPM-north catalog (Léppine Bongiorno 2007). Detailed study of the current and future common proper motion pairs of this type should help to explain the scatter in the semi-empirical initial-final, Detailed study of the current and future common proper motion pairs of this type should help to explain the scatter in the semi-empirical initial-final Bournaud ct al.,Bournaud et al. 2011). as suggested by local ULIRGs and ολων being dominated by gasricli major mergers (6.8. Sanders et al.," 2011), as suggested by local ULIRGs and SMGs being dominated by gas-rich major mergers (e.g. Sanders et al." 1988)., 1988). Iudeed. AIS galaxies aud outliers appear to be in different star formation reginies: a quasisteady. louglasting mode for disks auc a more rapid. starburst mode in major mergers or in the deusest SE regions (Daddi et al.," Indeed, MS galaxies and outliers appear to be in different star formation regimes: a quasi--steady, long–lasting mode for disks and a more rapid, starburst mode in major mergers or in the densest SF regions (Daddi et al." 2010b: Genzel et al., 2010b; Genzel et al. 2010)., 2010). So far it has been uncle by which of these two modes most of the stars in galaxies were formed., So far it has been unclear by which of these two modes most of the stars in galaxies were formed. While MS ealaxies are optically thin in the UV. (Dadi ct al., While MS galaxies are optically thin in the UV (Daddi et al. 2005: 2007). MS outliers are eencrallv optically thick (Goldacder et al.," 2005; 2007), MS outliers are generally optically thick (Goldader et al." 2002. Chapiuan et al.," 2002, Chapman et al." 2005) anc far-IR observations are required to reliably derive their SFRs., 2005) and far-IR observations are required to reliably derive their SFRs. The PACS caniera (Poelitsch et al., The PACS camera (Poglitsch et al. 2010) onboard Herschel (Pilbratt et al., 2010) onboard Herschel (Pilbratt et al. " 2010) now allows for the first time to obtain deep far-IR observation probing SFRs down to MS levels for typicalgalaxies with AL,~LOMAL. at 2~2. e. at the peak epoch of the cosinic SFR density aud of the space density of SAIGs (Chapman et al."," 2010) now allows for the first time to obtain deep far-IR observation probing SFRs down to MS levels for typicalgalaxies with $M_*\sim10^{10}M_\odot$ at $z\sim2$, i.e., at the peak epoch of the cosmic SFR density and of the space density of SMGs (Chapman et al." 2005)., 2005). Tn this letter we colmbine wide area PACS observatious of the COSMOS field with deeper data in the GOODS field. both taken as a part of the PEP survey (Lutz et al.," In this letter we combine wide area PACS observations of the COSMOS field with deeper data in the GOODS field, both taken as a part of the PEP survey (Lutz et al." 2011). aud obtain a first accurate estimate of the relative role of MS and outlier galaxies on the formation of stars at 2~2.," 2011), and obtain a first accurate estimate of the relative role of MS and outlier galaxies on the formation of stars at $z\sim2$." Red and dead (passive) galaxies. though. exist at these cosmic epochs. and form a separate sequence below the AIS of star-forming galaxies.," Red and dead (passive) galaxies, though, exist at these cosmic epochs, and form a separate sequence below the MS of star-forming galaxies." Their contribution will be ignored in this Letter., Their contribution will be ignored in this Letter. We use a Salpeter IAIF aud a standard WMAP cosinologv., We use a Salpeter IMF and a standard WMAP cosmology. Iu order to obtain a iiecaniueful ceusus of star-forming ealaxies on aud off the MS. oue has to cover the AV. plane down to low SER aud AL. levels. aud do so over a laree area to include rare objects with the highest SFRs.," In order to obtain a meaningful census of star-forming galaxies on and off the MS, one has to cover the $-M_*$ plane down to low SFR and $M_*$ levels, and do so over a large area to include rare objects with the highest SFRs." We reach this goal bv combining fu-IB-selected (.6.. SFR-selected) aud neimr-IB-selected (Le. M. -selected) star-forming samples in the COSMOS aud in GOODS-South fields. having both UV- and far IR-based SER determinations.," We reach this goal by combining far-IR-selected (i.e., SFR-selected) and near-IR-selected (i.e., $M_*$ -selected) star-forming samples in the COSMOS and in GOODS-South fields, having both UV- and far IR-based SFR determinations." We first describe the datasets used. saluple selections and SFR and AL. measurements.," We first describe the datasets used, sample selections and SFR and $M_*$ measurements." We consider ouly galaxies within the redshift range of 1.5«2 <2. based either on spectroscopic or photometric redshifts.," We consider only galaxies within the redshift range of $1.56 and flux limit 1 ph s! cm""? should have been detected bySWIFT."," More specifically, the model predicts that in two years 13 GRBs at $z\ga 6$ and flux limit $1$ ph $^{-1}$ $^{-2}$ should have been detected by." So far only 1 GRB has robust redshift estimate at z>6., So far only 1 GRB has robust redshift estimate at $z>6$. " On the other hand, while it is difficult to quantify the efficiency of the redshift determination, especially for very high redshift events, this could well be less than 10 per cent."," On the other hand, while it is difficult to quantify the efficiency of the redshift determination, especially for very high redshift events, this could well be less than $10$ per cent." " The exploited galaxy formation model also enables us to directly predict the properties of the GRB host galaxies (SFR, magnitude, stellar mass, average metallicity, extinction) as function of the halo mass and age as well as the luminosity function (LF) and the corresponding SFR distribution of the overall population."," The exploited galaxy formation model also enables us to directly predict the properties of the GRB host galaxies (SFR, magnitude, stellar mass, average metallicity, extinction) as function of the halo mass and age as well as the luminosity function (LF) and the corresponding SFR distribution of the overall population." " As discussed in 2.1, during the evolution of individual galaxies, the metallicity ofthe star-forming gas attains the threshold Zeit=0.1—0.2Zo quite rapidly, within tei,&5x107, and this timescale is basically independent of the host halo mass."," As discussed in 2.1, during the evolution of individual galaxies, the metallicity of the star-forming gas attains the threshold $Z_{\rm crit}=0.1-0.2 \, Z_{\odot}$ quite rapidly, within $t_{\rm crit}\approx 5\times 10^7$, and this timescale is basically independent of the host halo mass." " Interestingly, since this is much shorter than the halo virialization timescale, teri:10^{11}\, M_{\odot}$ , which exceed a few per cent of the total GRB hosts only at $z\la 6$ (cf." Fig., Fig. 1)., 1). " The AB absolute magnitude at 1350 A, M1350, is reported inFig."," The AB absolute magnitude at 1350 , $M_{1350}$ , is reported inFig." 7 for various halo masses and redshifts z=3 and z= 6., 7 for various halo masses and redshifts $z=3$ and $z=6$ . where we made use of the fact that the cuthalpy vanishes on the stellar surface.,where we made use of the fact that the enthalpy vanishes on the stellar surface. Note that the radius. rec of poiut Cis not known a priori.," Note that the radius, $\hat{r}_C$, of point C is not known a priori." " For the rigid rotation o, is independent of A.", For the rigid rotation $\hat{\phi}_{\rm rot}$ is independent of $A$. We solve Eqs. (20)), We solve Eqs. \ref{eq:Hac0}) ) and (21)) with respect to c aud My for cult.M obtained in the first step.," and \ref{eq:Hac1}) ) with respect to $\hat{c}$ and $\hat{h}_0$ for $\hat{\phi}_g(\hat{r},\theta)$ obtained in the first step." With these values of fy aud ce. we thea search for the location where the RUS of Eq. position(22))," With these values of $\hat{h}_0$ and $\hat{c}$, we then search for the location where the RHS of Eq. \ref{eq:Hac2}) )" takes the maxima value., takes the maximum value. The maxi of the RIS of Eq. for(22)), The maximum of the RHS of Eq. \ref{eq:Hac2}) ) thus obtained gives > in turn., thus obtained gives $\beta$ in turn. We are nowina to update ptr.0). solving the Bernoulli equation (18)) Og.0).Joby. aud e obtained so far.," We are nowin a position to update $\hat{\rho}(\hat{r},\theta)$, solving the Bernoulli equation \ref{eq:Ber2}) ) for $\hat{\phi}_g(\hat{r},\theta),\beta,\hat{h}_{0},$ and $\hat{c}$ obtained so far." We then repeat the procedure until a suffiieut convergence is achieved., We then repeat the procedure until a sufficient convergence is achieved. We move on to the multidavered case., We move on to the multi-layered case. Although. for simplicity. we consider ouly two-lavered structures iu the following. the extension toconfigurations with a larger umber oflavers is straightforward.," Although, for simplicity, we consider only two-layered structures in the following, the extension toconfigurations with a larger number oflayers is straightforward." Then we have again two unknown fuuctious ωμή. and. ptr.0) aud this time five coustauts 3. Pgs). aud ο ta Eqs. (6))," Then we have again two unknown functions $\hat{\phi}_g(\hat{r},\theta)$ and $\hat{\rho}(\hat{r},\theta)$ and this time five constants $\beta$, $\hat{h}_{0(i)}$ and $\hat{c}_{(i)}$ in Eqs. \ref{eq:Ber}) )" aud (2))., and \ref{eq:gravity}) ). Another iuportaut function to be 0)determined is the laver boundary expressed by a fiction 0)., Another important function to be determined is the layer boundary expressed by a function $\hat{r}_{b}(\theta)$. Just as in the sinele laver case. the choice of variables aud the iteration scheme are critically iuportaut to make the scheme convergeat," Just as in the single layer case, the choice of variables and the iteration scheme are critically important to make the scheme convergent." We first write down the equations capies to obtain the uukuowu constants. which correspond to Eqs. (20))-(22))alodus," We first write down the equations employed to obtain the unknown constants, which correspond to Eqs. \ref{eq:Hac0}) \ref{eq:Hac2}) )" for the sinele-lavered case., for the single-layered case. Asexplained above. the pressure should be continuous across the laver boundary.," Asexplained above, the pressure should be continuous across the layer boundary." " this condition on the equator (point Ly. in Figure 1)) aud on the rotation axis (poiut. P» iu the same figure). we write down the Bernoulli equation for both sides of the laver boundary at these points: where we out over the noniualized variablesfor notational simplicity aud πω rp,, are the radii of poiuts £j» and Py. respectively."," Employing this condition on the equator (point $E_{12}$ in Figure \ref{fig:multi}) ) and on the rotation axis (point $P_{12}$ in the same figure), we write down the Bernoulli equation for both sides of the layer boundary at these points: where we omit $\hat{ }$ over the normalized variablesfor notational simplicity and $r_{E_{12}}$, $r_{P_{12}}$ are the radii of points $E_{12}$ and $P_{12}$, respectively." " Note that I7j4,(p)4ffp2)(p) because the EOS’s are ciffereut frou laver to laver.", Note that $H_{(1)}(p)\ne H_{(2)}(p)$ because the EOS's are different from layer to layer. We employ the previous conditions at points E. P aud C. which are written asNote thatin Eq. (29))," We employ the previous conditions at points $E$, $P$ and $C$, which are written asNote thatin Eq.\ref{eq:cond7}) )" "we do not knowa priori in which laver the maximain density point C lies,",we do not knowa priori in which layer the maximum density point $C$ lies. Using Eqs. (23))- (29)), Using Eqs. \ref{eq:cond2}) \ref{eq:cond7}) ) " we can determine for the given EOS's aud rotation laws seven uukuown coustauts out of JJ. Moy. μον ορ]. (2) PEq VES Which pg,—pre.7/2) aud pp,—plrp,,.0)."," we can determine for the given EOS's and rotation laws seven unknown constants out of $\beta$, $h_{0(1)}$, $h_{0(2)}$, $c_{(1)}$, $c_{(2)}$, $p_{E_{12}}$, $p_{P_{12}}$, $r_p$, $r_{E_{12}}$, $r_{P_{12}}$, in which $p_{E_{12}}\equiv p(r_{E_{12}},\pi/2)$ and $p_{P_{12}}\equiv p(r_{P_{12}},0)$." This implies that oue can give threeconstants to ΕθνspecifyUp the modelV, This implies that one can give threeconstants to specify the model. "Ps As argued shortly. however. pp, aud Γρ as well as pe, aud rg, can not be specified incependcutly."," As argued shortly, however, $p_{P_{12}}$ and $r_{P_{12}}$ as well as $p_{E_{12}}$ and $r_{E_{12}}$ can not be specified independently." This cau be uuderstood by considering a nou-rotating but two-lavered configuration., This can be understood by considering a non-rotating but two-layered configuration. In this case one can coustruct au equiBbriiun configuration bv integrating Eq. (1)),In this case one can construct an equilibrium configuration by integrating Eq. \ref{eq:hydro2}) ) " radially from the center to rp, with the use of the .", radially from the center to $r_{P_{12}}$ with the use of the gravitational potential $\int^r_0 4\pi {r'}^2 \rho dr'/r^2$. : ut2 ∶↴∙⊾↥⋅⋜↧↖↽↕↑⋜↧⊓∪∐⋜↧↕↻∪↑↸∖∐↑⋯↕∙∕⊍↓⊼∣⋮∣∣≻↙∕∣∣∣∣⋮−∙↽∕∏∐∖∐↕↑↕↴∖↴∪↴⋝↖⇁↕≺∏↕↴∖↴↑∐⋜↧↑∣↗∫≽∟≖, Then it is obvious that $p_{P_{12}}$ depends on $r_{P_{12}}$ and vice versa (note that the maximum density is also fixed). ≺∐∖↻↸∖∐≼↧↴∖↴∪∐∣∣∫≽⊓⋜⋯≼↧↖↽↕↸⊳↸∖↖↽↸∖↥⋅↴∖↴⋜↕≺∐∪↑↸∖↑∐⋜↧↑↑↕∐∖: ∙∙ ⋅ ⋅ ⋯⋜⋯↕∐⋯⋯≼∐∖∐↴∖↴↕↑⋅↖↽↕↴∖↴⋜↕↕↴∖↴∪∱∎↕⊼↸∖≺⊔⋅≼∶∪↕∐∶↴∙⊾↴⋝⋜↧↸⊳↨↘↽↑∪↑∐↸∖∐∐," Going back to the multi-layered rotational case, we have found that the combination of $r_p$, $r_{P_{12}}$ and $r_{E_{12}}$ is a good choice." ∏↑↕≓↕⋜↧⋅↖↽↸∖↥⋅↸∖≼↧↥⋅∪↑⋜↧↑↕∪∐⋜↧↕↸⊳⋜↧↴∖↴↸∖∙↖↖↽↸∖∐⋜∏↽↸∖↕⋟∪∏∐≼↧∐⋜↧↑↑∐↸∖↸⊳∪∐∐⋝↕∐⋜," The triplet of $r_p$, $p_{P_{12}},$ and $p_{E_{12}}$ can be an alternative." ↧↑↕∪∐ ∪↕≯∣⋮∣↗∙∣⋮∫≽∟≖⋜⋯≼↧∣⋮⋮⊓↕↴∖↴⋜↧∶↴∙⊾∪≺⋉⇂↸⊳∐∪↕↸⊳↸∖∙⊺∐↸∖⊓⋅∏≻↕↸∖↑∪↕≯∣⋮∣↗∙∣↗∫≽∟↗∙⋜⋯≼↧∣↗⋮⊓⋯, Note that the inclusion of $r_p$ seems to be mandatory as has been demonstrated by the HSCF scheme. ∐↴⋝↸∖⋜⋯⋜↧↕↑↸∖↥⋅∐⋜↧↑↕↖↽↸∖∙⋀∖⊽∪↑↸∖↑∐⋜↧↑↑∐↸∖↕↕∐⊳↕∏↴∖↴↕∪∐," To summarize, Eqs. \ref{eq:cond2}) \ref{eq:cond7}) )" ∪↕≯∣⋮∣↗↴∖↴↸∖↸∖⋯↴∖↴↑∪↴⋝↸∖⋯⋜⋯≼⇂⋜↧↑∪↥⋅⋅↖↽⋜↧↴∖↴∐⋜↧↴∖↴↴⋝↸∖↸∖∐≺∐∖⋯∪∐↴∖↴⊓⋅⋜↧↑↸∖≼⇂↴⋝∙↖↽↑∐↸∖∐≋≼⊲⋮↴∖↴↸⊳↕∐∖⋯↸∖∙⊺∪↴∖↴∏∐∐⊔⋜∐⋅↕∑↸∖∙⊏≺∣↴∖↴∙⊔∶≩⊔⊣⊇≝⊔⋝⋜∐⋅↸∖∏↴∖↴↸∖≼↧ we proceed to the iteration scheme proposed in this paper.," are used to obtain either $\beta$ , $c_{(1)}$ , $c_{(2)}$ , $h_{0(1)}$ ,$h_{0(2)}$ , $p_{E_{12}}$ and $p_{P_{12}}$ for given $r_p$ , $r_{E_{12}}$ and $r_{P_{12}}$ or $\beta$ , $c_{(1)}$ , $c_{(2)}$ , $h_{0(1)}$ , $h_{0(2)}$ , $r_{E_{12}}$ and $r_{P_{12}}$ for given $r_p$ , $p_{E_{12}}$ and $p_{P_{12}}$ Now we proceed to the iteration scheme proposed in this paper." After solving the Poisson equation for the trial density distribution. Eqs. (23))-(29))," After solving the Poisson equation for the trial density distribution, Eqs. \ref{eq:cond2}) \ref{eq:cond7}) )" are solved for the variables chioseu iu the previous section., are solved for the variables chosen in the previous section. The procedure is divided into the following three, The procedure is divided into the following three The procedure is divided into the following three , The procedure is divided into the following three The procedure is divided into the following three s, The procedure is divided into the following three The procedure is divided into the following three st, The procedure is divided into the following three The procedure is divided into the following three ste, The procedure is divided into the following three The procedure is divided into the following three step, The procedure is divided into the following three The procedure is divided into the following three steps, The procedure is divided into the following three The procedure is divided into the following three steps:, The procedure is divided into the following three Our knowledge of molecular clouds and of the processes in the interstellar medium (hereafter ISM) that lead to the birth of stars Is mostly based on Galactic studies.,Our knowledge of molecular clouds and of the processes in the interstellar medium (hereafter ISM) that lead to the birth of stars is mostly based on Galactic studies. Local Group galaxies are however sufficiently close to allow individual massive stars and molecular clouds to be detected., Local Group galaxies are however sufficiently close to allow individual massive stars and molecular clouds to be detected. M33. at a known distance. has a high star formation rate per unit area and a low overall extinction compared to M31. owing to the moderate gas content and low inclination.," M33, at a known distance, has a high star formation rate per unit area and a low overall extinction compared to M31, owing to the moderate gas content and low inclination." It is therefore an ideal laboratory for the investigation of the relationship of molecular clouds to other ISM components and evolutionary scenarios involving blue. low-luminosity galaxies.," It is therefore an ideal laboratory for the investigation of the relationship of molecular clouds to other ISM components and evolutionary scenarios involving blue, low-luminosity galaxies." Recent high-resolution optical (HST). infrared (Spitzer: hereafter. IR) and 21-em observations (VLA) have traced star formation and the ISM throughout the M33 disk with high accuracy.," Recent high-resolution optical (HST), infrared (Spitzer; hereafter, IR) and 21-cm observations (VLA) have traced star formation and the ISM throughout the M33 disk with high accuracy." Our investigation of the IR emission in M33 (????) via Spitzer high-resolution images has unveiled a variety of star formation sites through infrared colors and optical-to-IR ratios.," Our investigation of the IR emission in M33 \citep{2007A&A...476.1161V,2009A&A...493..453V,2010A&A...510A..64V, 2009A&A...495..479C} via Spitzer high-resolution images has unveiled a variety of star formation sites through infrared colors and optical-to-IR ratios." In particular. our analysis has shown the existence of two types of IR selected sources: sources with only diffuse or very faint Ha emission. and sources with a definite Ha counterpart.," In particular, our analysis has shown the existence of two types of IR selected sources: sources with only diffuse or very faint $\alpha$ emission, and sources with a definite $\alpha$ counterpart." In the former sample we can find sites at an early stage of massive star formation which give us the opportunity to study individual embedded newly born HII regions in a galaxy different than our own., In the former sample we can find sites at an early stage of massive star formation which give us the opportunity to study individual embedded newly born HII regions in a galaxy different than our own. Young stellar clusters prior to the phase of gas removal. due to photoionization or mechanical force by stellar winds. are embedded into molecular gas and detectable only at infrared and radio wavelengths.," Young stellar clusters prior to the phase of gas removal, due to photoionization or mechanical force by stellar winds, are embedded into molecular gas and detectable only at infrared and radio wavelengths." Previous searches in M33 have not been successful in detecting embedded clusters., Previous searches in M33 have not been successful in detecting embedded clusters. A radio-selected sample of sources in M33 has been analyzed by ? who found optically visible counterparts with ages between 2-10 Myr., A radio-selected sample of sources in M33 has been analyzed by \citet{2006ApJS..162..329B} who found optically visible counterparts with ages between 2-10 Myr. Similar ages have been derived by ? by analyzing the spectral energy distribution of a sample of compact HII regions.," Similar ages have been derived by \citet{2010arXiv1006.1281G} by analyzing the spectral energy distribution of a sample of compact HII regions." These results point out the paucity of embedded clusters which might be a short-lived phase of the cluster lifetime., These results point out the paucity of embedded clusters which might be a short-lived phase of the cluster lifetime. A dust abundance lower than usual or à mass spectrum of molecular clouds steeper than in our Galaxy might be responsible for this result., A dust abundance lower than usual or a mass spectrum of molecular clouds steeper than in our Galaxy might be responsible for this result. ? suggest to analyze an IR selected sample. an approach that is now possible thanks to M33 Spitzer images and 24 ssource catalogue of ?..," \citet{2006ApJS..162..329B} suggest to analyze an IR selected sample, an approach that is now possible thanks to M33 Spitzer images and 24 source catalogue of \citet{2007A&A...476.1161V}." Mid-IR sources Which have no visible counterpart in the Ha emission map are generally faint and their nature is not obvious., Mid-IR sources which have no visible counterpart in the $\alpha$ emission map are generally faint and their nature is not obvious. Candidates include evolved clusters. evolved stars with dusty envelopes (such as pulsating asymptotic giant branch. hereafter AGBs. carbon stars ete.).," Candidates include evolved clusters, evolved stars with dusty envelopes (such as pulsating asymptotic giant branch, hereafter AGBs, carbon stars etc.)," embedded star forming sites. small young clusters which lack massive stars and hence ionizing photons.," embedded star forming sites, small young clusters which lack massive stars and hence ionizing photons." From the available catalogues we can exclude evolved clusters (aswellasPlan-etaryNebulae:see ?). since these have already removed their dusty envelope.," From the available catalogues we can exclude evolved clusters \citep[as well as Planetary Nebulae: see][]{2007A&A...476.1161V}, since these have already removed their dusty envelope." Bright evolved stars have also been catalogued and in this paper we discuss the likely presence of contamination., Bright evolved stars have also been catalogued and in this paper we discuss the likely presence of contamination. The presence of molecular clouds around these sources Would instead confirm ongoing star formation., The presence of molecular clouds around these sources would instead confirm ongoing star formation. A full imaging of molecular clouds complexes in. M33 has been completed by the BIMA interferometer (?) and the FCRAO-14m telescope (?2) using the ΙΟ J=1-0 line.," A full imaging of molecular clouds complexes in M33 has been completed by the BIMA interferometer \citep{2003ApJS..149..343E} and the FCRAO-14m telescope \citep{2003MNRAS.342..199C,2004ApJ...602..723H} using the $^{12}$ CO J=1-0 line." In our Galaxy. Giant Molecular Clouds (hereafter GMCs) break up into smaller subunits when observed at high spatial resolution (?)..," In our Galaxy, Giant Molecular Clouds (hereafter GMCs) break up into smaller subunits when observed at high spatial resolution \citep{2003ApJ...599..258R}." However. in M33 both surveys (FCRAO and BIMA) do not find any complex above the survey completeness limit (~10° M4) beyond a galactocentric radius of 4 kpe.," However, in M33 both surveys (FCRAO and BIMA) do not find any complex above the survey completeness limit $\sim 10^5$ $_\odot$ ) beyond a galactocentric radius of 4 kpc." On the other hand. star formation drops only at 7 kpe. well beyond the region where giant complexes are confined.," On the other hand, star formation drops only at 7 kpc, well beyond the region where giant complexes are confined." Recent single dish M33 surveys (??) have shown that a population of low-mass molecular clouds indeed exists and becomes the dominant one beyond 4 kpe.," Recent single dish M33 surveys \citep{2007A&A...473...91G,2010arXiv1003.3222G} have shown that a population of low-mass molecular clouds indeed exists and becomes the dominant one beyond 4 kpc." Here. molecular clouds no longer aggregate into large complexes but form predominantly in smaller mass units.," Here, molecular clouds no longer aggregate into large complexes but form predominantly in smaller mass units." This i5 likely due to the lack of spiral arms which in this flocculent spiral fade away around 4 kpe., This is likely due to the lack of spiral arms which in this flocculent spiral fade away around 4 kpc. This population of molecular elouds may be more easily affected or dispersed by the growth of HII regions and therefore their properties and detectability might be strongly linked to the evolution of the associated HII region., This population of molecular clouds may be more easily affected or dispersed by the growth of HII regions and therefore their properties and detectability might be strongly linked to the evolution of the associated HII region. However. since the aim of the all-disk surveys was to map large areas of the M33 disk. their sensitivity was not sufficient to unveil the presence of molecular gas around most of the IR sources detected by Spitzer.," However, since the aim of the all-disk surveys was to map large areas of the M33 disk, their sensitivity was not sufficient to unveil the presence of molecular gas around most of the IR sources detected by Spitzer." Thus. the nature of IR sources without associated Ha emission needs additional efforts to be clarified.," Thus, the nature of IR sources without associated $\alpha$ emission needs additional efforts to be clarified." For the aim of this paper we have restricted our sample to a few IR sources which are isolated. mostly located beyond 4 kpe. in the outer regions of M33.," For the aim of this paper we have restricted our sample to a few IR sources which are isolated, mostly located beyond 4 kpc, in the outer regions of M33." Our sample spans a variety of F(24um)y/F(CHo) flux ratios., Our sample spans a variety of $\mu$ $\alpha$ ) flux ratios. The IR fluxes and sizes of the sources suggest that they may host small young clusters, The IR fluxes and sizes of the sources suggest that they may host small young clusters The relation L—6 is not lightly constrained either.,The relation $L -\sigma$ is not tightly constrained either. Laor (2001). citing Nelson Whittle (1996). takes Lc6. and using AdeexL5 (Magorrian et al.," Laor (2001), citing Nelson Whittle (1996), takes $L \sim \sigma^{3}$, and using $M_{\rm bulge}\propto L^{1.18}$ (Magorrian et al." 1998) gets MieXe07., 1998) gets $M_{\rm bulge}\propto \sim \sigma^{3.5}$. Using this relation in equation (1)) gives ο)=1.2., Using this relation in equation \ref{eq:corr1}) ) gives $\beta=1.2$. Warring Ris (2004) find ;2=1.12x0.06. and Mpy/Mig=0.14640.04% for Mise05x10M.," Härring Rix (2004) find $\beta=1.12\pm 0.06$, and $M_{\rm BH}/M_{\rm bulge}=0.14\% \pm 0.04\%$ for $M_{\rm bulge} \sim 5\times 10^{10} M_\odot$." Based on these considerations. and for the purpose of the present paper. I assume the deviation [rom a linear Api—Mus relation to be due to an additional dependance on the dispersion velocity where O~LO* and X70—I.," Based on these considerations, and for the purpose of the present paper, I assume the deviation from a linear $M_{\rm BH} - M_{\rm bulge}$ relation to be due to an additional dependance on the dispersion velocity where $\Theta \simeq 10^{-3}$ and $\chi \simeq 0-1$." The above expression is an average one. as the relations between the SAIBIT mass. the bulge mass. and (he dispersion velocity are somewhat clilferent for ellipical ealaxies. classical bulges and pseudo-bulges (Gadotti Ixauffinann 2009).," The above expression is an average one, as the relations between the SMBH mass, the bulge mass, and the dispersion velocity are somewhat different for elliptical galaxies, classical bulges and pseudo-bulges (Gadotti Kauffmann 2009)." In (his first presentation of the idea I ignore these dillerences., In this first presentation of the idea I ignore these differences. In this paper I will ev to account for relation (2)) with a feedback mechanism based on jets launched by the SMDIL., In this paper I will try to account for relation \ref{eq:corr2}) ) with a feedback mechanism based on jets launched by the SMBH. The feedback mechanism where AGN jets (outflow: wind) suppress gas [rom cooling to low temperatures and from forming stars was discussed [or both cooling flows in galaxies and clusters of galaxies (e.g.. Dinnev Tabor 1995: Nulsen Fabian 2000: Revnolds et al.," The feedback mechanism where AGN jets (outflow; wind) suppress gas from cooling to low temperatures and from forming stars was discussed for both cooling flows in galaxies and clusters of galaxies (e.g., Binney Tabor 1995; Nulsen Fabian 2000; Reynolds et al." 2002: Omma Binney 2004: Soker Pizzolato 2005). and in galaxy formation (e... Silk Rees 1098; Fabian 1999: Ning 2003: Croton et al.," 2002; Omma Binney 2004; Soker Pizzolato 2005), and in galaxy formation (e.g., Silk Rees 1998; Fabian 1999; King 2003; Croton et al." 2006: Bower et al., 2006; Bower et al. 2008: Shabala Alexander 2009)., 2008; Shabala Alexander 2009). I note that some of the papers (e.g.. Silk Rees 1998: Ixing 2003) make use of the Eddington Iuninosity. limit: (le model proposed here make no use of the Eddington luminosity limit.," I note that some of the papers (e.g., Silk Rees 1998; King 2003) make use of the Eddington luminosity limit; the model proposed here make no use of the Eddington luminosity limit." Most models (e.g.. Silk Rees 1993: Fabian 1999) do not consider the geometry explicitly: here the geometry of (he narrow jets and the motion of their source are kev issues.," Most models (e.g., Silk Rees 1998; Fabian 1999) do not consider the geometry explicitly; here the geometry of the narrow jets and the motion of their source are key issues." Bower et al. (, Bower et al. ( 2003) numerically tried to derive the Alpi—Mise correlation.,2008) numerically tried to derive the $M_{\rm BH}-M_{\rm bulge}$ correlation. In the present paper I (ry to present the basic physics that I propose leads to this correlation., In the present paper I try to present the basic physics that I propose leads to this correlation. I do not consider the formation of the seed SMDII. but rather assume its existence.," I do not consider the formation of the seed SMBH, but rather assume its existence." The proposed mechanism is based on the following assumptions., The proposed mechanism is based on the following assumptions. our data).,our data). Some insights about (his are were previously reported by van der ναί (1978) using photographie plates., Some insights about this arc were previously reported by van der Kruit (1978) using photographic plates. The position of the streams progenitor remains unknown — il mav be completely disrupted or max lie hidden behind (the galaxys clisk., The position of the stream's progenitor remains unknown — it may be completely disrupted or may lie hidden behind the galaxy's disk. Our BBO image of the nearby galaxy NGC 1084 (Fig.1b) also displays three. eiant disconnected plumes of similar width extending a large galactocentric distance (~ 30 kpc) into its halo., Our BBO image of the nearby galaxy NGC 1084 (Fig.1b) also displays three giant disconnected plumes of similar width extending a large galactocentric distance $\sim$ 30 kpc) into its halo. Two of these tails emerge in opposite directions [rom the inner region of the ealaxy while a third one appears completely disconnected from (he galaxy., Two of these tails emerge in opposite directions from the inner region of the galaxy while a third one appears completely disconnected from the galaxy. These features were first detected alter a close visual inspection of SDSS images., These features were first detected after a close visual inspection of SDSS images. However. il remains difficult to assert if this collection of arcing features is associated: with one or several different merger events.," However, it remains difficult to assert if this collection of arcing features is associated with one or several different merger events." In addition to the remains of presumably lone disrupted companions. our data also capture the ongoing tidal disruption of satellite galaxies that are still visible. seen as long tails extending [rom the progenitor satellite.," In addition to the remains of presumably long disrupted companions, our data also capture the ongoing tidal disruption of satellite galaxies that are still visible, seen as long tails extending from the progenitor satellite." Perhaps. the most conspicuous exanmples can be seen in the image of NGC 4216 (Fig.," Perhaps, the most conspicuous examples can be seen in the image of NGC 4216 (Fig." 1c)., 1c). This panoramic view of the galaxy. shows two satellites with distinct cores ancl extremely long tails (hat extend several kiloparsecs into the principal galaxys halo., This panoramic view of the galaxy shows two satellites with distinct cores and extremely long tails that extend several kiloparsecs into the principal galaxy's halo. The host galaxy. also clisplavs a prominent (thick disk with several pillars arising from it., The host galaxy also displays a prominent thick disk with several pillars arising from it. The nature of these features (tidal debris or rai pressure signabures) is discussed at length in Martinez-Delgado et al. (, The nature of these features (tidal debris or ram pressure signatures) is discussed at length in Martinez-Delgado et al. ( 2010).,2010). Among the most conspicuous features found in our survey are coherent structures that resemble an open umbrella and extending tens of kiloparsees into (he host spiral's halo., Among the most conspicuous features found in our survey are coherent structures that resemble an open umbrella and extending tens of kiloparsecs into the host spiral's halo. These spectacular formations are often located on both sides of the principal galaxy and display long narrow shafts that terminate in a giant. partial shell of debris.," These spectacular formations are often located on both sides of the principal galaxy and display long narrow shafts that terminate in a giant, partial shell of debris." The most remarkable example so [ar detected is in NGC 4651. shown in Figure Id.," The most remarkable example so far detected is in NGC 4651, shown in Figure 1d." This is also the brightest tidal stream detected in our pilot survey (visible even in very short exposure times)., This is also the brightest tidal stream detected in our pilot survey (visible even in very short exposure times). The jet-like feature is strikingly coherent aud narrow., The jet-like feature is strikingly coherent and narrow. This feature was, This feature was shape of the PMS.,shape of the PMS. We identify the cluster PMS as best represented by the 1 Myr isochrone indicating that Tr114 is a very young stellar population., We identify the cluster PMS as best represented by the 1 Myr isochrone indicating that 14 is a very young stellar population. The derived distance modulus (DM=11.8X:0.4 mag) corresponds to a distance of ~2.3+0.4 kpc., The derived distance modulus $DM=11.8\pm0.4$ mag) corresponds to a distance of $\sim2.3\pm0.4$ kpc. The uncertainty is estimated by finding the closest and farthest distance which gives an acceptable approximation of the PMS of the cluster., The uncertainty is estimated by finding the closest and farthest distance which gives an acceptable approximation of the PMS of the cluster. " The extinction was simultaneously derived to Ax,=0.38+0.03 mag, using Ry=4.16 (Carraroetal.2004) and the relation of visual and near-infrared extinction according to Cardelli et al. ("," The extinction was simultaneously derived to $A_{K_S}=0.38\pm0.03$ mag, using $R_V=4.16$ \cite{carraro} and the relation of visual and near-infrared extinction according to Cardelli et al. (" 1989).,1989). " The error on the average extinction is estimated by shifting the isochrone towards the blue and red boundary of the upper PMS, respectively."," The error on the average extinction is estimated by shifting the isochrone towards the blue and red boundary of the upper PMS, respectively." " 'The distance of 2.3 kpc is comparable, though slightly smaller, to earlier derived distance estimates."," The distance of 2.3 kpc is comparable, though slightly smaller, to earlier derived distance estimates." " For example, Carraro et al. ("," For example, Carraro et al. (" "2004) locates Tr114 at a distance of 2.5 kpc, while Tapia et al. (","2004) locates 14 at a distance of 2.5 kpc, while Tapia et al. (" 2003) estimated a somewhat larger distance of 2.63 kpc.,2003) estimated a somewhat larger distance of 2.63 kpc. " Comparing our extinction estimate, which corresponds to an Ay=3.0+0.4 mag following the applied extinction law, reveals a slightly higher average extinction towards Tr114 compared to earlier values, e.g. Ay—2.6€0.2 mag (Tapiaetal.2003) or Αν=2.00.2 mag (Carraroetal."," Comparing our extinction estimate, which corresponds to an $A_V=3.0\pm0.4$ mag following the applied extinction law, reveals a slightly higher average extinction towards 14 compared to earlier values, e.g. $A_V=2.6\pm0.2$ mag \cite{tapia03} or $A_V=2.0\pm0.2$ mag \cite{carraro}." "2004).. We benefit from a higher angular resolution, and the improved photometry might explain the slight differences observed in the different studies."," We benefit from a higher angular resolution, and the improved photometry might explain the slight differences observed in the different studies." " The best fitting values, distance=2.3+0.4 kpc and Ax,=0.38+0.03 mag, are derived using a 1 Myr PMS isochrone."," The best fitting values, $=2.3\pm0.4$ kpc and $A_{K_S}=0.38\pm0.03$ mag, are derived using a 1 Myr PMS isochrone." This isochrone fits the PMS-MS colour width and shape of the PMS best., This isochrone fits the PMS-MS colour width and shape of the PMS best. " With a different combination of distance and extinction (distance=2.6+0.4 kpc, Ax,=0.36+0.03 mag), a slightly younger isochrone (0.5 Myr) represents the PMS-MS colour difference well, but the PMS shape is less well reproduced refcmd))."," With a different combination of distance and extinction $=2.6\pm0.4$ kpc, $A_{K_S}=0.36\pm0.03$ mag), a slightly younger isochrone (0.5 Myr) represents the PMS-MS colour difference well, but the PMS shape is less well reproduced \\ref{cmd}) )." For the 2 Myr isochrone the colour difference between MS and PMS is very narrow compared to the observations., For the 2 Myr isochrone the colour difference between MS and PMS is very narrow compared to the observations. We therefore adopt an uncertainty of 0.5 Myr on the age., We therefore adopt an uncertainty of 0.5 Myr on the age. " However, very young stellar ages should be dealt with carefully as evolutionary models have large uncertainties for ages <1 Myr, given the strong dependence of the predicted luminosities and temperatures on the initial conditions of the computation (e.g.Baraffeetal."," However, very young stellar ages should be dealt with carefully as evolutionary models have large uncertainties for ages $\lesssim 1$ Myr, given the strong dependence of the predicted luminosities and temperatures on the initial conditions of the computation \cite[e.g.][]{baraffe}." "2002).. Comparing the CMD with the Siess isochrones, we find the 1 Myr isochrone to best resemble the PMS."," Comparing the CMD with the Siess isochrones, we find the 1 Myr isochrone to best resemble the PMS." " However, at 14 mag«Ks<16 mag we identify a number of stars with colours bluer than the isochrone."," However, at 14 $νε, called thecase,, the spectrum is Initially the jet propagates as if it were spherical with an equivalent isotropic energy of Eque=05Fiso/2, where 0; is the half-opening angle of the jet."," The flux at the observer, $F_\nu$, is given by For $\nu_{\rm m}>\nu_{\rm c}$, called the, the spectrum is Initially the jet propagates as if it were spherical with an equivalent isotropic energy of $E_{\rm true} = \theta_{j}^2E_{\rm iso}/2$, where $\theta_{j}$ is the half-opening angle of the jet." " Even if the prompt emission is highly collimated, the Lorentz factor drops a«€0;! around the time and the jet starts to expand sideways (Ioka&Mészáros 2005)."," Even if the prompt emission is highly collimated, the Lorentz factor drops $\gamma_{\rm d} < \theta_{j}^{-1}$ around the time and the jet starts to expand sideways \citep{ioka2005}." ". Consequently, the jet becomes detectable by the off-axis observers."," Consequently, the jet becomes detectable by the off-axis observers." These afterglows are not associated with the prompt GRB emission., These afterglows are not associated with the prompt GRB emission. " Due to relativistic beaming, an observer located at Oops, outside the initial opening angle of the jet (θους> 6;), will observe the afterglow emission only at t~tg, when Ya= 'The"," Due to relativistic beaming, an observer located at $\theta_{obs}$ , outside the initial opening angle of the jet $\theta_{obs}> \theta_j$ ), will observe the afterglow emission only at $t \sim t_\theta$, when $\gamma_{\rm d} = \theta_{j}^{-1}$." " 0;.received afterglow flux by an off-axis observer in the point source approximation, valid for 055,>> 01, is related to that seen by an on-axis observer by (Granot where and 3=,/1—1/42."," The received afterglow flux by an off-axis observer in the point source approximation, valid for $\theta_{obs} \gg \theta_{j}$ , is related to that seen by an on-axis observer by \citep{granot2002,totani2002,Japelj2011} where and $\beta = \sqrt{1-1/\gamma_{\rm d}^2}$." " The time evolution of the Lorentz factor in given by where t; is the jet break time, c0.7(1+ days (Sarietal.1999)."," The time evolution of the Lorentz factor in given by where $t_j$ is the jet break time, $\approx 0.7(1+z)(E_{51}/n)^{1/3}(\theta_j/0.1)^2$ days \citep{sari1999}." ". Figure 2 shows four examples of afterglows as a function of observed angle 055, for the case of 0;=0.1 at z=3 for typical parameters described in the figure.", Figure \ref{fig:GRBafterglow} shows four examples of afterglows as a function of observed angle $\theta_{obs}$ for the case of $\theta_{j} = 0.1$ at $z =3$ for typical parameters described in the figure. The flux is calculated for an observational frequency v=5x1014Hz within the Gaia bandwidth., The flux is calculated for an observational frequency $\nu = 5\times 10^{14} \rm{Hz}$ within the Gaia bandwidth. " Depending on the parameters of the afterglow, the light curve can appear above the Gaia observational limits."," Depending on the parameters of the afterglow, the light curve can appear above the Gaia observational limits." " Due to the large quantity of free parameters, a Monte Carlo approach is essential to explore the detectability of a large number of events and will be explained in the next section."," Due to the large quantity of free parameters, a Monte Carlo approach is essential to explore the detectability of a large number of events and will be explained in the next section." A fraction of GRBs with X-ray or radio afterglows can be hidden by dust absorption from their host galaxies., A fraction of GRBs with X-ray or radio afterglows can be hidden by dust absorption from their host galaxies. " The observed flux after extinction correction can be simply written as (see,e.g,Elíasdóttiretal.2009) where A) is the extragalactic extinction along the line of sight, A).ert, as a function of the wavelength A plus the extinction from the Milk Way, A).mw."," The observed flux after extinction correction can be simply written as \citep[see, e.g,][]{eliasdottir2009} where $A_{\lambda}$ is the extragalactic extinction along the line of sight, $A_{\lambda;ext}$, as a function of the wavelength $\lambda$ plus the extinction from the Milk Way, $A_{\lambda;MW}$." " For A);ext, we adopted a simple Small Magellanic Cloud (SMC) type extinction model."," For $A_{\lambda;ext}$, we adopted a simple Small Magellanic Cloud (SMC) type extinction model." " The SMC model was already shown to provide good fits for several GRB afterglows observations (see,e.g,Elíasdóttir 2009)."," The SMC model was already shown to provide good fits for several GRB afterglows observations \citep[see, e.g,][]{eliasdottir2009}." . For Ax;rw; we use the average value 0.15 from observations of Schadyetal.(2012) and adopt a typical value of 0.3 for Ay.," For $A_{\lambda;MW}$, we use the average value 0.15 from observations of \citet{schady2012} and adopt a typical value of 0.3 for $A_{V}$." " In Fig. 3,,"," In Fig. \ref{fig:dust}," " we show the SMC extinction curve in comparison with other popular models, Large MagellanicCloud (LMC) and MilkyWay (MW)."," we show the SMC extinction curve in comparison with other popular models, Large MagellanicCloud (LMC) and MilkyWay (MW)." " The model choice has no significant effect on our results, since all of them have a similar trend in the G band range."," The model choice has no significant effect on our results, since all of them have a similar trend in the G band range." lower surface densities the migration was always divergent.,lower surface densities the migration was always divergent. In a second run of experiments. we have fixed the surface density to be X2 trying instead dillerent aspect ratios.," In a second run of experiments, we have fixed the surface density to be $\Sigma =\Sigma_0$ trying instead different aspect ratios." For the Sub-Jupiter gas giant we have managed to achieve the convergent migration of the planets for 7=0.03 (model 12)., For the Sub-Jupiter gas giant we have managed to achieve the convergent migration of the planets for $h=0.03$ (model 12). For this choice of parameters. the relative migration of the planets is too fast and they passed through the 1:2 mean motion resonance without being captured. into this commensurability.," For this choice of parameters, the relative migration of the planets is too fast and they passed through the 1:2 mean motion resonance without being captured into this commensurability." μον migrated. further until the Earth was trapped at the edge of the eap alter 2400 orbits., They migrated further until the Super-Earth was trapped at the edge of the gap after 2400 orbits. Suecessively the migration reversed as it is shown in Fig., Successively the migration reversed as it is shown in Fig. 1l (left panel) and the planets. passed again through the resonance region without being captured., \ref{res} (left panel) and the planets passed again through the resonance region without being captured. In order to slow down the relative racial motion of the planets. we have assumec in model 13 the higher aspect ratio of the disc bh=0.04. without changing other parameters.," In order to slow down the relative radial motion of the planets, we have assumed in model 13 the higher aspect ratio of the disc $h=0.04$, without changing other parameters." In this case. the relative migration of the planets at the beginning was slowly convergent but later on became divergent.," In this case, the relative migration of the planets at the beginning was slowly convergent but later on became divergent." " Finally. we have achieved the 1:2) mean motion resonance [or a disc with h=0.03. p=2-10” an No05M, (model 14)."," Finally, we have achieved the 1:2 mean motion resonance for a disc with $h=0.03$, $\nu=2 \cdot 10^{-6}$ and $\Sigma=0.5\Sigma_0$ (model 14)." The lower surface density. causes a slower migration of the Super-Earth and the convergen relative migration of the planets was slower than in moce 12., The lower surface density causes a slower migration of the Super-Earth and the convergent relative migration of the planets was slower than in model 12. In Fig., In Fig. I1. (right panel) we present the semi-major axis ratio of the planets., \ref{res} (right panel) we present the semi-major axis ratio of the planets. Phe divergent migration curing the firs 1000 is orbitscaused w the gas giant during the eap opening process., The divergent migration during the first 1000 orbits is caused by the gas giant during the gap opening process. It can be x(en that after 3000 orbits the planets approach the comunxnsurabilitv. both resonant angles ane the angle between aysiclal lines starts to librate around x and the eccentricities of the planets increase.," It can be seen that after 3000 orbits the planets approach the commensurability, both resonant angles and the angle between apsidal lines starts to librate around $\pi$ and the eccentricities of the planets increase." However. at the end. the planets migrate out of the resonance.," However, at the end, the planets migrate out of the resonance." " The Earth with mass of 10 AZ, opens a shallow dip. which moves along with the migrating planet."," The Super-Earth with mass of 10 $M_{\oplus}$ opens a shallow dip, which moves along with the migrating planet." The superposition of the dip and the outer edge of the gap creates a trap ancl leads to the capture of the Super-Earth., The superposition of the dip and the outer edge of the gap creates a trap and leads to the capture of the Super-Earth. From the above investigations we conclude that mean motion resonances between a gas giant and a Super-Earth which is located. further away in the disc should. be rare., From the above investigations we conclude that mean motion resonances between a gas giant and a Super-Earth which is located further away in the disc should be rare. If the mass of the gas giant. is higher than O.7AL;. the gap opened by the planet is wide and the Super-Earth is captured in the trap before reaching the mean motion commensurability.," If the mass of the gas giant is higher than $0.7M_J$, the gap opened by the planet is wide and the Super-Earth is captured in the trap before reaching the mean motion commensurability." For lower mass gas giants the gap is narrower and allows in principle the occurrence of the 1:2 resonance. but the migration of the gas giant is too Last for that.," For lower mass gas giants the gap is narrower and allows in principle the occurrence of the 1:2 resonance, but the migration of the gas giant is too fast for that." Our analysis. in which dillerent disc parameters have been examined. shows that it is possible to obtain the short-lasting 1:2 mean motion commensurability between a Jupiter mass gas giant on the internal orbit and a Super-Earth on the external one only for very thin clises with low surlace density.," Our analysis, in which different disc parameters have been examined, shows that it is possible to obtain the short-lasting 1:2 mean motion commensurability between a Sub-Jupiter mass gas giant on the internal orbit and a Super-Earth on the external one only for very thin discs with low surface density." The large-scale orbital migration in voung planetary systems mieht plav an important role in shaping up their architectures., The large-scale orbital migration in young planetary systems might play an important role in shaping up their architectures. The tidal gravitational forces are able to rearrange the planet positions according to their masses and clise parameters., The tidal gravitational forces are able to rearrange the planet positions according to their masses and disc parameters. The final configuration after the disc dispersal might be what we actually observe in extrasolar systems., The final configuration after the disc dispersal might be what we actually observe in extrasolar systems. In. particular. in a svstem with a gas giant and a Super-Earth the convergent migration can leac to mean motion resonant locking or the Super-Earth is captured at the outer edge of the gap.," In particular, in a system with a gas giant and a Super-Earth the convergent migration can lead to mean motion resonant locking or the Super-Earth is captured at the outer edge of the gap." Phe final outcome depends on the masses of the planets and on the dise parameters., The final outcome depends on the masses of the planets and on the disc parameters. We have investigated the evolution of the Super-Earth ancl of the gas giant embedded in à gaseous disc when the Super-Earth is on the external orbit and the eas giant on the internal one similarly as in PNOS., We have investigated the evolution of the Super-Earth and of the gas giant embedded in a gaseous disc when the Super-Earth is on the external orbit and the gas giant on the internal one similarly as in PN08. " However. we have concentrated here on systems with outer planet no more massive than 1037, and we have explored in details the evolution of such svstenis extending in this way the investigations done in PNOS."," However, we have concentrated here on systems with outer planet no more massive than $10 M_\oplus$ and we have explored in details the evolution of such systems extending in this way the investigations done in PN08." We have changed the initial radial location of the Super-Earth. the masses of the planets anc the cise parameters in order to check the possibility of locking into the 2:8 and 1:2 commensurabilities.," We have changed the initial radial location of the Super-Earth, the masses of the planets and the disc parameters in order to check the possibility of locking into the 2:3 and 1:2 commensurabilities." What we have found. is tha it is clillicult to obtain mean motion resonant configurations »ween. planets., What we have found is that it is difficult to obtain mean motion resonant configurations between planets. For the set of dise parameters ancl plane masses considered in this paper. it turns out that either the migration is divergent. or the Super-Earth mierates faster wn the Jupiter until it is trapped at the outer edge of 1e gap opened hy the gas giant.," For the set of disc parameters and planet masses considered in this paper, it turns out that either the migration is divergent, or the Super-Earth migrates faster than the Jupiter until it is trapped at the outer edge of the gap opened by the gas giant." Thus. the trapping of the uluper-Earth at the edge of the gap prevents the capture in 10 mean motion resonance because the gap is too wide ane 1e resonant region is inside it.," Thus, the trapping of the Super-Earth at the edge of the gap prevents the capture in the mean motion resonance because the gap is too wide and the resonant region is inside it." " 1n our studies we have investigated the behaviour of a uluper-Earth. which means a planet with a mass not bigger iun 1037,. in the presence of a gas giant."," In our studies we have investigated the behaviour of a Super-Earth, which means a planet with a mass not bigger than $10M_{\oplus}$, in the presence of a gas giant." Switching on 1e accretion. would result in exceeding the mass limit for Super-Earth. so we didn't take aceretion into account.," Switching on the accretion, would result in exceeding the mass limit for a Super-Earth, so we didn't take accretion into account." —owever. if we allow the planets to accrete the matter than 10 planet is released from the trap and it forms the resonant μαructure. as it has been shown in PNOS.," However, if we allow the planets to accrete the matter than the planet is released from the trap and it forms the resonant structure, as it has been shown in PN08." If the mass of the gas giant. is low enough the gap is narrow and the 1:2 mean motion resonance is allowed., If the mass of the gas giant is low enough the gap is narrow and the 1:2 mean motion resonance is allowed. For a system with a Sub-Jupiter mass planet on the internal orbit and a Super-Earth on the external one. we have observed the resonant configuration only for very thin clises with low surface densitv.," For a system with a Sub-Jupiter mass planet on the internal orbit and a Super-Earth on the external one, we have observed the resonant configuration only for very thin discs with low surface density." Phe resonant configuration dic not hold during the evolution. so no mean motion resonance has been observed at the end of our simulations.," The resonant configuration did not hold during the evolution, so no mean motion resonance has been observed at the end of our simulations." Moreover. for a gas giant planet. with Jupiter mass we have obtained a configuration in which the apsidal resonance is present if the Super-Earth is captured at the edge of the gap.," Moreover, for a gas giant planet with Jupiter mass we have obtained a configuration in which the apsidal resonance is present if the Super-Earth is captured at the edge of the gap." Similar structures between apsidal lines are actually observed. in core and 470Ala exirasolar planetary svstenis., Similar structures between apsidal lines are actually observed in $\upsilon And$ and $47 UMa$ extrasolar planetary systems. The dise properties used here have been determined by the requirement of convergent migration in the disc., The disc properties used here have been determined by the requirement of convergent migration in the disc. In the relatively thin disc with aspect ratio /=0.03 (models 3-6) we have found that the eccentricity of the gas giant increases. while the eccentricity of the Super-Earth remains very low.," In the relatively thin disc with aspect ratio $h=0.03$ (models 3-6) we have found that the eccentricity of the gas giant increases, while the eccentricity of the Super-Earth remains very low." The growth of the Jupiter cecentricity is modest but well pronounced., The growth of the Jupiter eccentricity is modest but well pronounced. The fact that the Super-Earth remains on an almost circular orbit. can have important implications for the habitability of such planets., The fact that the Super-Earth remains on an almost circular orbit can have important implications for the habitability of such planets. As an example. let us consider à svslem containing a gas giant inside the habitable zone.," As an example, let us consider a system containing a gas giant inside the habitable zone." Then. small planets or planetary. embryos can survive the evolution of the svstem being captured at the outer edge of the gap opened by the giant planet and thus can be located exactly in the habitable zone.," Then, small planets or planetary embryos can survive the evolution of the system being captured at the outer edge of the gap opened by the giant planet and thus can be located exactly in the habitable zone." One of the possible. places to look for such configurations is the svstenm LID 27442., One of the possible places to look for such configurations is the system HD 27442. Another interesting object is pCrD. a star with a," Another interesting object is $\rho$ CrB, a star with a" effects that will beam/focus more of the emission down towards the disk: Martocchia Matt 1996).,effects that will beam/focus more of the emission down towards the disk; Martocchia Matt 1996). We first investigate whether a correlation exists between flux and the various fit parameters. and in particular whether changes in reflection are dramatic.," We first investigate whether a correlation exists between flux and the various fit parameters, and in particular whether changes in reflection are dramatic." We do so by first fitting a simple model that consists of a power law and redshifted Gaussian to the 3-10 keV band. and comparing that with a power law fit to the 10-20 keV band.," We do so by first fitting a simple model that consists of a power law and redshifted Gaussian to the 3-10 keV band, and comparing that with a power law fit to the 10-20 keV band." In doing so. we find that while the intrinsic 3-10 keV power law slope increases. yooo appears to flatten with increasing flux (Fig. 59).," In doing so, we find that while the intrinsic 3-10 keV power law slope increases, $\Gamma_{10-20}$ appears to flatten with increasing flux (Fig. \ref{fig5-gammagamma}) )." Additionally. the iron Ixo flux {ας does not change with any statistical significance while the flux between the lowest and highestf4 flux nearly doubles (Table 2)): similar results for the constancy of the iron line in 6-30-15 was noted by MeHardy et al. (," Additionally, the iron $\rm K\alpha$ flux $F_{\rm K\alpha}$ does not change with any statistical significance while the flux between the lowest and highest flux nearly doubles (Table \ref{tab1-pl}) ); similar results for the constancy of the iron line in $-$ 6-30-15 was noted by McHardy et al. (" 1998). and by Chiang et al. (,"1998), and by Chiang et al. (" 1999) for Seyfert | galaxy NGC5548.,1999) for Seyfert 1 galaxy NGC5548. The ratio plot of data-to-model using a simple power law fit to the 3-20 keV data clearly illustrates the difference in the line and reflection component between the lowestand highest flux states in Fig., The ratio plot of data-to-model using a simple power law fit to the 3-20 keV data clearly illustrates the difference in the line and reflection component between the lowestand highest flux states in Fig. Jaa. Having demonstrated the existence of a strong reflection component in Fig., \ref{fig7-ratioplts}a a. Having demonstrated the existence of a strong reflection component in Fig. Jaa. and assessed its nature with more complicated tits in Lee et al. (," \ref{fig7-ratioplts}a a, and assessed its nature with more complicated fits in Lee et al. (" 1999) for this data set. we next investigate the features of reflection in detail for the different fluxes by fitting the data with a multicomponent model that includes the reflected spectrum.,"1999) for this data set, we next investigate the features of reflection in detail for the different fluxes by fitting the data with a multicomponent model that includes the reflected spectrum." The underlying continuum is fit with the model which is a power law with an exponential eut off at high energies reflected by an optically thick slab of neutral material (Magdziarz Zdziarski 1995)., The underlying continuum is fit with the model which is a power law with an exponential cut off at high energies reflected by an optically thick slab of neutral material (Magdziarz Zdziarski 1995). We fix the inclination angle of the reflector at 30 so as to agree with the disk inclination one obtains when fitting accretion disk models o the iron line profile as seen by (Tanaka et al., We fix the inclination angle of the reflector at $30^\circ$ so as to agree with the disk inclination one obtains when fitting accretion disk models to the iron line profile as seen by (Tanaka et al. 1995)., 1995). Due o the strong coupling oetween the fit parameters of L'. abundances. and reflection. we fix he low- and iron abundance respectively a 0.5 and 2 solar abundances ds determined by Lee et al. (," Due to the strong coupling between the fit parameters of $\Gamma$, abundances, and reflection, we fix the low-Z and iron abundance respectively at 0.5 and 2 solar abundances as determined by Lee et al. (" 1999) for the fits presented in Table 3:: the high energy cutoff is fixed at 100 keV appropriate for this object (Guainazzi et al.,1999) for the fits presented in Table \ref{tab2-pexrav}; the high energy cutoff is fixed at 100 keV appropriate for this object (Guainazzi et al. 1999: Lee et al., 1999; Lee et al. 1999)., 1999). An additional Gaussian component is added to model the iron line., An additional Gaussian component is added to model the iron line. " Using this complex model. we find that the 4-20 keV power law slope and reflection fraction /? increases with flux (Table 91) while the strength of theiron line. , decreases (Fig."," Using this complex model, we find that the 4-20 keV power law slope and reflection fraction $R$ increases with flux (Table \ref{tab2-pexrav}) ) while the strength of theiron line, $F_{\rm K\alpha}$ decreases (Fig." Gau). the latter in contrast to the findings for a constant 1; discussed in the contextof simpler fits.," \ref{fig6-refewfe}a a), the latter in contrast to the findings for a constant $F_{\rm K\alpha}$ discussed in the contextof simpler fits." " (Pi, is defined as the total number of photon flux in the line.)", $F_{\rm K\alpha}$ is defined as the total number of photon flux in the line.) We note that 7j; is consistent with constancy if unity abundances are assumed: this is in agreement with simple power law fits., We note that $F_{\rm K\alpha}$ is consistent with constancy if unity abundances are assumed; this is in agreement with simple power law fits. However. this leaves us with to-constrain errors. and worse fits in a 47 sense. (," However, this leaves us with difficult-to-constrain errors, and worse fits in a $\chi^2$ sense. (" With the exception of Pi. all other parameters as e.g. E shown in Table 3. follow similar trends whether unity or non-unity abundanees are assumed.),"With the exception of $F_{\rm K\alpha}$, all other parameters as e.g. $\Gamma$ shown in Table \ref{tab2-pexrav} follow similar trends whether unity or non-unity abundances are assumed.)" It is clear that degeneracies exist and cannot be resolved with 20 keV data - we suspect that the dependence on abundance is largely due to the modelling of the iron edge in these complex tits., It is clear that degeneracies exist and cannot be resolved with $-$ 20 keV data - we suspect that the dependence on abundance is largely due to the modelling of the iron edge in these complex fits. Nevertheless. we test this hypothesis by including an edge feature to the simple power law model of Table 2..," Nevertheless, we test this hypothesis by including an edge feature to the simple power law model of Table \ref{tab1-pl}." " These results presented in Table 4. show that 7, is indeed consistent with constancy and strengthens the argument that the behaviour of the iron line as given by the complex model of Table 3 is complicated with degeneracies.", These results presented in Table \ref{tab-powithedge} show that $F_{\rm K\alpha}$ is indeed consistent with constancy and strengthens the argument that the behaviour of the iron line as given by the complex model of Table \ref{tab2-pexrav} is complicated with degeneracies. This and the flux constancy of the iron line is well illustrated in Fig., This and the flux constancy of the iron line is well illustrated in Fig. 7bb which shows the ratio of the best-tit data against the model of Table 3.., \ref{fig7-ratioplts}b b which shows the ratio of the best-fit data against the model of Table \ref{tab2-pexrav}. Certainly. the case is strong for a requirement of supersolar iron abundances and is reflected in the strength of the iron line.," Certainly, the case is strong for a requirement of supersolar iron abundances and is reflected in the strength of the iron line." We discuss this in depth in Lee et al. (, We discuss this in depth in Lee et al. ( 1999).,1999). " While fic, apparently decreases with flux from complex fits. we find that the reflection fraction. and absolute normalization of he reflection component {ΠΟ ΓΗ) increases with flux (Table and Fig.6bb)."," While $F_{\rm K\alpha}$ apparently decreases with flux from complex fits, we find that the reflection fraction, and absolute normalization of the reflection component $Rnorm$ ) increases with flux (Table \ref{tab2-pexrav} and \ref{fig6-refewfe}b b)." We define /?rorm=Ax2. where -4 is the ;»ower law flux at | keV. in units of LO phem7s!keV.!. (," We define $Rnorm = A * R$, where $A$ is the power law flux at 1 keV, in units of $10^{-3}$ $\ph\cm^{-2}\s^{-1}\keV^{-1}$. (" Fig.,Fig. Jaa clearly shows that stronger reflection is present during ligher flux states.), \ref{fig7-ratioplts}a a clearly shows that stronger reflection is present during higher flux states.) The anticorrelation between fy... and reflection (Fig., The anticorrelation between $F_{\rm K\alpha}$ and reflection (Fig. " 6ος) can be due to an ""artificial effect in which the presence of a strong reflection spectrum during the high flux states has he effect of removing part of the flux from the line in the tits. thereby resulting in lower observed P, during the higher flux states."," \ref{fig6-refewfe}c c) can be due to an `artificial' effect in which the presence of a strong reflection spectrum during the high flux states has the effect of removing part of the flux from the line in the fits, thereby resulting in lower observed $F_{\rm K\alpha}$ during the higher flux states." This is linked to the strong coupling between the fit parameters of D.A.and.abundance. discussed previously.," This is linked to the strong coupling between the fit parameters of $\Gamma,\ R, {\rm and}\ abundance$, discussed previously." Thereis the possibility that iron becomes more ionized as the flux increases which will weaken the observed line flux. (, Thereis the possibility that iron becomes more ionized as the flux increases which will weaken the observed line flux. ( We discuss ionization scenarios in Section 7.),We discuss ionization scenarios in Section 7.) " As always we caution the effect ( ""inadequate spectral resolution and possibly incomplete models.", As always we caution the effect of inadequate spectral resolution and possibly incomplete models. Additionally. we find that ll anticorrelates with /? (Fig.," Additionally, we find that $W_{\rm K\alpha}$ anticorrelates with $R$ (Fig." 6dd)., \ref{fig6-refewfe}d d). " This lack of proportionality between /? and VW, is unexpected in the context of the standard corona/disk geometry. the implications of which are discussed in Section 7."," This lack of proportionality between $R$ and $W_{\rm K\alpha}$ is unexpected in the context of the standard corona/disk geometry, the implications of which are discussed in Section 7." Chiang et al. (, Chiang et al. ( 1999) tind similar results in their multi-wavelength campaign of NGC:S48.,1999) find similar results in their multi-wavelength campaign of NGC5548. In light of degeneracies associated with complex tits. we primarily present our results from simple power law fits.," In light of degeneracies associated with complex fits, we primarily present our results from simple power law fits." We next investigate in greater detail the time sequences surrounding the brightest and flares., We next investigate in greater detail the time sequences surrounding the brightest and flares. In. particular. we are prompted by the peculiar behaviour of the iron line surrounding the time interval of the flare as reported by I99 for this time sequence as seen in the data.," In particular, we are prompted by the peculiar behaviour of the iron line surrounding the time interval of the flare as reported by I99 for this time sequence as seen in the data." According to 199. there is," According to I99, there is" of uucertain properties were selected for further testing here: Berkeley Ll. Turner 1. and Collinder 119.,"of uncertain properties were selected for further testing here: Berkeley 44, Turner 1, and Collinder 419." All three clusters possess BHuited published optical observations. and provide good examples of where 2\LASS observations may help to clarify previous conchisions about cluster properties.," All three clusters possess limited published optical observations, and provide good examples of where 2MASS observations may help to clarify previous conclusions about cluster properties." The sparse northern hemisphere cluster Berkeley Li (Fig. 3)), The sparse northern hemisphere cluster Berkeley 44 (Fig. \ref{fig3}) ) has been identified as au old eroup bx Carraro.Subramaniam&Janes(2X106).. although with some question about its reality )ecause of aubieuitics in the star counts and the similarity of its coloranagnitude diagram to that of stars 1u the siuroundiue refercuce field.," has been identified as an old group by \citet*{ca06}, although with some question about its reality because of ambiguities in the star counts and the similarity of its color-magnitude diagram to that of stars in the surrounding reference field." " The published co-ordiuates for the cluster by Diasetal.2002) aud Carraroetal.