ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 1998 and references therein): a fat spectrum up to a break frequency in the vicinity of a few Iz aud spectrum falling steeply thereafter., 1998 and references therein): a flat spectrum up to a break frequency in the vicinity of a few Hz and spectrum falling steeply thereafter.3 The narrow quasi-periodic oscillation (QPO) along with its first harmonic. seen durius the other low-hard states of CRS 1915|105 (Paul et al.," The narrow quasi-periodic oscillation (QPO) along with its first harmonic, seen during the other low-hard states of GRS 1915+105 (Paul et al."4 1997: Morgan et al., 1997; Morgan et al.5 1997). is evident in the PDS.," 1997), is evident in the PDS."6 Iu the ligh state the PDS is a featureless power-law above 0.2 IIz., In the high state the PDS is a featureless power-law above 0.2 Hz.7 In the high state of July 20. however. there is a low frequency QPO at 0.13 Iz.," In the high state of July 20, however, there is a low frequency QPO at 0.13 Hz."8 The salieut. features of the PDS in the two states are even in Table 2., The salient features of the PDS in the two states are given in Table 2.9 To hiehlieht the differences iu tlhe PDS at the low and high frequencics. we have fitted the PDS with a power-lav and a Lorentzian (whenever a OPO is present) in the frequency ranges 0.1 1 Uz aud 1 10," To highlight the differences in the PDS at the low and high frequencies, we have fitted the PDS with a power-law and a Lorentzian (whenever a QPO is present) in the frequency ranges 0.1 $-$ 1 Hz and 1 $-$ 10"10is approximated by another log-linear with slope -0.16 (thick dashed line).,is approximated by another log-linear with slope -0.16 (thick dot-dashed line).11" This translates into a difference in the FP slope from our fiducial case around Py,27 of just about3%.. much less than the statistical uncertainties."," This translates into a difference in the FP slope from our fiducial case around $\Gamma_{\rm m}12\simeq 7$ of just about, much less than the statistical uncertainties."13 Similar is the case when different cut-off angles are considered., Similar is the case when different cut-off angles are considered.14 In the lower panel of Fig., In the lower panel of Fig.15" Al) we show how the observed correlations are skewed due to relativistic beaming when 6,=10 ¢dot-dashed contours and thick. dot-dashed line) or ϐ,=20° (dashed contours and thick dashed line).", \ref{fig:fp_gamma} we show how the observed correlations are skewed due to relativistic beaming when $\theta_c=10^{\circ}$ (dot-dashed contours and thick dot-dashed line) or $\theta_c=20^{\circ}$ (dashed contours and thick dashed line).16" Also in these cases the difference with respect to our fiducial ease corresponds to a difference in the ""corrected"" FP coefficients of less than ~3% at Ly,&7."," Also in these cases the difference with respect to our fiducial case corresponds to a difference in the “corrected” FP coefficients of less than $\sim$ at $\Gamma_{\rm m}17\simeq 7$."18 In summary. for any value of mean jet Lorentz factor of the sampled AGN. Li. we have shown that it is possible to derive statistically an intrinsic (un-boosted) radio core luminosity based on the observed hard X-ray one. Lx and on the black hole mass. App according to: where we have defined the new constant cen by.," In summary, for any value of mean jet Lorentz factor of the sampled AGN, $\Gamma_{\rm m}$, we have shown that it is possible to derive statistically an intrinsic (un-boosted) radio core luminosity based on the observed hard X-ray one, $L_{\rm19X}$ and on the black hole mass, $M_{\rm BH}$ according to: where we have defined the new constant $c_{\rm R}=\xi_{\rm RR}b_{\rm20R}+b_{\rm RR}$ ."21 The term in the first parenthesis in the right hand side thus represents our simple way to estimate the relativistic beaming bias introduced in the samples used originally to define the FP relation., The term in the first parenthesis in the right hand side thus represents our simple way to estimate the relativistic beaming bias introduced in the samples used originally to define the FP relation.22 Its numerical value do indeed depends on the assumptions of our fiducial Monte Carlo model. but to an extent that is negligible when compared to the statistical uncertainties on the FP parameters themselves.," Its numerical value do indeed depends on the assumptions of our fiducial Monte Carlo model, but to an extent that is negligible when compared to the statistical uncertainties on the FP parameters themselves."23 This above relation. then allows a meaningful statistical test of the intrinsic correlation between radio core luminosity and kinetic power of AGN jets. as we show in section 3..," This above relation, then allows a meaningful statistical test of the intrinsic correlation between radio core luminosity and kinetic power of AGN jets, as we show in section \ref{sec:rad}."24the 83D A and £ values and the tomographic r and { values.,the 3D $k$ and $\ell$ values and the tomographic $r$ and $\ell$ values.25 We will discuss the Limber approximation further in Section 4., We will discuss the Limber approximation further in Section \ref{Tomography from 3D Cosmic Shear}.26 In Figure 4 we show the elect of the Limber approximation on the 3D cosmic shear power spectrum., In Figure \ref{limberplot} we show the effect of the Limber approximation on the 3D cosmic shear power spectrum.27 Me find that the Limber approximation is a remarkably good approximation to the full caleulation for scales £z100. with residuals of ~10+ over all radial and azimuthal scales.," We find that the Limber approximation is a remarkably good approximation to the full calculation for scales $\ell\gs 28100$, with residuals of $\sim 10^{-4}$ over all radial and azimuthal scales."29 The break at koμοι In the power spectra at each f£. caused. by the Bessel function inequality ji(Ar()~0. ds reproduced through the inequality expressed. after equation (14)).," The break at $k\sim \ell/r_{\rm max}$ in the power spectra at each $\ell$, caused by the Bessel function inequality $j_{\ell}(kr \ls \ell)\sim 0$, is reproduced through the inequality expressed after equation \ref{l2}) )."30 For larger scales (<100. there is a larger effect on the power spectrum.," For larger scales $\ell < 100$, there is a larger effect on the power spectrum."31 In Figure 5 we show the elect of the Limber approximation on the expected. cosmological errors., In Figure \ref{limberfisherplot} we show the effect of the Limber approximation on the expected cosmological errors.32 We find that in most parameter combinations some information is inevitably lost. through the largest scales being down weighted. the increase in errors is between 1 30% with an average increase of ~ LOK.," We find that in most parameter combinations some information is inevitably lost, through the largest scales being down weighted, the increase in errors is between $1$ $30\%$ with an average increase of $\sim 10\%$ ."33 We conclude that the Limber approximation is adequate for forecasting purposes. but if computer time allows. it is preferable to use the full expressions in data analysis.," We conclude that the Limber approximation is adequate for forecasting purposes, but if computer time allows, it is preferable to use the full expressions in data analysis."34 We now approximate the 3D. shear fick further and. show how in the discrete real-space limit the tomographic power spectra can be reproduced., We now approximate the 3D shear field further and show how in the discrete real-space limit the tomographic power spectra can be reproduced.35 There have been some implicit references to this derivation. for example in Hu (1999). here we will show explicitly how the 3D shear field is related to the tomographic power spectrum.," There have been some implicit references to this derivation, for example in Hu (1999), here we will show explicitly how the 3D shear field is related to the tomographic power spectrum."36 Weak lensing tomography is a flavour of 3D weak lensing in which the angular anc redshilt information of each. galaxy is used., Weak lensing tomography is a flavour of 3D weak lensing in which the angular and redshift information of each galaxy is used.37 The practical distinction between 31) cosmic shear and tomography is that tomography divides the redshift range into a series of bins and the 2D shear transform in each bin is constructed., The practical distinction between 3D cosmic shear and tomography is that tomography divides the redshift range into a series of bins and the 2D shear transform in each bin is constructed.38 The auto (in à single bin) and cross (between bins) power spectra are used. to constrain cosmological parameters., The auto (in a single bin) and cross (between bins) power spectra are used to constrain cosmological parameters.39 Given the expressions in equations (14)) to (17)) we can now derive the weak lensing tomographie power spectra clirecthy from the 3D shear field., Given the expressions in equations \ref{l2}) ) to \ref{l4}) ) we can now derive the weak lensing tomographic power spectra directly from the 3D shear field.40" Lo Appendix Bowe show how the 3D cosmic shear power spectrum using the Limber approximation can be written as where we define a weight factor as where 7=(Gb; and ptrz])=ptrz]lezs]) is the redshift probability distribution. equivalent to p(z|2,) in equation (12))."," In Appendix B we show how the 3D cosmic shear power spectrum using the Limber approximation can be written as where we define a weight factor as where $r_i = \ell/k_i$ and $p(r[z])=p(r[z]|r[z_p])$ is the redshift probability distribution, equivalent to $\bar p(z|z_p)$ in equation \ref{Gcont}) )."41 We condense the notation here and in Appendix B to match the literature for the tomographic case., We condense the notation here and in Appendix B to match the literature for the tomographic case.42 This is still a full 3D estimator where rj=rsp) and po= can take any value. and in practice would be a sum over all galaxy pairs.," This is still a full 3D estimator where $r_1=r(z_1)$ and $r_2=r(z_2)$ can take any value, and in practice would be a sum over all galaxy pairs."43 This is a key result. of this article. using only two integrals a full 3D shear power spectrum can be computed from the 3D matter power spectrum (as simple as the standard tomographic approximation).," This is a key result of this article, using only two integrals a full 3D shear power spectrum can be computed from the 3D matter power spectrum (as simple as the standard tomographic approximation)."44 Inspection of the previous equations shows that they are the usual expressions for the (auto- or cross-) power spectrum of tomography. from which we see that. under the Limber approximation. tomography samples discrete sets of physical wavenumbers. in an £-dependent way: for shells at distances πι...," Inspection of the previous equations shows that they are the usual expressions for the (auto- or cross-) power spectrum of tomography, from which we see that, under the Limber approximation, tomography samples discrete sets of physical wavenumbers, in an $\ell$ -dependent way: for shells at distances $r_i$, $k = \ell/r_i$."45 1n summary to convert from 3D cosmic shear to weak lensing omography we see that the following three steps must be aken The second step is benign in that no information. should be lost. however the first and third steps do result. in information loss (see Section 3.1. and 4.1)).," In summary to convert from 3D cosmic shear to weak lensing tomography we see that the following three steps must be taken The second step is benign in that no information should be lost, however the first and third steps do result in information loss (see Section \ref{Convergence of the 3D Cosmic Shear} and \ref{Comparison46 to 3D shear}) )."47 Interestingly [or à specific redshift bin (r) and a specific azimuthal {- the tomographic approximation only probes a single physical &-mode A=(fr from the full 3D shear field: in contrast in 3D cosmic shear we have control over the & and { modes over the whole redshift range., Interestingly for a specific redshift bin $r$ ) and a specific azimuthal $\ell$ -mode the tomographic approximation only probes a single physical $k$ -mode $k=\ell/r$ from the full 3D shear field; in contrast in 3D cosmic shear we have control over the $k$ and $\ell$ modes over the whole redshift range.48 Clearly by fixing the distances of the tomographic binning. we lose some [lexibilitv over the physical wavenumbers probed. so there is a risk that either not all useful modes ave included. (increasing statistical errors). or that. for the nearby shells. the physical wavenumber range sampled extends to too high. a value of A. where theoretical uncertainties become a potential source of svstematic error.," Clearly by fixing the distances of the tomographic binning, we lose some flexibility over the physical wavenumbers probed, so there is a risk that either not all useful modes are included (increasing statistical errors), or that, for the nearby shells, the physical wavenumber range sampled extends to too high a value of $k$, where theoretical uncertainties become a potential source of systematic error."49 None of this is a fundamental problem for tomography: it simply requires that the £ range chosen should be redshilt- increasing Ax=σι for the distant shells. and reducing it for nearby. shells.," None of this is a fundamental problem for tomography; it simply requires that the $\ell$ range chosen should be redshift-dependent – increasing $\ell_{\rm max}=r[z]k_{\rm max}$ for the distant shells, and reducing it for nearby shells."50 In a similar manner to Section 2. we can also keep, In a similar manner to Section \ref{Photometric 3D Shear Estimator} we can also keep51Ideally we would like to use the muicrolensing flux ratios to constrain the size of the quasar as a functiou of waveleneth: however. only weak constraints can be derived without a detection of time variability due to microlensing (?)..,"Ideally we would like to use the microlensing flux ratios to constrain the size of the quasar as a function of wavelength; however, only weak constraints can be derived without a detection of time variability due to microlensing \citep{Wyithe2002}."52 Iustead we use a senmi-enpircal model for the infrared SED topredict what the flux ratios should be as a function of waveleneth and compare these predictions with the observed flux ratios to confirm the plausibility of this model., Instead we use a semi-empirical model for the infrared SED to what the flux ratios should be as a function of wavelength and compare these predictions with the observed flux ratios to confirm the plausibility of this model.53 We coustructed a semi-cimpirical model for the flux ratios to compare to the observed IRAC flux ratios as follows., We constructed a semi-empirical model for the flux ratios to compare to the observed IRAC flux ratios as follows.54 We asstune that the spectra cousists of a power-law component due to an accretion disk (we are modchne the region from Ο.Ε LOgam which is well longward of the peak of the disk spectrum and is only a decade in frequency. so a power-law should be an adequate approximation of a disk spectrum) aud a sinele-temperature thermal dust cussion component. representing the inner edge of the a dusty torus.," We assume that the spectrum consists of a power-law component due to an accretion disk (we are modeling the region from $0.4 - 4.0 \mu$ m which is well longward of the peak of the disk spectrum and is only a decade in frequency, so a power-law should be an adequate approximation of a disk spectrum) and a single-temperature thermal dust emission component, representing the inner edge of the a dusty torus."55 We fit the spectral cnerey distribution from 0.1 to. L0 nücrous in the rest frame with these two compoucuts. determining their relative streneth at cach wavelength.," We fit the spectral energy distribution from 0.4 to 4.0 microns in the rest frame with these two components, determining their relative strength at each wavelength."56 The best fit is shown in Figure 8: the model provides a good fit to the four IRAC data points., The best fit is shown in Figure \ref{fig:q2237sed}; the model provides a good fit to the four IRAC data points.57 We have not attempted to correct for mücroleusiug. nor possible time-variability as the SED data are not simultaneous.," We have not attempted to correct for microlensing, nor possible time-variability as the SED data are not simultaneous."58 However. this will likely have a sinall effect on the SED as suunnaiug over all four images reduces the impact of mucroleusing aud im the infrared quasars are weakly variable.," However, this will likely have a small effect on the SED as summing over all four images reduces the impact of microlensing and in the infrared quasars are weakly variable."59 With these two fts we determined the minima possible source sizes to reproduce the observed fux with thermal enission as follows., With these two fits we determined the minimum possible source sizes to reproduce the observed flux with thermal emission as follows.60" For the power-law component. we assumed a disk ecometry with a temperature that is à power-law in radius. re finding Toxe99, and found that tbe hal£-light radius should scale with waveleugtli as where A is measured iu microns iu the rest frame of the quasar."," For the power-law component, we assumed a disk geometry with a temperature that is a power-law in radius, $r$, finding $T \propto r^{-0.66}$, and found that the half-light radius should scale with wavelength as where $\lambda$ is measured in microns in the rest frame of the quasar."61" At this radius the standard disk model is well outside the immer edee and thus is expected to lave a temperature dependence of Toxà7/73, which is close to the measured dependence."," At this radius the standard disk model is well outside the inner edge and thus is expected to have a temperature dependence of $T \propto r^{-3/4}$, which is close to the measured dependence."62 We asstuned that the dust component either las an ciissivity described by optically-thin interstellar medii (ISM) dust with the model of ? or cuits as au optically-thick blackbody (BB)., We assumed that the dust component either has an emissivity described by optically-thin interstellar medium (ISM) dust with the model of \citet{Draine2003} or emits as an optically-thick blackbody (BB).63 These two extremes were chosen to bracket the range of possible behaviors for the hottest dust at the inner edge of the torus (we did not use the best-fit Fritz model due to the differcut peak waveleneth)., These two extremes were chosen to bracket the range of possible behaviors for the hottest dust at the inner edge of the torus (we did not use the best-fit Fritz model due to the different peak wavelength).64 We found best-fit temperatures of the dust of 1168 In (ISM), We found best-fit temperatures of the dust of 1168 K (ISM)65The theoretical approach presented here allows us to determine the spectrum and the anisotropy in the particle distribution for arbitrary shock velocity ancl arbitrary scattering properties of the fluid.,The theoretical approach presented here allows us to determine the spectrum and the anisotropy in the particle distribution for arbitrary shock velocity and arbitrary scattering properties of the fluid.66 In (his section we show that we can reproduce the results expected in (he non-relativistic limit., In this section we show that we can reproduce the results expected in the non-relativistic limit.67 We calculated the spectral slope and (he angular part of the distribution function for several values of the shock velocity and shock compression factor r., We calculated the spectral slope and the angular part of the distribution function for several values of the shock velocity and shock compression factor $r$.68 We also calculated (he return. probability [rom the downstream and upstream sections., We also calculated the return probability from the downstream and upstream sections.69" The expected return. probability in the Newtonian limit is 77opπαdug. very. accurately reproduced by our calculation. for instance for uy107 (DPZ,=0.96) and for uy=2x103 (P!,— 0.92)."," The expected return probability in the Newtonian limit is $P_{ret}^d=1-4 u_d$, very accurately reproduced by our calculation, for instance for $u_d=10^{-2}$ $P_{ret}^d = 0.96$ ) and for $u_d=2\times 10^{-2}$ $P_{ret}^d =700.92$ )."71 In all cases that we considered. the condition is confirmed for any value of jy within a part in 103.," In all cases that we considered, the condition is confirmed for any value of $\mu_0$ within a part in $10^4$."72 As a matter of fact. we checked. (hat the above equality is satisfied in all cases we studied. relativistic or otherwise.," As a matter of fact, we checked that the above equality is satisfied in all cases we studied, relativistic or otherwise."73 The slope of the spectrum of accelerated particles for u=3x107? and uy=107 (compression [actor 3) as calculated wilh our approach is 4.5. in agreement wilh the theoretical prediction (Bell 1973).," The slope of the spectrum of accelerated particles for $u=3\times7410^{-2}$ and $u_d=10^{-2}$ (compression factor 3) as calculated with our approach is 4.5, in agreement with the theoretical prediction (Bell 1978)."75 We obtain the same slope in botli cases of small pitch angle scattering with &=0.01 and large angle scattering. that we simulate by choosing ¢=100 (but any large value gives (he same result).," We obtain the same slope in both cases of small pitch angle scattering with $\sigma=0.01$ and large angle scattering, that we simulate by choosing $\sigma=100$ (but any large value gives the same result)."76 The [act that in the newtonian limit the slope of the spectrum does not depend on the scattering properties of the fIuid is also in agreement with the theoretical prediction of Bell (1978)., The fact that in the newtonian limit the slope of the spectrum does not depend on the scattering properties of the fluid is also in agreement with the theoretical prediction of Bell (1978).77" It is worth stressing that (his universality in the spectrum of the accelerated.particles does not reflect in the universality of the return probabilities 7; and P,.", It is worth stressing that this universality in the spectrum of the acceleratedparticles does not reflect in the universality of the return probabilities $P_d$ and $P_u$.78 In Fig., In Fig.79 1 we plot μμ.) ancl Pug.ji) as fncetions of ji for the values of ji inclicatecl in the figure ancl assuming «4=0.03.440.01 and a=0.01.," \ref{fig:PdPu001} we plot $P_d(\mu_0,\mu)$ and $P_u(\mu_0,\mu)$ as functions of $\mu$ for the values of $\mu_0$ indicated in the figure and assuming $u=0.03,u_d=0.01$ and $\sigma=0.01$."80 The same functions are plotted in Fig., The same functions are plotted in Fig.81 2 for the case of large angle scattering (a= 100)., \ref{fig:PdPu100} for the case of large angle scattering $\sigma=100$ ).82 As stressed. above. our method is based on the introduction of the (wo probability clistvibutions £2 and {η (hat can be calculated by solving (wo integral equations. Eqs. (16))," As stressed above, our method is based on the introduction of the two probability distributions $P_d$ and $P_u$ , that can be calculated by solving two integral equations, Eqs. \ref{eq:Pd}) )"83velocitv of the two cvlinders). as only differential rotation plavs a role in the generation ol turbulence.,"velocity of the two cylinders), as only differential rotation plays a role in the generation of turbulence."84" Defining w=v—Qyre,. and ©=0—Ouf (so that w and © are the velocity and azimuthal coordinate in (he rotating frame. respectively). the Navier-Stokes equation for w=(iw.ie.ete.) becomes where w.V'w=(w.Vie,je,+(w.Vi4)e;(w.Vi.)e.."," Defining ${\bf w}={\bf v}-\Omega_0 r85{\bf e}_{\phi}$, and $\phi=\theta-\Omega_0 t$ (so that ${\bf w}$ and $\phi$ are the velocity and azimuthal coordinate in the rotating frame, respectively), the Navier-Stokes equation for ${\bf w}=(w_r,\ w_\phi,\ w_z)$ becomes where ${\bf w}.\nabla'{\bf w}\equiv({\bf w}.\nabla w_r)86{\bf e}_r+({\bf w}.\nabla w_{\phi}) {\bf e}_{\phi}+({\bf w}.\nabla87w_z) {\bf e}_z$."88 For future reference. I refer to (he terms (5/r and 2w;ico/r as “geometric ternis. as they arise because of the cylindricalgeonietrv.," For future reference, I refer to the terms $w_{\theta}^2/r$ and $2w_rw_\theta/r$ as “geometric terms"", as they arise because of the cylindrical."89. For these flows. (he rotation parameter defined in Eq. (5))," For these flows, the rotation parameter defined in Eq. \ref{Ro}) )"90 reads where g=—(r/Q)(dQ/dr) is the parameter defined by Balbusοἱaf(1996). to characterize rotation profiles., reads where $q\equiv -(r/\Omega)(d\Omega/dr)$ is the parameter defined by \citet{BHS96} to characterize rotation profiles.91 The flow is stable according to Ravleigl’s criterion when 4<2. ie. wheΕν S«—1. quite similarly (ο rotating Couette and [ree flows. allhough (hie processes (hroug[un which instability occurs are dillerent.," The flow is stable according to Rayleigh's criterion when $q<2$, i.e. when $S<-1$, quite similarly to rotating Couette and free flows, although the processes through which instability occurs are different."92 Note also that Eqs. (4)), Note also that Eqs. \ref{NSR}) )93 and (3)) diller only through the geometric and centrifugal terms., and \ref{NSCT}) ) differ only through the geometric and centrifugal terms.94 The fact that the minimum Revnolds nunber for developed (turbulence is identical in plane Couette and. Couette-Tavlor flows with Ar/rX1/20 and the inner evlinder at rest can be understood in the following wav., The fact that the minimum Reynolds number for developed turbulence is identical in plane Couette and Couette-Taylor flows with $\Delta r/r\lesssim 1/20$ and the inner cylinder at rest can be understood in the following way.95 First. the advection term Gvhichli is the source of the turbulence cascade as indicated by the very existence of the Revnolds imunber) dominates over (he geometric terms when rAQ/ArorAQ/r. ie. Ar/r<1.," First, the advection term (which is the source of the turbulence cascade as indicated by the very existence of the Reynolds number) dominates over the geometric terms when $r\Delta\Omega/\Delta r\gg r\Delta\Omega/r$, i.e. $\Delta r/r\ll 1$."96 Second. AQ=© (one cvlinder being at rest). so that the Coriolis term is also very small compared to the advection term. and Eq. (8))," Second, $\Delta\Omega=\Omega$ (one cylinder being at rest), so that the Coriolis term is also very small compared to the advection term, and Eq. \ref{NSCT}) )"97 nearly reduces to Eq. (1))., nearly reduces to Eq. \ref{NSC}) ).98 Note furthermore that the Coriolis force does nol appear to significantly affect (he minimal lRevnolds number for the onset of turbulence for the values of q of interest here (Le. q>1 log~1 - 2). both in the limiting plane Couette regime and in the rotation regime. as exemplified bv the data of Wendt(1933). Lor nearly neutral flows. which follow the same law for the minimal Revnolds number. down to the plane Couette limit.," Note furthermore that the Coriolis force does not appear to significantly affect the minimal Reynolds number for the onset of turbulence for the values of $q$ of interest here (i.e., $q\gg 1$ to $q\sim 1$ - $2$ ), both in the limiting plane Couette regime and in the rotation regime, as exemplified by the data of \citet{Wen33} for nearly neutral flows, which follow the same law for the minimal Reynolds number, down to the plane Couette limit."99(2002. 2004).,"(2002, 2004)."100 It is easy to show that C(p) is related: to the Cp) through the relation Cp)|lífüol=ερ)., It is easy to show that $U(p)$ is related to the $\hat{U}(p)$ through the relation $\hat U(p)+1/R_tot = U(p)$.101 The dotted. and. dashed. lines are. the results. obtained with the caleulation of Alalkoyv (1997) with a Bohm aud Ixolmogorov. cillusion respectively., The dotted and dashed lines are the results obtained with the calculation of Malkov (1997) with a Bohm and Kolmogorov diffusion respectively.102 For Bohm clilfusion the two approaches give very similar results., For Bohm diffusion the two approaches give very similar results.103 For Ixolmogorov diffusion the dilferencies are larger. as expected.," For Kolmogorov diffusion the differencies are larger, as expected."104 In Fig., In Fig.105 5 we plot the spectra of the accelerated particles. as obtained in this paper (solid line) and for a Bohm (dotted line) and Ixolmosgorov. (dashed line) diffusion coellicient. as derived by carving out the caleulation of Malkov. (1997).," \ref{fig:malk_spec} we plot the spectra of the accelerated particles, as obtained in this paper (solid line) and for a Bohm (dotted line) and Kolmogorov (dashed line) diffusion coefficient, as derived by carrying out the calculation of Malkov (1997)."106 We recall that from the theoretical point of view the ohm dilfusion is in lact what should. be expected. in the proximity of a shock if the turbulence. necessary for. the acceleration is strong and generated by the same cosmic ravs that are being accelerated (Lagage Cesarsky 1983)., We recall that from the theoretical point of view the Bohm diffusion is in fact what should be expected in the proximity of a shock if the turbulence necessary for the acceleration is strong and generated by the same cosmic rays that are being accelerated (Lagage Cesarsky 1983).107 In this perspective. we look at the results illustrated in this section as very encouraging in using the approach presented in Blasi (2002. 2004). since it is simple and at the same time accurate in reproducing the major physical aspects of particle acceleration at cosmic ray modified shocks.," In this perspective, we look at the results illustrated in this section as very encouraging in using the approach presented in Blasi (2002, 2004), since it is simple and at the same time accurate in reproducing the major physical aspects of particle acceleration at cosmic ray modified shocks."108 The presence of multiple solutions is typical of many non-linear problems anc should not be surprising from the mathematical point of view., The presence of multiple solutions is typical of many non-linear problems and should not be surprising from the mathematical point of view.109 In terms of physical understanding however. multiple solutions may be disturbing.," In terms of physical understanding however, multiple solutions may be disturbing."110 The typical situation that takes place in nature when multiple solutions appear in the description of other non linear svstems is that (at least) one of the solutions is unstable and the svstem in a stable solution when perturbed., The typical situation that takes place in nature when multiple solutions appear in the description of other non linear systems is that (at least) one of the solutions is unstable and the system in a stable solution when perturbed.111 The stable solutions are the only ones that are physically meaningful., The stable solutions are the only ones that are physically meaningful.112 Some attempts to. investigate the stability of cosmic ray modified shock waves have been mace by Mond Drury (1998) and Toptyein (1999). but all of them refer to the two-Luicl models.," Some attempts to investigate the stability of cosmic ray modified shock waves have been made by Mond Drury (1998) and Toptygin (1999), but all of them refer to the two-fluid models."113 A step forward is being carried out by Blasi Vietri (in preparation) in the context of kinetic mocels., A step forward is being carried out by Blasi Vietri (in preparation) in the context of kinetic models.114 In acicdition to the stability. another issue that enters the physical. description of our problem is the identification of possible processes that determine some tvpe of backreaction on the system.," In addition to the stability, another issue that enters the physical description of our problem is the identification of possible processes that determine some type of backreaction on the system."115 Ht may be expected that when some types of processes of self-regulation are included. the phenomenon of multiple solutions is reduced.," It may be expected that when some types of processes of self-regulation are included, the phenomenon of multiple solutions is reduced."116 In this section we investigate, In this section we investigate117IW Pup CUP 36762) is a relatively Taint (Via;=10.36) contact binary which has not had any photometric or radial velocity observations.,HI Pup (HIP 36762) is a relatively faint $V_{\rm max}=10.36$ ) contact binary which has not had any photometric or radial velocity observations.118 Discovered in 1949. (he svstem was Classified ancl its light curve constructed from photographic observations by Hoffineister (1956).," Discovered in 1949, the system was classified and its light curve constructed from photographic observations by \citet{hoff56}."119. Sahade&DerónDavila(1963). suggested (hat it is a possible member of the open cluster Cr 173. but this matter has not been established vet.," \citet{sahade63} suggested that it is a possible member of the open cluster Cr 173, but this matter has not been established yet."120 The Tveho-2 mean B-W=0.51 corresponds to a spectral type about FOV. but there exist no direct classifications of the star.," The Tycho-2 mean $B-V=0.51$ corresponds to a spectral type about F6V, but there exist no direct classifications of the star."121 A companion with 8—V=1.68 (approximately M3V) is located 52 arcsec away (ESA1997).. but the star is not included as a visual double svstem in the WDS Catalog.," A companion with $B-V =1.68$ (approximately M3V) is located 52 arcsec away \citep{hip}, but the star is not included as a visual double system in the WDS Catalog."122 We have only 5 radial velocity observations for HI Pup. so the radial velocity orbit must be considered very preliminary.," We have only 5 radial velocity observations for HI Pup, so the radial velocity orbit must be considered very preliminary."123" The mass ratio is small. qi,=0.19a0.06."," The mass ratio is small, $q_{\rm sp}=0.19 \pm 0.06$."124 TZ Pvx (HIP. 42619) was discovered as a variable star by Strohmeier(1966). who determined the orbital period to be 0.697 davs (Strolimeier1961b)., TZ Pyx (HIP 42619) was discovered as a variable star by \citet{stroh66} who determined the orbital period to be 0.697 days \citep{stroh67b}.125. Later Llipparcos observations (ESA1997) showed that the binary has an orbital period of 2.3 days with a light curve showing relatively short. well defined eclipses.," Later Hipparcos observations \citep{hip}126 showed that the binary has an orbital period of 2.3 days with a light curve showing relatively short, well defined eclipses."127" It is definitely a detached binary with well separated. components. vet the star still appears as a W UMa-tyvpe binary in the Simbad database with the spectral (ype as an uncertain A. The Tyeho-2 photometric data. 0.27. suggest a spectral type A3/9V at Vi,=10.63."," It is definitely a detached binary with well separated components, yet the star still appears as a W UMa-type binary in the Simbad database with the spectral type as an uncertain A. The Tycho-2 photometric data, $B-V=0.27$ , suggest a spectral type A8/9V at $V_{\rm max}=10.68$."128 Our radial velocity orbit is the best among this group of targets. mostly because of sharp signabures in the broadening functions which were easy (o measure for radial velocities.," Our radial velocity orbit is the best among this group of targets, mostly because of sharp signatures in the broadening functions which were easy to measure for radial velocities."129 The Mass ratio is very close to unitv. ονdu=0.9652:0.020. with the slightlySuet less-niassive component (the one showing the larger semi-amplitude) giving a mareinally stronger signature in ihe DF's.," The mass ratio is very close to unity, $q_{\rm sp}=0.965 \pm 0.020$, with the slightly less-massive component the one showing the larger semi-amplitude) giving a marginally stronger signature in the BF's."130 The current paper is the second and last of the (wo papers describing a short program of radial velocity observations of southern contact binary stus conducted at the European Southern observatory in December 1996 and. August 1998., The current paper is the second and last of the two papers describing a short program of radial velocity observations of southern contact binary stars conducted at the European Southern observatory in December 1996 and August 1998.131 Paper I eave the full background and explanations for the rationale of this program. and contained results for 17 targets observable in the August season in 1998.," Paper I gave the full background and explanations for the rationale of this program, and contained results for 17 targets observable in the August season in 1998."132of its counterpart can be estimated. from the reddening clerived from the measurement and ealaxy counts.,of its counterpart can be estimated from the reddening derived from the measurement and galaxy counts.133" From the reddening map in Burstein Leiles (1982) we obtain a colour excess EGD13)zm0.054 for a halo source at §=46728584"" and b=36711573"".", From the reddening map in Burstein Heiles (1982) we obtain a colour excess $E(B-V) \approx 0.054$ for a halo source at $l = 46^{\circ} 28' 58.4''$ and $b = -36^{\circ} 11' 57.3''$.134" ""Ehe corresponding extinctions are chyzm(Q.17. chy&O.1l and cl,=0.09."," The corresponding extinctions are $A_V \approx 0.17$, $A_R \approx 0.11$ and $A_I \approx 0.09$."135" Llence. the extinction-corrected magnitudes of a 0.7 AL. star at a distance of 15 kpe are m,zz22.0. m,c22.2 and m,2 21.5."," Hence, the extinction-corrected magnitudes of a 0.7 $_\odot$ star at a distance of 15 kpc are $m_{_V} \approx 22.9$, $m_{_R} \approx 22.2$ and $m_{_I} \approx 21.7$ ."136 From the PCA count rates and the distance estimate (5.15 kpc). we obtain an estimate of ~10ores for the X-ray luminosity during ALJD zz24505)9)2451105.," From the PCA count rates and the distance estimate $5 - 15$ kpc), we obtain an estimate of $\sim 1 \times 10^{37}~{\rm erg\,s^{-1}}$ for the X-ray luminosity during MJD $\approx 2450995 - 2451105$."137 A fraction (OS)(πα) of the N-ravs would intercept the companion star. where [ο is the radius of the companion star and e the orbital separation.," A fraction $(\pi138R_2^2)/(4 \pi a^2)$ of the X-rays would intercept the companion star, where $R_2$ is the radius of the companion star and $a$ the orbital separation."139 I£ we substitute the values of {ο and Mo calculated. in. £44. this corresponcls o à fraction of ~3 per cent.," If we substitute the values of $R_2$ and $M_2$ calculated in 4, this corresponds to a fraction of $\sim 3$ per cent."140" Therefore. energy. will be deposited into the companion star's atmosphere at a rate of 5.LO35eres""."," Therefore, energy will be deposited into the companion star's atmosphere at a rate of $\sim 5 \times14110^{35}~{\rm erg\,s^{-1}}$."142 Xn unheated 0.7- M. main-sequence. star as à bolometric luminosity of about 1.1075eres+ and an ellective surface temperature of about 4800 Ix. The intrinsic uminositv of the companion star is therefore much lower han the power of the intercepted X-rays.," An unheated 0.7 $_\odot$ main-sequence star has a bolometric luminosity of about $1 \times 10^{33}~{\rm erg\,s^{-1}}$ and an effective surface temperature of about 4800 K. The intrinsic luminosity of the companion star is therefore much lower than the power of the intercepted X-rays."143 We suppose that a cquasi-edquilibrium state is set up at the heated surface of the companion star such that the rate of energy. radiated away is the same as the rate of energy. deposited., We suppose that a quasi-equilibrium state is set up at the heated surface of the companion star such that the rate of energy radiated away is the same as the rate of energy deposited.144 The effective surface temperature of the irraciatively-heatecl atmosphere of the companion star could then reach 20000 Ix. During our observations. the svstem was in the process of returning to its quiescent state.," The effective surface temperature of the irradiatively-heated atmosphere of the companion star could then reach 20000 K. During our observations, the system was in the process of returning to its quiescent state."145 On August 23. the ASAI count rate had. already dropped to the pre-outburst level (Fig., On August 23 the ASM count rate had already dropped to the pre-outburst level (Fig.146 1). which may. be considered. consistent. with zero.," 1), which may be considered consistent with zero."147 Although the X-ray activity seemed. to have ceased. the accretion disc hack not completely. dissipated. ancl the companion star's atmosphere hack not completely cooled down.," Although the X-ray activity seemed to have ceased, the accretion disc had not completely dissipated, and the companion star's atmosphere had not completely cooled down."148 Our photometric data obtained on August 19 and 20 show that the minimum brightness in the W-. 2 and {- light-curves was V.2:20.8. 220.5 and {zz20.5.," Our photometric data obtained on August 19 and 20 show that the minimum brightness in the $V$ -, $R$ - and $I$ -band light-curves was $V \approx 20.8$, $R \approx 20.5$ and $I \approx 20.5$."149 The V-band brightness continued to drop and reached 21.4 mag on August 23., The $V$ -band brightness continued to drop and reached 21.4 mag on August 23.150 The star was finally not visible in the D-. H- and V-band data that we obtained on August 25 and 26 tthe #-bancl brightness of 21.5 mage on August 26 and 27. Zurita Casares 1998. which would imply a distance of 11 kpc if it is taken as the quicscent brightness of the companion star).," The star was finally not visible in the $B$ -, $R$ - and $V$ -band data that we obtained on August 25 and 26 the $R$ -band brightness of 21.5 mag on August 26 and 27, Zurita Casares 1998, which would imply a distance of $\sim 11$ kpc if it is taken as the quiescent brightness of the companion star)."151 The optical brightness of RATE 058 was observed to decline at a rate of 0.1 magd+ in carly August (Zurita. Casares Hyvnes 1998).," The optical brightness of RXTE $-$ 058 was observed to decline at a rate of 0.1 ${\rm mag\,d^{-1}}$ in early August (Zurita, Casares Hynes 1998)."152 We observed a decline rate 0.200+0.001magd in the V-band. brightness between August IS and 20.," We observed a decline rate $0.200 \pm 0.001\,{\rm mag\,d^{-1}}$ in the $V$ -band brightness between August 18 and 20."153 X decline is also seen in our Z?- and I-band data but at less rapid rates of 0.085+0.002magd and 0.020+0.010magd respectively.," A decline is also seen in our $R$ - and $I$ -band data but at less rapid rates of $0.085 \pm 0.002\,{\rm154mag\,d^{-1}}$ and $0.020 \pm 0.010\,{\rm mag\,d^{-1}}$ respectively."155 (X. linear decline in brightness is equivalent to an exponential decline in luminosity., A linear decline in brightness is equivalent to an exponential decline in luminosity.156 The faster decline in the Y magnitude may indicate the fading or dissipation of the accretion disc (which was bluer than the companion star) after mass transfer ceased. in addition to the cooling of the atmosphere of the companion star.," The faster decline in the $V$ magnitude may indicate the fading or dissipation of the accretion disc (which was bluer than the companion star) after mass transfer ceased, in addition to the cooling of the atmosphere of the companion star."157 The photometric data also show hints of an ellipsoidal modulation around. phase 0.5. which became more evident in our later observations.," The photometric data also show hints of an ellipsoidal modulation around phase 0.5, which became more evident in our later observations."158 As we show in Fig., As we show in Fig.159 3. the V-band light-curve deviates from a sinusoidal-Iike curve by developing first a Hat top around phase 0.5 on August 18. and then à local minimum on August 20.," 3, the $V$ -band light-curve deviates from a sinusoidal-like curve by developing first a flat top around phase 0.5 on August 18, and then a local minimum on August 20."160 We attribute the eradual development of the secondary. mininium. at. phase 0.5 to the fading of the accretion disk. which reveals the ellipsoidal modulation of the companion star.," We attribute the gradual development of the secondary minimum at phase 0.5 to the fading of the accretion disk, which reveals the ellipsoidal modulation of the companion star."161 We carried. out a svnergetic study of the X-ray transient RATE 0585., We carried out a synergetic study of the X-ray transient RXTE $-$ 058.162 The photometric observations were carried out from 1998 August 14 to 26. when the svstem was in transition from the outburst to the quiescent state.," The photometric observations were carried out from 1998 August 14 to 26, when the system was in transition from the outburst to the quiescent state."163 data were obtained in the V. 2 and £ bands. which show approximately sinusoidal oscillations with a linear brightness decline when folded: on a period of 0.24821. d. The rate of decline measured from the V brightness during our observations was 0.20040.001magd.+. more rapid than that the rate of 0.085£0.002magd.+ for the & brightness and of 0.020270010magd.+ for the £ brightness.," High-quality data were obtained in the $V$, $R$ and $I$ bands, which show approximately sinusoidal oscillations with a linear brightness decline when folded on a period of 0.24821 d. The rate of decline measured from the $V$ brightness during our observations was $0.200 \pm 0.001\,{\rm mag\,d^{-1}}$, more rapid than that the rate of $0.085 \pm 0.002\,{\rm mag\,d^{-1}}$ for the $R$ brightness and of $0.020 \pm 0.010\,{\rm mag\,d^{-1}}$ for the $I$ brightness."164 Tho folded light-curves deviate significantly. from a sinusoidal curve around phase 0.5. showing hints of ellipsoidal mocdulations. which tend to become progressively more evident.," The folded light-curves deviate significantly from a sinusoidal curve around phase 0.5, showing hints of ellipsoidal modulations, which tend to become progressively more evident."165 This sugeests the presence of a fading accretion disc as well as an irraciativelv-heatecd companion star., This suggests the presence of a fading accretion disc as well as an irradiatively-heated companion star.166 We thank Allvn Tennant. Helen Johnston. Mike Dessell and Peter Wood for discussions. and. Don Melrose. ancl John Greenhill for their commentson the manuscript.," We thank Allyn Tennant, Helen Johnston, Mike Bessell and Peter Wood for discussions, and Don Melrose and John Greenhill for their commentson the manuscript."167 We also thank John Greenhill and Jorge Casares for their sharing some of the data obtained by the UTas. L-m telescope., We also thank John Greenhill and Jorge Casares for their sharing some of the data obtained by the UTas 1-m telescope.168 KW acknowledges the support. from the ARC through an Australian Research Fellowship., KW acknowledges the support from the ARC through an Australian Research Fellowship.169 This work is partially supported by the URC. University of Sydney.," This work is partially supported by the URG, University of Sydney."170interface fluxes. PF;i.,interface fluxes $F_{i+\frac{1}{2}}$.171 In general. an initial discontinuity at 7+ due to U; and U;4 will evolve into four piecewise constant states separated by three waves.," In general, an initial discontinuity at $i+\frac{1}{2}$ due to $U_{i}$ and $U_{i+1}$ will evolve into four piecewise constant states separated by three waves."172" The left-most and waves nav be either shocks or rarefaction waves. while the middle wave is always a contact. discontinuity,"," The left-most and right-most waves may be either shocks or rarefaction waves, while the middle wave is always a contact discontinuity."173 The determination of these [our piecewise constant states can. in eeneral. be achieved only by iterativelv solving nonlinear equations.," The determination of these four piecewise constant states can, in general, be achieved only by iteratively solving nonlinear equations."174 Thus (hie computation of the fluxes necessitates a step which can be computationally expensive., Thus the computation of the fluxes necessitates a step which can be computationally expensive.175 For this reason much attention has been eiven to approximate. but sufficiently accurate. techniques.," For this reason much attention has been given to approximate, but sufficiently accurate, techniques."176 One notable method is that due to Wartenetal.(1983.IILE).. in which the middle wave. ancl the two constant states that it separates. are replaced by a single piecewise constant state.," One notable method is that due to \citet[HLL]{hlv}, in which the middle wave, and the two constant states that it separates, are replaced by a single piecewise constant state."177 One benefit of this approximation. which smears the contact discontinuitv somewhat. is io eliminate the iterative step. (hus sienilicantlv improving efficiency.," One benefit of this approximation, which smears the contact discontinuity somewhat, is to eliminate the iterative step, thus significantly improving efficiency."178 However. the IILL method requires accurate estimates of the wave speeds for the left- and right-moving waves.," However, the HLL method requires accurate estimates of the wave speeds for the left- and right-moving waves."179 EFinfeldt(1988). analvzed the HLL method and found good estimates for the wave speeds., \citet{ein} analyzed the HLL method and found good estimates for the wave speeds.180 The resulting method combining the original ILL method with Einfeldts improvements (the IILLE method). has been taken as a starting point for our simulations.," The resulting method combining the original HLL method with Einfeldt's improvements (the HLLE method), has been taken as a starting point for our simulations."181 In our implementation we use wave speed estimates based on a simple application of the relativistic addition of velocities formula for the individual components of the velocities. and the relativistic sound speed ο. assuming that the waves can be decomposed into components moving perpendicular io the three coordinate directions.," In our implementation we use wave speed estimates based on a simple application of the relativistic addition of velocities formula for the individual components of the velocities, and the relativistic sound speed $c_s$, assuming that the waves can be decomposed into components moving perpendicular to the three coordinate directions."182" In order to compute the pressure p and sound speed c; we need (he rest. [rame mass density » and energy density ο,", In order to compute the pressure $p$ and sound speed $c_s$ we need the rest frame mass density $n$ and energy density $e$.183 However. these quantiües are nonlinearly coupled to the components of the velocity as well as to the laboratory [rame variables via (he Lorentz transformation: where >=(1—07)LV? is the Lorentz factor and (?=(07)?+(09)?(i)?.," However, these quantities are nonlinearly coupled to the components of the velocity as well as to the laboratory frame variables via the Lorentz transformation: where $\gamma = ( 1 - v^2 )^{-1/2}$ is the Lorentz factor and $v^2 =184(v^{x})^2 + (v^{y})^2 + (v^{z})^2$."185 Whenthe acdiabaticindex is constant it is possible to reduce (he computation of n. e. οὖν e aad e to," Whenthe adiabaticindex is constant it is possible to reduce the computation of $n$ ,$e$ , $v^{x}$ , $v^{y}$ and $v^{z}$ to"186configurations that are unlikely to occur in the negative specific heat branch are those with very negative values of TT.,configurations that are unlikely to occur in the negative specific heat branch are those with very negative values of $W_*$.187 Since the absolute value of TT. depends on the Inverse separation between particles. such configurations will have particles that are very close to cach other. aud therefore are likely to be uustable to mergers.," Since the absolute value of $W_*$ depends on the inverse separation between particles, such configurations will have particles that are very close to each other, and therefore are likely to be unstable to mergers."188 Together with the roughly 20% statistical variation over time of c about c. any configuration with a value of c iu the negative specific heat brauch may be a chance configuration of a cluster that has a negative specific heat.," Together with the roughly $20\%$ statistical variation over time of $\psi$ about $\overline{\psi}$, any configuration with a value of $\psi$ in the negative specific heat branch may be a chance configuration of a cluster that has a negative specific heat."189 Since the 6.N-dimeusional phase space configuration of subcelusters im a cell is directly related to tlic cells potential aud kinetic euereies aud thus its virial ratio. we cau use the theory to study the internal structure and shapes within a cell.," Since the $6N$ -dimensional phase space configuration of subclusters in a cell is directly related to the cell's potential and kinetic energies and thus its virial ratio, we can use the theory to study the internal structure and shapes within a cell."190 To do this. we relate the euergey calculated froii the observed iustautauceous pliase space configuration to the ensemble average euereics in quasi-equilibriuni," To do this, we relate the energy calculated from the observed instantaneous phase space configuration to the ensemble average energies in quasi-equilibrium."191 This hiehlliehts the fact that chisters of ealaxics are not iu strict equilibrimm and hence their poteutial and kinetic cuergies fluctuate about the eusenible average cnerey., This highlights the fact that clusters of galaxies are not in strict equilibrium and hence their potential and kinetic energies fluctuate about the ensemble average energy.192 The spatial configurations of clusters change as a result of these fluctuations., The spatial configurations of clusters change as a result of these fluctuations.193 Because the average thermocdvuamic quantities of an eusenible of cells iu quasiequilibriuumi change very slowly compared to the ανασα timescale of a single cell. the quasi-equilibriuim energies are approximately time averages.," Because the average thermodynamic quantities of an ensemble of cells in quasi-equilibrium change very slowly compared to the dynamical timescale of a single cell, the quasi-equilibrium energies are approximately time averages."194 We use the spectrum of fluctuations to determine the probability that a cell may have a particular mstantaneous virial ratio., We use the spectrum of fluctuations to determine the probability that a cell may have a particular instantaneous virial ratio.195 This is a uccessary but not sufficient coudition for a cell to lave a given configuration., This is a necessary but not sufficient condition for a cell to have a given configuration.196 To compare different coufigurationus. we therefore compare the probability that a cell has a virial ratio which could eive rise to a given configuration.," To compare different configurations, we therefore compare the probability that a cell has a virial ratio which could give rise to a given configuration."197 Based on the range of fluctuations in virial ratio observed in N-body simulations by Aarsetl&Saslaw (1972). we conclude that cells that have a ποσανο specific leat may have almost anv spatial configuration.," Based on the range of fluctuations in virial ratio observed in $N$ -body simulations by \citet{1972ApJ...172...17A}, we conclude that cells that have a negative specific heat may have almost any spatial configuration."198 These configurations are likely to be chance configurations of fuctuating cells that are nearly vinalized., These configurations are likely to be chance configurations of fluctuating cells that are nearly virialized.199 Cells with positive specific heat have a rauge of eucreies corresponding to fewer spatial configurations., Cells with positive specific heat have a range of energies corresponding to fewer spatial configurations.200 Iu our comparisons between line aud rug configurations. the probability that a cell will have a line coufiguration rather than a ring configuration varies depending ou the clustering parameter 6 and the nuuber JN of subclusters in the cell.," In our comparisons between line and ring configurations, the probability that a cell will have a line configuration rather than a ring configuration varies depending on the clustering parameter $b$ and the number $N$ of subclusters in the cell."201 Therefore we prescut the following procedure for comparing the shapes of two clusters: The first step is to define a region of space that covers the cluster., Therefore we present the following procedure for comparing the shapes of two clusters: The first step is to define a region of space that covers the cluster.202 The size aud shape of this region of space define the cell size., The size and shape of this region of space define the cell size.203 Within the cell. identity the subelusters whose masses are within an order of niaenitude of the largest subchister.," Within the cell, identify the subclusters whose masses are within an order of magnitude of the largest subcluster."204 The positions of these subclusters aro directly related to the scaled potential energy Ws of the claster., The positions of these subclusters are directly related to the scaled potential energy $W_*$ of the cluster.205 Frou the observed W. or the peculiar velocity information. estimate the virial ratio c.," From the observed $W_*$ or the peculiar velocity information, estimate the virial ratio $\psi$."206 The next step is to use the cell size to calculate the ΠΟ aud variance of the counts-in-cclls distribution of similarly-sized subclusters for a larger saurple to obtain the clustering parameter b (e.g. Sivakotf&Saslaw2005:Yaug&Saslaw 2011)).," The next step is to use the cell size to calculate the mean and variance of the counts-in-cells distribution of similarly-sized subclusters for a larger sample to obtain the clustering parameter $b$ (e.g. \citealt{2005ApJ...626..795S,2011ApJ...729..123Y}) )."207 Then using the observed paramcters c and b. calculate the probability of finding a cell with a similar virial ratio using equation(78).," Then using the observed parameters $\psi$ and $b$, calculate the probability of finding a cell with a similar virial ratio using equation."208. This probability should then be compared to a reference cell that has a different structure to deteriuiue the relative probabilities of different configurations., This probability should then be compared to a reference cell that has a different structure to determine the relative probabilities of different configurations.209 Although the configurations that we use here are highly idealized. our comparison of a line aud a ring configuration is generallv consistent with observations of the cosmic web.," Although the configurations that we use here are highly idealized, our comparison of a line and a ring configuration is generally consistent with observations of the cosmic web."210 This simple test of our theory gives a reasonable result., This simple test of our theory gives a reasonable result.211 We intend to make more detailed comparisons with observations and more realistic cases which may include dark matter in a forthcoming paper., We intend to make more detailed comparisons with observations and more realistic cases which may include dark matter in a forthcoming paper.212 We wish to acknowledge the preliminary work of Chuah Boon Leng who helped explore some of the concepts discussed in this paper., We wish to acknowledge the preliminary work of Chuah Boon Leng who helped explore some of the concepts discussed in this paper.213 We also wish to thank Phil Chan and Bernard Leong for many helpful discussions on this topic., We also wish to thank Phil Chan and Bernard Leong for many helpful discussions on this topic.214 To illustrate the effect of having multiple mass compouents iu a cluster. we consider the case where a cluster has two populations of subclusters.," To illustrate the effect of having multiple mass components in a cluster, we consider the case where a cluster has two populations of subclusters."215 For simplicity. we assume that these subclusters are poiut masses. and the masses of cach subchister are iy and ie with 227ny for subchisters iu each population.," For simplicity, we assume that these subclusters are point masses, and the masses of each subcluster are $m_1$ and $m_2$ with $m_2 > m_1$ for subclusters in each population."216 Iu such a cluster. we can consider the interactions of particles from each population such that the total potential of the cluster is (c.f.," In such a cluster, we can consider the interactions of particles from each population such that the total potential of the cluster is (c.f."217 Equation 503) where the superscripts denote members of the different populations. aud x denotes position.," Equation \ref{eq-PEBinary}) ) where the superscripts denote members of the different populations, and $\mathbf{x}$ denotes position."218 The three terms iu equation come from considering each mass component as a separate system. and adding their mutual iuteractious.," The three terms in equation come from considering each mass component as a separate system, and adding their mutual interactions."219 Therefore. equation is similar in form to equation(50).. even though we do not place any constraints on tle positions of mdividual particles.," Therefore, equation is similar in form to equation, even though we do not place any constraints on the positions of individual particles."220 We can take the average of the sums in equation such that where Ny aud No are the mumbers of particles in cach population. and (1/7515 is the average inverse separation between members of population 1.," We can take the average of the sums in equation such that where $N_1$ and $N_2$ are the numbers of particles in each population, and $\langle 1/r^{(1)} \rangle$ is the average inverse separation between members of population 1."221 Iu the case where both populations are similarly distributed throughout the cell. the," In the case where both populations are similarly distributed throughout the cell, the"222"Each of our hierarchical models shows a very wide range of extinction optical depths }} and scattering (7,4)) when the nebula is viewed from various directions.",Each of our hierarchical models shows a very wide range of extinction optical depths ) and scattering ) when the nebula is viewed from various directions.223 The ancl Observed for a reflection nebula represent a view of the dust [rom one direction., The and observed for a reflection nebula represent a view of the dust from one direction.224 There is a very wide range of optical properties (à.g) that can [it a given observation.," There is a very wide range of optical properties $a,\,g$ ) that can fit a given observation."225 Will one or more hierarchical models we can fit the best observed UV reflection nebula.7023.. with albedos > 0.5 over the range of g thal we tested (0.6 /— 0.85) and with a variety of averaged optical depths through the mocel.," With one or more hierarchical models we can fit the best observed UV reflection nebula, with albedos $\ge$ 0.5 over the range of $g$ that we tested (0.6 – 0.85) and with a variety of averaged optical depths through the model."226 In general. reflection nebulae have substantial optical depths ~ 1—3) otherwise. the scattered Iuxes are too faint.," In general, reflection nebulae have substantial optical depths $\sim1-3$ ); otherwise, the scattered fluxes are too faint."227 At substantial optical depths. uniform models ean underestimate the albedo rather severely because they overestimate the scattered light.," At substantial optical depths, uniform models can underestimate the albedo rather severely because they overestimate the scattered light."228 Unless the star happens to be embedded within a dense clump. radiation can leak oul of hierarchical clumps much more easily than from uniform dust.," Unless the star happens to be embedded within a dense clump, radiation can leak out of hierarchical clumps much more easily than from uniform dust."229 The Diffuse Galactic Light (DGL) has been interpreted (IIenry. 2002) with a recipe that predicts much more scattering Irom each star than our models. resulting in a low estimates ol the UV albedo.," The Diffuse Galactic Light (DGL) has been interpreted (Henry 2002) with a recipe that predicts much more scattering from each star than our models, resulting in a low estimates of the UV albedo."230 Murthy et al. (, Murthy et al. (2311991) failed to detect UV. DGL. but our fractal models olten have many directions from whieh the star and scattered light are very faint.,"1991) failed to detect UV DGL, but our fractal models often have many directions from which the star and scattered light are very faint."232 Thus. we do not believe that the faintness of the DGL in particular directions necessarily signifies a low albedo.," Thus, we do not believe that the faintness of the DGL in particular directions necessarily signifies a low albedo."233 The determination of both @ and g depends upon the variation of reflected intensity across the face of a centrally illuminated reflection nebula. while we have only considered the [αν of the seattered light.," The determination of both $a$ and $g$ depends upon the variation of reflected intensity across the face of a centrally illuminated reflection nebula, while we have only considered the flux of the scattered light."234 We feel that if the flux is as weakly constrained as our models show. (he intensity will be similarly subject to variation because of the unknown placement of the star relative to the surrounding dust.," We feel that if the flux is as weakly constrained as our models show, the intensity will be similarly subject to variation because of the unknown placement of the star relative to the surrounding dust."235 Even the relative variation of albedo with wavelength is difficult to determine from reflection nebulae if there are significant changes in opacitv among the waveleneths., Even the relative variation of albedo with wavelength is difficult to determine from reflection nebulae if there are significant changes in opacity among the wavelengths.236 The problem is that Che geometry is not really the same when the opacity changes., The problem is that the geometry is not really the same when the opacity changes.237 As opacity per IL atom increases. opticallv thin chunps become thick and scatter light with a different eeonmeltrical arrangement. so the geometry of the nebula depends on wavelength.," As opacity per H atom increases, optically thin clumps become thick and scatter light with a different geometrical arrangement, so the geometry of the nebula depends on wavelength."238 Our overall assessment is that the optical properties of grains are probably as well constrained by (heorv as by observations., Our overall assessment is that the optical properties of grains are probably as well constrained by theory as by observations.239 This statement is made in spite of well-known uncertainties in the theory of interstellar grains., This statement is made in spite of well-known uncertainties in the theory of interstellar grains.240 These uncertainties are major: whether (vpical large grains are chemically homogeneous (e.g.. silicate or carbonaceous) or composite. whether grains contain voids. or if grains have very loose (“fractal”) structure.," These uncertainties are major: whether typical large grains are chemically homogeneous (e.g., silicate or carbonaceous) or composite, whether grains contain voids, or if grains have very loose (“fractal”) structure."241 However. theory does not permit the large range of possible albedos provided bv reflection nebulae.," However, theory does not permit the large range of possible albedos provided by reflection nebulae."242 Al fist glance. various theories seem quite different.," At first glance, various theories seem quite different."243 Weingartner Draine (2001) have, Weingartner Draine (2001) have244The VVDS-Deep sample is magnitude limited in the Iap band with 17.5€Ine<24 and covers an area of 0.49 deg? without any color or shape restrictions imposed.,"The VVDS-Deep sample is magnitude limited in the $I_{AB}$ band with $17.5 \le I_{AB} \le 245 24$ and covers an area of 0.49 $deg^2$ without any color or shape restrictions imposed."246" ''he spectroscopic observations were taken with the Visible Multiple-Object Spectrograph (VIMOS, Le Févvre et al."," The spectroscopic observations were taken with the Visible Multiple-Object Spectrograph (VIMOS, Le Fèvvre et al."247" 2003) at the ESO VLT, whereas the Virmos Deep Imaging survey (VDIS) BVRI photometric data (LeFévreetal.2004) was obtained with the wide field 12k mosaic camera at the CFHT (Canada-France-Hawaii telescope) and is complete and free from surface brightness selection effects (McCrackenetal.2003)."," 2003) at the ESO VLT, whereas the Virmos Deep Imaging survey (VDIS) BVRI photometric data \citep{lef04} was obtained with the wide field 12k mosaic camera at the CFHT (Canada-France-Hawaii telescope) and is complete and free from surface brightness selection effects \citep{mcc03}."248". 'The sample contains 6582 galaxies with secure redshifts, ie. known at a confidence level >80%."," The sample contains 6582 galaxies with secure redshifts, i.e. known at a confidence level $\ge 80 \%$."249 These galaxies have a mean redshift of z = 0.83., These galaxies have a mean redshift of z $\approx$ 0.83.250 Fig., Fig.251" 1 shows the absolute magnitude of these galaxies as a function of redshift alongwith the different luminosity-threshold subsamples selected, where the luminosity threshold is assumed to evolve according to the relation Mp(z)=—1.15z+Mp(z0)."," \ref{FigMvsZ} shows the absolute magnitude of these galaxies as a function of redshift alongwith the different luminosity-threshold subsamples selected, where the luminosity threshold is assumed to evolve according to the relation $M_B(z)252 = -1.15z + M_B(z=0)$."253" The factor of ’-1.15’ arises from the redshift evolution of the characteristic absolute magnitude, Mg, of galaxies as measured in the luminosity function."," The factor of '-1.15' arises from the redshift evolution of the characteristic absolute magnitude, $M_B^*$, of galaxies as measured in the luminosity function."254 This value has been determined using the luminosity function measurements obtained within the same sample by Ilbert et al. (, This value has been determined using the luminosity function measurements obtained within the same sample by Ilbert et al. (2552005).,2005).256" An evolving luminosity threshold needs to be taken into consideration when comparing samples at different epochs, as it provides us with statistically similar samples at different redshifts, having similar evolved luminosities."," An evolving luminosity threshold needs to be taken into consideration when comparing samples at different epochs, as it provides us with statistically similar samples at different redshifts, having similar evolved luminosities."257" Assuming that the global evolution of galaxies has as a main consequence to increase the global luminosity of galaxies, we follow the evolution of galaxies with similar properties on average."," Assuming that the global evolution of galaxies has as a main consequence to increase the global luminosity of galaxies, we follow the evolution of galaxies with similar properties on average."258 This falls within the boundaries of standard practice of galaxy evolution studies., This falls within the boundaries of standard practice of galaxy evolution studies.259" As our subsamples are nearly volume complete, and as we are using all types of galaxies together, we may follow the global increase in the halo mass of an average galaxy."," As our subsamples are nearly volume complete, and as we are using all types of galaxies together, we may follow the global increase in the halo mass of an average galaxy."260" However, we do recognize that this way of selecting galaxies does not garantee to follow the exact same population with cosmic time."," However, we do recognize that this way of selecting galaxies does not garantee to follow the exact same population with cosmic time."261" Unfortunately, there is no single prescription enabling to tag galaxies and exactly follow their precursors / descendants."," Unfortunately, there is no single prescription enabling to tag galaxies and exactly follow their precursors / descendants."262" Indeed, if this were possible it would be the solution to galaxy evolution."," Indeed, if this were possible it would be the solution to galaxy evolution."263" To try to quantify the impact of our selection on the average halo mass, we have used the Millennium simulation."," To try to quantify the impact of our selection on the average halo mass, we have used the Millennium simulation."264 This will be further discussed in the next section., This will be further discussed in the next section.265" Samples using a similar type of selection, i.e. using ]uminosity thresholds, have been extensively studied within a theoretical framework (Zehavietal.2005;Coil2006;Conroyetal.2006;Zheng 2007)."," Samples using a similar type of selection, i.e. using luminosity thresholds, have been extensively studied within a theoretical framework \citep{zeh05, coi06, con06, zhe07}."266". The corresponding HOD parametrisation requires fewer parameters to be fitted as compared to differential, luminosity binned samples."," The corresponding HOD parametrisation requires fewer parameters to be fitted as compared to differential, luminosity binned samples."267" However, this means that one is biased towards increasingly brighter galaxies at higher redshifts, simply due to the fact that the sample is selected in apparent magnitude."," However, this means that one is biased towards increasingly brighter galaxies at higher redshifts, simply due to the fact that the sample is selected in apparent magnitude."268" As can be seen in Fig. 1,"," As can be seen in Fig. \ref{FigMvsZ},"269 there is a change of about 5 in the B-band absolute magnitude over the redshift, there is a change of about 5 in the B-band absolute magnitude over the redshift270ü The search for extrasolar planets has garnered enormous attention in recent vears. due primarily to the successtul Huplementation of radial velocity searches (Alavor& 1995.. Marev&Butler 1996)).," The search for extrasolar planets has garnered enormous attention in recent years, due primarily to the successful implementation of radial velocity searches \cite{mandq1995}, \cite{mandb1996}) )."271 These searches have led to the discovery of a population of massive. close-in planets with orbital separations of e<0.1AU.," These searches have led to the discovery of a population of massive, close-in planets with orbital separations of $a \la 0.1~\au$."272 Recently. it was discovered that one such planet. the companion to IID 209158. also trausits its parent star (Clarbouneauetal. 2000: Παινetal. 2000)). vielding a measurement of the lass. radius. aud deusitv of the companion.," Recently, it was discovered that one such planet, the companion to HD 209458, also transits its parent star \cite{charbon2000}; \cite{henry2000}) ), yielding a measurement of the mass, radius, and density of the companion."273 Clearly. transit observations can be used to extract additional information about known companions.," Clearly, transit observations can be used to extract additional information about known companions."274 Thediscovery of an extrasolar —planet using transits. however. has remained elusive.," The of an extrasolar planet using transits, however, has remained elusive."275 There are two primary difficultics with detecting plauets with trausits., There are two primary difficulties with detecting planets with transits.276" First. the photometric requireiieuts are quite stringent: a planct of radius. fh,Ry (ποσο Ry isthe radius of Jupiter) transiting an primary of radius AH.=HR. would produce a fractional deviation of z1% during the course of the transit."," First, the photometric requirements are quite stringent: a planet of radius $\rp\le\rjup$ (where $\rjup$ isthe radius of Jupiter) transiting an primary of radius $\rs=\rsun$ would produce a fractional deviation of $\la 1\%$ during the course of the transit."277 Second. the probability that a planet will trausit its parent is small: for a planet with separation z0.05AU orbiting a star with AR.=R.. the probability is <10.," Second, the probability that a planet will transit its parent is small: for a planet with separation $\ge 0.05~\au$ orbiting a star with $\rs=\rsun$, the probability is $\la 10\%$."278 Several methods for dealing will the small probability have been proposed., Several methods for dealing will the small probability have been proposed.279 For instance. one can monitor eclipsing binary stars. where the orbital plane is known to be (nearly) perpendicular to the sky (Deceetal. 1998)).," For instance, one can monitor eclipsing binary stars, where the orbital plane is known to be (nearly) perpendicular to the sky \cite{deeg}) )."280 Another wav of overcoming this small probability is to siuplv mouitor many stars sinultaneouslv., Another way of overcoming this small probability is to simply monitor many stars simultaneously.281 This can be doue by euiploviug a camera with a laree field-of-view. or by inonitoring very deuse stellar fields.," This can be done by employing a camera with a large field-of-view, or by monitoring very dense stellar fields."282 Were I focus on the latter possibility., Here I focus on the latter possibility.283 Specifically I determine the uuuber of planets that imieht be detected in a campaign monitorine stars toward the Galactic bulee., Specifically I determine the number of planets that might be detected in a campaign monitoring stars toward the Galactic bulge.284" The dux of a star beiug occulted by a plauct is given by. where Fy is the unocculted flux of the star. Fy, is the total flux from auv unrelated sources. aud ó(£) is the fractional deviation of the flux due to the transit. which depends on the radius of the plauct relative to the star. the inclination angle. 7. aud the lamh-darkening of the star (Sackett 1999))."," The flux of a star being occulted by a planet is given by, where $F_0$ is the unocculted flux of the star, $F_b$ is the total flux from any unrelated sources, and $\delta(t)$ is the fractional deviation of the flux due to the transit, which depends on the radius of the planet relative to the star, the inclination angle, $i$, and the limb-darkening of the star \cite{sackett1999}) )."285" For a small planet «f.) aud no liuib-darkeniug. ó=(RV/Rοι.r)Lwhere(74, O7) is the step functiou. and 7 is à normalized tine. 7=(f.ty)/fr."," For a small planet $\rp \ll \rs$ ) and no limb-darkening, $\delta=(\rp/\rs)^2\Theta(1-\tau)$, where $\Theta(x)$ is the step function, and $\tau$ is a normalized time, $\tau \equiv {({ t-t_0}) / \tt}$."286" Tere fy is the time of the midpoint of the transit. aud fT is one-half the transit duration. which for circular orbits 15. Tu reality. 6 depends very scusitively on 74, aud cosi. and less so on the liiib-darkeniug."," Here $t_0$ is the time of the midpoint of the transit, and $\tt$ is one-half the transit duration, which for circular orbits is, In reality, $\delta$ depends very sensitively on $\rp$ and $\ci$, and less so on the limb-darkening."287 I will therefore use the explicit form for ó eiven iu Sackett (1999). but πιο uo Iuub-darkening.," I will therefore use the explicit form for $\delta$ given in Sackett (1999), but assume no limb-darkening."288" Since the proposed search for plauets will be carried out iu dense stellar fields. and transits produce time-dependent varlatious in the flux of the stars. the data will likely be reduced with inage-ubtraction techniques (Tomancy&Crotts 1996.. Alard&Lupton 0051),"," Since the proposed search for planets will be carried out in dense stellar fields, and transits produce time-dependent variations in the flux of the stars, the data will likely be reduced with image-subtraction techniques \cite{tandc1996}, , \cite{andlup1998}) )."289 With imaee-subtraction. oue mcasures only the time variable portion of the 8ux. F(t)=Fy|étt)].," With image-subtraction, one measures only the time variable portion of the flux, ${\tilde F(t)}=F_0[\delta(t)]$."290 There are three requirements to detect a plauet of separation e aud radius Πρ around a star of mass M. radius ΠΠ. aud flux Fy.," There are three requirements to detect a planet of separation $a$ and radius $\rp$ around a star of mass $M$, radius $\rs$ and flux $F_0$ ."291 These are: (1) the planet must transit the star. (2) at least two transits nist occur duiug the time when observations are made. aud(3) the transit must cause a detectable deviation in the lieht curve.," These are: (1) the planet must transit the star, (2) at least two transits must occur during the time when observations are made, and(3) the transit must cause a detectable deviation in the light curve."292 If the, If the293outo massive syste.,onto massive systems.294 Timing our attention to the evolution of the maxima stellar mass. as shown iu the bottom panels. similar treuds are apparent.," Turning our attention to the evolution of the maximum stellar mass, as shown in the bottom panels, similar trends are apparent."295 While the maxiuun mass in the cooling moclel iucreases monotonically. the ACN feedback model is divided iuto two regions: oue at high redshift in which the maxim stellar mass mereases aloug with the nonlinear lass scale. and one at low redshift in which the maxi stellar mass stays fixed as the scale at which new ealaxics are formuug becomes snaller.," While the maximum mass in the cooling model increases monotonically, the AGN feedback model is divided into two regions: one at high redshift in which the maximum stellar mass increases along with the nonlinear mass scale, and one at low redshift in which the maximum stellar mass stays fixed as the scale at which new galaxies are forming becomes smaller."296 The general properties of cooling aud ACN feedback iodels are sununuarized iu Table 1., The general properties of cooling and AGN feedback models are summarized in Table 1.297" Finally, we poiut out that not only the temporal. but thespatial distribution of AGN in our feedback model is suggestive of recent observations."," Finally, we point out that not only the temporal, but the distribution of AGN in our feedback model is suggestive of recent observations."298 Usiug over 20.000 ealaxies from the 2dF QSO Redshift Survey. Croom (2005) have studied the spatial clustering of QSOs near the characteristic scale in the optical Iuninositv function.," Using over 20,000 galaxies from the 2dF QSO Redshift Survey, Croom (2005) have studied the spatial clustering of QSOs near the characteristic scale in the optical luminosity function."299" ""They measure bias values which. when converted iuto (+) values using standard expressious (Mo White 1996). evolve frou 2.5characte0.9 at 2=2.18 clown to 1.1€0.2 at dowusizine=0.56.The ristic scale of low-redshift Αν is from the rarest to the most. common objects. spreading the heated eas that extinguishes the formation of galaxies to this dax."," They measure bias values which, when converted into $\nu(z)$ values using standard expressions (Mo White 1996), evolve from $2.5 \pm 0.2$ at $z=2.48$ down to $1.1 \pm 0.2$ at $z=0.56.