(2006) do not match the optical density peak visible on the Palomar Observatory Skv Survev, and au alternate cluster center (Fig. 3))"," The published co-ordinates for the cluster by \citet{di02} and \citet{ca06} do not match the optical density peak visible on the Palomar Observatory Sky Survey, and an alternate cluster center (Fig. \ref{fig3}) )" was adopted here., was adopted here. The eroup Les more than 37 from the Galactic plane. so contamination by foreground carly-type stars should be relatively low.," The group lies more than $3^{\circ}$ from the Galactic plane, so contamination by foreground early-type stars should be relatively low." However. the extreme faüntuess of cluster stars makes it uecessary to consider both high quality and low quality 2MASS data for the field. with nucertaintics of +£0.05 representing the demarcation.," However, the extreme faintness of cluster stars makes it necessary to consider both high quality and low quality 2MASS data for the field, with uncertainties of $\pm0^{\rm m}.05$ representing the demarcation." " The 241ASS JER, data for Berkeley Li (Fie. 0) ", The 2MASS $_s$ data for Berkeley 44 (Fig. \ref{fig4}) ) confirm that if is an old open cluster., confirm that it is an old open cluster. The cluster color-color diagram is devoid of carly-type stars lving within 2’ of the adopted cluster ceuter. most cluster members being cooler late-tvpe stars.," The cluster color-color diagram is devoid of early-type stars lying within $2\arcmin$ of the adopted cluster center, most cluster members being cooler late-type stars." A few stars of inferred spectral types G aud Is appear to be essentially unreddened. with most stars of spectra types Foor later reddened by similar amouuts.," A few stars of inferred spectral types G and K appear to be essentially unreddened, with most stars of spectral types F or later reddened by similar amounts." The cluster color-maguiticle diagram reveals a well-defined chump of rec ejauts at 212.2 with nuplied spectral tvpes of carly Ik. so the identification of this cluster as an old cluster is coufirmed.," The cluster color-magnitude diagram reveals a well-defined clump of red giants at $J \simeq 12.2$ with implied spectral types of early K, so the identification of this cluster as an old cluster is confirmed." The optiuuu fit bv eve to theJHA. observations vields a reddening of IT) =0.295+0.02 =L100 +£0.07) and a distance modulus of Ad;=12.1£0.1 ,The optimum fit by eye to the$_s$ observations yields a reddening of $=0.295\pm0.02$ $ = 1.00 \pm0.07$ ) and a distance modulus of $_J = 12.1 \pm0.1$ other stars. probably from the IRS 16 region of blue. hot. and windy stars (?)..,"other stars, probably from the IRS 16 region of blue, hot, and windy stars \citep{1997A&A...325..700N}." Probing the MIR source size as a function of wavelength over the N-band also probes the location of the dust giving rise to the high line-of-sight extinction in that band. dominated by the silicate absorption. as was done for (?)..," Probing the MIR source size as a function of wavelength over the $N$ -band also probes the location of the dust giving rise to the high line-of-sight extinction in that band, dominated by the silicate absorption, as was done for \citep{2007arXiv0711.0249P}." In that article. we presented first observational evidence. based on the exceptional angular resolution of an optical interferometer. for an unusual dust chemistry and silicate overabundance in the interstellar dust around GCIRS 3. located (projected) 200 mpe away of the MBH only. and the here presented MIDI experiment was designed to extend this evidence by observing another star in that region.," In that article, we presented first observational evidence, based on the exceptional angular resolution of an optical interferometer, for an unusual dust chemistry and silicate overabundance in the interstellar dust around GCIRS 3, located (projected) 200 mpc away of the MBH only, and the here presented MIDI experiment was designed to extend this evidence by observing another star in that region." In. this article. we report. ón our recent. effort. to confirm experimentally the compactness and symmetry of IRS 7 at A-band wavelengths and at OLBI baselines as a necessary preparation for future OLBI imaging and astrometric observations of the GC.," In this article, we report on our recent effort to confirm experimentally the compactness and symmetry of IRS 7 at $K$ -band wavelengths and at OLBI baselines as a necessary preparation for future OLBI imaging and astrometric observations of the GC." In addition. first MIR-fringes on IRS 7. taken with the VLTI-MIDI instrument. are presented and discussed.," In addition, first MIR-fringes on IRS 7, taken with the VLTI-MIDI instrument, are presented and discussed." In the following section the observations. and data reduction process are described. including a discussion of the measurement uncertainties.," In the following section the observations, and data reduction process are described, including a discussion of the measurement uncertainties." Sect., Sect. 3. discusses the merits of the presented data in the appropriate scientific context. separately for the K- and N-band.," \ref{sec:3} discusses the merits of the presented data in the appropriate scientific context, separately for the $K$ - and $N$ -band." The main conclusions are summarized in Sect. 4.., The main conclusions are summarized in Sect. \ref{sec:4}. The first successful near infrared fringe detection on IRS 7 was achieved with the VLTI first generation science beam combiner AMBER (?) in March 2006 on the short UT3-UT4 baseline., The first successful near infrared fringe detection on IRS 7 was achieved with the VLTI first generation science beam combiner AMBER \citep{2007A&A...464....1P} in March 2006 on the short UT3-UT4 baseline. In June 2006. the high-angular-resolution dataset could be extended by a MIDI UT2-UT3 observation.," In June 2006, the high-angular-resolution dataset could be extended by a MIDI UT2-UT3 observation." " Each observation was followed by the measurement of a calibrator star. of known diameter with negligible uncertainty with respect to the precision of our observations. given in Table |.. taken from ESO's observations preparation pages"".. and measured with the identical instrumental setup of the IRS 7 observations. to calibrate for systematic instrumental and atmospheric visibility corruptions."," Each observation was followed by the measurement of a calibrator star of known diameter with negligible uncertainty with respect to the precision of our observations, given in Table \ref{tab:1}, taken from ESO's observations preparation pages, and measured with the identical instrumental setup of the IRS 7 observations, to calibrate for systematic instrumental and atmospheric visibility corruptions." A complete log of all relevant VLTI observations is given in Table |., A complete log of all relevant VLTI observations is given in Table \ref{tab:1}. Since IRS 7 is close to the sensitivity limit of AMBER. we chose the low spectral resolution mode (8.~ 30) and a detector," Since IRS 7 is close to the sensitivity limit of AMBER, we chose the low spectral resolution mode $R\,\sim 30$ ) and a detector" To extract the resolution of the MILES spectra we follow a similar procedure as in Sánchez-Blázquezetal.(2006).,To extract the resolution of the MILES spectra we follow a similar procedure as in \citet{SanchezBlazquez2006}. . We first divide each spectrum in 11 regions equally spaced in log space to be able to assess the dependence of the resolution with wavelength., We first divide each spectrum in 11 regions equally spaced in log space to be able to assess the dependence of the resolution with wavelength. We then derive the broadening of each MILES star with respect to a library of templates at higher resolution (Indo-U.S.. MARCS. ELODIE v3.1) by using the Penalized Pixel-fiting method (pPXF) of Cappellari&Em-sellem(2004) and taking into account the resolution of each template.," We then derive the broadening of each MILES star with respect to a library of templates at higher resolution (Indo-U.S., MARCS, ELODIE v3.1) by using the Penalized Pixel-fitting method (pPXF) of \citet{Cappellari2004} and taking into account the resolution of each template." pPXF performs the fitting in the pixel scale between an observed spectrum and a linear combination of templates., pPXF performs the fitting in the pixel scale between an observed spectrum and a linear combination of templates. pPXF also allows the use of additive and multiplicative Legendre polynomials to adjust the continuum shape of the template to the one of the spectrum to be analysed., pPXF also allows the use of additive and multiplicative Legendre polynomials to adjust the continuum shape of the template to the one of the spectrum to be analysed. We made some checks and found that the final results are consistently good by adding or not these polynomials., We made some checks and found that the final results are consistently good by adding or not these polynomials. Therefore for the general test we decide not to use them., Therefore for the general test we decide not to use them. The comparison between the results of two empirical libraries and a theoretical library gives us indication not only on the resolution of MILES but also on the actual resolution of the empirical templates we use., The comparison between the results of two empirical libraries and a theoretical library gives us indication not only on the resolution of MILES but also on the actual resolution of the empirical templates we use. Hence. by using the same method. we additionally estimate the actual FWHM of the Indo-U.S. library using as templates MARCS and ELODIE v3.1 libraries.," Hence, by using the same method, we additionally estimate the actual FWHM of the Indo-U.S. library using as templates MARCS and ELODIE v3.1 libraries." Note that the very high resolution of our templates - ELODIE v3.1 (R=42000) and MARCS (R=20000) - make us confident in our results since any error in the nominal resolution has very little impact on the final derived value., Note that the very high resolution of our templates - ELODIE v3.1 (R=42000) and MARCS (R=20000) - make us confident in our results since any error in the nominal resolution has very little impact on the final derived value. After obtaining the values of the broadening for each MILES star we derive the median of FWHMs to avoid being dominated by spurious values., After obtaining the values of the broadening for each MILES star we derive the median of FWHMs to avoid being dominated by spurious values. Errors for each wavelength bin were estimated as the standard deviation of the FWHMs., Errors for each wavelength bin were estimated as the standard deviation of the FWHMs. This estimation is validated by the fact that the typical distribution of FWHM is close to a Gaussian (see Fig.1 for one example)., This estimation is validated by the fact that the typical distribution of FWHM is close to a Gaussian (see \ref{fig:Fig1} for one example). In Fig., In Fig. 2. we show the results for each wavelength bin and for each template library as described below., \ref{fig:Fig2} we show the results for each wavelength bin and for each template library as described below. With the same procedure we derived the resolution of the MILES-based SSP of Maraston&Strémbiick(2010) by using à representative subsample of them covering the whole age range - 6.5 Myr. IGyr and 10 Gyr.," With the same procedure we derived the resolution of the MILES-based SSP of \citet{Maraston2010} by using a representative subsample of them covering the whole age range - 6.5 Myr, 1Gyr and 10 Gyr." This is important as the fractional contribution of dwarfs and giants to the integrated stellar population spectrum changes with age., This is important as the fractional contribution of dwarfs and giants to the integrated stellar population spectrum changes with age. We use solar metallicity models with a Salpeter IMF., We use solar metallicity models with a Salpeter IMF. In all tests we decided to exclude the last wavelength bin at >70004 bbecause the fit was not as reliable as in the other bins for none of the MILES stars., In all tests we decided to exclude the last wavelength bin at $>7000$ because the fit was not as reliable as in the other bins for none of the MILES stars. In the following we describe the results for each template separately., In the following we describe the results for each template separately. Note that in all cases we decided to remove the reddest wavelength interval (6937—7428 A)) as we could not obtain a good fit to the spectra. possibly due to the lack to strong absorption features to constrain the fit.," Note that in all cases we decided to remove the reddest wavelength interval $6937-7428\;$ ) as we could not obtain a good fit to the spectra, possibly due to the lack to strong absorption features to constrain the fit." As a first test we follow the same procedure of Sánchez-Blázquezetal. (2006)., As a first test we follow the same procedure of \citet{SanchezBlazquez2006}. . We first fitted each 985 MILES spectra with a linear combination of Indo-U.S. spectra (1274 templates)., We first fitted each 985 MILES spectra with a linear combination of Indo-U.S. spectra (1274 templates). Then we applied the same technique to a subsample of stars chosen among the MILES and Indo-U.S. solar metallicity stars FeHsun+0.01) finding 42 and 44 stars. respectively.," Then we applied the same technique to a subsample of stars chosen among the MILES and Indo-U.S. solar metallicity stars $\pm0.01$ ) finding 42 and 44 stars, respectively." " This could give indications about possible bias in the selection of the stars,", This could give indications about possible bias in the selection of the stars. We did not find any bias between the initial sample and the final one. which excludes template mismatch and an insufficient number of templates.," We did not find any bias between the initial sample and the final one, which excludes template mismatch and an insufficient number of templates." In the following we will use only the solar metallicity subsample., In the following we will use only the solar metallicity subsample. The results are shown in panel a) of Fig., The results are shown in panel a) of Fig. 2. (see the distribution of blue and red point in Fig., \ref{fig:Fig2} (see the distribution of blue and red point in Fig. 2 panel a) for differences between all MILES stars and the solar metallicity subsample.)., \ref{fig:Fig2} panel a) for differences between all MILES stars and the solar metallicity subsample.). "We find that the early-time (/< /),) flux decline is well-constrained. a,=—1.05x0.02.","We find that the early-time $t<\tb$ ) flux decline is well-constrained, $\alpha_1=-1.05\pm 0.02$." The slope of the optical spectrum al (his time is 9=—0.9. taking into account. Milkv. Way (MW) extinelion only. but can be as shallow as 9=—0.1 if SMC-0vpe host. extinction is included. (IRhoads&Fruchter2000:Jensenοἱal.2001).," The slope of the optical spectrum at this time is $\beta=-0.9$, taking into account Milky Way (MW) extinction only, but can be as shallow as $\beta=-0.7$ if SMC-type host extinction is included \citep{randf2000,jensen2001}." . For v>vw. (the SBPs most consistent with the data). (he value of ay implies p2.07 and thus 9=—1.03. which is only slightly steeper than the observed spectrum for MW extinction.," For $\nu > \nu_c$ (the SBPs most consistent with the data), the value of $\alpha_1$ implies $p\simeq 2.07$ and thus $\beta=-1.03$, which is only slightly steeper than the observed spectrum for MW extinction." " For v,,«p«€ν and fk=0, a,=—1.05 implies p=2.4 and (thus 6= —0.7. consistent with observations;f SMC-tvpe host extinction is adopted."," For $\nu_m < \nu < \nu_c$ and $k=0$, $\alpha_1=-1.05$ implies $p=2.4$ and thus $\beta=-0.7$ , consistent with observations SMC-type host extinction is adopted." " If the break at /~8days is due to a jel. (hen simple analylic models predict that the change in temporal [τις index a should be Aa=(p+3)/4 for hk=0 and b,p. and &=0 or 2 (Sari.Piran.&Halpern1999:Panaitesen&INiunar 2001)."," If the break at $t\sim 8~{\rm days}$ is due to a jet, then simple analytic models predict that the change in temporal flux index $\alpha$ should be $\Delta\alpha=(p+3)/4$ for $k=0$ and $\nu_m < \nu < \nu_c$ or $\Delta\alpha=(p+2)/4$ for $\nu>\nu_c$ and $k=0$ or $2$ \citep{sph1999,pandk2001}." . Kiar Panaitesen (2000) find. using a semi-analvtic model. that the jet break is rather smooth. especiallyfor a wind environment (7= 2). and therefore inconsistent. with the sharp break Chat we infer.," Kumar Panaitescu (2000) find, using a semi-analytic model, that the jet break is rather smooth, especiallyfor a wind environment $k=2$ ), and therefore inconsistent with the sharp break that we infer." However. initial results of numerical calevdlations of the jet break (Granotetal.2001).. based on a 2D hvdrodynanmic simulation of the jet lor 7=0. indicate that the break can be rather sharp (with s~4.5 for an observer along the jet axis). ancl (hat à» is smaller by ~0.35 compared to the simple analvtie predictions mentioned above. making Aq larger by a similar factor.," However, initial results of numerical calculations of the jet break \citep{granot2001}, based on a 2D hydrodynamic simulation of the jet for $k=0$, indicate that the break can be rather sharp (with $s\sim 4.5$ for an observer along the jet axis), and that $\alpha_2$ is smaller by $\sim 0.35$ compared to the simple analytic predictions mentioned above, making $\Delta\alpha$ larger by a similar factor." Nevertheless. ihe sharpness of the break still presents a serious problem [or the model where the jet propagates into a stellarwind (&= 2).," Nevertheless, the sharpness of the break still presents a serious problem for the model where the jet propagates into a stellarwind $k=2$ )." " Also. the SBP is expected to become more uniform al 2df, compares to /\tb$ compares to $t<\tb$ \citep{iandn2001,pana2001}. ." Since we assume, Since we assume process. Whose importance within (he overall scheme of nucleosvnüthesis is nol vel involves the inelastic scattering of neutrinos olf of nuclei and is referred. to as neulrino nucleosvuthesis. or the r-process.,"process, whose importance within the overall scheme of nucleosynthesis is not yet well-quantified, involves the inelastic scattering of neutrinos off of nuclei and is referred to as neutrino nucleosynthesis, or the $\nu$ -process." " Neutrino nucleosvnthesis was discussed by Donmogatskyv. Eramzhvan. Naclvozhin (1978). who focussed mainly on iis role in the production of the lightest elements. such as ?IL ""He. *Li. or D. Later. Woosley IHaxton (1983) expanded on the role of the z-process in the production of fIuorine aud subsequently. Wooslev et al. ("," Neutrino nucleosynthesis was discussed by Domogatsky, Eramzhyan, Nadyozhin (1978), who focussed mainly on its role in the production of the lightest elements, such as $^{2}$ H, $^{3}$ He, $^{7}$ Li, or $^{11}$ B. Later, Woosley Haxton (1988) expanded on the role of the $\nu$ -process in the production of fluorine and subsequently, Woosley et al. (" 1990) published predicted vields for a imber of species. including Li and E. The neutrinos involved in the v-process are produced as à result of (he gravitational collapse of a stellar core to a neutron star during a supernova οἱ Type HL (SN I1).,"1990) published predicted yields for a number of species, including Li and F. The neutrinos involved in the $\nu$ -process are produced as a result of the gravitational collapse of a stellar core to a neutron star during a supernova of Type II (SN II)." " The v-process may result in signilicant svnthesis of certain low-abundance isotopes that lie one mass unit below abundant nuclei. such as PC eiving rise to D. or ?"" Ne resulting in F via neutrino-induced spallation."," The $\nu$ -process may result in significant synthesis of certain low-abundance isotopes that lie one mass unit below abundant nuclei, such as $^{12}$ C giving rise to $^{11}$ B, or $^{20}$ Ne resulting in $^{19}$ F via neutrino-induced spallation." It is the association of PF. the only stable isotope of fIuorine. with the v-process that makes its abundance of interest as à potential probe of neutrino nucleosvnthlesis.," It is the association of $^{19}$ F, the only stable isotope of fluorine, with the $\nu$ -process that makes its abundance of interest as a potential probe of neutrino nucleosynthesis." In addition to the v-process. PF is possibly produced during He-burning thermal pulses on the asvinplotic eiant branch (AGB). as first suggested by Forestini οἱ al. (," In addition to the $\nu$ -process, $^{19}$ F is possibly produced during He-burning thermal pulses on the asymptotic giant branch (AGB), as first suggested by Forestini et al. (" 1992).,1992). Mevnet Arnould (2000) also pointed out that Wolf-IRavet stars. via the same sets of reactions as in the AGB stars. nav also produce significant amounts of PE. with the caveat that large αλα stellar winds must remove a significant. amount of mass. exposing the inner lavers where fluorine is produced. belore it is burned away.," Meynet Arnould (2000) also pointed out that Wolf-Rayet stars, via the same sets of reactions as in the AGB stars, may also produce significant amounts of $^{19}$ F, with the caveat that large dM/dt stellar winds must remove a significant amount of mass, exposing the inner layers where fluorine is produced before it is burned away." Observations of fIuorime abundances. spanning a range of stellar metallicities ancl across a variety of stellar populations. are needed in order to sort out relative contributions from AGB stars. Woll-Ravet stars. or neutrino nucleosvnthesis.," Observations of fluorine abundances, spanning a range of stellar metallicities and across a variety of stellar populations, are needed in order to sort out relative contributions from AGB stars, Wolf-Rayet stars, or neutrino nucleosynthesis." In (his paper. we use high-resolution IR spectra Irom Phoenix on Gemini-South to derive MF abundances (from HE). along with C abundances (from CO). and O abundances (from OIL) in three low-mass members of the Orion Nebula cluster.," In this paper, we use high-resolution IR spectra from Phoenix on Gemini-South to derive $^{19}$ F abundances (from HF), along with $^{12}$ C abundances (from CO), and $^{16}$ O abundances (from OH) in three low-mass members of the Orion Nebula cluster." Carbon aud oxveen provide comparison abundances to those derived from fIluorine., Carbon and oxygen provide comparison abundances to those derived from fluorine. Both C and O have been studied previously in Orion members by Cunha Lambert (1994): their study analyzed hot ο and D stars., Both C and O have been studied previously in Orion members by Cunha Lambert (1994); their study analyzed hot O and B stars. In addition. some oxveen abundanuces in Orionanember F aud G main-sequence ancl pre-anain-sequence stus have been published by Cunha. Smith. Lambert (1998).," In addition, some oxygen abundances in Orion-member F and G main-sequence and pre-main-sequence stars have been published by Cunha, Smith, Lambert (1998)." These previous studies provide a background on which (he abundances derived [rom Ix aud M tvpe stars can be compared., These previous studies provide a background on which the abundances derived from K and M type stars can be compared. Apart [rom the interest in the carbon and oxvgen abundances in voung stellar svstems. C and O provide important comparisons for the fIuorine abundances.," Apart from the interest in the carbon and oxygen abundances in young stellar systems, C and O provide important comparisons for the fluorine abundances." The Orion Nebula cluster stars are very voung and will reflect (he eurrent Galactic E/O ratio in the disk., The Orion Nebula cluster stars are very young and will reflect the current Galactic F/O ratio in the disk. Also. previous stellar IF. abundances (derived from HIE) have come only [from red eiants (Jorissen. Smith. Lambert 1992: Cunha et al.," Also, previous stellar $^{19}$ F abundances (derived from HF) have come only from red giants (Jorissen, Smith, Lambert 1992; Cunha et al." 2003). while here we undergo a pilot study to use cool dwarl stars as sources wilh which to probe fluorine abundances.," 2003), while here we undergo a pilot study to use cool dwarf stars as sources with which to probe fluorine abundances." Odd iuteg‘ands integrate to zero in our straight-line integration approximation.,Odd integrands integrate to zero in our straight-line integration approximation. " The accuuulated s— velocity is the residual CA motion after the eucounter. but it is at most of order 10> ol"" ty. so may be uimneasureable."," The accumulated $x-$ velocity is the residual CM motion after the encounter, but it is at most of order $10^{-2}$ of $v_0$, so may be unmeasureable." However the 2. estimate of Eq (21 ) is substantial., However the $P_z$ estimate of Eq \ref{deltavz}) ) is substantial. Notice tha these estimated kicks are for black hole with spin., Notice that these estimated kicks are for black hole with spin. " If both are spiuinug. the symmetries of the equal mass orbit dictate that a;—(a,ασ}"," If both are spinning, the symmetries of the equal mass orbit dictate that $a_i \rightarrow (a_1 -a_2)_i$." Heuce equal magnuituce oppositely cirected spin «oubles this kick velocity., Hence equal magnitude oppositely directed spin doubles this kick velocity. At this point we recall the limitations of these calculations. principally that the calelation ol the dyuamics is Newtouian.," At this point we recall the limitations of these calculations, principally that the calculation of the dynamics is Newtonian." Our result is completely cousisteut aud accurate in the Newtoulau stnall-cdeflection limit. but the estimate Eq (21)) is au extravagant extrapolation to ei=c.," Our result is completely consistent and accurate in the Newtonian small-deflection limit, but the estimate Eq \ref{deltavz}) ) is an extravagant extrapolation to $v_0=c$." In the absence of a General relativistic 2-body simulation. we can make oily qualitative adaptations to relativity.," In the absence of a General relativistic 2-body simulation, we can make only qualitative adaptations to relativity." One point to notice is that 4t is half the deflection angle in the hieh-speecl Newtouiau limit., One point to notice is that $\frac{m}{b}$ is half the deflection angle in the high-speed Newtonian limit. For a test body moving uear &—€ past a central mass. in Cereral Relativity the deflection t a given impact parameter and ass is twice the Newtoniar result assuimiug ¢=c.," For a test body moving near $v=c$ past a central mass, in General Relativity the deflection at a given impact parameter and mass is twice the Newtonian result assuming $v=c$." This suggests that we might obtain the result estimated above from motion with twice the impact parameter., This suggests that we might obtain the result estimated above from motion with twice the impact parameter. " To cout""ast our Lly-by caleulatious above. we now calculate the kicks when equal mass black ioles (1=mio an) are in a circular orbit in the w-y plane. ("," To contrast our fly-by calculations above, we now calculate the kicks when equal mass black holes $m_{1}=m_{2}=m$ ) are in a circular orbit in the $x$ $y$ plane. (" lu fact. the loss of energy. means he orbit spials inword. so is only. quasi-circular. but we assume a circular orbit. with the orbital separation a1 adjustably shrinking quantity to mimic this enerey loss.),"In fact, the loss of energy means the orbit spirals inword, so is only quasi-circular, but we assume a circular orbit, with the orbital separation an adjustably shrinking quantity to mimic this energy loss.)" " We choose the first black iole initially (t—0) at position ;c=+d. where the secouc black hole would be at cr=—d. with 2d as the ""circilar orbit separation”."," We choose the first black hole initially (t=0) at position $x = +d$, where the second black hole would be at $x = -d$, with $2d$ as the “circular orbit separation”." The third derivatives of the mass quadrupole components [or just the first black hole are thus: aud other components are zero., The third derivatives of the mass quadrupole components for just the first black hole are thus: and other components are zero. The total differentiated mass quadrupole for the two systel is twice that giveu in Eqs (22))., The total differentiated mass quadrupole for the two equal-mass system is twice that given in Eqs \ref{circMQ}) ). The spin multipoles are calculated with the method described iu ; 2.2 so that for one black hole. the two spin charges per component can be summed usine the following coordinates:," The spin multipoles are calculated with the method described in $\S$ 2.2 so that for one black hole, the two spin charges per component can be summed using the following coordinates:" Gaussian on a tapered map. where the source is not resolved.,"Gaussian on a tapered map, where the source is not resolved." The sum of the flux. densities of the two blobs does. not account for the emission of the entire nebula., The sum of the flux densities of the two blobs does not account for the emission of the entire nebula. An inspection of the residual maps (the maps after. subtraction of the fitting Gaussians) indicates that about 4.3 mv at 4.8 Cillz and 0.5 mJy at 8.4 Ciz remain unmatched., An inspection of the residual maps (the maps after subtraction of the fitting Gaussians) indicates that about 4.3 mJy at 4.8 GHz and 0.5 mJy at 8.4 GHz remain unmatched. This means that - besides the two peaks - weak extended emission is present and is recovered by tapering., This means that - besides the two peaks - weak extended emission is present and is recovered by tapering. We performed. for the first. time multi-frequency observations of HUAS 01005|7910. 17516-2525. 21546|4721. 22023|5249. 22495|5134. and 22568|6141.," We performed for the first time multi-frequency observations of IRAS 01005+7910, 17516-2525, 21546+4721, 22023+5249, 22495+5134, and 22568+6141." We fitted the data points to derive the spectral indices. which turned out to match very well with what expected for optically thin shells (a~ -0.1). as can be seen in Table 2..," We fitted the data points to derive the spectral indices, which turned out to match very well with what expected for optically thin shells $\alpha\sim$ -0.1), as can be seen in Table \ref{fits}." Since the emission is optically thin. we can also derive the emission measure for each of these sources as where fxegg. is the Fux density at 8.4 Giz in mJy. and @ the angular radius in aresee (‘Terzian&Dickey 1973).," Since the emission is optically thin, we can also derive the emission measure for each of these sources as where $F_{8.4 \, GHz}$ is the flux density at 8.4 GHz in mJy, and $\theta$ the angular radius in arcsec \citep{terzian}." . The only target that is resolved. at our angular resolution is αλ 22568|6141 Ty). whose northern ancl southern blobs of emission are listed separately in Table 2..," The only target that is resolved at our angular resolution is IRAS 22568+6141 \ref{para22568}) ), whose northern and southern blobs of emission are listed separately in Table \ref{fits}." Gaussian fitting of the two peaks allows us to determine their positions as RA=22:58:5144 DEC261:57:45.2 (North peak) and RA=22:58:51.68 DIC—61:57:42.8 (South peak)., Gaussian fitting of the two peaks allows us to determine their positions as RA=22:58:51.44 DEC=61:57:45.2 (North peak) and RA=22:58:51.68 DEC=61:57:42.8 (South peak). " The peaks are about 37 apart. with PA~ 146""."," The peaks are about $''$ apart, with $\sim$ $^\circ$." To calculate. their emission measures. we need to estimate the angular sizes of our sources.," To calculate their emission measures, we need to estimate the angular sizes of our sources." In Table 2.. we list the major and minor axes of the convolution beam.," In Table \ref{fits}, we list the major and minor axes of the convolution beam." For those sources that have been resolved with high-angular resolution observations in C'errigoneetal(2008). (IAS. 18442-1144. 19336-0400. 19590-1249. and 22023|5249). the geometric mean of the axes is an approximate estimation of their diameters. therefore we take into account this value in our calculations.," For those sources that have been resolved with high-angular resolution observations in \cite{cerrigone} (IRAS 18442-1144, 19336-0400, 19590-1249, and 22023+5249), the geometric mean of the axes is an approximate estimation of their diameters, therefore we take into account this value in our calculations." IRAS 17423-1755. (Llen3-1475) is a well. known point-symmetric pre-PN at à. distance. of about 5.8. kpe., IRAS 17423-1755 (Hen3-1475) is a well known point-symmetric pre-PN at a distance of about 5.8 kpc. [i shows OLL maser emission. lines from ionised elements. and recombination lines due to shocks propagating in its CSE (Rieraetal2003).," It shows OH maser emission, lines from ionised elements, and recombination lines due to shocks propagating in its CSE \citep{riera}." . SánchezContreras&Sahai(2001) find that two wind components are present in the vicinity of the star (~ 07.7): a fast and an ultra-fast wind (150 and 2300 km t respectively). both with kinematical ages of tens of vears.," \citet{sanchez01} find that two wind components are present in the vicinity of the star $\sim0''.7$ ): a fast and an ultra-fast wind (150--1200 and 2300 km $^{-1}$ respectively), both with kinematical ages of tens of years." Decreasing velocities from. 1000. to 150 km are found in the knots in its bipolar outllow. traced by optical. and near-L imaging. over - (Itera. 2003).," Decreasing velocities from 1000 to 150 km $^{-1}$ are found in the knots in its bipolar outflow, traced by optical and near-IR imaging over $''$ \citep{riera}." . Millimeter and cem observations trace much smaller structures. likely associated to a circumstellar clisk (millimeter observations) and a compact tonised region (centimeter observations) (Llugeinsetal2004).," Millimeter and cm observations trace much smaller structures, likely associated to a circumstellar disk (millimeter observations) and a compact ionised region (centimeter observations) \citep{huggins}." . Several models have been applied to this source to account for its kinematical anc morphological properties., Several models have been applied to this source to account for its kinematical and morphological properties. A possible explanation is that its pecularities are the result of an ejection variability of the central source (Rieractal, A possible explanation is that its pecularities are the result of an ejection variability of the central source \citep{riera}. 