$ The characteristic scale of low-redshift AGN is downsizing from the rarest to the most common objects, spreading the heated gas that extinguishes the formation of galaxies to this day."300 We thank Biman Nath. Chis Reynolds. and Toimasso Treu for helpful comments.," We thank Biman Nath, Chris Reynolds, and Tomasso Treu for helpful comments."301 This work was initiated duriug a visit bv JS to the KITP as part of the Galaxs-ICM Tuteractious Program., This work was initiated during a visit by JS to the KITP as part of the Galaxy-IGM Interactions Program.302 ES was supported by the NSF under erant PITY99-07919., ES was supported by the NSF under grant PHY99-07949.303"The minimum photon energy needed to produce muons with energy E, in the atmosphere is E75,~10xΕμ.",The minimum photon energy needed to produce muons with energy $E_{\mu}$ in the atmosphere is $E_{\gamma th} \sim 10 \times E_{\mu}$.304" In the Tupi experiment the muon energy threshold is estimated as Ej,~0.1GeV.", In the Tupi experiment the muon energy threshold is estimated as $E_{\mu} \sim 0.1GeV$.305" It means that the minimum proton energy is Ez,~1.0GeV.", It means that the minimum proton energy is $E_{\gamma th} \sim 1.0GeV$.306" However, Monte Carlo results Porieretal.(2002) showed that an effective photon energy threshold for muon production in the atmosphere is E44,~10GeV (see Fig. 5))."," However, Monte Carlo results \cite{poirier02} showed that an effective photon energy threshold for muon production in the atmosphere is $E_{\gamma th}\sim 10 GeV$ (see Fig. \ref{fig5}) )."307" The specific yield function, i.e. the number of muons at sea level per photon, as a function of photon energy near the vertical direction, is determined according to the FLUKA Monte Carlos results Porieretal.(2002)."," The specific yield function, i.e. the number of muons at sea level per photon, as a function of photon energy near the vertical direction, is determined according to the FLUKA Monte Carlos results \cite{poirier02}."308". This FLUKA result can be described by the following fit Ay=(6.16==0.60)x1075, y=1.183+0.014, Eo=7.13+0.56 GeV, A=1.5840.12."," This FLUKA result can be described by the following fit where $A_\mu = (6.16 \pm 0.60) \times 10^{-5}$, $\nu=1.183 \pm 0.014$, $E_0=7.13 \pm 0.56$ GeV, $\lambda=1.58 \pm3090.12$."310" We whereassumed that at the top of the atmosphere the energy spectrum of the arrived photons (from GRB) with E.> 10GeV) can be expressed by a single power law function The total number of muons with energies above Εμ covering an effective area Serf at the sea level, during time T, is a convolution between Eq.2 (or Eq.3) and Eq.4,"," We assumed that at the top of the atmosphere the energy spectrum of the arrived photons (from GRB) with $E_{\gamma}\geq 10GeV$ ) can be expressed by a single power law function The total number of muons with energies above $E_{\mu}$ covering an effective area $S_{eff}$ at the sea level, during time T, is a convolution between Eq.2 (or Eq.3) and Eq.4,"311"by the Chandra observatory, and computed the frequency band-averaged SZ flux decrement in the frequency interval [86 GHz, 94 GHz].","by the Chandra observatory, and computed the frequency band-averaged SZ flux decrement in the frequency interval [86 GHz, 94 GHz]."312 The ALMA telescope will observe at a frequency 90 GHz with higher sensitivity and resolution than that of the GBT; comparison the sensitivity of the GBT with the ALMA telescope has already been, The ALMA telescope will observe at a frequency 90 GHz with higher sensitivity and resolution than that of the GBT; comparison the sensitivity of the GBT with the ALMA telescope has already been.313 In Fig., In Fig.314" [I] we show thestudied]. dependence of the generalized spectral function G(x,T.) at a frequency 90 GHz (x=1.59), derived from Eq. (5))"," \ref{Fig90} we show the dependence of the generalized spectral function $G(x, T_{\mathrm{e}})$ at a frequency 90 GHz (x=1.59), derived from Eq. \ref{G}) )"315 on temperature., on temperature.316 We find that the absolute value of the generalized spectral function at a frequency 90 GHz significantly (and monotonically) decreases with electron temperature., We find that the absolute value of the generalized spectral function at a frequency 90 GHz significantly (and monotonically) decreases with electron temperature.317 The Kompaneets approximation is valid when the change of a photon frequency due to Compton scattering is much smaller than an initial photon frequency Av/v«1., The Kompaneets approximation is valid when the change of a photon frequency due to Compton scattering is much smaller than an initial photon frequency $\Delta\nu/\nu\ll1$.318" Since the average photon frequency change per inverse Compton scattering equals Av/v=4kyT./(m.c?) (for non-relativistic electrons, see, e. g., Rybicki Lightman 1979), the Kompaneets approximation is invalid when kyT,=(mec?)/4, i.e. when kyT,~128keV."," Since the average photon frequency change per inverse Compton scattering equals $\Delta\nu/\nu=4k_{\mathrm{b}} T_{\mathrm{e}}/(m_{\mathrm{e}}319c^2)$ (for non-relativistic electrons, see, e. g., Rybicki Lightman 1979), the Kompaneets approximation is invalid when $k_{\mathrm{b}} T_{\mathrm{e}}\simeq (m_{\mathrm{e}}c^2)/4$, i.e. when $k_{\mathrm{b}} T_{\mathrm{e}}\simeq 128 \mathrm{keV}$."320" Thus, strong deviations from the intensity value (and from the spectral function value of g(1.59)& —3.28) derived in the Kompaneets approximation arise at high temperatures."," Thus, strong deviations from the intensity value (and from the spectral function value of $g(1.59)\approx-3.28$ ) derived in the Kompaneets approximation arise at high temperatures."321" The given estimate of the regime of breakdown of the Kompaneets approximation is an approximation and significant deviations (although not of order unity) take place at much lower temperatures, even at 30 keV (e.g. Fabbri 1981)."," The given estimate of the regime of breakdown of the Kompaneets approximation is an approximation and significant deviations (although not of order unity) take place at much lower temperatures, even at 30 keV (e.g. Fabbri 1981)."322" An interesting feature of the SZ effect is that at frequency 217 GHz (x=3.83) where the SZ effect in the framework of the Kompaneets approximation is zero, the SZ effect from an AGN cocoon is dominated by the high temperature electron component (Τε>10° K)."," An interesting feature of the SZ effect is that at frequency 217 GHz (x=3.83) where the SZ effect in the framework of the Kompaneets approximation is zero, the SZ effect from an AGN cocoon is dominated by the high temperature electron component $T_{\mathrm{e}}\gg 10^8$ K)."323" Therefore, the SZ effect at frequency 217 GHz is an interesting tool for analyzing the hot electron component in AGN cocoons."," Therefore, the SZ effect at frequency 217 GHz is an interesting tool for analyzing the hot electron component in AGN cocoons."324 Note that Colafrancesco (2005) has considered a measurement of the SZ effect at a frequency 217 GHz to analyze a non-thermal electron component in radio lobes., Note that Colafrancesco (2005) has considered a measurement of the SZ effect at a frequency 217 GHz to analyze a non-thermal electron component in radio lobes.325" Since the value of G(3.83,Τε) is small when the temperature is either much lower than 10? K or higher than 1010 K, we conclude that this function should have an absolute maximum at an intermediate temperature."," Since the value of $G(3.83,326T_{\mathrm{e}})$ is small when the temperature is either much lower than $10^{8}$ K or higher than $10^{10}$ K, we conclude that this function should have an absolute maximum at an intermediate temperature."327" Dependence of the generalized spectral function G(x,Τε) at a frequency 217 GHz (x=3.83) on temperature derived from Eq. (6))"," Dependence of the generalized spectral function $G(x,328T_{\mathrm{e}})$ at a frequency 217 GHz (x=3.83) on temperature derived from Eq. \ref{G}) )"329 is shown in Fig. D]., is shown in Fig. \ref{Fig217}.330" The extremum of a curve G(3.83,Το) is at a temperature T,~160 keV (51.9x10? K) which is in the temperature range found from numerical simulations of cocoons."," The extremum of a curve $G(3.83, T_{\mathrm{e}})$ is at a temperature $T_{\mathrm{e}}\approx 160$ keV $\approx 1.9\times10^9$ K) which is in the temperature range found from numerical simulations of cocoons."331 Therefore analysis of the SZ effect at this frequency should be a promising way of demonstrating the existence of an electron component at high temperature., Therefore analysis of the SZ effect at this frequency should be a promising way of demonstrating the existence of an electron component at high temperature.332 Note that combined generalized functions defined in Sect., Note that combined generalized functions defined in Sect.333 2.2 are also shown in Fig. D]., 2.2 are also shown in Fig. \ref{Fig217}.334 Measurements at the frequency of 217 GHz are sensitive to the spectral response of the detectors., Measurements at the frequency of 217 GHz are sensitive to the spectral response of the detectors.335 In Appendix B we show how the broad detector spectral response impacts on the possibility of an analysis of high temperature plasmas., In Appendix B we show how the broad detector spectral response impacts on the possibility of an analysis of high temperature plasmas.336 In Sect., In Sect.337" 2.2, we investigate the possibility of constraining the properties of high energy particle populations by means of SZ intensity measurements at two frequencies."," 2.2, we investigate the possibility of constraining the properties of high energy particle populations by means of SZ intensity measurements at two frequencies."338 Measurements of the SZ effect at a frequency 217 GHz is a unique way of revealing a population of mildly relativistic electrons in AGN cocoons if the intensity distortion is observed at a single frequency., Measurements of the SZ effect at a frequency 217 GHz is a unique way of revealing a population of mildly relativistic electrons in AGN cocoons if the intensity distortion is observed at a single frequency.339" We propose below a new method for excluding the contribution from the low energy, non-relativistic electrons to the SZ effect by means of observations at two frequencies."," We propose below a new method for excluding the contribution from the low energy, non-relativistic electrons to the SZ effect by means of observations at two frequencies."340" By αι,Χο,Το), we denote a combined generalized spectral function which corresponds to a relativistic contribution to the generalized function at a frequency x; taking into account a measurement at a frequency x2 and is defined as At low temperatures T,«105 K, the limiting case http://safe.nrao.edu/wiki/bin/view/GBT/GBTSensitivityComparison(1) holds (see Sect."," By $C (x_{1}, x_{2}, T_{e})$, we denote a combined generalized spectral function which corresponds to a relativistic contribution to the generalized function at a frequency $x_{1}$ taking into account a measurement at a frequency $x_{2}$ and is defined as At low temperatures $T_{\mathrm{e}}\ll 10^8$ K, the limiting case (1) holds (see Sect."341" 2.1) and, therefore the combined"," 2.1) and, therefore the combined"342We have searched for quiescent. persistent. radio emission from the northern hemisphere supersoft X-ray sources. and taken a high resolution image of the one known source with emission.,"We have searched for quiescent, persistent radio emission from the northern hemisphere supersoft X-ray sources, and taken a high resolution image of the one known source with emission."343 We have improved the radio positions. source size and Hux from the persistent emitter AG Dra with MIEILIN.," We have improved the radio positions, source size and flux from the persistent emitter AG Dra with MERLIN."344 The core is resolved at the milliaresee scale into two components with a combined [lux of  1000 μ.]ν., The core is resolved at the milliarcsec scale into two components with a combined flux of $\sim$ 1000 $\umu$ Jy.345 Lt is possible that the core detected in the VLA image has significant nebulosity and is resolved out. by the higher ALERLIN resolution., It is possible that the core detected in the VLA image has significant nebulosity and is resolved out by the higher MERLIN resolution.346 A possible south component. detected: by the VLA was unconfirmed. although this could be due to it having a Hux lower than the noise in the ALERLIN image. or also being resolved out.," A possible south component detected by the VLA was unconfirmed, although this could be due to it having a flux lower than the noise in the MERLIN image, or also being resolved out."347 No new emission was detected from RN JOOL9S|2156 To Pyx and V1974 Cvgni down to a la RAIS noise level of around .20 [Jy n.," No new emission was detected from RX J0019.8+2156, T Pyx and V1974 Cygni down to a $\sigma$ RMS noise level of around 20 $\umu$ Jy $^{-1}$."348 No. emissionos was detected from⋅ any oeviouslv known Galactic or extragalactic source in the 3. 104 square aresec fields imaged. and we place upper-IHimits o radio emission from these sources.," No emission was detected from any previously known Galactic or extragalactic source in the 3, 104 square arcsec fields imaged, and we place upper-limits to radio emission from these sources."349 We have investigated: possible causes of radio emission rom a wind environment. both directly from the secondary star. and also as à consequence of the high X-ray. luminosity. rom the WD.," We have investigated possible causes of radio emission from a wind environment, both directly from the secondary star, and also as a consequence of the high X-ray luminosity from the WD."350" A total of 17 new point-sources were imaged with Iuxes oetween LOL) and 1500 s an estimate to the density of sources with a flux > ""0 b. wy of2) per square degree. at 5 Cillz. in this region sky."," A total of 17 new point-sources were imaged with fluxes between 100 and 1500 $\umu$ Jy giving an estimate to the density of sources with a flux $>$ 100 $\umu$ Jy of 200 per square degree, at 5 GHz, in this region of the sky."351 RNO wishes to thank the hospitality of the ALERLIN national facility at the Jodrell Bank Observatory. especially ‘Yom Muxlow.," RNO wishes to thank the hospitality of the MERLIN national facility at the Jodrell Bank Observatory, especially Tom Muxlow."352 SC acknowledges support from erant. F/00-A from the Leverhulme Trust., SC acknowledges support from grant F/00-180/A from the Leverhulme Trust.353 The tional liadio Astronomy Observatory ds à facility of theNational Science Foundation operated: under cooperative agreement by Associateck Universities. Inc. ALERLIN is a national facility operated by the University of Manchester on behalf of PPARC.," The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. MERLIN is a national facility operated by the University of Manchester on behalf of PPARC."354 This research has mace use of the SIMIAD database. operated at CDS. Strasbourg. France," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France"355Classification. ⊲⋅⊀⊀in astronomy has ο to many advances which. iive revealed important. informationun. about the UniverseD. in. which. we live.,Classification in astronomy has led to many advances which have revealed important information about the Universe in which we live.356. For. example. the classification⊲⋅⊀ of stars w their. colours ancl brightnesses. in. the Llertzsprung-; wor . ↘⊔⊳∖⊳∖∢⋅⊔∖↓∐↘∃∠⊔⋜↧⋏∙≟↓⋅⋜⋯↓↓∢⊾∠⇂⋯⋜⋯⊔⊔∠⇂⋖⊾↓⋅⊳∖⇂⋜⋯∠⊔⊔⋏∙≟∪⇂⊳∖∩⋅∐⋜⊔⋅⋅ structure and. evolution.," For example, the classification of stars by their colours and brightnesses in the Hertzsprung-Russel (HR) diagram led to an understanding of stellar structure and evolution."357. sThe It undiagram continues. to »: employed as a means to to determine. the ages and metallicitesD. of. stellar populations.. whether they are simple. stellar populations. as in globular clusters. or in composite »opulations. such as dwarf galaxies (?2?27)..," The HR diagram continues to be employed as a means to to determine the ages and metallicites of stellar populations, whether they are simple stellar populations, as in globular clusters, or in composite populations, such as dwarf galaxies \citep{Dolphin2003, 358Monelli2010, Williams2010}."359 Even when it is impossible to resolve stars. entire galaxies are classified w their colours and magnitudes.," Even when it is impossible to resolve stars, entire galaxies are classified by their colours and magnitudes."360 However. galaxies display resolved structure anc morphology that stars do not. and using this morphology can reveal much about the evolution of galaxies.," However, galaxies display resolved structure and morphology that stars do not, and using this morphology can reveal much about the evolution of galaxies."361 Early methods. used. for the classification of galaxies were based on morphology., Early methods used for the classification of galaxies were based on morphology.362 The ? Classification System is a method. used to categorise. galaxies. by their. morphology. ancl although it: has been the dominant: morphological. tool since. the mid-1920s.:5 over time. it. has proven to be deficientD. . ↓⊔⊳∖∢⊾∖⇁⋖⋅↓⋅⋜↧," The \citet{Hubble1926} Classification System is a method used to categorise galaxies by their morphology, and although it has been the dominant morphological tool since the mid-1920s, over time it has proven to be deficient in several areas."363↓⋜⊔⋅⋖⊾⋜↧⊳∖⊳⇀∖↓≻↓⋅∪⊔∐⊔∢⋅⊔↿∠⊔⊳∖⋯⇂∖⇁⋜⋯↿⋜↧⋏∙≟∢⊾∩⊓∼↓⋜↧⊳∖⊳∖↓⇂∙∖⇁↓⊔⋏∙≟. . VEN ealaxies. based on their. morphological. features⋅ alone is. that it Do.is subjective⊲⊀ with. respect to distance: (or resolution). ancl inclination., A prominent disadvantage to classifying galaxies based on their morphological features alone is that it is subjective with respect to distance (or resolution) and inclination.364"⋠⋠⋠ Furthermore∖ it⋠ has led to the grouping⋠ of⋅ a wide⋠ range of⋅ asymmetric. galaxies. as simply. .""irregularL", Furthermore it has led to the grouping of a wide range of asymmetric galaxies as simply “irregular”.365 As both ground- and space-based imaging has improved. and we probe higher redshifts. it has become apparent that classilving galaxies as “irregular” means ignoring a vast amount of. morphological information.," As both ground- and space-based imaging has improved, and we probe higher redshifts, it has become apparent that classifying galaxies as “irregular” means ignoring a vast amount of morphological information."366 ? attempted. to improve upon the 7 Classification System bv introducing “later ἵνρο as a sub-class of galaxies: however. this system still refers to. local. axisvmametric ealaxies as reference points. and. again. was based solely on morphology.," \citet{deVaucouleurs1959} attempted to improve upon the \citet{Hubble1926} Classification System by introducing “later types” as a sub-class of galaxies; however, this system still refers to local, axisymmetric galaxies as reference points, and, again, was based solely on morphology."367(sceBeckert&Duschl2004).. one finds an upper limit for the cloud size and a corresponding mass llere c is the cloud-internal speed. of pressure waves which is of the order of Tkms+.,"\citep[see][]{Bec04}, one finds an upper limit for the cloud size and a corresponding mass Here $c_{\rm s}$ is the cloud-internal speed of pressure waves which is of the order of $1\,{\rm km\,s^{-1}}$."368 We use this value as the unit for ὃς in the following., We use this value as the unit for $\csound$ in the following.369 This speed. characterizes the cloud. internal pressure whichis required to balance. self-gravity. and can be understood. as the speed. of supersonic turbulence in the clouds.," This speed characterizes the cloud internal pressure whichis required to balance self-gravity, and can be understood as the speed of supersonic turbulence in the clouds."370 Alternatively. the clouds may be magnetically supported+.," Alternatively, the clouds may be magnetically supported."371 Due to their large cross section. these clouds dominante the absorption. scattering. and. LR re-emission.," Due to their large cross section, these clouds dominante the absorption, scattering, and IR re-emission."372 From the relations for Z4 and. Aa. we get an upper envelope for the opacity of Hep=OTAyon(eMIT).," From the relations for $\Rcl$ and $\Mcl$, we get an upper envelope for the opacity of $\kappa_{\rm cl}= 0.7\kappa_0 \cdot \rpc^{3/2}/(\csound \Msev^{1/2})$."373 The distance from the black hole re is measured in pc and the speed c in km +., The distance from the black hole $\rpc$ is measured in pc and the speed $c_{\rm s}$ in km $^{-1}$.374 For clouds smaller than the shear limit. the opacity ποxLy becomes smaller.," For clouds smaller than the shear limit, the opacity $\kappa_{\rm cl}\propto \Rcl$ becomes smaller."375 With Eqn. (1)).," With Eqn. \ref{Ledd_classic}) ),"376 we obtain the IEddington limit for clouds in a clumipy torus. which are directly exposed to the primary ACN radiation. This is of the same order as in the classical Eddington limit (Eqn. 2))," we obtain the Eddington limit for clouds in a clumpy torus, which are directly exposed to the primary AGN radiation, This is of the same order as in the classical Eddington limit (Eqn. \ref{Ledd_std}) )"377 and is consistent with observed ACN luminosities and. black hole masses., and is consistent with observed AGN luminosities and black hole masses.378 Since LopXxX5s+ the Ecelington limit lor small clouds is even Larger than in Eqn. (7)).," Since $\Ledd \propto \kappa^{-1}$, the Eddington limit for small clouds is even larger than in Eqn. \ref{Ledd_clumpy}) )."379 Eqn.: - (7)), Eqn. \ref{Ledd_clumpy}) )380 shows that LiiilixrBIDο This o, shows that $\Lecl \propto r^{-3/2}$.381culosimplies. that at larger distances. ποσαν>αποe clouds which are directly exposedὃν to the AGN radiation. become unbound by the raciation pressure.," This implies that at larger distances, self-gravitating clouds which are directly exposed to the AGN radiation become unbound by the radiation pressure."382 Εις. distant clouds have to be shielded against the AGN radiation by clouds at. small radii.," Thus, distant clouds have to be shielded against the AGN radiation by clouds at small radii."383 As a consequence. there should be no significant vertical Daring for a clumpy torus: i.e... we expect ἐνzconst.," As a consequence, there should be no significant vertical flaring for a clumpy torus; i.e., we expect $H/r\approx{\rm const}$."384 Further consequences of this behaviour will be discussed in Sect. ??.., Further consequences of this behaviour will be discussed in Sect. \ref{Lhigh}.385 In the previous section. we argued that the Eddington imit for clumpwv dust tori is well in agreement with the range of observed AGN luminosities and black hole masses.," In the previous section, we argued that the Eddington limit for clumpy dust tori is well in agreement with the range of observed AGN luminosities and black hole masses."386 To be clumpy. a torus requires a small volume filling factor by<< or the dusty clouds.," To be clumpy, a torus requires a small volume filling factor $\pv\ll1$ for the dusty clouds."387" In the context of a SA model. BeckertDuschl(2004) find a mass transport rate through the orus Adpagusπμ, where v=IG-a is the elective viscosity for a torus and X is the surface H7Ok&Rdensity."," In the context of a SA model, \citet{Bec04} find a mass transport rate through the torus $\Mdtor = 3 \pi \nu \Sigma$, where $\nu= \frac{\tau}{1+\tau^2} H^2 \Omega_{\rm Kepler}$ is the effective viscosity for a torus and $\Sigma$ is the surface density."388 For an obscuring torus. the scale height. 44. cannot be smaller than the mean free path of clouds. {4ft=(4/34ὧν.," For an obscuring torus, the scale height, $H$, cannot be smaller than the mean free path of clouds $H \ge l = (4/3)R_{\rm cl}/\pv$."389 Otherwise the torus would become transparent for GIN photons., Otherwise the torus would become transparent for AGN photons.390 The parameter 7 in the viscosity. prescription measures the ratio 7=f/f., The parameter $\tau$ in the viscosity prescription measures the ratio $\tau=l/H$.391 Phe ecometric thickness of the torus and the viscosity is maximised for 7=1., The geometric thickness of the torus and the viscosity is maximised for $\tau = 1$.392 For ff/ the cloud density in the torus growth rapidly and the torus would collapse to a thin disk., For $H \gg l$ the cloud density in the torus growth rapidly and the torus would collapse to a thin disk.393 We therefore adopt Lf=f for a working mocel., We therefore adopt $H=l$ for a working model.394 After replacing the mean free path by the appropriate expression from Beckert&Duschl(2004)... we eet d in terms of Aqua The volume filling factor only depends on the mass transport rate through the torus. which we parametrized by Alans=O41.veLas:(gr/0.05)+ (soe Sect; 2)).," After replacing the mean free path by the appropriate expression from \citet{Bec04}, we get $\pv$ in terms of $\Mdtor$, The volume filling factor only depends on the mass transport rate through the torus, which we parametrized by $\Mdtor=0.4\,\Msy\times L_{45}\cdot(\eta\tau/0.05)^{-1}$ (see Sect. \ref{EddLimTor}) )."395 ὃν substituting Aa we obtain ahard lower luminosity for the existence of an obscuring torus according to the SA model. at which dy=1.," By substituting $\Mdtor$, we obtain ahard lower luminosity for the existence of an obscuring torus according to the SA model, at which $\pv=1$."396 For clumpy obscuring tori as described. it is necessary that the ACN luminosity is £7» dine ," For clumpy obscuring tori as described, it is necessary that the AGN luminosity is $L\gg L_{\rm low}$ ."397WEL&Ling. the volume filling factor becomes ο...," If $L \ga L_{\rm low}$, the volume filling factor becomes $\pv\rightarrow1$."398 At this point. theSA model would require that the torus collapses to a geometrically thin disk.," At this point, theSA model would require that the torus collapses to a geometrically thin disk."399 As a consequence. most of the cust would be driven away (see Sect. 22)).," As a consequence, most of the dust would be driven away (see Sect. \ref{sdd}) )."400 Lt is. however. known that this situation can be avoided: Lower Iuminosities &o along with lower accretion rates.," It is, however, known that this situation can be avoided: Lower luminosities go along with lower accretion rates."401 Vollmeretal.(2004) showed that for low mass accretion rate. a ¢lumpy ancl almost transparent (f>> Lf) circumnuclear clisk (CND) can form similar to what hasbeen found around the central black hole in our Galaxy (Ciüstenetal. 1987)..," \citet{Voll04} showed that for low mass accretion rate, a clumpy and almost transparent $l \gg H$ ) circumnuclear disk (CND) can form similar to what hasbeen found around the central black hole in our Galaxy \citep{Gue87}. ."402 Phe cüllerence between the clumpy torus and the CND is that the latter one loses most of its obscuration properties while there can still be LR. reprocessing., The difference between the clumpy torus and the CND is that the latter one loses most of its obscuration properties while there can still be IR reprocessing.403 Several observational studies show that at/ about 1077ergs tthe Lia Lsun- or Lx Lsun-relation show a significant change in behaviour compared to. higher luminosities (e...Lutzetal.2004:Llorstct2006).," Several observational studies show that at about $10^{42}\,\ergs$, the $L_{\rm bol}-L_{\rm MIR}$ - or $L_{\rm X}-L_{\rm MIR}$ -relation show a significant change in behaviour compared to higher luminosities \citep[e.g.,][]{Lut04,Hor06}."404. Apparently. the main source of MIIU emission at Lo—1077ergs is not the proposed. geometrically thick torus anymore.," Apparently, the main source of MIR emission at $L\sim10^{42}\,\ergs$ is not the proposed, geometrically thick torus anymore."405 AX similar low-luminosity limit has been found for models where the cust clouds are not. produced in a torus but released into a wind from an aceretion disk(Elitzur&Shlosman 2006)., A similar low-luminosity limit has been found for models where the dust clouds are not produced in a torus but released into a wind from an accretion disk\citep{Eli06}.406. Phe eutolT at lower Iuminositios is a result of the fact that the mass outflow rate in the wind cannot exceed the mass acerction rate in the disk., The cutoff at lower luminosities is a result of the fact that the mass outflow rate in the wind cannot exceed the mass accretion rate in the disk.407 Taking the same T and g as used in Elitzur&Shlosman (2006). we obtain Lys—20007eres ," Taking the same $\tau$ and $\eta$ as used in \citet{Eli06}, , we obtain $L_{\rm low}=2\times10^{42}\,\ergs$ ."408In Sect. ??7.. ," In Sect. \ref{clumpytorus}, ,"409we have shown that the Eddington luminosity ⋠⋠⋅for clouds in. the clumpy torus.ili £44. depends on the cloud-ACN distance as r ," we have shown that the Eddington luminosity for clouds in the clumpy torus,$\Lecl$ , depends on the cloud-AGN distance as $r^{-3/2}$ ."410A large [fraction, A large fraction411decrement as the only likely explanation.,decrement as the only likely explanation.412 This assumption is at odds. with the standard. AGN unified model. and deserves some further discussion., This assumption is at odds with the standard AGN unified model and deserves some further discussion.413 In what follows we address 10 question on whether 111320|551 is consistent with an bsorbed/reddened type Ll Sevfert or not., In what follows we address the question on whether H1320+551 is consistent with an absorbed/reddened type 1 Seyfert or not.414 Word et al (1988) studied the Balmer decrement of rw tvpe L AGN in the Piecinotti ct al (1982) sample., Ward et al (1988) studied the Balmer decrement of the type 1 AGN in the Piccinotti et al (1982) sample.415 The eood linear correlation. between Balmer decrement versus 10 ratio between 2-10 keV luminosity (mostly. unallected ον reddening/absorption) and 11:3 luminosity (a &ood tracer NW absorption) prompted Ward. ct al. (1988) to. suggest wt Balmer decrement is determined by nuclear reddening. rather than being intrinsic to the DL1It (see their fig.," The good linear correlation between Balmer decrement versus the ratio between 2-10 keV luminosity (mostly unaffected by reddening/absorption) and $\beta$ luminosity (a good tracer of absorption) prompted Ward et al (1988) to suggest that Balmer decrement is determined by nuclear reddening, rather than being intrinsic to the BLR (see their fig."416 4)., 4).417 Thev also find an approximately constant 2-10 keV to Ia ratio for the sample (see their Fig., They also find an approximately constant 2-10 keV to $\alpha$ ratio for the sample (see their Fig.418 5)., 5).419 In fact. Ward ct al (1988) conclude that in spite of the extreme conditions of he BLR. the intrinsic Balmer clecrement is ~3.5 for the vpe 1 AGNs.," In fact, Ward et al (1988) conclude that in spite of the extreme conditions of the BLR, the intrinsic Balmer decrement is $\sim 3.5$ for the type 1 AGNs."420 Now. 111320|551 has a Balmer clecrement which is more han half à decade larger than what would. be expected rom its 2-10 keV to L3 ratio.," Now, H1320+551 has a Balmer decrement which is more than half a decade larger than what would be expected from its 2-10 keV to $\beta$ ratio."421 Reddening correction will not ing this into agreement with the Sevfert Ls. as both the Balmer decrement and the X-ray. to 11.1 ratio will decrease if reddening corrected.," Reddening correction will not bring this into agreement with the Seyfert 1s, as both the Balmer decrement and the X-ray to $\beta$ ratio will decrease if reddening corrected."422 On the contrary. the 2-10 keV. to llo ratio is entirely consistent with that of the Sevfert s.," On the contrary, the 2-10 keV to $\alpha$ ratio is entirely consistent with that of the Seyfert 1s."423 All that means that the large BLE. decrement for this particular Seyfert 1.8/1.9. together with its unabsorbecl X-rav spectrum cannot be explained as a Sevfert 1 AGN viewed through obscuring material.," All that means that the large BLR decrement for this particular Seyfert 1.8/1.9, together with its unabsorbed X-ray spectrum cannot be explained as a Seyfert 1 AGN viewed through obscuring material."424" XMM-Newton X-ray observations of the 111320|551. which is classified by its optical spectrum as a type L1.8/1.9 ACN, reveal no absorption."," XMM-Newton X-ray observations of the H1320+551, which is classified by its optical spectrum as a type 1.8/1.9 AGN, reveal no absorption."425 Lf the non-simultaneous optical ancl X-ray observations both trace the true state of this source. we conclude that the large Balmer decrement of the BLR. which determines its 1.8/1.9 spectroscopic type. is not due to reddening by clusty absorbing material along the line of sight.," If the non-simultaneous optical and X-ray observations both trace the true state of this source, we conclude that the large Balmer decrement of the BLR, which determines its 1.8/1.9 spectroscopic type, is not due to reddening by dusty absorbing material along the line of sight."426" A variety of models can explain a large intrinsic value of the Balmer decrement. among them the failure of the standard. “case Bo recombination"" and/or optically thick BLR clouds."," A variety of models can explain a large intrinsic value of the Balmer decrement, among them the failure of the standard “case B recombination” and/or optically thick BLR clouds."427 In any case. the AGN unified mocoel fails completely in this source.," In any case, the AGN unified model fails completely in this source."428 Regardless on whether the unusual opticalN-rav absorption properties of 111320|551 are due to variations or not. they raise an important issue for unified ACN models for the N-rav. background.," Regardless on whether the unusual optical/X-ray absorption properties of H1320+551 are due to variations or not, they raise an important issue for unified AGN models for the X-ray background."429 1113201551 is a source with a relatively soft. unabsorbed N-rav. spectrum that. ds expected to typically have a type LXGN optical counterpart., H1320+551 is a source with a relatively soft unabsorbed X-ray spectrum that is expected to typically have a type 1 AGN optical counterpart.430 Llowever. we identify it with a Sevfert. 1.8/1.9.. breaking again the one-to-one identification between X-ray absorption and optical obscuration that the NLRB models use.," However, we identify it with a Seyfert 1.8/1.9, breaking again the one-to-one identification between X-ray absorption and optical obscuration that the XRB models use."431 Similarly. other relatively soft X-ray sources with no X-ray absorption might have optical counterparts which deviate from the standard: Sevfert 1 character.," Similarly, other relatively soft X-ray sources with no X-ray absorption might have optical counterparts which deviate from the standard Seyfert 1 character."432 LE the DLIU properties are not alwavs linked to the absorption clisplaved by ACN. then Seyfert 1.8/1.9/2. galaxies might appear as optical counterparts of soft. X-ray selected sources as well as type 1 Sevferts often appear as optical counterparts to hard. X-ray SOULCOS.," If the BLR properties are not always linked to the absorption displayed by AGN, then Seyfert 1.8/1.9/2 galaxies might appear as optical counterparts of soft X-ray selected sources as well as type 1 Seyferts often appear as optical counterparts to hard X-ray sources."433 We are grateful to Steve Sembay and Martin Turner for help with EPIC calibration issues., We are grateful to Steve Sembay and Martin Turner for help with EPIC calibration issues.434 Phe referee is also thanked for important suggestions on the original version of this paper., The referee is also thanked for important suggestions on the original version of this paper.435 The WIUE telescope is operated on the island of La Palma by the Isaac Newton Croup of Telescopes in the spanish Observatorio del Roque de Los Muchachos of the Instituto de sica de Canarias., The WHT telescope is operated on the island of La Palma by the Isaac Newton Group of Telescopes in the spanish Observatorio del Roque de Los Muchachos of the Instituto de sica de Canarias.436 Partial financial support for this work was provided by the Spanish Ministry of Science and Technology uncler project AY.A2000-1690., Partial financial support for this work was provided by the Spanish Ministry of Science and Technology under project AYA2000-1690.437and extend our use of clusters as tools for cosmology (Haiman.Mohr.&Holder2001).,and extend our use of clusters as tools for cosmology \citep{hai01}.438. At the lower end of the mass scale. Chandra anc XMM-Nesston will permit the poorer. lower luminosity clusters anc groups (svstems wilh temperatures <2 keV) to be systematically detected for the first time to redshilis of a lew tenths.," At the lower end of the mass scale, Chandra and XMM-Newton will permit the poorer, lower luminosity clusters and groups (systems with temperatures $<2$ keV) to be systematically detected for the first time to redshifts of a few tenths."439 Previous survevs for these svstems have often had to rely on prior optical catalogs. complicating the estimation of statistical completeness and bias (Aluichaev&Zabludolf1995).," Previous surveys for these systems have often had to rely on prior optical catalogs, complicating the estimation of statistical completeness and bias \citep{mul98}."440. A common aspect of X-ray group and cluster surveys has been the frequent. (although nol universal) choice of a pass-band trom 0.5-2keV. Such a band typically helps minimize the contribution of soft Galactic emission. and harder particle background. while maximizing sensitivitv to general cluster emission (MeLEucdyοἱal.1993:Rosatiet1995).," A common aspect of X-ray group and cluster surveys has been the frequent (although not universal) choice of a pass-band from 0.5-2keV. Such a band typically helps minimize the contribution of soft Galactic emission, and harder particle background, while maximizing sensitivity to general cluster emission \citep{mch98,ros95}."441. Previous imaging X-rav observatories have also not had the good spectral resolution of Chandra or XMM-Newton. so the choice of band was less controllable.," Previous imaging X-ray observatories have also not had the good spectral resolution of Chandra or XMM-Newton, so the choice of band was less controllable."442 In this short paper I present a set of simple calculations aimed at determining a set of optimal pass-bands for thermal plasmas over a range of temperatures and redshifts., In this short paper I present a set of simple calculations aimed at determining a set of optimal pass-bands for thermal plasmas over a range of temperatures and redshifts.443 I also demonstrate the relationship to the commonly used 0.5-2 keV band. and argue that [uture survevs of cooler svstems must take the band-pass explicitly into account. or risk seriously biasing (heir estimates of the space density of such svstenis.," I also demonstrate the relationship to the commonly used 0.5-2 keV band, and argue that future surveys of cooler systems must take the band-pass explicitly into account, or risk seriously biasing their estimates of the space density of such systems."444 The signal-to-noise criterion | use here is S/VN. where S is the source photon count. AN is the appropriate backeround count.," The signal-to-noise criterion I use here is $S/\sqrt N$, where $S$ is the source photon count, $N$ is the appropriate background count."445 This is chosen as a decent. approximation to the various [forms ol detection significance criteria used in X-ray survevs [or extended. sources., This is chosen as a decent approximation to the various forms of detection significance criteria used in X-ray surveys for extended sources.446 Typically. a mean background count per skv area is estimated. and the deviation of the count rale in a given area. minus the background. is compared to the statistical (usually. Poisson) fInetuation in the background over that area.," Typically, a mean background count per sky area is estimated, and the deviation of the count rate in a given area, minus the background, is compared to the statistical (usually Poisson) fluctuation in the background over that area."447 A typical background spectrum is derived across the full instrument. band-pass by combining high Galactic latitude data (<nif>~1x 107!) in which bright sources and periods of high particle background (flares) have heen removed.," A typical background spectrum is derived across the full instrument band-pass by combining high Galactic latitude data $<nH>\sim 1\times44810^{21}$ ) in which bright sources and periods of high particle background (flares) have been removed."449 For Chandra. the data was culled by combining archival fields ancl (he online background data.," For Chandra, the data was culled by combining archival fields and the online background data."450 Similarly. for NMM. archival PV data and online background data was utilized.," Similarly, for XMM, archival PV data and online background data was utilized."451 The background spectrum is derived by binning photons from the entire field-of-view and perlorming a simple. linear.," The background spectrum is derived by binning photons from the entire field-of-view and performing a simple, linear,"452because By= Oat r=BD),because $B_\theta \ne 0$ at $r=R(t)$.453 Phe shell and (lux rope solutions have perfectly rellecting solutions in which the total energy in rcAF) is conserved., The shell and flux rope solutions have perfectly reflecting solutions in which the total energy in $r<R(t)$ is conserved.454 I. means that the solutions are energy eigenstates of the svstem., It means that the solutions are energy eigenstates of the system.455 The eigenstates can be obtained by adjusting the parameter A., The eigenstates can be obtained by adjusting the parameter $k$.456 In this paper. we obtained solutions for freely expanding magnetic loops. te. Def)!