2003).. Velázquezctal(2004) have moclellecl this nebula with a precessing jet of periodically variable ejection velocity superimposed to a linear increase. which propagates into an Interstellar Mecium. (18M). previously perturbed by an AGB wind.," \citet{velazquez} have modelled this nebula with a precessing jet of periodically variable ejection velocity superimposed to a linear increase, which propagates into an Interstellar Medium (ISM) previously perturbed by an AGB wind." The velocity variability in their model has a period of 120 vr and a half-amplitude of 150 km +., The velocity variability in their model has a period of 120 yr and a half-amplitude of 150 km $^{-1}$. " The jet has therefore an ejection velocity of the form vj,=ry|cusin(2z((ο)τὸat. with ey=400 km e=150 km lL fj=G40yr. r= 120 wr. and a=lkms tye 5. Lee&S"," The jet has therefore an ejection velocity of the form $v_{jet} = v_0 + v_1 sin (2 \pi(t - t_0 ) / \tau) + a t$ , with $v_0= 400$ km $^{-1}$, $v_1 = $ 150 km $^{-1}$, $t_0=-640 yr$, $\tau=$ 120 yr, and $a = $ 1 km $^{-1}$ $^{-1}$." ahai(2003). present a general model to shape pre-PN with Collimated Fast Winds (CEW) interacting with a spherical AGB wind and they compare their results with observations of CIUL 618., \citet{lee} present a general model to shape pre-PN with Collimated Fast Winds (CFW) interacting with a spherical AGB wind and they compare their results with observations of CRL 618. Phey introduce periodic variations of the density and velocity of the fast wind in such a wav that the mass-loss rate (M=πι py) is kept constant: the density varies as p———ÀPt—- and the velocity às (=ey(1|Asin 225)., They introduce periodic variations of the density and velocity of the fast wind in such a way that the mass-loss rate $\dot{\mathrm{M}}=4\pi$ $^2\rho$ v) is kept constant: the density varies as $\rho=\frac{\rho_f}{1+A \sin\frac{2\pi t}{\tau}}$ and the velocity as $v=v_f (1+A \sin\frac{2\pi t}{\tau})$ . In particular. to compare their model to CHL 618 they consider a period of 22 vr and a velocity amplitude of 150 km s," In particular, to compare their model to CRL 618 they consider a period of 22 yr and a velocity half-amplitude of 150 km $^{-1}$." Racio continuum data since 1991 are available in the VLA archive., Radio continuum data since 1991 are available in the VLA archive. We retrieved the data. reduced them following the same recipe as for the rest of our data. ancl found a flux density of 0.3640.04 mJv in 1991 and O.5640.04 mJy in 1993. both at S.4 Cllz.," We retrieved the data, reduced them following the same recipe as for the rest of our data, and found a flux density of $\pm$ 0.04 mJy in 1991 and $\pm$ 0.04 mJy in 1993, both at 8.4 GHz." As shown in Figure 2.. the combination of our 2001 and 2009 observations with the archive data clearly shows variability of the radio Dux density.," As shown in Figure \ref{17423_lightcurve}, the combination of our 2001 and 2009 observations with the archive data clearly shows variability of the radio flux density." Unfortunately. our temporal sampling is too coarse to conclusively assess whether the variability is regular or not.," Unfortunately, our temporal sampling is too coarse to conclusively assess whether the variability is regular or not." Nevertheless. we show that the data are well fitted by periodic functional Forms similar to those introduced by Velázquezetal(2004) ancl Lee&Sahai(2003): We are fitting four points with functions having three degrees of freedom. therefore the procedure should not. be over-interpreted.," Nevertheless, we show that the data are well fitted by periodic functional forms similar to those introduced by \citet{velazquez} and \citet{lee}: We are fitting four points with functions having three degrees of freedom, therefore the procedure should not be over-interpreted." Both fits give periods around 19 vr (18.6 and 18.7 vr. for the dashed and dotted curves. respectively). comparable to the periodicity in the model of CRL 618 bv Lee&Sahai(2003).. but cdillerent [rom the period introduced in the model of URAS 17423-1755 by Velazquezetal (2004).," Both fits give periods around 19 yr (18.6 and 18.7 yr, for the dashed and dotted curves, respectively), comparable to the periodicity in the model of CRL 618 by \citet{lee}, but different from the period introduced in the model of IRAS 17423-1755 by \citet{velazquez}." .. Our 2009 observations indicate that the emission. is optically thin. with a spectral index of -0.4 (Table 2)).," Our 2009 observations indicate that the emission is optically thin, with a spectral index of -0.4 (Table \ref{fits}) )." Nevertheless. the observations reported in Cerrigoneοἱal(2008) at S.4 ancl 22.4 (111 indicate optically thick emission between these frequencies with a spectral index around. 1.," Nevertheless, the observations reported in \citet{cerrigone} at 8.4 and 22.4 GHz indicate optically thick emission between these frequencies with a spectral index around 1." In the cited. paper. it was assumed that no variation had occurred in the source between 2001 (epoch of the SA Cllz data) and 2003 (epoch of the 22.4 CGllz data).," In the cited paper, it was assumed that no variation had occurred in the source between 2001 (epoch of the 8.4 GHz data) and 2003 (epoch of the 22.4 GHz data)." Figure 2 shows that this assumption is not correct and that in 2003 the Dux density at SA Cllz was smaller than in 2001. if the variability is regular.," Figure \ref{17423_lightcurve} shows that this assumption is not correct and that in 2003 the flux density at 8.4 GHz was smaller than in 2001, if the variability is regular." This does not alfect the conclusion that the spectral index was positive in 2003 and likely around 1. considering errors.," This does not affect the conclusion that the spectral index was positive in 2003 and likely around 1, considering errors." Η the radio emission is due to the stellar wind. the radius Roof the emitting region depends on the frequeney as Hp)e7 (Panagia&Felli1975).. in the optically thick regime. as is the case in the 2003 observations.," If the radio emission is due to the stellar wind, the radius R of the emitting region depends on the frequency as $\nu$ $\sim\nu^{-0.7}$ \citep{panafelli}, in the optically thick regime, as is the case in the 2003 observations." Since any variation in the wind will propagate outwards ancl the emission at higher frequency arises from. inner regions. a light curve at a lower [requeney will be delayed. compared," Since any variation in the wind will propagate outwards and the emission at higher frequency arises from inner regions, a light curve at a lower frequency will be delayed compared" (HerbigandReadhead1992).. so it 1s not easy to simply extrapolate from one frequency to another.,"\citep{herbig92}, so it is not easy to simply extrapolate from one frequency to another." The mean spectral index from 21 em to | em is approximately à=—0.7. where Sv)xwi (Coorayetal...1998). but there is significant dispersion in the observed spectral indices (CoorayTayloretal 2001).," The mean spectral index from 21 cm to 1 cm is approximately $\alpha =-0.7$ , where $S(Jy) \propto \nu^\alpha$ \citep{cooray98} but there is significant dispersion in the observed spectral indices \citep{cooray98,taylor01}." . At | cm. there are no large scale deep surveys for point sources that can be used to accurately characterize the point source population. but there are a large number of pointed observations toward clusters for SZ effect observations (Carlstrometaf2000) at this wavelength.," At 1 cm, there are no large scale deep surveys for point sources that can be used to accurately characterize the point source population, but there are a large number of pointed observations toward clusters for SZ effect observations \citep{carlstrom99} at this wavelength." The majority of observed clusters has at least one point source with a flux at | cm greater than | mJy., The majority of observed clusters has at least one point source with a flux at 1 cm greater than 1 mJy. When compared with the point source abundance in fields not containing clusters. it 15 clear that most point sources in fields with galaxy clusters must be physically associated with the galaxy clusters (Coorayeraf...1998). most likely the galaxy cluster members.," When compared with the point source abundance in fields not containing clusters, it is clear that most point sources in fields with galaxy clusters must be physically associated with the galaxy clusters \citep{cooray98}, most likely the galaxy cluster members." Radio emission from galaxy cluster members has been studied in detail (LedlowandOwen1996) at 21 em (v=1.4 GHz). with the fraction of galaxies at a given radio luminosity (per log interval) nearly flat at radio powers (at 21 em) below 1075 HHz' and falling quickly above this power.," Radio emission from galaxy cluster members has been studied in detail \citep{ledlow96} at 21 cm $\nu=1.4$ GHz), with the fraction of galaxies at a given radio luminosity (per log interval) nearly flat at radio powers (at 21 cm) below $10^{24.8}$ $^{-1}$ and falling quickly above this power." To the optical and radio flux limits of their survey. roughly of cluster members showed some amount of point source emission.," To the optical and radio flux limits of their survey, roughly of cluster members showed some amount of point source emission." Assuming a typical spectral index à2—0.7 and our fiducial cosmology. the break power at 21 cm corresponds to an observed flux at | em of7 mJy for a source at z20.2 and | mJy forasource at z20.5.," Assuming a typical spectral index $\alpha=-0.7$ and our fiducial cosmology, the break power at 21 cm corresponds to an observed flux at 1 cm of 7 mJy for a source at $z=0.2$ and 1 mJy for a source at $z=0.5$." This flux level is in rough agreement with the typical point source fluxes observed by the OVRO/BIMA SZ imaging experiment (Carlstrometa/2000;Reese 2002).," This flux level is in rough agreement with the typical point source fluxes observed by the OVRO/BIMA SZ imaging experiment \citep{carlstrom99, reese02}." ". If no point source subtraction of any kind were done. these point sources would be a non-negligible fraction of the thermal SZ signal from massive clusters (~10247!M, )."," If no point source subtraction of any kind were done, these point sources would be a non-negligible fraction of the thermal SZ signal from massive clusters $\sim 10^{15} h^{-1}M_\odot$ )." The nearly flat probability distribution Gn log flux) with point source flux leads to the typical galaxy cluster having the brightest point source dominating the total radio flux., The nearly flat probability distribution (in log flux) with point source flux leads to the typical galaxy cluster having the brightest point source dominating the total radio flux. From an observational standpoint this is desirable. since an SZ experiment only needs to remove a bright point source or two to be confident that the measurementis not contaminated by radio emission from galaxy cluster members.," From an observational standpoint this is desirable, since an SZ experiment only needs to remove a bright point source or two to be confident that the measurementis not contaminated by radio emission from galaxy cluster members." " The expected integrated thermal SZ signal for a 1057!M, at z0.5 is on the order of 10-20 mJy (at 30 GHz) (HolderCarlstrom 2001).. and should scale as M**."," The expected integrated thermal SZ signal for a $10^{15} h^{-1}M_\odot$ at $z \sim 0.5$ is on the order of 10-20 mJy (at 30 GHz) \citep{holder01}, and should scale as $M^{5/3}$." This is in agreement with current observations (Carlstromerαἱ.2000).. but current data does not extend over a large range in mass.," This is in agreement with current observations \citep{carlstrom99}, but current data does not extend over a large range in mass." " The radio point source flux should scale approximately with the number of galaxies. which scales às the mass (Carlbergetal, 1996).."," The radio point source flux should scale approximately with the number of galaxies, which scales as the mass \citep{carlberg96}." A typical point source flux for massive galaxy clusters at this redshift is on the order of 1 mJy at 30 GHz and is therefore roughly of the total thermal SZ flux., A typical point source flux for massive galaxy clusters at this redshift is on the order of 1 mJy at 30 GHz and is therefore roughly of the total thermal SZ flux. The relative importance of point sources should therefore scale with mass as M. while the redshift evolution of the relative importance will scale as (1-2)? for a flat spectral index.," The relative importance of point sources should therefore scale with mass as $M^{-2/3}$, while the redshift evolution of the relative importance will scale as $(1+z)^{-3}$ for a flat spectral index." None of these numbers are particularly well constrained observationally. but these estimates constitute our baseline model.," None of these numbers are particularly well constrained observationally, but these estimates constitute our baseline model." At some level. all clusters have radio point sources.," At some level, all clusters have radio point sources." Ideally. one would be able to identify and remove all point sources in the field of view with a beam size that is matched to the size of the point source and much smaller than the extent of the SZ signal.," Ideally, one would be able to identify and remove all point sources in the field of view with a beam size that is matched to the size of the point source and much smaller than the extent of the SZ signal." In such a case. the amount of SZ flux removed would be negligible.," In such a case, the amount of SZ flux removed would be negligible." Not surprisingly. this 1s exactly the attempted strategy of choice for interferometric SZ experiments. such as the Ryle Telescope (Jonesetαἰ.1993). and OVRO/BIMA (Carlstrom.Joy.andGrego—1996).. where high angular resolution. measurements are performed. simultaneously. for point source removal.," Not surprisingly, this is exactly the attempted strategy of choice for interferometric SZ experiments, such as the Ryle Telescope \citep{jones93} and OVRO/BIMA \citep{carlstrom96}, where high angular resolution measurements are performed simultaneously for point source removal." It is not feasible to detect all point sources in a field. but such methods can easily remove point sources to a flux level below 10% of the peak SZ flux. with an effective resolution of roughly 107 or better.," It is not feasible to detect all point sources in a field, but such methods can easily remove point sources to a flux level below $10\%$ of the peak SZ flux, with an effective resolution of roughly 10” or better." With such a strategy. the residual effect of point sources on the SZ power spectrum would be negligible.," With such a strategy, the residual effect of point sources on the SZ power spectrum would be negligible." Such a strategy. is not currently feasible for CMB experiments such as CBI., Such a strategy is not currently feasible for CMB experiments such as CBI. As primarily a CMB experiment. CBI is not concerned with point sources that do not contribute more than about 10 μΚ to the rms temperature fluctuations.," As primarily a CMB experiment, CBI is not concerned with point sources that do not contribute more than about 10 $\mu K$ to the rms temperature fluctuations." This translates into a flux threshold of a few mJy at 30 GHz., This translates into a flux threshold of a few mJy at 30 GHz. Clusters with masses near 10/777!M.. have a total SZ flux of a mJy or less (HolderandCarlstrom2001).. so à 1 mJy point source could be problematic.," Clusters with masses near $10^{14} h^{-1} M_\odot$ have a total SZ flux of a mJy or less \citep{holder01}, so a 1 mJy point source could be problematic." If all clusters had point sources near | mJy. effectively no clusters below ~2«10/7!M... in figure | would contribute to the anisotropy. with a somewhat reduced contribution from slightly larger clusters.," If all clusters had point sources near 1 mJy, effectively no clusters below $\sim 2 \times 10^{14} h^{-1} M_\odot$ in figure \ref{fig:dcl} would contribute to the anisotropy, with a somewhat reduced contribution from slightly larger clusters." At (=1000 the difference would be noticeable but at (=4000 it might be expected that as much as half of the power could be missing., At $\ell=1000$ the difference would be noticeable but at $\ell=4000$ it might be expected that as much as half of the power could be missing. There are two leading strategies for dealing with point sources., There are two leading strategies for dealing with point sources. One strategy is to identify possible point sources in catalogs at 21 em and follow up with pointed observations at high angular resolution., One strategy is to identify possible point sources in catalogs at 21 cm and follow up with pointed observations at high angular resolution. Another strategy 1s to combine the data in a way that it is insensitive to any amount of flux coming from positions of known point sources. known as a constraint matrix approach (Bond.Jaffe.andKnox1998).," Another strategy is to combine the data in a way that it is insensitive to any amount of flux coming from positions of known point sources, known as a constraint matrix approach \citep{bond98}." ". Both methods are susceptible to point sources with ""inverted"" spectra. where the flux is higher at higher frequencies. and therefore could be missed in the 21 em catalog."," Both methods are susceptible to point sources with “inverted” spectra, where the flux is higher at higher frequencies, and therefore could be missed in the 21 cm catalog." Such inverted sources are rare. and are not expected to be a dominant source of error.," Such inverted sources are rare, and are not expected to be a dominant source of error." For extraction of primary CMB anisotropies both methods work quite well (Padinetαἱ.2000:Halversonaf... 2002).. but for the SZ effect. point source subtraction will remove all SZ fluxwithin the point source subtraction beam area from the map at the position of the point source.," For extraction of primary CMB anisotropies both methods work quite well \citep{padin01,halverson01}, , but for the SZ effect, point source subtraction will remove all SZ fluxwithin the point source subtraction beam area from the map at the position of the point source." Finally. we have also computed the results in the case of the guided thermal disturbance.,"Finally, we have also computed the results in the case of the guided thermal disturbance." We find that the thermal mode behavior is the same in the waveguide case and in the free propagation case., We find that the thermal mode behavior is the same in the waveguide case and in the free propagation case. Hence. this mode is not affected by the variation of the propagation angle and no further comments are needed.," Hence, this mode is not affected by the variation of the propagation angle and no further comments are needed." In this work. we have studied the effect of heliumr and i) on the time damping of thermal and MHD waves in a partially i0nized. prominence plasma.," In this work, we have studied the effect of helium and ) on the time damping of thermal and MHD waves in a partially ionized prominence plasma." This is an extension of previous investigations by Fortezaetal.(2007.2008) in which helium was not taken into account.," This is an extension of previous investigations by \citet{forteza07,forteza08} in which helium was not taken into account." We conclude that. although the presenee of neutral helium increases the eficiency of both ion-neutral collisions and thermal conduction. its effect is not important for realistic helium abundances in prominences.," We conclude that, although the presence of neutral helium increases the efficiency of both ion-neutral collisions and thermal conduction, its effect is not important for realistic helium abundances in prominences." In addition. due to the very small abundarce for central prominence temperatures. its presence is irrelevant to the wave behavior.," In addition, due to the very small abundance for central prominence temperatures, its presence is irrelevant to the wave behavior." This coiclusion applies both to the free propagation case and the coistrained propagation by à waveguide case., This conclusion applies both to the free propagation case and the constrained propagation by a waveguide case. Although the role of (or even um) could be larger for typical prominence-corona traasition region temperatures. the present result allows future studies of MHD waves and oscillatior si prominences to neglect the presence of helium.," Although the role of (or even ) could be larger for typical prominence-corona transition region temperatures, the present result allows future studies of MHD waves and oscillations in prominences to neglect the presence of helium." The formation of binary ancl multiple svstems provides one of the most exacting areas in which star formation theory can be compared. with observational data.,The formation of binary and multiple systems provides one of the most exacting areas in which star formation theory can be compared with observational data. Stars are known to have a binary. frequency in excess of50%.. both in the field. (Ducucnnoy Mayor 1991. henceforth DAIOL: Fisher Marcy 1992: Halbwachs ct al.," Stars are known to have a binary frequency in excess of, both in the field (Duquennoy Mayor 1991, henceforth DM91; Fisher Marcy 1992; Halbwachs et al." 2003) and in clusters (Ixóhhler Leinert 1998: Patience et al., 2003) and in clusters (Köhhler Leinert 1998; Patience et al. 1998: Alathieu et al., 1998; Mathieu et al. 2000: Bouvier et al., 2000; Bouvier et al. 2001)., 2001). For pre-main-sequence stars this frequency seems to be even higher (Reipurth Zinnecker 1993: Simon et al., For pre-main-sequence stars this frequency seems to be even higher (Reipurth Zinnecker 1993; Simon et al. 1995: Duchenne 1999: Reipurth 2000)., 1995; Duchênne 1999; Reipurth 2000). Thus. understanding the formation of multiple stars becomes necessary if we are to understand star formation in general.," Thus, understanding the formation of multiple stars becomes necessary if we are to understand star formation in general." Recently. Date. Bonnell Brom (2003: henceforth BBB) have shown that multiple stars are a natural byproduct of the collapse and fragmentation of turbulent molecular clouds.," Recently, Bate, Bonnell Bromm (2003; henceforth BBB) have shown that multiple stars are a natural byproduct of the collapse and fragmentation of turbulent molecular clouds." In particular. close binary stars can be incirectly formed. out of the fragmentation of a molecular cloud core by means of clynamical interactions," In particular, close binary stars can be indirectly formed out of the fragmentation of a molecular cloud core by means of dynamical interactions" 10145.10232 10722 these (e.g.Cao&Solomon2001:Juneau2009).," $10^{11}-10^{12}$ $>10^{12}$ \citep[e.g.][]{GS04,Juneau09}." . (Lagacheetal.2005) (ee.LeFlochetal.2005:Pérez-Gouzalez2005:Rodighiero," \citep{Lagache05} $z \sim 1$ \citep[e.g.,][]{LeFloch05, PPG05, Rodighiero10}." "etal.2010).. (SMCs:e.g.Blainetal.2002).. (οιο,Tacconi2008)."," $z \gtrsim 2$ \citep[SMGs; e.g.][]{Blain02}. \citep[e.g.][]{Tacconi08}." . ποια those of local galaxies of similar ΠΠηλ. Papo, from those of local galaxies of similar luminosity. vichetal.(2007). found that the 70 pan (observed) outputs teuded to be weaker rclative to those at 21 pau (observed) than expected. frou local templates., \citet{Papovich07} found that the 70 $\micron$ (observed) outputs tended to be weaker relative to those at 24 $\micron$ (observed) than expected from local templates. Many authors have found that the arolmatic bands iu thesePa ealaxies appear to be simular in structure to those iu sieuificautlv lower-Iuninositv οσα]. galaxies (e.g.Rigby 2010).," Many authors have found that the aromatic bands in these galaxies appear to be similar in structure to those in significantly lower-luminosity local galaxies \citep[e.g.,][]{Rigby08, Farrah08, Takagi10}." . The far infrared SEDs appear to be cold. again sinülar to those of lower bhuuinositv ocal galaxies (e...PopeWw MLO)...," The far infrared SEDs appear to be cold, again similar to those of lower luminosity local galaxies \citep[e.g.,][]{Pope06, Symeonidis09, Muzzin10}." These findingse sieves an underlying physical liffereuce between local Iuniiunous infrared galaxies aud rose at hieh redshift., These findings suggest an underlying physical difference between local luminous infrared galaxies and those at high redshift. Rigbyetal(2008) suggested at such a difference might arise either through reduced uetallicity or lower optical depth due to a greater exteut of the enüttiug regions., \citet{Rigby08} suggested that such a difference might arise either through reduced metallicity or lower optical depth due to a greater extent of the emitting regions. " Exbetal.(2006) fud that the uctallicitics ave of order three times lower at 2~~ for a eiven galaxy λα»,", \citet{Erb06} find that the metallicities are of order three times lower at $z \sim 2$ for a given galaxy mass. Eugelbrachtetal.(2008) show that. or local galaxies. there is ouly a weak trend in 8 pu vs. ddown to 1/3 solar metallicity. and that at lower netallicity the 8 gan luminosity is suppressed.," \citet{Engelbracht08} show that, for local galaxies, there is only a weak trend in 8 $\micron$ vs. down to $1/3$ solar metallicity, and that at lower metallicity the 8 $\micron$ luminosity is suppressed." This correlation is also reported for 2o2 galaxies by Reddyetal. (2010).," This correlation is also reported for $z \sim 2$ galaxies by \citet{Reddy10}." . We conclude that reduced metallicity is unlikely to be the primary cause of the chanecs iu SED with redshift., We conclude that reduced metallicity is unlikely to be the primary cause of the changes in SED with redshift. We therefore turu our attention to the second possibility. tha the galaxies have structures different from local ouesofsimular hnuuinosity.," We therefore turn our attention to the second possibility, that the galaxies have structures different from local onesofsimilar luminosity." Recent hieliesolution studies of SMCS in thesubiuilliinieter.racio. aud rear-IR have shown that their star-forming regions are senucrallv relatively extended. with cianeters of order 110 kpe," Recent high-resolution studies of SMGs in thesubmillimeter,radio, and near-IR have shown that their star-forming regions are generally relatively extended, with diameters of order $1-10$ kpc" we use D=0.98kpc (van Langevelde et HS90)).,"we use $D = 0.98\,{\rm kpc}$ (van Langevelde et \\cite{LHS90}) )." Starting with the parameters of previous radiative. transfer models forpresented by Rowan—Robinson (1982)). Bedijn (1987)). and Suh (1991)). we achieved a satisfactory mateh of the observed SED with the set of parameters given in Table 2 after a few trials.," Starting with the parameters of previous radiative transfer models forpresented by Rowan–Robinson \cite{RowRob82}) ), Bedijn \cite{Bed87}) ), and Suh \cite{Suh91}) ), we achieved a satisfactory match of the observed SED with the set of parameters given in Table \ref{tab-14} after a few trials." Henceforth we will refer to this parameter set as model A. and we will first discuss its properties before we use it as a reference for an investigation of the sensitivity of the results on the parameters.," Henceforth we will refer to this parameter set as model A, and we will first discuss its properties before we use it as a reference for an investigation of the sensitivity of the results on the parameters." The SED of model A is shown in refsed-14.., The SED of model A is shown in \\ref{sed-14}. Figure 7 displays an enlargement of the 525nu region with the 9.7jn. silicate feature.," Figure \ref{lrs-14} displays an enlargement of the $5-25\,{\rm\mu m}$ region with the $9.7\,{\rm\mu m}$ silicate feature." From the shortest wavelength at À=1.25;uu up to A=1.25unu model A provides a good fit to the observations.," From the shortest wavelength at $\lambda = 1.25\,{\rm\mu m}$ up to $\lambda = 1.25\,{\rm mm}$ model A provides a good fit to the observations." The location. shape and strength of the silicate feature around 105220 18. well reproduced with the adopted optical data from Ossenkopf et ((1992)).," The location, shape and strength of the silicate feature around $10\,{\rm\mu m}$ is well reproduced with the adopted optical data from Ossenkopf et \cite{OHM92}) )." Only in the 15au region is there a noticeable deviation because the model shows a weak. broad emission which ts absent in the IRAS LRS spectrum.," Only in the $18\,{\rm\mu m}$ region is there a noticeable deviation because the model shows a weak, broad emission which is absent in the IRAS LRS spectrum." " —n addition to the input parameters. Table 2 also lists the derived properties of model A. Our value for the bolometric luminosity at earth of fj,=31019Win.? is consistent with the values of 2.11019Win7 determined by van der Veen Rugers (1989))."," In addition to the input parameters, Table \ref{tab-14} also lists the derived properties of model A. Our value for the bolometric luminosity at earth of $f_{\rm b} = 3\, 10^{-10}\,{\rm W m^{-2}}$ is consistent with the values of $2.4\, 10^{-10}\,{\rm W m^{-2}}$ determined by van der Veen Rugers \cite{VeRu89}) )." With Tig=200018 the angular stellar diameter is @.=7.5ias and we obtain a stellar radius R.=T90R. and a luminosity £L.=9000L.. adopting a distance D=0.98kpc.," With $T_{\rm eff}=2000\,{\rm K}$ the angular stellar diameter is $\theta_{*}=7.5\,{\rm mas}$ and we obtain a stellar radius $R_{*}=790\,{\rm R_{\odot}}$ and a luminosity $L_{*}=9000\,{\rm L_{\odot}}$ adopting a distance $D=0.98\,{\rm kpc}$." The bolometric flux should be quite accurate considering the quality of the fit., The bolometric flux should be quite accurate considering the quality of the fit. However. the errors in the distance determination 05=0.31. van Langevelde et citeLHS90)) and the uncertainty in the determination of Tig from the radiative transfer modeling (see ref Teff-effects)) are rather large. resulting in correspondingly large uncertainties for L.. Fl. and Aly.," However, the errors in the distance determination $\sigma_{D}=0.34$, van Langevelde et \\cite{LHS90}) ) and the uncertainty in the determination of $T_{\rm eff}$ from the radiative transfer modeling (see \\ref{Teff-effects}) ) are rather large, resulting in correspondingly large uncertainties for $L_{*}$ , $R_{*}$ and $\dot{M}_{\rm d}$." The derived dust mass loss rate of 2.710*M.xr| is close to the values derived from radiative transfer models by other authors.," The derived dust mass loss rate of $2.7\, 10^{-7}\,{\rm M_{\odot} yr^{-1}}$ is close to the values derived from radiative transfer models by other authors." Bressan et ((1998)) obtain L510*AD.wr.|l and the model of Bedijn (1987)) 110“ALyr1H.," Bressan et \cite{BGS98}) ) obtain $4.5\, 10^{-7}\,{\rm M_{\odot} yr^{-1}}$, and the model of Bedijn \cite{Bed87}) ) $4\, 10^{-7}\,{\rm M_{\odot}yr^{-1}}$." " From a relation between the strength of the LOjin feature and the color temperature Schutte Tielens (1989)) obtained M4=2.110*Myr.+ for2200. and Heske et ((1990)) estimated E—1210""Misr! from the GOjiu IRASflux."," From a relation between the strength of the $10\,{\rm\mu m}$ feature and the color temperature Schutte Tielens \cite{SchTi89}) ) obtained $\dot{M}_{\rm d} = 2.4\, 10^{-7}\,{\rm M_{\odot} yr^{-1}}$ for, and Heske et \cite{HFOVH90}) ) estimated $\dot{M}_{\rm d} = 1.2\,10^{-7}\,{\rm M_{\odot} yr^{-1}}$ from the $60\,{\rm\mu m}$ IRASflux." All together the parameters and derived properties of model A lie in the typical range of values obtained from radiative transfer models for OH/IR stars showing the silicate feature in absorption., All together the parameters and derived properties of model A lie in the typical range of values obtained from radiative transfer models for OH/IR stars showing the silicate feature in absorption. In the calculations of Lorenz—Martins de Araujjo (1997)) Tie ranges from 15800Ts to 2 LOOT. Ty from 6501 to 1200 Kk. and 75; from 7 to 17.Justtanont Tielens (1992)) derive dust mass loss rates between 2.610*Mxr|! and," In the calculations of Lorenz–Martins de Araújjo \cite{LMA97}) ) $T_{\rm eff}$ ranges from $1800\,{\rm K}$ to $2400\,{\rm K}$ , $T_{1}$ from $650\,{\rm K}$ to $1200\,{\rm K}$ , and $\tau_{9.7}$ from 7 to 17.Justtanont Tielens \cite{JusTi92}) ) derive dust mass loss rates between $2.6\, 10^{-7}\,{\rm M_{\odot}yr^{-1}}$ and" the sample anc the number of galaxies in the sample.,the sample and the number of galaxies in the sample. At distances D 10^7$ years. Globular cluster central escape velocities are ) km 1, Globular cluster central escape velocities are $\leq$ 50 km $^{-1}$. If all kick velocities are ~ 250 km s. then no pulsars born from isolated stars are retained!," If all kick velocities are $\sim$ 250 km $^{-1}$, then no pulsars born from isolated stars are retained!" Lf the distribution is maxwellian. then the fraction retained is about0.254... which is still extremely low!," If the distribution is maxwellian, then the fraction retained is about, which is still extremely low!" Yet. he retention fraction of neutron stars is claimed to be of the order of (Phinney 1993))3) or higher πι! and Verbunt 1983).," Yet, the retention fraction of neutron stars is claimed to be of the order of (Phinney 1993) or higher (Hut and Verbunt 1983)." However. it is possible that binaries. either wimordial or dvnamically formed. could be responsible for he pulsars found in globular clusters (see Hut et al.," However, it is possible that binaries, either primordial or dynamically formed, could be responsible for the pulsars found in globular clusters (see Hut et al." 1992: Drukier 1996)., 1992; Drukier 1996). Drandt and Pocdsiadlowski (1995iocis) lind that EA ol binaries remain bound if the kick is 200 xIM ἐν which is the right order of magnitude to explain the required. mass in clark massive remnants.," Brandt and Podsiadlowski (1995) find that $\sim 17 \%$ of binaries remain bound if the kick velocity is 200 km $^{-1}$, which is the right order of magnitude to explain the required mass in dark massive remnants." However. this is ikelv to be an upper limit on the retention fraction because even systems which remain bound can receive significant centre-ol-mass velocities.," However, this is likely to be an upper limit on the retention fraction because even systems which remain bound can receive significant centre-of-mass velocities." Thus. Drukier (1996). using the results of Lyne Lorimer and Drandt Pocdsiadlowski. has shown that most elobular clusters would retain 1σα of their neutron stars.," Thus, Drukier (1996), using the results of Lyne Lorimer and Brandt Podsiadlowski, has shown that most globular clusters would retain $\sim 1-5 \%$ of their neutron stars." In the light of this. we should. point out that the lack of a low velocity tail in our distribution is not an artefact of the Viu weighting.," In the light of this, we should point out that the lack of a low velocity tail in our distribution is not an artefact of the $V_{\rm max}$ weighting." Of the 51 pulsars in our sample with ages less than 105 vears. the lowest transverse velocity is T0 kms+.," Of the 51 pulsars in our sample with ages less than $10^7$ years, the lowest transverse velocity is 70 km $^{-1}$." Lf there are voung pulsars with very small velocities. then they have not been measured ," If there are young pulsars with very small velocities, then they have not been measured yet." Another possible complication 1s je creation of fast (I? «0.1 s) pulsars with initial timing ages 210' vears., Another possible complication is the creation of fast (P $<$ 0.1 s) pulsars with initial timing ages $> 10^7$ years. The birthrate of such oulsars is not constrained by our analysis because of both our age cutoll ancl the restriction of our analysis to the carly Molonglo and Green Bank surveys., The birthrate of such pulsars is not constrained by our analysis because of both our age cutoff and the restriction of our analysis to the early Molonglo and Green Bank surveys. In conclusion. we have shown that the clistribution of voung pulsar proper motions. corrected for. selection ellects. is Consistent with a characteristic kick velocity at birth of ~ 250-300 km ," In conclusion, we have shown that the distribution of young pulsar proper motions, corrected for selection effects, is consistent with a characteristic kick velocity at birth of $\sim$ 250-300 km $^{-1}$." We find little evidence for a significant low velocity tail to the kick. distribution., We find little evidence for a significant low velocity tail to the kick distribution. Our method is robust in its reproduction of the mean velocity and low velocity shape of the distribution., Our method is robust in its reproduction of the mean velocity and low velocity shape of the distribution. However. the shape of the distribution at velocities 2- 300 kms * is not well constrained. by this method because of poor statistics.," However, the shape of the distribution at velocities $>$ 300 km $^{-1}$ is not well constrained by this method because of poor statistics." Our results are in good agreement with he properties of j(naries containing neutron stars ancl pleasantly close to he value inferred. from. numerical supernova simulations (c.g. Burrows. llaves Fryxell 1996. who inferred. kicks of ~300kms lopfrom core recoil. during. the collapse. but neglected. asvnumetries in the initial mass distribution. see Durrows Llaves 1996. which. could lead. to even. higher velocities).," Our results are in good agreement with the properties of binaries containing neutron stars and pleasantly close to the value inferred from numerical supernova simulations (e.g. Burrows, Hayes Fryxell 1996, who inferred kicks of $\sim 300 \, \rm km \, s^{-1}$ from core recoil during the collapse, but neglected asymmetries in the initial mass distribution, see Burrows Hayes 1996, which could lead to even higher velocities)." Finally. we have shown that the pulsars with long characteristic ages show the asymmetric drift. corresponding o à dynamically old population.," Finally, we have shown that the pulsars with long characteristic ages show the asymmetric drift, corresponding to a dynamically old population." The velocity distribution of these pulsars is alfected by their genesis in binaries as well as their subsequent motion through the galaxy., The velocity distribution of these pulsars is affected by their genesis in binaries as well as their subsequent motion through the galaxy. This work was sua by NSE erant .AST93-15455 and NASA erant NACGS5S-2756., This work was supported by NSF grant AST93-15455 and NASA grant NAG5-2756. di forWe would like to thank the referee. Philip Podsiad comments on the original nianuscript., We would like to thank the referee Philip Podsiadlowski for comments on the original manuscript. us the usual projected rotational velocity of the star as a whole.,is the usual projected rotational velocity of the star as a whole. An obvious feature of the convolution expressed by Eq., An obvious feature of the convolution expressed by Eq. is the singularity of the integrand at €=+7. re.. the presence of sharp spikes.," is the singularity of the integrand at $\xi=\pm\vsinimu$, i.e., the presence of sharp spikes." One might already suspect at this point that their presence will be apparent in the fully disk-integrated profile., One might already suspect at this point that their presence will be apparent in the fully disk-integrated profile. Numerically. one can handle the singularities by analytically integrating the expression over each resolution element assuming a certain functional dependence of /6) within them. and summing over all contributions in the interval 0.-9].," Numerically, one can handle the singularities by analytically integrating the expression over each resolution element assuming a certain functional dependence of $\I(v)$ within them, and summing over all contributions in the interval $\left[-\vsinimu, +\vsinimu\right]$." " We assumed a constant behavior of iin each resolution element so that the integral of the kernel function over a resolution element stretching over an interval [€,.€| can be conveniently expressed as y."," We assumed a constant behavior of in each resolution element so that the integral of the kernel function over a resolution element stretching over an interval $\left[\xi_1,\xi_2\right]$ can be conveniently expressed as )." The disk-integrated. rotationally-broadened flux profile FQ) is obtained by integrating oover the disk according to the standard relation F((v)4. =2n wa," The disk-integrated, rotationally-broadened flux profile $\Frot(v)$ is obtained by integrating over the disk according to the standard relation (v) = ) )." The second approximate equality is the discrete approximation to the integral employing a total number of llimb-angles of weight aat Positions 4t., The second approximate equality is the discrete approximation to the integral employing a total number of limb-angles of weight at positions $\mu_\imu$. The original implementation of Dravins NNordlund did not use a formulation as convolution but a discrete integration. over p-circles using polar coordinates., The original implementation of Dravins Nordlund did not use a formulation as convolution but a discrete integration over $\mu$ -circles using polar coordinates. While mathematically equivalent to Eq.(," While mathematically equivalent to Eq.," 1)... it somewhat obscures the critical role of the most extreme velocities on a peeircle for the smoothness of the rotationally broadened spectrum., it somewhat obscures the critical role of the most extreme velocities on a $\mu$ -circle for the smoothness of the rotationally broadened spectrum. Figure 2 illustrates the result of a test of Dravins NNordlund’s procedure., Figure \ref{f:irot2} illustrates the result of a test of Dravins Nordlund's procedure. We broadened an artificial Gaussian line profile with a rotational speed Vsin(/) of three times the line’s Doppler width., We broadened an artificial Gaussian line profile with a rotational speed $\vsini$ of three times the line's Doppler width. The rotational speed was chosen to be particularly critical., The rotational speed was chosen to be particularly critical. Effeets of smaller rotational velocities become less pronounced due to the smoothing by the Gaussian line profile. at larger rotational speeds deviations are less conspicuous since less localized.," Effects of smaller rotational velocities become less pronounced due to the smoothing by the Gaussian line profile, at larger rotational speeds deviations are less conspicuous since less localized." For the test case we assumed that the relative line shape is independent of yz. and that the intensity in the continuum follows a linear limb-darkening law with a limb-darkening coefficient of 0.6.," For the test case we assumed that the relative line shape is independent of $\mu$, and that the intensity in the continuum follows a linear limb-darkening law with a limb-darkening coefficient of 0.6." Hence. standard flux convolution can be applied to obtain the disk-integrated line profile.," Hence, standard flux convolution can be applied to obtain the disk-integrated line profile." " Figure 2. shows the convergence of the numerical approximation towards the exact result with an increasing total number of limb-anglesN,.", Figure \ref{f:irot2} shows the convergence of the numerical approximation towards the exact result with an increasing total number of limb-angles. ". As evident in the figure. noticeable deviations between the exact and the numerical result are present up to and including jV,=3."," As evident in the figure, noticeable deviations between the exact and the numerical result are present up to and including $\nmu=3$." The major reason for the “wiggly” behavior of the broadened line profile shown in Fig., The major reason for the “wiggly” behavior of the broadened line profile shown in Fig. 2. are the pronounced spikes in the integrand in Eq. (1)., \ref{f:irot2} are the pronounced spikes in the integrand in Eq. . . One can reduce their impact by associating a given. /(i) not only with an infinitely thin µ- but with a (see Fig. 1)), One can reduce their impact by associating a given $\I(\mu)$ not only with an infinitely thin $\mu$ -circle but with a (see Fig. \ref{f:scheme}) ) of finite extent., of finite extent. The contribution Fo to the rotationally broadened flux profile stemming from the stellar disk area subtended by µε[uj.1] is given by the convolution ," The contribution $\Frot(\mu)$ to the rotationally broadened flux profile stemming from the stellar disk area subtended by $\mu\in\left[\mu_\imu,1\right]$ is given by the convolution ) =." lis again given by relation(2)., is again given by relation. . Here. we assume that the intensity profile is constant within [μμ1| represented by the intensity at ge=fo — presumably but not necessarily lying in the interval [μῃ.1].," Here, we assume that the intensity profile is constant within $\left[\mu_\imu,1\right]$ represented by the intensity at $\mu=\mu_0$ – presumably but not necessarily lying in the interval $\left[\mu_\imu,1\right]$." Note. that relation takes into account the surface area corresponding to the interval [μμ1].," Note, that relation takes into account the surface area corresponding to the interval $\left[\mu_\imu,1\right]$ ." Its result is a flux-like integral. different from the result of relation which expresses an average intensity since the kernel function is normalized to one.," Its result is a flux-like integral, different from the result of relation which expresses an average intensity since the kernel function is normalized to one." " A jering extending over the interval [15.4454] can be obtained by subtracting contributions [15,1,.1] from the contribution of [Mn1| (assuming 4454> 4t4) keeping the same intensity at pio."," A $\mu$ -ring extending over the interval $\left[\mu_\imu,\mu_\imupone\right]$ can be obtained by subtracting contributions $\left[\mu_\imupone,1\right]$ from the contribution of $\left[\mu_\imu,1\right]$ (assuming $\mu_\imupone > \mu_\imu$ ) keeping the same intensity at $\mu_0$." One can build up the whole visible stellar disk by à number of gerings., One can build up the whole visible stellar disk by a number of $\mu$ -rings. Their surface area is reflecting the integration weight tin Eq., Their surface area is reflecting the integration weight in Eq. (4). As stated before. in each ring the intensity is assumed to be pz-independent.," As stated before, in each ring the intensity is assumed to be $\mu$ -independent." Figure 3 illustrates the outcome of this procedure., Figure \ref{f:irot1} illustrates the outcome of this procedure. A comparison with Fig., A comparison with Fig. 2 shows a more rapid convergence towards the exact result., \ref{f:irot2} shows a more rapid convergence towards the exact result. The improvement is related to the fact that the new method can atleast handle exactly the simple case of a globally z-independent intensity which is not the casefor, The improvement is related to the fact that the new method can atleast handle exactly the simple case of a globally $\mu$ -independent intensity which is not the casefor Assuming only the luminosity evolution mocdel (since this is more Commonly accepted). a single power law mocdel has been fitted to cach individual NLP corresponding to cdilferent redshift shells and a different slope has been found for each. as shown on the plots.,"Assuming only the luminosity evolution model (since this is more commonly accepted), a single power law model has been fitted to each individual XLF corresponding to different redshift shells and a different slope has been found for each, as shown on the plots." Note that it is more common to fit a LE with two power laws. but in this calculations. a single power law gave a reasonably &ood fit (Lhe goodness of the fits can be tested. using the 2D Iv-5 test).," Note that it is more common to fit a LF with two power laws, but in this calculations, a single power law gave a reasonably good fit (The goodness of the fits can be tested using the 2D K-S test)." Finding cdillerent slopes for cach redshift shell. suggests that these AGNs have evolved cillcrently at dillerent. periods of time.," Finding different slopes for each redshift shell, suggests that these AGNs have evolved differently at different periods of time." The XLF is used to caleulate the selection function. which is used in dipole ancl correlation. function. analysis.," The XLF is used to calculate the selection function, which is used in dipole and correlation function analysis." 1n dipole analysis. the weight corresponding to each object is proportional to the inverse of the selection function.," In dipole analysis, the weight corresponding to each object is proportional to the inverse of the selection function." Also in the analysis of the spatial correlation function. the random sample is selected so as to have the same selection function (ic.," Also in the analysis of the spatial correlation function, the random sample is selected so as to have the same selection function (ie." the same redshift distribution) as the original sample., the same redshift distribution) as the original sample. In most common cases of Εαν limited. extragalactic object catalogues. one has to take into account the cllects of the consequent undersampling of the density field: especially at laree distances. where the radial selection functions rapidly decline.," In most common cases of flux limited extragalactic object catalogues, one has to take into account the effects of the consequent undersampling of the density field especially at large distances, where the radial selection functions rapidly decline." Assuming that the unobserved galaxies are spatially correlated. with those included. in catalogue. the usual procedure to correct for the missing population is to weight cach observed object at a distance r by a factor x go Which is the reciprocal of the portion of the LF that can not be sampled at that distance due to the Dux limit of the catalogue.," Assuming that the unobserved galaxies are spatially correlated with those included in catalogue, the usual procedure to correct for the missing population is to weight each observed object at a distance r by a factor $\propto$ $\frac {1}{\Phi(r)}$, which is the reciprocal of the portion of the LF that can not be sampled at that distance due to the flux limit of the catalogue." Therefore. the weight becomes: where: is the selection function.," Therefore, the weight becomes: where: is the selection function." O(L) is the luminosity function. Lniinird=Jmur7555 ds the minimum luminosity that an extragalactic object can have in order to be visible at a distance r which is determined bv the flux limit of the sample.," $\Phi(L)$ is the luminosity function, $L_{min(r)} = 4 \pi r^{2} S_{lim}$ is the minimum luminosity that an extragalactic object can have in order to be visible at a distance r which is determined by the flux limit of the sample." Liu. is the maximum luminosity of such an object., $L_{max}$ is the maximum luminosity of such an object. " Note that the average density. n. is calculated as: where Lia, 15 the minimum luminosity of the object."," Note that the average density, n, is calculated as: where $L_{min}$ is the minimum luminosity of the object." Note that the selection function is inversly proportional to r. and this acts as a compensating ellect for the fact that poor sampling occurs at large redshifts.," Note that the selection function is inversly proportional to r, and this acts as a compensating effect for the fact that poor sampling occurs at large redshifts." 1n this section. we give a summary on how to calculate the amplitude of the dipole growth curve as a function of the radial distance.," In this section, we give a summary on how to calculate the amplitude of the dipole growth curve as a function of the radial distance." Basically. the dipole moment is defined as:," Basically, the dipole moment is defined as:" As presented in section 4 (see also Figures 5 and 6). the tight relation between Mgy and metallicity sensitive line ratios indicates that the Lagn-Zpie correlation is driven mostly by the Mgy-Zpee relation (and not by any L/Lygj-Zgi g relation).," As presented in section 4 (see also Figures 5 and 6), the tight relation between $M_{\rm BH}$ and metallicity sensitive line ratios indicates that the $L_{\rm AGN}$ $Z_{\rm BLR}$ correlation is driven mostly by the $M_{\rm BH}$ $Z_{\rm BLR}$ relation (and not by any $L/L_{\rm Edd}$ $Z_{\rm BLR}$ relation)." The Λάμη-ζμικ relation can be understood in the following terms., The $M_{\rm BH}$ $Z_{\rm BLR}$ relation can be understood in the following terms. If the Mgy-Mpy relation observed in the local universe (Magorrian et al., If the $M_{\rm BH}$ $M_{\rm bul}$ relation observed in the local universe (Magorrian et al. 1998) holds at z~2—3 (Janke et al., 1998) holds at $z \sim 2 - 3$ (Janke et al. 2009). the Mebuy-Zpce relation obtained in this study implies a Mou-Zpi n relation.," 2009), the $M_{\rm BH}$ $Z_{\rm BLR}$ relation obtained in this study implies a $M_{\rm bul}$ $Z_{\rm BLR}$ relation." In addition. if the BLR metallicity ts associated with the metallicity of the host galaxy. the Mpg-Zpii relation would simply trace the well-known correlation between the mass and metallicity in galaxies. Le. the Mpu-Zpuy relation (Lequeux et al.," In addition, if the BLR metallicity is associated with the metallicity of the host galaxy, the $M_{\rm BH}$ $Z_{\rm BLR}$ relation would simply trace the well-known correlation between the mass and metallicity in galaxies, i.e., the $M_{\rm bul}$ $Z_{\rm bul}$ relation (Lequeux et al." 1979: Tremonti et al., 1979; Tremonti et al. 2004: Maiolino et al., 2004; Maiolino et al. 2008)., 2008). " This implies that the origin of the {λον-Ζμικ relation is the Mpu- Zou relation (or. more simply. the ""mass-metallicity relation"")."," This implies that the origin of the $L_{\rm AGN}$ $Z_{\rm BLR}$ relation is the $M_{\rm bul}$ $Z_{\rm bul}$ relation (or, more simply, the “mass-metallicity relation”)." The one potential problem of this interpretation 15 the lack of redshift evolution of the Lagn-Zpie. out to z~6 (Nagao et al.," The one potential problem of this interpretation is the lack of redshift evolution of the $L_{\rm AGN}$ $Z_{\rm BLR}$, out to $z \sim 6$ (Nagao et al." 2006a; Juarez et al., 2006a; Juarez et al. 2009; see also Dietrich et al., 2009; see also Dietrich et al. 2003). which is at odds with the redshift evolution of the mass-metallicity relation observed in galaxies (Maiolino et al.," 2003), which is at odds with the redshift evolution of the mass-metallicity relation observed in galaxies (Maiolino et al." 2008. Mannueci et al.," 2008, Mannucci et al." 2009)., 2009). There are two possible solution to this problem., There are two possible solution to this problem. More recently. Mannucci et al. (," More recently, Mannucci et al. (" 2010) have found that the mass-metallicity relation in galaxies also depends on the SFR. more active galaxies being characterized by lower metallicity.,"2010) have found that the mass-metallicity relation in galaxies also depends on the SFR, more active galaxies being characterized by lower metallicity." They also found that. such mass-metallicity-SFR relation does not evolve with redshift out to z~2.5: previous claims on the evolution of the mass-metallicity relation were simply a consequence of the fact that high-z surveys have probed galaxies on average with higher SFR at high redshift.," They also found that, such mass-metallicity-SFR relation does not evolve with redshift out to $z \sim 2.5$; previous claims on the evolution of the mass-metallicity relation were simply a consequence of the fact that $z$ surveys have probed galaxies on average with higher SFR at high redshift." If quasar host galaxies at different redshifts are characterized by similar SER. (e.g.. Maiolino et al.," If quasar host galaxies at different redshifts are characterized by similar SFR (e.g., Maiolino et al." 2007a; Netzer et al., 2007a; Netzer et al. 2007: Lutz et al., 2007; Lutz et al. 2008). this would imply that they are likely characterized by the mass-metallicity relation.," 2008), this would imply that they are likely characterized by the mass-metallicity relation." However. this explanation is not totally satisfactory. since actually there is evidence that even the mass-metallicity-SFR relation evolves at zo» 3(Mannuccet et al.," However, this explanation is not totally satisfactory, since actually there is evidence that even the mass-metallicity-SFR relation evolves at $z > 3$ (Mannucci et al." 2010). while the Lagn-Zpee in quasars does not evolve out to z-6.," 2010), while the $L_{\rm AGN}$ $Z_{\rm BLR}$ in quasars does not evolve out to $z \sim 6$." Another effect. which goes in the direction of making the non-evolution of the LacGw-Zpgig relation even more problematic. is that at high redshift the Mpy-Mpy relation seems to evolve towards higher Mgy/Mpu relative to the local relation (Walter et al.," Another effect, which goes in the direction of making the non-evolution of the $L_{\rm AGN}$ $Z_{\rm BLR}$ relation even more problematic, is that at high redshift the $M_{\rm BH}$ $M_{\rm bul}$ relation seems to evolve towards higher $M_{\rm BH}/M_{\rm bul}$ relative to the local relation (Walter et al." 2004: Woo et al., 2004; Woo et al. 2006. 2008: Miiolino et al.," 2006, 2008; Maiolino et al." 200705: Lamastra et al., 2007b; Lamastra et al. 2010: Merloni et al., 2010; Merloni et al. 2010)., 2010). As a consequence. for a given black hole mass (hence similar luminosities. for a given. accretion rate) high redshift AGNs should be associated with less massive. hence lower metallicity. host galaxies relative to AGNs at lower redshift.," As a consequence, for a given black hole mass (hence similar luminosities, for a given accretion rate) high redshift AGNs should be associated with less massive, hence lower metallicity, host galaxies relative to AGNs at lower redshift." A possible redshift evolution of the aceretion rate L/Liu (at a given black hole mass. Netzer Trakhtenbrot 2007). would make the problem of the non evolution of the Lagn- Zyyy relation even more serious.," A possible redshift evolution of the accretion rate $L/L_{\rm Edd}$ (at a given black hole mass, Netzer Trakhtenbrot 2007), would make the problem of the non evolution of the $L_{\rm AGN}$ $Z_{\rm BLR}$ relation even more serious." Indeed. at a given luminosity ahigh-z AGN would have a black hole mass lower than a lower redshift AGN. hence should be associated with a less massive. and less enriched. host galaxy.," Indeed, at a given luminosity a $z$ AGN would have a black hole mass lower than a lower redshift AGN, hence should be associated with a less massive, and less enriched, host galaxy." A possible explanation is that luminous quasars host galaxies do not follow the same secular evolutionary process as most of the galaxies used to investigate the metallicity evolution. but are instead characterized by vigorous star formation likely associated with merging events (e.g.. Shao et al.," A possible explanation is that luminous quasars host galaxies do not follow the same secular evolutionary process as most of the galaxies used to investigate the metallicity evolution, but are instead characterized by vigorous star formation likely associated with merging events (e.g., Shao et al." 2010). yielding a very rapid co-evolution of the black hole and its host galaxy. implying a very rapid metals enrichment.," 2010), yielding a very rapid co-evolution of the black hole and its host galaxy, implying a very rapid metals enrichment." Within such strong an rapid co-evolutionary scenario it is likely that the metallicity investigation of quasars host galaxies through the cosmic epochs is subject to strong selection effects., Within such strong an rapid co-evolutionary scenario it is likely that the metallicity investigation of quasars host galaxies through the cosmic epochs is subject to strong selection effects. More specifically. as discussed in detail in Juarez et al. (," More specifically, as discussed in detail in Juarez et al. (" 2009). because of the co-evolutionary link between black holes and their host galaxies. quasars are detectable in. flux-limited surveys only once their host galaxies are already evolved and chemically enriched. and this connection is the same at any epoch. regardless of redshift (see also Kawakatu et al.,"2009), because of the co-evolutionary link between black holes and their host galaxies, quasars are detectable in flux-limited surveys only once their host galaxies are already evolved and chemically enriched, and this connection is the same at any epoch, regardless of redshift (see also Kawakatu et al." 2003)., 2003). In section 4. we have also found that the emission-line flux ratios involving are related to {χμ whereas the other two emission-line flux ratios. Le.. andiv. do not show any dependence on L/Lyuy.," In section 4, we have also found that the emission-line flux ratios involving are related to $L/L_{\rm Edd}$ whereas the other two emission-line flux ratios, i.e., and, do not show any dependence on $L/L_{\rm Edd}$." If the relation betweer the Eddington ratio and emission-line flux. ratios involving vis aseribed to a L/Liag-Zgirg relation. then the other two emission-line flux ratios should also show dependence ori L/Lygg. since all four emission-line flux ratios are sensitive to the gas netallicity of the BLR.," If the relation between the Eddington ratio and emission-line flux ratios involving is ascribed to a $L/L_{\rm Edd}$ $Z_{\rm BLR}$ relation, then the other two emission-line flux ratios should also show dependence on $L/L_{\rm Edd}$, since all four emission-line flux ratios are sensitive to the gas metallicity of the BLR." These results thus indicate that emission-line flux ratios involving do not simply depenc on metallicity but also on other independent parameters., These results thus indicate that emission-line flux ratios involving do not simply depend on metallicity but also on other independent parameters. One possible idea ts that the difference of the behavior between flux ratios with and without may be associated with the different enrichment timescale of nitrogen relative to other elements., One possible idea is that the difference of the behavior between flux ratios with and without may be associated with the different enrichment timescale of nitrogen relative to other elements. Recent studies on local AGNs have shown that nuclear star formation and AGN activity are not coeval (Davies et al., Recent studies on local AGNs have shown that nuclear star formation and AGN activity are not coeval (Davies et al. 2007: see also Wild et al., 2007; see also Wild et al. 2010)., 2010). More specifically. black hole accretion appears to occur in post-starburst nuclei. with a delay of ~10® years from the starburst.," More specifically, black hole accretion appears to occur in post-starburst nuclei, with a delay of $\sim 10^8$ years from the starburst." Probably during the active starburst phase powerful supernova explosions expel the circumnuclear gas preventing it to reach the black hole. while the more gentle winds of AGB stars occurring on timescales of 10° years are capable of stirring the interstellar matter (ISM). making it loose angular momentum and then feed the AGN.," Probably during the active starburst phase powerful supernova explosions expel the circumnuclear gas preventing it to reach the black hole, while the more gentle winds of AGB stars occurring on timescales of $10^8$ years are capable of stirring the interstellar matter (ISM), making it loose angular momentum and then feed the AGN." The production of nitrogen is delayed with respect to other elements. and indeed produced mostly by AGB stars whereas other elements (1.e.. Si. O. and Al) are produced by massive stars on much shorter timescale.," The production of nitrogen is delayed with respect to other elements, and indeed produced mostly by AGB stars whereas other elements (i.e., Si, O, and Al) are produced by massive stars on much shorter timescale." Carbon originates mainly from low-mass stars (Chiappini et al., Carbon originates mainly from low-mass stars (Chiappini et al. 2003): their life time Is 1077 years., 2003); their life time is $\sim 10^{9-10}$ years. This means that carbon would not be associated with black hole accretion., This means that carbon would not be associated with black hole accretion. Moreover. since C2549 is a strong coolant of the BLR. its intensity is little sensitive to the carbon abundance.," Moreover, since $\lambda$ 1549 is a strong coolant of the BLR, its intensity is little sensitive to the carbon abundance." As a consequence. if also," As a consequence, if also" sinele close passage of LAIC ancl (he swing to larger galactic longitude going backward in time at redshift about unity.,single close passage of LMC and the swing to larger galactic longitude going backward in time at redshift about unity. Models 4 and 5 illustrate the need for three massive actors in addition to LMC to account for the motion of LAIC out of the LMC-MW-NM323I. plane. (, Models 4 and 5 illustrate the need for three massive actors in addition to LMC to account for the motion of LMC out of the LMC-MW-M31 plane. ( As noted in P9. the gravitational interaction among three galaxies. LAIC. MW and M31. in an otherwise empty universe drives motions confined to the plane of the three galaxies.),"As noted in P9, the gravitational interaction among three galaxies, LMC, MW and M31, in an otherwise empty universe drives motions confined to the plane of the three galaxies.)" The models without a laree external mass solve the problem by promoting M33 to a massive actor., The models without a large external mass solve the problem by promoting M33 to a massive actor. This is unlikely but a useful illustration of what the measured LMC motion requires., This is unlikely but a useful illustration of what the measured LMC motion requires. And it is to be noted that the LAIC orbits relative to MW in Models 4 and 5 share the general features of (the other solutions., And it is to be noted that the LMC orbits relative to MW in Models 4 and 5 share the general features of the other solutions. The same is true of the still more schematic model in P9., The same is true of the still more schematic model in P9. Since the motion of LMC at low redshifts is dominated bv (he mass in MW. it is nol surprising that the orbits in Figure 3. at low redshift all are similar and agree with models with MW alone (Besla et al.," Since the motion of LMC at low redshifts is dominated by the mass in MW, it is not surprising that the orbits in Figure \ref{Fig:3} at low redshift all are similar and agree with models with MW alone (Besla et al." 2007) or with MW and M31. CIxallivavalil et al., 2007) or with MW and M31 (Kallivayalil et al. 2009: Shattow Loeb 2009)., 2009; Shattow Loeb 2009). The swing toward larger galactic longitude at larger redshift. and the single close approach of LMC to MW. are less intuitive. but they have proved to be stable results of the measured. LMC motion unuder the cosmological initial condition that the primeval peculiar velocities are growing.," The swing toward larger galactic longitude at larger redshift, and the single close approach of LMC to MW, are less intuitive, but they have proved to be stable results of the measured LMC motion under the cosmological initial condition that the primeval peculiar velocities are growing." Besla et al. (, Besla et al. ( 2007) and Shattow Loeb (2009) present models in which LAIC has completed more than one orbit around MW.,2007) and Shattow Loeb (2009) present models in which LMC has completed more than one orbit around MW. This is not found in the present analvsis., This is not found in the present analysis. The random starting orbils were designed to reach plausible solutions with (wo close passages. but the lack of discovery of examples must be balanced against the experience that the action method is not well adapted to capturing this case.," The random starting orbits were designed to reach plausible solutions with two close passages, but the lack of discovery of examples must be balanced against the experience that the action method is not well adapted to capturing this case." The argument from astronomy. against an earlier close passage is (hal it müght be expected to have stripped away the (van den Bergh 2006)., The argument from astronomy against an earlier close passage is that it might be expected to have stripped away the (van den Bergh 2006). Thus Besla et al. (, Thus Besla et al. ( 2010) find that the single orbit allows a model for the origin of the Magellanic stream bv tidal interaction between the Large and Small \lagellanic Clouds.,2010) find that the single orbit allows a model for the origin of the Magellanic stream by tidal interaction between the Large and Small Magellanic Clouds. The computation allows considerable [reeclom in the mass of LMC. and indeed (he mass in Model 3 is one tenth that of Model 2.," The computation allows considerable freedom in the mass of LMC, and indeed the mass in Model 3 is one tenth that of Model 2." However. the more plausible Models 1 and 2 put the mass of LMC at 1 to 2x10H»...," However, the more plausible Models 1 and 2 put the mass of LMC at 1 to $2\times 10^{11}m_\odot$." This is ten times the mass within LO kpe (van der Marel οἱ al., This is ten times the mass within 10 kpc (van der Marel et al. 2002). but at Iuminositv Lj~3xI0L. a conventional dark matter halo could make up the difference.," 2002), but at luminosity $L_B\sim 3\times 10^9L_\odot$ a conventional dark matter halo could make up the difference." Indeed. Besla et al. (," Indeed, Besla et al. (" "2010) present an independent argument for an LMC mass ~2x10, from the relation between luminosity and halo mass found in numerical simulations of structure formation in the standard cosmology.",2010) present an independent argument for an LMC mass $\sim 2\times 10^{11}m_\odot$ from the relation between luminosity and halo mass found in numerical simulations of structure formation in the standard cosmology. IF LAIC had a massive halo as it approached MW. then this dark matter would now be far from smoothly distributed as (he halo merges with the MW halo., If LMC had a massive halo as it approached MW then this dark matter would now be far from smoothly distributed as the halo merges with the MW halo. A halo merger does not seem likely to have had a significant effect on the motion of the stellar part of LAIC as it plunges into the dominant, A halo merger does not seem likely to have had a significant effect on the motion of the stellar part of LMC as it plunges into the dominant While the majority of MS stars (aside Irom the coolest ones) have effective temperatures (oo high for sienilicant molecular formation. the ability for this molecule to form on the SGD and RGB increases with Iuninositv as the star expands ancl its surface temperature drops.,"While the majority of MS stars (aside from the coolest ones) have effective temperatures too high for significant molecular formation, the ability for this molecule to form on the SGB and RGB increases with luminosity as the star expands and its surface temperature drops." The result of this is that. all things being equal. we expect to see increased CN absorption on the RGB when compared to the SGB and this elfect must be accounted for in (he analvsis prior to inlerring anv abundance differences.," The result of this is that, all things being equal, we expect to see increased CN absorption on the RGB when compared to the SGB and this effect must be accounted for in the analysis prior to inferring any abundance differences." Furthermore. for clusters of moderate metallicity. when the CN aborption strengths are plotted as a function of luminosity or temperature. (wo groups generally appear one CN-weak (sometimes referred to as CN-normal). the other CN-strong (enrielied).," Furthermore, for clusters of moderate metallicity, when the CN aborption strengths are plotted as a function of luminosity or temperature, two groups generally appear – one CN-weak (sometimes referred to as CN-normal), the other CN-strong (enriched)." A linear relationship is then fit to the CN-weak locus. aud the vertical difference in 5(3839)« between each point and the baseline is measured. as illustrated lor M2 in the bottom-lelt panel of Figure 4..," A linear relationship is then fit to the CN-weak locus, and the vertical difference in $_{\rm N}$ between each point and the baseline is measured, as illustrated for M3 in the bottom-left panel of Figure \ref{figdcngenhist}." This vertical difference is denoted as 05(3839) x. and is taken (o be a temperature-corrected measure of CN absorption.," This vertical difference is denoted as $\delta$ S(3839) $_{\rm N}$, and is taken to be a temperature-corrected measure of CN absorption." The other panels in (his ligure are generalized histograams of this temperature-corrected index for our sample of clusters. discussed in detail below.," The other panels in this figure are generalized histograms of this temperature-corrected index for our sample of clusters, discussed in detail below." The raw and corrected values are listed for each cluster in Table 3.., The raw and corrected values are listed for each cluster in Table \ref{tabcnch}. The slope of the relationship between CN bandstrength ancl luminosity is metallicity dependent. so each cluster must be corrected individually prior to constructing comparisons across {he sample.," The slope of the relationship between CN bandstrength and luminosity is metallicity dependent, so each cluster must be corrected individually prior to constructing comparisons across the sample." Figure 5. shows this relationship between the CN slope and.