=0.," In this paper, we obtained solutions for freely expanding magnetic loops, i.e., $Dv / Dt = 0$."457 We assumed that the magnetic loops have sulliciently large energy to drive the expansion., We assumed that the magnetic loops have sufficiently large energy to drive the expansion.458 When the ux function ;l increases with time. the toroidal magnetic fieles will also increase with time.," When the flux function $\tilde{A}$ increases with time, the toroidal magnetic fields will also increase with time."459 Phe toroidal magnetic fields will then allect the dynamics through the magnetic pressure., The toroidal magnetic fields will then affect the dynamics through the magnetic pressure.460 Such solutions can describe the accelerating magnetic loops., Such solutions can describe the accelerating magnetic loops.461 Magnetic fields can be expressed as the sum of the Fourier modes in the polar angle., Magnetic fields can be expressed as the sum of the Fourier modes in the polar angle.462 Phe modes and their amplitudes should be determined at the boundary where the magnetic twist is injected on the surface of the star., The modes and their amplitudes should be determined at the boundary where the magnetic twist is injected on the surface of the star.463" H0 is not shown but we can construct more complex solutions that the poloidal magnetic fields are expressed by the sum of the Fourier modes. i... .1xsin""@ "," It is not shown but we can construct more complex solutions that the poloidal magnetic fields are expressed by the sum of the Fourier modes, i.e., $\tilde A \propto \sin^n \theta$."464In actual explosion. the opening angle of the expanding magnetic loops depends on the location at which the magnetic twist is injected on the surface of the central star.," In actual explosion, the opening angle of the expanding magnetic loops depends on the location at which the magnetic twist is injected on the surface of the central star."465 Such a solution may be expressed as the sum of the Fourier nmiocdes for the poloidal and toroidal magnetic fields., Such a solution may be expressed as the sum of the Fourier modes for the poloidal and toroidal magnetic fields.466 We should note that SCR Mares are not necessarily axisvmmetric., We should note that SGR flares are not necessarily axisymmetric.467 Models including the non-axisvmmetrically expanding magnetic loops will be a subject of future works., Models including the non-axisymmetrically expanding magnetic loops will be a subject of future works.468 We are erateful to the anonymous referee for constructive comments improving the paper., We are grateful to the anonymous referee for constructive comments improving the paper.469 Fruitful discussions with Tomovuki Ianawa. Akira Mizuta. and Tomohisa Ixawashima at Chiba University are greatly appreciated.," Fruitful discussions with Tomoyuki Hanawa, Akira Mizuta, and Tomohisa Kawashima at Chiba University are greatly appreciated."470 This work was supported by the Grants-in-Aid for Scientific Research of Ministry of Education. Culture. Sports. Science. and Technology (11:20340040).," This work was supported by the Grants-in-Aid for Scientific Research of Ministry of Education, Culture, Sports, Science, and Technology (RM:20340040)."471pulse is extracted. trom the reference signal bv a high speed (lip-flop ancl fed into a field xoerammable eate array (FPGA).,pulse is extracted from the reference signal by a high speed flip-flop and fed into a field programmable gate array (FPGA).472 This FPGA develops all of the various timing signals used in the antenna., This FPGA develops all of the various timing signals used in the antenna.473 There are two tvpes of svnthesizers in the svstem (Figure 3))., There are two types of synthesizers in the system (Figure \ref{fig:if}) ).474 The LO signals to the receivers and/or converters for all bands except X-band are produced. by a conventional Yttrium Iron Garnet (YIG) oscillator that is phase locked to a harmonic of the 512 MIIz relerence. offset bv the 128 MlIIz reference. which produces tones in the Lrequency range of 11.776 Gllz to 19.968 GIIz in 256 MlIz steps.," The LO signals to the receivers and/or converters for all bands except X-band are produced by a conventional Yttrium Iron Garnet (YIG) oscillator that is phase locked to a harmonic of the 512 MHz reference, offset by the 128 MHz reference, which produces tones in the frequency range of 11.776 GHz to 19.968 GHz in 256 MHz steps."475 Since the outputs of these svnthesizers are used as the first (and in some cases second) LO. the svuthesizers ave designed to produce exceptionally clean. low phase noise CW signals with minimal harmonics.," Since the outputs of these synthesizers are used as the first (and in some cases second) LO, the synthesizers are designed to produce exceptionally clean, low phase noise CW signals with minimal harmonics."476 This is especially critical flor the Ix. Ίνα and Q band receivers where the LO is multiplied by an additional factor of two or three inside the receiver.," This is especially critical for the K, Ka and Q band receivers where the LO is multiplied by an additional factor of two or three inside the receiver."477 The LO signals to the main downconverters are generated by the second (wpe of saithesizers (FigureES 3))., The LO signals to the main downconverters are generated by the second type of synthesizers (Figure \ref{fig:if}) ).478 These units are unique microwave svnthesizers based on two YIG oscillators and two direct digital svnthesizer (DDS) chips., These units are unique microwave synthesizers based on two YIG oscillators and two direct digital synthesizer (DDS) chips.479 The svnthesizers produce tones in the Irequency range of 10.8 Gllz to 14.3 Giz in microhertz steps., The synthesizers produce tones in the frequency range of 10.8 GHz to 14.8 GHz in microhertz steps.480 The design of this svnüthesizer was verv challenging because the phase of ils output signal was required to be controllable as the lrequencey is changed., The design of this synthesizer was very challenging because the phase of its output signal was required to be controllable as the frequency is changed.481 The fine tuning requirement for (he svnthesizer was necessary for the transition mode operation of the EVLA system., The fine tuning requirement for the synthesizer was necessary for the transition mode operation of the EVLA system.482 In this mode. the very fine tuning capability of the svnthesizer is used to produce a differential rate between antennas to allow the interlerometer [ringes to track (he source.," In this mode, the very fine tuning capability of the synthesizer is used to produce a differential rate between antennas to allow the interferometer fringes to track the source."483 The EVLA data transmission svstem (DTS) dieitizes the IF signals at the antennas and transmits them to the correlator located in the central control building., The EVLA data transmission system (DTS) digitizes the IF signals at the antennas and transmits them to the correlator located in the central control building.484 The DTS consists of a formatter module in the antenna. optical fibers between (he antenna and the control building. and deformatters in the control building (Figure 5)).," The DTS consists of a formatter module in the antenna, optical fibers between the antenna and the control building, and deformatters in the control building (Figure \ref{fig:dts}) )."485 The deformatters also include signal processing circuiüry and cdigitial-Lo-analog converters to allow (he digital data produced bv the EVLA antennas to be processed bv the analog inputs to the existing VLA correlator during the (transition period., The deformatters also include signal processing circuitry and digitial-to-analog converters to allow the digital data produced by the EVLA antennas to be processed by the analog inputs to the existing VLA correlator during the transition period.486 The data path from the antenna to the control building can be summarized as follows., The data path from the antenna to the control building can be summarized as follows.487 An EVLA receiver can provide an instantaneous bandwidth of up to 3 GlIz in each of two polarizations., An EVLA receiver can provide an instantaneous bandwidth of up to 8 GHz in each of two polarizations.488 The receiver output is partitioned into eight. 2 Giz wide. IF bands bv the svstem (Figure 5 shows (wo of the eight bands).," The receiver output is partitioned into eight, 2 GHz wide, IF bands by the LO-IF system (Figure \ref{fig:dts} shows two of the eight bands)."489 Each IF band can be sampled with 4 Gllz, Each IF band can be sampled with 4 GHz4902010)).,).491" The leus galaxy redshift (τη) range is 0.05<2,<0.5. with a median of uo0.2."," The lens galaxy redshift $z_{l}$ ) range is $0.05\leq z_l\leq4920.5$, with a median of $z_{l} \sim 0.2$."493 Our ο is selected: 1) to have a measured Dumstem radius in Table 3 of A|09. 2) to be classified as elliptical or SU. 3) to have a measured V-band effective radius (anecasured at the intermediate axis).," Our sample is selected: 1) to have a measured Einstein radius in Table 3 of A+09, 2) to be classified as elliptical or S0, 3) to have a measured $V$ -band effective radius (measured at the intermediate axis)."494 Of the 85 lenses from this latest SLACS release. 66 passed our selection criteria.," Of the 85 lenses from this latest SLACS release, 66 passed our selection criteria."495 Asa lc0 comparison sample. we use the collection of 330 ETCs over the same mass rauge analyzed iu T|09 and NRTLO.," As a $z\sim0$ comparison sample, we use the collection of 330 ETGs over the same mass range analyzed in T+09 and NRT10."496 To estimate stellar qmass-to-light ratios (Y.) aud star formation bistorics. we analyze spectral energy distributions (SEDs) based on broad-baud Sloan Digital Sky Survey (SDSS) photometry (uameh. grit).," To estimate stellar mass-to-light ratios $\Upsilon_\star$ ) and star formation histories, we analyze spectral energy distributions (SEDs) based on broad-band Sloan Digital Sky Survey (SDSS) photometry (namely, $ugriz$ )."497 Our general procedure is to adopt a set of syvuthetic spectra from the prescription of Druzual&Charlot(2003).. a uuiform ietallicity Z. an age f characterizing the time of star formation onset. and au exponcutially declining star formation rate with timescale 7.," Our general procedure is to adopt a set of synthetic spectra from the prescription of \citet{BC03}, a uniform metallicity $Z$, an age $t$ characterizing the time of star formation onset, and an exponentially declining star formation rate with timescale $\tau$."498 For cach galaxy. Z.t. aud 7 are fitted parameters. with the determined Y. based on a EKroupa(2001) IME: uncertainties ou the estimated parameters have been quantified via Moute Carlo simulations: further details are provided iu T109 aud NRTIO alone wit1 explorations of «ποιατς uncertainties and degencracjes.," For each galaxy, $Z$ , $t$, and $\tau$ are fitted parameters, with the determined $\Upsilon_{\star}$ based on a \citet{Kroupa01} IMF; uncertainties on the estimated parameters have been quantified via Monte Carlo simulations: further details are provided in T+09 and NRT10 along with explorations of systematic uncertainties and degeneracies."499 The oulv change here is to shift the spectral resonses of the SDSS flters to correspond to the lous redshifts before couvolving with the model SEDs., The only change here is to shift the spectral responses of the SDSS filters to correspond to the lens redshifts before convolving with the model SEDs.500 We ave checked that inposiug restrictions on Z or r. or adosting the stellar populations results from A|}09 or Cailoetal.(2009).. does not qualitatively affect the resuls described below.," We have checked that imposing restrictions on $Z$ or $\tau$, or adopting the stellar populations results from A+09 or \citet{Grillo+09}, does not qualitatively affect the results described below."501 We derive the deprojected total mass from dyaiunies and lensing observables. and separate the DAL from the stellar componcuts using the stellar mass estimates discussed in the previous section.," We derive the deprojected total mass from dynamics and lensing observables, and separate the DM from the stellar components using the stellar mass estimates discussed in the previous section."502 We adopt the stellar effective radius. aas the fiducial reference poiut for mass comparisons., We adopt the stellar effective radius as the fiducial reference point for mass comparisons.503 For the leus galaxies. is measured. in. the V-baud. corresponcdiug approximately to the rest-frame D-bandused for the local galaxies.," For the lens galaxies, is measured in the $V$ -band, corresponding approximately to the rest-frame $B$ -bandused for the local galaxies."504 Iu both galaxy samples. the mass constraints are ecnerally based on icasurements at sanaller radii (~OLR aud ~O.5 Rog. respectively). aud therefore some extrapolation is required.," In both galaxy samples, the mass constraints are generally based on measurements at smaller radii $\sim 0.1 \Re$ and $\sim 0.5 \Re$ , respectively), and therefore some extrapolation is required."505 For the total lass distribution we adopt a singular isothermal sphere (SIS) with density p(r)=σαι.(2xGi?) (o.@. etal— 2006.. Cavazzictal.—.(2007.. IKoopiuausetal. 20093). where oup is an unknown normalization to be determined by fitting the observables.," For the total mass distribution we adopt a singular isothermal sphere (SIS) with density $\rho(r) = \sigma_{\rm SIS}^{2} / (2 \pi G506r^{2})$ (e.g. \citealt{SLACS3}, , \citealt{Gavazzi07}, \citealt{Koopmans+09}) ), where $\sigma_{\rm SIS}$ is an unknown normalization to be determined by fitting the observables."507 For the stars. we adopt a constant-Y. mass profile based on the (1990) model.," For the stars, we adopt a $\Upsilon_*$ mass profile based on the \citet{H90} model."508" To estimate dynamical masses we have used the SDSS stellar velocity dispersious σωμα. nieasured within a circulus aperture of R4,=1.5%."," To estimate dynamical masses we have used the SDSS stellar velocity dispersions $\sigma_{\rm SDSS}$ , measured within a circular aperture of $R_{\rm ap} = 1.5''$."509" Briefly, we have adopted the spherical Jeaus equation to derive the surface brightuess weighted velocity dispersion 0,318 within R4, (see T|09 for further details}. to be matched to Capss."," Briefly, we have adopted the spherical Jeans equation to derive the surface brightness weighted velocity dispersion $\sigma_{\rm ap,SIS}$ within $R_{\rm ap}$ (see T+09 for further details), to be matched to $\sigma_{\rm SDSS}$."510 As discussed in T]09. there is some deeree of svsteiiatic uncertainty from asswuptions of sphericity and orbital isotropy. which we can now check in the case of the lenses by using the independent leusine- asses (Gvhieh do have their own uncertainties from mass-sheoet deeeueracies).," As discussed in T+09, there is some degree of systematic uncertainty from assumptions of sphericity and orbital isotropy, which we can now check in the case of the lenses by using the independent lensing-based masses (which do have their own uncertainties from mass-sheet degeneracies)."511" For the lensing mass estimates. we have used the Einstein radiusRe. to derive a model independent measurement of projected inass (νο). withinfig. since Mg=Afni(RE)zBNet. where Meat=eD,IxGD;Dji,. with Dy. D; aud Dj, the observer - source. observer - lens aud leus - source comoving aueular diameter distances. respectively,"," For the lensing mass estimates, we have used the Einstein radius, to derive a model independent measurement of projected mass $M_{\rm proj}$ ) within, since $M_{E}=M_{\rm proj}(\RE) = \pi512\RE^{2} \Sigma_{\rm crit}$, where $\Sigma_{\rm crit} = c^{2}513D_{s}/4 \pi G D_{l} D_{ls}$ , with $D_{s}$, $D_{l}$ and $D_{ls}$ the observer - source, observer - lens and lens - source comoving angular diameter distances, respectively."514 Finally we match the svediction of the SIS model projected mass. Muisis with Mr to have a further coustraiut on the ouly free uodel parazuueter for cach galaxy. yyy.," Finally we match the prediction of the SIS model projected mass, $M_{proj,SIS}$ with $M_{E}$ to have a further constraint on the only free model parameter for each galaxy, $\sigma_{\rm SIS}$."515" The best fitted ayy can be derived indepeudently usine either technique to estimate the best 3D deprojected uass profile which we extrapolate to r=Ruy to obtain our reference mass values,", The best fitted $\sigma_{\rm SIS}$ can be derived independently using either technique to estimate the best 3D deprojected mass profile which we extrapolate to $r = \Re$ to obtain our reference mass values.516 Using this approach. we fud hat lensing and dvuamics provide consistent results. nodulo a ~ (and a scatter of ~25%) higher mass roni dvnanucs. correspouding to a change of 0.03+0.10 in fp.," Using this approach, we find that lensing and dynamics provide consistent results, modulo a $\sim$ (and a scatter of $\sim 25\%$ ) higher mass from dynamics, corresponding to a change of $0.03 \pm 0.10$ in $f_{\rm DM}$."517" Thus. we adopt a combination of the coustraiuts or our final masses. by minimizing with respect to 31a a combined \? function including oue term for dynamics and one for lensing observables. given by where 6, aud 6) ave the wmucertaitics ou typsyy ancl Alp. respectively9."," Thus, we adopt a combination of the constraints for our final masses, by minimizing with respect to $\sigma_{\rm SIS}$ a combined $\chi^2$ function including one term for dynamics and one for lensing observables, given by where $\delta_{d}$ and $\delta_{l}$ are the uncertainties on $\sigma_{\rm SDSS}$ and $M_{E}$, respectively."518 Tn the following we will focus ou the central 3D deprojected aand the mean DAI density withinRuy. defined as (pom=Mpw/tl3aRug?)j where Mp=AeAL at is the DAL mass.," In the following we will focus on the central 3D deprojected and the mean DM density within, defined as $\langle \rho_{\rm519DM}\rangle= M_{\rm DM}/(4/3 \pi \Re^3)$ where $M_{\rm DM}=M_{\rm520tot}-M_\star$ at is the DM mass."521 Asin T00 and NRTLO. to interpret the observational results. we construct a series of tov mass models based ou ACDAL cosmological simulations.," Asin T+09 and NRT10, to interpret the observational results, we construct a series of toy mass models based on $\Lambda$ CDM cosmological simulations."522" For cach biu in M,. we use the average Rog-age relations from 1ο combined. leus|local sample. ancl pareuneterize the virial DM mass by a star formation efficicuev egg=ALOna MU). where O44=O17 (Sperecletal. 2007)) is the barvou densityparaucter."," For each bin in $M_\star$, we use the average $\Re$ -age relations from the combined lens+local sample, and parameterize the virial DM mass by a star formation efficiency $\epsilon_{\rm SF}=M_\star/(\Omega_{\rm bar} M_{\rm tot})$ , where $\Omega_{\rm bar}=0.17$ \citealt{WMAP2}) ) is the baryon densityparameter."523 The halo deusitics are initially characterized as Navarroοal.(1997). profiles following al average nanss-concentraion relation. adjusted by (1| for the leus galaxies.," The halo densities are initially characterized as \citet{NFW} profiles following an average mass-concentration relation, adjusted by $(1+z)^{-1}$ for the lens galaxies."524 A recipe for AC frou barvou settling isthen applied (Guedinetal. 2001)..., A recipe for AC from baryon settling isthen applied \citep{Gnedin+04}. .525 The tov models for egg=0.03.0.1.L3 ave shown iu th. Fies.," The toy models for $\eSF = 0.03,0.1,0.3$ are shown in both Figs."526 aud 3..,\ref{fig: fig1} and \ref{fig: fig3}..527"where L, is the luminosity of the star, a is the semi-major axis of the orbit and e is the eccentricity of the orbit.","where $L_*$ is the luminosity of the star, $a$ is the semi-major axis of the orbit and $e$ is the eccentricity of the orbit."528 T'his analysis was performed on all planets that met our average incident flux cut (F)<2x105 erg s? cm? and had a mass greater than 20 Ma-since our model is primarily designed to describe giants with masses greater than Neptune., This analysis was performed on all planets that met our average incident flux cut $\langle F \rangle < 2 \times 10^8$ erg $^{-2}$ $^{-2}$ and had a mass greater than 20 $M_{\oplus}$ –since our model is primarily designed to describe giants with masses greater than Neptune.529 Note these heavy element masses should be taken asmasses since if the planet is internally heated or if higher atmospheric opacities (due to metal-enhanced atmospheres), Note these heavy element masses should be taken as since if the planet is internally heated or if higher atmospheric opacities (due to metal-enhanced atmospheres)530Iu the high pattern speed limit (model 05E). the orbital structure maplies iuner bar that is short. round aud cau trap a good fraction of stars.,"In the high pattern speed limit (model 05E), the orbital structure implies inner bar that is short, round and can trap a good fraction of stars."531 As pointed out iu Section 3.1.3. its end dis not well defined. and the transition region to the outer bar maw look like an isophotal twist (Figure 2. top panels).," As pointed out in Section 3.1.3, its end is not well defined, and the transition region to the outer bar may look like an isophotal twist (Figure 2, top panels)."532 The size of this transition zone increases with immer bars pattern speed (see left-hand cols of Figure 3 for models 05 aud O5E). and one may expect that at still higher pattern sxeeds the morphology im the inner bar region is dominated by the isoplotal twist.," The size of this transition zone increases with inner bar's pattern speed (see left-hand columns of Figure 3 for models 05 and 05E), and one may expect that at still higher pattern speeds the morphology in the inner bar region is dominated by the isophotal twist."533 Iu the low pattern speed iuit (nodel 02). the orbital structure nuplies iuuner bar that is lone. eccentric aud can trap onlv a sinall fraction of stars.," In the low pattern speed limit (model 02), the orbital structure implies inner bar that is long, eccentric and can trap only a small fraction of stars."534 Such bar has a well defined eud iu terms ο Sorbits that support it. but as these orbits do not trap sars well. the bars cud may uot be defined that well in stellar distribution.," Such bar has a well defined end in terms of orbits that support it, but as these orbits do not trap stars well, the bar's end may not be defined that well in stellar distribution."535 Further decreasing of pattern speed of the iuner bar erases the supporting orbits abruptly aid completely., Further decreasing of pattern speed of the inner bar erases the supporting orbits abruptly and completely.536" Thus there is a well defined lowest possibο, critical pattern speed of the inner bar."," Thus there is a well defined lowest possible, critical pattern speed of the inner bar."537 For pattern speeds lower than that. there are still regular orbits within the iuuer bar. but their appearance is dramatically different. aud they no longer support the shape of the immer bar.," For pattern speeds lower than that, there are still regular orbits within the inner bar, but their appearance is dramatically different, and they no longer support the shape of the inner bar."538 Most of thei remain xrpeudieular to the immer bar., Most of them remain perpendicular to the inner bar.539 If the presence of such orbits were a mere cousequence of this bar having an ILR. they should be also preseut in models 01. 03 ane I2. as all these models have an ILR (see fig.9 in ΑΤΑΟΣ).," If the presence of such orbits were a mere consequence of this bar having an ILR, they should be also present in models 04, 03 and 02, as all these models have an ILR (see fig.9 in MA08)."540 We searched for such orbits in those models. but we di rot flucl au.," We searched for such orbits in those models, but we did not find any."541 Also. if the structure of the immer aud the outer bar were simular. families of orbits both parallel aux xrpeudieular to the bar should coexist within the same uodoel. which is not the case in our models.," Also, if the structure of the inner and the outer bar were similar, families of orbits both parallel and perpendicular to the bar should coexist within the same model, which is not the case in our models."542 The abrupt disappearance. at low pattern speeds. of orbits aligue with the ner bar. aud their replacement throughout the extent of the bar by orbits perpendicular to it. which were abseut at higher pattern speeds. reflects the nonlinear interaction between the bars in doubly barred galaxies.," The abrupt disappearance, at low pattern speeds, of orbits aligned with the inner bar, and their replacement throughout the extent of the bar by orbits perpendicular to it, which were absent at higher pattern speeds, reflects the nonlinear interaction between the bars in doubly barred galaxies."543 The value of the critical pattern speed found im this paper is specific to the set of models considered here. aud it is uot clear by what plysical mechanisin it is determined.," The value of the critical pattern speed found in this paper is specific to the set of models considered here, and it is not clear by what physical mechanism it is determined."544 It is close to twice the pattern speed of the outer har. and one can hypothesize that the low-order resonance between the bars destroys the support of the inner bar.," It is close to twice the pattern speed of the outer bar, and one can hypothesize that the low-order resonance between the bars destroys the support of the inner bar."545" However, no transition in orbital structure is seen when the pattern speed of the inner bar is three times that of the outer bar."," However, no transition in orbital structure is seen when the pattern speed of the inner bar is three times that of the outer bar."546 Receutly a iiethod. has been proposed for extracting inner bars from observations of carly-type spirals by modelling aud subtracting the disk. bulge aud the outer bar.," Recently a method has been proposed for extracting inner bars from observations of early-type spirals by modelling and subtracting the disk, bulge and the outer bar."547 The results for two ealaxics have already Όσοι presented (Exwin 2010)., The results for two galaxies have already been presented (Erwin 2010).548 The two extracted mner bars are quite differcut from cach other., The two extracted inner bars are quite different from each other.549 One (in NGC 1513) contains a small fraction ofthe total stellar elit )). its eccentricity is hieh (axial ratio of 1). and its extent rather well defined. with isophotes aligued throughout the bar.," One (in NGC 1543) contains a small fraction of the total stellar light ), its eccentricity is high (axial ratio of 4), and its extent rather well defined, with isophotes aligned throughout the bar."550 The other bar (ii NGC 2859). to the coutrary. contaius a mmch larger fraction of the total helt ). its eccentricity is lower (axial ratio of 2). iud its outer part smoothly turus mto a region of twisted isophotes outside it. which at larger radii become round and similar to those of the subtracted components of the galaxy iu the sine region.," The other bar (in NGC 2859), to the contrary, contains a much larger fraction of the total light ), its eccentricity is lower (axial ratio of 2), and its outer part smoothly turns into a region of twisted isophotes outside it, which at larger radii become round and similar to those of the subtracted components of the galaxy in the same region."551 Based ou our knowledge of single bars. one should not necessarily expect correlatious between the three characteristics above (eccentricifv. luass. and outer isophotal shape).," Based on our knowledge of single bars, one should not necessarily expect correlations between the three characteristics above (eccentricity, mass, and outer isophotal shape)."552 It is therefore siguificaut that iu the observations they correlate iu the same way as 1n our two models of extreme pattern speeds., It is therefore significant that in the observations they correlate in the same way as in our two models of extreme pattern speeds.553 Orbits supporting the slowly rotating ΠΙΟ bar iu our models map onto looS that are eccentric. hence large axial ratio of such a bar. but they do uot trap stars well. hence simall mass fraction in the bar.," Orbits supporting the slowly rotating inner bar in our models map onto loops that are eccentric, hence large axial ratio of such a bar, but they do not trap stars well, hence small mass fraction in the bar."554 We also showed that because of its orbital structure the extent of a slow bar is well defined., We also showed that because of its orbital structure the extent of a slow bar is well defined.555 The inner bar in NGC 15[3 is eccentric. contaius small iiass raction and has a well defined exteut. which suggests at it rotates slowly in the seuse that its pattern specd is close to the lowest possible onc.," The inner bar in NGC 1543 is eccentric, contains small mass fraction and has a well defined extent, which suggests that it rotates slowly in the sense that its pattern speed is close to the lowest possible one."556 Ou the other haud. iu our models orbits supporting ie -inner bar of hieh patteru speed nap onto loops jit become increasingly round as the pattern speed of 15 bar increases. therefore the observed axial ratio of wat bar should be small.," On the other hand, in our models orbits supporting the inner bar of high pattern speed map onto loops that become increasingly round as the pattern speed of the bar increases, therefore the observed axial ratio of that bar should be small."557 These orbits trap stars very eficicuth. heuce the majority of the stars within the extent of the bar follow that bar aud the mass fraction in the bar is large.," These orbits trap stars very efficiently, hence the majority of the stars within the extent of the bar follow that bar and the mass fraction in the bar is large."558 Outer loops of fast rotating iuner wars become monotomically rounder as their major axes increase. and cuter a transition region that looks like au isophotal twist. so that the end of the bar is not well defined.," Outer loops of fast rotating inner bars become monotonically rounder as their major axes increase, and enter a transition region that looks like an isophotal twist, so that the end of the bar is not well defined."559 The inner bar of NGC 2859 is less eccentric han in NGC 15123. contains a high mass fraction aud is urrounded by au isophotal twist which sugeests that he angular velocity of the iuuer bar in NGC 2859 is considerable larger than its lowest clvnamically possible value. and that the structure of this iuner bar is close to he structure iu models of fast inner bars preseuted here.," The inner bar of NGC 2859 is less eccentric than in NGC 1543, contains a high mass fraction and is surrounded by an isophotal twist which suggests that the angular velocity of the inner bar in NGC 2859 is considerably larger than its lowest dynamically possible value, and that the structure of this inner bar is close to the structure in models of fast inner bars presented here."560 Thus. we propose that from the morphology of extracted iuuer bars we can discriminate between slow xus. Whose pattern speed is close to the minimal dynamically possible value. aud fast bars. whose patter speed is cousicderably above this limit (possibly two nues higher).," Thus, we propose that from the morphology of extracted inner bars we can discriminate between slow bars, whose pattern speed is close to the minimal dynamically possible value, and fast bars, whose pattern speed is considerably above this limit (possibly two times higher)."561 This distinction can be based on the characteristics listed imm Table 2., This distinction can be based on the characteristics listed in Table 2.562 Note that by slow and fast immer bars we do not mean the ratio of the cheth of the bar to its corotation radius. which iu our models is virtually coustaut.," Note that by slow and fast inner bars we do not mean the ratio of the length of the bar to its corotation radius, which in our models is virtually constant."563" Our slow bars lave oittern speeds in a range whose lower lait is set bv 10 orbital support for the iuner bar. while our fast bars vecolme increasingly rounder as their angular velocity Increases, and eventually they caunot be distinguished Toni axisviunetrie components of the galaxy."," Our slow bars have pattern speeds in a range whose lower limit is set by no orbital support for the inner bar, while our fast bars become increasingly rounder as their angular velocity increases, and eventually they cannot be distinguished from axisymmetric components of the galaxy."564Active Galactic Nuclet (AGNs) show significant variability over a large range of timescales.,Active Galactic Nuclei (AGNs) show significant variability over a large range of timescales.565 Usually. a variety of information can be extracted from the data with statistical methods based on Fourier techniques.," Usually, a variety of information can be extracted from the data with statistical methods based on Fourier techniques."566 In the X-ray domain. for example. variability iu acereting compact objects has commonly been described by means of power spectral densities (PSD). characterizing the. amount of variability power P(w) as a function of temporal frequencies ω. or timescales 1/« (e.g.. van der Klis 1997).," In the X-ray domain, for example, variability in accreting compact objects has commonly been described by means of power spectral densities (PSD), characterizing the amount of variability power $P(\omega)$ as a function of temporal frequencies $\omega$, or timescales $1/\omega$ (e.g., van der Klis 1997)."567 For (Seyfert) AGNs the resultant PSDs quite often appear to follow power laws P(w)«qw. which on long timescales (small frequencies) are approximately described by f£ close to | (flicker noise). but break to a steeper slope (= 2) on timescales shorter than à break timescale tp.," For (Seyfert) AGNs the resultant PSDs quite often appear to follow power laws $P(\omega)\propto \omega^{-\beta}$, which on long timescales (small frequencies) are approximately described by $\beta$ close to $1$ (flicker noise), but break to a steeper slope $\geq 2$ ) on timescales shorter than a break timescale $t_B$."568 Active Galactic Nuclei thus vary more strongly towards lower frequencies (longer timescales)., Active Galactic Nuclei thus vary more strongly towards lower frequencies (longer timescales).569 Recent studies have shown that the X-ray PSDs of AGNs can be qualitatively similar to the high state of black hole X-ray binary systems (e.g.. McHardy et al.," Recent studies have shown that the X-ray PSDs of AGNs can be qualitatively similar to the high state of black hole X-ray binary systems (e.g., McHardy et al."570 2004. 2006).," 2004, 2006)."571 Based on these and other similarities. AGNs have sometimes been interpreted as scaled-up Galactic black hole In the very-high-energy (VHE) domain. the experimental situation is usually much less favorable.," Based on these and other similarities, AGNs have sometimes been interpreted as scaled-up Galactic black hole In the very-high-energy (VHE) domain, the experimental situation is usually much less favorable."572 However. one object where it became recently possible to employ similar analysis techniques is the TeV blazar PKS 2155-304 (z= 0.116).," However, one object where it became recently possible to employ similar analysis techniques is the TeV blazar PKS 2155-304 $z=0.116$ )."573 Usually detected only with a low VHE flux of ~10% of the Crab nebula. PKS 2155-304 underwent a dramatic outburst in July 2006. with VHE flux levels varying between | and 15 Crab units. allowing an unprecedented variability analysis (Aharonian et al.," Usually detected only with a low VHE flux of $\sim 10\%$ of the Crab nebula, PKS 2155-304 underwent a dramatic outburst in July 2006, with VHE flux levels varying between 1 and 15 Crab units, allowing an unprecedented variability analysis (Aharonian et al."574 2007; Abramowski et al., 2007; Abramowski et al.575 2010; Degrange et al., 2010; Degrange et al.576 2008)., 2008).577 The Fourier analysis of its WHE light curve of. e.g.. MJD 53944 indicates a red (Brownian) noise-type VHE PSD with an exponent close to 2 within the frequency range [1077 Hz. 107 Hz] (Aharonian et al.," The Fourier analysis of its VHE light curve of, e.g., MJD 53944 indicates a red (Brownian) noise-type VHE PSD with an exponent close to 2 within the frequency range $[10^{-4}$ Hz, $10^{-2}$ Hz] (Aharonian et al."578 2007)., 2007).579 Similar results have been obtained in X-rays (1.5-10 keV) with BeppoSAX in 1996 and 1997 (Zhang et al., Similar results have been obtained in X-rays (1.5-10 keV) with BeppoSAX in 1996 and 1997 (Zhang et al.580 1999)., 1999).581 Moreover. similar to findings in the X-ray domain (Zhang et al.," Moreover, similar to findings in the X-ray domain (Zhang et al."582" 1999, 2005). where linear relations between (absolute) rms variability amplitude and (mean) X-ray flux have been previously reported. a significant rms-flux correlation has been observed in the VHE data set (Degrange et al."," 1999, 2005), where linear relations between (absolute) rms variability amplitude and (mean) X-ray flux have been previously reported, a significant rms-flux correlation has been observed in the VHE data set (Degrange et al."583 2008)., 2008).584 This is known to be characteristic of a non-linear. log-normal stochastic process where the relevant. normally distributed variable 1$ the logarithm of the flux logCX). and not just the flux itself (see Uttley et al.," This is known to be characteristic of a non-linear, log-normal stochastic process where the relevant, normally distributed variable is the logarithm of the flux $\log(X)$, and not just the flux itself (see Uttley et al."585 2005 for a general treatment. and Superina et al.," 2005 for a general treatment, and Superina et al."586 2008 for application to PKS 2155)., 2008 for application to PKS 2155).587 A log-normal distribution can be thought of as the result of many multiplicative random effects. whereas additive effects would give rise to a normal (Gaussian) distribution.," A log-normal distribution can be thought of as the result of many multiplicative random effects, whereas additive effects would give rise to a normal (Gaussian) distribution."588 Dideed. if the variability would be caused merely by an additive stochastic process. the fluxes would be normally distributed and no linear rms-flux relation would be expected. becatse all Fourier. coefficients. would be statistically. independert.," Indeed, if the variability would be caused merely by an additive stochastic process, the fluxes would be normally distributed and no linear rms-flux relation would be expected, because all Fourier coefficients would be statistically independent."589 Therefore. the finding that the variations on short timescales (determining the rms) decrease in amplitude when the long timescale variations (determining the mean flux) decrease. indicates that the process driving the variations is a multiplicative process (as 1n a cascade) and not just an additive one (e.g.. shot-noise). nor one resulting from independent variations in many separate regions (Uttley et al.," Therefore, the finding that the variations on short timescales (determining the rms) decrease in amplitude when the long timescale variations (determining the mean flux) decrease, indicates that the process driving the variations is a multiplicative process (as in a cascade) and not just an additive one (e.g., shot-noise), nor one resulting from independent variations in many separate regions (Uttley et al."590 2005: McHardy In acereting galactic black hole (BH) systems. these variations have been frequently related to small. independent fluctuations 1n the accretion rate. occurring on local viscous timescale {μι over a range of disk radi r that are large compared to the inner radius of the disk (Lyubarskii. 1997; King et al.," 2005; McHardy In accreting galactic black hole (BH) systems these variations have been frequently related to small, independent fluctuations in the accretion rate, occurring on local viscous timescale $t_{\rm visc}(r)$ over a range of disk radii $r$ that are large compared to the inner radius of the disk (Lyubarskii 1997; King et al."591 2004: Arevalo Uttley 2006)., 2004; Arevalo Uttley 2006).592 If not damped. these fluctuations can propagate inwards and couple together in à way to produce the multiplicative characteristics. noted above.," If not damped, these fluctuations can propagate inwards and couple together in a way to produce the multiplicative characteristics noted above."593 Any emission process linked to the the innermost region (e.g.. as X-ray production or jet launching site) may then eventually be modulated over a frequency interval ranging from the inverse accretion time hear the outer to the one at the innermost disk radius. respectively.," Any emission process linked to the the innermost region (e.g., as X-ray production or jet launching site) may then eventually be modulated over a frequency interval ranging from the inverse accretion time near the outer to the one at the innermost disk radius, respectively."594 While this scenario sounds very attractive (cf., While this scenario sounds very attractive (cf.595 also Giebels Degrange 2009 for BL Lac). a generalization to a supermassive source like PKS 2155-304 seems challenging given the detected VHE minimum variability (doubling) timescale of 4.