|Fe/1I].. obtained by dividing our entire sample into 0.1-dex wide metallicity bins and fitting a line to the CN-weak locus of each bin.," Figure \ref{figcnfehbin} shows this relationship between the CN slope and, obtained by dividing our entire sample into 0.1-dex wide metallicity bins and fitting a line to the CN-weak locus of each bin." Note the trend of decreasing CN slope with decreasingFe/H].. which is similar to the trend for field giants from DR? reported by(2010).," Note the trend of decreasing CN slope with decreasing, which is similar to the trend for field giants from DR7 reported by." . When the slope of each panel in their Figure 6 is plotted as a function of metallicity. we obtain a linear relationship for field giants:," When the slope of each panel in their Figure 6 is plotted as a function of metallicity, we obtain a linear relationship for field giants:" We observed Οίας with the EVLA on Apri 20.1920.26 at central frequencies. of L96 GIIz ux S16 ας.,We observed 10fqs with the EVLA on April 20.19–20.26 at central frequencies of 4.96 GHz and 8.46 GHz. We added together two adjacent 128 MIIZ subbands with full polarization to maximize continui sensitivity., We added together two adjacent 128 MHz subbands with full polarization to maximize continuum sensitivity. Amplitude and bandpass calibration was achieved using a single observation of J1331|3030. aac phase calibration was carricd out every 10 mun bv switching between the target field and the poiut source J1239|0730.," Amplitude and bandpass calibration was achieved using a single observation of J1331+3030, and phase calibration was carried out every 10 min by switching between the target field and the point source J1239+0730." The visibility data were calibrated aac -inaged in theALPS package following standard practice., The visibility data were calibrated and imaged in the package following standard practice. A radio point source was uot detected at the position of the transient., A radio point source was not detected at the position of the transient. After removing extended emission from the host galaxy. the 20 limits for a point source are 93 Jv aud 63 Jy at 1.96 GITz aud 8.16 CGIIz. respectively.," After removing extended emission from the host galaxy, the $3\sigma$ limits for a point source are 93 $\mu$ Jy and 63 $\mu$ Jy at 4.96 GHz and 8.46 GHz, respectively." " At the distauce of M99. this corresponds to £,<2.1«107 ove s1 |."," At the distance of M99, this corresponds to $L_{\nu} < 2.1 \times 10^{25}$ erg $^{-1}$ $^{-1}$." Comparing with the compilation in Chevalieretal.(2006).. this upper Πατ is at the level of the faintest Type IEP 2200141: Beswickot.al. 2005)) and Type Ic 22002ap: Dergeretal. 20021) supernovae.," Comparing with the compilation in \citet{cfn06}, this upper limit is at the level of the faintest Type II-P 2004dj; \citealt{bma+05}) ) and Type Ic 2002ap; \citealt{bkc02}) ) supernovae." As noted by Bereeretal.(2009)... the nearby NQGQC300-OTT was also not detected in the radio to deeper DIuniuositv linüts.," As noted by \citet{bsc+09}, the nearby NGC300-OT was also not detected in the radio to deeper luminosity limits." We observed Οίας withGALEN (Alartinctal.2005) on two consecutive orbits starting at 2010 April 21387 (total exposure of 281655)., We observed 10fqs with \citep{mfs+05} on two consecutive orbits starting at 2010 April 24.387 (total exposure of s). All images were reduced and coadded using the standardGALEN pipeline and calibration (Morrisseyetal.2007)., All images were reduced and coadded using the standard pipeline and calibration \citep{mcb+07}. . To create a refercuce nuage. we coadded 22 nuages of AI99 prior to 2005 April 2 (total exposure of 185715).," To create a reference image, we coadded 22 images of M99 prior to 2005 April 2 (total exposure of s)." Next. we subtracted the reference image frou observations of LIOfÉqs (see Figure 6)).," Next, we subtracted the reference image from observations of 10fqs (see Figure \ref{fig:galex}) )." No source is detected., No source is detected. We find a 30 upper limit of NUV 22.7 AD imag iu an aperture consistent with aGALEN point source (τον τι]. , We find a $\sigma$ upper limit of NUV 22.7 AB mag in an aperture consistent with a point source $7.5\arcsec \times 7.5\arcsec$ ). To constrain the pre-explosion counterpart. we measured the laniting magnitude at the position of 1Ll0fqs in the coadded reference image.," To constrain the pre-explosion counterpart, we measured the limiting magnitude at the position of 10fqs in the coadded reference image." The faintest detected object consistent with being a point source within the ealaxy had NUV = 20.1 AB mage., The faintest detected object consistent with being a point source within the galaxy had NUV = 20.1 AB mag. The 36 Iiiuit based on measuring the sky root-nean square (πάς) is NUV > 21.5 AB imag., The $\sigma$ limit based on measuring the sky root-mean square (rms) is NUV $>$ 21.8 AB mag. We observed PTFLOfqs with Swift/XNRT ou April 20.166 for2507.3ss and April 22.021 for ss. No source is detected to a 30 Bnitiug count rate (assume an Ls” radius) of LG«10! counts !., We observed PTF10fqs with /XRT on April 20.466 fors and April 22.024 for s. No source is detected to a $3\sigma$ limiting count rate (assuming an $18''$ radius) of $4.6 \times 10^{-4}$ counts $^{-1}$ . Assmnine a power-law model with a photon iudex of two. this," Assuming a power-law model with a photon index of two, this" "In most observations of the 10 - 15 um range, the dominant 11.2 um feature appears with a dwarfed satellite feature at 11.0 um. This has been attributed to the solo C-H out-of-plane bending modes of PAH* (?????)..","In most observations of the 10 - 15 $\mu$ m range, the dominant 11.2 $\mu$ m feature appears with a dwarfed satellite feature at 11.0 $\mu$ m. This has been attributed to the solo C-H out-of-plane bending modes of $^+$ \citep{hudgins,peeters, hony, baus, baus09}." " We observe the highest [11.0]/[11.2] um ratio closest to the source star, which is also where the abundance of PAH* is greatest."," We observe the highest [11.0]/[11.2] $\mu$ m ratio closest to the source star, which is also where the abundance of $^+$ is greatest." A comparison of observed spectra from a PAH* dominated region and a VSG dominated region are shown in Figure 9.., A comparison of observed spectra from a $^+$ dominated region and a VSG dominated region are shown in Figure \ref{fig:analysis}. " It is important to recall that regardless of position in the PDR, the 11.2 um PAH? feature significantly dominates the 11.0 44m PAH"" feature."," It is important to recall that regardless of position in the PDR, the 11.2 $\mu$ m $^0$ feature significantly dominates the 11.0 $\mu$ m $^+$ feature." " The separate contributions of PAH* and PAH? to the 11.0 and 11.2 pm features respectively, agrees with previous spectroscopic laboratory and quantum chemical calculation studies by e.g. 255 255 25 ? and ?.."," The separate contributions of $^+$ and $^0$ to the 11.0 and 11.2 $\mu$ m features respectively, agrees with previous spectroscopic laboratory and quantum chemical calculation studies by e.g. \citet{hudgins}; \citet{hony}; \citet{peeters}; \citet{baus} and \citet{cami}." " In our decomposition analysis, the 11.0 um band is clearly associated with the PAH* component (Signal 2) based upon the strong 6.2 and 7.7 um bands, while the 11.2 pm band is attributed to the neutral component (?).."," In our decomposition analysis, the 11.0 $\mu$ m band is clearly associated with the $^+$ component (Signal 2) based upon the strong 6.2 and 7.7 $\mu$ m bands, while the 11.2 $\mu$ m band is attributed to the neutral component \citep{Olivier}." Hence we suggest that the variation of the [11.0]/[11.2] um ratio is due to a changing abundance of PAH* to ΡΑΗΟ., Hence we suggest that the variation of the [11.0]/[11.2] $\mu$ m ratio is due to a changing abundance of $^+$ to $^0$. " As mentioned in the introduction, the 11.2 um band has an observed asymmetry with a varying red wing (?).."," As mentioned in the introduction, the 11.2 $\mu$ m band has an observed asymmetry with a varying red wing \citep{roche}." This wing has been attributed to anharmonicity or to different species of PAHs with a shifted solo mode peak emission (??)..," This wing has been attributed to anharmonicity or to different species of PAHs with a shifted solo mode peak emission \citep{pech, peeters}." Observations of the 11.2 um feature show that the shape and peak position can vary., Observations of the 11.2 $\mu$ m feature show that the shape and peak position can vary. " In their analysis of the skewed variations in the 11.2 um profile, ? empirically divided observations of the feature into two categories: one group is characterized by a peak between 11.20 and 11.24 um and a more skewed red wing, while the other peaks at 11.25 um and is much more symmetric."," In their analysis of the skewed variations in the 11.2 $\mu$ m profile, \citet{peeters} empirically divided observations of the feature into two categories: one group is characterized by a peak between 11.20 and 11.24 $\mu$ m and a more skewed red wing, while the other peaks at 11.25 $\mu$ m and is much more symmetric." " In agreement with this, it has also"," In agreement with this, it has also" however. was much different. wilh no apparent rebrightening phase. while the plateau phase had small amplitude variations during the whole duration of the outburst.,"however, was much different, with no apparent rebrightening phase, while the plateau phase had small amplitude variations during the whole duration of the outburst." The main purpose of (he present work is (o (rv to account [or the observed sequence of temperatures using a numerical model for the accretional heating ancl subsequent cooling ol the accreting white dwarf., The main purpose of the present work is to try to account for the observed sequence of temperatures using a numerical model for the accretional heating and subsequent cooling of the accreting white dwarf. In the next section we address the issue of the accuracy of the temperature determination during the outburst and cooling periods. together with an overview of the estimates of the WD temperature and accretion rate.," In the next section we address the issue of the accuracy of the temperature determination during the outburst and cooling periods, together with an overview of the estimates of the WD temperature and accretion rate." We present the code we use to carry out (he simulations of the heating and cooling of the WD in section 3., We present the code we use to carry out the simulations of the heating and cooling of the WD in section 3. The results are presented in section 4., The results are presented in section 4. In the last section we discuss the possible origin of the observed high temperatures and slow cooling of the white dwar!, In the last section we discuss the possible origin of the observed high temperatures and slow cooling of the white dwarf. In the present work we consider (he observations of WZ See carried out in the Far Ultraviolet for which the temperature of the accreting white dwarl and/or the mass accretion rate of the system were assessed., In the present work we consider the observations of WZ Sge carried out in the Far Ultraviolet for which the temperature of the accreting white dwarf and/or the mass accretion rate of the system were assessed. These observations monitor changes in the FUV component of the svstem during its different phases. over a time span of 20 months.," These observations monitor changes in the FUV component of the system during its different phases, over a time span of 20 months." ancl reveal a cooling of the WD in response to the outburst of about 12.000Ix. Namely. we consider 4 FUSE and 11 IIST/STIS observations as follows: one FUSE observation obtained during the plateau phase. one IIST observation obtained during the dip. two LST and one FUSE observations obtained during (he rebrightening phase and 2 FUSE with 8 HIST observations obtained during the cooling phase.," and reveal a cooling of the WD in response to the outburst of about 12,000K. Namely, we consider 4 FUSE and 11 HST/STIS observations as follows: one FUSE observation obtained during the plateau phase, one HST observation obtained during the dip, two HST and one FUSE observations obtained during the rebrightening phase and 2 FUSE with 8 HST observations obtained during the cooling phase." A total of 15 observations together with their references ave recapitulate in Table 1., A total of 15 observations together with their references are recapitulated in Table 1. In order to estimate the temperature one generates a grid of theoretical spectra for different. values of the surface temperature. gravity. aud composition. using the synthetic speclra generator codes TLUSTY and SYNSPEC (IIubeny1988:IIubeny.etal.llubeny&Lanz 1995).," In order to estimate the temperature one generates a grid of theoretical spectra for different values of the surface temperature, gravity and composition, using the synthetic spectra generator codes TLUSTY and SYNSPEC \citep{hub88,hub94,hub95}." One then masks regions of the observed spectrum that are nol characteristic of a WD atmosphere (such are emission lines for example). and a A? fitting technique is used to find the best fit model.," One then masks regions of the observed spectrum that are not characteristic of a WD atmosphere (such are emission lines for example), and a $\chi^2$ fitting technique is used to find the best fit model." The mass accretion rate is estimated im a similar manner using different options in the synthetic spectra generator codes TLUSTY (the older version is known as TLDISIX) and SYSNDPEC., The mass accretion rate is estimated in a similar manner using different options in the synthetic spectra generator codes TLUSTY (the older version is known as TLDISK) and SYSNPEC. the following mass accretion rates were estimated in the references mentioned in Table 1 and should be considered only as an order of estimate., the following mass accretion rates were estimated in the references mentioned in Table 1 and should be considered only as an order of estimate. From Table 1. we see that the mass accretion rate estimate during the plateau phase is," From Table 1, we see that the mass accretion rate estimate during the plateau phase is" The soft. X-ray transients. a subclass of the low-mass X-ray binaries distinguished by their X-ray outbursts. have prove to be an ideal hunting erounc for stellar-mass black hole candidates (Lanaka Shibazaki 1996).,"The soft X-ray transients, a subclass of the low-mass X-ray binaries distinguished by their X-ray outbursts, have proved to be an ideal hunting ground for stellar-mass black hole candidates (Tanaka Shibazaki 1996)." ‘The λα Nova Sco 1994 (—GhO 165540) is particularly interesting. since as well as being a source of superluminal jets (Zhang et al..," The system Nova Sco 1994 (=GRO J1655–40) is particularly interesting, since as well as being a source of superluminal jets (Zhang et al.," 1994: Harmon et al..," 1994; Harmon et al.," 1995). its optical brightness ancl partia eclipse features mean that it is one of the few systems tha jas. vielded a reliable estimate for the mass of the collapse star.," 1995), its optical brightness and partial eclipse features mean that it is one of the few systems that has yielded a reliable estimate for the mass of the collapsed star." Nova Seo 1994 was discovered. on July 27 1994 with BAPSE on board the Compton Camma tay Observatory (Zhang et ab.," Nova Sco 1994 was discovered on July 27 1994 with BATSE on board the Compton Gamma Ray Observatory (Zhang et al.," L994)., 1994). It has been studied extensively during 1ο past few vears in X-rays and at οXical ancl racio =μαavelengths. (Bailyn et al.," It has been studied extensively during the past few years in X-rays and at optical and radio wavelengths (Bailyn et al.," 1995a and b. Zhang et al.," 1995a and b, Zhang et al.," rm905. van der Loolt οἱ al.," 1995, van der Hooft et al." 1998)., 1998). Strone evidence that 16 compact object in Nova Sco 1994 is à black hole was presented. by Bailvn et ((1995b) who initially established. a spectroscopic. period. of. 2.6)]+0.027 days. Jassified the secondary as an F6íe type star and suggested. a. mass function [(M )23.164:0.15 M..," Strong evidence that the compact object in Nova Sco 1994 is a black hole was presented by Bailyn et (1995b) who initially established a spectroscopic period of $2.601\pm0.027$ days, classified the secondary as an $\sc iv$ type star and suggested a mass function $f(M)$ $\pm$ 0.15 $_{\odot}$ ." An improved. value of f(AL)=3.24-£0.09 A. was presented by Orosz Bailvn (1997) using |roth quiescent and outburst data. derivec [rom a radial velocity semi-amplitucde of 228.2+2.2," An improved value of $f(M)$ $\pm$ 0.09 $_{\odot}$ was presented by Orosz Bailyn (1997) using both quiescent and outburst data, derived from a radial velocity semi-amplitude of $\pm$ 2.2." Shahbaz οἱ al. (, Shahbaz et al. ( 1900) using only quiescent data. determined. the true racial velocity. seni- A»—215.532.4 which In1ves a revised value for the mass function of f(AL) = 2.7340. OAL...,"1999) using only quiescent data, determined the true radial velocity semi-amplitude $K_{2}$ $\pm$ which gives a revised value for the mass function of $f(M)$ = $\pm$ 0.09 $_{\odot}$." " They also measured the rotational broadening of the secondary star which then gives the binary mass ratio q~0.39 (=Al, Aly. where M, and Als are the masses of the compact object and secondary star respectively)."," They also measured the rotational broadening of the secondary star which then gives the binary mass ratio $q\sim 0.39$ $_{2}$ $_{1}$, where $_{1}$ and $_{2}$ are the masses of the compact object and secondary star respectively)." " The οσοι of heating of the πόσοιary ds to shift the ""ellective centre! of the secondary. weighted by the strength of the absorption lines. from the centre of mass of the star."," The effect of heating of the secondary is to shift the `effective centre' of the secondary, weighted by the strength of the absorption lines, from the centre of mass of the star." One expects hat this results in a signiicant distortion of the racial velocity curve and renders a sinusoidal fit clearly inadequate. leading to a spuriously high racial velocity scmi-amplitucde.," One expects that this results in a significant distortion of the radial velocity curve and renders a sinusoidal fit clearly inadequate, leading to a spuriously high radial velocity semi-amplitude." In. order to quantify this effect we have determined the racial velocity variations of the secondary star in Nova Seo 1994. when it was in outburst ancl compared our resultswih others obtained using data taken when the source was in dillerent X-ray states.," In order to quantify this effect we have determined the radial velocity variations of the secondary star in Nova Sco 1994, when it was in outburst and compared our resultswith others obtained using data taken when the source was in different X-ray states." "Researchers have been able to reproduce outburst light curves and mean times between outbursts using oj,;20.1 and cuu;c0.01.","Researchers have been able to reproduce outburst light curves and mean times between outbursts using $\alpha_{hot} \simeq 0.1$ and $\alpha_{cold} \simeq 0.01$." " Another oft discussed possibility is that a obevs a scaling relation such as a=αρ), where £7 is the disk scale height aud r the local radius."," Another oft discussed possibility is that $\alpha$ obeys a scaling relation such as $\alpha = \alpha_0 (H/r)^q$, where $H$ is the disk scale height and $r$ the local radius." To our knowledge this prescription has been used iu the DN coutext oulv to study decay properties of the outhurst helt curves., To our knowledge this prescription has been used in the DN context only to study decay properties of the outburst light curves. Both these preseriptious for varving o are phenomenologically motivated: while there exist some theoretical justifications for varying o. inour view they are not strouely plivsicallvy 1iotivated.," Both these prescriptions for varying $\alpha$ are phenomenologically motivated; while there exist some theoretical justifications for varying $\alpha$, in our view they are not strongly physically motivated." " What thenis Rey, n cowarf nova disks?", What then is $Re_M$ in dwarf nova disks? " For definiteness. we focus on a nearby. well-studied system: SS νο,"," For definiteness, we focus on a nearby, well-studied system: SS Cygni." SS (νο has a 1.2M. white chwart accretiug from a disk fed bv a (FAL. ΙΟΥ companion. a period of σ.σ. a distance from the primary to the L1 poiut. of about 6«1019c1. a mean interval between outbursts of Ld. and a characteristic decay time from outburst of 2.td. The mean accretion rate is not well known but is of order 10PADyr31 (Canuizzo (1993a))).," SS Cyg has a $1.2 \msun$ white dwarf accreting from a disk fed by a $0.7 \msun$ K5V companion, a period of $6.6$ hr, a distance from the primary to the L1 point of about $6 \times 10^{10} \cm$, a mean interval between outbursts of $40$ d, and a characteristic decay time from outburst of $2.4$ d. The mean accretion rate is not well known but is of order $10^{-9} \msun \yr^{-1}$ \cite{can93a}) )." We require a teniperature aud density to estimate the resistivity in SS Cyeni in quicscence., We require a temperature and density to estimate the resistivity in SS Cygni in quiescence. These are ouly weakly constrained by observations., These are only weakly constrained by observations. Iu the absence of direct Iuüeasurenients. we must turn to a theoretical model for the disk evolution: the staucdid disk stability model.," In the absence of direct measurements, we must turn to a theoretical model for the disk evolution: the standard disk instability model." Future observations niav provide better constraints on physical conditions in the disk., Future observations may provide better constraints on physical conditions in the disk. SS Cre has been theoretically studied in detail using the standard thermal luit evele model (see Canulzzo(19934) for the most cetailed study to date)., SS Cyg has been theoretically studied in detail using the standard thermal limit cycle model (see \cite{can93a} for the most detailed study to date). " We have run our own evolutionary models of SS (νο to estimate plivsical conditions in the quiescent disk. using a modern. dependent. Πιτ, adaptive erid code (IEbuueuryctal. (19973))."," We have run our own evolutionary models of SS Cyg to estimate physical conditions in the quiescent disk, using a modern, time-dependent, implicit, adaptive grid code \cite{ham97}) )." " We adopt the same paramcters for SS Cre as Cannizzo's standard model (05,;= 0.1.0,= 0.02). and our calculated X aud T; are sinular to those in liis standard model"," We adopt the same parameters for SS Cyg as Cannizzo's standard model $\alpha_{hot} = 0.1$, $\alpha_{cold} = 0.02$ ), and our calculated $\Sigma$ and $T_c$ are similar to those in his standard model." At a radius of2.10!”ci from the primary a typical stnface density in quiescence is 200¢cm2. aud a typicalcentral toupevature is 30001.," At a radius of $2 \times 10^{10}\cm$ from the primary a typical surface density in quiescence is $200 \gm \cm^{-2}$, and a typical temperature is $3000 \K$." " Then ο=L5«10ὃν4. e,=35«dOaus t=ο=7.7«Wem. and pcMÁAQID)2913410Sean?."," Then $\Omega = 4.5 \times 10^{-3} \sec^{-1}$, $c_s = 3.5 \times 10^5 \cm\sec^{-1}$, $H = c_s/\Omega = 7.7 \times 10^7 \cm$, and $\rho \simeq \Sigma/(2 H) = 1.3 \times 10^{-6} \gm \cm^{-3}$." In LTE hydroseu is then predominantly molecular., In LTE hydrogen is then predominantly molecular. The disk is mareinally optically thick iu à Rosselaud mean seuse., The disk is marginally optically thick in a Rosseland mean sense. The resistivity is given by where is an effective collision frequency for electrons., The resistivity is given by where $\nu_c$ is an effective collision frequency for electrons. " Since electron-neutral collisions dominate. we take vo σοι Where, is the neutral umber density. σι 1s the electrou-ueutral momentum exchange cross section. are eomοOni)."," Since electron-neutral collisions dominate, we take $\nu_c = n_n \sigma_{en} v$ , where $n_n$ is the neutral number density, $\sigma_{en}$ is the electron-neutral momentum exchange cross section, and $v = \sqrt{128 k T/(9\pi m_e)}$." " At OU000IN 0,=13«10on? (IIlavashi (1981))).", At $3000\K$ $\sigma_{en} = 1.3 \times 10^{-15} \cm^2$ \cite{hay81}) ). Then y=1.67«Lnfae., Then $\eta = 1.67 \times 10^4 n_n/n_e$. The electron abundance at this temperature is determine: primarily by iouizatioun of Na. and to a lesser extent. Ca aud [KK πο assume solar abuudauces)," The electron abundance at this temperature is determined primarily by ionization of Na, and to a lesser extent, Ca and K (we assume solar abundances)." " A cdoetaile solution for ionization equilibrium (ve have used a code kindly provided to ux bx Dr. P. Woefich. but à simplificc calculation involving Na. C. and I& eives nearly ideutica results) eives n,=X03&d0l*αι7. audon? soy =7.295lOeni?d."," A detailed solution for ionization equilibrium (we have used a code kindly provided to us by Dr. P. Hoeflich, but a simplified calculation involving Na, C, and K gives nearly identical results) gives $n_n = 3.73 \times 10^{17} \cm^{-3}$, and, so $\eta = 7.29 \times 10^{9} \cm^{2} \sec^{-1}$." " The natural leusth aud velocity scales iu disks are fF aud es. respectively,"," The natural length and velocity scales in disks are $H$ and $c_s$, respectively." " The disk magnetic Revnolds Πεο is then Reg,—elf."," The disk magnetic Reynolds number is then $Re_M \equiv c_s H/\eta$." " Using the resistivity just calculated. Rea,=3670."," Using the resistivity just calculated, $Re_M = 3670$." This is below the value at which ΑΠΟ turbulence is depressed in the simmlations of IIGD., This is below the value at which MHD turbulence is depressed in the simulations of HGB. " Similarly low values of Rea, ave obtaimed at other radii iu our niodel.", Similarly low values of $Re_M$ are obtained at other radii in our model. " Of course. this Rea, was obtained asstunine Ceol=0.02."," Of course, this $Re_M$ was obtained assuming $\alpha_{cold} = 0.02$." " At lower a the disk will be cooler aud deuser. and then Rea, will be simaller since 5 is very sensitive to temperature."," At lower $\alpha$ the disk will be cooler and denser, and then $Re_M$ will be smaller since $\eta$ is very sensitive to temperature." Since a depends on the resistivity as well. there could be a runaway decay of MIID turbulence.," Since $\alpha$ depends on the resistivity as well, there could be a runaway decay of MHD turbulence." " All this suggests that. at least in SS νο, angular mionientuni transport may die away once the disk s&oes iuto quiescence."," All this suggests that, at least in SS Cygni, angular momentum transport may die away once the disk goes into quiescence." Before going onu. let us briefly consider two other jsxues.," Before going on, let us briefly consider two other issues." First. does ambipolar diffusion plav auv role?," First, does ambipolar diffusion play any role?" " The relative importance of ambipolar diffusion aud resistivity is controlled by the product of the electron and iou Tall paralcters. DR=ww(MenVin). Where uw; are the ion and electron cyclotron frequencies aud É;, is the ion-neutral collision frequency: when DRο1d ambipolar diffusion dominates."," The relative importance of ambipolar diffusion and resistivity is controlled by the product of the electron and ion Hall parameters, $DR = \omega_e \omega_i/(\nu_{en}\nu_{in})$, where $\omega_{e,i}$ are the ion and electron cyclotron frequencies and $\nu_{in}$ is the ion-neutral collision frequency; when $DR > 1$ ambipolar diffusion dominates." Asstmine cquipartition magnetic fields at our fiducial point in the SS (νο disk. we find DR=0.02.," Assuming equipartition magnetic fields at our fiducial point in the SS Cyg disk, we find $DR = 0.02$." Since the field is likely to be weaker than this. resistivity dominates ambipolar diffusion.," Since the field is likely to be weaker than this, resistivity dominates ambipolar diffusion." Second. can nouthermal ionization save the dav?," Second, can nonthermal ionization save the day?" " Tere the chief concern is N-vavs: cawarf novae typically lave L,~l0Ueest but SS Cre ds particularly: brisbt in hard A-vavs in quiescence. with L,(1B37keV)x1.5«1075eresLo( Yoshidaetal. (19923))."," Here the chief concern is X-rays; dwarf novae typically have $L_x \simeq 10^{30}\erg \sec^{-1}$, but SS Cyg is particularly bright in hard X-rays in quiescence, with $L_x (1-37 \kev) \simeq 1.5 \times 10^{32} \erg \sec^{-1}$ \cite{yio92}) )." Oulyphotous with Ezl0keV will penetrate the disk., Onlyphotons with $E \gtrsim 10 \kev$ will penetrate the disk. These will Compton scatter and diffuse downward ito a laver of thickness ~30gein2? coxrespondiug to iu effective optical depth of 1 (Cdasseoldetal.(1997).. Igea.&|Cassgold (19973)).," These will Compton scatter and diffuse downward into a layer of thickness $\simeq 30 \gm \cm^{-2}$ corresponding to an effective optical depth of $1$ \cite{gni97}, \cite{ig97}) )." The imtercepted flux per unit area of the disk is fcL4IH/c)/tlxr?).," The intercepted flux per unit area of the disk is $f_x \simeq L_x (H/r)/(4\pi r^2)$." Suppose this fux diffuses iuto a laver of thücknuess JF aud produces 1 ion per E;=36eV., Suppose this flux diffuses into a layer of thickness $H$ and produces 1 ion per $E_i = 36 \ev$. " Then the volume ionization rate is £=L,/(lzi?Ej)eun...", Then the volume ionization rate is $\xi = L_x /(4 \pi r^3 E_i) \cm^{-3}$. Balancing this against dissociative recombination at a rate yoNT10OF Mean? we find os=Ldsσι7.," Balancing this against dissociative recombination at a rate $n_e^2 \times 8.7 \times 10^{-6} T^{-1/2} \cm^{-3}$ we find $n_e = 1.1 \times 10^9 \cm^{-3}$." Since this is much less than the LTE electron. number density we can neglect A-vav iouization in the bulk of the disk., Since this is much less than the LTE electron number density we can neglect X-ray ionization in the bulk of the disk. It is possible. however. that a thin laver ou the surface of the disk will be ionized by N-ravs. aud. accretion will proceed in that laver iu a 11anner similar to that described by Camunic(1996) in the contest of protoplanctary disks.," It is possible, however, that a thin layer on the surface of the disk will be ionized by X-rays, and accretion will proceed in that layer in a manner similar to that described by \cite{gam96} in the context of protoplanetary disks." A thin partially ionized laver could explain eclipse maps of quiescent dwarf novae (Woodctal.(1992).. IIorne (1993))). whichare interpreted as showing cussion frou. a wann optically thin disk.," A thin partially ionized layer could explain eclipse maps of quiescent dwarf novae \cite{whv92}, \cite{hor93}) ), whichare interpreted as showing emission from a warm optically thin disk." Suppose that MITID turbulence dies away in SS (ντος disk iu quiescence., Suppose that MHD turbulence dies away in SS Cyg's disk in quiescence. It i8 possible that some weaker residual transport process will be present in the disk., It is possible that some weaker residual transport process will be present in the disk. Let us consider some of the possibilities., Let us consider some of the possibilities. Convective turbulence is ruled out for at least two reasons; the disk is only iuargimallv optically thick. so convection will uot be present. aud even it were present. recent studies showthat convective turbulence produces ρα augular monentun transport (να&Coodman (1992).. Stone (1996).. Cabot (1996))).," Convective turbulence is ruled out for at least two reasons: the disk is only marginally optically thick, so convection will not be present, and even it were present, recent studies showthat convective turbulence produces angular momentum transport \cite{rg92}, , \cite{sb96}, , \cite{cab96}) )." Turbulence due to nonlinear hvdrodyauauie instability also seenus uulikelv in lieht of recent analytic and munerical work, Turbulence due to nonlinear hydrodynamic instability also seems unlikely in light of recent analytic and numerical work siuuple of stars (1200 GC members). analyzed in a very homogeucous aud accurate way. revealed that while the © auticorrelation is present iu all the GCs (i.e. the second generation is nof a “perturbation”). the shape of the © distribution waries from cluster to cluster (Carretta et al.," $-$ sample of stars $\sim$ 1200 GC members), analyzed in a very homogeneous and accurate way, revealed that while the $-$ O anticorrelation is present in all the GCs (i.e. the second generation is not a “perturbation""), the shape of the $-$ O distribution varies from cluster to cluster (Carretta et al." 20096)., 2009c). Ou the other haud. the analysis of UVES spectra for ~ 200 stars by Carretta oet al. (," On the other hand, the analysis of UVES spectra for $\sim$ 200 stars by Carretta et al. (" 20095) has shown that the Al auticorrelation is not present iu all GCs.,2009b) has shown that the $-$ Al anticorrelation is not present in all GCs. Both these indications sugecst that the typical polluter masses chanee from cluster to cluster: this variation is apparently driven by a combination of cluster luminosity aud metallicity., Both these indications suggest that the typical polluter masses change from cluster to cluster: this variation is apparently driven by a combination of cluster luminosity and metallicity. Iu this context. lithium abundances offer a coniplemieutary approach to p-capture elements allowing to address several important issues.," In this context, lithium abundances offer a complementary approach to $p$ -capture elements allowing to address several important issues." If no Li is produced bv the polluters. the inultiple. population scenario predicts that Li aud. O are positively correlated. while Li aud Na anticorrelated.," If no Li is produced by the polluters, the multiple population scenario predicts that Li and O are positively correlated, while Li and Na anticorrelated." Na-poor. O/Li-vich stars are the first population born in the cluster (they share the sale chemical composition of field stars at the same metallicity). aud Na-vich. O/Li-poor stars constitute the second generation.," Na-poor, O/Li-rich stars are the first population born in the cluster (they share the same chemical composition of field stars at the same metallicity), and Na-rich, O/Li-poor stars constitute the second generation." Within the same hypothesis. Li is an excellent tracer of the dilution process acting within each star: only through Li abundance deteriiuationus we can determine the amount of pristine (and of pollute) material present m cach star.," Within the same hypothesis, Li is an excellent tracer of the dilution process acting within each star: only through Li abundance determinations we can determine the amount of pristine (and of polluted) material present in each star." In particular. we hope to answer two fuudinental questions: do polluted stars (Li-0) exist or even the most extreme population still contains a certain fraction of primordial matter?," In particular, we hope to answer two fundamental questions: do polluted stars $\sim$ 0) exist or even the most extreme population still contains a certain fraction of primordial matter?" Also. is the minium measurable Li couteut the same or all GC's or does it vary from cluster to cluster?," Also, is the minimum measurable Li content the same for all GCs or does it vary from cluster to cluster?" Ou the other haud. Li offers the exciting chance to observationally coustrain the nature of the polluters.," On the other hand, Li offers the exciting chance to observationally constrain the nature of the polluters." If he progenitors of second ecueration stars are FRAIS. hey have destroved their original Li couteut.," If the progenitors of second generation stars are FRMS, they have destroyed their original Li content." " Ou the other hand. if ACD stars are responsible for iutra-cluster xollutiou. they may have non-neglieible Li vield. given he Li production via the ""*De transport” πουλάήστι (Cameron Fowler 1971)."," On the other hand, if AGB stars are responsible for intra-cluster pollution, they may have non-negligible Li yield, given the Li production via the $^7$ Be transport"" mechanism (Cameron Fowler 1971)." As à consequence. we cau reveal if AGB stars are responsible for GC pollution," As a consequence, we can reveal if AGB stars are responsible for GC pollution" CA=0.5) can then move the afterglow locus onto he stellar locus in color-color space.,$A_V = 0.5$ ) can then move the afterglow locus onto the stellar locus in color-color space. Wowever. this effect is only important for Milkv-Way type dust.," However, this effect is only important for Milky-Way type dust." The most important consequence of dust for color-aged afterglow searches is therefore uot reddeniug ut extinction. which cau reduce the received fiux vclow the detection hit of the search whatever he reddening law.," The most important consequence of dust for color-based afterglow searches is therefore not reddening but extinction, which can reduce the received flux below the detection limit of the search whatever the reddening law." " However. GRBs cau destroy dust at distances up to LOpe (Wasinan Draine 2000) or bevoud (Fruchter. το], Rhoads 2001). reducing these concerns substantially for bursts at high Galactic latitude."," However, GRBs can destroy dust at distances up to $10~\pc$ (Waxman Draine 2000) or beyond (Fruchter, Krolik, Rhoads 2001), reducing these concerns substantially for bursts at high Galactic latitude." Archival iulicolor data is available for a few CRB fields fron the U.S. Naval. Observatorv's GRB followup emn (see Ienden et al 2000)., Archival multicolor data is available for a few GRB fields from the U.S. Naval Observatory's GRB followup team (see Henden et al 2000). I have used this data for the field of CRB 000301C. together with piDlished photometry of the afterglow (Jensen et al 2000). for an empirical demonstration of color-based optical afterglow searches.," I have used this data for the field of GRB 000301C, together with published photometry of the afterglow (Jensen et al 2000), for an empirical demonstration of color-based optical afterglow searches." Two color-color plots for this field are shown i- figure 3.., Two color-color plots for this field are shown in figure \ref{301c}. In both cases. we see that the afterglow i4. an outlier iu color-color space.," In both cases, we see that the afterglow is an outlier in color-color space." " Iun tho Ποιο, there are a few other outliers. all of which are systematically redder than the afterglow in both colors."," In the figure, there are a few other outliers, all of which are systematically redder than the afterglow in both colors." Inthe plot. the afterglow is the single most dramatic outlier and would be the first tarect chosen for prompt spectroscopy or other rapid uarrow-field followup observations.," In the plot, the afterglow is the single most dramatic outlier and would be the first target chosen for prompt spectroscopy or other rapid narrow-field followup observations." Color-based searches have the poteutial to identify GRD afterglows faster than a two-cpoch variability search. aud hence to allow more thorough ollowup of many afterglows.," Color-based searches have the potential to identify GRB afterglows faster than a two-epoch variability search, and hence to allow more thorough followup of many afterglows." There are three basic color sclection criteria available for afterelows: IR excess (“IRNο. UV excess ΟΤΕΝο). aud Eia weak.," There are three basic color selection criteria available for afterglows: IR excess (“IRX”), UV excess (“UVX”), and Lyman break." The appropriate combination of these depends on both the redshift of the burst aud the available instrumentation., The appropriate combination of these depends on both the redshift of the burst and the available instrumentation. The primary focus of lis paper is on color-color plane methods. which combine the IR excess aud UV excess criteria aud ire therefore more robust than either criterion alouc.," The primary focus of this paper is on color-color plane methods, which combine the IR excess and UV excess criteria and are therefore more robust than either criterion alone." magnetic field line (Mestel1005): These can be interpreted respectively as the conservation along magnetic field lines of mass to magnetic [αν ratio. angular velocity. specific angular momentum. ancl specilic energy.,"magnetic field line \citep{m68}: These can be interpreted respectively as the conservation along magnetic field lines of mass to magnetic flux ratio, angular velocity, specific angular momentum, and specific energy." llere fy is the specific enthalpy ancl the subscript p indicates a quantity in the poloidal (2. zc) plane.," Here $h$ is the specific enthalpy and the subscript $p$ indicates a quantity in the poloidal $z$, $\varpi$ ) plane." In our simulations. & and O are prescribed. while L and £ are to be determined numerically.," In our simulations, $\kappa$ and $\Omega$ are prescribed, while $L$ and $E$ are to be determined numerically." All of our simulations have been performed using the Zevs3D MIID code (Clarke.Fiedler 1994).. with modifications as described in NLB99 and ILDBO03.," All of our simulations have been performed using the 3D MHD code \citep{cnf94}, with modifications as described in KLB99 and KLB03." Most of the modifications are related to boundary and initial conditions. which we describe briefly below.," Most of the modifications are related to boundary and initial conditions, which we describe briefly below." The outer boundaries of the simulation box at z=zy44 and 2—zy use the standard outflow boundary. conditions present in the 33D code., The outer boundaries of the simulation box at $z=z_{\rm{max}}$ and $\varpi= \varpi_{\rm{max}}$ use the standard outflow boundary conditions present in the 3D code. Specifically the values of all the variables in the ghost zones are set equal to the the values al 2=τµας OF T=cya, Specifically the values of all the variables in the ghost zones are set equal to the the values at $z=z_{\rm{max}}$ or $\varpi=\varpi_{\rm{max}}$. Ihe axial boundary a=0 is handled. with standard. reflection boundary conditions. (he ehost zone values of the variables are reflections of the simulation zone quantities wilh a sien change in the z and © (but not 2) components of vector quantiles.," The axial boundary $\varpi=0$ is handled with standard reflection boundary conditions, the ghost zone values of the variables are reflections of the simulation zone quantities with a sign change in the $\varpi$ and $\phi$ (but not $z$ ) components of vector quantities." The z=0 boundary is ihe most problematic of the boundaries to implement., The $z=0$ boundary is the most problematic of the boundaries to implement. We have divided the 2=0 surface into two regions: an inner launching surface ancl an outer surface along which the plasma loaded onto the last. field line slides., We have divided the $z=0$ surface into two regions: an inner launching surface and an outer surface along which the plasma loaded onto the last field line slides. For the region interior to the maximum launching radius zy. we pin the fiekl lines at their foot points. bul allow them to bend freely in the racial and azimuthal directions.," For the region interior to the maximum launching radius $\varpi_{0}$, we pin the field lines at their foot points, but allow them to bend freely in the radial and azimuthal directions." This is accomplished (through imposing conditions on the electromotive force field £ in the ghost zones (INLD99)., This is accomplished through imposing conditions on the electromotive force field $\mathbf{\cal E}$ in the ghost zones (KLB99). Exterior to ay. we demand that the last field line to lie exactly on (he equator (so that ve.=D. 0).," Exterior to $\varpi_{0}$, we demand that the last field line to lie exactly on the equator (so that $v_z=B_z=0$ )." " The requirement is enforced through £,(—:)=-€,(2). £4(—:)=—£4(z). aud €.(—2)=€.(2)."," The requirement is enforced through ${\cal E} _{\phi}(-z)=-{\cal E}_{\phi}(z)$, ${\cal E}_{\varpi}(-z)=-{\cal E} _{\varpi}(z)$, and ${\cal E}_{z}(-z)={\cal E}_{z}(z)$." For the initial distribution of magnetic field in (he active zones of the simulation box. we adopt a potential configuration computed using the prescribed magnetic flux distribution on the launching," For the initial distribution of magnetic field in the active zones of the simulation box, we adopt a potential configuration computed using the prescribed magnetic flux distribution on the launching" star.,star. This corresponds to hoe> 16.5., This corresponds to $_{\rm sec} \geq$ 16.5. " Assuming 80 << 128 pe. the absolute// magnitude of the secondary star is in the range 11.0 < Aly x 12.0. consistent. with an early/miid-L dwarl,"," Assuming 80 $\leq$ d $\leq$ 128 pc, the absolute magnitude of the secondary star is in the range 11.0 $\leq$ $_{\rm H}$ $\leq$ 12.0, consistent with an early/mid-L dwarf." Thus. EF Evi joins WZ See (see Lowell et al.," Thus, EF Eri joins WZ Sge (see Howell et al." 2004) as the cataclysmic variables with the strongest evidence lor harboring brown clwarl-like secondary stars., 2004) as the cataclysmic variables with the strongest evidence for harboring brown dwarf-like secondary stars. We have obtained phase-resolved infrared spectroscopy of EF Eri aud conclude that the large amplitude variations seen in its infrared light curve are not due (o a heated brown cwarf. but has its origin in evclotron emission.," We have obtained phase-resolved infrared spectroscopy of EF Eri and conclude that the large amplitude variations seen in its infrared light curve are not due to a heated brown dwarf, but has its origin in cyclotron emission." EF Eri appears to join the small family of polars where the accretion rate has dropped to a very low level., EF Eri appears to join the small family of polars where the accretion rate has dropped to a very low level. Unlortunately. our data are inadequate to allow us unravel the complex evelotron emission that is present in EF Eri.," Unfortunately, our data are inadequate to allow us unravel the complex cyclotron emission that is present in EF Eri." Phase-resolved band spectroscopy is required to make further progress on disentangling the evelotron spectrum of EF Evi., Phase-resolved -band spectroscopy is required to make further progress on disentangling the cyclotron spectrum of EF Eri. Given that the mean J-band magnitude of EF Evi is 17.3. multiple orbits of data on 8 m-class telescopes will be needed to obtain spectra with sullicient S/N. To fully interpret the spectroscopic observations. phase-resolved. broacd-banclJL polarimetric observations of EF Evi will be essential.," Given that the mean -band magnitude of EF Eri is 17.3, multiple orbits of data on 8 m-class telescopes will be needed to obtain spectra with sufficient S/N. To fully interpret the spectroscopic observations, phase-resolved, broad-band polarimetric observations of EF Eri will be essential." It would also be extremely. useful to have a radial velocity. curve lor the EF Eri svstem to allow us to properly phase. and coadd (he infrared spectra to search for features [rom the secondary star.," It would also be extremely useful to have a radial velocity curve for the EF Eri system to allow us to properly phase, and coadd the infrared spectra to search for features from the secondary star." Such data could be acquired through optical spectroscopy of the Zeeman absorption features of 11 I. acknowledges partial support under NSF erant AST 99-86323., Such data could be acquired through optical spectroscopy of the Zeeman absorption features of H I. \acknowledgements{TEH acknowledges partial support under NSF grant AST 99-86823. We would like to thank T. Geballe for his help in planning and executing our NIBI observations. and B. Campbell and G. Wirth for assistance wilh NIRSPEC.," We would like to thank T. Geballe for his help in planning and executing our NIRI observations, and R. Campbell and G. Wirth for assistance with NIRSPEC." DII acknowledges support from the National Science Foundation under NFS grant. N-Stars RR185-258. and [rom NASA under," DH acknowledges support from the National Science Foundation under NFS grant N-Stars RR185-258, and from NASA under" 1999).,. ".. In this context. the simplest parametrization of the Dark IZnergy. equation of state ele) depending on the cosmic scale factor e reads (ChevallicrPolarski2001:Linder 2003): where wy is the present-day value of the equation of state and ew, accounts for its time-depencdence."," In this context, the simplest parametrization of the Dark Energy equation of state $w(a)$ depending on the cosmic scale factor $a$ reads \citep{chevallier2001a,linder2003a}: where $w_0$ is the present-day value of the equation of state and $w_a$ accounts for its time-dependence." Alternative approaches describe cosmic acceleration as a manifestation. of new gravitational physics rather than Dark Energy (sec.e.g.Dellavet2001:Delfavetetal.2002: 2007)..," Alternative approaches describe cosmic acceleration as a manifestation of new gravitational physics rather than Dark Energy \citep[see, e.g.,][]{deffayet2001a,deffayet2002a, carrol2004a, nojiri2006a,amendola2007a}." Instead. of adding an extra term to the energv-momentum tensor on the right side of Einstein's equations. these modify the geometry terms on their Left side in order to reproduce the observations.," Instead of adding an extra term to the energy-momentum tensor on the right side of Einstein's equations, these modify the geometry terms on their left side in order to reproduce the observations." llence. we face the situation that apart. from ACDAL a large variety of cosmological models has been proposed to account for cosmic acceleration.," Hence, we face the situation that apart from $\Lambda$ CDM a large variety of cosmological models has been proposed to account for cosmic acceleration." Testing their validity is an important but challenging task., Testing their validity is an important but challenging task. Phe present-day nearby Universe is fairly well-known and therefore all models uncer consideration reproduce its characteristics. or contain free parameters that can be tuned to do so.," The present-day nearby Universe is fairly well-known and therefore all models under consideration reproduce its characteristics, or contain free parameters that can be tuned to do so." This degencracy is cillieult to break with currently available cata., This degeneracy is difficult to break with currently available data. Usually. Dark Energy models are constrained by starting out from a Lriedman cosmology in which the expansion function // is parametrized. in terms of the contributions of radiation (r). matter (m). curvature (A). and Dark Energy (do) to the energy density as where /fy and ο denote the Lubble constant and the present-day density. parameters. corresponding to the ciffercnt components.respectively.," Usually, Dark Energy models are constrained by starting out from a Friedman cosmology in which the expansion function $H$ is parametrized in terms of the contributions of radiation (r), matter (m), curvature $k$ ), and Dark Energy (de) to the energy density as where $H_0$ and $\Omega_{\ldots 0}$ denote the Hubble constant and the present-day density parameters corresponding to the different components,respectively." Aj possible time-dependence of the Dark Encrey equation of state is captured bv the function £(a) The cosmological parameters occurring in Iq. (2)), A possible time-dependence of the Dark Energy equation of state is captured by the function $F(a)$ The cosmological parameters occurring in Eq. \ref{eq:dark1}) ) are determined. from fits to observations and Dark Energy niocels are usually assessed by confronting their predictions to these parameters., are determined from fits to observations and Dark Energy models are usually assessed by confronting their predictions to these parameters. The significance of this approach is. however. limited since it automatically assumes a Friedman model.," The significance of this approach is, however, limited since it automatically assumes a Friedman model." When working with SNe la this constraint is unnecessary as they probe the geometry of the Universe directly. ancl no assumptions on the form of the enereyv-momentum tensor are required to. derive. the. expansion history of the Universe., When working with SNe Ia this constraint is unnecessary as they probe the geometry of the Universe directly and no assumptions on the form of the energy-momentum tensor are required to derive the expansion history of the Universe. Consequently. our analvsis follows à recently developed method (Mignone&Bartelmann2008) to reconstruct the expansion history of the Universe in a mocdoel-indepencdent fashion from luminosity distance data.," Consequently, our analysis follows a recently developed method \citep[]{mignone2008a} to reconstruct the expansion history of the Universe in a model-independent fashion from luminosity distance data." The idea of a mocdeLindependent reconstruction extracted: straight from the data was already. proposed in Starobinsky(1998). ane reconstructions of this kind. were carried. out by Shalielooetal.(2006):Shalieloo(2007) using SN la data. by Fay&Tavakol(2006) adding constraints from. measurements of barvon acoustic oscillations (D.XO) to the SN la cata. and by Daly&Djorgovski(2003.2004). combining SNe Ia luminosity distances with angular-diameter distances from radio galaxies.," The idea of a model-independent reconstruction extracted straight from the data was already proposed in \citet{starobinsky1998a} and reconstructions of this kind were carried out by \citet{shafieloo2006a,shafieloo2007a} using SN Ia data, by \citet{fay2006a} adding constraints from measurements of baryon acoustic oscillations (BAO) to the SN Ia data, and by \citet{daly2003a,daly2004a} combining SNe Ia luminosity distances with angular-diameter distances from radio galaxies." Seikel&Schwarz(2008.2000). tested. the significance of cosmic expansion directly from SN la data in a model-independent way.," \citet*{seikel2008a,seikel2009a} tested the significance of cosmic expansion directly from SN Ia data in a model-independent way." The goal of this work is to apply the method of MignoneDartelmann(2008). to the most complete SN La data set currently available and to constrain some Uavors of Dark Iinergv models.," The goal of this work is to apply the method of \citet{mignone2008a} to the most complete SN Ia data set currently available and to constrain some flavors of Dark Energy models." This is intended as a of the eencral power of SN Ia distance measurcmients for testing Dark Enerey models when analvzed in a mocel-independent wav., This is intended as a of the general power of SN Ia distance measurements for testing Dark Energy models when analyzed in a model-independent way. A rigorous statistical treatment that would let us rule out specific models is bevond the scope of this paper., A rigorous statistical treatment that would let us rule out specific models is beyond the scope of this paper. The paper is organized as follows., The paper is organized as follows. In Section 2.. the essential aspects of the mocdel-independent methodology are reviewed.," In Section \ref{sec:method}, the essential aspects of the model-independent methodology are reviewed." The application of the method. to. luminosity-distance measurements ds discussed. in Section 3., The application of the method to luminosity-distance measurements is discussed in Section \ref{sec:data}. X comparison between SN Ia data and several Dark Energy models is presented in Section. 4., A comparison between SN Ia data and several Dark Energy models is presented in Section \ref{sec:application}. In Section 5... the predictions [or the expansion history of the Universe of several non-standard. cosmologies are confronted with our reconstruction from SN la data.," In Section \ref{sec:alternative}, the predictions for the expansion history of the Universe of several non-standard cosmologies are confronted with our reconstruction from SN Ia data." Ways of improving the reconstruction with new data that may become available through current surveys are. pointed. out in Section 6.., Ways of improving the reconstruction with new data that may become available through current surveys are pointed out in Section \ref{sec:improve}. This shows that our mocel-independent analysis can be instrumental in planning observational campaigns., This shows that our model-independent analysis can be instrumental in planning observational campaigns. Moreover. it can also point to potential svstematics in the data that do not generally. arise from traditional wavs of analysis.," Moreover, it can also point to potential systematics in the data that do not generally arise from traditional ways of analysis." “This aspect is highlighted in Section 7.., This aspect is highlighted in Section \ref{sec:systematics}. Finally. conclusions are clrawn ancl future perspectives are discussed.," Finally, conclusions are drawn and future perspectives are discussed." The minimal assumptions adopted by Mignone&Bartcl-mann(2008) are that the expansion rate is a reasonably smooth function. and. that the Universe. is topologically simply connected. homogeneous and. isotropic. Π ds characterized by a Robertson-Walker metric: The Robertson-Walker metric allows us to define an angular-ciameter distance by with the comoving angular-diamoeter distance and the comoving distance 'hrough. Etherineton’s relation. (Etherington 1933).. which holds for any space-time. we can relate the Iuminosity distance to the angular-ciameter distance: This allows us to write the former as an integral of the inverse of the expansion rate," The minimal assumptions adopted by \citet{mignone2008a} are that the expansion rate is a reasonably smooth function and that the Universe is topologically simply connected, homogeneous and isotropic, it is characterized by a Robertson-Walker metric: The Robertson-Walker metric allows us to define an angular-diameter distance by with the comoving angular-diameter distance and the comoving distance Through Etherington's relation \citep{etherington1933a}, which holds for any space-time, we can relate the luminosity distance to the angular-diameter distance: This allows us to write the former as an integral of the inverse of the expansion rate" "discussed above, peculiar velocities make studies of voids smaller than h-! MMpc very hard, so we need not be concerned about the smallest voids at all.","discussed above, peculiar velocities make studies of voids smaller than $\,h^{-1}$ Mpc very hard, so we need not be concerned about the smallest voids at all." " As a in Figure we show one line-of- the qualitativesimulated example,volume."," As a qualitative example, in Figure \ref{los11} we show one line--of--sight through the simulated volume." " We [0]plot the 1D gas density sightfield in real throughspace (top the simulated flux (middle panel) in redshift space, and the panel), peculiar velocity field in km/s in real space."," We plot the 1D gas density field in real space (top panel), the simulated flux (middle panel) in redshift space, and the gas peculiar velocity field in km/s (bottom panel) in real space." gasThe z-axis indicates the comoving (bottom panel)coordinate the line-of-sight., The $x$ –axis indicates the comoving (real space) coordinate along the line–of–sight. Flux absorption is (realusually space)produced by gas alongoverdensities shifted by the peculiar associated to the same gas element., Flux absorption is usually produced by gas overdensities shifted by the peculiar velocity associated to the same gas element. " For example, the velocityabsorption in the flux at is produced by the gas peak at around MMpc/h, MMpc/hshifted by ~200 km/s — which densitycorresponds to roughly 2h-! MMpc."," For example, the absorption in the flux at $h$ is produced by the gas density peak at around $/h$, shifted by $\sim 200$ km/s – which corresponds to roughly $h^{-1}$ Mpc." 'The shaded regions show the intersections with the line-of- of 3D voids in the dark matter distribution identified with the void finder algorithm described above., The shaded regions show the intersections with the line--of--sight of 3D voids in the dark matter distribution identified with the void finder algorithm described above. " In the middle panel we overplot the mean flux level as a dotted line, with the flux smoothed on a scale of h- MMpc, as in Section ."," In the middle panel we overplot the mean flux level as a dotted line, with the flux smoothed on a scale of $h^{-1}$ Mpc, as in Section \ref{1Dsect}." We find that the choice of threshold overdensity! δε=—0.5 for the 3D void finder results in a good correspondence of the resulting voids with voids defined in the flux distribution., We find that the choice of threshold overdensity $\delta_{t}=-0.5$ for the 3D void finder results in a good correspondence of the resulting voids with voids defined in the flux distribution. " From the bottom panel of Figure it is clear that the void regions are expanding, and he gas βvelocity fields for the largest voids are of the order of + octN00 km/s (see the void centered on around MMpc/h)."," From the bottom panel of Figure \ref{los11} it is clear that the void regions are expanding, and the gas velocity fields for the largest voids are of the order of $\pm$ 200 km/s (see the void centered on around $/h$ )." " These igh redshift voids in the IGM will keep growing, get emptier matter and could be the progenitors of lower redshifts voids sizes similar to the Tully void (?))."," These high redshift voids in the IGM will keep growing, get emptier of matter and could be the progenitors of lower redshifts voids of sizes similar to the Tully void \cite{tully}) )." The peculiar velocities Pootong the line-of-sight rise smoothly from negative values to οσοositive ones and are sandwiched in which the peculiar < shows a negative bywhich regionscould be the signature a elocitymoderate shock.," The peculiar velocities along the line–of–sight rise smoothly from negative values to positive ones and are sandwiched by regions in which the peculiar velocity shows a negative gradient, which could be the signature of a moderate shock." " It is worth gradient, that these velocity rofiles are not completely emphasizing because the line-ovo does not always pierce the 3D symmetricvoids in their centers.", It is worth emphasizing that these velocity profiles are not always completely symmetric because the line--of--sight does not necessarily pierce the 3D voids in their centers. " Moreover,—sight from the top necessarilypanel it is clear that the 1D density profile inside the void is quite complex, showing small density peaks, which correspond to small haloes that most likely host the observed void galaxy population."," Moreover, from the top panel it is clear that the 1D density profile inside the void is quite complex, showing small density peaks, which correspond to small haloes that most likely host the observed void galaxy population." " In order to provide a more quantitative picture, in Figure [10] we plot the underlying mean values of 1D quantities obtained once the 3D voids have been identified (using 0;=—0.5)."," In order to provide a more quantitative picture, in Figure \ref{figfinal} we plot the underlying mean values of 1D quantities obtained once the 3D voids have been identified (using $\delta_{t}=-0.5$ )." " The top panel represents the probability distribution function of the sizes of such 1D flux voids, while in the other three panels each point shows, from top to bottom, the mean gas overdensity, flux and peculiar velocity field for a given 3D DM void."," The top panel represents the probability distribution function of the sizes of such 1D flux voids, while in the other three panels each point shows, from top to bottom, the mean gas overdensity, flux and peculiar velocity field for a given 3D DM void." " Note that while in Section [4.1] we were interested in measuring the properties of voids once the mean flux threshold was set as a criterion to define voids, here we use the 3D DM distribution to look for the corresponding 1D forest) flux—related quantities."," Note that while in Section \ref{1Dsect} we were interested in measuring the properties of voids once the mean flux threshold was set as a criterion to define voids, here we use the 3D DM distribution to look for the corresponding 1D forest) flux–related quantities." " The overall (Lyman-apicture suggests that large voids (> are usually related to flux values above the mean, andMMpc/h) the mean values of gas density and peculiar velocitiescorresponding have less scatter than smaller voids."," The overall picture suggests that large voids $>7-10$ $/h$ ) are usually related to flux values above the mean, and the corresponding mean values of gas density and peculiar velocities have less scatter than smaller voids." " The corresponding mean value for the gas is =—0.43, so the 3D void region is slightlyoverdensity denser in gasὄωβς than in dark matter, that can be expected since baryons feel pressure and somethingare thus more diffused than the collisionless dark matter (e.g. ?))