~200 sec.," also Giebels Degrange 2009 for BL Lac), a generalization to a supermassive source like PKS 2155-304 seems challenging given the detected VHE minimum variability (doubling) timescale of $t_v \sim 200$ sec."596 As we show below. a consistent approach along this line may require the presence of a putative binary BH system in PKS 2155-304 (cf.," As we show below, a consistent approach along this line may require the presence of a putative binary BH system in PKS 2155-304 (cf."597Polu-aiug galaxies (PRC) are peculiar objects iu which a polar or very inclined ving surround the host galaxy.,Polar-ring galaxies (PRG) are peculiar objects in which a polar or very inclined ring surround the host galaxy.598 Thev teach us a lot on galaxy formation., They teach us a lot on galaxy formation.599" At least two niain scenarios are invoked to form these svstenmis either the major merecr scenario. with a head-on mereiue of two galaxies with their disks oriented. perpendicularly (οιο, Bekki 1998). or the accretfion scenario. where a ga-Yich donor loses matter to form the rug (e.e.. Scloweizer et al."," At least two main scenarios are invoked to form these systems: either the major merger scenario, with a head-on merging of two galaxies with their disks oriented perpendicularly (e.g., Bekki 1998), or the accretion scenario, where a gas-rich donor loses matter to form the ring (e.g., Schweizer et al."600 1983. Reshetuikov Sotuikova 1997).," 1983, Reshetnikov Sotnikova 1997)."601 The accretion scenario itself could either correspond to a sil colupanion being disrupted durius a niünor merecr. or a major chcounter with tidal mass transfer from a massive donor to the host (Bowrnaud Combes 2003. hereafter BC03).," The accretion scenario itself could either correspond to a small companion being disrupted during a minor merger, or a major encounter with tidal mass transfer from a massive donor to the host (Bournaud Combes 2003, hereafter BC03)."602 In previous simmlations. BCO3 have shown that the accretion scenario offers more chances to form the observed svstenmis. aud that a discriminating characteristic can be the existence. in the merecr scenario. of a diffuse stellar backerouud around the polarring svstem.," In previous simulations, BC03 have shown that the accretion scenario offers more chances to form the observed systems, and that a discriminating characteristic can be the existence, in the merger scenario, of a diffuse stellar background around the polar-ring system."603 Iu the accretion scenario. the matter is not as much dispersed spatially.," In the accretion scenario, the matter is not as much dispersed spatially."604 It is naportaut ο test on several πο]ουρανος polar-rving systems the possible scenarios. aud the prescut system offers a good example.," It is important to test on several well-observed polar-ring systems the possible scenarios, and the present system offers a good example."605 The southerm peculiar ealaxy AAD 1931-563. was classified by Whitmore et al. (, The southern peculiar galaxy AM 1934-563 was classified by Whitmore et al. (6061990) (PRC. polar rines catalogue) as a good candidate for polarring galaxics. (,"1990) (PRC, polar rings catalogue) as a good candidate for polar-ring galaxies. ("607The object name is PRC B-18 according to the PRC.),The object name is PRC B-18 according to the PRC.)608" The füut extended feature crosses the iain ealaxy (disturbed edge-on galaxy with inclined. dust lane) at au anele of about GO"" from the major axis (Figs.", The faint extended feature crosses the main galaxy (disturbed edge-on galaxy with inclined dust lane) at an angle of about $^{\rm o}$ from the major axis (Figs.609 1 aud 2)., 1 and 2).610 Both components the main body aud the suspected rine are slightly S-shaped., Both components – the main body and the suspected ring – are slightly S-shaped.611 ANT 1931-563 has two nearby coupanious of similar size and magnitude (Fies., AM 1934-563 has two nearby companions of similar size and magnitude (Figs.612 1 aud 2)., 1 and 2).613 These are POC 100092 (NW conipanuion) and POC 390718 {5 conrpaniion). both of unknown redshift.," These are PGC 400092 (NW companion) and PGC 399718 (S companion), both of unknown redshift."614 Other galaxies of comparable iaeuitudes are located about 10 N of AM 1931-563 and belong to the AM. 1931-562 exoup of ealaxies., Other galaxies of comparable magnitudes are located about $'$ N of AM 1934-563 and belong to the AM 1934-562 group of galaxies.615 AMO 1931-563. is an almost unexplored galaxy., AM 1934-563 is an almost unexplored galaxy.616 Deshetnikov et al. (, Reshetnikov et al. (6172001) have found fast rotation of the eas in the central region of the ealaxy. as far as sigus of Sv2 or LINER activity.,"2001) have found fast rotation of the gas in the central region of the galaxy, as far as signs of Sy2 or LINER activity."618 van Del et al. (, van Driel et al. (6192002) have detected the 21-cii HI liue cussion toward AM. 1931-563 but the observed III xofile can be confused with another galaxy of the triplet.,2002) have detected the 21-cm HI line emission toward AM 1934-563 but the observed HI profile can be confused with another galaxy of the triplet.620 We present here new photometric aud spectroscopic data for AAT 1931-563 and two companion galaxies., We present here new photometric and spectroscopic data for AM 1934-563 and two companion galaxies.621 The ιο data reveal that the three galaxies forma a plivsical viplet., The new data reveal that the three galaxies form a physical triplet.622 Global observational structure and kinematies of ANTI 1931-563 allow to conclude that this ealaxy is a real x»bur-riug galaxy with a spiral host and inclined rine/cdisk structure., Global observational structure and kinematics of AM 1934-563 allow to conclude that this galaxy is a real polar-ring galaxy with a spiral host and inclined ring/disk structure.623 We also moclel our observations usiue N-body miuerical siuulations., We also model our observations using N-body numerical simulations.624 We study different formation scenarios for this polar ring. aud fud that ouly one is likely o reproduce the observed properties of AM 1931-563.," We study different formation scenarios for this polar ring, and find that only one is likely to reproduce the observed properties of AM 1934-563."625 We hen couclude that this polar ring las been formed bv idal accretion of material frou a eas-vich ealaxy. that uav still be observed today in the triplet.," We then conclude that this polar ring has been formed by tidal accretion of material from a gas-rich galaxy, that may still be observed today in the triplet."626 Let us stress hat AAD 1931-563. with its massive spiral lost. is peculiar among PRs. which most frequently have a small carly-vpe hosts (often SOs).," Let us stress that AM 1934-563, with its massive spiral host, is peculiar among PRGs, which most frequently have a small early-type hosts (often S0s)."627 Thus. we study the formation of ANL 1931-563 in particular. aud do uot pretend that our results will strictly extent to PRCs in general. even if may PRGs have probably formed through the same accretion mechamisi (see Ὀς09).," Thus, we study the formation of AM 1934-563 in particular, and do not pretend that our results will strictly extent to PRGs in general, even if many PRGs have probably formed through the same accretion mechanism (see BC03)."628 The observations that have beeu made are preseuted iu Sect., The observations that have been made are presented in Sect.629 2., 2.630 Their results are analyzed in Sect., Their results are analyzed in Sect.631 3., 3.632 Iu Sect., In Sect.633 1 we model this svstem. and discuss its formation mechlanisu.," 4, we model this system, and discuss its formation mechanism."634 The photometric observations were performed with the l.Gau telescope at the ΟΡΙΟ (AICT/LNA). Brasil ou Aueust 2002.," The photometric observations were performed with the 1.6-m telescope at the OPD (MCT/LNA), Brasil on August 2002."635 The telescope was equipped with direct Huaging camera 11 and a thick. back-alluuinated," The telescope was equipped with direct imaging camera 1 and a thick, back-illuminated"636or escaping along open magnetic field lines via direct electron measurements near the Earth (see777.[orareview)..,"or escaping along open magnetic field lines via direct electron measurements near the Earth \citep[see][for a review]{Aschwanden02,BrownKontar05,Benz08}."637 The first in-situ observations of energetic particles (72) opened up the non-electromagnetic window of flare accelerated. particle observations.," The first in-situ observations of energetic particles \citep{vanAllen65}638 opened up the non-electromagnetic window of flare accelerated particle observations."639 Solar impulsive electron events detected in-situ generally clisplay broken power-law energy distributions with lower energies having softer spectra (7).., Solar impulsive electron events detected in-situ generally display broken power-law energy distributions with lower energies having softer spectra \citep{Lin85}.640 These events also show near time-ol-I[light velocity dispersion and a beamed pitch-angle distribution (e.g.???)..," These events also show near time-of-flight velocity dispersion and a beamed pitch-angle distribution \citep[e.g.][]{Lin85,Krucker_etal1999,Krucker_etal07}."641 From (his evidence. it is often believed that such electrons propagate scatter-Dree [rom the Sun to the Earth (e.g.?)..," From this evidence, it is often believed that such electrons propagate scatter-free from the Sun to the Earth \citep[e.g.][]{Wang_etal06}."642 The observed. correlation between (he spectral indices of energetic electrons at the Sun ου data and (he Earth trom in-situ data (??) is often viewed as an additional support for {his model.," The observed correlation between the spectral indices of energetic electrons at the Sun from X-ray data and the Earth from in-situ data \citep{Lin85,Krucker_etal07} is often viewed as an additional support for this model."643 At the same time. impulsive solar energetic electron events are closely related observalionally (e.g.2??7?77) and theoretically (22277???) to Type II solar radio bursts.," At the same time, impulsive solar energetic electron events are closely related observationally \citep[e.g.][]{Li_etal1981,Ergun_etal98,Gosling_etal2003,Cane2003,Krucker_etal07}644 and theoretically \citep{GZ1958,Zaitsev_etal72,Grognard1982,Melrose90,Melnik99,Kontar01a,Ledenev04}645 to Type III solar radio bursts."646 The stzncdaid model of Type HI solar radio bursts (7). suggests that electron. beams propagating in the ambient solar wind plasma from the Sun (to the Earth can excite Langmuir waves. which in turn generate escaping plasma radio emission (see7.lorareview)...," The standard model of Type III solar radio bursts \citep{GZ1958}647 suggests that electron beams propagating in the ambient solar wind plasma from the Sun to the Earth can excite Langmuir waves, which in turn generate escaping plasma radio emission \citep[see][for a review]{Melrose_85}."648 Ii a treatment assuming travel along magnetic field lines. as faster electrons outpace slower electrons a positive gradient is formed in velocity space.," In a one-dimensional treatment assuming travel along magnetic field lines, as faster electrons outpace slower electrons a positive gradient is formed in velocity space."649 Η (his positive gradient gets large enough to start the generation of waves. electron energy is resonantly transferred to Langmuir waves in (he background plasma.," If this positive gradient gets large enough to start the generation of waves, electron energy is resonantly transferred to Langmuir waves in the background plasma."650 This transler of energv reduces the gradient in velocitv. space forming; a plateau (??)..," This transfer of energy reduces the gradient in velocity space forming a plateau \citep{Vedenov_etal1962,Drummond_Pines1962}."651 For a spatially limited electron beam cloud. the plasma waves generated al the front. of the cloud. are absorbed by the electron beam al the back allowing the electrons to travel through the corona with small energy losses aud with a velocity that decreases with time due to plasma inhomogeneity (?)..," For a spatially limited electron beam cloud, the plasma waves generated at the front of the cloud are absorbed by the electron beam at the back allowing the electrons to travel through the corona with small energy losses and with a velocity that decreases with time due to plasma inhomogeneity \citep{Kontar01a}."652 Although this broad picture is often supported by observations. the detailed picture of electron transport and plasma radio emission is far from well-understood.," Although this broad picture is often supported by observations, the detailed picture of electron transport and plasma radio emission is far from well-understood."653 This is largely due to electron beam propagation and radio emission being essentially a non-linear multi-scale problem. aud is the solar imp," This is largely due to electron beam propagation and radio emission being essentially a non-linear multi-scale problem, and is the subject of a large number of ongoing simulation efforts \citep[e.g.][]{Melnik99,Kontar01a,KontarPecseli02,Ledenev04,Li_etal2006,2008ApJ...677..676G}."654ulsive electron events can span a broad range of energies. [rom a lew keV to hundreds of keV. (?)..," Solar impulsive electron events can span a broad range of energies, from a few keV to hundreds of keV \citep{Lin_etal1996}."655 Their energy distribution forms a broken power-law spectrum with the break enerey in deca-keV range., Their energy distribution forms a broken power-law spectrum with the break energy in deca-keV range.656 Despite often showing the near time-ol-Ilight. dispersion. lower energv electrons appear to arrive sooner (han expected [rom a scatter-Iree mocel (7?)..," Despite often showing the near time-of-flight dispersion, lower energy electrons appear to arrive sooner than expected from a scatter-free model \citep{Wang_etal06}."657 Since the low energy electrons of a few keV should lose their energy collisionally in the low corona. these electrons are believed to be accelerated high in the corona (?)..," Since the low energy electrons of a few keV should lose their energy collisionally in the low corona, these electrons are believed to be accelerated high in the corona \citep{Lin_etal1996}."658 Recent time-ol- analvsis (7) assuming scatter-[ree propagation of solar energetic electrons suggests the existence of two electron populations. one low energy beam injected before the start οἱ the tvpe HIE burst and one high energy beam injected alter the tvpe II burst.," Recent time-of-injection analysis \citep{Wang_etal06} assuming scatter-free propagation of solar energetic electrons suggests the existence of two electron populations, one low energy beam injected before the start of the type III burst and one high energy beam injected after the type III burst."659 In this Letter. we investigate the electron propagation from the Sun to the Earth taking," In this Letter, we investigate the electron propagation from the Sun to the Earth taking"660observed Lya region and (4) consistency of the scale factor-derived distance with the adopted distance or distance constraint.,observed $\alpha$ region and (4) consistency of the scale factor-derived distance with the adopted distance or distance constraint.661 In other words. the fitting solution may not necessarily be the model with the lowest 47 value but rather all other available constraints are used such as constraints on the distance. reliable svstem parameters if available. absorption line fits. especially (he να wings but sometimes even Si II. Si HI. C III. C II. si IV and $i II when (hese features are in absorption aud do not have an origin in a wind or corona.," In other words, the fitting solution may not necessarily be the model with the lowest $\chi^{2}$ value but rather all other available constraints are used such as constraints on the distance, reliable system parameters if available, absorption line fits, especially the $\alpha$ wings but sometimes even Si II, Si III, C III, C II, Si IV and Si II when these features are in absorption and do not have an origin in a wind or corona."662 We also search for anv statistically significant improvement in the fitting by combining white dwarf models and disk models together using a X7 minimization routine called DISKFIT., We also search for any statistically significant improvement in the fitting by combining white dwarf models and disk models together using a $\chi^{2}$ minimization routine called DISKFIT.663 Once again. we find the minimum 4? value achieved for the combined models. and check the combined model consistency. wilh the observed continuum slope and Lya region. aud consistency of the scale factor-derived distance wilh the adopted clistance or distance constraints.," Once again, we find the minimum $\chi^{2}$ value achieved for the combined models, and check the combined model consistency with the observed continuum slope and $\alpha$ region, and consistency of the scale factor-derived distance with the adopted distance or distance constraints."664 For the white dwarl radii. we use the mass-radius relation from (he evolutionary model grid of for C-O cores.," For the white dwarf radii, we use the mass-radius relation from the evolutionary model grid of \citet{Wood1990} for C-O cores."665 For a non-magnetic nova-like variable during its high state. it is reasonable to expect that a steady state optically Chick accretion disk might provide a successful fit (see (2003))).," For a non-magnetic nova-like variable during its high state, it is reasonable to expect that a steady state optically thick accretion disk might provide a successful fit (see \citet{Hamilton2008}) )."666 This was our intial expectation lor all three nova-likes. DIx Lyn. V380 Oph and V751 Cveni.," This was our intial expectation for all three nova-likes, BK Lyn, V380 Oph and V751 Cygni."667 For BI. Lyn. the most striking feature of its spectrum is the sharp. narrow Lya line in combination with a steeply rising continu.," For BK Lyn, the most striking feature of its spectrum is the sharp, narrow $\alpha$ line in combination with a steeply rising continuum."668 The narrowness of the Lya ancl steep continuum slope suggested (he possiblity (hat the FUV flux originates [rom a hot white cwarf photosphere., The narrowness of the $\alpha$ and steep continuum slope suggested the possiblity that the FUV flux originates from a hot white dwarf photosphere.669 But a fit to the the continuum slope with a hot photosphere αἱ T=300001. and a nominal white dwarl gravity of log e=8.0. vields a svnthetüie Ίωνα absorption feature which is [ar (oo broad.," But a fit to the the continuum slope with a hot photosphere at T=30000K and a nominal white dwarf gravity of log g=8.0, yields a synthetic $\alpha$ absorption feature which is far too broad."670 ILowever. a narrower prolile is obtained bv increasing the effective temperature and/or lowering the gravitv.," However, a narrower profile is obtained by increasing the effective temperature and/or lowering the gravity."671 The continuum slope and narrow Lya feature of the observed spectrum can be matched with a white dwarf photosphere with T-—380001Ix. aud log g—T., The continuum slope and narrow $\alpha$ feature of the observed spectrum can be matched with a white dwarf photosphere with T=38000K and log g=7.672 A surface gravity Chis low would not be inconsistent with the low white dwarl mass derived by Dobrzveka&Lowell(1992)., A surface gravity this low would not be inconsistent with the low white dwarf mass derived by \citet{Dobrzycka1992}.673. However. the distance implied by the fit is 1200 pc while the stellar radius approached (hat of a hot subclwarl," However, the distance implied by the fit is 1400 pc while the stellar radius approached that of a hot subdwarf."674 Moreover. the V-band magnitude ol this model fit is 20.6. which is about [ive magnitudes fainter than the observed magnitude.," Moreover, the V-band magnitude of this model fit is 20.6, which is about five magnitudes fainter than the observed magnitude."675 The narrowness of the Lya prolile also suggested (he possibility that it is of interstellar origin., The narrowness of the $\alpha$ profile also suggested the possibility that it is of interstellar origin.676 First. if the svstem were being viewed at low inclination. then the emission lines which are presumed to be formed in the disk. would not be as broad as observed.," First, if the system were being viewed at low inclination, then the emission lines which are presumed to be formed in the disk, would not be as broad as observed."677 This makes il likely that the narrow Lya absorption. given that it is not cue to a low gravity white dwarl," This makes it likely that the narrow $\alpha$ absorption, given that it is not due to a low gravity white dwarf"678it is interesting to examine whether such a possibility could be acceptable using additional constraints.,it is interesting to examine whether such a possibility could be acceptable using additional constraints.679 CMB is known to provide such constraints on the quintessence scenario. eg (?22)..," CMB is known to provide such constraints on the quintessence scenario, eg \citep{spergel03,nous2003,odman2004}."680 We therefore examine CMB constraints on the type of models introduced above. although we leave to a future work a full investigation of the constraints that can be set on this type of model.," We therefore examine CMB constraints on the type of models introduced above, although we leave to a future work a full investigation of the constraints that can be set on this type of model."681 We use the WMAP 3 data-set. as well as CBI. VSA and Boomerang data at small scales. and a version of the CAMB cosmological code (2) that we have modified.," We use the WMAP 3 data-set, as well as CBI, VSA and Boomerang data at small scales, and a version of the CAMB cosmological code \citep{CAMB} that we have modified."682 Modifications of the code are straightforward since its public version includes models with constant We In which we have implemented the energy density ροίς) and the pressure Po) as a function of redshift., Modifications of the code are straightforward since its public version includes models with constant $w_\QUINT$ in which we have implemented the energy density $\rho_\QUINT (z)$ and the pressure $P_\QUINT(z)$ as a function of redshift.683 Our ansatz for the equation of state parameter wo(z) allows us to integrate the conservation equation to obtain an analytical form for po(z)!., Our ansatz for the equation of state parameter $w_\QUINT(z)$ allows us to integrate the conservation equation to obtain an analytical form for $\rho_\QUINT(z)$.684. The angular power spectrum of CMB fluctuations in the presence of dark energy is modified mainly through the modification of the angular distance (?) (see Fig., The angular power spectrum of CMB fluctuations in the presence of dark energy is modified mainly through the modification of the angular distance \citep{bl84} (see Fig.685 3 ?)., \ref{fig:cmbCl} ).686 Although a strong dependence appears. this is. partially lost through parameter degeneracies which strongly weaken the final constraints.," Although a strong dependence appears, this is partially lost through parameter degeneracies which strongly weaken the final constraints."687 In addition. ISW will contribute to lower levels as the transition is assumed at lower redshift. and this effect contributes to modify the angular power spectrum of the CMB fluctuations.," In addition, ISW will contribute to lower levels as the transition is assumed at lower redshift, and this effect contributes to modify the angular power spectrum of the CMB fluctuations."688 We have investigated the CMB constraints on models with rapid transitions described by Eq. 2.., We have investigated the CMB constraints on models with rapid transitions described by Eq. \ref{wqz}. .689 Γ was set to 10., $\Gamma$ was set to 10.690 We have checked that varying E above 5 produces no appreciable differences., We have checked that varying $\Gamma$ above 5 produces no appreciable differences.691 The other parameters that were left free are the Hubble constant Ho. the dark energy density at the present day Qo. the index of the primordial spectrum 7. the amplitude of fluctuations ος and the transition epoch aq=1/(1+τι).," The other parameters that were left free are the Hubble constant $H_0$, the dark energy density at the present day $\Omega_\QUINT$, the index of the primordial spectrum $n$, the amplitude of fluctuations $\sigma_8$ and the transition epoch $a_\TRANS = 1 / (1 + z_\TRANS)$."692" From the contours obtained in figure 4.. one can see that the constraints that can be set on the transition redshift z, from the CMB are rather stringent. z;>0.54 (lo on one parameter) when Qo represents less than 50% of the total density."," From the contours obtained in figure \ref{fig:CD2}, one can see that the constraints that can be set on the transition redshift $z_\TRANS $ from the CMB are rather stringent, $z_\TRANS > 0.54 $ $\sigma$ on one parameter) when $\Omega_\QUINT$ represents less than $50\%$ of the total density."693" These constraints being slightly dependent on Ho we have also examined whether a combination of CMB and supernova data allows to improve the transition epoch constraints. but although the SNIa data restricted the dark energy density much more around Og~0.7. the final constraints do not represent a significant improvement: the final constraint I8 z,>0.66 (26 on one parameter)."," These constraints being slightly dependent on $H_0$ we have also examined whether a combination of CMB and supernova data allows to improve the transition epoch constraints, but although the SNIa data restricted the dark energy density much more around $\Omega_\QUINT \sim 0.7$, the final constraints do not represent a significant improvement: the final constraint is $z_\TRANS > 0.66 $ $\sigma$ on one parameter)."694 Some different dark energy models could in principle lead to different conclusions in the case where the sound speed varies in a way that significantly affects the integrated. Sachs-Wolfe effect on large angular scales. even though no such model was found in our analysis.," Some different dark energy models could in principle lead to different conclusions in the case where the sound speed varies in a way that significantly affects the integrated Sachs-Wolfe effect on large angular scales, even though no such model was found in our analysis."695 Clearly. better constraints could be obtained from additional data of cosmological relevance. but this is beyond the scope of the present paper.," Clearly, better constraints could be obtained from additional data of cosmological relevance, but this is beyond the scope of the present paper."696 In order to distinguish quintessence models from a pure cosmological constant. it is crucial to be able to track the dark energy evolution as early as possible.," In order to distinguish quintessence models from a pure cosmological constant, it is crucial to be able to track the dark energy evolution as early as possible."697 The main impact of darkenergy comes from its influence on the expansion rate of the universe., The main impact of darkenergy comes from its influence on the expansion rate of the universe.698 An important question is therefore until what epoch, An important question is therefore until what epoch699convolved with a Gaussian of full width half maximum + pixels (850. μπι) or 3 pixels (450 sem) giving final resolutions of 14.2 (850 jim) and 8.6 aresees (450 fam).,convolved with a Gaussian of full width half maximum 4 pixels (850 $\mu$ m) or 3 pixels (450 $\mu$ m) giving final resolutions of $14.2$ (850 $\mu$ m) and $8.6$ arcsecs (450 $\mu$ m).700 The convolved maps with signal-to-noise (S/N) contours are shown in reftig:allmaps.., The convolved maps with signal-to-noise (S/N) contours are shown in \\ref{fig:allmaps}.701 We observed each field with the IRAC (at 4.5 and 8.0 jim) and MIPS (at 24 jim) cameras on-board theTelescope., We observed each field with the IRAC (at 4.5 and 8.0 $\mu$ m) and MIPS (at 24 $\mu$ m) cameras on-board the.702 IRAC observations were made between 2005 March and 2005 July while the MIPS observations were made between 2005 March and 2005 December., IRAC observations were made between 2005 March and 2005 July while the MIPS observations were made between 2005 March and 2005 December.703 For the IRAC observations we used 5-pt Gaussian dithers with frame times of 100 or 200s depending on the predicted brightness of the target., For the IRAC observations we used 5-pt Gaussian dithers with frame times of 100 or 200s depending on the predicted brightness of the target.704 Frame times for the MIPS observations were between 3 and 10 s. These observations are summarised in Table 3.., Frame times for the MIPS observations were between 3 and 10 s. These observations are summarised in Table \ref{table:spitlog}.705 The IRAC frames were processed by the Science Center using the standard pipeline version S1:4.0.0., The IRAC frames were processed by the Science Center using the standard pipeline version S14.0.0.706 The images were then cropped to only include the region of constant exposure time: this allows catalogues to be constructed from regions with similar noise properties., The images were then cropped to only include the region of constant exposure time; this allows catalogues to be constructed from regions with similar noise properties.707 Source extraction was performed with (Bertin Arnouts 1996) with a fixed aperture of 3.5” and a local background fit., Source extraction was performed with (Bertin Arnouts 1996) with a fixed aperture of $3.5^{\prime\prime}$ and a local background fit.708 Aperture corrections of 1.6 and 2.13 were applied to the 4.5 and 8.0 jim flux densities respectively. in accord with the values determined from theSpicer First Look Survey (Lacy et al.," Aperture corrections of $1.6$ and $2.13$ were applied to the 4.5 and 8.0 $\mu$ m flux densities respectively, in accord with the values determined from the First Look Survey (Lacy et al."709 2005)., 2005).710 For MIPS observations. the 24 ;7m BCD images were fitted with a plane after first masking out the bright objects.," For MIPS observations, the $24~\mu$ m BCD images were fitted with a plane after first masking out the bright objects."711 This plane was then subtracted from each. BCD frame resulting in a flat background image., This plane was then subtracted from each BCD frame resulting in a flat background image.712 These images were then combined with the task using the astrometric solution from each individual BCD image., These images were then combined with the task using the astrometric solution from each individual BCD image.713 This procedure resulted in a much improved 24 j/m image. free of the jail-bar pattern common to the PBCD images supplied from theSpizer pipeline.," This procedure resulted in a much improved 24 $\mu$ m image, free of the jail-bar pattern common to the PBCD images supplied from the pipeline."714 Again. only the central 3.3 aremin? region of the images was used to detect sources.," Again, only the central $3\times 3$ $^2$ region of the images was used to detect sources."715 We used to find sources and thePHOT script in IDL to measure their flux density within a 13 aresec radius aperture., We used to find sources and the script in IDL to measure their flux density within a $13$ arcsec radius aperture.716 All flux densities were then subjected to an aperture correction of 1.167 (see Seymour et al., All flux densities were then subjected to an aperture correction of 1.167 (see Seymour et al.717 2007)., 2007).718 Our philosophy is to match our analysis as closely as possible to that performed by the SHADES consortium (Coppin et al., Our philosophy is to match our analysis as closely as possible to that performed by the SHADES consortium (Coppin et al.719 2006) thus allowing a direct comparison of the number counts determined for blank fields and those in the highly biased regions of the Universe surrounding our QSOs., 2006) thus allowing a direct comparison of the number counts determined for blank fields and those in the highly biased regions of the Universe surrounding our QSOs.720 Most of the analysis in this section pertains to the 850. jam data., Most of the analysis in this section pertains to the 850 $\mu$ m data.721 For the 450 jim data we extract a catalogue at a fixed. S/N threshold but do not compute number counts., For the 450 $\mu$ m data we extract a catalogue at a fixed S/N threshold but do not compute number counts.722 We adopt the source extraction algorithm described by Scott et, We adopt the source extraction algorithm described by Scott et723"posterior distribution of 0 aud c is Πωαο, poe.110.0) is given by Equation (11)). and pf=10.0) is the probability of including a source in one’s sample. given the model parameters. 0 and (0 I have left off the subscripts for the data poiuts in Equation (11)) because the iuteerals are the same for each (rj.d;£j.4).","posterior distribution of $\theta$ and $\psi$ is Here, $p(x_i,y_i|\theta,\psi)$ is given by Equation \ref{eq-obslik2}) ), and $p(I=1|\theta,\psi)$ is the probability of including a source in one's sample, given the model parameters, $\theta$ and $\psi$: I have left off the subscripts for the data points in Equation \ref{eq-detprob}) ) because the integrals are the same for each $(x_j,y_j,\xi_j,\eta_j)$."724 IE one asstunes the Gaussian mixture model of Sections L1 and L3.. then ple.gil.c) is eiven by Equations (16)) or (30)).," If one assumes the Gaussian mixture model of Sections \ref{s-normreg} and \ref{s-multreg}, then $p(x_i,y_i|\theta,\psi)$ is given by Equations \ref{eq-bobslik}) ) or \ref{eq-mobslik}) )."725 The posterior mode can then be used as au estimate of 0 aud c. which is found by maximizing Equation (10)).," The posterior mode can then be used as an estimate of $\theta$ and $\psi$, which is found by maximizing Equation \ref{eq-trunclik}) )."726 Iu addition to issues related to the sample selection method. if is Common in astronomical data to have nou-detections.," In addition to issues related to the sample selection method, it is common in astronomical data to have non-detections."727 Such uou-detections are referred to as ‘censored’ data. and the standard procedure is to place an upper and/or lower limit ou the censored data poit.," Such non-detections are referred to as `censored' data, and the standard procedure is to place an upper and/or lower limit on the censored data point."728 Methods of data analysis for ceusored data have been reviewed aud proposed in the astronomical literature. (e.g...Feigelson&Nelson1985:Sclunitt1985:Magshall1992:Αίας&Siebert 1996).. and Isobeetal.(1986). describe censored regression when the variables are measured without error.," Methods of data analysis for censored data have been reviewed and proposed in the astronomical literature, \citep[e.g.,][]{feig85,schmitt85,marsh92,akritas96}, and \citet{isobe86} describe censored regression when the variables are measured without error."729 See Feigelsou(1992). for a review of censored. data in astronomy., See \citet{feig92} for a review of censored data in astronomy.730 To facilitate the inclusiou of censored data. [introduce au additional indicator variable. D. indicating whether a data poiut is censored or not on the depeudent variable.," To facilitate the inclusion of censored data, I introduce an additional indicator variable, $D$, indicating whether a data point is censored or not on the dependent variable."731 Tf y; is detected. then D;=1. else if y; is censored then D;= 0.," If $y_i$ is detected, then $D_i = 1$, else if $y_i$ is censored then $D_i = 0$ ."732 It is commonly the case that a source is cousidered “detected if its iieasured fiux falls above some iuultiple of the background5 noise level. sav 3o.," It is commonly the case that a source is considered `detected' if its measured flux falls above some multiple of the background noise level, say $3\sigma$."733 Then. in this case. the probability of detecting the source given the measured source flux y; is p(D;—Uys)= 1f uy;>36. and p(D;=Oly) Lif yy<30.," Then, in this case, the probability of detecting the source given the measured source flux $y_i$ is $p(D_i=1|y_i) = 1$ if $y_i > 3\sigma$, and $p(D_i=0|y_i) = 1$ if $y_i < 3\sigma$."734 Since source detection depeuds ou the measured flix. some sources with iutrinsie flux y above the flux limit will have a measured fiux y that falls below the flux limit.," Since source detection depends on the measured flux, some sources with intrinsic flux $\eta$ above the flux limit will have a measured flux $y$ that falls below the flux limit."735 Similarly. some sources with iutriusic flux below the flux Limit will have a imieasured fiux above the flix lint.," Similarly, some sources with intrinsic flux below the flux limit will have a measured flux above the flux limit."736 Tassie that a sample ds selected based on the independeut variables. ie. μονο)=pe).," I assume that a sample is selected based on the independent variables, i.e., $p(I|x,y) = p(I|x)$."737 It is ifhcult to duagine obtaining a censored sample if the sample is selected based ou its dependent variable. as μαome of the values of y are censored aud thus unknown.," It is difficult to imagine obtaining a censored sample if the sample is selected based on its dependent variable, as some of the values of $y$ are censored and thus unknown."738 Therefore. I ouly investigate the effects of ceusoriug on y When the probability that a source is included in the sample is independent of y. given we.," Therefore, I only investigate the effects of censoring on $y$ when the probability that a source is included in the sample is independent of $y$, given $x$."739 Ta addition. I o not address the issue of censoring on the independent variable.," In addition, I do not address the issue of censoring on the independent variable."740 Although such methods can be developed. --- is probably simpler to just omit such data as inference on the regression paramicters is unaffected when a sample is selected based oulv ou the independent variables (cf. 5.1.1)).," Although such methods can be developed, it is probably simpler to just omit such data as inference on the regression parameters is unaffected when a sample is selected based only on the independent variables (cf., \ref{s-seffects_x}) )."741 The observed data Likelihood for au a-selected sample isgiveu by Equation (39))., The observed data likelihood for an $x$ -selected sample isgiven by Equation \ref{eq-indlik}) ).742 We can modifv this likelihood. to account for censored y by including the indicator variable D and again inteerating over the mussing data:, We can modify this likelihood to account for censored $y$ by including the indicator variable $D$ and again integrating over the missing data:743non-barvonie compact objects (ο explain microlensing events.,non-baryonic compact objects to explain microlensing events.744" This conclusion will be made much stronger if larger future quasar samples demonstrate the limit on ο, to be <0.01. the fraction of barvons unexplained in the current. census (?).."," This conclusion will be made much stronger if larger future quasar samples demonstrate the limit on $\Omega_c$ to be $\lesssim7450.01$, the fraction of baryons unexplained in the current census \citep{misc:silk-baryons}."746" Also below this threshold. microlensing by ordinary stars in galaxies may become more significant. since ο,zz0.006 (7)."," Also below this threshold, microlensing by ordinary stars in galaxies may become more significant, since $\Omega_\ast \approx 0.006$ \citep*{misc:baryon-budget}."747 There are some important points to keep in mind when considering (hie analvsis leading to these constraints., There are some important points to keep in mind when considering the analysis leading to these constraints.748 The first is that. because the three sets of emission lines are [rom only one sample of quasars. the constraints are independent and cannot in general be combined io derive a stronger limit.," The first is that, because the three sets of emission lines are from only one sample of quasars, the constraints are independent and cannot in general be combined to derive a stronger limit."749 Rather the three sets of limits serve in some sense as checks on one another., Rather the three sets of limits serve in some sense as checks on one another.750 The second point concerns the absence of quoted lower limits., The second point concerns the absence of quoted lower limits.751" While ihe maxinmm-likelihood analysis formally. produces a nonzero most-likely value for ©, in sole cases. along with a lower limit. this should not be interpreted as an unambiguous detection of compact dark matter."," While the maximum-likelihood analysis formally produces a nonzero most-likely value for $\Omega_c$ in some cases, along with a lower limit, this should not be interpreted as an unambiguous detection of compact dark matter."752 It may very. well be Chat the intrinsic distribution at low equivalent widths departs from a simple lognormal: (his could be easily be misconstrued as evidence for lensing at low O.., It may very well be that the intrinsic distribution at low equivalent widths departs from a simple lognormal; this could be easily be misconstrued as evidence for lensing at low $\Omega_c$.753 Another wav of saving this is that because probability must be non-negative. anv departure [rom the exponentially small intrinsic probability at low equivalent width will result in a positive detection of compact dark matter. real or not.," Another way of saying this is that because probability must be non-negative, any departure from the exponentially small intrinsic probability at low equivalent width will result in a positive detection of compact dark matter, real or not."754 The other side of this argument is that if the actual unleused distribution does in fact have some probability al low equivalent widths not represented in the model. then the limits from the simple lognormal-based model will necessarily be conservative.," The other side of this argument is that if the actual unlensed distribution does in fact have some probability at low equivalent widths not represented in the model, then the limits from the simple lognormal-based model will necessarily be conservative."755 A large source of svstematic uncertainty in (his analvsis is the Daldwin effect. which deserves a much more thorough treatment (han was possible in this paper.," A large source of systematic uncertainty in this analysis is the Baldwin effect, which deserves a much more thorough treatment than was possible in this paper."756 The requirements of an acdequately parameterized distribution has led to (he introduction of a number of (?).. (D.VandenBerk2003.privatecommunication).. ?..," The maximum-likelihood requirements of an adequately parameterized distribution has led to the introduction of a number of \citep{sdss:qso-belr-shifts}. \citetext{D. Vanden Berk 2003,757 private communication}. \citet{lens:press-gunn},"758stals were eliuinated because of their large proper motions. which would skew the zero point of the proper motions.,"stars were eliminated because of their large proper motions, which would skew the zero point of the proper motions."759" The ""eSlt of steps 1 — Y was a set of parallaxes. proper motious. aud formal errors for all he stals whic ilad been measured in each Ποιά."," The result of steps 1 – 7 was a set of parallaxes, proper motions, and formal errors for all the stars which had been measured in each field."760 Table 2 (available in full in the electronic versiol of this paper) presents this information. aloug with the celestial coordinates. V. aid V=f anaguitueS. RMS residuas of the fits. aud statistical weights.," Table 2 (available in full in the electronic version of this paper) presents this information, along with the celestial coordinates, $V$ and $V-I$ magnitudes, RMS residuals of the fits, and statistical weights."761 A COLοςion to absolute parallax was estimated as follows., A correction to absolute parallax was estimated as follows.762 For each star ied for the reference frame. a «lstance was estimated from the measred £ au V—TJ color. using typical maln-sequeice values ta)lated by Pickles(1998)..," For each star used for the reference frame, a distance was estimated from the measured $I$ and $V-I$ color, using typical main-sequence values tabulated by \citet{pickles}."763 The straigit mean of the estimated refe'euce-star parallaNOS was usec to correct the relative parallax ¢» absolute., The straight mean of the estimated reference-star parallaxes was used to correct the relative parallax to absolute.764 Reddeuiug of lie refereuce stars was IOl taken Ito accoLit. nor was the possibility that they uight be giants. which we cauιοί exclude.," Reddening of the reference stars was not taken into account, nor was the possibility that they might be giants, which we cannot exclude."765 At hieh latitudes. οiauts of the apparent 1uagnitL(e of the refereice stars would be far out iu the alo ancl hence unliselypriori at lower latitucles. where many more rele‘ence stars were avallabe. a few Wus-1ceutified giants w«jid lead to a slig|t overestimation of the very stall «'Orrection.," At high latitudes, giants of the apparent magnitude of the reference stars would be far out in the halo and hence unlikely; at lower latitudes, where many more reference stars were available, a few mis-identified giants would lead to a slight overestimation of the very small correction."766" The use of £1iagnitucdes mitigaed the ellects of vbsorption to sole extent: in aly Case. ulaccouatecd-for extluction would somew""hat couuter-iutuively tend to make the stars appear ck»er than their true clistalces. because the ‘ecldlening woul uake the stars appear later-tvpe. aid |ence absolutely fainte ‘ancl hence closer than their true ¢]stance."," The use of $I$ magnitudes mitigated the effects of absorption to some extent; in any case, unaccounted-for extinction would somewhat counter-intuitively tend to make the stars appear closer than their true distances, because the reddening would make the stars appear later-type, and hence absolutely fainter, and hence closer than their true distance."767 Tje extinction would also make le slars appear fainter (and. hence fartler away). but Ie former effect more than compeus:ves for the latter.," The extinction would also make the stars appear fainter (and hence farther away), but the former effect more than compensates for the latter."768 Accordinely. this estimate is in ellec ali 1pper limit to the correction.," Accordingly, this estimate is in effect an upper limit to the correction."769 Tle COLrrecious were in all Cases stuall. of order 1 1jas. aud the unce‘tainty in the correction was iguorect.," The corrections were in all cases small, of order 1 mas, and the uncertainty in the correction was ignored."770 The number of stars measured i1 each field was large enough to allow au alter.ate calculation of the parallax error. as follows.," The number of stars measured in each field was large enough to allow an alternate calculation of the parallax error, as follows."771 A se olsars was Chosen for proximity οἱ the sky aid similarity in brightuess. aud the scatter of the fitted parallaxes o -AMliese stars was take Las au alterlale allax uncertainty.," A set of stars was chosen for proximity on the sky and similarity in brightness, and the scatter of the fitted parallaxes of these stars was taken as an alternate parallax uncertainty."772 The magnitude and. radius wiudow was adjisted o include ~10 stars ο: ore in the sample: typically stars within 3 arciiin aud xL mage of the program star were included. but this varied witely based on how mauy stars were available.," The magnitude and radius window was adjusted to include $\sim 10$ stars or more in the sample; typically stars within 3 arcmin and $\pm 1$ mag of the program star were included, but this varied widely based on how many stars were available."773 T10 scater was computed both arolic Zero aud around the stars’ pl1oloLjetric parallaxes. ut the shotomeric parallax adjustimeuts we'e small ellois0h. aud the errors large enough. that tiis inade little clierence in. practice.," The scatter was computed both around zero and around the stars' photometric parallaxes, but the photometric parallax adjustments were small enough, and the errors large enough, that this made little difference in practice."774 This measure of parallax 1ucertaluty weis swally somewliat greater 1 li1ο fit. errors above. but they were uot dram:ically larger. indjcatiiig that the fit eVOrs were dt 00 far olf.," This measure of parallax uncertainty was usually somewhat greater than the fit errors above, but they were not dramatically larger, indicating that the fit errors were not too far off."775 Nonetheless. these meast are probably more faithful indicators of the rue external error. aud they were tsel in the dista estiuates given later. except in those cases 1 which the estimated external erroFr wasfess than fortral error. which could happen because o “the sinall nuiyer of stars involved.," Nonetheless, these measures are probably more faithful indicators of the true external error, and they were used in the distance estimates given later, except in those cases in which the estimated external error was than the formal error, which could happen because of the small number of stars involved."776 The scater arouud the parallax and proper motion fits for the best. stablest comparison stars is around 6 uas (vector rius error).," The scatter around the parallax and proper motion fits for the best, stablest comparison stars is around 6 mas (vector rms error)."777 This is abou double the error obtained at USNO with a similar CCD and slightly poorer unage scale (Dalinetal.2002)., This is about double the error obtained at USNO with a similar CCD and slightly poorer image scale \citep{dahn02}.778. The short exposure times used in the oesent study may coutribute to tlis in the following, The short exposure times used in the present study may contribute to this in the following779Classical Be stars cau share many similar observational features with ILA&eDe star aud are likely to be more prevalent in the Galaxy. aud SAIC/LAIC. eiveu the short pre-inain sequence lifetimes of iuterinediate-niass stars.,"Classical Be stars can share many similar observational features with HAeBe star and are likely to be more prevalent in the Galaxy and SMC/LMC, given the short pre-main sequence lifetimes of intermediate-mass stars."780 Thus. establishing that ESIIC. and ΕΠΟ stars are in fact pre-1uain sequence objects requires clear evidence that their observed behavior is iucousisteut with that expected from classical De stars.," Thus, establishing that ESHC and ELHC stars are in fact pre-main sequence objects requires clear evidence that their observed behavior is inconsistent with that expected from classical Be stars."781 Figure 2 illustrates that the IR colors of mown SMC/LMC. classical Be stars share COMMLOL parameter space both with maux ESIIC/ELIIC stars and with some Calactic WAcBe stars., Figure \ref{2cdfig} illustrates that the IR colors of known SMC/LMC classical Be stars share common parameter space both with many ESHC/ELHC stars and with some Galactic HAeBe stars.782 Moreover. deWitetal.(2005) show that this degeneracy persists after corrections are made to ceredden the colors of Galactic ILÀAeDe stars to attempt to match the lower metallicity content of the Magellanic Clouds.," Moreover, \citet{dew05} show that this degeneracy persists after corrections are made to deredden the colors of Galactic HAeBe stars to attempt to match the lower metallicity content of the Magellanic Clouds."783 Thus the magnitude of he near-IR excess associated with ESIIC aud ELIIC stars alone is insufficient to conclusively cletermine whether hese objects are ITAcBe stars or classical Be stars., Thus the magnitude of the near-IR excess associated with ESHC and ELHC stars alone is insufficient to conclusively determine whether these objects are HAeBe stars or classical Be stars.784 Some aspects of the maguitude and time-scale of the shotometric variability exhibited by ILA&eDe stars aud classical Be stars cau be used to help identity the nature of ELIIC aud ESIC stars., Some aspects of the magnitude and time-scale of the photometric variability exhibited by HAeBe stars and classical Be stars can be used to help identify the nature of ELHC and ESHC stars.785 Classical Be stars are known o aperiodically exhibit dramatic eveuts whereby thev completely lose their disks or regenerate a new disk frou a disk-less stage (normal D to Be to normal D transitious: Underhill&Doazan1982:MeSwiiuctal.2009:Wis-niewskietal.2010:Draper 2011)).," Classical Be stars are known to aperiodically exhibit dramatic events whereby they completely lose their disks or regenerate a new disk from a disk-less stage (normal B to Be to normal B transitions; \citealt{und82,mcs09,wis10,dra11}) )."786 During these eveuts the stars optical photometry has been observed to change ~0.5 (Bjorkmanetal.2002) to ~0.7 magnitudes (IIlununel1998:Gaudetetal.2002:Miroshuicheukoal. 2003).," During these events the stars optical photometry has been observed to change $\sim$ 0.5 \citep{bjo02} to $\sim$ 0.7 magnitudes \citep{hum98,gan02,mir03}."787. .J.ILI&-baud. brishtuess variatious of <0.5 (0.95 imaenuitudes have been reported by Ashoketal.(1981). aud Doueherty&Tavlor(1991) over time-scales of huudreds of davs to tens of vears: the largest of these IR variations Likely correspond to large disk loss/disk-renewal eveuts.," J,H,K-band brightness variations of $<$ 0.5 - $\sim$ 0.95 magnitudes have been reported by \citet{ash84} and \citet{dou94} over time-scales of hundreds of days to tens of years; the largest of these IR variations likely correspond to large disk loss/disk-renewal events."788 Dougherty&Tavlor(1991) Sugeest that a 70.5 magnitude variation corresponds to a change in the density of au optically thin disk of a, \citet{dou94} suggest that a $\sim$ 0.5 magnitude variation corresponds to a change in the density of an optically thin disk of a789The identification. of possible dvnamical familics )etween the irregular satellites of the giant planets had oen a common task to all the studies. performed. on he subject.,The identification of possible dynamical families between the irregular satellites of the giant planets had been a common task to all the studies performed on the subject.790 Lhe existence of collisional families could. in winciple be explained by invoking the effects. of impacts »tween pairs of satellites ancl between satellites and roclies on heliocentric orbits., The existence of collisional families could in principle be explained by invoking the effects of impacts between pairs of satellites and between satellites and bodies on heliocentric orbits.791 “Lhe impact rate between satellite pairs is low even on timescales of the order of the Solar System age. with the only ex‘option of impacts amongst the most massive irregular satellites.," The impact rate between satellite pairs is low even on timescales of the order of the Solar System age, with the only exception of impacts amongst the most massive irregular satellites."792 The eravitational interactions between the giant. planets and the planctesimals in the early. Solar System may have pushe some of them in planetcrossing orbits., The gravitational interactions between the giant planets and the planetesimals in the early Solar System may have pushed some of them in planet–crossing orbits.793 This process is still active at the present time and C'entaurs may cross the Ην sphere of the planets., This process is still active at the present time and Centaurs may cross the Hill's sphere of the planets.794 However. Zahnleetal.(2003) showed that the present. Dux. of bodies. combined. with the small size of irregular satellites. is unable to supply an adequate impact. rate.," However, \cite{zah03} showed that the present flux of bodies, combined with the small size of irregular satellites, is unable to supply an adequate impact rate."795 ΙΓ collisions between planetesimals and satellites are responsible for the formation of families. these events should. date back sometime between the formation of the giant planets ancl the Late Heavy. The possible existence of dynamical families in. the Saturn satellite system has been explored by using cilferent approaches.," If collisions between planetesimals and satellites are responsible for the formation of families, these events should date back sometime between the formation of the giant planets and the Late Heavy The possible existence of dynamical families in the Saturn satellite system has been explored by using different approaches."796 Photometric comparisons has been exploited ov Gravetal.(2003):&Holman(2004):Burattietal.(2005). anc were limited. to a few bright objects.," Photometric comparisons has been exploited by \cite{gra03,gra04,bea05} and were limited to a few bright objects."797 Dynamical methods have been used by Crayetal.(2003):resvornyetal.(2003):Grav&LHolman(2004) but on he limited sample (about one third of the presently known population) of irregular satellites available at that ime.," Dynamical methods have been used by \cite{gra03,nes03,gra04} but on the limited sample (about one third of the presently known population) of irregular satellites available at that time."798 These methods aimed to identify those satellites which could. have originated. from a common parent body ollowing one or more breakup events., These methods aimed to identify those satellites which could have originated from a common parent body following one or more breakup events.799 The identification was based on the evaluation through Gauss equations of he dispersion in orbital element space due to the collisional ejection velocities., The identification was based on the evaluation through Gauss equations of the dispersion in orbital element space due to the collisional ejection velocities.800 In this paper we apply the (hereinafter UCAL)) described. in Zappaláetal.(1990.1904). to the irregular satellites of Saturn.," In this paper we apply the (hereinafter ) described in \cite{zap90,zap94} to the irregular satellites of Saturn."801 HCM is a clusterdetection algorithm which looks for groupings within a population of minor bodies with small nearestneighbour distances in orbital clement space., HCM is a cluster–detection algorithm which looks for groupings within a population of minor bodies with small nearest–neighbour distances in orbital element space.802 These distances are translated. into cillerences in. orbita velocities via Gauss equations and. the membership to a cluster or [αν is defined by giving a limiting velocity dillerence (cutoll)., These distances are translated into differences in orbital velocities via Gauss equations and the membership to a cluster or family is defined by giving a limiting velocity difference (cutoff).803 Nesvornyetal.(2003). adopted a cutoll velocity. value of LOO m/s according to hycrocode mocels (Benz&Aspaugh1999)., \cite{nes03} adopted a cutoff velocity value of $100$ m/s according to hydrocode models \citep{ben99}.804. Llere we prefer to relax this value to 200 m/s considering the possible range of variability of the mean orbital elements. because of dynamical. effects., Here we prefer to relax this value to $200$ m/s considering the possible range of variability of the mean orbital elements because of dynamical effects.805 The results we obtained are summarised in table 3 anc interpreted as in the By inspecting our data. we conclude that. as already argued by Nesvornyetal.(2003)... the velocity. dispersion of prograde ancl retrograde. satellites (about 500. m/s [or progrades and more than GOO mj/s for retrogracles) makes extremely implausible that cach of the two groups originated by a single. parent body.," The results we obtained are summarised in table \ref{families} and interpreted as in the By inspecting our data, we conclude that, as already argued by \cite{nes03}, the velocity dispersion of prograde and retrograde satellites (about $500$ m/s for progrades and more than $600$ m/s for retrogrades) makes extremely implausible that each of the two groups originated by a single parent body."806 In. addition. the classification in dynamical groups based. on the values. of he orbital inclination originally proposed. by Cladimanal.(2001). and. reported by other authors (see Sheppare(2006) and references within) is probably misleading.," In addition, the classification in dynamical groups based on the values of the orbital inclination originally proposed by \cite{gla01} and reported by other authors (see \cite{she06} and references within) is probably misleading."807" ""roerade satellites like Ixiviuq. LDiraq. Siarnaq ancl Paaliac do share the same inclination but. as à group. they have a velocity. dispersion of over 450 m/s. hardly deriving rom the breakup of a single. parent. body."," Prograde satellites like Kiviuq, Ijiraq, Siarnaq and Paaliaq do share the same inclination but, as a group, they have a velocity dispersion of over $450$ m/s, hardly deriving from the breakup of a single parent body."808 Lhe enlarge population of retrograde satellites we have analysed show hat the clustering around a single inclination and their association to Phoebe (Cladmaneal.2001) is not an indication of à common origin., The enlarged population of retrograde satellites we have analysed show that the clustering around a single inclination \citep{gla01} and their association to Phoebe \citep{gla01} is not an indication of a common origin.809 The required velocity dispersion is in fact about 650 We found. two potential dynamical. familics between the prograde satellites: the couple WiviucLiraq and what we term asfamily. composed of Alhiorix. Erriapo. Jarvos and 8/2004 S11.," The required velocity dispersion is in fact about $650$ We found two potential dynamical families between the prograde satellites: the couple Kiviuq–Ijiraq and what we term as, composed of Albiorix, Erriapo, Tarvos and S/2004 S11."810 The analysis of the retrograde satellites is more complex., The analysis of the retrograde satellites is more complex.811 There are three possible groups each composed of three. satellites and two others. by two satellites. all characterised by acceptable values of the velocity dispersion. (between 100. and. 170. m/s)," There are three possible groups each composed of three satellites and two others by two satellites, all characterised by acceptable values of the velocity dispersion (between $100$ and $170$ m/s)."812 A sixth possible group satisfying our acceptance criterion is composed of Narvi and 8/2004 S18. but its interpretation is quite tricky.," A sixth possible group satisfying our acceptance criterion is composed of Narvi and S/2004 S18, but its interpretation is quite tricky."813 This group shows a high velocity dispersion. at the upper limit of our range. but the dynamical evolution of both satellites is uncertain on a timescale of 10. vears.," This group shows a high velocity dispersion, at the upper limit of our range, but the dynamical evolution of both satellites is uncertain on a timescale of $10^{9}$ years."814 The orbits of both bodies have the most extreme values of inclination among all retrograde satellites., The orbits of both bodies have the most extreme values of inclination among all retrograde satellites.815 Our numerical experiments with test particles showed that for such bodies the cecentricity dis. strongly coupled to the inclination (sce fie. 27))., Our numerical experiments with test particles showed that for such bodies the eccentricity is strongly coupled to the inclination (see fig. \ref{forced-e}) ).816 In our simulations. initially circular. orbits became highly eccentric in less than LO? vears.," In our simulations, initially circular orbits became highly eccentric in less than $10^{6}$ years."817 Lt is possible that Narvi ane 5/2004 SIS had. similar orbits in the past which later civerged due to the inclinationeecentricity Some of our candidate Families merge at higher values of the velocity dispersion forming bigeer groups we calledclusters., It is possible that Narvi and S/2004 S18 had similar orbits in the past which later diverged due to the inclination–eccentricity Some of our candidate families merge at higher values of the velocity dispersion forming bigger groups we called.818 Phe most relevant one is that termed. as cluster A jn table 3.., The most relevant one is that termed as cluster A in table \ref{families}.819 It is made of two thiree-body. families and an incliviclual satellite and it is defined at à velocity cut.oll of 150 m/s. At à velocity cut.olf of 202 m/s cluster A moerges with the twoΡον family related to 8/2004 S15 forming cluster D. Confirming these dynamical groups by comparing their colour. indices is a οποια task because of the limited amount of data available in the literature., It is made of two three-body families and an individual satellite and it is defined at a velocity cut–off of $150$ m/s. At a velocity cut–off of $202$ m/s cluster A merges with the two–body family related to S/2004 S15 forming cluster B. Confirming these dynamical groups by comparing their colour indices is a difficult task because of the limited amount of data available in the literature.820 The only spectrophotometric cata concerning Saturn's retrograde satellites are those of Phoebe and Ymir. which. according to our analysis. are separated. by a velocity dispersion of more than GOO m/s. Phoebe appears to have colours not compatible with any other irregular satellite of the system. supporting our claim that Phoebe is not related to the rest of Saturn's present population of irregular The situation looks more favourable for prograde families: the colours of three members of the possible Albiorix family are available. with two sets of data for Albiorix itself.," The only spectrophotometric data concerning Saturn's retrograde satellites are those of Phoebe and Ymir, which, according to our analysis, are separated by a velocity dispersion of more than $600$ m/s. Phoebe appears to have colours not compatible with any other irregular satellite of the system, supporting our claim that Phoebe is not related to the rest of Saturn's present population of irregular The situation looks more favourable for prograde families: the colours of three members of the possible Albiorix family are available, with two sets of data for Albiorix itself."821 The colour data are reported in table 4 with the corresponding le errors., The colour data are reported in table \ref{family-colour} with the corresponding $1\sigma$ errors.822 These data seem. to be compatible with the hypothesis of a common origin of the eroup at a 37 level., These data seem to be compatible with the hypothesis of a common origin of the group at a $3\sigma$ level.823(Watson 11995).,(Watson 1995).824 The observed variation of the light curves with the colour ratios suggests that the absorption process is likely to be bouncd-free absorption of the Balmer continuum., The observed variation of the light curves with the colour ratios suggests that the absorption process is likely to be bound-free absorption of the Balmer continuum.825 This is predominantly in the U-band. and the variations in the colour ratios and light curves are explained by variations in the amount and density of material confined by the magnetic Ποιά Hines of the white ciwart.," This is predominantly in the U-band, and the variations in the colour ratios and light curves are explained by variations in the amount and density of material confined by the magnetic field lines of the white dwarf."826 The phase of the onset of the trough is later than that of the pre-eclipse dip seen in the light curves of HU «qe Allin 11999: Bridge 22002). which was identified as the eclipse of the accretion region by the strongly collimated. accretion. stream.," The phase of the onset of the trough is later than that of the pre-eclipse dip seen in the light curves of HU Aqr (Harrop-Allin 1999; Bridge 2002), which was identified as the eclipse of the accretion region by the strongly collimated accretion stream."827 “This phase is determined by the geometry of the field. lines carrving the acereting material. so a cillerence between systems is not unexpected.," This phase is determined by the geometry of the field lines carrying the accreting material, so a difference between systems is not unexpected."828 While the onset of the trough feature is Consistent with an eclipse caused. by the accretion stream. an extended accretion curtain would cause absorption over an extended phase range (previous section) and. produce the observed Hat light curves during the trough (Figures E: and 2)).," While the onset of the trough feature is consistent with an eclipse caused by the accretion stream, an extended accretion curtain would cause absorption over an extended phase range (previous section), and produce the observed flat light curves during the trough (Figures \ref{fig:whitelight} and \ref{fig:UBVRcurves}) )."829 The extent of this accretion curtain can be estimated using the eclipse light curve features and the ecometric model introduced earlier., The extent of this accretion curtain can be estimated using the eclipse light curve features and the geometric model introduced earlier.830" A value of 4, can be estimated by varying the parameter until the field lines begin to eclipse the accretion region. at the phase set by the start of the trough in the ligh curve."," A value of $R_{\mu}$ can be estimated by varying the parameter until the field lines begin to eclipse the accretion region, at the phase set by the start of the trough in the light curve."831" For those eveles with brighter streams and accretion regions. where the onset of the trough is earlier. we finc values of £2,~Ode (lor 5=65) and 0.19 (for 7= Ls"")."," For those cycles with brighter streams and accretion regions, where the onset of the trough is earlier, we find values of $R_{\mu}\sim0.14a$ (for $\beta=65^{\circ})$ and $0.19a$ (for $\beta=18^{\circ}$ )."832" For those eveles where the onset of the trough is later a 6=0.90. we find 2,~0.16a (for 3= 65) and 0.22« (for j— ISO."," For those cycles where the onset of the trough is later at $\phi=0.90$, we find $R_{\mu}\sim0.16a$ (for $\beta=65^{\circ}$ ) and $0.22a$ (for $\beta=18^{\circ}$ )."833 The outer edge of the curtain. where materia ireads closest to the secondary. can be estimated from. 1e end of the egress of bright. stream material around © = 1.1. and is independent. of 3.," The outer edge of the curtain, where material threads closest to the secondary, can be estimated from the end of the egress of bright stream material around $\phi$ = 1.1, and is independent of $\beta$."834 This assumes there is no significant continuum emission from the ballistic section of 10 accretion stream. where material is expected to be faint nd cooling as it falls.," This assumes there is no significant continuum emission from the ballistic section of the accretion stream, where material is expected to be faint and cooling as it falls."835 For those eveles where the bright gaream egress is clearly seen. we find a value of ~θεα.," For those cycles where the bright stream egress is clearly seen, we find a value of $\sim0.42a$."836 For rose evcles with Lauter streams the egress ofthe stream is =[udot seen., For those cycles with fainter streams the egress of the stream is not seen.837 We therefore infer that brighter streams result in a wider accretion curtain. with more material in the accretion gaream penetrating further into the magnetosphere.," We therefore infer that brighter streams result in a wider accretion curtain, with more material in the accretion stream penetrating further into the magnetosphere."838 For faint stream eveles a decline in [ux is seen immecdiately before the eclipse of the accretion region (see Section 3.2))., For faint stream cycles a decline in flux is seen immediately before the eclipse of the accretion region (see Section \ref{sec:streameclipse}) ).839 This could be due to the eclipse of stream material which is threacing early in the trajectory. and which should emit through magnetic heating.," This could be due to the eclipse of stream material which is threading early in the trajectory, and which should emit through magnetic heating."840 Alternatively the decline could be caused by absorption by material along the line of sight to the white dwarl and accretion region (see Section 4.3))., Alternatively the decline could be caused by absorption by material along the line of sight to the white dwarf and accretion region (see Section \ref{sec:trough}) ).841 The trough is absent in. the observations οἱ temillard ((1991) ancl SMO97., The trough is absent in the observations of Remillard (1991) and SM97.842 “Phe stream also appears to be fainter in both previous observations. although this may be due to 16 poorer sampling.," The stream also appears to be fainter in both previous observations, although this may be due to the poorer sampling."843 The lack of a bright stream may. be 1e cause of this absence of a trough in their light curves. if 1e two are linked as we suggest.," The lack of a bright stream may be the cause of this absence of a trough in their light curves, if the two are linked as we suggest."844" An extended: accretion curtain with material. being weacded at dillerent Z6, would allow material to accrete over uj extended. region on the white dwarf.", An extended accretion curtain with material being threaded at different $R_{\mu}$ would allow material to accrete over an extended region on the white dwarf.845 The foot points of 1e field lines form an arc shape on the white dwarf surface., The foot points of the field lines form an arc shape on the white dwarf surface.846 uluch an extended accretion region would be consistent with 10 optical1 evelotron models of SM97 which show evidence or an accretion arc or ribbon., Such an extended accretion region would be consistent with the optical cyclotron models of SM97 which show evidence for an accretion arc or ribbon.847 We have analysed the first high signal-to-noise ratio and hieh time resolution data of EP Dra taken on two consecutive nights at the WITT using S-Came2., We have analysed the first high signal-to-noise ratio and high time resolution data of EP Dra taken on two consecutive nights at the WHT using S-Cam2.848 The eclipse light curves show variability in the accretion stream and accretion region over the timescale of the orbital period., The eclipse light curves show variability in the accretion stream and accretion region over the timescale of the orbital period.849 We see no direct evidence in the light curves for the expected. rapid. eclipse of a small accretion region on the white cwark, We see no direct evidence in the light curves for the expected rapid eclipse of a small accretion region on the white dwarf.850 The rapid eclipse seen in the light curves is à combination of emission from the white chwarl photosphere and the accretion region., The rapid eclipse seen in the light curves is a combination of emission from the white dwarf photosphere and the accretion region.851 We see evidence for the variability of the aceretion region from the variation in brightness of the rapid eclipse ingress with the varving aceretion stream brightness., We see evidence for the variability of the accretion region from the variation in brightness of the rapid eclipse ingress with the varying accretion stream brightness.852 Variability seen in the light curves on a longer timescale is inlluenced to some extent by evelotron beaming., Variability seen in the light curves on a longer timescale is influenced to some extent by cyclotron beaming.853 However from the colour dependence. there is. probably also a contribution from absorption. and this is seen às a trough in the light curves of the second. night.," However from the colour dependence, there is probably also a contribution from absorption, and this is seen as a trough in the light curves of the second night."854 We attribute the absorption to. bound-free. absorption by material in an extended. acerction curtain obscuring the accretion region ancl white dwarf., We attribute the absorption to bound-free absorption by material in an extended accretion curtain obscuring the accretion region and white dwarf.855 Phere may also be significant absorption by material located close to the white dwarf above the accretion reeion., There may also be significant absorption by material located close to the white dwarf above the accretion region.856 Accreting material is threaded. onto many field. lines along the accretion stream trajectory. ancl the location in phase of the onset of the trough or absorption dip provides an estimate of the location of the edge of the accretion curtain.," Accreting material is threaded onto many field lines along the accretion stream trajectory, and the location in phase of the onset of the trough or absorption dip provides an estimate of the location of the edge of the accretion curtain."857 Variations in the brightness of the accretion stream seen after the ingress of the white cwarl and the accretion region are caused by a change in the location of bright stream material in the accretion curtain and/or a change in the extent of the curtain., Variations in the brightness of the accretion stream seen after the ingress of the white dwarf and the accretion region are caused by a change in the location of bright stream material in the accretion curtain and/or a change in the extent of the curtain.858 From the extent of the accretion curtain we infer the presence of an extended. accretion arc at the foot points of the acereting field. lines. however this region is still small compared with the size of the white cart.," From the extent of the accretion curtain we infer the presence of an extended accretion arc at the foot points of the accreting field lines, however this region is still small compared with the size of the white dwarf."859 We acknowledge the contributions of other members of the Research and. Seientifie Support Department of, We acknowledge the contributions of other members of the Research and Scientific Support Department of860—,.861 Allowing for enerev-clepenclent diffusion. we get. inserting into(38).. Εν 12 Ey 4)4.," Allowing for energy-dependent diffusion, we get, inserting into, -1 ) ( - E_0 )."862 As in the ease of(40)... also does not depend on the magnitude of the cdilfision coefficient. only on the distance r; to the source. ancl via(36).. on the Gime since the injection of the particles into the ISM.," As in the case of, also does not depend on the magnitude of the diffusion coefficient, only on the distance $r_i$ to the source, and via, on the time since the injection of the particles into the ISM."863 In the limit of E—0. reduces to(40).," In the limit of $E\rightarrow 0$, reduces to."864. We calculated (the contribution from Geminea and BOGSG+14 (o the positron LIS [or distances of ppc (Caraveoetal.1996) and ppc (Manchesteretal.2005) respectively (assuming 7— 2Okvr and J= 60kvr). in addition to the expected anisotropies in the positron LIS.," We calculated the contribution from Geminga and B0656+14 to the positron LIS for distances of pc \citep{C96} and pc \citep{atnf} respectively (assuming $T\,=\,20\,$ kyr and $T\,=\,60\,$ kyr), in addition to the expected anisotropies in the positron LIS."865 The results for birth periods of 4d0nmuns and GOmams are plotted in (he left panels of Figs., The results for birth periods of ms and ms are plotted in the left panels of Figs.866 1 and 2.. where we compare our calculations with the measurements from Doezioetal.(2000) and DuVernoisetal.(2001)..," \ref{fig:geminga} and \ref{fig:bo656}, where we compare our calculations with the measurements from \citet{2000ApJ...532..653B} and \citet{2001ApJ...559..296D}."867 We have shown that one can expect a non-negligible Cli positron component in the LIS from nearby pulsars that may become dominant above several GeV. in agreement with Ἀίοναetal.(1995) who showed that the high-energv positron LIS may be explained by a voung. nearby source.," We have shown that one can expect a non-negligible CR positron component in the LIS from nearby pulsars that may become dominant above several GeV, in agreement with \citet{1995PhRvD..52.3265A} who showed that the high-energy positron LIS may be explained by a young, nearby source."868 In (he context of our model. we are able to constrain the permissible pulsar birth period. £2). depending on the magnitude of the interstellar diffusion coefficient.," In the context of our model, we are able to constrain the permissible pulsar birth period $P_0$, depending on the magnitude of the interstellar diffusion coefficient."869 For the two nearest pulsars with characteristic ages in the range vvr to vvr. Geminga and D06564-14. we show that in particular lor D0656--14 one can expect. in the absence of a backeround flux. an anisotropy in the positron LIS of up to almost3%.. significantly larger than the expected value of 220.257€ [or Geminga.," For the two nearest pulsars with characteristic ages in the range yr to yr, Geminga and B0656+14, we show that in particular for B0656+14 one can expect, in the absence of a background flux, an anisotropy in the positron LIS of up to almost, significantly larger than the expected value of $\approx$ for Geminga."870 As shown in Figs., As shown in Figs.871 1. and 2.. the observed anisotropy also gives an estimate of the contribution of (he pulsar to the positron LIS.," \ref{fig:geminga} and \ref{fig:bo656}, the observed anisotropy also gives an estimate of the contribution of the pulsar to the positron LIS."872 On the, On the873orotherwise only Dey;4 and use,There are several other for which we consider the following truncation.874 2 > Dp ⋅⋡↴⋟∖⊽∩∐⋜↙∫⋟3 Sul aglr ga)⋅↽↴∩≼←⋟⋅+, We refer the reader to \cite{allrpaper} for a discussion.875 ; ↜∣ hy)1ro which(3), This implies where $R$ is the Ricci scalar.876 Sane↜∣ a σα(r+hk a sufficientapproximation since Y alwavs comeswith a [actor of e. Theevent horizonis," For our ansatz to constitute a solution, it must satisfy the equations of motion for the, the moduli $Y^I$,the auxiliary field $T_{01}^-$, as well as the fields $A_a$, and either $V_a$ or $D$ depending on the compensating multiplet used."877 locatedal r = innerhorizonal tobe valid.we require ..