."," The corresponding mean value for the gas overdensity is $\delta_{\mbox{GAS}}=-0.43$, so the 3D void region is slightly denser in gas than in dark matter, something that can be expected since baryons feel pressure and are thus more diffused than the collisionless dark matter (e.g. \cite{viel02}) )." " The different value of dGag than the one found in Section [1-3] does not contradict our earlier findings, since now the requirement to define a void isless stringent."," The different value of $\delta_{\mbox{GAS}}$ than the one found in Section \ref{1Dflux} does not contradict our earlier findings, since now the requirement to define a void is stringent." " Now, the actual void has to be a quasi-spherical 3D region in the DM distribution and not a connected 1D region with flux above the mean flux."," Now, the actual void has to be a quasi–spherical 3D region in the DM distribution and not a connected 1D region with flux above the mean flux." " This means that in 1D one is more sensitive to clumps of matter producing absorptions, while the same clump will have a smaller impact on the mean density of the 3D region surrounding it."," This means that in 1D one is more sensitive to clumps of matter producing absorptions, while the same clump will have a smaller impact on the mean density of the 3D region surrounding it." " Cases for which the flux voids correspond to actual DM voids are avaraged out statistically by small lumps of gas around the mean density along the line-of-sight, that cause absorption and do not alter the global 3D DM density of the void region For this population of large voids the typical scatter in the peculiar velocity field is 170kkm/s. We thus have shown that the population of 1D large flux voids, i.e. regions above the mean flux level, as estimated from a set of mock high resolution spectra at z~2, traces reasonably faithfully a population of 3D dark matter voids of similar with a typical ὃν=—0.5."," Cases for which the flux voids correspond to actual DM voids are avaraged out statistically by small lumps of gas around the mean density along the line–of–sight, that cause absorption and do not alter the global 3D DM density of the void region For this population of large voids the typical scatter in the peculiar velocity field is km/s. We thus have shown that the population of 1D large flux voids, i.e. regions above the mean flux level, as estimated from a set of mock high resolution spectra at $z\sim 2$, traces reasonably faithfully a population of 3D dark matter voids of similar sizes, with a typical $\delta_{t}=-0.5$." " We have also sizes,checked that the scatter plots of Figure [IQ] are not sensitive to the cosmological model (i.e. different values of og), verywhich means that the voids physical properties are the same for different values of the power spectrum amplitude."," We have also checked that the scatter plots of Figure \ref{figfinal} are not very sensitive to the cosmological model (i.e. different values of $\sigma_8$ ), which means that the voids physical properties are the same for different values of the power spectrum amplitude." " We used forest QSO spectra to constrain the void population at z~2 at a range of scales and redshifts, which cannot be probed by other observables."," We used forest QSO spectra to constrain the void population at $z\sim 2$ at a range of scales and redshifts, which cannot be probed by other observables." The main conclusions can be summarized as follows:, The main conclusions can be summarized as follows: heating of the high-redshift IGM in 38..,heating of the high-redshift IGM in \ref{example}. Finally. we concludein S9..," Finally, we concludein \ref{disc}." Because of the wide range of interactions available to fast electrons. we use a Monte Carlo model to track their fates.," Because of the wide range of interactions available to fast electrons, we use a Monte Carlo model to track their fates." Our procedure is very similar to?) (see also 2. and 2). except that we use updated cross-sections and include (and track) more interaction processes.," Our procedure is very similar to \citet{shull85} (see also \citealt{shull79} and \citealt{valdes08}) ), except that we use updated cross-sections and include (and track) more interaction processes." An alternative. fully analytic. approach uses the degradation equation (22).. but we find that to be more cumbersome.," An alternative, fully analytic, approach uses the degradation equation \citep{spencer54, xu91}, but we find that to be more cumbersome." As inputs. the model requires only the number densities anc ionized fractions of hydrogen and helium.," As inputs, the model requires only the number densities and ionized fractions of hydrogen and helium." We will see that the ionized fractions have an important effect on the results but tha the absolute number densities have only a slight impact (through the Coulomb logarithm)., We will see that the ionized fractions have an important effect on the results but that the absolute number densities have only a slight impact (through the Coulomb logarithm). For simplicity. we will typically assume that the HI and Hel fractions are identical Gr;) and that the Hell fraction is με," For simplicity, we will typically assume that the HI and HeI fractions are identical $x_i$ ) and that the HeII fraction is $1-x_i$." The presence of HellI does not significantly affect our results., The presence of HeIII does not significantly affect our results. As a fiducial value. we use the mean density of the Universe at >=10 (according to the cosmological parameters recommended by 1). but taking any density n=LO”em* only changes our reported values by a few percent.," As a fiducial value, we use the mean density of the Universe at $z=10$ (according to the cosmological parameters recommended by \citealt{dunkley09}) ), but taking any density $n \la 10^8 \cmden$ only changes our reported values by a few percent." Note that our mode assumes a static IGM and does not self-consistently account for the ionization Cand heating) produced by each electron., Note that our model assumes a static IGM and does not self-consistently account for the ionization (and heating) produced by each electron. The model begins with a single electron of energy £ eV: lower energy particles can only interact with the electron gas and so automatically deposit all of their energy as heat., The model begins with a single electron of energy $E >10.2 \eV$ ; lower energy particles can only interact with the electron gas and so automatically deposit all of their energy as heat. Our goal is to compute the fraction of this energy that is deposited in ionizing each of the relevant IGM species (HI. Hel. or Hell). the Traction of energy that is lost to collisional excitations producing shotons with /£«13.6eV Cand additionally the fraction that ends up in HI photons). and the fraction of energy that is deposited as heat in the IGM.," Our goal is to compute the fraction of this energy that is deposited in ionizing each of the relevant IGM species (HI, HeI, or HeII), the fraction of energy that is lost to collisional excitations producing photons with $E<13.6 \eV$ (and additionally the fraction that ends up in HI photons), and the fraction of energy that is deposited as heat in the IGM." We also follow collisional excitations that oroduee higher energy photons (from helium). but the resulting οποίους are re-absorbed by the IGM and so are not the ultimate oroduets of the process.," We also follow collisional excitations that produce higher energy photons (from helium), but the resulting photons are re-absorbed by the IGM and so are not the ultimate products of the process." To this end. we compute the cross-sections (weighted by the number densities of each species) for the electron to interact with he IGM in several different ways: collisional ionization tof any of the three species above). collisional excitation (again of any of the three species. and including explicitly all levels η< 4). and electron-electron collisions.," To this end, we compute the cross-sections (weighted by the number densities of each species) for the electron to interact with the IGM in several different ways: collisional ionization (of any of the three species above), collisional excitation (again of any of the three species, and including explicitly all levels $n \le 4$ ), and electron-electron collisions." Below we describe our treatment of each of these processes in detail., Below we describe our treatment of each of these processes in detail. From these cross-sections we randomly choose one such process for the electron to undergo and update its energy. and the energy deposition fractions. accordingly.," From these cross-sections we randomly choose one such process for the electron to undergo and update its energy, and the energy deposition fractions, accordingly." If it ionizes an atom or ion. we add a new secondary electron of the appropriate energy to the array of particles: if it collisionally excites helium. we add a new photon to the We repeat this process until the primary electron’s energy falls below 10.2 eV: beyond that point. the only available process is a collision with an electron. so we assign all its energy to heat.," If it ionizes an atom or ion, we add a new secondary electron of the appropriate energy to the array of particles; if it collisionally excites helium, we add a new photon to the We repeat this process until the primary electron's energy falls below 10.2 eV; beyond that point, the only available process is a collision with an electron, so we assign all its energy to heat." We then track each of the secondary electrons through the same machinery. and finally we randomly determine (from the photoionization cross-sections weighted by number density) the species that each secondary photon ionizes and follow the resulting electrons through their entire energy loss cascade.," We then track each of the secondary electrons through the same machinery, and finally we randomly determine (from the photoionization cross-sections weighted by number density) the species that each secondary photon ionizes and follow the resulting electrons through their entire energy loss cascade." At each step. we track the energy lost to each of the aforementioned processes.," At each step, we track the energy lost to each of the aforementioned processes." " For our final results. we follow 10 input electrons at each of 258energies (logarithmically spaced from 10 eV to 9900 eV) at each of fourteen ionized fractions from .r;=10. to 0.999,"," For our final results, we follow $10^5$ input electrons at each of 258energies (logarithmically spaced from 10 eV to 9900 eV) at each of fourteen ionized fractions from $x_i=10^{-4}$ to 0.999." This encompasses the range expected in the early IGM (where .r; is set by the relie density following recombination: 2)) up to the point at which the neutrals are no longer signiticant energy sinks., This encompasses the range expected in the early IGM (where $x_i$ is set by the relic density following recombination; \citealt{seager99}) ) up to the point at which the neutrals are no longer significant energy sinks. To generate random numbers. we use the Mersenne Twister algorithm. which has a period of at least ο1 (2.," To generate random numbers, we use the Mersenne Twister algorithm, which has a period of at least $2^{19937}-1$ \citep{matsumoto98}." For ££<1Κον. we take the collisional ionization cross-sections from the CCC an online collection of cross-sections calculated with the convergent close-coupling (CCC) method.," For $E<1 \keV$, we take the collisional ionization cross-sections from the CCC an online collection of cross-sections calculated with the convergent close-coupling (CCC) method." The CCC approach is accurate whenever the target particle can be well-modelled by one or two valence electrons above a Hartree-Fock core: obviously this is an excellent approximation for hydrogen and helium., The CCC approach is accurate whenever the target particle can be well-modelled by one or two valence electrons above a Hartree-Fock core; obviously this is an excellent approximation for hydrogen and helium. The relevant physies. and references to many of the original papers for hydrogen and helium. can be found in ?..," The relevant physics, and references to many of the original papers for hydrogen and helium, can be found in \citet{bray02}." We use cubic splines to interpolate the database values., We use cubic splines to interpolate the database values. At higher energies. we assume that cross-sections follow the Bethe approximation limit (2)..," At higher energies, we assume that cross-sections follow the Bethe approximation limit \citep{bethe30}. ." Then the cross-section for ionization from the ground state in species / is (CA | Bi) may. where αν is the Bohr radius and 24; and D; are coefficients.," Then the cross-section for ionization from the ground state in species $i$ is ( A_i + B_i ) a_0^2, where $a_0$ is the Bohr radius and $A_i$ and $B_i$ are coefficients." These are usually fixed by demanding that the cross-section map onto the first Born approximation at high energies., These are usually fixed by demanding that the cross-section map onto the first Born approximation at high energies. This asymptotic behavior compares well to the calculated behavior at /71keV. and we extrapolate to higher energies by fitting a function of this form to the uppermost energy bin in the CCC results.," This asymptotic behavior compares well to the calculated behavior at $E \sim 1 \keV$, and we extrapolate to higher energies by fitting a function of this form to the uppermost energy bin in the CCC results." The resulting parameters ely and 2y differ from the analytic estimates of by ~15% and 30%. respectively. but their exact values make little difference to our final results (largely because it is the relative importance of each ionization and excitation process that matters).," The resulting parameters $A_H$ and $B_H$ differ from the analytic estimates of \citet{johnson72} by $\sim 15\%$ and $30\%$, respectively, but their exact values make little difference to our final results (largely because it is the relative importance of each ionization and excitation process that matters)." Whenever a species is collisionally ionized. it also produces a secondary electron. so we must select the final energies of the incident and ejected electrons.," Whenever a species is collisionally ionized, it also produces a secondary electron, so we must select the final energies of the incident and ejected electrons." We use the probability distributions of 2?.. which are adapted from the measurements of ?:: see also ? for a discussion of the energy spectra of secondaries.," We use the probability distributions of \citet{dalgarno99}, which are adapted from the measurements of \citet{opal71}; see also \citet{shull79} for a discussion of the energy spectra of secondaries." This prescription assumes thatthe probability for the secondary to have an energy 5 is proportional to where =;=5.15.8. and 32.6eV for HI. Hel. and Hell. respectively. (," This prescription assumes thatthe probability for the secondary to have an energy $\varepsilon$ is proportional to ), where $\bar{\varepsilon}_i= 8,\,15.8$, and $32.6 \eV$ for HI, HeI, and HeII, respectively. (" We always identify the “secondary” as having the lower energy of the two final photons. so thats<(/7.—£7) /2.),"We always identify the “secondary"" as having the lower energy of the two final photons, so that $\varepsilon < (E-E_i)/2$ .)" Note that secondary electrons are typically ejected with a modest energy somewhat below the ionization threshold of their original host atom: the median energies are 7.2. 14.2. and 28.5eV for the three species. althoughthere is a tail to much higher =.," Note that secondary electrons are typically ejected with a modest energy somewhat below the ionization threshold of their original host atom: the median energies are $7.2,\,14.2$ , and $28.5 \eV$ for the three species, althoughthere is a tail to much higher $\varepsilon$ ." As discussed in ?.. the secondary energy increases logarithmically with the incident energy for fast ? provides an alternate estimate of the secondary electron," As discussed in \citet{shull79}, , the secondary energy increases logarithmically with the incident energy for fast \citet{johnson72} provides an alternate estimate of the secondary electron" physically realistic density parameter.,physically realistic density parameter. The best fit values for the model parameters D and A are determined., The best fit values for the model parameters $B$ and $K$ are determined. I is found that the model admits dark οποίον density close to that predicted by observations in CDM cosmologv., It is found that the model admits dark energy density close to that predicted by observations in $\Lambda$ CDM cosmology. Phe analysis we adopted here involves kinematies only and it would be interesting to analyze and determine the model constraints using the dynamical aspects like structure formation etc., The analysis we adopted here involves kinematics only and it would be interesting to analyze and determine the model constraints using the dynamical aspects like structure formation etc. Also it is worthwhile to note that the parameter fy should in principle be fixed from the initial conditions itself., Also it is worthwhile to note that the parameter $K$ should in principle be fixed from the initial conditions itself. more stringent constraint on the EU may be obtained for a viable candidate for cosmology., A more stringent constraint on the EU may be obtained for a viable candidate for cosmology. ALL these issues will be considered elsewhere., All these issues will be considered elsewhere. SC would like to thank CSIR for awarding Senior Rescarch Fellowship., SG would like to thank CSIR for awarding Senior Research Fellowship. BCP and PP would like to thank IUCUAA Resource Centre. NBU for providing research facilities.," BCP and PT would like to thank IUCAA Resource Centre, NBU for providing research facilities." BCP would like to thank UGC. New Delhi for financial support (Grant No.," BCP would like to thank UGC, New Delhi for financial support (Grant No." 36 205(919) dated 28 Alar... 2009).," 36 365/(SR) dated 28 Mar., 2009)." communiiv as part of the effort which [funds the infrastructure suppor(üng astronomical research.,community as part of the effort which funds the infrastructure supporting astronomical research. In addition. it is essential (hat we promote and encourage policies (hat foster and facilitate the growth of the digital scholarly environment that the Virtual Observatory has been envisioning.," In addition, it is essential that we promote and encourage policies that foster and facilitate the growth of the digital scholarly environment that the Virtual Observatory has been envisioning." The recent funding of dieital preservation frameworks such as the Data Conservancy project suggests that the time has come for the VO to play a major role in the capture ancl preservation of the astronomy research lifeevcle., The recent funding of digital preservation frameworks such as the Data Conservancy project suggests that the time has come for the VO to play a major role in the capture and preservation of the astronomy research lifecycle. We look [orwarel for the members of the International Virtual Observatory Alliance to take a pro-active role over the next decade in order to make this vision a reality., We look forward for the members of the International Virtual Observatory Alliance to take a pro-active role over the next decade in order to make this vision a reality. uncertainties on (he positions and magnification ratio to be unimportant.,uncertainties on the positions and magnification ratio to be unimportant. We celine (he goodness-ol-fit parameter as in which primed quantities are (hose determined by Che model. and unprimed quantities are those observed.," We define the goodness-of-fit parameter as in which primed quantities are those determined by the model, and unprimed quantities are those observed." In addition. we reject models (hat predict a third image brighter than the upper limit.," In addition, we reject models that predict a third image brighter than the upper limit." This is computationally faster (han the more orthodox procedure of adding another error term to Eq., This is computationally faster than the more orthodox procedure of adding another error term to Eq. 2. for the third-image flux. but we have verified that the results are verv nearly equivalent.," \ref{eq:chisq} for the third-image flux, but we have verified that the results are very nearly equivalent." This is because (he {lux of the third image depends sensitively on the parameters in our models. causing 47 to increase very rapidly across the boundary in parameter space where the (hird-image constraint is violated.," This is because the flux of the third image depends sensitively on the parameters in our models, causing $\chi^2$ to increase very rapidly across the boundary in parameter space where the third-image constraint is violated." Although in principle there could be a complicated angular structure in the lens model. due to the ellipticity of the lens galaxy and due (o external perturbations. we do not have enough constraints to explore such models.," Although in principle there could be a complicated angular structure in the lens model, due to the ellipticity of the lens galaxy and due to external perturbations, we do not have enough constraints to explore such models." Instead. we use mass models with circular svimnmetirv. (o which we add an external shear field. (of strength + ancl position angle 6.) to simulate the combined effect of galaxy. ellipticity. ancl tidal fields from neighboring mass concentrations.," Instead, we use mass models with circular symmetry, to which we add an external shear field (of strength $\gamma$ and position angle $\theta_\gamma$ ) to simulate the combined effect of galaxy ellipticity and tidal fields from neighboring mass concentrations." " We begin with global power-law models. for which p(r)xr""."," We begin with global power-law models, for which $\rho(r) \propto r^{-\beta}$." " The model has 7 [ree parameters: 3. 5. 6.. (he mass normalization. the source location (ry. y.). and the position angle of the source jet o,."," The model has 7 free parameters: $\beta$, $\gamma$, $\theta_\gamma$, the mass normalization, the source location $(x_s,y_s)$ , and the position angle of the source jet $\phi_{\rm s}$ ." We applied the 8 constraints of Table 2. using a \7-minimization code.," We applied the 8 constraints of Table \ref{tbl:model-constraints-1} using a $\chi^2$ -minimization code." Because (he constraint on the third-image flux is one-sided. and because of the wav in which we have implemented that constraint. the allowed models fit the constraints perfectly (42= 0).," Because the constraint on the third-image flux is one-sided, and because of the way in which we have implemented that constraint, the allowed models fit the constraints perfectly $\chi^2=0$ )." The optimal value is 3=2.05 and the 26 bounds are 1.95<32.28., The optimal value is $\beta=2.05$ and the $2\sigma$ bounds are $1.95 < \beta < 2.28$. This range brackets the isothermal value ;?=2., This range brackets the isothermal value $\beta=2$. The upper bound is enforced by the observed jet orientations., The upper bound is enforced by the observed jet orientations. The lower bound is enforced by the upper limit on the flux of the third image., The lower bound is enforced by the upper limit on the flux of the third image. The lower bound is robust. even if our upper limit on t/j] is too strong due to the possible extinction of a third image by [ree-Iree absorption. or (he lowering of its peak Πας density by scatter-broadening.," The lower bound is robust, even if our upper limit on $\mu_3/\mu_{\rm A}$ is too strong due to the possible extinction of a third image by free-free absorption, or the lowering of its peak flux density by scatter-broadening." For example. if we weaken (he limit on the third-image flux density by a factor of 10 (papi< 0.01). the lower bound changes only slightly: ," For example, if we weaken the limit on the third-image flux density by a factor of 10 $\mu_3 / \mu_{\rm A} < 0.01$ ), the lower bound changes only slightly: $1.91 < \beta < 2.28$ ." Interestingly. {here is a different (weaker) lower bound on 3 that results from the relative positions of A and D with respect to the lens center.," Interestingly, there is a different (weaker) lower bound on $\beta$ that results from the relative positions of A and B with respect to the lens center." For 2<1.83. the radial critical curve is sullicientlv large to encompass D. In such models. the parity of D is reversed. aud a brighter (hire imageispredicted in a location outside (he radial critical curve: image D becomes the," For $\beta < 1.83$, the radial critical curve is sufficiently large to encompass B. In such models, the parity of B is reversed, and a brighter third imageispredicted in a location outside the radial critical curve; image B becomes the" component in the quiescent spectrum of ,component in the quiescent spectrum of . "Whereasthe ddatacouldnotconstramlhepowerlawinder,] thelargercollecti cear qed pprovidesbellerconsiraints forthe fliresundercon sideration,"," Whereas the data could not constrain the powerlaw index, the larger collective area of provides better constraints for the fluxes under consideration." ὃν using a combinecl anc model o fit the deata. we obtain a powerlaw index of D—1.7+0.5. Le. in between the values of P—1 and E—2 considered. by(," By using a combined and model to fit the data, we obtain a powerlaw index of $\Gamma=1.7\pm0.5$, i.e., in between the values of $\Gamma=1$ and $\Gamma=2$ considered by." 2000)... αςGt furthermore vields Ny= and Ak=17.81 km. when fixing the neutron star mass to a canonical value of Ans=1.4M. and he distance to D=1.4 kpc2008).," Thisfit furthermore yields $N_{\mathrm{H}}=(7\pm2)\times10^{20}~\mathrm{cm}^{-2}$ and $R_{\mathrm{NS}}=17.8\pm1$ km, when fixing the neutron star mass to a canonical value of $M_{\mathrm{NS}}=1.4~\Msun$ and the distance to $D=7.4$ kpc." . The resulting »owerlaw component contributes LO percent to the total unabsorbed 0.5.LO keV Lux., The resulting powerlaw component contributes $\sim10$ percent to the total unabsorbed 0.5–10 keV flux. Fhis is lower than the ~15.20 »ercent inferred from the oobservations performed. in. 2008 mid-October2009)., This is lower than the $\sim15-20$ percent inferred from the observations performed in 2008 mid-October. . The obtained hwdrogen column clensity is consistent with values found for cdauring its outburst2: ]sidoliü5., The obtained hydrogen column density is consistent with values found for during its outburst; . The oobservations obtained in 2009 February ancl June are well-fitted by an absorbed mocel and do not require an additional powerlaw component., The observations obtained in 2009 February and June are well-fitted by an absorbed model and do not require an additional powerlaw component. However. the 2010. April cata shows evidence for such a hard tail. as significant residuals are present above the model [it for energies Z23 keV. H£ we include a powerlaw with photon index P= 1.7. as was found from fitting the ddata (see above). this model component contributes ~10. 5 and ~15 percent to the total unabsorbed 0.5.10 keV flux for the data taken in. 2009 February. June ancl 2010 April. respectively.," However, the 2010 April data shows evidence for such a hard tail, as significant residuals are present above the model fit for energies $\gtrsim2-3$ keV. If we include a powerlaw with photon index $\Gamma=1.7$ , as was found from fitting the data (see above), this model component contributes $\sim10$, $\sim5$ and $\sim15$ percent to the total unabsorbed 0.5–10 keV flux for the data taken in 2009 February, June and 2010 April, respectively." Fig., Fig. 3. compares the sspectral data obtained on 2008 October and. 2010. April. showing that both spectral components decreased over the lS-month time span that separates the two observations.," \ref{fig:spec} compares the spectral data obtained on 2008 October and 2010 April, showing that both spectral components decreased over the 18-month time span that separates the two observations." We found no spectral dilferences between the two separate exposures performed in 2009 February and therefore we tied all spectral parameters between these two spectra in the fits., We found no spectral differences between the two separate exposures performed in 2009 February and therefore we tied all spectral parameters between these two spectra in the fits. The ddata do not provide sullicicnt statistics to constrain the presence of a hard spectral. component., The data do not provide sufficient statistics to constrain the presence of a hard spectral component. We co include a powerlaw in the fits. but fix both the index and the normalisation of this component (see Section ??)).," We do include a powerlaw in the fits, but fix both the index and the normalisation of this component (see Section \ref{subsec:evolution}) )." Since it is unclear how the powerlaw exactly. evolves over time. we adjust the powerlaw normalisation for the oobservations such that it always contributes LO percent of the total unabsorbed 0.5.LO keV. Dux.," Since it is unclear how the powerlaw exactly evolves over time, we adjust the powerlaw normalisation for the observations such that it always contributes $10$ percent of the total unabsorbed 0.5–10 keV flux." After treating cach oobservation separately. we found that the thermal. Dux and neutron star temperature did not evolve significantly between consecutive observations.," After treating each observation separately, we found that the thermal flux and neutron star temperature did not evolve significantly between consecutive observations." To improve the statistics. we therefore sum the delata into groups spanning 14 weeks of observations. resulting in exposure times of 1020 ks (see Table 2)).," To improve the statistics, we therefore sum the data into groups spanning $\sim1-4$ weeks of observations, resulting in exposure times of $\sim10-20$ ks (see Table \ref{tab:spec}) )." The summed spectra were >grouped. to contain a minimum of 20 photons per bin., The summed spectra were grouped to contain a minimum of 20 photons per bin. As discussed in Section ??.. the quiescent spectrum of ccan be described by a combination of a neutron star atmosphere model and. a non-thermal powerlaw tail.," As discussed in Section \ref{subsec:spectraldata}, the quiescent spectrum of can be described by a combination of a neutron star atmosphere model and a non-thermal powerlaw tail." We littecl the aancl cdata simultaneously within to a combined and model subject to interstellar absorption. to explore the best-fit values for the neutron star mass and radius. source distance ancl hvdrogen column density.," We fitted the and data simultaneously within to a combined and model subject to interstellar absorption, to explore the best-fit values for the neutron star mass and radius, source distance and hydrogen column density." We include the first set of oobservations obtained in 2008 October in the analysis., We include the first set of observations obtained in 2008 October in the analysis. As before. we use the model with the default abundances and cross-sections to take into account the neutral hydrogen absorption along the line ofsight.," As before, we use the model with the default abundances and cross-sections to take into account the neutral hydrogen absorption along the line of sight." Phe powerlaw index is fixed to P=1.7 (the best fit-value obtained from oobservations: see Section ??)). because there are not sullicient counts at higher energies in the sspectra to allow this component to vary.," The powerlaw index is fixed to $\Gamma=1.7$ (the best fit-value obtained from observations; see Section \ref{subsec:spectraldata}) ), because there are not sufficient counts at higher energies in the spectra to allow this component to vary." Phe powerlaw normalisation is left as a free parameter., The powerlaw normalisation is left as a free parameter. If the neutron star mass and radius are [fixed to canonical values of Adns=1.4M. and xs=10 km. and in addition the source distance is fixed to D=7.4 kpc. the hydrogen column density pees at its lower limit (Vy=0).," If the neutron star mass and radius are fixed to canonical values of $M_{\mathrm{NS}}=1.4~\Msun$ and $R_{\mathrm{NS}}=10$ km, and in addition the source distance is fixed to $D=7.4$ kpc, the hydrogen column density pegs at its lower limit $N_{\mathrm{H}}=0$ )." When the cistance is left to vary ουν. the best-Lit value is 4640.8 kpe. which is just outside the range obtained from X-ray burst analysis2008).," When the distance is left to vary freely, the best-fit value is $4.6\pm0.3$ kpc, which is just outside the range obtained from X-ray burst analysis." . Therefore. we choose to keep the distance fixed at 7.4 kpe. and instead allow the neutron star radius to vary.," Therefore, we choose to keep the distance fixed at 7.4 kpc, and instead allow the neutron star radius to vary." Phis way. we obtain best-fit values of Ny=(7x1)107Encm2 and R=195.050.5 km.," This way, we obtain best-fit values of $N_{\mathrm{H}}=(7\pm1)\times10^{20}~\mathrm{cm}^{-2}$ and $R=15.6\pm0.8$ km." UW additionally jo neutron star niass is left free to vary in the fit. this parameter is not stronglv constrained (Ades~1.62:0.6 M).," If additionally the neutron star mass is left free to vary in the fit, this parameter is not strongly constrained $M_{\mathrm{NS}}\sim 1.6\pm 0.6~\Msun$ )." In the final fits we choose to fix the neutron star mass to Ανω=1.4 M.because otherwise the uncertainty in this quantity will dominate the errors of the other parameters.," In the final fits we choose to fix the neutron star mass to $M_{\mathrm{NS}}= 1.4~\Msun$ ,because otherwise the uncertainty in this quantity will dominate the errors of the other parameters." For the final spectral analysis. we fit allVALAL-New/lon.. aand delata with an absorbed plus moclel. where Ng27107em7. Mya=L4M. Res=15.6 km. D—74 kpe and P=L7 are fixed. while the neutron star effective temperature is left as a free parameter.," For the final spectral analysis, we fit all, and data with an absorbed plus model, where $N_{\mathrm{H}}=7\times10^{20}~\mathrm{cm}^{-2}$, $M_{\mathrm{NS}}=1.4~\Msun$, $R_{\mathrm{NS}}=15.6$ km, $D=7.4$ kpc and $\Gamma=1.7$ are fixed, while the neutron star effective temperature is left as a free parameter." The powerlaw normalisation is left to vary freely for the aand oobservations. but fixed for the data (so that this component contributes. 10 percent to yw total unabsorbed 0.5.10 keV. flux).," The powerlaw normalisation is left to vary freely for the and observations, but fixed for the data (so that this component contributes 10 percent to the total unabsorbed 0.5–10 keV flux)." We fit all cata in 10 0.5.10 keV energy range and deduce the absorbed. ancl inabsorbed. Ηχος in this band., We fit all data in the 0.5–10 keV energy range and deduce the absorbed and unabsorbed fluxes in this band. The thermal model fit is extrapolated to the energy range of 0.01.100 keV to estimate 1ethermal bolometric Hux., The thermal model fit is extrapolated to the energy range of 0.01–100 keV to estimate thethermal bolometric flux. The results from fitting the X-ray spectra in this way are presented in Table 2.. The effective temperatures and thermal bolometric fluxes derivedrom Chondra.. aancd," The results from fitting the X-ray spectra in this way are presented in Table \ref{tab:spec}.. The effective temperatures and thermal bolometric fluxes derivedfrom , and" "SBI pair (Rastegaevοἱal.2007) ancl a common proper motion companion D at 34"" 2000)..","SB1 pair \citep{rastegaev_2007} and a common proper motion companion D at $34''$ \citep{allen}." Dased on the data from Allenetal.(2000).. the evolutionary (racks from Daralfeοἱal.(1997).. and on our speckle interferometric measurements. we evaluated the period ratio of the three G&9-14 subsystems: 0.52: 3 000: 650 000 vr.," Based on the data from \citet{allen}, , the evolutionary tracks from \citet{baraffe}, and on our speckle interferometric measurements, we evaluated the period ratio of the three G89-14 subsystems: 0.52: 3 000: 650 000 yr." Another well-known metal-poor quadruple svstem is (Tokovinin1997). with |Fe/II]=—1.05 (Nordstrómοἱal., Another well-known metal-poor quadruple system is \citep{tokovinin_1997} with $\mathrm{[Fe/H]}=-1.05$ \citep{nordstrom}. 2004).. This multiple star was repeatedlv observed on the BTA by means of speckle interferometry (e.g... Dalega 2006)).," This multiple star was repeatedly observed on the BTA by means of speckle interferometry (e.g., \citealt{balega_2006}) )."