ο forall£-functions for r 2jrWewere not ablet," In the cases that we solved, we observed that when using the hypermultiplet compensating multiplet, the equation of motion for $D$ has an overall factor of $(k^3-k_0)^2$, after substituting the ansatz."878o extendthis requirement Although the approximation breaksdownat," For $k^3=k_0$, one has to take this limit only after solving the equations of motion, in order not to lose a constraint."879 the innerhorizon. the solutions are valid inthe physical regionof," The Einstein-Hilbert term in the Lagrangian, determines that “Newton's constant” is given by the unscaled Kähhler potential: Usually one fixes $G_N=1$ as the dilatational $D$ -gauge choice."880 interest. [romthe eventhorizon," This, however, is too restrictive and does not always allow a solution."881 to infinity.Ir addition we setthe boundary," Therefore $G_N$ is a function of the radial coordinate, resembling the case of dilaton gravity."882" conditions: lim,ος £(r)—0.", The metric in the Einstein frame is given by $g^E_{\mu\nu}=G_N^{-1}g_{\mu\nu}$.883 This givesan asvinploticallyflat solution. The equations of motionfor the vectorfield strengths were derivedin Fy) iB EDT = (iGo," The ADM mass (in Planck units) for a non-normalized metric is given by One may see this by applying the coordinate transformation $t\rightarrow(-g^E_{tt}(\infty))^{-1/2}t,~r\rightarrow g^E_{rr}(\infty)^{-1/2}r$ to get the conventionally normalized line element."884HF+5 (Εν+FaAES iF. SE, The central charge is given by885HF+5 (Εν+FaAES iF. SEA, The central charge is given by886 (2???) (e.g.222?)..," $0 < z \lesssim8871$ \citep{CFRS95,ECBHG96,LYCE97,CNOC299} \citep[e.g.\ ][]{KIFD01,DFKI01,Vogtetal96,BZB96}."888 (??2?) K- (999)..," \citep{KWG93,SP99,CLBF00} $K$ \citep{RR93,KC98a,BE00}."889 K-band ~3 K-band ? ~5000 2)). 3)) A-band (84)). (35)). £25;=0.3.Q4=0.7 Hy=100//kms7!Mpe7!. Ji=0.60 /i ," $K$ $\sim 3$ $K$ \citet{MUNICS1} $\sim 5000$ \ref{s:sample}) \ref{s:photred}) $K$ \ref{s:integ_mf}) \ref{s:discuss}) $\Omega_M = 0.3$$\Omega_{\Lambda} = 0.7$ $H_0 = 100\ h\ \mathrm{km\ 890 s^{-1}\ Mpc^{-1}}$ $h = 0.60$ $h$ "891were obtained by Schwarz et al. (,were obtained by Schwarz et al. (8922004) to determine the orbital period of the svslem.,2004) to determine the orbital period of the system.893 They [found a period of 1.7 hours from the fit to the radial velocity curve as determined from the convolution of double Gaussians (o the line profiles (Schafter 1985)., They found a period of 1.7 hours from the fit to the radial velocity curve as determined from the convolution of double Gaussians to the line profiles (Schafter 1985).894 Unlortunately the derived. period was similar in length to the total observing time and couldn't be classified as a definite period due to undersampling., Unfortunately the derived period was similar in length to the total observing time and couldn't be classified as a definite period due to undersampling.895" Nevertheless the Ila emission showed a clear periodic change in its blue and red components during the observing run which supported a short orbital period (tvpical of WZ See svstems,", Nevertheless the $\alpha$ emission showed a clear periodic change in its blue and red components during the observing run which supported a short orbital period typical of WZ Sge systems.896 An optically thin disk. showing the WD absorption. is indicative of a short period. low-ii2 svstem (i.e. below (he period eap).," An optically thin disk, showing the WD absorption, is indicative of a short period, $\dot{m}$ system (i.e. below the period gap)."897 Likewise. (he lack of an accretion disk in the optical spectrum placed a firm upper limit of 3 hours on the orbital period of PQ And.," Likewise, the lack of an accretion disk in the optical spectrum placed a firm upper limit of 3 hours on the orbital period of PQ And."898 schwarz et al., Schwarz et al.899 also determined the effective temperature and surface gravity of the white dwarl (WD) using svnthetic spectra from model atmospheres., also determined the effective temperature and surface gravity of the white dwarf (WD) using synthetic spectra from model atmospheres.900" The best fits gave T,y; = 12.000 zx 1.000 Α΄ and log(g) = 7.7 + 0.3 (egs units) which placed PQ And in the region of the ZZ Celi instability strip (Bergeron el al."," The best fits gave $_{eff}$ = 12,000 $\pm$ 1,000 K and $g$ ) = 7.7 $\pm$ 0.3 (cgs units) which placed PQ And in the region of the ZZ Ceti instability strip (Bergeron et al."901 1995: 2004)., 1995; 2004).902 Thev noted that with its low accretion rate. PQ And was an excellent candidate {ο search [or non-racial oscillations which have recently been observed in other WZ Sge novae.," They noted that with its low accretion rate, PQ And was an excellent candidate to search for non-radial oscillations which have recently been observed in other WZ Sge novae."903 In (his paper we present the results of a photometric campaign {ο search [or non-radial pulsations in PQ And., In this paper we present the results of a photometric campaign to search for non-radial pulsations in PQ And.904 Section 2 provides details of the observations., Section 2 provides details of the observations.905 The analvsis of the data are given in Section 3 and our conclusions follow in Section 4., The analysis of the data are given in Section 3 and our conclusions follow in Section 4.906 Our photometric observations were carried out using the Orthogonal Parallel Transfer Tinaging Camera (OPTIC. see Howell et al. 2003) at the WIYN observatory 3.5-in telescope located on Wilt Peak.," Our photometric observations were carried out using the Orthogonal Parallel Transfer Imaging Camera (OPTIC, see Howell et al, 2003) at the WIYN observatory 3.5-m telescope located on Kitt Peak."907 OPTIC is (he only prototvpe orthogonal (ransler CCD imager operating (see Tonrv el al..," OPTIC is the only prototype orthogonal transfer CCD imager operating (see Tonry et al.,"908 2002) and consists of two 2IX by 4x CCLD-28 OTCCDs in a single dewar mounted adjacent to each other with a small gap in between the chips., 2002) and consists of two 2K by 4K CCID-28 OTCCDs in a single dewar mounted adjacent to each other with a small gap in between the chips.909 OPTIC is controlled by standard. SDSU-2 electronics running custom mierocode and reads out (he two OTCCDs via 4 video channels. one located in each corner of the device.," OPTIC is controlled by standard SDSU-2 electronics running custom microcode and reads out the two OTCCDs via 4 video channels, one located in each corner of the device."910 OPTIC has a read noise of <4 electrons when read at a normal rate of 160 kpix/sec and a gain of 1.45 e/ADU., OPTIC has a read noise of $<$ 4 electrons when read at a normal rate of 160 kpix/sec and a gain of 1.45 e/ADU.911 We used OPTIC in conventional mode placing the target star and all comparison stars of interest in one of the CCDs., We used OPTIC in conventional mode placing the target star and all comparison stars of interest in one of the CCDs.912 Two {ime series data seis. were obtained. the first was on the night of 1H September 2004 UT and the second on 13 October 2004 UT.," Two time series data sets were obtained, the first was on the night of 14 September 2004 UT and the second on 13 October 2004 UT."913 The September observations consisted of ~125. 45 second observations using a Johnson V filter.," The September observations consisted of $\sim$ 125, 45 second observations using a Johnson V filter."914 The CCD was binned 2 X 2 (the seeing on this night was 1.67) and the readout (ime was 8 seconds.," The CCD was binned 2 X 2 (the seeing on this night was 1.6"") and the readout time was 8 seconds."915 The October observations consisted of ~100 60 second V-band integrations using 1 X 1 binning (reaclout time was 24 seconds) and {he seeing was 0.5*," The October observations consisted of $\sim$ 100 60 second V-band integrations using 1 X 1 binning (readout time was 24 seconds) and the seeing was 0.5""."916 The data were reduced using the standard IRAF packages., The data were reduced using the standard IRAF packages.917 Relative photometry was performed using four different background stars as references., Relative photometry was performed using four different background stars as references.918 Figure 1 shows a plot of ihe magnitude difference as a function of time for both nights., Figure 1 shows a plot of the magnitude difference as a function of time for both nights.919 The squares represent, The squares represent920older starbursts are related to galactic mergers themselves or to the putative coalescence of the central black holes in post-merger galaxies.,older starbursts are related to galactic mergers themselves or to the putative coalescence of the central black holes in post-merger galaxies.921 The latter possibility can be viably tested by comparing the starburst ages to the dynamic ages of the active and passive lobes in the X-shaped objects., The latter possibility can be viably tested by comparing the starburst ages to the dynamic ages of the active and passive lobes in the X-shaped objects.922 The KS-test applied to the distributions of the most recent starburst ages gives a statistical significance of 2.30 for the two samples being different., The KS-test applied to the distributions of the most recent starburst ages gives a statistical significance of $\sigma$ for the two samples being different.923" To account for a possible dependence of this difference on the galactic type, we apply the KS-test to the X-shaped sample and the subsample of control ellipticals."," To account for a possible dependence of this difference on the galactic type, we apply the KS-test to the X-shaped sample and the subsample of control ellipticals."924 The results of the test show that the starburst ages of the X- sources and the control ellipticals are still different at a statistical significance of 2.1o., The results of the test show that the starburst ages of the X-shaped sources and the control ellipticals are still different at a statistical significance of $\sigma$.925" In Fig. 8,,"," In Fig. \ref{fig9},"926 histograms of the logarithm of the ratio of the dynamic age and most recent starburst age are plotted for the X-shaped sources and control sources of Region 0., histograms of the logarithm of the ratio of the dynamic age and most recent starburst age are plotted for the X-shaped sources and control sources of Region 0.927" The mean logarithmic ratios are —1.29+0.23 and —0.14+0.18 for the X-shaped objects and the control sample, respectively."," The mean logarithmic ratios are $-1.29 \pm 0.23$ and $-0.14928\pm 0.18$ for the X-shaped objects and the control sample, respectively."929" The X-shaped sources tend to have starburst ages that are older than the dynamic ages of the radio lobes, while in both the control sample and the control subsample of ellipticals these ages are comparable."," The X-shaped sources tend to have starburst ages that are older than the dynamic ages of the radio lobes, while in both the control sample and the control subsample of ellipticals these ages are comparable."930 The starburst activity in X-shaped sources is therefore likely not related to the active lobes., The starburst activity in X-shaped sources is therefore likely not related to the active lobes.931 The KS-test shows that the ratio distributions are different at a statistical significance of 2.8σ., The KS-test shows that the ratio distributions are different at a statistical significance of $\sigma$.932 This difference in the starburst/dynamic age ratios may support the scenario in which the active lobes of the X-shaped sources are due to a possible reorientation caused by a black hole merger (Merritt Ekers 2002)) that leaves the old low-surface-brightness lobes inactive., This difference in the starburst/dynamic age ratios may support the scenario in which the active lobes of the X-shaped sources are due to a possible reorientation caused by a black hole merger (Merritt Ekers \cite{merritt}) ) that leaves the old low-surface-brightness lobes inactive.933" Assuming that the low-surface-brightness lobes became inactive when the high-surface ones were activated, the dynamic age of the passive lobes during their active stage can be determined using Eq. 5.."," Assuming that the low-surface-brightness lobes became inactive when the high-surface ones were activated, the dynamic age of the passive lobes during their active stage can be determined using Eq. \ref{wings}."934 The ratio of the total dynamic age of the active plus passive lobes to the starburst age is plotted in Fig., The ratio of the total dynamic age of the active plus passive lobes to the starburst age is plotted in Fig.935" 8 (second panel), and it indicates that the starburst age still remains older than the total dynamic age of the lobes."," \ref{fig9} (second panel), and it indicates that the starburst age still remains older than the total dynamic age of the lobes."936" This suggests that the starburst activity in X-shaped sources had occured before the possible reorientation owing to a black hole merger, and it may have been related to the galactic merger itself."," This suggests that the starburst activity in X-shaped sources had occured before the possible reorientation owing to a black hole merger, and it may have been related to the galactic merger itself."937" Instead of analyzing all the X-shaped sources with optical spectra available, we can constrain the X-shaped sample to only the X-shaped radio galaxies included in the bona fide sample of Landt et al. (2010))."," Instead of analyzing all the X-shaped sources with optical spectra available, we can constrain the X-shaped sample to only the X-shaped radio galaxies included in the bona fide sample of Landt et al. \cite{landt2010}) )."938" This implies taking out 10 of the 29 X-shaped sources included in our sample, which leads to a 50% increase in the statistical erros, but does not change the obtained results."," This implies taking out 10 of the 29 X-shaped sources included in our sample, which leads to a $\%$ increase in the statistical erros, but does not change the obtained results."939" The statistical studies would be improved, on the other hand, by the addition of more X-shaped radio sources to the sample."," The statistical studies would be improved, on the other hand, by the addition of more X-shaped radio sources to the sample."940 This will be done with the availability of new optical spectra., This will be done with the availability of new optical spectra.941One of the fundamental problems in (he search for exoplanets via transits is (he relatively small fraction of svstems exhibiting periodic (ransils that are found {ο be caused by exoplanets alter lollow-up observations reveal the nature of the orbiting body.,One of the fundamental problems in the search for exoplanets via transits is the relatively small fraction of systems exhibiting periodic transits that are found to be caused by exoplanets after follow-up observations reveal the nature of the orbiting body.942 The process of verification consumes a great deal of telescope time on top-class instruments., The process of verification consumes a great deal of telescope time on top-class instruments.943 This process would be, This process would be944orders of magnitude shorter than a usual OSSE exposure.,orders of magnitude shorter than a usual OSSE exposure.945 OSSE observed GRO J1655-40 during the 1996 outburst VHS when the source was very variable on time scales of hours and longer., OSSE observed GRO J1655-40 during the 1996 outburst VHS when the source was very variable on time scales of hours and longer.946 In this case the long accumulation time can result in a biases in the observed spectral shape., In this case the long accumulation time can result in a biases in the observed spectral shape.947 We suggest that the presence of the extended power law up to ~700 keV in OSSE spectra can be a result of the long accumulation time scale when specific details of the spectra can be biased particularly at high energies., We suggest that the presence of the extended power law up to $\sim 700$ keV in OSSE spectra can be a result of the long accumulation time scale when specific details of the spectra can be biased particularly at high energies.948" Despite the fact that HEXTE is not sensitive above 300 keV, it is able to sample the source spectrum with much more detailed temporal resolution."," Despite the fact that HEXTE is not sensitive above 300 keV, it is able to sample the source spectrum with much more detailed temporal resolution."949 Our analysis of the PCA/HEXTE from XTE 1550-564 indicates that VHS spectra do show exponential turnover at energies about 200 keV Fig. , Our analysis of the PCA/HEXTE from XTE 1550-564 indicates that VHS spectra do show exponential turnover at energies about 200 keV (see Fig. \ref{cutoff_vs_index_1998}) ).950"Moreover, our results clearly show that the (seecutoff energy4)). changes gradually from the LHS through the IS towards the HSS."," Moreover, our results clearly show that the cutoff energy changes gradually from the LHS through the IS towards the HSS."951 It is worth noting that Mottaetal. concluded that the cutoff power law in the PCA/HEXTE(2009) spectrum of GX 339-4 is most likely due to one spectral component., It is worth noting that \citet{motta} concluded that the cutoff power law in the PCA/HEXTE spectrum of GX 339-4 is most likely due to one spectral component.952" These facts indicate strongly that HEXTE more be more reliable source of information on the hard tails of X-ray spectra, at least, up to 300 keV than OSSE."," These facts indicate strongly that HEXTE more be more reliable source of information on the hard tails of X-ray spectra, at least, up to 300 keV than OSSE."953" In fact, there are more physical arguments in favor of the versus OSSE observations of the hard X-ray tails in PCA/HEXTEBH X-ray binaries."," In fact, there are more physical arguments in favor of the PCA/HEXTE versus OSSE observations of the hard X-ray tails in BH X-ray binaries."954" Specifically, the dynamical time scale which is related to the magneto-acoustic oscillations of the Compton cloud (CC) is ta~ where L.. is the CC size and V, is the magnetoacoustic2Lec/Va velocity [see e.g. Titarchuk&Sha- (2005)]."," Specifically, the dynamical time scale which is related to the magneto-acoustic oscillations of the Compton cloud (CC) is $t_d\sim 2L_{cc}/V_a$ where $L_{cc}$ is the CC size and $V_a$ is the magnetoacoustic velocity [see e.g. \cite{ts05}] ]."955" With the assumption that the characteristicCC size L4. in the HSS is of the order of (5—10)(3Rs)~108(m/10), where Rg=3x is the Schwarchild radius, m is a BH mass in solar units, V,~10'(kT,/1 keV) cm s-!, KT. is Compton cloud temperature, we obtain that tg~20[(m/10)/(kT./lkeV)| s. Thus, the dynamical time scale of the Compton cloud £4 is only one order magnitude140.AAA shortera than the PCA/HEXTE spectrum accumulation time of ~105 s and we rather believe that the PCA/HEXTE spectra including its turnover more precisely describe the shape of the emergent spectra than that by the OSSE spectrahigh/soft averaged over 2 magnitudes longer periods."," With the assumption that the characteristicCC size $L_{cc}$ in the HSS is of the order of $(5-10) (3 R_S) \sim 10^8(m/10)$, where $R_S=3\times 10^5m$ is the Schwarchild radius, $m$ is a BH mass in solar units, $V_a\sim 10^7 (kT_e/1$ keV) cm $^{-1}$, $kT_e$ is Compton cloud temperature, we obtain that $t_d\sim 20[(m/10)/(kT_e/1$ keV)] s. Thus, the dynamical time scale of the Compton cloud $t_d$ is only one order magnitude shorter than the PCA/HEXTE spectrum accumulation time of $\sim 10^3$ s and we rather believe that the PCA/HEXTE spectra including its turnover more precisely describe the shape of the high/soft emergent spectra than that by the OSSE spectra averaged over 2 magnitudes longer periods."956 We present further observational evidence supporting the theory of the bulk motion (converging) flow near accreting black holes., We present further observational evidence supporting the theory of the bulk motion (converging) flow near accreting black holes.957" We show that when sufficient cooling is provided by the mass supply from the donor star, the Comptonizing media is completely cooled down and the origin of the extended cutoff power law is due to non-thermal bulk motion process."," We show that when sufficient cooling is provided by the mass supply from the donor star, the Comptonizing media is completely cooled down and the origin of the extended cutoff power law is due to non-thermal bulk motion process."958 The energy of the high energy cutoff observed during 1998 outbursts from XTE J1550-564 (as well as during 2007 outburst from GX 339-4 reported by Mottaetal. (2009))) behaves in striking agreement with the bulk motion scenario., The energy of the high energy cutoff observed during 1998 outbursts from XTE J1550-564 (as well as during 2007 outburst from GX 339-4 reported by \citet{motta}) ) behaves in striking agreement with the bulk motion scenario.959 Combined with the previously reported effect of index saturation in BH X-ray binaries (Shaposhnikov&Titarchuk2009) the cutoff energy behavior provides robust observational signature of the bulk motion region near the accreting object., Combined with the previously reported effect of index saturation in BH X-ray binaries \citep{st09} the cutoff energy behavior provides robust observational signature of the bulk motion region near the accreting object.960" As a direct consequence of the specific drain properties of the BH, this signature presents the most direct observational evidence of the existence of the astrophysical black holes."," As a direct consequence of the specific drain properties of the BH, this signature presents the most direct observational evidence of the existence of the astrophysical black holes."961 The RXTE data for this work was aquired through HEASARC., The data for this work was aquired through HEASARC.962 Authors acknowledge the support of this research by NASA grant NNX09AF02G., Authors acknowledge the support of this research by NASA grant NNX09AF02G.963characteristic of accretion on a putative compact object and is. for now. the main reason to assune that SPAT are binary svstenus.,"characteristic of accretion on a putative compact object and is, for now, the main reason to assume that SFXT are binary systems."964 As the sources are flaring at most once per dav. their average lard X-ray Iuuiuositv is very low. reaching (0.2Ls1024 erg/s.," As the sources are flaring at most once per day, their average hard X-ray luminosity is very low, reaching $(0.2-4)\times 10^{34}~\rm{erg/s} $ ."965 It is therefore very unlikely that those systenis have average orbital raclius lower than 1tHanie ~10R.., It is therefore very unlikely that those systems have average orbital radius lower than $10^{13}~\rm{cm}$ i.e. $\sim 10~R_*$.966 One expects orbital periods larger than 15 davs and underflow Roche lobe systems (note that no orbital period has vet been derived in any of these systenis)., One expects orbital periods larger than 15 days and underflow Roche lobe systems (note that no orbital period has yet been derived in any of these systems).967 The average hard Nay huuinosity of the SENT svstems in quiescence is <6.6&1075ere/s (which corresponds to 0.2 cet/s)., The average hard X-ray luminosity of the SFXT systems in quiescence is $< 6.6 \times 10^{33}~\rm{erg/s}$ (which corresponds to 0.2 ct/s).968 This is au upper Πιτ as the mosaics used to measure those quiesceut fiuxes most probably coutain faint flares. not detected dunues single poiutines.," This is an upper limit as the mosaics used to measure those quiescent fluxes most probably contain faint flares, not detected during single pointings."969 The INTEGRAL data alone do not exclude that there is no quiescent hard N-ray ΕΜ xvsteuis., The INTEGRAL data alone do not exclude that there is no quiescent hard X-ray emission in these systems.970 The interaction of a compact object with a dense chup formed in the wind of a massive companion leads to lucreased accretion rate and hard ταν cussion (7?).., The interaction of a compact object with a dense clump formed in the wind of a massive companion leads to increased accretion rate and hard X-ray emission \citep{Leyder2007}.971" The free-fall time from the accretion radius 2,=2«1010cni towards the compact object is of the order of (2.3)ς10%s", The free-fall time from the accretion radius $R_a = 2\times 10^{10}~ \rm{cm}$ towards the compact object is of the order of $(2-3)\times10^2~\rm{s}$.972 As the intrinsic aneular momenta of the accreted σας is πα (2). the Πα is mostly radial (down to the Compton radius) aud proceeds at the Dondi-ITovle accretion rate., As the intrinsic angular momentum of the accreted gas is small \citep{Illarionov2001} the infall is mostly radial (down to the Compton radius) and proceeds at the Bondi-Hoyle accretion rate.973 The accretion could slow down if the wind clumps have internal turbulence or harbor significant intrinsic aneular ποιοιτα (77).," The accretion could slow down if the wind clumps have internal turbulence or harbor significant intrinsic angular momentum \citep{Theuns1996,Krumholz2005}."974 This is however uulikelv iu a lighly supersonic wind. aud supported by the very sharp N-rayv Hare cutoff observed ou time scale of the order of few 100 sin some of these systems (27)..," This is however unlikely in a highly supersonic wind, and supported by the very sharp X-ray flare cutoff observed on time scale of the order of few 100 s in some of these systems \citep{ZuritaWalter2007, gonzalez04aa}."975 With a duration of fj;=2LO ks. the observed short rard N-ray fares are siguificautly longer than the frec-fall ine.," With a duration of $t_{fl}=2-10$ ks, the observed short hard X-ray flares are significantly longer than the free-fall time."976" The flare duration is therefore very probably linked with the thickness of the clumps which. for a clump radial velocity V,=105cns. is ha=Vy\tH~(210)«10H cu."," The flare duration is therefore very probably linked with the thickness of the clumps which, for a clump radial velocity $V_{cl}=10^8 ~\rm{cm/s}$, is $h_{cl} = V_{cl} \times t_{fl} \sim (2-10) \times 10^{11}~\rm{cm}$ ."977 The average hard A-rav Iuninositv resulting frou an interaction between the compact object aud the chimp cau be evaluated as Ly=6€δωJDέμ Gvhere €~ 0.1) aud the mass of a clump can then be estimated as where Ry is the radius of the clump perpendicular to the radial distance., The average hard X-ray luminosity resulting from an interaction between the compact object and the clump can be evaluated as $L_X = \epsilon~M_{acc}c^2/t_{fl}$ (where $\epsilon\sim0.1$ ) and the mass of a clump can then be estimated as where $R_{cl}$ is the radius of the clump perpendicular to the radial distance.978" In the case of a spherical clump. If N is the rate of chuups emitted by the star. the observed hard Nav fhue rate is given by Thed rate ofH niasz-loss iu+ the form. of. wind. chumps can then be estimated as For ao =l velocity law aud spherical clumps. the munber of chumps located between 1.0572 aud H4, cal be evaluated as where t(r) is the wind flight time (?).."," In the case of a spherical clump, If $\dot{N}$ is the rate of clumps emitted by the star, the observed hard X-ray flare rate is given by The rate of mass-loss in the form of wind clumps can then be estimated as For a $\beta=1$ velocity law and spherical clumps, the number of clumps located between $1.05R_*$ and $R_{orb}$ can be evaluated as where t(r) is the wind flight time \citep{Hamann2001}."979 Assuming spherical chuups. the chunpdensity at the orbital radius is py=weanLy-)τνag10ll©GaycllB and the corresponding (homogeneous wind cdoensitv is pn—o—ME-LLqpVa).(10d1loseL;uua3umx)yr1.5«10σσ ?.," Assuming spherical clumps, the clumpdensity at the orbital radius is $\rho_{cl}=\left(\frac{L_X}{10^{36}~\rm{erg/s}}\right) ~7\times 10^{-14} ~\rm{g~cm}^{-3}$ and the corresponding homogeneous wind density is $\rho_h=\dot{M}_{cl}/(4\pi~R_{orb}^2~V_{cl})=980\left(\frac{10~\rm{d}}{T}\frac{L_X}{10^{36}~\rm{erg/s}}\frac{t_{fl}}{3~\rm{ks}}\right)981~1.5\times 10^{-15}~\rm{g~cm}^{-3}$ ."982 The ehuup voluue filling factor at the orbital radius is fy=‘=](445)f0.02.E and (<4)15«1022 an.," The clump volume filling factor at the orbital radius is $983f_V = \frac{\rho_h}{\rho_{cl}} = 984\left(\frac{10~\rm{d}}{T}\frac{t_{fl}}{3~\rm{ks}}\right)985~0.02$ and the corresponding porosity length \citep{owocki2006,OskinovaHamannFeldmeier2007} is $h=\frac{R_{cl}}{f_V}=986\left(\frac{T}{10~\rm{d}}\right)987~15\times 10^{12} ~\rm{cm}$ ."988" Tt the deusitv+ of. a clump decreases withB radiusH as rrD7Ἱ andl its mass remains constant. the averaged hionnogeuceous wind deusitv within A4, is pj=NALA(imYu)Hobosfuz)=7.10+5οxem3? aud the average↜ chup. volume filling factor aud porosity leugth could be estimated. as 0.1. and 3.<10132cui respectively."," If the density of a clump decreases with radius as $r^{-2\beta}$ and its mass remains constant, the averaged homogeneous wind density within $R_{obs}$ is $\overline{\rho_{h}}=N M_{cl}/(\frac{4}{3}\pi 989R_{orb}^3990) = 991\left(\frac{10~\rm{d}}{T}\frac{L_X}{10^{36}~\rm{erg/s}}\frac{t_{fl}}{3~\rm{ks}}\right)992~7\times 10^{-15} ~\rm{g~cm}^{-3}$ and the average clump volume filling factor and porosity length could be estimated as 0.1 and $3\times10^{12} ~\rm{cm}$, respectively."993. The variety of ty. T aud Εμ tha are observed probably reflects a rauge of clump parameters aud orbital radii.," The variety of $t_{fl}$, $T$ and $F_{fl}$ that are observed probably reflects a range of clump parameters and orbital radii."994 Several of the average clump parameters estimated above. im particular the chuup deusitv. filling factor aud porosity leugth do uot depend ou the orbital radius. which is unknown. and only slowly depend on the observed quautitics.," Several of the average clump parameters estimated above, in particular the clump density, filling factor and porosity length do not depend on the orbital radius, which is unknown, and only slowly depend on the observed quantities."995 These average parameters match the macro-clumping scenario proposed bv ? to reconcile clunipiug auc niass-loss rates.," These average parameters match the macro-clumping scenario proposed by \cite{OskinovaHamannFeldmeier2007}996 to reconcile clumping and mass-loss rates."997" Their model depeuds on a free parameter Ly=Liga?Vir)Voxj3)E?, where Lir) is the chump separation in unit of A..."," Their model depends on a free parameter $L_0=L(r) (r^2V(r)/V(\infty))^{-1/3}$, where $L(r)$ is the clump separation in unit of $R_*$."998 Our average clumping parameters correspond to Ly=0.35., Our average clumping parameters correspond to $L_0=0.35$.999 The muuber of clumps derived above is also comparable to evaluations by ? and ??..," The number of clumps derived above is also comparable to evaluations by \cite{Lepine1999} and \cite{OskinovaFeldmeierHamann2006, OskinovaHamannFeldmeier2007}."1000 The ποιο filling factor and the clamp mass-loss rate are also sinular to those derived bv ?. from the study of ultraviolet and optical line profiles iu two super-elaut stars., The volume filling factor and the clump mass-loss rate are also similar to those derived by \cite{Bouret2005} from the study of ultraviolet and optical line profiles in two super-giant stars.1001 The cohunu density through a clump can also be estimated as Nyy=can(wt:un)5«102o02 3.," The column density through a clump can also be estimated as $N_H = \frac{M_{cl}}{R_{cl}^2m_p}=1002\left(\frac{L_X}{10^{36}\rm{erg/s}}\frac{t_{fl}}{3\rm{ks}}\right)1003~5\times 10^{22}\rm{cm}^{-2}$ ."1004 The chumps remain optically thin iu tle N-ravs., The clumps remain optically thin in the X-rays.1005 The activity surrounding some of the most significant flares unav be related to tidal effects on the clumps themself aud induced turbulence., The activity surrounding some of the most significant flares may be related to tidal effects on the clumps themself and induced turbulence.1006 The long flare that has, The long flare that has1007p(r)οςr .,"$\rho(r) \propto1008r^{-\gamma}$ ."1009 7 defines an upper limit to the slope; a steeper slope would require more mass interior to r than is measured., $\gamma$ defines an upper limit to the slope; a steeper slope would require more mass interior to $r$ than is measured.1010 We note that this measure was used by ? for resimulated haloes of different masses but comparable particle resolution in their study of the universality of the mass profile., We note that this measure was used by \citet{2004MNRAS.349.1039N} for resimulated haloes of different masses but comparable particle resolution in their study of the universality of the mass profile.1011" In we plot the radial variation of + for all haloes that satisfy the FigureselectionB] criteria of and are in the same mass- as those used in D.2]colour-coded according to the spectral index n of the model insectionB.3},which they form."," In Figure \ref{fig:maxslope_rr2} we plot the radial variation of $\gamma$ for all haloes that satisfy the selection criteria of \ref{sec:halo_selection} and are in the same mass-range as those used in section \ref{sec:fitting}, colour-coded according to the spectral index $n$ of the model inwhich they form."1012" Note that we have normalised these profiles to r_2, the radius at which the differential mass profile pr? reaches a maximum."," Note that we have normalised these profiles to $r_{-2}$, the radius at which the differential mass profile $\rho\,r^2$ reaches a maximum."1013" For a NFW profile, r_2 is identical to the scale radius rs and so it provides an attractive non-parametric measure ofconcentration}."," For a NFW profile, $r_{-2}$ is identical to the scale radius $r_s$ and so it provides an attractive non-parametric measure of."1014" When normalising the radius in this manner, we find excellent agreement between the average shapes of the Υ profiles between the different n models."," When normalising the radius in this manner, we find excellent agreement between the average shapes of the $\gamma$ profiles between the different $n$ models."1015" However, the scatter between profiles within a given simulation is significant (cf."," However, the scatter between profiles within a given simulation is significant (cf."1016" upper panel of figure)), which strengthens our argument that it is essential to use a statistical sample of haloes when discussing the asymptotic inner slope."," upper panel of figure \ref{fig:maxslope_rr2}) ), which strengthens our argument that it is essential to use a statistical sample of haloes when discussing the asymptotic inner slope."1017" It is noticeable that the average profile in each model we have looked at continues to becomes shallower with decreasing radius, without showing evidence for convergence to an asymptotic value (c.f.?).."," It is noticeable that the average profile in each model we have looked at continues to becomes shallower with decreasing radius, without showing evidence for convergence to an asymptotic value \citep[c.f.][]{2004MNRAS.349.1039N}."1018 We find similar behaviour when considering only haloes in the high-mass This figure also confirms our suspicion that it is the scale radius r_2 or concentration cvi;=Tvir/7—2 rather than the slope α that varies with n., We find similar behaviour when considering only haloes in the high-mass This figure also confirms our suspicion that it is the scale radius $r_{-2}$ or concentration $c_{\rm vir}=r_{\rm vir}/r_{-2}$ rather than the slope $\alpha$ that varies with $n$.1019 We find that haloes forming in the n=—0.5 model tend to be more concentrated (cf., We find that haloes forming in the $n=-0.5$ model tend to be more concentrated (cf.1020 figure Al below)than haloes forming in runs with steeper spectral indices., figure \ref{fig:concentration} below)than haloes forming in runs with steeper spectral indices.1021 Therefore fits with a generalised NFW profile (cf., Therefore fits with a generalised NFW profile (cf.1022" equation [9)) tend to favour smaller values of a for steeper n because these haloes tend to be less concentrated, and so we resolve the profile to smaller fractions of r_—2, Where the flattening of the profile is more apparent."," equation \ref{eq:extend_nfw}) ) tend to favour smaller values of $\alpha$ for steeper $n$ because these haloes tend to be less concentrated, and so we resolve the profile to smaller fractions of $r_{-2}$, where the flattening of the profile is more apparent."1023 Therefore a shallower effective slope a will tend to be preferred., Therefore a shallower effective slope $\alpha$ will tend to be preferred.1024 It is a relatively straightforward exercise to obtain expressions for equation [T1] for the NFW profile and the ? profile., It is a relatively straightforward exercise to obtain expressions for equation \ref{eq:maxslope} for the NFW profile and the \citet{1998ApJ...499L...5M} profile.1025" Two other analytical model profiles have been promisingly applied to halo density profiles, the ? and ? profiles, which provide better fits than the NFW profile."," Two other analytical model profiles have been promisingly applied to halo density profiles, the \citet{1965Einasto} and \cite{1997A&A...321..111P} profiles, which provide better fits than the NFW profile."1026" ? argue that the Einasto model performed best in fitting halo profiles, followed closely by the Prugniel-Simien model."," \citet{2006AJ....132.2685M}1027 argue that the Einasto model performed best in fitting halo profiles, followed closely by the Prugniel-Simien model."1028 Expressions for Υ for the Einasto and Prugniel-Simien models are given in the Appendix [B]., Expressions for $\gamma$ for the Einasto and Prugniel-Simien models are given in the Appendix \ref{app:maximumslope}.1029 In the lower panel of figure B] we over-plot the averaged -curves with the theoretical predictions derived for the four analytic profiles mentioned above., In the lower panel of figure \ref{fig:maxslope_rr2} we over-plot the averaged $\gamma$ -curves with the theoretical predictions derived for the four analytic profiles mentioned above.1030 We find that the Moore profile is unable to reproduce the observed behaviour., We find that the Moore profile is unable to reproduce the observed behaviour.1031" The NFW profile is consistent with our data for the 512-0.50 and 512-1.50 runs, but it fails to reproduce the continual flattening of  to small radii."," The NFW profile is consistent with our data for the 512-0.50 and 512-1.50 runs, but it fails to reproduce the continual flattening of $\gamma$ to small radii."1032" In contrast, both the Einasto and Prugniel-Simien profiles capture the behaviour of our data well at small "," In contrast, both the Einasto and Prugniel-Simien profiles capture the behaviour of our data well at small ."1033"Interestingly we note that all of the analytical profiles tend to radij].overestimate the slope of the density profile at large r/r_2, which appears to roll over and flatten off."," Interestingly we note that all of the analytical profiles tend to overestimate the slope of the density profile at large $r/r_{-2}$, which appears to roll over and flatten off."1034" This is most apparent for the data points from the n=—0.5 In Figure we make explicit the connection between r..» and the concentrationA] cyir=Tvir/r—2, showing how cvi, varies with halo mass (given by the number of particles within the virial radius Nyir; upper panel), and the spectral index n (lower panel)."," This is most apparent for the data points from the $n=-0.5$ In Figure \ref{fig:concentration} we make explicit the connection between $r_{-2}$ and the concentration $c_{\rm vir}=r_{\rm1035 vir}/r_{-2}$, showing how $c_{\rm vir}$ varies with halo mass (given by the number of particles within the virial radius $N_{\rm vir}$; upper panel), and the spectral index $n$ (lower panel)."1036" A similar figure can befound in ?,, who looked at scale-free models with spectral indices of n=—0.5,—1.0, —1.5, but who derived their concentrations from fits ofNFW profiles."," A similar figure can befound in \cite{1997ApJ...490..493N}, , who looked at scale-free models with spectral indices of $n=-0.5, -1.0, -1.5$ , but who derived their concentrations from fits ofNFW profiles."1037" Although our concentrations are calculated in a non-parametric manner, it is reassuring that we see a similar trend to that reported in ?.."," Although our concentrations are calculated in a non-parametric manner, it is reassuring that we see a similar trend to that reported in \cite{1997ApJ...490..493N}. ."1038Data from global helioseismologv. (Thompsonetal.2003) have shed some light on ihe internal rotation of the sun.,Data from global helioseismology \citep{Thompson03} have shed some light on the internal rotation of the sun.1039 Throughout the convective envelope. the rotation rate decreases monotonicallv Coward (he poles.," Throughout the convective envelope, the rotation rate decreases monotonically toward the poles."1040 Near the base of the convection zone. there is a sharp (transition between differential rotation in the convective envelope and. nearly uniform rotation in the radiative interior.," Near the base of the convection zone, there is a sharp transition between differential rotation in the convective envelope and nearly uniform rotation in the radiative interior."1041 This (ransition region has become known as the, This transition region has become known as the1042in OSC'A (no focal or Lvot mask) is illustrated in Fig. 7..,in OSCA (no focal or Lyot mask) is illustrated in Fig. \ref{aperture}.1043 The normalised. peak intensity ratio of the PSE produced bv this aperture compared to the same aperture without segmentation (with no phase mismatching) is 0.97., The normalised peak intensity ratio of the PSF produced by this aperture compared to the same aperture without segmentation (with no phase mismatching) is 0.97.1044 From this simple calculation it is seen that a scementec AO system is of lower contrast by design compared to a continuous [ace-sheet mirror., From this simple calculation it is seen that a segmented AO system is of lower contrast by design compared to a continuous face-sheet mirror.1045 Llowever. the loss in performance when using a coronagraph with a segmentecl mirror is much more than34.," However, the loss in performance when using a coronagraph with a segmented mirror is much more than."1046. The reason for this is can be seen by examining the distribution of light in the pupil plane after the application of the focal stop. an example is given in Fig. 9((," The reason for this is can be seen by examining the distribution of light in the pupil plane after the application of the focal stop, an example is given in Fig. \ref{pupil_phase}( ("1047a).,a).1048 For the case of a Gaussian focal plane mask applied. to the PSE obtained by using the aperture in Vig. ΤΡ]. , For the case of a Gaussian focal plane mask applied to the PSF obtained by using the aperture in Fig. \ref{aperture}( (1049it is found that of the total light in the pupil is clistributecl about the segment. edges.,"b), it is found that of the total light in the pupil is distributed about the segment edges."1050 So if à normal Lyot mask is used here (primary. secondary. ancl vane masking) a significant proportion of the light from that remaining of the masked star will stav in the final image. thus reducing the suppression performance.," So if a normal Lyot mask is used here (primary, secondary and vane masking) a significant proportion of the light from that remaining of the masked star will stay in the final image, thus reducing the suppression performance."1051 The use of a more complex Lyot mask which masks the individual mirror segments as well as the telescope primary and secondary gives improved suppression performance compared to a Lvot mask which only masks the telescope primary and secondary., The use of a more complex Lyot mask which masks the individual mirror segments as well as the telescope primary and secondary gives improved suppression performance compared to a Lyot mask which only masks the telescope primary and secondary.1052 The individual segments in NAOALL are T.6mim across with a ~0.loim gap between each one., The individual segments in NAOMI are 7.6mm across with a $\sim$ 0.1mm gap between each one.1053 The ratio of gap to segment size is the same order of magnitude to those proposed. lor future. segmented extremely large telescopes (ELS). ic. lim segments with IO0mm gaps.," The ratio of gap to segment size is the same order of magnitude to those proposed for future segmented extremely large telescopes (ELTs), i.e. 1m segments with 10mm gaps."1054 Hence these results have relevance for high contrast imaging with 1911»., Hence these results have relevance for high contrast imaging with ELTs.1055 To model the effect of the gaps between the NAOALL segments more pixels are required across the aperture., To model the effect of the gaps between the NAOMI segments more pixels are required across the aperture.1056 The results shown in Fig., The results shown in Fig.1057 S were obtained using 1024. pixels across the aperture diameter with a 2 pixel ga ονου the mirror segments.," \ref{grid_plot}1058 were obtained using 1024 pixels across the aperture diameter with a 2 pixel gap between the mirror segments."1059 Due to the size of this array this was à static simulation (i.e. not an AO simulation). a 2 times padding factor was used in the FETs.," Due to the size of this array this was a static simulation (i.e. not an AO simulation), a 2 times padding factor was used in the FFTs."1060 The lines show the mean trends (a convolution filter has been applied to flatten out the high frequeney periodicity) that the segementect aperture produces., The lines show the mean trends (a convolution filter has been applied to flatten out the high frequency periodicity) that the segmented aperture produces.1061 In the high contrast. direction (45° to image axes) the benefit is most evident at. distance 75 aresec [from the centre. reducing counts by 2. orders. of magnitude.," In the high contrast direction $45^\circ$ to image axes) the benefit is most evident at distance $>5$ arcsec from the centre, reducing counts by 2 orders of magnitude."1062 For the racial averaged lines (which include the bright axial dilfraction peaks) the benefit of the grid. Lyot mask is noticeable from 1 arcsec., For the radial averaged lines (which include the bright axial diffraction peaks) the benefit of the grid Lyot mask is noticeable from 1 arcsec.1063 For the full AO simulations (with 256 pixels across the aperture. 4. padding and no gaps). the clleet of phase mismatching between the segments can be seen as an about the segments in the pupil plane subsequent to the application of the occulting mask. as shown in Fig. 9((," For the full AO simulations (with 256 pixels across the aperture, $4\times$ padding and no gaps), the effect of phase mismatching between the segments can be seen as an about the segments in the pupil plane subsequent to the application of the occulting mask, as shown in Fig. \ref{pupil_phase}( ("1064d).,d).1065" Segments with the greatest intensity are those that are ""turned off and so have the greatest phase step between them and adjacent segments.", Segments with the greatest intensity are those that are `turned off' and so have the greatest phase step between them and adjacent segments.1066 Taking gaps and. phase errors between segments into consideration the benefit of a Lyot mask which masks the individual mirror segments becomes apparent., Taking gaps and phase errors between segments into consideration the benefit of a Lyot mask which masks the individual mirror segments becomes apparent.1067 A Lyot mask matched to the NAOMIE mirror segments under sizing of segments) was created with OSCA (shown in Fig., A Lyot mask matched to the NAOMI mirror segments under sizing of segments) was created with OSCA (shown in Fig.1068 2. (inset top. left-hand mask)) but is as vet untested on-sky.," \ref{lyot} (inset top, left-hand mask)) but is as yet untested on-sky."1069 The mask requires very careful alignment and there has been insullicient. commissioning time to trial this new mask., The mask requires very careful alignment and there has been insufficient commissioning time to trial this new mask.1070 Telescope schedules allowing. trials may. be performed towards the end of 2005.," Telescope schedules allowing, trials may be performed towards the end of 2005."1071 Aspatially filtered collimated 613nm laser beam and a series of lenses and masks were arranged in the laboratory to simulate an ideal coronagraphic svstem., A spatially filtered collimated 613nm laser beam and a series of lenses and masks were arranged in the laboratory to simulate an ideal coronagraphic system.1072 A simple iris was used. for the entrance. aperture and. another one at dizuneter to act as the Lyot mask., A simple iris was used for the entrance aperture and another one at diameter to act as the Lyot mask.1073 Images were recorded at the final focus for a variety of different occulting spots using a Santa Barbara Instrument. Croup (SBLC) camera. this consists of a 3755242 pixel. Pelticr-coolec CCD.," Images were recorded at the final focus for a variety of different occulting spots using a Santa Barbara Instrument Group (SBIG) camera, this consists of a $375\times242$ pixel, Peltier-cooled CCD."1074 The usual calibrations were taken - dark frames and background images between every image., The usual calibrations were taken - dark frames and background images between every image.1075 These tests were performed. after OSCA had. been galipped to the WIEEF., These tests were performed after OSCA had been shipped to the WHT.1076. Phe Gaussian masks were 'ominmissioned. at a later date anc a method. to compare rem. to the standard. masks on OSCA was devised., The Gaussian masks were commissioned at a later date and a method to compare them to the standard masks on OSCA was devised.1077 The lithography5 template plate was used in 1place of a 0.5 aresec isc occulting mask. approximately the same as the full-width half-maximum of the Gaussian masks.," The lithography template plate was used in place of a 0.5 arcsec disc occulting mask, approximately the same as the full-width half-maximum of the Gaussian masks."1078 The ND value X this mask was also closely matched to the max ND level at 16 peak of the Gaussian mask so ollered a good comparison between the two dilferent shapes of mask., The ND value of this mask was also closely matched to the max ND level at the peak of the Gaussian mask so offered a good comparison between the two different shapes of mask.1079 The 1.0 aresee mask tested here was a spare from OSCA and had an ND level of 245.5 (compared to 72.5 for the 0.5 aresee mask ancl Gaussian) at this wavelength., The 1.0 arcsec mask tested here was a spare from OSCA and had an ND level of $\sim$ 5.5 (compared to $\sim$ 2.5 for the 0.5 arcsec mask and Gaussian) at this wavelength.1080 Images were taken at the focus for all 3 cülferent occulting masks. both with and without the Lyot mask.," Images were taken at the focus for all 3 different occulting masks, both with and without the Lyot mask."1081 The images were reduced (dark and background subtracted auc scaled for exposure dilferences) and then radial averages were plotted about the PSE peak., The images were reduced (dark and background subtracted and scaled for exposure differences) and then radial averages were plotted about the PSF peak.1082 Fig., Fig.1083 10. shows the racial averages of the 3 dillerent masks using the same Lyot mask., \ref{lab_masks} shows the radial averages of the 3 different masks using the same Lyot mask.1084 The 1.0 arcesec mask performs best of all. entirely due to its much larger size (covers 4. the area thus removing much more of the PSE) anc greater opacity.," The 1.0 arcsec mask performs best of all, entirely due to its much larger size (covers $4\times$ the area thus removing much more of the PSF) and greater opacity."1085 Comparing the other two masks which diller mainly in their shape rather than any other factors it can be seen that as the simulations predicted. the Gaussian shaped mask provides ereater suppression closer in to the centre than the disc mask does.," Comparing the other two masks which differ mainly in their shape rather than any other factors it can be seen that as the simulations predicted, the Gaussian shaped mask provides greater suppression closer in to the centre than the disc mask does."1086 Fie., Fig.1087 LL shows the significant ellect adding a Lyot stop has on the suppression with the Gaussian mask. the CCD count at LO pixels from the centre is 5«107. compared to 1.2.104 for the 0.50 aresce dise.," \ref{gausa_graph} shows the significant effect adding a Lyot stop has on the suppression with the Gaussian mask, the CCD count at 10 pixels from the centre is $5\times10^3$, compared to $1.2\times10^4$ for the 0.50 arcsec disc."1088 Without a Lyot stop the value at. 10 pixels from the centre for the Gaussian mask is, Without a Lyot stop the value at 10 pixels from the centre for the Gaussian mask is1089description of the functional form of the above operators is given.,description of the functional form of the above operators is given.1090 The current version of the code uses also some improvements over MK95., The current version of the code uses also some improvements over MK95.1091 Thus for synchrotron radiatior relativistic electrons emit the full photon spectrum (see.e.g.?) instead of the delta-function approximation used in MK95.," Thus for synchrotron radiation relativistic electrons emit the full photon spectrum \citep[see, e.g.][]{blum70} instead of the delta-function approximation used in MK95."1092 Also. for inverse Compton scattering. while the electro: cooling still uses the technique described in MK95. the electro emissivity uses relation (2.48) of ?..," Also, for inverse Compton scattering, while the electron cooling still uses the technique described in MK95, the electron emissivity uses relation (2.48) of \citet{blum70}."1093 Numerical tests have shown that this approach balances electron energy losses anc total photon radiated power to within 90% of each other., Numerical tests have shown that this approach balances electron energy losses and total photon radiated power to within $\%$ of each other.1094 Furthermore. departing from the approach of MK97. we implement an acceleration term in the electron kinetic equatior which is characterized by an appropriate timescale (έως) anc is accompanied by a term which deseribes particle injectior at some low energy (first term in RHS of Eq.," Furthermore, departing from the approach of MK97, we implement an acceleration term in the electron kinetic equation which is characterized by an appropriate timescale $\tacc$ ) and is accompanied by a term which describes particle injection at some low energy (first term in RHS of Eq."1095 ?? where Q(r) is the rate of electrons which are injected at low energies yoHt;c)., \ref{eq1} where $Q(t)$ is the rate of electrons which are injected at low energies $\gamma_0m_\mathrm{e}c^2$ ).1096 This modification allows us to follow particles as they accelerate from low to high energies., This modification allows us to follow particles as they accelerate from low to high energies.1097 Note that this approach is similar to the one taken in KRM., Note that this approach is similar to the one taken in KRM.1098 However. the present work differs from KRM in that we adopt here a one-zone model.," However, the present work differs from KRM in that we adopt here a one-zone model."1099 There are six parameters that are required to specify the source in a stationary state., There are six parameters that are required to specify the source in a stationary state.1100 These include 1., These include 1.1101 The Doppler factor 6=[ΓΙ—8cos0)]7!., The Doppler factor $\delta=[\Gamma(1-\beta \cos\theta)]^{-1}$.1102 2., 2.1103 The radius R of the source (or. equivalently. the crossing time in the rest frame of the source 44= R/c).," The radius $R$ of the source (or, equivalently, the crossing time in the rest frame of the source $\tcross=R/c$ )."1104 3., 3.1105 The magnetic field strength B., The magnetic field strength $B$.1106 4., 4.1107" The acceleration timescale ¢,... which by the setup of the problem must obey the relation face>fa."," The acceleration timescale $\tacc$, which by the setup of the problem must obey the relation $\tacc\ge\tcross$."1108 5., 5.1109 The timescale of particle escape of the system fa..., The timescale of particle escape of the system $\tesc$.1110 6., 6.1111 The rate of injected electrons Qo — we note. however. that the solution turns to be largely independent of the exact choice of yo as long as this ts not larger than 10.," The rate of injected electrons $Q_0$ – we note, however, that the solution turns to be largely independent of the exact choice of $\gamma_0$ as long as this is not larger than 10."1112" As was shown in KRM this prescription (under. the assumption of synchrotron radiation losses only) leads to an electron distribution function which in steady state reads ""ὃς. for yo€yyu. Where yu, is the Lorentz factor at which electron energy losses balance acceleration."," As was shown in KRM this prescription (under the assumption of synchrotron radiation losses only) leads to an electron distribution function which in steady state reads ) for $\gamma_0\le\gamma\le\gammamax$, where $\gammamax$ is the Lorentz factor at which electron energy losses balance acceleration."1113" For example. in the pure synchrotron case. where5,=torpor with cy the Thomson cross section."," For example, in the pure synchrotron case, where $\beta_s={4\over 3}\sigma_T c {B^2\over{8\pi m_ec^2}}$ with $\sigma_T$ the Thomson cross section."1114 However. the present approach incorporates. in addition to synchrotron. SSC losses which render the derivation of an analytic solution impossible due to complications arising from the Klein-Nishina limit.," However, the present approach incorporates, in addition to synchrotron, SSC losses which render the derivation of an analytic solution impossible due to complications arising from the Klein-Nishina limit."1115 One further notes that for £4: and fa. both independent of energy. as it was assumed in deriving the above solution. the electron distribution function is a power law of index s2-2--(face—fostae (as long as y<< ος," One further notes that for $\tacc$ and $\tesc$ both independent of energy, as it was assumed in deriving the above solution, the electron distribution function is a power law of index $s=-2-({\tacc-\tesc})/{\tesc}$ (as long as $\gamma<<\gammamax$ )."1116 note also that tests on the code in the pure synchrotron loss case have shown that the electron distribution above yy; does not drop to zero abruptly. but rather. due to numerical diffusion. a very steep power law ts produced.," We note also that tests on the code in the pure synchrotron loss case have shown that the electron distribution above $\gammamax$ does not drop to zero abruptly, but rather, due to numerical diffusion, a very steep power law is produced."1117 The above description changes during a flare: Assume that the system has reached some stationary state., The above description changes during a flare: Assume that the system has reached some stationary state.1118 If this ts perturbed in some way. 1.9. by injecting an increased number of particles in the acceleration mechanism for some time interval Ar. then a wave of fresh particles will move to high energies.," If this is perturbed in some way, i.e. by injecting an increased number of particles in the acceleration mechanism for some time interval $\Delta\tau$, then a wave of fresh particles will move to high energies."1119 Assuming that the episode starts at some instant. fo. then at each time ¢>f+Ar the fresh particles will have Lorentz factors Yniin()€YYnaa(O with Yana=yortntaec and γη)=yoeUnATVface.," Assuming that the episode starts at some instant $t_0$, then at each time $t>t_0+\Delta\tau$ the fresh particles will have Lorentz factors $\gamflmn(t)\le\gamma\le\gamflmx(t)$ with $\gamflmx(t)=\gamma_0e^{(t-t_0)/\tacc}$ and $\gamflmn(t)=\gamma_0e^{(t-t_0-\Delta\tau)/\tacc}$."1120 This relation holds as long as YoanaxSYmas, This relation holds as long as $\gamflmx\le\gammamax$.1121 AS the time evolving particle distribution will have a higher amplitude than the steady state one. this will cause a flare in photons which will relax back to the pre-flare state once particles of Lorentz factor yg start becoming of order yis.," As the time evolving particle distribution will have a higher amplitude than the steady state one, this will cause a flare in photons which will relax back to the pre-flare state once particles of Lorentz factor $\gamflmn$ start becoming of order $\gammamax$."1122 Ht is interesting to note that as losses do not come solely from synchrotron radiation but from SSC as well. the flaring event could have an impact on the determination of yq.," It is interesting to note that as losses do not come solely from synchrotron radiation but from SSC as well, the flaring event could have an impact on the determination of $\gammamax$."1123" More specifically. the presence of extra photons during a flare in the system will increase the total electron energy losses and. depending on the specific conditions. could cause yy, to drop."," More specifically, the presence of extra photons during a flare in the system will increase the total electron energy losses and, depending on the specific conditions, could cause $\gammamax$ to drop."1124 We begin by using the model described in the previous section to fit the X/TeV data as given in Fig., We begin by using the model described in the previous section to fit the X/TeV data as given in Fig.1125 21 of Ἱ.(July 9. 2005. observations).," 21 of \citet{albert07} (July 9, 2005, observations)."1126 We have solved the set of stiff differential equations (??)) and (22)) using the numerical techniques às these were described and tested in MK95., We have solved the set of stiff differential equations \ref{eq1}) ) and \ref{eq2}) ) using the numerical techniques as these were described and tested in MK95.1127 The parameters used for the steady state fit are R=1.510U em. ó=60. B=05 G. fae=NOa. foe=4.17%. yo=10° and Q=510° em see7ere7!.," The parameters used for the steady state fit are $R=1.5~10^{14}$ cm, $\delta=60$, $B=0.5$ G, $\tacc=3\tcross$, $\tesc=4.17\tcross$, $\gamma_0=10^{0.05}$ and $Q=5~10^6$ $^{-3}$ $^{-1}$ $^{-1}$."1128" The cosmological parameters used are Hy=70kms!Μρο. Q,=0.7 and Q=0.3."," The cosmological parameters used are $H_0=70\ \mathrm{km}\ \mathrm{s}^{-1}\1129\mathrm{Mpc}^{-1}$, $\Omega_\Lambda=0.7$ and $\Omega=0.3$."1130 The spectrum is shown with solid line in Fig. ].., The spectrum is shown with solid line in Fig. \ref{fig1}.1131" The resulting electron distribution function is a power-law of slope s=—1.7 up to an energy Yu,=210°.", The resulting electron distribution function is a power-law of slope $s=-1.7$ up to an energy $\gammamax= 2~ 10^5$.1132 Perturbing the steady state as given above we found that a change in. Q(r) always produces a hard lag flare as the one observed., Perturbing the steady state as given above we found that a change in $Q(t)$ always produces a hard lag flare as the one observed.1133 However. this method of simulating a flaring activity causes the flux in each energy band to increase approximately by the same amplitude — see ?..," However, this method of simulating a flaring activity causes the flux in each energy band to increase approximately by the same amplitude – see \citet{mamo09}."1134 If. as the observations seem to suggest. the flare is becoming harder as well. 1.e. more flux is emitted in the higher energy bands. then in order to get à fit to the TeV lighteurve one needs. in addition. to decrease foe and/or B during the flaring episode.," If, as the observations seem to suggest, the flare is becoming harder as well, i.e. more flux is emitted in the higher energy bands, then in order to get a fit to the TeV lightcurve one needs, in addition, to decrease $\tacc$ and/or $B$ during the flaring episode."1135 This can be explained from an inspection of rel. (, This can be explained from an inspection of rel. (11364).,4).1137 A spectral hardening of the flare requires an increase of yj; during the episode and this can be achieved. within the context of the present model. only by reducing one. or both. of the aforementioned parameters.," A spectral hardening of the flare requires an increase of $\gammamax$ during the episode and this can be achieved, within the context of the present model, only by reducing one, or both, of the aforementioned parameters."1138 Figures 2 and 3 depict the lightcurves resulting from such a flaring episode., Figures 2 and 3 depict the lightcurves resulting from such a flaring episode.1139 Here the observed flare comes from an impulsive change of Q by a factor of ~13 for Ar=If anda decrease of f; and B by a factor of 1.7 for Ar=30f4 which Is approximately equal to the duration of the flaring episode. i.e. to the time needed for the injected particles to reach yy.," Here the observed flare comes from an impulsive change of $Q$ by a factor of $\sim13$ for $\Delta\tau=1t_\mathrm{cr}$ and a decrease of $\tacc$ and $B$ by a factor of 1.7 for $\Delta\tau=30t_\mathrm{cr}$ which is approximately equal to the duration of the flaring episode, i.e. to the time needed for the injected particles to reach $\gammamax$ ."1140 In order to keep the spectral slope unchanged (see rel., In order to keep the spectral slope unchanged (see rel.1141 3) we also vary fa. by the same factor., 3) we also vary $\tesc$ by the same factor.1142 Fig., Fig.1143 2 shows the lightcurve at the lowest energy range (0.15-0.25 TeV) of the MAGIC, 2 shows the lightcurve at the lowest energy range (0.15-0.25 TeV) of the MAGIC1144nunodel is appropriate for the prototvpe lywpernova SN L998Dw Cwamoto et 11998: Ναι et22001),model is appropriate for the prototype hypernova SN 1998bw (Iwamoto et 1998; Nakamura et.11452.. Teh/WolfRavet stars are known to lose a substantial fraction of their cuvelopes in a stellar wind., Helium/Wolf-Rayet stars are known to lose a substantial fraction of their envelopes in a stellar wind.1146 To take this iuto account. we assume that the helimu star has lost au amount AM.=g(MA.Mp) before the explosion. where Af is the initial mass| of the compact reninaut (neutron star or black hole).," To take this into account, we assume that the helium star has lost an amount $\Delta M_{\rm He}1147= g\, (M_{\rm He}^0-M_{\rm BH}^0)$ before the explosion, where $M_{\rm BH}^0$ is the initial mass of the compact remnant (neutron star or black hole)."1148 We use the parameter g to vary the total amount of wind mass loss before the supernova., We use the parameter $g$ to vary the total amount of wind mass loss before the supernova.1149 At the time of the explosion. the masses of the primacy and secondary are Mg aud AL. respectively.," At the time of the explosion, the masses of the primary and secondary are $M_{\rm He}$ and $M_2^0$, respectively."1150 When the primary collapses. it first forms a compact remnant of ass Alf).," When the primary collapses, it first forms a compact remnant of mass $M_{\rm1151BH}^0$."1152" The rest of the envelope is assumed to be ejected initially, but part of it (Menace) Will subsequently: fall back. either because it did not achieve escape velocity or was pushed back by a reverse shock in the euvelope (see Woosley Weaver 1995)."," The rest of the envelope is assumed to be ejected initially, but part of it $M_{\rm fallback}$ ) will subsequently fall back, either because it did not achieve escape velocity or was pushed back by a reverse shock in the envelope (see Woosley Weaver 1995)."1153" The fallback matter inereases the mass of the compact remmant to Af, (udeed. it may be this fallback that leads to the conversion of the compac remnant into a black hole)."," The fallback matter increases the mass of the compact remnant to $M_{\rm BH}^1$ (indeed, it may be this fallback that leads to the conversion of the compact remnant into a black hole)."1154 Figure 3a schematically illustrates the definition of these various mass parameters., Figure 3a schematically illustrates the definition of these various mass parameters.1155 Tu the simple model we consider first. we assiuune that of the matter that falls back has moved bevoud the position of the secondary (n 3.2 we shall critically assess this assuniptiou).," In the simple model we consider first, we assume that of the matter that falls back has moved beyond the position of the secondary (in 3.2 we shall critically assess this assumption)."1156 Therefore. the secondary can be pollutefice with supernova material. first bv all the materia hat is ejected and then bv material that fallsρα back.," Therefore, the secondary can be polluted with supernova material, first by all the material that is ejected and then by material that falls back."1157" We asstune that the fraction of matter that is captured is given w the geometric fraction of the secondary (10μη,x 0.03. where RY=OsR.(ALYALT ds the radius of the secondary aud ay the initial orbital separation) nues some efficiency factor f. where we assume ciffereut cficiency factors for matter that passes the secoucdary in the initial ejection (fjccrion) aud for matter that falls ack feattback)."," We assume that the fraction of matter that is captured is given by the geometric fraction of the secondary $[R_2^0/2 a_0]^2\simeq 0.01\,$ $\,$ 0.03, where $R_2^0 =11580.8\Rs\,(M_2^0/\Ms)^{0.8}$ is the radius of the secondary and $a_0$ the initial orbital separation) times some efficiency factor $f$, where we assume different efficiency factors for matter that passes the secondary in the initial ejection $f_{\rm ejection}$ ) and for matter that falls back $f_{\rm fallback}$ )."1159 The efficiency factors can be much smaller han 1. for example. if the supernova leads to stripping of inatter from the secoudarv {(Alavietta. Burrows. Fivecll 2000 and 3.1). or larger than 1 if eravitational ocusing is duportant.," The efficiency factors can be much smaller than 1, for example, if the supernova leads to stripping of matter from the secondary (Marietta, Burrows, Fryxell 2000 and 3.1), or larger than 1 if gravitational focusing is important."1160 The latter requires that the relative velocity of the material is less than the escape velocity of he secondary and can plausibly only occur for fallback. uaterial., The latter requires that the relative velocity of the material is less than the escape velocity of the secondary and can plausibly only occur for fallback material.1161 We also take iuto account the pollution of the secondary that has occurred before the supernova because of the capture of wind material by the secondary (where we assunie a capture efficiency of 1)., We also take into account the pollution of the secondary that has occurred before the supernova because of the capture of wind material by the secondary (where we assume a capture efficiency of 1).1162 The matter that is captured by the secondary. has a much arecr nean molecular weielit than the composition of the secondary. a relatively unevolved star at this stage.," The matter that is captured by the secondary has a much larger mean molecular weight than the composition of the secondary, a relatively unevolved star at this stage."1163 This is secularlv unstable aud leads to thermohaline mixing iu he secondary (0.8.. Ixippeulalin. Ruscheuplatt Thomas 1980).," This is secularly unstable and leads to thermohaline mixing in the secondary (e.g., Kippenhahn, Ruschenplatt Thomas 1980)."1164 Since the time scale for thermohaline wining is short compared to the evolutionary time scale of the secondary. we assume that the material captured x the secondary is completely mixed with the rest of the star after the supernova.," Since the time scale for thermohaline mixing is short compared to the evolutionary time scale of the secondary, we assume that the material captured by the secondary is completely mixed with the rest of the star after the supernova."1165 Iu order to be able to follow the post-superuova evolution. we assume that the pre-supernova system is circular aud that the supernova explosion is spherically svuuimetric in the frame of the primary.," In order to be able to follow the post-supernova evolution, we assume that the pre-supernova system is circular and that the supernova explosion is spherically symmetric in the frame of the primary."1166 It is then straightforward to estimate the post-supernova paraiecters of the svstenm (ve follow Brandt Podsiadlowski 1995. but for otler equivalent treatiuents; see. e.g... Dhattacharya van deu Heuvel 1991: Nelemans et 11999).," It is then straightforward to estimate the post-supernova parameters of the system (we follow Brandt Podsiadlowski 1995, but for other equivalent treatments, see, e.g., Bhattacharya van den Heuvel 1991; Nelemans et 1999)."1167 The ecceutzricitv of the post-supernova binary is giveu by where AMax=Mp.Mig. the post-supernova major axis by where eg is the initial orbital separation.," The eccentricity of the post-supernova binary is given by where $\Delta1168M_{\rm SN}\equiv M_{\rm He}-M_{\rm BH}^1$, the post-supernova semi-major axis by where $a_0$ is the initial orbital separation."1169" The post-supernova svsteni kick velocity can be obtained frou equation (2.10) in Brandt Podsiadlowski (1995) as where e¢!), ds the pre-supernova orbital velocity of the system.", The post-supernova system kick velocity can be obtained from equation (2.10) in Brandt Podsiadlowski (1995) as where $v_{\rm orb}^0$ is the pre-supernova orbital velocity of the system.1170 Here we have neglected. the simall change iu the uass of the secoudary due to the capture of ejected uaterial from the primary (typically ~0.2M LJ. as well as any kick associated with the interaction of the superuova fast wave with the secoudary (see Marietta et 22000).," Here we have neglected the small change in the mass of the secondary due to the capture of ejected material from the primary (typically $\sim 0.2\Ms$ ), as well as any kick associated with the interaction of the supernova blast wave with the secondary (see Marietta et 2000)."1171 After the supernova. the binary parameters will coutinue o evolve.," After the supernova, the binary parameters will continue to evolve."1172 The svstem will first re-cireularize. obtaining a jew orbital separation Once the secondary starts to fill(1 its Roche lobe. it will start o lose mass. of which a fraction οὐ will be accreted by the mumary. while the rest will be ejected from the svstem.," The system will first re-circularize, obtaining a new orbital separation Once the secondary starts to fill its Roche lobe, it will start to lose mass, of which a fraction $\beta$ will be accreted by the primary, while the rest will be ejected from the system."1173 We asstune that the matter that is lost from the svsteni carries away the same specific augular momenta as the primary (see. e... Podsiadlowski Rappaport. Pfall 2001).," We assume that the matter that is lost from the system carries away the same specific angular momentum as the primary (see, e.g., Podsiadlowski Rappaport, Pfahl 2001)."1174 This is appropriate if the mass loss occurs from a region near the primary. as sugeested by the relativistic jets observed from Nova Sco (IIjelliiiug Rupen 1995).," This is appropriate if the mass loss occurs from a region near the primary, as suggested by the relativistic jets observed from Nova Sco (Hjellming Rupen 1995)."1175 Even though this model is still relatively simple (for example. it docs not take iuto account a kick due to an asvuuuetric explosion). it still contains a large umber of essentially unspecified parameters Whe AM: Misglback- Faeenions νοκ. Ge J}.," Even though this model is still relatively simple (for example, it does not take into account a kick due to an asymmetric explosion), it still contains a large number of essentially unspecified parameters $M_{\rm He}^0$, $M_{\rm BH}^0$, $M_{\rm fallback}$, $f_{\rm1176ejection}$, $f_{\rm fallback}$, $g$, $\beta$ )."1177" For givou values of fojection aud füdbaee We have sampled all the other parzuceters iu a failv svsteimnatic and comprehensive fashion. although we eoncrally do not change the present masses of tle Nova Sco comiponeuts, but keep them fixed at amd. AL."," For given values of $f_{\rm ejection}$ and $f_{\rm fallback}$, we have sampled all the other parameters in a fairly systematic and comprehensive fashion, although we generally do not change the present masses of the Nova Sco components, but keep them fixed at and ,."1178..respectively... In practice. we proceed iu he following wav.," In practice, we proceed in the following way."1179 For each of the 7 superuova imoclels (ie. each combination of helium star mass aud explosion energv). we systematically vary the initial black-hole Lass. Mii the fallback amass. AJggnaae the wind-loss xuaneter. g. aud the mass-accretion parameters. 3 (the atter two are varied from 0 to 1).," For each of the 7 supernova models (i.e., each combination of helium star mass and explosion energy), we systematically vary the initial black-hole mass, $M_{\rm BH}^0$, the fallback mass, $M_{\rm fallback}$, the wind-loss parameter, $g$, and the mass-accretion parameters, $\beta$ (the latter two are varied from 0 to 1)."1180 Mavine fixed these waraluctors. we can use the present orbital period aud nasses to reconstruct the pre-superhova lasses aud pre- orbital period using the formalisinoutlined above.," Having fixed these parameters, we can use the present orbital period and masses to reconstruct the pre-supernova masses and pre-supernova orbital period using the formalismoutlined above."1181 If this recoustruction shows that the radius of the, If this reconstruction shows that the radius of the1182computed. for dillerent assumptions of smooth matter density. photometric error. ancl direction. of the galactic transverse velocity.,"computed for different assumptions of smooth matter density, photometric error, and direction of the galactic transverse velocity."1183 Since the probability functions referred to above were computed from. a derivative analysis. the statistics that we compute in this paper are quantitatively similar for the different possible models.," Since the probability functions referred to above were computed from a derivative analysis, the statistics that we compute in this paper are quantitatively similar for the different possible models."1184 “Pherefore we present only results from models with no smooth matter. a transverse velocity direction along the image C-D axis and simulated: photometric errors assigned according to à Gaussian distribution with half widths of @=AAL/2 in images A and D. and 8$=AA in images C and D. Both the microlensing rate cue to a transverse velocity. (ee.," Therefore we present only results from models with no smooth matter, a transverse velocity direction along the image C-D axis and simulated photometric errors assigned according to a Gaussian distribution with half widths of $\sigma=\Delta M/2$ in images A and B, and $\sigma=\Delta M$ in images C and D. Both the microlensing rate due to a transverse velocity (eg."1185 Witt. Iaiser Refsdal 1903). as well as the corresponding rate due to proper motions (WAWLO0a) are not functions of the details of the microlens mass distribution. but rather are only dependent. on the mean microlens mass.," Witt, Kaiser Refsdal 1993), as well as the corresponding rate due to proper motions (WWT00a) are not functions of the details of the microlens mass distribution, but rather are only dependent on the mean microlens mass."1186 We therefore limit our attention to models in which all the microlenses have the same mass since the results obtained will be applicable to other models with different forms for the mass function., We therefore limit our attention to models in which all the microlenses have the same mass since the results obtained will be applicable to other models with different forms for the mass function.1187 The determination. of probability for. the quantity ΓΕΝim) from the OQ2237|0305 monitoring data is quite robust., The determination of probability for the quantity $v_{eff}\sqrt{\langle m\rangle}$ from the Q2237+0305 monitoring data is quite robust.1188 However the probability for the source size Is derived from a single poorly sampled. LATE., However the probability for the source size is derived from a single poorly sampled HME.1189 The small number of observations cleseribing the LOSS peak (ία et al., The small number of observations describing the 1988 peak (Irwin et al.1190 1989: Corrigan et al 1991) introduces the potential for a systematic error in the source size equal to the ratio of the true event length. and the inferred. event. length. of ~52 days. (twice the estimated rise time)., 1989; Corrigan et al 1991) introduces the potential for a systematic error in the source size equal to the ratio of the true event length and the inferred event length of $\sim 52$ days (twice the estimated rise time).1191 This can be compared to the  100 dav separation of the two points that provide an on the event duration., This can be compared to the $\sim$ 100 day separation of the two points that provide an on the event duration.1192 The resulting systematic error in the estimate of source size is therefore smaller than a [actor of ~2., The resulting systematic error in the estimate of source size is therefore smaller than a factor of $\sim 2$.1193 In addition there may also be à component of svstematic error from the assumption that the LOSS peak was due to a single caustic crossing., In addition there may also be a component of systematic error from the assumption that the 1988 peak was due to a single caustic crossing.1194 “Phe statistics presented in the following sections are therefore computed assuming prior probabilities for S assuming no systematic error. and systematic errors of 2 and 5 in 5: and Our source size estimate was mace from cata collected in the 1t and r bands. while the OGLE light-curves showing the features that we wish to investigate are in the V band.," The statistics presented in the following sections are therefore computed assuming prior probabilities for $S$ assuming no systematic error, and systematic errors of $\times 2$ and $\times 5$ in $S$: and Our source size estimate was made from data collected in the R and r bands, while the OGLE light-curves showing the features that we wish to investigate are in the V band."1195 This introduces the possibility for another source of systematic error if the source has significantly dillerent sizes in the It/r ancl V bands., This introduces the possibility for another source of systematic error if the source has significantly different sizes in the R/r and V bands.1196 To investigate individual ΗΛΙΟΣ we must look at light- statistics for single images., To investigate individual HMEs we must look at light-curve statistics for single images.1197 Therefore unlike the calculation of ps. pe and pi. which used. difference light- intrinsic source variation may be important.," Therefore unlike the calculation of $p_{s}$, $p_{v}$ and $p_{m}$, which used difference light-curves, intrinsic source variation may be important."1198 This cannot be directly. measured. however in Wvithe. Webster. Turner Agol (2000). (hereafter WAWLAOO) limits are placed on the intrinsic variability power-spectreum and it is shown that intrinsic variability should not be an important consideration curing LEMEs.," This cannot be directly measured, however in Wyithe, Webster, Turner Agol (2000) (hereafter WWTA00) limits are placed on the intrinsic variability power-spectrum and it is shown that intrinsic variability should not be an important consideration during HMEs."11992004).,.1200. This work is supported by a RGC erant of the Hong Kong government of the SAR of China., This work is supported by a RGC grant of the Hong Kong government of the SAR of China.

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